Coupled theory of poroelasticity is used to develop a generic analytical solution for the time-dependent solid stress and pore fluid pressure of the subsurface rocks. A uniaxial model comprising three layers of rock formations, namely, the reservoir, caprock and burden rock is considered. The model entails different mechanical and flow properties for the considered rock layers. A linear stress–displacement formulation at the interface of the caprock and overburden defined and is calibrated to account for the confinement effect of the burden rock. The closed-form solution to the considered coupled, poroelastic problem is derived in Laplace transform space. The time-domain solution is retrieved by numerical inversion of the solution in Laplace transform space.

The obtained general solution is used to assess the coupled pore fluid pressure and stress evolution of rock layers in the following applied problems. (1) Caprock integrity upon fluid injection into the reservoir. (2) Seal rock efficiency of containing fluid transport from an abnormally pressured reservoir compartment. Findings indicate that the time evolution of pore fluid transport within and in between the rock layers is influenced by the relative magnitude of both flow and mechanical properties of the reservoir and caprock. In particular, the contrast between the elastic moduli of the reservoir and caprock are found to have substantial effect on the rate and magnitude of overpressure dissipation from the reservoir. Coulomb’s shear failure criterion, together with Terzaghi’s effective stress criterion for tensile failure, is used to assess the time-dependent failure tendency of the caprock upon exposure to excess pressure of the reservoir in the case of fluid injection problem. Findings suggest that higher injection rate, stiffer overburden, thinner reservoir and stiffer reservoir rock would enhance the failure tendency of the caprock.

孔隙弹性耦合理论用于为地下岩石随时间变化的固体应力和孔隙流体压力开发通用的解析解。考虑包括三层岩层的单轴模型，即储集层，盖层和承重层。对于所考虑的岩层，该模型需要不同的机械和流动特性。定义并校准了盖层和覆盖层交界处的线性应力-位移公式，以说明承重岩的约束作用。在拉普拉斯变换空间中，得出了所考虑的耦合多孔弹性问题的闭式解。通过在Laplace变换空间中对解进行数值反演来检索时域解。

所获得的一般解用于评估以下应用问题中的耦合孔隙流体压力和岩层应力演化。（1）流体注入油藏时盖层完整性。（2）密封岩石的效率，即从异常压力的储层室输送流体。研究结果表明，岩层内部和之间的孔隙流体传输的时间演化受储层和盖层的相对流动和力学性质的大小影响。特别是，发现储层和盖层的弹性模量之间的反差对储层超压消散的速度和幅度有实质性影响。库仑的剪切破坏准则以及Terzaghi的拉伸破坏有效应力准则，在流体注入问题的情况下，当油藏暴露于储层的过大压力下时，使用“应力分析”来评估盖层随时间变化的破坏趋势。研究结果表明，较高的注入速率，较硬的覆盖层，较薄的储层和较硬的储层岩石将增强盖层的破坏趋势。