Bulletin 19, Spring 2006 - Plaxis

Plaxis finite element code for soil and rock analyses 

Plaxis Bulletin 

issue 19 / March 2006 

Simulation of soil nail in large scale 

direct shear test 

Finite element modelling of ice rubble 

Staged construction of embankments on Soft Soil using Plaxis

Editorial 

Colophon 

Ronald Brinkgreve 

Editorial 

New Developments 

Plaxis Practice 

Finite element 

modelling of ice rubble 


Simulation of soil nail in 

large scale direct shear 

test 


Staged construction of 

embankments on Soft 

Soil using Plaxis 

Recent activities 

3 

4 

6 

12 

16 

18 

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 geotechnical 

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 

bulletin@plaxis.nl 

or by regular mail to: 

Plaxis Bulletin 

c/o Erwin Beernink 

PO Box 572 

2600 AN Delft 

The Netherlands 

The Plaxis Bulletin has a total circulation of 10.000 copies and is distributed worldwide. 

Editorial Board: 

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 kernel 

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. 

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 3D was used for the validation of punch testing results 

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 compromise 

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 issues. 

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). 

Wout Broere 


Erwin Beernink 

François Mathijssen





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 -3 ) 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, smallstrain 

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 smallstrain 

stiffness formulation was based on research by Thomas Benz at the Federal Waterways 

Engineering and Research Institute (BAW) in Karlsruhe, and supervised by the 

Institut für Geotechnik of the University of Stuttgart [1,2]. 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, G 0 , and the shear strain at which the shear modulus has reduced to 

0.7 times G 0 (g 0.7 

); 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 

S-curves of several different types of soil that the particular shape of the S-curves 

does not change much and that g 0.7 

is generally around 10 -4 . G 0 generally ranges from 

around 10 times G ur for soft soils, down to 2.5 times G ur for harder types of soil, where 

G ur = E ur / (2(1+n ur )). 

Figure 2 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 

ref ref 

taken G 0 = 3 G ur and g 0.7 

= 10 -4 . 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 [3], 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 

12 m), which corresponds well with the results of the 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, applying 

a harmonic horizontal prescribed displacement at the bottom. Figure 3 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. 

Figure 3: Shear stress as function of shear strain, indicating hysteresis 

Blue: Mohr-Coulomb model 

Red: Hardening Soil model 

Gold: HSsmall model 

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. 

References: 

[1] Benz T. (2006). Small-strain stiffness of soils and its numerical consequences. 

Ph.D. Thesis. Institut für Geotechnik, Universität Stuttgart. 

Figure 1: S-curve for reduction of shear modulus with shear strain 

Figure 2: Example excavation project. 

Above using the existing HS model 

Below using the new HSsmall model 

[2] Benz T., Schwab R. and Vermeer P.A. (2006). A small strain overlay model I: 

model formulation. Int. J. Numer. Anal. Meth. Geomech., in progress. 

[3] Peck R.B. (1969). Deep excavations and tunneling in soft ground. 

State of the art report. Proceedings 7th ICSMFE, Mexico.




Pavel Liferov. Barlindhaug Consults AS, Norway; NIP-Informatica, Russia 

Introduction 

A 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 2. 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 25 – 30 m. 

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 material. 

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 thermodynamic 

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 continuum 

model of ice rubble is also presented as a tool to describe and analyse the characteristic 

behaviour of ice rubble at failure. 

Figure 3: Barge test set-up (from Jensen, 2002) 

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 4 shows a cross-section along the centreline of the ridge with the corresponding 

test locations. 

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 3D tunnel for the circular plate 

test as described by Liferov et al. (2002, 2003). The finite-element model of the circular 

plate punch test is shown in Figure 5. 

Punch testing of ice rubble 

During the design phase offshore structures are subjected to physical model testing. 

Figure 5: Finite-element model of the simulated punch tests 

Figure 1: Sea ice cover 

Figure 2: Cross-section of an ice ridge 

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, 2002. The use of the barge concept for export of oil includes the following 

four major phases: initial approach to the loading facility, final approach and hookup, 

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 3 shows an illustration of the test with the barge and the STL going 

through the ice ridge. 

