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Plaxis finite element code for soil and rock analyses
Simulation of soil nail in large scale direct shear testFinite element modelling of ice rubble
Staged construction of embankments on Soft Soil using Plaxis
issue 19 / March 2006Plaxis Bulletin
� �
this issue of the Plaxis Bulletin features three articles by Plaxis users covering discrete
modeling of ice rubble for offshore construction projects, large-scale shear testing of dike
reinforcement and speed versus safety during road embankment construction. in addition
there is information about Plaxis related activities.
the first article describes how Plaxis �d was used for the validation of punch testing re-
sults on ice rubble. the strength of ice rubble had been determined to provide information
for offshore construction projects such as oil platforms. Plaxis was used to back-calculate
the test results and a finite element analysis approach was used to model discrete ice
particles. this was actually a mix of continuum and discrete approaches.
the second article discusses the use of Plaxis to simulate large-scale shear testing of
dike reinforcement.
the third article looks at the stage-by-stage construction of road embankments. a com-
promise always has to be struck between speed of construction and safety. Plaxis was
used to analyze stability as a function of consolidation time and turned out to be an ideal
tool for this type of work.
this issue also contains contributions from Plaxis and information on Plaxis related is-
sues. these include the relevance of small strain stiffness and the latest information
on the cooperation between Plaxis and Geodelft. Here joint research and development
projects will benefit from the combined expertise of the two companies (finite-element
modeling + geo-engineering).
Ronald Brinkgreve
Editorial
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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any correspondence regarding the Plaxis Bulletin can be sent by email to
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Plaxis Bulletinc/o erwin Beernink
Po Box 57�
�600 an delft
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the Plaxis Bulletin has a total circulation of 10.000 copies and is distributed worldwide.
Editorial Board:
Wout BroereRonald BrinkgreveErwin BeerninkFrançois Mathijssen
Colophon
The Plaxis company has now been in existence for 12.5 years. last year our
emphasis was on quality and involved procedures such as automatic GUi and ker-
nel testing, improved planning, version control, a system for bug reporting and
monitoring, release test procedure and improved documentation. The new quality
procedures have now been integrated into all Plaxis developments. We are also
refactoring – improving the design of our existing code.
Editorial
New Developments
Plaxis PracticeFinite element
modelling of ice rubble
Plaxis PracticeSimulation of soil nail in
large scale direct shear test
Plaxis PracticeStaged construction of embankments on Soft
Soil using Plaxis
Recent activities
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12
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New DevelopmentsNew Developments
New Developments
Ronald Brinkgreve
the accuracy of results from Plaxis calculations depend in particular on the type of soil
model being used and the selection of the corresponding model parameters.
from the beginning of Plaxis, much effort has been put into development, improvement
and implementation of soil models. over the years more advanced soil models became
available, taking into account more and more aspects of soil behaviour. most Plaxis users
nowadays recognize the advantages of models like the Hardening soil (Hs) model with
its stress(path)-dependent stiffness behaviour. despite the larger number of stiffness
parameters that have to be entered, the parameter selection is easier than for simplified
models, because of the clear meaning of the individual stiffness parameters in the Hs
model.
one feature of soil behaviour that was still missing in the Hs model is the high stiffness
at small strain levels (< 10-5). even in applications that are dominated by ‘engineering
strain levels’ (> 10-�) small-strain stiffness can play an important role. it is generally
known that conventional models over-predict heave in excavation problems. these models
also overpredict the width and underpredict the gradient of the settlement trough behind
excavations and above tunnels. small-strain stiffness can improve this. moreover, small-
strain stiffness can reduce the influence of the particular choice (position) of the finite
element model boundaries. last but not least, small-strain stiffness can be used to model
the effect of hysteresis and hysteretic damping in applications involving cyclic loading
and dynamic behaviour.
recently, the Plaxis Hs model was extended with small-strain stiffness. the small-
strain stiffness formulation was based on research by thomas Benz at the federal Wa-
terways engineering and research institute (BaW) in karlsruhe, and supervised by the
institut für Geotechnik of the University of stuttgart [1,�]. the extended Hs model, named
Hssmall, has been implemented in a special Plaxis version for Pdc members (Pdc =
Plaxis development community). the extra information on which the small strain stiffness
formulation is based comes from s-shaped curves where the shear modulus, G, is plotted
as a (logarithmic) function of the shear strain, g, ranging from very small strain levels
(vibrations) up to large strain levels. the s-curve is characterised by the small-strain
shear modulus, G0, and the shear strain at which the shear modulus has reduced to
0.7 times G0 (g0.7); see figure 1. these two parameters are the only extra parameters
compared to the original Hs model. in fact, it has been demonstrated by comparing
figure 1: s-curve for reduction of shear modulus with shear strain
s-curves of several different types of soil that the particular shape of the s-curves
does not change much and that g0.7 is generally around 10-�. G0 generally ranges from
around 10 times Gur for soft soils, down to �.5 times Gur for harder types of soil, where
Gur = Eur / (�(1+nur)).
figure � shows compuational results of an example excavation project in medium stiff
soil, where both the Hs model and the Hssmall model with similar parameters were
used to model the soil behaviour. the additional parameters in the Hssmall model were
taken G0ref = � Gur
ref and g0.7 = 10-�. the results indicate that the Hssmall model gives
a stiffer over-all behaviour and a smaller (less wide) settlement trough behind the
retaining wall. according to Peck [�], the width of the settlement trough behind the retaining
wall in relatively stiff soils extends to a maximum of two times the excavation depth (here
1� m), which corresponds well with the results of the Hssmall model.
figure �: example excavation project. above using the existing Hs model Below using the new Hssmall model
Variations with the position of the bottom and side boundaries have indicated that the
Hssmall model is indeed less sensitive for the precise position of the boundaries than
other Plaxis soil models.
