JABATAN PENGAIRAN DAN SALIRAN (JPS) KEMENTERIAN SUMBER ASLI DAN ALAM SEKITAR (NRE)

MALAYSIA

NOTA KURSUS TAHUN 2006

KM 7, JALAN AMPANG 68000 AMPANG, KUALA T Lw'PU

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1 KURSUS KESTABILAN CERUN DAN 1 TEMBOK PENAHAN

PADA 16 - 18 ME1 2006

DESIGN OF RETAINING STRUCTURES

NG KOK SENG Penolong Pengarah Kanan

Bahagian Struktur, Geoteknik dan Empangan Cawangan Ampang, K.L. e-mail : ngks@water.gov.my Tel: 03- 42552509

SHEAR STRENGTH OF SOILS AND RELATED SOIL INVESTIGATION

REQUIREMENTS

Shear Strength of soils

State of stress of soils

-Terzaghi's Principle of Stresses in soil

0' = 0 - u and u = us + u,

o Total normal stress on a plane

' Effective normal stress on the plane, (due to inter-contact of soil particles)

U pore water pressure (due to water in void)

us static water pressure in voids

u, excess pore water pressure in voids

- When saturated soils are loaded,

- Total stress increases, o

- soil particles (incompressible) rearrange by slidinglrolling - o ' - water pressure in voids immediately increases - excess pore water pressure, u,

- U, dissipate in time if allow to seep * Before full dissipation 3 applied stress carried by soils particles +water i.e.

undrained condition * Full dissipation of excess pore pressure, i.e. u, = 0 ,

3 soil particles rearranged to take full applied stress with decrease in volume i.e. drained condition

Shear Strength of soils

State of stress of soils

- Soil deform and fail when

> applied stresses > shear strength of soil

- Stability of slope and retaining structures required shear resistance I strength of the soils, i.e. Limit Equilibrium method analysis.

Shear Strength of soils (cont ...)

Coulomb's shear strength - 2 components of shear strength i.e.

- 0 (angle of internal friction) i.e. sliding friction between grains & stress dependent ,

- C cohesion, non- stress dependent

Thus, Coulomb's equation

s = c + a' tan I$ Where,

s = shear strength or shear resistance, kNlm2

c = cohesion, kNlrn2 (not dependent on normal stress)

a' - intergranular pressure acting perpendicular to the shear plane, k N h 2

= (o - u ) o = total pressure

u = pore water pressure

= angle of internal frictional of soil, degrees.

Note : a' tan I$ = frictional resistance between soil grains and proportional to normal pressure

Shear Strength of soils

- Graphical Representative of Coulomb's (straignt Line)

S Granular/ cohesionless / non- cohesive or frictional soil

b.) (coarse grained soil)

s = o' tan I$ where c = 0 0'

Fine-grained or cohesive soil

(fined-grained eg clay, silt & colloids)

f. s = C o '

where 0 = 0

Shear Strength of soils - by Mohr Circles Envelope

Mohr Circle Envelope - represent shear stresses on failure plane at failure as function of normal stress on that plane i.e.

s,=f (0,)

By carrying a series of tests with varying normal

Initial Conditions

stresses until failure (triaxial), a plot of increasing normal stresses (resembling confining pressures in

1 'T cell

in-situ) versus shear strength at failure, give the graph below: - -n-

Mohr Failure Envelope

4

t At failure

1 axial (at f a ) 1 1 cell (at fail) J Oqf

- cell (at fail) - 3f

Shear Strength of soils - Mohr-Coulomb's Envelope

Mohr Failure 01 ' Envelope

I

- Mohr-Coulomb's Envelope

- a state where combination of shear stress and normal stress give the stress conditions at the failure plane at failure.

- 4 and c known as strength parameters , important in stability and foundation analysis.

f Mohr-Coulomb's Envelope

0'

a) For cohesionless soils

- the slope of the straight line tangent to the series of Mohr circles represents I$

- Q more pronounced for cohesionless soils and approach zero for soft cohesive soil.

- series of varying confining pressures in Triaxial tests are reflected by the plotting of the Mohr Circles

- +, c can be determined from undisturbed samples but usually from SPT and in-situ penetration cone , direct shear test

- apparent cohesion, c" i.e. cohesionless soil exhibit characteristic of cohesive soils (evident - stand vertical when cut)

% due either t o capillary attractive forces (when dry of saturation) or mineralogy action. For capillary action, it usually disappear with time, thus normally ignore in stability analysis.

Shear Strength of soils - Mohr-Coulomb's Envelope

0'

SPT Vs 41 for cohesionless soils

Type of soil Penetration Anale o f Internal friction (kN/m2) Resistance, N Peck (1974) Meyerhof (1956)

Very Loose sand < 4 < 29 < 30

Loose sand 4 - 10 29 - 30 30 - 35

Medium Sand 10 - 30 30 - 36 35 - 40

Dense Sand 30 - 50 36 - 41 40 - 45

V. Dense Sand > 50 > 41 > 45

Mohr-Coulomb's Envelope

1 s = c

b) For cohesive soil

- shear strength due to atomic attraction forces between soils particles

- independent of the confining pressures

- Intercept a t shear strength axis, 'c' (where principle stress, 0 = zero)

- Soft clay, I$ - o, s= in-situ shear strength, 'c'

- 'c' obtained from triaxial tests, cone penetration tests, vane shear and unconfined undrained (UU) compression test

Total Stress Vs. Effective stress Analysis

c', $, S, changes with time (in relationship to excess pore water pressure)

When load applied on soil mass, add'l load taken by: - - Soil skeleton - Pore water , 3 result in excess pore pressure

Excess pore press. will dissipate in time by seepage, hence c', I$, will change with

time

Designer need to determine critical soil parameters i.e.

- short-term or total stress under undrained conditions analysis (immediately I during construction)

- long-term or effective stress (after dissipation of excess pore pressure i.e. drained condition)

- Short- or long-term afialysis depend on Type of soil - coarse grains or cohesionless soil - fine grain or cohesive soil

- Permeability

- Compressibility

- Soil thickness

- Type of drainage

-1 depend 0+

Total Stress Vs. Effective stress Analysis (cont ...)

Cohesionless Soils - (sandy 1 granular soils)

- Stability = f ( I$' , y , u)

- High permeability + Excess pore water pressure dissipate rapidly

- Need only consider long-term parameters

- Effective stress analysis

For sand, 4 = $' and c' = 0

- Influence of Pore pressure

Submergence no effect on strength

- Shear strength Tests:

C-D Triaxial (not common)

Direct shear test

SPT relationship

Total Stress Vs. Effective stress Analysis (cont ....)

SPT Vs I$ for cohesionless soils

Type of soil Penetration Resistance, N

Very Loose sand < 4

Loose sand 4 - 10

Medium Sand 10 - 30

Dense Sand 30 - 50

V. Dense Sand > 50

Anqle of Internal friction Peck (1974) Meyerhof (1956)

< 29 < 30

29 - 30 30 - 35

30 - 36 35 - 40

36 - 41 40 - 45

> 41 > 45

Total Stress Vs. Effective stress Analysis (cont ....)

Cohesive Soils - (clayey soils) - Low permeability 3 Excess pore water pressure dissipate slowly

- Analysis using either total or effective stress analysis (or check for both)

a) Effective stress stability

- drained conditions

+ = and c = c'

- Shear strength Tests:

- CU I CD Triaxial

- SPT relationship

b)Total Stress stability

- Undrained condition - In-situ undrained strength with

c=su, r$ = o - Applied when soil saturated - Shear strength not affected by

position of water table or phreatic surface - Shear strength Tests:

- UU 1 CU Triaxial - Vane shear in-situ test - Correlation with Plasticity

Index (PI) i.e. C,/cr,' = 0.1 1 + 0.0037 (PI)

- Clay with >25% PI -3 can develop low residual shear angles when disturbed

Total Stress Vs. Effective stress Analysis (cont.. ..)

Examples of Time Dependent Shear Strength (cohesive soil)

I Embankment

I Cutting

Height

Pore water pressure (u)

FOS

Steps Involved in Slope Stability and Retaining Structure Analysis - Design

1. Determine Type of Analysis and Parameters Required

2. Determine Type and Method of Geotechnical lnvestigation Required

3. lnterpret Geotechnical lnvestigation Results

4. Analysis & Design

Steps Involved in Slope Stability and Retaining Structure Analysis - Design

Determine Type of Analysis and Parameters Required

Determine Type and Method of Geotechnical lnvestigation Required

lnterpret Geotechnical lnvestigation Results

Analysis & Design

1. Determine Type of Analysis and Parameters Required

Type of Analysis Required

k Stability @ Slope Stability C? Retaining wallslsheet piles @ Bearing Capacity

Parameter Required

> Shear Strength @ Cohesion, c - Triaxial 4 Internal frictional angle, $ - Triaxial

1. Determine Type of Analysis and Parameters Required (cont ...)

Others Parameter Required

(3 Unit Weight, y - Lab

@ Moisture Content - Lab @ Soil Classification - Lab (3 Plastic 1 liquid limit - Lab

@ Sensitivity - Lab @ Phreatic Line (Water Table) - In-situ

Steps Involved in Slope Stability and Retaining Structure Analysis - Design

1. Determine Type of Analysis and Parameters Required

2. Determine Type and Method of Geotechnical Investigation Required

3. Interpret Geotechnical lnvestigation Results

4. Analysis & Design

-- -- - -

2. Type and Method of Ground Investigation Required

*3 Boreholes with Field Tests + Laboratory Tests

2.1 Boreholes (BS 5930: 1981) - General

Include sampling, in-situ testing and water table observations

Depth > 100 m

Drill through all soils and core through rocks

Types

J Rotary drilling by circulating fluid - most common

J Wash boring utilizes the percussive action of a chisel bit to break up materials and flush to the surface by water or drilling fluid pumping down the hollow drill rods

2.2 Boreholes - Sampling

a) Wash samples

J Soil Strata Description

b) Install piezometers to measure ground water level

c) Disturbed Samples

J Split Spoon samples after SPT

2.2 Boreholes -Sampling (Cont.. ...)

d) Undisturbed Samples - laboratory strength and consolidation tests

J Thin wall sampler o Cohesive soils up to firm consistency (N <I 0) and free

from large particles eg. marine deposits

J Thin wall piston sampler o Cohesive soils with low strength like very soft to soft clay

J Continuous sampler o Identifying sand lenses, description/classification tests o Usually for soft marine deposits

J Mazier Sampler

o Triple-tube core-barrels containing detachable liners within the inner barrel

o Undisturbed soil samplers from stiffer soil stratum

2.3 Boreholes - Field Tests

a) Standard Penetration Test (SPT)

b) MackintoshIJKR Probe

c) Field Vane Shear Test eg. Geonor vane - to determine in-situ undrained shear strength (S, ) of soft cohesive soil - give good results due to insitu testing - usually overestimate S, , thus need to be corrected by Bjerrum's

correction factor related to Plasticity Index

d) Static Cone Penetration Test

- Undrained shear strength

- Soil Type

e) Pressuremeter Test

- Borehole (Menard) or self boring

f) Permeability Test

2.4 Boreholes - Laboratow Tests

a) Classification

J Bulk Density

J Moisture Content

J Specific Density

J Gradation

J Atterberg limits

b) Strength

J Unconfined Compression

J Triaxial Tests (UU, CU, CD with pore pressure measurement)

J Shear Box

2.4 Boreholes - Laboratory Tests

c) Consolidation

4 One-dimensional test

d) Compaction

J Standard Proctor Compaction

4 Relative Density

e) Permeability

4 Triaxial cell

4 Hydraulic consolidation cell

4 Constant Head permeability test

f) Chemical

J Organic content, sulphate, pH test

Steps Involved in Slope Stability and Retaining Structure Analysis - Design

1. Determine Type of Analysis and Parameters Required

2. Determine Type and Method of Geotechnical Investigation Required

3. Interpret Geotechnical lnvestigation Results

4. Analysis & Design

3. Interpret Geotechnical Investigation Results

3.1 Field Tests - Mackintosh / JKR Probe

9 Suitable in softlweak layer

9 Determine hard layer or shallow bedrock

9 Preliminary subsoil info

9 Assist in interpolation between boreholes

9 Limited Use

J Shallow Bedrock profile

J Weak zone at shallow depth

J Shallow foundation

o No recent fill and future settlement

o Structure of low risk

o if in doubt, use borehoie

3.2 Correlations between SPT and S,

i. S, = 20 N kNlm2 (Meyerhof)

ii. 2 S,= 13N kNlm2 (Terzaghi & Peck)

iii. S, = 70 N kNlm2 (Reese, Touma & O'Neil)

iv. S, = 4 to 6 N kNlm2 (Stroud & Butler)

v. 2 S, = 0.1 + 0.15 N kNlm2 (Fukuoka) -

(Ref: Fleming et al, Piling Engineering Survey Uni. Press, Glasgow (1985))

vi. ForCHClay

2 S, = 13.7N kNIm2 ) Sambhandharaksa & Pitupakor, ) 1985

2 S, = 10.4N kNIm2 ) for Bangkok Clays

1 Note; N = SPT 'N' corrected I

3.3 Relationship Between SPT, JKRlMackintosh Probe and Unconfined Compression Strength of Cohesive Soil

Consistency (Blowlft)

15 - 30 Very stiff +

Bulk Unit Unconfined JKR Probe Weight, y, Compressive (Blowlft) kN/mZ Strength q, (kNI mZ)

Note:- S, = q , where S, = undrained shear strength,

3.4 Relationship Between SPT, JKR /Mackintosh Probe, Allowable Soil Pressure, Soil Density, Internal Frictional Angle for Granular Soils

N (Blowlft)

Allowable Soil Pressure Probe

(blowllft)

Not suitable 0 - 10

0 - 80 10-30 4 - 10

10 -30

30 -50

> 50

Consistency

Loose

Medium

Dense

Very Dense

Bulk Unit Weight, y, kN/mZ

Internal Friction anale. &I

15 -20

17- 21

17 - 22

> 21

28 - 30

30 - 36

36-41

41

3.5 Relationship Between SPT and 0

- Recommended for Cohesionless soils as representative sample of in-situ is almost impossible to achieve for lab. test

N,,= Corrected N value

N = Actual SPT - N value

o ,, = Vertical effective stress ton/ft2

Anale of Sheanna Resistance. d. darees 1

3.6 Sample Triaxial Test Results

Interpreted From Mohr " ' I I000

Effective Stress

1b00 ZQQO Z ~ O Q ZLOQ NORMAL STRESS lkNfn7

3.7 Example of Some Undrained Shear Strengths by Various Test Methods

0 I I I I

!

Depth vs. Typical Undrained Shear Strength by various Methods for Morgan City recent Alluvium, ie.

- Unconfined Compression

- Undrained Triaxial

- Laboratory Vane

- Field Vane

snastreogh an'

3.8 Mackintosh Value Vs Allowable Bearing Capacity

I Macintosh Value (blowslft) I Allowable Bearinn Ca~acitv Vs Mackintosh Probe

M.P. < 10,

Very loose, wet, fine sand, silt or clay, genrally unstable.

M.P. 10 - 40

Moist, fine sand or sand with large amount of clay from soft to firm consistency

M.P. > 40.

Moist sand and clayed sand from firm to very hard consistency.

Note: - 1. Used for square foundation only, normally founded at least 5' below finished level.

2. Generally can be applied to moist clayey sand soils

3. Mackintosh probe < 18 blowslft, need special treatment

4. If foundation near slope, stability of slope need to be considered

3.9 JKR Probe Vs Allowable Bearing Capacity

(Ooi & Ting, 1975)

. Plate bearing test on sand A plate bearing test on'

I Residual granite soil

10 20 30 40 50 SO 70 80 90 100 PENETRATION RESISTANCE (B lows/ft)

3.10 Atterbern Limits to predict soil strenath:

Undrained shear strength&

9 Peck (1 940) - for Chicago clay

9 Skempton (1954)

for normally consolidated clays : C, = (0.1 1 + 0.37 PI) * o

9 P.1 used as Correction Factor for C, measured by Vane Shear test

Effective Stress Parameter

9 Bjerrum and Simons (1 960)

4' for normally consolidated clays assuming C' = 0

Relationship between sin 4' , and Plasticity Index for Normally consolidated Soils (Kenney 1959)

Sample of Soil Profile Used for Designlanalysis

0 SPT'N' A JKR Probe

Relevant B.S. for Geotechnical Enginnering

1 BS 1377 (1 990) Methods of Test for soils in Civil Enginneering Purposes

2 BS 5930 (1981) COP for Site Investigations

3 BS6031(1981) COP for Earthworks

4 BS 8002 (1 994) COP for Earth Retaining Structures

5 BS 8004 (1 986) COP for foundations

6 BS 8005 (1986) COP for StrengthenedlReinforced soils and other Fills

7 BS 8081 ( I 989) COP for Ground Anchors

Steps Involved in Slope Stability and Retaining Structure Analysis - Design

1. Determine Type of Analysis and Parameters Required

2. Determine Type and Method of Geotechnical Investigation Required

3. Interpret Geotechnical lnvestigation Results

4. Design Analysis - Slope Stability Analysis - Retaining Structures

Kursus Analisa Kesta bilan Cerun dan Rekabentuk Tembok Penahan

pada 16 - 18 Mei 2006

Design Guide For Retaining Walls (Adopted from Design Office, JPS Malaysia)

I . 1 SCOPE OF THIS DESIGN G U I D E

T h e s c n o t e s a r e i n t e n d e d a s a G u i d e f o r u s e i n t h e e s t i m a t i o n of

e a r t h p r e s s u r e f o r c e s , and For t h e d e s i g n a n d c o n s t r u c t i o n o f r e t a i n i n g

w a l l s a n d o t h e r e a r t h Y e t a i n i n g s t r u c t u r e s . Recommended m e t h o d s

a r e g i v e n For most a s p e c t s o f d e s i g n , e x c e p t f o r r e i n f o r c e d c o n c r e t e , where

g u i d a n c e is g i v e n on o n l y a few s p e c i a l p o i n t s . T h r o u g h o u t t h e G u i d e ,

r e f e r e n c e i s made t o r e l e v a n t t e x t b o o k s , C o d e s a n d p u b l i s h e d p a p e r s , a n d t h e

r e a d e r s h o u l d c o n s u l t t h o s e o r i g i n a l ' d o c u m e n t s f o r more d e t a i l e d c o v e r a g e o f

p a r t i c u l a r a s p e c t s o f t h e s u b j e c t m a t t e r .

I t i s i m p o r t a n t to remember t h a t e n g i n e e r i n g j u d g e m e n t s h o u l d

a l w a y s b e e x e r c i s e d i n a p p l y i n g t h e t h e o r i e s a n d d e s i g n m e t h o d s g i v e n i n t h e

G u i d e - I n p a r t i c u l a r , t h e p r a c ~ i t i o n e r m u s t b e a w a r e o f c h e l i m i t a t i o n s on

t h e b a s i c a s s u m p t i o n s employed i n a p a r t i c u l a r l y t h e o r e t i c a l o r c o m p u t a t i o n a l

method .

1 . 2 RETAINING WALL DESIGN PRINCIPLES

1 . 2 . 1 F/ree-4-tand&tg Re,ta&&~g ~~ I n t h e d e s i g n o f f r e e - s t a n d i n g r e t a i n i n g w a l l s , t h e f o l l o w i n g

a s p e c t s need t o be i n v e s t i g a t e d :

(a) t h e s t a b i l i t y o f t h e s o i l a r o u n d t h e w a l l ,

(b) t h e s t a b i l i t y o f t h e r e t a i n i n g w a l l i t s e l f ,

( c ) t h e s t r u c t u r a l s t r e n g t h o f t h e w a l l ; and

(d) damage t o . a d j a c e n t s t r u c t u r e s d u e t o w a l l c o n s t r u c t i o n -

The m a g n i t u d e o f t h e e a r t h p r e s s u r e w h i c h w i l l b e e x e r t e d o n a

wall i s d e p e n d e n t on t h e amount o f movement t h a t t h e w a l l u n d e r g o e s .

I t is u s u a l t o assume f o r f r e e - s t a n d i n g r e t a i n i n g w a l l s i h n t .

s u f f i c i e n t outward movement o c c u r s t o a l l o w act ive (minim~im) e a r t h p r e s s r j t c s

t o deve lop . The d e s i g n e r must e n s u r e cha t s u f f i c i e n t movemcnt cnn t a k e p l a c c

w i t h o u t a f f e c t i n g t h e s e r v i c e a b i l i t y o r appearance of t h e wa l l .

Mlere i t is n o t p o s s i b l e f o r t h e r e q u i r e d outward movement t o

o c c u r , f o r i n s t a n c e due t o wa l l o r founda t ion r i g i d i t y , h igher p r e s s u r e s

w i l l deve lop and t h e w a l l must b e des igned For these . Fur the r guidance on

t h i s m a t t e r i s given i n S e c t i o n 3.2.

1 . 2 . 2 0;thm Retaivtirtg S . t h u c t w r e ~

I f a s t r u c t u r e p r e v e n t s outward movement of the s o i l , t h e w a l l

w i l l u s u a l l y be s u b j e c t t o s t a t i c e a r t h p r e s s u r e s g r e a t e r than a c t i v e . This

o c c u r s where a w a l l r e t a i n i n g e a r t h is p a r t o f a more e x t e n s i v e s t r u c t u r e ,

s u c h a basement w a l l i n a b u i l d i n g o r an abutment wa l l of a p o r t a l

s t r u c t u r e . It a l s o o c c u r s when t h e w a l l i s connected t o ano the r s t r u c t u r e , .

s u c h a s a b r i d g e abutment connected t o t h e s u p e r s t r u c t u r e .

1 .3 LOAD CASES

1 . 3 . 1 8 a h - i ~ Loadingd

The b a s i c p r e s s u r e l o a d i n g t o be cons ide red f o r des ign is :

fiormal l o a d i n g = s t a t i c e a r t h p r e s s u r e + wate r p r e s s u r e +

p r e s s u r e due t o l i v e loads o r su rcharge .

The p o s s i b l e o c c u r r e n c e o f o t h e r d e s i g n c a s e s , or v a r i a t i o n s oC t h e

o n e above , caused by c o n s t r u c t i o n sequence o r f u t u r e development of s u r r o u n d i n g

a r e a s shou ld a l s o be c o n s i d e r e d . For i n s t a n c e , a d d i t i o n a l s u r c h a r g e s may s e e d - E d e c o n s i d e r e d and a l lowance made f o r any p o s s i b l e f u t u r e removal of ground

i n - --. f r o n t of --- - t h e w a l l i n c o n n e c t i o n w i t h s e r v i c e s , p a r t i c u l a r l y i f t h e p a s s i v e

r e s i s t a n c e of t h i s m a t e r i a l is i n c l u d e d 3.n t h e s t a b i l i t y . c a l c u l a t i o n s .

The e f f e c t of e x c k t i o n on t h e w a l l b e a r i n g c a p a c i t y may a l s o need t o b e

c o n s i d e r e d ,

For t h e d e t e r m i n a t i o n of e a r t h p r e s s u r e s , i t is u s u a l t o c o n s i d e r

a u n i t l e n g t h of t h e c r o s s - s e c t i o n of t h e w a l l and r e t a i n e d s o i l . A . u n i t

- l e n g t h is a l s o ussd i n t h e s t r u c t u r a l d e s i g n o f c a n t i l e v e r w a l l s and o t h e r

w a l l s w i t h a uniform c r o s s - s e c t i o n .

2 . 1 G E N E R A L

For a l l w a l l s h i g h e r than 5 met res , e s p e c i a l l y those w i t h s l o p i n g

b a c k f i l l , t h e s o i l p r o p e r t i e s of t h e n a t u r a l ground and b a c k f i l l s l iould be

e s t i m a t e d i n advance of d e s i g n from t e s t s on samples of t h e m a t e r i a l s i n v o l v e d .

In a d d i t i o n , s p e c i a l a t t e n t i o n should be paid t o t h e de te rmina t ion o f ground

G a t e r l e v e l s , p a r t i c u l a r l y w i t h r e s p e c t t o maximum probable v a l u e s .

. .

For l e s s i m p o r t a n t w a l l s , . a n e s t i m a t i o n of the s o i i p r o p e r t i e s

may be made frbm p r e v i o u s tests on s i m i l a r m a t e r i a l s . A c a r e f u l v i s u a l

examina t ion of t h e m a t e r i a l s , p a r t i c u l a r l y t h a t a t t h e proposed founda t ion l e v e l

shou ld b e made and index tests c a r r i e d o u t t o e n s u r e t h a t the assumed m a t e r i a l

type is c o r r e c t .

2 - 2 SELECTION AMI USE OF BACKFl LL

The i d e a l b a c k f i i l f o r a minimum s e c t i o n wa l l i s a f r e e d r a i n i n g

g r a n u l a r m a t e r i a l of h i g h s h e a r i n g . s t r e n g t h . However,- the f i n a l c h o i c e o f

m a t e r i a l shou ld b e based o n t h e c o s t s and a v a i l a b i l i t y of such m a t e r i a l s

ba lanced a g a i n s t t h e c o s t of more expens ive w a l l s .

I n g e n e r a l , t h e u s e of f i n e - g r a i n e d c layey b a c k f i l l s i s n o t recommended.

Clays a r e s u b j e c t t o s e a s o n a l v a r i a t i o n s i n mois tu re con ten t and consequent

s w e l l i n g and s h r i n k a g e . T h i s e f f e c t may l e a d t o an i n c r e a s e i n p r e s s u r e a g a i n s t - a w a l l when t h e s e s o i l s a r e used a s b a c k E i l l . Due t o c o n s o l i d a t i o n , l o n g

term s e t t l e m e n t problems are c o n s i d e r a b l y g r e a t e r than wi th c o h e s i o n l e s s

m a t e r i a l s ,

For c o h e s i v e b a c k f i l l s , s p e c i a l a t t e n t i o n must be pa id t o t h e

p r o v i s i o n of d r a i n a g e t o p r e v e n t t h e build-up of water p r e s s u r e . F r e e d r a i n i n g

c o h e s i o n l e s s ~ t e r i a l s may n o t r e q u i r e t h e same amount of a t t e n t i o n i n t h i s

r e s p e c t - They may s t i l l r e q u i r e p r o t e c t i o n by p roper ly des igned f i l t e r ' l a y e r s .

The w a l l d e f l e c t i o n r e q u i r e d t o produce t h e a c t i v e s t a t e i n c o h e s i v e

m a t e r i a l s wi th a s i g n i f i c a n t c l a y c o n t e n t may be up t o 10 t imes g r e a t e r t h a n .

f o r c o h e s i o n l c s s m a t e r i a l s . T h i s , t o g e t h e r wi th t h e f a c t tha t tile former

g e n e r a l l y have lower va lues of s l ~ c a r i n g s t r e n g t h , means t h a t t h e amount o f

. s h e a r s t r e n g t h mobi l i sed f o r any g iven w a l l movement is c o n s i d e r a b l y lower

f o r c o h e s i v e m a t e r i a l s than f o r c o h e s i o n l e s s m a t e r i a l s . The c o r r e s p o n d i n g

e a r t h p r e s s u r e on t h e a c t i v e s i d e f o r a p a r t i c u l a r w a l l movement w i l l t h e r c f o r r ?

be h igher i f c o h e s i v e s o i l is used f o r b a c k f i l l .

Rock f i l l is a very s u i t a b l e m a t e r i a l f o r u s e a s a b a c k f i l l t o

r e t a i n i n g w a l l s and c o n s i d e r a t i o n shou ld be given t o i t s use when a v a i l a b l e .

I n g e n e r a l , t h e r o c k f i l l should b e w e l l g;aded and have a nominal maximum s i z e

o f 200mm. A well-graded densely compacted r o c k f i l l s h o u l d not have more t h a n

abou t 2% f i n e r than 75um i f i t .is t o remain f r e e - d r a i n i n g .

Movement o f s o i l , due t o seepage , i n t o t h e r o c k f i l l needs t o b e

p reven ted . T h i s may r e q u i r e t h e p r o v i s i o n o f p r o p e r l y des igned f i l t e r l a y e r s .

between t h e s o i l and t h e r o c k f i l l .

I t is e s s e n t i a l t o s p e c i f y and s u p e r v i s e t h e p l a c i n g of b a c k f i l l t o . e n s u r e t h a t i t s s t r e n g t h and u n i t weight p r o p e r t i e s a g r e e with t h e d e s i ~ n

assumpt ions bo th f o r l a t e r a l e a r t h p r e s s u r e and dead we igh t c a l c u l a t i o n s . Jn

t h i s r e g a r d , i t i s p a r t i c u l a r l y impor tan t t o e n s u r e . t h a t the b a c k f i l l b e h i n d

a w a l l and on a s l o p e is p roper ly compacted. The b a c k f i l l shou ld normal ly

b e compacted i n t h i n l a y e r s u s i n g l i g h t compaction p l a n t f o r t h e reasons

o u t l i n e d i n S e c t i o n -3.10.

The a c t i v e e a r t h p r e s s u r e is s u b s t a n t i a l l y reduced, p a r t i c u l a r l y f o r

a s t e e p l y s l o p i n g b a c k f i l l , i f t h e f a i l u r e - p l a n e o c c u r s . i n a m a t e r i a l w i t h a

h i g h a n g l e of s h e a r i n g r e s i s t a n c e . I n some c i r c u m s t a n c e s , i t may be economical

t o r e p l a c e weaker m a t e r i a l so ' t h a t t h e above s i t u a t i o n occurs .

2 . 3 UNIT WEIGIfJ

The u n i t we igh t of s o i l depends on t h e s p e c i f i c g r a v i t y of t h e

s o l i d p a r t i c l e s and t h e p r o p o r t i o n s of s o l i d , a i r and w a t e r i n t h e , s o i l .

The p ropor t ion of t h e t o t a l volume t h a t is made up o f c h i s s o i i d m a t e r i a l

i s dependent on t h e degree o f compaction o r c o n s o l i d a t i o n .

A s e s t i m a t e of t h e u n i t weight of b a c k f i l l m a t e r i a l t o b e used

b e h i n d a r e t a i n i n g - s t r u c t u r e may br ohin ined f ron s t a n d a r d I aborntory

compact ion t e s t s on samples of t h e m a t e r i a l o r from r e c o r d s oE f i e l d ' t e s t i n g . - The u n i t weighe chosen must c o r r e s p o n d t o t h e compaction and mois ture c o n d i t i o n s

t h a t w i l l a p p l y i n t h e a c t u a l f i e l d s i t u a t i o n .

The u n i t we igh t of n a t u r a l s o i l should be ob ta ined from u n d i s t u r b e d -

s a m p l e s kep t a t t h e f i e l d m o i s t u r e c o n t e n t and volume. For i n i t i a l d e s i g n

p u r p o s e s , d r y d e n s i t i e s i n t h e range 1750 t o 1850kg/m3 nay be assumed f o r

a l l s o i l s compacted n e a r optimum m o i s t u r e c o n t e n t .

