PLAXIS

PLAXIS

PLAXIS

PLAXIS Nº 12 - JUNE 2002

Editorial

Some time has passed since the appearance

of our last bulletin no 11, but the PLAXIS

team did not sit still. Not only was a new

director appointed for PLAXIS B.V. which

will be introduced further on, also a

number of other new team-members have

come to work for PLAXIS. The Plaxis-team

has extended with four new people in

order to improve the capability to

accommodate for the demand on new

plaxis developments. The Plaxis-team

consist of 14 people. In the next bulletin,

we will briefly introduce them to you.

New Developments which will be discussed in

the contribution by Dr Brinkgreve, the head of

our development team. He will discuss further

developments such as for the release of Plaxis

Version 8, the progress on the PLAX-flow

program and the other 3D developments. With

respect to PLAXIS 2D, Version 8 is due to be

expected after the summer holidays, as Beta

testing of this new program is underway, and

the users in our regular PLAXIS course in

Noordwijkerhout in January and also the

attendants of the advanced course have had

some opportunity to experience this new

program.

In his regular column Prof. Vermeer will discuss

the use of soil parameters and especially

parameter estimation. Not always is it possible

to do a direct test for a parameter. Or sometimes

in a pre-design stage there is only limited

information of the soil stratification. In that case

it is often very convenient to have some

correlations between different soil-parameters

in order to be able to proceed with a

geotechnical design. In this issue Prof. Vermeer

discusses Oedometer stiffness of Soft Soils.

In addition to the aforementioned, Prof.

Schweiger who also is a regular contributor to

our bulletin discusses the relation between

Skemptons pore pressure parameters A and B

and the performance of the Hardening Soil

model.

Furthermore we are fortunate to have new

contributions with respect to Benchmarking;

two contributions on benchmarking are

presented here, one on Shield tunnelling and

another on excavations.

Again we are glad to have a number of practical

applications; Among which are a contribution

by Dr. Gysi, on a multi-anchored retaining wall,

and another one by Mr. Cheang from

Singapore on a complicated retaining wall with

Jack-In Anchors.

Finally in the Users Forum it is shown how a

more complicated 3D situation of a Retaining

wall with anchors is practically modelled with

PLAXIS 2D.

Editorial Staff:

Martin de Kant, Plaxis Users Association (NL)

Marco Hutteman, Plaxis Users Association (NL)

Peter Brand, Plaxis B.V.

Scientific Committee:

Prof. Pieter Vermeer, Stuttgart University

Dr. Ronald Brinkgreve, Plaxis bv

1

Bulletin of thePLAXISUsers Association (NL)

Plaxis bulletinPlaxis B.V.P.O. Box 5722600 AN DelftThe NetherlandsE-mail:bulletin@plaxis.nl

IN THIS ISSUE:

Editorial 1

Column Vermeer 2

New developments 4

Note on pore pressure 6

Benchmarking I 9

Benchmarking II 12

Recent Activities 13

Plaxis practice I 14

Plaxis practice II 17

Users forum 22

Some Geometries 22

Agenda 24

PLAXIS

PLAXIS

Fig. 1: Atterberg limits of 21

different soils that weretested by Engel

Column Vermeer

ON THE OEDOMETER STIFFNESS

OF SOFT SOILS

For normally consolidated fine-grained

soils, we have the logarithmic compression

law, �e = Cc �log�’, where De is the change

of the void ratio, Cc the compression index

and �’ the vertical effectivestress in one-

dimensional compression. The compression

index Cc is measured in oedometer tests,

together with other stiffness related

parameters such as the swelling index and

the preconsolidation stress. In this column

I will discuss correlations for the

compression index Cc.

It should be realized that Terzaghi and other

founding fathers of Soil Mechanics lived in the

10-log-paper period and their findings have to

be reformulated for use in computer codes.

Hence, we have to change from a 10-log to a

natural logarithm in order to obtain the

reformulated law,

�e = - � �ln�’, where �= Cc �ln10. On top of

this it is convenient to use strain instead of

void ratio, which leads to the compression law,

where �� = �* �ln�’, �* = ��(1+e) and �� is a

finite strain increment. I will address Cc, as well

as the modified compression index �* and in

addition the oedometer modulus Eoed.

One of the best-known geotechnical

correlations reads Cc� 0.9 (wL - 0.1), where wL

is the liquid limit. For details, the reader is

referred to the book by Terzaghi and Peck

(1967). Wroth and Wood (1978) proposed the

seemingly different correlation Cc� 1.35IP,

where IP is the plasticity index. In reality the

two correlations are virtually identical, as the

plasticity index can usually be approximated as

IP � 0.73 (wL - 0.1). Indeed, with the exception

of sandy silts, data for IP and wL tend to be on

a straight line that is parallel to the so-called

A-line in Casagrande’s plasticity chart (see

Fig. 1). On using the Ip-wL correlation, the

Terzaghi-Peck correlation reads Cc � 1.23IP,

which is very close to the finding of Cc � 1.35IPby Wroth and Wood. Considering the large

amount of evidence on the correlations,

Cc � 1.35IP and IP � 0.73 (wL - 0.1), I conclude

that we may use both

Cc � 1.35IP and Cc � wL - 0.1 (1)

The latter one is only slightly different from

the earlier one by Terzaghi and Peck and to my

judgement also slightly better. Let us now

address the modified compression index �* as

used in all advanced Plaxis models. The

relationship between the traditional

compression index Cc and the modified one

�* is expressed by the equation

�*=Cc �

Cc(2)

(1+e) In10 4.6

The approximation follows for e=1. In general

it is crude to assume e�1, but it works within

the context of the correlations for soft soils.

In combination with the correlations for Cc it

leads to:

�* � 0.3lp and �* � 0.2(wL- 0.1) (3)

For a direct assessment of these correlations,

we will consider data by Engel (2001). This

database contains modified compression

indices for 21 different clays and silts, with a

liquid limit ranging from 0.2 up to 1.1 and a

plasticity index between 0.03 and 0.7, as can

2

PLAXIS

PLAXIS be seen in Fig. 1. Engel’s data for �* leads to

Figures 2 and 3. From Fig. 2 it can be

concluded that the correlation

�* � 0.3lp has some shortcomings. A close

inspection shows that it is nice for clays with

plasticity indices above the A-line in

Casagrande’s plasticity chart, but not for silts

with Ip below the A-line. To include such silts

one could better use the correlation,

�* � 0.2(wL- 0.1) as demonstrated in Fig. 3. On

plotting �* as a function of the liquid limit, as

done in Fig. 3, it is immediately clear that there

is an extremely nice correlation.

It should also be recalled that the correlation

�* � 0.2(wL- 0.1) is not only supported by

Engel’s database, but that it is also fully in line

with the work of Wroth & Wood as well as

Terzaghi & Peck on correlations for Cc.

Let us now consider the oedometer stiffness.

To this end the logarithmic compression law

�� = �* . �ln�’ can be written in the differential

form d�/dln� = �* and one obtains

d�’/ d� = �’/� The tangent stiffness in

oedometer-compression, also refered to as

the constrained modulus, is thus proportional

to stress. Hence, Eoed =�'/�*, where Eoed is also

denoted as M or Es, depending on conventions

in different countries. This linear stress

dependency of soil stiffness is nice for fine-

grained NC-soils, but not for coarse-grained

ones. Therefore Ohde (1939) and Janbu (1963)

proposed a generalisation of the form:

Eoed = Eoed (�'/Pref)m with Pref = 100kPa (4)

where m is an empirical exponent. This

equation reduces to the linear stress

dependency of soil stiffness for m=1.

