Relating $K_{\alpha }$ to Relative State Parameter Index

The effect of an initial static shear stress on the undrained cyclic loading resistance of saturated sand, as observed in laboratory testing, is often expressed in terms of a correction factor, $K_{\alpha }\text{.}$ Prior research has demonstrated that $K_{\alpha }$ depends on the state of the sand, as commonly represented by its relative density and confining stress conditions. This dependence of $K_{\alpha }$ on state is intuitively consistent with critical state concepts, but the implementation of this dependence in practice has been hindered by the absence of simple methods for estimating state and its effects without having to perform an extensive program of laboratory testing. In this paper, a simple index for representing state is derived from Bolton’s (1986) relative dilatancy index and shown to provide a reasonable and practical index for describing the variation of $K_{\alpha }$ with both relative density and confining stress.