## 4 Results and Discussion
### Stress Path for a Soil Element around the Cavity  
For the soil element located at any position around the cavity, the same effective stress path (ESP) in \(p^{\prime}\)-q plane is followed; therefore, only the ESP for a soil element at the cavity wall is analyzed. The ESPs for \(R=1\), \(1.2\), \(3\), and \(10\) are plotted in Figure 13, respectively. In these figures, points \(A\), \(B\), \(C\), and \(D\) denote four stress variation points, i.e., the initial stress point (\(p_{0}\), \(q_{0}\)), the initial yield stress point, the crushing beginning point, and the final critical state point, respectively. The \(B\), \(B^{\prime}\), and \(B^{\prime\prime}\) were used to distinguish the initial yield stresses for \(R_{s}=1.0\), \(1.2\), and \(1.5\), respectively. Note that the comparisons of ESPs between the present solution and Chen and Abousleiman's solution [22] were shown by comparing the case of \(R_{s}=1.0\) with that of \(R_{s}=1.2\) and \(1.5\).  
Figure 12: Influences of initial structure and destructuration on the distributions of \(p^{\prime}\), \(q\) and \(\Delta u\) around the cavity: (**a**) \(R=1\); (**b**) \(R=1.2\); (**c**) \(R=3\); (**d**) \(R=10\).  
From Figure 13, it is clear that the initial yield surface and yield stress increase as \(R_{s}\) increases. During the elastic deformation, the ESPs follow the vertical line until the stress state reaches the initial yield stress point \(B\), \(B^{\prime}\), or \(B^{\prime\prime}\), except for the ESP for \(R=1\) with \(R_{s}=1.0\). Thereafter, the ESPs turn left or right with the development of plastic deformation, which depends on whether the soils experience hardening (the stress ratio at \(B\), \(B^{\prime}\), or \(B^{\prime\prime}\) is smaller than \(M\)) or softening (the stress ratio at \(B\), \(B^{\prime}\), or \(B^{\prime\prime}\) is larger than \(M\)).  
For \(R_{s}=1.0\), the ESPs go monotonously to the left or right after the initial yielding, until the final critical state point \(D\) is reached. For \(R_{s}=1.2\) and \(1.5\), the ESPs turn left and reach the point \(C^{\prime}\) or \(C^{\prime\prime}\) when hardening occurs, and then travel along the CSL, owing to the structure crushing, until reaching the final critical state point \(D\), as shown in Figure 11a,b. In contrast, the ESPs turn right and move toward the critical line when softening occurs, and then change their directions and travel downwards until they reach point \(D\), as shown in Figure 13c,d. That the same point \(D\) is reached for the soils with different \(R_{s}\) indicates that the final critical state is irrespective of the initial structure, although it has significant influences on the ESPs, which can also be found in the shearing test results of structured soils [37]. In addition, it can be seen from Figure 13b that because of the 'false' over-consolidated behavior of structured soils, the slightly over-consolidated soils with \(R=1.2\) exhibit partial characteristics of the heavily over-consolidated soils when the \(R_{s}\) increases to \(1.5\), namely, the initial yield stress point \(B^{\prime\prime}\) was located at the left side of CSL, as shown in Figure 13b.  
Figure 13: Effective stress paths for the structured and the corresponding reconstituted soils: (**a**) \(R=1\); (**b**) \(R=1.2\); (**c**) \(R=3\); (**d**) \(R=10\).