2 Stability Analysis

Push In

Basal Heave

Overall Shear Failure

Overall shear failure modes：

Stability Analysis

Overall Shear Failure Mode: PUSH-IN

failure surface

{strut

wall

settlement

wall bottom "kick out"

It is mainly due to the unbalance between passive earth

pressure (inside) and active earth pressure (outside)

Strut settlement

failure surface

bottom heave

Overall Shear Failure Mode: BASAL HEAVE

It is mainly due to

bearing capacity of the

soil beneath the

excavation bottom

pp

aL

pL

sM

pP

strut

ap

aP

ANALYSIS OF PUSH-IN

The factor of safety against push-in:

aa

spp

d

rp

LP

MLP

M

MF

+==

Distribution of earth pressures for cohesive soil：

(4.16)

(4.17)

(4.18)

(4.19)

acava cKK 2-= ss

)1(c

cKK

w

aac+=

pcpvp cKK 2+= ss

)1(c

cKK w

ppc+=

(5.6)

Cast-in-place pile

API

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

a

vu /s s

FIGURE 4.12 Relation between adhesion and undrained shear

strength of clay

uwsc a=

Factor of safety

（Diaphragm walls）

（Steel sheet piles）

=1.2~1.3

Cohesionless soil（sandy, gravel）

Distribution of water pressures ：

Gross water pressure distribution ？

Net water pressure distribution？

uw sc 67.0=

uw sc 5.0=

pF

(a) (b)

fu fu

Strut

Strut

id

jd

FIGURE 5.7 Distribution of water pressure due to seepage (a)

distribution of water pressure (b) net water pressure

(note: = water pressure due to seepage)f

u

Cohesionless soil（sandy, gravel）

Distribution of earth pressures：Caquot-Kerisel's or Coulomb's active earth pressure should be adopted

for the active earth pressure.

Caquot-Kerisel's passive earth pressure should be adopted for the

passive earth pressure. When , Coulomb's passive earth

pressure coefficient is quite close.

Caquot-Kerisel's earth pressure theory's , and have

some relationship. Section 4.5.3 has summarized some findings on

values of .

Clough's research：concluded that between concrete (cast in steel

mold) and sand, is about .

2/fd <

aK pK d

d

d f0.8

0.0

0.2

0.4

0.6

0.8

1.0

0.8 1.0 1.2 1.4 1.6 1.8

pF

eH(%

)/

eH

FIGURE 5.8 Factors of safety against push-in for excavations in

sand (all cases are safe cases; is assumed)

hm

d

hmd

hmd

fd =

Conclusion：

Assumption that seems to be reasonable.

For conservative reason, we usually assume

=0.5

=1.2~1.3

=d

pF

d f

f

(a)

Strut

(b)

anL

pnL

pnP

anP

sM

FIGURE 5 . 9 Analysis of- push in by the net pressure method ( a ) distribution of net earth pressure

( b ) force equilibrium of the retaining wall as a free body

The analyses of the basal heave failure are only applicable to clayey

soils.

Like Terzaghi, Bjerrum and Eide,

Tschebotarioff, Terzaghi and Peck,

Clough and O'Rourke, etc.

But the most commonly applied of which are Terzaghi's method,

Bjerrum and Eide, and the slip circle method.

ANALYSIS OF BASAL HEAVE

(1) Bearing capacity method (modified Terzaghi’s method)

(a) (b)

(c) (d)

d

a b c

a b c a b c

a b c

d

d d

2/1

BB =2/

1BB =

1BB 1B

1B1B

o45

eH

o45

FIGURE 5.10 Analysis of push-in by bearing capacity method

(a) a wide trial failure surface

(b) a second wide trial failure surface

(c) a third wide trial failure surface

(d) both sides of the excavation produce failure surfaces

1B

1B

1B

FIGURE 5.11 Excavation profile of the assumed excavation case

X

2.5m

eH

62.19=satg 3

m/kN

Bearing capacity method

Negative bearing capacity method

Slip circle method (side strength neglected)

