interface enabling constitutive models coded as user...

Centre for Offshore Foundation Systems

The University of Western Australia

CENTRE FOR OFFSHORE FOUNDATION SYSTEMS

Interface enabling constitutive models coded as user materials to

be employed in explicit analysis

Research report

by

B. BIENEN1, S. STANIER

1, C. VULPE

1 & D. MAŠÍN

2

1 Centre for Offshore Foundation Systems, University of Western Australia

35 Stirling Hwy, Crawley, Perth, WA 6009, Australia

2 Faculty of Science, Charles University in Prague

Albertov 6, 12843 Prague 2, Czech Republic

NOVEMBER 2014 GEO: 14756

INTERFACE ENABLING CONSTITUTIVE MODELS CODED PAGE | 2

AS USER MATERIALS TO BE EMPLOYED IN EXPLICIT ANALYSIS GEO: 14756



TABLE OF CONTENTS

1. INTRODUCTION ........................................................................................................................................... 1

2. CONSTITUTIVE RELATIONS USED AS EXAMPLES ........................................................................... 2

3. INTERFACE ENABLING USE OF CURRENT IMPLICIT IMPLEMENTATION IN EXPLICIT

LARGE DEFORMATION ANALYSIS ................................................................................................................. 4

4. EXAMPLE ANALYSES – COMPARISON OF IMPLEMENTATIONS.................................................. 6

5. EXAMPLE LARGE DEFORMATION ANALYSIS WITH THE NEW USER SUBROUTINE ............ 8

6. CONCLUDING REMARKS .......................................................................................................................... 8

LIST OF TABLES

Table 1. Hypoplastic parameters of Hochstetten sand (von Wolffersdorff 1996, Niemunis and

Herle 1997). ................................................................................................................................ 14

Table 2. Hypoplastic parameters of Weald clay (Mašín 2014 model, αG=1)............................. 14

Table 3. Hypoplastic parameters of UWA silica sand (cf. Pucker et al. 2013). ......................... 14

LIST OF FIGURES

Figure 1. Oedometer tests on Hochstetten sand: comparison of experimental data Abaqus

implicit and explicit simulations for initial void ratios e0 = 0.695, 0.73 (von Wolffersdorff

1996). .......................................................................................................................................... 16

Figure 2. Oedometer tests on Hochstetten sand including stress cycles as simulated by Abaqus

implicit and explicit using (a) the hypoplastic model by von Wolffersdorff (1996), and (b) the

same model with the intergranular strain concept extension (Niemunis and Herle 1997)......... 16

Figure 3. Undrained triaxial tests on Weald clay: comparison of experimental data with Abaqus

implicit and explicit simulations using the Mašín (2014) model in (a) q-p space, and (b) q-εa

space. .......................................................................................................................................... 17

Figure 4. Penetration of a large diameter (D = 12 m) conical footing with an enclosed angle of

150º into medium dense sand (Dr = 45%) (a) load-penetration curve, (b) mobilised friction

angle at a penetration depth of 0.3D. ......................................................................................... 18





Interface enabling constitutive models coded as user materials to be

employed in explicit analysis

Research report GEO 14756

1. INTRODUCTION

The soil constitutive model is a key part of any numerical analysis in geotechnical engineering.

A large number of constitutive models are reported in the literature, though typically their

numerical implementation is not readily available to the readership. To overcome this problem,

a group of researchers (G. Gudehus, A. Amorosi, A. Gens, I. Herle, D. Kolymbas, D. Mašín,

D. Muir Wood, R. Nova, A. Niemunis, M. Pastor, C. Tamagnini, and G. Viggiani) established

the “soilmodels.info” project (Gudehus et al. 2008, www.soilmodels.info) in 2007. The

soilmodels.info project is an “open-source database of constitutive models for numerical

analysis in geotechnical engineering implemented in a standardized format”. The chosen

standardised format is that of the user subroutine UMAT within the commercial software

package Abaqus (an interface is available for Plaxis). The unrestricted access to the source

code has the added benefit of allowing rigorous validation by researchers and practitioners

alike, internationally.

