Answer the following problems 3 and 4 regarding (soil structure interaction):

PROBLEM 3 A normally consolidated inhomogeneous soil of thickness H has stiffness varying with depth, z, according to the equation G(z)=G.z", G and being constants. Assuming constant density p with depth and n 0.5 determine a first gross estimate of the fundamental natural period of the soil by means of dimensional analysis. Assume a numerical value for p 1.7Mg/m', H=35m and G-15,000KN/m52. Compare your answer to established procedures like those recommended by NEHRP and Towhata (1996). (Hint: Assume that T depends on unknown powers of H, p and PE normally-consolidated soil H G = G-z" = constant Figure 3 PROBLEM 4 A circular footing of radius Ra=2m resting on the surface of the above soil layer has vertical stiffness K=100,000KN/m. Using dimensional analysis determine the corresponding stiffness Kof a similar footing on the same soil layer having radius Ro=4m. PROBLEM 3 A normally consolidated inhomogeneous soil of thickness H has stiffness varying with depth, z, according to the equation G(z)=G.z", G and being constants. Assuming constant density p with depth and n 0.5 determine a first gross estimate of the fundamental natural period of the soil by means of dimensional analysis. Assume a numerical value for p 1.7Mg/m', H=35m and G-15,000KN/m52. Compare your answer to established procedures like those recommended by NEHRP and Towhata (1996). (Hint: Assume that T depends on unknown powers of H, p and PE normally-consolidated soil H G = G-z" = constant Figure 3 PROBLEM 4 A circular footing of radius Ra=2m resting on the surface of the above soil layer has vertical stiffness K=100,000KN/m. Using dimensional analysis determine the corresponding stiffness Kof a similar footing on the same soil layer having radius Ro=4m