Slip circle method (side strength considered)

0 1 2 3 40

1

2

3

eHX

Fb

)/25(2

mKNSu=

FIGURE 5.12 Relations between failure circle sizes and factors of safety against basal heave obtained by the bearing capacity method, negative bearing capacity

method, and the slip circle method

0 1 2 3 40

1

2

3

eHX

bF





)3.0/( =vuS s

FIGURE 5 . 13 Relations between failure circle sizes and factors of safety

against basal heave obtained by the bearing capacity method ,

negative bearing capacity method , and the slip circle method

Terzaghi's method

Stiff soil

B

a b

c

d

1us

2us

2/B 2/B

2/B

sqsq

o45

eH

D

FIGURE 5.14 Analysis of basal heave using Terzaghi's method

2/)( BDa

When , the formation of a failure surface is not

restrained by the stiff soil.

Vertical plane bc can offer shear resistance and the

factor of safety against basal heave will be：

(5.7)

(5.8)

(5.9)

2/BD

2)()1)(( 1

BqHBqHW sese

+=×+= gg

2)7.5()1(7.5 212

BsBsQ uuu

=×=

euHs

1

euse

u

eu

ub

HsBqH

Bs

HsW

QF

1

2

1 2/)(

2/7.5

-+=

-=

g

D

D

B

D

1us

2us

sqsq

DeH

2/)( BDb <

Stiff soil


2/)( BDb <

When , the failure surface will be restrained by the stiff soil.

(5.10)

Clough suggested that, Terzaghi's factor of safety should be

greater than or equal to 1.5.

2/BD <

)(b

F

euse

u

eu

ub

HsDqH

Ds

HsW

QF

1

2

1 )(

7.5

-+=

-=

g

B 1B

(a)

Bd

a b c

(b)

FIGURE 5.15 Relation between the embedded part of the retaining wall and the failure surface

(a) large penetration depth (b) small penetration depth

d

a b

90 °

90 °

eH

e

eH

(2) Negative bearing capacity method (modified Bjerrem and Eide’s method)

1B1B

B

Assumed failure surface

(a) (b)

(c)

sqsq sqsq

eH

eH

12 B

12 B

sq

eH

sq

FIGURE 5.16 Analysis of basal heave by negative bearing capacity method (a) a wide failure

surface (b) another wide failure surface (c) Failure surface covers the whole

excavation bottom

12B

12B

FIGURE 5.11 Excavation profile of the assumed excavation case

X

2.5m

eH

62.19=satg 3

m/kN





0 1 2 3 40

1

2

3

eHX

F b


method, and the slip circle method )/25(

2

mKNSu=

0 1 2 3 40

1

2

3

eHX

bF





)3.0/( =vuS s


against basal heave obtained by the bearing capacity method , negative bearing capacity method , and the slip circle method

sq

eH

sq

FIGURE 5.16c

Bjerrum and Eide's method

(5.12) se

uc

bqH

sNF

+×

×=

g

0 1 2 3 4 54

5

6

7

8

9

1=BL

23

BHe

cN

FIGURE 5.17 Skempton's bearing capacity factor

(rectangular) (square)= (5.11) cNcN )16.084.0(

L

B+

Modified Bjerrum and Eide's method：

(5.13)

(5.14)

e

sdscu

bH

ffNsF

g

,1=

L

Bf s 2.01 +=

D 10

9

8

7

6

5.53

2.62.42.22.01.81.61.41.2

1.00.80.60.40.25.53

5

4

3

2

1

0

0.2

0.3

0.40.5

Nc,s

12 uu ss

12 uu ss

BD /

BD /

Nc,s

112<

uu ss 112>

uu ss

undrained shear strength profile

eH

u1s

u2s

B

1

2

(a) for failure circles passing two soil layersN c,s

If / exceeds the values in the figure, the failure circle

will be tangent to the top of the lower soil layer.

