Numerical analysis of diaphragm wall behavior in a jet-grouted deep excavation: a random field case study

Deep excavations in densely built urban areas frequently employ jet grouting to enhance base stiffness and limit diaphragm wall deformation. However, most design approaches treat the improved soil mass as homogeneous and rarely consider the spatial variability inherent in jet-grouted materials, which may lead to biased deformation predictions and incomplete risk evaluation. This study investigates the influence of spatial variability in the secant stiffness modulus (E₅₀) of jet-grouted soil on diaphragm wall displacement using a probabilistic numerical framework. A two-dimensional lognormal random field of E₅₀ was generated using the spectral representation method and incorporated into a finite element model within the Random Finite Element Method (RFEM) framework. The mean stiffness of the improved soil was taken as 1336.85 MPa based on laboratory testing, while variability was characterized by coefficients of variation (COV) ranging from 0.34 to 0.8 and spatial correlation lengths defined by scales of fluctuation of SOFₓ = 3-5 m and SOF_γ = 0.5-2 m. Monte Carlo simulations were conducted with a converged sample size of 40 realizations. The results indicate that spatial variability significantly affects both the magnitude and dispersion of wall displacement, with predicted maximum values generally ranging from 11.0 to 11.8 mm and following a lognormal distribution. For an allowable displacement of 11.44 mm, the exceedance probability decreases from approximately 58% at COV = 0.34 to about 35% at COV = 0.8. Changes in spatial correlation length have comparatively smaller effects, although vertical correlation shows a slightly stronger influence than horizontal correlation. These findings demonstrate that deterministic analyses assuming uniform ground improvement may underestimate the range of possible wall movements, while incorporating spatial variability provides a more realistic basis for reliability-based assessment and risk-informed design of jet-grouting-reinforced excavations.