in another application a small soil column was modelled in a dynamic application, ap-
plying a harmonic horizontal prescribed displacement at the bottom. figure � shows the
results in terms of shear stress vs. shear strain for a stress point near the bottom of
the model. the Hs and the mc model do not show any hysteresis, whereas the Hssmall
model clearly shows hysteresis for subsequent loading cycles, resulting in more realistic
material damping.
in the coming period the Hssmall model will be further tested in various applications.
therefore, different material data sets will be defined for different types of soil, and it
will be validated to what extend these data sets can be used in various applications.
meanwhile, a small group of users can already get familiar with the new model.
figure �: shear stress as function of shear strain, indicating hysteresis Blue: mohr-coulomb model red: Hardening soil model Gold: Hssmall model
References:[1] Benz t. (�006). Small-strain stiffness of soils and its numerical consequences.
Ph.d. thesis. institut für Geotechnik, Universität stuttgart.
[�] Benz t., schwab r. and Vermeer P.a. (�006). A small strain overlay model I:
model formulation. int. J. numer. anal. meth. Geomech., in progress.
[�] Peck r.B. (1969). Deep excavations and tunneling in soft ground.
state of the art report. Proceedings 7th icsmfe, mexico.
6 7
Introductiona characteristic feature of ice-covered waters is the presence of ice ridges. they are
formed by compression or shear in the ice cover and are often found in the shear zone
between the land fast ice, i.e. frozen to the shore and the drift ice. a high ridging intensity
may also be found in straits and sounds with strong currents. ice ridges are in general
long and curvilinear features. ridges often exist in combination with rafted ice and this
combination is named a ridge field. ice ridges do in many cases give the design loads for
such structures as offshore platforms and bridge piers. they may also cause significant
impediment to navigation. When drifting into the shallow waters, ice ridges may scour the
seabed and create a serious threat to all seabed installations such as pipelines, cables,
wellheads etc. the loads from ice ridges on various structures are not clear, and one of
the major deficiencies is that the mechanical properties, in time and space, of first-year
sea ice ridges are not well known.
a typical view of the sea ice cover (in the area of high interest with respect to oil and gas
exploration) is shown in figure 1.
a typical section of the first-year ice ridge is schematically shown in figure �. a first-year
ice ridge consists of the sail, the consolidated layer and the keel. the sail is visible, or
above the water surface part of a ridge (ref. figure 1), similar to that of an iceberg.
the keel is a part of a ridge that is below the water surface. the consolidated layer is the
uppermost refrozen part of the keel. the keel draught can reach �5 – �0 m.
figure 1: sea ice cover
figure �: cross-section of an ice ridge
loads from sea ice ridges on offshore structures are usually estimated by calculating the
loads from the sail, the consolidated layer and the keel separately and adding them at
the end. the consolidated layer is often considered to be a thick level ice sheet so that the
thickness and the strength (flexural and compressive) become the vital parameters. the
sail and the keel are normally called ice rubble and are often treated as a granular mate-
rial. a number of testing programmes was conducted both in the laboratory and in-situ
during the last three decades. ice rubble was normally described either as tresca or as
mohr-coulomb material. the cohesion and the angle of internal friction of ice rubble were,
and still are a subject for investigation and discussion. Variation in the above strength
parameters was, in particular for the laboratory tests, exceedingly high and there are a
number of reasons for this. in contrast with other granular materials, the lifetime of ice
rubble within the ice ridge is limited to a few months. during this period the ice rubble
constantly evolves throughout the initial, main and the decay phases. laboratory tests on
ice rubble are normally conducted during the initial phase, which is believed to be the
most sensitive with respect to the testing conditions. When modelling ice rubble, the ther-
modynamic similarity is of high significance in addition to geometric, kinetic and dynamic
similitude between the prototype and the model. all this, even intending, is very difficult
to achieve in reality. different interpretation of test result with subsequent comparison
neither helped to meet the agreement on how to describe the ice rubble strength.
this article briefly descries how PlaXis was used to simulate some physical tests on
ice rubble with respect to derivation of its strength. the developed pseudo-discrete con-
tinuum model of ice rubble is also presented as a tool to describe and analyse the char-
acteristic behaviour of ice rubble at failure.
Punch testing of ice rubbleduring the design phase offshore structures are subjected to physical model testing.
action from the ice and the ice ridges is studied in ice basins. in the course of conceptual
design of the arctic shuttle Barge equipped with the submerged turret loading system,
the model tests were conducted at the Hamburg ship model Basin (tmr Programme
from the european commission through contract n°erBfmGect950081) as described in
details by Jensen, �00�. the use of the barge concept for export of oil includes the follow-
ing four major phases: initial approach to the loading facility, final approach and hook-
up, loading and departure. during loading the major concerns are related to ice loads on
the tanker from ice ridges and mooring/riser interference with ice when the ridges are
passing by. figure � shows an illustration of the test with the barge and the stl going
through the ice ridge.
one of the major problems with laboratory testing is scaling. Gravity forces dominate the
problem studied and thus the froude scaling was used: the gravity field was not scaled
and the basic scaling unit was the length (l). the flexural strength of the ice was scaled,
but not that of the ice rubble as there are no standardised methods for ridge production
in ice facilities. it was therefore of high importance to conduct separate tests on ice
rubble in order to estimate its strength so it could be related to the full-scale values.
two types of tests were conducted and analysed: plane strain and circular plate punch
tests. figure � shows a cross-section along the centreline of the ridge with the corre-
sponding test locations.
as shown in figure �, the plain strain test was performed in such a way that it was pos-
sible to observe the failure inside the rubble behind the transparent lexan glass wall.
