raisa ehsan past paper

8/12/2019 Raisa Ehsan Past Paper

1/24

2012/13 ICE G&S Papers Competition Entry

Raisa Ehsan

A Study of Geotechnical ConstitutiveModels using PLAXIS 2D

This paper is document is published as a guide to show prospective ICE G&S Papers Competitionentrants what judges are looking for in a winning entry. Please respect the intellectual rights of the

author over this work. If you wish to use this paper for any other reason, please contact ICERegional Communications Executive Annette Honeyball ([email protected] or 0118 986

9442)
mailto:[email protected]:[email protected]:[email protected]:[email protected]


2/24

Synopsis: A Study of Geotechnical Constitutive Models Used in PLAXIS 2D

In this report, the author has attempted to carry out an investigation on the constitutive models utilised

in geotechnical finite element modelling programs, primarily Plaxis2D. The purpose of this study is to evaluate the performance of geotechnical structures in deep excavations using finite element analysis comprising of the elastic perfectly plastic Mohr Coulomb model and the more complex non linear Hardening Soil and Hardening Soil with Small Strain model.

Detailed research was carried out on each of the constitutive models present in PLAXIS 2D V9, including a detailed summary of each input parameter. Based on the comparison, a conclusion is derived at in the

form of the limitations and advantages of both the simple Mohr Coulomb model and the complex non

linear models.

The report also consists of the research done on the correlation of parameters with testing, which

includes a full break down of model input parameters and possible derivations from standard laboratory

and insitu testing. A clear guide is provided on what each parameter means in the constitutive models and where it is derived from.

A series of case studies are chosen with available monitoring data for deep excavations. Then a comparison between results from PLAXIS runs for each constitutive model and field instrumentation data found in case studies is made. The results demonstrate that more realistic predictions of wall deflections can be obtained by the Hardening Soil with Small Strain model.


3/24

A Study of Geotechnical ConstitutiveModels Used in Plaxis 2D

ByRaisa Ehsan


4/24

Raisa Ehsan G&S Papers Competition 2013

2

1 IntroductionThe major challenge involved for the geotechnical engineers is the task of accurately

predicting the performance of deep excavations. Numerical analysis such as the finite

element method is almost always used to make predictions of ground behaviour. However, in

an attempt to model a geotechnical problem so that it reflects real soil behaviour, the engineer

faces complex constitutive models.

1.1 Constitutive ModelsConstitutive modelling of soils is a mathematical form of describing the stress-strain

behaviour of soils in response to applied loads. It introduces or describes the physical

properties of a given material and also distinguishes between elastic and plastic deformations.

2 Mohr Coulomb Model (MC Model)The Mohr-Coulomb yield criterion is a first order approximation of soil behaviour, and due to

the simplicity of the model, is employed extensively in geotechnical analysis.

Figure 1 : Mohrs circles at yield, one touching Coulombs envelope ( Brinkgreve R.B.J et al

2004)

The combination of Mohr failure envelope and the Coulomb strength parameters is referred to

as the Mohr-Coulomb failure criterion. The failure criterion states that a material fails and not

from their maximum normal or shear stress alone, but because of a critical combination of

normal stress and shear stress. This is the only failure criterion that predicts the stresses on

the failure plane at failure.


5/24


3

In PLAXIS, the Mohr Coulomb model uses an elastic perfectly-plastic constitutive model for

three-dimensional state of stress. According to Smith et al (1982), when formulated in terms

of yield stresses, the full Mohr-Coulomb yield condition consists of six separate yield

functions. The yield functions together gives rise to a fixed hexagonal cone in principal stress

space as shown in Figure 2 .

Figure 2 : The Mohr Coulomb yield surface in principal stress space for c=0 ( BrinkgreveR.B.J 2004)

Figure 2 illustrates that changes of stress remaining inside the yield surfaces are associated

with stiff (elastic) response, and hence are recoverable deformations. On the other hand the

changes of stress which are on the yield surfaces are associated with plastic response, and

hence are irrecoverable deformations.

Comments on Strength and Stif fness

Stiffness behaviour before reaching the local shear strength is poorly modelled in the Mohr

Coulomb model in PLAXIS, where it assumes the stiffness behaviour to be linear elastic

below the failure surface. This limits its abilities to model deformation behaviour before

yielding.

