plaxis bulletin autmn 2009

Title

Identification of constitutive parameters of reconstituted and natural Pisa clay

Local ice crushing analyses of OPEN CELL SHEET PILE® Wall by 3DFoundation

Influence of a revetment geometry on liquefaction susceptibility

Editorial

Issue 26 / Autumn 2009

Plaxis bulletin

Table of contents

Pag

e 4

Pag

e 6

Pag

e 12

Pag

e 18

Pag

e 22

Editorial03New developments04

Recent activities22


18


12


06

PLAXIS Expert Services assist in optimizing pile raft foundation design

05

ColophonAny correspondence regarding the Plaxis bulletin can be sent by e-mail to:

[email protected]

or by regular mail to:

Plaxis Bulletinc/o Erwin BeerninkPO Box 5722600 AN DelftThe Netherlands

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

Editorial board:Wout BroereRonald BrinkgreveErwin BeerninkArny Lengkeek

Design: Blemmodesign

For information about Plaxis software contact your local agent or Plaxis main office:

Plaxis bvP.O. Box 5722600 AN DelftThe Netherlands

[email protected]

Tel: +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 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 plain unformatted text. 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 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 vector based format (eps,ai). If photographs or ‘scanned’ figures are used the author should ensure that they have a resolution of at least 300 dpi or a minimum of 3 megapixels. The use of colour in figures and photographs is encouraged, as the Plaxis bulletin is printed in full-colour.

www.plaxis.nl l Autumn issue 2009 l Plaxis bulletin 3

Editorial

» After the release of the previous bulletin we obtained several positive responses on

the new Plaxis corporate identity. Recently, we have also launched the restyled Plaxis web site following the same identity. Herewith we present to you the second Bulletin in the new style, which contains again some interesting contributions from Plaxis users about geo-engineering projects they have been working on.

The first contribution is a research project on automatic parameter identification using a population-based stochastic optimization method. Different material models were used to simulate the behaviour of reconstituted and natural Pisa clay. The corresponding model parameters were optimized by matching oedometer test data. Plaxis considers adopting this method in the soil test facility such that all users can benefit from this feature. Please let us know what you think about this by sending your e-mail to [email protected].

The second contribution is the analysis of a patented wall structure against ice loads using 3DFoundation. Key issue was the development of failure criteria for the structure and to prove that it would not fail under extreme conditions. It turned out that soil improvement was needed in order to meet the requirements. Coloured plots nicely show the impact of the ice load on the structure.

The third contribution demonstrates the use of PLAXIS to analyse the liquefaction potential of a revetment geometry using the cyclic stress approach. A comparison is made between the PLAXIS results and the results of a 1D program

that is generally used in geotechnical earthquake analysis. Considering the limitations of the 1D program, results seem consistent. Hence, despite the fact that a true liquefaction model is missing in PLAXIS, there are possibilities to analyse the liquefaction potential.

In addition to the contributions by PLAXIS users, there is a joint presentation about a project where Plaxis has provided expert services to a client. Furthermore, there are the ‘standard’ columns on new developments and recent activities, followed by the agenda of upcoming activities. We wish you an interesting reading experience and look forward to receive your comments on this 26th Bulletin.

The Editors

Editorial

4 Plaxis bulletin l Autumn issue 2009 l www.plaxis.nl

New developments

»In recent years, a considerable amount of resources in Plaxis development were spent

on 3D modelling, and this will definitely continue after the upcoming release of PLAXIS 3D. For those who like to ‘taste’ this completely new PLAXIS version with general 3D modelling facilities, we like to invite you to participate in the European Plaxis Users Meeting in Karlsruhe on November 11-13, 2009 (see agenda for more details).

In addition to the major 3D developments, we are making considerable investments in new features and calculation options for PLAXIS 2D. By far the majority of world-wide PLAXIS calculations are (still) 2D, and we do like to satisfy new modelling requirements from this ever growing group of PLAXIS users. In this respect we would like to mention some of the features that we have worked on and that will become available in PLAXIS 2D in

the coming years:• Fully coupled flow-deformation analysis and

unsaturated soil behaviour (see Bulletin 24)• New features in dynamic calculations (a.o. free

vibration analysis, independent horizontal and vertical prescribed displacements or accelerations, liquefaction).

• Facilities to perform SLS and ULS calculations according to design codes (a.o. using partial factors for loads and model parameters).

• Hoek-Brown continuum model for rock behaviour and reinforcement elements.

• Advanced concrete models and non-linear plate elements for more realistic structural behaviour.

• Improved automatic mesh generation, resulting in high-quality meshes (Fig. 1).

• Visualisation of stresses and forces on selected (sub-)structures (Fig. 2), with facilities to enable equilibrium checks.

… and several minor items that make your geo-engineering work efficient and enjoyable. New technical / scientific features are first verified in collaboration with universities and research in-stitutes, after which beta-testers will apply the new features in practical applications. In parallel; unit tests, application tests and finally a release test are defined and performed by our QA department. The production process is highly automated using a build / test server, to ensure constant high-quali-ty software products.

We welcome your comments and suggestions on new PLAXIS developments via [email protected].

In the previous bulletin (25) we made a suggestion to compose, with your help, predefined material data sets based on the

HSsmall model. We invited all Plaxis users to submit data sets with some additional data, in return for which they would obtain

a spreadsheet to estimate all HSsmall model parameters on the basis of a single property, namely the Relative Density (RD)

for sands or the Plasticity Index (PI) for clays. Data sets from existing projects can still be submitted by using the SendMaterial

tool, which is available in the download area on the Plaxis website. All this is meant to stimulate the use of advanced soil

models and to make better predictions in geo-engineering applications. We are counting on your input!

Author: Ronald Brinkgreve, Plaxis bv

Figure 1: Comparison of generated meshes:Left: Using ‘old’ mesh generator in PLAXIS 2DRight: Improved mesh using new mesh generator

Figure 2: Visualisation of stresses on sub-structuresLeft: Model detail with effective stresses (red), pore pressures (green) and equivalent forcesRight: Deformed mesh of total model


»Blank-Lehrer specializes in soil mechanics, foundation engineering and geotechnical

risk management analysis. They provide geotechnical consulting services, including infrastructure investigation, geotechnical reviews, geophysical study coordination, foundation systems analysis, soil structure interaction analysis, geology services, construction guidelines and site supervision. Blank-Lehrer is one of the leaders in Israeli engineering in these fields with more than thirty years experience in Israel and abroad.

Project DescriptionThe project deals with the design of a piled-raft foundation for a 300m high building. The concrete raft is 3.5 meters thick and will be cast at a depth of 15 meters below soil level. The high rise building will be founded on a on the soil substratum which is made of two sand layers (from +4m to -12m and from -12m to -30m) with respectively Eoed = 60000 kPa and Eoed = 100000 kPa. In order to reduce settlements 20m long piles will be placed under the raft. Each individual pile is expected to have a skin friction of 100 kN/m2 and an end-bearing capacity of 4000 kN/m2.The aim of the project is to design the piles in such a way that:• between 60% and 70% of the load will be car-

ried by the piles,• under ultimate limit state, the load on each

pile is not greater than 80% of the ultimate pile bearing capacity.

PLAXIS Expert Services Added-ValuePLAXIS has been assigned for providing an optimized FE model that will be used by Blank-Lehrer for further parametrical studies (pile number, pile properties, pile location, ..). In this context, a FE model of pile raft foundation has been set-up using 3DFoundation program.The model has been set-up based on best FE

practices (model size, geometrical modeling of constitutive members, material model) offering an optimized mesh (results accuracy and computational performance) and proper modeling of piles through embedded pile elements.

A comprehensive memorandum has also been delivered highlighting all model assumptions and providing a clear description of defined calculation phases and main recommendations regarding further model changes to be done by the client along with result interpretation.

Lastly, extensive user support has then be provided to Blank-Lehrer during their final design assessment with 3DFoundation.

Customer Quote “Our office uses the PLAXIS 2D and the 3DFoundation softwares regularly. In spite of that, we have decided that in complex project such as the one we are facing, an expert advice should be used in the model assembly stage. The embedded piles dimensions were determined after testing the behavior of volume piles. The Plaxis expert advice assisted in building a flexible model which enables to test the sensitivity of the solution to different engineering parameters (i.e. number of piles and soil characteristics).There is no doubt that the solution reached, following the expertise is the most economical one”.

Plaxis was asked by Blank-Lehrer to be assisted with an advanced consulting project requiring the construction of a 3D pile raft

foundation finite element model. In the framework of PLAXIS Expert Services, a successful modeling partnership has enabled

Blank-Lehrer to quickly achieve a reliable design.

Author: Ady Lehrer, Managing Director, Blank-Lehrer

PLAXIS Expert Services assist in optimizing pile raft foundation design


experiments as numerical element tests are done in PLAXIS 2D. Based on this a population-based stochastic optimization method is applied to minimize the absolute error between experimental and numerical curves.

Constitutive models for clayUnderneath, a selection of constitutive models and their parameters are briefl y described.