2 . 4 EFFECT1 V E STRESS AND PORE PRESSURE

An e f f e c t i v e s t r e s s may be c o n s i d e r e d t o be t h e s t r e s s t r a n s m i t t e d

t h r o u g h the p o i n t s of c o n t a c t between t h e s o l i d p a r t i c l e s of t h e s o i i . I t

is t h i s stress t h a t d e t e r m i n e s t h e s h e a r i n g r e s i s t a n c e of t h e s o i l . The

e f f e c t i v e stress, a l , . a t any p o i n t i n a s a t u r a t e d s o i l mass may be o b t a i n e d

by s u b t r a c t i n g t h e p r e s s u r e transmitted by w a t e r i n t h e v o i d s , u , (pore

w a t e r p r e s s u r e ) from t h e t o t a l s t r e s s , a , t h u s :

o l = o - u . . . . . ( 1 )

An i n c r e a s e d pore w a t e r p r e s s u r e g i v e s a reduced e f f e c t i v e s t r e s s

and ' t h e r e f o r e a reduced s o i l s h e a r i n g r e s i s t a n c e . Th i s l e a d s t o an i n c r e a s e d

f o r c e a g a i n s t a w a l l i n t h e a c t i v e c a s e . Converse ly , an i n c r e a s e i h t h e

n e g a t i v e pore p r e s s u r e ( i - e . a pore s u c t i o n ) g i v e s an i n c r e a s e d s h e a r i n g

r e s i s t a n c e and reduces t h e f o r c e a g a i n s t a w a l l i n t h e a c t i v e case .

P o s i t i v e p o r e w a t e r p r e s s u r e r e s u l t s from a number of f a c t o r s ,

t h e most i m p o r t a n t b e i n g s t a t i c wa te r p r e s s u r e , seepage o f

groundwater o r r a i n f a l l and seepage from o t h e r s o u r c e s , such as b u r s t o r

l e a k i n g w a t e r supp ly mains. I n some s o i l s , shock o r v i b r a t i o n can c a u s e

t r a n s i e n t i n c r e a s e s i n pore p r e s s u r e . I n low p e r m e a b i l i t y s o i l s , changes

i n pore w a t e r p r e s s u r e can r e s u l t from changes i n t o t a l s t r e s s due t o

ground l o a d i n g , dewate r ing o r e x c a v a t i o n . These p o r e p r e s s u r e s d i s s i p a t e

w i t h t ime, b u t may n e e d t o b e c o n s i d e r e d i n d e s i g n . P o r e w a t e r p r e s s u r e s -

due t o s t a t i c w a t e r p r e s s u r e and seepage of w a t e r a r e covered i n Chap te r 5 - .

- ..- - - - - - -

Negat ive .pore p r e s s u r e s a r e p r e s e n t i n many p a r t i a l l y s a r u r a ~ c u

s o i l s . S o i l suc t ion may be destroyed by s u r f a c e i n f i l t r a t i o n

o r seepage , m d , - k t i l more i n f o r m a t i o n o n its magni tude , d i s t r i b u t i o n a n d

behaviour becomes a v a i l a b l e , i t s e f f e c t on t h e s h e a r r e s i s t a n c e o f t l ic s o i l

should no t be used i n r e t a i n i n g wal l des ign .

2 . 5 SHEAR STRENGTIf

I n a l l e a r t h p r e s s u r e prohlems t h e magni rude of e a r t h p r e s s u r e on

a p a r t i c u l a r s t r u c t u r e is a f u n c t i o n of the s h e a r s t r e n g t h of t h e s o i l .

The s h e a r s t r e n g t h is not a unique p roper ty of t h e m a t e r i a l but depends upon

t h e c o n d i t i o n s t o which the s o i l i s s u b j e c t e d when i t is s h e a r e d . Where a

r e t a i n i n g s t r u c t u r e supports a s a t u r a t e d c l a y s o i 1 aE low p e r m e a b i l i t y , t h e

undrained s h e a r s t r e n g t h can be used t o c a l c u l a t e t h e e a r t h p r e s s u r e f o r

short-term stability, because the s h e a r s t r e n g t h o E such s o i l does n o t change

a s i t i s sheared quickly ( i . e . t h e excess p o r e w a t e r p r e s s u r e s cannot

d i s s i p a t e d u r i n g s h e a r ) . However, Hong Kong r e s i d u a l s o i l s a r e no t s a t u r a t e d .

and they have r e l a t i v e l y high p e r m e a b i l i t i e s . The wate r c o n t e n t , t h e r e f o r e ,

can change q u i t e r a p i d l y , wi th a consequent change i n pore p r e s s u r e and , h e n c e ,

wi th a change i n shear s t r e n g t h . I t is n e c e s s a r y , t h e r e f o r e , f o r e a r t h

p r e s s u r e s i n Hong Kong s o i l s t o be c a l c u l a t e d from s h e a r s t r e n g t h s e x p r e s s e d

i n terms of effective stresses.

.-

The s h e a r s t r e n g t h of a s o i l is p r o p o i ~ i o n a l t o t h e e f f e c t i v e stress

which a c t s on t h e f a i l u r e p lane . Laboratory t e s t s c a n . b e c a r r L e d o u t t o

e s t a b l i s h t h e r e l a t i o n s h i p between s t r e n g t h , S, e f f e c t i v e s t r e s s , a ' , and t h i s

is commonly termed the strength envelope. The e n v e l o p e w i l l g e n e r a l l y b e

curved, b u t p o r t i o n s of t h e c u r v e can be approx imated by t h e r e l a t i o n s h i p :

- s = C ' + o ' t a n 0 ' ....- ( 2 )

where c t and 0' a r e termed t h e effective strength parameters. These p a r a m e t e r s

should b e used f o r e a r t h p r e s s u r e c a l c u l a t i o n s i n Hong Kong s o i l s . It is

i m p o r t a n t t o n o t e t h a t t h e d e s i g n s t r e n g t h p a r a m e t e r s must be t h o s e de te rmined

i n t h e l a b o r a t o r y f o r t h e r a n g e o f e f f e c t i v e stress which is a p p r o p r i a t e t o the

f i e l d s i t u a t i o n .

Laboratory t r i a x i a l t e s t s o r s h e a r b o x tests a r e conononly used to

d e t e r m i n e t h e s t r e n g t h e n v e l o p e of a s o i l . Guidance on r h e s e met'hods of.

s - t r e n g t h measurement and on t h e i n t e r p r e t a t i o n o f t e s t r e s u l t s c a n b e - o b t a i n e d

f rom Lambe & W h i t s n ( 1 9 6 9 ) and from t h e C e o t e c h n i c a l Manual f o r S l o p e s

( G e o t e c h n i c a l Conzrol O f f i c e , 1979).

The f o l i o w i n g two t y p e s o f t r i a x i a l t e s t s c a n be u s e d :

( a ) Conso l ida t ed -undra ined t e s t s w i t h p o r e p r e s s u r e measurement

(CG t e s t s ) c a r r i e d o u t on spec imens s a t u r a t e d u s i n g back

p r e s s u r e .

( b ) Drzined t e s t s (CD t e s t s ) on s a t u r a t e d spec imens . .

S h e a r bcx t e s t s a r e s i m p l e r t o c a r r y o u t t h a n t r i a x i a l t e s t s b u t

o n l y d r a i n e d t e s t s can b e conduc ted on Hong Kong r e s i d u a l s o i l s . Ca re s h o u l d

b e t aken t o er is t j re cha t t e s t . spec imens a r e soaked f o r a s u f f i c i e n t p e r i o d p r i o r

t o t e s t i n g and t h z t submergence is m a i n t a i n e d d u r i n g s h e a r .

The s h e a r s t r e n g t h , o f a b a c k f i l l m a t e r i a l d e p e n d s on i t s d e n s i t y ,

. and l a b o r a t o r y s t r e n g t h tests s h o u l d b e c a r r i e d o u t on s p e c i m e n s compacted

t o t h e d e n s i t y t h a z w i l l e x i s t i n s i t u . Where i n a d e q u a t e s h e a r , s t r e n g t h

i n f o r m a t i o n is a v a i l a b l e a t t h e t ime o f p r e l i m i n a r y d e s i g n , t h e f o l l o w i n g

v a l u e s may be t a k e s a s g u i d a n c e t o t h e p r o p e r t i e s o f compac ted llong Kong - s o i l s : - -

For deconposed v o l c a n i c s , 'c ' = 0 , 0 ' = 35'. ~d = 1 750kg/m3 0

For decocposed g r a n i t e , c ' = 0, 0 ' = 39 , y d = 1850kg/m3

2 . 6 BASE SHEAR RESISTANCE

The amount o f s h e a r i n g r e s i s t a n c e a v a i l a b l e b e t w e e n t h e b a s e o f

t h e w a l l and t h e f o u n d a t i o n s o i l will depend on t h e n a t u r e o f m a t e r i a l s u s e d

t o c o n s t r u c t t h e bzse and o n t h e c o n s t r u c t i o n t e c h n i q u e .

The b a s e f r i c t i o n t o be used f o r w a l l s w i t h o u t a k e y i s 26'/3.

When i t can b e ensu red t h a t t h e e x c a v a t i o n o f t h e b a s e w i l l be c a r r i e d o u t

in t h e d r y s e a s o n and t h a t d i s t u r b a n c e and d e t e r i o r a t i o n - . o f t h e s u b s o i l is

p r e v e n t e d by c o n s t r k t i o n of a n a d e q u a t e b l i n d i n g l a y e r inmediately a f t e r

f o u n d a t i o n e x p o s u r e , and where t h e r e is p r o f e s s i o n a l s i t e s u p e r d i s i o n i t may

b e p o s s i b l e t o j u s t i f y a h i g h e r p r o p o r t i o n of 0'. V a l u e s o f b a s e a d h e s i o n ,

c b , used i n c a l c u l ' a t i o n s shou ld be taken a s z e r o u n l c s s ,specific d a t a proving

o t h e r w i s e a r e a v a i l a b l e .

I f a s h a l l o w b a s e key i s u s e d , t h e f a i l u r e p lane w i l l g e n e r a l l y be- -

th rough t h e f o u n d a t i o n s o i l ( s e e F i g u r e 1 ) and , t h e r e f o r e , the s h e a r i n g

r e s i s t a n c e may be taken a s t h a t of t h e s o i l (6b = 0 ' and cb = c ' ) . Fur ther '

comment on t h i s is given i n S e c t i o n 6 . 2 .

2.7 W A L L FRICTION

The magnitude and d i r e c t i o n of t h e developed wal l f r i c t i o n depends

on t h e r e l a t i v e movement between t h e w a l l and t h e s o i l . En the active c a s e ,

oe moves t h e maximum v a l u e o f w a l l f r i c t i o n deve lops o n l y when the s o i l wed,

s i g n i f i c a n t l y downwards r e l a t i v e t o t h e r e a r f a c e o f t h e w a l l . Ln some c a s e s ,

w a l l f r i c t i o n c a n n o t deve lop . These i n c l u d e c a s e s where t h e wa l l moves d o n

w i t h t h e s o i l , s u c h a s a g r a v i t y w a l l on a y i e l d i n g founda t ion o r a s h e e ~ p i l e

w a l l w i th i n c l i n e d a n c h o r s , and c a s e s where t h e f a i l u r e s u r f a c e forms away

from t h e w a l l , s u c h a s i n c a n t i l e v e r and c o u n t e r f o r t w a l l s (F igure 9 ) .

The maximum v a l u e s of w a l l f r i c t i o n may b e t aken a s fo l lows :

Timber , s t e e l , p r e c a s t c o n c r e t e , 0 ' 6 rnax. = - 2

Cast i n - s i t u c o n c r e t e , 2 0 ' 6 max. = - 3

In g e n e r a l , t h e e f f e c t of w a l l f r i c t i o n is t o reduce a c t i v e p r e s s u r e .

The e f f e c t i s s m a l l and o f t e n d i s r e g a r d e d .

The e f f e c t of w a l l f r i c t i o n on passzve pressures is l a r g e ( s e e

S e c t i o n 3 ) .

C o n s i d e r a b l e s t r u c t u r a l movements may be n e c e s s a r y , however, to

m o b i l f s e maximum w a l l f r i c t i o n , f o r w h i c h , t h e s o i l i n t h e pass ive zone needs

t o move upwards r e l a t i v e t o t h e s t r u c t u r e . G e n e r a l l y , maximum w a l l E r i c r i o n

is on ly m o b i l i s e d where t h e w a l l t e n d s t o move downwards, f o r examplc, i d a

w a l l is founded on c o m p r e s s i b l e s o i l , o r f o r s h e e t p i l e d w a l l s w i t h i n c l i n e d

t e n s i o n e d members. Some gu idance on t h e p r o p o r t i o n o f maximum w a l l f r i c ~ i o n

which may d e v e l o p i n v a r i o u s c a s e s is given i n Table 1 .

T a b l e 1 . . I n d i c a t i v e P r o p o r t i o n s oE Maximum Wall Fri.c t ion Developed 4Cranu la r S o i l s - P a s s i v e Case) (Roue 6 P e a k e r , 1965)

Shee t w a l l s w i t h freedom t o move down- wards under a c t i v e f o r c e s o r i n c l i n e d anchor l o a d s

S t r u c t u r e Type

C r a v i t y o r f r e e s t a n d i n g w a l l s wi th h o r i z o n t a l movement. Shee t p i l e w a l l s b e a r i n g on hard s t r a t u m

Developed P r o p o r t i o n of Maximum Wall . F r i c t i o n

Wal ls where p a s s i v e s o i l may s e t t l e under e x t e r n a l l o a d s

Where a w a l l w i l l be s u b j e c t e d t o s i g n i f i c a n t . v i b r a t i o n , w a l l

f r i c t i o n s h o u l d n o t be i n c l u d e d .

Loose

0

Anchorage b l o c k s , e t c . which have freedom t o move upwards on m o b i l i z a t i o n of p a s s i v e p r e s s u r e .

i

2 . 8 COEFFICIENT OF SUBGRADE KEACTION

Dense

0.5

0

I n t h e d e s i g n of Foot ings and w a l l f o u n d a t i o n s , . the s i m p l i f i e d

concept of subgrade can be used t o de te rmine w a l l r o t a t i o n s . T h i s concept

0

0

i s based on t h e assumpt ion t h a t t h e s e t t l e m e n t , A , of any e lement of a

loaded a r e a i s e n t i r e l y independent of t h e load on t h e a d j o i n i n g e lements .

I t is f u r t h e r assumed t h a t t h e r e i s a c o n s t a n t r a t i o , K s , between t h e

i n t e n s i t y , 4, of t h e Eoundation p r e s s u r e on t h e e lement and t h e c o r r e s p o n d i n g

I I

0

s e t t l e m e n t , A , given by :

The f o u n d a t i o n p r e s s u r e , q , is called t h e subgrade reaction, and t h e r a t i o , -

K,, is known as t h e coefficient of subgrade reaction. -- -. - -

EARTH PRESSURES

3 . 1 STATES OF STRESS

The s t r e s s e s a t any po in t w i t h i n a s o i l mass may be represen ted on

t h e Mohr c o - o r d i n a t e system i n terms of s h e a r s t r e s s , T , and e f f e c t i v e normal

s t r e s s , u'. In t h i s system, t h e s h e a r i n g s t r e n g t h o f t h e s o i l a t v a r i o u s

e f f e c t i v e normal s t r e s s e s g i v e s an envelope o f t h e combinat ions of s h e a r .?nd

normal s tress. When t h e maximum s h e a r i n 5 s t r e n g t h is f u l l y mobi l ised a l o n g

a s u r f a c e w i t h i n a s o i l mass, a F a i l u r e - c o n d i t i o n k n o w a s a state of pZa.?tic

equi libriurn is reached.

Where t h e combinations of s h e a r and normal s t r e s s w i t h i n a s o i l mass

a l l l i e below t h e l i m i t i n g enve lope , t h e s o i l i s i n a state of elastic

equilibrium ( ~ e r z a ~ h i & Peck, 1967) . A s p e c i a l c o n d i t i o n of e l a s t i c e q u i l i b r i u m

is t h e ' a t - r e s t ' s t a t e , where t h e s o i l is preven ted from espanding o r compress in^

l a t e r a l l y w i t h changes i n t h e v e r t i c a l s t r e s s . Any l a t e r a l s t r a i n i n t h e s o i l

a l t e r s i t s h o r i z o n t a l s t r e s s c o n d i t i o n . Depending on t h e s t r a i n invo lved , t h e

f i n a l h o r i z o n t a l s t r e s s can l i e anywhere between two l i m i t i n g ( f a i l u r e )

c o n d i t i o n s , known a s t h e active and passive f a i l u r e s t a t e s .

3 . 2 AML)UNT AND ' TYPE OF WALL MOVEMENT

The e a r t h p r e s s u r e which a c t s on a n e a r t h r e t a i n i n g s t r u c t u r e is

s t r o n g l y dependent on t h e l a t e r a l de format ions which occur i n t h e s o i l -

Hence, u n l e s s t h e deformat ion c o n d i t i o n s can be e s t i m a t e d wi th r e a s o n a b l e

a c c u r a c y , r a t i o n a l p r e d i c t i o n o f t h e magnitude and d i s t r i b u t i o n o f e a r t h

p r e s s u r e i n t h e structure is n o t p o s s i b l e .

The minimum active p r e s s u r e which c a n b e e x e r t e d a g a i n s t a w a l l

o c c u r s when t h e w a l l moves s u f f i c i e n t l y E a r o u t w a r d s f o r t h e s o i l behind the

wall t o expand l a t e r a l l y and r e a c h a state of p l a s t i c e q u i l i b r i u m . Sf rn i l a r ly ,

t h e maximum passive p r e s s u r e o c c u r s when the w a l l movement is towards t h e

s o i l . The amount of movement n e c e s s a r y t o r e a c h t h e s e f a i l u r e c o n d i t i o a s is

dependent p r i m a r i l y on t h e t y p e of b a c k f i l l m a t e r i a l . Some guidance on t h e s e

mWementS i s given i n Tab le 3.

10

Table 3

Soi 1-

Sand

Clay

Wall Displacements Required t o Develop Act ive and P a s s i v e Ear th P r e s s u r e s (Wu, 1975) .

i t a t e of S t r e s s

Ac t i v e

A c t i v e

P a s s i v e

P a s s i v e

A c t i v e

A c t i v e

P a s s i v e

Type of Movement

-- P a r a l l e l t o w a l l

Ro ta t ion about base

P a r a l l e l t o w a l l

Rota t ion about base

P a r a l l e l t o w a l l

Rorat ion about b a s e

Necessary Displacement

0.001H

0.001H

0 .05 11

For w a l l d i s p l a c e m e n t s l e s s than those necessa ry t o produce the

f a i l u r e c o n d i t i o n s , t h e magnitude of the p r e s s u r e on t h e wa l l l i e s between

the ex t reme v a l u e s . F i g u r e 2 shows the t y p i c a l v a r i a t i o n i n w a l l p r e s s u r e

wi th movement.

For a r i g i d w a l l Eree t o t r a n s l a t e o r r o t a t e about its b a s e , t h e

a c t i v e o r p a s s i v e c o n d i t i o n o c c u r s i f s u f f i c i e n t movement can t a k e p l a c e , and

the p r e s s u r e d i s t r i b u t i o n remains approximate ly t r i a n g u l a r f o r u n i f o r m ~ l o p j - n g

ground ( F i g u r e 3 ( a ) ) .

In some c a s e s , r o t a t i o n about t h e b a s e o r t r a n s l a t i o g o f a f r e e

s t a n d i n g w a l l may be l i m i t e d by a s t r o n g founda t ion o r by some o t h e r r e s t r a i n t

such a s o c c u r s i n b r i d g e abutments o r w a l l s f ramed-in .wi th the s u p e r s t r u c t u r e .

S t r u c t u r a l de fo rmat ions f o r w a l l s a r e not u s u a l l y s u f f i c i e n t a l o n e t o a l l o w

development of a c t i v e p r e s s u r e s , and hence t h e w a l l is s u b j e c t t o p r e s s u r e s

near t h o s e f o r a t - r e s t c o n d i t i o n s (F igure 3 ( b ) ) o r those caused by compact ion

( S e c t i o n 3 .10) . Thermal expansion of - the s t r u c t u r e may f o r c e t h e r e t a i n i n g

w a l l s n t o t h e s o i l producing h i g h e r e a r t h p r e s s u r e s (Broms & I n g e l s o n 1 9 7 1 ) -

When t h e t o p o f t h e w a l l i s r e s t r a i n e d w h i l e the base c a n r o t a t e , n o t

a l l o f t h e r e t a i n e d s o i l p a s s e s i n t o t h e a c t i v e s t a t e . Limited movement n e a r

t h e t o p of t h e w a l l , t o g e t h e r w i t h a rch ing , leads t o an a p p r o x i m a t e l y p a r a b o l i c

p r e s s u r e d i s t r i b u t i o n , w i t h a cor respond ing f o r c e on t h e w a l l 10 t o 15% h i g h e r

than t h e f o r c e f o r t h e a c t i v e cond- i t ion ( F i g u r e 3(c)) . .

An approx ima te c a l c u l a t i o n o f t h e magn i tude o f t h e t i l t i n g movement . i . - kj t h a t r e s u l t s from t h e b a c k f i l l i n g o f a r e t a i n i n g w a l l may-be o b t a i n e d - b y

s i m u l a t i n g t h e Eoundation s o i f a s a ser ies o f s p r i n g s w i t h a n a p p r o p r i a t e .

c o e f f i c i e n t o f subgrade r e a c t i o n ( s e e S e c t i o n 2 . 8 ) . The b a s e r o t a t i o n , Ob, - . ( r a d i a n s ) is t h e n g iven by :

0 ( Eor eb S - 6 )

L ': 1.2 where V is t h e v e r t i c a l component o f t h e f o u n d a i i o n b e a r i n g p r e s s u r e ,

1- eb is t h e e c c e n t r i c i t y o f t h e l o a d on t h e base p -J

L , 0 a r e l e n g t h and b r e a d t h of t h e b a s e s r e s p e c t i v e l y , "

and Ks is t h e c o e f f i c i e n t o f s u b g r a d e r e a c t i o n (Eqn. 3 ) .

F l e x i b l e w a l l s a l l ow complex d e f o r m a t i o n s a n d r e d i s t r i b u t i o n o f l o a d s .

Loads v a r y on i n d i v i d u a l s u p p o r t s d e p e n d i n g l s r g e l y on t h e s t i f f n e s s

'': c h a r a c t e r i s t i c s o f t h e s u p p o r t s t h e m s e l v e s .

. . tr,: 7- - , - - L: S t r u t t e d w a l l s have a p p r o x i m a t e f i n a l d e f o r m a t i o n p a t t e r n s a s shown

,, i n F i g u r e 3 ( d ) . T h i s p r o f i l e is s t r o n g l y i n f l u e n c e d by c o n s t r u c t i o n d e t a i l s !.:. . . [:-.and p r o c e d u r e s , and s o p r e s s u r e e n v e l o p e s c o v e r i n g p o s s i b l e a c t u a l p r e s s u r e

d i s t r i b u t i o n s a r e used f o r r e t a i n e d h e i g h t s of g r e a t e r t h a n 6 met res . ' ( F i g u r e - (- 2 4 ) *

i:. -

.. Compaction of t h e b a c k f i l l c a n produce p r e s s u r e s h i g h e r t h a n a c t i v e . L : (2,

This i s d i s c u s s e d i n S e c t i o n s 3.10 & 3.11. -

ii 3 . 3 RANKINE EARTH PRESSURE THEORY . * . . . , ,.- iz R a n k i n e ' s e q u a t i o n s g i v e t h e e a r t h p r e s s u r e on a v e r t i c a l p l a n e which

i:. ... 1s somet imes c a l l e d t h e virtual back o f t h e w a l l . The e a r t h p r e s s u r e on the . .. .:I & . v e r t i c a l p l a n e a c t s i n a d i r e c t i o n p a r a l l e l t o t h e g r o u n d s u r f a c e and is -

d i r e c t l y p r o p o r t i o n a l t o t h e v e r t i c a l d i s t a n c e b e l o w t h e g r o u n d s u r f a c e . -x. {:;The p r e s s u r e d i s t r i b u t i o n is t r i a n g u l a r - %

- 7.-- ; 2. ;. -. R a n k i n e ' s c o n d i t i o n s are t h e o r e t i c a l l y o n l y a p p l i c a b l e t o r e r a i n i n g L

walls when t h e w a l l does n o t i n t e r f e r e w i t h t h e f o r m a t i o n o f a n y p a r t o f t h e

r.i f a i l u r e wedges t h a t form on e i t h e r s i d e o f t h e v e r t i c a l p l a n e , as s h o r n i n 1 ::

-*&Figures 1 & 9 o; v h e r e . a n imposed bounda ry p r o d u c e s t h e c o n d i t i o n s o f stress - - t h a t would e x i s t i n t h e u & t e r r u p t e d s o i l wedges. These k o n d i t i o n s r e q u i r e t h a t 1.' :

I . . . :- t h e a n g l e o f w a l l f r i c t i o n is e q u a l t o t h e b a c k f i l l s l o p e ( 6 = m )

P a s s i v e c a l c u l a t i o n s u s i n g Rankine

d i r e c t i o n of w a l l f r i c t i o n w i l l b e i n c o r r e c t

a r e n o t recommended, s i n c e t h e

and an u n d e r e s t i m a t i o n of

p a s s i v e r e s i s t a n c e w i l l r e s u l t . --

3 . 4 COULOMB EARTH PRESSURE THEORY

Coulomb theory assumes t h a t a wedge o f s o i l bounded by a p l a n a r

f a i l u r e s u r f a c e s l i d e s on t h e back of t h e w a l l . Hence s h e a r i n g r e s i s t a n c e is

m o b i l i s e d on both back of t h e c a l l and t h e f a i l u r e s u r f a c e . The r e s u l t a n t

p r e s s u r e c a n be c a l c u l a t e d d i r e c t l y f o r a r ange of w a l l f r i c t i o n s , s l o p e s -

o f wa l l and b a c k f i l l s l o p e s .

Where t h e wa l l f r i c t i o n is a t a n g l e s o t h e r than t h e b a c k f i l l s l o p e

' a n g l e t h e e q u a t i o n s a r e an approx imat ion due t o t h e curved n a t u r e oE t h e

a c t u a l f a i l u r e s u r f a c e and t h e f a c t t h a t s t a t i c e q u i l i b r i u m i s n o t always

s a t i s f i e d . The e r r o r is s l i g h t l y on t h e u n s a f e s i d e f o r t h e a c t i v e c a s e , and

more s e r i o u s f o r t h e p a s s i v e c a s e . For s i m p l e g e o m e t r i e s , the c h a r t e d v a l u e s

o f K, g i v e n i n F igures 4 & 5 (Caquot & K e r i s e l , 1948) may be used ; t h e s e were

o b t a i n e d f o r t h e more a c c u r a t e E a i l u r e mechanism i n v o l v i n g curved f a i l u r e

s u r f a c e s .

3 . 5 TRl A t WEDGE METHOD

D i f f i c u l t i e s a r i s e i n t h e u s e o f c h a r t s o r e q u a t i o n s where t h e

, ground s u r f a c e is i r r e g u l a r , where t h e b a c k f i l l p o s s e s s e s some ccohesion,

where w a t e r p r e s s u r e s e x i s t i n the b a c k f i l l o r where t h e b a c k f i l l - c o k p r i s e s

more t h a n one s o i l type.

The s i m p l e s t approach f o r e a r t h p r e s s u r e d e t e r m i n a t i o n i n t h e s e

c a s e s is t o use a g r a p h i c a l p rocedure making t h e assumpt ion of p l a n a r f a i l u r e

s u r f a c e s based on Coulomb t h e o r y . The method i s v e r y powerful i n t h a t

s o l u t i o n s t o most a c t i v e p r e s s u r e problems are p o s s i b l e and it a l s o h a s the

advan tage t h a t t h e d e s i g n e r c a n s e e t h e s o l u t i o n d e v e l o p i n g and g a i n s an

a p p r e c i a t i o n of the s i g n i f i c a n c e of t h e c o n t r i b u t o r y f a c t o r s invo lved .

. There a r e , however, c e r t a i n l i m i t a t i o n s in t h e u s e o f t h e method for t h e

d e t e r m i n a t i o n of p a s s i v e p r e s s u r e s . The p r o c e d u r e is knpcm a s t h e T r i a l Wedge

Method o r t h e Coulomb Wedge Method.

-- . -The method -is o u t l i n e d i n F i g u r e s 6 ,7 & 8. The b a c k f i l l is - -.

d i v i d e d i n t o wedges by s e l e c t i n g p l a n e s through the h e e l of t h e w a l l . The .

f o r c e s ac t ing- on each of t h e s e wedges a r e combined i n a f o r c e polygon s o c h a t .-- t h e magni tude of t h e r e s u l t a n t e a r t h p r e s s u r e can be o b t a i n e d . A ~ o r c ' e polygon

is c o n s t r u c t e d , a l t h o u g h t h e f o r c e s a c t i n g on- the wedge a r e i n g e n e r a l no t i n

moment e q u i l i b r i u m . T h i s method i s t h e r e f o r e an approximat ion w i t h the same

assumpt ions a s t h e e q u a t i o n s For Coulomb's c o n d i t i o n s , and, f o r a 'g round

s u r f a c e w i t h a un i fo rm s l o p e , g i v e s t h e same r e s u l t . When t h e v a l l f r i c t i o n '

c o r r e s p o n d s t o t h a t impl ied by t h e Rankine c a s e , t h e v a l u e of e a r t h p r e s s u r e

o b t a i n e d Erorn t h e T r i a l Wedge Method is e q u a l t o :hat o b t a i n e d from ank kine's

e q u a t i o n .

F i g u r e 8 shows t h e . g e n e r a 1 method of d e a l i n g w i t h a c t i v e p r e s s u r e s

i n more complex ground . c o n d i t i o n s u s i n g t h e T r i a l Wedge Method. I t should

b e n o t e d t h a t t h e method can b e r a t h e r l a b o r i o u s i n t h e s e s i t u a t i o n s .

The a d h e s i o n of t h e s o i l t o t h e back or' t h e w a l l i n cohes ive s o i l s

is u s u a l l y n e g l e c t e d , s i n c e i ts v a l u e i s d i f f i c u i t t o d e t e r m i n e and the

s i c a p l i f i c a t i o n is c o n s e r v a t i v e . For t h e a c t i v e c a s e , t h e maximum value of t h e

e a r t h p r e s s u r e c a l c u l a t e d f o r t h e v a r i o u s wedges is r e q u i r e d . T h i s i s a b t a i n e d

by i n t e r p o l a t i n g between the c a l c u l a t e d v a l u e s (see F i g u r e 6 ) . For the p a s s i v e

case, t h e r e q u i r e d minimum v a l u e is s i m i l a r l y ob:ained. The d i r e c t i o n o f t h e

r e s u l t a n t e a r t h p r e s s u r e i n t h e f o r c e ~ o l y g o n s should be o b t a f n e d b y c o n s i d e r i n g

the d i r e c t i o n of t h e r e l a t i v e movement between iiie w a l l and s o i l . F o r c a s e s

where t h i s force a c t s p a r a l l e l t o t h e ground s u r f a c e , a s u b s t i t u t e cons fan t

s l o p e shou ld be used f o r s o i l b o t h w i t h and without cohes ion ( F i g u r e 10) -

T h e o r e t i c a l l y , i n c o h e s i v e s o i l s , t ens ion exists t o a depth To below

b o t h h o r i z o n t a l and s l o p i n g ground s u r f a c e s . .

where c

Y

B

- Yo = - d

Zc t a n (45' +- . . . .. ( 5 ) Y -

is the cohesion of the s o i l i n terms of t o t a l s t r e s s ,

is the bulk u n i t w e i g h t of t h e soil, arrd

is. the a n g l e of s h e a r i n g r e s i s t a n c e of the s o i l i n te&s of total stress.

