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.

Rock mass quality prediction on tunnel faces with incomplete multi-source dataset via tree-augmented naive Bayesian network

Rock mass quality serves as a vital index for predicting the stability and safety status of rock tunnel faces.In tunneling practice,the rock mass quality is often assessed via a combination of qualitative and quantitative parameters.However,due to the harsh on-site construction conditions,it is rather difficult to obtain some of the evaluation parameters which are essential for the rock mass quality prediction.In this study,a novel improved Swin Transformer is proposed to detect,segment,and quantify rock mass characteristic parameters such as water leakage,fractures,weak interlayers.The site experiment results demonstrate that the improved Swin Transformer achieves optimal segmentation results and achieving accuracies of 92%,81%,and 86%for water leakage,fractures,and weak interlayers,respectively.A multisource rock tunnel face characteristic(RTFC)dataset includes 11 parameters for predicting rock mass quality is established.Considering the limitations in predictive performance of incomplete evaluation parameters exist in this dataset,a novel tree-augmented naive Bayesian network(BN)is proposed to address the challenge of the incomplete dataset and achieved a prediction accuracy of 88%.In comparison with other commonly used Machine Learning models the proposed BN-based approach proved an improved performance on predicting the rock mass quality with the incomplete dataset.By utilizing the established BN,a further sensitivity analysis is conducted to quantitatively evaluate the importance of the various parameters,results indicate that the rock strength and fractures parameter exert the most significant influence on rock mass quality.

Stability analysis of tunnel face reinforced with face bolts

Face bolting has been widely utilized to enhance the stability of tunnel face,particularly in soft soil tunnels.However,the influence of bolt reinforcement and its layout on tunnel face stability has not been systematically studied.Based on the theory of linear elastic mechanics,this study delved into the specific mechanisms of bolt reinforcement on the tunnel face in both horizontal and vertical dimensions.It also identified the primary failure types of bolts.Additionally,a design approach for tunnel face bolts that incorporates spatial layout was established using the limit equilibrium method to enhance the conventional wedge-prism model.The proposed model was subsequently validated through various means,and the specific influence of relevant bolt design parameters on tunnel face stability was analyzed.Furthermore,design principles for tunnel face bolts under different geological conditions were presented.The findings indicate that bolt failure can be categorized into three stages:tensile failure,pullout failure,and comprehensive failure.Increasing cohesion,internal friction angle,bolt density,and overlap length can effectively enhance tunnel face stability.Due to significant variations in stratum conditions,tailored design approaches based on specific failure stages are necessary for bolt design.

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.

Three-dimensional pseudo-dynamic reliability analysis of seismic shield tunnel faces combined with sparse polynomial chaos expansion

To address the seismic face stability challenges encountered in urban and subsea tunnel construction,an efficient probabilistic analysis framework for shield tunnel faces under seismic conditions is proposed.Based on the upper-bound theory of limit analysis,an improved three-dimensional discrete deterministic mechanism,accounting for the heterogeneous nature of soil media,is formulated to evaluate seismic face stability.The metamodel of failure probabilistic assessments for seismic tunnel faces is constructed by integrating the sparse polynomial chaos expansion method(SPCE)with the modified pseudo-dynamic approach(MPD).The improved deterministic model is validated by comparing with published literature and numerical simulations results,and the SPCE-MPD metamodel is examined with the traditional MCS method.Based on the SPCE-MPD metamodels,the seismic effects on face failure probability and reliability index are presented and the global sensitivity analysis(GSA)is involved to reflect the influence order of seismic action parameters.Finally,the proposed approach is tested to be effective by a engineering case of the Chengdu outer ring tunnel.The results show that higher uncertainty of seismic response on face stability should be noticed in areas with intense earthquakes and variation of seismic wave velocity has the most profound influence on tunnel face stability.

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.

