We present a novel poro-damage-viscoelastic model for predicting the failure response of fluid-saturated porous geomaterials. The Generalized Maxwell model is introduced for the representation of the viscoelastic behavior of the solid skeleton, which is achieved by a standard Prony-series type expansion. Damage regularization is obtained by an non-local integral-type formulation and damage behavior is described by Mazars model with the modified von Mises-type equivalent strain measure. The poromechanics parameters (Biot’s coefficient, Biot’s modulus) are functions of damage, and the fluid flow obeys Darcy’s seepage law in the entire domain, while the permeability is assumed to be anisotropic and strain dependent. The coupled system is discretized in time using a backward Euler scheme. The non-linear system is linearized using a Newton Raphson scheme and solved monolithically every time step. A consistent Jacobian matrix and residual vector are derived analytically. Several numerical examples are studied in order to investigate the performance of the proposed approach, including (i) a column undergoing hysteresis from cyclic loading, stress relaxation, creep and variable strain rate loading tests and (ii) fluid-driven fracturing in a 2D poro-viscoelastic domain. The numerical time-dependent results exhibit mesh insensitivity for all field variables, and confirm the feasibility and applicability of the proposed non-local damage model for simulating hydraulic fracture.

我们提出了一种新的孔隙损伤粘弹性模型，用于预测流体饱和多孔土工材料的失效响应。引入广义麦克斯韦模型来表示实体骨架的粘弹性行为，这是通过标准的 Prony 级数类型展开实现的。损伤正则化由非局部积分型公式获得，损伤行为由 Mazars 模型用改进的 von Mises 型等效应变测量来描述。孔隙力学参数（Biot 系数、Biot 模量）是损伤的函数，流体流动在整个域内遵循 Darcy 渗流定律，而渗透率假设为各向异性和应变相关。耦合系统使用时间离散化后向欧拉方案。非线性系统使用 Newton Raphson 方案进行线性化，并在每个时间步进行单片求解。分析得出一致的雅可比矩阵和残差向量。为了研究所提出方法的性能，研究了几个数值示例，包括 (i) 柱在循环加载、应力松弛、蠕变和可变应变率加载测试中经历滞后，以及 (ii) 二维孔隙中的流体驱动压裂-粘弹性域。数值时间相关结果显示出对所有场变量的网格不敏感，并证实了所提出的非局部损伤模型模拟水力压裂的可行性和适用性。