In the special case of m=1, one thus obtains

the logarithmic compression law for fine-

grained NC-soils. For coarse grained soils, much

lower exponents of about m=0.5 are reported

by Janbu (1963), Von Soos (2001) and other

researchers.

The above power law of Ohde, Janbu and Von

Soos has been incorporated into the Hardening

Soil Model of the Plaxis code. Here it should be

noted that the above authors define

Eoed = v . Pref, where v is a so-called modulus

number. Instead of the dimensionless modulus

number, the Hardening Soil Model involves

Eoed as an input parameter, i.e. the constrained

modulus at a reference stress of

�’= pref = 100kPa. For the coming Version 8 of

the Plaxis code, we have also considered the

use of alternative input parameters. Instead of

Eoed , we have discussed the modulus number

1/�* as well as the modified compression index

itself, as it yields

�* Pref / Eoed (5)

In fact, this simple relationship between the

oedometer stiffness and the modified

compression index triggered our thinking on

alternative input parameters. Finally we decided

3

Fig. 2:Compression indices asmeasured by Engel as a

function of Ip

ref

ref

ref

ref

ref

Fig. 3:Compression indices

correlate nicely with theliquid limit

PLAXIS

PLAXIS to go one step further and use the traditional

compression index Cc by implementing the

equations:

Eoed = Pref

= (1+e) ln10

. Pref (6)�* Cc

Within the new Version 8, users will have the

choice between the input of Eoed and the

alternative of Cc. Similarly, the so-called swelling

index Cs will be used as an alternative input

parameter for the unloading-reloading stiffness

Eur. On inputting Cc one also has to prescribe

a value for the void ratio.

Here, a default value of e=1 will be introduced.

This will make the Hardening Soil Model easier

to use in the field of soft soil engineering.

P.A. Vermeer, Stuttgart University

REFERENCES:

Engel, J., Procedures for the Selection of

Soil Parameters (in German), Habilitation study,

Department of Civil Engineering, Technical

University of Dresden, 2001, 188 p.

Janbu, N., "Soil Compressibility as Determined

by Oedometer and Triaxial Tests", Proceedings

3rd European Conference on Soil Mechanics

and Foundation Engineering, Vol. 1,

Wiesbaden, 1963, pp. 19-25.

Ohde, J. , "On the Stress Distribution in the

Ground" (in German), Bauingenieur, Vol. 20, No.

33/34, 1939, pp. 451-459.

Terzaghi, K. and Peck, R. B., "Soil Mechanics in

Engineering Practice", 2nd Ed, John Wiley and

Sons, New York, 1967, 729 p.

Soos von, P., "Properties of Soil and Rock" (in

German), Grundbautaschenbuch, Vol. 1, 6th

Ed., Ernst & Sohn, Berlin, 2001, pp. 117-201

Wroth, C. P. and Wood, D. M. , "The Correlation

of Index Properties with Some Basic

Engineering Properties of Soils", Canadian

Geotechnical Journal, Vol. 15, No. 2, 1987, pp.

137-145.

New Developments

In a few months, Plaxis version 8 will be

released. This new 2D program is one of the

results of a recently finished two-years

project on Plaxis developments. Another

results of this project is the 3D Tunnel

program, which was released last year. In

this bulletin some new features of Plaxis

version 8 will be mentioned. The new

features are divided into three groups:

Modeling features, calculation options and

user friendliness.

MODELING FEATURES

Plaxis (2D) version 8 has several new features

for the modeling of tunnels and underground

structures. Some of these features were

already implemented in the 3D tunnel

program, such as:

- Extended tunnel designer, including thick

tunnel linings and tunnel shapes composed

of arcs, lines and corners.

- Application of user-defined (pore) pressure

distribution in soil clusters to simulate grout

injection.

- Application of volume strain in soil clusters

to simulate soil volume loss or

compensation grouting.

- Jointed Rock model

Other new modeling features are aimed at

the modeling of soil, structures and soil

structure interaction:

4

ref

PLAXIS

PLAXIS - Input of Skempton's B-factor for partially

undrained soil behavior.

- Hinges and rotation springs to model beam

connections that are not fully rigid.

- Separate maximum anchor forces

distinction between extension and

compression).

- De-activation of interface elements to

temporarily avoid soil-structure interaction

or impermeability.

- Special option to create drains and wells for

a groundwater flow calculation.

CALCULATION OPTIONS

Regarding the new calculation options, most

new features are in fact improvements of

'inconsistencies' from previous versions.

Examples of such improvements are:

- Staged Construction can be used as loading

input in a Consolidation analysis.

- A Consolidation analysis can be executed as

an Updated Mesh calculation.

- In an Updated Mesh calculation, the update

of water pressures with respect to the

deformed position of elements and stress

points can be included. In this way, the

settlement of soil under a continuous

phreatic level can be simulated accurately.

- Loads can be applied in Staged

Construction, which enables a combination

of construction and loading in the same

calculation phase. The need to use

multipliers to apply loading has decreased.

This makes the definition of calculation

phases more logical and it enhances the

flexibility to use different load combinations.

- Preview (picture) of defined calculation

phase in a separate calculations tab sheet.

- Improved robustness of steady-state

groundwater flow calculations. Simplified

input of groundwater head boundary

conditions based on general phreatic level.

In addition, a separate program for transient

groundwater flow is planned to be released

at the end of 2002.

USER FRIENDLINESS

Many new features in the framework of 'user

friendliness' are based on users' suggestions

from the past. Examples of these features are:

- Reflection of input data and applied loads

in the output program.

- Report generation, for a complete

documentation of a project (including input

data and applied loads).

- Complete output of stresses (effective, total,

water), presented both as principal stresses,

cartesian stresses;

also available in cross sections and in the

Curves program.

- Equivalent force in cross-section plots of

normal stresses.

- Force envelopes, showing the maximum

values of structural forces over all

proceeding calculation phases.

- Scale bar of plotted quantities in the output

program.

- Color plots plotted as bitmaps rather than

meta-files. This avoids the loss of colors

when importing these plots in other

software.

- Parameters in material data sets can be

viewed (not modified) in Staged

Construction.

- User-defined material data set colors.

A special feature that is available in Version 8 is

the user-defined soil models option. This

feature enables users to include self-

programmed soil models in the calculations.

Although this option is most interesting for

researchers and scientists at universities and

research institutes, it may also be interesting

for practical engineers to benefit from this

work. In the future, validated and well-

documented user-defined soil models may

become available via the Internet. More

information on this feature will be placed on

our web site www.plaxis.nl.

Registered Plaxis users will be informed when

the new version 8 is available; they can benefit

from the reduced upgrade prices. Meanwhile,

new developments continue. More and more

developments are devoted to 3D modeling. We

will keep you informed in future bulletins.

Ronald Brinkgreve, PLAXIS BV

5

PLAXIS

PLAXIS NOTE ON PORE

PRESSURE

SOME REMARKS ON PORE PRESSURE

PARAMETERS A AND B IN UNDRAINED

ANALYSES WITH THE HARDENING SOIL

MODEL

In undrained analyses Skempton’s pore

pressure parameters A and B (Skempton,

1954) are frequently used to estimate

excess pore pressures. If we consider triaxial

conditions, Skempton’s equation reads

�u = B [ ��3 + A ( ��1 - ��3 ) ]

where ��1 and ��3 are changes in total minor

and major principal stresses respectively. For

fully saturated conditions, assuming pore water

being incompressible, B is 1.0. Furthermore,

for elastic behaviour of the soil skeleton, A

turns out to be 1/3.

