Plaxis finite element code for soil and rock analyses

Modeling passive earth pressures on bridge abutments for nonlinear Seismic Soil - Structure interaction using Plaxis

Prediction of soil deformations during excavation works for the renovation of

“Het Nieuwe Rijksmuseum” in Amsterdam, The Netherlands

Comparison of the effectiveness of Deep Soil Mix columns

using 2-D and 3-D Plaxis

issue 20 / October 2006Plaxis Bulletin

�

the Plaxis Bulletin is the combined magazine of Plaxis B.V. and the Plaxis Users

association (nl). the Bulletin focuses on the use of the finite element method in geotech-

nical engineering practise and includes articles on the practical application of the Plaxis

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Editorial Board:

Wout BroereRonald BrinkgreveErwin BeerninkFrançois Mathijssen

Colophon

Editorial

New Developments

Plaxis BenchmarkResults from the ERTC7

benchmark exercise

Plaxis PracticeModeling passive earth

pressures on bridge abutments for nonlinear Seismic Soil - Structure interaction using Plaxis

Plaxis PracticePrediction of soil deformations

during excavation works for the renovation of “Het Nieuwe Rijksmuseum” in Amsterdam,

The Netherlands

Plaxis PracticeComparison of the

effectiveness of Deep Soil Mix colomns using 2-D

and 3-D Plaxis

Recent activities

Activities 2006-2007

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4

5

8

16

20

23

24

3

in the first paper anoosh shamsabadi and steinar nordal focus on the development of

stiffness degradation due to earthquakes for the earth pressure behind bridge abutments.

this problem has recently been studied at several universities and research institutes

in the Usa. Back calculations of the test results using Plaxis 3-d tunnel and 3-d

foundations show that Plaxis is an extremely valuable tool for the practicing bridge

engineer for capturing realistic nonlinear soil-abutment-structure interaction curves.

the second contribution by H.d. netzel and d. Vink of crux engineering discusses the

geotechnical design calculations used in the recent renovation of the world famous

rijksmuseum in amsterdam. Plaxis was used on this project. the calculations are part

of the risk assessment strategy for predicting the influence of ground deformation due to

excavation close to buildings.

in the third paper Hester leung, cristien Gani, Wataru okada and sergei terzaghi of skm

auckland and skm sydney compare the behaviour of deep soil mixing columns predicted

by Plaxis �-d and 3-d programs. these columns are one of the remedial solutions for slip

repair works on state highways in the northland region of new Zealand. slope failure is

quite common in this region due to heavy rainfall, particularly in winter months. �-d and

3-d Plaxis were used as concerns were raised about the suitability of only two rows of

columns in the design.

this last paper shows the growing importance of 3d modelling. in recent years we

have done a great deal of development work in this area. We are currently working on a

general 3d finite element program in which different types of geotechnical applications with

arbitrary geometries will eventually be combined.

We hope that you will find this �0th edition instructive and enjoyable.

Editorial

“after some challenging activities during the past summer period including a

number launches and user meetings we can proudly conclude that Plaxis Practice

is still increasing world-wide. a spin-off of some of these activities can be found

in this 20th issue of the Plaxis bulletin. This comprehensive issue contains very

interesting papers by users about the contribution of Plaxis programs to everyday

soil and rock anaylses.”

�

New Developments

Ronald Brinkgreve, Plaxis BV

New Developments

in recent years much development work has been spend on 3d modelling. in addition to

3d tunnel, which was the first 3d program developed by Plaxis, most 3d developments by

now have been performed in the foundation program. and there is more to come. Plaxis

is working on a general 3d finite element program in which, eventually, different types of

geotechnical applications with arbitrary geometries can be combined, while maintaining

the familiar ‘easy-to-use’ modelling concepts. However, it will take some time before a

first release of this general 3d program becomes available. meanwhile, developments in

the 3d foundation program also continued and will make the program more versatile. the

upcoming Version � will not only aim at the modelling of foundations (including multiple

piles), but also more at excavations and slopes, although the name ‘3d foundation’ is

retained. in this contribution i will reveal some of its new features.

in Bulletin 17 i already mentioned the embedded pile option based on the embedded

beam concept [ata.1998]. although originally planned for last year’s release of 3d

foundation, we decided that this new technology would require more testing and

validation, and therefore intermediate versions 1.5 and 1.6 were released without embedded

piles. nevertheless, a first implementation was ready then for research and testing

purposes. meanwhile, an extensive testing and validation programme is being carried

out in cooperation with our network of contacts at universities and research institutes.

main focus of the embedded pile option is on axially loaded bored piles in compression

and piles in extension. it is particularly useful for the optimisation of piled-raft founda-

tions where the interplay between the raft, the piles and the soil is essential to make an

economic design. in addition, we will also evaluate the possibilities for laterally loaded

piles, although the embedded beam concept is not primarily meant for this type of

applications. it is also not very suitable for displacement piles or driven piles, since it

does not take into account the increase in lateral stress and the effects of densification

in the soil around the pile. nevertheless, the embedded pile option provides a valuable

extension to the foundation program.

the embedded beam concept has also been combined with node-to-node anchors to

model ground anchors in which the embedded beam acts as the grout body whereas

the node-to-node anchor acts as the anchor rod. Ground anchors can be placed on work

planes (at walls, beams or other structures) and can go arbitrarily into the ground. the

anchor bearing capacity must be specified by the user in terms of a maximum friction

force along the grout body. this feature is also being tested at the moment.

since foundation version 1.5, the modelling of slopes and embankments has improved by

means of the ‘triangulate’ meshing option (to create straight slopes and sharp edges).

now, with version �, the well-known phi-c reduction procedure for the calculation of global

safety factors will also be available as a standard calculation option. moreover, the

new embedded pile and ground anchor can also be used to model reinforced slopes and

embankments. Hence, version � further facilitates the modelling and analysis of these

types of applications.

for users of large 3d models that have been somewhat disappointed with the slow

performance of the existing output program, there is good news. the output program has

been completely refactored and supports openGl (hardware accelerated graphics). this

means that all graphic operations in the output program are dramatically faster, provided

that the computer’s graphic card has sufficient memory (>6� mB). rotation and zooming

into the model can be done using the mouse and scroll wheel, just like in popular cad

programs. also the speed of output tables has been increased significantly, and several

features have become more user-friendly. a particular feature to mention is the output of

volume piles, which will be automatically provided in terms of structural forces, just as

for the embedded piles, rather than as stress plots only.

at the moment a full-function beta version of the new 3d foundation V� is being tested

by a selected group of users. in the coming two months we will complete the testing

programme and apply our Quality assurance procedures for the final release of this new

product, which is planned for January �007.

References:ata n.1998. etude du comportement des micropieux sous chargement lateral:

construction numerique des courbes (p-y) et coumplage fluide-squelette. Pld thesis,

lille University of technology.

Results from the ERTC7 benchmark exercise

5

Abstracta benchmark example addressing ultimate limit state (Uls) design of an embedded

retaining wall has been specified by the ertc7 on the occasion of the 6th european

conference on numerical methods in Geotechnical engineering. the main goal of the

exercise was to highlight possibilities and limitations of numerical methods for Uls

design with particular reference to eurocode7 (ec7), where three design approaches (da1,

da� and da3) have been specified. these design approaches differ in the way partial

factors of safety are introduced in the analysis. However, the exercise was not restricted

to the use of ec7 and thus a wide spectrum of results, which are summarized in this

contribution, could be expected. some of the 13 submissions did not actually present de-

sign values as requested but provided parametric studies showing the influence of vari-

ous design assumptions or did an analysis using characteristic values, some introduced

factors without given explicit reference to a particular code or standard.

Specification of ERTC7 benchmarkthe benchmark is a deep excavation problem supported by a single strut. the geometry

is depicted in figure 1. the significant difference to examples previously examined by

various working groups around europe (orr, �005) is that it was the intention here to solve

this problem, including determination of the required embedment depth (!), by means

of numerical methods, although a check by simple limit equilibrium calculations was

certainly recommended. as the emphasis is on the Uls design and not on the serviceability

limit state (sls) only parameters required for simple elastic-perfectly plastic analysis

have been provided (table 1). these parameters have to be considered as characteristic

values and not design values. the following construction steps should be modelled in the

numerical analysis:

- initial phase (k0 = 0.5)

- activation of diaphragm wall (wished-in-place)

- activation of surcharge loads

- excavation step 1 to level -�.0 m

- activation of strut at level -1.50 m, excavation step � to level -�.0 m,

- groundwater lowering inside excavation to level -6.0 m

- excavation step 3 to level -6.0 m

the surcharge of 10 kPa is a permanent load, the surcharge of 50 kPa is a variable load.

