A simple cycle loading CSUH model

Soil exhibits hysteresis characteristic under cycle loading. Under the basic framework of the unified hardening model for clays and sands, a simple H-CSUH model considering cycle 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+ps) space is modified to be nonlinear by introducing parameters κ0 and w, where parameter κ0 is used to reflect the initial unloading modulus and parameter 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 Hh, is established by constructing a multiplier ζ, which improves the model's plastic stiffness under low stress. Compared with existing models, the H-CSUH model has a simpler form and fewer parameters, and achieves a unified description of the hysteretic behavior of clay and sand under cycle loading. The model's validity was confirmed through comparisons of drainage and undrained test results across various types of clays and sands.