A frequently asked question in PLAXIS courses

is “What pore pressure parameters A and B does

PLAXIS use”, if an undrained analysis is

performed in terms of effective stresses setting

the material type to undrained? The answer is

“You don’t know”, except for the trivial cases

of elastic or elastic-perfectly plastic behaviour.

In order to investigate this in more detail

undrained triaxial stress paths are investigated

with the Mohr Coulomb model with and

without dilatancy, and with the Hardening Soil

model. In the latter the influence of various

assumptions of E50 and Eoed has been studied.

Soil Parameters

The following parameter sets have been used

and the model number given below is referred

to in the respective diagrams. A consolidation

pressure of 100 kN/m2 has been applied to all

test simulations followed by undrained

shearing of the sample.

Pore Pressure Parameter B

In order to check the value of parameter B in

an undrained PLAXIS analysis a hydrostatic

stress state has been applied after

consolidation. By doing so, the parameter A

does not come into picture and B can be

directly calculated from �u and ��3, when

using undrained behaviour as material type.

PLAXIS does not yield exactly 1.0 because a

slight compressibility of water is allowed for

numerical reasons and therefore a value of

0.987 is obtained for the given parameters for

the Mohr Coulomb model. For the HS model

the value depends slightly on E50 and Eoed, but

also on the power m and changes with loading.

The differences however are in the order of

about 3.0 to 5.0 % for the parameter sets

investigated here. So it is correct to say that

Skempton’s pore pressure parameter B is

approximately 1.0 in PLAXIS, when using

undrained behaviour as material type.

Pore Pressure Parameter A

The value of parameter A is more difficult to

determine. However one can evaluate A from

the results of the numerical simulations and

this has been done for various parameter

combinations for the Hardening Soil model and

the Mohr Coulomb model.

6

Table 1 Parametersets for Hardening

Soil model

Model Number E50ref Eur

ref Eoedref � c ur pref m K0

nc Rf

kN/m2 kN/m2 kN/m2 ° ° kN/m2 - kN/m2 - - -

HS_1 30 000 90 000 30 000 35 0 / 10 0.0 0.2 100 0.75 0.426 0.9

HS_2 50 000 150 000 50 000 35 0 0.0 0.2 100 0.75 0.426 0.9

HS_3 15 000 45 000 15 000 35 0 0.0 0.2 100 0.75 0.426 0.9

HS_4 30 000 90 000 40 000 35 0 0.0 0.2 100 0.75 0.426 0.9

HS_5 30 000 90 000 15 000 35 0 0.0 0.2 100 0.75 0.426 0.9

HS_6 50 000 150 000 30 000 35 0 0.0 0.2 100 0.75 0.426 0.9

Parameters for MC Model: E = 30 000 kN/m2; = 0.2; � = 35°; = 0° and 10°

PLAXIS

PLAXIS Comparison Mohr Coulomb –

Hardening Soil

In this comparison we consider the Mohr

Coulomb criterion and the parameter set 1 for

the Hardening Soil model for dilatant ( = 10°)

and non dilatant ( = 0°) behaviour. The p’-q-

diagramm (Fig. 1) firstly shows that the

effective stress path observed in a typical

undrained triaxial test is only obtained for the

Hardening Soil model because the Mohr

Coulomb model remains in the elastic range

and thus no change in effective mean normal

stress takes place. The well known fact that

dilatant behaviour leads to an increase of

strength in the undrained case is reproduced

by both models in a similar way. It is important

to point out that although the effective

strength parameters are the same for both

models the undrained shear strength is

different due to different effective stress paths

produced by both models, the Hardening Soil

model giving an almost 15% lower value (see

also Fig. 2). The pore pressure vs vertical strain

diagram in Fig. 3 shows the expected increase

of excess pore water pressure followed by a

rapid decrease for the dilatant material

behaviour. It is worth noting that in the case

of the Mohr Coulomb model there is a sharp

transition when the excess pore water pressure

starts to decrease (at the point where the

failure envelope is reached) whereas for the

Hardening Soil model this transition is smooth.

The pore pressure parameter A (Fig. 4) is 1/3

for the non dilatant Mohr Coulomb model (this

is the theoretical value for elastic behaviour)

and is independent of the loading stage and

thus the vertical strain. For the Hardening Soil

model A is not a constant but increases with

deviatoric loading to a final value of approx.

0.44 for this particular parameter set. Of course

the parameter A tends to become negative for

dilatant behaviour.

Hardening Soil – Influence of E50ref and

Eoedref

The reference parameter set is HS_1 of Table

1. Based on this, the reference values of E50

and Eoed have been varied (HS_2 to HS_6). Only

non dilatant material behaviour is considered.

Fig. 5 shows effective stress paths in the p’-q-

space and it is interesting to see that for E50

= Eoed the stress path is the same for all values

of E50 leading to the same undrained shear

strength although the vertical strain (and thus

the shear strain) at failure is different (Fig. 6).

If E50 is different from Eoed, different stress

paths and hence different undrained shear

7

Fig. 1 Stress path in

p’-q-space / MC – HS model

Fig. 2q-�1 - diagram /MC – HS model

Fig. 3 �u-�1 - diagram /

MC – HS model

Fig. 4A-�1 - diagram /MC – HS model

par

amet

er A

exce

ss p

ore

pre

ssu

re [k

N/m

2 ]q

[kN

/m2 ]

q [k

N/m

2 ]

PLAXIS

PLAXIS strengths are predicted. The difference

between HS_4 and HS_5 is more than 30%

which is entirely related to the difference in

Eoed. This is perhaps not so suprising because

Eoed controls much of the volumetric

behaviour which in turn is very important for

the undrained behaviour. However one has to

be aware of the consequences when using

these parameters in boundary value problems.

In Fig. 6 deviatoric stress is plotted against

vertical strain and – unlike in a drained test

where Eoed has only a minor influence on the

q-�1-curve – both parameters have a strong

influence on the results. E50 governs, as

expected, the behaviour at lower deviatoric

stresses but when failure is approached the

influence of Eoed becomes more pronounced.

A very similar picture is obtained when excess

pore pressures are plotted against vertical

strain (Fig. 7). In Fig. 8 the pore pressure

parameter A is plotted against vertical strain

and it follows that for Eoed > E50 (parameter

set HS_4) the pore pressure parameter A is

approx. 0.34, i.e. close to the value for elastic

behaviour. If Eoed < E50 (parameter sets HS_5

and HS_6) the parameter A increases rapidly

with loading, finally reaching a value of

approximately A = 0.6.

Summary

It has been shown that the pore pressure

parameters A and B obtained with PLAXIS from

undrained analysis of triaxial stress paths using

a Mohr Coulomb failure criterion are very close

to the theoretical values given by Skempton

(1954) for elastic material behaviour, i.e. B is

approx. 1.0 and A is 1/3. For more complex soil

behaviour as introduced by the Hardening Soil

model the parameter A is no longer a constant

value but changes with loading and is

dependent in particular on the value of Eoed in

relation to E50. For a given E50 the parameter

A at failure is higher for lower Eoed-values,

which in turn results in lower undrained shear

strength. Eoed < E50 is usually assumed for

normally consolidated clays experiencing high

volumetric strains under compression which

corresponds to a higher value for A in the

undrained case. It is therefore justified to say

that PLAXIS predicts the correct trend, care

however has to be taken when choosing Eoed,

because the influence of this parameter, which

may be difficult to determine accurately for in

situ conditions, is significant and may have a

strong influence on the results when solving

practical boundary value problems under

undrained conditions.