in the circular plate test, the large circular platen with diameter of 0.7 m was loaded by
��0 kg of steel weights. Penetration force (Fz) and displacements of the platen (Z1) and
of the surrounding ice (Z2) were measured in both tests.
the derivation of the rubble strength from punch tests where boundary conditions are not
properly controlled is not straight forward. two approaches have been used in the past
to interpret the test results: analytical and numerical. among the analytical approaches
both the different forms of limit equilibrium method and the upper bound theorem of plas-
ticity were used. the major problem was associated with the use of the two-parametric
mohr-coulomb failure criterion since tests result in one equation and two unknowns in
this case. simplifications were done and ice rubble was considered either as a friction-
less or as a cohesionless material. in the latter case, however, unrealistically high values
figure �: Barge test set-up (from Jensen, �00�)
figure �: Punch tests set-up
of the internal friction angle were obtained. as the analytical approaches do not take
the complexity of deformation mode into account, they may yield to unreliable results.
numerical modelling of punch tests turned out to be a useful tool for assessment of the
ice rubble strength. finite-element simulations of the physical tests described above were
conducted in Plaxis 8 for the plain strain test and in Plaxis �d tunnel for the circular plate
test as described by liferov et al. (�00�, �00�). the finite-element model of the circular
plate punch test is shown in figure 5.
the quasi-static approach was used in the simulations and the iterative calculations
were carried out until the prescribed displacement level was reached. the initial stress
state inside the ice rubble was neglected, i.e. the ice rubble was considered as a weight-
less material. the level ice and the consolidated layer were modelled as an elastic mate-
rial and their elastic properties were estimated during physical model testing. ice rubble
was modelled as the elastic-perfectly plastic mohr-coulomb material. the ice sheet was
modelled resting on the underlying elastic layer whose properties were calibrated such
that it simulated the water for the particular needs (elastic padding). in the part of the
cross-section under the ice rubble the elastic layer underneath was deactivated as it
could impose incorrect boundary conditions at the bottom of the keel. in this area the
buoyancy force was modelled as an imposed traction load applied to the bottom of the
consolidated layer and it was set proportional to the displacement of the ice sheet in
Z-direction. as the ice became fully submerged, the buoyancy load was set to a constant
value. the displacement of the platen was prescribed to a value that was recorded during
the experimental testing. the material properties of the ice rubble were then adjusted
in order to fit the recorded load - displacement curves Fz versus Z1 and Z2. in case of
the plain strain test, the failure mechanism observed through the transparent wall was
an extra “input” to the curve fitting. an example of the experimental and the simulated
failure mechanisms inside the rubble is shown in figure 6.
the goal of the finite element modelling was to evaluate the strength of the model ice
Finite element modelling of ice rubble
Plaxis PracticePlaxis Practice
Pavel liferov. Barlindhaug Consults as, Norway; NiP-informatica, Russia
figure 5: finite-element model of the simulated punch tests
8 9
Finite element modelling of ice rubble
rubble by fitting the experimental curves by the simulated ones. Both the shape of the
curves and their ultimate values were fitted. nevertheless, no particular efforts were put
into “refining” of the fitting and the attention was rather focused on the parametric study.
examples of results from the circular plate test simulations is shown in figure 7 where the
experimental (recorded) and the simulated load – displacement curves are shown.
two stiffness regions separated at about 1-� mm displacement were obtained as a result
a: experimental
b: simulation (total strains)
figure 6: failure mechanism in plain strain test
figure 7: load-displacement curves, circular plate test (note: recorded force includes the buoyancy load that is �0 kn at �0 mm displacement).
of the simulations shown in figure 7. this coincides well with the experimental records.
the analysis of the material state at the transition point shows that in the first high stiff-
ness region the ice rubble fails in tension in the lower part of the ridge as shown in figure
8 (cross-section taken at the centreline of the plate, prescribed displacement not shown).
after that a shear slip surface begins to develop through the keel and a substantial part
of the rubble experiences tensile distortion (figure 9) and the stiffness drops approaching
zero at failure (figure 10).
(a) Plastic (red) and tension cut-off (white) points (b) relative shear stresses (red = 1) figure 8. stress state inside the ice rubble at 1.5 mm displacement of the plate.
(a) Plastic (red) and tension cut-off (white) points (b) relative shear stresses (red = 1) figure 9. stress state inside the ice rubble at 6 mm displacement of the plate.
(a) Plastic (red) and tension cut-off (white) points (b) relative shear stresses (red = 1)
figure 10. stress state inside the ice rubble at the ultimate failure.
the simulations revealed that the failure mechanism of ice rubble consisted of the plate
bending and the punch through modes. curve fitting showed that frictional resistance
of the ice rubble against the pushing load was minor compared to the cohesive compo-
nent. it became apparent that the frictional resistance could not be mobilized along the
entire failure plane because of the extensive tensile zone in the lower part of the rubble.
the parametric study showed that the strength parameters of the material do not contrib-
ute independently to the peak load. Basically, it was found that strength of the ice rubble
in the punch test is largely dominated by cohesion and tensile strength. the local failure
mode is rather complex and depends on combination of the material properties. it was
also shown that increase of the friction angle may cause decrease of the attained peak
load when the bending of the ice formation is not prevented. it may also be pointed out
that the cohesion of the simulated ice rubble could be in order of 0.5 kPa while its tensile
strength is about 0.�5 kPa. these values correspond to the assumed angle of internal
friction of �5º and they provide the best fit of the experimental curves. this corresponds to
the full-scale cohesion value of 1�.5 kPa that is in a fairly good agreement with what was
experimentally measured in the full-scale punch tests in-situ.
