## 2 Analytical Method
### Analytical Method for the Strength Parameters of Gas Hydrate-Bearing Sediments  
Mohr-Coulomb (M-C) strength criterion is always used to describe the strength property of gas hydrate-bearing sediments; therefore, cohesion (\(c\)) and the internal friction angle (\(\varphi\)) are two important strength parameters [23; 36]. As a widely accepted yielding parameter, plastic shear strain (\(\gamma^{\mathrm{P}}\)) [32; 33; 34; 36] is adopted here to investigate the evolution of strength parameters during the yielding process. A common approach to calculating plastic shear strain is shown in the following equation [26; 38]:  
\[\gamma^{\mathrm{P}}=\epsilon_{1}^{\mathrm{P}}-\epsilon_{3}^{\mathrm{P}} \tag{1}\]  
where \(\epsilon_{1}^{\mathrm{P}}\) and \(\epsilon_{3}^{\mathrm{P}}\) are the axial and lateral plastic strain measured in the triaxial compression experiments, respectively. By conducting cyclic loading-unloading tests, plastic strain can usually be obtained according to the irreversible strain in each cycle. However, there should be a lot of cycles for recording a detailed evolution process with increasing plastic strain, and it is not easy to carry out a series of tests with so many cycles. Hence, a simplified method is used extensively in many research studies by assuming a series of unloading stress-strain curves with a certain unloading modulus in every cycle [34; 38; 41; 42]. It should be noted that the unloading modulus indicates the slope of the unloading stress-strain curve. In this way, at any post-yielding stress level, the irreversible plastic strain can be calculated. This method will be introduced in more detail in Figure 1 as follows:  
1. Identifying the yielding stress. According to the stress-strain curve under triaxial compression, the elastic stage of GHBS samples is not as obvious as that of rock samples. In this study, the yielding stress is defined as the stress level at which the axial strain reaches 0.2% (i.e., \(\sigma_{0.2}^{\prime}\), as shown in Figure 1). The period before this stress level is considered as the elastic stage, and the secant modulus based on \(\sigma_{0.2}^{\prime}\) is adopted to define the initial modulus. 2. Identifying the plastic strain for each cycle. For each stress level \(\sigma_{1,i}^{\prime}\) at the post-yielding stage, a line can be drawn with the tangent value equal to the unloading modulus, and the plastic axial strain \(\epsilon_{1,i}^{\mathrm{P}}\) can be obtained. In the research on rock samples, the unloading modulus is usually considered to be equal to the initial modulus [26; 34; 36; 38]. Nevertheless, it is found that the unloading modulus is about 4-8 times the initial modulus for the GHBS samples [23]. So, the unloading modulus should be identified according to the tested properties of the GHBS samples. In a similar way, the lateral plastic strain \(\epsilon_{3,i}^{\mathrm{P}}\) can also be identified for each stress level \(\sigma_{1,i}^{\prime}\)  
Figure 1: Sketch of the method for determining plastic strains at the corresponding stress levels. For each stress level \(\sigma^{\prime}_{1,i^{\prime}}\), the plastic shear strain \(\gamma^{\mathrm{P}}_{i}\) can be calculated by \(\left(\dot{e}^{\mathrm{P}}_{1,i}-\dot{e}^{\mathrm{P}}_{3,i}\right)\) based on Equation (1). Thereafter, a series of stress levels \(\sigma^{\prime}_{1}\) can be obtained with increasing plastic shear strain \(\gamma^{\mathrm{P}}\) at different effective confining pressures \(\sigma^{\prime}_{3}\).