Tunnel face reliability analysis using active learning Kriging model——Case of a two-layer soils

This paper is devoted to the probabilistic stability analysis of a tunnel face excavated in a two-layer soil. The interface of the soil layers is assumed to be positioned above the tunnel roof. In the framework of limit analysis, a rotational failure mechanism is adopted to describe the face failure considering different shear strength parameters in the two layers. The surrogate Kriging model is introduced to replace the actual performance function to perform a Monte Carlo simulation. An active learning function is used to train the Kriging model which can ensure an efficient tunnel face failure probability prediction without loss of accuracy. The deterministic stability analysis is given to validate the proposed tunnel face failure model. Subsequently, the number of initial sampling points, the correlation coefficient, the distribution type and the coefficient of variability of random variables are discussed to show their influences on the failure probability. The proposed approach is an advisable alternative for the tunnel face stability assessment and can provide guidance for tunnel design.

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.

Influences of anisotropy and inhomogeneity on supporting pressure of tunnel face with kinematical approach

Based on the active failure mechanism generated by a spatial discretization technique, the stability of tunnel face was studied. With the help of the spatial discretization technique, not only the anisotropy and inhomogeneity of the cohesion but also the inhomogeneity of the internal friction angle was taken into account in the analysis of the supporting forces. From the perspective of upper bound theorem, the upper bound solutions of supporting pressure were derived. The influence of the anisotropy and heterogeneity on the supporting forces as well as the failure mechanisms was discussed. The results show that the spatial discretization characteristics of cohesion and internal frictional angle impose a significant effect on the supporting pressure, which indicates that above factors should be considered in the actual engineering.

Seismic reliability analysis of shield tunnel faces under multiple failure modes by pseudo-dynamic method and response surface method

In order to investigate the stability problem of shield tunnel faces subjected to seismic loading,the pseudodynamic method(P-DM)was employed to analyze the seismic effect on the face.Two kinds of failure mechanisms of active collapse and passive extrusion were considered,and a seismic reliability model of shield tunnel faces under multifailure mode was established.The limit analysis method and the response surface method(RSM)were used together to solve the reliability of shield tunnel faces subjected to seismic action.Comparing with existing results,the results of this work are effective.The effects of seismic load and rock mass strength on the collapse pressure,extrusion pressure and reliability index were discussed,and reasonable ranges of support pressure of shield tunnel faces under seismic action were presented.This method can provide a new idea for solving the shield thrust parameter under the seismic loading.

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.

Dynamic collapse characteristics of the tunnel face induced by the shutdown of earth pressure balance shields(EPB):A 3D material point method study

The collapse of the tunnel face is a prevalent geological disaster in tunnelling.This study employs a three-dimensional(3D)material point method(MPM)to simulate the dynamic collapse process and post-failure mechanisms of the tunnel face.The specific focus is on the scenario where the auxiliary air pressure balanced shield with a partially filled chamber is shut down.To assess the suitability of the 3D MPM,numerical solutions are compared with the results from small-scale experimental tests.Subsequently,a series of large-scale numerical simulations is conducted to explore the dynamic collapse characteristics of the tunnel face induced by the shutdown of the EPB shield under various support air pressures and cutter head conditions.The temporal evolution of the accumulated soil masses in the soil chamber and ground responses under different support air pressures,cutter head types and opening ratios are discussed.In particular,the associated surface subsidence due to the tunnel face collapse is determined and compared with empirical solutions.Numerical results confirm the applicability of the 3D MPM for simulating the large-scale tunnel face collapse scenarios,spanning from small to large deformation analysis.

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.

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.

Pseudo-dynamic analysis of a 3D tunnel face in inclined weak strata

A new discretization technique is proposed for a three-dimensional(3D)tunnel face in weak strata with a random position in space.This method limits the angle,height,and thickness of the strata on the tunnel face.The original whole piece of soil is separated by a series of parallel planes,and two parallel planes are used as a stratum.Each radial discrete plane is separated when it passes through the strata,and the change in the soil properties of discrete points on the truncated plane is considered separately inside the strata.Considering the spatial and temporal characteristics of seismic waves,a pseudo-dynamic analysis of the tunnel face is carried out.The tunnel face active damage types under earthquake conditions are quantitatively analyzed,and the corresponding support pressure design diagrams are given for the case without weak strata.For the case containing weak strata,the presence of weak strata can have adverse effects on the face.The failure mechanism of the weak strata is given by the discretization method.For different friction angles,the presence of the weak strata changes the friction angles of the soils.For the thickness,location and angle of the weak strata,the variation in the support pressure is given in this paper.To more intuitively depict the change in the failure mechanism in the presence of weak strata,the change in the failure mechanism under different thicknesses and weaknesses of weak strata is plotted.