Bedrock was assumed at a depth of �0 m below ground surface. the axial stiffness of the

strut was set to ea = 1.5e6 kn/m.

results to be provided:

- embedment depth of wall

- design bending moment for the wall

- design strut force

on purpose it was not specified how the water drawdown inside the excavation should be

taken into account because different codes and standards would allow different

assumptions. the same argument holds for wall friction because individual national

standards would have different requirements. the choice of the dilatancy angle,

Results from the ERTC7 benchmark exercise

H.F. schweiger, Computational Geotechnics Group, institute for soil Mechanics and Foundation Engineering, Graz University of Technology, Graz, austria

Plaxis Benchmark

rarely given in a conventional geotechnical report, is also left to the user in most cases

and was therefore not given.

figure 1. Geometry of benchmark example

table 1. material properties for soil and wall

E ν ϕ’ c’ γ kN/m2 - ° kN/m2 kN/m3

soil 30 000 0.3 �7.5 10 �0 / 19

Wall 3.0e7 0.18 - - ��

Submitted resultsnotes on individual submissions

13 results have been submitted, but as mentioned previously not all of them have

provided the results in the form as specified. Because all entries are considered in the

comparison presented in this paper a very brief summary of individual assumptions - as

far as described by the authors - is given in the following. this should help explaining - at

least to some extent - the differences observed in the results.

no.1: gives no information at all on analysis.

no.�: provides results for ec7 design approaches da� and da3, uses different wall

friction on active and passive side (�/3ϕ and 1/3ϕ). Partial factor of 1.� on soil

weight on active side (does not conform to ec7 > possibly national annex (italy)).

no.3: does not apply any safety factors, wall friction 0.9ϕ.

no.�: provides finite element and limit equilibrium results, global safety factor applied,

6

stiffness of strut/per unit length of excavation obviously different from

specification, wall friction 0.8ϕ.

no.5: compares finite element and beam spring results, loads, soil weight and strength

parameters factored (similar to da3) but with different factors than in ec7,

cohesion and friction angle have different partial factors, wall friction 0.3ϕ, refers

to russian code of practice.

no.6: applies dutch cUr-method, which has some similarity with design approaches in

ec7 but with different partial factors, wall friction �/3ϕ.

no.7: load factors on service loads according to British (1.�) or australian standards

(1.5), partial factor on soil strength of 1.�, provides additional results with

subgrade reaction method, wall friction �/3ϕ.

no.8: provides finite difference and subgrade reaction analyses under various

assumptions (e.g. undrained conditions), wall friction �/3ϕ and 1/3ϕ, does not

explicitly provide design results, no safety factor given or applied to actions or

parameters.

no.9: a second submission applying the dutch cUr-method, wall friction �/3ϕ.

no.10: compares ec7 design approaches da� and da3 with partial factors according to

ec7 and eaB (German recommendation for deep excavations) respectively, wall

friction 0.5ϕ, assumes stiffness increasing with depth.

no.11: does not apply a particular code but determines embedment from finite element

analysis employing the strength reduction technique on the basis of a global

factor of safety of 1.5, design bending moment obtained from calculated value at

final excavation step multiplied by 1.5, wall friction 0.5ϕ.

no.1�: does not apply a particular code but determines embedment from finite element

analysis employing the strength reduction technique on the basis of a global

factor of safety of �.0, wall friction �/3ϕ, drucker-Prager failure criterion for soil.

no. 13: assumes in an alternative calculation capillary cohesion above groundwater level

(determined from seepage analysis), design approach da3 according to ec7 and

analysis with characteristic soil parameters, wall friction �/3ϕ.

the lowering of the groundwater table was taken into account by means of phreatic

levels by no.3, 5, 9, 10 and no.6, 7, 11 performed an additional interpolation in order to

achieve continuous pore pressures at the base of the wall. no.�, 8, 1� and 13 performed a

seepage analysis.

Resultsfigure � shows the variation in embedment depth of all entries. as indicated in the previous

section some submissions provided more than one solution (depending on assumptions

made) and this is why there is more than one result plotted in these cases. it follows that

the minimum embedment depth is 1.8 m and the maximum 5.5 m, but there is a tendency

towards an embedment depth between 3.0 to �.0 m.

figure �. embedment length - all entries

the maximum embedment depth of no.� (5.5 m) is obtained by conventional analysis

applying a global factor of safety η = 1.5. the same embedment depth has been used

in the numerical analysis. no.3 indicated a factor of safety of 1.76, no.� factored the

soil weight and no.1� obtained a factor of safety from strength reduction technique of

�.0. thus these higher embedment depths can be explained by higher safety levels as

compared to the other submissions. at the lower end (embedment depths around � m)

it is found that these results are obtained from numerical analyses, either by means of

a strength reduction technique or by factoring soil strength parameters. However, no.7

employed a factor of safety of η = 1.� which is lower than in ec7. no.13 indicated that the

low depth is possible only by modelling the groundwater lowering by means of a �-phase

flow formulation resulting in suction effects above groundwater. from comments provided

it can be concluded these two authors would not have designed a wall for a real project

with this low embedment depth.

only 3 authors explicitly used ec7 for their analysis (da� and da3), 3 authors used

an approach similar to ec7 but with different partial factors of safety. it is somewhat

encouraging to see that except for no.� (where the soil weight was factored) the

embedment depth is between 3.0 and �.0m despite differences in assumptions of partial

factors and wall friction. no.10 investigated the difference between da� and da3 and

obtained a slightly shorter wall with da3.

Continuation

Results from the ERTC7 benchmark exercise

Plaxis Benchmark

7

figure 3. Bending moments - all entries

figure �. strut forces - all entries

figure 3 shows bending moments and there we find a difference of approx. 300% but this

includes values which are obviously not Uls-design values. this is however not surprising

considering the different assumptions made in the various analyses. if we consider again

the ec7 and related approaches (i.e. no. 5, 6, 9, 10 and 13) we see a range from �01 to

�78 knm/m for da3. da� results in approximately �0% higher bending moments. if we

multiply obvious sls-bending moments by a partial factor of 1.35 we find that results

also fall in this range.

a similar picture is obtained for strut forces. considering all solutions submitted the

range is from 60 to 363 kn/m (including values representing sls) and in this case also

the ec7 and related approaches show a significant difference with the minimum being

19� and the maximum force being 363 kn/m.

Conclusionthe results from a benchmark exercise addressing the design of a diaphragm wall for a

deep excavation problem have been presented. Unfortunately not all of the submissions

provided their results in form of design values but discussed the influence of various

modelling assumptions without a clear statement on what they would use for design.

However the results gave some valuable insight into the way design calculations are

performed in different countries applying their respective codes of practice and standards

and the differences in results are not surprising and not larger than in similar exercises

which have been performed using conventional limit equilibrium analysis (orr, �005).

it can be considered encouraging that the calculated embedment depth based on

numerical analysis applying ec7 design approaches are within reasonable limits.

differences in bending moments and strut forces are less encouraging and clearly show

the need for recommendations of good practice in numerical modelling in geotechnical

engineering.

ReferencesBauduin, c., de Vos, m. & simpson, B. �000. some considerations on the use of finite

element methods in ultimate limit state design. Proc. int. Workshop on limit state design

in Geotechnical engineering, melbourne.

Bauduin, c., de Vos, m. & frank, r. (�003). Uls and sls design of embedded walls

according to eurocode 7. Proc.Xiii ecsmGe, Prague (czech republic), Vol. �, �1-�6

orr, t.l.l. �005. review of workshop on the evaluation of eurocode 7. Proc. int. Workshop

on the evaluation of eurocode 7, dublin, 31.3.-1.�.�005, 1-10.

schweiger, H.f. �005. application of fem to Uls design (eurocodes) in surface and near

surface geotechnical structures. Proc. 11th int. conference of iacmaG, turin, italy, 19-��

June �005. Bologna: Patron editore. �19-�30.

schweiger, H. f. 1998. results from two geotechnical benchmark problems. Proc. �th

european conf. numerical methods in Geotechnical engineering, cividini, a. (ed.),

springer, 6�5-65�.

schweiger, H.f. �00�. results from numerical benchmark exercises in geotechnics. Proc.

5th european conf. numerical methods in Geotechnical engineering (P. mestat, ed.),

Presses Ponts et chaussees, Paris, �00�, 305-31�.

schweiger, H.f. �006. results from the ertc7 benchmark exercises. Proc. nUmGe �006.

