interface formulation problem in finite software

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- 2035 -

Interface Formulation Problem in

Geotechnical Finite Element Software

Adis SkejicM.Eng.

Civil Engineering faculty Sarajevo, BiH

[email protected]

ABSTRACTA serious problem has been discovered in the interface formulation in one of the most popular

finite element software programs used in geotechnical practice. This paper analyses the problem of

interface formulation which is not in agreement with the definition given in program manuals.

Problem explained appears to have been solved in the most recent version, but the author finds itimportant to discuss the implications of this problem, because there are so many investigation

conclusions given in the recent past without being aware of this problem. A simple example of

sliding block on elastic soil is used for this investigation and the results with discussions are

presented, with intimate details of the computational model.KEYWORDS: interface, finite element method, Plaxis 2D.

INTRODUCTION

Very often in Geotechnical enginering practice using the advanced tool of the finite element

technique, interface elements are used to model soil structure interaction. Modeling of discontinuities

in rocks, soil – geogrid interaction modeling in reinforced soil, soil – pile interaction for pile capacity

calculations are only few examples where interface plays a crucial role. Interface formulation given in

programs manuals is not in agreemnet with program code, what makes the conclusions reached using

the numerical model imprecise. After a brief interface formulation, details of practical example

numerical model shall be presented, to prove the point of this article. Same problem was analysed

with Plaxis version 2011, and problem was not found. To end this introduction, an interestingquotation given by Kulhawy (2011) is reminded: “Please do not use software if you do not understand

what is it doing.

MATERIALS AND METHODS

Numerical model of sliding block on elastic soil, is used to analyse the stress state on the

discontinuity between block and soil medium. Plane strain model with 6-node triangular finite

elements is employed. The soil – block contact is modeled by interface element. An isoparametric



Vol. 17 [2012], Bund. N 2036

zero thickness interface element (Goodman et al. 1968, Ghaboussi et al., 1973; Carol and Alonso,

1983; Wilson, 1977; Desai et al. 1984, Beer, 1985). Interface is defined as thick layer connected with

soil and structure elements with 2 degrees of freedom. (Figure 1)

Figure 1: Geometry and interface slippage criterion for 6 node element (Modified from VanLangen & Vermeer, 1990)

The soil behaviour in this discontinuity can be different from soil behaviour, what it confirmed by

many experimental investigations (Potyondy 1961, Desai, 1981, Acar et al., 1982, Desai et al. 1985,

Boulon i Plytas, 1986, Boulon, 1989). Interface stiffness matrices formed according to constitutive

low of its behavior, are assembled in stiffness matrice of particular problem as whole structure. After

slippage occurs, volumetric as well as shear deformations occurs on interface. Volumetric strain

magnitude, are controled by dilatancy angle (ψ) which defines the constitutive low flow rule.

Figure 2: Interface modeling and interface deformations definition

The constitutive law of interface behavior is defined by:

( )e p D Dσ ε ε ε = = −

where e nad p indexes defined elastic and plastic part of deformation respectively. For elasticdeformations the stress and strain increment can be related by interface shear an normal stifness, k s

and k n respectively.

0

0

en s s

en n n

k

k

τ ε

σ ε

=



Vol. 17 [2012], Bund. N 2037

,

0

0

i

ein s

eoed in n

i

G

t

E

t

τ ε

σ ε

=

Where Gi and Eoed,i are shear and oedometer modulus of interface. The relative thickness factor is

taken as default value 0,1, and will not be analyzed in this article. Using the theory of plasticity terms

(flow rule, consistency condition) the scalar multiplicator magnitude can be calculated, andelastoplastic stifness matrix can be derived as :

,

0

0

i

in s

oed in n

i

G

t g

E

t

τ ε µ

σ σ ε

∂ = − ∂

2

2

0 tan '1

0 (tan ') (tan ') (tan ') (tan ') (tan ')

n s s s n s

n n s n s n n n

k k k k

k k k k k k

τ ϕ ε

σ ϕ ψ ψ ϕ ψ ε

− ⋅ ⋅ = −

+ ⋅ ⋅ − ⋅ ⋅ ⋅ ⋅

For Plaxis 2D, the strength and stiffness of interface are defined as part of the strength and

stiffness of soil adjusted to interface strength according to :

soil ii c Rc ⋅=

soil ii R ϕ ϕ ⋅=

while in Reference manual, the last relation is defined as soil ii R ϕ ϕ tantan ⋅=

soil ii G RG ⋅=2

,

12 ; 0.451 2

ioed i i i

i

E G ν

ν ν

−= =−

where R i is reduction coefficient. Also, for:

ψi = 0 for R i < 1, ψi = ψtla for R i = 1

where: c – cohesion of soil material

φ – soil friction angle

ψ – soil dilatancy angle

νi – Poisson ratio for interface

And finally we can write the slippage criterion as :

''tan)( iinn c f +⋅−= ϕ σ τ σ

Next, the details of numerical model are presented. Refer to Figure 3 and Table



Vol. 17 [2012], Bund. N 2038

Figure 3: Numerical model with material parameters shown in Table 1.