Shear s t r e n g t h pa ramete r s i n t e rms of e r ' f e c t i v e stress (c' 6 9') be

u s e d i n e q u a t i o n ( 5 ) . -

+

V e r t i c a l t e n s i o n c r a c k s w i l l deve lop i n t h i s zone s i n c e s o i l canno t

s u s t a i n t e n s i o n and w i l l become w a t e r f i l l e d . One o f t h e s e c r a c k s w i l l ex tend

down t o t h e f a i l u r e s u r f a c e and s o reduce t h e l e n g t h on which cohesion a c t s .

The e f f e c t of t h i s , t o g e t h e r w i t h t h e s l i g h t l y s m a l l e r wedge we igh t , is t h e

same a s n e g l e c t i n g the r e d u c t i o n i n t o t a l p r e s s u r e provided by t h e t e n s i o n

zone a c c o r d i n g t o t h e Rankine and Coulomb e q u a t i o n s . Figure 7 shows t h e wedge

a n a l y s i s Eor t h i s case .

For an i r r e g u l a r ground s u r f a c e t h e p r e s s u r e d i s t r i b u t i o n a g a i n s t t h e

w a l l i s no t t r i a n g u l a r . However, i f t h e ground d o e s n o t depar t s i g n i f i c a n t l y

from a p l a n e s u r f a c e , a l i n e a r p r e s s u r e d i s t r i b u t i o n may be assumed, and t h e

c o n s t r u c t i o n given i n ' F i g u r e 1 1 used t o d e t e r m i n e t h e p o i n t of a p p l i c a t i o n o f

t h e a c t i v e f o r c e . A more a c c u r a t e method i s g i v e n i n Figure 1 2 . The L a t t e r

should be used when t h e r e a r e a b r u p t changes i n t h e ground s u r f a c e , o r t h e r e

a r e non-uniform surcharges i n v o l v e d .

3 . 6 PASSIVE EARTH PRESSURES

The shape o.£ t h e f a i l u r e s u r f a c e f o r p a s s i v e f a i l u r e i s c u r v e d , more

s t r o n g l y when w a l l f r i c t i o n is p r e s e n t . Both Coulomb and the T r i a l Wedge

t h e o r i e s assume plane f a i l u r e s u r f a c e s and l e a d t o s u b s t a n t i a l e r r o r s i n

c a l c u l a t e d v a l u e s of p a s s i v e r e s i s t a n c e .

Methods us ing curved f a i l u r e s u r f a c e s , such a s l o g - s p i r a l and - c i r c u l a r , may be used w i t h o u t i n t r o d u c t i o n of s i g n i f i c a n t e r r o r . Caquot &

K e r i s e l ( 1 9 4 8 ) have p r e s e n t e d c h a r t s f o r s i m p l e g e o m e t r i e s ( F i g u r e s 4 5 )

based on a combination of l o g - s p i r a l and a p l a n e . For more complex g e o m e t r i e s

p a s s i v e p r e s s u r e may b e c a l c u l a t e d u s i n g t h e c i r c u l a r a r c method o u t l i n e d i n

F i g u r e 13. T h i s method i s q u i t e l a b o r i o u s f o r e v e n r e l a t i v e l y s imple

c o n d i t i o n s .

The t r i a l wedge method may b e used t o d e t e r m i n e p a s s i v e r e s i s t a n c e .

However, s e r i o u s o v e r e s t i m a t i o n of t h e p a s s i v e p r e s s u r e r e s u l t s when t h e a n g l e

of w a l l f r i c t i o n 6 is g r e a t e r t h a n 2 0 ' 1 3 (Morgens te rn & E i s e n s t e i n , 1970).

Care s h o u l d b e taken t h e n t o e n s u r e t h a t 6 is not o v e r e s t i m a t e d , a s t h e e r r o r

is on t h e u n s a f e

d e t e r m i n 2 t i o n of

s i d e , and the trial wedge .method shou ld n o t be used' f o r the

p a s s i v e p r e s s u r e s when 6 > 0 ' / 3 . -

-

3'. 7 EARTH PRESSURES FOR SMALL WALL DEFLECTIONS

F o r c e r t a i n w a l l t y p e s , such- a s propped c a n l i l e v e r s and anchored

diaphragm w a l l s , o n l y - s m a l l w a l l movements occur and e l a s t i c c o n d i t i o n s apply .

-- Where no l a t e r a l movement t a k e s p l a c e from t h e i n s i t u c o n d i t i o n ,

- t h e ' a t - r e s t ' e a r t h p r e s s u r e a p p l i e s . For t h e c a s e of a v e r t i c a l wall and

a h o r i z o n t a l ground s u r f a c e , i t h a s been shown e m p i r i c a l l y by Jaky ( 1 9 4 4 ) t h a t

the c o e f f i c i e n t of ' a t - r e s t ' e a r t h p r e s s u r e , K O , f o r normal ly c o n s o l i d a t e d

m a t e r i a l s may be taken a s :

KO = 1 - s i n 0 ' . . . . . ( 6 )

where 0' is t h e ang le of s h e a r i n g r e s i s t a n c e o f t h e s o i l i n t e r n s of e f f e c t i v e

s t r e s s .

Because of t h e l a c k of d a t a on t h e v a l u e s of K O ,

v a l u e s a d o p t e d f o r d e s i g n should n o t b e l e s s t h a n 0 .5 even f o r s o i l s w i t h h igh

E r i c t i o n a n g l e s . It shou ld be no ted t h a t , i n some s i t u a t i o n s , va lues much

h i g h e r t h a n KO = 0.5 may be found.

For a s l o p i n g ground s u r f a c e , KO v a r i e s from t h a t g i v e n by equa t ion

( 6 ) . The Danish Code (Danish C e o t e c h n i c a l I n s t i t u t e , 1978) s u g g e s t s f o r a

v e r t i c a l w a l l and ground s l o p i n g a t an a n g l e , w, t h a t t h e ' a t - r e s t ' e a r t h .

p r e s s u r e c o e f f i c i e n t i s KO ( 1 + s i n w ) . For o t h e r w a l l a n g l e s and b a c k f i l l

s l o p e s , i t may assumed t h a t t h e a t - r e s t p r e s s u r e c o e f f i c i e n t v a r i e s p ropor t ion-

a l l y t o t h e ' a c t i v e ' e a r t h p r e s s u r e c o e f f i c i e n t , Ka . ' ~ t - r e s t ' e a r t h p r e s s u r e s ,

excep t f o r over -conso l ida ted s o i l s , may b e assumed t o i n c r e a s e l i n e a r l y wi th

depth from z e r o a t t h e ground s u r f a c e . The t o t a l a t - r e s t e a r t h p r e s s u r e f o r c e

is g i v e n by Po = UoY H'. T h i s a c t s a t H/3 from c h e b a s e of t h e wa i l o r from

t h e bo t tom of t h e key f o r w a l l s w i t h keys .

I n c o h e s i o n l e s s s o i l s , f u l l ' a t - r e s t ' e a r t h p r e s s u r e s occur o n l y w i t h

t h e most r i g i d l y suppor ted w a l l s ( s e e S e c t i o n 3 .10) . I n h i g h l y p l a s t i c c l a y s ,

P r e s s u r e s approaching a t - r e s t may deve lop u n l e s s w a l l movement can c o n t i n u e

w i t h time.

3 . 8 INFLUENCE O F GEOMETiZfCAL S f l A P E OF R E T A I N I N G STRUCTURE ON WALL F R T C T I O N

When r e l a t i v e movement c a n o c c u r between a w a l l and t h e s u p p o r t e d

s o i l , che e f f e c t o f w a l l f r i c t i o n must be t a k e n i n t o accoun t . I n some c a s e s --

t h e w a l l is f r e e t o move w i t h t h e s o i l , s u c h a s i n t h e c a s e of l a g g i n g

b e t w e e n s o l d i e r p i l e s . I n t h e s e c a s e s l i t t l e o r no w a l l f r i c t i o n i s n w b i l i s c a .

When t h e o u t e r f a i l u r e s u r f a c e from t h e h e e l of t h e w a l l i n t e r s e c t : s

o r l i e s w i t h i n t h e w a l l Coulomb's c o n d i t i o n s a p p l y . Rank ine ' s c o n d i t i o n s o n l y

a p p l y t o c a s e s where t h i s f a i l u r e s u r f a c e d o e s no t i n t e r s e c t t h e w a l l , a s shown

i n F i g u r e 9.

3.9 INFLUENCE OF L I M I T E D BACKFl LL

The methods given above assume t h a t t h e s o i l is homogeneous f o r a

s u f f i c i e n t d i s t a n c e b e h i n d t h e w a l l t o e n a b l e an i n n e r . f a i l u r e s u r f a c e t o

fo rm i n t h e p o s i t i o n where s t a t i c e q u i l i b r i u m is s i t i s f i e d ( F i g u r e 12) . Where

a n e x c a v a t i o n i s made t o accommodate t h e w a l l , t h e u n d i s t u r b e d i n s i t u material

may have a s t r e n g t h d i f f e r i n g from t h e b a c k f i l l . I f e q u a t i o n s a r e u s e d , t h e .

p o s i t i o n o f t w o . f a i l u r e p l a n e s s h o u l d be c a l c u l a t e d , one u s i n g t h e p r o p e r t i e s

of t h e b a c k f i l l m a t e r i a l a n d o n e u s i n g t h e p r o p e r t i e s of t he u n d i s t u r b e d m a t e r i a l -

IE b o t h f a l l w i t h i n t h e p h y s i c a l l i m i t o f t h e b a c k f i l l , t h e c r i t i c a l E a i l u r e

p l a n e i s o b v i o u s l y t h e o n e c a l c u l a t e d u s i n g t h e b a c k f i l l p r o p e r t i e s .

S i m i l a r l y , i f t h e y b o t h come w i t h i n t h e u n d i s t u r b e d m a t e r i a l , t h e c r i t i c a l o n e

is t h a t f o r t h e u n d i s t u r b e d m a t e r i a l p r o p e r t i e s . - . .

Two o t h e r p o s s i b l e s i t u a t i o n s may a r i s e : f i r s t l y where c r i t i c a l f a i l u r e

p l a n e s o c c u r i n b o t h m a t e r i a l s , i n which c a s e t h e one g i v i n g t h e maximum e a r t h

p r e s s u r e i s u s e d , and s e c o n d l y where t h e f a i l u r e p l a n e c a l c u l a t e d w i t h t h e

b a c k f i l l p r o p e r t i e s would f a l l w i t h i n t h e u n d i s t u r b e d m a t e r i a 1 , a n d t h e f a i l u r e

p l a n e f o r u n d i s t u r b e d m a t e r i a l would f a l l w i t h i n t h e b a c k f i l l . I n t h e l a t t e r

c a s e , which o c c u r s when t h e u n d i s t u r b e d m a t e r i a l h a s a h i g h s t r e n g t h , t h e - b a c k f i l l may b e assumed t o s l i d e on t h e p h y s i c a l boundary be tween t h e two

materials. The e a r t h p r e s s u r e e q u a t i o n s d o n o t a p p l y i n t h i s c a s e , b u t t h e

wedge method may b e u s e d w i t h t h e a l r e a d y s e l e c t e d f a i l u r e p l a n e and t h e

b a c k f i l l s o i l p r o p e r t i e s . The t o t a l p r e s s u r e t h u s c a l c u l a t e d i s less than

the active v a l u e a s s u m i n g u n i f o r m m a t e r i a l b e h i n d t h e w a l l . The v a r i a t i o n of

p r e s s u r e w i t h d e p t h i s not l i n e a r , and s h o u l d be de te rmined by t h e p r o c e d u r e

g i v e n i n F i g u r e 12-. .

T h e d e p t h , hc , be low wh ich a c t i v e p r e s s u r e due t o t h e weight

o f t h e o v e r l y i n g s o i l e x c e e d s t h e c o m p a c t i o n i n d u c e d p r e s s u r e i s o b t a i n e d

from :

The eEEect of c o m p a c t i o n o n l a t e r a l p r e s s u r e i s s h o w i n F igu re

1 4 ( i i ) ( a ) & ( b ) and t h e r e s u l t i n g p r e s s u r e d i s t r i b u t i o n For u s e i n d e s i g n ,

ba sed o n t h i s s i m p l i f i e d t h e o r y , i s shown i n F i g u r e i 4 ( i i ) ( c ) . I n g o l d ' s d e s i g n

p r e s s u r e d i s t r i b u t i o n c a n b e s e e n t o b e v e r y s i m i l a r t o t h a t oE Brons shown i n

F i g u r e 14 ( i ) .

3.11 EFFECTS OF COMPACTION ON CONVENTIONAL WALL DESIGN

The l a t e r a l p r e s s u r e s i nduced by c o m p a c t i o n ( F i g u r e 1 4 ) can be up

t o t w i c e t h e a c t i v e p r e s s u E e s o b t a i n e d by c o n v e n t i o n a l a n a l y s i s . These

c o m p a c t i o n p r e s s u r e s l e a d t o h i g h e r s t r u c t u r a l l o a d s , which nay c a u s e d i s t r e s s

o r r e s u l t i n s e r v i c e a b i l i t y p r o b l e m s w i t h a w a l l .

- I f movement oE t h e w a l l is a l l o w e d t o t a k e p l a c e t h e s e compaction-

i nduced p r e s s u r e s a r e . r e d u c e d . T r a n s l a t i o n s o r r o t a t i o n s of t h e o r d e r o f

H/500 are s u f f i c i e n t t o r e d u c e t h e p r e s s u r e s t o n e a r t h e a c t i v e s t a t e . The

f i n a l p r e s s u r e d i s t r i b u t i o n is p a r a b o l i c r a t h e r t h a n t r i a n g u l a r , and t h u s t h e

l i n e o f t h r u s t is r a i s e d .

It i s s a t i s f a c t o r y t o u s e t h e a c t i v e p r e s s u r e d i s t r i b u t i o n when

d e t e r m i n i n g t h e f a c t o r o f s a f e t y a g a i n s t s l i d i n g . The bend ing moments a f t e r

s l i d i n g h a s t a k e n p lace . may s t i l l b e u p t o 50X h i g h e r t han t h o s e p r e d i c t e d

u s i n g a t r i a n g u l a r a c t i v e p r e s s u r e d i s t r i b u t i o n . C a l c u l a t i o n s o f b e a r i n g

p r e s s u r e s a n d o v e r t u r n i n g moments s h o u l d t a k e in to a c c o u n t t h e h i g h e r p o s i t i o n

o f t h e l i n e of t h r u s t .

m 4

EFFEGTS OF SURCHARGES

4 . 1 UNIFORM SURCHARGES

Loads imposed

d e s i g n .

on t h e s o i l b e h i n d t h e w a l l s h o u l d be a l l o w e d f o r i n

Uniform s u r c h a r g e l o a d s may be c o n v e r t e d t o an e q u i v a l e n t h e i g h t O F

f i l l and t h e e a r t h p r e s s u r e s c a l c u l a t e d f o r t h e c o r r e s p o n d i n g l y g r e a t e r h e i g h t

I n t h i s case the d e p t h of t h e t e n s i o n z o n e s i n c o h e s i v e m a t e r i a l is c a l c u l a t e d

from t h e t o p of t h e e q u i v a l e n t a d d i t i o n a l f i l l . The d i s t r i b u t i o n o f p r e s s u r e

f o r t h e g r e a t e r h e i g h t ' i s d e t e r m i n e d by t h e p r o c e d u r e s g i v e n i n C h a p t e r 3 . The

t o t a l l a t e r a l e a r t h p r e s s u r e i s c a l c u l a t e d f rom t h e p r e s s u r e d i a g r a m , n e g l e c t i n g

t h e p a r t i n t e n s i o n a n d / o r t h e p a r t i n t h e h e i g h t o f f i l l e q u i v a l e n t t o t h e

s u r c h a r g e , a s shown i n F i g u r e 1 2 .

B u i l d i n g s w i t h s h a l l o w f o u n d a t i o n may b e t a k e n a s a u n i f o r m

s u r c h a r g e of lOkPa p e r s t o r e y .

The s t a n d a r d l o a d i n g s f o r highway s t r u c t u r e s i n a r e

expres sed i n terms o f HA and HB l o a d i n g a s d e f i n e d i n BS 5400 : Part 2 : 1978.

I n t h e a b s e n c e o f - m o r e e x a c t c a i c u l a t i o n s , t h e n o m i n a l l oad d u e t o l i v e load -

s u r c h a r g e may be t a k e n from T a b l e 4 .

The two l o a d i n g c a s e s shown i n F i g u r e 16 need t o b e c o n s i d e r e d .

Tab le 4 Sugges t ed S u r c h a r g e Loads t o b e Used in. t h e Des ign o f R e t a i n i n g ~ t r u c t u r e s ( P u b l i c Works D e p a r t m e n t , ' l 9 7 7 )

r YeMC U N t )

E q u i v a l e n t Surcharge

20kPa

1SkPa

1 OkPa

5kPa

t

Road c l a s s

Urban t r u n k R u r a l t r u n k (Road l i k e l y t o b e - r egu la r ly used by heavy i n d u s t r i a l t r a f f i c )

Primry d i s t r i b u t o r Rura l main r o a d

District and l o c a l d i s t r i b u t o r s O the r r u r a l r o a d s Access Roads, C a r p a r k s

1 - Foo tpa ths , i s o l a t e d f rom r o a d s P l a y a r e a s

Note : 1. It is recommended t h a t t h e s e s u r c h a r g e s b e a p p l i e d . t o t h e 1 i n 10 y e a r s t o r m c o n d i t i o n .

2 . For f o o t p a t h s n o t i s o l a t e d f rom roadways , t h e s u r c h a r g e a p p l y i n g f o r t h a t - r o a d c lass s h o u l d b e u s e d -

T y p e o f l i v e l o a d i n g

HA + 45 u n i t s of HB

HA + 37% u n i t s o f HB

HA

4 . 2 t 1 NE LOADS - - , - -

Where t h e r e is a superimposed l i n e load running f o r a c o n s i d e r a b l e

l e n g t h p a r a l l e l t o the w a l l , t h e Wedge Method of des ign may be used , and t h e

weight p e r u n i t Length of t h i s l o a d can be added t o t h e weight of t h e

p a r t i c u l a r t r i a l wedge t o which i t is a p p l i e d . A s t e p thus a p p e a r s i n t h e

a c t i v e f o r c e l o c u s , a s t h e we igh t of t h e t r i a l wedge suddenly i n c r e a s e s when

t h e l i n e l o a d i s inc luded. The i n c r e a s e d t o t a l e a r t h p r e s s u r e w i l l be g i v e n

from t h e t r i a l wedge procedure , b u t the l i n e load w i l l a l s o change t h e p o i n t

oE a p p l i c a t i o n oE t h i s t o t a l p r e s s u r e . The method given i n F igure 15 may be

used t o g i v e t h e d i s t r i b u t i o n of p r e s s u r e .

When t h e l i n e load is s m a l l compared t o t h e a c t i v e e a r t h p r e s s u r e ,

the e E f e c t o f t h e l i n e load 0:: i t s own should b e determined by t h e mechod g i v e n

I n F i g u r e 15. Th i s is based on s t r e s s e s i n an e l a s t i c medium modiEied by

exper imenr . The p ressures t h u s determined a r e superimposed on t h o s e d u e t o

a c t i v e e a r t h p r e s s u r e and o t h e r p r e s s u r e s a s a p p r o p r i a t e .

4 . 3 P07NTLOAVS .

P o i n t loads cannot b e taken i n t o account by t r i a l wedge p r o c e d u r e s .

The method based on Bouss inesq ' s equa t ions g iven i n F igure 15 may be u s e d ,

b u t i t shou ld be noted t h a t t h e method is only approximate a s t h e s t i f - E n e s s

of the w a l l i s not taken i n t o accoun t .

c m 5

EFFECTS OF WATER

5.1 GENERAL

The p r e s e n c e of w a t e r beh ind a w a l l h a s a marked e f f e c t on t h e

p r e s s u r e s a p p l i e d t o t h e w a l l . When t h e p h r e a t i c s u r f a c e i n t e r s e c t s t h e w a l l ,

a h y d r o s t a t i c p r e s s u r e i s e x e r t e d a g a i n s t t h e w a l l , t o g e t h e r w i t h u p l i f t

p r e s s u r e s a l o n g t h e b a s e o f t h e w a l l . Even when t h e r e is no w a t e r i n d i r e c t

c o n t a c t w i t h t h e wall., s u c h a s w h e n a d e q u a t e d r a i n a g e is p r o v i d e d , t h e r e is a n

i n c r e a s e d p r e s s u r e on t h e w a l l d u e t o t h e i n c r e a s e d e a r t h p r e s s u r e ( S e c t i o n

5 .2) . The e f f e c t of w a t e r b e h i n d t h e w a l l i s s i g n i f i c a n t ; t h e t o t a l f o r c e

may b e more than doub le t h a t a p p l i e d For d r y b a c k f i l l . Many r e c o r d e d w a l l

f a i l u r e s c a n be a t t r i b u t e d t o t h e p r e s e n c e o f w a t e r .

The h e i g h t t o which w a t e r can r i s e i n t h e b a c k f i l l , and t h e volume .

of f l o w , are b o t h of pr ime c o n c e r n . To d e t e r m i n e t h e s e t h e ground w a t e r

c o n d i t i o n s must be e s t a b l i s h e d . These may b e b e s t d e r i v e d from t h e

o b s e r v a t i o n of groundwater c o n d i t i o n s p r i o r t o c o n s t r u c t i o n u s i n g p i e z o m e t e r s

and by a p p l y i n g t h e p r i n c i p l e s o u t l i n e d i n t h i s S e c t i o n . N o t w i t h s t a n d i n g t h e

r e s u l t s o f g roundwate r m o n i t o r i n g , t h e groundwater l e v e l assumed f o r d e s i g n

s h o u l d b e n o t lower t h a n o n e - t h i r d of t h e r e t a i n e d h e i g h t . .-

The e f f e c t of l e a k a g e f rom s e r v i c e s c a n b e s i g n i f i c a n t . T h e r e i s

e v i d e n c e f rom f i e l d measurements and f a i l u r e s i n Hong ~ o n g t h a t t h i s l e a k a g e

c o n t r i b u t e s s u b s t a n t i a l l y t o b o t h pe rched and main g roundwate r t a b l e s .

Where i n a d e q u a t e d r a i n a g e i s p r o v i d e d b e h i n d a r e t a i n i n g s t r u c t u r e ,

t h e r e may b e a d a r n i n g effect which would r e s u l t i n r a i s i n g g r o u n d w a t e r l e v e l s

l o c a l l y and i n t h e g e n e r a l area. Such a rise may a d v e r s e l y a f f e c t t h e

s t a b i l i t y o f s l o p e s and r e t a i n i n g w a l l s . E f f e c t i v e d r a i n a g e m e a s u r e s s h o u l d

a lways be p rov ided i n s u c h cases.

5.2 EFFECT OF WATER ON EARTH PRESSURES

When a s o i l is submerged, i t s e f f e c t i v e u n i t we igh t is r e d u c e d t o

Y ' = Y sa t ' Y W . The l a t e r a l e a r t h p r e s s u r e s h o u l d , i n t h i s case, be

c a l c u l a t e d u s i n g Y ' i n e q u a t i o n s o r c h a r t s . A l t e r n a t i v e l y , i n g r a p h i c a l

. - - - - - -

p r o c e d u r e s such a s the t r i a l wedge method, a l l f o r c e s a c t i n g on t h e s o i l .

wedge, i n c l u d i n g the h y d r o s t a t i c normal u p l i f t p r e s s u r e on t h e f a i l u r e p lane

and t h e l a t e r a l h y d r o s t a t i c p r e s s u r e , may be included i n t h e t r i a l wedge

p r o c e d u r e . his is i l l u s t r a t e d i n Figure 6 t o 8.

In low p e r m e a b i l i t y cohes ive s o i l s , t h e pore wa te r p r e s s u r e s s e t up

d u r i n g c o n s t r u c t i o n may be i n e x c e s s of any h y d r o s t a t i c pore p r e s s u r e , s o an

u n d r a i n e d a n a l y s i s may be more a p p r o p r i a t e .

When t ens ion c r a c k s o c c u r , l a t e r a l h y d r o s t a t i c wa te r p r e s s u r e shou ld

be i n c l u d e d For t h e f u l l depth o f t h e t r a c k , a s g iven i n S e c t i o n 3 .5 o r f o r

H / 2 , w h i c h e v e r ' i s l e s s . F u l l l a t e r a l ' w a t e r p r e s s u r e must be al lowed f o r

below t h e i n v e r t of the lowest weep h o l e s o r o t h e r d ra inage o u t l e t s .

IF the water i n t h e s o i l v o i d s ' i s f lowing , t h e pore wa te r p r e s s u r e s ,

a r e changed from the h y d r o s t a t i c v a l u e s t o values de temined by the seepage p a t t e r n .

These v a l u e s have t o be used i n a t r i a l wedge s o l u t i o n t o determine t h e e a r t h

p r e s s u r e .

The a c t u a l f low p a t t e r n developed i s very dependent on t h e

u n i f o r m i t y and homogeneity o f . t h e ground, and on t h e p o s i t i o n of any d r a i n s . *

F i g u r e 1 7 ( a ) shows t h e f low n e t produced by s t e a d y seepage i n t o a v e r t i c a l . .

d r a i n when t h e p h r e a t i c s u r f a c e i s below ground l e v e l and t h e b a c k f i l l

un i fo rm and i s o t r o p i c . R a i n f a l l of i n t e n s i t y e q u a l t o o r g r e a t e r than t h e

p e r m e a b i l i t y of t h e b a c k f i l l w i l l change t h i s f l o w n e t t o t h a t s h o w i?

F i g u r e 17(b) if t h e r e i s no s u r f a c e p r o t e c t i o n t o p r e v e n t i n f i l t r a t i o n .

There i s a s i g n i f i c a n t i n c r e a s e i n . w a t e r p r e s s u r e on t h e f a i l u r e s u r f a c e f o r t h i s

l a t t e r c a s e . It is thus d e s i r a b l e , f o r t h i s d r a i n a g e arrangement , t o p r e v e n t - w a t e r e n t e r i n g t h e b a c k f i l l from the s u r f a c e . F i g u r e 17(c ) shows t h e f l o w

n e t due t o heavy r a i n f a l l i n f i l t r a t i o n i n t o a n i n c l i n e d d r a i n . The e f f e c t

o f t h i s d r a i n a g e arrangement i s t o reduce t h e w a t e r p r e s s i r e i n t h e b a c k f i l l

t-o z e r o ; t h i s is t h e r e f o r e a v e r y e f f e c t i v e d r a i n a g e measure.

The pore wa te r p r e s s u r e s normal t o t h e a c t i v e o r p a s s i v e wedge

f a i l u r e s u r f a c e a f f e c t t h e f o r c e s a c t i n g on a w a l l . The r e s u l t a n t t h r u s t on

t h e f a i l u r e s u r f a c e , determined from a flow n e t , is a p p l i e d in t h e f o r c e

polygon f o r t h e s o i l wedge t o g e t h e r with any l a t e r a l water p r e s s u r e a t t h e

w a l l a s shown i n Fdgures 6 t o 8. The method o f de te rmin ing w a t e r p r e s s u r e s

from t h e f low n e t , and hence t h e water Eorce, is shown i n F i g u r e 1 7 . -

~0.r methods o f d e a l i n g wi th seepage through a n i s o t r o p i c and

non-homogeneous b a c k f i l l s , r e f e r e n c e may be made t o Cedergren ( 1 9 7 7 ) .

5.3 DRAINAGE PROVISIONS

Water p r e s s u r e s must b e included i n t h e f o r c e s a c t i n g on t h e w a l l

k n l e s s s u i t a b l e d ra inage i s provided. Good p r a c t i c e r e q u i r e s t h a t d r a i n a g e

is always provided.

For w a l l s l e s s than 2 metres h i g h , d r a i n a g e m a t e r i a l is u s u a l l y

on ly provided on t h e back f a c e of t h e v a l l , w i t h weep h o l e s t o r e l i e v e w a t e r

P r e s s u r e . I n some low r i s k s i t u a t i o n s , i t may be g e o t e c h n i c a l l y t o l e r a b l e

and economical ly advantageous t o omit t h e d r a i n and design f o r t h e h y d r o s t a t i c

water p r e s s u r e .

With c o r r e c t l y des igned i n c l i n ~ d d r a i n a g e systems, such a s t h o s e

shown i n F i g u r e s 18(a) & ( c ) , wa te r p r e s s u r e s may be neg lec ted b o t h on t h e w a l l

i t s e l f and on t h e s o i l f a i l u r e p lane . A l t e r n a t i v e d ra inage d e t a i l s a s shown

i n F i g u r e s 18(b) & (d) may be used. I n t h e s e c a s e s , the appropr i -a te w a t e r

P r e s s u r e shou ld be cons idered i n des ign. H y d r o s t a t i c p r e s s u r e w i f l act on

t h e w a l l be low t h e lowest d r a i n a g e o u t l e t .

For a d r a i n t o b e e f f e c t i v e i t must b e a b l e t o c a r r y t h e d e s i g n £ l o $

'of w a t e r w i t h o u t backing up o r b locking. T h i s d e s i g n flow s h o u l d i n c l u d e t h e

. f l o w s from l e a k i n g o r b u r s t s e r v i c e c o n d u i t s where a p p r o p r i a t e .

To p r e v e n t b lockage , t h e d r a i n must b e p r o t e c t e d by a n a d e q u a t e

! filter, des igned accord ing t o t h e r u l e s g i v e n i n S e c t i o n 5 . 4 .

The r a t e of seepage i n t o t h e d r a i n from t h e s o i l c a n be !

determined f rom a flow n e t t o g e t h e r w i t h a knowledge of t h e p e r m e a b i l i t i e s

' o f t h e s o i l s invo lved and a flow-net. - n e w a t e r f low rate t h a t t h e d r a i n a g e l a y e r can accommodate depends

.on t h e p e r m e a b i l i t y of t h e d r a i n a g e medium, t h e t h i c k n e s s o f t h e d r a i n and the

- - -

h y d r a u l i c g r a d i e n t - i n t h e d r a i n . In some c a s e s , i t may be in tended t h a t the

f i l t e r i t s e l f shou-ld a c t a s a d r a i n ; i f so, i t should be des igned t o have ,

adequa te c a p a c i t y . -- -

By the use of a c o n v e n t i o n a l f low n e t s k e t c h , t h e approximate r a t e

of Elow i n t o t h e d r a i n may be e s t i m a t e d . Using an a p p r o p r i a t e value O F

h y d r a u l i c g r a d i e n t , i, and t h e v a l u e of p e r m e a b i l i t y f o r t h e d ra inage m a t e r i a l ,

ki, t h e r e q u i r e d a r e a of d r a i n a g e m a t e r i a l , A , normal t o t h e d i r e c t i o n - of

Flow can be determined by a p p l i c a t i o n of ~ a r c y ' s law :

where 'Q is t h e f low r a t e through t h e d r a i n .

