System reliability-based geotechnical design of braced excavations in soft clays

This paper presents a preliminary study on the system reliability for the geotechnical design of braced excavations in soft clays. In this system reliability geotechnical analysis, both ultimate limit state (ULS) and serviceability limit state (SLS) are considered. Herein, the ULS failure refers to the basal heave failure, while the SLS failure refers to failures sue to excessive ground-surface settlement and excessive wall deflection. The major uncertain soil parameters are identified and modelled as multivariate normal and lognormal distribution in Monte Carlo simulations. This procedure for the system reliability-based geotechnical design of braced excavations in soft clays is demonstrated through a hypothetical case. Key failure mode affecting system reliability in various case scenarios is discussed. In addition to uncertainty in soil parameters, the model bias factors are also considered to quantify the uncertainty in system reliability analysis. Keywords: Braced excavation; wall deflection; ground-surface settlement; basal heave; system reliability. 1. Introduction For the design of braced excavations in soft clays, a geotechnical engineer needs to consider the uncertainties in soil parameters and models to make structure satisfy the guideposts requirement in relevant codes. To ensure the safety and usability through quantifying uncertain in design, the reliability approaches can be a preferable choice. Many efforts have been dedicated in excavations, including the reliability analysis on ultimate limit state (ULS) in terms of basal-heave (e.g., Goh et al. 2008, Wu et al. 2012), serviceability limit state (SLS) in terms of ground-surface settlement (e.g., Hsiao et al. 2008) and wall deflection (e.g., Wu et al. 2015). Most previous investigators studied either ULS or SLS failure of braced excavation. The safety of a braced excavation is affected by multiple failure modes. Taiwan Geotechnical Society (TGS 2001) indicates that the requirements of the factor of safety against basal-heave, maximum ground-surface settlement and maximum wall deflection should be satisfied simultaneously in a geotechnical design. Therefore, the system reliability of braced excavation should be explicitly considered. The reliability analysis quantifies the parametric uncertainty and model uncertainty. The parameter uncertainty refers to the uncertain soil parameters in this study. In geotechnical engineering, uncertain soil parameters are generally modeled as normal or lognormal distributions. In addition to parameter uncertainty, model uncertainty should also be considered in reliability analysis, as a geotechnical model is actually an abstract of a real engineering problem. (Zhang et al 2014). This paper investigates both ULS failure and SLS failure in a system reliability analysis of braced excavations in soft clays. Specifically, ULS failure refers to the basal heave failure, while the SLS failure refers to failures due to excessive lateral wall deflection and excessive ground-surface settlement. The system reliability analysis is realized through Monte Carlo simulations of a hypothetical braced excavation example. The probability of failure for each single failure mode and the system failure is examined. The key failure mode in various case scenarios is also simply analyzed. 6 Asian-Pacific Symposium on Structural Reliability and its Applications (APSSRA6) 28-30 May 2016, Shanghai, China H.W. Huang, J. Li, J. Zhang & J.B. Chen (editors) In addition to the parameter uncertainty in soil, the bias factors (BFs) are introduced to quantify the effect of model uncertainty in the reliability analysis of braced excavations. 2. Limiting design criteria In this study, the geotechnical design criteria for braced excavations in Shanghai (PSCG 2000) are adopted to be standards. These standards are adopted to determine the specific failure modes, as listed in Table 1. In Table 1, δ!" = maximum ground-surface settlement, δ!" = maximum lateral wall deflection, Fs = factor of safety against basal heave, H! = final excavation depth. In this paper, the level 3 in Table 1 is employed in the reliability assessment. It should be noted that in this study basal heave failure occurs if Fs <1. Table 1. Example limiting criteria for braced excavations in Shanghai, China (PSCG 2000) Excavation protection level Limiting criteria 1 1. δ!" ≤ 0.14%H! 2. δ!" ≤ 0.1%H! 3. F! ≥ 2.2 2 1. δ!" ≤ 0.3%H! 2. δ!" ≤ 0.2%H! 3. F! ≥ 2.0 3 1. δ!" ≤ 0.7%H! 2. δ!" ≤ 0.5%H! 3. F! ≥ 1.5 3. Models for predicting excavation-induced responses In this paper, the KJHH model (Kung et al. 2007) is used to predict the maximum wall deflection and the maximum ground-surface settlement. The slip circle method (JSA 1988; PSCG 2000, TGS 2001) is used to calculate the Fs against basal heave. 3.1 Maximum wall deflection Eq. (1) is used to calculate maximum wall deflection. δ!" mm = b! + b!X! + b!X! + b!X! + b!X! + b!X! + b!X!X! + b!X!X! + b!X!X! (1) where X! = t H! ; X! = t[ln S ] , S = EI/γ!h!"# ! ; X! = t(B/2); X! = t(s!/σ!) ; and X! = t(E!/σ!). Here, He = excavation depth; S=system stiffness; EI = wall stiffness; γ! = unit weight of water; havg = average support spacing; B = excavation width; su = undrained shear strength of soil; σ! = vertical effective stress; Ei = initial Young’s modulus of soil. The coefficients for Eq. (1) are: b0=−13.41973; b1=−0.59351; b2=0.09872; b3=−0.06025; b4=0.23766; b5=−0.15406; b6=0.00093; b7=0.00285; and b8=0.00198. The variables Xi (i=1~5) are defined as X = t x = a!x + a!x + a! (2) The coefficients are listed in Table 2. Table 2. Coefficients for Eq. (2) (adapted from Kung et al. 2007) x H! ln(S) B/2 s!/σ! E!/σ! a! -0.4 11.5 -0.04 3225 0.00041 a! 24 -295 4 -2882 -1 a! -5