Fractional-Order Stress Relaxation Model for Unsaturated Reticulated Red Clay Slope Instability

Triaxial suction-controlled relaxation tests were performed on unsaturated reticulated red clay from a highway cut slope to quantify the coupled influence of matric suction (50–200 kPa), net confining pressure (100–300 kPa), and axial strain (2–8%) on time-dependent stress decay. The results reveal that 60–80% of deviatoric stress dissipates instantaneously, with the remaining loss evolving nonlinearly toward a stable residual; higher suction or confinement raises residual capacity but enlarges absolute relaxation, whereas increasing strain accelerates damage and intensifies stress drop. A parsimonious three-element fractional Poynting–Thomson (FPTh) model that embeds Caputo-derived Koeller dashpot and the exponential damage variable of the viscous coefficient was formulated. The proposed model demonstrates a superior performance compared with the Merchant, Burgers, and Nishihara models (R2 > 0.99 and RMSE < 3.5). The FPTh model faithfully reproduces the rapid and attenuating relaxation phases, offering a robust predictive tool for the long-term stability assessment of unsaturated clay slopes.