Nc,s

5

10

20

30

40

50

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

3.02.5

2.01.45

1.251.2

BD

Nc,s

12 uu ss

(b) for failure circles tangent to the top of the lower soil layer

DM7.2 suggested that Bjerrum and Eide's factor of safety

should be greater than or equal to 1.5.

FIGURE 5.18 Extended Bjerrum and Eide's method

(a) for failure circles passing two soil layers

(b) for failure circles tangent to the top of the lower soil layer

(c) width modification factorNc,s

df

df

(c)

0 1 2 3 4 5 61.0

1.1

1.2

1.3

1.4

1.5

BH e /

Nc,s

bF

(3) Slip circle method

O

W

r

us

Lowest level of struts

A

B

FIGURE 5.19 Location of the center of a failure circle for the slip circle method

(5.15)

X

O

ab

d f

e c

(a)

W

OsM

(b)


N

N

N N

N

N

N

us

us

X

s

g

s

d

a

FIGURE 5.20 Analysis of basal heave by the slip circle method

(a) the failure surface (b) balance of the a free body

2

)(2

0

XW

MdXsX

M

MF

su

d

r

b

×

+

==

+ap





0 1 2 3 40

1

2

3

eHX

bF



2

mKNSu=

FIGURE 5.13 Relations between failure circle sizes and factors of safety against basal heave obtained by the bearing capacity method,

negative bearing capacity method, and the slip circle method

)3.0/( =vuS s

0 1 2 3 40

1

2

3

eHX

bF





Lowest level

of struts

FIGURE 5.21 Factor of safety increasing due to the failure circle exceeding

the excavation width


u1s

u2s

u2u1 SS >

FIGURE 5.22 Analysis of basal heave in layered soft soils





0 1 2 3 40

1

2

3

eHX

bF



2

mKNSu=

0 1 2 3 40

1

2

3

eHX

bF





)3.0/( =vuS s


against basal heave obtained by the bearing capacity method , negative bearing capacity method , and the slip circle method

(5) Applicability to sandy soils

B

a b

c

d

1us

2us

2/B2/B

2/B

sqsq

o45

eH

D

Stiff soil

2/)( BDa

D

D

B

DStiff soil

1us

2us

sqsq

DeH


2/)( BDb <

X

O

ab

d f

e c

(a)

W

OsM

(b)


N

N

N N

N

N

N

us

us

X

s

g

s

d

a

FIGURE 5.20 Analysis of basal heave by the slip circle method

(a) the failure surface (b) balance of the a free body

北投自強路 excavation failure case

5.5.3 Case Study of Overall Shear Failure

The excavation case was located in Taipei. The width of the

excavation was 17.6m； the length was 100.1m ；the depth was

13.45m. The excavation adopted a 70cm thick , 34, deep

diaphragm wall as the retaining wall. There four levels of struts

and the excavation was carried out in 5 stages.

力霸百老匯excavation failure

力霸百老匯 excavation failure case

SM

OL-ML

SP-SM

CL

¡E

GL-4.5 m

GL-8.7 m

GL-10.7 m

GL-13.45 m

GL-2.8 m

GL-10.15 m

GL-24.0 m

14.7 2m/kN

FIGURE 5.23 Stability analysis of an excavation case history

(a) excavation and geological profiles

o18=uf

2/7.16 mkNcu

=

3/8.18 mkNt

=g

0=c

3/7.19 mkNt

=g

o10=uf

2/98.0 mkNcu

=

3/6.15 mkNt

=g

o33=f0=c

3/3.20 mkNt

=g

o32=f

and

will be 1.5

will be 2.3

were the total stress strength parameters of the clay soils,

obtained from the triaxial CU test

adopt by the original designer

We assume the soil below the lowest level of struts (GL-10.15 m)

to be a clayey layer, the adhesion between the retraining wall and

the soil

and the normalized undrained shear strength

(4.16)

