plaxis bulletin autmn 2015

Title Title

Issue 38 / Autumn 2015

Plaxis Bulletin

PLAXIS 2D and 3D applications in geotechnical earthquake engineering

2D FEM analysis compared with the in-situ deformation measurements: A small study on the performance of the HS and HSsmall model in a design

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Table of contents

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Colophon

Any correspondence regarding the Plaxis Bulletin can be sent by e-mail to:

[email protected]

or by regular mail to:

Plaxis Bulletinc/o Annelies VogelezangPO Box 5722600 AN DelftThe Netherlands

The Plaxis Bulletin is a publication of Plaxis bv and is distributed worldwide among Plaxis subscribers

Editorial board:Ronald BrinkgreveErwin BeerninkYos SimanjuntakMartin de KantArny Lengkeek

Design: Judi Godvliet

For information about PLAXIS software contact your local agent or Plaxis main offi ce:

Plaxis bvP.O. Box 5722600 AN DelftThe Netherlands

[email protected]: +31 (0)15 251 7720Fax: +31 (0)15 257 3107

The Plaxis Bulletin is the combined magazine of Plaxis bv and the Plaxis users association (NL). The Bulletin focuses on the use of the fi nite 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 e-mail) 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 fi gures are used in the text, it should be indicated where they should be placed approxi-mately in the text. The fi gures themselves have to be supplied separately from the text in a vector based format (eps,ai). If photographs or ‘scanned’ fi gures are used the author should ensure that they have a resolution of at least 300 dpi or a minimum of 3 mega pixels. The use of colour in fi gures and photographs is encouraged, as the Plaxis Bulletin is printed in full-colour.

Editorial03

04 New developments


06

PLAXIS Expert Services update05


10

Recent activities18

Upcoming events20

www.plaxis.com l Autumn issue 2015 l Plaxis Bulletin 3

We are delighted to publish the autumn 2015 edition of the Plaxis Bulletin, including two new user articles. Following the release of PLAXIS 2D 2015 and 2D Thermal module earlier this year, PLAXIS 3D AE has just been delivered with new additions and improvements relevant to the fi eld of tunnelling, offshore geotechnics and rock mechanics.

To overcome the limitations of the fi nite element method (FEM) especially when dealing with large deformations and material fl ow, the New Develop-ment column puts forward PLAXIS MPM version that is being developed based on the Material Point Method (MPM). As well as a brief explanation about this method, an early implementation of PLAXIS MPM in the area of offshore geotechnics is presented.

In the PLAXIS Expert Services update, we take a look at a benchmark study dealing with 3D dynamic analysis that Plaxis provided to Langan. In addition to this, a two-day in-house training focused on the use of PLAXIS 3D and 3D Dynamics module was also delivered at Langan’s New York City offi ce in the USA. This way, the engineers are equipped with the backgrounds of advanced soil modelling, consolidation, undrained behaviour and 3D dynamic analysis using PLAXIS.

The need of more accurate information on the earthquake design ground motion has led to an increased use of numerical codes. Without doubt, a good knowledge on modelling facilities and their applicability to different conditions are of great importance when choosing a proper numerical code for geotechnical earthquake engineering projects.

The fi rst user’s article emphasizes the modelling aspects in PLAXIS to correctly perform a dynamic analysis. Particular attention is given to geometry and lateral boundary conditions, constitutive models, input motion and bottom boundary conditions, mesh and calculation parameters, and output facilities.

The second user’s article involves the excavation of a building pit in the city of Amsterdam. Two distinctive constitutive models in PLAXIS, namely the Hardening Soil (HS) model and the Hardening Soil with small-strain stiffness (HSsmall) model, were applied to assess the soil deformations as a result of excavation.

This article highlights the performance of the HS model and HSsmall model. In view of validation, the results obtained using PLAXIS were compared with the measured data.

In our Recent Activities section, we look back at some of the events that our Asiapac and Americas offi ces hosted or participated in and report the 21st European Plaxis Users Meeting (EPUM) in Gescher, Germany, which was sponsored by HUESKER.

For our worldwide presence on events or hosted courses, we refer you to the upcoming events listed on the backside of this Bulletin.

We wish you a pleasant reading experience and look forward to receiving your feedback on the autumn 2015 edition of the Plaxis Bulletin.

The Editors

Editorial

4 Plaxis Bulletin l Autumn issue 2015 l www.plaxis.com

New developments

Ronald Brinkgreve, Plaxis bv

In the last 25 year, the � nite element method (FEM) has evolved from a research tool to a daily analysis and design tool in geotechnical engineering practice. Plaxis has played a pioneering role in this process and continues to provide new features to make geotechnical � nite element simulations comfortable and more realistic. As with all numerical methods, FEM also has its limitations; for example when it comes to very large deformations and material � ow. To overcome this limitation, Plaxis is working on a new development based on the Material Point Method (MPM). This article gives some explanation about the method and shows a very early application.

The Material Point Method has similarities with FEM. However, the soil domain is now modelled with ma-terial points (comparable with stress points in FEM) whereas the underlying element mesh is only used as a calculation grid. After calculating deformations in each load step, the calculation grid is restored whilst the material points remain at their deformed position. In this way, material points may move from one cell to another. The MPM calculation process is visualised in Figure 1:

Challenges of MPM calculationsThe use of MPM in practical applications brings some challenges, such as:

• Points moving from one cell to another• Dealing with empty cells• Determining active model boundaries• Connecting MPM to FEM domain• Application of loads and boundary conditions• Smoothing of stresses and strains• Cohesive-frictional contact formulation• Stability of the calculation process

The Plaxis research and development team is working on these challenges to ensure that the fi rst PLAXIS MPM version is robust and user-friendly, just as our FEM versions.

Applications in offshore geotechnicsPLAXIS 3D can be used very well to analyse the bearing capacity of offshore foundations, like mud mats, piles, suction anchors and spud cans. There are, however, limitations when it comes to installation effects and penetration of piles and anchors in the seabed. MPM can overcome these limitations, and is capable of analysing the path and resistances related to spudcan penetration and extraction as well as cable and pipeline movements.

