Endochronic Constitutive Law for Liquefaction of Sand

A nonlinear constitutive law is developed, together with the previously established model for an inelastic two-phase medium, to give a realistic prediction of the pore pressure buildup and associated liquefaction of sand due to cyclic shear. The law is of the endochronic type and consists of quasi-linear first-order differential equations expressed in terms of intrinsic time, which is an independent variable whose increments depend on the strain increments. This accounts for the accumulation of particle rearrangements, which are characterized by a parameter termed the rearrangement measure. The basic extensions of this work with regard to the application of endochronic theory to metals are due to the fact that sands densify upon shearing and are sensitive to confining stress; these two features are shared with the formulation of endochronic theory for concrete. Several typical examples are given to illustrate densification, hysteresis, and liquefaction tendency of sands subjected to cyclic shear in laboratory tests.