Abstract
SummaryThis paper presents a u‐p (displacement‐pressure) semi‐Lagrangian reproducing kernel (RK) formulation to effectively analyze landslide processes. The semi‐Lagrangian RK approximation is constructed based on Lagrangian discretization points with fixed kernel supports in the current configuration. As a result, it tracks state variables at discretization points while allowing extreme deformation and material separation that is beyond the capability of Lagrangian formulations. The u‐p formulation following Biot theory is incorporated into the formulation to describe poromechanics of saturated geomaterials. In addition, a stabilized nodal integration method to ensure stability of the domain integration and kernel contact algorithms to model contact between bodies are introduced in the u‐p semi‐Lagrangian RK formulation. The proposed method is verified with several numerical examples and validated with an experimental result and the field data of an actual landslide.
Highlights
This is the author manuscript accepted for publication and has undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record
smoothed particle hydrodynamics (SPH) suffers from tensile instability and boundary deficiency since the kernel approximations are inconsistent [18], while parameters of element-to-element contact models used in discrete element method (DEM) are difficult to calibrate and can significantly impair the accuracy [20]
This paper presents an extension of the Reproducing Kernel Particle Method (RKPM), the semi-Lagrangian RKPM, for analyzing entire landslide processes within one mathematical framework
Summary
This is the author manuscript accepted for publication and has undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. SPH suffers from tensile instability and boundary deficiency since the kernel approximations are inconsistent [18], while parameters of element-to-element contact models used in DEM are difficult to calibrate and can significantly impair the accuracy [20] Since it is extremely challenging or even impractical to apply one of these numerical methods to effectively and accurately analyze whole landslide processes, some researchers have suggested or employed coupled methods such as FEM-SPH [21] or FEM-DEM [22, 23], to handle different stages of landslide processes with suitable numerical methods by defining certain strain criteria to switch between methods. Besides the capability to analyze slope stability as effectively as FEMs, the present method can naturally model run-out simulation This is due to the construction of the approximation functions in the current configuration [32, 33], which readily allows extreme deformation and material separation. The domain integration method and contact algorithms are addressed in a two-field framework due to the incorporation of the two-field formulations using Biot theory [35] with the semi-Lagrangian RKPM to properly describe mechanics of porous media
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