## 4 Discussion
### Temperature-Induced Stress  
The development of cracks in the CMS reflects the soil sample affected by temperature. From Figure 12, we observed six prominent cracks on the sample surface for the temperature setting of 0 \({}^{\circ}\)C. At 35 \({}^{\circ}\)C, cracks began to develop and penetrate the soil, thereby generating a small number of tiny cracks. The sample surface exhibited increased fragmentation due to fissures. At 70 \({}^{\circ}\)C, the primary cracks on the surface were connected, and the soil particles at the crack edges were dissolved. The cracks became blurred and more tiny cracks were formed. Here, we focused on the prominent cracks in the C-M-S samples at different temperatures. However, the smaller fissures gradually increased with increasing temperature. Thus, we could conclude that the temperature effected the soil pore structure mainly in the form of smaller-cracks development.  
Next, to explore the reason for the temperature's cracking of soil samples, we analyzed the thermal stress of the C-M-S sample. As per thermodynamic principles, thermal expansion of the soil constrains the generated thermal stress. Soil expansion and stress are caused by changes in temperature. The temperature-induced stress could be obtained as follows [45]:  
\[\sigma_{X(Y)}=\frac{\alpha E}{1-\mu}\biggl{[}-T(Z)+\frac{1}{L-0.01}\int_{0.01} ^{L}T(Z)dZ\biggr{]} \tag{13}\]  
where \(\alpha\) denotes the thermal expansion coefficient of the CMS (\(\alpha=0.5\times 10^{-6}\)/\({}^{\circ}\)C), \(E\) the Young's modulus (\(E=2\times 10^{6}\) Pa), \(\mu\) is the Poisson's ratio (\(\
u=0.25\)), and \(L\) is the radius of CMS sample, \(T(Z)\) is the distribution of temperature along the \(Z\)-axis.  
The distribution of temperature along the \(Z\)-axis could be obtained as follows [41]:  
\[T(Z)=T_{0}\biggl{[}1-\frac{Z^{2}}{m}\biggr{]} \tag{14}\]  
where \(T_{0}\) denotes the temperature at the surface andm the temperature-distribution coefficient.  
When \(Z=0.01\) m, \(T(Z)=35\), and when \(Z=\)0.0 4 m, \(T(Z)=70\). Substituting these boundary conditions into Equation (14), we could calculate the distribution of temperature along the \(X\)-axis as follows:  
\[T(Z)=32.67\Bigl{[}1+714.28Z^{2}\Bigr{]} \tag{15}\]  
\[\sigma_{X(Y)}=\frac{4}{3}\Bigl{[}47335.53Z^{2}-32.66\Bigr{]} \tag{16}\]  
Figure 12: Crack generation in C-M-S samples at different temperatures after three dry–wet cycles: (a) T = 0 \({}^{\circ}\)C, (b) T = 35 \({}^{\circ}\)C, (c) T = 70 \({}^{\circ}\)C.  
From Equations (15) and (16), we could infer that the temperature-induced stress distribution along the X-direction. Figure 13 depicts the temperature-induced stress distribution along the X-direction, plotted as per Equation (16), wherein we noted that the temperature decreases with increase of the internal depth of the sample. The compressive stress at the inner center had a maximum value of 0.44 Mpa, whereas the temperature-induced tensile stress at the outer boundary had a maximum value of 0.57 Mpa. The zero-stress point was located at \(Z=0.015\) m, which corresponded to the transition point between compressive and tensile stress. It could be observed that when \(Z\in(0.015,\ 0.04)\), if the stress is greater than the tensile strength, cracks occur and develop. The tensile stress on the surface of the sample was relatively large, which explained the surface-crack increase after each dry-wet cycle and high-temperature exposure.