Surface Settlement Due to Shear Stresses at Depth

Mindlin's solution for surface vertical displacement due to a horizontal force at depth is first examined and then integrated for shear stresses acting on a long rectangular reinforcing strip. Four types (constant, linear decrease, power‐law decrease, and triangular) of shear stress variations, are considered. These variations are possible as a result of interaction between a reinforcement strip and the soil. The constant variation of shear stress corresponds to full mobilization, whereas the triangular one corresponds to a linearized approximation of Binquet and Lee's shear‐stress variation. Results presented quantify the effects of length, depth, and distance of the loaded area from the surface point; and of the Poisson's ratio of the soil on the displacement of the surface point. The heave or the settlement reductions are noted to be largest if the reinforcement strip on which shear‐stress variations are considered has a length 2.5 to 3.0 times the width of the surface load or is located at a depth 0.25 to 0.375 times the width of the same. The results are useful in estimating settlement reduction due to strip reinforcement of soil beneath surface loads.