1. Mohr-Coulomb modelThe Mohr-Coulomb model (MC) is introduced in PLAXIS (see more information in the PLAXIS 2D Material Manual [1]). For the Mohr-Coulomb model only fi ve constitutive parameters (Young’s modulus E, Poisson’s ratio y, friction angle {’, cohesion c and dilatancy angle } ) are needed to describe the soil behavior. These parameters can be determined from the results of standard geotechnical testing.

2. Soft Soil creep modelThe Soft Soil Creep model (SSC) is a standard model in PLAXIS (see more information in the PLAXIS 2D Material Manual [1]). The parameters of the SSC model (modified compression index m*, modifi ed swell index l*, modifi ed creep index µ*, coeffi cient of earth pressure at rest K0,nc,y,{’, c and } ) can be determined from standard triaxial and oedometer tests with time measurement.

3. S-CLAY1S modelThe S-CLAY1S model can be used in PLAXIS as a user-defi ned model. It is an elastic-plastic model, which accounts for plastic anisotropy and destructuration of normally or lightly over consolidated clays [6]. Therefore, an “intrinsic yield surface” (IYS) is introduced (Figure 1). The IYS refers to equivalent unbounded soils having the same shape and orientation at the same void ratio within the yield surface. Using an initial inclination of the yield surface a0 anisotropy is considered for

Identifi cation of constitutive parameters of reconstituted and natural Pisa clay

»In this article a back analysis approach is used to determine the parameters for several

constitutive models for clays with different level of complexity. These models can be used with the help of PLAXIS 2D, to simulate the oedometric behavior of Pisa Clay. The simulation of the lab

Parameters of constitutive models are generally obtained by comparing results of numerical forward simulations with

measurement data. Often the parameter values are varied by trial-and error in order to reach an improved fi t and to obtain

plausible results. However, the description of complex soil behavior requires advanced constitutive models (e.g. [9]). The rising complexity of these models mainly increases the number of unknown constitutive parameters. Thus an effi cient “by hand” identifi cation becomes quite diffi cult for most practical problems.

Authors: T. Knabe*, Graduiertenkolleg 1462, Bauhaus-Universität Weimar and T. Schanz, Laboratory of Foundation Engineering, Soil and Rock Mechanics, Ruhr-Universität Bochum* [email protected]

Table 1: Model parameter for the S-CLAY1S model

Parameter Comment

e0: Initial void ratio Standard laboratory test

M: Value of the stress ratioh at critical state

Triaxial test

a0: Initial size and inclination of the

yield curve Anisotropy: Estimated via { ’

n: Absolute effectiveness of rotational hardening

Anisotropy: typical values:

10 / m - 20 / m

b: Relative effectiveness of rotational hardening Anisotropy: Estimated via { ’

x0: Initial bonding effect Destructuration: St - 1

a: Absolute effectiveness of destructurational hardening Destructuration: typical values : 8 - 11

b: Relative effectiveness of destruc-turational hardening

Destructuration: typical values : 0, 2-0, 3



the plastic behavior. The additional constitutive parameters for anisotropy and destructuration for the S-CLAY1S models are summarized in Table 1. They cannot all be determined directly from standard laboratory tests. This means that some parameters have no “real” physical meaning and can only be obtained by estimation via other soil parameters or can only be identifi ed by back calculation.

4. Multilaminate model for Structured ClayThe Multilaminate Model (ML) for Structured Clay is a user-defi ned model in PLAXIS. The model was developed by Galavi 2007 [4] and is based on the Multilaminate framework [7]. Anisotropy, destructuration and softening can be taken into account. The deformation behavior of the soil is obtained by integrating the response of a particular number of differently oriented “sampling planes” (Figure 2). Each stress integration point is associated with a certain number of these planes at different orientations. The stress-strain relations are formulated locally at the microscopic level, except for the elastic part, which is calculated at the macroscopic level. The global strains are obtained by numerical integration of the inelastic contribution of each sampling plane and the global elastic contribution. Therefore, induced anisotropy can be considered without further material parameters. In order to include the inherent anisotropy, a so-called micro structure tensor is implemented. To take destructuration into account, it is assumed that destructuration starts at gross yield. It is related to the damage strain fdi, where an increase leads to a decrease of structure and depends on the bonding parameter b and the volumetric rate of the destructuration hv. The additional constitutive parameters describing anisotropy and destructuration of the Multilaminate Model for Structured Clay are summarized in Table 2. Not all parameters can be determined by standard laboratory tests.

Figure 2: Multilaminate model (integration planes) [4]

Figure 1: S-CLAY 1S model (principle stress space) according to [6]


Plaxis practice: Identification of constitutive parameters of reconstituted and natural Pisa clayPlaxis Practice: Crane Monopile Foundation Analysis

Laboratory testing and numerical modelingDrained oedometer tests on natural and reconstituted Pisa clay, a soft, marine clay from Italy, were chosen to calibrate the constitutive soil parameters [8]. High quality Laval samples were retrieved from the subsoil of the Tower of Pisa from a depth of 10 – 12 m (Upper Clay). Pisa Clay has a metastable structure and a high sensitivity. The over consolidation rate is about 1 – 2. The oedometer tests are simulated in PLAXIS 2D as plane strain element tests. Optimization 1. Parameter IdentificationDue to lack of knowledge of the constitutive parameters a back analysis in terms of direct or inverse approaches can be used to calibrate the material model parameters [3]. In this article the direct approach is used, which is based on an iterative procedures correcting the trial values of the unknown parameters by minimizing an objective function. Here the material parameters are the unknowns and the objective function consists of measured and simulated data. Additionally bound constraints are considered on the optimization variables x to ensure that the global minima lie within a restricted search space corresponding to the range of realistic constitutive parameter values

xmin ≤ x ≤ xmax

where xmin and xmax are the lower and upper bounds of x, respectively. Schematically this procedure is given in Figure 3. The objective function reads:

with fi = (yi,meas – yi,calc)

where wi are weighting factors, i = 1, …, n is the counter of loading steps used in the optimization process. In this paper the Particle Swarm Optimizer (PSO) is used to minimize the objective function. The PSO approach is based on a population of individuals [5]. Each particle represents a solution to the optimization problem. While searching for optima, each particle adjusts its trajectory according to its own previous best position and the best previous position attained by any member of its neighbors.

2. Start valuesFor the identification process it is necessary to assume initial start values for each constitutive parameter. These values can be adopted by e.g. engineering experience or from literature. The assumed constitutive parameters for reconstituted Pisa Clay for the different models with their minima and maxima boundaries are summarized in Table 3. The cohesion c is assumed as 2.4 kN/m2 and the friction angle {’ as 25.6°. Dilatancy is not taken into account } = 0). For the S-CLAY1S model the slope M of the Critical State Line supposed to be 1.0 [2,8]. The Poisson’s ratio is also adopted to be 0.2. These parameters are held constant in the

Figure 3: Identification procedure

Parameter Comment

Ad: Parameter for proportion of plastic strains

Destructuration and anisotropy: 0 -1

Ar: Anisotropy ratio Anisotropy

b0: Size initial value of bonding Destructuration:

hv : Volumetric rate of destructuration Destructuration: typical values 10 - 30

v' * vy

v'vy- 1

Table 2: Model parameter for the Multilaminate Model for Structured Clay

F=yi.meas

2

i=1

n/fi

2 .wi

i=1

n

/

Plaxis Practice: Crane Monopile Foundation Analysis

Table 3: Constitutive parameters for reconstituted Pisa Clay from literature

Constitutiveparameter

Start value

Boundariesminimum

Boundariesmaximum

m i

*

[-] 0.15 0.08 0.25

l i

*

[-] 0.02 0.01 0.03

m i [-] 0.23 [2] 0.15 0.35

l i [-] 0.035 [2] 0.025 0.045

Gref.i [kN/m2] 1500 1000 2500

c [kN/m2] 2.4 [8] fixed in oedometric conditions

{ [o] 25.6 [8] fixed in oedometric conditions

M [-] 0.984 [8] fixed in oedometric conditions

a0 [-] 0.54 0.20 0.60

n [-] 30 20 50

b [-] 0.94 0.85 1.05

Ar [-] 1 0.7 1.5

Ad [-] 0 [4] fixed in oedometric conditions

n [-] 0.0001 fixed

e0,i [-] 1.4 [10] fixed

Table 4: (Additional) Constitutive parameters for natural Pisa Clay


Start value

Boundariesminimum

Boundariesmaximum

Gref [kN/m2] 2500 1500 4000

m*

[-] 0.2 0.1 0.3

l*

[-] 0.025 0.015 0.035

x0 [-] 10 1 20

b [-] 0.3 0.2 0.4

a [-] 10 7 15

hv [-] 10 5 20

b0 [-] 2 1 5

e0 [-] 1.72 [10] fixed



Table 3: Constitutive parameters for reconstituted Pisa Clay from literature


Start value

Boundariesminimum

Boundariesmaximum

m i

*

[-] 0.15 0.08 0.25

l i

*

[-] 0.02 0.01 0.03

m i [-] 0.23 [2] 0.15 0.35

l i [-] 0.035 [2] 0.025 0.045

Gref.i [kN/m2] 1500 1000 2500

c [kN/m2] 2.4 [8] fixed in oedometric conditions

{ [o] 25.6 [8] fixed in oedometric conditions

M [-] 0.984 [8] fixed in oedometric conditions

a0 [-] 0.54 0.20 0.60

n [-] 30 20 50

b [-] 0.94 0.85 1.05

Ar [-] 1 0.7 1.5

Ad [-] 0 [4] fixed in oedometric conditions

n [-] 0.0001 fixed

e0,i [-] 1.4 [10] fixed

Table 4: (Additional) Constitutive parameters for natural Pisa Clay


Start value

Boundariesminimum

Boundariesmaximum

Gref [kN/m2] 2500 1500 4000

m*

[-] 0.2 0.1 0.3

l*

[-] 0.025 0.015 0.035

x0 [-] 10 1 20

b [-] 0.3 0.2 0.4

a [-] 10 7 15

hv [-] 10 5 20

b0 [-] 2 1 5

e0 [-] 1.72 [10] fixed



identifi cation of the oedometer tests, because the sensitivity of these parameters is very low in oedometric conditions in comparison to the other parameters. The (additional) parameters for natural Pisa Clay are summarized in Table 4.

