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.

An efficient probabilistic design approach for tunnel face stability by inverse reliability analysis

In order to maintain the safety of underground constructions that significantly involve geo-material uncertainties,this paper delivers a new computation framework for conducting reliability-based design(RBD)of shallow tunnel face stability,utilizing a simplified inverse first-order reliability method(FORM).The limit state functions defining tunnel face stability are established for both collapse and blow-out modes of the tunnel face failure,respectively,and the deterministic results of the tunnel face support pressure are obtained through three-dimensional finite element limit analysis(FELA).Because the inverse reliability method can directly capture the design support pressure according to prescribed target reliability index,the computational cost for probabilistic design of tunnel face stability is greatly reduced.By comparison with Monte Carlo simulation results,the accuracy and feasibility of the proposed method are verified.Further,this study presents a series of reliability-based design charts for vividly understanding the limit support pressure on tunnel face in both cohesionless(sandy)soil and cohesive soil stratums,and their optimal support pressure ranges are highlighted.The results show that in the case of sandy soil stratum,the blowout failure of tunnel face is extremely unlikely,whereas the collapse is the only possible failure mode.The parametric study of various geotechnical uncertainties also reveals that ignoring the potential correlation between soil shear strength parameters will lead to over-designed support pressure,and the coefficient of variation of internal friction angle has a greater influence on the tunnel face failure probability than that of the cohesion.

Effect of cutterhead configuration on tunnel face stability during shield machine maintenance outages

Owing to long-distance advancement or obstacles,shield tunneling machines are typically shut down for maintenance.Engineering safety during maintenance outages is determined by the stability of the tunnel face.Pressure maintenance openings are typically used under complicated hydrogeological conditions.The tunnel face is supported by a medium at the bottom of the excavation chamber and compressed air at the top.Owing to the high risk of face failure,the necessity of support pressure when cutterhead support is implemented and a method for determining the value of compressed air pressure using different support ratios must to be determined.In this study,a non-fully chamber supported rotational failure model considering cutterhead support is developed based on the upper-bound theorem of limit analysis.Numerical simulation is conducted to verify the accuracy of the proposed model.The results indicate that appropriately increasing the specific gravity of the supporting medium can reduce the risk of collapse.The required compressed air pressure increases significantly as the support ratio decreases.Disregarding the supporting effect of the cutterhead will result in a tunnel face with underestimated stability.To satisfy the requirement of chamber openings at atmospheric pressure,the stratum reinforcement strength and range at the shield end are provided based on different cutterhead aperture ratios.

Face stability of shield tunnels considering a kinematically admissible velocity field of soil arching

Existing mechanism of simulating soil movement at tunnel face is generally based on the translational or rotational velocity field,which is,to some extent,different from the real soil movement in the arching zone.Numerical simulations are carried out first to investigate the characteristics of the velocity distribution at tunnel face and above tunnel vault.Then a new kinematically admissible velocity field is proposed to improve the description of the soil movement according to the results of the numerical simulation.Based on the proposed velocity field,an improved failure mechanism is constructed adopting the spatial discretization technique,which takes into account soil arching effect and plastic deformation within soil mass.Finally,the critical face pressure and the proposed mechanism are compared with the results of the numerical simulation,existing analytical studies and experimental tests to verify the accuracy and improvement of the presented method.The proposed mechanism can serve as an alternative approach for the face stability analysis.

Experimental study of face passive failure features of a shallow shield tunnel in coastal backfill sand

Face passive failure can severely damage existing structures and underground utilities during shallow shield tunneling,especially in coastal backfill sand.In this work,a series of laboratory model tests were developed and conducted to investigate such failure,for tunnels located at burial depth ratios for which C/D=0.5,0.8,1,and 1.3.Support pressures,the evolution of failure processes,the failure modes,and the distribution of velocity fields were examined through model tests and numerical analyses.The support pressure in the tests first rose rapidly to the elastic limit and then gradually increased to the maximum value in all cases.The maximum support pressure decreased slightly in cases where C/D=0.8,1,and 1.3,but the rebound was insignificant where C/D=0.5.In addition,the configuration of the failure mode with C/D=0.5 showed a wedge-shaped arch,which was determined by the outcropping shear failure.The configuration of failure modes was composed of an arch and the inverted trapezoid when C/D=0.8,1,and 1.3,in which the mode was divided into lower and upper failure zones.

Face stability analysis of a shield tunnel excavated along inclined strata

The horizontally layered or even inclined strata are often encountered in practical shield tunneling.The influence of inclined strata on face stability of shield tunnels is not fully investigated by the existing studies.This paper adopts both theoretical analysis and numerical simulation to carry out research on face stability in inclined strata.The spatial discretization technique is adopted to construct a threedimensional(3D)kinematic failure mechanism considering intersection between inclined soil interface and tunnel face.An analytical solution for critical support pressure is obtained.Besides,the critical support pressure and 3D kinematic mechanism are compared with numerical results to verify accuracy and effectiveness of analytical model.The influences of dip and position of inclined strata on face stability are thoroughly studied.The proposed failure mechanism can serve as a reference for face stability analysis in inclined strata.