In the figure below, two circular loads with respective diameters of 10 inches (254 mm) and 20 inches (508 mm) on centres are applied to a homogeneous half-space. 50 psi (345 kPa) of pressure is exerted on the circle. The elastic modulus of the half-space is 10,000 psi (69 MPa), and its Poisson ratio is 0.5. Find the vertical strain, deflection, and stress at point A, which is 10 in. (254 mm) below the centre of one circle.

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Methods to Determine Vertical Stress

The load applied to the soil is transferred to the underground. The presence of water at soil pores and solid grains above the soil are the primary components that are responsible for the effective load transfer. Due to the load acting, the internal component of the soil or the underground formations undergoes deformations or a tectonic shift. The amount of deformation depends upon the amount of load acting on the soil surface, which indeed, depends on the weight of everything present above the soil. Due to this, the underground soil element develops internal stresses which try to resist the tectonic changes.