A particular problem with severe consequences is the situation when a spudcan is installed in a seabed that consists of a strong soil layer overlying a weak layer. During ballasting of the offshore platform, the spudcan could punch through the strong layer, whilst the weak layer will provide insuffi cient resistance to stop the penetration. As a result, the platform could encounter large differential settlements and, in the worst case, it could even fall over. This situation was modelled in a very preliminary MPM version of PLAXIS, based on Case 2 of the publication by Khoa (2013).

The dimensions of the spudcan and soil layers are given in Figure 2, while the layer properties are given in Table 1. The resulting load-displacement curve is shown in Figure 3, with an indication of the punch-through point.

References• Khoa, H. D. V. (2013). Large deformation fi nite

element analysis of spudcan penetration in layered soils, Proceedings of the 3rd International Symposium on Computational Geomechanics (COMGEO III), Krakow, 570–584.

Clay Layer A Clay Layer B

SuA = 11.0 kN/m2 SuB = 38.3 kN/m2

EA = 4934 kN/m2 EB = 17178 kN/m2

Figure 1: Three phases in an MPM calculation step

Figure 2: Spudcan geometry

Table 1: Layer properties

Figure 3: Load-displacement curve

1. Initialisation Phase 2. Lagrangian Phase 3. Convection Phase


Konstantinos Syngros, Ph.D., PE, Langan, New York, USA

PLAXIS Expert Services update

Langan has performed FEM modelling in support of tall building projects on challenging soil and rock conditions all around

the world. The modelling requirements for these projects have become increasingly more demanding, with some involving the

evaluation of time dependent settlements, factors of safety for slope stability, and time-domain dynamic analyses.

Langan presented PLAXIS Expert Services with a complex 3D model for a 3D-dynamic-analysis benchmark study and requested that PLAXIS 3D is used to obtain the solution. Following the benchmark study, we partnered with PLAXIS Expert Services to provide a two-day in-house training course on the modelling aspects of this benchmark problem.

The training course was held at Langan’s New York City offi ce and consisted of 10 engineering professionals. The purpose of the workshop was to educate engineers about the backgrounds of advanced soil and structural modelling, soil consolidation, soil undrained behavior, and 3D dynamic analyses using PLAXIS.

With this specialized training, the participants have become well-versed in setting up PLAXIS 3D models for complex excavations with multiple construction stages and changing water conditions, as well as to perform site response and liquefaction analysis using the features of the PLAXIS Dynamics module.

About LanganFounded in 1970, Langan is a multi-discipline con-sulting fi rm that provides geotechnical, site/civil and environmental engineering services. The fi rm employs more than 900 professionals and has 28 offi ces all over the world (United States, Middle East, South America). Langan has been involved in the geotechnical and seismic design of many signature projects, such as the Kingdom Tower (the next tallest building in the world), and the Jakarta Signature Tower.

“We were very pleased with the support and training we received from

PLAXIS Expert Services. Plaxis presented very advanced material in a

very organized and professional manner, and answered clearly all our

questions. We consider this training a very successful event, and we are

all better equipped to meet the challenges of our projects.”


• the appropriate selection of the calculation pa-rameters for the time-step integration

Geometry and lateral boundary conditionsReality consists of an infi nite continuous soil medium that has to be reduced to a finite representative model. The geometry of the model infl uences the mesh settings and the choice of the most appropriate boundary conditions to represent the far-fi eld medium or to perform a 1D wave propagation analysis. The far-fi eld medium is simulated with the use of free-fi eld elements (Figure 1), where the vertical boundaries absorb the incident waves and are linked to each other through the earthquake signal, while tied degrees-of-freedom allow to model a reduced geometry by connecting the nodes at the same elevation on the vertical boundaries. The main advantage of theuse of tied degrees-of-freedom is the reduced computational cost for one-dimensional wave propa-gation analysis with the advantage of using more representative soil constitutive models compared to the equivalent-linear visco-elastic codes.

Constitutive modelsRelevant results have been achieved in PLAXIS by implementing and validating constitutive models for seismic analysis. Every constitutive model allows to model some aspects of the material behaviour but it always involves a certain number of limitations. To choose the most representative material model, it is important to identify the dominating aspects of the material behaviour for the specifi c case-study.

In earthquake engineering problems, the soil is subjected to cyclic shear loading, showing a non-linear dissipative behaviour. Its stiffness decays with the increasing strain level induced by the loading, and the sequence of loading and unloading paths generates an hysteretic loop with dissipation of energy and consequent damping (Figure 2). Some of the traditional constitutive models, as for example Mohr-Coulomb, cannot describe the hysteretic damping. Instead, the total amount of damping is introducedthrough the frequency-dependent Rayleigh formu-lation in terms of viscous damping, that has to be


For years, the site response analysis has been usuallyperformed using the equivalent-linear visco-elastic approach, provided in well-known one-dimensional codes. However, this approach implies important limitations that can be overcome with the use of numerical models. In particular, PLAXIS allows to:

• reproduce the non-linear dissipative behaviour of the soil subjected to cyclic loading, taking into account the effect of cyclic degradation

• model the soil-fl uid interaction, accounting for the possible seismically induced excess pore water pressures by means of fully coupled effective stress analysis and the use of advanced constitutive models

• create one-, two- or three-dimensional models, based on the specifi c design conditions and/or the local site characteristics

Detailed information on the facilities implemented inPLAXIS for dynamic analysis and the description of theavailable constitutive models can be found in the PLAXIS Manuals. In addition, some elaborated ex-amples are published in the PLAXIS Knowledge Base platform to help engineers with the use of PLAXIS for seismic analysis (Laera & Brinkgreve, 2015). The most relevant aspects related to this type of projects are:

• the defi nition of an appropriate geometry and the corresponding required lateral boundary conditions

• the selection of the most representative constitutive models for the soil involved and the calibration of the model parameters

• the application of the input motion and defi nition of the bottom boundary condition

• the discretization of the model in terms of type and dimension of the element in the fi nite element mesh

Anita Laera, MSc., Plaxis bv

In current design practice, geotechnical earthquake engineers are often responsible for providing the appropriate design ground

motions for structural analysis, studying the effects of earthquakes and elaborating methods to mitigate these effects. A site

response analysis is required to investigate the complex interaction between the seismic waves and the local site conditions.

