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.

Two-dimensional face stability analysis in rock masses governed by the Hoek-Brown strength criterion with a new multi-horn mechanism

The face stability problem is a major concern for tunnels excavated in rock masses governed by the Hoek-Brown strength criterion.To provide an accurate prediction for the theoretical solution of the critical face pressure,this study adopts the piecewise linear method(PLM)to account for the nonlinearity of the strength envelope and proposes a new multi-horn rotational mechanism based on the Hoek-Brown strength criterion and the associative flow rule.The analytical solution of critical support pressure is derived from the energy-work balance equation in the framework of the plastic limit theorem;it is formulated as a multivariable nonlinear optimization problem relying on 2m dependent variables(m is the number of segments).Meanwhile,two classic linearized measures,the generalized tangential technique(GTT)and equivalent Mohr-Coulomb parameters method(EMM),are incorporated into the analysis for comparison.Surprisingly,the parametric study indicates a significant improvement in support pressure by up to 13%compared with the GTT,and as expected,the stability of the tunnel face is greatly influenced by the rock strength parameters.The stress distribution on the rupture surface is calculated to gain an intuitive understanding of the failure at the limit state.Although the limit analysis is incapable of calculating the true stress distribution in rock masses,a rough approximation of the stress vector on the rupture surface is permitted.In the end,sets of normalized face pressure are provided in the form of charts for a quick assessment of face stability in rock masses.

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.

Face stability analysis of circular tunnels in layered rock masses using the upper bound theorem

An analysis of tunnel face stability generally assumes a single homogeneous rock mass.However,most rock tunnel projects are excavated in stratified rock masses.This paper presents a two-dimensional(2D)analytical model for estimating the face stability of a rock tunnel in the presence of rock mass stratification.The model uses the kinematical limit analysis approach combined with the block calculation technique.A virtual support force is applied to the tunnel face,and then solved using an optimization method based on the upper limit theorem of limit analysis and the nonlinear Hoek-Brown yield criterion.Several design charts are provided to analyze the effects of rock layer thickness on tunnel face stability,tunnel diameter,the arrangement sequence of weak and strong rock layers,and the variation in rock layer parameters at different positions.The results indicate that the thickness of the rock layer,tunnel diameter,and arrangement sequence of weak and strong rock layers significantly affect the tunnel face stability.Variations in the parameters of the lower layer of the tunnel face have a greater effect on tunnel stability than those of the upper layer.

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.

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.

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.

Experimental investigation of face instability for tunnels in sandy cobble strata

In order to investigate the influence of face instability for tunnels with different burial depths in sandy cobble strata on earth pressure and the instability region,geomechanical model tests and numerical simulations were performed.The continuous excavation method was adopted to reduce the pressure of the soil bin and restore the real engineering situation.Earth pressure in three directions of the obser-vation section in front of the tunnel face was monitored during the tunneling of the shield.Evolutions of the lateral stress ratios at dif-ferent stages were also investigated.The instability area of the shield tunnel face in sandy cobble strata with different burial depth ratios during the instability stage was obtained based on the change ratio of earth pressure and compared with existing researches.The earth pressure began to change when the excavation was one shield diameter away from the observation section,and when the excavation reached the observation section,the earth pressure decreased significantly.The burial depth of shield tunnel in the sandy cobble strata has a significant impact on the evolution of soil arch and the size of the failure area.The numerical simulation of the continuum medium cannot reflect the stress redistribution characteristics of the granular body like sandy cobble strata,and the failure area or stress distur-bance area obtained by the model test is larger than the numerical simulation result.Existing methods have deviations in analyzing the failure area of shield tunnel face in sandy cobble strata.It provides not only guidance for shield tunnel excavation engineering in sandy cobble strata,but also a reference for the theoretical research on failure areas.

Hard rock tunnel boring machine penetration test as an indicator of chipping process efficiency

The transition from grinding to chipping can be observed in tunnel boring machine(TBM) penetration test data by plotting the penetration rate(distance/revolution) against the net cutter thrust(force per cutter) over the full range of penetration rates in the test.Correlating penetration test data to the geological and geomechanical characteristics of rock masses through which a penetration test is conducted provides the ability to reveal the efficiency of the chipping process in response to changing geological conditions.Penetration test data can also be used to identify stress-induced tunnel face instability.This research shows that the strength of the rock is an important parameter for controlling how much net cutter thrust is required to transition from grinding to chipping.It also shows that the geological characteristics of a rock will determine how efficient chipping occurs once it has begun.In particular,geological characteristics that lead to efficient fracture propagation,such as fabric and mica contents,will lead to efficient chipping.These findings will enable a better correlation between TBM performance and geological conditions for use in TBM design,as a basis for contractual payments where penetration rate dominates the excavation cycle and in further academic investigations into the TBM excavation process.

Analytical solutions of limit support pressure and vertical earth pressure on cutting face for tunnels

This paper focuses on theoretical analytical models to calculate the limit support pressure and vertical earth pressure on the cutting face for tunnels.The failure zone is divided into two parts:a sliding failure zone and an upper loosen zone,and the limit support pressure calculation equation is derived.To verify the rationality of the theoretical model,it was compared with the existing theory,numerical simulation,and centrifugal test,and then the parameter analysis was carried out.The results show that the results of this paper agree well with the existing theory,numerical simulation,and centrifugal test.The inclination angle of the proposed mechanism is determined based on the results of the existing centrifuge test,and the recommended inclination angle is between 52°+φ/2 and 54°+φ/2.The method is proven to be safe and accurate.It can provide a theoretical basis for similar projects.

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.

Construction strategies for a NATM tunnel in Sao Paulo, Brazil, in residual soil

Due to the fast growth of urban areas worldwide,the demand for tunnels in developed areas is increasing.The design and construc-tion of those tunnels are complex because of their shallow depths and their interaction with existing aboveground and buried structures,which results in rather limited allowable ground deformations induced by the tunnel excavation and support.In tropical regions,residual porous soils near the surface are common.Those soils are highly deformable;thus,tunneling may induce large ground deformations that may damage nearby structures.The new Austrian tunneling method(NATM)and the sprayed concrete lining(SCL)technique are being widely employed in several big cities in tropical regions,but little research has been conducted to assess the induced ground deformations in residual soils,common in tropical areas.This paper provides insight into this issue.A well-documented metro tunnel in Sa˜o Paulo,Brazil,in a residual red porous clay,was analyzed using 3D finite element method(FEM).The behavior of the residual red porous clay was approximated by an advanced constitutive soil model calibrated with triaxial tests on intact samples extracted at the site.Predictions of the tunnel deformations during construction matched the field data.The calibrated model was then used to explore the tunnel per-formance under different construction strategies.The influence of partial face excavation,unsupported span length,support stiffness and pipe roof umbrella were assessed.The numerical results showed that partial face excavation was effective to reduce ground deformations ahead of the face of the tunnel and to improve face stability;however,the settlements behind the face increased because of the delay in closing the primary lining.The installation of a stiffer liner closer to the face reduced the ground deformations significantly.The pipe roof umbrella was the most effective technique to reduce the ground deformations around the tunnel;however,the numerical results did not consider deformations that could be induced by the drilling and grouting operations.The results shown in this paper provide both qual-itative and quantitative information about the ground deformations induced by NATM tunneling in residual porous soils,that could help designers and contractors choose the optimum support and construction methods to minimize ground deformations.