Simulation of the localization and development of plastic shear bands in fluid-saturated rocks is considered using a nonlinear poroelastoplastic model generalizing Biot’s model for a two-phase fluid-saturated porous medium under small and finite strains. A Drucker-Prager yield criterion and a non-associated plastic flow rule are applied to describe an accumulation and localization of plastic strains in a rock. Additionally, a nonlinear dependence of the model parameters (elastic moduli, Biot’s modulus, permeability, etc.) on porosity is considered as well as a dynamic variation of porosity due to the volumetric deformation of the pore space. An isoparametric spectral element method is used to discretize a geometric model and PDEs on curvilinear unstructured meshes of high order in space. A distinctive feature of the developed algorithm for numerical solving the system of nonlinear PDEs of poroelastoplasticity is the use of the dynamic relaxation method, which provides a quasi-stationary solution using an explicit time integration scheme and an optimal choice of the damping parameter. The suggested algorithm allows efficient implementation on a massively parallel high-performance computing system using CUDA technology. The spectral element mesh is naturally mapped onto the CUDA Grid representing GPU’s multiprocessors, and accordingly, each spectral element is mapped onto a streaming block, within which element’s internal nodes are processed by the corresponding threads of the block. Numerical results of solving a series of model problems of the development of plastic shear bands nearby a borehole drilled in a porous fluid-saturated rock are presented. The dynamic variations of porosity and permeability because of the accumulation of plastic deformations are analyzed.

考虑使用非线性孔弹塑性模型模拟流体饱和岩石中塑性剪切带的定位和发展，该模型推广了 Biot 的模型，用于在小应变和有限应变下的两相流体饱和多孔介质。应用 Drucker-Prager 屈服准则和非关联塑性流动规则来描述岩石中塑性应变的积累和局部化。此外，还考虑了模型参数（弹性模量、Biot 模量、渗透率等）对孔隙度的非线性依赖性，以及由于孔隙空间的体积变形引起的孔隙度动态变化。等参谱元法用于离散空间中高阶曲线非结构化网格上的几何模型和偏微分方程。所开发的用于数值求解多孔弹塑性非线性 PDE 系统的算法的一个显着特征是使用动态松弛方法，该方法使用显式时间积分方案和阻尼参数的最佳选择提供准稳态解。建议的算法允许在使用 CUDA 技术的大规模并行高性能计算系统上高效实现。光谱元素网格自然映射到代表 GPU 的多处理器的 CUDA 网格上，因此，每个光谱元素都映射到一个流块上，其中元素的内部节点由块的相应线程处理。给出了解决在多孔流体饱和岩石中钻孔附近的塑性剪切带发展的一系列模型问题的数值结果。分析了塑性变形累积引起的孔隙度和渗透率的动态变化。