Numerical modeling of stress–strain behavior of sand under cyclic loading

Analysis of soil response to cyclic loading is a complex problem due to the participation of a large number of loading conditions and physical properties. In this study, a promising variant of genetic programming (GP), namely multi expression programming (MEP) is utilized to model stress–strain behavior of sands subjected to large amplitude regular cyclic loading. Generalized MEP-based formulations are derived to simulate hysteresis strain–stress curves. To construct the hysteresis curves, functional relationships are obtained between maximum shear stress at different loading cycles and several influencing parameters. New constitutive correlations are further developed for the assessment of damping ratio and shear modulus. The proposed correlations are established based on several drained strain-controlled cyclic torsional simple shear tests performed on samples of Toyoura sand. The correlations take into account the effects of initial effective confining pressure, initial relative density, initial anisotropic stress state, strain amplitude, and shear history. A subsequent parametric study is carried out and the obtained trends are confirmed with the experimental study results. For more validity verification, the MEP-based correlations are applied to simulate the stress–strain curves of a part of the laboratory results beyond the training data domain. The proposed models are effectively capable of capturing the complex hysteresis behavior of sandy soils under cyclic loading conditions. The derived correlations are particularly valuable for providing an analysis tool accessible to practicing engineers.