Energy-Based and Strain-Based Methods for Estimation of Pore Water Pressure within Liquefied Soil Layers

The evaluation of the excess pore water pressure ratio ($r_{\mathrm{u}}$), the ratio of the excess pore water pressure of the soil, is a defining approach to assessing liquefaction occurrence. Rarely is $r_{\mathrm{u}}$ measured, so surficial observations of sand boils, fissures, and soil settlements have provided indirect evidence of liquefaction occurrence in case histories. Acceleration responses during undrained cyclic loadings incorporate shear strain and stress responses of the liquefied soil. Therefore, the use of acceleration responses can provide another indirect indication of liquefaction as the sudden drop in the frequency in the time–frequency domain in acceleration records. This study aimed to develop strain-based and energy-based methods for estimating the pore water pressure buildup based on the acceleration responses of liquefiable sand layers. The strain-based method linked the liquefaction-induced shear strain of the soil with $r_{\mathrm{u}}$ through the shear modulus that is a function of the effective stress. An alternative approach used an energy-based method that linked pore-pressure generation with the energy dissipated in the soil. Centrifuge model tests for the liquefaction of soil were used to develop and validate the two methods, and these were applied to a case history, the 1987 Superstition Hill earthquake at the Wildlife site, for validation. To capture the variation of $r_{\mathrm{u}}$ from its contractive to dilative responses, the amount of $r_{\mathrm{u}}$ drop was estimated based on the peak shear stress when dilation spikes occurred. For the energy-based method, the centrifuge test results were used to derive empirical relations between $r_{\mathrm{u}}$ and cumulative dissipated energy done by liquefiable soil. The estimated $r_{\mathrm{u}}$ time-histories from the established methods were consistent with the measured responses in the centrifuge tests and the case history.