Plaxis Benchmark

8

the passive earth pressure stiffness has been studied in experiments where

external loads are applied by hydraulic jacks to push the abutment against the soil. the

passive earth pressure stiffness has also been studied through analyzing strong motion

records from bridges exposed to earthquakes. seismic instruments have been installed in

many bridge structures through out the world to improve our understanding of the global

behavior and potential damage of the bridge structures during a seismic event. the

information provided by monitoring structural responses led to better scientific under-

standing of nonlinear behavior of various components of the bridge system. Post-earth-

quake studies of various components of the bridge structures using system identification

techniques has indicated that stiffness of the bridge abutment-backfill depends on the

level of shaking and it varies significantly during the shaking. all the results indicate

that significant nonlinearity and stiffness degradation occur within the bridge abutment-

backfill system due to hysteretic soil behavior. therefore, reliable soil models are needed

to predict the nonlinear force-deformation of the mobilized passive soil wedge as a

function of bridge superstructure displacement in order to capture the global seismic

behavior of the bridge structure model.

direct three-dimensional continuum finite element modeling of the surrounding soil and

the bridge structure is by no means simple and computationally very expensive. as an

alternative to the three-dimensional fem, some simplifications are needed to enable

the bridge engineer to simulate the global seismic response of the bridge structure.

Beam elements are typically used to model columns and the superstructure. simple and

practical soil springs connected to the beam elements are widely used to represent the

pile foundations. therefore, the nonlinear abutment-backfill behavior should be modeled

as nonlinear discrete soil springs as well.

a nonlinear-continuum finite-element model can be used to develop the abutment-back-

fill nonlinear discrete soil springs in terms of backbone curves. in the global analysis of

the bridge system the nonlinear hysteretic damping of the soil is then included using a

masing rule based on the nonlinear curves obtained from the soil continuum model.

figure 1 shows how the nonlinear discrete abutment springs are attached to a typical

Abstractseismic design of bridge structures is based on a displacement-performance

philosophy. full-scaled field experiments, observations from the major seismic events

and post-earthquake studies have indicated that the bridge abutment-backfill exhibits

strength and stiffness degradation. Hence it is important to incorporate the degradation

of the abutment-backfill in the bridge global model in relation to it’s the seismic response

and performance. this article’s focus is on the development of stiffness degradation

(nonlinear load deformation curve) for the earth pressure behind bridge abutments. this

problem has recently been studied experimentally at several universities and research

institutes in the Usa and good-quality, large-scale test results are available. Back-

calculations of the test results using Plaxis 3d tunnel and 3d foundations are shown

herein. the Hardening soil model has been used to simulate the nonlinear abutment-

backfill force-deformation relationship from some of these tests. the Plaxis results are

in good agreement with the experimental results and the simulations provide valuable

information on the soil behavior and the soil parameters. it is concluded that Plaxis is an

extremely valuable tool for the practicing bridge engineer in capturing realistic nonlinear

soil-abutment-structure interaction curves.

Introductionduring a seismic event, the bridge deck moves laterally and collides with the abutment

backwall. the passive resistance provided by the abutment reduces the displacement

demands on the bridge columns. the basic idea of the displacement-performance-based

design is to prevent total collapse by allowing selected components of the bridge system

to yield with predictable large plastic deformations. easily reparable components are

preferably selected to yield. this concept allows the bridge engineers to limit the super-

structure forces and displacements to acceptable levels. often the abutment-backwall

is designed to break off during a major seismic event in order to protect the abutment

pile-foundation from plastic action. this implies that the passive earth pressure of a soil

wedge in between the wingwalls is of special importance.

figure 1. two-span box-girder bridge used in global bridge analysis

Modeling passive earth pressures on bridge abutments for nonlinear Seismic Soil - Structure interaction using Plaxis

anoosh shamsabadi, senior Bridge Engineer, Office of Earthquake Engineering, sacramento, Usa steinar Nordal, Professor of civil engineering, Norwegian University of science and Technology, Trondheim, Norway

Plaxis Practice

9

Plaxis Practice

nonskewed two-span single-column highway overcrossing bridge. figure � shows a

typical seat type bridge abutment, indicating how the bridge may move in the longitudinal

direction and collide with the abutment backwall during a seismic event. the back wall is

designed to shear off and allows the mobilized passive soil pressure to be developed as a

result of backwall horizontal displacement.

the effect of an actual earthquake is shown in figure 3. this is an example of the

passive wedge formed when a bridge superstructure is pushed into the abutment-backfill

due to longitudinal seismic excitation. the surface cracks were developed in the roadway

pavement behind the northern (�3.5-m wide, near-normal 5o skew) abutment of the

shiwei Bridge in taiwan during the chi-chi earthquake (kosa et al, �001).

a typical highway bridge is wide and has a moderate back wall height, often 1

to � meters. the earth pressure problem is then a plane strain problem and �d fem

simulations may be sufficient to simulate the soil response. However, for the skewed

bridges the superstructure undergoes significant rotations about the vertical axis

during seismic events that result in permanently lateral offset of the deck at seat-type

abutments. due to deck rotation the obtuse corners of the deck collides with the

abutment wall and the acute corners of the deck move away from the abutment back-

wall. as a result asymmetric soil reactions are developed between the acute and obtuse

corner of the abutment wall (shamsabadi et. al, �006), therefore, 3d analysis is needed

to capture the nonlinear response of the backfill in between the wing walls for bridges

with skewed abutments.

Plaxis simulations of experimental dataPassive resistance behind walls has been studied in centrifuge tests (such as by Gadre

and dobry, 1998), laboratory tests (such as by fang et al, 199�), and large-scale or full-

scale tests (such as by romstad et al., 1995 and documented by martin et al., 1997).

recent full-scale tests at Bingham young University (ByU) are reported by rollins and

cole (�006). large-scale tests are currently being performed at University of california

san diego and at University of california los angeles to capture the nonlinear force-

deformation characteristics of the abutment-backfill for the seismic design of bridge

structures.

figure �. seat-type abutment and foundation system

a series of full-scale static load tests was performed by rollins and cole (�006) on a 5.18

m by 3.05 m pile cap with a height of 1.1� m embedded in five types of soil backfills.

the backfill was placed in layers and compacted to approximately 95% modified Proctor

density. the pile cap rested on a 3 by � group of 3��-mm diameter steel pipe piles driven

in saturated low-plasticity silts and clays. the resistance of the piles was subtracted

from the measured total horizontal resistance of the pile cap to determine the mobilized

passive resistance of the backfill. depending on the backfill properties, the measured

earth pressure force on the back wall varied from 750 kn to �000 kn at a horizontal wall

displacement of about 6 cm.

figure � shows the schematics of a typical ByU pile cap field experiment with the three-

dimensional passive wedge bounded by a logarithmic-spiral type failure surface, based

on field measurements of observed cracking patterns and wedge deformations by rollins

and cole (�006).

Mobilized limit-equilibrium methodsthe results of the experimental nonlinear force-deformation response from a number of

full-scale tests, centrifuge model tests and small-scale laboratory tests for walls, bridge

abutments and pile caps in a variety of structure backfills have been studied using a

model by shamsabadi et al. (�006). this two-dimensional plane-strain model is based

on limit-equilibrium using a logarithmic-spiral failure surface coupled with a modified

Hyperbolic stress-strain relationship (“lsH”). Good agreement was found between the

“lsH” model and the experimental data. the computed results from the “lsH” model

were multiplied by an adjustment factor a varying between 1.� and 1.� to account for the

three-dimensional shape of the mobilized passive wedge in the backfill (see figure �).

the force-deformation relationships calculated using 3d Plaxis were compared against

experimental data without any adjustment factor.

figure 3. Passive wedges caused by an earthquake, shiwei Bridge

Heaved roadwayand Backfill due to Passive Wedge

10

Computation of stiffness parametersin the Hardening soil model, the applied stiffness for sand follows expressions of this

type:

E50 = E50ref σ3’ + a (1)

p’ref + a

Where a = c / tan φ, σ3’ is the minor principal stress, and the reference pressure

is p’ref = 100 kPa. the applied stiffness in the Hardening soil model

in Plaxis is hence not only a function of the input stiffness parameter, E50ref, but also a

function of the stress level and the cohesion, c.

the reference input stiffness parameters E50ref for sand and gravel are normally in the

range 15 mPa to 50 mPa. Here significantly higher values are used, actually 100 mPa,

except for the silty sand. the backfill material is well compacted, which justifies high

stiffness. However, the main reason for selecting higher stiffness values is related to the

low initial stresses behind the wall. When the term σ3’+ a in equation 1 is low then the

applied stiffness, E50, will be low. conventional experience on using reference stiffness

in the range 15 to 50 mPa is primarily obtained from natural sands and valid primarily

at higher stress levels, (σ3’- values). the present experimental results indicate that for

problems with low σ3’- stresses, higher input stiffness parameters than normal may be

relevant.