The database currently comprises the following constitutive models:

The elasto-plastic model for structured clay by Liu and Carter (2002),

The elasto-plastic model for sand SANISAND by Dafalias and Manzani (2004),

The hypoplastic model for granular material by von Wolffersdorff (1996), available

with the small-strain extension by Niemunis and Herle (1997),

The hypoplastic model for clay by Mašín (2014), available with the small-strain

extension by Niemunis and Herle (1997).

Currently, these models are available as a UMAT, which limits their application to

Abaqus/Standard (and Plaxis) and thus small strain finite element analyses that employ an

implicit solution scheme. However, many geotechnical problems are better suited to explicit

integration, such as those involving large deformations (in particular problems with more

complex footing geometries) or highly dynamic events. These analyses require a user routine

http://www.soilmodels.info/





called a VUMAT, which differs from a UMAT in several aspects as detailed later. The

numerical implementation of the constitutive models not being readily available as a VUMAT

is an obstacle to their widespread application in large deformation geotechnical problems

suited to analysis using an explicit scheme. This paper introduces an interface coded to enable

the freely available UMAT user routines of advanced constitutive relations to be used in

Abaqus/Explicit. The interface is not model specific, i.e. it can be used together with any

UMAT user routine. The accuracy and reliability of its implementation is demonstrated here

through several examples assuming hypoplastic constitutive relations to represent soil

behaviour.

The following provides a brief description of the hypoplastic constitutive models currently

available for granular materials and clays, respectively, before the user routine requirements

and interface coding is discussed. The correct implementation is demonstrated through

examples of element test simulations, performed using two different hypoplastic models

representing the response of both sand and clay soils. These are analysed both using

Abaqus/Standard with the UMAT routine as available on www.soilmodels.info, and using

Abaqus/Explicit with the VUMAT routine, achieved by combining the UMAT with the new

interface. The paper concludes with an example large deformation application, utilising the

VUMAT interface introduced here.

The new VUMAT interface is freely available on www.soilmodels.info.

2. CONSTITUTIVE RELATIONS USED AS EXAMPLES

The constitutive models used as examples in this paper are the hypoplastic relations for

granular (von Wolffersdorff 1996, Niemunis and Herle 1997) and clay soils (Mašín 2014),

respectively. While it is not the scope of this Note to discuss details of the model formulation

and validation, we provide a brief description of the models only. For additional information,

the readers are referred to the cited publications.

Hypoplasticity for granular soils

The hypoplastic constitutive model by von Wolffersdorff (1996) has both been widely used

and relied upon as a reference model to which extensions have been added. This model

originated from a series of research developments undertaken at Karlsruhe University. The

performance of this model under cyclic loading was improved by the intergranular strain

concept introduced by Niemunis and Herle (1997). Niemunis (2003) further used the von







Wolffersdorff model as a basis for a visco-hypoplastic model and generalised hypoplasticity.

For further details on the model calibration and validation, see Herle and Gudehus (1999).

The model by von Wolffersdorff (1996) can be described by a non-linear tensorial equation

that yields the objective stress rate

T as a function of the stretching rate D:

(1)

where is a fourth order tensor, is a second-order tensor, is a barotropy factor including

the influence of mean stress and is a pyknotropy factor including the influence of relative

density. In the hypoplastic formulation, the strain is not divided into elastic and plastic

components.

The constitutive model is able to realistically reproduce the nonlinear and inelastic behaviour

of sands. The stiffness and the peak friction angle depend on the current stress state T

(barotropy) and the current void ratio (pyknotropy). The latter enables changes from

contractive to dilatant behaviour to be modelled and a critical state can be obtained. The failure

surface of the model matches the failure criterion of Matsuoka and Nakai (1974).