3. Results of parameter identifi cationFor the oedometer test on reconstituted Pisa Clay the results of the optimized simulation results compared with the measurement data are shown in Fig. 4. Due to its limitations it was not possible to improve the simulation of the MC model. The simulated stress-strain curves of the SSC, S-CLAY1S and ML models result in a good agreement with the measurements. The associated optimized parameter set can be seen in Table 5 (left). For the oedometer test on natural Pisa Clay the S-CLAY1S and the ML models can predict the behavior after gross yield best, as they can consider destructuration (Fig. 5). Because of this they can predict the metastable structure what results in an abrupt yield. The SSC model reaches the fi nal measured strains at a stress of 3250 kPa. However, this model is not able to predict the correct destructuration behavior after yielding. The associated optimized parameter set for natural Pisa Clay can be seen in Table 5 (right). Cohesion c, friction angle {, Poisson’s ratio y are also held constant.

ConclusionsThe description of complex behavior of clay requires advanced constitutive models with a large number of unknown parameters. Thus an effi cient manual identifi cation becomes quite diffi cult for most practical problems. Due to the complex problems a back analysis in terms of an inverse approache is used. For laboratory tests on reconstituted and natural Pisa Clay, it is possible to get good results of constitutive parameter sets. It was shown that the SSC, S-CLAY1S and ML models for reconstituted Pisa Clay are able to predict the correct soil behavior. The MC model is not able to simulate essential features of soil behavior because of limitations. Only the S-CLAY1S and ML models are able to predict the natural behavior of Pisa Clay because these models can consider destructuration.The next step would be the identifi cation of the parameters on triaxial tests and fi nally on oedometer and triaxial tests simultaneously to obtain the best fi t for all experiments.

AcknowledgementsThe presented developments have been carried out within the frame of the DFG Research Training Group 1462 “Model Validation in Structural Engineering”. Special thanks go to the PLAXIS Company for allocating PLAXIS 2D/3D and Martin Zimmerer for providing his identifi cation program VARo2PT. The authors are thankful to Luigi Callisto as well for the laboratory test results.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.910 100 1000 10000

ε y [-

]

σy [kPa]

measurementMC

SSCS-CLAY1S

ML

Figure 4: Observed and simulated vertical strain of an oedometer test on reconstituted Pisa Clay with optimized parameters (according to [8])

Figure 5: Observed and simulated vertical strain of an oedometer test on natural Pisa Clay with optimized parameters (according to [8])


References[1] R. B. J. Brinkgreve and P. A. Vermeer. PLAXIS Finite Element Code for Soil and Rock Analysis. Volume 8, Material Models Manual. Rotterdam: A.A Balkema.

[2] L. Callisto and S. Rampello. An interpretation of structural degradation for three natural clays. Canadian Geotechnic Journal, 41:392-407, 2004.

[3] A. L. Cividini, L. Jurina, and G. Gioda. Some aspects of characterization problems in geomechanics. Int. J. Rock. Mech. Min. Sci. and Geomech., 18:487-503, 1981.

[4] V. Galavi. A Multilaminate Model for Structured Clay incorporating Inherent Anisotropy and Strain Softening. PhD thesis, Technische Universität Graz, 2007.

[5] J. Kennedy and R. Eberhard. Particle swarm optimization. In U. Publishing company Piscataway, NJ, editor, Proc. of IEEE Int. Conf. on Neural Networks, 1995.

[6] M. Koskinen, M. Karstunen, and S. Wheeler. Modeling destructuration and anisotropy of a natural soft clay. In P. MEstat, editor, Proc. of the 5th European Conf. on Numerical Methods in Geotechnical Engineering, Paris. Press de lENPC/LCPC, 1992.

[7] G. N. Pande and K. G. Sharma. Multilaminate model of clays - a numerical evaluation of the influence of rotation of principal stress axes. Int. J. of Numerical and Analytical Methods in Geomechanics, 7:397-418, 1983.

[8] S. Rampello and L. Callisto. A study on the subsoil of the tower of pisa based on results from standard and high-quality samples. Canadian Geotechnic Journal, 35:1074.1092, 1998.

[9] S. J. Wheeler, M. Cudny, H. P. Neher, and C. Wiltafsky. Some developments in constitutive modeling of soft clays. In International Workshop on Geotechnics of Soft Soils-Theory and Practice, 2003.

Table 5: Optimized parameter sets for reconstituted (left) and natural (right) Pisa Clay

MC End value

SCC End value

S- EndCLAY value

ML End value

Gref 2600 m*

0.127 m i0.19 m i

0.27

l* 0.013 l 0.029 l 0.039

ao0.3 Ar 1.3

n 60 Ad 0

b 0.9

x03.9 b0

2.8

a 12 hv15

b 0.25

MC End value

SCC End value

S- EndCLAY value

ML End value

Gref.i 1900 0.107 m i0.19 m i

0.27

0.028 l i0.027 l i

0.035

c 2.4 c 2.4 M 1 c 2.4

{ 25.6 { 25.6 { 25.6

y 0.2 y 0.2 y 0.2 y 0.2

n 0.0001 a00.28 Ar 1.3

n 60 Ad 0

b 0.94

li*

mi*


Geometry and geotechnical InformationThe proposed OPEN CELL SHEET PILE retaining wall extends from an elevation of +12 feet above the mean sea level to elevation of natural seabed -40 feet. The assumed geotechnical profi le consists of an assumed sandy gravel fi ll above elevation -40 feet. A layer of very stiff interbedded and sometimes intermixed clayey silt and fi ne silty sand was utilized for depths between -40 feet to -45 feet. Below the silt, sands with varying amounts of silt and fi ne gravel were assumed from elevations -45 to -50 feet. The sand layer was then underlain by well graded sandy gravel. The fi ll material was fi rst assumed to be placed in a somewhat loose condition. However, subsequent analyses indicated that compaction of the soil behind the sheet piles would be necessary for wall stability and additional ice resistance. Figure 2 depicts the assumed geometry and soil profi le.

Soil parameters utilized in the analyses are listed in Table 1.

Three-dimensional analysesPLAXIS 3D fi nite element modelingA soil model section with a dimension of 310 feet x 95 feet x107 feet (LxBxH) was developed in 3DFoundation. Horizontal displacements were fi xed at the boundaries along the soil block perimeter. The length of 107 feet was chosen to enable modeling three cells of the OPEN CELL

ParameterDry Unit Weight

(kcf)

Elastic modulus (ksf)

Poisson’s ratio

Cohesion (ksf)

Friction Angle (deg)

Sandy Gravel Fill 0.12 3100 0.3 0.02 34

Clayey Silt 0.1 544 0.35 0.8 25

Silty Sand 0.12 450 0.33 0.05 33

Deep Sandy Gravel 0.12 4000 0.3 0.02 34

SHEET PILE structure to appropriately evaluate the local ice crushing resistance of the system by loading the center cell. The face sheet piles of these structures are typically constructed with nineteen 19.69-inch-wide fl at sheet piles arranged in the curvilinear pattern, which results in cell widths of approximately 30 feet width. For this analysis, the face sheet piles were connected structurally to tail wall sheets that extended about 45 feet into compacted granular fi ll. A plan layout of OPEN CELL SHEET PILE wall is shown in Figure 3.

