Inverse reliability analysis and design for tunnel face stability considering soil spatial variability

The traditional deterministic analysis for tunnel face stability neglects the uncertainties of geotechnical parameters,while the simplified reliability analysis which models the potential uncertainties by means of random variables usually fails to account for soil spatial variability.To overcome these limitations,this study proposes an efficient framework for conducting reliability analysis and reliability-based design(RBD)of tunnel face stability in spatially variable soil strata.The three-dimensional(3D)rotational failure mechanism of the tunnel face is extended to account for the soil spatial variability,and a probabilistic framework is established by coupling the extended mechanism with the improved Hasofer-Lind-Rackwits-Fiessler recursive algorithm(iHLRF)as well as its inverse analysis formulation.The proposed framework allows for rapid and precise reliability analysis and RBD of tunnel face stability.To demonstrate the feasibility and efficacy of the proposed framework,an illustrative case of tunnelling in frictional soils is presented,where the soil's cohesion and friction angle are modelled as two anisotropic cross-correlated lognormal random fields.The results show that the proposed method can accurately estimate the failure probability(or reliability index)regarding the tunnel face stability and can efficiently determine the required supporting pressure for a target reliability index with soil spatial variability being taken into account.Furthermore,this study reveals the impact of various factors on the support pressure,including coefficient of variation,cross-correlation between cohesion and friction angle,as well as autocorrelation distance of spatially variable soil strata.The results also demonstrate the feasibility of using the forward and/or inverse first-order reliability method(FORM)in high-dimensional stochastic problems.It is hoped that this study may provide a practical and reliable framework for determining the stability of tunnels in complex soil strata.

Reliability assessment for serviceability limit states of stiffened deep cement mixing column-supported embankments

The reliability and deterministic analyses of wood-cored stiffened deep cement mixing and deep cement mixing column-supported embankments(referred to as WSCSE and DCSE,respectively)considering serviceability limit state requirements are presented in this paper.Random field theory was used to simulate the spatial variability of soil
cement mixing(SCM)material in which the adaptive Kriging Monte Carlo simulation was adopted to estimate the failure probability of a column
supported embankment(CSE)system.A new method for stochastically generating random values of unconfined compressive strength(qu)and the ratio(Ru)between the undrained elastic modulus and qu of SCM material based on statistical correlation data is proposed.Reliability performance of CSEs concerning changes in the mean(μ),coefficient of variation(CoV),and vertical spatial correlation length(θv)of qu and Ru are presented and discussed.The obtained results indicate that WSCSE can provide a significantly higher reliability level and can tolerate more SCM material spatial variability than DCSE.Some performance of DCSE and WSCSE,which can be considered satisfactory in a deterministic framework,cannot guarantee an acceptable reliability level from a probabilistic viewpoint.This highlights the importance and necessity of employing reliability analyses for the design of CSEs.Moreover,consideration of only μ and CoV of qu seems to be sufficient for reliability analysis of WSCSE while for DCSE,uncertainties regarding the Ru(i.e.both μ and CoV)and θv of qu cannot be ignored.

Reliability-based settlement analysis of embankments over soft soils reinforced with T-shaped deep cement mixing piles

This paper presents a reliability-based settlement analysis of T-shaped deep cement mixing(TDM)pile-supported embankments over soft soils.The uncertainties of the mechanical properties of the in-situ soil,pile,and embankment,and the effect of the pile shape are considered simultaneously.The analyses are performed using Monte Carlo Simulations in combination with an adaptive Kriging(using adaptive sampling algorithm).Individual and system failure probabilities,in terms of the differential and maximum settlements(serviceability limit state(SLS)requirements),are considered.The reliability results for the embankments supported by TDM piles,with various shapes,are compared and discussed together with the results for conventional deep cement mixing pile-supported embankments with equivalent pile volumes.The influences of the inherent variabilities in the material properties(mean and coefficient of variation values)on the reliability of the piled embankments,are also investigated.This study shows that large TDM piles,particularly those with a shape factor of greater than 3,can enhance the reliability of the embankment in terms of SLS requirements,and even avoid unacceptable reliability levels caused by variability in the material properties.