Strength behaviour, however, is modelled better in the Mohr Coulomb model. Goldscheiders

(1982) work shows that the hexagonal shape of the Mohr Coulomb yield surface illustrated


6/24


4

by Figure 2 has a good agreement with the stress combination causing failure in real soil

samples in true triaxial tests.

The use of effective strength parameters in undrained analysis of Mohr-Coulomb model may

result in an over estimation of the shear strength of the material in undrained conditions. The

differing effective stress paths followed for real soil behaviour and Mohr- Coulomb model

predictions in the p-q plane are elaborated in Figure 3.

Figure 3 : Effective stress paths followed in real soil and in MC model. (Pickles A.R 2005)

To avoid such a problem a total stress analysis is preferred, where the cohesion parameter is

used to model the actual undrained shear parameter (c=C u) and the friction angle is set to be

equal to zero ( =0). Doing so will run an analysis where consolidation and dissipation of

excess pore water pressure is not automatically taken into account, and hence no increase in

shear strength will result.

2.1 Mohr Coulomb Model (MC model) input parametersThis model requires a total of five parameters:

TWO stiffness parameters

E : Effective Youngs Modulus ' : Effective Poissons ratio


7/24


5

Instead of using Youngs modulus, alternative stiffness parameters G and E oed can be entered.

These alternative parameters are inf luenced by the input values of E and . Entering a

particular value for one of the alternatives, G or E oed, results in a change of the Youngs

modulus E.

Advanced Parameters are used when stiffness is defined as varying with depth in MC model.

By including the depth effect, an attempt can be made to provide a more realistic model of

natural soils and it is generally acknowledged that soil stiffness does increase with depth.

E inc : increment of stiffness per unit of depth

yref : for y-coordinate above y ref stiffness is equal to E ref and below y ref stiffness is given by

(2.1)

THREE strength parameters

cref : Effective cohesion : Effective friction angle : Dilatancy angle

Advanced Parameters may be used when cohesion is defined as varying with depth in MC

model.

c inc : increment of effective cohesion per unit of depth

yref : for y-coordinate above y ref stiffness is equal to c ref and below y ref cohesion is given by (2.2)

F ri ction angle

The friction ang le determines the shear strength by means of Mohrs stress circles as shown

by Figure 4. Part a corresponds to the friction angle used to model the effective friction of the

soil, where as part b shows how the friction angle is set to zero when cohesion parameter is

equal to the undrained shear strength of the soil.


8/24


6

Figure 4 : Stress circles at yield: one touches the Coulombs envelope (Brinkgreve R.B.J 2004)

Dilation

The angle of dilation is the measure of the change in volumetric strain with respect to thechange in shear strain. Clayey soils tend to show little dilatancy ( 0) and for frictional

angle values of less than 30 the angle of dilatancy is taken as zero in PLAXIS by default.

Poor prediction of dilation occurs in the Mohr Coulomb model, where the magnitude of

plastic volumetric strains is much larger than that encountered in real soils. This model

allows the soil to dilate forever once the soil yields and shear deformation occurs without any

volume change. The strength of the soil maybe overestimated in an undrained effective stressanalysis, where a positive value of the dilatancy angle, combined with restrictions to volume

changes, result in a generation of tensile pore stresses.

Determination of Parameter sThe determination of Youngs modulus can be done from the conventional triaxial

compression test. The experimental results of the test are represented as stress-strain curves

from which the basic elastic constants (Youngs Modulus, E, and Poissons ratio, ) can be

determined. Clayton,C.R.I et al (2005) summarises some of the common in situ and

laboratory tests to determine basic parameters.

The dilatancy angle can be examined in plane strain situations. Data can be extracted from a

typical drained, plain strain, compression test described by Barden, Ismail and Tong (1969)

and then the angle of dilatancy as defined by Bolton (1986) is


9/24


7

(2.3)

where the ps subscript means plain strain.