(4.18)

pF

bF

3/2 uw sc =

22.0/ =vus s

acava cKK 2-= ss

pcpvp cKK 2+= ss

ucuf

At the depth of GL-10.15 m

2/5.18545.17.192.46.155.43.20 mkNv

=×+×+×=s

2/1.7281.9)8.215.10( mkNu =×-=

2/3.113 mkNuvv

=-= ss

2/9.243.11322.022.0 mkNs vu

=×== s

2

, /2.1213

21)9.24(25.185)1(2 mkN

s

cKsK

u

wauavah

=+-=+-= ss


Before excavation─

after excavation was started, on the passive side, but

value stayed unchanged.

Thus,

2/0.24875.28.1855.07.195.185 mkNv

=×+×+=s

2/5.10481.9)8.245.13( mkNu =×-=

2/5.143 mkNuvv

=-= ss

2/6.315.14322.022.0 mkNs vu

=×== s

0=vs us

2

, /5.813

21)6.31(20)1(2 mkN

s

cKsK

u

wpupvph

=++=++= ss


The active side─2

/3.44655.108.180.248 mkNv=×+=s

2/0.20881.9)8.224( mkNu =×-=

2/3.238 mkNuvv

=-= ss

2/4.523.23822.022.0 mkNs vu

=×== s

2

, /0.3113

21)4.52(23.446)1(2 mkN

s

cKsK

u

wauavah

=+-=+-=ss


The passive side─

After excavation was start stayed constant,us2

/3.198)45.130.24(8.18 mkNv=-×=s

2

, /6.3333

21)4.52(23.198)1(2 mkN

s

cKsK

u

wpupvph

=++=++= ss

The factor of safety against push-in as

(b)

81.5

121.2

311.0333.62

mkN

2mkN

2mkN

2mkN

GL-10.15 m

GL-13.45 m

GL-24.0 m


(b) distribution of earth pressure for the push-in analysis

89.03/285.135.085.13)2.1210.311(2/85.1385.132.121

)3.33/255.10(5.055.10)5.816.333()3.32/55.10(55.105.81=

××××-+××

+××××-++××=pF

Compute the factor of safety against basal heave

according to Slip circle method ：Similarly, assuming the soil below the lowest level of

struts is clay, the average value of the undrained shear

strengths (the active side) of the soil between GL-10.15 m

and GL-24.0 m would be

The average value of the undrained shear strengths of

the soil between GL-13.45 m and GL-24.0 m would be

2

, /7.382

4.529.24mkNs au

=+

=

2

, /0.422

4.526.31mkNs pu

=+

=

The radius of the failure circular arc would be

The central angle of the failure circular arc on the active side

would be

The central angle of the failure circular arc on the passive

side would be

The factor of safety against circular arc failure would be

m85.1315.1024 =-

57.12==

p

33.1)85.13

3.3(cos

1 == -

94.023786

22370

2/85.1385.13

85.137.3857.185.1385.130.4233.185.13

)45.13(

==+×

=-GLv

bFs

× × × × ×

××

Computing the factor of safety against basal heave

following Terzaghi's method：

The width of the excavation , was larger than the

penetration depth (10.55 m). Assumed failure surface will pass below the

bottom of the retaining wall.

