# A Modified Bearing Capacity Model for Inclined Shallow Anchor Cable with Experimental Verification
## 5 Conclusions and Discussion  
In this study, a bearing capacity calculation formula was derived based on the common failure mode of shallow-embedded anchors, specifically the inverted cone failure mechanism, with consideration of the anchor inclination angle. To validate the proposed formula, a series of indoor pull-out tests were conducted on anchors with varying inclination angles. The experimental results were compared with the calculated values from the formula, showing good agreement. Furthermore, the formula was compared with previous research to ensure its accuracy and reliability. The key conclusions drawn from this study are as follows:  
1. Under conditions of constant burial depth and anchoring length, as the inclination angle increases, the horizontal component of the force acting on the anchor cable decreases, leading to a gradual reduction in the ultimate bearing capacity of the anchor cable. Additionally, the maximum failure diameter (\(b\)) decreases with the increase in inclination angle, and the magnitude of this decrease diminishes as the angle increases;
2. The failure modes obtained from the pull-out of anchor cables at different angles all presented as an asymmetrical \"inverted trumpet shape. The failure angle at the loading end (\(\beta_{2}\)) increased with the increase in the anchor cable tilt angle, approximately 0.6 times the anchoring angle, the peak angle of failure (\(\theta\)) decreased as the tilt angle of the anchor cable increased, while the failure angle (\(\beta_{1}\)) away from the loading end did not change significantly with the increase in the anchoring angle, and remained relatively stable at around 54\({}^{\circ}\). 3. The results indicate that the maximum deviation between the values calculated using the proposed model and the experiments reported in the literature ([PERSON] (1978) [34], [PERSON] (1970) [35], and [PERSON] (1973) [36]) is approximately 17%. This level of discrepancy falls within the acceptable range for engineering applications, demonstrating the reliability of the proposed model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Reference**} & \multirow{2}{*}{\begin{tabular}{c} **Internal** \\ **Friction Angle,** \\ **\(\varphi\) (\({}^{\circ}\))** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Buried Depth,** \\ **\(h_{\mathbf{a}}\) **(m)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Cohesion, \(c\)** \\ **(kPa)** \\ \end{tabular} } & \multicolumn{2}{c}{**Bearing Capacity (kN)**} & \multirow{2}{*}{**Error (\%)**} \\ \cline{4-4} \cline{6-7}  & & & & & **Experiment** & **Projected Value** \\ \cline{4-4} \cline{6-7}  & & & & **Literature** & **Model** & \\ \hline [PERSON] (1978) [34] & 30 & 5 & 20 & 850–950 & 911.44 & 7.2 \\ [PERSON] (1970) [35] & 35 & 6 & 15 & 1200–1300 & 1250.56 & 4.2 \\ [PERSON] (1973) [36] & 30 & 5 & 15 & 900–1100 & 911.44 & 17.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results comparison. These results indicate that the inclination of the anchor cable has a more significant effect on the bearing capacity. Therefore, in order to accurately predict the bearing capacity of an anchor cable, the effect of its inclination must be considered in addition to its burial depth and anchorage length. However, these results were obtained under limited experimental conditions (only one soil condition was considered in the experiment). Further laboratory tests are needed in the future to consider more characteristics of anchor cable bearing in different soil conditions, making it suitable for a wider range of engineering applications. Conceptualization, L.D. and T.C. ; methodology, Z.-Z., L.D. and T.C. ; formal analysis, investigation, resources, G.X., L.D. and T.C. ; validation, analysis, data curation, investigation, resources, data curation, and writing--original draft preparation, G.X. ; writing--review and editing, Z.Z., G.X., L.D., T.C., B.X., M.C. and J.Y. ; visualization, L.D., T.C., J.Y., M.C. and B.X. ; supervision, Z.Z., L.D. and T.C. ; project administration, Z.Z., L.D.