Application of Fatigue Theories to Seismic Compression Estimation and the Evaluation of Liquefaction Potential

Earthquake-induced liquefaction of saturated soils and seismic compression of unsaturated soils are major sources of hazard to infrastructure, as attested by the wholesale condemnation of neighborhoods surrounding Christchurch, New Zealand. The hazard continues to grow as cities expand into liquefaction- and seismic compression-susceptible areas hence accurate evaluation of both hazards is essential.

The liquefaction evaluation procedure presented herein is based on dissipated energy and an SPT liquefaction/no-liquefaction case history database. It is as easy to implement as existing stress-based simplified procedures. Moreover, by using the dissipated energy of the entire loading time history to represent the demand, the proposed procedure melds the existing stress-based and strain-based liquefaction procedures in to a new, robust method that is capable of evaluating liquefaction susceptibility from both earthquake and non-earthquake sources of ground motion.

New relationships for stress reduction coefficient (r_d) and number of equivalent cycles ($neq$) are also presented herein. The r_d relationship has less bias and uncertainty than other common stress reduction coefficient relationships, and both the $neq$ and $rd$ relationships are proposed for use in active tectonic and stable continental regimes. The $neq$ relationship proposed herein is based on an alternative application of the Palmgren-Miner damage hypothesis, shifting from the existing high-cycle, low-damage fatigue framework to a low-cycle framework more applicable to liquefaction analyses.

Seismic compression is the accrual of volumetric strains caused by cyclic loading, and presented herein is a "non-simplified" model to estimate seismic compression. The proposed model is based on a modified version of the Richart-Newmark non-linear cumulative damage hypothesis, and was calibrated from the results of drained cyclic simple shear tests. The proposed model can estimate seismic compression from any arbitrary strain time history. It is more accurate than other "non-simplified" seismic compression estimation models over a greater range of volumetric strains and can be used to compute number-of-equivalent shear strain cycles for use in "simplified" seismic compression models, in a manner consistent with seismic compression phenomenon.