Analytical solution for stress and settlement of strip footings resting on orthotropic jointed rocks: a parametric study

Large-scale engineering structures with substantial loads, such as dams, towers, and bridges, are currently being constructed on rocks as a good load-bearing foundation. Because many rocks are jointed and thus inherently discontinuous, the analysis of stress and settlement is crucial to ensure a safe and reliable foundation design with no potential for failure or excessive settlement. This paper presents a new analytical solution based on the complex variable method for calculating stresses and settlements under vertically loaded strip footings. The rock mass was assumed to be elastic and intersected by two perpendicular joint sets parallel and normal to the rock surface. The jointed rock was modeled as an equivalent orthotropic continuum to obtain the analytical solution, and the theory of anisotropic elasticity was applied. Comparisons with the available isotropic solutions and results from Finite Element and Distinct Element models are also provided to verify the accuracy of the proposed solution. Finally, a number of parametric studies are conducted to investigate the effects of various joint characteristics and Poisson’s ratios on the results. The proposed solution offers a quick assessment tool for designing footings on jointed rocks without requiring complicated numerical simulations or relying on oversimplified isotropic solutions.