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.

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.

Design Theory of Full Face Rock Tunnel Boring Machine Transition Cutter Edge Angle and Its Application

At present, the inner cutters of a full face rock tunnel boring machine (TBM) and transition cutter edge angles are designed on the basis of indentation test or linear grooving test. The inner and outer edge angles of disc cutters are characterized as symmetric to each other with respect to the cutter edge plane. This design has some practical defects, such as severe eccentric wear and tipping, etc. In this paper, the current design theory of disc cutter edge angle is analyzed, and the characteristics of the rock-breaking movement of disc cutters are studied. The researching results show that the rotational motion of disc cutters with the cutterhead gives rise to the difference between the interactions of inner rock and outer rock with the contact area of disc cutters, with shearing and extrusion on the inner rock and attrition on the outer rock. The wear of disc cutters at the contact area is unbalanced, among which the wear in the largest normal stress area is most apparent. Therefore, a three-dimensional model theory of rock breaking and an edge angle design theory of transition disc cutter are proposed to overcome the flaws of the currently used TBM cutter heads, such as short life span, camber wearing, tipping. And a corresponding equation is established. With reference to a specific construction case, the edge angle of the transition disc cutter has been designed based on the theory. The application of TBM in some practical project proves that the theory has obvious advantages in enhancing disc cutter life, decreasing replacement frequency, and making economic benefits. The proposed research provides a theoretical basis for the design of TBM three-dimensional disc cutters whose rock-breaking operation time can be effectively increased.

Wear Analysis of Disc Cutters of Full Face Rock Tunnel Boring Machine

Wear is a major factor of disc cutters’ failure. No current theory offers a standard for the prediction of disc cutter wear yet. In the field the wear prediction method commonly used is based on the excavation length of tunnel boring machine（TBM） to predict the disc cutter wear and its wear law, considering the location number of each disc cutter on the cutterhead（radius for installation）; in theory, there is a prediction method of using arc wear coefficient. However, the preceding two methods have their own errors, with their accuracy being 40% or so and largely relying on the technicians’ experience. Therefore, radial wear coefficient, axial wear coefficient and trajectory wear coefficient are defined on the basis of the operating characteristics of TBM. With reference to the installation and characteristics of disc cutters, those coefficients are modified according to penetration, which gives rise to the presentation of comprehensive axial wear coefficient, comprehensive radial wear coefficient and comprehensive trajectory wear coefficient. Calculation and determination of wear coefficients are made with consideration of data from a segment of TBM project（excavation length 173 m）. The resulting wear coefficient values, after modification, are adopted to predict the disc cutter wear in the follow-up segment of the TBM project（excavation length of 5621 m）. The prediction results show that the disc cutter wear predicted with comprehensive radial wear coefficient and comprehensive trajectory wear coefficient are not only accurate（accuracy 16.12%） but also highly congruous, whereas there is a larger deviation in the prediction with comprehensive axial wear coefficient（accuracy 41%, which is in agreement with the prediction of disc cutters’ life in the field）. This paper puts forth a new method concerning prediction of life span and wear of TBM disc cutters as well as timing for replacing disc cutters.

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.

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.

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.

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.

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.

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.

Mechanism analysis of foam penetration in EPB shield tunnelling with a focus on FER and soil particle size

Parameters of foam penetration in earth pressure balance(EPB)shield tunnelling,such as permeability coefficients and penetration distances,significantly impact tunnel face stability.However,existing studies have faced inaccuracies in analysing these parameters due to imitations in experimental methods.This study addresses this issue by employing enhanced methods for a more precise analysis of foam penetration.Experiments involving three distinct sand types(coarse,medium,and fine)and three foam expansion ratios(FER)(10,15,and 20)are conducted using a modified model test setup.Benefiting from a novel computer vision-based method,the model test outcomes unveil two distinct foam penetration paths:liquid migration(L_(w))and bubble migration(L_(f)).Three penetration phases-namely,injection,blockage&drainage,and breakage—are identified based on L_(w)and L_(f)variations.The initial"injection"phase conforms to Darcy’s law and is amenable to mathematical description.The foam with FER of 15 has the maximum viscosity and,hence the L_(f)and permeability in the penetration tests with FER of 15 are the lowest in the same sand.The bubble size distribution of foam with different FER shows minor differences.Nevertheless,the characteristics of foam penetration vary due to the distinct particle size distribution(PSD)of different sands.Foam penetration creates low-permeability layers in both medium and fine sands due to the larger bubble size of the foam compared to the estimated pore sizes of medium and fine sands.While the coarse sand results in a different situation due to its large pore size.The distinctive characteristics of foam penetration in different sand strata are notably shaped by FER,PSD,and pore size distributions.These insights shed light on the complex interactions during foam penetration at the tunnel face,contributing valuable knowledge to EPB shield tunnelling practices.

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.

Machine learning-based classification of rock discontinuity trace:SMOTE oversampling integrated with GBT ensemble learning

This paper presents a hybrid ensemble classifier combined synthetic minority oversampling technique(SMOTE),random search(RS)hyper-parameters optimization algorithm and gradient boosting tree(GBT)to achieve efficient and accurate rock trace identification.A thirteen-dimensional database consisting of basic,vector,and discontinuity features is established from image samples.All data points are classified as either‘‘trace”or‘‘non-trace”to divide the ultimate results into candidate trace samples.It is found that the SMOTE technology can effectively improve classification performance by recommending an optimized imbalance ratio of 1:5 to 1:4.Then,sixteen classifiers generated from four basic machine learning(ML)models are applied for performance comparison.The results reveal that the proposed RS-SMOTE-GBT classifier outperforms the other fifteen hybrid ML algorithms for both trace and nontrace classifications.Finally,discussions on feature importance,generalization ability and classification error are conducted for the proposed classifier.The experimental results indicate that more critical features affecting the trace classification are primarily from the discontinuity features.Besides,cleaning up the sedimentary pumice and reducing the area of fractured rock contribute to improving the overall classification performance.The proposed method provides a new alternative approach for the identification of 3D rock trace.