Seepage‐stress coupling is a key problem in the field of geotechnical engineering, and the finite element method is one of the main methods to study seepage‐stress coupling in rock masses. However, the finite element method has issues of poor stability, low efficiency, and low accuracy in the simulation of the seepage‐stress coupling problem. In this paper, the homogeneous saturated rock mass is taken as the object to deduce the control equation based on the Biot's theory. Considering the singularity of the coupling matrix, the discrete equation is converted into a precise integral format, and the equation is solved by the precise integration method to avoid instability and low precision. The precise integration method in this paper has good numerical stability, fast convergence speed, and high simulation accuracy, which effectively facilitates the rapid and stable numerical simulation of the seepage‐stress coupling problem using the equivalent continuum medium model. The validity and accuracy of the precise integration method for seepage‐stress coupling problems are verified by numerical examples.

中文翻译：

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具有耦合矩阵奇异可能性的岩体渗流应力耦合问题精细积分方法

渗流-应力耦合是岩土工程领域的关键问题，有限元法是研究岩体渗流-应力耦合的主要方法之一。但是，有限元方法在模拟渗流应力耦合问题时存在稳定性差，效率低和精度低的问题。本文以Biot理论为基础，以均质饱和岩体为对象，推导了控制方程。考虑耦合矩阵的奇异性，将离散方程转换为精确的积分格式，并通过精确积分的方法求解该方程，以避免不稳定和精度低。本文的精确积分方法数值稳定性好，收敛速度快，仿真精度高，这有效地促进了使用等效连续介质模型对渗流-应力耦合问题进行快速稳定的数值模拟。数值算例验证了渗流耦合问题精确积分方法的有效性和准确性。