Pseudo-discrete modelling of ice rubbledetailed analysis of the in-situ tests on ice rubble described by liferov and Bonnemaire
(�00�) revealed that there exist essentially two failure modes of the ice rubble. the pri-
mary failure mode is associated with breakage of the initial rubble skeleton. the skeleton
consists of the ice blocks that are fused together by freeze bonds. the secondary failure
mode is associated with propagating failure and mobilization of the frictional resistance.
incorporation of these experimentally observed failure modes into modelling of rubble
– structure interaction can provide an opportunity to conduct more physically sound
simulations and to verify the existing models.
the pseudo-discrete continuum model of ice rubble deformation is a combination of
a discrete particles assembly (i.e. ice rubble accumulation) and a fe analysis of this
assembly. the primary rational for developing such a model was to produce a tool that
would enable a numerical study of the primary failure mode of ice rubble that in many
cases can dominate the global rubble resistance. this model, described by liferov (�00�),
provides the possibility to simulate contacts between ice blocks and to account for their
local failure. the modelling procedure consists of two basic steps. first, the assembly
of blocks is generated. a block generator was developed to fulfil this task. in the second
step, the generated assembly is used as a geometrical input for the fe analysis to study
its behaviour under different boundary conditions. a typical view of the direct shear box
fe model is shown in figure 11.
a series of experiments was conducted to study the variation of the interface strength
reduction factor R, the confining pressure p, the angle of internal friction of the parent
ice blocks j and the contact area between the blocks A. three randomly generated block
assemblies were used for each set of the parametric analysis. figure 1� shows an
example of simulation results: the influence of confining pressure p on the rubble shear
resistance t. for the range of the present analysis t increased non-linearly with increasing
p as shown in figure 1�.
Plaxis PracticePlaxis Practice
Prescribed displacement
Primary failure planes
Punch platesecondary failure planes
Continuation
figure 11: fe model of the direct shear box test
lid
Horizontal translation is constrained Vertical translation is constrained
interface elementto simulatefreeze bond
10 11
at the confining pressure p of 1 kPa the rubble failed in tension, i.e. the tensile stresses
at the contacts between the blocks exceeded their tensile strength. the failure mode
changed with increase of p and became a combination of tension and shear modes. shear
failure dominated at p = 10 kPa.
a good correlation was found between the interface strength (i.e. freeze bond strength) in
the pseudo-discrete model and the equivalent cohesion (i.e. shear strength) in the con-
tinuum model. at present, a research project is ongoing to study the freeze bond strength
between the ice blocks in-situ. this knowledge would enable to provide better assessment
of the ice rubble shear strength, both in time and space, which can then be used in practi-
cal engineering applications.
Discussionmechanical properties of ice rubble is a relatively new item in the engineering ice
research. Practical difficulties with conducting both the laboratory and the in-situ tests
figure 1�: direct shear box test: t vs. p diagram
Finite element modelling of ice rubble
Plaxis Practice
Plaxis and GeoDelft
since GeoDelft and Plaxis signed their Memorandum of Understanding on further cooperation, much progress has been made.
among other things, Geodelft and Plaxis have undertaken the update of their
mutual product Plaxflow. as a first step that will eventually lead to the development of
Plaxflow �d, an update of the present �d product Plaxflow was decided for. the direct
occasion to undertake this job was the development of the multi-language user interface
for Plaxis �d, which will eventually enable a chinese and Japanese version of the Plaxis
User interface. this update is in a finishing stage when you read this Bulletin.
Besides that, a new product development line has been undertaken in a mutual project
between Geodelft, stuttgart University (Prof Pieter Vermeer) and Plaxis. the project is
aimed at the development of a new analysis tool for large deformations, such as for
cone-penetration and excavation problems, see figure 1, and most likely for a number of
offshore problems such as spud can installation.
the method, known as material Point method or sometimes referred to as Particle in cell
method, has shown some major progress in the last decade. originally some two decades
ago, the method appeared in fluid dynamics. later on the method was adopted by some
universities which modified the equations to solve geotechnical problems. amongst these
first geotechnical developers are well-known researchers as Prof schreyer, University
of albuquerque in new mexico, Prof. Wieckowski from lodz University in Poland, and dr
coetzee from stellenbosch University in south africa. With the latter a cooperation and
support agreement has been achieved to upgrade his �d formulation into a �d version
using Plaxis. for those who are familiar with the formulation of the finite element method,
the material points in mPm might roughly be compared to moving integration points in a
fem formulation. therefore it was decided to use the Plaxis �d source code as a basis for
the further development of a �d mPm code. at this moment dr claus Wisser has started
working at stuttgart University iGs with Prof Vermeer, to develop a static version of the
code. We are looking forward for his first results in roughly about one and a half years.
further Plaxis and Geodelft intend to upgrade the compatibility between the Plaxis and
Geodelft software by making interactions between a number of delft Geosystem software
products and Plaxis V8. the results of these developments are foreseen in the upcoming
year. on the longer term it is decided to match the Plaxis and Geodelft software range upto
a compatible series of software for geotechnial purposes, where delft geosystem software
is aimed at application oriented software products for Geotechnical design and Plaxis is
aimed at general purpose analysis software for geo-engineering in �d and �d.
further Plaxis and Geodelft have decided to increase their cooperation with respect to
international marketing by using their mutual international networks and e.g. combining
efforts in the case of presence at international conferences and business fairs.
resulted in a quite approximate description of the ice rubble strength. the numerical
tools such as fem in general and the PlaXis code in particular are believed to be useful
in planning and analysing the non-standard tests as well as performing further applied
analyses. ice rubble resembles granular materials and therefore the soil material models
can be used to simulate its behaviour.
ReferencesJensen, a., �00�. evaluation of concepts for loading of hydrocarbons in ice-infested
waters. Phd thesis, norwegian University of science and technology, department of
structural engineering.