A s a very g e n e r a l g u i d e d r a i n a g e m a t e r i a l should have a pe rmeab i l i ty

a t l e a s t 100 t imes t h a t of t h e m a t e r i a l i t is meant t o d r a i n . If t h i s is

a c h i e v e d , pore w a t e r p r e s s u r e s due t o s e e p a g e w i l l b e minimised a t the

boundary, and t h e s o i l mass w i l l d r a i n a s though i t had a f r e e boundary.

P e r m e a b i l i t i e s of g r a n u l a r ( d r a i n a g e ) m a t e r i a l s a r e g iven i n F igure 20.

I n s o m e - c a s e s , F igure 19 (Cedergren 1977) nay be u s e f u l i n

d e t e r n i n i n g t h e t h i c k n e s s of t h e f i l t e r o r d r a i n , b u t i t should be nored t h a t

c o n s t r u c t i o n c o n s i d e r a t i o n s o f t e n govern t h i c k n e s s . A

he maximum a l l o w a b l e h y d r a u l i c g r a d i e n r i n t h e d r a i n depends on

t h e l a r g e s t h y d r o s t a t i c head t h a t c a n s a f e l y d e v e l o p wi thou t c a u s i n g

u n d e s i r a b l e h y d r o s t a t i c p r e s s u r e s o r i n f i l t r a t i o n i n t o t h e b a c k f i l l .

I t shou ld be noted t h a t a c l e a n wel l -graded rock b a c k f i l l p ro tec ted

by an a p p r o p r i a t e F i l t e r would be a n e x c e l l e n t s o l u t i o n i n any l o c a t i o n where

seepage f rom t h e s o i l o r l e a k a g e from s e r v i c e c o n d u i t s may be a problem.

5.4 FILTER RE(LU2REMENTS

5 . 4 - 1 Grraded F i B m

All drainage t h a t is prov ided shou ld b e a d e q u a t e l y p ro tec ted by

p r o p e r l y d e s i g n e d f i l t e r l a y e r s a g a i n s t b lockage-due t o t h e movement of the

f i n e r s o i l p a r t i c L e s . ~ i l t e r s s h o u l d b e more permeable than t h e p r o t e c t e d

s o i l , and f i l t e r m a t e r i a l s s h o u l d be t r a n s p o r t e d and placed c a r e f u l l y s o t h a t

. s e g r e g a t i o n , and c o n t a m i n a t i o n by f i n e s , does n o t o c c u r .

Where f i l t e r m a t e r i a l s a r e used i n c o n j u n c t i o n w i t h a c o a r s e r free-

drainage m a t e r i t l such a s c rushed rock, the g r a d i n g o f t h e c o a r s e r m a t e r i a l

should c o n f o m t o t h e f i l t e r d e s i g n c r i t e r i a g i v e n i n Tab le 5 , t o p r o t e c t

the f i l t e r fro= e r o s i o n .

Table 5 F i l t e r C r i t e r i a ( G e o t e c h n i c a l Nanual f o r S l o p e s , 1979)

Rule tiumber F i l t e r Design Rule .

D15F, < 5 Da5Sf

D15F, < 20 x D15Sf

D15Ff > 5 x D15S,

D50Fc < 25 x U50Sf

1JniEormity c o e f f i c i e n t 4 < D60F D 1 OF

Should n o t b e gap g raded

Maximllm p a r t i c l e s i z e : 7 5 m m

Not more than 5 % tro p a s s 63um s i e v e , and t h i s f r a c t i o n t o b e c o h e s i o n l e s s

* For well-graded base s o i l t h i s c r i t e r i o n can b e extended t o

I n t h i s t a b l e , DI5F is used t o d e s i g n a t e t h e 15% s i z e of t h e f i l t e r

m a t e r i a l ( i - e . the s i z e o f t h e s i e v e t h a t a l l o w s 15% by we igh t of t h e f i l t e r

m a t e r i a l t o pass tlirough i t ) . S i m i l a r l y , Da5S d e s i g n a t e s t h e s i z e o f s i e v e

that a l l o w s 65X by weight of the base s o i l t o p a s s t h r o u g h i t . D60Fc

i n d i c a t e s t h e D s i z e on t h e c o a r s e s i d e o f t h e f i l t e r enve lope . D ~ o F E

i n d i c a t e s t h e Dl0 s i z e on t h e f i n e s i d e of the f i l t e r enve lope .

When c e r t a i n g r a d i n g s o f decomposed v o l c a n i c . m a t e r i a l s w i t h a n

a p p r e c i a b l e f i n e s c o n t e n t a r e b e i n g used a s b a c k f i l l , the f i l t e r d e s i g n may

r e q u i r e s p e c i a l care.

- - I n some c a s e s , it may b e p o s s i b l e t o u s e man-made f i b r o u s woven

and non-woven f a b r i c s , known as p o t e z t i l e s , t o p r o t e c t t h e d r a i n a g e

f a c i l i t i e s .

There are o b j e c t i o n s t o 2 t h & u s e of Some of these mater ia ls , such - -

a s s e r i o u s d e t e r i o r a t i o n on exposure t o s u n l i g h t and u l t r a - v i o l e t l i g h t ,

c logg ing due t o movement of f i n e s , . r e d u c t i o n i n p e r m e n h i l i t y due t o compression,

c o n s t r u c t i o n a l d i f f i c u l t i e s and m a t e r i a l s Forming p l a n e s of weakness ifl the -

works. IF t h e s e o b j e c t i o n s a r e overcome by a t t e n t i o n t o d e s i g n , cons t ruc t ion .

and q u a l i t y c o n t r o l , then t h e a v a i l a b i l i t y of g e o t e x t i l e s p rov ides new

o p p o r t u n i t i e s Eor i n n o v a t i v e f i l t e r l d r a i n d e s i g n and c o n s t r u c t i o n .

F a b r i c f i l t e r s s h o u l d be p r o p e r l y des igned t o be i n f i l t e r

r e l a t i o n s h i p w i t h t h e s u r r o u n d i n g s o i l . Care must b e taken t o s e l e c t n

g e o t e x t i l e which is a p p r o p r i a t e t o t h e g r a d i n g of t h e s o i l i t i s in tended t o

p r o t e c t and h a s a d e q u a t e d r a i n a g e c a p a c i t y Eor t h e p a r t i c u l a r a p p l i c a t i o n .

A summary o f d e s i g n c r i t e r i a f o r f a b r i c f i l t e r s is g iven i n t h e book by

Ranki lor (1981) .

A v a i l a b l e l i t e r a t u r e s u g g e s t s t h a t E a b r i c s wi th an e q u i v a l e n t

opening s i z e oE l e s s than 15Opm (o r a n open a r e a of l e s s than 4 % ) and t h e

t h i c k e r non-woven f a b r i c s , may b e more prone t o c l o g g i n g than o t h e r v a r i e t i e s .

The u s e of t h e s e types ' shou ld t h e r e f o r e be avoided u n l e s s t h e s a t i s f a c t o r y

performance of t h e p a r t i c u l a r soil/fabric/drainage-medium system has been

demonstra ted by p e r m e a b i l i t y t e s t . On t h e o t h e r h a n d , some o f t h e very . t h i n

f a b r i c v a r i e t i e s e x h i b i t q u i t e l a r g e v i s i b l e - g a p s caused by uneven

d i s t r i b u t i o n oE f i b r e s , and , t h e u s e of such d e f e c t i v e m a t e r i a l s should a l s o

be avo ided . - During c o n s t r u c t i o n , s t r i n g e n t measures a r e r equ i red t o erisure t h a t

t h e m a n u f a c t u r e r ' s i n s t r u c t i o n s concern ing s t o r a g e and hand l ing a r e s t r i c t l y

fo l lowed , and t h a t s t o r a g e , p lacement and b a c k f i l l i n g of f a b r i c s a r e

c a r e f u l l y c o n t r o l l e d t o a v o i d e x c e s s i v e exposure t o u l t r a - v i o l e t l i g h t ,

mechanical damage and i n e f f e c t i v e o v e r l a p p i n g . It is prudent t o use t w o

l ayer s of f a b r i c as a p r e c a u t i o n a g a i n s t impairment of t h e f i l t e r f u n c t i o n by

mechan ica l damage d u r i n g p lacement .

6.1 GENERAL

The s t a b i l i t y of a f r e e s t a n d i n g r e t a i n i n g s t r u c t u ~ e and t h e s o i l

conta ined by i t i s de te rmined by computing f a c t o r s of s a f e t y ( o r s t a b i l i t y

factors), which may be d e f i n e d i n genera l t e r m s a s :

F, = Moments o r f o r c e s a i d i n g s t a b i l i t y . . . . . ( 1 1 ) .Moments o r f o r c e s c a u s i n g i n s t a b i l i t y

F a c t o r s o f s a f e t y s h o u l d b e c a l c u l a t e d f o r t h e f o l l o v i n g s e p a r a t e

modes of f a i l u r e and should a p p l y t o the 1 i n 10 y e a r groundwater c o n d i t i o n :

( a ) s l i d i n g of t h e wal l outwards from t h e r e t a i n i n g s o i l ,

( b ) o v e r t u r n i n g of t h e r e t a i n i n g w a l l about i t s t o e ,

(c> f o u n d a t i o n b e a r i n g f a i l u r e , and

(d) l a r g e r s c a l e s l o p e o r o t h e r f a i l u r e in t h e su r rounding s o i l .

The f o r c e s t h a t produce o v e r t u r n i n g and s l i d i n g a l s o produce t h e

foundat ion b e a r i n g p r e s s u r e s and , t h e r e f o r e , ( a ) and ( b ) above a r e i n t e r - r e l a t

with ( c ) i n most s o i l s . -

I n c a s e s where t h e f o u n d a t i o n material is s o i l , o v e r t u r n i n g s t a b i l i t

is u s u a l l y s a t i s f i e d i f b e a r i n g c r i t e r i a a r e s a t i s f i e d . However, o v e r t u r n i n g

s t a b i l i t y may be c r i t i c a l - f o r s t r o n g founda t ion m a t e r i a l s such a s rock , o r whc

the base of t h e w a l l i s propped, o r when t h e b a s e o f t h e w a l l i s small, f o r

i n s t a n c e w i t h c r i b w a l l s . -

I n g e n e r a l , t o l i m i t s e t t l e m e n t and t i l t i n g of w a l l s on s o i l m a t e r i a l s ,

t h e r e s u l t a n t of t h e l o a d i n g on t h e base s h o u l d b e w i t h i n t h e middle t h i r d .

For rock f o u n d a t i o n m a t e r i a l , t h e r e s u l t a n t s h o u l d b e w i t h i n t h e middle h a l f

of t h e b a s e .

men c a l c u l a t i n g o v d r a l l s t a b i l 2 t y o f a w a l l , t h e l a t e r a l ' e a r t h -

P r e s s u r e is c a l c u l a t e d t o t h e bo t tom of t h e b l i n d i n g Layer, o r i n t h e c a s e o f

a base w i t h a k e y , t o the bot tom o f t h e key where t h e a c t u a l ' f a i l u r e mechanism

extends Co t h a t pcint. - . . - - -

If the pas s ive r e s i s t ance of t h e s o i l i n f ron t of a w a l l is included

in t h e c a l c u l a t i o n s for s l i d i n g s t a b i l i t y , only 502 of the c a l c u l a t e d pas s ive

r e s i s t a n c e should b e used, because oE the l a r g e deformations requi red t o

mob i l i s e the Eull pas s ive r e s i s t ance . . .

S t a b i l i t y c r i t e r i a For Erec s t and ing r e t a i n i n g w a l l s a r e summarised

i n F igure 22.

SLIDING STABT LITY

6 . 2 . 1 gane wdhuUR a Key

Sl id ing occurs along the unders ide of the base ( s e e Sec t ion 2 .6

Eor f u r t h e r d i scuss ion) .

The f a c t o r of s a f e t y , Fs, a g a i n s t s l i d i n g should not be less than

Fs ( s l i d i n g ) = (Wt + P,)tan 6b + ctB + O . W D

H

where Wt is t he weight of t he w a l l

P, i s t he v e r t i c a l component of e a r t h p re s su re fo rce

PH is the ho r i zon ta l component of e a r t h p r e s s u r e f o r c e

6b is the angle of base Eriction - cb i s the adhesion at t h e base of the w a l l

B is the base width, and

Pp i s the passive p re s su re fo rce .

The effects of water fo rces should be taken i n t o account i n chis

equat ion , inc luding u p l i f t p ressures below the wal l base , u n l e s s d r a i n s t h a t

permanently and e f f e c t i v e l y e l imina te u p l i f t water p re s su re s a r e provided- -

6 . 2 . 2 4ade utith a Key - - -.

Huntington (1961) sugges ts t h a t w a l l s with shal-low key& should b e

analysed assuming t h a t s l i d i n g occurs on a horizontaP p l ane through t h e s o i l

a t t h e bottom of t h e key-. Both active and pass iqe forces should-. be- a d j u s t e d

t o t ake i n t o account t h e depth of t h e key. The weight of s o i l i n f r o n t of the

key and be low- the base , d o n t o the f a i l u r e su r f ace , should b e included i n the

t o t a l w e i g h t , W c . F i g u r e 1 shows t h e f o r c e s i n v o l v e d . The f a c t o r o f s a f e t y

a g a i n s t s l i d i n g s h o u l d be as g iven i n S e c t i o n 6 .2 .1 , w i t h t h e a n g l e of b a s e

[ r i c t i o n , 6t,, r e p l a c e d by t h e a n g l e of s h e a r i n g r e s i s t a n c e , 0', of t h e

f o u n d a t i o n s o i l .

6 .2 .3 S f i c f i n g on a Rock Foundat;con

I t is p o s s i b l e t o a n a l y s e t h e s l i d i n g of a r e t a i n i n g w a l l on a

rock f o u n d a t i o n i n a s i m i l a r manner t o s l i d i n g of rock a l o n g a rock joint.-

The b a s i c f r i c t i o n a n g l e may be i n c r e a s e d by a w a v i n e s s a n g l e , i,, based on

the measured w a v i n e s s of t h e exposed rock s u r f a c e .

The wav iness must be of a s u f f i c i e n t s i z e s o tha: s h e a r i n g ~ h r o u g h

t h e a s p e r i t y d o e s n o t o c c u r . In a d d i t i o n , t h e r e must be a s i g n i f i c a n t

component of t h e rock s u r f a c e i n c l i n e d a t i, i n t h e d i r e c r i o n of s l i d i n g .

, 6 . 3 OVERTURNING STAB1 LlTY

6 . 3 . 1 G ~ ~ J u !

Moments c a l c c l a t e d about t h e bot tom o f t h e f r o n t o f t h e t o e s h o u l d

g i v e a f a c t o r of s a f e t y , F,, a g a i n s t o v e r t u r n i n g of n o t l e s s t h a n 2 .

Fs ( o v e r t u r n i n g ) = M,

.. . . . (13)

- vhere.Mr i s t h e a l g e b r a i c sum of moments r e s i s t i n g o v e r t u r n i n g and

Pi i s t h e a l g e b r a i c sum o f moments c a u s i n g o v e r t u r n i n g . --

F o r s e m i g r a v i t y c a n t i l e v e r and c o u n t e r f o r t / a l l s , o n l y t h e .

o v e r t x n i n g f a c t o r o f s a f e t y f o r t h e ~ w a l l as a whole is s i g n i f i c a n t . Fo r

crib w a l l s a n d s o l i d g r a v i t y w a l l s f o r which t h e b a s e and t h e u p p e r p o r t i o n - of t h e w a l l a re u s u a l l y s e p a r a t e u n i t s , t h e f a c t o r o f s a f e t y o f t h e u p p e r

P o r t i o n a g a i n s t o v e r t u r n i n g a b o u t i ts t o e shou ld b e c h e c k e d .

P a s s i v e r e s i s t a n c e s h o u l d n o t b e i n c l u d e d i n c a l c u l a t i o n s f o r Fs

( o v e r t u r n i n g ) for c o n v e n t i o n a l walls.

There a r e number o f ways i n w h i c h a f a c t o r o f s a f e t y a g a i n s t

o v e r t u r n i n g may be d e t e r m i n e d , and t h e s e l e a d t o s i g n i f i c a n t d i f f e r e n c e s i n

t h e computed v a l u e of F,. --

I n o r d e r t o u n d e r s t a n d . w h y some of t h e s e d i f f e r e n c e s o c c u r , t h e

f o r c e s a c t i n g on t h e s i m p l e r e t a i n i n g w a l l i l l u s t r a t e d i n F i g u r e 22(a ) w i l l

b e examined. Dry b a c k E i l l o n l y i s c o n s i d e r e d , and t e rms a r e d e f i n e d on the

d i ag ram.

A p p l i c a t i o n o f e q u a t i o n (13) g i v e s ( F i g u r e 22) :

W .a Fs ( o v e r t u r n i n g ) = .- PA-m

It may be n o t e d t h a t , f o r t h e u s u a l p r o p o r t i o n s of s o l i d g r a v i t y

r e t a i n f n g w a l l s , t h e b a t t e r o f t h e back i s u s u a l l y s u c h t h a t t h e f i n e of a c t i o n

of PA p a s s e s below t h e t o e . he l e v e r - a r m , m , i s t h u s n e g a t i v e and PA

c o n t r i b u t e s t o t h e s t a b i l i t y o f t h e w a l l . A n e g a t i v e value o f . F s t h u s indicates

t h a t t h e w a l l c a n n o t o v e r t u r n .

I t is u s u a l i n retaining wall d e s i g n t o work i n terms of - t h e

h o r i z o n t a l and v e r t i c a l components o f t h e o v e r t u r n i n g f o r c e P A . These E o r c e s ,

m u l t i p l i e d by t h e i r r e s p e c t i v e l e v e r a rms and s u b s t i t u t e d i n t o equa t ion - (14 )

f o r t h e s i m p l e c a s e a s i l l u s t r a t e d i n F i g u r e 2 2 ( a ) . -

g i v e

It i s commonly assumed however

resisting o v e r t u r n i n g and o n t h i s basis,

t h a t t h e component Pv c o n t r i b u t e s t o

the f a c t o r o f s a f e t y becomes

- . . . . . (16)

E q u a t i o n s (15) and (16) d o n o t , o f c o u r s e , g i v e t h e same value of

factor of safety.

I t can b e seen t h a t , according t o e q u a t i o n ( 1 6 ) , t h e o v e r t u r n i n g

f a c t o r of s a f e t y is t h a t number by which t h e h o r i z o n t a l component of t h e e a r t h

p r e s s u r e would need . to be mu1~; ip l i ed t o c a u s e o v e r t u r n i n g , t h e v e r t i c a l

component of t h i s p r e s s u r e remaining unchanged. I t i s un l i k e l y , howcvcr , 1 h n L

t h e h o r i z o n t a l component of t h e r e s u l t a n t e a r t h p r e s s u r e would i n c r e a s e and

t h e v e r t i c a l component remain unchanged. O n t h i s b a s i s , i t would appear chat

t h e procedure r e p r e s e n t e d by equa t ion (16) is no t l o g i c a l .

Although equa t ion (16) l eads t o a more c o n s e r v a t i v e r e s u l t than t h e

procedure based on equa t ion ( 1 5 ) , i t is n o t recommended and t h e d e s i g n c h t a

given in Figure 22 i s based on the more l o g i c a l p rocedure r e p r e s e n t e d by

e q u a t i o n ( 1 5 ) - Huntington (1961) d i s c u s s e s t h i s t o p i c . . .

6.3 .3 W& 14~Lth Oeep Keg4

Appl ica t ion of an a n a l y s i s o f r o t a t i o n a l s t a b i l i t y of w a l l s w i t h

deep keys t o t h e r e a l s i t u a t i o n is found t o be very u n c e r t a i n , a s t h e f o r c e s

a c t i n g a r e dependent on t h e r e l a t i v e s t i f f n e s s o f t h e w a l l and the supporting

s o i l , and on t h e deformat ion t h a t t akes p l a c e . I n view of c o n s t r u c t i o n a l

d i f f i c u l t i e s a n c ! l i k e l y l a r g e d e f o r m a t i o n s , w a l l s w i t h deep keys shou ld i n

g e n e r a l be avoided ( s e e S e c t i o n 1 1 . 7 ) .

6 . 4 FOUtdIATlON BEARING PRESSURE

The u l t i n a t e b e a r i n g c a p a c i t y o f t h e f o u n d a t i o n s o i l on which a n

e a r t h r e t a i n i n g s t r u c t u r e r e s t s should g e n e r a l l y be de t t nnined.[rcm a t h e o r e t i c a l

a n a l y s i s of t h e f o u n d a t i o n , u s i n g the s o i l p r o p e r t i e s o b t a i n e d from l a b o r a t o r y

t e s t s . Where a p p r o p r i a t e , t h e s e s h e a r s t r e n g t h p r o p e r t i e s shou ld be rev iewed

a s t h e c o n s t r u c t i o n proceeds. The a p p l i e d l o a d i n g s h o u l d p r o v i d e a f a c t o r o f

s a f e t y of 3.0 a g a i n s t u l t i m a t e b e a r i n g f a i l u r e .

Foundat ions of r e t n i n i n g w a l l s a r e u s u a l l y s u b j e c t e d t o i n c l i n e d and

e c c e n t r i c loads , t h e founda t ion i t s e l f may b e t i l t e d a t an a n g l e t o t h e

h o r i z o n t a l and sometimes t h e w a l l i s founded on s l o p i n g ground. A g e n e r a l

e x p r e s s i o n for t h e u l t i m a t e b e a r i n g c a p a c i t y of s h a l l o w f o u n d a t i o n s which c a n

deal with these s i t u a t i o n s h a s been g i v e n by Vesic (19751, and t h i s is presen ted

in S e c t i o n 6 -4-2.

. -

Other f a c t o r s which may i n l l u e n c e t h e b e a r i n g c a p a c i t y a r e t h e

founda t ion d e p t h , - s o i l c o m p r c s s j b i l i c y , s c a l e e f f e c t s and non-homogeneous s o i l

c o n d i t i o n s . These a r e d i s c u s s e d by Vesic (1975) . -

6.4.2 8e&q Capaccty F c r c t o a

The u l t i m a t e b e a r i n g c a p a c i t y of a shal low (DSD) s t r i p foundat ion

is given by :

- term r e l a t i n g t o e f f e c t s oE cohesion )

+ !2 v 8, N S i, t, gy - term r e l a t i n g to i n f l u e n c e 1

Y Y o f u n i t weight of s o i l ) .... ( t i ) 1

- term r e l a t i n g t o s u r c h a r g e ) e f f e c t s - . - - .. . -

The b e a r i n g c a p a c i t y f a c t o r s , N c , N y , Nq .are f u n c t i o n s of t h e a n g l e

of s h e a r i n g r e s i s t a n c e , 0, of the s o i l and a r e modified a s a p p r o p r i a t e u s i n g .

f a c t o r s f o r t h e shape o f f o o t i n g , S,, Sy , S S , i n c l i n a t i o n o f l o a d , ic, iy, i (1 '

t i l t of f o o t i n g base , t,, t y , t q , and s l o p e of ground, g c , g y , g q - Values

f o r t h e s e f a c t o r s a r e g i v e n i n Figure 23.

The above b e a r i n g c a p a c i t y F a c t o r s have been de te rmined on t h e

assumption t h a t t h e f o u n d a t i o n m a t e r i a l is reasonably i n c o m p r e s s i b l e , so t h a t

f a i l u r e would occur by g e n e r a l s h e a r i n g . For compress ib le m a t e r i a l s , f a i l u r e

o c c u r s by l o c a l o r punching f a i l u r e . For t h e s e m a t e r i a l s Terzagh i (1943)

recommended t h a t t h e v a l u e of cohesion used should be reduced t o 2 ~ 7 3 , and t h e - 1

a n g l e of s h e a r i n g r e s i s t a n c e t o t a n ( ( 2 t a n 0')/3). A more a c c u r a t e s o l u t i o n

c o n s i d e r i n g both c o m p r e s s i b i l i t y and' s i z e e f f e c t s is g iven by Vesic ( 1975).

F o r f o u n d a t i o n s c o n s t r u c t e d on s a t u r a t e d c l a y e y s o i l s of low

p e r m e a b i l i t y , t h e shor t - t e rm s t a b i l i t y is c r i t i c a l , and t h e y a r e u s u a l l y

a n a l y s e d i n - t e rns of undra ined s t r e n g t h ( 0 ' _= 0 a n a l y s i s ) - --

Where a w a l l i s founded on compacted f i l l o v e r l y i n g e i t h e r s o f t

c l a y o r l o o s e f i l l , p a r t i c u l a r c a r e must b e taken. Reference should be made

t o Vesic ( 1 9 7 5 ) . -

6 . 4 . 3 E66ect 0 6 G~owtdwcLtm Lev&

Equation (17) a p p l i e s when t h e groundwater t a b l e is a t a d i s t a n c e

of a t l e a s t B below t h e b a s e of t h e f o u n d a t i o n . When t h e water t a b l e is a t

the same Level a s t h e f o u n d a t i o n , t h e submerged u n i t weight of t h e s o i l b e l o w '

the founda t ion shou ld be used. For i n t e r m e d i a t e l e v e l s of thc. .r ;ntcr t a b l e ,

the u l t i m a t e b e a r i n g c a p a c i t y shou ld be i n t e r p o l a t e d between ~ h c abov'c

l i m i t i n g v a l u e s .

6.5 ECCEMRZC LOADS - .

- When t h e load on the f o u n d a t i o n i s e c c e n t k i c , t h i s s n b s t a n c i a l l y

reduces t h e b e a r i n g c a p a c i t y . To a l l o w f o r t h i s , the base w i d t h , B , is

reduced t o an e f f e c t i v e width B ' g iven by :

B where eb i s the load e c c e n t r i c i t y (eb 5 1.

For a f o o t i n g e c c e n t r i c a l l y loaded i n two d i r e c t i o n s , t h e e f f e c t i v e

dimensions of t h e b a s e become such t h a t t h e c e n t r e of an a r e a , A ' . c o i n c i d e s

with t h e v e r t i c a l component, V, of t h e a p p l i e d l o a d . Then :

where L ' = L - 2eI, and B' = B - 2 e l , and e l , eb a r e t h e load e c c e n t r i c i t i e s #

i n t h e two d i r e c t i o n s . - .

L' and B ' a r e then used i n p l a c e of L and B i n a l l eqi1at ions .

- - - - -.

The f a c t o r of s a f e t y is g iven by :

F, ( b e a r i n g ) = q-fi ... 4 a l l .

V - f o r a c o n t i n u o u s Where qall. = f o r a r e c t a n g u l a r f p o t i n g , and- q a l l - - B'

strip f o o t i n g ( u n i t l e n g t h c o n s i d e r e d ) .

6 . 6 FOUNDATTONS COIJSTRUCTED ON SLOPING GROUND AM) NEAR SLOPE CRESTS

The u l t i m a t e b e a r i n g c a p a c i t y of f o u n d a t i o n s c o n s t r u c t e d -on s l o p e s

i s lower than t h a t f o r f o u n d a t i o n s c o n s t r u c t e d on l e v e l ground. The ground

s l o p e f a c t o r s of Vesic (l975), given i n F igure 23 , a r e d e v i s e d t o t a k e t h i s

i n t o a c c o u n t . .- -

Where a Eoundation is c o n s t r u c t e d on the. c r e s t of a s l o p e , t h e

b e a r i n g c a p a c i t y i n c r e a s e s with d i s t a n c e from t h e c r e s t t o a maximum va lue a t --

d i s t a n c e s from t h e c r e s t g r e a t e r than approximately f o u r t i m e s t h e founda t ian

w i d t h . No e x a c t s o l u t i o n is a v a i l a b l e f o r t h i s c a s e . The procedure o u t l i n e d

by Bowles (1977) could be a p p l i e d ' t o t h e va lues g iven by Vesic i n Figure 23.

A l t e r n a t i v e l y , a s a conserva t ive assumption, a l i n e a r v a r i a t i o n between t h e

two extreme v a l u e s may be used.

The b e a r i n g c a p a c i t y c a l c u l a t i o n s d o no t c o n s i d e r the f a c t t h a t t h e

s o i l on t h e s l o p e i s a l r e a d y under s t r e s s . Th i s is p a r t i c u l a r l y important w h e r e

t h e i n c l i n a t i o n of the s l o p e is g r e a t e r than 0 ' / 2 . The o v e r a l l s t a b i l i t y of

t h e s l o p e under t h e in f luence of the loaded f o o t i n g must t h e r e f o r e be checked ,

in a d d i t i o n t o t h e bear ing capac i ty c a l c u l a t i o n .

6.7 FOUNDATIONS ON ROCK

Foundations on cont inuous sound rock seldom p r e s e n i ptoblems s i n c e

t h e rock i s s t r o n g e r than most foundat ion m a t e r i a l s . S t r u c t u r a l d e f e c t s and

d i s c o n t i n u i t i e s , o r the c o m p r e s s i b i l i t y of t h e rock mass below the f o u n d a t i o n ,

u s u a l l y c o n t r o l the a l lowable bear ing p r e s s u r e .

Where d i s c o n t i n u i t y - c o n t r o l l e d f a i l u r e mechanisms a r e p o s s i b l e , j o i n t

s u r v e y s should b e c a r r i e d out i n the excavat ion and a d j a c e n t s l o p e s . -

The c o m p r e s s i b i l i t y of the rock mass below Eoundation l e v e l depends

on t h e f requency of j o i n t s and on t h e amount and type of i n f i l l i n g ~f t h e s e

j o i n t s i n t h e zone of i n f l u e n c e of t h e founda t ion . RQD (Rock Q u a l i t y D e s i g n a t i o n

i s d e f i n e d as :

RQD (X) = 100 x Length of unweathered c o r e . 2 1OOm.m Length of b o r e h o l e

I n unweathered rocks , RQD i n d i c a t e s the j o i n t i n t e n s i t y , whereas

i n weathered rock i t g i v e s a measure o f t h e amount of compress ib le m a t e r i a l

- b u t no i n d i c a t i o n of t h e i n f i l l c o m p r e s s i b i l i t y .

Where o n l y t i g h t c l e a n j o i n t s a r c p r e s e n t , t h e c o r r e l a t i o n between

RQD and a l l o v a b l e b e a r i n g p r e s s u r e p roposed by Peck et a l ( I 9 7 4 ) , g iven i n

Table b , aay b e u s e d .

T a b l e G . - A l l o w a b l e B e a r i n g P r e s s u r e on J o i n t e d Rock ( P e c k , l l anson & Thornburn , 1974 )

A 1 l o v a b l e P r e s s u r e ( k P a )

Note : ( 1 ) Use a l l o w a b l e p r e s s u r e or

u n c o n f i n e d c o m p r e s s i v e s t r e n y r t O F i n t a c t r o c k , wh icheve r is l e s s .

( 2 ) ROD is f o r rock i n t h e zone of i n f l u e n c e o f t h e f o u n d a t i o n .

For i n f i l l e d j o i n t s d e f o r m a t i o n w i l l b e l a r g e r , and e s t i m a t e s o f

t h e j o i n t i n f i l l c o m p r e s s i b i l i t y may b e r e q u i r e d . The e f f e c t of j o i n t i n f i l l i n g

On a l l o w a b l e b e a r i n g p r e s s u r e f o r a l i m i t e d r a n g e o f j o i n t s p a c i n g and t h i c k n e s s

is g i v e n i n t h e C a n a d i a n F o u n d a t i o n Manual (Canad ian G e o t e c h n i c a l S o c i e t y , 1 9 7 8 ) .

