Precise integration method for solving the seepage‐stress coupling problem in rock mass with singular possibilities of the coupling matrix. (27th April 2020)

• Record Type: Journal Article
• Authors: Liu, Zhen; Ming, Weihua; Du, Zuolei; Zhou, Cuiying
• Is Part Of: International journal for numerical and analytical methods in geomechanics. Volume 44:Number 11(2020)
• Page Start: 1587
• Page End: 1600
• Publication Date: 2020-04-27
• Subjects: Biot's theory -- coupled matrix singularity -- finite element method -- high simulation accuracy -- precise integration method -- seepage‐stress coupling; Soil mechanics -- Mathematics -- Periodicals; Rock mechanics -- Mathematics -- Periodicals; 624.1510151
• DOI: 10.1002/nag.3083
• Languages: English
• ISSNs: 0363-9061

Abstract

Summary: 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.