## 3 Uniaxial Compressive Constitutive Equation Establishment
### Applicability of the Modified Constitutive Equation
The results of the curve shape parameter calculation are shown in Table 7. The fitting curves with the largest and smallest R\({}^{2}\) in this study and typical literature are shown in Figure 13. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen Source**} & \multirow{2}{*}{**Region**} & \multirow{2}{*}{**Specimen Working Condition**} & \multicolumn{4}{c}{**Rising Section**} & \multicolumn{4}{c}{**Descending Section**} \\  & & & \(\mathbf{a_{1}}\) & \(\mathbf{b_{1}}\) & \(\mathbf{R^{2}}\) & \(\mathbf{a_{2}}\) & \(\mathbf{b_{2}}\) & \(\mathbf{c_{2}}\) & \(\mathbf{R^{2}}\) \\ \hline This test & Xinjiang & L\({}_{100}\)-28-0.2 & 0.274 & 2.363 & 0.995 & \(-\)2.505 & 8.808 & \(-\)7.013 & 0.895 \\ This test & Xinjiang & L\({}_{100}\)-28-1.0 & 0.219 & 2.332 & 0.997 & \(-\)2.010 & 7.056 & \(-\)5.190 & 0.927 \\ This test & Xinjiang & L\({}_{100}\)-28-3.0 & 0.271 & 2.319 & 0.983 & \(-\)2.204 & 7.476 & \(-\)0.506 & 0.911 \\
[38] & Shanxi & L\({}_{100}\)-28-3.0 & 0.308 & 2.302 & 0.998 & \(-\)2.850 & 9.199 & \(-\)6.845 & 0.919 \\
[34] & Shanxi & L\({}_{100}\)-28-2.0 & 0.374 & 2.208 & 0.993 & \(-\)2.801 & 10.463 & \(-\)9.125 & 0.863 \\
[34] & Xinjiang & L\({}_{100}\)-28-2.0 & 0.302 & 2.181 & 0.991 & \(-\)2.701 & 9.341 & \(-\)7.403 & 0.949 \\
[34] & Fujian & L\({}_{100}\)-28-2.0 & \(-\)0.110 & 3.193 & 0.995 & \(-\)1.720 & \(-\)7.506 & \(-\)6.495 & 0.902 \\
[34] & Heilongjiang & L\({}_{100}\)-28-2.0 & 0.250 & 2.660 & 0.984 & \(-\)2.010 & 8.402 & \(-\)7.378 & 0.788 \\
[36] & Shanxi & L\({}_{100}\)-28-3.0 & 0.402 & 2.021 & 0.994 & \(-\)2.303 & 8.768 & \(-\)7.406 & 0.873 \\
[36] & Shanxi & L\({}_{100}\)-28-1.0 & 0.201 & 2.271 & 0.986 & \(-\)2.340 & 10.493 & \(-\)10.228 & 0.841 \\
[39] & Shanxi & L\({}_{100}\)-28-0.5 & 0.330 & 2.036 & 0.987 & \(-\)2.520 & 9.436 & \(-\)7.693 & 0.834 \\
[39] & Shanxi & L\({}_{100}\)-28-1.0 & 0.420 & 1.691 & 0.983 & \(-\)2.901 & 9.938 & \(-\)7.693 & 0.929 \\
[39] & Shanxi & L\({}_{100}\)-28-5.0 & 0.302 & 2.278 & 0.993 & \(-\)2.746 & 9.523 & \(-\)7.811 & 0.925 \\
[39] & Shanxi & L\({}_{100}\)-28-7.0 & 0.346 & 2.150 & 0.996 & \(-\)2.784 & 10.096 & \(-\)8.549 & 0.846 \\ \hline \hline \end{tabular} Note: L\({}_{100}\)-28-0.2 (0.5, 1.0, 2.0, 3.0, 5.0, 7.0) m represents the cube specimens with side length of 100 mm. The curing age is 28 days, and the loading rate is 0.2 (0.5, 1.0, 2.0, 3.0, 5.0, 7.0) mm-min\({}^{-1}\).  
\end{table} 
Table 7: Fitting parameters of constitutive equation of different earth specimens. Figure 12: Summary of the original uniaxial compressive stress-strain curves in the related literature: (**a**) Earth from Xinjiang; (**b**) Earth from Shanxi; (**c**) Earth from Fujian; and (**d**) Earth from Heilongjiang. The following patterns can be observed in Table 7 and Figure 13:
* There are certain differences in the values of the parameters of the shape of the constitutive equation curves of the standard specimens in different regions. At the same loading rate, the best-fitting results of the constitutive equation were obtained for the soil in Xinjiang. The R\({}^{2}\) of the ascending section is 0.991, and the R\({}^{2}\) of the descending section is 0.949. The fitting effect of the constitutive equation for the soil in Heilongjiang is relatively lower. The reason for this is that the earth material in Heilongjiang is mainly black soil, which contains more humus [40], further aggravating the inhomogeneity of the earth material. Considering that soils containing humus are not suitable for use in building structures and that the agricultural value of black soil is greater than the value of building materials, the use of black soil as a building material is not recommended. * The present constitutive equation is a good fit for the rising section of the uniaxial compression test curve, and the descending section is relatively slightly lower. Take the Heilongjiang test data, where the fit is weakest, as an example. The R\({}^{2}\) of the ascending section is 0.983, and the R\({}^{2}\) of the descending section is 0.788.