Keywords: nonlinear soil, permanent strain, energy distribution, shear horizontal waves, strong ground motion, Lax-Wendroff numerical scheme, flexible foundation.

A nonlinear soil-linear structure system excited by strong ground shear horizontal wave motion is considered. The wave equation in the domain consisting of soil, foundation, and superstructure is solved using the Lax-Wendroff numerical scheme [1]. We studied the influence of the interaction in the creation and development of permanent strains in the soil and energy distribution in the system.

The input energy to the system, the scattered energy from the foundation, the energy in the building, and the hysteretic energy spent for creation and development of permanent strains are computed for half-sine pulses with the same amplitude but different durations. In the analyses we use dimensionless frequency, which is ratio between the radius of the semicircular foundation and the half wavelength of the input pulse. In our study the range of this dimensionless frequency is from 0.05 (long pulses) to 2 (short pulses).

The energy in the structure mostly depends upon the foundation stiffness. This is not the case for the hysteretic energy in the nonlinear soil. For some frequency ranges and angles of incidence the hysteretic energy of the model with softer foundation is larger than the one of the model with stiffer foundation and opposite for other frequency ranges and other angles of incidence. This is the outcome of the complicated pattern of interference among the incoming field, reflected from the free surface field, and scattered field, for different ranges of dimensionless frequency.

For long waves, soft foundations, and small incident angles, the effect of the interaction on the nonlinear response of the soil is small. As the foundation becomes stiffer, zones of large permanent strains develop around the foundation. For stiff foundations, short waves, and large incident angles, a zone of permanent strains develops behind the foundation, which appears to be due to the concentration of rays associated with diffraction of the waves from the foundation. The zones of large permanent strains are responsible for the damage and failures in the shallow infrastructure (water and gas pipes, underground cables, etc.) that accompany large earthquakes and cause interruptions of gas and water supplies [2,3].

1

G. Sod, "Numerical Methods in Fluid Dynamics", Cambridge Univ. Press, UK, 1985.

2

M.D.Trifunac, M.I. Todorovska, "Northridge, California, earthquake of 17 January 1994: Density of pipe breaks and surface strains", Soil Dynamics and Earthquake Eng., 16(3), 193-207, 1997. doi:10.1016/S0267-7261(96)00042-5

3

M.D. Trifunac, M.I. Todorovska, "The Northridge, California, earthquake of 1994: Fire ignition by strong shaking", Soil Dynamics and Earthquake Eng., 17(3), 165-175, 1998. doi:10.1016/S0267-7261(97)00040-7

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