Porous media containing cracks, fractures, or internal discontinuities arise throughout subsurface geomechanics, biomechanics, and materials science. Numerical simulation of the coupled hydromechanical response is inherently challenging because the pressure and displacement fields are tightly coupled through the Biot equations, requiring stable mixed formulations. These difficulties are compounded when cracks are present, because standard mesh-conforming approaches require costly, labor-intensive, body-fitted meshing, while unfitted methods often require cut-cell integration, enrichment functions, or additional stabilization. In this work, we use an alternative approach, we adapt the shifted interface method to coupled transient poroelasticity with embedded interfaces. The method replaces the true crack by a surrogate approximation where interface conditions are transferred through local expansions. A unified derivation yields shifted forms for both hydraulic transmission and mechanical traction coupling. Two enforcement strategies are extensively compared: a weak (integral) enforcement and a strong (pointwise) enforcement. Four test cases of increasing geometric complexity (offset mesh-aligned, boundary-intersecting angled, embedded angled, and multi-crack configurations) validate the formulation. Away from crack tips, interface residuals converge as O(h); near tips, localized post-processing artifacts degrade the global rate, but first-order convergence is recovered when a small tip region is excluded. A multi-crack demonstration with four simultaneously embedded cracks of distinct geometry and interface properties confirms the practical applicability of the framework. These results support the shifted interface method as a practical framework for poroelastic crack modeling on non-body-fitted meshes with geometrically complex embedded interfaces.

翻译：含裂纹、裂隙或内部间断的多孔介质广泛存在于地下地质力学、生物力学及材料科学中。由于压力场与位移场通过Biot方程紧密耦合，需采用稳定的混合格式，因此对耦合水力力学响应进行数值模拟本身就具有挑战性。当存在裂纹时，这些困难进一步加剧：标准网格贴合方法需要昂贵且劳动密集的体适应网格划分，而非贴合方法常需采用切割单元积分、富集函数或额外稳定化处理。本文采用替代方法，将移位界面方法适配至含嵌入界面的瞬态多孔弹性耦合问题。该方法通过局部展开传递界面条件，以近似替代真实裂纹。统一推导给出了水力传输与力学牵引耦合的移位形式，并系统比较了两种强制执行策略：弱（积分）形式与强（逐点）形式。四个几何复杂度递增的算例（偏移网格对齐裂纹、边界相交斜裂纹、嵌入斜裂纹及多裂纹构型）验证了该公式的有效性。远离裂纹尖端处，界面残差以O(h)收敛；尖端附近，局部后处理伪影降低了全局收敛阶，但排除小尖端区域后恢复一阶收敛。一个同时嵌入四条不同几何形状与界面属性裂纹的多裂纹算例验证了该框架的实用适用性。这些结果表明，移位界面方法为非体适应网格上含几何复杂嵌入界面的多孔弹性裂纹建模提供了实用框架。