P. liferov, a. Jensen, k.V. Høyland and s. løset, �00�. on analysis of punch tests on ice
rubble. 16th international symposium on ice (iaHr’0�), dunedin, new Zealand, december
�00�, vol. �, pp. 101-110.
P. liferov, a. Jensen and k.V. Høyland, �00�. �d finite element analysis of laboratory punch
tests on ice rubble. Proceedings of the 17th conference on Port and ocean engineering
under arctic conditions (Poac), trondheim, norway, June 16-19, vol. �, pp. 611-6��.
liferov, P. and Bonnemaire, B., �00�. ice rubble behaviour and strength, Part i: review
of testing methods and interpretation of results. Journal of cold regions science and
technology, �1: 1�5-151.
liferov, P., �00�. ice rubble behaviour and strength, Part ii: modelling. Journal of cold
regions science and technology, �1: 15�-16�.
Dead Load
figure 1: example of �d material Point method analysis for large deformation analysis, e.g. bucket excavation, by coetzee
Virgin Material
Bucket Displacement = 800 mm
Continuation Klaas Jan Bakker
1� 1�
Simulation of soil nail in large scale direct shear test
Plaxis PracticePlaxis Practice
arny lengkeek, Witteveen+BosMarco Peters, Grontmij Netherlands
Introductionin the netherlands we have a history of living with water. dikes, both at the sea and at riv-
ers, need to protect us against flooding. the height of the dikes in the netherlands needs
to be increased in the future. adjustment is needed because of climate changes, raising
sea level and ongoing settlements. if raising of the crest level is required, stability is best
increased by widening the dike. However, this is not possible in case of existing buildings
at the land side and in the case narrowing of the river flow section is not allowed. Within
this framework the project innovations on stability improvement enabling dike elevations
(inside) started in �001.
consortium inside squad, a dutch co-operation between Boskalis b.v., Van Hattum en
Blankevoort b.v., Grontmij b.v. and Witteveen+Bos b.v. developed a new concept “dijkver-
nageling”, which stands for reinforcing dikes by soil nailing. this way steeper slopes are
possible. figure 1 shows the typical failure mechanism of a dike and the reinforcing by
soil nailing. the soil nails add to the stability of the dike, but do not take over the full load.
the dike keeps functioning the way it did for hundreds of years. the soil nails increase the
internal strength of the dike in three ways:
- anchorage of the sliding section;
- increasing of the contact stress at the shear plane;
- shear connection of the sliding section.
Researchreinforcing embankments by soil nailing is a proven method to stabilise, especially in
case of constructing a steeper slope in granular soils. But how does it work in dikes
consisting of soft clay?
the main investigation goals were defined as:
- what is the behaviour of soil nails in soft clay in a direct shear mode;
- what are the �d and group effects of the soil nails;
- is it possible to develop a design model.
figure 1: typical section of reinforced dike by soil nailing
dike reinforcement by soil nailing is mainly achieved by the anchorage. However, the
shear connection by the soil nails is important for the performance of the soil nail. the
research is focued on the shear connection in clayey soils, as there is little experience on
this subject.
to investigate the behaviour of soil nail in clayey soils, large scale direct shear tests were
executed to explore the strengthening effects with different types of soil nails in clayey
soils. the tests were executed in the laboratory by two circular steel structures with a
diameter of 0.9 m and a total height of 1.� m. the soil nail was placed centric in the cyl-
inder with a rotation possibility at the bottom. the upper ring could displace by horizontal
loading, while the lower ring was fixed.
Before performing the large scale direct shear tests, analytical and numerical finite ele-
ment analyses (fem) were carried out to define the soil nail properties such as diameter
and bending stiffness in relation to the soil strength and the soil stiffness. after the
tests, postdiction analyses were made to understand the behaviour and improve the fem
model.
a total of fifteen large scale direct shear tests have been performed with different soil
nails. three of these tests have been performed without soil nails for reference, six tests
have been performed on very soft clay and two tests have been performed with three soil
nails in one cylinder.
typical soil nails that were used are:
- steel rods with a grout body of about � to 6 cm;
- carbon rods with a grout body of about � to 6 cm;
- HdPe strips with a width of 10 to 15 cm.
figure �: large scale direct shear test
Soil behaviour in direct shear testa proper way to investigate the maximum shear stress in soil is the direct shear test. this
test shows the relation between the present normal stress and the maximum mobilised
shear stress. for a drained situation coulomb derived the relation as:
t = c + sn tanj
in the case of undrained situations, one may asscume j = 0 and c = cu. although the
maximum shear stress could directly be obtained, there are some disadvantages about
the direct shear test. the location of the deformation plane is prescribed, and the stress
situation in the soil sample is not uniformly recorded. in contrast of the simple shear test,
the displacements in a direct shear test are not homogeneous but lenticular shaped as
shown in figure �.
Test resultfigure � presents the test results of the large scale direct shear tests on soft clay. the
saturated density is 17 kn/m³ and the undrained shear strength is 9 kn/m². the total jack
force has been normalised by the total undrained shear strength of the cross section; this
is called the strengthening ratio. a ratio of 1.0 is equal to the maximum strength of the
soil, any increase is caused by the soil nails. the maximum strengthening of 1 soil nail
at �0 cm displacement is about �5% (ratio is 1.�5). for � soil nails it is 75%. the force
by � soil nails is equal to � times that of 1 soil nail. it can be concluded that there is no
negative group effect for soil nails in a close grid (less than 0.5 m).
figure �: strengthening by soil nail in direct shear test with soft clay
FE model in prediction analysisdue to nonsymmetrical loading, numerical analysis was not possible with axi-symmetric
�d calculations. the use of PlaXis �d tunnel makes it possible to simulate these large
scale direct shear tests and �d effects of the soil nailing properly.
