Computation of Number of Equivalent Strain Cycles: A Theoretical Framework

The equivalent uniform cycle concept was originally developed for evaluating metal fatigue and has its roots in the macro cumulative damage fatigue hypothesis posed by Palmgren and Miner. The premise of the concept is that a random load can be represented by an equivalently damaging number of uniform cycles, which greatly facilitates testing specimens in the laboratory. The concept has proven to be very useful in geotechnical earthquake engineering, and a variant of the Palmgren-Miner hypothesis has been adopted to compute the equivalent number of uniform strain cycles for evaluating the seismic compression of unsaturated fills. Inherent to the Palmgren-Miner hypothesis is the assumed linear accumulation of damage. Whence, the sequencing of the pulses in a random motion is not considered in computing the equivalent number of uniform cycles. The implications of this inherent assumption for evaluating seismic compression are examined herein. It is found that because the sequencing of the pulses in a random motion does influence volumetric strain in soil, the macro cumulative damage fatigue hypothesis proposed by Richart and Newmark is better suited for computing the equivalent number of uniform strain cycles than the Palmgren-Miner hypothesis. The framework for using the Richart-Newmark hypothesis for computing the number of equivalent strain cycles is outlined and two examples are presented. In the cases analyzed, although limited, the Palmgren-Miner hypothesis over-predicted the number of equivalent uniform strain cycles, as compared to the Richart-Newmark hypothesis.