6 . & SLOPE FA7 LURE I N SURROUNDING SO7 L

The o v e r a l l s t a b i l i t y oE t h e g r o u n d ' s u r r o u n d i n g t h e r e t a i n i n g w a l l

s h o u l d be i n v e s t i g a t e d , and c a l c u l a t i o n s s h o u l d b e c a r r i e d o u t on t h e f u l l

r ange o f p o t e n t i a l f a i l u r e s u r f a c e s t o e n s u r e t h a t an a d e q u a t e f ac to r -o f s a f e t y

, a g a i n s t o v e r a l l s l o p e f a i l u r e i s m a i n t a i n e d . The c a l c u l a t i o n s s h o u l d i n c l u d e

t h e i n f l u e n c e of t h e s u r c h a r g e f rom t h e w a l l on t h e s l o p e . ' The minimum f a c t o r

of s a f e t y r e q u i r e d a t a s i t e is d e p e n d e n t on i t s h a z a r d p o t e n t i a l .

SHEET RETA I N I NG STRUCTURES

7, I GENERAL

Walls which h a v e u n i f o r m c r o s s - s e c t i o n w i t h d e p t h a r e c o n s i d c r c d i n

t h i s c h a p t e r . These i n c l u d e f l e x i b l e s h e e t s t r u c t u r e s , s u c h a s s h e e t - p i l e d and

s o l d i e r - p i l e d w a l l s , a n d more r i g i d w a l l s , i n c l u d i n g d i aph ragm and c a i s s o n

w a l l s .

The e a r t h p r e s s u r e which a c t s on an e a r t h s u p p o r t i n g s t r u c t u r e is

s t r o n g l y dependen t on t h e amount o f l a t e r a l d e f o r m a t i o n which o c c u r s i n t h e

soi l . Fo r f l e x i b l e s h e e t w a l l s , t h e d e t e r m i n a t i o n o f d e f o r m a t i o n s , and h e n c e

t h e e a r t h p r e s s u r e s , i s n o t s i m p l e , because t h e y i e l d of one p a r t o f a f l e x i b l e . --

w a l l t h r o w s p r e s s u r e - on t o t h e more r i g i d p a r t s . Hence, t h e p r e s s u r e s i n - t h e

v i c i n i t y o f t h e s u p p o r t s a r e h i g h e r t h a n i n t h e unsuppor t ed a r e a s , and t h e

l o a d s on i n d i v i d u a l s u p p o r t s v a r y depend ing on t h e s t i f f n e s s c h a r a c t e r i s t i c s

of t h e s u p p o r t s t h e m s e l v e s .

De fo rma t ion o f t h e ground a d j a c e n t to e x c a v a t i o n s may c a u s e b r e a k a g e

of w a t e r - c a r r y i n g s e r v i c e s . In s i t u a t i o n s where l a r g e f l o w s may r e s u l t , t h e

p r u d e n t d e s i g n e r w i l l a l l o w f o r t h e wacer t a b l e b e i n g a t :he ground s u r f a c e

when c a l c u l a t i n g l o a d s t o b e r e t a i n e d . M

7 . 2 STRW7EV EXCAVATTONS

S t r u t t e d s h e e t p i l i n g is o f t e n u sed t o p r o v i d e t empora ry s u p p o r t f o r

t h e s i d e s o f deep e x c a v a t i o n s . The s h e e t p i l e s a r e u s u a l l y d r i v e n f i r s t w i t h

s u p p o r t s t r u t s b e i n g i n s t a l l e d a s t h e e x c a v a t i o n p r o c e e d s . The f i n a l

d e f o r m a t i o n s of t h e w a l l are h i g h l y dependen t on t h e c o n s t r u c t i o n s e q u e n c e a n d

. d e t a i l i n g . This is d e p i c t e d i n a s i m p l i f i e d manner i n F i g u r e 28.

- - .. -

F a i l u r e o f a s t r u t t e d w a l l o f t e n r e s u l t s from t h e i n i t i a l f a i l u r e

of o n e o f t h e s t r u t s , r e s u l t i n g i n t h e p r o g r e s s i v e f a i l u r e o f t h e w h o l e . s y s t e m * - .-

The f o r c e s i n i d e n t i c a l s t r u t s i n a n y p a r t i c u l a r s u p p o r t s y s t e m may d i f f e r

Wide ly b e c a u s e t h e y depend on s u c h f a c t o r s as t h e way i n wh ich t h e s t r u t s are

P t e l o a d e d and t h e time. be tween e x c a v a t i o n and i n s t a l l a t i o n o f s t r u t s . Loads

i n S i m i l a r struts i n any set of o b s e r v a t i o n s h a v e been found t o v a r y from t h e

a v e r a g e value by up t o 5 60 p e r c e n t (Lambe e t al. 1970).

Since f a i l u r e of strutted c u c s o f t e n o c c u r s b y s t r u c t u r a l f a i l u r e ,

p a r t i c u l a r a t t e n t i o n shou ld be p a i d t o thc s t ~ ~ ~ c t u r n l d e t a i l i n g o f he

i n c e r n a l s t rut t inp,. Cu idancc on r.lic s t r r ~ c t i i r a l dcs i .gn o f srrcli w:tl l s , t o g e t h e r

w i t h t y p i c a l d e t a i l s o f c o n n c c t i o n s and s t r u t t i n g s y s t e m s , n r e gjvcn by

Goldberg e t a 1 (1975) . S t r u t s mrlst bc su f f i c i c?nc f o r 311 s t o g c s o f . . ._ - - --

c o n s t r u c t i o n . -

The d i s t f i b u t i o n of p r e s s u r e on a- a t r u ~ l e d e x c a v a t i o n is complex,

and i t i s normal t o use a p r e s s u r e enve lope c o v e r i n g t h e normal range p r e s s u r e

d i s t r i b u t i o n s . The e n v e l c p e s (F-igure 2 4 ) p,jven b y P e c k ( 1 9 6 9 ) , and t h e .Japan

S o c i e t y o f C i v i 1 Engineers ( 1 9 7 7 ) , toqect ier w i t h l o a d i n g s from groundwater a n d

s u r c h a r g e , s h o u l d . b e used t o de te rmrnc s t r u t loads f o r a l l i n t e r n a l l y s t r u t t e d

e x c a v a t i o n s . In a s s e s s i n g l o a d i n g from groundwate r , t h e e f f e c t of a c c i d e n ~ a l .

b r e a k a g e of w a t e r c a r r y i n g s e r v i c e s shou ld be c o n s i d e r e d .

The ioad c a r r i e d by each i n t e r n a l s t r u t is e s t i m a t e d by assuming

t h a t t h e s h e e t p i l e is s imply s u p p o r r e d between s t r u t s , and t h a t a r e a c t i o n

below t h e base o f t h e excavat io i i e x i s t s . T h i s reac:tion is provided by t h e

p a s s i v e r e s i s t a n c e of the s o i l b e n e a t h the c u t .

The d e p t h of p e n e t r a t i o n o f t h e w a l l below the base o f t h e e x c a v a t i o n

shou ld be s u f f i c i e n t t o p rov ide c h i s r e a c t i o n .

-. -

Since t h e wal l moves towards t h e e x c a v a t i o n , i t may be assumed t h a t

a c t i v e and p a s s i v e p r e s s u r e s deve lop a g a i n s t t h e w a l l below t h e e x c a v a t i o n

l e v e l , - a n d h o r i z o n t a l e q u i l i b r i u m nay be used t o d e t e r m i n e t h e d e p t h o f

p e n e t r a t i o n . The p a s s i v e r e s i s t a n c e shou ld be f a c t o r e d by 2.0.

For s o f t c l a y s * n e g l i b l e p a s s i v e r e s i s t a n c e s d e v e l o p , and t h e lower

s e c t i o n o f t h e w a l r must be des igned as a c a n t i l e v e r , and t h e bending moment

and d e f l e c t i o n must be checked.

The maximum bending movement a t , o r below, t h e lowes t s t r u t s h o u l d be

checked against o v e r s t r e s s i n g of t h e w a l l .

I n s t a b i l i t y of t h e base of a n - e x c a v a t i o n can o c c u r due t o s h e a r

f a i l u r e i n s o f t t o f i r m c l a y s (known as base heave). I n g r a n u l a r m a t e r i a l s ,

p i p i n g o r heave a s s o c i a t e d w i t h groundwater f l o w c a n o c c u r .

T h e F a c t o r - o f s a f e t y w-i th r e s p e c t t o s h e a r f a i l u r e is g i v e n b y :

where t h e t e r m s a r e d e f i n e d i n F i g u r e 25. Where Fs is less t h a n 2 s u b s t a n t i a l

d e f o r m a t i o n s may o c c u r w i t h c o n s e q u e n t loss o f g r o u n d , a n d t h e p r o b a b i l i t y o f

f a i l u r e e x i s t s . Where s o f t c l a y e x t e n d s t o c o n s i d e r a b l e d e p t h b e l o w t h e

e x c a v a t i o n , t h e e f f e c t o f i n c r e a s e d s h e e t i n g s t i f E n e s s , o r d e p t h , i s min imal .

However d r i v i n g t h e s h e e t i n g i n t o a h a r d s t r a t u m b e f o r e commencing t h e

e x c a v a t i o n c a n a p p r e c i a b l y r e d u c e t h e d e f o r m a t i o n s .

C o n t r o l o f t h e g r o u n d w a t e r a a y b e n e c e s s a r y t o p r e v e n t p i p i n g o r

heave a s s o c i a t e d w i t h g r o u n d w a t e r f l o w . M e t h o d s t o a c h i e v e t h i s a r e d i s c u s s e d

i n S e c t i o n 5 .5 .

7.3 A N C W R E D FLEXIBLE WALLS

7.3.1 W& Anchurred ncmt {he Top The d e f o r m a t i o n o f a n a n c h o r e d s h e e t p i l e d e p e n d s on t h e r e l a t i v e

s t i f f n e s s o f t h e p i l e l s o i l s y s t e m . For a r e l a t i v e l y r i g i d s y s t e m , s u c h a s a

heavy s e c t i o n i n a l o o s e s a n d , t h e e a r t h p r e s s u r e d i s t r i b u t i o n c o r r e s p o n d s

c l o s e l y t o t h e t r i a n g u l a r a c t i v e a n d p a s s i v e c o n d i t i o n s . The t o e o f t h e p i l e

is assumed p i n n e d , and t h e F r e e E a r t h S u p p o r t d e s i g n method a s o u t l i n s d by

Teng (1962) is a p p r o p r i a t e .

AS t h e s t i f f n e s s o f t h e s y s t e m d e c r e a s e s t h e p r e s s u r e d i s t r i b u t i o n

a l t e r s I n s u c h a way a s t o r e d u c e t h e b e n d i n g moment i n t h e p i l e . AS a

c o n s e q u e n c e , t h e s h e e t p i l e s e c t i o n u s e d may b e r e d u c e d a s compared w i t h a n

i n f i n i t e l y s t i f f w a l l . Rowe ' s T h e o r y o f Moment R e d u c t i o n (1952, 1 9 5 5 , 1957)

t a k e s t h i s e f f e c t i n t o a c c o u n t ; i t is s u m m a r i s e d by T e n g (1962) a n d i n XIRIA

R e p o r t NO. 54 ( 1 9 7 4 ) .

When c a l c u l a t i n g t h e t o e p e n e t r a t i o n , i t is recommended t h a t no

f a c t o r o f s a f e t y s h o u l d b e a p p l i e d t o t h e a c t i v e p r e s s u r e s . The p a s s i v e

may b e f a c t o r e d b y 2.0, o r , a s recommended i n t h e C I R I A r e p o r t , t h e

f o l l o w i n g f a c t o r e d v a l u e s o f 0' a n d 6 , i . e. Q r F and 6F, may be u s e d t o c a l c u l a t e -

t h e p a s s i v e r e s i s t a n c e :-

and

-

For s a n d s , F, = 1 .5 s h o u l d be u s e d , which g i v e s an a p p r o x i m a t e f a c t o r

o f 2.0 on t h e d e r i v e d K p v a l u e s . I f , however , t h e v a l u e s o f 0 ' and 6 a r e

u n c e r t a i n , t h e n F, = 2.0 s h o u l d b e u s e d .

For t h e s h o r t t e rm s t a b i l i t y o f w a l l s i n c l a y s , a f a c t o r 2 . 0 5 Fs 5 3.0

s h o u l d b e a p p l i e d t o the v a l u e o f u n d r a i n e d c o h e s i o n , c , depend ing o n t h e

r e l i a b i l i t y of t h e pa rame te r s . For l ong t e rm s t a b i l i t y , t h e f a c t o r on t a n @ '

c a n b e taken a s I . 2 . S FS 5 1 . 5 .

P a s s i v e and a c t i v e p r e s s u r e s s h o u l d b e c a l c u l a t e d u s i n g t h e methods

g i v e n in Chap te r 3 .

The m u l t i p l e - a n c h o r e d sys t em o f w a l l s u p p o r t r e s u l t s i n t h e - r e t a i n i n g

structure b e i n g p r o g r e s s i v e l y f i x e d . C o n s e q u e n t l y , t h e l a t e r a l d e f o r m a t i o n s

are l i m i t e d t o s u c h ail e x t e n t t h a t f a i l u r e w i t h i n t h e r e t a i n e d s o i l is u n l i k e l y .

The e a r t h p r e s s u r e which f i n a l l y a c t s on t h e w a l l d e p e n d s on t h e r e l a t i v e

s t i f f n e s s of t h e w a l l t o t h e s o i l , t h e a n c h o r s p a c i n g , t h e anchor y i e l d and

t h e p r e s t r e s s l ocked i n t o t h e a n c h o r s a t i n s t a l l a t i o n .

e

The e a r t h p r e s s u r e d i s t r i b u t i o n h a s been shown t o he s i m i l a r t o t h a t

o b t a i n e d f o r i n t e r n a l l y b r a c e d e x c a v a t i o n s . - A r e c t a n g u l a r p r e s s u r e e n v e l o p e . .

s i m i l a r t o t h a t adopted by Peck ( F i g u r e 2 4 ) is a p p r o p r i a t e . The e a r t h p r e s s u r e 8

c o e f f i c i e n t may b e taken a s Ka. However, i t is common t o use a v a l u e be tween

Ka and KO, s u c h a s (K, + K0)/2 , i n a n a t t e m p t t o c o n t r o l s u r f a c e movements .

S u c c e s s f u l d e s i g n s have been made u s i n g t r i a n g u l a r p r e s s u r e

d i s t r i b u t i o n s w i t h e a r t h p r e s s u r e c o e f f i c i e n t s v a r y i n g between K a and KO.

However, b e c a u s e o f t h e mechanism i n v o l v e d , the r e c t a n g u l a r d i s t r i b u t i o n is

c o n s i d e r e d more a p p r o p r i a t e (Hanna, 1980). Anchor l o a d s may be c h e c k e d u s i n g

b o t h d i s t r i b u t i o n s , and t h e w o r s t c a s e t a k e n .

- The d e t e r m i n a t i o n o f v e r t i c a l and h o r i z o n t a l s p a c i n g o f a n c h o r s u s i n g - -

t h e p r o c e d u r e f o r i n t e r n a l s t r u t s p a c i n g g i v e s a c c e p t a b l e r e s u l t s . -Ano the r

app roach is t h e s e m i - e m p i r i c a l d e s i g n m e t h o d o f James 6 J a c k (1974) w h i c h

s i m u l a t e s t h e f i e l d c o n s t r u c t i o n p rocedure us ing t r i a n g u l a r p r e s s u r e

d i s t r i b u t i o n s . T h i s . method a l l o w s d e t e r m i n a t i o n of t h e dep th o f p e n e t r a t i o n

r e q u i r e d , and r e s u l t s cor respond w e l l t o f i e l d and l a b o r a t o r y t e s t s .

Anchors a r e u s u a l l y i n c l i n e d downwards, t r a n s m i t t i n g t h e v e r t i c a l

component of t h e anchor f o r c e i n t o t h e anchored member. T h i s Eorce s h o u l d . b e

c o n s i d e r e d i n d e s i g n , t o g e t h e r wi th t h e weight of t h e member i t s e l f (White ,

1 9 7 4 ) .

A number of c a s e s have been recorded where s o l d i e r p i l e s have f a i l e d

i n end b e a r i n g due t o t h e v e r t i c a l component of t h e anchor f o r c e .

7 . 4 C W l L E V E R E D WALLS . . -

These r e l y e n t i r e l y on t h e development of p a s s i v e r e s i s t a n c e i n f r o n t of t h e - wal l f o r t h e i r s t a b i l i t y . A s a consequence, c o n s i d e r a b l e movement must o c c u r

be fore e q u i l i b r i u m is reached, and deep p e n e t r a t i o n is r e q u i r e d . The d e f l e c t i o n

a t the t o p of t h e w a l l may be t h e governing c r i t e r i o n . Such w a l l s should n o t

normally be used a s permanent s t r u c t u r e s t o r e t a i n a h e i g h t of more than 5m

u n l e s s c a n t i l e v e r e d from rock.

The p r e s s u r e d i s t r i b u t i o n . a t f a i l u r e approximates t h e c l a s s i c a l

t r i a n g u l a r p a t t e r n . F u l l a c t i v e p r e s s u r e should be used and t h e p a s s i v e

p r e s s u r e shou ld be f a c t o r e d wi th Fs = 3 on t a n 0' and t a n 6 ( r e f e r t o S e c t i o n

2-7 f o r a p p r o p r i a t e v a l u e s o f 6). T h i s h i g h e r f a c t o r of s a f e t y is r e q u i r e d

because o f t h e l a r g e de format ions needed t o develop f u l l p a s s i v e r e s i s t a n c e .

?owever, i f i t can be shown t h a t w a l l deformat ions w i l l n o t c a u s e d i s t r e s s

t.0 n e i g h b o u r i n g s t r u c t u r e s o r s e r v i c e s , then a lower f a c t o r may be

?PPPopria te . -

f - The dep th o f p e n e t r a t i o n is ob ta ined by t a k i n g moments abou t t h e ke* The maximum bending moment may b e ob ta ined by t a k i n g moments of t h e

e s s u r e ~ , above v a r i o u s c u t s , u n t i l t h e maximum v a l u e is determined

I n s t a l l a t i o n o f a d r a i n a g e and f i l t e r medium behind t h e w a l l may b e

f i c u l t and so f u l l h y d r a s t a t i c p r e s s u r e may have t o be c o n s i d e r e d f o r the

RE1 NFORCED EARTH RETAIN I NG WAUS

It is recommended, a t p r e s e n t , t h a t d e s i g n s shou ld be i n a c c o r d a n c e

wi th t h e T e c h n i c a l Mernorandurrl ( B r i d g e s ) B E 3/78 (Department of T r a n s p o r t , UK, - . - . -

19781. I t fi a l s o recommended t h i t f o r t h e b a c k f i l l , t h e g r a d i n g and p l a s t i c i t y

index r e q u i r e m e n t s of t h e Federa l Highways A d m i n i s t r a t i o n (1978) , o u t l i n e d i n

Tab le 7 , shou ld a l s o b e met , because of t h e l i m i t e d documented e x p e r i e n c e o f

r e i n f o r c e d e a r t h r e t a i n i n g w a l l s c o n s t r u c t e d u s i n g m a t e r i a l s w i t h a h i g h f i n e s

c o n t e n t and p l a s t i c i t y index .

C lose s u p e r v i s i o n i s r e q u i r e d t o e n s u r e t h a t c o n s t r u c t i o n p r o c e e d s

accord ing t o s p e c i f i c a t i o n , p a r t i c u l a r l y a l l a s p e c t s of t h e b a c k f i l l

s p e c i f i c a t i o n . D i f f i c u l t i e s wi th l a t e r p r o v i s i o n of s e r v i c e s and t h e -

s t e r i l i z a t i o n of l a n d above f o r b u i l d i n g development may p r e c l u d e t h e u s e of

r e i n f o r c e d e a r t h i n c e r t a i n c i r c u m s t a n c e s .

T a b l e 7 Minimum S p e c i f i c a t i o n f o r S e l e c t B a c k f i l l For Re in forced E a r t h R e t a i n i n g Walls ( a f t e r F e d e r a l Highway A d m i n i s t r a t i o n , 1978)

S i e v e S i z e Percen tago P a s s i n g

and P1 < 6

OR I f p e r c e n t a g e p a s s i n g 75urn i s g r e a t e r t h a n 25%, - and p e r c e n t a g e f i n e r t h a n 15pm i s less than t 5 % , m a t e r i a l is a c c e p t a b l e i f 0 5 30' as de te rmined by the a p p r o p r i a t e t e s t and P . I . < 6 .

I . I GENERAL

A c r i b w a l l s t r u c t u r e is made by p l a c i n g a number o f c r i b l i k e c e l l s

o g e t h e r and f i l l i n g them w i t h s o i l o r rock f i l l t o g i v e them s ~ r e n g t h and

re ight . The w a l l e s s e n t i a l l y a c t s a s a g r a v i t y r e t a i n i n g w a l l . C r i b wa l l

i n i t s may b e b u i l t of p r e c a s t c o n c r e t e , s t e e l o r of t r e a t e d t i m b e r . The

j a n u f a c t u r e r s o f c r i b w a l l u n i t s produce d e s i g n d a t a f o r c r i b w a l l s , bu t i n

g e n e r a l c a r e must be exercised i n t h e i n t e r p r e t a t i o n and a p p l i c a t i o n o f t h i s

d a t a .

The f r o n t f a c e of a c r i b w a l l u s u a l l y c o n s i s t s of a g r i d of c o n c r e t e

members s o spaced t h a t t h e s o i l ' i n f i l l a t i t s angle o f r e p c s e d o e s not s p i L l

through t h e s p a c e r s . H o r i z o n t a l members o f such a grid a r e t e m e d stretckers.

The f a c e members a r e c o n n e c t e d by t r a n s v e r s e members termed h e ~ d a r s t o a s f m i l a r

g r i d of s t r e t c h e r s , p a r a l l e l t o t h e f a c e , forming :he back f a c e o f t h e wall

( F i g u r e 2 6 ) . The minimum t h i c k n e s s of w a l l s s h o u l d be one n e t r e , excep t c h e r e

the w a l l is non-suppor&ing f o r l a n d s c a p i n g . A 1.2 n t h i c k n e s s is u s u a l l y a

b e t t e r e z g i n e e r i n g s o l u t i o n . A d d i t i o n a l s p a c e r s be tween t h e s t r e t c h e r s - w i t h i n

t h e f r o n t and back grids may be used i f t h e s y s t e n r e q u i r e s i t , a n d t h e s e a r e

termed false headers o r piZlow bZocks. Headers s h o u l d i n g e n e r a l be

Prepend i ' cu l a r t o t h e face of t h e w a l l , a l t h o u g h s o m e a v a i l a b l e systems have

v a r i a t i o n s t o t h i s .

The sys t em u s u a l l y a l l o w f o r t h e a d d i t i o n of one o r more g r i d s of

p a r a l l e l t o the f a c e and s i t u a t e d behind the s t r u c t u r e d e s c r i b e d above, - B0 forming m u l t i p l e d e p t h wal ls of g r e a t e r h e i g h t , Such a d d i t i o n a l g r i d s are- P

- connec ted t o t h e grid i n the f r o n t by a h e a d e r s y s t m .

9.2 DESIGN

The g e n e r a l d e s i g n criteris f o r g r a v i t y valls a p p l y co c r i b wa l l s .

The p r e s s u r e s a c t i n g on a c r i b w a l l s h o u l d be d e t e r a i n e d by the methods given

- i n C h a p t e r 3. The resultant shou ld a lways l i e i n the midd le t h i r d o f t h e -&ill

c r o s s - s e c t i o n . Figure 26 shows t h e e a r t h p r e s s u r e d i s t r i b u t i o n a c t i n g on a

t y p i c a l w a l l and some t y p i c a l c o n s t r u c t i o n d e t a i l s - F i g u r e 27 gives desigzt

curves which may b e used f o r p r e l i m i n a r y d e s i g n o n l y .

TO a g r e a t e x t e n t , t h e per formance o f a c r i b w a l l d e p e n d s on t h e

a b i l i t y of t he c r i b m e m b e r s t o c o n t a i n t h e e n c l o s e d s o i l . A n a l y s i s of t h e

stresses and l o a d i n g s i n t h e c r i b members and c o n n e c t i o n s i s b a s e d on t h e

e a r t h p r e s s u r e i n s i d e t h e c r i b . The i n d i v i d u a l u n i t s f o r c r i b w a l l s s h o u l d b e

d e s i g n e d t o w i t h s t a n d t h e . t o r s i o n , bend ing moments, s h e a r f o r c e s and t e n s i l e

f o r c e s e x e r t e d on them. The t h e o r e t i c z l d e t e r m i n a t i o n o f t h e ~ o r c e s on c r i b

u n i t s and t h e a c t u a l s t r e n g t h o f t h e u n i t s i s d i f f i c u l t and is u s u a l l y b a s e d

o n e a r t h p r e s s u r e s f r o m b i n p r e s s u r e t h e o r i e s ( S c h u s t e r e t a l , 1975;

T s c h e b o t a r i o f f , 1951), t h e s t r u c t u r a l form o f t h e c r i b u n i t s and t h e e a r t h

p r e s s u r e from t h e b a c k f i l l . However, i t h a s been found by S c h u s t e r e t a 1 ( 1 9 7 5 )

t h a t s t r e s s e s measu red ' i n c r i b w a l l u n i t s a r e much h i g h e r chan t h o s e p r e d i c t e d

u s i n g l o a d s on t h e u n i t s f rom b i n p r e s s u r e t h e o r i e s . S p e c i f i c a t i o n CD209 -

C r i b w a l l i n g and Notes ( M i n i s t r y o f Works and Development N . 2 . , 1980) s p e c i f i e s

t h a t c r i b u n i t s b e a b l e t o w i t h s t a n d l o a d i n g s which imply e a r t h p r e s s u r e s t w i c e

t h o s e g iven by b i n p r e s s u r e s . T h i s r equ i r emen t f o l l o w e d an e x a m i n a t i o n o f

s a t i s f a c t o r y and u n s a t i s f a c t o r y c r i b w a l l u n i t s . Good d e t a i l i n g and d e s i g n i s

r e q u i r e d a t t he c o n n e c t i o n be tween u n i t s t o e n s u r e t h e s a t i s f a c t o r y t r a n s f e r o f

f o r c e s . Cr ib w a l l f a i l u r e s h a v e o c c u r r e d b e c a u s e o f poor s t e e l r e i n f o r c e m e n t

d e t a i l i n g .

The S p e c i f i c a t i o n CD209 a l s o g i v e s u s e f u l a d v i c e on r e q u i r e m e n t s f o r

t h e s t r e n g t h and t e s t i n g of c r i b u n i t s and t h e c o n s t r u c t i o n of c r i b w a l l s .

C a r e f u l q u a l i t y c o n t r o l d u r i n g m a n u f a c t u r e o f t h e c r i b u n i t s is r e q u i r e d .

. e s p e c i a l l y w i th r e g a r d t o c o n c r e t e c o v e r , t h e p l a c e m e n t o f s t e e l r e i n f o r c e m e n t ,

c o n c r e t e n i x d e s i g n , and t h e d i m e n s i o n a l t o l e r a n c e s o f i n d i v i d u a l u n i t s -

Many c r i b w a l l s h a v e f a i l e d because o f d i f f e r e n t i a l s e t t l e m e n t o f t h e

w a l l s t r u c t u r e . B e c a u s e o f t h i s , a l l c r i b w a l l s s h o u l d b e founded a t l eas t 3 0 0 ~

below ground l e v e l o n a c a s t i n - s i t u r e i n f o r c e d c o n c r e t e b a s e s l a b of 150nm

minimum t h i c k n e s s o v e r t h e whole p l a n a r e a o f t h e w a l l . -

9 . 3 BACKFILL

The c r i b w a l l u n i t s s h o u l d a lways b e i n f i l l e d w i t h a f r e e - d r a i n i n g

m a t e r i a l p l a c e d a n d w e l l compac ted i n l a y e r s i n a w a y t h a t d o e s n o t d i s t u r b

t h e c r i b u n i t s . Where s o i l i s u s e d , a r e l a t i v e c o m p a c t i o n o f at leas t 98%- t o . - ' 8 5 1377 : 1975 Test 12 s h o u l d b e o b t a i h e d . Where r o c k f i l l is u s e d , t h e

r e l a r i v e d e n s i t y t o be o b t a i n e d s h o u l d b e s p e c i f i e d . The s t r e n g t h o f t h e completed vall d e p e n d s on the s t a n d a r d o f t h i s b a c k f i l l i n g .

9 .4

the . .

was

PROVISION OF 'DRAINAGE Adequate d r a i n a g e o f t h e whole c r i b s t r u c t u r e is e s s e n t i a l . -Many of

F a i l u r e s i n c r i b w a l l s have o c c u r r e d because m a t e r i a l of low p e r m e a b i l i t y

used a s b a c k f i l l , t h u s deve lop ing high s t a t i c o r seepage w a t e r p r e s s u r e s .

h s u b s o i l d r a i n s h o u l d be i n s t a l l e d a t t h e h e e l of t h e wa l l k h e r e v e r p o s s i b l e ,

o t h e r w i s e ponding may o c c u r .

9 . 5 MULTIPLE DEPTH WALLS

The s t a b i x i t y o f w a l l s o f more than s i n g l e d e p t h s h o u l d be checked

a t t h e c h a n g e s f rom s i n g l e t o double and double t o t r i p l e , e t c . , t o e n s u r e

t h a t t h e r e s u l t a n t f o r c e l ies w i t h i n t h e middle t h i r d of each s e c t i o n

cons idered , and t h a t . - t h e o v e r t u r n i n g c r i t e r i o n s t a t e d i n F i g u r e 22 is m e t .

- - 9 .6 WALLS CURVED IN PLAN

C r i b walls w i t h a convex f r o n t f a c e a r e much more s u s c e p t i b l e t o

damage b y transverse d e f o r m a t i o n s than a r e concave w a l l s .

Gabion wall are aesthetically appealing For the purpose of design, the lateral earth and many configurations are possible a s pressure coeff~cient Ka is derived from the shown below: -- equations a s follows:

I I /

I: i = backfill inclination a = wall inclination 4 = internal friction - -

angle of soil 6 = wail friction angle.

a. Embankment

sin2(a + qD )

s m (@ + 61 s ~ n 1

stn ( a - 6 ) s m ln + r I

For vertical wall with horizontal backfill, ( i = 6 = 0 and a = 90")

b. Wall with footing

c. Tilted

In terms of design..the external stability of gabion wall is treated a s with any other gravity structures. Active earth pressure conditions are assumed in the design. Adequate safety factor must be provided against sliding and overturning of the gabion structure.

- - The foundation soil must be checked against bearing failure.