Bd

a b c

(b)

90°

eH

FIGURE 5.15 Relation between the embedded part of the retaining wall and the failure surface

(b) small penetration depth

mB 6.17= 2/B

The average undrained shear strength of soil within the range of

the failure circle can be calculated as follows：

of soil deep below the ground surface--mB 9.252/45.13 =+

2/1.482)45.1390.25(8.180.248 mkNv

=-+=s ×

2/5.25581.9)8.290.25(1.482 mkNuvv

=--=-= ss ×

2/2.565.25522.022.0 mkNs vu

=== s ×

The average undrained shear strength within the range of the

failure circle would be

As computed earlier, the total stress outside the excavation zone

at the depth equaling the excavation surface would be

2/9.432/)2.566.31( mkNsu

=+=

2/0.248 mkNv

=s

To simplify the analysis and be conservative, we assume the

soil above the excavation surface is clay and has soil shear

strength expressed as . The average undrained shear

strength of the soil outside the excavation zone and the excavation

surface would be

The factor of safety according to Terzaghi's method would be

22.0/ =vus s

2)45.13(/8.15

2

6.31

2

22.0mkNs

GLv

u==

=

-s

08.12874

3118

45.138.152/6.170.248

2/6.179.437.5

1

==-

=-

=eu

u

bHsW

QF

× ×

× ×

The factor of safety following Bjerrum and Eide's method would be

10.10.248

2.69.43==

+=

se

cub

qH

NsF

g

×

Undrained shear strength and the depth：

)(2mkN

Active side ),( uuc f

0.22/ =vus s

Passive side ),(uuc f

(c)


(c) the undrained shear strength used in the analysis

25

2

0

15

10

5

00 50 100 150 200

dept

h(m

)

us

【Example 5.1】Assume a 9.0 m deep excavation in a sandy

ground and the lowest level of struts is 2.5m above the

excavation surface. The level of groundwater outside the

excavation zone is ground surface high while that within the

excavation zone is as high as the excavation surface. The

unit weight of saturated sandy soils , the

effective cohesion and the effective angle of friction

. Because of the difference between the levels of

groundwater , seepage will occur. Assume that the friction

angles ( ) between the retaining wall and soil on both the

active and passive sides are and the factor of safety

against push-in, . Compute the required penetration

depth( ).

20=satg 3

m/kN

o30=f

0=c

d

f5.05.1=

pF

pH

jd

id

x

x

a

b

ccu

wjep dHH g)( -+

(a)

bu

(b)

FIGURE 4.22 Simplified analysis method for seepage

(a) distribution of water pressure (b) net water pressure

z

z

wip dH g)( -

eH

pH

1.determine the coefficient of the earth presure

Compute both the active and passive earth pressures following

Caquot-Kerisel's earth pressure theory. When , the

coefficients of active and passive earth pressure can be found from

Figure 4.9 and Figure 4.10 to be 0.3 and 4.6 separately. Thus, the

coefficients of the horizontal active and passive earth pressure

would be

【Solution】

f=d 5.0

29.05.0cos3.0cos3.0,=== fd

haK

4.45.0cos6.4cos6.4,=== fd

hpK

2. Compute the effective active active earth pressure on the wall

According to Eq. 4.51the porewater pressure at x away from upstream

water level would be

At the lowest level of strut (z=6.5m, x=6.5m) --

havha K ,,ss = 2

kN/m1305.620 ==vs ×

5.4

77.63

92

81.95.62

2

)(2

+=

+=

--+

-=

p

p

p

p

jiep

wip

H

H

H

H

ddHH

dHxu

g × × ×

5.4

49.187.3729.0)

5.4

77.63130()( ,,

+-=

+-=-=

p

p

P

p

hahaH

H

H

HKuss ×

At the bottom of the retaining wall( , )─pHz +=9 pHx +=9

)5.4

60.2584.28.52.52(

29.0)5.4

29.8881.920180(

2

2

,

+

+-+=

×+

+-+=

p

pp

p

p

pp

pha

H

HHH

H

HHHs

ppv HH 20180)9(20 +=+=s ×

5.4

29.8881.9

92

81.9)9(2

2

)(22

+

+=

+

+=

--+

-=

p

pp

p

pp

jiep

wip

H

HH

H

HH

ddHH

dHxu

g × × ×

3. Compute the lateral effective passive earth pressure on the wall

At the bottom of the retaining wall（）─pHz =

ppv HH 2020 =×=s

5.4

29.8881.92

+

+=

p

pp

H

HHu

5.4

48.38816.4388

4.4)5.4

29.8881.920(

2

2

,

+

+-=

×+

+-=

p

pp

p

p

pp

php

H

HHH

H

HHHs

4. Compute the maximum net water pressure (at the

excavation surface)

