INSTITUTT FOR GEOTEKNIKK. NTH PROSJEKT NR. NOT1AT NR. IDATO (;[(1"'"EC:'-'~~iCAL DIVISIOll. 0.82.02 I 1. 9. 19~

I : PROSJEKTTITTELi 01 ro I SUBROJECT CNRD 13-2c

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:::::> CD w0 NOTATET GJELDER ~-----------------+----'< A

" I

TABLE OF CONTENTS

1. INTRODUCTION Page 1

2. UNDRAINED SHEAR STRENGTH 1

3. STRESS CHANGES DURING INSTALLATION 2

4. EXCESS PORE PRESSURE DISSIPATION 3

5. NORMAL STRESS CHANGES DURING CONSOLIDATION 4

6. ULTIMATE CAPACITY OF SEGMENT PILE 5

7. LOAD DISPLACEMENT CURVES 5

8. REFERENCES 7

TABLE OF FIGURES

Fig. 1 UNDRAINED SHEAR STRENGTH

11 2 PREDI

II

1

1. INTRODUCTION

On the following pages are presented the NTH predictions in

connection with the seqment pile tests of project CNRD 13-2.

Only static behaviour is included herein. The predictions

are based on the Ertec report No.82-200-1, the NG! report

81222-2 and our own report No.0.82.02-1.

The cyclic responce will be attempted predicted in a later

technical note.

2. UNDRAINED SHEAR STRENGTH

As a supplement to the undrained shear strength profile in

Plate 30 of the Ertec Report No.82-200-1, an evaluation of

the undrained shear strength (c ) by the "Undrained Effective u

Stress Approach" (Svan 1981) is performed. The main assump

tion is that the undrained excess pore pressure (~u) due to

a change in total stresses is given by

~u = ~a - D oct ~ad ( 1)

where 1 a = (ooct 3 + a +a l x y z

D = dilatancy parameter, determined by triaxial tests. (Janbu, 1977)

Assuming an initial K 0' state of stresses, Eq. (1) can be

developed into

x(p' +a) (2)v

where K' .l (1+b -3D) (1-K'0 + 3 0 0X = ~ (N-1)

11 + - ( 1 +b-3D) (N-1)3

2

and

a = attraction = c/tan

c = cohesion

N = tan 2 ( 4 5 +PI 2)

tanp= mobilized friction

tan= friction at failure

Ko I = (ph +a) I (p; +a) p' = effective overburden pressurev

p' = earth pressure at resth b = (0 2 -0 3 ) I (o 1 -o ) (final state of stress)3 bo = (0 20 -0 30 ) I (0 -0 ) (initial state of stress)10 30

Eq.(2) is valid for K' < 1, and gives the undrained shear 0

strength if N = Nf = tan 2 (45+/2).

Interpretation of the available triaxial tests gives the a,

tan and K; at Fig.1. Dis judged to D = -0.3 in Stratum II

and D = -0.5 in strata I and III in average. With these para

meters, and p ' equal to the interpreted maximum past effective v

pressure o~ in Plate 12 A of the Ertec report No.82-200-1,

the undrained shear strength profile in Fig.2 is obtained.

This approach gives a slightly higher c than the Ertec u

average c in Stratum II, but as a whole the differences are u

not scaring. Hence, the interpreted o ' may be close to the vm

correct value, but eventual separate porepressure measurements

will confirm this.

3. STRESS CHANGES DURING INSTALLATION

The stress changes due to installation of the segment pile

are computed according to expansion of cavities theory.

Hence, the normal stress change at the pile surface is

!:J.o n (3)

3

where

- (ro- tir)2 G R ~/r o' ( 4)ro cr 2 u

0

G is average secant shear modulus, r is radius of pile,0

and fir is radial soil displacement (fir ~ wall thickness) .

The undrained excess pore pressure at pile surface due to

installation is according to Wroth, Carter and Randolph

(1979):

ln R ,. ' tiu = 2c (5)u - uOoct ro

tio' is change in mean effective stress. tia' is eastioct oct mated through Eqs. (1) and (2) resulting into

tia' = - 0.041 (p' + a) for Strata I and IIIoct v tia' = - 0.027 (p' + a} for Stratum IIoct v

The major factor of influence is the ratio G/c . Based on u the triaxial and direct simple shear tests, a ratio between

40 and 60 is judged adequate for the exoansion of cavities

calculations. This results into the plots in Figs. 2, 3

and 4, giving pore pressure in excess of the ambient pore

pressure, normal stress increase due to installation and

expected normal stress during installation respectively.