some further comments are given in the following paragraphs regarding the selection of

stiffness parameters. observation of the ByU nonlinear experimental force-deformation

relationship indicates an average stiffness (k50) of about 100 kn/mm for the sand and

gravel backfill. assume that the deformation behind a wall with the height H is equal to

dh due to an average horizontal strain within an influence zone L. let L be in the order of

2H. an average stiffness (E) may then be introduced by the following equation:

dh = σh L =

σh 2H = Pp 2H =

Pp 2H = 2Pp =

2k50 σh (�) E E AE WHE WE WE

Input parameters to finite element studiesthe pilecap experiments conducted at (ByU) demonstrated significant 3d effects as

shown in figure 5 . Both the Plaxis 3d tunnel and Plaxis 3d foundation were used to

simulate the pile cap experiments. table 1 shows the backfill strength values and the

stiffness parameters used in the Hardening soil model available in Plaxis. selection of

the stiffness parameters used in Plaxis is a compromise between simplicity and a reason-

able match with experimental data. Perfect match could have been obtained if strength

and stiffness variation were utilized for every separate test. But keeping the strength the

same as proposed by the experimentalists and using the stiffness parameters shown in

table 1, the results obtained using 3d Plaxis are in good agreement with experimen-

tal data. the stiffness parameters listed in table 1 provide realistic force-deformation

relationships of the bridge abutment-backfill and appears reasonable for practical

design. for the parameters not listed in table 1 the default values recommended in the

Plaxis user manuals are used. the plate element with linear elastic and high stiffness is

used to model the rigid back wall.

table 1. input parameters for �d and 3d Plaxis analyses

BYUSoil γ ϕ c ψ Rinter Rf E50ref Eur

ref

[kN/m3] Friction [kPa] Dilatancy Wall [MPa] [MPa]

interface

clean sand 18.� 390 � 90 0.70 0.97 100 �00

fine Gravel �0.8 3�0 � �0 0.70 0.97 100 �00

coarse Gravel �3.� �00 1� 100 0.70 0.97 100 �00

silty sand 19.� �70 31 00 0.70 0.97 50 100

Plaxis Practice Plaxis Practice

Continuation

figure �. full-scale static ByU load test on silty-sand Backfill

Modeling passive earth pressures on bridge abutments for nonlinear Seismic Soil - Structure interaction using Plaxis

11

Computed resultsBoth the 3d tunnel and the 3d foundation programs were used in this study. the simula-

tions were done using a half-wall-width model due to symmetry of the problem. figure 6

shows the half-model of the geometry used with a medium coarse mesh as applied in the 3d

foundation program. the use of a finer mesh did not change the results significantly, but

made convergence at large deformations considerably more difficult.

Sequence of the eventsall the analysis was performed in steps to simulate sequence of the real events during the

field experiments. the computations were simulated using the following steps:

1- starting with a level ground the initial stresses were calculated.

�- excavation was performed by deactivating clusters of elements in the front of the pile

cap.

3- in 3d tunnel, displacements were applied while in 3d foundations distributed normal

stresses were applied to push the pile cap up to backfill failure.

Before the field experiment, the backfill was placed and compacted behind the wall.

the backfill was extended to the sides behind the pilecap, but no backfill was placed

along the sides of the pile cap. this is why the simulations were performed as shown in

figure 5. the “free” vertical soil face in the model is supported by a ko pressure and

increased linearly below ground surface. this pressure is kept constant throughout the

test. the wall was pushed then horizontally without any vertical movement. in Plaxis 3d

foundations, horizontal translation was obtained by adding an extended “handle” normal

to the wall plate (see figure 5) and specifying the appropriate horizontal line fixity on the

“handle’s” lower edge.

the simulated load deformation curves are shown in figure 6 to figure 9. figure 6 shows

the sandy gravel experiment, giving an ultimate load for the 5.18 x 1.1� m� wall of about

1000 kn. the initial stiffness is in the order of 1500 kn/cm which corresponds to about

�50 kPa/cm. figure 7 shows results for coarse Grained Gravel and figure 8 shows results

for fine Grained Gravel where the ultimate capacity is about �000 kn and 780 kn, respec-

tively. the initial stiffness is however about the same as for sandy Gravel. figure 9 shows

the result of the simulation for the silty sand backfill. there is a good agreement between

the Plaxis simulations and the experimental curves.

some of the load-deformation curves simulated by both Plaxis 3d foundation and

tunnel are not smooth and show some minor irregularities. some of this is related to the

development of alternative plastic failure mechanisms as illustrated by figure 10 and

figure 11. figure 10 shows two failure “competing” mechanisms. figure 11 shows that

one mechanism becomes more dominant as deformation increases. figure 7 shows the

change in the inclination of the simulated nonlinear load-deformation curve at about

3 cm. this is a reflection of the fluctuating failure mechanism. such behavior was seen

in several simulations and is believed to be attributed to the inherent minor instability

of non-associative plasticity. the authors believe that such feature may also be seen in

real soil behavior.

where Pp is 50% of the ultimate passive earth pressure force acting over a total back wall

area of A = W·H, and σh’ = Pp /A. the fraction 50% is chosen to give a “half way to

failure” average stiffness. the wall width W is 5,180 mm in the ByU test (figure �).

turning equation � around we obtain:

E = 2k50 = 2.100kN / mm= 40MPa (3)

W 5180mm

We note that �0mPa is a stiffness considerably lower than the input values used, but

the average stiffness of �0mPa is not a reference stiffness. applying rough, average

parameters (a=5 kPa, p’ref=100 kPa, σ3=15 kPa), the input stiffness parameter e50ref can

be estimated to:

E50ref = E50

p’ref + a = 40MPa 100kPa + 5kPa

= 90MPa (�) σh + a 15kPa + 5kPa

Please keep in mind that this is a crude estimate. it may still indicate why we apply the

input reference stiffness (100 mPa ) for the high-quality gravel and sand backfill.

the parameters used in the Hardening soil model are identical to the parameters used in

the “lsH” model proposed by shamsabadi et al (�006). following the recommendation

by shamsabadi et al. (�006), the Hyperbola cut off parameter, rf, was set equal to 0.97.

this gives a better match with the measured nonlinear force-deformation than the default

value of 0.90 proposed in the Plaxis user manual. a pre-consolidation effect due to com-

paction of the backfill was originally used, but resulted in a rather sharp drop in stiffness

as the applied load was increased beyond the pre-consolidation pressure. such a drop is

not observed in the experimental data. therefore, the ocr was set equal to one and the

effect of the backfill compaction was taken into account using the stiffness parameters

listed in table 1.

Plaxis Practice

figure 5. a half model of the ByU field test, medium coarse mesh, 3d foundations

1�

figure 7. load deflection curves for coarse Grained Gravel

figure 8. load deflection curves for fine Grained Gravel

figure 9. load deflection curves for silty sand

figure 10. coarse Grained Gravel, incremental shear strain contours at 3 cm

deformation

figure 1� show examples of the logarithmic spiral failure surface mechanism using

the Plaxis 3d tunnel. there is a good match between simulated deformed shapes of the

passive wedges from the 3d Plaxis and the ByU pile cap experiments mapped in the

field.

Plaxis Practice Plaxis Practice

Continuation

Modeling passive earth pressures on bridge abutments for nonlinear Seismic Soil - Structure interaction using Plaxis

figure 6. load deflection curves for clean sand

test data

3d tunnel

3d found

test data

3d tunnel

3d found

test data

3d tunnel

3d found

test data

3d tunnel

3d found

13

figure 11. coarse Grained Gravel, incremental shear strain contours at 6 cm deformation

Simulation timethe computer simulations were fast using the Plaxis default coarse mesh. the coarse

mesh was found to be too rough and mesh refinement with several mesh densities have

been tried. the time required for each computer simulation depends primarily on the mesh

density but also on the selection of parameters for the iterative procedure to obtain proper

convergence. convergence was more slow for certain combinations of stiffness, friction,

cohesion and dilatancy parameters. still coarse meshes were analyzed in a few minutes

while the ones shown above take from half an hour to more than an hour on a Personal

computer. it is confirmed that simulating an indentation problem to large deformations

are numerically challenging and hence manual iteration control was used. the over-

relaxation factor was often set to 1.0 while low values were selected for the desired

number of iterations. some of the results are obtained by using a tolerated error of 3%.

it was observed that using high tolerated errors even up to 10% did not change the

computed results significantly compared to a 1% tolerated error analysis. a proposed

explanation for this may be that divergence tendencies, when they occur, appears to be

related to zones with tension and stress concentrations in corners, not so much to the

volume of soil mainly providing the passive resistance. still, high tolerated errors should

never be used uncritically.