According to Eq. 4.53, the maximum net water pressure

would be

5.4

29.88

92

81.992

2

))((2

+=

+

×××

=--+

--+=

p

p

p

p

jiep

wipjie

bH

H

H

H

ddHH

dHddHu

g

5. The effective earth pressure on both sides of the wall and the

distribution of the net water pressure are as shown in Figure

5.24

Lowest level

of struts

FIGURE 5.24 Distribution of lateral earth pressure

o

b

2.5

9

pH

bu9

5.6 bu

netu

hp ,s

ha,s

5.4

48.38816.4388

2

+

+-

p

pp

pH

HHH

5.4

60.2584.28.52.52

2

+

+-+

p

pp

pH

HHH

5.4

49.187.37

+-

p

p

H

H

6. Compute the driving moment ( ) and the resistant moment

( ) for the free body below the lowest level of strutsrM

dM

bppp

p

pp

p

bbppb

p

p

pp

p

p

p

p

ahad

uHHHH

HHH

uuHHu

H

H

HHH

H

H

H

LPM

]84.225.117.0[)5.2)(5.4

62.1195.093.168.23(

32

5.22

9

5.2

2

5.2

9

5.6)

35.2(

2

32

)5.2(2)

5.4

11.784.28.55.14(

2

)5.2()

5.4

49.187.37(

22

2

22

222

,

+++++

+-+=

×

××+×++×+

×

+×

+

+-++

+×

+-=

=

bppp

p

pp

p

bbppb

p

p

pp

p

p

p

p

ahad

uHHHH

HHH

uuHHu

H

H

HHH

H

H

H

LPM

]84.225.117.0[)5.2)(5.4

62.1195.093.168.23(

32

5.22

9

5.2

2

5.2

9

5.6)

35.2(

2

32

)5.2(2)

5.4

11.784.28.55.14(

2

)5.2()

5.4

49.187.37(

22

2

22

222

,

+++++

+-+=

×

××+×++×+

×

+×

+

+-++

+×

+-=

=

)3

25.2)(

5.4

24.19458.2144(

)3

25.2(

2)

5.4

48.38816.4388(

23

2

2

,

p

p

pp

p

pp

p

pp

p

phpr

H

H

HHH

HH

H

HHH

LPM

++

+-=

+××

+

+-=

=

7. determine the penetration depth

Then we have m

pH

5.1==

d

rp

M

MF

25.7=pH

【Example 5.2】An excavation in clay goes 9.0m in to the

ground . The groundwater outside the

excavation zone is at the ground surface level while

that within the excavation zone is at the level of the

excavation surface. . The

undrained shear strength .

Suppose the excavation width B =10m and the

excavation length L =30m. Compute the factor of

safety against basal heave according to Terzaghi's

method and Bjerrum and Eide's method,

respectively.

=17.0

=45

9.0m)( =e

H

satg 3

m/kN

2m/kNus

【Solution】

In this example, the surcharge

According to Terzahi's method,

0=sq

7.2

107.0

4517

457.5

9

1

7.0

7.51=

×-

×=

-

××=

B

s

s

HF

u

u

e

b

g

According to Bjerrum and Eide's method,

According to Figure 5.17, we have

0.310

30==

B

L

9.010

9==

B

He

1.7=cN

09.2917

1.745=

×

×==

et

cub

H

NsF

g

Upheaval

Impermeable layer

Permeable layerw

HWater pressure

1h

2h

1tg

2tg

The factor of safety against upheaval should be larger than or equal to 1.2

FIGURE 5.31 Analysis of upheaval

(5.17)

ww

iiti

upH

h

Fg

g

×

×

=

upF

(CL)

