Nonlinear soil-linear structure interaction: Energy and strain distribution

The wave propagation approach in solving the problem is considered. The wave equation is solved numerically in the domain consisting of the soil, foundation, and superstructure using the explicit Lax-Wendroff numerical scheme. An artificial boundary is incorporated to simulate the Sommerfeld radiation boundary condition at infinity. The velocities and the displacements at the points of the stress-free boundaries are updated in each time step using the vacuum formalism approach. The system consists of rectangular structure having circular foundation embedded in nonlinear soil. The aim of this study is to present the permanent strain distribution in a soil and to calculate energy distribution in a nonlinear system excited by SH waves in form of half-sine pulses. For that purpose, the superstructure and the foundation are assumed linear, while the soil as material is non-linear and is allowed to yield. Due to the plane waves, the input energy to the system, the hysteretic energy spent for creation and development of nonlinear strains, the scattered energy from the foundation, and the energy in the building are determined for half-sine pulses with same amplitude but different durations (frequencies). For transient response, we use dimensionless frequency, which is ratio between the radius of the semicircular foundation and half wavelength of the input pulse. The range of this dimensionless frequency in our analyses is from 0.05 (long pulses) to 2 (short pulses).