Morphology, stratigraphy, water conditions and soil properties have a high in� uence not only on the characteristics of the earthquake

(for example in terms of duration, peak acceleration and frequency content) but also on the modelling strategy.

Figure 1: Free-fi eld boundaries in a 2D dynamic analysis


consistent with the level of strain induced by the earthquake. In PLAXIS, material models capable of capturing the soil damping through the hysteretic loop are available in the library or as user-defi ned soil model, such as the HSsmall and the Generalised Hardening Soil model. Advanced constitutive models usually require an adequate knowledge of the model parameters and a good calibration strategy. For this reason, some examples have been published in the PLAXIS Knowledge Base (Laera & Brinkgreve, 2015), showing the applicability of the material models men-tioned above and the parameter calibration based on well-known geotechnical tests and literature data. The case-study has been validated against the results of the analysis performed with a one-dimensional code, showing comparable results with several advantages in the modelling process and with the important capability of determining the excess pore pressures.

Due to the increasing interest towards liquefactionanalysis, a site response analysis has been performedand published in the PLAXIS Knowledge Base (Laera &Brinkgreve, 2015) using the UBC3D-PLM model, available as a user-defi ned soil model in PLAXIS. This model accounts for the accumulation of strains and pore pressures in sandy soils, that is determinant to capture the onset of liquefaction. The calibration of the parameters and the comparison with the results of a simplifi ed procedure are described, showing that PLAXIS can be used to trigger liquefaction.

Input motion and bottom boundary conditionAmong the other input data to the design project, the seismic motion has to be correctly assigned at the base of the model (Figure 3). PLAXIS allows to model the bottom boundary as either a fully refl ective boundary or a compliant base. The former represents the case of a very soft soil overlying a rigid bedrock, while the latter can model an absorbent boundary. In both cases, the signal can be applied through a prescribed displacement in terms of time-history accelerations, velocity or displacement. No conversion into a load-history signal is required, since PLAXIS automatically transforms the input into stresses applied to the main domain. The input signal required in the two possible alternatives at the base of the model is

Figure 2: Hysteretic behaviour in the HSsmall model

τ (k

Pa)

γ (%)



different, since a fully refl ective boundary requires the full input motion (given by the superposition of upward and downward waves) as measured at the bedrock depth, while the compliant base formulation is based only on the upward motion (in the case of both the horizontal and vertical component of the earthquake), which could be roughly considered as half of the motion measured at the outcropping rock.

Mesh and calculation parametersThe accuracy of the calculation depends also on the size and distribution of the elements in the mesh. In PLAXIS the mesh generation is based on a robust triangulation procedure (Figure 4). In the case of a dynamic analysis, the size of the elements needs to be

chosen based on the characteristics of both the soil and the input signal. The average element size must be less than or equal to one-eight of the wavelength, which depends on the lowest shear wave velocity in the soil and the maximum frequency component of the input wave (i.e. the highest frequency component that contains appreciable energy). These aspects are taken into account also in the calculation process, where the calculation parameters should be consist-ently specifi ed.

The dynamic equations of motion are integrated basedon time-stepping schemes characterized by calculationfeatures related to the accuracy, numerical damping and stability (the number of steps and substeps,

the Newmark damping coeffi cients and the mass matrix, among the others). The automatic procedure implemented in PLAXIS ensures that a wave does not cross more than one element per time step: the critical time step is fi rst estimated according to the element size and the material stiffness, then the time step is adjusted based on the number of data points specifi ed as dynamic multipliers.

Output facilitiesA considerable amount of output information can be inspected in the PLAXIS Output program. At the end of the calculation, the deformed mesh can be viewed and, based on the stored number of steps, it is possible to create an animation.

Figure 4: 3D geometry and mesh

Figure 3: Time history acceleration

t (sec)

a x (g

)



Besides the quantities that can be displayed in termsof contour plots for any kind of calculation, additional dynamic parameters can be chosen, as for example velocities and accelerations. For soils, in the case of advanced constitutive models like HSsmall, Generalized Hardening Soil and UBC3D-PLM, other parameters, such as the stiffness, the accumulated excess pore pressures and their ratio with respect to the initial effective stresses, that allows to evaluate the onset of liquefaction in the case the UBC3D-PLM material model has been used (Figure 5), can be inspected. As for structures, it is possible to evaluate the stresses distribution and the amount of displacements at the end of the dynamic analysis.

In design projects, it is often required to extract time history quantities and response spectra at some desired depths, as for example the foundation level. Via the Curve facility in PLAXIS, it is possible to create several plots for preselected points (nodes or stress points) in the mesh. Charts of time-history displacements, velocities and accelerations at the selected nodes can be generated and also trans-formed in their corresponding representation in the frequency-domain. Among the other curves, response spectra can be generated for preselected nodes. They represent the locus of the maximum response of a structure, idealized as a single degree

of freedom system, for different values of stiffness and damping ratio. The response spectra in terms of accelerations, known as PSA spectra, are useful to determine the predominant period, i.e. the period related to the peak PSA value, and the acceleration associated to the natural period of vibration of the design structure (Figure 6).

ConclusionsIn this article, a general overview of PLAXIS capabilitiesin geotechnical earthquake engineering projects hasbeen presented. The dynamic analysis of a geo-technical system depends on an extensive site characterization, a good knowledge on the advan-tages and limitations of the numerical codes and an appropriate choice of the several components that defi ne the model.

Several new features have been implemented in PLAXIS in the last years and more documentation arenow available to provide a useful framework for dy-namic fi nite element analysis. Further studies aiming at investigating and extending the validation of PLAXIS in different dynamic environments are encouraged.

Figure 5: Pore pressure ratio for triggering liquefaction Figure 6: PSA spectrum

References• Laera, A., Brinkgreve, R.B.J. (2015). Ground response

analysis. Plaxis Knowledge Base.• Laera, A., Brinkgreve, R.B.J. (2015). Site response

analysis and liquefaction evaluation. Plaxis Know-ledge Base.