4. EXCESS PORE PRESSURE DISSIPATION

The excess pore pressure dissipation is estimated based

on linear elastic theory and radial transport of excess

water (Torstenson 1978), Randolph and Wroth (1979)). The

major factors of influence are the ratio between radius of

plastified zone and radius of the pile (R/r ), and the radial 0

coefficient of consolidation (ch) .

4

For the test site, McClelland, NGI and NTH report vertical

c in the order 0.8 to 1.5 m2 /year at the relevant effective v

stress levels. The Ertec cv-values are significantly higher

(3 to 7 m2 /year). Based on the lower cv-range, the

consolidation plot in Fig. 5 has been developed. Observe

that the time needed for 90% consolidation (t 90 ) is 4 to

12 days. Only if ch is greater than 3 m2 /year, willt 90 be 72 hours or less.

5. NORMAL STRESS CHANGES DURING CONSOLIDATION

According to linear elastic theory, very high normal

effective stresses will occur at the pile surface at the

end of consolidation, leading to local K~ values

considerably greater than unity. These high K -values are 0

highly questionable. The stress increase is restricted

to a rather small zone around the pile, and as the consoli

dation proceeds, creep,relaxation and stress redistribution

effects may easily counterbalance most of the effective

stress increase tendencies.

To illustrate, the free creep between and t would bet 70 9 0 1 t

~s = 0.75% according to Janbu's (1970} formula ~s = r ln -t~-1 s . ref"' r ln t 90/t 71> (t 9 0 /t 70 :::: 4. 6) . The creep number rs lS

setsequal to 200 as obtained by reinterpreting test lNODl,

NTH Report No. 0.82.02-1. (Typical ranges for rs is 100 to

500 for NC-clays, 1000 to 5000 for QC-clays}. Multiplying

~s with a swelling modulus of 10 times the compression

modulus gives an effective stress reduction at 35 meters

depth of 100 kPa, i.e. of the same order of magnitude as the

total normal stress increase due to pile insertion.

This highly tentative (and theoretically incorrect} estimate

gives the background for assuming an earth pressure coeffi

sient K' ~ 0.7 to 0.8 at the end of consolidation. (Assumed0

initial K~ ~ 0.55 to 0.6}.

5

6. ULTIMATE CAPACITY OF SEGMENT PILE

The undrained shear strength after reconsolidation is not

expected to be much different from the c before pileu

installation in this plastic to highplastic underconsoli

dated clay. If so, the a-factor giving the estimated unit

skin friction Tu by the formula Tu = a cu could be 0.65 to 0.8, giving Tu equal to 0.18 to 0.2 times (p~ + a). Tu is plotted in Fig. 6. This Tu is lower than the API

unit skin friction in Plate 31 of Ertec's Report No.

82-200-1, whe.re a = 1 has been assumed.

Janbu's effective stress method is generally a method for

estimating the longterm capacity of piles in clay, silt or

sand, and it does strictly not apply to the shortterm

capacity of piles in clay, and especially not in highplastic

clays with high clay contents. However, if the method is

used it gives a negative skin friction factor S in the vn order of 0 .12 to 0 .14 for a roughness ratio r = 0. 7 to 0 .. 9 (see Janbu, 1974). The corresponding ultimate unit skin

friction T = S (p 1 + a) is dotted in Fig. 6, where p'u vn v -v equal to Ertec's interpreted maximum part effective vertical

stress has been used. This serves as as estimate of the

longterm capacity of the segment pile.

7. LOAD - DISPLACEMENT CURVES .

A single slice model is used for the computation of t - w

curves, t beeing skin friction per meter (kN/m) and w vertical

displacement. Here, the displacement increment ~w due to a

unit skin friction increment ~T at the pile surface becomes0

6

r 1 r1

6T J dr6w = f G dr = 6T 0 r o r G

ro ro

( 6)

Here it is assumed that the shear stress increment at a

distance r from the pile centerline is 6T = 6T 0 r 0 /r, r 0 being the pile radius. Exgressing the tangent shear

modulus as G = G. (1 - .!__) , where T is ultimate skinl T U

friction, and expressingu T at a radial distance r as

T = T r /r, Eq. (6) becomes after rearrangements0 0

= 1 6w 2 - ( 7)K d

where

sl dsK = f ,[1-*r

u

and d = 2 r = pile diameter 0

s = r/r 0

=s1 rl/ro

Judged from the triaxial, direct simple shear and consoli

dation tests as a whole, suitable pairs of G./T and n l u

seem to be 155 and 2.25 or 100 to 115 and 2.0 for Stratum II,

and 105 and 2.25 or 75 to 85 and 2.0 for Strata I and III,

respectively. (Note, Tu is ultimate unit skin friction,

and not undrained shear strength). The resulting normalized

t - w curves are given in Fig. 7. An axis for absolute

displacement in mm of 3" segment pile is included.

