A conservative and consistent Lagrangian gradient smoothing method for earthquake-induced landslide simulation

Abstract

Numerical study of earthquake-induced landslides plays an important role in the disaster prevention and post-earthquake managements. Thanks to its mesh-free feature, the SPH (Smoothed Particle Hydrodynamics) method has significant advantages over the traditional grid-based methods in dealing with extremely large deformation problems such as high-speed fluid-like landslides. However, SPH is unstable when the material is in tension, which is widely known as the ‘tensile instability’ problem in SPH. Although the instability issue can be removed to certain stand by particular ad-hoc techniques, the root cause of the problem is not addressed. In addition, such ad-hoc techniques require additional user-defined parameters, which is difficult to make universally applicable. In this study, a conservative and consistent Lagrangian Gradient Smoothing Method (L-GSM) is proposed for fluid-like landslide simulations based on the recently developed meshfree L-GSM. In the present L-GSM, the strong-form of governing equations is discretized using the GSM gradient operator in a conservative and consistent manner. Moreover, a simple and accurate boundary treatment for free surface and solid boundary is newly proposed for L-GSM to handle the complicated free surface and solid boundary existed in the landslide problems. Finally, the proposed conservative and consistent L-GSM framework is validated by a soil column collapse benchmark and three real landslide problems. Results show that our L-GSM can give an accurate and reliable solution to the fluid-like landslide problem with a high efficiency. The treatments for free surface and solid boundary are also proven very effective in producing desired boundary conditions. Both cohesive soil column collapse example and Wangjiayan landslide example demonstrate that L-GSM is indeed free from the tensile instability problem.