1.00

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The deformation behaviour as a result of excava-tion of a building pit in the inner city of Amsterdam is studied using the small strain stiffness model in PLAXIS 2D. The numerical results of deformations on the sheet pile wall during the different excavation stages obtained using PLAXIS are compared with the measured data. The objective of this study is to investigate the differences in computed deformation of the sheetpile wall when using the Hardening Soil model (HS) and the Hardening Soil Small Strain Stiff-ness model (HSsmall) employing the correlations of Alpan (1970) and Benz & Vermeer (2007) compared with the inclinometer data to asses their performance in an actual design process.

Background on the Small Strain Stiffness modelIt has been discovered from dynamic response analysis (Seed & Idriss, 1970), that most soils exhibit curvilinear stress-strain relationships. The shear modulus G (see Figure 1) is usually expressed as the secant modulus found at the extreme points of the hysteresis loop. The damping factor is proportional to the area found inside the hysteresis loop. The applied terminology of damping usually means the dissipation of strain energy during cyclic loading. From the defi nition of both physical properties, it shows that each of them will depend on the magnitude of the strain for which the hysteresis loop is determined. Thereby, both the shear moduli and damping factors must be determined as functions of the induced strain in a soil. Several studies have shown that the shear moduli of most soils decay monotonically with strain. Cavallaro et al. (1999), Mayne & Schneider (2001), and Benz et al. (2009) suggest that when the maxima are at very small strain levels, i.e. less than 10-6 to 10-5, which is associated to recoverable, the material behaviour is almost purely elastic (see Figure 2).

Ir. Martin A. op de Kelder, CRUX Engineering bv

Small-strain stiffness is seen as a fundamental property that almost all soils ranging from colloids to gravels and even rocks exhibit.

This is the case for static and dynamic loading, and for drained and undrained conditions. In literature, small-strain stiffness is

assumed to exist due to inter-particle forces within the soil skeleton. Therefore, it can be altered only if these inter-particle forces

are rearranged (Benz et al., 2009).

Figure 1: a) Defi nition of the secant shear stiffness Gsec of the hysteresis loop, b) Decrease of Gsec from its maximum value Gmax with increasing shear strain amplitude γampl [after Wichtmann & Triantafyllidis (2009)]

Figure 2: Characteristic stiffness-strain behaviour in logarithmic scale [after Atkinson & Sallfors (1991) and Mair (1993)]



The difference between ‘small’ strains and ‘large’ strains is usually taken at the point where classical laboratory testing, such as triaxial or oedometer testing without special instrumentation like local strain gauges has reached its limits, i.e. around 10-3 or 0.1%.

The preferred approach for the establishment of small strain stiffness parameters, which can be used in routine design obviously, starts with laboratory testing. The small strain stiffness implementation in PLAXIS is based on the small strain overlay model (Benz et al., 2009). Parameters G0 and γ0.7 are required input parameters. At the absence of experimental data for the determination of these two required parameters, approximations through correlations can be appropriate.

One of the often used correlations is the one sug-gested by Alpan (1970), where he used a single curve that describes the relationship between ‘static’ and ‘dynamic’ Young’s moduli. However, in his paper it does not become exactly clear what he means with the ‘static’ modulus as controversially discussed in literature by Benz & Vermeer (2007) and Wichtmann & Triantafyllidis (2007, 2009). Alpan (1970) reported the tangent elastic modulus E i as the inclination of the nearly linear initial portion of the deviatoric stress – strain curve, implying a stiffness for the fi rst loading, like today we would use E50. Wichtmann & Triantafyllidis (2009) further add to this that un- and reload cycles are not discussed in the paper of Alpan (1970) although Benz & Vermeer (2007) argued for Eur. Benz (2007) further adds that Alpan’s Estat is the apparent elastic Young’s modulus in conventional soil testing, e.g. (εa ≈ 10-3) in triaxial testing. According to Benz (2007) for soils with known Young’s modulus in triaxial unloading-reloading, the Alpan (1970) chart can provide an estimate for its very small-strain modulus E0.

In Deutsche Gesellschaft für Geotechnik (DGGT) (2001), the correlation between dynamic and static stiffness modulli is given in terms of the modulus M for one-dimensional compression (zero lateral strain). The correlation has been derived from the curve of Alpan (1970), but in contrast to that curve, DGGT (2001)

provides upper and lower boundaries for different types of soils. Unfortunately, no testing procedure for the determination of Mstat is prescribed, however because no un- and reloading cycles are mentioned in that research, the input parameter Mstat is probably meant as the stiffness modulus during fi rst loading. According to Wichtmann & Triantafyllidis (2009), the chart is used in this way in practice. Benz & Vermeer (2007) provided an alternative correlation between Mdyn/Mstat and Mstat, which is also based on the curve of Alpan (1970). In 2009, Wichtmann & Triantafyllidis have reported that for a given value of Mstat, the ratio of Mdyn/Mstat predicted by the correlation of Benz & Vermeer (2007) lay signifi cantly higher than those obtained from the relationship recommended in DGGT (2001).

They suggested that this is probably due to a different interpretation of Alpan’s Estat. Furthermore, Wichtmann & Triantafyllidis (2009) tested four samples of sand with different grain size distributions. If Estat is approximated by Estat = Eur ≈ 3E50 (Benz & Vermeer, 2007), instead of Estat ≈ E50 (Alpan, 1970), the obtained results can give a good fi t for sands. The curve of Alpan (1970) underestimates in the same experiment the obtained values Edyn/E50 by a factor in the range between 1,5 and 2,5. Both Benz & Vermeer (2007) and Wichtmann & Triantafyllidis (2009) concluded that if the original correlation by Alpan (1970) can be interpreted as Estat = Eur ≈ 3E50, based on both authors experiences, Alpan’s chart would provide reasonable estimates for the stiffness of soils.

Figure 3: Comparison of the correlations between Edyn/Estat and Estat according to Alpan (1970), DGGT (2001) and by Benz & Vermeer (2007) [after Wichtmann & Triantafyllidis (2009)]


As shown in Figure 3 and based on the aforemen-tioned statements, the following can be summarized in regard to the interpretation of Alpan’s Estat:

• Alpan (1970) Estat = Eur ≈ 3 E50

• DGGT (2001) Estat = Eur ≈ 3 E50

• Benz & Vermeer (2007) Estat = Eur ≈ 3 E50

Once Estat or Mstat has been determined, which is the static Young’s modulus E or the one-dimensional compression modulus M at very small strains in essence of E0 and M0 respectively, the small strain shear modulus G0 can be calculated if the Poisson ratio ν is known, or an estimation of it can be used.