8

Fig. 5 Stress path in

p’-q-space /Hardening Soil

Fig. 6q-�1 - diagram /Hardening Soil

Fig. 7�u-�1 - diagram /

Hardening Soil

Fig. 8A-�1 - diagram /Hardening Soil

par

amet

er A

exce

ss p

ore

pre

ssu

re [k

N/m

2 ]q

[kN

/m2 ]

q [k

N/m

2 ]

PLAXIS

PLAXIS Reference

Skempton, A.W. (1954). The Pore-Pressure

Coefficients A and B. Geotechnique, 4, 143-

147.

H.F. Schweiger

Graz University of Technology

Benchmarking I

PLAXIS BENCHMARK NO.1: SHIELD TUNNEL

1 - RESULTS

Introduction

Unfortunately the response of the PLAXIS

community to the call for solutions for the

first PLAXIS benchmark example was not a

success at all. Probably the example

specified gave the impression of being so

straightforward that everybody would

obtain the same results and thus it would

not be worthwhile to take the time for this

exercise. However, I had distributed the

example on another occasion within a

different group of people dealing with

benchmarking in geotechnics. In the

following I will show the results of this

comparison together with the few PLAXIS

results I have got. As mentioned in the

specification of the problem no names of

authors or programs are given, so I will not

disclose which of the analyses have been

obtained with PLAXIS.

I hope, that the summary of the first

benchmark example provides sufficient

stimulation for taking part in the second call

for solutions for PLAXIS Benchmark No.2,

published in this bulletin, so that we can go

ahead with this section and as awareness for

necessity of validation procedures grow,

proceed to more complex examples. The

specification of Benchmark No.1 is not repeated

here; please refer to the Bulletin No.11.

Results Analysis A – elastic, no lining

Figure 1 shows calculated settlements of the

9

Fig. 1:Surface

settlements -analysis A

Fig. 2: Horizontal

displacements atsurface -analysis A

Fig. 3:Displacements of

slected points -analysis A

Fig. 4:Surface

settlements -analysis B

Fig. 5:Horizontal

displacements atsurface -analysis B

ho

rizo

nta

l dis

pla

cem

ents

[mm

]ve

rtic

al d

isp

lace

men

ts [m

m]

dis

pla

cem

ents

[mm

]h

ori

zon

tal d

isp

lace

men

ts [m

m]

vert

ical

dis

pla

cem

ents

[mm

]

PLAXIS

PLAXIS surface and it follows that even in the elastic

case some scatter in results is observed.

Some of the discrepancies are due to different

boundary conditions. ST5, for example,

restrained vertical and horizontal displacements

at the lateral boundary, others introduced an

elastic spring or a stress boundary condition.

The effect of the lateral boundary is not so

obvious from Figure 1 but becomes more

pronounced when Figure 2, showing the

horizontal displacement at the surface, is

examined. Figure 3 summarizes calculated

values at specific points, namely at the surface,

the crown, the invert and the side wall (for

exact location see specification). A maximum

difference of 10 mm (this is roughly 20%) in

the vertical displacement of point A (at the

surface) is observed and this is by no means

acceptable for an elastic analysis.

Results Analysis B – elastic-perfectly

plastic, no lining

Figures 4 and 5 show settlements and

horizontal displacements at the surface for the

plastic solution with constant undrained shear

strength. In Figure 4 a similar scatter as in

Figure 1 is observed with the exception of ST4,

ST9 and ST10 which show an even larger

deviation from the "mean" of all analyses

submitted. Again ST5 restrained vertical

displacements at the lateral boundary and thus

the settlement is zero here. ST9 used a von-

Mises and not a Tresca failure criterion which

accounts for the difference. The strong

influence of employing a von-Mises criterion

as follows from Figure 4 has been verified by

separate studies. It is emphasized therefore

that a careful choice of the failure criterion is

essential in a non-linear analysis even for a

simple problem as considered here. The

significant variation in predicted horizontal

displacements, mainly governed by the

placement of the lateral boundary condition,

is evident from Figure 5. Figure 6 compares

values for displacements at given points. Taking

the settlement at the surface above the tunnel

axis (point A) the minimum and maximum

value calculated is 76 mm and 159 mm

respectively. Thus differences are - as expected

- significantly larger than in the elastic case but

again not acceptable.

10

Fig. 6:Displacements of

selcted points -analysis B

Fig. 7:Surface

settlements -analysis C

Fig. 8:Horizontal

displacements atsurface analysis C

Fig. 9:Displacements of

selcted points -analysis C

Fig. 10:Normal forces andcontact pressure -

analysis C

no

rmal

fo

rces

[kN

]/co

nta

ct p

ress

ure

[kP

a]d

isp

lace

men

ts [m

m]

ho

rizo

nta

l dis

pla

cem

ents

[mm

]ve

rtic

al d

isp

lace

men

ts [m

m]

dis

pla

cem

ents

[mm

]

PLAXIS

PLAXIS Results Analysis C – elastic-perfectly

plastic, lining and volume loss

Figure 7 plots surface settlements for the

elastic-perfectly plastic analysis with a specified

volume loss of 2% and the wide scatter in

results is indeed not very encouraging. The

significant effect of the vertically and

horizontally restrained boundary condition

used in ST5 is apparent. However in the other

solutions no obvious cause for the differences

could be found except that the lateral

boundary has been placed at different

distances from the symmetry axes and that

the specified volume loss is modelled in

different ways. Figure 8 shows the horizontal

displacements at the surface and a similar

picture as in the previous analyses can be

found. Figure 9 depicts displacements at

selected points. The range of calculated values

for the surface settlement above the tunnel

axis is between 1 and 25 mm and for the

crown settlement between 17 and 45 mm

respectively. The normal forces in the lining

and the contact pressure between soil and

lining do not differ that much (variation is

within 15 and 20% respectively), with the

exception of ST9 who calculated significantly

lower values (Figure 10).

Results with lateral boundary at distance

of 100 m from tunnel axis

Due to the obvious influence of the lateral

boundary conditions a second round of analysis

has been performed asking all authors to redo

the analysis with a lateral boundary at 100 m

distance from the line of symmetry with the

horizontal displacements fixed. As follows from

Figures 11 and 12 which depicts these results

for case A, all results are now within a small

range and thus it has been confirmed that the

discrepancies described from the previous

chapter are entirely caused by the boundary

condition. In addition to finite element results

an analytical solution by Verruijt is included for

comparison. Vertical displacements are in very

good agreement and also horizontal

displacements are acceptable in the area of

interest (i.e. in the vicinity of the tunnel). For

case B similar results are obtained although

some small differences are still present. For case

C the comparison also matches much better

now but some differences remain here and this

is certainly due to the fact that the programs

involved handle the specified volume loss in a

different way.

