Vahid Galavi

Experimental studies show that initial fabric and its evolution under different stress paths highly influence soil behaviour. Even though different sample preparation methods create different inherent anisotropies and cause different material responses, the same initial fabric structure under different stress paths also results in different material behaviours. In this paper, a simple state-dependent, bounding surface-based elastoplastic constitutive model, that can simulate the anisotropic nature of sands including the effect of principal stress rotation, is described. The model is developed based on a semi-micromechanical concept within the multilaminate framework and, to include the inherent anisotropy of sand, a deviatoric fabric tensor describing the initial microstructure is introduced. In addition, a fabric evolution rule compatible with anisotropic critical state theory (ACST) is employed to describe the evolving fabric structure and induced anisotropy towards the critical s...

In the last decades an important number of constitutive models based on the concept of angular discretization of space have been developed. Two of the most important families of this kind of models are referred to as microplane (MPM) and multilaminate (MLM) theories. Both frameworks represent the behaviour of the material by considering the response on several so-called “integration planes” or “microplanes”, where the yield surface and plastic potential are defined individually. Thus an initially isotropic material becomes anisotropic after loading, capturing plastic flow induced anisotropy intrinsically. Also, both frameworks allow considering inherent anisotropy as a particular case in a straightforward manner without mathematical complexity. In this paper the basics of each formulation will be explained and their similarities and differences, as well as their corresponding advantages, disadvantages, capabilities and limitations will be discussed. Some numerical simulation of simp...

Both the Material Point Method (MPM) and meshfree schemes based on optimal transport theory have been developed for efficient and robust integration of the weak form equations originating from computational mechanics. Although the methods are derived in a different fashion, their algorithms share many similarities. In this paper, we outline the close resemblance of MPM and Optimal Transportation Meshfree (OTM) schemes. Aside from a theoretical analysis, the methods are compared numerically using a one-dimensionalbenchmark.

This paper presents a three dimensional formulation of a simple and practical constitutive model developed for evaluating seismic liquefaction in sands. The model is an extension of the two dimensional UBC-SAND model developed at University of British Colombia (Beaty & Byrne 1998) which utilises isotropic and simplified kinematic hardening rules for primary and secondary yield surfaces, in order to take into account the effect of soil densification and predict a smooth transition into the liquefied state during undrained cyclic loading. By means of a simplified Rowe stress-dilatancy theory the model is capable of modelling cyclic liquefaction for different stress paths. To show the capability of the model to predict cyclic liquefaction in soils, the mechanical behaviour of some sands is numerically studied under direct simple shear conditions and compared with experimental data. The effect of densification and parameters selection on the results is discussed. Finally, the model is used for simulating an experimental dynamic centrifuge test and the numerical results are compared with the real measurements. function based on Drucker-Prager criterion is used in order to maintain the assumption of stress-strain coaxiality in the deviatoric plane for a stress path beginning from the isotropic line (Tsegaye 2010). In the proposed formulation of the UCB3D-PLM model a soil densification rule is added to predict more realistic evolution of excess pore pressures during cyclic loading. A correct procedure of counting the cycles during dynamic and cyclic loading is implemented in order to achieve higher accuracy in the stress paths which do not start from the isotropic line. The densification rule allows the increase of thepore pressures with a decreasing rate during shearing which is observed during experimental studies by different researchers (Martin et al. 1975). Moreover, a rule which governs the predicted behaviour during post-liquefaction is introduced in order to model the degradation of the stiffness during the liquefied state. This also allows the prediction of cyclic mobility in dense sands and solves the issue of volumetric locking which was encountered in previous formulations. Finally, a rule for taking into account the non-symmetry in cycles is implemented in order to correct the evolution of excess pore pressure during loading. The main characteristics of the model are presented in the next section after which a validation of the model is presented.

Static liquefaction is one of the principal triggering mechanisms of failure in fully saturated loose sand slopes both in offshore and onshore regions. Static liquefaction induced landslides are known for their significant softening and a fluid-like behavior at the onset of failure. However, the literature lacks experimentally verified advanced numerical approaches which are capable of simulating static liquefaction. In this study, an advanced constitutive model based on the multilaminate framework is used in a finite element code. Multilaminate model accounts for significant features such as rotation of principal stresses, anisotropy in the material, strain softening due to static liquefaction and stress and strain dependency of the stiffness which enable us to achieve a more realistic soil behavior. The analysis results are verified by a set of large scale experiments of static liquefaction failures in submerged slopes under monotonic loading. Presented numerical approach can be u...