(ML)

(SM)

GL-0.0m

GL-8.0m

GL-25.0m

GL-32.5m

GL-36.0m

GL-40.5m

Grouting

Gravel

2.9m -Stage 1

5.9m -Stage 2

8.8m -Stage 311.9m -Stage 4

14.4m -Stage 5

17.5m -Stage 6

20.0m -Stage 722.5m -Stage 825.1m -Stage 9

27.55m -Stage 10

30.6m -Stage 11

(SF)

GL-58.5m GL-58.0m

GL-63.0m

33.7m -Stage 12

36.75m -Stage 13

40.5m -Stage 14

GL-10.0m(CL)

(SP-SM)GL-15.0m

(CL)

(SM)GL-43.0m

Case Study

ww

iiti

upH

h

Fg

g

×

×

=

ww

i

iti

upH

h

Fg

g

=

Upheaval failure:

1H

2H

z

Upward water flow

u

0

Saturated soil

A

C

B

2H

hzh

FIGURE 5.32 Total stresses, effective stresses, and change of porewater pressure in

sandy soils acted on by an upward water flow

wH g1 wH g

1

satw HH gg21

+whHH g)( 21

++whH gg -

2

s s

Sand Boiling --- Factor of safety and failure mechanism

The critical hydraulic gradient is then

Besides, according to the phase relationship of soil, the

submerged unit weight is

(5.24)

(5.25)

-w

s

e

Ggg |

+

=1

1

e

Gi

s

cr+

-=

1

1

)max(exit

crs

i

iF = (5.26)

(5.26)

A

wHD

pH

FIGURE 5.33 Seepage in soil below sheetpiles

Impermeable layer

Wall

Sand boiling zone

)max(exit

cr

si

iF =

Terzaghi's method：

=(the volume of the soil column)

The factor of safety is

(5.27)

(5.28)

(5.29)

wavgpwaviHi gg 2

2

1)( =×

ggg =-= 22

2

1)(

2

1pwsatp HHW

wavg

siU

WF

g

g =

=

U

Provided the computed factor of safety is too small, we can

consider placing filters at the exits of seepage. Assuming the

weight of filters is Q, the factor of safety will be

(5.30)

In general, the required for the above equation should

be greater than of equal to 1.5sF

U

QWFs

+=

Marsland's method：

DM7.1 suggested that the reasonable factor of safety against piping

in an excavation be around 1.5 to 2.0.

Retaining wall

2.0

1.5

1.0

0.5

00.5 1.0 1.5 2.0

2.0

1.5

2.0

1.5

1.0

1.0sF

Loose sandDense sand

wH

PH

B

(a)

)2/(w

HB

wp

HH

/

FIGURE 5.34 Relations between wall penetration depths and factors of safety against sand boiling

(a) dense and loose sands with the impermeable layer located at the infinite depth

FIGURE 5.34 Relations between wall penetration depths and factors of safety against sand boiling

(b) dense sand with the impermeable layer located at a finite depth

2.0

1.5

1.0

0.5

00.5 1.0 1.5 2.0

2.0

1.5

1.01.0

2.0

1.5

wH

B

D

Impermeable layer

(b)

sF

PH

)2/( wHB

2=wHD

1=wHD

wp

HH

/

One dimension seepage method：

id

FIGURE 5.35 Analysis of sand boiling

wH

Sandy soil

a

bc

d

pH

eH

jd

D

The total head at the upstream elevation (point a) will be

The difference of the total heads between upstream and

downstream levels will be

If we assume the datum is at the downstream level, the total

head at the elevation of downstream (point d) will be

(5.31)

(5.32)

(5.33)