The following relationship (Eq. 1) can be used to estimate the initial shear modulus G0 (Wichtmann & Triantafyllidis, 2009):

where:E0 = the Young’s modulus at very small strains [MPa]

ν = Poisson’s ratio [-]

For the calculation of the threshold shear strain γ0.7 at which the normalized small strain shear modulus G/G0 has reduced to 70%, the following relationship (Eq. 2) is used (Hardin & Drnevich, 1972):

where:c' = drained cohesion [kN/m2]

φ' = drained angle of internal friction [deg]

k0 = neutral earth pressure coefficient [-]

σ1' = effective vertical stress

(usually equal to σ3' = 100 kPa) [kN/m2]

Case Study - Vijzelhof ProjectThe Vijzelhof project in Amsterdam consists of a single storey underground parking space, which will be realised by the construction of a building pit using sheet piles and a single strut layer. Considering the non-linear behaviour of soils, a higher order constitutive model to capture most of the actual soil behaviour is needed. Herein, the deformation behaviour and its impact on the surrounding buildings will be analysed using the FEM code PLAXIS 2D. Measurements were carried out by the in-situ monitoring. In view of validation, the numerical results of horizontal deformations will be compared with the measured data. In order to capture the deformation behaviour of the sheet piles, several inclinometers were installed at the project site. The corresponding soil profile is presented in Figure 4. In this paper, the study is concentrated on the cross-section 1-1 because this was the most critical area. An overview of where the buidling pit is constructed can be seen in Figure 5.

Results and DiscussionsTo assess the deformations as a result of excavation, two phased calculations were performed. For both calculation phases, the predicted deformations of the left sheetpile will be compared with the measured data obtained during the construction of the building pit. The objective of this study is to investigate the performance of the HS model and HSsmall model employing the correlations of Alpan (1970) and Benz & Vermeer (2007), and to compare the numerical results with the inclinometer data so as to asses the model performance during the design process.

( ) ( )0 0 0

1 1 2

2 1 2 1G E M

νν ν

− ⋅= ⋅ = ⋅

⋅ + ⋅ −

( )( ) ( ) ( ){ }' ' ' '0.7 1 0

0

12 1 2 1 2

9c cos K sin

Gγ ϕ σ ϕ≈ ⋅ ⋅ ⋅ + ⋅ + ⋅ + ⋅ ⋅

⋅

Figure 4: Geotechnical soil profiles based on CPT’s and borings (op de Kelder, 2013)

( ) ( )0 0 0

1 1 2

2 1 2 1G E M

νν ν

−= =

+ − (1)

(2)( ) ( )'0.7 1 0

0

12 ' 1 cos 2 ' 1 sin 2 '

9c k

Gγ ϕ σ ϕ ≈ + + +

2D FEM analysis compared with in-situ deformation measurements: A small study on the performance of the HS and HSsmall model in a design


2D FEM analysis compared with in-situ deformation measurements:A small study on the performance of the HS and HSsmall model in a design

Figure 5: Study area [CRUX (2011), op de Kelder (2013)]

Figure 6: Global dimensions of the FEM model (top), zoomed in view (bottom)


It has to be noted that in any nummerical model, the presented results are not only affected by the selected small-strain stiffness parameters and used correlations but also by the other soil parameters, modelling assumptions, applied boundary conditions, phasing, etc. Keeping that in mind, in this article, the first and the last excavation phase will be discussed.

Phase 1The first excavation phase covers the modelling of excavation of the soils to a level of NAP +0.00m and of those that slope to NAP -0.50m (Figure 7). Figure 8 shows the predicted and measured horizontal displacements of the sheet pile. It can be seen that there is a large difference in deformations between the HS and HSsmall model. When compared to the

Figure 7: Configuration of phase 1

measured data, the HSsmall model underestimates the sheet pile horizontal deformation at the upper part of the sheet pile, whilst the HS model overestimates the horizontal deformation almost over the entire length of the sheet pile. The HS model in particular shows a good agreement with the measured data around the upper part of the pile. Clearly, the discrepancy between the numerical results obtained using the HS model and the field measurements is due to the inability of the HS model to incorporate small-strain stiffness behaviour.

Comparing the HSsmall model with the measured data, the numerical results at top level of the sheet-pile are approximately three times lower than the measured data. This is due to the very stiff response

of the soil in the first excavation phase as strains are still in the very small strain domain, thus a very stiff response results in small deformations. As the depth increases, the deformation decreases. Consequently, the soil response is stiffer at greater depth due to its stress-dependent stiffness moduli, and the relative numerical deformation difference between the HS model and HSsmall model becomes relatively small.

For the calculation of HSsmall parameters several correlations are available. For the calculation of the shear modulus G0, the correlation of Benz & Vermeer (2007) and that of Alpan (1970) interpreted according to Benz & Vermeer (2007), i.e. Estat ≈ Eur ≈ 3E50 was used. The threshold shear strain γ0.7 is calculated using Eq. (2).

Alpan (1970) Benz & Vermeer (2007)

Layer nameγunsat γsat c' ϕ’ νur k0 E50

ref Eoedref Eur

ref m G0 γ0.7 G0 γ0.7

[kN/m3] [kN/m3] [kPa] [deg] [-] [-] [kPa] [kPa] [kPa] [-] [kPa] [-] [kPa] [-]

Sand (anthropogenic) 15 18,4 0,1 30 0,15 0,50 2,00E+04 2,00E+04 6,00E+04 0,80 9,31E+04 1,55E-04 2,13E+05 6,78E-05

Estuary clay 16,9 16,9 6 26 0,15 0,50 1,00E+04 4,00E+03 2,50E+04 0,80 5,57E+04 2,74E-04 1,22E+05 1,25E-04

Holland peat 10,5 10,5 5 20 0,15 0,65 2,00E+03 1,00E+03 1,00E+04 0,80 3,39E+04 4,05E-04 7,18E+04 1,91E-04