Figure 4: Punch tests set-up 

As shown in Figure 4, the plain strain test was performed in such a way that it was possible 

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 

230 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 plasticity 

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 frictionless 

or as a cohesionless material. In the latter case, however, unrealistically high values 

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 weightless 

material. The level ice and the consolidated layer were modelled as an elastic material 

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




Continuation 

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 1-2 mm displacement were obtained as a result 

Primary failure planes 

Secondary failure planes 

Punch plate 

Figure 7: Load-displacement curves, circular plate test (Note: recorded force includes the 

buoyancy load that is 40 kN at 40 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 stiffness 

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). 

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 component. 

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 contribute 

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 0.25 kPa. These values correspond to the assumed angle of internal 

friction of 35º and they provide the best fit of the experimental curves. This corresponds to 

the full-scale cohesion value of 12.5 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 rubble 

Detailed analysis of the in-situ tests on ice rubble described by Liferov and Bonnemaire 

(2004) revealed that there exist essentially two failure modes of the ice rubble. The primary 

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 (2004), 

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 12 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 12. 

a: Experimental 

Lid 

Prescribed displacement 

(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. 


Figure 9. Stress state inside the ice rubble at 6 mm displacement of the plate. 

Interface element 

to simulate 

freeze bond 

b: Simulation (total strains) 

Figure 6: Failure mechanism in plain strain test 


Figure 10. Stress state inside the ice rubble at the ultimate failure. 

Horizontal translation is constrained 

Vertical translation is constrained 

Figure 11: FE model of the direct shear box test



Plaxis and GeoDelft 

Continuation 

Klaas Jan Bakker 

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 continuum 

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 practical 

engineering applications. 

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. 

References 

Jensen, A., 2002. 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, 2002. On analysis of punch tests on ice 

rubble. 16 th International Symposium on Ice (IAHR’02), Dunedin, New Zealand, December 

2002, vol. 2, pp. 101-110. 

P. Liferov, A. Jensen and K.V. Høyland, 2003. 3D finite element analysis of laboratory punch 

tests on ice rubble. Proceedings of the 17 th Conference on Port and Ocean Engineering 

under Arctic conditions (POAC), Trondheim, Norway, June 16-19, vol. 2, pp. 611-623. 

Liferov, P. and Bonnemaire, B., 2004. Ice rubble behaviour and strength, Part I: Review 

of testing methods and interpretation of results. Journal of Cold Regions Science and 

Technology, 41: 135-151. 

Liferov, P., 2004. Ice rubble behaviour and strength, Part II: Modelling. Journal of Cold 

Regions Science and Technology, 41: 153-163. 

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 3D, an update of the present 2D product PlaxFlow was decided for. The direct 

occasion to undertake this job was the development of the multi-language user interface 

for Plaxis 2D, 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 2D formulation into a 3D 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 3D source code as a basis for 

the further development of a 3D 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 2D and 3D. 

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. 

Figure 12: Direct shear box test: t vs. p diagram 

Discussion 

Mechanical 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 

Dead Load 

Virgin Material 

Bucket Displacement = 800 mm 

Figure 1: Example of 2D Material Point Method analysis for large deformation analysis, e.g. bucket excavation, by Coetzee 

10 11



Simulation of soil nail in large scale direct shear test 

Arny Lengkeek, Witteveen+Bos 

Marco Peters, Grontmij Netherlands 

Introduction 

In the Netherlands we have a history of living with water. Dikes, both at the sea and at rivers, 

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 2001. 

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 “Dijkvernageling”, 

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. 

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 1.2 m. The soil nail was placed centric in the cylinder 

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 element 

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 3 to 6 cm; 

- carbon rods with a grout body of about 3 to 6 cm; 

- HDPE strips with a width of 10 to 15 cm. 

Soil behaviour in direct shear test 

A 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 + s n tanj 

In the case of undrained situations, one may asscume j = 0 and c = c u . 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 2. 

Test result 

Figure 3 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 20 cm displacement is about 25% (ratio is 1.25). For 3 soil nails it is 75%. The force 

by 3 soil nails is equal to 3 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). 

FE model in prediction analysis 

Due to nonsymmetrical loading, numerical analysis was not possible with axi-symmetric 

2D calculations. The use of PLAXIS 3D Tunnel makes it possible to simulate these large 

scale direct shear tests and 3D effects of the soil nailing properly. 

