## 3 Experiment Results and Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**S (\%)**} & \multirow{2}{*}{\(\sigma_{3}\) (kPa)} & \multirow{2}{*}{\(\mathrm{FTC}\) = 0} & \multirow{2}{*}{\(\mathrm{FTC}\) = 1} & \multirow{2}{*}{\(\mathrm{FTC}\) = 5} & \multirow{2}{*}{\(\mathrm{FTC}\) = 10} & \multirow{2}{*}{\(\mathrm{FTC}\) = 30} & \multirow{2}{*}{\(\mathrm{FTC}\) = 60} & \multirow{2}{*}{\(\mathrm{FTC}\) = 120} \\ \cline{5-8}  & & & & & & & & \\ \hline \multirow{3}{*}{0.0} & 100 & 330 & 218 & 204 & 180 & 172 & 170 & 127 \\  & 200 & 418 & 294 & 274 & 246 & 242 & 239 & 184 \\  & 300 & 469 & 363 & 351 & 328 & 320 & 314 & 243 \\ \hline \multirow{3}{*}{0.5} & 100 & 308 & 209 & 191 & 169 & 160 & 153 & 114 \\  & 200 & 369 & 273 & 266 & 231 & 224 & 218 & 165 \\  & 300 & 434 & 341 & 324 & 306 & 299 & 289 & 217 \\ \hline \multirow{3}{*}{1.0} & 100 & 298 & 204 & 187 & 161 & 153 & 144 & 92 \\  & 200 & 357 & 262 & 246 & 226 & 214 & 209 & 116 \\  & 300 & 412 & 331 & 317 & 294 & 289 & 272 & 176 \\ \hline \multirow{3}{*}{2.0} & 100 & 297 & 191 & 177 & 157 & 145 & 140 & 81 \\  & 200 & 348 & 243 & 232 & 219 & 209 & 204 & 100 \\  & 300 & 377 & 307 & 298 & 285 & 273 & 265 & 152 \\ \hline \multirow{3}{*}{3.0} & 100 & 301 & 192 & 182 & 163 & 147 & 140 & 60 \\  & 200 & 356 & 247 & 239 & 228 & 216 & 202 & 93 \\  & 300 & 416 & 318 & 313 & 298 & 283 & 266 & 122 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Failure principal-stress deviation \((\sigma_{1}-\sigma_{3})_{f}\) of samples. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\sigma_{3}\) (kPa) & **S (\%)** & \(\mathrm{A_{1}}\) & \(\mathrm{B_{1}}\) & \(\mathrm{C_{1}}\) & \(\mathrm{D_{1}}\) & \(\mathrm{R^{2}}\) \\ \hline \multirow{3}{*}{100} & 0.0 & 132.67 & \(-\)1.82 & 197.32 & \(-\)0.0035 & 0.985 \\  & 0.5 & 122.73 & \(-\)1.61 & 185.26 & \(-\)0.0039 & 0.989 \\  & 1.0 & 115.46 & \(-\)1.64 & 182.53 & \(-\)0.0053 & 0.984 \\  & 2.0 & 120.69 & \(-\)2.04 & 176.31 & \(-\)0.0057 & 0.984  
into a new dynamic and stable equilibrium state [10; 30]. Therefore, the decreasing rate of \((\sigma_{1}-\sigma_{3})_{f}\) was obviously reduced when samples underwent 30 and 60 cycles. However, as the number of FTCs increased, pores in the soil gradually spread into cracks, so soil strength had an accelerated decline after 120 cycles. The exponential function can reflect the relationship between \((\sigma_{1}-\sigma_{3})_{f}\) and FTC. Correlation coefficient R\({}^{2}\) was above 0.93, so this function is suitable to explain the relationship between \((\sigma_{1}-\sigma_{3})_{f}\) and FTC. \((\sigma_{1}-\sigma_{3})_{f}\) increased with confining pressure, which indicated that the latter could inhibit pore-volume changes caused by axial pressure. So, confining pressure can slightly enhance the strength of the samples and have a certain inhibitory effect on deformation and failure [11; 31]. c and the \(\varphi\) are two important indices for evaluating soil's shear strength that are mainly affected by particle-size composition, arrangement, and cementation [32; 33; 34]. Recurrent FTC and changes in S change these factors, thus affecting soil c and \(\varphi\). According to the experiment data, c and \(\varphi\) of the sample could be obtained, as shown in Table 4. As shown in Figure 3, c and \(\varphi\) were related to FTCs. The exponential function (Equation (1)) could explain the relationship between c and FTC, while the  
Figure 2: Variation of failure principal-stress difference \((\sigma_{1}-\sigma_{3})_{f}\) with FTC: (**a**) \(\sigma_{3}=100\) kPa; (**b**) \(\sigma_{3}=200\) kPa; (**c**) \(\sigma_{3}=300\) kPa. Fourier function could explain the relationship between \(\varphi\) and FTC. The two functions' parameters are shown in Table 5.  
The Fourier function is as follows:  
\[y=\text{A}_{2}+\text{B}_{2}*\cos(\text{B}_{2}*x)+\text{C}_{2}*\sin(\text{D}_{2}* x), \tag{2}\]  
where \(x\) is the number of FTCs the samples underwent, and A\({}_{2}\), B\({}_{2}\), C\({}_{2}\), and D\({}_{2}\) are the fitting parameters.