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.

A novel image-based approach for interactive characterization of rock fracture spacing in a tunnel face

This paper presents a novel integrated method for interactive characterization of fracture spacing in rock tunnel sections.The main procedure includes four steps:(1)Automatic extraction of fracture traces,(2)digitization of trace maps,(3)disconnection and grouping of traces,and(4)interactive measurement of fracture set spacing,total spacing,and surface rock quality designation(S-RQD)value.To evaluate the performance of the proposed method,sample images were obtained by employing a photogrammetrybased scheme in tunnel faces.Experiments were then conducted to determine the optimal parameter values(i.e.distance threshold,angle threshold,and number of fracture trace grouping)for characterizing rock fracture spacing.By applying the identified optimal parameters involved in the model,the proposed method could lead to excellent qualitative results to a new tunnel face.To perform a quantitative analysis,three methods(i.e.field,straightening,and the proposed method)were employed in the same study and comparisons were made.The proposed method agrees well with the field measurement in terms of the maximum and average values of measured spacing distribution.Overall,the proposed method has reasonably good accuracy and interactive advantage for estimating the ultimate fracture spacing and S-RQD.It can be a possible extension of existing methods for fracture spacing characterization for two-dimensional(2D)rock tunnel faces.

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.

Anisotropy of multi-layered structure with sliding and bonded interlayer conditions

A better understanding of the mechanical behavior of the multilayered structure under extermal loading is the most important item for the structural design and the risk asssment.The objective of this study are to propose and develop an analytical solution for the mechanical behaviors of multi-layered structure generated by axisy mmetric loading,and to investigate the impact of anisotropic layers and interlayer conditions on the multi-layered structure.To reach these objectives,first,according to the goveming equations,the analytical solution for a single layer was formulated by adopting the spatial Hankel transform.Then the global matrix technique is applied to achieve the analytical solution of multi-layered structure in Hankel domain.The sliding and bonded interlayer conditions were considered in this process.Finally,the numerical inversion of integral transform was used to solve the components of displacement and stress in real domain.Gauss-Lcgendre quadrature is a key scheme in the numerical inversion process.Moreover,following by the verification of the proposed analytical solution,one typical three-layered flexible pavement was applied as the computing carrier of numerical analysis for the multi-layered structure.The results have shown that the anisotropic layers and the interlayer conditions significantly affect the mechanical behaviors of the proposed structure.