Old marine clay 16,5 16,5 7 33 0,15 0,50 9,00E+03 4,30E+03 2,50E+04 0,80 5,57E+04 3,13E-04 1,22E+05 1,42E-04

Mudflat deposits sand 17,9 17,9 2 35 0,20 0,40 1,20E+04 5,00E+03 3,30E+04 0,56 6,26E+04 2,43E-04 1,39E+05 1,09E-04

Mudflat deposits clay 15,2 15,2 8 34 0,15 0,58 9,00E+03 6,10E+03 1,80E+04 0,80 4,63E+04 4,04E-04 1,01E+05 1,86E-04

Base peat 11,7 11,7 6 21 0,15 0,65 2,00E+03 1,00E+03 1,00E+04 0,80 3,39E+04 4,30E-04 7,18E+04 2,03E-04

1st sand layer 19,8 19,8 0,1 33 0,20 0,40 4,00E+04 3,00E+04 2,00E+05 0,50 1,92E+05 7,40E-05 4,62E+05 3,08E-05

Alleröd, clay 18,5 18,5 3 33 0,20 0,40 1,70E+04 1,30E+04 4,50E+04 0,50 7,51E+04 2,02E-04 1,69E+05 8,96E-05

2nd sand layer 19 19 0,1 35 0,20 0,40 3,50E+04 3,50E+04 1,90E+05 0,50 1,85E+05 7,88E-05 4,47E+05 3,27E-05

Table 1: Soil properties



Figure 8: First excavation phase

Phase 2The last excavation phase focusses on the deformation behaviour as a result of the excavation to NAP -2.55 m and fi nishing off the granular fi ll layer (top level NAP -2.30 m) as shown in Figure 9. The black dotted line in Figure 9 roughly indicates the surface level inside the building pit, in which the arrow represents the strut level.

The predicted horizontal deformations are presented in Figure 10. It can be sen that the numerical results obtained using the HSsmall model are in good agreement when compared to the measured data. Particularly in the lower part of the pile, the predicted deformations obtained using the HSsmall model underestimate the actual deformations.

This is likely caused by the relative high small-strain stiffness behaviour in the cohesive soil layers. In con-trast, the HS model overestimates the deformations of the sheet pile due to its inabbility to capture the actual small-strain behaviour in the soil troughout the excavation phasing.

The relative difference of deformations at the middle section of the sheet pile decreases as the excavation level increases. The deformations when obtained using the HSsmall model for both correlations are roughly two times lower than those of the HS model. The small-strain stiffness behaviour at this depth suggests that the G/Gur ratio in the mudfl at deposits layer containing sand is between 3 and 4. In the mudfl at deposits layer containing clay it is between 4 and 5.

In the base peat layer it is between 5 and 6. Compared to earlier phases (which are not all discussed in this article), the response of the soil is stiffer meaning that there is an increase in small-strain behaviour.

The stiffer response of the soil is probably triggered by the fact that the granular fi ll results in a ‘load trans-versal’ (after unloading from the excavation sequence the soil is compressed again), which causes a part of the elastic straining to be recovered in the HSsmall model and higher stiffness of the soil is observed.

The ordinary HS model has a lack of the ability to take into account this kind of small strain soil behaviour and therefore does not produce similar numerical results.



Figure 9: Confi guration of last excavation phase and application of granular fi ll layer

Figure 10: Last excavation phase, strut-window still in place



Conclusions Acknowledging that in any numerical model, the presented results are not only affected by the se-lected small-strain stiffness parameters and used correlations but also by the other soil parameters, modelling assumptions, applied boundary conditions, phasing, etc. the following conclusions can be drawn.

By means of the FEM code PLAXIS 2D the deforma-tion behaviour as a result of excavation of a building pit in the inner city of Amsterdam was investigated. Two different constitutive models, namely the HS model and HSsmall model were used in the analysis. Furthermore, the HSsmall model was distinguished based on either the Benz & Vermeer (2007) or Alpan (1970) correlations. To validate the model, the numeri-cal results are compared with the measured data.

When compared to the measured data, this study suggests that the HSsmall model employing either the Benz & Vermeer (2007) correlation or the Alpan (1970) correlation are better in capturing the soil behaviour than employing the HS model. When using the aformentioned correlations Estat should be interpreted as Estat = Eur ≈ 3E50. Then, the small strain stiffness behaviour which soils do exibit can be included in the numerical computation by employ-ing the HSsmall model. The Alpan (1970) correlation provides lower small strain stiffness moduli G0 and thus will be more conservative when applied in design compared to Benz & Vermeer (2007).

Secondly, this study also suggests that the HSsmall model, when using the presented correlations of Alpan (1970) and Benz & Vermeer (2007) in combination with the presented parameterset, tends to overestimate small-strain stif fness behaviour in the cohesive layers. Relatively high G/Gur ratios were computed in the cohesive layers compared to the non-cohesive layers that can result in smaller deformations. This may be related to the fact that the small-strain stiffness correlations of Alpan (1970) and Benz & Vermeer (2007) used in this study, are established

based on primarily tests of non-cohesive materials like sands and gravels. Only a small amount of tests have so far been conducted on cohesive materials like clays and peats.

The correlations provided by Alpan (1970) or Benz & Vermeer (2007) in combination with the unload-reload stiffness Eur and other soil properties such as c, φ, k0 and ν, can be used to determine the actual small-strain stiffness parameters G0, γ0.7 used in the HSsmall model of PLAXIS. At the absence of experi-mental data for the determination of parameters G0 and γ0.7, approximations through correlations can be appropriate. Keeping in mind that the standard procedure for estimating Eur through correlations in PLAXIS is to use Eur equals to 3E50.

References• Alpan, I. (1970). The geotechnical properties of soils.

Earth-Science Reviews, Vol. 6, pp 5–49.• Atkinson, J.H., Sallfors, G. (1991). Experimental

determination of soil properties. Proceedings of the 10th ECSMFE, Vol. 3, Florence, pp 915-956.

• Benz, T. (2007). Small-strain stiffness of soils and its numerical consequences. PhD Thesis, Dissertationsschrift. Mitteilung 55 des Instituts für Geotechnik, Universität Stuttgart.