000,=+=+=

pedt hhh

jiejiepeat ddHddHhhh -+=+-+=+= 0,

jiedtatw ddHhhH -+=-=,,

D

Suppose the seepage is one dimensional and the hydraulic

gradients for each depth along the flow path abcd are equal. the

hydraulic gradient will be

The factor of safety against boiling will be

The required for the above equation should be greater than

or equal to 1.5.

jipe

w

ipije

wavg

ddHH

H

dHddH

Hi

--+=

-++-=

2)(2

DD

ww

jipe

avg

cs

H

ddHH

i

iF

Dg

g )2( --+==

sF

Case Study

FIGURE 5.36 Excavation of Siemen Station of Taipei Rapid Transit System

(a) excavation and geological profiles

SM

CL

SM

CL

SM

EL.+72.5m

EL.+69.4m

EL.+63.4m

EL.+59.6m

EL.+56.4m

Sungshan III formation

Sungshan II formation

. . .. . . .. . . .. . . . . ... .. . .. .... .. .... .

EL.+81.8m

EL.+87.2m

EL.+95.0m

EL.+104.5m

Sungshan IV formation

Sungshan VI formation

Groundwater level EL.+98.0mEL.+98.0m

CL

SM

CL

Chingmei formation

EL.+88.0m

EL.+80.0m

Sand boiling

23.25m

(a)

Sungshan V formation

Sungshan I formation


(b) plan view

6.2m

5.0m

23.25m

sump

bore

Diaphragm wall

N

(b)

SM

CL

SM

CL

SM

EL.+80.0m

EL.+72.5m

EL.+69.4m

EL.+63.4m

EL.+59.6m

EL.+56.4m

Casing

5m 6m

4m

Sump

8m9m

. . . . . .

. .

. . . . . . . .. .. .. . . . .. . . . .

. .

. . . . .. . . .

(c)

. . . .

. .


(c) process of sand boiling

Sungshan III

Sungshan I

Sungshan II

Marsland’s method {Fig. 5.34,1.5}(1, 5)

Terzaghi’s method {Eq. 5.30

assuming Ms=0}(1)

Overall shear failure

Push-in Basal heave

Gross pressure method

{Eq. 5.5, ｝(1)

Short term behaviors can

be ignored while long

term behaviors may need

consideration. The

analysis methods are the

same as those for sand

and gravel.

Sand boiling Upheaval

San

d o

r g

rav

e A

lter

nat

ed l

ayer

s of

sand

(or

gra

vel

) an

d c

lay

Cla

y ˍˍ

ˍˍ ˍˍ

ˍˍ

TABLE 5.2 Stability analysis methods for strutted walls and the required minimum factors of safety


{Eq.5.5, 1.2,

Harza’s method {Eq. 5.26,

2.0}(4)

1.5~2.0}(4)

}(1, 5)

Simplified 1-D seepage

method {Eq. 5.35,

Terzaghi’s method

Bjerrum and Eide’s

Slip circle method {Eq. 5.15,

}(1)


{Eq. 5.5, ｝(1)

assuming Ms=0}(1)

assuming Ms=0}(1)

Terzaghi’s method {Eq. 5.9 or

5.10, }(1,2,3)

Bjerrum and Eide’s method{Eq.

5.12 or 5.13, }(4,3)

Slip circle method {Eq. 5.15,

}(1,3)

{Eq. 5.17, Fup≧1.2}(1)

pF

sF

sF

sF

0.2sF

2.1bF

2.1pF

2.1pF

5.1bF

2.1bF

2.1bF

NOTE:

(1) The methods and factors of safety are suggested by TGS (2001)

and JSA (1988)

(2) The factor of safety is suggested by Mana and Clough (1981)

(3) It is only when clay is the dominant soil layer that the analysis of

basal heave is required

(4) The factor of safety is suggested by NAVFAC DM 7.1 (1982)

(5) TGS (2001) and JSA (1988) suggest the conservative value

obtained by Terzaghi's method or the simplified 1-D seepage be

adopted for design.

Documents

2 Stability Analysis