Analytical Solution of Stress in a Transversely Isotropic Floor Rock Mass under Distributed Loading in an Arbitrary Direction

Abstract

Rock masses with a distinct structure may present a transversely isotropic character; thus, the stress state in a transversely isotropic elastic half-plane surface is an important way to assess the behavior of the interaction between the distributed loading and the surroundings. Most previous theoretical analyses have considered a loading direction that is either vertical or horizontal, and the stress distribution that results from the effect of different loading directions remains unclear. In this paper, based on the transversely isotropic elastic half-plane surface theory, a stress solution that is applicable to distributed loading in any direction is proposed to further examine the loading effect. The consistency between the analytical solution and numerical simulations showed the effectiveness of the proposal that was introduced. Then, it was utilized to analyze the stress distribution rule by changing the Poisson’s ratio and Young’s modulus of the model. The effects of the formation dip angle on the stress state are also examined. The stress distribution, depending on the physical property parameters and relative angle, is predicted using an analytical solution, and the mechanisms associated with the transversely isotropic elastic half-plane surface subjected to the loading in any direction are clarified. Additionally, extensive analyses regarding this case study, with respect to the mechanical behavior associated with changes in the stress boundary, is available. Hence, the proposed analytical solution can more realistically account for the loading problem in many engineering practices.

Keywords

• transversely isotropic
• elastic foundation
• distributed loading
• arbitrary direction