For cohesionless soil with a sloping surface behind a smooth vertical retaining wall, (a = 90. 6 = 0) ci

J- )COS r COS I + COS I -COS 51, I

Typical safe soil bearing capacities (Ref. B.S. code CPI 01. 1963)

kN/m2 -

Soft clay & silts 50- 1 00 Stiff G sandy clay 200-400 Loose sand dry 1 00-200 Loose sand submerged 50-100 Compacted sand or loose graded sand dry 200400 Compacted sand or loose graded sand submerged i 00-200 Compacted gravel-sand mixture dry 400600 Compacted gravel-sand mixture submerged 200-300 Shale G soft sandstone 1000-2000 Limestone G hard sedimentary rock 3004000 Sound igneous rock -1 0000

Example: Horrizontal backfill with surcharge.

For the purpose of the following design, the wall friction is neglected. Given : H = 3 m Soil Parameters : 'y, = 16 kN/mJ

4, = 30"

7, = 18 kN/mJ

gabion structure = l ~ k ~ / ~ "

t

2 Check against Overturning By taking moments about pt.A: '

Disturbing moment.

M, = 23.76(1) + 14 85(1.5) -- = 46.04 kN.m

Restoring moment

M, = 6(18) (1.5) + jl(i6) (2.5) + 0.5 (16) (2.75))

= 224 kN.m

1 Check against sliding

I 2 Lateral earth force. Pa = -Ka -yH 2

Surcharge force, P, = 1.5 x K , qH

= 1.5(0. !3)(10)(3) = 14.85.kN/ m

Disturbing forces = 23.76 t 14.85 = 38-61 kN/m

Restoring force, F, = ( W, i- W,)tan d,

=[6(18) + 1.5( 16)]ran.30° = 132 tan 30" =76.21 kN/m

Safety Factor.

Safety factor against overturning with respect to the toe should be at least 2.0.

3.Bearing Capacity

The vertical componeni R acting on the . base is equal to the s u n of the forces aciing downward. and x i i l have an eccentricity e with resperi to !he g e ~ ~ n e t r i c a f center of i h l base. By taking moments about ~ t . A (toe)

3 224 -46.04 = 0 . ,5 eccentricity. e = - -

2 122

Hence eccentricity i s within middle third.

maximum R 6 e pressure. 6 max = i(l + T)

76.21 Thus, safety Factor S = - 38.61 The safety factor against bearing failure

= 1.97 > 1.5 must be at least 2.0. Hence :he ultimate bearing capacity of the foundation soil - -

Safety factor against s!iding should be at must exceed; least 1.5 for cohesionless backfill and 2.0 for cohesive backfill. 57.2 x 2 = 114.4 kN/m2

WE ASPECTS OF REINFORCED CONCRETE DESIGN AN[> DETAILING -

1 1 . 1 IMRODUCTION

T h i s chap te r d o e s n o t aim t o c o v e r a l l a s p e c t s of r e i n f o r c e d c o n c r e t e

des ign a s i t a p p l i e s t o r e t a i n i n g w a l l s . T h e r e a r e , however, s e v e r a l a s p e c t s

of the d e s i g n and d e t a i l i n g which a r e n o t a d e q u a t e l y covered i n t h e commonly

a v a i l a b l e l i t e r a t u r e o r p r e s e n t Codes and R e g u l a t i o n s , and some g u i d a n c e is

given h e r e on t h e s e . . I n p a r t i c u l a r , t h e j u n c t i o n s between members a r e o f t e n

poorly d e t a i l e d and s u g g e s t i o n s a r e c o n t a i n e d i n S e c t i o n 1 1 . 9 f o r improvements

R e f e r e n c e s h o u l d b e made t o comprehensive p u b l i c a t i o n s on r e i n f o r c e d

c o n c r e t e ( e . g . S c o t t e t a l , 1965; Park & Paulay, 1975) f o r comple te d e t a i l s o f

c o n c r e t e r e t a i n i n g w a l l d e s i g n and d e t a i l i n g .

.11.2 GENERAL NOTES

11.2.1 C o d a

R e i n f o r c e d c o n c r e t e s t r u c t u r a l d e s i g n should be i n a c c o r d a n c e w i t h

the a p p r o p r i a t e s t a n d a r d c u r r e n t l y used.

The Code b e i n g used w i l l s p e c i f y t h e load f a c t o r s o r p a r t i a l f a c t o r s

t o be used.

1 1 . 2 . 3 C o v a .to Reivl~o/rcment

P a r t i c u l a r a t t e n t i o n s h o u l d b e g i v e n t o t h e c o v e r of r e i n f o r c e m e n t ,

both i n t h e d e t a i l i n k and d u r i n g c o n s t r u c t i o n . B l i n d i n g concreGe s h o u l d a lways - Se used on s o i l - l i k e m a t e r i a l s .

13.3 TOE DESIGN

S h e a r i n a t o e is u s u a l l y t h e c r i t i c a l l o a d i n g c a s e . The c r i t i c a l

s e c t i o n o f t h e t o e may b e t a k e n a t d i s ~ a n c e ' d ' o u t from t h e f a c e o f t h e

s u p p o r t a s shown i n F i g u r e 32. The d e t a i l i n g of t h e c u r t a i l m e n t a n d anchorage

of r e i n f o r c e m e n t is i m p o r t a n t (see S e c t i o n 11.8) . -

1 1 . 4 . 1 SZof tondirq . - For t h e stem des ign c a n t i l e v e r and c o u n t e r f o r t w a l l s , i t is n o r n ~ a l

p r a c t i c e t o t a k e the e a r t h p r e s s u r e a c t i n g on t h e v e r t i c a l p l a n e chrough the

r e a r o f t h e h e e l a s being p r o j e c t e d o n t o t h e s tem ( s e e F igure I ) . tiowever, i n

n e a r l y a l l w a l l s , the e a r t h p r e s s u r e a c t i n g on t h e s t r u c t u r a l s e c t i o n o f the

w a l l is d i f f e r e n t From t h i s , because of t h e l a t e r a l p r e s s u r e s cha t d e v c l n p

d u r i n g t h e compacting of t h e b a c k f i l l . Such l a t e r a l p r e s s u r e s a r c u s u a i l y m u c h

h i g h e r than a c t i v e and can be h i g h e r than a t - r e s t p r e s s u r e s . .The magnitude of

such l a t e r a l p r e s s u r e s is d i s c u s s e d i n S e c t i o n s 3.10 & 3 .1 1 . -

T h e r e f o r e , i n d e s i g n i n g s tem of a w a l l th-e e a r t h pressi1rc.s f r o m

compaction should always be c a l c u l a t e d . In many c a s e s , t h i s w i l l be t h e

c r i t i c a l load ing . There is L i t t l e e v i d e n c e t o show t h a t t h e d e f l e c t i o n o f

c a n t i l e v e r w a l l s w i l l reduce t h e compaction p r e s s u r e s . (See S e c t i o n 3 . 1 1 ) . - .

1 1 .4.2 B i n d i n g Mamenb and Sheaa F a a c u in Xlze SXern~ oh CounXe/r~on-t Waled

The bottom of a stem, where i t j o i n s t h e h e e l , shou ld be r e i n f o r c e d

f o r v e r t i c a l spanning a c t i o n i n a d d i t i o n t o h o r i z o n t a l spann ing a c t i o n .

H o r i z o n t a l s t e e l should be con t inuous in b o t h faces-. H o r i z o n t a l bend ing moment

v a r i a t i o n s w i t h height should be c a t e r e d f o r by v a r y i n g t h e r e i n f o r c e m e n t

s p a c i n g i n p r e f e r e n c e t o changing t h e b a r s i z e s . - * .

Shear f o r c e s should b e c a l c u l a t e d a t t h e Face oE. t h e c o u n t e r f o r t s .

Shear s t r e s s e s w i l l u s u a l l y govern t h e stem t h i c k n e s s .

The bending moments and s h e a r f o r c e s i n s tems shou ld b e c a l c u l a t e d

by methods which p roper ly t a k e i n t o a c c o u n t t h e f i x i t y of each= edge of the

stem s l a b and t h e d i s t r i b u t i o n of p r e s s u r e s on t h e s l a b . Hunt ing ton (1961) - g i v e s u s e f u l guidance on t h i s based on work done by t h e US P o r t l a n d Cement

A s s o c i a t i o n . B o w l e s (1977) g i v e s similar i n f o r m a t i o n . - - - - -

- -

1 7 . 5 HEEL SLAB DESIGN -- .- - - - --

- 1 7 -5.1 L O & ~

The design loading on t h e h e e l s l a b is shown i n F i g u r e SO. The - --.

b e a r i n g p r e s s u r e s f o r u s e i n s r r u c r u r a l d e s i g n are n o t t h e same as t h o s e - u s e d

t o check t h e F a c t o r of s a f e t y a g a i n s t u l t i m a t e b e a r i n g f a i l u r e (Section 6 . 4 ) .

They a r e normal ly taken a s t h e b e a r i n g p r e s s u r e s a t working Loads, a s Eollows:

I f t h e r e s u l t a n t p a s s e s through t h e base w i t h i n t h e r ~ i t l t i l c

t h i r d , t h e t o e and h e e l p r e s s u r e s f o r s t r u c t u r a l d e s i g n nwy

be c a l c u l a t e d from

where V is t h e normal component of the r e s u l t i i n t l o a d i n g on - . -

t h e b a s e , B i s t h e b a s e w i d t h , and L is t h e l e n g t h o f w a l l

f o r which t h e r e s u l t a n t e a r t h p r e s s u r e i s c a l c u l a t e d ( u s u a l l y

u n i t y ) , and eb is t h e e c c e n t r i c i t y of t h e l o a d . -

I f t h e r e s u l t a n t L i e s o u t s i d e t h e midd le t h i r d :

7 1 . 5 . 2 H e d SLabn 60h Courztw~boat O d L s

The h e e l s l a b f o r c o u n t e r f o r t w a l l s s h o u l d be d e s i g n e d a s a s l a b

spanning i n two d i r e c t i o n s , The r e f e r e n c e s g i v e n i n S e c t i o n 1 1 . 4 . 2 may be

c o n s u l t e d f o r t h i s purpose .

A s i n S e c t i o n 11.4..2, t h e c r i t i c a l s e c t i o n f o r s h e a r i s a t t h e f a c e

of t h e c o u n t e r f o r t s . Again, s h e a r stresses u s u a l l y govern t h e h e e l t h i c k n e s s . -

17.6 COUNTERFORT D E S I G N - -

. . V e r t i c a l s t e e l i n t h e c o u n t e r f o r t is r e q u i r e d t o ca-r ry t h e n e t t e n s i l e

load from each s t r i p of t h e h e e l s l a b i n t o t h e c o u r l t e r f o r t . The main moment

r e i n f o r c e m e n t f o r t h e w a l l is. u s u a l l y c o n c e n t r a t e d a t t h e back o f t h e c o u n t e r f o r t

H o r i z o n t a l s teel i n t h e c o u n t e r f o r t is r e q u i r e d t o c a r r y t h e n e t load on each

h o r i z o n t a l s t r i p o f s t e m . The d e t a i l i n g of t h i s steel shou ld b e done So as t o

provide a d e q u a t e anchorage between t h e s t e m s l a b and t h e c o u n t e r f o r t ( F i g a r e

3 1 ) . C o n s i d e r a t i o n should b e g i v e n t o s t a g g e r i n g t h e l a p s i n t h e s e anchorage

b a r s .

Cut-off p o s i t i o n s f o r t h e main t e n s i l e s t s e l i n t h e c o u n t e r f o r t s

a r e shown i n F i g u r e 3 1 .

1 1 . 7 KEY DESIGN

I n g e n e r a l the r a t i o of d e p t h t o t h i c k n e s s oE rhc kcy s l io*~ld bt.

less than 2 .0 . I t is d i f f i c u l t t o p r e d i c t w h a t ' t h e force a c t i n g on the key

w i l l be. Approximately :

Design h o r i z o n t a l - h o r i z o n t a l l o a d s t o t a l v e r t i c a l l o a d s - t end iqg t o c a u s e - 0 .4 x load on key above b l i n d i n g layer

s l i d i n g

I t may be assumed t h a t t h i s load a c t s a c o n e - t h i r d of the key h e i g h t

from t h e bot tom of key. The key shou ld be d e t a i l e d i n accordaqce wich S e c t i o n

11.8 & 11.9. Note t h a t t e n s i l e s t r e s s e s a r e c a r r i e d from t h e k e y i n t c t h e

bottom of t h e h e e l s l a b , and t h e r e f o r e some r e i n f o r c e m e n t is c a l l e d fo r i n t h a t

a r e a .

I l . 8 CURTAILMENT AND ANCHORAGE OF RETNFORCEMEM

The c u r t a i l m e n t of r e in fo rcement i n r e t a i n i n g w a l l s is c r i t i c a l . A

b a r must ext-end beyond the p o i n t where i t is t h e o r e t i c a l l y no longer r ~ q u i r e d . .

t o a l l o w f o r i n a c c u r a c i e s i n l o a d i n g and a n a l y s i s , t o a l low f o r i n a c c u r a c i e s . .

i p p l a c i n g b a r s , and t o avoid l a r g e c r a c k s a t t h e c u r t a i l m e n t s e c t i o n . Such

c r a c k s reduce t h e r e s i s t a n c e t o s h e a r f o r c e s and i n t r o d u c e h i g h peak s c r e s s c s

i n t h e t e n s i o n re in fo rcement .

1 1 . 9 VETAT L1 NG OF' REZNFORCED CONCRETE CORNERS A I W J O I N S

Many r e i n f o r c e d c o n c r e t e w a l l s invo lve c a n t i l e v e r s t h a t meet at

r i g h t a n g l e s . A t t h i s j u n c t i o n , t h e r e i s - ' t h e - c o m b i r i a t i m of peak bending

moments and peak $hear f o r c e s . Such c a n t i l e v e r s and c o v e r s G u s t be c a r e f u l l y

l e t a i l e d t o a v o i d wide c r a c k width,, and s o e n s u r e t h e . s t r e n g t h and s e n i c e a b i l i t y

)f t h e s t r u c t u r e s . Some guidance on s u i t a b l e d e t a i l i n g is g i v e n i n t h i s Chapter-

. . .- Research work by N i l s s o n 6 Losberg (1976) h a s shown t h a t r e i n i o r c e m i n t

jetails commonly used i n c a n t i l e v e r w a l l s have ultimate c a p a c i t i e s s i g n i f i c a n t l ~

Less t h a n are u s u a l l y assumed i n c a l c u l a t i o n s , a n d t h e y r e s u l t i n e x c e s s i v e l y

l i d e c o r n e r c r a c k w i d t h s a t what would normally be working l o a d s . For

u l t i m a t e c a p a c i t y , and a t a load o f 55% o f t h e c a l c t l l a t e d ul t i rna t c r.:lp;ici t y ,

t h e r e was a c o r n e r c r a c k 2.51nm w i d e . . The d e t a i 1 shown i n F i g u r e 33b. w h i I t .

_ hav ing s u f f i c i e n t u l t i m a t e monlenc c a p a c i t y . had 3 c o r n e r c r a c k 5.3mn1 widc s t

a l o a d o f 55% o f t h e c a l c u l a t e d u l t iniate 'caplc i c y . O t h e r conunonly used

d e t a i l s had a n even w o r s e p e r f o r m a n c e . T h e s e t e s t s were a t r e l a t i v e l y s m a l l

s t e e l p e r c e n t a g e s of 0 . 5 t o 0.8;;. Swann ( 1 4 6 9 ) c.21-ricd t ~ u t a s l n l j l n r srric:s

of tests a t t h e h i g h e r steel p e r c e n t a g e of 3.i and significantly worsc nion~cnt

c a p a c i t i e s were o b t a i n e d . Such j o i n t s s h o u l d be c a p a b l e of r e s i s t i n g a moment

a t l e a s t a s l a r g e a s t h e c a l c u l a t e d f a i l u r e moment i n a d j a c e n t c r o s s section:;.

The c r a c k s t h a t form i n t h e i n s i d e o f c o r n e r s s h o u l d h a v e a c c e p t a b l e c r a c k

w i d t h s f o r l o a d s i n t h e w o r k i n g r a n g e . A l s o t h e r e i n f o r c e m e n t i n c o r n e r s

shou ld b e e a s y t o f a b r i c a t e and p o s i t i o n , and t h i s s h o u l d no rma l ly a v o i d t h e

need f o r s r i r r u p s or t ies.

F o r t h e r e i n f o r c e m e n t o f c o r n e r s s u b j e c t e d t o a n open ing bend ing - - rncment, N i l s s o n & Losbe rg (1976) recommended t h a t t h e r e i n f o r c e m e n t l o o p f r m

e a c h a d j a c e n t p a r t of t h e s t r u c t u r e s h o u l d b e t a k e n o u t i n t o t h e c o r n e r . r e g i o n , a s f a r as c o v e r r e s t r i c t i o r ~ s a l l o w , and s h o u l d t h e n be b r o u g h t back

i n t o t h e same c r o s s - s e c t i o n a d j a c e n t co the i r - icl incd r e i n f o r c e m e n t ( s e c

F i g u r e s 32(c) and 3 2 ( d ) ) . The main r e i n f o r ~ c m e n r s h o u l d be d e s i g n e d on t h e

b a s i s o f the moments i n c h c ,d j , iccnt s e c t i o n s ( P I 1 6 F:2) , i g n o r i n g t h e

e f f e c t o f r e i n f o r c e m e n t l o o p c u r t a i l m e n t i n t h e c o m p r e s s i o n zone and t h e

i n c l i n e d r e i n f o r c e m e n t . The c r o s s - s e c t i o n a l a r e a o f t h 2 i n c l i n e d

r e i n f o r c e m e n t shou ld b e a p p r o x i m a t e l y o n e - h a l f t h e a r e a o f t h e l a r g e s t main

r e i n f o r c e m e n t . Bars s h o u l d n e v e r be s p l i c e d i n t h e c o r n e r r e g i o n .

1 1 - 9 . 2 R eirzdmung S Z e d DetaiLcng R@culnrnc?~~dc&o~~,.

B a s e d ' o n t h e recommendat ions i n S e c t i o n 11 .9 .1 , &he c o r n e r s i n

r e t a i n i n g w a l l s shou ld b e r e i n f o r c e d a c c o r d i n g t o t h e g e n e r a l s o l u t i o n s g i v e n

i n t h e f o l l o w i n g p a r a g r a p h s .

\ h e n t h e l e n g t h

s h o u l d b e r e i n f o r c e d a s a

r e i n f o r c e m e n t i n t h e . b a s e

c o v e r r e q u i r e m e n t p e r m i t s

When t h e l e n g t h

o f t h e t o e is Less t h a n t h e s t e m t h i c k n e s s , t h e j o i n t

c o r n e r s u b j e c t e d t o a n o p e n i n g moment. The

s l a b s h o u l d b e t a k e n o u t i n t o t h e t o e a s f a r a s t h e

(see F i g u r e 3 2 ( c ) ) .

o f t h e t o e i s g r e a t e r t h a n t h e s tern t h i c k n e s s , and I

t h e l e n g t h o f t h e t o e is s u f f i c i e n t t o p r o v i d e a d e q u a t e a n c h o r a g e l e n g t h ,

r e i n f o r c e m e n t c a n b e a s i n F i g u r e 3 2 ( d ) . The c o n c r e c e Code o r R e g u l a t i o n

r e q u i r e m e n t s r e g a r d i n g bend ing r a d i u s , s p a c i n g o f b e n r b a r s and c o v e r s h o u l d

hc b o r n e i n mind. To l i m i t c o r n e r c r a c k widths, i n c l i n e d r e i n f o r c e m e n t

c r o s s - s e c t i o n a l a r e a a p p r o x i m a t e l y o n e h a l f t h e a r e a o f t h e l a r g e s t main

r e i n f o r c e m e n t s h o u l d be used . The L i m i t a t i o n s on s t e e l p e r c e n t a g e g i v e n i n

S e c t i o n 1 1 . 9 . 1 a p p l y o n l y t o t h e main r e i n f o r c e m e n t , a n d t h e d i a g o n a l b a r s

s h o u l d n o t b e i n c l u d e d i n t h i s p e r c e n t a g e .

Haunches i n t h e r e - e n t r a n t c o r n e r , accommodating s u b s t a n t i a l d i a g o n a l

f l e x u r a l b a r s , f o r c e t h e p l a s t i c h i n g e away from t h e f a c e o f t h e j o i n t . T h i s . - .

improves t h e a n c h o r a g e o f t h e main t e n s i l e s t e e l where i t e n t e r s t h e j o i n t .

The i n c r e a s e d i n t e r n a l l eve r -a rm w i t h i n t h e j o i n t , i n t u r n , r e d u c e s t h e

i n t e r n a l t e n s i l e f o r c e . [ launching would a l l o w t h e u s e o f h i g h e r s teel - - -

P e r c e n t a g e s , b u t N i l s s o n & - L a s b e r g (1976) make no s p e c i f i c recommendations on

a l l o w a b l e s teel p e r c e n t a g e s f o r haunched r i g h t a n g l e d c o r n e r s . C

F o r l a r g e j o i n t s w i t h u p t o 0.5% s t e e l , - P a r k & P a u l a y (1975)

recommended t h e u s e o f d i a g o n a l b a r s a c r o s s t h e c o r n e r e q u a l i n a r e a t o 50%

of t h e main r e i n f o r c e m e n t .

Above 0.54 o f s t e e l , t h e y p roposed t h a t r a d i a l hoops ( F i g u r e 3 2 ( e ) )

be p r o v i d e d , t h e a r e a o f one r a d i a l hoop b e i n g g i v e n by :

where D = h- i n t h e c r i t i c a l member, b . d,

n = no. o f ' l e e s .

A,1 = area o f s t e e l l i m i t i n g t h e magni tude o f t h e moment t h a t can

b e a p p l i e d t o t h e j o i n t ,

fyj = y i e l d stress o f r a d i a l hoops . -- -. -

I t s h o u l d b e emphas i sed t h a t problems o f c o n s t r u c t i o n may a r i s e

b e c a u s e of s teel c o n g e s t i o n a t s u c h c o r n e r s , and i t is u s u a l l y a b e t t e r -- .. - - -

s o l u t i o n t o t h i c k e n t h e c o n c r e t e s e c t i o n s i n v o l v e d .

Where t h e bac l t f i l . l cd f a c e s o f a r e t a i n i n g w a l l meet a t an a c u t e

a n g l e i n p l a n , t hen s i m i l a r c o n s i d e r a t i o n s t o t l ~ o s e . above s h o u l d be g i v e n to

t h e d e t a i l i n g o f t he r e i n f o r c i n g s t e e l . A d d i t i o n a l h o r i z o n t a l r c i n f o r c i r i g

s t e e l w i l l be r e q u i r e d i n t i le c u c s i d c f a c e of t h e wa l l .

V e r t i c a l j o i n t s a r e r e q u i r e d i n r e t a i n i n g w a l l s t o rninirnise t h e

e f f e c t s o f t e m p e r a t u r e changes and s h r i n k a g e , and b e c a u s e of c o n s t r u c t i o n

s t a g e s . I n r e i n f o r c e d c o n c r e t e w a l l s , v e r t i c a l .construe t i o n j o i n t s w i t h

V-notches a t t h e f a c e shou ld be p r o v i d e d a t s e c t i o n s p r e f e r a b l y no t o v e r lorn

a p a r t , t o g e t h e r w i t h r e i n f o r c e m e n t t h r o u g h t h e j o i n t s . Expans ion j o i n t s

w i t h g rooved s h e a r keys s h o u l d be p r o v i d e d n o t more t h a n 3 0 m a p a r t , t h e

r e i n f o r c e m e n t n o t be ing c a r r i e d t h r o u g h s u c h j o i n t s . I n g r a v i t y c o n c r e t e

w a l l s , s imi la r e x p a n s i o n j o i n t s s h o t ~ l d b e p r o v i d e d , p r e f e r a b l y no t more

t h a n lorn a p a r t . Where t h e w a t e r t a b l e is h i g h , w a t e r s t o p s s h o u l d b e

p r o v i d e d a t a l l c o n s t r u c t i o n and e x p a n s i o n j o i n t s .

Where t h e r e are l a r g e t e m p e r a t u r e v a r i a t i o n s , e x p a n s i o n j o i n t s may

r e q u i r e r e s i l i e n t j o i n t i n g m a t e r i a l t o a l l o w movement.

-

S e c t i o n s where t h e r e i s a s u b s t a n t i a l c h a n g e i n w a l l s t i f f n e s s or

w a l l t y p e ( e - g . c o u n t e r f o r t t o c a n t i l e v e r ) , o r w h e r e t h e n a t u r e of t h e

f o u n d a t i o n c h a n g e s (e .g . from f i l l t o r o c k ) , r e q u i r e c a r e f u l d e t a i l i n g . A t

s u c h l o c a t i o n s , i t i s u s u a l i y p o s s i b l e t o work o u t t h e d i r ~ c t i o n o f movemcr

t h a t may o c c u r and t o p rov ide a d e q u a t e c l e a r a n c e t o accommodate t h e movements.

It is u s u a l l y b e s t t o p rov ide a s t r u c t u r a l s e p a r a c i o n , ' r a t h e r t h a n t o a t t e m p t

t o r e i n f o r c e t h e j u n c t i o n t o t a k e t h e b e n d i n g rnocents and s h e a r s i n v o l v e d .

The s t a n d a r d o f roughness and c l e a n - u p o n h o r i z o n t a l c o n s t r u c t i o n

j o i n t s s h o u l d b e c l e a r l y s p e c i f i e d and c o n t r o l l e d . Keys i n s u c h j o i n t s s h o u l d - b e a v o i d e d , and w a t e r s t o p s s h o u l d be p r o v i d e d in j o i n t s b e l o w t h e w a t e r t a b l e ,

The c o n s t r q c t i o n j o i n t a t t h e b a s e o f a c a n t i l e v e r s t e m s h o u l d

a l w a y s b e d e t a i l e d a s be ing a t l e a s t 1OOm.m a b o v e t h e h e e l s l a b , ' t o e n a b l e t h e . . >

c o n c r e t e formwork t o be h e l d ' d u r i n g c o n s t r u c t i o n .

1i t h e stem of a w a l l , t h e p o s i t i o n of all c o n s t r u c t i o n j o i n t s should

be c a r e f u l l y considered from the p o i n t of view o f appearance a s we l l a s

s t r u c t u r a l performance ( s e e Sec t ion 1 1 . 1 2 ) .

t l . l f C O N T R O t O F C R A C K 7 N G

TO prevent unacceptable c r a c k i n g of r e t a i n i n g s t r u c t u r e s the f o l l o w i n g

s t e p s s h o u l d b e taken, i n a d d i t i o n t o normal good q u a l i t y c o n c r e t e p r a c t i c e :

(a) Provide sh r inkage and t e m p e r a t u r e re in fo rcement . This s t e e l

should be i n accordance wi th C h a p t e r 4 of t h e PWD C i v i l

Engineering ~ a n u a i t o ensure t h a t t h e c r a c k wid ths g iven i n . --

t h a t c h a p t e r a r e n o t exceeded: Note t h a t t h e r e i s a

r e l a t i o n s h i p between t h e r e i n f o r c i n g b a r s i z e , s t e e l p e r c e n t a g e

and c r a c k width i n v o l v e d . In n o c a s e shou ld the s t e e l

percentage used be l e s s 0.3% o f t h e g r p s s c o n c r e t e a r e a of t h e

wal l both h o r i z o n t a l l y and v e r t i c a l l y . I n t h e stem of t h e

wa l l exposed t o t h e a i r two t h i r d s of t h i s s t e e l should be

face .

(b ) Speci fy t h a t t h e c o n c r e t e p l a c i n g and temperature is t o be - .

kept a s low a s practical, e s p e c i a l l y i n t h e summer p e r i o d . .

(c) Speci fy s u c c e s s i v e bay, not a l t e r n a t e bay , c o n s t r u c t i o n .

(d l Speci fy e a r l y c u r i n g f o r the purpose o f c o b l i n g , s o a s t o

minimise the h e a t r i s e .

( e l Spec i fy good q u a l i t y c o n c r e r e a n d , where a p p r o p r i a t e , l i m i t

t h e cement c o n t e n t .

( f ) Addi t iona l a g a i n s t c r a c k i n g can be given by p a i n t i n !

t h e e a r t h f a c e o f a w a l l wi th , f o r i n s t a n c e , two c o a t s of

a s b e s t o s f i l l e d bi tuminous o r - a s p h a l t i c p a i n t . -

REFERENCES

Aggour, M.S. & Brown, C.B. ( 1 9 7 4 ) . The prediction of earth pressure on

retaining walls due to con~~action. Ceotechnique, Vol 2 4 , pp 489-502.

Bjerrim, L. C Eide, 0. (1956). Stability of strutted excavations in clay.

Geotechnique, Vol. 6, pp 32-47.

Bowles, J.E. ( 1 9 7 7 ) . Foundation Analysis and Des ip . McGraw Hill, New York

British Standards Institution ( 1 9 7 2 ) . Code o f Practice for the Structural Use

o f Concrete, CP 110:3u072. British Standards Institution, London, 54 p.

British Standards Institution ( 1972). Code of Practice for Foundations,

CP 2004:1972. British Standards Institution, London, 158 p.

British Standards Institution ( 1 9 7 8 ) . SteeZ, concrete and composite bridges - Speci f icat ion for loads, BS 5400:Part 2: 1978. ~riiish Standards

Institution, London, 158 p.

Broms, B.B. ( 1 9 7 1 ) . Lateral Earth Pressure Due to Compaction of Cohesionless

Soils. Proceedings of the 5th Gudapest Conference on Sci2 )!ecjknzids

and Foundation Engineers, Budapest, pp 373-384.

c '~roms, B.B. 6 Ingelson, I. ( 1 9 7 1 ) . Earth pressure against the abutments'of

a rigid frame bridge. Geotechnique, Vol. 21, pp 15-28.

Caquot, A. h Kerisel, J. ( 1 9 4 8 ) . Tables for the CaZculation of Passive Pressure

Active Press y e and Bearing Ccrpacitzj o f Foundations. (Translated from

the French by H . A . Bec, London) Gauthier - ViLlars, Paris; 120 p .

- Canadian Geotechnical Society ( 1 9 7 8 ) . Canadian Fowzdation Engineering Manual,

P a r t 4. Canadian Geotechnical Society, Ottawa, 68 p.

Cedegren, H . R . ( 1 9 7 7 ) . Seepage, Drainage & F Z a , Nets. 2nd Ed. Wiley, N e w

York, 534 p.

C1RI.A (1974) . A cornparison of quay wall design methods. ~ o n s t r u c t i o n Industry

Reseprch & Information Association, London, Report No 54 , 125 P - I

Danish Geo-technical I n s t i t u t e (1978) . Code of P r a c t i c e f o r Foundarion

Engineer ing . Bu LZe tin Wo. 32, Danish Geotechnical i n s titzcte, 5 2 p .

Davies , R . V . & Henkel, D . J . (1980) . Geo techn ica l problems assoc iaecd w i t h the

c o n s t r u c t i o n of C h a t e r S t a t i o n [long Kong. Proceedivgs of the Conferencn

on Mass Transportation i n Asia, Hong Kong, Sess ion 53, pp 1-31.

Department of Transporc , U.K. (1978).

Re inforced e a r t h r e t a i n i n g w a l l s apd b r i d g e abutments f o r embankments.

Department of Transport, Technical I-femorandzun (Bridges) GE 3/78 , 80 p .

