SUMMARYSimulation of large deformation and post-failure of geomaterial in the framework of smoothed particle hydrodynamics (SPH) are presented in this study. The Drucker-Prager model with associated and non-associated plastic flow rules is implemented into the SPH code to describe elastic-plastic soil behavior. In contrast to previous work on SPH for solids, where the hydrostatic pressure is often estimated from density by an equation of state, this study proposes to calculate the hydrostatic pressure of soil directly from constitutive models. Results obtained in this paper show that the original SPH method, which has been successfully applied to a vast range of problems, is unable to directly solve elastic-plastic flows of soil because of the so-called SPH tensile instability. This numerical instability may result in unrealistic fracture and particles clustering in SPH simulation. For non-cohesive soil, the instability is not serious and can be completely removed by using a tension cracking treatment from soil constitutive model and thereby give realistic soil behavior. However, the serious tensile instability that is found in SPH application for cohesive soil requires a special treatment to overcome this problem. In this paper, an artificial stress method is applied to remove the SPH numerical instability in cohesive soil. A number of numerical tests are carried out to check the capability of SPH in the current application. Numerical results are then compared with experimental and finite element method solutions. The good agreement obtained from these comparisons suggests that SPH can be extended to general geotechnical problems.

Most slope stability analyses have employed limit equilibrium methods (LEMs) or the finite-element method (FEM) as the standard approach. However, slope instability is often accompanied by discontinuous failure of the soil, which cannot be modelled by either LEMs or FEM. To overcome this limitation, this paper presents an extension of the smoothed particle hydrodynamics (SPH) method to evaluate the stability of a slope, and to simulate the post-failure behaviour of soil. For the slope stability analysis, the shear strength reduction technique with a modified failure criterion for distinguishing convergent from non-convergent solutions is applied to estimate the safety factor of a slope, and the critical slip surface is determined from a contour plot of accumulated plastic strain. To take the pore water pressure into account, a new SPH formulation for soil motion is developed. It is suggested that this equation can be applied to further developments of SPH for saturated soil. As an application of the proposed method, several smoothed particle slope stability analyses and corresponding slope failure simulations are presented, and compared with other solutions. The results show good agreements with other methods in terms of the safety factor and the critical slip surface. As compared with such traditional methods, however, an advantage of SPH is that it can simulate large deformation and post-failure of soil, and can thereby treat a wide range of applications in computational geomechanics, especially those that include large deformation and failure of geomaterials.La plupart des analyses de stabilité des pentes emploient, comme méthodes standards, des méthodes d'équilibre limite et la méthodes aux éléments finis. Toutefois, l'instabilité des pentes s'accompagne fréquemment d'une rupture discontinue du terrain, qui ne peut être modélisée avec les méthodes d'équilibre limite ou aux éléments finis. Pour résoudre ce problème, la présente communication se penche sur une extension de la méthode de l'hydrodynamique par particules adoucies [smoothed particle hydrodynamics (SPH)] pour évaluer la stabilité d'une pente et simuler le comportement de post-rupture du sol. Pour la stabilité de la pente, on emploie la technique de réduction de la résistance au cisaillement, en ajoutant un critère de rupture' modifié pour distinguer les solutions convergentes des solutions non convergentes, afin d'estimer le facteur de sécurité de la pente, et on détermine une surface de glissement critique sur la base d'un tracé des déformations plastiques accumulées. Afin de tenir compte de la pression interstitielle, on a développé une nouvelle formulation SPH pour le mouvement du sol. On propose que cette équation pourrait être appliquée pour des développements ultérieurs du SPH pour des sols saturés. A titre d'application de la méthode proposée, plusieurs analyses de la stabilité de pentes, par la methode SPH, et leurs simulations correspondantes de la rupture de pentes, sont présentées et comparées avec d'autres solutions. Les résultats démont...

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SUMMARYThe method of smoothed particle hydrodynamics (SPH) has recently been applied to computational geomechanics and has been shown to be a powerful alternative to the standard numerical method, that is, the finite element method, for handling large deformation and post-failure of geomaterials. However, very few studies apply the SPH method to model saturated or submerged soil problems. Our recent studies of this matter revealed that significant errors may be made if the gradient of the pore-water pressure is handled using the standard SPH formulation. To overcome this problem and to enhance the SPH applications to computational geomechanics, this article proposes a general SPH formulation, which can be applied straightforwardly to dry and saturated soils. For simplicity, the current work assumes hydrostatic pore-water pressure. It is shown that the proposed formulation can remove the numerical error mentioned earlier. Moreover, this formulation automatically satisfies the dynamic boundary conditions at a submerged ground surface, thereby saving computational cost. Discussions on the applications of the standard and new SPH formulations are also given through some numerical tests. Furthermore, techniques to obtain the correct SPH solution are also proposed and discussed throughout. As an application of the proposed method, the effect of the dilatancy angle on the failure mechanism of a two-sided embankment subjected to a high groundwater table is presented and compared with that of other solutions. Finally, the proposed formulation can be considered a basic formulation for further developments of SPH for saturated soils.