in the prediction analysis, several models were developed to simulate undrained
behaviour of natural clay, see figure �. in �d tunnel, the tunnel structure will normally be
generated in a horizontal z-direction. to model an undrained situation without increas-
ing effective stresses in y-direction perpendicular to the tunnel lining, the initial stress
condition was created in the first calculation step by using a uniformly distributed z-load.
the material model used in the prediction analysis is the mohr-coulomb model, with
c = cu , E = Eundr;50 and j set to zero. the different soil nails were modelled by a linear
elastic tunnel structure with bending stiffness ei and extension stiffness ea.
a
B
c
figure �: developed models in prediction analysis
1� 15
Simulation of soil nail in large scale direct shear test
Plaxis PracticePlaxis Practice
Postdiction modelto postdict the large scale direct shear tests more properly and to obtain more accurate
stress results, the �d tunnel model was modified by using gravity loading with an adapt-
ing gravitation direction parallel to the tunnel lining and with adapted boundary condi-
tions. moreover, an improved modelling of soil behaviour was considered by using the
Hardening soil model and by distinguishing between effective stresses and (excess) pore
pressures using the undrained setting.
figure 5: Postdiction reference model without nail, shear stresses
figure 6: Postdiction model with soil nail, total stresses
figure 5 presents the postdiction reference model without soil nail (half symmetric).
the maximum calculated shear stress tyz was in fact equal to the input value used for the
undrained shear stress (c = cu ). the shear stresses in the symmetric cross section also
showed a lenticular development. figure 6 presents the postdiction model with soil nail.
there is an obvious interaction between the soil nail and the horizontal stresses.
soil properties prediction postdiction
model prediction a, B, c mohr coulomb Hardening soil
analysis drained undrained
material type (clay) undrained undrained
Unit weight 18.� kn/m� 18.� kn/m�
elastic modulus e50 (ref.) 700 kPa 700 kPa
elastic modulus eoed (ref) - 197� kPa
elastic modulus eur (ref) - �100 kPa
Power m - 0.8
Poisson’s ratio 0.�9 0.�0
friction angle 1° 1°
cohesion �7.5 kPa �7.5 kPa
shear stress a: x-y plane z-x plane
B + c: z-x plane
initial stress z-load gravity loading (drained)
table 1: material models and material properties
figure 7: Postdiction model results, load-displacement curves with and without soil nail
the strengthening by a soil nail in a large scale direct shear test can also be determined
with the postdiction model. first step is to perform postdiction analyses with soil nail.
second step is to switch off the soil nail and repeat the calculation. figure 7 shows the
difference between load-displacement curves of clay with soil nail and without soil nail.
the strengthening ratio can be determined by the ratio of both analyses results.
Comparison of resultsthe strengthening effect has been determined by the interpretation of the measurements
and the postdiction analyses with the �d tunnel model. the results of the strengthening
ratio are presented in figure 8. the symmetry line represents the ideal relation between
measurement and model. most results do have a margin of less than 10% from this line.
the results are very satisfying in particular because a variety of soil nails have been
tested in normal and very soft clay. the �d tunnel model is capable to perform good
postdiction analyses and can be used for future designs.
figure 8: comparison of strengthening ratio by interpretation of measurements and by
the postdiction model
Conclusions on modellingWith regard to the presented results, one can conclude that PlaXis �d tunnel offers a
good tool to model the large scale direct shear tests. However, some suggestions how to
obtain better results are presented below, as there is always room for improvement.
mesh refinement with smaller element sizes might lead to even better results, but using
smaller elements could increase calculation time dramatically. Using a half space sym-
metric model was one of the methods to reduce calculation time.
further investigation on the influence of shaft friction between nail and soil and between
soil and inner side of cylinder is recommended. the actual undrained shear strength is
not constant in the different stress paths in the used model. overconsolidation has been
taken into account, but the degree of overconsolidation in the used clay after installation
in the test rings is not recorded.
one of the advantages of the �d tunnel postdiction model is the fact that identical soil
conditions are compared with and without the application of a soil nail. in this way, some
of the inadequacies in modelling leading to different results can be faded out.
Continuation
16 17
Staged construction of embankments on Soft Soil using Plaxis
Plaxis PracticePlaxis Practice
Gautam Bhattacharya, Professor, Department of Civil Engineering, Bengal Engineering and science University, shibpur, Howrah 711 103, iNDiasudip Nath, Graduate student, Department of Civil Engineering, Bengal Engineering and science University, shibpur, Howrah 711 103, iNDia
Introductiona problem, which is rather common in the fields of geotechnical and highway engineering,
arises when road embankments of moderate to large heights are to be constructed on very
soft soils with low shear strength and high compressibility in the shortest possible time.
But, owing to the low shear strength of the subgrade (foundation) soil, the full height of
the embankment cannot be built at a time and the so-called staged construction has to
be resorted to. to implement such a phased construction it is required to carry out an
analysis to determine beforehand the sequence of construction to be followed in a given
situation such that the embankment can be constructed as quickly as possible while
ensuring a reasonable margin of safety.
Analysis of embankment stability using PlaxisPlaxis (Version 8.0) has the provision for �d (plane strain) stress-displacement as well
as safety factor analysis of road embankments founded on layered deposit having any
complex soil and pore water pressure conditions. analysis can be done based on a number
of options available, e.g., type of element, coarse mesh or fine mesh, soil models such as
mohr-coulomb model (mc), soft soil creep model (ssc), Hardening soil model (Hs) etc.
further, the updated mesh and consolidation options can be invoked for a more rigorous
determination of embankment displacements and excess pore pressure dissipation.