The model has been used in complex boundary value problems, many of them employing

explicit solution schemes (the analyses relied on in-house coding of the constitutive model as a

VUMAT user routine). These include dynamic soil improvement (Grabe 1992), prediction of

soil settlements (Hügel 1995), investigation of the effect of installation method on soil

plugging of open ended pile profiles (Henke and Grabe 2008), the numerical simulation of the

installation process of full displacement piles (Pucker and Grabe 2012), and development of a

CPT based approach to predict the load-penetration curve of footings on sand (Pucker et al.

2013). The model has also been used in reproducing experiments from geotechnical centrifuge

tests (Ng et al. 2013, Pucker et al. 2013, Bienen and Qiu 2014).

Hypoplasticity for clay soils

Mašín (2005) based the development of a hypoplastic model for clay soils on a modification

(Herle and Kolymbas 2004) of the above model by von Wolffersdorff (1996), in combination

with traditional critical state soil mechanics. The Matsuoka-Nakai (1974) failure surface forms

the limit stress criterion. The primary equation is identical to that of the sand model (1), which

allows for a unified implementation strategy of both models.





Further recent developments involved explicit incorporation of the asymptotic state boundary

surface (Mašín 2012a,b), which led to the updated version of the hypoplastic model (Mašín

2013) and finally to a model that caters for stiffness anisotropy in clays (Mašín 2014). The

model has been used in various boundary value problem simulations (Mašín 2009a, Svoboda et

al. 2010, Najser et al. 2012, Blecha and Mašín 2013). These models are rate independent. Rate

dependency is captured in visco-hypoplastic models (Niemunis 2003, Niemunis et al. 2009),

which have been used in boundary value problems of granular columns in soft soil (Meier

2009) and spudcan footing penetration in sand overlying clay (Qiu and Grabe 2012). Once

again, the explicit implementation of these models involved in-house code development. For

validation of different model properties on the element test level, the readers are further

referred to Mašín et al. (2006), Hájek et al. (2009) and Mašín (2009b).

Current implementation

The constitutive relations, coded as UMAT routines by C. Tamagnini, D. Mašín and P.-A. von

Wolffersdorff for use in conjunction with the commercial software package Abaqus, are

available under www.soilmodels.info.

Although the intricacies of the clay and sand models differ, their overall numerical

implementation is similar. The implementation of both models uses the explicit, adaptive

second order Runge-Kutta-Fehlberg (RKF23) scheme with local time step extrapolation to

integrate the constitutive relation.

3. INTERFACE ENABLING USE OF CURRENT IMPLICIT IMPLEMENTATION

IN EXPLICIT LARGE DEFORMATION ANALYSIS

Differences in user routine requirements

There are a number of significant differences between the UMAT and VUMAT definitions.

While a UMAT is called in Abaqus/Standard for every integration point in every increment,

Abaqus/Explicit is written to take advantage of vector processing and thus calls a VUMAT for

a block of material calculation points. The material Jacobian matrix does not need to be defined

in a VUMAT, whereas it must be supplied in a UMAT. Abaqus/Explicit stores the stress and

strain components internally in a different order: 11, 22, 33, 12, 23, 13; compared to 11,

22, 33, 12, 13, 23 in Abaqus/Standard. The shear strain components in a VUMAT are stored

as tensor components. This is different from a UMAT, which uses engineering components.






Full definitions of the UMAT and VUMAT requirements and conventions are detailed in the

Abaqus User Subroutines Reference Manual (Dassault Systèmes, 2012).

Interface coding

The interface has been coded to perform the necessary changes to achieve compatibility

between the existing UMAT and VUMAT requirements. This includes re-ordering stress

components from Abaqus/Standard to Abaqus/Explicit storage schemes, conversion of tensor

to engineering shear strains and assignment of further variables used by UMAT.