' .

7

I ,

8. REFEREHCES

Janbu, N. (1970): "Grunnlag i geoteknikk".

Tapir forlag, Trondheim.

Janbu, N. (1977): "Slopes and excavations".

Re. General .report, Main Sess. 3, Proc. 9th ICSMFE,

Tokyo, Vol. 2, pp. 549 - 566.

Randolph, M.F. and C.P. Wroth (1979): "An analytical

solution for the consolidation around a driven

pile".

Int. Journal for Numerical and Analytical Methods

in Geomechanics, Vol. 3, No. 3.

Svan, G. (1981): "Undrained effective stress analysis".

Dr.ing. thesis, NTH.

Torstenson, B.A. (1978): "The pore pressure Probe".

Geoteknikkdagen, Norsk Geoteknisk Forening,

Oslo, 11 nov. 1977, pp. 34.1 - 34.15.

Wroth, C.P., J.P. Carter and M.F. Randolph (1979):

"Stress changes around a pile driven into cohesive

soil".

Recent developments in the design and construction

of piles. 21 - 22 March 1979, London, pp. 255 - 264.

(kPa)

AO

Friction tan Undrained shear strength cz uen

-l 0 ( 0.2 0.4 0.6 0 20 40 60-l n I I I Ic z 0 t I I ~

a == 10 kPa,, ~ I-'0 \.N D ::: -0. 5:0 I N 10G) K'

0 = 0.6 I . m

0 I ez -I0 -l -I IT1 I A m :r: z

I V> 0 ~ .. NTH-theoreticalz -0 I:0 0 20:;:i::; IT1 z I

I i ~ \:\~A t::l .... -0 a == 20 kPa I ("') ....z

I _.,. r 1D = -0.3 ..... IT10"" w 0 .b 30z V> K' = o.ss

0(/) .....-l -.. c Ul 0 I:0 0::t::l ERTEC0 wV> -< I I z m E-1 0 wG"> I I I average::E:I 3: 40mm 9z zs:: H~

-0 I...... Cl a = 20 kPar w m Ill~I I so D = -0.5 ? ~ w

Ul K' = 0.6 0;?;

0 1-=l Iw 60Ill

I ~ 0 QI

... E-1~10 ~ 111-l 0 Iw

.... r' 0 ~ ~ Cl I.70. ~ 0 N 0 Ertec CIUC

Ertec CKoUC McClelland CK 0UC NTH CKaUC .post cyclic ______,----------

I

.

b

--------------------------------------------,

IO p.. ~

z 0 H E-4p:; :i (/.)

z H

:i ..:I H p..

0 E-4

:i :::> Cl

:i (/.) ,ct :ip:; u z H

:ip:; :::> ti) (/.) :ip:; Q) p.. r-1 :i .-I p:; 0. 0 p.. ..

c Cl Q) :i E E-4 tJ"I u Q) H II) Cl :i = p:; M p..

~ c 0 M

0 0 N

0 0 ..-

0

0 0 0 0 0 0 0 0..,...-- N M lf) \0 r- E (SE8.L3W NI) G8HV3S MO'l38 H.Ld3G

PROSJEKT

CNRD 13-2 TENSION PILE STUDY 0,82.02 NTH-PREDICTIONSJ SEGMENT PILE DATO

INSTITUTT FOR GEOTEKNIKK, N-7034 TRONDHEIM - NTH FIG.

