## 3 Test Results and Analysis
### Conventional Triaxial Compression Strength
#### 3.2.3 The Nonlinear Characteristics of the Shear Strength of Gravel Soil  
Typically, the stress path of gravel soil under different confining pressures is represented by the changes in stress on the maximum shear stress plane \((p^{\prime},q)\). The maximum shear stress plane stress is determined according to Equations (2) and (3). \[p^{\prime}=(\sigma_{1}+\sigma_{3})/2 \tag{2}\]  
\[q=(\sigma_{1}-\sigma_{3})/2 \tag{3}\]  
where \(\sigma_{1}\) and \(\sigma_{3}\) represent the axial stress and confining pressure, respectively. Due to the inability of conventional triaxial compression tests to determine the shear stress and normal stress in the shear plane for gravel soils, the relationship between the stress \((p^{\prime},q)\) in the maximum shear stress plane at different confining pressures is described by a power function (Equation (4)) as proposed in reference [23]. \[\frac{q}{p_{\text{a}}}=A\left(\frac{p^{\prime}}{p_{\text{a}}}\right)^{B} \tag{4}\]  
where \(p_{\text{a}}\) is the atmospheric pressure, set at 101.3 kPa; A and B are constants of the function. However, the actual shear strength of gravel soil exhibits nonlinearity, making the Mohr-Coulomb criterion inappropriate. Therefore, the strength envelope is represented by the tangent to the appropriate points on the power function curve, as shown in Figure 7.  
Using Equation (4), with \(p^{\prime}/p_{\text{a}}\) as the horizontal coordinate and \(q/p_{\text{a}}\) as the vertical coordinate, the values of \((p^{\prime}/p_{\text{a}},q/p_{\text{a}})\) at different confining pressures can be obtained from the stress-strain curve of the gravel soil, as shown in Figure 8.  
Figure 7: Mohr–Coulomb quasi-measurement envelope and true intensity envelope. From Figure 8, the tangent slope and intercept of a given fitted curve can be determined. The actual shear strength parameters can then be calculated using Equations (5) and (6). \[k^{\prime}=\sin\varphi_{\rm c} \tag{5}\]  
\[p_{\rm a}a^{\prime}=C_{\rm c}\cos\varphi_{\rm c} \tag{6}\]  
where \(k^{\prime}\) and \(a^{\prime}\) are the tangent slope and intercept of the power function fit curve at a given confining pressure, while \(C_{\rm c}\) and \(\varphi_{\rm c}\) are the true cohesion and internal friction angles of the gravel soil, respectively. The results of the calculations using Equation (2) to Equation (6) are shown in Table 6. It can be seen that \(R^{2}\) is greater than 0.9, indicating a high degree of curve fitting. The true cohesion and angle of friction of the stabilized gravel soil were calculated using Equations (5) and (6) as shown in Figure 9. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Sample**} & \multicolumn{2}{c}{**Confining**} & \multirow{2}{*}{\(k^{\prime}\)} & \multirow{2}{*}{\(a^{\prime}\)} & \multirow{2}{*}{\(R^{2}\)} & \multirow{2}{*}{\(C_{\rm c}\)/(kPa)} & \multirow{2}{*}{\(\varphi_{\rm c}\)/\(\varsigma\)} \\  & **Pressure/(kPa)** & & & & & \\ \hline \multirow{4}{*}{Natural soil} & 100 & 0.495 & 0.300 & & 34.97 & 29.68 \\  & 200 & 0.500 & 0.402 & 0.999 & 47.05 & 30.07 \\  & 300 & 0.520 & 0.541 & & 64.14 & 31.32 \\ \hline \multirow{4}{*}{2\% Xanthan gum} & 100 & 0.503 & 0.551 & & 64.57 & 28.29 \\  & 200 & 0.519 & 0.630 & 0.980 & 74.68 & 31.30 \\  & 300 & 0.540 & 0.727 & & 87.53 & 32.73 \\ \hline \multirow{4}{*}{4\% Xanthan gum} & 100 & 0.529 & 0.577 & & 68.90 & 31.97 \\  & 200 & 0.540 & 0.660 & 0.992 & 79.49 & 32.76 \\  & 300 & 0.557 & 0.770 & & 93.95 & 33.90 \\ \hline \multirow{4}{*}{6\% Xanthan gum} & 100 & 0.541 & 0.730 & & 87.92 & 32.77 \\  & 200 & 0.557 & 0.801 & 0.997 & 97.70 & 33.87 \\ \cline{1-1}  & 300 & 0.576 & 0.850 & & 105.37 & 35.21 \\ \hline \end{tabular}
\end{table} 
Table 6: Parameters of shear strength of gravelly soils. Figure 8: Characteristic power function-fitted curves for shear strength of gravelly soils.