Comparison undrained – drained

conditions

In order to show that the influence of the

lateral boundary is especially important under

undrained conditions (constant volume) an

11

Fig. 11:Surface

settlementsanalysis A / lateralboundary at 100 m

Fig. 12:Horizontal

displacements atsurface analysis A/ lateral boundary

at 100 m

Fig. 13:Surface

settlementsanalysis A /undrained -

drained

Fig. 14:Horizontal

displacements atsurface analysis A

/ undrained -drained

ho

rizo

nta

l dis

pla

cem

ents

[mm

]ve

rtic

al d

isp

lace

men

ts [m

m]

ho

rizo

nta

l dis

pla

cem

ents

[mm

]ve

rtic

al d

isp

lace

men

ts [m

m]

PLAXIS

PLAXIS

Fig. 1:Geometric data

benchmark excavation

Table 1. Parameters for

sheet pile wall and strut

analysis has been performed for case A with

exactly the same parameters except for

Poisson's ratio, chosen now to correspond to

a drained situation, i.e. deformation under

constant volume is no longer enforced (for

simplicity the difference of Young's module

between drained and undrained conditions has

been neglected). It follows from Figure 13 that

for the drained case the surface settlements

are virtually independent of the distance of the

lateral boundary (results for mesh widths of

50 m and 100 m are shown respectively). The

horizontal displacements (Figure 14) show

some differences of course but in the area of

interest they are negligible in the drained case.

Summary

The outcome of this benchmark example

clearly emphasizes the necessity of performing

these types of exercises in order to improve

the validity of numerical models. Given the

discrepancies in results obtained for this very

simple example much more scatter can be

expected for real boundary value problems.

One of the lessons learned from this example

is that the influence of the boundary

conditions can be much more severe in an

undrained analysis than in a drained one and

whenever possible a careful check should be

made whether or not the placement of the

boundary conditions affects the results one is

interested in. One may argue that this is a trivial

statement, practice however shows that due

to time constraints in projects it is not always

feasible to check the influence of all the

modelling assumptions involved in a numerical

analysis of a boundary value problem. It is one

of the goals of this section to point out

potential pitfalls in certain types of problems

which may not be obvious even to experienced

users and to promote the development of

guidelines for the use of numerical modelling

in geotechnical practice.

Helmut F. Schweiger, Graz University of

Technology

Benchmarking II

PLAXIS BENCHMARK NO. 2: EXCAVATION 1

The second benchmark is an excavation in

front of a sheet pile wall supported by a

strut. Geometry, excavation steps and

location of the water table are given in

Figure 1. Fully drained conditions are

postulated. The soil is assumed to be a

homogeneous layer of medium dense sand

and the parameters for the Hardening Soil

model, the sheet pile wall and the strut are

given in Tables 1 and 2 respectively.

The following computational steps have to be

performed in a plane strain analysis:

- initial phase (K0 = 0.426)

- activation of sheet pile, excavation step 1

to level – 2.0 m

12

�dry �wet E50ref Eur

ref Eoedref � c ur pref m K0

nc Rf Rinter T-Strength

kN/m3 kN/m3 kPa kPa kPa ° ° kPa - kPa - - - - kPa

19.0 20.0 45 000 180 000 45 000 35 5 1.0 0.2 100 0.55 0.426 0.9 0.7 0.0

Table 2. Parameters for HS-model

EA EI W V

kN/m kN2/m kN/m/m -

Sheet pile wall 2.52E6 8064 0.655 0.0

Strut 1.5E6

PLAXIS

PLAXIS

13

- activation of strut at level –1.50 m,

excavation step 2 to level – 4.0 m,

- groundwater lowering inside excavation to

level – 6.0 m

- excavation step 3 to level – 6.0 m

- phi-c-reduction

REQUIRED RESULTS

1. bending moments and lateral deflections of

sheet pile wall (including values given in a

table)

2. surface settlements behind wall (including

values given in a table)

3. strut force

4. factor of safety obtained from phi-c-

reduction for the final excavation step

Note: As far as possible results should be

provided not only in print but also on disk

(preferably EXCEL) or in ASCII-format respectively.

Alternatively, the entire PLAXIS-project may be

provided. Results may also be submitted via e-

mail to the address given below.

Results should be sent no later than

August 1st, 2002 to:

Prof. H.F. Schweiger

Institute for Soil Mechanics and Foundation

Engineering

Computational Geotechnics Group

Graz University of Technology

Rechbauerstr. 12, A-8010 Graz

Tel.: +43 (0)316 – 873-6234

Fax: +43 (0)316 – 873-6232

E-mail: schweiger@ibg.tu-graz.ac.at

http://www.tu-graz.ac.at/geotechnical_group/

Recent Activities

NEW DIRECTOR OF PLAXIS B.V.

We are pleased to introduce the new

director of PLAXIS BV, Dr. Klaas Jan Bakker.

Dr. Bakker who started the first of February

takes over the chair of Mr. Hutteman, who

temporary occupied the chair on behalf of

MOS Grondmechanica BV.

Since the very beginning Dr. Bakker has been

actively involved in the program(ming) of

PLAXIS and is a key figure in the PLAXIS

network. In his last position he was Head of

Construction and Development at the Tunnel-

engineering department for the Dutch Ministry

of Public Works. Furthermore he is a lecturer

at Delft University of Technology.

COURSES

In 2001 over 400 people attended one of

the 13 Plaxis courses that were held in

several parts of the world. Most of these

courses are held on a regular basis, while

others take place on an single basis.

Regular courses:

Traditionally, we start the year with the standard

International course “Computational

Geotechnics” that takes place during the 3rd

week of January in the Netherlands. The

Experienced users course in the Netherlands

is traditionally organised during the 4th week

of March each year. Besides these standard

courses in the Netherlands, some other regular

courses are held in Germany (March), England

(April), France (Autumn), Singapore (Autumn),

Egypt, and the USA. For the USA the course

schedule is a bit different, as we plan to have

an Experienced users course per two years and

two standard courses in the intermediate

periods. In May, 2002, we had the Experienced

users course in Boston, which was organised

in cooperation with the Massachusetts Institute

of Technology (MIT). For January 2003, a

standard course is scheduled in Berkeley in

PLAXIS

PLAXIS cooperation with the University of California.

For August, 2003, another standard course is

organised in Boulder in cooperation with the

University of Colorado. It is our intention to

repeat this scheme of courses for the Western

hemisphere. For the Asian region, we have

planned a similar schedule that also includes

an experienced users course once every two

years.

Other courses:

Besides the above regular courses, other

courses are organised in different parts of the

world. In the past year, courses were held in

Mexico, Vietnam, Turkey, Malaysia, etc. On the

last page of this bulletin, you can see the

agenda, which lists all scheduled courses and

some other events. Our web-site www.plaxis.nl

on the other hand will always give you the

most up-to-date information.

PLAXIS Practice I

1. Introduction

In Würenlingen (Switzerland), for the

temporary storage of nuclear waste, an

extension of the existing depository was

required. To facilitate this, a 7.5 - 9.0 m deep

excavation was necessary. This bordered

immediately adjacent pre-existing

structures. Furthermore, along one of it‘s

sides there is a route used for the

transportation of nuclear waste.

2. Project

Length of excavation: 98 m

Width of excavation: 33 m

Maximum depth: 9 m

Start of works: Spring 2001

End of construction: Summer 2001

3. Geotechnical conditions

In the Würenlingen area, significant deposits

of the Aare River dominate, which comprises

predominantly gravels and sands. The

groundwater table lies at a depth of ca. 9.5 m

below the surface prior to excavation. The

gravels and sands are known as good

foundation material, with some low apparent

cohesion, allowing for the temporary

construction of vertical cuttings of low height.

