Probabilistic analysis of tunnel face seismic stability in layered rock masses using Polynomial Chaos Kriging metamodel

Face stability is an essential issue in tunnel design and construction.Layered rock masses are typical and ubiquitous;uncertainties in rock properties always exist.In view of this,a comprehensive method,which combines the Upper bound Limit analysis of Tunnel face stability,the Polynomial Chaos Kriging,the Monte-Carlo Simulation and Analysis of Covariance method(ULT-PCK-MA),is proposed to investigate the seismic stability of tunnel faces.A two-dimensional analytical model of ULT is developed to evaluate the virtual support force based on the upper bound limit analysis.An efficient probabilistic analysis method PCK-MA based on the adaptive Polynomial Chaos Kriging metamodel is then implemented to investigate the parameter uncertainty effects.Ten input parameters,including geological strength indices,uniaxial compressive strengths and constants for three rock formations,and the horizontal seismic coefficients,are treated as random variables.The effects of these parameter uncertainties on the failure probability and sensitivity indices are discussed.In addition,the effects of weak layer position,the middle layer thickness and quality,the tunnel diameter,the parameters correlation,and the seismic loadings are investigated,respectively.The results show that the layer distributions significantly influence the tunnel face probabilistic stability,particularly when the weak rock is present in the bottom layer.The efficiency of the proposed ULT-PCK-MA is validated,which is expected to facilitate the engineering design and construction.

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.

Analysis of tunnel face stability with advanced pipes support

To keep the tunnel face stable is very important for tunnel construction.In this paper,the tunnel face stability under the advanced pipe was analyzed using the Winkler foundation model and rigid limit equilibrium.The tunnel face deformation characteristics were also analyzed using the numerical simulation.The influence of parameters on the deflection of the pipe roof and the stability of the tunnel face were discussed.The results show that the tunnel face stability can be improved through increasing the pipe diameter,decreasing the initial displacement at the beginning of the pipe seat,and adopting the short round length and small excavation height.With the increase of tunnel burial depth,the safety factor of tunnel face stability first decreases,then increases,and then remains unchanged.The deformation at the center of the tunnel face is larger than the deformation at the surround sides and at the corner.The horizontal displacement varies little with the increasing of the pipe length.The horizontal displacement at the center of the tunnel face increases with the increase of the pipe ring spacing and the pipe longitudinal spacing.There is an optimum external angle.

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.

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.

Three-dimensional seismic face stability of shield tunnels inundrained clay

Tunnel face stability has received increasing research interest over the past few decades. However, computing time-efficient and safethree-dimensional solutions under seismic loading is still an unsolved problem, while case studies indicate that seismic loading can be onecritical destabilizing factor affecting tunnel stability. The primary objective of this work is to fill this gap in knowledge by providing compromisingand computationally efficient solutions, along with their respective lower and upper bounds, to compute face stability underseismic conditions. The analyses employ the finite element limit analysis method to evaluate the limit support pressure in undrained clay,considering horizontal pseudo-static seismic forces pointing outwards from the face. Moreover, the analyses employ both constant andlinearly increasing shear strengths with depth. The results are summarized as dimensionless stability charts and tables to facilitate theirinterpretation and future use for tunnel design. A new design equation has been developed to evaluate the stability of the tunnel faceconsidering the effect of seismic forces. Additionally, the effects of different parameters on the shape of the failure mechanism have beeninvestigated by analysing the distribution of shear dissipation.

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.

Numerical and analytical studies on the coupling effects of unloading and cutterhead vibration on tunnel face in dry sandy ground

When tunnelling in difficult ground conditions,shield machine would inevitably produce significant ground loss and vibration,which may disturb the ground ahead of the tunnel face.In this paper,discrete element models calibrated by model tests were established to investigate the response of tunnel face under the coupling effects of unloading and cutterhead vibrations.The results show that the friction angle reduction under cyclic loading and vibration attenuation in the sandy ground are significant and can be estimated by the fitted exponential functions.Under cutterhead vibration,the tunnel face stability is undermined and the limit support pressure(LSP)increases to 1.4 times as that in the static case with the growth of frequency and amplitude.Meanwhile,the loosening zone becomes wider and the arching effect is weakened with the reduction of peak horizontal stress and the increase of vertical stress above the tunnel.Based on the numerical results,a pseudo-static method was introduced into the limit equilibrium analysis of the wedge-prism model for calculating the LSP under vibration.With an error rate less than 5.2%,the proposed analytical method is well validated.Further analytical calculation reveals that the LSP would increase with the growth of vibration amplitude,vibration frequency and covered depth but decrease with the increase of friction angle.This study can not only lay a solid foundation for the further investigation of ground loss,ground water and soft-hard heterogeneous ground under cutterhead vibration,but also provide meaningful references for the control of environmental disturbance in practice.

MCS-based quantile value approach for reliability-based design of tunnel face support pressure

This paper develops a new approach for reliability-based design(RBD)of tunnel face support pressure from a quantile value perspective.A surrogate model is constructed to calculate the collapse pressures of the random samples generated by a single run of Monte Carlo simulation(MCS).The cumulative distribution function(CDF)of the collapse pressure is then obtained and the support pressure aiming at a target failure probability is chosen as the upper quantile value of the collapse pressures.The proposed approach does not require repetitive reliability analyses compared to the existing methods.Moreover,a direct relationship between the target failure probability and the required support pressure is established.An illustrative example is used to demonstrate the implementation procedure.The accuracy of the reliability-based support pressures is verified by direct MCS incorporating with three-dimensional numerical simulations.Finally,the influencing factors,including the sample size of MCS,the correlation coefficient between random variables,the choice of experimental points,and the surrogate model,are investigated.This method can play a complementary role to available approaches due to its advantages of simplicity and efficiency.

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 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.

Investigation of the failure mechanism and theoretical model of bolt-reinforced shallow tunnel faces with different bolt lengths

Using fiberglass bolts to reinforce a tunnel face is a practical auxiliary technology for ensuring tunnel face stability in soft ground.The reinforcing effect and the economics of this technology are significantly affected by bolt length.However,to date,the failure mechanism of bolt-reinforced tunnel faces with different bolt lengths has rarely been investigated.To reveal the failure mechanism of bolt-reinforced shallow tunnel faces,in this study,the stability of bolt-reinforced tunnel faces with different bolt lengths was investigated by using laboratory tests and numerical simulations,and a simplified theoretical model for practical engineering was proposed.The face support pressure and failure pattern for different bolt lengths during the face collapse process were obtained,and the influence of bolt length on face stability was clearly revealed.More specifically,the results show that face stability increases with increasing bolt length,and the reinforcing effect of face bolts is governed by the shear failure at the soil-grout interface first in the stable zone of the tunnel face and then in the failure zone.Once the bolt length in the stable zone is larger than that in the failure zone,face stability will not be improved with increasing bolt length;thus,this bolt length is referred to as the optimal bolt length L_(opt).The L_(opt)value is slightly larger than the initial failure range(in the unreinforced condition)and can be approximately calculated by L_(opt)=(1-0.0133u)D(u is the friction angle of the soil,and D is the tunnel diameter)in practical engineering.Finally,a simplified theoretical model was established to analyse the stability of reinforced tunnel faces,and the results are in good agreement with both laboratory tests and numerical simulations.The proposed model can be used as an efficient tool for the design of face bolts.