Failure responses of rock tunnel faces during excavation through the fault-fracture zone

It is essential to cast light on the construction risks in tunnel excavations through the fault-fracture zone(FFZ).This study adopts the material point method(MPM)to simulate the failure responses of a rock tunnel face during excavation through the FFZ.A numerical study was conducted to compare a physical model test and validate the feasibility of using the MPM in simulating tunnel face failure.One hundred ninety numerical simulation cases were constructed to represent a rock tunnel excavation project with different site con-figurations.The simulation results suggest that the cohesion and the friction angle significantly influence failure responses.The tunnel cover depth can magnify the failure responses,and the FFZ thickness significantly affects the mobilized rock mass volume when the FFZ consists of a weak rock mass.The numerical simulation results suggest three deformation patterns:face bulge,partial failure,and slide collapse.The failure responses can be characterized by stress arch,slip surface,angle of reposing,and influence range.The insights suggested by the face failure responses during excavation through the FFZ can aid field engineers in determining the scope of possible damage,and in establishing emergency measures to minimize losses if such failure occurs.

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.

Hard-rock tunnel lithology identification using multiscale dilated convolutional attention network based on tunnel face images

For real-time classification of rock-masses in hard-rock tunnels,quick determination of the rock lithology on the tunnel face during construction is essential.Motivated by current breakthroughs in artificial intelligence technology in machine vision,a new automatic detection approach for classifying tunnel lithology based on tunnel face images was developed.The method benefits from residual learning for training a deep convolutional neural network(DCNN),and a multi-scale dilated convolutional attention block is proposed.The block with different dilation rates can provide various receptive fields,and thus it can extract multi-scale features.Moreover,the attention mechanism is utilized to select the salient features adaptively and further improve the performance of the model.In this study,an initial image data set made up of photographs of tunnel faces consisting of basalt,granite,siltstone,and tuff was first collected.After classifying and enhancing the training,validation,and testing data sets,a new image data set was generated.A comparison of the experimental findings demonstrated that the suggested approach outperforms previous classifiers in terms of various indicators,including accuracy,precision,recall,F1-score,and computing time.Finally,a visualization analysis was performed to explain the process of the network in the classification of tunnel lithology through feature extraction.Overall,this study demonstrates the potential of using artificial intelligence methods for in situ rock lithology classification utilizing geological images of the tunnel face.

Face stability analysis for a longitudinally inclined tunnel in anisotropic cohesive soils

A stability analysis approach of tunnel face considering a longitudinally inclined tunnel angle and anisotropic purely cohesive soils based on a continuous velocity field (CVF) is investigated in this study. Based on the kinematic approach of limit analysis and the discretization technique, an improved three-dimensional CVF model for longitudinally inclined tunnels driven by pressurized shields is proposed. With the proposed model, the critical support pressure acted on tunnel face is determined by the work-balance equation. A serial of finite element numerical models are conducted to validate the proposed model. Finally, the effects of tunnel inclination angles, several dimensionless parameters as well as soil anisotropy on the critical support pressure are investigated. The numerical results show that the effects of the soil anisotropy and the tunnel inclination angle on tunnel faces should be considered in the actual design of tunneling engineering.

Energy analysis of face stability of deep rock tunnels using nonlinear Hoek-Brown failure criterion

The nonlinear Hoek-Brown failure criterion was introduced to limit analysis by applying the tangent method. Based on the failure mechanism of double-logarithmic spiral curves on the face of deep rock tunnels, the analytical solutions of collapse pressure were derived through utilizing the virtual power principle in the case of pore water, and the optimal solutions of collapse pressure were obtained by using the optimization programs of mathematical model with regard of a maximum problem. In comparison with existing research with the same parameters, the consistency of change rule shows the validity of the proposed method. Moreover, parametric study indicates that nonlinear Hoek-Brown failure criterion and pore water pressure have great influence on collapse pressure and failure shape of tunnel faces in deep rock masses, particularly when the surrounding rock is too weak or under the condition of great disturbance and abundant ground water, and in this case, supporting measures should be intensified so as to prevent the occurrence of collapse.