Mesh size3d simulations accentuate mesh dependency since normally a rather low number of

elements is used to avoid excessive computation times. at the same time 3d

simulations require lower order elements. in order to get a feeling for the effect of

mesh refinement and compare �d simulations to 3d simulations, a true �d problem

was analyzed using both Plaxis �d and Plaxis 3d foundations, figure 13 and figure 1�.

three different mesh densities were used in 3d with a mohr coulomb soil with

γ = �� kn/m3, e = 30 mPa, ν = 0.3, c = �0 kPa, ϕ = 38,70 and ψ = 100.

drained conditions and no groundwater are assumed. the same soil parameters and a

very fine mesh were used for Plaxis �d.

Plaxis Practice Plaxis Practice

(a) typical deformed mesh with total displacement contours

(b) typical shaded plot of total displacement contours

(d) cross section of plastic points in the incremental shear strain zone

figure 1�. results from a half wall width simulation with 3d tunnel.

(c) cross section of incremental shear strain

1�

(a) coarse mesh

(b) medium mesh

{c) fine mesh

figure 13. effect of mesh sensitivity using Plaxis 3d foundations

Conclusionsa full 3d Plaxis stiffness degradation model for the bridge abutment-backfill has been

presented. the model simulates stiffness degradation behavior of the abutment-back-

fill to replicate the stiffness the degradation which has been observed during a major

seismic event. the authors found that there is a very good agreement between the

nonlinear experimental force-deformation behavior of the mobilized passive wedge and

the 3d Plaxis simulations using the Hardening soil model.

for simulation of wide bridge abutments where plane-strain conditions can be

assumed, it is the authors recommendation that the Plaxis �d should be used without any

adjustment factors for the 3d effects. in other cases such as skewed abutment due

to bridge rotation, a 3d simulation is more relevant. Based on the full-scaled experi-

ments of the more narrow abutments studied in this article, the 3d effect can result in

increase of �0 to �0% in passive soil resistance compared to a plane-strain case. the

analyses indicate that 3d simulations give realistic results. a medium mesh size is found

to give reasonable results for geotechnical applications. the Plaxis results are in good

agreement with the experimental results and the simulations provide valuable information

on the soil parameters and the failure mechanism. Plaxis can be a valuable analysis tool

for the researchers and practicing bridge engineers to evaluate realistic nonlinear soil-

abutment-structure interaction behavior.

Continuation

Modeling passive earth pressures on bridge abutments for nonlinear Seismic Soil - Structure interaction using Plaxis

Plaxis Practice Plaxis Practice

all the load deflection curves given in figure 1� are identical up until about 50% of

the capacity where after they deviate. the deviation is considerable for the coarse 3d

mesh. this might be expected since it is very coarse with only two elements over the wall

height. some uncertainty is related to the irregularity of the curves. the medium 3d mesh

appears to perform satisfactorily, and the overshoot for rather crude meshes is less than

�0%. some overshoot can be expected unless very fine meshes are used. if the expected

percentage of overshoot is roughly known, a reasonably good simulation can be achieved

using a medium dense mesh. for geotechnical applications, a medium dense mesh

appears to be an decent trade-off between accuracy and computing time.

figure 1�. load deflection curves illustrating mesh dependency

15

Plaxis Practice Plaxis Practice

References:PlaXis �d

PlaXis 3d tunnel

PlaXis 3d foundations

fang, y.-s., chen, t.-J., and Wu, B.-f. (199�). Passive earth Pressures with Various Wall

movements. Journal of Geotechnical engineering, asce, Vol. 1�0, no. 8, pp. 1307-13�3.

Gadre, a. d., and dobry, r. (1998). centrifuge modeling of cyclic lateral response of Pile-

cap systems and seat-type abutments in dry sand. report mceer-98-0010, rensaeler

institute, civil engineering dept., troy, ny.

Gadre, a.d. (1997), lateral response of Pilecap foundation system and seat-type

abutment in dry sand, Phd dissertation, rPi.

martin, G. r., yan, l.-P., and lam, i. P. (1997). development and implementation of

improved seismic design and retrofit Procedures for Bridge abutments, final report,

research Project funded by the california department of transportation, september.

romstad, k., kutter, B., maroney, B., Vanderbilt, e., Griggs, m., and chai, y. H. (1995).

experimental measurements of Bridge abutment Behavior. department of civil and

environmental engineering, University of california, davis, report no. Ucd-str-95-1,

september.

rollins, k.m., and cole, r.t. (�006), “cyclic lateral load Behavior of a Pile cap and

Backfill,” accepted for publication, Journal of Geotechnical and Geoenvironmental

engineering.

shamsabadi, a., kapuskar, m. and a. Zand (�006), “three-dimensional nonlinear finite

element soil-abutment-structure interaction for skewedBridges,” fifth national seismic

conference on Bridges & Highways” september 18-�0, �006 in san francisco

shamsabadi, a., rollins, k., and kapuskar, m. (�006), “nonlinear soil-abutment-Bridge

structure interaction for seismic Performance-Based design,” Journal of Geotechnical

and Geoenvironmental engineering, asce (under review for publication).

shamsabadi, a., and kapuskar, m. (�006), “Practical nonlinear abutment model for

seismic soil-structure interaction analysis,” �th int’l Workshop on seismic design and

retrofit of transportation facilities, san francisco, march 13-1�.

16

Dipl.-ing. H.D. Netzel (CRUx Engineering b.v.)ir. D. Vink (CRUx Engineering b.v.)

Prediction of soil deformations during excavation works for the renovation of “Het Nieuwe Rijksmuseum” in Amsterdam, The Netherlands

Introductionthe “rijksmuseum” in amsterdam is one of the most important 19th century monumental

buildings in the netherlands. the showpiece of the museum is the world famous the

night Watch by rembrandt. Presently the building is being renovated in order to meet

the modern standards for international museums. the design of the renovation has

been drawn by cruz y ortiz from sevilla. the constructive design is being carried out by

arcadis in cooperation with crUX engineering and Wareco for the assessment of the

geotechnical and hydrological implications of the project. the most striking feature in

the new design is a semi-underground square of approximately 3000 m� in between the

existing monumental building. this square is situated in the existing court yards and

will serve as main entrance to the museum. the geotechnical design calculations are

carried out by crUX using the finite element program PlaXis. the calculations are part

of the risk assessment strategy in order to predict and judge the influence of ground

deformations due to the excavations on the surrounding building. intensive monitoring

is used to control the deformations of the structure and the sheet pile walls during the

construction work.

Generalthe realization of the lowered square and underground facility rooms requires the

construction of concrete cellars with a depth of 6 m or more, right next to the existing

wooden foundation piles of the monumental building. the cellars will be cast in building

pits, the excavation of which will cause relaxation of the soil, inducing deformations in

figure 1. artist impression of the lowered court yards (source JndG-amsterdam)

the near vicinity of the pits. these deformations, caused by the excavation works, have

been predicted using PlaXis. figure 1 shows an artist impression of the court yards with

lowered ground level. figure � shows the museum in cross section. Below the court yards

cellars will be realised for use as conference rooms, an auditorium and the kitchen.

Soil Conditionsfor the project 18 electric cone penetration tests (cPt) have been performed. the cPts

show the soil profile that is typical for amsterdam. the top layer of � m to 3 m below

surface level consists of anthropogenic sand. Below this toplayer the Holocene deposits

are found to a depth of about 13 m below surface level. the Holocene formation can be

divided (from top to bottom) into 1 m to � m peat (Hollandveen), 1 m to � m clay (oude

Zeeklei), 3 m silty sand (Wadzand), 3 m clay (Hydrobiaklei) and 0,� m peat (Basisveen).

the soft Holocene has been deposited on top of the stiff Pleistocene sands consisting of

the so called first sand layer of � to 3 m thickness, an intermediate silty, clayey sand layer

(allerod) of � m and the second sand layer of at least 5 m thickness. the phreatic water

level is about 0,� m below surface level. the artesian water level in the first sand layer

lies � m below the phreatic water level.

