Download - 20 PLAXIS Bulletin (1)
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
programs, case studies and backgrounds on the models implemented in Plaxis.
the Bulletin offers a platform where users of Plaxis can share ideas and experiences with
each other. the editors welcome submission of papers for the Plaxis Bulletin that fall in
any of these categories.
the manuscript should preferably be submitted in an electronic format, formatted as
plain text without formatting. it should include the title of the paper, the name(s) of the
authors and contact information (preferably email) for the corresponding author(s). the
main body of the article should be divided into appropriate sections and, if necessary,
subsections. if any references are used, they should be listed at the end of the article.
the author should ensure that the article is written clearly for ease of reading.
in case figures are used in the text, it should be indicated where they should be placed
approximately in the text. the figures themselves have to be supplied separately from the
text in a common graphics format (e.g. tif, gif, png, jpg, wmf, cdr or eps formats are all
acceptable). if bitmaps or scanned figures are used the author should ensure that they
have a resolution of at least 300 dpi at the size they will be printed. the use of colour in
figures is encouraged, as the Plaxis Bulletin is printed in full-colour.
any correspondence regarding the Plaxis Bulletin can be sent by email to
or by regular mail to:
Plaxis Bulletinc/o erwin Beernink
Po Box 57�
�600 an delft
the netherlands
the Plaxis Bulletin has a total circulation of 11.000 copies and is distributed worldwide.
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
3
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 [email protected].
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
x
y
h(t)
h(t)
h(t)
0 1
23 4
5 6
78 9
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: [email protected]
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
6005
587