Nonlinear Components in Soil Response

The constructed models of soil behavior allow us to study soil profiles as nonlinear systems converting input motion to soil layers into motion on the surface. To estimate nonlinear components in soil response, nonlinear identification methods are used based on the calculation of high-order impulse characteristics of nonlinear systems. Under conditions of stationarity, analyticity, and finite memory of a nonlinear system, the response of the system can be represented as a Volterra-Wiener series, i.e. a sum of multiple integrals of the input signal. Knowing the input and output signals, we can conclude about the types and quantitative characteristics of the system’s nonlinearity. The Chapter describes nonlinear identification of the soil profiles and estimation of nonlinear components in the soil response in the near-fault zones of the studied earthquakes. It was obtained that the estimates of nonlinear components of the soil response are comparable to the estimates of shear moduli reduction in the layers during strong motion. Subsurface soils possess mostly odd-type nonlinearities (cubic and other higher-order odd-type nonlinearities), because hysteretic stress–strain relations are essentially odd functions. Nonlinearities of even types are usually weak, but become significant in cases when loading and unloading curves of the stress–strain relations acquire noticeable even components (as in liquefied soils or at the moments of most intense motion).