PLAXIS Modela schematic soil profile that best fits the cPts has been constructed for the model

geometry. for modelling the soil layers the Hardening soil model has been adopted. this

model is most suitable for excavations. it is capable of describing reduction of stiffness

as well as irreversible deviator strains due to deviatoric stress. in the vicinity of the

excavation (on the active side) deviatoric stress applies. the horizontal stresses are

reduced more compared to the vertical stresses. this results in friction hardening which is

a feature of the Hardening soil model. friction hardening also occurs at the passive side

of the sheet pile (that is, below the bottom of the pit). Here horizontal stress increases

compared to the vertical stress due to (horizontal) movement of the sheet pile on the one

hand and reduction of vertical stress as a result of the excavation on the other hand.

in order to get parameters for the Hardening soil material set, almost 50 samples have

been taken from 13 borings. four soil layers have been tested: Hollandveen, oude Zeeklei,

Wadzand and Hydrobiaklei. these layers are considered to be most important regarding

deformations due to the excavation. Besides testing the volumetric weight (γ), triaxial

tests and oedometer tests have been performed for determining stiffness parameters

(e50, eoed) and strength parameters (c’, ϕ’). the parameters from the laboratory tests

figure �. cross section

Plaxis PracticePlaxis Practice

17

have been compared to available parameter sets from other projects in the central part of

amsterdam. they generally show a good agreement. for the calculations the mean values

of stiffness have been taken whereas for the strength the low representative values apply.

table 1 contains the soil parameters for the Hardening soil material data set.

the cross section shown in figure � has been modelled in Plaxis �d using the plane strain

model consisting of a mesh of triangular elements with 15 nodes. in total 89 clusters

have been defined. the generated mesh contains1906 elements. a picture of the model

geometry is shown in figure �.

due to the considerable length of the cross section only part of it has been modelled in

order to reduce the number of elements and calculation time. the western court yard

with its sloping bottom has been entirely included in the model geometry; however only

one symmetric half of the eastern court yard has been taken into account. the distance

between the boundaries on the left and the right side of the model geometry is 100 m.

the bottom level is set at naP -30 m; the top level at naP +0,0 m. no existing structural

elements such as foundation piles, foundation beams or floors have been modelled.

Hence, the model considers a green field calculation in which the stiffness of these

elements is neglected. this is a conservative approach regarding the expected differential

deformations of the adjacent structure. existing loads from the building on the stiff sands

at pile tip level have however been taken into account.

the sheet pile walls (three in number) have been modelled as a beam element with the

characteristics of aZ 18 profiles. the piles of the underwater concrete floor are loaded by

tensional forces during pumping dry the building pits. anchor elements and geotextile

Plaxis PracticePlaxis Practice

table 1. Hardening soil parameter set

ID Name Type γunset γset kx ky E50ref Eoed

ref Eurref cref ϕ ψ

[kN/m3] [kN/m3] [kN/m3] [m/day] [m/day] [kN/m2] [kN/m2] [kN/m2] [kN/m2] [º] [º]

1 1st sand layer drained 19,8 19,8 1,3e+01 1,3e+01 35000 �0000 100000 1,0 33,0 3

� �nd sand layer drained 19 19 8,0e+00 8,0e+00 3�000 �5000 80000 1,0 33,0 3

3 allerod Undrained 18,5 18,5 �,6e+00 �,6e+00 15000 91�0 30000 3,0 �8,0 0

� Hollandveen Undrained 10,5 10,5 1,7e-03 8,6e-0� ��00 1187 8817 1�,1 18,� 0

5 top layer drained 17 18,� 8,6e-01 8,6e-01 17000 15000 50000 1,0 �7,0 0

6 oude zeeklei Undrained 15,� 15,� 1,3e-0� 1,3e-0� 9�00 5��9 �0000 �,8 �7,� 0

7 wadzand Undrained 18,1 18,1 8,6e-03 8,6e-03 11600 �90� �5000 �,0 3�,9 �,9

8 Hydrobiaklei Undrained 1�,7 1�,7 9,0e-05 9,0e-05 5700 3791 11�00 13,3 �3,3 0

11 basisveen Undrained 11,7 11,7 1,0e-03 1,0e-03 �000 100� 7000 6,0 �1,0 0

figure 3. characteristic soil profile

ID Name kur pref Power Ko:nc

c_incr yref Pf T-Strength Rinter

[-] [kN/m2] [-] [-] [kN/m3] [m] [-] [kN/m2] [-]

1 1st sand layer 0,� 100 0,5 0,�0 0 0 0,9 0 0,67

� �nd sand layer 0,� 100 0,5 0,�6 0 0 0,9 0 0,375

3 allerod 0,� 100 0,5 0,50 0 0 0,9 0 0,67

� Hollandveen 0,15 100 0,7� 0,69 0 0 0,9 0 0,5

5 ophooglaag 0,15 100 0,8 0,55 0 0 0,9 0 0,67

6 oude zeeklei 0,15 100 0,57 0,5� 0 0 0,9 0 0,67

7 wadzand 0,� 100 0,75 0,�3 0 0 0,9 0 0,67

8 Hydrobiaklei 0,15 100 0,59 0,60 0 0 0,9 0 0,67

11 basisveen 0,� 100 0,8 0,65 0 0 0,9 0 0,5

18

elements have been chosen to model the tension piles. the tensional stiffness of these

elements has been adapted as to match the stiffness of the line of piles by dividing the

axial pile stiffness by the center-to-center distance of �,5 m of the piles.

Construction phasestable � shows the construction phases with a short description. except for the consolidation

phases, all phases are of plastic analysis type. consolidation phases have been defined

in order to allow for dissipation of excess pore (under)pressures that develop during

excavation.

table �: overview of construction phases

Phase Description soil behaviour

foundation load on and load passage on loads from pile groups and load of passage activated (historic higher surface level) drained

load passage off load of passage deactivated in accordance with actual surface level drained

sheet pile walls on beams activated; reset displacements from previous stages to zero drained

east: strut +0,0; excavation -�,6; water level -3,8 strut court yard east activated; lowering of water level in eastern pit to naP-3,8 m and excavation to naP-�,6m (this dry excavation step is necessary due to the soil decontamination in the above layers) undrained

West: strut +0,5; excavation -�,6; water level -3,8 strut court yard west activated; lowering of water level in western pit to naP-3,8 m and excavation to naP-�,6m (this dry excavation step is necessary due to the soil decontamination in the above layers) undrained

consolidation �1d consolidation phase, �1 days consolidation

water level -0,8 water level in both pits rises from naP-3,8m to naP-0,8m undrained

east: excavation -7,0; water level -0,8 final excavation pit east to naP-7,0m; water level in pit remains naP-0,8m undrained

West: excavation -7,7/-7,0; water level -0,8 final excavation pit west to depth of naP-7,0m to naP-7,7m; water level in pit remains naP-0,8m undrained

consolidation 30d consolidation phase, 30 days consolidation

east & West: underwater concrete underwater concrete clusters activated and material set applied undrained

east: pump dry water in pit east is removed undrained

West: pump dry water in pit west is removed undrained

Risk assessment of influence on the existing building and its foundationthe calculated greenfield deformations are used to access the influence on the existing

rijksmuseum building. the following aspects are considered:

- Horizontal soil displacements can cause lateral pile loading affecting the bending

capacity of the existing wooden foundation piles of the rijksmuseum.

- Vertical soil displacements on surface and pile toe level (1st sand layer) can cause pile

and consequently (differential) building deformations. Vertical soil displacement at

surface level needs to be controlled because settling soil may lead to an increase in

negative shaft friction on the existing wooden foundation piles.

- reduction of effective stress at pile tip level due to the excavation may lead to reduced

bearing capacity of the end-bearing piles of the rijksmuseum close to the excavation.

these aspects are analysed with numerical, analytical and empirical prediction methods

in order to quantify the damage risks.

