## 2 Materials and Methods
### Ring-Shear Test  
Ring-shear tests were conducted on the prepared specimens with different initial moisture contents after various F-T cycles. The tests were performed using a 27-WF2202 Bromhead automatic ring-shear instrument, manufactured by Controls of Milan, Italy. Prior to testing, error calibration of the normal stress sensor, shear stress sensor, and vertical displacement sensor within the data acquisition system must be performed, followed by comprehensive checks of the upper/lower shear plates and parameter configuration system. Additionally, strict regulation of laboratory ambient temperature (\(\pm 1\)\({}^{\circ}\)C) is critical throughout the experimental process. Neglecting these protocols may introduce systematic errors, ultimately compromising the reliability of mechanical parameters and rendering the results inapplicable to geotechnical engineering practice. The instrument was slightly modified to increase the specimen height and reduce test errors and costs.  
The specimen was carefully placed into the lower shear box, followed by placing the upper shear box equipped with a permeable stone on the specimen's upper surface. The torque was applied to the shear box using the torque rings on both sides of the shear box. Normal stresses of 200 kPa, 400 kPa, and 600 kPa were applied using weights loaded on a pallet balance with a leverage ratio of 10:1. The shear rate was maintained at a constant value of 20 mm/min, and the loading mode followed a single-stage application. The shear stress was calculated using Equation (1) in accordance with Test Method BS 1377-7:1990 [73]:  
\[\tau=\frac{0.239(A+B)LRF*10^{3}}{{R_{1}}^{3}-{R_{2}}^{3}} \tag{1}\]  
In the equation: \(A\) and \(B\) represent the torque values of torque rings 1 and 2, respectively, in units of N-m; \(L\) denotes the distance between the force application points on the torque beam, measured in mm; \(R_{F}\) is the dimensionless average force ring coefficient; \(R_{1}\) and \(R_{2}\) correspond to the outer and inner radii of the specimen, respectively, expressed in mm. Error analysis (including mean and standard deviation) of the shear stress values under each experimental condition was performed in Microsoft Excel 2016, and the strength variation patterns were analyzed through shear stress versus average linear displacement curves with error bars. Subsequently, curve fitting for the shear strength parameters of Hipparion laterite under varying F-T cycles and moisture content levels was conducted in OriginPro 2021, establishing high-correlation functions to predict the degradation of soil cohesion. These results provide theoretical support for practical slope engineering applications.  
In ring-shear testing, the peak strength of soil represents the maximum shear stress resisting shear failure during the shearing process, typically corresponding to the apex of the shear stress versus mean linear displacement curve. The residual strength denotes the stabilized shear stress after shear failure, corresponding to the plateau segment following the peak point. For this study, the residual-to-peak strength ratio falling below 0.85 was established as the shear failure criterion. Post-failure shearing was continued to monitor stress evolution, with test termination triggered under a cumulative mean linear displacement reaching 200 mm. Operator-defined termination protocols (e.g., early stoppage for highly sensitive clays or energy-constrained scenarios) were permitted but required explicit documentation of deviations from standard procedures to ensure reproducibility.