2

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0 0 .._~~~-4-~~~-+-~~~~~~~~1--~~~-+-~-+--+-+-~~~--;

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(SH3~3W NI) 03ffil3S M0~3H H~d3G

PROSJEKT

0.82.02CNRD 13-2 TENSION PILE STUDY DATONTH-PREDICTIONSJ SEGMENT PILE

FIG. INSTITUTI FOR GEOTEKNIKK, N-7034 TRONDHEIM - NTH 3

. I

0 0 \0

0 0 ...-~~~+-~~~--~~~....-~~~--~~~--~~~--._.,.....~--~

""'

0 0 t--~~~+-~~~-+-~~~-+-~~~--~~~--+..-....._~'---+-~~~-1 N

0 00 ..--~~~+-~~~+-~~~-+-~~~-+-~..,,..~~--.,.C--~-t--:::i.,..,C-~-;

0 0 J--~~~+-~~~+-~~~+.......-~~-;.z..,,1---_,,..w-r;.y_~~~-+-~._c.~-1 co

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00 .--~~~+-...........f'--7"---::0.-C----+-~~~--+-~~~-+-~~~-+-~~~-1 ""'

0 0 t--,~=--~+-~~~-+-~~~-+-~~~-+-~~~-+-~~~-4-~~~~ N

o.__~~~..._~~~-'-~~~_:_~~~-L-~~~....._~~~-=-~~~-' E

0 0 0 0 0 0 N M 11) \.0 r-

SE3~3W NI G3HV3S M0~3H H~d3G

PROSJEKT

CNRD 13-2 TENSJON PILE STUDY 0.82.02 DATONTH-PREDICTJONSJ SEGMENT PILE

FIG. INSTITUTI FOR GEOTEKNIKK, N-7034 TRONDHEIM - NTH 4

.c N

1-l IO (!)

>t ........ "' E co

0

II

~

II) -0 w

I .c I \0

Lf)

N

-0 co

.c co N

-0 -.;t'

.c -.;t'

\0

.c N M

.c \0

-0 N

-0 ~

0) r-l -r-1 P..

.. s:: (!)

E tri 0) ti)

: M

..c co

z 0 H E:-i ~ H H ~ E:-i (/)

z H

.c N

::i ...:l H ~

p:: ::i E:-i

\0

-0s:: fU

\0

~ ~

::i ~ H E:-i

II 0

J...I ........ p::

0 co N 0

0 0 0 0

PROSJEKT

CNRD 13-2 TENSION PILE STUDY 0.82.02 DATONTH-PREDICTIONS~ SEGMENT PILE

FIG INSTITUTT FOR GEOTEKNIKK, N-7034 TRONDHEIM - NTH 5

I ,

ULTIMATE SKIN FRICTION (kPa)

0 20 40 60 80 100 kPa 0

10

20

ased)

API O'. 1

30

Cl) (Janb model,p::;

8 :i

eff. stress ased) -:i 40 ..::... z H

Q :i co 50 ~ :i Cl)

!!:: 0 ...:i :i 60 co ::r:: 8 P. :i Q

70m

\ ' \' \ ~ :'

\ -\ :_\

\

\ \ \

PAOSJEKT

0.82.02 DATO

FIG. 6

. . ------------ -------- --

CNRD 13-2 TENSION PILE STUDY NTH-PREDICTIONSJ SEGMENT PILE

INSTITUTI FOR GEOTEKNIKK, N-7034 TRONDHEIM NTH

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-------

f:.;.

w/d ( % )

w (mm)

w/d (%)

:t RUV pr,.hc:.kf' c:.

1 0 .

' G./1 =1 ..

J_ u n=2.25

0.8

= 100 n 2.0

G. /1 115 2.0= n .l u

0.6 :::1

I-' ....... I-'

0 H 0.48

~ [/} [/} .:i

0.2~ 8 U)

~ STRATUM I I .::t: .:i ::r:

0U) 0 1 2 3 4 5

0 2 3 4, 1 . 0

G. /1 105 .. .... .l u ...

n = 2. 0.8

=85 n= 0

0.6 ~ =75 n= .0

I-' ....... I-'

0 H 0.48

~ U) ti) .:i ~ 8

0.2 (/)

