Stress solutions for an inhomogeneous plane strain transversely isotropic rock subjected to horizontal and vertical line loads

摘要

This article yields the stress solutions subjected to horizontal and vertical line loads acting in a continuously inhomogeneous plane strain transversely isotropic rock with Young’s and shear moduli varying exponentially with depth. The governing equations can be obtained by combining the generalized Hooke’s law, the strain-displacement relationships, and the equilibrium equations. Then, utilizing the Fourier integral transforms, the governing equations are transformed into ordinary differential equations. In addition, by means of the variation of parameters, the solutions of displacements in the Fourier domain are derived. However, the stress solutions in the same domain also can be acquired by utilizing the stress-strain-displacement relationships.Finally, performing the inverse Fourier integral transforms by using numerical integration program, QDAGI in FORTRAN language, the stresses due to horizontal and vertical line loads can be estimated. The solutions show that the stresses are remarkably affected by: (1) the in homogeneity parameter, (2) the type and degree of rock anisotropy, (3) the types of loading, (4) the nondimensional horizontal distance. The present solutions are the same with those of Wang and Liao (1999) by suitable integrations, when the rock mass is a homogeneous plane strain transversely isotropic medium. A parametric study is conducted to elucidate the effect of aforementioned factors on the yielded vertical normal stress. The results reveal the computations of stresses ought to take the inhomogeneous characteristic into account when transversely isotropic rocks subjected to applied loads.