The definition of dilatancy angle can also be derived from the stress strain curves from

triaxial compression test as expressed by Schanz,T. et al (1996a) :

(2.4)

Correlation of parameters to get E

If the data from the stress-strain curves is not available, the undrained shear strength, Cu is

often used in correlations on stiffness parameters for clays. Gaba A.R et al (2003)

recommends the following relationship:

(2.5)

Hence the undrained Youngs moduli can be easily converted to effective Youngs moduli by

the following equation which is based on Hookes law:

(2.6)

3 Hardening Soil Model (HS model)The hardening soil model is an advanced elasto-plastic soil model and differs from the Mohr-

Coulomb model by its approach to stiffness. Here, it is possible to model the soil moreaccurately with the use of three different input stiffness. As a result this model attempts a

better approximation to real soil behaviour as illustrated by Figure 5.


10/24


8

Figure 5: Comparison of HS and MC model with real soil response (internet source)

Unlike the elastic perfectly-plastic Mohr-Coulomb model, there is no fixed yield surface. Due

to plastic straining the yield surface can expand homothetically, i.e. it changes dimensions but

not in shape. In such a case the hardening is isotropic, as shown in Figure 6.

Figure 6: Isotropic Hardening (Robert Nova 2002)

The idea behind the formulation of this model is the hyperbolic relationship between the

vertical strains, 1 and the deviatoric stress, q in primary triaxial loading. Hardening Soil

model uses theory of plasticity and includes soil dilatancy and a yield cap.

This Hardening Soil model is a double hardening model based on the Mohr coulomb failure

criterion and consists of two main types of hardening, namely shear hardening and volumetric

hardening as illustrated in Figure 7. The shear hardening part models the plastic shear strain

in deviatoric loading and volumetric hardening considers the volumetric strain in primary

compression.


11/24


9

The volumetric hardening part is accounted by the yield cap surface in the model. In

isotropic compression, the measured plastic volumetric strain is not included in the shear

yield surface in Figure 7 a. To close this elastic region in the effective stress, p -axis, a second

type of yield surface is introduced. As illustrated by Figure 7 b, the shape of the cap yield is

an ellipse in p-q plane.

(a) Shear Strain Hardening

(b) Volumetric Strain Hardening

Figure 7: (Brinkgreve R.B.J 2004)

The presence of this yield cap enables the user to independently enter the two input

parameters of triaxial and oedometer modulus. The shear yield surface and the magnitude of

plastic shear strains associated with this yield surface are controlled by the triaxial modulus.

On the other hand the yield cap surface and the magnitude of plastic shear strains originating

from this yield surface are controlled by the oedometer modulus.

Yield cap


12/24


10

In the analysis of over consolidated clays, shear strain hardening is a dominant characteristic,

whereas volumetric strain hardening is dominant in the analysis of normally consolidated

clays. As a result, the soil behaviour of both soft and stiff soils can be analysed using the

Hardening Soil model in PLAXIS.

Figure 8 illustrates the total yield contour of Hardening Soil model, i.e. the yield surface

combined with the shear and cap yield surface in principal stress space. The expansion of the

shear yield surface occurs until it reaches the Mohr-Coulomb failure surface, whereas the

expansion of the yield cap is a function of the pre-consolidation pressure.

Figure 8: Representation of total yield contour of the Hardening Soil model in principal stressspace (Brinkgreve R.B.J 2004)

Drawbacks of the model would include its lack of ability in modelling anisotropic strength

and stiffness, time-dependant behaviour such as creep effects and post peak softening

observed in dense sands and stiff clays. The model does not account for large amplitudes of

soil stiffness related to transition from very small strain to engineering strain levels (10 -3 to

10 -2). The model also the lacks the capability to reproduce hysteretic soil behaviour observed

during cycling loading.

3.1 Soil Hardening Model (HS model) input parameters

The Stiffness parameters to be entered in PLAXIS are: : Secant stiffness in standard drained trixial test [kN/m 2]


13/24


11

: Unloading/ reloading stiffness (default ) [kN/m 2]: Tangent stiffness for primary oedometer loading [kN/m 2]

m : Power for stress-level dependency of stiffness [-]

The three strength parameters are the same as Mohr Coulomb model

Sti ff ness moduli and

The Hardening Soil model uses a power law formulation for stress dependant stiffness. The

hyperbolic relationship in the Hardening Soil model is illustrated in Figure 9.