Varied mesh size were applied to soil blocks and OPEN CELL SHEET PILE structure to save computation time. A very fi ne mesh was assigned to the middle cell and the enclosed granular fi ll right behind it where the ice force was directly applied. The rest of the soil blocks, as well as the adjacent two cell structures, share a medium, fi ne mesh. The strategic mesh refi nement led to a mesh of approximately 12,700 elements and approximately 63,000 nodes. The sensitivity studies indicate that deformation discrepancy of sheet pile wall system with very fi ne mesh and medium mesh is within an acceptable range of 5%. A fully meshed PLAXIS 3D model is presented in Figure 4. The elastic-plastic Mohr-Coulomb constitutive soil model for the soil layers in the drained conditions was applied. The most complex portion of modeling of OPEN CELL SHEET PILE wall for this project was to

Figure 2. OPEN CELL SHEET PILE Wall Geometry and Soil Profi le

Table 1. Soil Properties Used in PLAXIS 3D Figure 3. Plan Layout of OPEN CELL SHEET PILE Wall


»The proposed retaining wall system must resist ice crushing against the vertical face

with thawed soil behind the cells. Since the sheet pile wall was constructed of fl at piles attached vertically to each other throughout the perimeter of the structure, the analysis examined whether the soil would deform under localized ice loads to such an extent that the sheet pile would come

apart along the vertical connection joints.In order to determine the capacity and potential improvements required for the system to resist localized ice loads, the author performed a series of fi nite element analyses with PLAXIS 3DFoundation v.2.1. Numerical analyses were utilized to predict defl ections of the sheet pile wall and associated soil mass. These computed

defl ections were then compared against measured ultimate defl ections of the sheet pile knuckles to analyze system performance.

Project descriptionOPEN CELL SHEET PILE systemThe OPEN CELL SHEET PILE system was developed, tested and patented by PND Engineers, Inc. initially in support of Alaska’s North Slope oil industry in the 1980s. Since then, over hundreds of OPEN CELL SHEET PILE structures have built throughout Alaska and the rest of the United States. International structures include a dock in Trinidad.

The concept of this type of retaining wall is geometrically similar to the closed cell except that approximately one-fourth of the cell is removed, allowing access to the interior of the cell for fi ll and compaction operations. The tail walls anchor the face sheets and are buried within the fi ll. The idea is to use fl at sheet piles as vertical soil friction anchors for a membrane wall system.

Figure 1 shows the stability mechanism of the OPEN CELL SHEET PILE system. The system functions as a horizontally tied membrane relying solely on the vertical fl at sheet pile tailwall to restrain the curved fl at sheet pile arch face. The bulkhead becomes a series of U-shaped vertical member structures that does not need toe embedment for stability. These structures have signifi cant advantages over cantilever, tied-back or reinforced earth abutment structures, particularly with regard to load resistance and ease of construction.

PLAXIS 3DFoundation was utilized in a recent analysis of ice loading to a vertical sheet pile wall. The analyzed retaining system consisted of an OPEN CELL SHEET PILE wall, which utilizes hoop tension in the steel to retain the soil behind, similar to a circular fl at sheet pile cell. Since the fl at sheet piles do not provide signifi cant structural resistance to external loadings, the soil must provide the capacity. 3DFoundation provides the ideal means of numerically modeling the system.

Local ice crushing analyses of OPEN CELL SHEET PILE® Wall by 3DFoundationAuthors: Kenton W. Braun, P.E., PND Engineers, Inc, Anchorage, Alaska USA, [email protected] Feifei Bai, PND Engineers, Inc, Anchorage, Alaska USA Guang Li, EPT, BP, Houston, Texas USA

Figure 1. Mechanism of OPEN CELL SHEET PILE Wall System



Geometry and geotechnical InformationThe proposed OPEN CELL SHEET PILE retaining wall extends from an elevation of +12 feet above the mean sea level to elevation of natural seabed -40 feet. The assumed geotechnical profi le consists of an assumed sandy gravel fi ll above elevation -40 feet. A layer of very stiff interbedded and sometimes intermixed clayey silt and fi ne silty sand was utilized for depths between -40 feet to -45 feet. Below the silt, sands with varying amounts of silt and fi ne gravel were assumed from elevations -45 to -50 feet. The sand layer was then underlain by well graded sandy gravel. The fi ll material was fi rst assumed to be placed in a somewhat loose condition. However, subsequent analyses indicated that compaction of the soil behind the sheet piles would be necessary for wall stability and additional ice resistance. Figure 2 depicts the assumed geometry and soil profi le.

Soil parameters utilized in the analyses are listed in Table 1.

Three-dimensional analysesPLAXIS 3D fi nite element modelingA soil model section with a dimension of 310 feet x 95 feet x107 feet (LxBxH) was developed in 3DFoundation. Horizontal displacements were fi xed at the boundaries along the soil block perimeter. The length of 107 feet was chosen to enable modeling three cells of the OPEN CELL

ParameterDry Unit Weight

(kcf)

Elastic modulus (ksf)

Poisson’s ratio

Cohesion (ksf)

Friction Angle (deg)

Sandy Gravel Fill 0.12 3100 0.3 0.02 34

Clayey Silt 0.1 544 0.35 0.8 25

Silty Sand 0.12 450 0.33 0.05 33

Deep Sandy Gravel 0.12 4000 0.3 0.02 34

SHEET PILE structure to appropriately evaluate the local ice crushing resistance of the system by loading the center cell. The face sheet piles of these structures are typically constructed with nineteen 19.69-inch-wide fl at sheet piles arranged in the curvilinear pattern, which results in cell widths of approximately 30 feet width. For this analysis, the face sheet piles were connected structurally to tail wall sheets that extended about 45 feet into compacted granular fi ll. A plan layout of OPEN CELL SHEET PILE wall is shown in Figure 3.

Varied mesh size were applied to soil blocks and OPEN CELL SHEET PILE structure to save computation time. A very fi ne mesh was assigned to the middle cell and the enclosed granular fi ll right behind it where the ice force was directly applied. The rest of the soil blocks, as well as the adjacent two cell structures, share a medium, fi ne mesh. The strategic mesh refi nement led to a mesh of approximately 12,700 elements and approximately 63,000 nodes. The sensitivity studies indicate that deformation discrepancy of sheet pile wall system with very fi ne mesh and medium mesh is within an acceptable range of 5%. A fully meshed PLAXIS 3D model is presented in Figure 4. The elastic-plastic Mohr-Coulomb constitutive soil model for the soil layers in the drained conditions was applied. The most complex portion of modeling of OPEN CELL SHEET PILE wall for this project was to

Figure 2. OPEN CELL SHEET PILE Wall Geometry and Soil Profi le

Table 1. Soil Properties Used in PLAXIS 3D Figure 3. Plan Layout of OPEN CELL SHEET PILE Wall



Plaxis practice: Local ice crushing analyses of OPEN CELL SHEET PILE® Wall by 3DFoundationPlaxis Practice: Mohr-Coulomb parameters for modelling of concrete structures

elevation -10 would generally be weaker and would not experience the confi nement necessary for large local loads. Therefore, lower compressive pressures were utilized for the upper and lower ice crushing zones.

For modeling purposes, the ice load was applied at the highest elevation within each boundary considering that this location would have the minimum soil mass behind the sheet pile to resist the crushing force.

Failure criteriaDevelopment of failure criteria for the analyzed structure presented a signifi cant challenge to the project. Considering the extreme nature of the ice loads, plastic soil movement behind the sheet piles was acceptable, as long as the sheet piles did not come apart. The bilinear behavior of the interlock hinges (as well as modeling limitations) also made it diffi cult to utilize structural stresses within the steel as an evaluation method. Ultimately, it was determined that the best measure of structure limit state was to examine the amount of rotation at the interlocks. The angle between adjacent sheet piles right before failure was defi ned as ultimate defl ection angle. This defl ection angle was derived from destructive sheet pile testing which indicated a 20 degree relative angle (between adjacent sheet piles) could be utilized as the failure criteria when evaluating the Plaxis results. A depiction of this criteria and the associated angle is presented in Figure 5.

It should be noted that there is likely much more reserve capacity in the sheet piles than that which was utilized in the modeling effort. The ultimate testing proved to be diffi cult in that plastic bending of the sheet piles generally occurred sooner than ultimate failure of the knuckles. Such results indicate that the sheet pile wall would likely bend and form plastic hinges prior to knuckle failure, which would allow for much greater defl ections and load absorption/distribution than that utilized in this analysis.

appropriately model the steel wall, especially the contiguous sheet piles vertically attached via interlocks. During an ice event, an interlock connection will fi rst freely rotate around the vertical axis when an inward out-of-plane load is applied. Under an increasing load, the interlocks will fi rst straighten, followed by continued inward defl ection. Eventually, the pile interlocks will bind and begin to resist load until, ultimately, the interlock pries apart.

The inappropriate application of isotropic steel properties could result in an extremely unconservative behavior whereby, in the most extreme condition of a solid steel plate, most of the ice loads could be carried by the OPEN CELL® structure rather than the enclosed soil body. Consequently, a series of fully decoupled nonlinear force strain (i.e. axial force-axial strain) or moment-curvature (i.e. bending moment-rotation curvature) relations were developed. A bilinear force-strain relation (large in-plane horizontal tension vs. small in-plane horizontal compression) was also applied to appropriately estimate the axial hoop tension in steel wall. The bending moment-rotation curvature to defi ne a hinge property caused by interlock rotation was derived and applied to the model based on the destructive sheet pile testing performed by the author. Full sheet pile section properties have been assigned to the sides of model (boundary). Considering the large dimension between adjacent OPEN CELL® structures and the local ice pressure that is only applied to the center of middle cell, the effects of the boundary cell (sides of the model) is neglected.