4. Construction procedure

Due to space restrictions, a sloped earthworks

profile is not possible. Therefore, it was

concluded to undertake the excavation using

14

Model Behavior �unsat �sat E50ref Eoed

ref m Eurref ur c � Rinter

- kN/m3 kN/m3 kPa kPa - KPa - kPa ° ° -

HS Drained 22.0 22.0 33 000 37 500 0.5 99 000 0.25 1.0 32 6 1.0

Table 1. Soil parameters

Photo 1: Participants in theExperienced users

course, March 2002, theNetherlands.

Photo 2: Plaxis short course,

October 2001, Mexico

Photo 3: Plaxis short course,

November 2001,Vietnam.

PLAXIS

PLAXIS a soil nailing option. Correspondingly, the

excavation had to proceed in benched stages.

Each bench had a height of 1.30 m and a width

of 4.5 to 6.0 m. The free face was immediately

covered with an 18 cm thick layer of shotcrete

and tied back with untensioned soil nails.

The bond strength of the soil nails was

established by pullout tests. Usually the soil

nails are cemented along their full length. For

the pullout tests, however, the bond length

was reduced to between 3.0 and 4.0 m with a

total length of 7.0 m. The individual nails have

a cross-sectional area of 25 mm and yield

strength of 246 kN. During the pullout tests,

it was possible to tension the nails to yield point

without any indication of creep or failure.

In total five benches were necessary to reach

excavation depth. The wall itself is vertical, with

nail spacing of 1.5 m and 1.3 m, horizontal and

vertical respectively. The nails were tightened

three days after installation with a torque key,

to secure a fast seat to the shotcrete. A pre-

tensioning with fully cemented nails is not

sensible (see fig. 1).

5. Calculations

The initial calculations were performed with

the usual statical programs based on beam

theory and limiting equilibrium loading. Due

to the particular safety requirements in

connection with nuclear transport additional

deformation predictions were made. These

calculations were carried out with Plaxis version

7. Geotextile elements were used to model the

nails. Due to the good bonding of the soil nails

proven by the pullout attempts, no reduction

was made for loading transfer along the

geotextile elements.

The calculations were performed with the

following parameters:

� Hardening soil model

� Plane strain with 6 node elements

� 649 elements

� Due to the simple geology, only one soil layer

was used (see table 1)

� Due to good bonding between soil and

shotcrete wall no reduction in interface

friction was made.

� The calculations were performed without

groundwater.

� Shotcrete wall of 18 cm thickness with

reinforced wire mesh, modeled as beam

elements. EA = 5.4 x 106 kN/m, EI =

1.458 x 104 kNm2/m and = 0.2

� Soil nails are modeled as geotextile elements.

EA = 6.87 x 104 kN/m and = 0.

� Results

Final excavation stage

Maximum deformation of shotcrete wall;

17 mm (see fig. 2a and fig. 3).

Maximum horizontal deformation of

shotcrete wall; 14 mm (see fig. 2d).

Maximum force in geotextile element; 49

kN/m, or 73.5 kN per nail (see fig. 4).

Maximum bending moment in shotcrete

wall; 11.5 kNm/m (see fig. 2b).

Maximum axial force in shotcrete wall; -67

kN/m (see fig. 2c).

It must be noted, that the tensile forces in the

geotextile elements at the final excavation

stage did not calculate to zero at the toe of

the nail, as should be in reality. This could be

due to a too wide FE-net around the geotextile

elements, additionally due to the use of only

6-nodes instead of the more precise 15-node

element.

6. Measurement on site

In total, deformation of the excavation was

taken at five stations. Prior to excavation

clinometers were placed ca. 1.0 m behind the

proposed shotcrete wall, with a depth of 7 m

below excavation level. Figure 7 shows the

measured horizontal deformations of two

cross-sections with equal depths (7.2 and 9.0

mm). Figure 6 contains the calculated

horizontal deformations along a vertical line

15

Fig. 1: Typical sectionwith horizontaldisplacements

PLAXIS

PLAXIS 1m behind the shotcrete wall (14.9 mm). A

comparison shows that the calculated

deformations are greater than the measured.

Conspicuous is, that below the excavation base

there is practically no movement measurable.

Plaxis, however, has predicted some 4 mm

deformation. This may be due to an initial

offset or due to stiffer behavior at the bottom

of the excavation.

The maximum measured horizontal

deformation was between 7.2 and 9.0 mm at

the wall head. Plaxis calculated 14.9 mm

horizontal deformation at this point.

If only relative measurements are considered,

assuming that no movement takes place at the

wall toe, then the prediction from Plaxis lays

very close to the actual maximum measured.

The forms of the measured and calculated

deformation curves correspondwell well with

each other.

7. Conclusions

The calculated deformation of the nailed wall

corresponds well with the measured values,

especially if the predicted deformations of

Plaxis below excavation level are not

considered.

The soil parameters used correspond to

conservative average values, evaluated from a

large number of previous sites under similar

conditions. It is plausible that the deformation

parameters are underestimated.

The Plaxis calculation illustrates

comprehensively, that the soil nailing system

(soil-nail-wall) works as an interactive system. It

shows further, that the maximum nail force

does not necessarily act at the nail head, but

according to the distribution of soil movements

may also lie far behind the head of the nail. This

means that displacements are necessarily taking

place before the nail force is activated.

On the one hand, it shows that the shotcrete

wall in vertical alignment is stressed by bending

and compression, and that the wall’s foot

transmits compressive stresses to the soil. On

the other hand, the shotcrete wall in horizontal

alignment is only loaded by bending, whereby

in the absence of lateral restrictions of

deformation there could also be tension. Finally

it is clear to see, that nail head support and

pullout failure should be considered (see fig. 4).

16

Fig. 2:Output in

shotcrete wall

Fig. 3: Deformation of

geotextile

Fig. 4: Axial Forces in

geotextile

Fig. 5:Measured

displacements

Fig. 6:Calculated

displacement

Thanks to prior deformation calculation with

Plaxis and measurement control by clinometer

installation during the construction stage, the

safety of the works in relation to nuclear

transportation could be assessed at all times.

H.J. Gysi, G.Morri, Gysi Leoni Mader AG,

Zürich - Switzerland

� Calculation procedure

Phase 1: Initial stresses, using Mweight = 1.

Phase 2: Live load (5 kN/m2 and 10 kN/m2)

Phase 3: Excavation to top level of

wall (-0.80 m).

Phase 4: First excavation stage,

including shotcrete of wall

and installation of first row

of soil nails (-2.10 m).

Phase 5: Second excavation stage with

shotcrete wall (-3.40 m).

Phase 6: Installation of second row

of soil nails.

Phase 7: Third excavation stage

with shotcrete wall (-4.70 m).

Phase 8: Installation of third row of soil nails.

Phase 9: Fourth excavation stage

with shotcrete wall (-6.00 m).

Phase 10: Installation of fourth row

of soil nails.

Phase 11: Fifth excavation stage

with shotcrete wall (-7.30 m).

Phase 12: Installation of fifth row of soil nails.

