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Calibration of a modified hardening soil model for kakiritic rocks
Étalonnage d'un modèle modifié d'écrouissage des sols pour les roches kakiritiques
Dong W., Anagnostou G.
ETH Zurich, Switzerland
ABSTRACT: The response of weak rocks to tunnel excavation is usually analysed by assuming that the ground behaves as a linearly
elastic, perfectly plastic material obeying the Mohr-Coulomb yield criterion. This model fails, however, to map the non-linear stress-
strain behavior and the stress dependency of stiffness observed in triaxial testing on typical weak tectonized rocks such as kakirites.
As a consequence, an equivalent Young’s modulus has to be adopted, which may prove to be a difficult task. The present paper shows
that a modified hardening soil model, whose parameters can be determined by common triaxial tests, describes the behavior observed
under triaxial testing conditions better than the Mohr-Coulomb model under different stress levels. It also eliminates the need for
more or less arbitrary assumptions concerning the Young’s modulus.
RÉSUMÉ : Lors de la conception, la réaction de la roche à l'excavation du tunnel en terrain tendre est généralement analysée en
assumant un comportement élastique linéaire, parfaitement plastique du matériau en utilisant le critère de plasticité de Mohr-
Coulomb. Cependant, ce modèle ne permet pas la description du comportement contrainte-déformation non-linéaire ainsi que la
dépendance de la rigidité à l'égard des contraintes observées dans les essais triaxiaux sur des roches tendres tectonisées comme les
kakirites. Par conséquent, le module d'Young équivalent doit être appliqué, ce qui peut, en fonction du degré de la non-linéarité
actuelle et de la variation de la contrainte de confinement, se révéler être une tâche difficile. Le présent document montre qu'un
modèle modifié d'écrouissage des sols, dont les paramètres peuvent être déterminés par des essais triaxiaux courants, décrit mieux le
comportement observé sous différents niveaux de contraintes dans des conditions de test triaxial qu'avec le modèle de Mohr-
Coulomb. Ce modèle élimine également le besoin de hypothèses plus ou moins arbitraires concernant le module d'Young. (roches
poussantes, modèle modifié d'écrouissage des sols, dépendance de la rigidité à l'égard des contraintes.)
KEYWORDS: squeezing ground, modified hardening soil model, stress dependent stiffness
1 INTRODUCTION
The relationship between rock pressure and displacement of the
excavation boundary is important for tunnel design particularly
under so-called squeezing conditions (Kovári 1998).
Considerable uncertainties persist with respect to quantifying
this relationship, because it depends essentially on the
constitutive behavior of the ground. The latter is usually
considered as a homogeneous, isotropic, linearly elastic and
perfectly plastic material obeying the Mohr-Coulomb yield
criterion. This model (hereafter referred to as “MC model”) is
widely used in engineering practice, because it accounts for
some important aspects of actual ground behavior, is relatively
simple and contains a small number of easily identifiable and
familiar parameters. However, the MC model cannot map some
features of the rock behavior observed in triaxial tests. More
specifically, triaxial tests on kakirite samples (a typical
squeezing rock from the Alps) show that the stress-strain
behavior is pronouncedly nonlinear and inelastic right from the
start of deviatoric loading, while the MC model exhibits linear
elastic behavior before yielding. Another drawback of the MC
model is that it cannot map the observed stress dependency of
stiffness. Applying the modulus determined at some stress
levels to other stress levels may lead to inaccurate predictions.
Due to the linearity of the MC model, an equivalent Young’s
modulus has to be adopted, which – besides being theoretically
questionable – may (depending on the degree of the actual non-
linearity and confining stress variety) prove to be a difficult
task.
The present paper investigates whether an alternative
constitutive model can better map the observed behavior under
triaxial conditions. The considered model represents a slight
modification of the well-known Hardening Soil model (“HS
model”) of the PLAXIS finite element code and will be referred
to hereafter as the “Modified Hardening Soil” model (“MHS
model”). Section 2 of the present paper introduces the model,
while Section 3 determines the model parameters using the
results of laboratory tests on kakiritic samples. Finally, the
capability of the MHS model is discussed by comparing it with
the MC model under triaxial drained shear conditions and
different confining pressures (Section 4).
2 MODIFIED HARDENING SOIL MODEL
The detailed description of the original HS model can be found
at Brinkgreve and Vermeer (1997). Benz et al. (2008) extended
the original model by formulating the yield function in terms of
the Lode angle. This makes it possible to replace the original
Mohr-Coulomb yield surface easily by alternative failure
criteria such as the Matsuoka-Nakai criterion, which considers
the effect of the intermediate stress, does not exhibit
singularities and simplifies, therefore, the numerical
implementation.
The MHS model is slightly different from the HS model with
respect, (i), to the dependency of the yield surface on the Lode
angle, (ii), to the dilatancy law and, (iii), to the cap hardening
part, which is not taken into account in the present model. The
present Section outlines the formulation of the MHS model
under triaxial test conditions. All stresses hereafter are effective
stresses. Compressive stresses are taken as positive.