Loading conditions The localized ice crushing force was set up as static ice pressure in Plaxis following the local pressure-area curves identifi ed in Table 2. From elevation +2 feet to -10 feet, ISO 19906 criteria were utilized considering this area could be exposed to confi ned ice with large compressive pressure. Above elevation +2, the ice would typically be rubbled and ice pressure is therefore greatly reduced. Similarly, ice located below

Figure 5. Sheet Pile Failure Criteria Diagram

Figure 4. Meshed 3D PLAXIS Model

Plaxis Practice: Mohr-Coulomb parameters for modelling of concrete structures

Figure 6. Maximum Horizontal Deformation of Fill and OPEN CELL SHEET PILE at Failure (200 psi with 100 ft2 contact area @ Elevation +4.5 feet)

Initial Analyses ResultsThe initial ice crushing analyses results are presented in Table 3. Results are organized corresponding to the varied ice contact areas and loading elevations defi ned in Table 2. The bold numbers indicate the relative defl ection angle between adjacent sheet piles exceeds the ultimate defl ection angle criteria of 20 degrees.

Selected deformation contours of the enclosed gravel fi ll and OPEN CELL SHEET PILE wall are also shown in Figure 6. In Figure 7, the total incremental soil defl ection contour (|u|) presents a very distinct failure surface in the soil block at the loaded area.

The analyzed sheet pile defl ections of the nineteen pile segments are presented in Figure 8. The defl ection of sheet pile along various wall elevations are plotted separately. The vertical axis represents the X coordinates (unit in feet) to locate each sheet pile segment in PLAXIS 3D. The plots also indicate the maximum pile defl ection occurs within the range of elevation +4 feet to elevation -6 feet, where 100 ft2 crushing ice was loaded.

Soil Reinforcement Initial numerical analysis (Table 3) indicated that thawed fi ll soil and sheet piles alone were not suffi cient to resist the local ice pressure at the higher elevations. Thus, soil improvement was recommended within this zone and the preliminary design assumed jet grouting was utilized for this purpose. A revised Plaxis model was then developed assuming the grouted columns were installed from approximately 8 feet below grade to 23 feet below grade, stiffening approximately 15 feet of soil at the face of the sheet piles. The initial cohesion c and friction angle { for jet grouting was assumed to be 22 ksf and zero

Calculation Case Max Horizontal Def. of Soil (in)

Max Relative Rotation Angle (deg)

Unfrozen SandyGravel

400 psi @ 2 ft2 0.5 3.7

3500 psi @ 2 ft2 31.0 40.0

300 psi @ 2 ft2 0.3 negligible

300 psi @ 10 ft2 16.0 28.0

1130 psi @ 10 ft2 57.0 78.0


200 psi @ 100 ft2 48.0 17.0

225 psi @ 100 ft2 32.0 13.0


Crushing Ice Contact Area

Crushing Load Elevation (feet)

Assumed Ice Crushing Pressure (psi)

2 ft2

+4.5 to +2 400

+2 to -10 3500

-10 to -39 300

10 ft2

+4.5 to +2 300

+2 to -10 1130

-10 to -39 200

100 ft2

+4.5 to +2 200

+2 to -10 225

-10 to -39 100

Table 2. Ice Loading Conditions in Plaxis

Table 3 Initial Ice Crushing Analyses Results Summary


Plaxis practice: Local ice crushing analyses of OPEN CELL SHEET PILE® Wall by 3DFoundationPlaxis Practice: Mohr-Coulomb parameters for modelling of concrete structures

elevation -10 would generally be weaker and would not experience the confi nement necessary for large local loads. Therefore, lower compressive pressures were utilized for the upper and lower ice crushing zones.

For modeling purposes, the ice load was applied at the highest elevation within each boundary considering that this location would have the minimum soil mass behind the sheet pile to resist the crushing force.

Failure criteriaDevelopment of failure criteria for the analyzed structure presented a signifi cant challenge to the project. Considering the extreme nature of the ice loads, plastic soil movement behind the sheet piles was acceptable, as long as the sheet piles did not come apart. The bilinear behavior of the interlock hinges (as well as modeling limitations) also made it diffi cult to utilize structural stresses within the steel as an evaluation method. Ultimately, it was determined that the best measure of structure limit state was to examine the amount of rotation at the interlocks. The angle between adjacent sheet piles right before failure was defi ned as ultimate defl ection angle. This defl ection angle was derived from destructive sheet pile testing which indicated a 20 degree relative angle (between adjacent sheet piles) could be utilized as the failure criteria when evaluating the Plaxis results. A depiction of this criteria and the associated angle is presented in Figure 5.

It should be noted that there is likely much more reserve capacity in the sheet piles than that which was utilized in the modeling effort. The ultimate testing proved to be diffi cult in that plastic bending of the sheet piles generally occurred sooner than ultimate failure of the knuckles. Such results indicate that the sheet pile wall would likely bend and form plastic hinges prior to knuckle failure, which would allow for much greater defl ections and load absorption/distribution than that utilized in this analysis.

appropriately model the steel wall, especially the contiguous sheet piles vertically attached via interlocks. During an ice event, an interlock connection will fi rst freely rotate around the vertical axis when an inward out-of-plane load is applied. Under an increasing load, the interlocks will fi rst straighten, followed by continued inward defl ection. Eventually, the pile interlocks will bind and begin to resist load until, ultimately, the interlock pries apart.

The inappropriate application of isotropic steel properties could result in an extremely unconservative behavior whereby, in the most extreme condition of a solid steel plate, most of the ice loads could be carried by the OPEN CELL® structure rather than the enclosed soil body. Consequently, a series of fully decoupled nonlinear force strain (i.e. axial force-axial strain) or moment-curvature (i.e. bending moment-rotation curvature) relations were developed. A bilinear force-strain relation (large in-plane horizontal tension vs. small in-plane horizontal compression) was also applied to appropriately estimate the axial hoop tension in steel wall. The bending moment-rotation curvature to defi ne a hinge property caused by interlock rotation was derived and applied to the model based on the destructive sheet pile testing performed by the author. Full sheet pile section properties have been assigned to the sides of model (boundary). Considering the large dimension between adjacent OPEN CELL® structures and the local ice pressure that is only applied to the center of middle cell, the effects of the boundary cell (sides of the model) is neglected.

Loading conditions The localized ice crushing force was set up as static ice pressure in Plaxis following the local pressure-area curves identifi ed in Table 2. From elevation +2 feet to -10 feet, ISO 19906 criteria were utilized considering this area could be exposed to confi ned ice with large compressive pressure. Above elevation +2, the ice would typically be rubbled and ice pressure is therefore greatly reduced. Similarly, ice located below

Figure 5. Sheet Pile Failure Criteria Diagram

Figure 4. Meshed 3D PLAXIS Model

Plaxis Practice: Mohr-Coulomb parameters for modelling of concrete structures

Figure 6. Maximum Horizontal Deformation of Fill and OPEN CELL SHEET PILE at Failure (200 psi with 100 ft2 contact area @ Elevation +4.5 feet)

Initial Analyses ResultsThe initial ice crushing analyses results are presented in Table 3. Results are organized corresponding to the varied ice contact areas and loading elevations defi ned in Table 2. The bold numbers indicate the relative defl ection angle between adjacent sheet piles exceeds the ultimate defl ection angle criteria of 20 degrees.

Selected deformation contours of the enclosed gravel fi ll and OPEN CELL SHEET PILE wall are also shown in Figure 6. In Figure 7, the total incremental soil defl ection contour (|u|) presents a very distinct failure surface in the soil block at the loaded area.

The analyzed sheet pile defl ections of the nineteen pile segments are presented in Figure 8. The defl ection of sheet pile along various wall elevations are plotted separately. The vertical axis represents the X coordinates (unit in feet) to locate each sheet pile segment in PLAXIS 3D. The plots also indicate the maximum pile defl ection occurs within the range of elevation +4 feet to elevation -6 feet, where 100 ft2 crushing ice was loaded.

Soil Reinforcement Initial numerical analysis (Table 3) indicated that thawed fi ll soil and sheet piles alone were not suffi cient to resist the local ice pressure at the higher elevations. Thus, soil improvement was recommended within this zone and the preliminary design assumed jet grouting was utilized for this purpose. A revised Plaxis model was then developed assuming the grouted columns were installed from approximately 8 feet below grade to 23 feet below grade, stiffening approximately 15 feet of soil at the face of the sheet piles. The initial cohesion c and friction angle { for jet grouting was assumed to be 22 ksf and zero



Unfrozen SandyGravel

400 psi @ 2 ft2 0.5 3.7

3500 psi @ 2 ft2 31.0 40.0


300 psi @ 10 ft2 16.0 28.0

1130 psi @ 10 ft2 57.0 78.0


200 psi @ 100 ft2 48.0 17.0

225 psi @ 100 ft2 32.0 13.0


Crushing Ice Contact Area

Crushing Load Elevation (feet)

Assumed Ice Crushing Pressure (psi)

2 ft2

+4.5 to +2 400

+2 to -10 3500

-10 to -39 300

10 ft2

+4.5 to +2 300

+2 to -10 1130

-10 to -39 200

100 ft2

+4.5 to +2 200

+2 to -10 225

-10 to -39 100

Table 2. Ice Loading Conditions in Plaxis



Plaxis practice: Local ice crushing analyses of OPEN CELL SHEET PILE® Wall by 3DFoundationPlaxis Practice: Simulation of Soil Nail Structures using PLAXIS 2D



Reinforced Soil

400 psi @ 2 ft2 0.4 3.5

3500 psi @ 2 ft2 1.8 6.0


300 psi @ 10 ft2 1.3 4.5

1130 psi @ 10 ft2 1.7 5.0


200 psi @ 100 ft2 1.6 3.5

225 psi @ 100 ft2 1.2 3.0



Figure 7. Soil Failure Surface at Failure-Total Incremental Deformation (200 psi with 100 ft2 contact area @ Elevation +4.5 feet)

degrees, respectively. Results from this revised analysis are presented in Table 4 and indicated positive behavior. Figure 9 also depicts the total incremental soil deformation contours associated with the analysis.

