Subsurface fluid operations alter the in-situ stress field, often reactivating displaced faults and inducing seismicity. Accurately evaluating fault slip and stress redistribution is crucial for geomechanical risk assessment. While previous studies derived closed-form analytical expressions for initial pre-slip Coulomb stresses on displaced faults (Jansen et al. 2019; Wu et al. 2021), calculating quasi-static slip evolution remains mathematically cumbersome. This limitation is particularly evident when interacting slip patches merge or within complex fault configurations, where traditional singular integral approaches become computationally restrictive. To address this, we introduce an efficient semi-analytical framework based on the eigenstrain theory to robustly determine true fault slip lengths. In this framework, the pressurized region and fault slip are modelled as Eshelby’s inclusion and dislocation (also known as displacement discontinuity), respectively.  We employ a high-precision Discontinuous Displacement Method (DDM) approach to compute stress and displacement fields along faults under fluid-induced pressure changes. Instead of relying on complex analytical inversion of Cauchy singular equations to track slip boundaries, our method utilizes an active-set iterative strategy to efficiently identify sliding and locked elements. This formulation automatically resolves true slip distributions during loading without a priori assumptions regarding slip patch locations. Furthermore, the DDM intrinsically accommodates complex geometrical features and heterogeneous frictional properties, providing a highly versatile tool for realistic subsurface scenarios.
 

Displacement Discontinuity Method,Injection-induced seismicity,Eshelby' s inclusion,Semi-analytical method