F e d e r a l Highway Admin is t ra t ion ( 1978) . Standar*d Spec i f i ca t iom ' f o r Constructio?t

o f Roads and Bridges on Federal Highway Projects. Federa l Highway

A d m i n i s t r a t i o n , . . Washington, D.C., 355 p. - . -

G e o t e c h n i c a l Cont ro l O f f i c e (1979). Geotechnical Manual for SZope~.

Government P r e s s , Hong Kong, 230 p. -

, -

Goldberg, D.T., Jaworsk i , W.E. & Gordon, M-D, (1975). L a t e r a l s u p p o r t sys tems

& underp inn ing : Vol. 1, Design and c o n s t r u c t i o n . Federal Highway

A h i n i s t r a t i o n Report No. Fh'WA RD-75- 128, 3 12 p . ( N a t i o n a l Techn ica l I n f o r m a t i o n S e r v i c e No. PB257210).

Gould, J .P . (1970). L a t e r a l p r e s s u r e s on r i g i d permanent s t r u c t u r e s .

Proceedings of the SpeciaZi t y Conference on Latera L S tresses i n the Grount

and Design of Earth Retaining Structures, Tthica, New York, pp 21 9-270-

Hanna, T.H. (1980). Design and c o n s t r u c t i o n o f ground anchors . Construction

Industry Research and Information Association, U. K . Repor f: No. 65 , 2nd

ed. , 67 p, -

Hunt ing ton , W. C. (1961). Earth Pressures and Retaining WaZZs. Miley , New - - - - - - York 534 p.

I n g o l d ,T.S. (1979). The e f f e c t s of compaction on r e t a i n i n g walls. Geo tech?~ ip

Vol. 2 9 , pp 265-284 .

J - (1944) The c o e f f i c i e n t of e a r t h p r e s s u r e s a t rest. JOUPWZZ o f the

Society of Hungarian Architects and Engineers, pp 355-358- -

, a- . - . *\ \

James, E.L. & J a c k , B . J . (1974) . A d e s i g n s t u d y 0f;diaphrag-m w a l l s , . - Proceedings o f the Conference on Diaphragm WaZZs and Anchorages, Londo?l,

Janbu, N . , Bjerrum, L 6 K j a e r n s l i , B . (1956) . V e i l e d n i n g r e d l o s n i n g av

foundementerrings-oppgaker ( S o i l Mechanics a p p l i e d t o some e n g i n e e r i n g

p rob lems) . Norwegian Geotechnical I n s t i t u t i o n , Publicatior; No 16, 9 3 p .

- -

Japan S o c i e t y of C i v i l E n g i n e e r s (1977) . Guide t o 2''unnsZZing b y Cut and C o m r

Method. Japan S o c i e t y of C i v i l E n g i n e e r s , Tokyo, 203 p .

Lambe, T.W. & Whitman, R.V. (1969) . Soil Mechanics, Wiley, New Y o r k , 5 5 3 p .

tambe, T.W., W o l f s k i l l , L.A.. t Wong, I.H. ( 1 9 7 0 ) .

Measured performance o f b r a c e d e x c a v a t i o n s .

Journal of the So i l Mechanics and Foundations Division, American Soc ie ty

of C i v i l Eng ineers ; Vol. 96, pp 817-836.

Lumb P . (1975.). Slope f a i l u r e s i n Hong Kong. Quarterly Jour?lal of Engineering

Geology, Vol. 8, pp 31-65.

M i n i s t r y o f works and Development, New Zealand (1980). Specification &I 209 - CribwaZZing and Notes. M i n i s t r y of Works and Development, New Zealand,

W e l l i n g t o n , 9 p. -

M i n i s t r y o f Works and Development, New Zea land ( 1 9 7 3 ) . Retaining Design

Notes. M i n i s t r y o f Works and Development, C i v i l D i v i s i o n P u b l i c a t i o n

CDP 702/C, 43 p.

Morgens te rn , N.R. and E i s e n s t e i n , Z. (1970). Methods o f . e s t i m a t i n g l a t e r a l

l o a d s and def o k a t i o n s . Proceedings of the Specialty Confe~ence on Lateral

Stresses i n the Ground and Design of Earth Retaining Structures. Ithica, . - N e u York, pp 51-102.

Morton, K., C a t e r , R.W. & Linney , L. (1980). Observed s e t t l e m e n t s o f b u i l d i n g s

a d j a c e n t t o s t a t i o n s c o n s t r u c t e d f o r t h e m o d i f i e d i n i t i a l sys tem of t h e

Mass T r a n s i t Railway, Hong Kong. Proceedings of the 6th Southeast Asian

Conference on So i l Engineering, Taipei. V o l . 1, pp 415-430.

I..

NAVFAC ( 197 1 ) . Design f i l a n u ~ l - Soi Z Mechanics, Foundat ions, and &lath - - Structures , Df = 7. Depar tment o f t h e Navy, Naval F a c i l i t i e s Eng inee r ing - -

, ,

Command, Clnshington, D . C . , 223 p.

N i l s s o n , L. H . E. & Losberg , A. (1976) . R e i n f o r c e d c o n c r e t e c o r n e r s ant1 j o i i ~ t s -

O'Rourke, T.D., Cording , E . J . & B o s c a r d i n , M. (1976) . The ground movements

r e l a t e d t o b raced e x c a v a t i o n and t h e i r i n f l u e n c e on a d j a c e n t b u i l d i n g s .

U S Depa?*trnmt of Transportat,ion, h'eport No. DOT-2-S- ' 3 , 7-22, 123 p.

Park , R. & Pau lay , T ( 1975) . Reillforced C m c ~ > e t e .Struc'L!araes, . Wi l e y , New Yorl-: . 769 p.

Peck, R . B . (1969) . Deep e x c a v a t i o n s and t u n n e l l i n g i n s o f t ground.

7 th I n t . Conf. . Soi l Mechs, and Foundation Exginee?..l:ng, Mexico C i t y .

S t a t e - o f - t h e - a r t Volume, pp 225-290.

Peck R.B. , Hanson !.I.E. & Thornburn T.H. ( 1 9 7 4 ) . IJo~.,ndation Eqirleellirtg.

2nd Ed. Wiley, New York; 514 p.

P u b l i c Works Depar tment , tiong on^ ( 1977) . Civ i i! E'qineeririg Mn)zua7., V C ~ . i' :

Roads. P u b l i c works Depar tmen t , Hong Kong, 350 p . . . .. . . - .

R a n k i l o r , P.R. (1081). Membranes. i n Crorcnd Engiweering. Wiley, C h i c h e s t e r 377

Rowe, P . W . ( 1952) . Anchored s h e e t p i l e w a l l s . ~roceedtngs of the ~ n s t i t u t i o ~

o f CiviZ Engineers. Vol . 1, pp 27-70.

Row, P.W. (1955). A t h e o r e t i c a l and e x p e r i m e n t a l a n a l y s t s of s h e e t p i l e . . w a l l s .

Proceeding of the InsTi tut ion o f Civ i l E@neers, Vol. 4 , pp 32-87.

Rowe, P.W. (1957). S h e e t p i l e w a l l s in clay-. Proceedings of the I?zsti tution ' 4

of CiviZ Engineers, Vol . 7 , pp 629-654.

Rowe, P.W. & Peake r , K. ( 1965) . P a s s i v e ear th p r e s s u r e measuremencs-

Geotechnique, Vol. 15, p p 57-78.

S c h u s t e r , R.L., J o n e s , W.V., Sack, R.L. & Smar t , S.M. (1975). Timber r e t a i n i n g

s t r u c t u r e s . Transport Research Board, National Research CounciZ.

Special Report 160: Low Volume Roads, pp 116-127.

S c o t t , G l a n v i l l e & Thomas (1965). Explamztor9 Ifamibook GN the i:. S. C d r of

Practice for ~ e i n j b r c e d Concrete C P 11 4 : 195 7, 2nd Ed. C o n c r e t e

P u b l i c a t i o n s , London, 172 p .

Seed, N.B. & Whitman, R.V. (1970) . Design o f e a r t h r e t a i n i n g s t r u c t u r e s f o r

dynamic loads . Proceedings of the Special ty Conference o7i LC t&mZ

Stresses i n the Ground and Design of Ea17th Retainixo Stmctttre:;, I t h i m ,

New York, pp 103-147.

Swann, R.A. ( 1 9 6 9 ) . , F l e x u r a l s t r e n g t h of c o r n e r s of r e i n f o r c e d c o n c r e t e p o r t a l

f r a m e s . Cement and Concrete Association, U. K . , Tec!tnical Report T U 434.

14 p .

Teng, W.C. (1962). Foundation Design. P r e n t i c e - H a l l , New J e r s e y , 466 p .

. .

Terzagh i , K:(1943). Theoretical Soil Mechanics. Wiley, New York, pp 129-130.

of C iv i l Engineers, Vol. 119, pp 1243-1324.

Terzagh i , K . & Peck R . B . (1967). Soil Mechanics i n Engi?zeering Practice,

2nd Ed., Wiley, New York, 729 p.

T s c h e b o t a r i o f f , G. P. (1951). Soi l Mechanics, Foundations and Earth Structures.

McGraw H i l l , New York, 1st Ed., 655 p .

Vesic, A . S . (1975). Bear ing c a p a c i t y of s h a l l o w founda t ions - -

Foundation Engineering Handbook, E d i t e d by H.F. Winterkorn and H . Y . Fang,

pp 121-147. Van Nostrand Reinhole Co., New York - .

* White, R.E. (1974). Anchored w a l l s a d j a c e n t t o v e r t i c a l rock c u t s . ~rocesd ipqs - .

o f the Conference an Diaphragm WaZ 2s and Anchorages, London, pp 18 1-1 88.

Wu, -T.H. (1975). R e h i n i n g . wa1l.s. - Foundation Engineering Handbook, Edited- b y

H:F. Winterkorn and H.Y. Fang, pp 402-417. Van Nostrand Re inho ld C O . ,

New York. * .

APPENDIX A

SYMBOL

Y

g

gcs gq* gy

H , HI , e t c .

a r ea of d ra inage m a t e r i a l

e f f e c t i v e a r e a of base

a rea o f c ros s - sec t ion of r e i n f o r c i n g s t e e l

base width of wa l l

e f f e c t i v e base width

d i s t a n c e from c r e s t of s l o p e t o foundat ion

cohesion of s o i l i n terms of t o t a l s t r e s s

adhesion a t base

cohesion of s o i l i n terms of e f f e c t i v e s t r e s s

e f f e c t i v e depth of w a l l s t e m

depth of foundat ion

e c c e n t r i c i t y of load on b a s e . i n t h e d i r e c t i o n s of length and b read th r e s p e c t i v e l y

f a c t o r of s a f e t y

moment arm of v e r t i c a l component of e a r t h p re s su re f o r c e

c h a r a c t e r i s t i c s t r e n g t h of reinforcement

a c c e l e r a t i o n duc t o g r a v i t y

foundat ion ground s l o p e f a c t o r s

he ight of p lane on which e a r t h p re s su re is c a l c u l a t e d (from unders ide of base- o r bottom of key t o ground s u r f a c e )

t a n g e n t i a l component of foundat ion 1,oading

d i s t a n c e of r e s u l t a n t fo rce . f rom w a l l t o e

c r i t i c a l dep th of f i l l where compaction p re s su res equa l . a c t i v e . p re s su re . . -

hydraulic g r a d i e n t

waviness of r o c k - j o i n t

bea r ing c a p a c i t y i n c l i n a t i o n f a c t o r s . -

c o e f f i c i e n t o f e a r t h p r e s s u r e a t r e s t

I

P, Pmax, Pt

c o e f f i c i e n t of a c t i v e e a r t h p r e s s u r e

c o e f f i c i e n t of p a s s i v e e a r t h p r e s s u r e

c o e f f i c i e n t of subgrade r e a c t i o n

c o e f f i c i e n t of p e r m e a b i l i t y

l e n g t h of base . . . . ~ - .. .

e f f e c t i v e l e n g t h of b a s e

l e n g t h of w a l l h e e l -

c l e a r span.between c o u n t e r f o r t s

l e n g t h of w a l l t o e

bending moments f o r r e i n f o r c e m e n t d e s i g n

sum of moments c a u s i n g o v e r t u r n i n g

sum of moments r e s i s t i n g o v e r t u r n i n g

s t a b i l i t y f a c t o r r e l a t i n g t o e x c a v a t i o n b a s e E a i l u r ~

b e a r i n g c a p a c i t y f a c t o r s

moment arm of r e s u l t a n t w a t e r f o r c e - on back of w a l l

e q u i v a l e n t l i n e l o a d due t o r o l l e r

a c t i v e e a r t h p r e s s u r e f o r c e

' a t r e s t ' e a r t h p r e s s u r e f o r c e

h o r i z o n t a l component of a c t i v e e a r t h p r e s s u r e f o r c e

normal component o f e a r t h p r e s s u r e f o r c e

p a s s i v e e a r t h p r e s s u r e f o r c e

t a n g e n t i a l component o f e a r t h p r e s s u r e f o r c e

l a t e r a l e a r t h p r e s s u r e d u e - t o l i n P o r p o i n t s u r c h a r ( p e r u n i t l e n g t h of w a l l ) -

v e r t i c a l component of e a r t h p r e s s u r e f o r c e

w a t e r f o r c e due t o w a t e r i n t e n s i o n c r a c k

p r e s s u r e for s t r u c t u r a l d e s i g n

t o t a l load

line load

Q~ po in t load

- - - - a i n t e n s i t y i f l o i d - o n base o r su rcharge l o a d

qa11 a l lowable b e a r i n g c a p a c i t y

9 d flow r a t e through d r a i n

quit u l t i m a t e b e a r i n g c a p a c i t y

R s R,, R p s RW r e s u l t a n t f o r c e s

6 s h e a r s t r e n g t h of s o i l

t o t a l s h e a r i n g r e s i s t a n c e a t u n d e r s i d e of b a s e

SC, s q t s foundation shape c o r r e c t i o n f a c t o r s

th ickness of w a l l stem .

t c , t q y t foundation t i l t f a c t o r s

U Y u p u2 r e s u l t a n t f o r c e due t o water p r e s s u r e s

U l ~ y U~~ h o r i z o n t a l and v e r t i c a l components o f r e s u l t a n t w a t e r f o r c e

pore water p r e s s u r e

normal cornponen t of foundat ion b e a r i n g p r e s s u r e

V shear force f o r reinforcement des ign

w, wb weight of b a c k f i l l

Wt weight of w a l l

X r e s u l t a n t h o r i z o n t a l r e a c t i o n

Y l a t e r a l deformat ion of r e t a i n i n g w a l l

Yo v e r t i c a l depth o f ' tens ion crack i n c o h e s i v e s o i l

Z depth below f i n a l f i l l l e v e l

zc depth below f i n a l f i l l l e v e l of maximum r e s i d u a l compaciibn. - p t e s s u r e

a , angle of i n c l i n a t i o n of founda t ion b a s e

6 a n g l e of i n c l i n a t i o n of t h e back of t h e ; e t a i n i n g vall . .

Y bulk u n i t weight of s o i l .

Y' e f f e c t i v e u n i t we igh t of submerged s o i l

u n i t weight o f w a t e r

s a t u r a t e d u n i t we igh t of s o i l

settlement of wall

angle of wall friction

angle of base friction

location angles for failure plane

angular rotation of foundation base

total and effective normal stress

angle of shearing resistance in terms of. total and effective stress

angle of ground slope

shear stress

DENSE SAND

PRINCETON TESTS

DENSE SAND

0.06 0.OL 0.02 0 0 -0 au. Y

WALL ROTAT ION -)I WALL ROTATION ~ ; i H

PASSIVE CASE ACTIVE CASE

f after Canadian Ceotechnicai Society, 1978 1

EFFECT OF WALL MOVEMENT'ON. whir PRESSURE .

I I ' f i x : .. ACTIVE STATE

STATE

WALL FREE TO TRANSLATE OR ROTATE ABOUT ITS BASE

NO DISPLACEMENT

RESTRAINED RIGID WALL

EXPANSION

BOTTOM OF WALL

DISPLACED OUTWARD MORE THAN TOP

OF WALL

TOP QF WALL RESTRAINED

EXPANSION

STRUTTED FLEXIBLE WALL

ANGLE OF SHEARING RESISTANCE, 8, DEGREES (Caguot b ~ e r i s e l , 1 9 4 8 )

1

NOTES

1 . The l a t e r a l e a r t h p r e s s u r e i s o b t a i n e d by s e l e c t i n g a number o f t r i a l f a i l u r e p l a n e s and d e t e r m i n i n g c o r r e s p o n d i n g v a l u e s o f P A (o r Pp) by d rab t in9 a f o r c e p o l y g o n - see ( a ) . F o r t h e a c t i v e p r e s s u r e case , t h e maxinlum va icle o f

7 4 i s r e q u i r e d and f o r t h e p a s s i v e case , t h e minimum Pp i s r e q u i r e d . These ~ r n i t i n g v a l u e s a r e o b t a i n e d b y i n t e r p o l a t i n g between t h e v a l u e s f o r t h e

wedges s e l e c t e d - see (b) . - 2. L a t e r a l . e a r t h p r e s s u r e may b e c a l c u l a t e d o n any s u r f a c e o r p l a n e t h r o u g h the

s o i I .

3 . See F igu res 1 1 and 12 f o ' r t h e p o i n t o f a p p l i c a t i o n o f PA.

4 . The t r i a l wedge me thod may a l s o b e used f o r a l e v e l or c o n s t a n t l y s l o p i n g g r o u n d s u r f a c e , i n w h i c h case i t s h o u l d y i e l d t h e same r e s u l t a s t h a t g i v e n b y R a n k i n e ' s o r Cov iomb ' s e q u a t i o n s ( w h i c h e v e r i s a p p i i c a b l e ) .

T R I A L W E D G E METHOD - COHESIONLESS SOIL'

SURFACE ON WHICH-PRESSURE - -

IS CALCULATED \

TENSION ZONE

- LEVEL

L

. -

FORCE POLYGON FOR TYPICAL WEDGE COMBINATION OF

ACTIVE PRESSURE -T

The above Cou l omb ' s

example shows ank kine' c o n d i t i o n s . (Adhes ion

FORCE POLYGONS .TO OBTAIN

MAX. PA s condi on the

t i o n s b u t the, back o f the wa

same 'p r inc ip le 1 1 i s ignored) .

2. Fo r d i r e c t i o n PA see F i g u r e 10 anki kine's cond i t i .ons) o r f i g u r e 6 ( ~ o u l o m b ' s - c o n d i t i o n s ) .

3 . See F igures 1 1 and 12 f o r p o i n t of a p p l i c a t i o n .

4. See F igu re 12 f o r r e s u l t a n t p ressu re diagram.

5 . The t r i a l wedge method may be used f o r a l e v e l o r c o n s t a n t l y s l o p i n g ground s u r f a c e .

TRIAL WEDGE METHOD - C O H E S ~ V E SOIL F IGURE 7

PROCEDURE

I . ' Draw t r i a l wedge I i n l a y e r (I) (as shown) a n d o b r a i n PA, ,,, b y v a r y i n g [ t i c f a i l u r e p l a n e and d r a w i n g t h e f o r c e p o l y g o n ( a ) .

2 - Draw t r i a l wedge 11 (as shown) by c h o o s i n g f a i l u r e p l a n e AB i n l a y e r ( 2 ) .

3 . F i n d X max b y v a r y i n g t h e i n c l i n a t i o n o f p l a n e BC f r o m 8 and d r a w i n g !he f o r c e p o l y g o n (b ) .

I . U s i n g X m a x draw f o r c e p o l y g o n ( c ) and f i n d PA2. ,

5 , Repeat s t e p s 2. t o 5 . u s i n g o t h e r t r i a l f a i - h r e p l a n e s A B ' , e t c . u n t i l P A 2 lllar

i s de te rm ined .

NOTE , ..

Where l a y e r 2 i s r o c k - l i k e m a t e r i a l , s u c h t h a t no e a r t h p r e s s u r e s a r e e x e r t e d i g a i n s t t h e w a l l , due accoun t s h o u l d however be t a k e n o f w a t e r p r e s s u r e s and j o i n t o n t r o l l e d f a i l u r e modes.

T R I A L W E D G E M E T H O D - L A Y E R E D S O I L A H D P O R E W A T E R P R E S S U R E ( A C T I Y E C A S E 1

-

MOJES WITH

MOVES WITH

NOTE

VIRTUAL BACK

( a ) R A N K I E 6 =IJ

SLOPING VIRTUAL BACK

( 1 ) I f 1 ine AB does not intersect the wal!, Rankine's conditions apply.

If line AB does intersect the wall, Coulomb's conditions apply. ,

I sin w ( 2 ) 6 = +(YO - 6') - f ( ~ - W) where ;in&=-- s i n 0'

PROCEDURE

Draw a line from the point 'where the ground surface intersects the back of the w a l l (B) to a point o n the ground surface located at a distance equal to 2H' from B.

The pressure on A-A' may be assumed to act para1 lel 'with this I ine.

APPRtlKlMBTf: METHOD FOR DETERMIHATIOH OF D l R E C T l O H BF R A N K I N E ACTIVE E A R T H PRESSURE F I G U R E 10

F'

TENS

ION

CRAC

K IN

,

SO

L WI

TH

COHE

SION

F

#--

---

---

I I

FAIL

UR

E P

LAN

E

I I

CEN

TRE OF G

RAV

ITY

( C.G

. )

OF

I

C. G

. OF

WED

GE

WED

GE

A A

"CD

EF

SUR

FAC

E ON

W

HICH

PR

ESSU

RE

I

I.

Draw a

li

ne th

roug

h th

e c.

g, of wedge AA"

CDEF pa

rall

el with th

e pr

evio

usly

obtained Fa

ilur

e plane, to

inte

rsec

t A

-A'

at point.)(.!

(For

constant b

ackf i

l l slope, A

-X

= -f-

A-A

")

. Fo

r cohes ion

less

so

i Is

th

e to

tal

wedge b

etwe

en th

e fa

ilur

e pl

ane

and th

e gr

ound

su

rfac

e is

A

used

.

2.

Draw a

I i

ne th

roug

h po

int

X pa

ral lel

to

BG' (s

ee

f iq

ure 10)

and

a ve

rtic

al li

ne th

roug

h th

e c.

g. of wedge A

BA

1 to in

ters

ect

at poinr'~.

I ,*

3.

PA

ac

ts th

roug

h po

int

Z at

an a

ngle

of 6" to th

e no

rmal

to

th

e su

rfac

e on w

hich th

e pr

essu

re is ca

lcul

ated

.

NOTE

:

a)

If th

e pr

essu

re is ca

lcul

ated

on a

ver

tica

l pl

ane

step

s 2

and

3 are u

nnec

essa

ry as P

A acts th

roug

h po

int

X.

b)

Llater' fo

rces

rilu

st

be 'co

ns id

rred

se

para

tely

.

SURCHARGE

T R I A L WEDGES PRESSURE ON A-6

Use when t t ~ c g r o u n d su r face i s v e r y i r r e g u l a r o r when a non-uniform su rcha rge i s c a r r i e d .

- PROCEDURE

1 . Subdiv ide the l ine A-6 i n t o about 4 equal p a r t s hl (below the depth yo of

tension c r a c k ),

2. ' Compute the ac t i ve e a r t h p r e s s u r e s P I , P2, P3, 'etc.. , as i f cach of r l w po in t s 1 , 2 , 3 , etc. , w e r e the base of the wa l l . The [ r i a l hedge method i s used f o r each computat ion.

3. De le rm ine the p r e s s u r e d i s t r i b u t i o n by w o r k i n g down f rom point 4 . A l i n e a r v a r i a t i o n of p r e s s u r e may be assumed between the points where p r e s s u r e h a s been ca lcu la ted .

4 . Dete rm ine t h e e leva t i on of the c e n t r o i d of the p r e s s u r e di.agram, 7 . Tti is. is the approx imate e leva t i on of the point of app l ica t ion of the resu l tan t e a r t h p r e s s u r e , PA.

NOTE : Water f o r c e s must b e cons ide red separa te ly .

POINT OF APPLICATION OF RESULTANT FORCE AND PRESSURE DISTRIBUTION F I G U R E 12

1 . De te rm ine the d i r e c t i o n s o f su r face o f s l i d i n g B A ' 3nd the p l a n e p o r t i o n A I M o f t h e s u r f a c e o f r u p t u r e from the f o l l o w i n g formulae :

6 , = f(90a + 0 ) - ! ( E + UJ) where, w = mean ground s l o p e

0 , = $(SO" + 0) $(E + ld) and s i n € = s i n w / s i n 0

1 2 . S e l e c t a reasonable p o s i t i o n f o r A ' and j o i n A ' H w i t h a s t r a i g h t I ine.

I 3 . C o n s t r u c t A'C p e r p e n d i c u l a r t o A I M a t A ' . Produce a p e r p e n d i c u l a r b i s e c t o r OP c u t t i n g A'C a t 0, draw a r c A A ' w i t h 0 as c e n t r e . -

I 4 . Dete rm ine U j & U2, r e s u l t a n t o f water p r e s s u r e on each p o r t i o n o f wedge.

5. Compute W 1 , W2 & W 3 and c o n s t r u c t f o r c e po lygons b , c t, d i n o r d e i t o o b t a i n P p

6. Draw t h e p ressu re l o c u s o f Pp i n ( a ) f o r v a r i o u s t r i a l p o s i t i o n s o f 8 ' .

7. Repeat s teps 2-6 w i t h d i f f e r e n t l o c a t i o n s o f A ' u n t i l t h e m i n . v a l u e o f Pp i s found.

PASSIVE F O R C E BY C I R C U L A R ARC METHOD I A Y F R E D S O I L A N D POREWATER P R E S S U R E I F I G U R E 13

I EARTH PRESSURE W E TO WEIGHT OF

- - . : BACKFILL u h o ~ ~ ~ . = l ~ k ~ r n ? , - ,

CRITICAL DEPTHS AH0 EARTH PRESSURE VALUES I

K 3 .3 t VIBRATORY ROLLER . I 0 5 2 1 19.0

% 1.L i VIBRATORY ROLLER I . 0 . 3 5 I 1 2 . 5

LOO kg VIBRATORY PLATE 1 6 . 0 COMPACTOR

1 2 0 kg VIBRATORY PLATE 0 . 3 2 11.5 COHPACTQR

NOTE. DIAGRAM DRAWN FOR 10.2 1 SMOOTH WHEEL ROLLER

ON FILL, @ r 3;. = 1 8 k N I m 3

X EFFECTIVE WEIGHT OF VIBRATORY ROLLERS ASSUMED TO B E TWICE TOTAL STATIC WEIGHT.

I i ) COMPACTION AGAINST UNYIELDING WALLS ( BROMS, 1971 1.

RESULTANT PRESSURl DISTRIBUTlON

HORIZONTAL EARTH PRESSURE

I \ HORIZONTAL WlH PRESSURE

COMPACTED LAYERS

HOmZOHTAL EARTH PRESSURE

(bj SHOWS IHFLUEHCE OF SUCCESSIYEU COHPACTIHG LAYERS OF SOIL BEGlNHlHG AT BASE OF WALL.

Q* hrn - MAXIMUM VALUE OF HORIZONTAC STRESS SUSTAINED AFTER COMPACTION.

*

--

WHERE p t ECNIYALENT LINE LOAD CUE TI ROLLER. FOR V18RATORI ROLLE CALCULATE p USING AN EQUIVALENT WEIGHT EQUAL T(

h, = DEADWEIGHT OF ROLLER PLUS Ka . CENTRIFUGAL FORCE INDUCED

BY ROLLER VIBRATING MECHANISM.

k] SHOWS PROPOSED DESIGN PRESSURE DIAGRAM-

( ii ) COMPACTION PRESSURES - DESIGN DATA (INGOLD, I979 I -.

'1 FIGURE 14

For m s O.L

H Q$--I = 0.20n QL (0.16t nZ I L

Po = 0. 5 5 tlL

For m > 0.4

PRESSURES FROM- LINE LOAD Q, ( MOOIFIEO BOUSSINESQ

RESULTANT Ps = KaQL

RESULTANT FORCE FROM LINE LOAD QL ( APPROX. METHOD FOR LOW RETAINING WALL 1

- -. UNE LOAD r TERZAGHI t PECK 1967 1

LATERAL LOADS ON WALL DUE TO

Fcr m 0.11

For m > 0. C

SECTION A -A

'RESSURE FROM POINT LOAO Qp

POINT LOAD r t w m ~ o msmsa 1

POINT AND LINE L O A D S U R C H A R G E S F I G U R E 15

I I I I - virtual back of wall

un i f o r m SUI-chat -qe

LOADING I

CRITICAL FOR BEARING PRESSURES WALL REINFORCEMENT

AND

uni f o r m surcharge ..

I

LOADING 2

CRITICAL FOR STABIL tTY

SURCHARGE LOAD CASES ! F I G U R E - 1 6

Water pressure distribution on

mtential failure plane due to

steady seepage.

(a1 NORMAL STEADY STATE SEEPAGE CONOiTlON

Infiltration

(VERTICAL DRAIN 1

. . - - --

Note increase in

water pressure on . potential failure

plane due to

surface infiltration.

(bJ SURFACE INFILTRATION (VERTICAL DAAIN 1

Note water pressure

is zero on potentiat

failure piane.

/

( FLOW NETS ASSUME HOMOGENEOUS. ISOTROPtC 9 1 L ]

Kote : For ease of c o n s t r u c t i o n . ~ ~ h e r e - f i l t e r l a y e r s a r e c o n s t r u c t e d a t a s teep i n c l i n e , f i l tcr m a t e r i a l may be p l a c e d i n h e s s i a n bags.

c o n s t r u c t i o n

d r a i a j q c ~ t a t e r i a l

cng i t u d i naI pcrous pi PC

\ l a t e r p r e s s u r e shou ld be cons itfcrVed i n d e s i g n ( S e c t i o n 5 . 3 )

e r , r i a l

nage r i a l

[b} CANTILEVER 1 COUNTERFORT used when .(a). is not possible

b l i n d i n g layerJ

CANTILEVER I COUNTERFORT Water p r e s s u r e shou ld be c o n s i d e r e d

i n d e s i g n ( S e c t i o n 5 - 3 1

\ - de ta i 1 as (a)

fc) GRAVITY TYPE

f i 1 t e r l a y e r des i gne accordance w i t h

---- ----

d r a i n a g e m a t e r i a l p l a c e d i n h e s s i a n

I b l i n d i n g l a y e r

(d) GRAVITY TYPE used when (c) is not possible

BASE

( a ) TYPICAL FLOW NE f' FOR SEEPAGE INTO INCLINED FILTER

Q f INCLINATION OF FILTER C SEE ABOVE 1

( b)' CHART DEVELOPED FROM FAMILY OF FLOW-NETS ( after Cedergren , t977 I

DESIGN dF INCLINED DRAINS 1 1 FIGURE 19

GRAIN SIZE ( m m )

COEFFICIENT OF PERI~EAEIL ITY

FOR CLEAtt C W S E - S3?AlfJf D DRAI Pi&€ MATERIAL

PERCENT BY WEIGHT WSSING 75 miuon

S E E ( a f t e r N A V F A C 014-7,. 1971)

P E R M E A B I L I T Y O F D R A I N A G E M A T E R I A L S ' F I G U R E 20

I PENETRATION REOUlRED FOR SHEETING I

- - - PEHETRATION REQUIRED FOR SHEETIUG

IN SANDS OF INFiHlTE DEPTH IN DENSE SAND OF FlNFlE DEPTH -

d -

\. ------ -0OSE SANO 6 \ - \

H" DENSE SAfiO \

'FACTOR OF SAFETY A t m m n u w t FACTOR OF SAFETY AGAINST PtPlNti LOOSE SAND OR PIPING IN MUSE SAND

a) SHEET PENETRATlON IN GRANULAR SOILS

Le t kl = k3

. HI < t i j i h e r e g e n e r ~ l l y i s more i low

than g i v e n i n g raph ( a ) ( i n f i n ; te ! 3 5 9 - ~ e .