Discussion and conclusionsPLAXIS 3DFoundation provides a very useful tool for analyzing the performance of an OPEN CELL SHEET PILE wall system under localized ice impact. The initial ice crushing analyses indicated that ice crushing loads on the sheet pile wall exceeded the strength capacity of the thawed granular fi ll soil and sheet piles alone. Subsequent analyses utilizing soil reinforcement was found to provide greater resistance and structural integrity within the failure zone and provided positive results. Shear strain analyses in Plaxis showed that the proposed jet grouting soilcrete could have some cracking develop under high crushing pressure between elevations +4.5 feet to -10 feet. Considering the frequency of any anticipated ice loading events and that the static ice crushing analyses in Plaxis is relatively conservative, the assumed width and depth of the jet grouting zone was believed to be adequate, but additional analyses may be required to further refi ne the design. For reinforced soil, the relative rotation angle of adjacent sheet piles was reduced signifi cantly with the use of soil reinforcement, resulting in a maximum value of 6 degrees as compared to a 78 degree angle for the unreinforced case. The very low result for reinforced soil indicates that jet grouting or other similar means could have voids yet still provide suffi cient resistance.

Plaxis Practice: Simulation of Soil Nail Structures using PLAXIS 2D

AcknowledgementThis project is supported by BP Exploration (Alaska), Inc. Special thanks are also given to Plaxis bv, Hayward Baker, Inc and Geoengineers, Inc for providing technical support to the analyses.

ReferencesBowles J. “Foundation Analysis and Design” •Fifth Edition, McGraw Hill (1996)ISO/DIS 19906 Draft Standard for Petroleum •and natural gas industries – Arctic Offshore structures (November 2008)Plaxis bv “3DFoundation User Manual” (2007)•

Figure 9. Maximum Total Incremental Deformation of Reinforced Soil (200 psi with 100 ft2 contact area @ Elevation +4.5 feet)

Figure 8. Perimeter Sheet Pile Defl ection at Failure (200 psi with 100 ft2 contact area @ Elevation +4.5 feet)


Plaxis practice: Local ice crushing analyses of OPEN CELL SHEET PILE® Wall by 3DFoundationPlaxis Practice: Simulation of Soil Nail Structures using PLAXIS 2D



Reinforced Soil

400 psi @ 2 ft2 0.4 3.5

3500 psi @ 2 ft2 1.8 6.0


300 psi @ 10 ft2 1.3 4.5

1130 psi @ 10 ft2 1.7 5.0


200 psi @ 100 ft2 1.6 3.5

225 psi @ 100 ft2 1.2 3.0



Figure 7. Soil Failure Surface at Failure-Total Incremental Deformation (200 psi with 100 ft2 contact area @ Elevation +4.5 feet)

degrees, respectively. Results from this revised analysis are presented in Table 4 and indicated positive behavior. Figure 9 also depicts the total incremental soil deformation contours associated with the analysis.

Discussion and conclusionsPLAXIS 3DFoundation provides a very useful tool for analyzing the performance of an OPEN CELL SHEET PILE wall system under localized ice impact. The initial ice crushing analyses indicated that ice crushing loads on the sheet pile wall exceeded the strength capacity of the thawed granular fi ll soil and sheet piles alone. Subsequent analyses utilizing soil reinforcement was found to provide greater resistance and structural integrity within the failure zone and provided positive results. Shear strain analyses in Plaxis showed that the proposed jet grouting soilcrete could have some cracking develop under high crushing pressure between elevations +4.5 feet to -10 feet. Considering the frequency of any anticipated ice loading events and that the static ice crushing analyses in Plaxis is relatively conservative, the assumed width and depth of the jet grouting zone was believed to be adequate, but additional analyses may be required to further refi ne the design. For reinforced soil, the relative rotation angle of adjacent sheet piles was reduced signifi cantly with the use of soil reinforcement, resulting in a maximum value of 6 degrees as compared to a 78 degree angle for the unreinforced case. The very low result for reinforced soil indicates that jet grouting or other similar means could have voids yet still provide suffi cient resistance.


AcknowledgementThis project is supported by BP Exploration (Alaska), Inc. Special thanks are also given to Plaxis bv, Hayward Baker, Inc and Geoengineers, Inc for providing technical support to the analyses.

ReferencesBowles J. “Foundation Analysis and Design” •Fifth Edition, McGraw Hill (1996)ISO/DIS 19906 Draft Standard for Petroleum •and natural gas industries – Arctic Offshore structures (November 2008)Plaxis bv “3DFoundation User Manual” (2007)•

Figure 9. Maximum Total Incremental Deformation of Reinforced Soil (200 psi with 100 ft2 contact area @ Elevation +4.5 feet)

Figure 8. Perimeter Sheet Pile Defl ection at Failure (200 psi with 100 ft2 contact area @ Elevation +4.5 feet)


Assessment of the liquefaction potential of sand supporting revetments is often performed by making a 1D analysis at several positions along the revetment (Figure 1). The earthquake-induced loading (CSR, Cyclic Stress Ratio) is commonly calculated using programs like SHAKE2000, which performs 1D calculations in the frequency domain. The liquefaction resistance (CRR, Cyclic Resistance Ratio) of a soil is assessed using empirical methods based on laboratory tests or fi eld tests. This article focuses on the loading phase (CSR).

The 1D analyses imply assumptions and simplifi cations. For example, the 1D assessments are valid for half-spaces (i.e. horizontal ground level and a horizontal soil stratigraphy), where in practice more complex (trapezoidal) geometries exist. This leads to the main research objective:

The main objective of this study is to investigate the infl uence of the revetment geometry on the susceptibility to liquefaction of the underlying sand layer.

Equivalent linear model It is well known that soil behaviour is non-linear, e.g. the shear modulus and the damping ratio are non-linear functions of strain. The non-linear

hysteretic stress-strain behaviour of cyclically loaded soils can be approximated by equivalent linear soil properties. A typical hysteresis loop during undrained symmetric cyclic loading as would be expected beneath a level ground surface far from adjacent structures, is shown in Figure 2. Hereby the equivalent linear shear modulus G is taken as the shear secant modulus to approximate the tangent modulus that varies along the hysteresis loop. The equivalent linear damping ratio p produces the same energy loss in a single cycle as the actual hysteresis loop.

The hysteretic damping ratio is calculated as:

Where:p = damping ratio [-]WD = dissipated energy [kNm]WS = maximum strain energy [kNm]AL = the area enclosed by the hysteresis loop [kPa]AT = the area of the shaded triangle in Figure 2 [kPa]

The linear approach used in SHAKE requires that G and p are constant for each soil layer. Therefore the values that are consistent with the level of strain induced by the earthquake need to be determined for each layer. Since the computed strain level depends on the values of the equivalent linear properties, an iterative procedure is used in SHAKE to compute these strain-compatible properties (Schnabel et al., 1972).

ApproachThe revetment geometry is divided into 4 zones that are approximated by 1D-situations (see Figure 1). The 4 1D shear columns are calculated with SHAKE2000 and PLAXIS, using the linear equivalent parameters G and p. However, the damping is defi ned differently in both computer programmes. SHAKE is performed in the frequency domain and uses the damping ratio p, which is frequency independent. PLAXIS on the other hand

calculates in the time domain and uses a viscous damping1 , more specifi cally Rayleigh damping, which is frequency dependent. The results of the two programs are compared using amplifi cation functions. Consider a soil column with two points at different depths, for example at the top and the bottom. Applying a steady state harmonic horizontal motion with a certain circular frequency at the bottom leads to different horizontal maximum displacements at the two points. In other words: amplifi cation takes place between the two points. A steady state harmonic motion with a different circular frequency leads to a different amplifi cation. The amplifi cation function is therefore the ratio of motion amplitudes between two points in a column as a function of frequency.

In this research, the approach is to modify the damping parameters in PLAXIS until the resulting amplifi cation function matches the outcome of SHAKE. Hereby the procedure described in the following is used. Thereafter the 2D simulation is performed in PLAXIS and the infl uence of the revetment geometry on the dynamic behaviour of the underlying sand is investigated.