Hence, following the subroutine header as set out in the Abaqus manual, the interface code

contains the following statements: The re-ordering and conversion of stress and strain

components reads

do 100 km = 1,nblock

do i = 1, ndir

stress(i) = stressOld(km,i)

dstran(i) = strainInc(km,i)/dt

enddo

stress(4) = stressOld(km,4)

dstran(4) = two * strainInc(km,4)/dt

if (nshr .gt. 1) then





endif





This is followed by the definition of variables that are used by UMAT but are not part of a

VUMAT or have different names in the two types of user subroutines. The UMAT is then

called. Prior to exiting the VUMAT the stress components are re-ordered as required:

do i = 1, ndir

stressNew(km,i) = stress(i)

enddo

stressNew(km,4) = stress(4)

if (nshrUMAT .gt. 1 ) then



endif

100 continue

As detailed, the interface is applied by simply inserting it around the UMAT code within the

target user subroutine. It is suitable for use with any UMAT coded constitutive model.

The interface introduced here enables existing UMAT constitutive models to be employed in

explicit analysis without the requirement for further coding. Awareness of the user of existing

modelling assumptions and limitations, both in the constitutive model and the numerical

method, remain central to obtaining reliable results that accurately model the key features of

the response.

4. EXAMPLE ANALYSES – COMPARISON OF IMPLEMENTATIONS

Two example element test simulations are first discussed here to illustrate the robust, accurate

and reliable performance of the interface: (1) an oedometer test on sand, (2) a triaxial test on

clay. The problems are analysed using (i) the UMAT implementation in conjunction with

Abaqus/Standard and (ii) the VUMAT implementation (i.e. the UMAT with the new interface)





in Abaqus/Explicit. The capabilities of the interface enabled constitutive formulation is then

further demonstrated through a large deformation analysis of a large diameter conical footing

penetrating into sand, carried out using the Coupled Eulerian-Lagrangian approach available in

Abaqus/Explicit.

Oedometer test

Von Wolffersdorff (1996) illustrated the capability of the hypoplastic model to reflect the

behaviour of sand of different relative densities by only varying the initial void ratio. The

general parameter set remains the same irrespective of the soil state. The hypoplastic

parameters are provided for Hochstetten sand in Table 1.

The implicit analysis performed using the UMAT routine from www.soilmodels.info produces

results (Fig. 1) that agree well with the experimental measurements and original calculated

response (von Wolffersdorff 1996). The concept of intergranular strains introduced by

Niemunis and Herle (1997) is shown to reduce the excessive ratcheting (Fig. 2).

The results of the implicit and explicit analyses are indistinguishable.

Triaxial test

The second example presents undrained triaxial tests on normally consolidated and over-

consolidated Weald clay (Parry 1960) with the hypoplastic model introduced by Mašín (2014).

Model parameters and the initial states assumed for the two analyses are provided in Table 2.

The results from implicit and explicit analyses of this study are compared with experimental

results in Figure 3. The two numerical predictions are indistinguishable, which confirms the

performance of the interface. The implicit results are further identical to those presented in

Mašín (2013), who discusses the constitutive modelling features and parameter values which

result in the differences between experimental results and numerical simulations.

These analyses confirm that the constitutive models available from www.soilmodels.info

perform as intended. They further demonstrate that:

The new interface provides a straightforward and viable approach to adapting

constitutive model user subroutines intended for implicit analysis to be employed in

explicit analysis.

The accuracy of the solution is maintained.





5. EXAMPLE LARGE DEFORMATION ANALYSIS WITH THE NEW USER

SUBROUTINE

Figure 4 shows the penetration resistance obtained from a large deformation analysis

performed using the Coupled Eulerian-Lagrangian approach in Abaqus/Explicit employing the

hypoplastic model for sand with the new interface. The simulation is a of a 12 m diameter

conical footing being penetrated into medium dense sand (with the parameters summarised in

Table 3) from the soil surface to a depth of approximately 4.5 m (measured from the footing

tip). This example is of a problem relevant to offshore practice, where jack-up rigs are used to

provide a platform from which to perform drilling of the seabed, facilitating the extraction of

oil and gas economically in water depths up to approximately 150 m.

