## 2 Structured Cam Clay Model  
The SCC model [37] involves only a few conveniently identified parameters; however, it is still capable of capturing the destructuration of natural soils, including the structure degradation and crushing [38]. According to the fact that the voids ratio of naturally structured soils \(e\) is larger than that of the corresponding reconstituted soils \(e^{*}\) at the same stress state [39], the isotropic compression behavior of structured soils in the SCC model is idealized, as shown in Figure 1, and the decrease of \(\Delta e\) (the difference between \(e\) and \(e^{*}\)represents the destructuration of soils. For isotropic compression virgin yield (\(p^{\prime}>p^{\prime}_{yi}\)), the additional voids ratio \(\Delta e\) of structured soils can be given by [37]  
\[\Delta e=(\Delta e_{i}-c)\left(\frac{p^{\prime}_{yi}}{p^{\prime}}\right)^{b}+c \tag{1}\]  
where \(p^{\prime}\) is the current mean effective stress, \(p^{\prime}_{yi}\) is the initial yield stress of structured soils under isotropic compression, and \(b\) is the isotropic compression destructuring index. \(\Delta e_{i}\) is the value of \(\Delta e\) at \(p^{\prime}=p^{\prime}_{yi}\), and \(c\) is a stable value of \(\Delta e\) when \(p^{\prime}\) is sufficiently large. As a Cam Clay model, it is assumed that the yield surface of structured soils in the \(p^{\prime}-q\) plane is elliptical, as shown in Figure 2, which is larger than that of the corresponding reconstituted soils, and can be formulated as [37]  
\[f=q^{2}-M^{2}p^{\prime}\left(p^{\prime}_{s}-p^{\prime}\right)=0 \tag{2}\]  
where \(M\), named the critical state stress ratio, represents the slope of the critical state line (CSL), \(q\) is the deviator stress that follows its standard three-dimensional definition in this study, and \(p^{\prime}_{s}\) is the isotropic yield stress denoting the size of the yield surface. Figure 1: Conceptual model of soil responses under isotropic compression. Figure 2: Yield surfaces of the structured Cam Clay soil. The initial yield surface of structured soils enlarges with the increase of structure, as shown in Figure 2. The equivalent yield surface for structured soils, i.e., the dashed line in Figure 2, is defined as a yield surface for the soils remolded with the same voids ratio and stress state [37]. The size of the equivalent yield surface is denoted by \(p^{\prime}_{e}\), whose value can be determined by the states (\(p^{\prime}\) and \(e\)) of structured soils, as follows:  
\[p^{\prime}_{e}=\exp\left(\frac{e^{*}_{IC}-e-\kappa\ln p^{\prime}}{\lambda- \kappa}\right) \tag{3}\]  
where \(e^{*}_{IC}\) is the voids ratio for reconstituted soils when \(p^{\prime}=1\) kPa, as shown in Figure 1. \(\lambda\) and \(\kappa\) denote the slopes of the compression and loading-reloading lines of the reconstituted soils, respectively. When the stress state reaches the structural yield surface with \(dp^{\prime}_{s}\
eq 0\), virgin yielding occurs and is accompanied by the destructuration, which is an irreversible process. Considering the contribution of shearing on the destructuration of soils, the plastic volumetric strain increment can be described as  
\[de^{p}_{v}=\left[\lambda-\kappa+b\left(\langle\Delta e-c\rangle+\frac{\gamma \eta\Delta e}{M-\eta}\right)\right]\frac{dp^{\prime}_{s}}{(1+e)p^{\prime}_{s}} \tag{4}\]  
where \(\eta=q/p^{\prime}\) is the stress ratio, \(\gamma\) is the shearing destructuring index, and \(<\,>\) is the Macaulay bracket. Additionally, it was observed that the flow rule, the strain increment ratio \(de^{p}_{d}/de^{p}_{v}\), is also significantly affected by the soil structure [40]. The non-associated flow rules, defining the yield surface as inconsistent with the plastic potential surface, are employed in the SCC model to incorporate the influences of structure.