Figure 9: Hyperbolic stress-strain relation in primary loading for a standard drained triaxialtest (Schanz, T 1999)

The parameter E 50, for plastic shear hardening , is the confining stress dependent stiffness

modulus for primary loading which can be given by:

(3.1)

For unloading and reloading another stress dependent stiffness modulus E ur is defined as:

(3.2)

Both E 50 and E ur can be extracted from standard drained triaxial test by plotting the deviator

stress,q versus the axial strain 1, as shown by Figure 9. Bishop A.W. et al (1957) has given

details on how to carry out the standard drained triaxial test.


14/24


15/24


13

In PLAXIS, the Hardening Soil model uses a reference stress of p ref = 100kN/m 2, which can

be substituted in for the vertical effective stress. Thus the equation to derive now arises

to:

(3.5)

The primary loading stiffness of clays can be measured quite well from oedometer tets.

Hence for normally consolidated clays, an approximate relation can be derived where the

reference oedometer stiffness is about half the reference triaxial stiffness at 50% of strength.

(3.6)

The unloading/ reloading stiffness was kept to PLAXIS default setting as:

(3.7)

Power L aw mThe amount of stress dependency is given by the power m. The value for this was derived

from the plots in Figure 11. The plots demonstrate how m can be determined if the exponents

m for different clays is plotted as a function of plasticity index at very small strains. This

relationship was proposed by Viggiani et al (1997), and Hicher (1996) had proposed a similar

relationship but with the liquid limit instead.


16/24


14

Figure 11: Power law exponent m as a function of plasticity index and liquid limit (BenzT.2007a)

All the other parameters were kept to PLAXIS default settings.

4 Hardening Soil with Small Strain (HSsmall model)The hardening soil model assumes elastic material during unloading and reloading. But in

real soil behaviour, the strain range where soils can recover from the applied straining

completely, i.e soil being truly elastic, is very small.

The Hardening Soil with Small Strain (HSsmall) model is an enhanced version of the

Hardening Soil model, where it takes into account small strain stiffness of the soil and models

soil stiffness to decay non-linearly with increasing strain amplitude. The advanced features of

the HS-Small Strain model are able to produce more accurate and reliable approximation of

displacements. The improved results are particularly found useful for dynamic applications or

in modelling unloading-conditioned problems, e.g. excavations with retaining walls or tunnel

excavations.

Formulation of the small strain stiffness is derived from the S shaped curves shown inFigure 12. The curves arise from the shear modulus G being plotted as a logarithmic function

of the shear strain . The plot rang es from very small to very large strain levels. The main

characteristic of the S curve is the small strain shear modulus G0 and the shear strain at

which the shear modulus 70% of G0, stated as 0.7.


17/24


15

Figure 12: S-curve for reduction of shear modulus with shear strain (Brinkgreve R.B.J et al2006)

4.1 Soil Hardening with Small Strain (HSsmall model) input parametersSince the HSsmall model is based on the Hardening Soil model, the input parameters are

almost entirely the same parameters, with the addition of two parameters:

reference shear modulus at very small strains (


18/24


16

Benz, T. (2007) b, in his paper has discussed a list of laboratory and field tests to measure the

small strain soil stiffness. Vojkan Jovicic (1997) has given a detailed description of the

bender element technique to derive the elastic shear modulus of a soil at very small strains.

Atkinson J. (2007) suggests that the simplest way to calculate the shear modulus at small

strains is from the velocity of dynamic waves. G 0 is then given by:

(4.3)

where V s is the velocity of the shear waves through the soil sample, is the unit weight of the

soil and g = 9.81m/s2

.

Corr elati on of shear strain 0.7

The correlation between the threshold shear strain and Plasticity Index can be used to

determine 0.7 . The value for the threshold shear strain is read off at G/G 0=0.7 and the

corresponding Plasticity Index.

Figure 14: Influnce of plasticity index on stiffness reduction (Vucetic et al 1991)

5 Case Studies ConsideredTo come to a conclusion on which constitutive model gave the best analysis results, i.e.

which analysis best represent real soil behaviour, benchmark results had to be identified.

