A simple cyclic loading CSUH model

Soil exhibits hysteresis characteristic under cyclic loading. Under the basic framework of the unified hardening model for clays and sands, a simple H-CSUH model considering cyclic loading is established by constructing elastic hysteresis loops and improving low stress plastic stiffness. The main works are as follows: (1) The elastic response of the unloading line in the e-ln(p+p_s) space is modified to be nonlinear by introducing parameters κ₀ and w, where κ₀ is used to reflect the initial unloading modulus and w is used to reflect the modulus change rate. The modified elastic unloading and reloading lines exhibit complete elastic hysteresis behavior. (2) A new hardening equation, denoted as H_h, is established by constructing a multiplier ζ, which improves the plastic stiffness of the model under low stress. Compared with the existing models, the H-CSUH model has a simpler form and fewer parameters, and achieves a unified description of the hysteretic behavior of clays and sands under cyclic loading. The validity of the model is confirmed through comparisons of drained and undrained test results across various types of clays and sands.