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.

Investigation of anisotropic strength criteria for layered rock mass

Layered rock mass is a type of engineering rock mass with sound mechanical anisotropy,which is generally unfavorable to the stability of underground works.To investigate the strength anisotropy of layered rock,the Mohr-Coulomb and Hoek-Brown criteria are introduced to establish the two transverse isotropic strength criteria based on Jaeger's single weak plane theory and maximum axial strain theory,and parameter determination methods.Furthermore,the sensitivity of strength parameters(K 1,K 2,and K 3)that are used to characterize the anisotropy strength of non-sliding failure involved in the strength criteria and confining pressure are investigated.The results demonstrate that strength parameters K 1 and K 2 affect the strength of layered rock samples at all bedding angles except for the bedding angle of 90°and the angle range that can cause the shear sliding failure along the bedding plane.The strength of samples at any bedding angle decreases with increasing K 1,whereas the opposite is for K 2.Except for bedding angles of 0°and 90°and the bedding angle range that can cause the shear sliding along the bedding plane,K 3 has an impact on the strength of rock samples with other bedding angles that the specimens'strength increases with increase of K 3.In addition,the strength of the rock sample increases as confining pressure rises.Furthermore,the uniaxial and triaxial tests of chlorite schist samples were carried out to verify and evaluate the strength criteria proposed in the paper.It shows that the predicted strength is in good agreement with the experimental results.To test the applicability of the strength criterion,the strength data of several types of rock in the literature are compared.Finally,a comparison is made between the fitting effects of the two strength criteria and other available criteria for layered rocks.

Dynamic response and failure process of horizontal-layered fractured structure rock slope under strong earthquake

Rock slope with horizontal-layered fractured structure(HLFS)has high stability in its natural state.However,a strong earthquake can induce rock fissure expansion,ultimately leading to slope failure.In this study,the dynamic response,failure mode,and spectral characteristics of rock slope with HLFS under strong earthquake conditions were investigated based on the large-scale shaking table model test.On this basis,multiple sets of numerical calculation models were further established by UDEC discrete element program.Five influencing factors were considered in the parametric study of numerical simulations,including slope height,slope angle,bedding-plane spacing and secondary joint spacing as well as bedrock dip angle.The results showed that the failure process of rock slope with HLFS under earthquake action is mainly divided into four phases,i.e.,the tensile crack of the slope shoulder joints and shear dislocation at the top bedding plane,the extension of vertical joint cracks and increase of shear displacement,the formation of step-through sliding surfaces and the instability,and finally collapse of fractured rock mass.The acceleration response of slopes exhibits elevation amplification effect and surface effect.Numerical simulations indicate that the seismic stability of slopes with HLFS exhibits a negative correlation with slope height and angle,but a positive correlation with bedding-plane spacing,joint spacing,and bedrock dip angle.The results of this study can provide a reference for seismic stability evaluation of weathered rock slopes.

A modified smoothed particle hydrodynamics method considering residual stress for simulating failure and its application in layered rock mass

Residual strength is an indispensable factor in evaluating rock fracture,yet the current Smoothed Particle Hydrodynamics(SPH)framework rarely considers its influence when simulating fracture.An improved cracking strategy considering residual stress in the base bond SPH method was proposed to simulate failures in layered rocks and slopes and verified by experimental results and other simulation methods(i.e.,the discrete element method).Modified Mohr–Coulomb failure criterion was applied to distinguish the mixed failure of tensile and shear.Bond fracture markψwas introduced to improve the kernel function after tensile damage,and the calculation of residual stress after the damage was derived after shear damage.Numerical simulations were carried out to evaluate its performance under different stress and scale conditions and to verify its effectiveness in realistically reproducing crack initiation and propagation and coalescence,even fracture and separation.The results indicate that the improved cracking strategy precisely captures the fracture and failure pattern in layered rocks and rock slopes.The residual stress of brittle tock is correctly captured by the improved SPH method.The improved SPH method that considers residual strength shows an approximately 13%improvement in accuracy for the safety factor of anti-dip layered slopes compared to the method that does not consider residual strength,as validated against analytical solutions.We infer that the improved SPH method is effective and shows promise for applications to continuous and discontinuous rock masses.

