## 3 Stability of Bentonite Slurry with Stratum C3
### Discussion of Calculation Results  
Firstly, the slurry trench models were built and analysed by FLAC2D v. 7.0, RS2 v. 11.0, and at a trench length of 6 m in 3D (FLAC3D v. 7.0, RS3 v. 4.0). The results demonstrate agreement between FLAC2D v. 7.0 and RS2 v. 11.0, and between FLAC3D v. 7.0 and RS3 v. 4.0, as depicted in Table 2 and Figures 5-8. In the case of temporary support with 10.5 kN/m\({}^{3}\) bentonite slurry and no surcharge load on the ground surface, the factors of safety (as analysed by RS2 v. 11.0 and FLAC2D v. 7.0) range from 1.26 to 1.32. However, with a surcharge load of 10.0 kPa on the ground surface under the same conditions, the factors of safety decrease and stabilise at values ranging from 1.148 to 1.19. Figure 6: The failure mode of trenches in FLAC 2D/3D and RS2/3 for the case of \(\gamma\)s = 10.5 kN/m\({}^{3}\) slurry and surcharge load of 10.0 kPa on the ground surface. Figure 7: The failure mode of trenches in FLAC 2D/3D and RS2/3 for the case of \(\gamma\)s = 12.0 kN/m\({}^{3}\) slurry and no surcharge load on the ground surface. Turning to the case of temporary support with \(\gamma_{\rm s}=12\) kN/m\({}^{3}\) bentonite slurry and no surcharge load on the ground surface, RS2 v. 11.0 and FLAC2D v. 7.0 estimate the factor of safety to range from 1.74 to 1.80. However, with an evenly distributed surcharge load of 10.0 kPa, the factor of safety remains between 1.456 and 1.540. After analysing the slurry trench with a length of 6 m in 3D, FLAC3D v. 7.0 and RS3 v. 4.0 were also used to conduct stability analysis with an extension of the trench length from 6 m to 54 m. The results show that initially, at a length of 6 m, the factor of safety in 3D is higher than in 2D by an average of 57.8% (Table 1, Figures 5-8). Figures 9 and 10 depict the critical slip surfaces identified, respectively, by FLAC and RS in both 2D and 3D configurations for the case of slurry \(\gamma_{\rm s}=10.5\) kN/m\({}^{3}\) (Figure 9) and 12.0 kN/m\({}^{3}\) (Figure 10). Slight differences in the localisation of slip surfaces obtained from both programs are visible. However, as the trench length increases, the factor of safety gradually decreases until, at a length of 54 m, the factors of safety for both 3D and 2D configurations are almost equal. The limit equilibrium method (LEM) of Bell-Washbourne was also applied to calculate the stability, as mentioned in Section 2.2. After obtaining the stability results using the Bell-Washbourne method, a comparison was made between the Bell-Washbourne method and the numerical one (FLAC, RS). It was observed that the shape of the slip wedge differed between the Bell-Washbourne method and FLAC3D v. 7.0, RS3 v. 4.0, as shown in Figures 11 and 12. The differences are most significant near the narrower edge of the trench. The shape of the slip surface resulting from the Bell-Washbourne method is solely a function of the internal friction angle, and it represents the flat plane close to the narrower end of the trench. The slip surface determined by the SSR method, as a function of the simultaneous reduction of friction and cohesion, is more curved. Figure 8: The failure mode of trenches in FLAC 2D/3D and RS2/3 for the case of \(\gamma_{\rm s}=12.0\) kN/m\({}^{3}\) slurry and surcharge load of 10.0 kPa on the ground surface. Figure 10: Critical slip surfaces identified by FLSC and RS for the case of slurry \(\gamma\)s = 12.0 kN/m\({}^{3}\). Figure 9: Critical slip surfaces identified by FLSC and RS for the case of slurry \(\gamma\)s = 10.5 kN/m\({}^{3}\). The results obtained using FLAC and RS programs were 1.1 to 1.4 times higher than those calculated using the Bell-Washbourne method (Figures 13-16). Figure 11: Shape of a slip wedge for a deep trench (Length < 2 Depth). Figure 12: Shape of a slip wedge for a shallow trench (Length > 2 Depth). Figure 13: Variation in FS with trench length using different analysis methods such as FLAC2D, RS2, Bell–Washbourne-2D, RS3, FLAC3D, Slide 3 (Bishop) and Bell–Washbourne-3D for stratum C3 and \(\gamma\)s = 10.5 kN/m\({}^{3}\).