Reduction of Structural Damage by Nonlinear Soil Response

Following the 1994 Northridge earthquake, the areas with a high density of reported breaks in water pipes in typical residential areas in San Fernando Valley and in Los Angeles often did not coincide with the areas having a high density of severely damaged (red-tagged) buildings. As the former is an indicator of large strains and nonlinear soil response, this observation suggests that the damage to buildings in some areas may have been smaller than expected because the soil dissipated part of the energy of the ground motion by nonlinear response. This paper presents an attempt to quantify this relationship between the density of red-tagged buildings, N (per km²), and the severity of shaking (via peak horizontal ground velocity, v_max, or modified Mercalli intensity, IM_M), including the density of breaks in water pipes, n (per km²), as a variable specifying the level of strain in the soil. Approximate empirical relationships for N = f(vmax, n) and N = f(I_MM, n) are presented. The trends in the data indicate that, for vmax in the range from ∼35 to ∼125 cm/s, the rate of growth of N versus v_max tends to decrease at sites with large strain in the soil (i.e., large n). For vmax beyond ∼150 cm/s, the beneficial effects of nonlinear soil response seem to fade out, as large differential motions associated with soil failure begin to contribute to the damage of structures. Assuming fairly uniform density and quality of building stock and of water pipes in the areas studied, the derived relationships are then used to map v_max and IM_M in San Fernando Valley and in Los Angeles. The resulting maps are more detailed than what could be obtained from the density of strong motion stations and of sites with reports on felt intensity.