## 4 Conclusions  
This article presented comprehensive stability analysis results for slurry trench walls in 2D and 3D configurations for the real conditions of Hue City (Vietnam). These analyses utilised limit equilibrium methods (Bell-Washbourne and Bishop) and numerical simulations based on the Shear Strength Reduction Technique. The stability and displacement distribution of the slurry trench model were obtained based on predictions from an RS software program (FEM) and an FLAC software program (FDM). A comprehensive series of laboratory tests was also conducted, based on which properties were determined and which individual layer types were identified. The FS values indicated good agreement between RS2 v. 11.0 and FLAC2D v. 7.0, and between RS3 v. 4.0 and FLAC3D v. 7.0. However, there were significant differences when these methods were compared with LEM results from the Bell-Washbourne and Bishop methods. Applying the SSR technique in 3D introduced an appropriate FS value for most cases. The 3D model considers each small element in three dimensions, considering complex geological geometries such as thin layers overlapping, arc-shaped slip surfaces, concave surfaces, etc. This approach is sufficiently realistic in analysis. In 2D, all analyses consider only two dimensions, whereas in 3D all three are considered. This means that, in 2D, the trench is analysed in width \(\times\) depth, while in 3D it is analysed in width \(\times\) length \(\times\) depth. This leads to a difference between 2D and 3D. The result obtained in 2D was equivalent to that in 3D for a certain length dimension, specifically corresponding to a trench length of more than 20-30 m (Figures 13-16). In the LEM of Bell-Washbourne, a simplified method was utilised. This method assumes the sliding mechanism occurs in straight lines rather than in sliding arcs (Figures 11 and 12) for simplicity in stability calculation. This may seem inconsistent with reality since, in reality, the sliding mechanism occurs in the form of a sliding arc. Although 3D analysis may be an effective method, slurry trench design also requires the consideration of flexibility, balancing safety [23], economy and construction conditions. This entails excavating trench panels, typically with a maximum length of 6 m, corresponding to the length of the wall section. This ensures safe and efficient construction and convenient on-site rotation of materials and machinery equipment. Therefore, a length of 6 m for slurry trench panels was chosen. Figure 16: 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 = 12.0 kN/m\({}^{3}\) and surcharge load 10 kPa. The factor of safety of the slurry trench panel length of 6 m, determined using numerical methods in 3D (RS3 v. 4.0 and FLAC3D v. 7.0), exceeded 1.5 (Table 1 and Figures 13-16). This factor of safety ensures safety and economic feasibility in the slurry trench design. The next step should be to verify the calculation and simulation results under in-situ conditions. Applying the presented computational methodology to real cases of trench walls supported with bentonite slurry would be beneficial. Practical verification could also be conducted by measuring displacements on the surface near the excavation, although this is technically challenging. With the increase in computer speed, 3D numerical analysis appears to be a relatively straightforward and rapid alternative to classical methods for the design and stability analysis of bentonite slurry trenches. Conceptualization, T.C.T.L. ; methodology, M.C. ; software, T.C.T.L. ; validation, M.C., A.S. and T.C.T.L. ; formal analysis, A.S.; investigation, T.C.T.L. ; resources, T.C.T.L. ; data curation, T.C.T.L. ; writing--original draft preparation, T.C.T.L. ; writing--review and editing, M.C. ; visualization, T.C.T.L. ; supervision, M.C. ; project administration, A.S. All authors have read and agreed to the published version of the manuscript.