Spatial Variability of Shear Wave Velocity and its effects on Seismic Ground Response

Abstract

Since it is unfeasible to sample every point at a site, there will always be a level of uncertainty in the mechanical properties that are used in geotechnical design. As the geotechnical community transitions towards reliability and risk-based designs, the formal treatment of these uncertainties throughout the analysis process becomes increasingly important. This study has two objectives. The first is to quantify the spatial variability of shear wave velocity based on 206 seismic cone penetration tests available for sites in British Columbia, Canada. The second is to assess how this spatial variability affects the response of a soil mass subject to earthquake ground motions.

The statistical properties of shear wave velocity were estimated using a multiplica- tive form, where the random shear wave velocity (V (d)) was expressed as the product of a deterministic trend (v̂(d)) and a lognormal random variable (Y ). The distribu- tion of Y was estimated using the method of moments, and the correlation length was estimated using two approaches, a commonly used direct-fitting method, as well as a bias-matched method. Additionally, a comparison is presented to the first-order, auto-regressive method to randomize shear wave velocity proposed by Toro (1995). Finally, a discrete-time, two-state Markov chain is used to generate realizations of soil layering, modeling the transitions between clay-like and sand-like materials. Several probabilistic, equivalent-linear ground response analyses (GRA) were com- pleted to assess how the spatial variability of shear wave velocity affects the peak ground acceleration, cyclic stress ratio, and spectral acceleration response spectra. In general, randomizing shear wave velocity was found to result in lower mean stresses and accelerations when compared against the results obtained from a deterministic approach using the mean shear wave velocity. The sensitivity of the results to the random field parameters was also explored. The distribution of peak ground accel- eration (PGA) and cyclic stress ratio (CSR) were found to be most sensitive to the coefficient of variation of shear wave velocity, with correlation length and correlation anisotropy having a smaller influence on the results.