Resultsfor all main construction stages the following relevant deformations and stresses have

been read from the output:

- horizontal deformation of the sheet pile wall;

- horizontal and vertical deformations in a horizontal cross-section at surface level;

- vertical deformation in a horizontal cross-section at pile tip level;

Continuation

Plaxis PracticePlaxis Practice

Prediction of soil deformations during excavation works for the renovation of “Het Nieuwe Rijksmuseum” in Amsterdam, The Netherlands

figure �. model geometry

19

- modification of effective soil stresses near pile tips of the existing piles of the

rijksmuseum.

figure 5 shows the deformed model and the contourplot of the deformations in the fully

excavated situation.

figure 6 shows the lateral deflections of the sheet pile wall in different stages of the

excavation.

the calculated maximum deformations are summarized in table 3.

table 3: maximum deformation

Type and location Value

maximum horizontal soil displacement at surface level at the location of the piles of the existing building (at closest distance to the sheet pile wall) 17mm

maximum surface settlement at the location of the piles of the existing building (at closest distance to the sheet pile wall) 1�mm

maximum settlement on pile toe level at the location of the piles of the existing building (at closest distance to the sheet pile wall) �mm

maximum lateral wall deflection of the sheet pile wall �9mm

reduction of vertical effective soil stress at at the location of the pile toes of the existing building (at closest distance to the sheet pile wall) 15%

Continuation

Plaxis PracticePlaxis Practice

Prediction of soil deformations during excavation works for the renovation of “Het Nieuwe Rijksmuseum” in Amsterdam, The Netherlands

these greenfield results are translated to the pile foundations and the adjacent building

of the rijksmuseum in order to quantify the impact on the adjacent structrure. the maxi-

mum cumulative deformation due to the different sources is predicted to be 5mm and

the angular distortion along the building is restricted to be 1/3000. the risk of damage

at the masonry structures is negligible and the bending capacity of the wooden piles is

sufficient in order to withstand the additional lateral pile loading due to the excavation.

figure 5. shadings plot of total deformations in final construction phase

figure 6. lateral deformation of the sheet pile wall

Conclusionin order to predict soil deformations in the vicinity of two excavation sites that are located

inside the monumental building of the rijksmuseum in amsterdam extensive PlaXis cal-

culations have been performed. the design of the excavation of the building pits with an

underwater concrete floor is predicted to cause an acceptable influence on the adjacent

structure. the locations and the extent of the monitoring of the building and the sheet

pile wall was derived from these risk analysis. the performance of the construction work

on the adjacent building will be frequently compared with the predicted deformations in

order to be able to anticipate in time with regard to unexpected deformation trends during

the construction process.

References:[1] a.m. de roo, H.d. netzel, P.J.m. den nijs; “omgaan met risico’s bij de renovatie van

Het Nieuwe rijksmuseum”; in dutch; journal GeotecHniek edition 3, juli �006.

Acknowledgments:the project organisation “Het Nieuwe rijkmuseum” is greatfully acknowledged for provid-

ing the permittion to publish this article.

�0

Hester leung, Cristien Gani, Wataru Okada sKM aucklandsergei Terzaghi, sKM sydney

Comparison of the effectiveness of Deep Soil Mix columns using 2-D and 3-D Plaxis

Plaxis Practice

Introduction the purpose of this paper is to compare the behaviour of deep soil mixing columns

predicted by Plaxis �d and 3d programmes in terms of stresses acting in columns and

calculated factor of safety (fos). deep soil mixing column has been used as one of the

remedial solutions on slip repair works of state highways in the northland region of

new Zealand. slope failure is common in northland region due to the unique characteristic

of the geology in this area and also the heavy rainfall experienced particularly in winter

months. Prior to installing the deep soil mixing columns, the road had to be repaired regularly

by smoothing of the pavement. a heavy rain event eventually caused sufficient significant

damage to the road such that slope stabilisation work was considered necessary.

one such study was selected to both illustrate the repair method, integration with Plaxis,

and also to illustrate the issues with the use of fe technology in routine design. experience

to date suggests that conventional limit equilibrium design was not capturing the field

behaviour of the columns, and greater understanding of the real behaviour was needed.

in this particular study, �-d and 3-d Plaxis was used, as concerns were raised about the

suitability of only two rows of columns in the design by the project reviewers. field experience

also indicates that the effectiveness of the columns is bounded. if columns are too close

there is no further gain in overall strength, and too far apart, and the columns begin

behaving individually with no net benefits. this paper illustrates some of these issues.

Slip DescriptionsTopography and Ground Condition

the slip discussed in this paper occurred in state Highway 11, northland. it was a road

slip which occurred in a section where the road has been constructed on a natural valley

feature. the upper slope of the valley above the road is hummocky and shows a number

of headscarp, creep and slump features. the area below the failure is highly vegetated

with trees and bush, with the lower flanks of the valley also containing houses. Borehole

logs indicate that the sub surface condition consist of soft to firm silty clay sandwiched

between fine to coarse grained gravel and firm to stiff silty clay. mudstone/sandstone

forms the bedrock.

Failure Mechanismsite observations suggest that the failure is likely to have resulted from a circular slip,

which has probably been induced by saturation of the slope during a heavy rainfall event.

creep movement was noted below the toe of the slip, which would have contributed to the

failure to some extent. a secondary deeper block failure was suspected to be responsible

for the crack adjacent to the road centreline. the slip is approximately 50 m long in the

longitudinal direction. Photographs of the slip are shown in figures 1 and �.

Deep Soil Mixing Column Assessmenttypically, geotechnical parameters used in the design are derived from laboratory test

results of selected core samples collected during the site investigation. in some cases,

geotechnical parameters are assessed from other site information based on the geology

and site observation. an initial analysis is carried out to verify the geotechnical

parameters used by simulating the actual slip failure in the model.

once the actual slope failure is successfully simulated, deep soil mixing columns are intro-

duced into the model. the columns are modelled as soil using volume elements. typically

the design unconfined compressive strength of a deep soil mixing column is about 1.5

mPa. in reality, the achieved strength is much higher in most cases.

in �d models, the column has been modelled using a replacement ratio method in the

out of plane direction. the columns are modelled together with the surrounding soil as

a block of composite material. this takes the column spacing into account by assigning

appropriate average composite properties. the 3d model uses the design properties of the

deep soil mixing column as input.

the columns are positioned in such a way that a block of improved soil bounded by the

columns is created in the pavement and the slope below the road.

for the purpose of this paper, the slope is assumed to be dry. adjustments have been

made to the subsurface parameters such that the dry slope models have a pre-existing

failure mechanism similar to the interpreted mechanism when taking groundwater into

consideration. two rows of 0.3 m by 0.3 m columns are installed and the lengths of the

columns are 5.0 m and 6.0 m. our research focus on the behaviour of columns for the

figure 1. slip on the shoulder of the road

figure �. close up of the slip

�1

Plaxis Practice

following scenarios:

- Variation on column spacing i.e. 0.6 m (� diameter spacing), �.5 m (8 diameter

spacing) and �.0 m (13 diameter spacing) in the longitudinal direction (parallel to

road). the �.5 m spacing is the practical maximum spacing we have adopted based on

field observations of completed projects.

- the effect of soil model used in the assessment i.e. mohr coulomb soil model and

Hardening soil model.

figure 3. cross section and parameters used in the model

Resultsthe output of Plaxis analysis for different scenarios with regard to factor of safety and

shear stress acting in column are given in tables 1 and � respectively. the factor of safety

prior to columns installation is 1.1 and 1.� as determined from �d and 3d modelling

respectively. Both models give a similar failure mechanism as shown in figure �.

the shear stress mobilised by the columns are determined from the deviatoric stress

given in the Plaxis output. in �d models, this needs to be converted to an equivalent shear

stress as the columns have been modelled as a block of composite material instead of

an individual column as in the case for 3d. the conversion is based on the assumptions

that the shear stress taken by each column is proportional to the stiffness of surrounding

soil and takes into consideration of column spacing. this aspect needs to be refined to

maximise the effectiveness of the columns.

table 1. comparison of factor of safety using Plaxis �d version 8.� and Plaxis 3d tunnel

Programme

Column spacing (m) Factor of safety (Fos) Mohr Coulomb Hardening soil Model 2D 3D 2D 3D Pre-existing case 1.10 1.�1 1.10 1.19

0.6 1.5� 1.55 1.53 1.5�

�.5 1.53 1.�5 1.5� 1.�5

�.0 1.5� 1.�3 1.51 1.��

table �. comparison of maximum shear acting in columns

Column spacing (m) Maximum shear stress (kPa) Mohr Coulomb Hardening soil Model 2D 3D 2D 3D 0.6 1�� 70 111 6�

�.5 3�6 73 �5� 5�

�.0 388 70 �87 50

figure �. failure mechanism

Discussion Factor of safety table 1 indicates that the computed factor of safety in 3d models are lower than �d

models by 5% to 7%, however this is not reflected for model with the column spaced at

0.6 m. this is because on 3d model, the actual position of column is modelled whilst on

�d model the variation of column spacing is modelled by adjusting the composite column

parameters, thus in �d model the effect of stress distribution for different column

spacing’s have not been taken into account. already we see the impact of the bounds

noted above. for this problem a spacing of �.5 m is the maximum, and probably a closer

spacing would be more beneficial in reality.

no significant difference is noted in terms of soil model used in the analysis. Both the

mohr coulomb model and Hardening soil model give in similar results for this particular

slip. this is possibly because the problem is modelled as dry thus the strength reduction

(and consequent change in stiffness due to strain) due to groundwater has not been seen

in the model which otherwise will be better represented by Hardening soil model.

shear stresses in Column�d models show significantly higher shear stress compared to 3d model as shown in

table � above because the shear stress in �d model is the equivalent shear stresses

acting in columns which calculated using the equivalent stiffness assumption whereas

the shear stress in 3d model is the actual stress determined from the finite element

analysis.

mohr coulomb models show higher shear stresses in the column in comparison to

Hardening soil model, if e of the mohr coulomb model is equal to e50ref of the Hardening

soil model. However, the impact of the columns being stiffer than the surrounding soil

modifies the stress regime and hence the actual stiffness, making the direct comparison

more difficult.