I f (11, - bI3) > .B use graph ( a ) ( i n 1 i n i t e ) .

I f (HI - t i J ) < B t h e r e i s n o r e f l c w ihsr i g i v e n i n g raph ( a ) ( i n f i n i t c ) . I F C; > - 10KI. f a i l u r e head [ I u i s equal t o H z .

I f Ill < ti s a f e l y f a c t o r s a r e i n c e c i c e d i a t c 3 between those f o r graph (a) ( F i n i t e ) . I f 11, > }I3 graph ( a ) ( F i n i t c ) i s con;er- v a t i v e .

I f - d! > 8 use graph ( a ) ( f i n i c c ) above. . . - - -

I f - d) c B p r e s s u r e re1 i c f r .equi r e d so t h a t unbalanced-head on f i n e l a y e r --

does n o t exceed we igh t of Hz.

I f f i n e l a y e r i s h i g h e r than b o t t o m o f e x c a v a t i o n t h e completed e x c a v a t i o n i s - s a f e , b u t d u r i n g c o n s t r u c t i o n a b l o w i n nlay o c c u r - p r e s s u r e r e l i e f t hen r e q u i red .

b ) PILING - PENETRATION TO PREVENT PIPING i otter NAVFAC OH-7, 1971 I

- V4LL YPE -

>- k - > 4 IY (3

- - m

i? 0

-4--

6 - $ - > I- - > Q (r:

-

(Y

W > u -1 - t- Z Q 0

- - V

r a J J t > C L I + -I - - L

z-2 Q c 2 3 - -

LOAD DIAGRAM

Rt;Z:E

VERTICAL ! I=* / STEM

STABILITY. CRITERIA

SLIDING

S + 0 . S P Fs (sliding) = > 1 - 5

p n + U ~ H

i.e. F.S. on any included ultimate passive > 3.0

Moments about the toe of the base

Homents resisting ovcrturninq fir $5 (overturning) = = -

Homcnts causing ovcrtufning n o

Mr = Vta (Fassive Resi srancc Pp ignored)

No = PA" + U1n t U2e

N.B. I t is illogical to take vertical conlpo- nenrs of the dist.urbing forces and use them as restoring rrionlcnts in the expression for F.S. see section 6 . 3 . 2

Cverturning may be ignored i f R, lies within middle third (soii), m;ddlc half (rock). For gravity type walls. overturning must be checked at selected ho;izontal plane;.the resulrant must remain within the rriddlc third.

LOCATION OF RESULTANT

Point where R, intersects base, from t o e .

Ula + P,f - P t ~ + Ulvc - Ul),d - U2e h =

Wt + Pv + 81" - U2 . (Passive resistance Pp isnored)

For soil foun.-?ation marcrial, Rw should lie within middle third o f the base

For a rock foundation, R, should lie within middle half of the base

BEARING PRESSURE

See section 6.4 for Calcu!ation of f ~ c t o r of safecy for bearing Fs (bearing)> 3.0

Ut = total weight of the wall incluPing soif on toe plus soil above^ heel (for cantilever walls only)

R, - resultant of W c . PA; U I C U2

SLOPE FA1 CURE I ti SURRCL;I+D I NG SO 1 L

With shear surfaces passing under the \.(all. the factors of safety st-~utd conply uith the requirements of Table 5.2 of the Geotechnical Hanual for Slopes.

W A T E R F O R C E S - *

- - . - - . .

Refrrence should be made'to Chapter 5 fo;- - cases ocher than those shcwn here.

3

S T A B I L I T Y C R I T E R I A F O R R E T A I N I N G W A L L S 1 F I G U R E 22

q u ~ t = cNc Sc ic \ gc +

- -

SHAPE FACTORS

8 N Sc = I + - a L N c

B S, = I - 0 . L - L

INCLINATION FACTORS

TILT FACTORS

WHERE d I S IN RADIANS

GROUND SLOPE FACTORS

q = SURCHARGE EFFECT

= $Dcosw

[ SECTION 6 .4 .3 1

2 + 7 W E R E rn, - PROVIDED THE ~NCLINATION OF LOAD IS IN THE

B DIRECTION OF B l + T

L

NOTE : Hmox - v tan4'+ A c

NOTES

1. DATA APPLES TO SHALLOW FOUNDATIONS

ONLY D 4 B.

2. FOR W > &. A arCK SHOULD ALSO BE MADE 2

FOR OVEAAU SLOPE STABILITY.

3. FOR THE EFFECTS OF NONHOXOGENEWS SOIL AND SOlL COMPRESSIBILTTY AM) SCALE EFFECTS REFERENCE SHOULD BE TO VESIC.

L. WHERE THE F W ~ T I O N IS KT BACX mat THE CREST OF THE SLOPE, REFER TO SECTION 6.6

L O O

3 0 0

0 5 10 15 2 0 2s 30 35 # LS 50

AHGLE OF SHEARING RESISTAHCE 9' . [ degrees )

BEARING WAClTY FXTORS

B E A R I N G CAPACITY DATA ( VESIC, 1975 ) I FIGURE 23

N.C CLAYS

. . --

& = RANKINE COEFFICIENT OF ACTIVE EARTH PRESSURE

N3TE WATER AND SURCHARGE LOAOlt;G5

0 c CLAYS SHOULD BE CONSIDERED

fa after Peck ,.I969

HARDCLAY(N,L) ,OGH

SOFT CLAY ( N * L 1

K = COEFFICIENT OF EARTH PRESSURE N = STANDARD PENETRATION TEST VALUE

I b ) af teg Japan Society of Civil Engineers ,1977

NbC F,( base l = - 3 H . q .

c = AVERAGE UNDRAINED SHEAR STRENGTH OF IHE SOIL FN(3-i BASE

H LEVEL TO A DEPTH Ct= 0 2SH BELOW THE BASE

Nb= STABILITY FACTOR

L = EXCAVATIW LENGTH

-

-

0, INFINITE STRIP

-

STABILITY FACTOR FOR VARKXIS a

GEOMETRIES OF CUT -

L - I I I I I I I i 1 I 0 i 2 3' L 5

H - ' 8

(After h n t u et al. 1956 )

F A C T O R 0 F SAFETY WITH RESPECT TO BASE HEAVE 1 FIGURE 25

t '

NOTES

1 . C r i b w a l l u n i t s t o be i ~ f i l l c d i-!il l~ I rpc.

d r ~ i n i n g m a t e r i a l , we1 1 compac i cd t n l a y e r s . Care s h o u l d be t a k e n t o ~ v o ~ d d i s t u r b i n g the u n i t s .

2. Des ign c r i t e r i a f o r g r a v i ~y w.11 1 s .2i : i : ;y

t o c r i b w a l l s . Wal I s e c t i o n rc\ i l . t i r ~ q o v e r t u r n i n g i s t a k e n a s a r c c t . ~ r ~ r . l c t l f d imens ion (ti x b ) .

. - 3 . L o w wa 1 I s ( unde r 1 . Sm h i g h ) may I)c' ~tr.ttlc

w i t h a plumb face . Higher- wa l 1s ~ I I o ~ I ~ ~ I be b a t t e r e d as shown.

sz24(b 4 . For h i g h wal i s (4m h i g h and over l r h c . b a t t e r i s i n c r e a s e d o r supp l cn l c r l l a r v

c r i b s a r e added a t t h e b a c k .

concrete base slab .

1

( a ) TYPICAL SECTION ( diagrammatic 1

ng ctoser

( b 1 TYPICAL FORM OF CRIB WALLING - --

I C R I B W A L L . D E T A I L S F I G U R E -26

ASSUMPTIONS : Soil properties : 9: c = 0 , r=19.5krilm3 0' = LO' Wll properties : 6-= f 8. Ww-15.5 k ~ l m 3

--- +' = 36 Wall slope : 0 = - IL' ( 1 in L I

CR~SWAU DESIGN CURVES FIGURE 27

TOE MOIAENT EFFECT ON HEEL

WElGHT OF BACKFILL ABOVE HEEL

SELF WEIGHT OF HEEL

LOADING FRGht TOE iAOMENT

ASSUMED KXJNDATION BEARING PRESSURES

RESULTANT LOADING ON HEEL ( MAY BE FULLY POSKNE )

NOTE : PRESSURE DIAGRAMS NOT TO SCALE - . --

DESIGN 'LOADING ON HEEL SLAB 1 F I G U R E 30

a1 UNSAS!SFACTORY DETAIL b ) UNSATISFACTORY DETAIL

CRITICAL SECTION

FOR SHEAR tN TOE

M;iICHEVEc IS T H E

c ) RECDMbEFJXD DETAlL FOR L; t T

R AOIAL HOOPS

4 j

ef RECOMMENDED DETAIL FOR

LARGE JCINTS (As1 > 0.5%

NOTES

1 . R c f e r t o S e c t i o n s 11.8 C 1 1 . ' ) l o r

d i s c u s s ion, i n c l u d i n a 1 i rn i t . ? t ior>s 4;n s t e e l p e r c e n t a s e .

2 . Fur c l a r i t y , n o t a i l s r r . c I i s ;!,r):rn i r : t h e s e s k e t c h e s . , AJd i i i o n s i s[ct:I f r l r t o e moment I 4 3 i s shown d c t l c d . lio shrinkage, t e m p e r a t u r e o r b i s t r i I::it i o n s t e e l i s shown.

3 . I f - d e s i r e d , a f i l l e t may . be included. ,

EXAMPLE OF CANTILEVER STEEL SHEET PILED WALL DESIGN

Example of Cantilever Steel Sheet Pile Wall Design

Dredge Line

Cantilever Sheet Piles Wall in Granular soils

Earth Pressures

Cantilever Sheet Piles Wall in Granular soils

Dredge Line

Earth Pressures

yDKa

Cantilever Sheet Piles Wall in Granular soils

Resultant I Net pressures

Dredge

' . L y D k p - , $ y(H+D)Ka ' y(H+D)ka y(H+D)kp-yDKa , bp - yDKa

Cross-section TDKP ~(H+D)KP Simplified Method

Max. Bendin

Cross-section Net Pressures Shear c end in^ Deflection Mom

Surcharge 10 kNlm2

Loose fine sand Min. unplanned excavation depth = y = 17.1 6 kNlm2

0.5~1 or lo% of \ dl=30° ,6=00 retained ht. (BS8002) Im

1 -sin 4 K~ = ----- = tan (45 - 4 1 2) = 0.33 Loose sand

Water l+ s in+ = 0.27 Compact sand pressure

1+s in4 - tan t (45 ++/ 2) = 3.0 Loose sand Kp=--_---

I-sln 4 = 3.7 Compact sand

Loose fine sand y= 17.1 6 kNlm2 @=30° ,6=00

Compact fine san y = 18.6 kNlm2. y ,=9.8 kNlm2. y' =10.8 kNlm2. @=35° ,6=00 . 1 C=O

Active Pressures

1

1 - 5( 69

Compact fine sand

Dist fr. Top (m)

Loose fine sand y= 17.16 kNlm2

passive 1 Active Pressures Pressures

O=3O0,6=O0

Dist Active (kNlm2) ". Vertical pressure Lateral pressure TOP

-

Active (kNImZ)

Passive (kNlmZ) 1

Vertical pressure

Vertical 1 Lateral pressure pressure 1

Lateral pressure

1 Surcharge b r 10 kNlm2

Compact fine sand y ,.,=9.8 kNlm2, (D=35°,6=00

n T

Loosefinesand y= 17.16 kNlm2 cD=30°,6=00 I

c ~ e t Diag. pressures

C=O

-. -. - . . . . . -. -. -. -. -. . . - . . . -. . . . . . , -. . . . 25.9

.... 0 ;= -+- -=- , 37.7 20 Location of

- -.I-..WT ,., : zero shear i.e.

-. -. - . . . . . -. -. -. -. -. . . - . . . -. . . . . . , -. . . . Location of

- -.I-..WT ,., i zero shear i.e.

y = 18.6 kNlm2. ,- -. - .+ ,/ max. bending y' 40.8 kNlm2, L:: moment C=O A-'212.4 c !.

Active fkNlm2)

Vertical pressure I Lateral pressure

Passive (kNim2)

Vertical Lateral pressure Net pressure press

0 0 3.3

0 0 25.9

17.16x1=17.2 17.2x3=51.6 -20

17.16x1=17.2 17.2~3.7~63.6 -37.7

18.6x1+17.16x 35.8~3.7432.5 -101.6 1=35.8

Ix17.2+1~18.6 68.2~3.7+9.8~3=2 -212.4 +2x10.8=68.2 81.4

Surcharge - - - - * [ I 10 kNlm2, 1- fi 3.3 Net Pressures , Diag.

I I - \ - - - I

1 13.3x4=13.2 I

1 5.56 1 73.4 Thus, D = 2.44m

212.4 Take moment about C 4

By Trial & Error -Assume

2 1 22.6 x 4 x K = 45.2 4.893 1 221.2 I Depth of penetration

Lat. Forces (kN/m)

6 -53.1D x D x % ~26.55 DZ Dl3 = 1.2 x 3.44 = 4.2m

Total length of SSP = 8.2m

Mom Arm @ C lml

Moment (kNrnlm) depth of D until Z = 0

Surcharge A [ - 1 10 kNlm2 ////

4n1

- .......................................

Net Pressures 1 Diag.

0.44m -k--. Y

0.56m Te--

max. bending moment

I I Lat. Forces (kNirn) I

Thus, obtain Y,

i.e. Ans. Y = 5.9m

I

Surcharge , - r y i 10 kNlm2 //I/

4r i

- - .................................

WT

Max Moment

Net Pressures fi "'"

u moment

Take Mom (max) @ point of kero shear

Repeat previous Table for determining D except to use Y C 5.9 m to obtain Max Moment

M max = 182.4 kNim2

Using Allowable Yield Stress = G =180kNlm2

Sect Modulus SSP required ,

= - M =182.4 x 1000 x 100 = 1413 cm31m, Choose LX 12, k 11208 cm3/m o 180x100

REINFORCED CONCRETE RETAINING WALL

- THEORY AND DESIGN

Types of Retaining Structures

A. Gravity Retaininq Walls

I. Mass Concrete Retaining Wall

2. Crib Wall

3. Gabions Wall 6

4. Reinforced Fill Retaining Walls

Types of Retaining Structures (conk..)

T-shaped L-shaped B. Reinforced Concrete Retaininq Walls

I. RC L- or inverted T-shaped Cantilever Retaining Wall (with or without key)

2. R.C. Counterfort Retaining Wall

3. R.C. Buttressed Retaining Wall

C. Cantilevered Retaininq Walls

1. Contiguous I Secant Bored pile wall or Sheet Pile (conc /steel) Retaining Walls

Types of Retaining Structures (cont ...)

Retaining Wall with Counterforts

Retaining Wall with Buttresses

Common Usage of Retaining Wall - in DID

Fill

Water

Gravity a. Stability by wt of wall

c. can incorporate features on surface

a. need large amt of space

b. support may be required during construction

a. Reasonably good fdn required

b.Large quantities conc, need curing time

c. Generallv H < 3 - 4 m

21 Crib Wall I a.Easy to construct & maintain b.Soil used as structural components, no I need manufactured materials

I c. Used manufactured elements. better

I quality 3 Gabions wall a.As (a). & (b) in uib wall

b. Permit construction on weaker fdn c. Flexible str, tolerate higher differential

settlement than conc wall

4 Reinforced Fill a. As in (a). (b), (c) in crib wall b. Can cope in tighter curve than conc

wall c. As in (b), (c), (d ) for gabions wall1

a. selfdrain fill reqd b. High cost for small quantities

c. Not suitable for ht > 7 m

a. As in (a) & (b) in Crib wall

a. Land take may be more than other gravity wall requirement

b. Reinforced zone required protection c. Stringent requirement for fills d. Patents aspects

e. Cost may be high for small quantities

Advantages and Disadvantages of different Types of Retaining Wall (Cont..)

Reinforced Concrete Retaining Wall

R.C. Cantilever Retaining Wall (L- T-shaped)

R.C. Counterfort or Buttress Retaining Wall

a. Provides stability by strength & stiffness of R. C & wt of Retained fill

b. Suitable for retaining fill, embankmentetc

a. Construction may required large excavation with supports

b. reasonable good fdn required

c. need curing time d. thin wall susceptible to damage by

impact

a.Conventional construction b. can incorporate features on

surface

I a. Reasonably good fdn required

b. Large quantities conc, need curing time

c. Generallv H < 7 m

a. Can be construct to higher than a. Formwork may be costly RC. Ret wall b. Generafyy H < 12 m

b. As in (a) (b) above

Advantages and Disadvantages of different Types of Retaining Wall (Cont..)

Cantilevered Retaining Wall

a. Provides stability by bending strength & stiffness of cantilever

b. Used where space limited & where bearing pressure to be kept low

c. Suitable where it can be supported B be part of adjacent structures

d. Temporary Cutting not required

a. May required substantial penetration into ground for stability if frock or strong bearing layer is not found at shallow depth

b. Cost 8 ground movement are generally much higher than gravity or RC retaining wall

c. Design very sensitive to changes to ground level

d. Impermeable wall may cause a rise in h e local oroundwater level.

I Retaining Structures - Design Philosophy

2 set of calculations

- Set of equilibrium calculations for proportions I geometric of structures to achieve equilibrium under earth pressures and forces

I - Structural design calculations for Reinforced Concrete sections propertiieslsize to resist bending momentsfshear forces

1. Assemble general info - topo, surveys etc.

2. Analyze subsoil conditions Ex. Ground

3. Compute Earth and surcharge pressures

4. Select tentative proportion of wall (for RC wall) Proposed

5. Analyze structural and foundation stability Retaining wall

6. Design structural elements

7. Select drainage backfill

8. Predict settlement and movement of wall

Topo of site - existing Structures, utilities, groundwater, tidal water, etc.

Controlling dimensions e.g. top and base elev. of wall, slope , alignment of wall , flood levels, drains, roads etc

Wall foundation supports - on earth, piles (need batter piles for lateral forces)

Determine bearing capacity of foundation soils.

Determine shear strength of soil, c', t+ ' (long vs. short term)

Investigation of lower strata - possible settlement and failure and piles bearing capacity (if required).

Determination of Soil Properties - Cohesionless Soils - Normally free draining, excess pore pressure dissipate rapidly Thus, effective stress used for both long-term & short-term, C= 0.4 = 4 ' Effect of Wall friction on wall, 6 on - Active pressure 3 normally ignored - Passive pressure 3 6 = 213

- Soil Properties - SPT - JKRI Mackintosh Probe - Shear Box Test

SPT Vs + for cohesionless soils

Type of soil Penetration Angle of Internal friction (degree! Resistance, N Peck (1974) Meyerhof (1956)

Very Loose sand c 4 < 29 < 30

Loose sand 4 - 10 29 - 30 30 - 35

Medium Sand 10 - 30 30 - 36 35 - 40

Dense Sand 30 - 50 36 - 41 40 - 45

V. Dense Sand > 50 > 41 > 45

Determination of Soil Properties - Cohesive Soils

Shear strength change over time due to excess pore pressure dissipation

Considered both long- and short-term - Short term (undrained) - immediately after construction 3 Total stress values - Long-term (drained) - effective stress values (i.e. values resemble cohesive

values)

Soil Properties - Total Stress Values (+ =o, c = c)

Direct shear test 3 Vane Shear (in-situ) Indirect Shear Test

9 Triaxial UU, CU 9 Unconfined Compression Test - undrained cohesive soil under zero

lateral pressure - Effective Stress Values - Triaxial CU with pore pressure meas

Triaxial CD (not common)

- Other soil parameters required - Moisture contents Density

= Soil dassifications

(Reference:

Determination of Soil Properties - Cohesive Soils (cont ....)

If no effective stress parameters are available from drained tests, this tables may be used only for initial studies and would tend to give conservative values (BSC - Piling Handbook)

Verysoft I > 80 1 c20 1 0 1 15

Description

Soft 1 80 / 20-40 / 0 1 15

Plasticity Index (%)

Very stiff 1 15 1 > I 5 0 / 0 1 30

Medium (firm)

Stiff

Undrained cohesion, c,

kN/m2

50

30

Drained Cohesion, c'

(kN/m2)

@ ' (degrees)

50 - 75

100 - 150

0

0

20

25

Determination of Soil Properties - Cohesive Soils (cont ....)

Relationship Between SPT, JKRMackintosh Probe and Unconfined Compression Strength of Cohesive Soil

1 . . 3. compute Earth anh Surcharge pi-essures

- Earth pressure on retaining structures depend on lateral movement of soils

Active pressure : - J Minimum pressure when wall moved outward away from soil

A > 0.003 H , Active forces (min)

Very small wall deflection needed to activation active force ,

* Passive pressure on Retaining Structures - J Maximum pressure when wall moved toward the soil

At-rest earth pressure on Retaining Structures

A t* . A > 0.05 H , Passive Forces (min)

J For very rigid I small wall deflection (eg. propped anchored wall)

KO = 1 - sin I$ ' - Jaky's

H

Normally KO 1 0.5

Very large wall deflection needed to activation passive force

Where K,, = Coefficient of lateral pressure at rest

Rankin's Theory For Coefficient of Lateral Pressures "

COS p - . J c 0 s Z p - C O S 2 4 Ka = cos p

COS + 4-i

Kp = cos p c o s p - J z j 7 G 2 4 c o s p + 4-4

Where

Ka = Coefficient o f active pressure I@ = Coefficient o f passive pressure

For Level backfill D

L$"i: Compute Earth and &rcharge,pressuPes ( ~ 6 ~ ; ~ ) f t

Active and Passive Lateral Pressures

Where Pa = Active Lateral Pressure (kWm2) on wall P, = Passive lateral Pressure (kN/mZ) on wall

Ka = Coefficient of active pressure Kp = Coefficient of passive pressure

Note:

Rankine's underestimate Passive BS8002 - ignore top pressure, however, frequently used as 0.5m of soil in passive it err on the conservative side for resistance force stability analysis.

Coulomb's Theory For Coefficient of Lateral Pressures

....................

- a R - -- - - -- --- -- -- cos2 0

sin($+&) sin(@-@) " = cod E +/-I cod C O S ~

where @ = angle of internal friction of soil 6 = angle of wall friction D = angle of the backfill with respect to horizontal

1. Overestimate Passive pressure , thus, limit to F <+'I3 (HK Ret. Wall guidelines)

2. Mobilised angle of wall friction 6, need to be assumed

Surcharge Loads

Permanent or temporary

Uniform distributed eg stacked materials, vehicles etc.

Concentrated Loads

9 Line loads eg loads from strip footing

9 Point Load eg. squarelcircular footing

Area loads eg, large area footing in relation to ht of wall

Seismic Loads

Nominal Uniform Surcharqe Load

BS 8002 (Earth Retaining Structures): min 10 kNlm2

HK Ret Wall guidelines: - J Buildings with shallow foundation = 10 kNlm2

4 Highway structures HA Loadings = 10 kNlm2

HB structures = 20 kNlm2

4 Footpaths, cycle trackslptay areas1 isolated roads = 5 kNlm2

Line Load Q, on Wall

(modified Boussinesq)

I m H C p FEZ- H

I \ 'or m 10

Point Load on Wall, Qp

(modified Boussinesq)

For m. 0

Water Pressure Loads

Many walls failed due to water behind wall

Importance to provide adequate drainage behind wall J prevent softening & loss of strength of cohesive backfill J prevent ingress of water into fissures formed during hot dry spells.

Design based on worst credible groundwater conditions during extreme events eg. flooding, severe rainfall, bursting of water mains, rapid drawdown

P, act on both passive and active side of wall

Groundwater Table assumed > 113 H

y ' = y ,- y , + Lateral pressure below / ..

WT calculated using y '

Water pressure on Wall- Drainage

Effects of providing drainage on phreatic line

Backfill for Wall

* Granular fill , preferably e.g well graded small rockfills, gravels, sands,

- Cohesive - used only if granular fill not possible leconomic reason

- Designed for in term of water pressure behind wall and construction

- Liquid Limit < 45 % and P.l < 25 %

. Batter = (1 : 50)

H If no in-situ info, used Hw = 213 x H

Base frictional angle = 213 x Soil int'l friction angle (drained condition) If undrained condition, use .r = C,

. +

B= (0.4 - 0.67 H)

Tw= (0.085 - 0.15H, min 0.25 - 0.3m ) -

5 Stability of Retaininqlqravity Wall - Mode of Failures

General Principle on Stability of Wall

FOS = Moments or Forces Aidincl Stability Moment or forces causing instability

5 Stability of Retaininq I qravitv Wall Mode of Failures

3. Base soil Bearing Failure

------..-......-.

5 Stabilitv of Retaining I qravitv Wall -

= 2.0

FOS

Rotation Failure

Sum bf Moments resistina overturning Sum of Moments causing overturning

J Passive Wall with deep keys should be avoided due to construction problem and uncertainty in resisting rotation

5 Stabilitv of Retainincllnravit~ Wall

Sliding Failure

FOS=(Wt+Pv)tan&, - +chB+0.5Pp -

Ph

Wt = Wt of Wall

Pv ) = Vertical component of earth pressure force

6, = angle of base friction

C , = adhesion at base of wall

B = Base width

Pp = passive pressure force

P, = horizontal component of earth pressure forces

FOS Sliding (min) = 1.5 (normal)

= 1.2 (Adverse)

5 Stability of Retain in~l~ravi ty Wall

Sliding Failure

S= Resisting lateral force due to base frictionladhesion

= Vertical force x Coefficient of friction at Base

Coefficient of friction at Base (cohesionless soil)

= tan 4 + for rough base (eg conc on soil)

Ref : Foundation Design- WC Teng

= 0.55 + Coarse grain soils (without silt)

= 0.45 + Coarse grain soils (with silt)

= 0.35 + silt

= 0.60 Sound rock (with rough surface)

Coefficient of friction at Base (cohesive soil)

= Cohesive strength, c (4 = 0)

Base on Piles

= No frictionladhesion on base and all lateral & vertical loads supported by piles

- -

5 Stability of Retaininnlnravitv Wall

I Shear Key

Used of Shear Key on base slab)

Increase lateral resistance ( but benefit generally small unless embedded in rock)

Best located directly under stem or inner half of base

Disavantages -Excavation for keys disturbed soils esp. in soft & purely granullar soils

5 Stability of Retaininnlsravitv Wall -

Base Soil Bearing Failure

Estimate the ultimate bearing capacity from theoretical analysis of the foundation

For foundation on saturated clayey soils of low permeability, short term is more critical, thus used undrained strength ( i.e. g' =O condition)

Submerged y should be used when foundation under water table

Base soil Bearing Failure FOS (min) = 2 - 3

Foundation Bearing Capacity (shallow Foundation i.e. D < B)

Refer to Geotechnical Guidelines For DID Works Pg 37 to 44

Qult=cNcscdcicbcgc +p,Nqsqd,iqbqg, +%yNysy dy i y b y g y

Effect of cohesion effect of surcharge effect of y

Brinch Hansen 's General Eqn

y = Density of soil below foundation level

B = Width of foundation C

C =undrained cohesion of soils t--------,

Po = effective overburden pressure of soil at foundation level B

N, , N,, N y = bearing capacity factors

d, , d,, d, = depth factors

s, , s,, s, = shape factors

i, , i,, iy = Load inclination factors

b, ,b,, b, = base inclination factors g, , g,, gy = ground surface inclination factors

Foundation Bearing Capacity (shallow Foundation i.e. D < B)

Qult=cNcscdcicbcgc +p,Nqsqdqiqbqgq +XyN,s,d, i, b,g,

Foundation Bearing Capacity (shallow Foundation i.e. D < B)

I Qult=cNcscdcicb,gc +p,Nqsqdqiqbqgq +KyN,s,d, i, b,g,

GROUND SLOPE FACTOW INCLIP~ATION FACTORS

9' - 9*-- I, - iq --!z% Na fan$

Ng tan@'

e of Design of RC Cantilever Retaining Wall (T- shaped)

- Dimensions of Wall

I I

0.5m or 10% of retained ht. of soil ignore in passive resistance due to unp(anod excavation

b) base mat1 =20° j$~n~~ty;bulk) y = 18kNlm3

aturated Densuity = 20kN/m3 ubmerged Density y' = 11 -00 kN/rn3 IF (base material) (Cb ) = 5 kNlmZ

II?Annl I bearina oressure allowable=150kNlm2 1

1 l4o0 1: ' I MATERIAL PROPERTIES I fcu =zNlmrn2 ym =1.5 (conc) fy = s N l m m 2 ym =1.15 (steel) Cover tension steel =50mm I

I""_' . 1 Concrete density =24kNlm3 I

Compute Lateral pressures

1 0.3 x 11 x 1 . 4 4 6 2

Earth

Compute Lateral prdssures

I Compute Lateral prqssures

Compute Lateral prqssures

0.3 x 11 x 1 .4462 10x l.4=14

Earth Surcharge Water

Compute Lateral Forces

Compute Lateral Forces

--

Compute Lateral Forces

Compute Vertical Force* Ws=lOx(Z-.35-.4)=12.5

Ka x surcharge=

Compute Vertical Forces

Mq=173.4 Ms=17.2

Compute Vertical Forces LFl rl

Compute Vertical Forces - m

{External Stabilii t

iOveruning Moment j t I I I

I Overuning Moment L I

- !!~!E!L-- _- 9.8 - - 0 4 7 _-A606 - j.4 3.4484 -L3.72 P p 3.3 0.16 0.528

Sum 45.85 55.876 78.966 68.81 i

Water 9,8 0.117 - 4.606 1 l 6.4484 13.72- Pp 3.3 0.16 0.528

Sum 45.85 55.876 78.966 68.81 H.

Design for Heel

Surcharge = 10 x 1.25 = 12.5

Soil = W3=18x1.25~2 + 20x(1.4 -0.35)x1.25=71.25

Conc Wt. = 0.35 x 24 x 1.25=20.5

=(I .25 1 ~ ) X I 18.6 =74.1

Design for Toe

Conc Wt. = 0.35 x 24 x 0.4=

3.18 118.6 y

Design for Stem

DElAlLIRG OF C A U T i l t l E R WALL RtlRiORCEAIENl . I FIGURE 32

thtes:

Backfill with free draining materials, well compacted layers

Stability analysis as for gravity wall

Battered as shown

List of References

BS8002: Code of Practices : Earth Retaining Structures

BSC Piling Handbook

Retaining Walls by DID Design Office

Geotechnical guidelines for DID Works - Design office JPT

Foundation Design - WC Teng

Steel Sheet Piling Design manual - United States Steel

Hong Kong Geotechnical Guidelines

An Introduction to Geotechnical Engineering - Robert D. Holtz & William D. Kovacs 8

Earth Retention Systems handbook -Alan Macnab

Soil Mechanics - GN smith