PLAXIS Practice II

FINITE ELEMENT MODELLING OF A DEEP

EXCAVATION SUPPORTED BY JACK-IN

ANCHORS

1. INTRODUCTION

A mixed development project that is located

at UEP Subang Jaya, Malaysia consists of three

condominium towers of 33 storeys and a single

20-storey office tower. Due to the huge

demand for parking space, an approximately

three storey deep vehicular parking basement

was required. The deep excavation, through a

filled layer of very loose silty sand and very soft

peaty clay varies from 11m to 13m. Due to the

presence of very soft soil condition and the

fast track requirement of the project,

Contiguous Bored Pile (CBP) walls supported

by soil nails were used to support the

excavation process. This hybrid technique was

envisaged and implemented due to its speed

in construction and the ability of the Jack-in

Anchors1) in supporting excavations in

collapsible soils, high water table and in soft

soils conditions (Cheang et al., 1999 & 2000,

Liew et al, 2000). The use of soil nailing in

excavations and slope stabilisation has gained

wide acceptance in Southeast Asia, specifically

in Malaysia and Singapore due to its

effectiveness and huge economic savings.

Adopting the observational method, numerical

analyses using ‘PLAXIS version 7.11’ a finite

element code were conducted to study the

soil-structure interaction of this relatively new

retaining system. Numerical predictions were

compared with instrumented field readings and

deformation parameters were back analysed

and were used in subsequent prediction of wall

movements in the following excavation stages.

2. SUBSURFACE GEOLOGY

The general subsurface soil profile of the site,

shown in Table 1 consists in the order of

succession of loose clayey SILT, loose to

medium dense Sand followed by firm to hard

clayey SILT. The residual soils (Figure 1) are inter-

layered by 9m thick soft dark peaty CLAY. For

analysis purposes the layers were simplified

PLAXIS

PLAXIS

17

Photo 1: Jack-in Anchor Technique

1) Jack-in Anchor Technique™ is a patentedproduct by Specialist Grouting EngineersSdn. Bhd. Malaysia

PLAXIS

PLAXIS into representative granular non-cohesive and

cohesive material, such as:

3. THE RETAINING SYSTEM

In view of the close proximity of commercial

buildings to the deep excavation, a very stiff

retaining system is required to ensure minimal

ground movements the retained side of the

excavation. Contiguous Bored Pile that acts as

an earth retaining wall during the excavation

works were installed along the perimeter of

the excavation and supported by jack-in

anchors. The retaining wall system consist of

closely spaced 1000mm diameter contiguous

bored piles supported by hollow pipes which

functions as soil nails are installed by hydraulic

jacking using the Jacked-in Soil Anchor

Technology™ as shown in photo 3. Figure 2

illustrates the soil nail supported bored pile wall

system.

18

Photo 2: The Retaining System:Contiguous Bored Pile

Wall Supported by Jack-in Anchors that function

as Soil Nails

Photo 3: Hydraulic Jacking Fig. 2b:

The Retaining System

Fig. 1:Typical Subsurface Profile

Fig. 2a:The Retaining System

DEPTH (m) DESCRIPTION SPT ‘N’ VALUE

LAYER 1 0 to 9 Clayey SILT <12

LAYER 2 9 to 18 Soft Dark Silty CLAY 0

LAYER 3 18 to 27 Medium Dense SAND >18

LAYER 4 27 to 35 Dense SILT >50

Table 1. Soil Layers

PLAXIS

PLAXIS This method has proven to be an efficient and

effective technique for excavation support,

where conventional soil nails and ground

anchors have little success in such difficult soft

soil conditions. Such conditions are sandy

collapsible soil, high water table and in very

soft clayey soils where there is a lack of short-

term pullout resistance.

Relatively, larger movements are required to

mobilise the tensile and passive resistance of

the jacked-in pipes when compared to ground

anchors. However it was anticipated that the

ground settlement at the retained side and

maximum lateral displacement of the wall

using this system would still be within the

required tolerance after engineering

assessment.

4. GEOTECHNICAL INSTRUMENTATION

In view of this relatively new excavation

support technique used for in-situ soft soil

conditions and the close proximity of the

commercial buildings to the deep excavation,

a performance monitoring program was

provided. Firstly, as a safety control. Second,

to refine the numerical analysis using field

measurements obtained at the early stages of

construction and third, to provide an insight

into the possible working mechanisms of the

system.

The geotechnical instrumentation program

consists of 18 vertical inclinometer tubes

located strategically along the perimeter

within the Contiguous Bored Pile wall and 30

optical survey makers (surface settlement

points) near the vicinity of the commercial

buildings. The locations of these instruments

are detailed in Fig. 4 for the inclinometers.

Fig. 5 illustrates the restrained trend of

horizontal displacement of the wall as

measured through inclinometers installed at

the site

5. FINITE ELEMENT MODELLING

EQUIVALENT PLATE MODEL

Equivalence relationships have to be developed

between the 3D structure and 2D numerical

model. Non 2-D member such as soil nails must

be represented with ‘equivalent’ properties that

reflect the spacing between such elements.

Donovan et al. (1984) suggested that properties

of the discrete elements could be distributed

over the distance between the elements in a

19

Fig. 4:GeotechnicalInstruments

Fig. 5:Measures deflection

profile

PLAXIS

PLAXIS uniformly spaced pattern by linear scaling.

Unterreiner et al. (1997) adopted an approach

similar to Al-Hussaini and Johnson (1978) where

an equivalent plate model replaces the discrete

soil-nail elements by a plate extended to full

width and breadth of the retaining wall. Nagao

and Kitamura (1988) converted the properties

of the 3-D discrete elements into an equivalent

composite plate model by taking into account

the properties of the adjacent soil. The two-

dimensional finite element analysis performed

hereafter uses the ‘composite plate model’

approach.

Finite Element Analysis

The finite element analyses were performed

using ‘PLAXIS’ (Brinkgreve and Vermeer, 1998).

The Contiguous Bored Pile wall and steel tubes

were modelled using a linear-elastic Mindlin

plate model (Figure 6). The nails were ‘pinned’

to the CBP wall. The soil-nail soil interface was

modelled using the elastic-perfectly-plastic

model where the Coulomb criterion

distinguishes between the small displacement

elastic behaviour and ‘slipping’ plastic behaviour.

The surrounding soils were modelled using the

Mohr-Coulomb soil model. Table 2 and 3 shows

the properties used for the analyses.

6. COMPARISON OF FIELD INSTRUMENTED

AND PREDICTED DISPLACEMENT READINGS

Measured And Predicted Lateral Deflection

Figure 7 compares the in-situ, predicted and

back analysed lateral deflection of the soil nail

supported wall. The measured lateral deflection

is showing a trend of restrained cantilever and

the jack-in anchors are restraining the

horizontal displacement of the wall. Initial finite

element prediction (Prediction No.1) based on

soil strengths correlated from laboratory

20

Table 2: Soil Properties

Layer 1 Layer 2 Layer 3 Layer 4

E (kN/m2) 34000 9000 30000 200000

�soil (kN/m3) 19 20 20 19

0.25 0.25 0.25 0.25

� 25 0 35 30

C 2 12 2 2

0 0 0 0

Table 3: Nail and Contiguous Bored Pile Wall Properties

ENAIL 2.90E+06 kN/m2

ECONC. 2.00E+07 kN/m2

Figure 7: Lateral Deflection of Soil Nailed

Contiguous Bored Pile Wall

Figure 8: Lateral Deflection of ‘Stiff’ and ‘Flexible’

Soil Nail System

Fig 6: 2-Dimensional finite element mode

PLAXIS

PLAXIS results. Excavation involves mainly the

unloading of adjacent soil, the ground stiffness

is dependent on stress level and wall

movements. These aspects were taken into

account in prediction no.2, the trend is similar

and a better prediction was obtained.

