Maximum ground surface motion in probabilistic seismic hazard analyses

The increasing use of Probabilistic Seismic Hazard Assessment for critical facilities leads to the consideration of earthquake scenarios with a probability of occurrence as low as 10(-7) per year. For such low probabilities the computed ground accelerations, based oil extrapolations of statistical ground-motion prediction relationships, may reach values as high as several g's, which poses tremendous difficulties for earthquake-resistant design. Obviously such large motions cannot exist at soil sites because, among other factors, the soil profile has a limited resistance capacity and cannot transmit unbounded motions. When failure is reached at any depth within the soil profile, the incident motion is filtered and no motion larger than the motion reached at that stage can be transmitted to the upper strata. The approach developed herein to estimate the maximum ground surface acceleration is based on an analytical solution to the wave equation in all inhomogeneous soil profile; the assumed soil constitutive behaviour is of the elastic perfectly plastic type, and is completely defined by the maximum shear stress and the yield strain at any depth. When compared to parametric numerical site response analyses based on a sophisticated non-linear soil constitutive model the methodology gives reasonable predictions. Comparison with recorded strong motion records do not show any contradiction between prediction and observation.