Illustrative ExampleDescriptionto illustrate the staged construction of a road embankment in the shortest possible time
compatible with the safety requirements at the intermediate stages of construction as
well as during its service life (long term), the embankment section exemplified in the
tutorial manual (lesson 5) has been selected for the present study (figure 1).
the geometry model, material sets, mesh generation and initial conditions adopted in the
tutorial manual (lesson 5) have been retained. specifically, a plane strain model with
15-node elements is utilized. the problem being symmetric, only one half is modeled.
the deformations of the deep sand layer are assumed to be zero; hence this layer is not
included in the model and a fixed base is used instead (figure �). the properties of the
different soil types are given in table 1. in the initial conditions, the hydrostatic pore water
pressures are based on a general phreatic level at the base of the clay layer.
safety analysis for staged constructionsince it is required to construct the embankment in the shortest possible time, the time
of construction in each stage should be such that it is just sufficient for the stability of
the embankment up to that height for a target factor of safety. the time of construction,
therefore, depends on the target factor of safety. the larger the factor of safety, longer
will be the time of construction in each stage. after the construction of a certain stage,
some time interval needs to be allowed for the improvement in undrained strength due to
consolidation, which is required for the stability of the increased height in the next stage.
further, after the construction of the total height is over, some amount of time needs
to be allowed for a certain percentage of consolidation to take place for which Plaxis
has a provision to calculate time of consolidation till the excess pore pressure becomes
less than a certain pre-assigned value (e.g., 1.0 kn/m�). thus, the total time required
includes the actual time of construction in each stage and the time interval between two
consecutive stages as well as after the final stage of construction. if the construction
sequence thus obtained is available to a practicing geotechnical engineer, for various
target factor of safety, it will enable him to make a trade-off between the time available
for the completion of the project and the amount of risk involved in selecting a particular
target factor of safety.
Resultssequence of constructionin the first stage, by trial runs, it has been observed that a height of �.0 m can be built by
allowing a minimum time of construction as �, �0, 50 and 70 days corresponding to target
factor of safety at the end of construction of 1.10, 1.15, 1.�0 and 1.�5 respectively. Before
the second stage of construction begins, it is required to allow a sufficient time interval
for substantial strength increase due to consolidation. However, it has been observed that
even after allowing a large time interval of more than 1000 days, the increased strength
is still not sufficient to raise the embankment by another �.0 m to its final height of �.0
m. it has therefore been decided to build the remaining height of �.0 m in two stages, 1m
in each stage, thus making it a �-stage construction. in the second stage, the required
minimum time interval comes out to be 75, 100 and 1�5 days corresponding to the target
factor of safety at the end of construction of 1.10, 1.15, 1.�0 and 1.�5 respectively. in this
case the minimum time of construction is �, 10, �5 and �5 days respectively. similarly, for
the third stage, the minimum time interval and time of construction have been obtained.
finally, the minimum time interval between the completion of construction and the time of
dissipation of excess pore water pressure to less than a value of 1 kn/m� has been found
out. the entire sequence of construction thus obtained has been presented in figure � for
various target factor of safety. the long term factor of safety of the completed embank-
ment is obtained as 1.�90.
Correlation Between Factor of safety and Displacementalthough safety analysis indicates the stability status of the embankment, a displace-
ment analysis is of interest to ensure its serviceability requirement; in other words, the
displacements occurring particularly at long term indicate whether the embankment
would perform satisfactorily during its design life. now, as discussed before, for the plan-
ning of staged construction, the geotechnical designer has to adopt a target factor of
safety. the engineering judgment to be applied in this case is obviously based on the
displacement estimated to take place at the end of construction as well as long term. for
the geotechnical engineer, therefore, it would be very useful, if a correlation is available
between the target factor of safety and the estimated vertical displacement at the end of
construction as well as at long term. figure � presents such a correlation in the form of a
plot of factor of safety against displacement.
Utilizing the Plaxis updated mesh option, the above mentioned displacements have been
re-evaluated and plotted against the target factor of safety in figure 5. it may be men-
tioned here that such an analysis does not provide values of safety factor and, therefore,
a revised construction sequence similar to figure � cannot be obtained. However, it is
observed that the time of consolidation following the end of construction comes out to
be appreciably less than in the original analysis. this may allow the engineer-in-charge
a little margin in this time interval before declaring the embankment ready for the con-
struction of pavement structure.
Summary and Conclusionin the present article an attempt has been made to demonstrate how the Plaxis (version
8) can be effectively utilized in providing the practicing geotechnical engineers with all
the relevant results of safety and displacement analyses that will enable him to exercise
engineering judgment in deciding on a judicious sequence of staged construction of a
road embankment. it is understandable that the sequence of construction depends on the
target factor of safety at the intermediate stages; the higher the target factor of safety the
longer it will take for the total construction to be completed. However, the displacement,
especially the vertical displacement at the end of construction as well as at the long term
should be of concern to the designer of such a project. the displacement is obviously
inversely proportional to the total time allowed and hence the target factor of safety. thus
it is a trade-off between the time available at hand and the maximum permissible vertical
displacement i.e. settlement of the embankment. keeping this in mind, the results of the
entire analysis have been summed up in the form of two plots – one giving the height of
construction vs. time for various factor of safety and the other, vertical displacement vs.
target factor of safety.
figure 1: road embankment on soft soil for the illustrative example
figure �: Plaxis model
figure �: construction sequence
figure �: Variation of top Vertical diplacement with fos
figure 5: Variation of top Vertical diplacement with fos (using Updated mesh)
table 1: material Properties of the road embankment and subsoil
18 19
Plaxis Practice
Recent activities
Plaxis StaffWe are pleased to announce that we appointed a new course coordinator. from february
1, �006, dennis Waterman will take over the position of Wout Broere. Wout was working
� days at Plaxis bv and � days at delft University . Wout got the opportunity to get a � days
job at the University and he will continue his part of writing manuals of upcoming new
Plaxis versions. dennis has already a long Plaxis history with support and programming
activities. Besides course coordination dennis will also stay responsible for the first line
support. during support peak periods he will be assisted by other Plaxis staff. Besides
these internal changes Plaxis staff is extended with eric Verschuur. eric studied technical
informatics and graduated at the Haagse Hogeschool and has a background in user inter-
face development. He is currently working on upgrading the �d Geothermic program.