Subsequent finite element runs were made

base on the improved parameters.

7. SOIL-NAIL-SOIL-STRUCTURE

INTERACTION

Lateral Bending Stiffness of Soil Nails

A flexible nail system with a bending stiffness

of 1/220 of the stiff nail system was numerically

simulated. It was hypothesised that if bending

stiffness of the inclusions were insignificant in

the performance of the nail system, there

would be no difference in the lateral

displacement of the wall. However figure 8

shows that bending stiffness is significant, at

least in a soil nail supported embedded wall.

With a stiff nail system, the lateral displacement

was significantly reduced. Figure 9 illustrates

that the influence increases as excavation

proceeds further, this is due to the fact that

larger movements are required to mobilised

lateral bending resistance of the nails.

8. CONCLUSION

The soil-nail-soil-structure interaction of a nailed

wall is complex in nature. Soil nails are subjected

to tension, shear forces and bending moments.

The outcome of this numerical investigation of

a real soil-nailed supported Contiguous Bored

Pile wall in soft residual soils is that nail bending

stiffness has a significant effect as deformation

progresses, at least in this hybrid support

system. Soil-nail lateral resistance is dependent

not only on the relative stiffness and yield

strengths of the soil and nail, but also on the

local lateral displacement across the shear zone.

Due to the hybrid nature of this system, the

results indicated that the relative stiffness of

the nail and wall too governs the development

of bending i.e., lateral resistance of the soil nail.

In soft soils, numerical results indicated greater

bending moments in the nails due to larger wall

deflection. The implication of this study is

additional analysis of different working

mechanisms in various soil types should be

envisaged.

9. REFERENCE

1. Al-Hussaini, M.M., Johnson, L., (1978),

Numerical Analysis of Reinforced Earth Wall,

Proc. Symp. On Earth Reinforcement ASCE

Annual Convention, p.p. 98-126.

2. Brinkgreve, R.B.J., Vermeer, P.A., (1998),

Plaxis- Finite Element Code for Soil and Rock

Analyses- Version 7.11,A.A.Balkema.

3. Cheang, W.L., Tan, S.A., Yong, K.Y., Gue, S.S,,

Aw, H.C., Yu, H.T., Liew, Y.L., (1999), Soil Nailing

of a Deep Excavation in Soft Soil,

Proceedings of the 5Th International

Symposium on Field Measurement in

Geomechanics, Singapore, Balkema.

4. Cheang, W.L., Luo, S.Q., Tan, S.A., Yong, Y.K.,

(2000), Lateral Bending of Soil Nails in an

Excavation, International Conference on

Geotechnical & Geological Engineering,

Australia. ( To be Published)

5. Donovan, K., Pariseau, W.G., and Cepak,

M.,(1984), Finite Element Approach to Cable

Bolting in Steeply Dipping VCR Slopes,

Geomechanics Application in Underground

Hardrock Mining, pp.65-90.New York: Society

of Mining Engineers.

6. Liew, S.S., Tan, Y.C., Chen, C.S., (2000), Design,

Installation and Performance of Jack-In-Pipe

Anchorage System For Temporary Retaining

Structures, International Conference on

Geotechnical & Geological Engineering,

Austraila. ( To be Published)

7. Nagao, A., Kitamura, T., (1988), Filed

Experiment on Reinforced Earth and its

Evaluation Using FEM Analysis, International

21

Figure 9: Influence ofNail Stiffness

PLAXIS

PLAXIS Symposium on Theory and Practice of Earth

Reinforcement, Japan, pp.329-334.

8. Unterreiner, P., Benhamida, B., Schlosser, F.,

(1997), Finite Element Modelling Of The

Construction Of A Full-Scale Experimental Soil-

Nailed Wall. French National Research Project

CLOUTERRE, Ground Improvement, p.p. 1-8.

W.L.Cheang, Research Scholar,

E-mail: engp9168@nus.edu.sg,

S.A.Tan, Associate Professor,

E-mail: cvetansa@nus.edu.sg,

K.Y.Yong, Professor, Department of Civil

Engineering, National University of

Singapore

Users Forum

BEAM TO PILE PROPERTIES

IN PLAXIS

Properties for anchors are entered per anchor

so : EA = [kN] per anchor

Ls = [m] is spacing centre to centre

Beams and geotextiles are continuous in the

z-direction (perpendicular to the screen).

Therefore, a beam /geotextile will be a

continuous plate/textile in the z-direction. The

properties are entered per meter

in the z-direction EA = [kN/m], EL = [kN/m2/m]

Modelling a row of piles or a row of grout

bodies in the z-direction can be done by

dividing the EAreal and ELreal by

the centre-to-centre distance Ls.

For a beam:

EAreal=Ereal*dreal*breal [kN]

EAplaxis= EAreal/Ls [kN/m]

For a grout body:

EAreal=Ereal*dreal*breal [kN]

EAplaxis= EAreal/Ls [kN/m]

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Fig 1. Partial geometryfor shieldtunnel

project

Some geometries

In the past bulletins, a few articles were related

to experience with the 3D Tunnel program.

Since it’s release last year, the 3D Tunnel

program has been used in practice for some

interesting projects. In the below graphs,

without further explanation you will find a brief

overview of possible projects and geometries.

The printed figures also indicate that the 3D

Tunnel program can deal with projects beyond

tunneling.

PLAXIS

PLAXIS

Fig 4. Partial geometry for anchored retaining wall.

Fig 5. Deformed mesh for interacting tunnels.

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Fig 2. Partialgeometry for pile-

raft foundation

Fig 3.Displacement

contours for shieldtunnel project

PLAXIS

PLAXIS ACTIVITIES

8-10 MAY, 2002

International course for experienced Plaxis users

(English)

Boston, USA

16 MAY, 2002

2nd French Plaxis Users meeting (French)

Paris, France

14-18 OCTOBER, 2002

Short course on Computational Geotechnics

(Arabic, English)

Cairo, Egypt

25-26 OCTOBER, 2002

Short course on Computational Geotechnics

(Portuguese, English)

Sao Paulo, Brazil

7-8 NOVEMBER, 2002

11th European Plaxis Users meeting (English)

Karlsruhe, Germany

18-20 NOVEMBER, 2002

Short course on Computational Geotechnics

(English)

Trondheim, Norway

27-29 NOVEMBER, 2002

Short course on Computational Geotechnics

(French)

‘Pratique des éléments finis en Géotechnique’

Paris, France

6-9 JANUARY, 2003

Short course on Computational Geotechnics &

dynamics (English)

Berkeley, USA

19-22 JANUARY, 2003

Short course on Computational Geotechnics

(English)

Noordwijkerhout, The Netherlands

10-12 MARCH, 2003

Short course on Computational Geotechnics

(German)

Stuttgart, Germany

23-26 MARCH, 2003

International course for experienced Plaxis users

(English)

Noordwijkerhout, The Netherlands

8-10 APRIL, 2003

Short course on Computational Geotechnics

(English)

Manchester, England

28-30 APRIL, 2003

Short course on Computational Geotechnics

(Italian)

Napoli, Italy

31 JULY–2 AUGUST, 2003

Experienced Plaxis users course (English)

Singapore

For more information on these activities

please contact:

PLAXIS bv

P.O. Box 572

2600 AN DELFT

The Netherlands

Tel: +31 15 26 00 450

Fax: +31 15 26 00 451

E-mail: info@plaxis.nl

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