## 3 Results
### Macroscopic Mechanical Properties of Hipparion Laterite Under F-T Effect
According to the Mohr-Coulomb shear mechanical strength theory, the normal stress acting on Hipparion laterite in the slip zone is related to both the peak and residual shear stresses, as described by the following equations:  
\[\tau_{p}=c_{p}+\sigma\tan\varphi_{p} \tag{2}\]  
\[\tau_{r}=c_{r}+\sigma\tan\varphi_{r} \tag{3}\]  
In the equation, \(\tau_{p}\) and \(\tau_{r}\) represent the peak shear strength and residual shear strength of the soil, respectively, expressed in kPa; \(c_{p}\) and \(c_{r}\) denote the peak cohesion and residual cohesion of the soil, also in kPa; \(\sigma\) is the effective normal stress in kPa; while \(\varphi_{p}\) and \(\varphi_{r}\) correspond to the peak internal friction angle and residual internal friction angle of the soil, measured in degrees (\({}^{\circ}\)). Based on these equations, the peak and residual shear strengths of Hipparion laterite specimens with varying numbers of F-T cycles and initial moisture contents were statistically determined and are presented in Figure 12.  
Nonlinear curve fitting was applied to the test data to establish a functional relationship between the number of F-T cycles and soil shear strength. The cohesion and internal friction angle exhibit distinct functional relationships with F-T cycles: the former conforms to a monotonically decreasing modified exponential function, while the latter angle follows a monotonically increasing exponential function. The relationships are as follows:  
\[C=a-b*c^{N} \tag{4}\]  
\[\varphi=m*exp\ (-N/t)+n \tag{5}\]  
In the equation, \(C\) represents the cohesion (kPa), \(\varphi\) denotes the internal friction angle (\({}^{\circ}\)), and \(N\) signifies the number of F-T cycles. The parameters \(m\), \(n\), \(t\), \(a\), and \(b\) are fitting constants derived from experimental data regression. Overall, the peak and residual cohesion of the Hipparion laterite specimens decreased with increasing numbers of F-T cycles and increasing moisture content. In contrast, the peak and residual internal friction angles exhibited a less consistent pattern with slight fluctuations. However, there was a general upward trend although the differences were minimal. For peak cohesion, losses of 26.76 kPa, 18.44 kPa, and 21.29 kPa were observed during 4 to 8 F-T cycles, respectively. From 8 to 10 cycles, the curve became slower with smaller slopes, and the strength remained almost constant. The residual cohesion of the Hipparion laterite specimen with 16% moisture content decreased by 34.17 kPa after two F-T cycles, representing a deterioration rate of 24.03%, highlighting the significant effect of F-T cycles. Subsequently, the slope of the curve line decreased, and the magnitude of the change became roughly similar to that of the peak cohesion. In contrast, the variation in the residual internal friction angle slightly differed from that of the peak internal friction angle. During the 2 nd to 4 th F-T cycles, the residual internal friction angles for different moisture contents reached low values of 15.77\({}^{\circ}\), 13.29\({}^{\circ}\), and 14.91\({}^{\circ}\), respectively. These values then gradually increased, with a higher total growth rate observed within the 0 th to 10 th cycle range, although this rate remained lower than that of the peak internal friction angle. This finding is consistent with observations of F-T damage in red sandstone [76; 77]. Figure 12: The relationship between the peak and residual shear strength of Hipparion laterite samples with different moisture contents and the number of F-T cycles. (**a**,**c**,**c**) Peak shear strength of specimens with moisture contents ranging from 16% to 24%; (**b**,**d**,**f**) residual shear strength of specimens with moisture contents ranging from 16% to 24%.