Stresses in a weighable half-plane with a semicircular notch

The influence of the surface roughness on the stress state of a rock is studied. For an elastic half-plane in the gravity field that contains a notch shaped like a semicircle, the stress distribution is constructed. It is shown that depending on the Poisson ratio, the notch bottom can be in a state of tension or compression. The polynomial dependence of pressure on depth is given on the axis of symmetry.