• Benz, T., Vermeer, P.A. (2007). Zuschrift zum Beitrag ”Über die Korrelation der ödometrischen und der ”dynamischen” Steifigkeit nichtbindiger Böden” von T. Wichtmann und Th. Triantafyllidis (Bautechnik 83, No. 7, 2006). Bautechnik, Vol. 84 (5), pp 361–364.

• Benz, T., Vermeer, P.A., Schwab, R. (2009). A small-strain overlay model. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 33, pp 25–44.

• Benz, T., Vermeer, P.A., Schwab, R. (2009). Small-strain stiffness in geotechnical analyses. Bautechnik, Vol. 86 (S1), pp 16-27.

• Cavallaro, A., Maugeri, M., Lo Presti, D.C.F., Pallara, O. (1999). Characterising shear modulus and damping from in situ and laboratory tests for the seismic area of Catania, Proceedings of

the 2nd International Symposium on Pre-Failure Deformation Characteristics of Geomaterials, Torino 27-30 September, Balkema, Vol. 1, pp 51-58.

• CRUX Engineering B.V. (2011). “Parkeergarage 'De Vijzelhof' Noorderstraat Amsterdam, Risicoanalyse omgevingsbeïnvloeding”, RA11249a2, pp 5 – 8.

• DGGT (2001). Empfehlungen des Arbeitskreises 1.4 ”Baugrunddynamik” der Deutschen Gesellschaft für Geotechnik e.V.

• Hardin, B.O., Drnevich, V.P. (1972). Shear modulus and damping in soils: design equations and curves. Journal of the Soil Mechanics and Foundations Division, Vol. 98 (SM7), pp 667–692.

• op de Kelder, M.A. (2013). 2D Finite Element Analysis of a building pit compared with in-situ measurements, M.Sc. Thesis, Faculty of Civil Engineering and Geosciences, Department of Geo-Engineering, Delft University of Technology

• Mair, R.J. (1993). Developments in geotechnical engineering research: application to tunnels and deep excavations. Proceedings of Institution of Civil Engineers, Civil Engineering, pp 27-41.

• Mayne, P.W., Schneider, J.A. (2001). Evaluating axial drilled shaft response by seismic cone. Foundations & Ground Improvement, GSP 113, ASCE, Reston/VA, pp 665-669.

• Seed H.B., Idriss, I.M. (1970). Soil moduli and damping factors for dynamic response analysis. Report 70-10, EERC, Berkeley, CA, U.S.A.

• Wichtmann, T., Triantafyllidis, T. (2007). Erwiderung der Zuschrift von T. Benz und P.A. Vermeer zum Beitrag ”Über die Korrelation der ödometrischen und der ”dynamischen” Steifigkeit nichtbindiger Böden” (Bautechnik 83, No. 7, 2006). Bautechnik, Vol. 84 (5), pp 364–366.

• Wichtmann, T., Triantafyllidis, T. (2009). On the correlation of ''static'' and ''dynamic'' stiffness moduli of non-cohesive soils. Bautechnik, Vol. 86 (S1), pp 28-39.



Recent activities

After the successful release of PLAXIS 2D 2015 as well as the new add-on 2D Thermal module, we proudly introduce PLAXIS 3D AE that has been delivered since the fi rst half of this year. It has been our attention that tunnels should be modelled in more convenient and structured way.

One of the major new additions to PLAXIS 3D AE is the 3D Tunnel designer that contains three modes, namely the cross-section, properties and trajectory. Aside from the option to import the tunnel cross-section from CAD fi les, the cross-section mode allows users to create the tunnel geometry and sub-sections, such as benches and side-wall drifts. In the proper-ties mode, plates, interfaces, loads and contraction can be assigned to the different parts of the tunnel cross-section. In the trajectory mode, users can now easily defi ne the tunnel path and excavation segments. This way, a tunnel including its properties, path and segments can be generated at once. Via the Tunnel designer, the created tunnel can be modifi ed and regenerated quickly as well.

The second major feature in PLAXIS 3D AE is the rigid body tool. This feature allows users to defi ne the degrees of freedom such as rotations, forces or

displacements of an object from a given reference point. It is particularly useful for offshore applications including suction piles and spud cans.

In the Output program of PLAXIS 3D AE, it is now possible to obtain the structural forces for cylindrical objects such as volume piles. The HTTP REST-based API (Advanced Programming Interface) with Python wrapper once introduced in PLAXIS 2D AE has now become available for PLAXIS 3D AE Output program. Through the Remote Scripting API, the interaction between the Input and Output programs can be defi ned. This way, users not only can retrieve numeri-cal result data, but also can partially automate back-calculations. To benefi t from this scripting interface, the subscription to PLAXIS VIP and a valid internet connection are necessary.

European Plaxis Users MeetingPlaxis is grateful to HUESKER for sponsoring the 21st European Plaxis Users Meeting (EPUM) at HUESKER Synthetic GmbH in Gescher, Germany held on the 28th and 29th of May, 2015. During this two-day meeting, the users were equipped not only with the information regarding the latest developments of PLAXIS including the new 2D Thermal module and

PLAXIS 3D, but also with the coupling technique between PLAXIS and SAP2000. Several research presentations on the use of PLAXIS were given by the users. Research topics presented include the slope stability analysis, adaptive foundation system for embankments, soft Scandinavian clay, and rota-tional failure of diaphragm walls. This meeting went with a great success and received a wide range of attendees ranging from consulting and contracting companies, public work bodies to universities. At the end of the second day of this meeting, there was an opportunity to look more closely at the facilities of HUESKER Synthetic in Germany.

June 2015 was particularly remarked as the month with full of events. Plaxis headquarters in Delft organized two workshops dealing with advanced modelling and dynamic behaviour in PLAXIS. In association with Univesidad de Buenos Aires, Plaxis organized introductory and advanced courses in Argentina. In the same month, two standard courses also took place in Europe. The one was co-organized with our agent, Wilde Analysis in Manchester, the UK, while the other was in Madrid, Spain. Besides the lectures on the fi nite element modelling and constitutive models, these courses focused on the practical application of PLAXIS on modelling of excavation, dams and embankments. Together with our agent, Terratek, the same course will also be provided from 22 to 24 October in Sao Paulo, Brazil.

