Аннотация:The presentation considers a generalization of classical Biot's equations to the poroelastoplastic
medium in order to simulate a shear banding phenomena taking place around the borehole
drilled in the prestressed solid under the artificial depression leading to the change in the pore
pressure in the surrounding rock as well as redistribution of stresses and accumulated plastic strains.
The mathematical problem formulation consists of a coupled system of dynamic poroelastoplastic
equations in a solid skeleton and a saturating fluid for the small strains case (geometrically linear
formulation): equilibrium equations, Darcy's law, and constitutive stress-strain and pore pressure
relations. Different physically nonlinear relations are taken into account: dynamic porosity and
permeability dependent on the pore pressure and volumetric strains, non-associative poroplasticity
taken into account irreversible plastic strans and change in fluid volume content, dynamic poroelastic
moduli (bulk, shear, Biot etc) dependent on the current porocity. A set of nonlinear PDEs is solved
using a novel approach based on the fully explicit time integration scheme and the high order spectral
element method (SEM) space discretization scheme. Two numerical algorithms are analyzed and
compared with each other: the first one is based on the direct Lagrangian formalism leading to the full
displacement integration and accumulation of the full plastic strains at each loading step, the second
one is based on the Euler formalism leading to the seeking a numerical solution in terms of the
relative displacements at each loading step (i.e. velocities) and accumulated stresses. Both approaches
are implemented for solving quasi-static poroelastoplastic equations using pseudo-transient scheme
with the inertia and dissipative terms allowing one to converge to the static solution at each loading
"time" step. Obtained numerical results as well as the performance of both approaches are analyzed
and compared with CAE Fidesys for the Drucker-Prager plasticity. CUDA technology is used to
parallelize the implemented algorithm on the massively parallel Tesla V100 GPU. Different
optimization strategies and details of parallelizing spectral element method using CUDA are
discussed. In particular, an algorithm for the mapping of an unstructured spectral element mesh of an
arbitrary order onto the grid of blocks of GPU multilevel thread hierarchy is presented. CUDA
kernels' design, memory access patterns, synchronization issues are considered. Performance analysis
is given for different SEM orders and mesh sizes as well as for the different floating-point precisions.
The reported study was funded by Russian Science Foundation project -19-77-10062 .