Number of Equivalent Cycles Concept for Liquefaction Evaluations—Revisited

The “equivalent number of cycles” concept is integral to cyclic liquefaction evaluations, whether applied directly in laboratory evaluations or via magnitude scaling factors in field evaluations. The premise of the concept is that the random motions of an earthquake can be represented by an equivalently damaging number of uniform stress cycles $\left(n_{\mathrm{eq}}\right)$ , which facilitates laboratory testing and provides a convenient metric for comparing the duration of earthquake motions. The most widely used procedure for computing $n_{\mathrm{eq}}$ was developed by the late Professor H.B. Seed and colleagues in the late 1960s to early 1970s and is based on the Palmgren–Miner $\left(P–M\right)$ cumulative damage hypothesis developed for metal fatigue evaluations. However, the original $P–M$ hypothesis is intended for high cycle fatigue conditions and therefore applies to conditions where the strains are constrained to the elastic range of the material. By contrast, low cycle fatigue conditions, such as the case of soils subjected to strong ground shaking, are characterized by significant amounts of plastic strain. The implications of using a high cycle fatigue hypothesis to compute $n_{\mathrm{eq}}$ for evaluating liquefaction are examined herein, and an alternative approach to implementing the $P–M$ fatigue hypothesis that more appropriately accounts for the nonlinear behavior of soil is proposed. The alternative implementation procedure equates energy dissipated in the soil subjected to the actual earthquake motions and $n_{\mathrm{eq}}$ uniform cycles. The results of a parametric study using the alternative implementation procedure show that $n_{\mathrm{eq}}$ varies as a function of earthquake magnitude, site-to-source distance, and depth in a soil profile.