A series of case studies were reviewed and three simple problems are chosen:


19/24


17

Case related to cantilevered retaining wall by A H Brookes et al (1996) Case related to singly propped retaining wall by D R Carder et al (1989)

Case related to Doubly propped retaining wall by A H Brookes et al (1996)

6 Soil Constitutive ModelsThree different types of retaining walls were modelled using the finite element package

PLAXIS. Each type of wall was modelled using three different types of soil constitutive

model, so that the analysis results could be compared.

Details of the soil profile had been taken for their respective case studies. As an example of

the PLAXIS model set up, Figure 15 shows the soil profile for the single propped wall.

Figure 15: Model set up for single propped wall in PLAXIS

Made Ground

Boulder Clay

London Clay

Cantilever Wall

Temporary StrutMade Ground

Slab acting as single prop

London Clay

Singly Propped WallSurcharge of 10kPa

Made Ground

Slab acting as single prop

London Clay

Singly Propped Wall


20/24


18

The walls and the slabs acting as props were modelled as plate elements, whereas the

temporary prop used in the modelling of singly propped wall was modelled as a fixed anchor.

All three models of the wall wer e done in plain strain. For the single and double propped

wall only one half of the excavation is considered in the analysis, since the model is

symmetric.

After setting up the model, a finite element mesh was composed of 15-node cubic strain

elements with global coarseness set to fine. A finer mesh was assigned in areas of higher

concentration in an attempt to get better analysis results. An example of the meshing done is

illustrated in Figure 16.

Figure 16: Deformed mesh for Cantilever Wall for model HS A

The analysis results for lateral movements, bending moments, shear forces and lateral stresses

results from the models analysed using the finite element software PLAXIS v.9 were compared

with the actual monitoring data from case studies. Evaluation of the model comparisons had

shown that the results from MC -model analytical runs had deviate the most from the actual field

monitoring data . This is because the small strain stiffness of soil is not taken into account in

the MC-Model. The HS model results also deviate from the measured values, but less than

the MC-model. The Hardening Soil model with Small Strain best portrayed real soil behaviour

by taking into account the very small strains in soil.

7 ConclusionThe primary aim of this report was to investigate the application of elasto-plastic non-linearmodels in PLAXIS 2D to predict efficiently ground deformations caused by deep


21/24


19

excavations. Detailed research was carried out on each of the constitutive models present in

PLAXIS 2D V9, including a detailed summary of each input parameter and correlations with

testing.

A series of case studies are chosen with available monitoring data for deep excavations.

These monitoring data were compared with the analysis results from the three different

constitutive models. It was come to the conclusion that the Hardening Soil model with Small

Strain showed best agreement between its results and the field monitoring data as it takes into

account the very small strains in soil.

8 Recommendations for further studyIn order to extend the findings of this report it is proposed that the behaviour of other

structures, for example a footing is analysed and the results compared with different types of

constitutive models.

The retaining walls considered here are all embedded in clay, meaning the evaluation of soil

behaviour and the parameter correlations made is based on clay only. It is proposed that same

evaluations and study is carried out for sand material.

The soil constitutive models used in this report are limited to Mohr Coulomb, Hardening Soil

and Hardening Soil with Small Strain model in finite element program PLAXIS 2D, version

9. Other constitutive models, such as the BRICK model, can also be used to evaluate and

compare results and hence check if this gives better prediction of real soil behaviour.

Only plain strain analysis is carried out during all analysis stages in 2D. It is worth performing 3D calculations to check if results are different and verify the 2-D numerical

analyses.

The effects of wall installation are not considered in this report and assumed no disturbance

was caused to the ground. Further studies need to be carried out to take the effects of stress

relief during deep excavations into account and how they affect the final analyses results.


22/24


20

9 References

A H Brookes and D R Carder (1996), Behaviour of a cantilever contiguous bored pile

wall in boulder clay at Finchley, TRL Report 244, Highways Agency

A H Brookes and D R Carder (1996), Behaviour of the diaphragm wall of a cut and cover

tunnel constructed in boulder clay at Finchley, TRL Report 187, Highways Agency

ASTM International. ASTM D2435 - 04 Standard Test Methods for One-Dimensional

Consolidation Properties of Soils Using Incremental Loading.

