# Evaluating Pile-Supported Embankment Considering the Soil Anisotropy Effect
## 4 Soil Arching Considering the Cohesion Anisotropy
### The Stress Distribution in Emhankments Is Influenced by the Anisotropy of Cohesive Force  
In order to study the influence of cohesion anisotropy on the stress distribution in embankments, the distribution of major principal stress and the change of pile-soil stress ratio under different degrees of cohesion anisotropy are analyzed, respectively. Figure 7 shows the vector diagram of the major principal stress of the embankment with different anisotropy coefficients \(k\). It can be seen from the figure that the direction of the major principal stress at the center of the two piles is close to the horizontal direction in the range of 0-1.5 m. At the same height in the embankment, from the center of the two piles to the upper position of the pile top, the major principal stress gradually deflects from the horizontal direction to the vertical direction and points to the pile top. As the anisotropy coefficient decreases, the major principal stress above the pile top decreases, indicating that the anisotropy leads to a decrease in strength, which weakens the horizontal transmission effect of vertical stress. This is consistent with [PERSON] and [PERSON]'s [53] proposal that 'with the application of gravity load, the major principal stress gradually turns to the vertical direction'. In the UMAT subroutine, the cohesive force is stored by the fourteenth state variable (SDV14). Figure 8 shows the anisotropic cohesive force distribution when the embankment model calculation is completed. It can be seen from the figure that the cohesion changes with the direction of the major principal stress. The closer to the center of the two piles, the smaller the cohesion, indicating that the vertical stress at this position is no longer the major principal stress, and the direction of the major principal stress tends to be horizontal. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Anisotropic Coefficient of Cohesion \(k\)**} & \multirow{2}{*}{\(\varphi\) (\({}^{\circ}\))} & \multicolumn{2}{c}{\(c\) (kPa)} \\ \cline{3-4}  & & \(c_{p}\) & \(c_{h}\) \\ \hline
1 & 30 & 5 & 5 \\
0.7 & 30 & 5 & 3.5 \\
0.5 & 30 & 5 & 2.5 \\
0.3 & 30 & 5 & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Anisotropic cohesion research model plan. Figure 6: Variation of the cohesive force in terms of \(i\) for various values of \(k\). When the cohesive force \(c_{p}=5\) kPa, the variation of the pile-soil stress ratio with the differential settlement in the embankment is shown in Figure 9. It can be seen from Figure 9 that with the increase in differential settlement, the pile-soil stress ratio gradually increases. When the differential settlement is less than 38 mm, the pile-soil stress ratio increases significantly. When the differential settlement is greater than 38 mm, the pile-soil stress ratio increases marginally. On the whole, with the increase in anisotropy, the pile-soil stress ratio decreases. It can be seen from the end point of the curve that the increase in anisotropy not only causes the increase in settlement but also leads to the decrease in the pile-soil stress ratio. This is consistent with [PERSON] and [PERSON] [54] 'anisotropic MIT-E3 elastoplastic constitutive model can produce greater vertical displacement'. The pile-soil stress corresponding to different anisotropy coefficients is shown in Figure 10. It can be seen that the pile-soil stress ratio is inversely proportional to the degree of anisotropy. The soil arching effect in the embankment depends on the shear stress in the soil. At this time, the major principal stress of the soil element in the soil arching range is no longer in the vertical direction. The stronger the anisotropy is, the more the cohesion decreases. Therefore, as the anisotropy coefficient decreases, the pile-soil stress ratio decreases gradually. As the anisotropy coefficient decreases from 1 to 0.3, the pile-soil stress ratio decreases from 36.1 to 28.8.