A Jacobi eigenvalue solver for material point models and one-dimensional consolidation simulations of a soil layer
A Jacobi eigenvalue solver for material point models and one-dimensional consolidation simulations of a soil layer
The Material-Point Method (MPM) is used in this study to identify the eigenfrequencies and mode shapes of an elastic plane strain slice (column) that resembles a soil layer. The soil layer is also subjected to one-dimensional consolidation under a uniform vertical stress and modelled with MPM. The eigenvalue identification of the soil column is based on a generalised Jacobi method using Material-Point stiffness and mass matrices. To simulate the consolidation process, an explicit v-w formulation for fully saturated soils has been implemented into a Material-Point algorithm following existing approaches and making use of similar computational schemes. Simulations with different plane strain elements and different levels of spatial discretisation are performed to compare numerical results with analytical solutions. Finally, the algorithm for explicit time-integration is found to be numerically stable when adopting time-step sizes below reference critical values, e.g., values based on
the Courant-Friedrichs-Lewy (CFL) stability condition, and on an analogy to a mass-spring oscillator that depends on the numerically obtained fundamental frequency of the model.
Cristian David Rodriguez Lugo; Lucian Canales Brenlla; Luis Felipe Prada-Sarmiento; T. Wichtmann
10th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE2023)
2. Finite element, finite difference, discrete element, material point and other methods
https://doi.org/10.53243/NUMGE2023-281
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