Displacement and stress distributions under a uniform inclined rectangular load on a cross‐anisotropic geomaterial

Abstract

SUMMARYIn practical engineering, an applied rectangular area load is not often horizontally or vertically distributed but is frequently inclined at a certain angle with respect to the horizontal and vertical axes. Thus, the solutions of displacements and stresses due to such a load are essential to the design of foundations. This article yields the analytical solutions of displacements and stresses subjected to a uniform rectangular load that inclines with respect to the horizontal and vertical axes, resting on the surface of a crossanisotropic geomaterial. The planes of cross-anisotropy are assumed to be parallel to the horizontal ground surface. The procedures to derive the solutions can be integrated the modified point load solutions, which are represented by several displacement and stresses elementary functions. Then, upon integrations, the displacement and stress integral functions resulting from a uniform inclined rectangular load for (1) the displacements at any depth, (2) the surface displacements, (3) the average displacements in a given layer, (4) the stresses at any depth, and (5) the average stresses in a given layer are yielded. The proposed solutions are clear and concise, and they can be employed to construct a series of calculation charts. In addition, the present solutions clarify the load inclinations, the dimensions of a loaded rectangle, and the analyzed depths, and the type and degree of geomaterial anisotropy profoundly affect the displacements and stresses in a cross-anisotropic medium. Parametric results show that the load inclination factor should be considered when an inclined rectangular load uniformly distributed on the cross-anisotropic material.

Elastic fields in two joined transversely isotropic media of infinite extent as a result of rectangular loading

“…Therefore, the findings presented in the paper would be useful for further examination of the behavior of two bonded transversely isotropic solids under distributed loads. (19) are given exactly as follows:…”

“…Þ , the above expressions in Equations (16) to (19) become indeterminate and has the form of 0/0. This degenerating case includes the elastic rock solid exhibiting isotropy.…”

“…For this case, the algebraic general solutions can be obtained by taking the limit as g 1k ! g 2k (k = 1, 2) in Equations (16) to (19) and can be expressed as follows:…”

“…Putting z = 0 into Equations (16) to (19), six independent algebraic equations governing the variables w (0) and Y z (0) at the interface can easily be obtained. By solving the linear algebraic equations, we can arrive at the solutions for w(0) and Y z (0) in terms of g. Substituting the solution of w(0) and Y z (0) into Equations (16) to (19), we further obtain the solution for the two vectors w(z) and Y z (z). The two vectors will be used to find the solution for displacements, stresses and strains in the physical domain.…”

“…Wang and Liao [17] developed a graphical procedure to calculate stresses in a transversely isotropic half-space subjected to a three-dimensional surface load. Furthermore, Wang and Liao [18] and Wang et al [19] developed elastic solutions for stresses in a transversely isotropic half-space and a cross-anisotropic geo-material subjected to threedimensional rectangular loads, respectively. Yue et al [20] investigated stresses and displacements of a transversely isotropic elastic half-space because of rectangular loadings.…”