Probabilistic analysis of crack width and deflection of an anchored diaphragm wall installed in sands

Abstract This paper deals with the probabilistic modelling of an anchored diaphragm wall installed in normally consolidated sand. The analysis uses the random finite element method and is based on N = 1000 Monte Carlo simulations. The model's geometry is based on the benchmark of the triple-anchored wall installed in the Berlin sand, published by Schweiger (Part i: Results of benchmarking. Part ii: Reference solution and parametric study. Technical Report CGG_IR006_2002, Institute for Soil Mechanics and Foundation Engineering, Graz University of Technology, Austria, 2002). A single spatially variable soil layer is assumed. The variability of the soil is modelled by two random fields that describe the normalised CPTu parameters $${Q}_{\text{tn}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mtext>tn</mml:mtext> </mml:msub> </mml:math> and $${F}_{r}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>r</mml:mi> </mml:msub> </mml:math> . The probability distribution, cross-correlation coefficient and vertical scales of fluctuations SOF for both random fields are identified based on CPTu tests from the central part of Poland. The Hardening Soil-brick model is used as the constitutive model of the soil. Its parameters are derived based on local values of normalised corrected tip resistance $${Q}_{\text{tn}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mtext>tn</mml:mtext> </mml:msub> </mml:math> and normalised friction ratio $${F}_{r}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>r</mml:mi> </mml:msub> </mml:math> according to the correlations found for this soil type by Truty (Sci Rep 140(1):15102, 2024). Based on the initial analysis conducted for mean soil parameters, steel reinforcement for the wall has been designed. The probabilistic analysis involves both the ultimate (ULS) and the serviceability (SLS) limit states; however, it is focused on the latter. In particular, the crack width and the wall deflection are investigated. The estimation of system probability considering both SLSs is based on the Nataf transformations. As shown, both states can significantly impact the failure’s probability, resulting in the system failure probability being substantially more significant than that for individual SLS.