Abstract
A new analytical approach is presented for gravity-induced stresses in elastic half plane with a slope. The half plane is mapped onto the unit circle in ζ plane by conformal transformations. The mapping function proposed by Schwarz-Christoffel is irrational and difficult to be applied to the problem in the paper. Therefore, the explicit expression of the mapping function, which is easy to use and has high precision, is proposed through power series approximation. Based on the complex potentials with body force, a simple method for solving gravity-induced stresses which do not involve analytic continuation and Cauchy integral is established. The analytic functions are expressed as power series. Through the stress boundary condition on the ground surface, a set of linear equations with the coefficients of the power series can be directly constructed and solved. The stress results obtained by the presented analytical method agree well with the numerical solution. The stress distributions under different Poisson’s ratio and slope angle are studied.
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