# A Modified Bearing Capacity Model for Inclined Shallow Anchor Cable with Experimental Verification
## 3 Validation by Model Experiment
### Experimental Result
To analyze the characteristics of the failure surfaces in greater detail, the failure surfaces for anchors at different inclination angles were treated geometrically; the surface's endpoint farthest from the borehole was designated as point A, the endpoint nearest to the borehole as point B, and the internal apex of the failure zone as point C, with the geometric center of the failure surface marked as point O. Lines AB, AC, and BC were connected to form a triangular representation of the failure zone, where AC was taken as \(b\), \(\angle BAC\) as \(\beta_{1}\), \(\angle ACB\) as \(\beta_{2}\), and \(\angle ABC\) as \(\theta\). These geometric connections approximate the failure surface as an inverted conical shape with quantifiable dimensions. From Figure 5, it is evident that with increasing inclination angle, the failure angle \(\beta_{2}\) gradually increases, highlighting the effect of inclination on the failure mechanism. Furthermore, to better understand the influence of anchor cable inclination on failure surface characteristics, statistical analyses of these geometrical parameters were performed across different inclination angles. The results of these analyses are presented in Figure 6, providing quantitative insights into the relationship between inclination and failure surface geometry. As illustrated in Figure 6a, the maximum failure diameter of the anchor cable (b) gradually decreased with increasing anchor inclination. Under constant burial depth and anchoring length, the horizontal component of the axial tensile force of the anchor cable diminished as the inclination angle increased, thereby reducing its influence range. Figure 7b shows that as the inclination angle of the anchor cable increases, the failure angle at the loading end (\(\beta_{2}\)) also increases, to approximately 0.6 times the anchor inclination of the anchor cable. Conversely, the vertex failure angle (\(\theta\)) decreases with increasing inclination angle. In contrast, the failure angle away from the loading end (\(\beta_{1}\)) did not exhibit significant variation with increasing anchoring angle, remaining relatively stable at around 54\({}^{\circ}\), which is consistent with the findings of [PERSON] [34]. Figure 6: Schematic diagram of failure model: (**a**) three-dimensional failure model; (**b**) cross-sectional view at a 30\({}^{\circ}\) inclination; (**c**) cross-sectional view at a 40\({}^{\circ}\) inclination; (**d**) cross-sectional view at a 50\({}^{\circ}\) inclination; (**e**) cross-sectional view at a 60\({}^{\circ}\) inclination; (**f**) cross-sectional view at a 70\({}^{\circ}\) inclination. Figure 7: Influence of inclination anchor cable on the geometric parameters of the failure surface: (**a**) maximum failure diameter; (**b**) failure angle. Figure 8 illustrates that as the inclination angle of the anchor cable increases, the bearing capacity gradually decreases. This trend is corroborated by both experimental and theoretical values, highlighting the significant impact of inclination on the performance of anchor cables under the same conditions. With a fixed burial depth and anchoring length, the increase in inclination angle results in a reduction in the horizontal component, which directly affects the frictional force between the anchor and the surrounding soil. The decrease in friction implies a weakened resistance to pull-out, consequently leading to a reduction in bearing capacity. The discrepancy observed at higher angles may be attributed to experimental errors or setup limitations, such as measurement inaccuracies or soil heterogeneity. However, this does not imply that the error increases with higher angles. The strong consistency between theoretical and experimental values, with a maximum error of around 10%, indicates that the theoretical model used provides a reliable basis for the design and calculation of anchor cables.