Average increase in vertical stress due to uniform embedded rectangular loadings in cross-anisotropic materials

•Average increase in vertical stress.•Uniform embedded rectangular loadings.•Cross-anisotropic material.•Consolidation settlement.

This study derives the closed-form solution for the average increase in vertical stress at the corner of uniform embedded rectangular loadings on cross-anisotropic materials. The solution is obtained by integrating the vertical point load solution of Wang and Liao, which is affected by the dimensions of the loaded rectangular area, the depth of the loading embedment, the depth below the loading, and the five elastic cross-anisotropic engineering constants. Additionally, to estimate the consolidation settlement at a particular cross-anisotropic layer due to embedded rectangular loadings, the average increase in vertical stress is obtained by applying the principle of superposition.