In the prediction analysis, several models were developed to simulate undrained 

behaviour of natural clay, see figure 4. In 3D Tunnel, the tunnel structure will normally be 

generated in a horizontal z-direction. To model an undrained situation without increasing 

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 = c u , E = E undr;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 1: Typical section of reinforced dike by soil nailing 

Figure 4: Developed models in prediction analysis 

Research 

Reinforcing 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 3D and group effects of the soil nails; 

- is it possible to develop a design model. 

Figure 2: Large scale direct shear test 

Figure 3: Strengthening by soil nail in direct shear test with soft clay 

12 13



Simulation of soil nail in large scale direct shear test 

Continuation 

Postdiction model 

To postdict the large scale direct shear tests more properly and to obtain more accurate 

stress results, the 3D Tunnel model was modified by using gravity loading with an adapting 

gravitation direction parallel to the tunnel lining and with adapted boundary conditions. 

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 presents the postdiction reference model without soil nail (half symmetric). 

The maximum calculated shear stress t yz was in fact equal to the input value used for the 

undrained shear stress (c = c u ). 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 18.4 kN/m 3 18.4 kN/m 3 

Elastic modulus E 50 (ref.) 700 kPa 700 kPa 

Elastic modulus E oed (ref) - 1973 kPa 

Elastic modulus E ur (ref) - 100 kPa 

Power m - 0.8 

Poisson’s ratio 0.49 0.20 

friction angle 1° 1° 

cohesion 7.5 kPa 27.5 kPa 

shear stress a: x-y plane z-x plane 

B + C: z-x plane 

initial stress z-load gravity loading (drained) 

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 results 

The strengthening effect has been determined by the interpretation of the measurements 

and the postdiction analyses with the 3D 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 3D Tunnel model is capable to perform good 

postdiction analyses and can be used for future designs. 

Conclusions on modelling 

With regard to the presented results, one can conclude that PLAXIS 3D 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 symmetric 

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 3D 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. 

Table 1: Material models and material properties 

Figure 5: Postdiction reference model without nail, shear stresses 

Figure 8: Comparison of strengthening ratio by interpretation of measurements and by 

the postdiction model 

Figure 7: Postdiction model results, load-displacement curves with and without soil nail 

Figure 6: Postdiction model with soil nail, total stresses 

14 15



Staged construction of embankments on 

Soft Soil using Plaxis 

Gautam Bhattacharya, Professor, Department of Civil Engineering, Bengal Engineering and Science University, Shibpur, Howrah 711 103, INDIA 

Sudip Nath, Graduate Student, Department of Civil Engineering, Bengal Engineering and Science University, Shibpur, Howrah 711 103, INDIA 

Introduction 

A 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 Plaxis 

Plaxis (Version 8.0) has the provision for 2D (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. 

Figure 1: Road embankment on soft soil for the illustrative example 

Figure 2: Plaxis model 

included in the model and a fixed base is used instead (Figure 2). 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 construction 

Since 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 2 ). 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. 

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 2.0 m to its final height of 4.0 

m. It has therefore been decided to build the remaining height of 2.0 m in two stages, 1m 

in each stage, thus making it a 3-stage construction. In the second stage, the required 

minimum time interval comes out to be 75, 100 and 125 days corresponding to the target 

factor of safety at the end of construction of 1.10, 1.15, 1.20 and 1.25 respectively. In this 

case the minimum time of construction is 2, 10, 25 and 35 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 2 has been found 

out. The entire sequence of construction thus obtained has been presented in Figure 3 for 

various target factor of safety. The long term factor of safety of the completed embankment 

is obtained as 1.390. 

Figure 4: Variation of Top Vertical Diplacement with FOS 

would perform satisfactorily during its design life. Now, as discussed before, for the planning 

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 4 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 mentioned 

here that such an analysis does not provide values of safety factor and, therefore, 

a revised construction sequence similar to Figure 3 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 construction 

of pavement structure. 

Summary and Conclusion 

In 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. 

