ARCS: A one dimensional nonlinear soil model for ground response analysis

This paper presents a one dimensional nonlinear stress-strain model called ARCS (Axis Rotation and Cubic Spline) capable of reproducing any user-input modulus reduction and damping curve. Unlike many previous nonlinear models, the ARCS model does not utilize Masing's rules, nor does it require a specific functional form for the backbone curve such as a hyperbola. Rather, the model matches the desired modulus reduction curve by fitting cubic splines to the implied stress-strain curve, and matches the damping curve by utilizing a coordinate transformation technique in which one axis lies along the secant shear modulus line with the other axis in the orthogonal direction for a particular unload-reload cycle. Damping is easily controlled in the transformed coordinate space. An inverse coordinate transformation returns the desired stress. The integration algorithm is independent of strain step size, meaning that the returned stress for a large strain increment is identical to the stress that would be returned by subdividing the strain increment into smaller increments. Small-strain damping may be modeled hysteretically, avoiding the need for supplemental viscous damping. The model is shown to match the results of laboratory cyclic simple shear tests involving deliberately irregular stain histories. The performance of the model is illustrated in a set of ground response simulations where its predictions are compared with those of existing models. The ARCS model does not explicitly account for rate effects, cyclic degradation, or pore pressure generation. However, the equations can potentially be adapted in more advanced constitutive models to capture these effects. Such implementations are reserved for future publications.