due to continued growth, Plaxis bv has
additional positions available for;
- software Quality engineer
- senior software development engineer
- Programmer Graphical User interface
- numerical Geophysicist/Geohydrologist
see our website for detailed information.
a visited laboratory of the Bundes anstalt für Wasserbau in karlsruhe, Germany
Erwin Beernink
Plaxis Asiain asia we will enforce our activities with the assistance of William cheang. William
will act on behalf of Plaxis bv under the flag of “Plaxis asia”. He will be involved in pre
and after sales activities in asian countries were we do not have an agent. furthermore
William will assist our agents to promote Plaxis products and services via conferences,
courses and seminars. you can already get acquinted with him at the asian experienced
Plaxis Users course and Users forum in Phuket, april 17-�0. William did his undergradu-
ate and masters of science degree at the University of east london, United kingdom.
furthermore he did a doctoral study at the national University of singapore under the
title “axial soil nail-soil interaction: Quasi-static Pullout Behaviour of Passive Bonded
inclusions in residual soils”.
for Plaxis activities in china a cooperation agreement has been signed between Prof. e.X.
song of tsinghua University, Beijing and Plaxis bv. Professor song has contributed in the
past to the development of the Plaxis finite element program and the education to the
Plaxis users. see also the updated Plaxis History at our website. last months Prof. song
performed a quality check on the chinese Plaxis version of the user interface and manual.
We will also cooperate in the organization of Post academic computational Geotechnical
courses in china.
12th European Plaxis User Meeting
around 80 participants attended the european Plaxis Users meeting �005, hosted by the
Bundesanstalt für Wasserbau in karlsruhe, Germany. many interesting presentations
were given by engineering consultants and researcher, on geotechnical engineering ap-
plications, research-like projects, soil modelling aspects, parameter selection and other
Plaxis-related subjects. in addition to the presentations, group discussions on special
themes resulted in the generation and distribution of knowledge and new ideas.
an extra day was devoted to user-defined soil models, where researchers presented
implementational aspects and applications of special soil models. this day was not only
visited by researchers, but also by consulting engineers with interest for advanced soil
modelling
Based on the number of participants and the positive comments during and after the
meeting it can be concluded that the meeting was again very succesful. We are look-
ing forward to the next european Plaxis users meeting in karlsruhe in november �006.
see the agenda on our website or the backcover of this bulletin for upcoming User
meetings and other activities.
New products/updates in �005 we worked hard on improvements of our products and services. latest extensions
can be downloaded from our website. Plaxis Version 8 update pack 7 has been extended
with;
- steady state groundwater flow for axisymmetric problems has been reintroduced
- the modified cam clay model (has been added to the available soil models)
- a set of revised manuals
- alternative examples (lesson � and 6) using the Hardening soil model
furthermore some bugs have been solved including problems on east asian Windows
systems. from update pack 7 also the chinese and Japanese version of Plaxis V8 are
available.
in Version 1.5 of �dfoundation many new features are included like;
- consolidation analyses
- creep: secondary compression with the soft soil creep model
- new vertical elements: vertical beams, vertical line loads and vertical fixities
- k0-procedure
- display of (volume) pile forces
- Usage of stress points and nodes of structural elements for curves
Plaxis User meeting �005
Plaxis finite element code for soil and rock analyses
Plaxis BVPo Box 57�
�600 an delft
the netherlands
tel: +�1 (0)15 �51 77 �0
fax: +�1 (0)15 �57 �1 07
e-mail: [email protected]
Website: www.plaxis.nl
13 - 15 March 2006finite elemente in der Geotechnik,
theorie und Praxis - stuttgart, Germany
20 - 23 March 2006international course for experienced
Plaxis Users - antwerp, Belgium
17 - 19 april 2006�nd asian course for experienced
Plaxis Users - Phuket, thailand
20 april 20061st asian Users day - Phuket, thailand
18 - 22 april 2006
100th anniversary earthquake conference
san fransisco, U.s.a.
22 - 27 april 2006ita �006 - seoul, south korea
9 - 11 May 2006Plaxis Workshop
cairo, egypt
15 - 18 May 2006curso internacional de Geomecanica
computational - Valparaiso, chile
16 May 2006french Plaxis Users meeting
Paris, france
29 - 31 May 2006Xiii. danube-european conference on
Geotechnical engineering
ljubljana, slovenia
1 - 3 June 2006international course on computational
Geotechnics - ljubljana, slovenia
31 May-2 June 200610th Piling and deep foundations
amsterdam, the netherlands
2 - 4 June 2006 Geoshanghai international conference
shanghai, china
20 - 22 June 2006course computational Geotechnics
manchester, United kingdom
28 - 30 June 2006icde �006 deep excavations -
singapore
July 2006short course on computational
Geotechnics - Boulder, Usa
16 - 18 august 2006standard course on computational
Geotechnics - Johannesburg, south africa
27 - 31 august 2006coBramseG �006 - curibita, Brazil
6 - 8 september 2006 6th european conference on numerical
methods in Geotechnical engineering
Graz, austria
29 - 30 september 2006Baugrund tagung - Bremen, Germany
9 - 11 November 2006european Plaxis User meeting
karlsruhe, Germany
13 - 15 November 2006short course on computational
Geotechnics - trondheim, norway
November 2006 Pratique éclairée des éléments finis
en Géotechnique - Paris, france
December 2006dutch Plaxis Users meeting
delft, the netherlands
Activities 2006
500�
866