Table 1: Material parameters

Soil & Interface Model γ [kN/m3] Eref [kPa] c [kPa] φ [ᵒ] ν [-]

Concrete block Linearelastic

25,0 3e7 - - 0,0

interface Mohr-

Coulomb

0,0 5e4 0,0 65 0,45

After generating initial stress state which is defined with self-weight of concrete block, prescribed

displacement are applied at the left boundary, to cause slippage of concrete block. Shear and normal

stresses are generated at the interface, and shear to normal stress ratios are analyzed to investigate the

definition of interface strength. The stress distributions along interface, as well as plastic points areshown to prove that the slippage occurs on soil – block contact.

Two different cases of reduction coefficient (R i) and relatively high value of internal friction

angle (φ = 65ᵒ) are used to show the difference between programs code and programs reference

manual definition of interface strength. First R i = 1,0, and then R i = 0,2. The ratio of average stressesvalues is also compared to show the described difference.

RESULTS AND DISCUSSION

The results of provided analysis, shows the shear and normal stress ratio for prescribed

displacement of 2,0 cm, when plastic points occurs along full length of interface (figure 5). As it is

said earlier, the strength of interface is actually defined as R i·φ, and not R i·tanφ, as it is written in programs manuals (figure 5). Of course for reduction coefficient equal 1,0 such a difference do net

exists (figure 5).



Vol. 17 [2012], Bund. N 2039

Figure 4: Slippage criterion difference in program’s code (R i·φ) and reference manual(R i·tanφ); (a) R i = 0.2; (b) R i = 1,0

As it can be seen, the slope of the line defined by normal and shear stresses on interface is defined

with tangent of angle of internal friction of interface itself, and it is 0.2309, what is exactly

tan(0.2 × 65), and not 0.2 × tan65.

Finite element mesh as well as plastic points are shown on the picture below.

Figure 5: Finite element mesh and plastic points for R i = 0.2

Finally, the results for normal and shear stress distribution along interface are shown.

Figure 6: Stress distribution along interface for prescribed displacement of 2.0 cm (R i = 0.2)

(a) (b)

(a) normal stress distribution

(b) shear stress distribution

219.32 kPa

470.34 kPa



Vol. 17 [2012], Bund. N 2040

As a discussion part, the author would like to underline that explained problem does not exist in

Plaxis version 2010 and 2011. The idea of this text is to show that some conclusions of investigations

done with previous versions (like 8.1 and 8.5) of this very popular software may be questionable. This

paper does not discuss the role of interface elements in practice of geotechnical engineering, but only

inform about a particular problem found in a widely used software program.

CONCLUSIONS

Interface formulation defined in Plaxis ver. 8.5 program manual does not agree with program’s

code. The problem is definition of interface strength which is defined as R i·tan·φsoil in manual, and

R i·φsoil in program’s code, according to calculation results shown in this paper. This problem becomes

more obvious for higher values of internal friction angles (φ), and lower values of reduction

coefficient (R i).

This problem should be on mind to everyone using named version of Plaxis software. Even for

using newer version which solved this problem, suggested values of reduction coefficients for

modeling any soil structure interaction problem investigated by doing back analysis with olderversions, should be taken with caution.

A very simple problem is analyzed in order to eliminate as many second order factors as possible.

REFERENCES

1.

Binesh, S.M., Hataf, N. and Ghahramani A. (2010) “Elasto-plastic analysis of reinforced soils

using mesh-free method”, Applied Mathematics and Computation, Elsevier Inc

2. Brinkgreve, R.B.J. (2002) PLAXIS – Finite Element Code for Soil and Rock Analyses:

User’s Manual – Version 8, A.A. Balkema, Rotterdam, Netherlands

3.

Coutinho, A.L.G.A., Martins, M.A.D., Sydenstricker, R.M., Alves, J.L.D. and Landau L(2003) “Simple zero thickness kinematically consistent interface elements”, Computers and

Geotechnics 30 347–374

4.

Grubić, N., Skejić, A. i Balić A. (2012) “Numerical modeling of interaction between stiff

reinforcing elements and granular backfill under pullout conditions”, 7th International

Conference on Computational Mechanics for Spatial Structures, IASS-IACM, Sarajevo

5. Li, J. & Kaliakin, V. N. (1993) “Numerical Simulation of Interfaces in Geomaterials :

Development of Zero Thickness Interface Elements, Department of Civil Engineering,

University of Delaware, Newark, Civil Engineering Report

6.

Skejić, A., Balic, A., Grubić, N. (2011) “Uloga Interface elemenata pri numeričkom

modeliranju armiranog tla”, Forth International conference Geotechnical aspect of

engineering, Zlatibor.

7. Van Langen H. and Vermeer P. A. (1991) “Interface elements for Singular Plasticity Points“,

International Journal for numerical and Analitical Methods in Geomechanics. Vol. 15, 301-3

15



Vol. 17 [2012], Bund. N 2041

8.

Van Langen, H. & Vermeer, P. A. (1990) “Automatic Step Size Correction for non-

associated Plasticity Problems”, International Journal for Numerical Methods in

Engineering , Vol. 29, 579-598

9.

Van Langen, H. (1991) Numerical Analysis of Soil Structure Interaction, PhD thesis, DelftUniversity

10. Wood D.M. (2004) Geotechnical Modeling, Spon Press

© 2012 ejge

interface formulation problem in finite software

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