��

Recent activities

Continuation

Comparison of the effectiveness of Deep Soil Mix columns using 2-D and 3-D Plaxis

figures 5 and 6 show the deviatoric stresses distribution for �.5 m column spacing

with Hardening soil model. figures 7 to 8 show principal stress direction prior and after

installation of deep soil mixing.

Dry slope versus Wet slopefor the purpose of this paper, the slope is assumed dry. However, the parameters have

been adjusted to simulate the condition where the ground water is approximately �.0 m

below road embankment.

comparison between the modified dry model and the original saturated model confirms a

similar failure mechanism on the embankment slope for both models. on the saturated

model, a deeper secondary failure mechanism is noted. the reported factor of safety for

both models however are the same since the main failure is on the slope.

it is noted that installing deep soil mixing columns have increased factor of safety by

�0% to �0%.

Modelling versus Realitythe column spacing of �.5 m was adopted in the final design. Whilst the factor of safety

for the �.5m spacing design appears the same as that of � m column spacing’s in the

�d models, the calculated shear stress significantly increases between the 0.6 and �.5 m

spacing and then appears to level out suggesting that the �.5 m spacing design appears

to be close to the threshold spacing for group effect. However, the same impact was not

noted in the 3d models on the shear stress, but rather on the factor of safety.

the deep soil mixing columns were constructed in november �003. the remedial work

has performed satisfactorily to date, and has undergone several events of heavy

rainfall without developing any signs of further instability in support of the design adopted

Conclusionsthis study clearly demonstrates the 3d effects of soil column interaction. for closer column

spacings of 0.6 m (two column diameters), interaction becomes more dominant, and �d

and 3d results coincide. for more typical column spacing of � to �.5 m, there are significant

differences between the �d and 3d models which need to be understood. at wider spacings,

the 3-d effects dominate, and the �-d results may not be reliable.

the key conclusion of this study is the need to understand the interaction of deep soil mix-

ing columns with surrounding soil mass. columns need to be designed so that they create

an arching effect, and change stress distribution. such change in stress distribution

should be readily visible in model output, whether in �d or 3d analyses, and should in

most cases be reflected in computed factors of safety.

field observations suggest 3d effects of column interaction play a key role in the field

performance of deep soil mixing columns in road remedial work.

figure 5. �d output - deviatoric stresses for column spacing at �.5m – Hardening soil model

figure 6. 3d output – deviatoric stresses for columns spacing at �.5m – Hardening soil model

figure 7. 3d output - Principal stress direction prior to column installation – mohr

coulomb model

figure 8. 3d output - Principal stress direction for column spacing at �.5m – mohr cou-

lomb model

Plaxis Practice

�3

Product updatesWe are quite happy to announce that in the recent period, Plaxis and Geodelft where

able to achieve an update of our mutual product for Groundwaterflow analysis. With this

update the stability and robustness of the program has been further improved. most

users of Plaxis V8 may not be aware, but the Plaxflow calculation kernel has been serving

smoothlessly their needs for stationary groundwaterflow analysis since the release of

Plaxis V8 in �00�. in addition to that, the Plaxflow software package for transient Ground-

waterflow became available one year later. especially after the number of Plaxflow users

kept growing and using the code for various different problems, our support desk experi-

enced that some users had difficulty to finish some complex problems in the combination

of flow and deformation analysis, and for some infiltration problems. therefore last year

it was decided to schedule an update of the code, and to build in the Unicode library for

compatibility with Version 8. this upgrade of Plaxflow, just improving the robustness,

without adding much new functionality is one of the examples of continuous service and

quality control for the Plaxis computer codes. We expect that especially those users that

are working on problems related to time dependent interaction between slope-stability

and groundwater flow will be pleased with the update of the program.

furthermore we recently launched Plaxis 8.� and 3dfoundation 1.6. release notes on

specific details can be found at the download area of our products. Plaxis Update Pack

8.� includes bugfixes for all registered Plaxis V8 users and offers some new special

extensions for V.i.Plaxis members.

V.I.Plaxisthe V.i.Plaxis service Program is an additional subscription system on top of the

traditionally Perpetual licenses. With the V.i.Plaxis service Program you benefit from the

latest releases of your Plaxis software, special extensions and support from Plaxis technical

experts. the V.i.Plaxis service Program protects your investment in geotechnical tools

because it will keep your Plaxis software up to date. each time a new version of your

Plaxis software is released, it is automatically available. it can’t get any easier than that.

the special extensions are modular enhancements to Plaxis software products and are

exclusively available to V.i.Plaxis members. the extensions provide new functionalities,

are fully compatible with the base product and are easy to learn. for members of the

V.i.Plaxis service Program the current available extensions for Plaxis �d are:

- a new soil model: Hardening soil with small strain stiffness

- soil tests: easy simulation of soil lab tests for Plaxis soil models

- sensitivity analysis; analysis of parameters with the relative influences on the results

- Parameter Variation; Upper and lower analysis for all possible combinations.

Recent activities

for detailed information on the V.i.Plaxis service Program like pricing and subscription

please contact us at sales@plaxis.com.

Plaxis StaffWe are pleased to announce that we extended our staff with Wendy merks-swolfs and

ronald Hordijk. Wendy studied civil engineering, and graduated at tU delft, specializing

in structural engineering and computational mechanics. Her main activity is the quality

control of Plaxis products. ronald studied computer science at the tU-delft where he

specialized in computer graphics. He will work on the output/presentation of all Plaxis

products. Plaxis bv will continuosly strenghten its team and has currently additional

positions available for;

- senior software development engineer

- Programmer Graphical User interface

- numerical Geophysicist/Geohydrologis

Upcoming eventslast half year we had some novelties in our agenda, like user meetings in south east

asia and russia (see photo), an advanced course in mexico and the first course ever in

south africa. if you are looking for an opportunity to network with nearby Plaxis users or

want to learn more about realistic simulations with Plaxis Products, please join us at the

european Plaxis User meeting �006 or one of the other events. final dates and locations

will be posted on regular base at the agenda of our website. for more details on current

planned activities, please check the backcover of this bulletin or the agenda on our website.

June �006, st. Petersburg, 1st russian Plaxis User meeting

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y

h(t)

h(t)

h(t)

0 1

23 4

5 6

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Erwin Beernink, Plaxis BV

Plaxis finite element code for soil and rock analyses

Plaxis BVPo Box 57�

�600 an delft

the netherlands

tel: +31 (0)15 �51 77 �0

fax: +31 (0)15 �57 31 07

e-mail: info@plaxis.nl

Website: www.plaxis.nl

5 October 2006funderingsdag �006

ede, the netherlands

28 October - 1 November 2006second national conference on

Geotechnical engineering

Wuhan, china

8 - 10 November 2006european Plaxis User meeting

karlsruhe, Germany

13 - 15 November 2006short course on computational Geotechnics

trondheim, norway

22 - 24 November 2006 Pratique éclairée des éléments

finis en Géotechnique

Paris, france

29 November - 1 December 2006�nd international Workshop of

characterisation and engineering Properties

of natural soils

singapore

14 - 16 December 2006indian Geotechnical conference �006

chennnai, india

11 - 13 December 2006Plaxis standard course

Jakarta, indonesia

8 - 12 January 2007short course on computational Geotechnics

Berkeley, california, U.s.a.

22 - 24 January 2007international course on computational

Geotechnics schiphol, the netherlands

18 - 21 February 2007Geocongres �007

denver, colorado, U.s.a.

21 - 23 February 2007course computational Geotechnics

chennai, india

7 - 9 March 2007Unsat �007 conference

Weimar, Germany

19 - 21 March 2007 course computational Geotechnics (German)

stuttgart, Germany

26 - 29 March 2007international course for experienced

Plaxis users

antwerpen, Belgium

25 - 27 april 2007nUmoG X

rhodes, Greece

8 - 11 May 200716th southeast asian Geotechnical

conference

selangor darul ehsan, malaysia

16 - 20 July 2007PcsmGe �007

isla de margarita, Venezuela

24 - 27 september 2007XiV ecsmGe

madrid, spain

10 - 14 December 2007asian regional conference

kolkata, india

Activities 2006-2007

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