Though the problem is axisymmetric, the CEL implementation in Abaqus is limited to three-

dimensional modelling with eight node elements with reduced integration the only choice for

the Eulerian part. Hence, a 90° section of the problem was analysed. Contact between Eulerian

(here: the soil) and Lagrangian (here: the footing, modelled as discretely rigid) bodies is

enforced using a general contact formulation that is based on a penalty method. Intermediate

roughness was assumed. Velocity boundary conditions were imposed that prevent vertical

movement at the base and lateral movement at the sides of the soil domain. The footing was

penetrated into the soil at a constant velocity of 1 m/s. This was selected based on

considerations of computational efficiency whilst ensuring the response remained quasi-static

(via the energy balance).

The load-penetration curve predicted in this numerical example compares well against

experimental data obtained from testing in a geotechnical centrifuge where the response is

expected to reflect that of the prototype as stress similitude is maintained. The prototype

diameter of the spudcan footing (a conical footing with a central tip, which influences the

initial part of the penetration) in these experiments was 10 m and the relative density of the

sand Dr = 37% (Bienen 2009). Hence, the response is a little softer as expected. Overall,

however, the numerical prediction agrees well with the data from physical tests, which

provides confidence in the simulation.

6. CONCLUDING REMARKS

An interface is described that enables constitutive models coded as user materials (UMAT) to

be employed in explicit analysis (VUMAT), rather than requiring coding of an entirely new





user routine. Reliability, robustness and accuracy of solution are demonstrated with examples

of oedometer and triaxial tests, before performance of the code is illustrated in a large

deformation explicit analysis of a footing penetrating into soil. The interface code is available

on www.soilmodels.info.

ACKNOWLEDGEMENTS

The first author is the recipient of an Australian Research Council (ARC) Postdoctoral

Fellowship (DP110101603). The work described here forms part of the activities of the Centre

for Offshore Foundation Systems (COFS), the ARC Centre of Excellence in Geotechnical

Science and Engineering, and Lloyd’s Register Foundation (LRF). LRF helps to protect life

and property by supporting engineering-related education, public engagement and the

application of research. This support is gratefully acknowledged.






REFERENCES

Bienen, B., Qiu, G. (2014). Numerical analysis of large penetration of a cone and a large

diameter footing into dense sand overlying clay. Proc. 14th

International Conference of the

International Association for Computer Methods and Advances in Geomechanics

(IACMAG), Kyoto, Japan.

Blecha, V., Mašín, D. (2013). Observed and calculated gravity anomalies above a tunnel driven

in clays - implication for errors in gravity interpretation. Near Surface Geophysics, Vol. 11,

No. 5, pp. 569-578.

Dafalias, Y.F., Manzari, M.T. (2004). Simple plasticity sand model accounting for fabric

change effects. Journal of Engineering Mechanics, Vol. 130, No. 6, pp. 622-634.

Dassault Systèmes. (2012). Abaqus User Subroutines Reference Manual. Providence, RI, USA.

Herle, I., Gudehus, G. (1999). Determination of parameters of a hypoplastic constitutive model

from properties of grain assemblies. Mechanics of Cohesive-Frictional Materials, Vol. 4, pp.

461-486.

Grabe, J. (1992). Experimentelle und theoretische Untersuchungen zur flächendeckenden

dynamischen Verdichtungskontrolle. PhD thesis, University of Karlsruhe, Germany.

Gudehus, G., Amorosi, A., Gens, A., Herle, I., Kolymbas, D., Mašín, D., Muir Wood, D.,

Niemunis, A., Nova, R., Pastor, M., Tamagnini, C., Viggiani, G. (2008). The

soilmodels.info project. International Journal of Numerical and Analytical Methods in

Geomechanics, Vol. 32, No. 12, pp. 1571-1572.

Hájek, V., Mašín, D., Boháč, J. (2009). Capability of constitutive models to simulate soils with

different OCR using a single set of parameters. Computers and Geotechnics, Vol. 36, No. 4,

pp. 655-664.

