Mechanism and stability analysis of trench wall instability in extra-deep irregular-shaped diaphragm wall trenching construction

• We derived an L-trench safety factor formula, turning complex engineering into math, enriching stability mechanisms. • Case studies validated the formula's accuracy and applicability. • FEM simulations found optimal slurry gravity for silt and silty clay in L-trench. • Software calculations confirmed formula feasibility (<15 % error). The instability of extra-deep irregular diaphragm wall trenches, particularly in L-shaped configurations, presents significant challenges in geotechnical engineering. This study develops a 3D failure model within a limit-equilibrium framework and derives a closed-form safety-factor expression for L-shaped trenches, explicitly coupling groundwater level, slurry density, layered soils, and surface overload. Finite-element analyses on three under-construction stations in Guangzhou, Jinan, and Shanghai validate the approach, with theory-FE deviations <15 %. Results show that reinforcement reduces the peak inward displacement from 168.5 mm to 67 mm. Recommended slurry densities are 1.25-1.30 g/cm³ for silt layers and 1.15-1.20 g/cm³ for silty clay. The outcomes provide a practical stability-assessment method and engineering guidance for L-shaped diaphragm-wall trenches under complex geological conditions.