~ STRATA I & II I.::t: .:i ::r:: [/} 0

0 1 2 3 4 5

PROSJEKT

CNRD 13-2 TENSION PILE STUDY 0.82.02 NTH-PREDICTIONS ... SEGMENT PILE DATO

FIG.INSTITUTT FOR GEOTEKNIKK, N-7034 TRONDHEIM - NTH 7

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UntitledINSTITUTT FOR GEOTEKNIKK. NTH PROSJEKT NR. NOT1AT NR. IDATO (;[(1"'"EC:'-'~~iCAL DIVISIOll. 0.82.02 1.9. 19~ I : PROSJEKTTITTELi 01 ro SUBROJECT CNRD 13-2c .~I ,,__ ()) (/) =o >roGAR TIL: Q) c ,_ TENSION PILE STUDYc Ctl ()) .c ;:::: 0 NOTATET GJELDER ~-----------------+----'< A TABLE OF CONTENTS 11INSERTION segment pile) 3 HORISONTAL STRESS INCREASE AT PILE SURFACE DUE TO PILE INSERTION 4 ESTIMATED TOTAL NORMAL STRESSES AT PILE SURFACE AFTER INSERTION 5 ESTIMATED PORE PRESSURE DISSIPATION 6 ESTIMATED ULTIMATE SKIN FRICTION 7 PREDICTED DIMENSIONLESS LOAD-DISPLACEMENT CURVES 1. INTRODUCTION .On the following pages are presented the NTH predictions in connection with the seqment pile tests of project CNRD 13-2. Only static behaviour is included herein. The predictions are based on the Ertec report No.82-200-1, the NG! report 81222-2 and our own report No.0.82.02-1. The cyclic responce will be attempted predicted in a later technical note. 2. UNDRAINED SHEAR STRENGTH As a supplement to the undrained shear strength profile in Plate 30 of the Ertec Report No.82-200-1, an evaluation of the undrained shear strength (c ) by the "Undrained Effective u Stress Approach" (Svan 1981) is performed. The main assumption is that the undrained excess pore pressure (~u) due to a change in total stresses is given by D = .dilatancy parameter, determined by triaxial tests. (Janbu, 1977) Assuming an initial K' state of stresses, Eq. (1) can be developed into x(p' +a) .(2)v where K' .l (1+b -3D) (1-K'0 + 3 0 0X = ~ (N-1) 11 + -( 1 +b-3D) (N-1)3 and a = attraction = c/tan c = cohesion N = tan( 4 5 +PI 2) tanp= mobilized friction tan= friction at failure Ko= (ph +a) I (p; +a) p' = effective overburden pressurev .p' = earth pressure at rest.h b = (0-0) I (o -o ) (final state of stress)3 bo = (0-0) I (0 -0 ) (initial state of stress)10 30 Eq.(2) is valid for K' < 1, and gives the undrained shear 0 strength if N = Nf = tan(45+/2). Interpretation of the available triaxial tests gives the a, tan and K; at Fig.1. Dis judged to D = -0.3 in Stratum II and D = -0.5 in strata I and III in average. With these parameters, and p ' equal to the interpreted maximum past effective v o~ in Plate 12 A of the Ertec report No.82-200-1, the undrained shear strength profile in Fig.2 is obtained. This approach gives a slightly higher c than the Ertec u average c in Stratum II, but as a whole the differences are u not scaring. Hence, the interpreted o ' may be close to the vm correct value, but eventual separate porepressure measurements will confirm this. 3. STRESS CHANGES DURING INSTALLATION The stress changes due to installation of the segment pile are computed according to expansion of cavities theory. Hence, the normal stress change at the pile surface is (3) .G is average secant shear modulus, r is radius of pile,0 and fir is radial soil displacement (fir ~ wall thickness) . The undrained excess pore pressure at pile surface due to installation is according to Wroth, Carter and Randolph (1979): ln R ,. ' tiu = 2c (5)-uOoct ro tio' is change in mean effective stress. tia' is eastioct oct mated through Eqs. (1) and (2) resulting into tia' = -0.041 (p' + a) for Strata I and IIIoct v tia' = -0.027 (p' + a} for Stratum IIoct v The major factor of influence is the ratio G/c . Based on u the triaxial and direct simple shear tests, a ratio between 40 and 60 is judged adequate for the exoansion of cavities calculations. This results into the plots in Figs. 2, 3 and 4, giving pore pressure in excess of the ambient pore pressure, normal stress increase due to installation and expected normal stress during installation respectively. 4. EXCESS PORE PRESSURE DISSIPATION The excess pore pressure dissipation is estimated based on linear elastic theory and radial transport of excess water (Torstenson 1978), Randolph and Wroth (1979)). The major factors of influence are the ratio between radius of ), and the radial 0 coefficient of consolidation (ch) . For the test site, McClelland, NGI and NTH report vertical c in the order 0.8 to 1.5 m/year at the relevant effective v stress levels. The Ertec cv-values are significantly higher (3 to 7 m/year). Based on the lower cv-range, the consolidation plot in Fig. 5 has been developed. Observe that the time needed for 90% consolidation (t) is 4 to 12 days. Only if ch is greater than 3 m/year, will90 be 72 hours or less. 5. NORMAL STRESS CHANGES DURING CONSOLIDATION According to linear elastic theory, very high normal effective stresses will occur at the pile surface at the K~ values considerably greater than unity. These high K -values are 0 highly questionable. The stress increase is restricted to a rather small zone around the pile, and as the consolidation proceeds, creep,relaxation and stress redistribution effects may easily counterbalance most of the effective stress increase tendencies. To illustrate, the free creep between and t would be70 9 0 1 t ~s = 0.75% according to Janbu's (1970} formula ~s = r ln -t~1 s . refln t 90/t 1> (t /t :::: 4. 6) . The creep number rs lS setsequal to 200 as obtained by reinterpreting test lNODl, NTH Report No. 0.82.02-1. (Typical ranges for rs is 100 to 500 for NC-clays, 1000 to 5000 for QC-clays}. Multiplying ~s with a swelling modulus of 10 times the compression modulus gives an effective stress reduction at 35 meters depth of 100 kPa, i.e. of the same order of magnitude as the total normal stress increase due to pile insertion. This highly tentative (and theoretically incorrect} estimate gives the background for assuming an earth pressure coeffi~ 0.7 to 0.8 at the end of consolidation. (Assumed0 K~ ~ 0.55 to 0.6}. 6. ULTIMATE CAPACITY OF SEGMENT PILE .The undrained shear strength after reconsolidation is not expected to be much different from the c before pileu installation in this plastic to highplastic underconsolidated clay. If so, the a-factor giving the estimated unit skin friction Tu by the formula Tu = a cu could be 0.65 to 0.8, giving Tu equal to 0.18 to 0.2 times (p~ + a). Tu is plotted in Fig. 6. This Tu is lower than the API unit skin friction in Plate 31 of Ertec's Report No. 82-200-1, whe.re a = 1 has b7. LOAD -DISPLACEMENT CURVES . A single slice model is used for the computation of t -w curves, t beeing skin friction per meter (kN/m) and w vertical displacement. Here, the displacement increment ~w due to a unit skin friction increment ~T at the pile surface becomes0 r 1 r1 .6T J dr.6w = f G dr = 6T0 r o r G .ro ro .r 1 r1 .6T J dr.6w = f G dr = 6T0 r o r G .ro ro .

