## 3 Evolution Characteristics of the Strength Parameters of Gas Hydrate-Bearing Sediments  
In order to calculate the values of strength parameters (\(c\) and \(\varphi\)) during the yielding process with the method introduced in Section 2, the unloading modulus for the stress-strain curves should be identified first. By conducting a series of cyclic loading-unloading experiments on GHBS samples with Toyoura sand, [PERSON] et al. [23] found that the unloading modulus is not constant at different cycles; however, the change is not significant compared with the variation affected by hydrate saturation. Hence, the unloading modulus can be considered as a constant value at different plastic strains for the samples with the same hydrate saturation. Based on a linear fitting of the data of the unloading modulus reported in [23], the unloading modulus can be obtained as 1.2, 2.4, and 3.0 GPa for the samples with the hydrate saturations \(s_{\mathrm{h}}=0\%\), 27-34%, and 41-45%, respectively. Nonetheless, the unloading-reloading curves for the lateral strain were not analyzed in reference [23]. In this study, we assume that the ratios between the unloading modulus and the initial modulus are the same for both the axial stress-axial strain and axial stress-lateral strain curves. Consequently, the unloading modulus for the axial stress-lateral strain curves can be calculated as \(-14.4\), \(-20.3\), and \(-30.1\) GPa for the samples with the hydrate saturation \(s_{\mathrm{h}}=0\%\), 27-34%, and 41-45%, respectively. Thereafter, plastic shear strain can be calculated at any stress level according to the method introduced in Section 2. A series of strength parameters (\(c\) and \(\varphi\)) can be obtained and plotted as the scattered data points in Figure 2 with the increasing plastic shear strain \(\gamma^{\mathrm{P}}\) based on Equation (2). The evolution characteristics of strength parameters (\(c\) and \(\varphi\)) can be concluded as follows:1. It can be observed that cohesion (\(c\)) increases quickly to a peak value and then decreases gradually to a residual value for the samples with different hydrate saturations (Figure 2a). Comparatively, previous studies show that only a decrease in cohesion (\(c\)) occurs for the rock samples [25, 27, 29, 30, 31]. The increasing stage should correspond to the compaction of the particles in the GHBS samples at the early stage of compression. The compaction was reported in [15] by analyzing the volumetric strain, while this behavior is not obvious in most rock samples. As the loading continues, dilatant behavior starts to occur [15], and cohesion (\(c\)) begins to drop. 2. The samples with higher hydrate saturations have higher initial values, peak values, and residual values of cohesion (\(c\)) (Figure 2a). This is probably due to the cementation effect of hydrate between sand grains [15]. However, cohesion (\(c\)) drops more significantly after the peak value for the samples with higher hydrate saturations, and this phenomenon is probably the result of a more significant degradation of the cementation effect during the dilatant stage of the samples with higher hydrate saturations. 3. The internal friction angle (\(\varphi\)) increases quickly with increasing plastic shear strain and then becomes stable at a residual value for all the samples with different hydrate saturations (Figure 2b). The increase in \(\varphi\) should be due to the enhanced friction effect between the particles led by the compaction of the specimens. 4. For the plastic shear strain between 0 and 4%, the values of \(\varphi\) are very close for the samples with various hydrate saturations. When the plastic shear strain is higher than 4%, the samples with higher hydrate saturations have higher internal friction angles (\(\varphi\)) during the whole test process with increasing plastic shear strain (Figure 2b). This indicates that the existence of hydrate supplies more friction effect between the particles.