Numerical aspects of seismic liquefaction in soils as implemented in the finite element code, PLAXIS, is described in this paper. After description of finite element equations of dynamic problems, three practical dynamic boundary conditions, namely viscous boundary tractions, tied degrees of freedom and free field elements are reviewed. Possibilities and limitation of each type of boundary condition is highlighted. The formulation of a constitutive model, called as UBC3D-PLM, which describes the mechanical behaviour of soils under cycUc loading is also presented. The model is an extension of the two dimensional UBCSAND model developed at University of British Colombia which utilises isotropic and kinematic hardening mles for primary and secondary yield surfaces to properly take into account accumulation of excess pore water pressure and effect of soil densification during cychc loading. By means of a simplified Rowe's stress-dilatancy theory, the model is capable of modelling li...

Constitutive models based on the multilaminate framework provide an alternative framework to more common formulations in terms of stress invariants. The basic feature of multilaminate models, namely the consideration of various integration planes to formulate the stress-strain relationship has the advantage that yield criteria, flow and hardening rules are formulated on planes rather than in three-dimensional stress space making the mathematics simpler. Stress or strain induced anisotropy is an intrinsic feature of these models and inherent anisotropy can be introduced by means of a structural tensor which allows the input of orientation dependent strength properties. A number of different constitutive equations for modelling clays and sands based on the multilaminate framework have been presented in the literature and more recently advanced formulations including small strain stiffness effects or non-local softening behaviour have been developed. In this paper only a very brief sum...

The material point method (MPM) is an effective computational tool for simulating problems involving large deformations. However, its direct mapping of the material-point data to the background grid frequently leads to severe inaccuracies. The standard function reconstruction techniques can considerably decrease these errors, but do not always guarantee the conservation of the total mass and linear momentum as the MPM algorithm does. In this paper, we introduce a novel technique, called Taylor Least Squares (TLS), which combines the Least Squares approximation with Taylor basis functions to reconstruct functions from scattered data. Within each element, the TLS technique approximates quantities of interest, such as stress and density, and when used with a suitable quadrature rule, it conserves the total mass and linear momentum after mapping the material-point information to the grid. The numerical and physical properties of the reconstruction technique are first illustrated on one-...

In this report the formulation of the UBC3D constitutive model as implemented in PLAXIS is presented. The UBC3D is a 3-D generalized formulation of the original 2-D UBCSAND model introduced by Puebla et al. (1997). The initial 3-D implementation in PLAXIS was presented by Tsegaye (2010). An improved version is developed by the authors and the final model is presented together with a validation in different monotonic and cyclic stress paths. UBC3D-PLM consists a relatively simple but powerful approach in order to model the onset of the liquefaction phenomenon. In Chapter 1 the main features of the UBC3D-PLM are presented. The model utilises isotropic and simplified kinematic hardening rules for primary and secondary yield surfaces, in order to take into account the effect of soil densification and predict a smooth transition into the liquefied state during undrained cyclic loading. By means of a simplified Rowe stress-dilatancy theory the model is capable of modelling cyclic liquefac...

Constitutive models based on the multilaminate framework provide an alternative framework to more common formulations in terms of stress invariants. The basic feature of multilaminate models, namely the consideration of various integration planes to formulate the stress-strain relationship has the advantage that yield criteria, flow and hardening rules are formulated on planes rather than in three-dimensional stress space making the mathematics simpler. Stress or strain induced anisotropy is an intrinsic feature of these models and inherent anisotropy can be introduced by means of a structural tensor which allows the input of orientation dependent strength properties. A number of different constitutive equations for modelling clays and sands based on the multilaminate framework have been presented in the literature and more recently advanced formulations including small strain stiffness effects or non-local softening behaviour have been developed. In this paper only a very brief sum...

... Vahid Galavi, Ph.D., Helmut F. Schweiger. Abstract. ... Since scaling of the softening rate has been found to work efficiently, this model can be applied to solve practical geotechnical boundary value problems. Basic Input Parameters of the Multilaminate Model. ...