The hysteretic damping ratio, which is used in SHAKE, is defi ned as the ratio between the damping and the critical damping in the single-degree-of-freedom system:

Where:c = damping [N s/m]ccrit = critical damping [N s/m]k = stiffness [N/m]m = mass [kg]

Figure 2: Typical hysteresis loop during undrained symmetric cyclic loading

1 Instead of viscous damping, hysteretic damping can be

used in PLAXIS by applying the HSsmall model

Infl uence of a revetment geometry on liquefaction susceptibility

p =ccrit

c=

2 km

c

p =4rWS

WD

=4rAT

AL


Many coastal zones around the world are characterized by the presence of soft soil sediments, which are prone to erosion. The critical areas are therefore protected by engineering structures, like revetments and breakwaters. The structures and their foundations should be able to resist earthquake loads and deformations should remain within acceptable limits.

»The cyclic loading during an earthquake causes pore pressure build-up in the

subsurface that may lead to liquefaction. Liquefaction is a threat to the stability of the engineering structures, since it signifi cantly reduces the strength of underlying soil.

The cyclic behaviour of sands is best explained using the critical state soil mechanics framework.

For cyclic loading, inducing excess pore pressures, two failure mechanisms have been recognised, namely by loss of cyclic stiffness and by cyclic mobility. For continuing cyclic loading around a non-zero mean mobilized effective stress level the mean shear strain can accumulate to very large magnitude (e.g. 20%), known as cyclic mobility. In this case critical state failure is defi ned in terms of the maximum accumulated shear strain causing the critical state of the structure. The engineer will aim at a design in which a state of cyclic shakedown is reached with smaller maximum shear strains.The other failure mechanism, involving the loss of cyclic stiffness, can occur for cyclic loading around a zero-mean effective stress level, inducing excessive cyclic shear strains (e.g. 10%). Consequently in this case critical state failure is due to excessive cyclic shear strains causing the critical state of the structure.

However, in this research (and in engineering practice) the cyclic stress approach is followed to assess initiation of liquefaction. Hereby the earthquake-induced loading, expressed in terms of cyclic shear stress ratio, is compared to the liquefaction resistance of the soil, also expressed

in cyclic shear stress ratio. The cyclic shear stress ratio is defi ned as the ratio of the shear stress amplitude and the initial effective vertical stress. At locations where the loading exceeds the

resistance, liquefaction is expected to occur. Using this approach the pore pressures that cause liquefaction are linked to cyclic shear stresses.

Author: Sanne Brinkman, MSc Student, Delft University of Technology

Figure 1: 2D revetment geometry (top) and 1D approximation (bottom)



Assessment of the liquefaction potential of sand supporting revetments is often performed by making a 1D analysis at several positions along the revetment (Figure 1). The earthquake-induced loading (CSR, Cyclic Stress Ratio) is commonly calculated using programs like SHAKE2000, which performs 1D calculations in the frequency domain. The liquefaction resistance (CRR, Cyclic Resistance Ratio) of a soil is assessed using empirical methods based on laboratory tests or fi eld tests. This article focuses on the loading phase (CSR).

The 1D analyses imply assumptions and simplifi cations. For example, the 1D assessments are valid for half-spaces (i.e. horizontal ground level and a horizontal soil stratigraphy), where in practice more complex (trapezoidal) geometries exist. This leads to the main research objective:

The main objective of this study is to investigate the infl uence of the revetment geometry on the susceptibility to liquefaction of the underlying sand layer.

Equivalent linear model It is well known that soil behaviour is non-linear, e.g. the shear modulus and the damping ratio are non-linear functions of strain. The non-linear

hysteretic stress-strain behaviour of cyclically loaded soils can be approximated by equivalent linear soil properties. A typical hysteresis loop during undrained symmetric cyclic loading as would be expected beneath a level ground surface far from adjacent structures, is shown in Figure 2. Hereby the equivalent linear shear modulus G is taken as the shear secant modulus to approximate the tangent modulus that varies along the hysteresis loop. The equivalent linear damping ratio p produces the same energy loss in a single cycle as the actual hysteresis loop.

The hysteretic damping ratio is calculated as:

Where:p = damping ratio [-]WD = dissipated energy [kNm]WS = maximum strain energy [kNm]AL = the area enclosed by the hysteresis loop [kPa]AT = the area of the shaded triangle in Figure 2 [kPa]

The linear approach used in SHAKE requires that G and p are constant for each soil layer. Therefore the values that are consistent with the level of strain induced by the earthquake need to be determined for each layer. Since the computed strain level depends on the values of the equivalent linear properties, an iterative procedure is used in SHAKE to compute these strain-compatible properties (Schnabel et al., 1972).

ApproachThe revetment geometry is divided into 4 zones that are approximated by 1D-situations (see Figure 1). The 4 1D shear columns are calculated with SHAKE2000 and PLAXIS, using the linear equivalent parameters G and p. However, the damping is defi ned differently in both computer programmes. SHAKE is performed in the frequency domain and uses the damping ratio p, which is frequency independent. PLAXIS on the other hand

calculates in the time domain and uses a viscous damping1 , more specifi cally Rayleigh damping, which is frequency dependent. The results of the two programs are compared using amplifi cation functions. Consider a soil column with two points at different depths, for example at the top and the bottom. Applying a steady state harmonic horizontal motion with a certain circular frequency at the bottom leads to different horizontal maximum displacements at the two points. In other words: amplifi cation takes place between the two points. A steady state harmonic motion with a different circular frequency leads to a different amplifi cation. The amplifi cation function is therefore the ratio of motion amplitudes between two points in a column as a function of frequency.

In this research, the approach is to modify the damping parameters in PLAXIS until the resulting amplifi cation function matches the outcome of SHAKE. Hereby the procedure described in the following is used. Thereafter the 2D simulation is performed in PLAXIS and the infl uence of the revetment geometry on the dynamic behaviour of the underlying sand is investigated.

The hysteretic damping ratio, which is used in SHAKE, is defi ned as the ratio between the damping and the critical damping in the single-degree-of-freedom system:

Where:c = damping [N s/m]ccrit = critical damping [N s/m]k = stiffness [N/m]m = mass [kg]

Figure 2: Typical hysteresis loop during undrained symmetric cyclic loading

1 Instead of viscous damping, hysteretic damping can be

used in PLAXIS by applying the HSsmall model


p =ccrit

c=

2 km

c

p =4rWS

WD

=4rAT

AL



Plaxis practice: Influence of a revetment geometry on liquefaction susceptibilityPlaxis Practice: Simulation of Soil Nail Structures using PLAXIS 2D

Figure 5: Cyclic stress values (CSR) as a function of depth in the sand layer at various locations along the revetment geometry. Red values represent the 1D approximation for the zone, blue values the 2D calculations. Locations A through M and the zones with 1D approximations are shown in Figure 4.

Figure 4: Geometry with locations of determined CSR values and zones with 1D approximations

Replacing the damping by c = am + bk and using that

k/m = ~ leads to:

Where:a = Rayleigh damping parameter [-]b = Rayleigh damping parameter [-]~= circular frequency [rad/s]

The frequency dependency of Rayleigh damping is shown in Figure 3. If the range of important frequencies (~ 1 and ~ 2) for the dynamic analysis can be estimated, then the values of a and b can be chosen to give tolerably constant damping over this frequency range. Using that in the approximation p = p at ~ = ~ 1 and at ~ = ~ 2 , the following is derived:

The conventional approach is to choose the first natural frequency from the soil column as ~ 1 and predominant frequency of the input motion as ~ 2. However, Park and Hashash (2004) show that much better results can be obtained by choosing the frequencies independent of soil column’s natural frequencies, with the aim of obtaining the best match with the frequency domain solution.

In this method, first ~ 1 and ~ 2 are selected such that the frequencies in between comprise the most important part of the earthquake spectrum, with the highest amplitudes. Solving Equation 4 for each layer individually leads to the initial values of a and b for that particular layer in the PLAXIS calculation. After the dynamic calculation, the resulting amplification function from PLAXIS is compared to the amplification function produced by SHAKE. If the amplification functions are not in agreement, ~ 1 and ~ 2 are adjusted. This leads to a new a and b for each layer and thus to a new PLAXIS solution with corresponding amplification function. The frequencies are adjusted by trial and error, but one uses the fact that the contribution of mass in the damping is primarily at low frequencies and the contribution of stiffness in the damping is largest at higher frequencies (Figure 3). The frequencies are adjusted until the amplification

functions of PLAXIS and SHAKE coincide.

Applying the above procedure for all zones provides the Rayleigh damping parameters for the entire geometry. Using these parameters the 2D-calculation is performed in PLAXIS.

ResultsThe cyclic shear stresses that result from the PLAXIS 2D calculation at various locations along the revetment geometry are compared to the 1D results of the corresponding zones (Figure 4 and Figure 5). It can be seen that the 1D approximations and the 2D results correspond well for zone 2, 3 and 4. The CSR values in these zones are low, indicating a low impact of the earthquake loading that will not lead to liquefaction. The low CSR values are caused by the overburden stress due to overlying material. Therefore it is concluded that the presence of the revetment geometry reduces the CSR in the underlying top few meters of sand.

