Quantification of hysteresis area and artificial intelligence-assisted prediction of cracking in biochar-amended soil under wet-dry cycles

This study investigates the coupled hysteresis-cracking interaction in expansive soil under wet-dry cycles, integrating artificial intelligence predictive modeling. Based on the Van Genuchten ( VG ) model, an analytical formula for hysteresis area and a one-dimensional crack depth equation considering hysteresis were developed. Laboratory experiments on expansive soil with varying biochar contents revealed hysteresis and crack patterns. Biochar optimizes soil structure via a bimodal pore system, reducing hysteresis and cracking. After 10 cycles, hysteresis area decreased by 37% in bare soil and 70% in 15% biochar-amended soil; the crack intensity factor after five cycles was 9.11 versus 15.17 for the control, confirming crack suppression. The analytical formula matched experimental data well ( R ²  > 0.98). Parameter sensitivity shows hysteresis area depends primarily on VG parameters α , n, and cycle number; higher α and n reduce hysteresis, and area stabilizes with increasing cycles. Hysteresis area strongly correlates with crack depth, serving as a cracking predictor. A mechanism-constrained random forest surrogate model ( R ²  = 0.93, RMSE  = 0.82) was developed for rapid crack depth assessment under various material compositions and cycling conditions. These findings offer a theoretical foundation and data-driven techniques for screening protective materials and evaluating damage evolution in unsaturated soils under wet-dry cycling.