Mem-modeling of strain ratcheting using early-time soil fatigue data

Stress–strain behavior of two different soil specimens subjected to cyclic compressive loading are studied herein, the goal being to present a simple dynamic uniaxial mem-modeling approach that aids physical insight and enables system identification. In this paper, “mem” stands for memory, i.e., hysteresis. Mem-models are hysteresis models transferred from electrical engineering using physical analogies. Connected in series, a mem-dashpot and mem-spring are employed to model inter-cycle strain ratcheting and intra-cycle gradual densification of the two soil specimens. Measured time histories of stress and strain are first decomposed so that the two modeling components, mem-dashpot and mem-spring, can be identified separately. This paper focuses on the mem-dashpot, a nonlinear generalization of a linear viscous damper. A mem-spring model is also devised built on an extended Masing model. Nonlinear dynamic simulations (with inertia) employing the identified mem-dashpot and mem-spring demonstrate how well the identified mem-models reproduce the measured early-time data (first 200 cycles of loading). Choices of state variables inherited from bond graph theory, the root of mem-models, are introduced, while MATLAB time integrators (i.e., ode solvers) are used throughout this study to explore a range of contrasting damper and spring models. Stiff solver and the state event location algorithm are employed to solve the equations of motion involving piecewise-defined restoring forces (when applicable). Computational details and results are relegated to the appendices. This is the first study to use single-degree-of-freedom (SDOF) system dynamic simulations to explore the consistency of mem-models identified from real-world data.