Plaxis is quite active in meeting with existing and new customers worldwide. The new PLAXIS 2D 2015 and PLAXIS 3D AE have been demonstrated to engineers and specialists in offshore structures during the 3rd ISFOG (International Symposium on Frontiers in Offshore Geotechnics) in Oslo, Norway. Quite recently, Plaxis was an exhibitor at the XVI European Conference on Soil Mechanics and Geotechnical Engineering (ECSMGE) in Edinburg, the UK. During this conference, a lot of interest in PLAXIS came from participants with a strong background in geology, geophysics and soil mechanics. In October 2015, Plaxis will participate in and exhibit at EUROCK 2015 & 64th Geomechanics Colloquium in Salzburg, Austria. As well as meeting with customers and practitioners in


the fi eld of tunnelling and rock mechanics, one of our researchers will give a poster presentation focussing on a fully-coupled THM (thermo-hydro-mechanical) model in PLAXIS. We will also be present at the 5th ISGSR (International Symposium on Geotechnical Safety and Risk) in Rotterdam, demonstrating the capability of PLAXIS in geotechnical risk assessment and management.

Plaxis AmericasMay 2015 saw a successful standard course being held on the UC Berkeley campus. This course brought together a diverse group of engineers from across the US and Canada, with some attendees having many years of PLAXIS experience while others were pretty new to the program. The last course day was dedi-cated to modelling dynamic behaviour, with relevant topics such as dynamic boundary conditions, damp-ing considerations, and evaluation of soil-structure interaction analysis. The next US course will be held in the Boston area, from 4 to 6 November 2015, with more information and registration on our website.Plaxis was an exhibitor at several events in the US

and Canada in the past months. There was a lot of interest in the latest developments regarding model-ling rock mechanics and geomechanics in PLAXIS at the ARMA 2015 seminar in San Francisco and at the combined CIM-ISRM conference in Montréal. RETC 2015 (Rapid Excavation and Tunnelling Conference) included several presentations utilizing PLAXIS, with PLAXIS being the most widely used software at RETC 2015 (as was the case at the previous RETC in 2013). This is a clear indication that PLAXIS is the preferred software in the North American excavation and tunnelling world.

In the months and years to come, we continue to visit and exhibit at numerous events across the US and Canada. You might see some new faces at the Plaxis booth as we are increasing our North American pres-ence. We are a growing company, and with our new staff we can serve our users even better. If you want to know when and where you can meet us in person, make sure you receive our electronic newsletters, check the online list of upcoming events or follow us on social media. We look forward to meeting you!

Plaxis AsiaPacMay 19th the Plaxis Indian User Meeting was held in Mumbai, India. We would like to thank all the participants for their presentations and participa-tion in discussions.

On the 16th and 17th of June, two workshops were organized in Hong Kong in collaboration with our partners. Both the workshops, covering the Introduc-tion to PLAXIS 3D and Introduction Geotechnical Modelling with PLAXIS, were well attended.

We are also proud to mention that our fi rst PLAXIS Seminar in the Philippines exceeded our expectations and we believe that this seminar will be a good start for more PLAXIS events in the Philippines. We would also like to mention the success of our Colombo workshop, held on August 8th in Sri Lanka.

PLAXIS AsiaPac was one of the orators at the Numerical Analysis in Geotechnics 2015 conference held in Hanoi Vietnam. Topics like embankments, reclamation and ground improved by vacuum consolidation were covered.

Together with JIP Techno Science Corporation we were present on the 50th Japan National Confer-ence on Geotechnical Engineering in Sapporo. The conference gave us the opportunity to strenghten our relation with our Japanese user-base.

In Taiwan we were accompanied by our partner Genesis on the 16th Conference on Current Researches in Geotechnical Engineering. Both our booth and our product demonstration were a success.

We hope to see you again at our upcoming events in your region.

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www.plaxis.com/jobsFore more information about our vacancies please take a look at our website

15 - 18 SeptemberPLAXIS Advanced CourseMelbourne, Australia

20 - 23 SeptemberGEOQuébec 2015Québec, Canada

21 - 24 SeptemberPLAXIS Standard CourseWellington, New Zealand

1 - 2 October BAW-KolloquiumKarlsruhe, Germany

7 - 10 OctoberEurock 2015Salzburg, Austria

12 - 15 October DFI 40th Annual Conferenceon Deep FoundationsOakland, California, USA

13 - 16 October5th ISGSR SymposiumRotterdam, The Netherlands

22 - 24 OctoberStandard Course on Computational GeotechnicsSao Paulo, Brazil

NovemberWorkshop on Advanced Modelling in PLAXISDelft, The Netherlands

1 - 4 November6th International Conference on Earthquake Geotechnical EngineeringChristchurch, New Zealand

3 - 6 NovemberStandard Course onComputational GeotechnicsParis Cedex 12, France

3 NovemberGeotechniekdag 2015Breda, The Netherlands

4 - 6 NovemberStandard Course on Computational GeotechnicsBoston, Massachusetts , USA

9 - 13 November15th ARC on Soil Mechanics and Geotechnical EngineeringFukuoka, Japan

10 NovemberWaterbouwdag 2015Rotterdam, The Netherlands

15 - 18 NovemberXV Pan-American Conference on Soil Mechanics and Geotechnical EngineeringBuenos Aires, Argentina

26 NovemberNorwegian Plaxis Users MeetingHøvik, Norway

1 - 2 DecemberSTUVA 2015Dortmund, Germany

18 - 21 January Standard Course on Computational GeotechnicsHoofddorp, The Netherlands

14 - 17 FebruaryGeotechnical & StructuralEngineering CongressPhoenix, Arizona, USA

15 - 17 FebruaryStandard Course on Computational GeotechnicsOstfi ldern, Germany

17 February6th Belgium Plaxis Users MeetingAntwerpen, Belgium

14 - 17 MarchAdvanced Course onComputational GeotechnicsHoofddorp, The Netherlands

22 - 28 AprilWTC2016/NAT 2016San Francisco, California, USA

Upcoming Events 2015 - 2016

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