Stresses induced by vertical rectangular uniform loads within ground based on Mindlin solution

The calculation of foundation settlement is usually based on the Boussinesq’s solution or Mindlin’s solution, which is suitable for considering the embedding depth to calculate the additional stress coefficient. In order to simplify the integration process, in the existing literatures the coordinate origin is often placed at the corner of rectangle in calculating the additional stress coefficient of vertical rectangular uniform loads acting on a semi-infinite elastic body, and the coefficients at a point under the corner of rectangule are calculated, so the relevant solutions have obvious limitations. In order to make the solution more general, on the basis of Mindlin’s solution of concentrated load, the analytic expressions for stress distribution at any point in a semi-infinite body suffering vertical rectanglar uniform loads on horizontal area and the analytic expression for with vertical rectanglar uniform loads on vertical area are deduced. Their correctness is verified by comparing with the existing literature, and the change laws of stress coefficient at different positions under different Poisson's ratios are analysed. The conclusions can be applied in engineering calculation.