( 6)Here it is assumed that the shear stress increment at a distance r from the pile centerline is 6T = 6T 0 r 0 /r, r0 being the pile radius. Exgressing the tangent shear modulus as G = G. (1 -.!__) , where T is ultimate skinl T U friction, and expressingu T at a radial distance r as T = T r /r, Eq. (6) becomes after rearrangements0 0= 1 6w 2 -( 7)K d where sl dsK = f u and d = 2 r = pile diameter 0 s = r/r0 =1 rl/ro Judged from the triaxial, direct simple shear and consolidation tests as a whole, suitable pairs of G./T and n l u seem to be 155 and 2.25 or 100 to 115 and 2.0 for Stratum II, and 105 and 2.25 or 75 to 85 and 2.0 for Strata I and III, respectively. (Note, Tu is ultimate unit skin friction, and not undrained shear strength). The resulting normalized t -w curves are given in Fig. 7. An axis for absolute displacement in mm of 3" segment pile is included. 8. REFEREHCES Janbu, .N. (1970): "Grunnlag i geoteknikk". Tapir forlag, Trondheim. Janbu, .N. (1977): "Slopes and excavations". Re. General .report, Main Sess. 3, Proc. 9th ICSMFE, Tokyo, Vol. 2, pp. 549 -566. Randolph, M.F. and C.P. Wroth (1979): "An analytical solution for the consolidation around a driven pile". Int. Journal for Numerical and Analytical Methods in Geomechanics, Vol. 3, No. 3. Svan, .G. (1981): "Undrained effective stress analysis". Dr.ing. thesis, NTH. Torstenson, B.A. (1978): "The pore pressure Probe". Geoteknikkdagen, Norsk Geoteknisk Forening, Oslo, 11 nov. 1977, pp. 34.1 -34.15. Wroth, .C.P., J.P. Carter and M.F. Randolph (1979): "Stress changes around a pile driven into cohesive soil". Recent developments in the design and construction of piles. 21 -22 March 1979, London, pp. 255 -264. P