Atkinson J.,(2007), The Mechanics of Soils and Foundations, Second Edition, Spon Text,

Ch13, pg 193

Barden L., Ismail H., and Tong P., (1969), Plane strain deformation of granular material

at low and high pressures, Geotechnique 19, No.4, pg 441-452

Benz, T. (2007)a. Small-strain stiffness of soils and its numerical consequences. Ph.D.

Thesis. Institut fr Geotechnik, Universitt Stuttgart.

Benz, T. (2007)b. Small-strain stiffness of soils and its numerical consequences. Ph.D.

Thesis. Institut fr Geotechnik, Universitt Stuttgart.

Bishop A.W. and Henkel D.J. (1957), The Measurement of Soil Properties in the Triaxial

Test, Edward Arnold (Publishers) LTD, London, pg122-131

Brinkgreve R.B.J. & Broere W, PLAXIS 2D Manual, 2004

Brinkgreve R.B.J., Bakker K.J., Bonnier P.G., (2006), The relevance of small-strain soil

stiffness in numerical simulation of excavation and tunnelling projects, Numerical

Methods in Geotechnical Engineering Schweiger (ed.), Taylor & Francis Group,

London


23/24


21

Carder D. R. and Brookes A. H. (1989), Long term performance of a propped retaining

wall embedded in stiff clay, TRL Report 187, Highways Agency

C.R.I. Clayton, M.C. Matthews and N.E. Simons,(2005), Site Investigation, Departmenet

of Civil Engineering, University of Surrey, 2nd Ed

Gaba A.R., Simpson B., Powrie W. and Beadman D.R., (2003), CIRIA C580, Embedded

retaining walls- guidance for economic design, London

Goldscheider, M., (1982), True triaxial tests on dense sand, G. Gudehus, F. Darve, I.

Vardoulakis (Eds.), Results of the Int. Workshop on Constitutive Relations for Soils,

Balkema, Rotterdam, The Netherlands (1982), pp. 11 54

Hicher P. Y.,(1996), Elastic Properties of soils, Journal of Geotechnical Engineering,

122(8), pg 641-648

Internet source, Constitutive Model in FE Analysis HS,

http://units.civil.uwa.edu.au/teaching/CIVL3140?f=260156

Pickles A.R. and Henderson TO (2005), Some thoughts on the use of numerical

modelling in geotechnical design poractice, Underground Singapore 2005-Specialty

Session on Numerical Analysis in Geotechnical Engineering, Singapore

Roberto Nova (2002) , Development of Elastoplastic Strain Hardening Models of Soil

Behaviour, Department of Structural Engineering, Milan University of Technology

(Politecnico), Milan, Italy, pg6

Schanz, T. and Vermeer, P.A., (1996a), Angles of Friction and Dilatancy of

Sand,Geotechnique. 46(1), 145-151.

Schanz, T., Vermeer, P.A. and Bonnier, P.G. (1999),The Hardening Soil Model:

Formulation and Verification. Beyond 2000 in Computational Geotechnics-10 years of

Plaxis, Balkema, Rotterdam.
http://units.civil.uwa.edu.au/teaching/CIVL3140?f=260156http://units.civil.uwa.edu.au/teaching/CIVL3140?f=260156


24/24


Smith, I.M, Griffith, D.V. (1982), Programming the Finite Element Method, John Wiley

and Sons, Chisester, U.K. Second edition

Vermeer P.A., Termaat R.J and Vergeer G.J.H. (1985), Failure by Large Plastic

Deformations, Proceedings of 11 th International Conference on Soil Mechanics and

Foundation Engineering, Balkema, Rotterdam.

Viggiani G.M.B., Rampello S. and Amorosi A.,(1997), Small strain stiffness of re-

constituted clay compressed along constant triaxial effective stress ratio paths,

Geotechnique, 47 (3), pg475-489

Vucetic M. and Dobry R., (1991) Effect of soil plasticity on cyclic response, Journal of

Geotechnical Engineering, ASCE, 117(1), pg 89-107

raisa ehsan past paper

Documents