Illustrative Example 

Description 

Figure 3: Construction sequence 

To 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 

Results 

Sequence of construction 

In the first stage, by trial runs, it has been observed that a height of 2.0 m can be built by 

allowing a minimum time of construction as 4, 20, 50 and 70 days corresponding to target 

factor of safety at the end of construction of 1.10, 1.15, 1.20 and 1.25 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 

Figure 5: Variation of Top Vertical Diplacement with FOS (using Updated Mesh) 

Correlation Between Factor of Safety and Displacement 

Although safety analysis indicates the stability status of the embankment, a displacement 

analysis is of interest to ensure its serviceability requirement; in other words, the 

displacements occurring particularly at long term indicate whether the embankment 

Table 1: Material Properties of the road embankment and subsoil 

16 17


Recent activities 

Erwin Beernink 

Plaxis Staff 

We are pleased to announce that we appointed a new Course Coordinator. From February 

12 th European Plaxis User Meeting 

Around 80 participants attended the European Plaxis Users Meeting 2005, hosted by the 

Plaxis Asia 

In Asia we will enforce our activities with the assistance of William Cheang. William 

New products/updates 

In 2005 we worked hard on improvements of our products and services. Latest extensions 

1, 2006, Dennis Waterman will take over the position of Wout Broere. Wout was working 

3 days at Plaxis bv and 2 days at Delft University . Wout got the opportunity to get a 4 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 interface 

development. He is currently working on upgrading the 3D 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. 

BundesAnstalt für Wasserbau in Karlsruhe, Germany. Many interesting presentations 

were given by engineering consultants and researcher, on geotechnical engineering applications, 

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 looking 

forward to the next European Plaxis users meeting in Karlsruhe in November 2006. 

See the agenda on our website or the backcover of this bulletin for upcoming User 

Meetings and other activities. 

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 17-20. William did his undergraduate 

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. 

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 4 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 3DFoundation 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 2005 

A visited laboratory of the Bundes Anstalt für Wasserbau in Karlsruhe, Germany 

18 19

Plaxis finite element code for soil and rock analyses 

Activities 2006 

13 - 15 March 2006 

Finite Elemente in der Geotechnik, 

Theorie und Praxis - Stuttgart, Germany 

2 - 4 June 2006 

GeoShanghai International Conference 

Shanghai, China 

20 - 23 March 2006 

International Course for Experienced 

Plaxis Users - Antwerp, Belgium 


Course Computational Geotechnics 

Manchester, United Kingdom 

17 - 19 April 2006 

2nd Asian Course for Experienced 

Plaxis Users - Phuket, Thailand 


ICDE 2006 Deep Excavations - 

Singapore 

20 April 2006 

1st Asian Users Day - Phuket, Thailand 

18 - 22 April 2006 

100th Anniversary Earthquake Conference 

San Fransisco, U.S.A. 

22 - 27 April 2006 

ITA 2006 - Seoul, South Korea 

9 - 11 May 2006 

Plaxis Workshop 

Cairo, Egypt 


Curso Internacional de Geomecanica 

Computational - Valparaiso, Chile 

16 May 2006 

French Plaxis Users Meeting 

Paris, France 


XIII. Danube-European Conference on 

Geotechnical Engineering 

Ljubljana, Slovenia 


International Course on Computational 

Geotechnics - Ljubljana, Slovenia 

31 May-2 June 2006 

10th Piling and Deep Foundations 

Amsterdam, the Netherlands 

July 2006 

Short Course on Computational 

Geotechnics - Boulder, USA 

16 - 18 August 2006 

Standard Course on Computational 

Geotechnics - Johannesburg, South Africa 

27 - 31 August 2006 

COBRAMSEG 2006 - Curibita, Brazil 

6 - 8 September 2006 

6th European Conference on Numerical 

Methods in Geotechnical Engineering 

Graz, Austria 

29 - 30 September 2006 

Baugrund Tagung - Bremen, Germany 

9 - 11 November 2006 

European Plaxis User Meeting 

Karlsruhe, Germany 

13 - 15 November 2006 

Short Course on Computational 

Geotechnics - Trondheim, Norway 

November 2006 

Pratique éclairée des éléments finis 

en Géotechnique - Paris, France 

December 2006 

Dutch Plaxis Users Meeting 

Delft, The Netherlands 

Plaxis BV 

PO Box 572 

2600 AN Delft 

The Netherlands 

Tel: +31 (0)15 251 77 20 

Fax: +31 (0)15 257 31 07 

E-Mail: info@plaxis.nl 

Website: www.plaxis.nl 

5004866

Bulletin 19, Spring 2006 - Plaxis

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?