Henke, S., Grabe, J. (2008). Numerical investigation of soil plugging inside open-ended piles

with respect to the installation method. Acta Geotechnica, Vol. 3, No. 3, pp. 215-223.

Herle, I., Kolymbas, D. (2004). Hypoplasticity for soils with low friction angles. Computers

and Geotechnics, Vol. 31, pp. 365-373.

Hügel, H.M. (1995). Prognose von Bodenverformungen. PhD thesis, University of Karlsruhe,

Germany.





Liu, M.D., Carter, J.P. (2002). A structured Cam Clay model. Canadian Geotechnical Journal,

Vol. 39, pp. 1313-1332.

Mašín, D. (2005). A hypoplastic constitutive model for clays. International Journal of

Numerical and Analytical Methods in Geomechanics, Vol. 29, No. 4, pp. 311-336.

Mašín, D. (2009a). 3D modelling of a NATM tunnel in high K0 clay using two different

constitutive models. Journal of Geotechnical and Geoenvironmental Engineering (ASCE),

Vol. 135, No. 9, pp. 1326-1335.

Mašín, D. (2009b). Comparison of predictive capabilities of selected elasto-plastic and

hypoplastic models for structured clays. Soils and Foundations, Vol. 49, No. 3, pp. 381-390.

Mašín, D. (2012a). Asymptotic behaviour of granular materials. Granular Matter, Vol. 14, No.

6, pp. 759-774.

Mašín, D. (2012b). Hypoplastic Cam-clay model. Géotechnique, Vol 62, No. 6, pp. 549-553.

Mašín, D. (2013). Clay hypoplasticity with explicitly defined asymptotic states. Acta

Geotechnica, Vol. 8, No. 5, pp. 481-496.

Mašín, D. (2014). Clay hypoplasticity model including stiffness anisotropy. Géotechnique,

Vol. 64, No. 3, pp. 232-238.

Mašín, D., Tamagnini, C., Viggiani, G. and Costanzo, D. (2006). Directional response of a

reconstituted fine-grained soil - Part II: performance of different constitutive models.

International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 30, No.

13, pp. 1303-1336.

Matsuoka, H., Nakai, T. (1974). Stress–deformation and strength characteristics of soil under

three different principal stresses. Proc. Japanese Soc. of Civil Engineers, Vol. 232, pp. 59-

70.

Meier, T. (2009). Application of hypoplastic and viscohypoplastic constitutive models for

geotechnical problems. PhD thesis, University of Karlsruhe, Germany.

Najser, J., Mašín, D., Boháč, J. (2012). Numerical modelling of lumpy clay landfill.

International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 36, No.

1, pp. 17-35.





Ng, C. W. W., Boonyarak, T., Mašín, D. (2013). Three-dimensional centrifuge and numerical

modeling of the interaction between perpendicularly crossing tunnels. Canadian

Geotechnical Journal, Vol. 50, No. 9, pp. 935-946.

Niemunis, A. (2003). Extended hypoplastic models for soils. Heft 34, Schriftreihe des Instituts

für Grundbau und Bodenmechanik der Ruhr-Universität Bochum, Germany.

Niemunis, A., Grandas-Tavera, C.E., Prada-Sarmiento, L.F. (2009). Anisotropic visco-

hypoplasticity. Acta Geotechnica, Vol. 4, No. 4, pp. 293-314.

Niemunis, A., Herle, I. (1997). Hypoplastic model for cohesionless soils with elastic strain

range. Mechanics of Cohesive-Frictional Materials,Vol. 2, pp. 279-299.

Parry, R.H.G. (1960). Triaxial compression and extension tests on remoulded saturated clay.

Géotechnique, Vol.10, pp. 166-180.

Pucker, T., Grabe J. (2012). Numerical simulation of the installation process of full

displacement piles. Computers and Geotechnics, Vol. 45, pp. 93-106.