Zone 1 is the critical zone as the CSR values are significantly higher than in the other zones. Indeed sand near the surface that is not overlain by revetment material is subject to liquefaction at the design earthquake loading. From Figure 5

Figure 3: Rayleigh damping and hysteretic damping ratio. From: Muir Wood (2004)

b =~1 + ~2

2pc

a =~1 + ~2

2pc~1~2

p =2~

a+2

b~


Figure 6: Geometry of revetment with possible deformation mechanism schematized in red. The 1D approximation leads to overestimation of the CSR in the zone indicated by + and underestimation in the zone indicated by -

it is seen that the 2D results at location A, B and D are in agreement with the 1D approximation of zone 1. At position E the 1D approximation gives higher values than the 2D analysis and therefore it is overestimating the CSR. The application of the 1D approximation will not lead to a dangerous situation for this location. However, at location C, just in front of the toe, the 1D approximation underestimates the CSR value considerably. The 2D analysis shows that the design earthquake will certainly lead to liquefaction at this location. The loss of strength in the liquefied area may in turn cause failure of the revetment (Figure 6). However, the revetment stability will not be significantly affected when the berm is constructed sufficiently wide, as liquefaction near the toe and subsequent deformation will occur solely in the berm.

Conclusions and recommendationsIn this research the influence of the revetment geometry on the susceptibility to liquefaction of the underlying sand layer is investigated. The following procedure is used, in which the cyclic stress approach is followed to assess initiation of liquefaction.

By separating the geometry into zones that are approximated by 1D shear columns, equivalent linear soil properties are obtained using the computer program SHAKE. This program uses an iterative procedure to obtain values for G and pof each soil layer that are consistent with the level of strain induced by the earthquake. The viscous damping parameters that are used as input for PLAXIS are determined from the strain equivalent damping ratios using an iterative method. Hereby the viscous damping parameters are adjusted until the amplification functions from both computer programs match.

After the strain equivalent parameters are derived, a 2D-calculation is performed in PLAXIS to investigate the influence of the revetment geometry on the susceptibility to liquefaction of the underlying sand layer. For the investigated situation it is found that sand near the surface that is not overlain by revetment material is subject to liquefaction at the design earthquake loading. The presence of the revetment geometry reduces the CSR in the top few meters of underlying sand.

However, the CSR close to the toe on the sea side is higher due to the presence of the revetment geometry. The 1D-approximation does not show this as a location that will be liquefied, as the 1D-approximation largely underestimates CSR values on the sea side of the toe. The loss of strength in the liquefied area may in turn cause collapse of the revetment. This is avoided by making the berm sufficiently wide, so possible liquefaction under the toe and subsequent failure of the berm do not affect the revetment stability significantly.

The influence of static shear stress and rotation of principal stress directions on the liquefaction resistance are not taken into account in this article. If further research shows that the influence is significant, it is recommended to use an advanced model that is able to predict pore pressure generation as a function of stress rotation and static shear stress.

ReferencesMuir Wood, D. (2004), Geotechnical modelling. •Spon Press, United KingdomPark, D. and Hashash, Y.M.A. (2004), “Soil •damping formulation in nonlinear time domain site response analysis”. Journal of Earthquake Engineering, Vol.8, No.2, pp.249-274Schnabel, P.B., Lysmer, J. and Seed, H.B. (1972), •“SHAKE: A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites”. Report No. EERC 72-12, University of California, Berkeley


Recent activities

New websiteIn September we released our new website. With this website we finished the transition to our new Corporate Identity which started with the new look of the previous bulletin (spring issue 2009). Besides a fresh look and feel, this website is more transparent. Gradually we will also release a webshop, specific technical information, papers and new videos.

Please check out our website on regular basis and give us your feedback.

PLAXIS 3D At the 17th International Conference for Geotechnical Engineering and Soil Mechanics in Alexandria, Egypt, Plaxis launched the new PLAXIS 3D Program.

PLAXIS 3D is a finite element package intendedfor three-dimensional analysis of deformation andstability in geotechnical engineering. Geotechnical applications require advanced constitutive models for the simulation of the non-linear, time-dependent and anisotropic behaviour

of soils and/or rock. In addition, since soil is a multi-phase material, special procedures are required to deal with hydrostatic andnon-hydrostatic pore pressures in the soil.Although the modelling of the soil itself is animportant issue, many tunnel projects involve the modelling of structures and the interaction between the structures and the soil.PLAXIS 3D is equipped with features to deal withvarious aspects of complex geotechnical structures.

Some features are:• Arbitrary 3D geometry for soil and structures• DXF or 3DS input of geometry (PLAXIS VIP)• Terrain geometry input tools• Multiple borehole wizard• Real and easy 3D interaction• Command line input• Model replay function• Advanced soil models• User defined soil models (PLAXIS VIP)• 64 bit calculation kernel (PLAXIS VIP)• Convenient construction stage definition


At our User Meeting from 11 till 13 November 2009 in Karlsruhe, Germany users and prospects will have the opportunity to get familiar with the new PLAXIS 3D program. Participants who bring their own laptop can install PLAXIS 3D and learn how easy one can operate this new flexible program. Participants will also get the possibility to take a time limited version of the program with them. Plaxis in ChinaIn China we noticed that there are an increasing number of large state-owned enterprises and private consultants using PLAXIS for their projects, as compared to one year ago, when only educational institutes used PLAXIS for their research projects. Companies like China Petroleum, China Airport Construction, China

Railway, CNPC Research Institute of Engineering Technology etc. are realising the importance of using Finite Element Method for the analysis of deformation, stability and groundwater flow for their day-to-day geotechnical engineering projects. The user friendliness, robust calculation procedures and continuous scientific research of the software are the key factors for the success in the Chinese market.

Plaxis Asia coursesThe first PLAXIS 3 day standard course in China was successfully conducted in April 2009 in Beijing with participants from Guangdong, Tianjin, Hebei, Beijing and other nearby provinces. The course was organised by our Plaxis agent in China, Beijing Civil King Software Tech. Co. Ltd and the

renowned Qinghua University in Beijing, and was presented by Prof. Song Erxiang from (Tsinghua Unversity, vice Prof. Yang Jun from Tsinghua University and Dr. William Cheang from Plaxis Asia.

Besides covering the preliminary principles of FEM for Geo-engineering, the methodology and the key parameters used in PLAXIS, the 3 day course also gave the participants hands-on experience and the chance to work on real projects using PLAXIS, followed by a Q&A session. The success of this course means that certainly more PLAXIS Courses shall be organised in China in the future.

Title

16 Jalan Kilang Timor#05-08 Redhill Forum

159308 Singapore

P.O. Box 572 2600 AN Delft

The Netherlands

www.plaxis.nlTel +31 (0)15 2517 720Fax +31 (0)15 2573 107

Plaxis AsiaSingapore

Tel +65 6325 4191

Plaxis bvDelftechpark 53

2628 XJ Delft

September 29 – October 2, 2009Curso Avanzado de Geotecnia ComputacionalQuerétaro, Mexico

October 5 – 9, 2009 17th ISSMGEAlexandria, Egypt

November 5, 2009GeotechniekdagRotterdam, The Netherlands

November 5 – 6, 2009PLAXIS CourseTaipei, Taiwan

January 19 – 22, 2010Short Course on Computational Geotechnics & Soil modelsWashington DC, USA

January 25 – 28, 2010Standard Course on Computational Geotechnics Schiphol, The Netherlands

February 15 – 17, 2010Curso de Geotecnia ComputacionalBarcelona, Spain

February 20 – 24, 2010GeoFloridaWest Palm Beach, U.S.A.

February 22 – 24, 2010Course “Finite Elementen in der Geotechnik“ Stuttgart, Germany

November 11 – 13, 200916th European Plaxis User MeetingKarlsruhe, Germany

November 19, 2009SeminarHong Kong

November 24, 20093D Launch SeminarLondon, U.K.

November 25 – 26, 2009PLAXIS CourseHong Kong, China SAR

March 2010Advanced Course on ComputationalGeotechnicsKuala Lumpur, Malaysia

March 2 – 5, 2010Curso de Geotecnia ComputacionalBogotá, Colombia

March 15 – 18, 2010Advanced Course on Computational GeotechnicsSchiphol, The Netherlands

May 10 – 13, 201017th Southeast Asian Geotechnical ConferenceTaipei, Taiwan

May 14 – 20, 201036th World Tunnel CongressVancouver, Canada

November 25 – 27, 2009Standard Course on Computational GeotechnicsParis, France

November 30 – December 4, 2009 Advanced Course on Computational GeotechnicsGold Coast, Australia

December 1 – 3, 2009STUVA’09 ConferenceHamburg, Germany

May 26 – 28, 201011th DFILondon, United Kingdom

June 2 – 4, 20107th NUMGETrondheim, Norway

June 7, 2010International GeotechnicalConferenceMoscow, Russia

June 8 – 10, 20109th Intertunnel 2010Turin, Italy

Activities 2009

Activities 2010

plaxis bulletin autmn 2009

Documents