Pucker, T., Bienen, B., Henke, S. (2013). CPT based prediction of foundation penetration in

siliceous sand. Applied Ocean Research, Vol. 41, pp. 9-18, doi:10.1016/j.apor.2013.01.005.

Svoboda, T., Mašín, D., Boháč, J. (2010). Class A predictions of a NATM tunnel in stiff

clay. Computers and Geotechnics, Vol. 37, No. 6, pp. 817-825.

Qiu, G., Grabe, J. (2012). Numerical investigation of bearing capacity due to spudcan

penetration in sand overlying clay. Canadian Geotechnical Journal, Vol. 49, pp. 1393-1407.

von Wolffersdorff, P.A. (1996). A hypoplastic relation for granular materials with a predefined

limit state surface. Mechanics of Cohesive-Frictional Materials, Vol. 1, pp. 251-271.





List of tables

Table 1. Hypoplastic parameters of Hochstetten sand (von Wolffersdorff 1996, Niemunis and

Herle 1997).

Table 2. Hypoplastic parameters of Weald clay (Mašín 2014 model, αG=1).

Table 3. Hypoplastic parameters of UWA silica sand (cf. Pucker et al. 2013).





TABLES

Table 1. Hypoplastic parameters of Hochstetten sand (von Wolffersdorff 1996, Niemunis

and Herle 1997).

Parameters for von Wolffersdorff (1996) model Intergranular strain extension

(Niemunis and Herle 1997)

C hs n ec0 ed0 ei0 β R mR mT βr χ

(º) (MPA) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-)

33 1,000 0.25 0.95 0.55 1.05 0.25 1.5 110-4

5.0 2.0 0.5 6.0

Table 2. Hypoplastic parameters of Weald clay (Mašín 2014 model, αG=1).

Parameters Initial state

C λ

* κ

* N ν e p q

(º) (-) (-) (-) (-) (-) (KPA) (KPA)

24 0.059 0.014 0.8 0.15 NC: 0.6225

OC: 0.5719

206.8

68.95

0

0

Table 3. Hypoplastic parameters of UWA silica sand (cf. Pucker et al. 2013).

C hs n ec0 ed0 ei0 β R mR mT βr χ

(º) (MPA) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-)

30 1,354 0.34 0.76 0.49 0.86 0.18 1.27 110-4

5.16 3.07 0.58 5.74





List of figures



1996).

Figure 2. Oedometer tests on Hochstetten sand including stress cycles as simulated by Abaqus

implicit and explicit using (a) the hypoplastic model by von Wolffersdorff (1996), and (b) the

same model with the intergranular strain concept extension (Niemunis and Herle 1997).

Figure 3. Undrained triaxial tests on Weald clay: comparison of experimental data with Abaqus

implicit and explicit simulations using the Mašín (2014) model in (a) q-p space, and (b) q-εa

space.

Figure 4. Penetration of a large diameter (D = 12 m) conical footing with an enclosed angle of

150º into medium dense sand (Dr = 45%) (a) load-penetration curve, (b) mobilised friction

angle at a penetration depth of 0.3D.





FIGURES



1996).

a) b)

Figure 2. Oedometer tests on Hochstetten sand including stress cycles as simulated by

Abaqus implicit and explicit using (a) the hypoplastic model by von Wolffersdorff (1996),

and (b) the same model with the intergranular strain concept extension (Niemunis and

Herle 1997).





a) b)

Figure 3. Undrained triaxial tests on Weald clay: comparison of experimental data with

Abaqus implicit and explicit simulations using the Mašín (2014) model in (a) q-p space,

and (b) q-εa space.





a)

b)

Mobilised friction angle 40.0º

37.5 º

35.0º

32.5º

30.0º

27.5º

25.0º

22.5º

20.0º

Figure 4. Penetration of a large diameter (D = 12 m) conical footing with an enclosed

angle of 150º into medium dense sand (Dr = 45%) (a) load-penetration curve, (b)

mobilised friction angle at a penetration depth of 0.3D.

interface enabling constitutive models coded as user...

Documents