Restraint effect of partition wall on the tunnel floor heave in layered rock mass

The presence of horizontal layered rocks in tunnel engineering significantly impacts the stability and strength of the surrounding rock mass,leading to floor heave in the tunnel.This study focused on preparing layered specimens of rock-like material with varying thickness to investigate the failure behaviors of tunnel floors.The results indicate that thin-layered rock mass exhibits weak interlayer bonding,causing rock layers near the surface to buckle and break upwards when subjected to horizontal squeezing.With an increase in the layer thickness,a transition in failure mode occurs from upward buckling to shear failure along the plane,leading to a noticeable reduction in floor heave deformation.The primary cause of significant deformation in floor heave is upward buckling failure.To address this issue,the study proposes the installation of a partition wall in the middle of the floor to mitigate heave deformation of the rock layers.The results demonstrate that the partition wall has a considerable stabilizing effect on the floor,reducing the zone of buckling failure and minimizing floor heave deformation.It is crucial for the partition wall to be sufficiently high to prevent buckling failure and ensure stability.Through simulation calculations on an engineering example,it is confirmed that implementing a partition wall can effectively reduce floor heave and enhance the stability of tunnel floor.

A three-dimensional numerical study on the stability of layered rock spillway tunnels in alpine canyon areas

Rock masses in alpine canyon areas exhibit strong heterogeneity,discontinuity,and are subject to strong tectonic effects and stress unloading,leading to extremely complex distribution of in-situ stress.In addition,the occurrence of layered rock masses makes it more complex,with obvious anisotropic mechanical properties.This study proposes a comprehensive method for evaluating the stability of layered rock spillway tunnels in a hydropower station in an alpine canyon.First,the failure criterion and mechanical model of layered rock masses considering the anisotropy induced by the bedding plane and the true triaxial stress regime were established;an inversion theory and calculation procedure for in-situ stress in alpine canyon areas were then introduced.Finally,by using a self-developed numerical tool,i.e.CASRock,the stability of the layered rock spillway tunnel in a hydropower station was numerically analyzed.The results show that,affected by geological structure and stratigraphic lithology,there is significant differentiation in the in-situ stress in alpine canyons,with horizontal tectonic stress as the main factor.The occurrence of layered rock masses in the region has a significant impact on the stability of surrounding rock,and the angle between the bedding strike and the tunnel axis as well as the bedding dip both exert a significant influence on the failure characteristics of the surrounding rock.

Mechanical properties and associated seismic isolation effects of foamed concrete layer in rock tunnel

Foamed concrete has a good energy absorption capability and can be used as seismic isolation material for tunnels. This study aims to investigate the mechanical properties and associated seismic isolation effects of foamed concrete layer in rock tunnel. For this, a series of uniaxial/triaxial compression tests was conducted to understand the effects of concrete density, confining stress and strain rate on the mechanical properties of foamed concrete. The direct shear tests were also performed to investigate the effects of concrete density and normal stress on the nonlinear behaviors of foamed concrete layer-lining interface. The test results showed that the mechanical properties of foamed concrete are significantly influenced by the concrete density. The foamed concrete also has high volumetric compressibility and strain-rate dependence. The peak stress. residual stress. shear stiffness and residual friction coefficient of the foamed concrete layer-lining interface are influenced by the foamed concrete density and normal stress applied. Then, a crushable foam constitutive model was constructed using ABAQUS software and a composite exponential model was also established to study the relationship between shear stress and shear displacement of the interface, in which their parameters were fitted based on the experimental results. Finally, a parametric analysis using the finite element method(FEM) was conducted to understand the influence of foamed concrete layer properties on the seismic isolation effect, including the density and thickness of the layer as well as the shear stiffness and residual friction coefficient of the interface. It was revealed that lower density and greater thickness in addition to smaller shear stiffness or residual friction coefficient of the foamed concrete layer could yield better seismic isolation effect, and the influences of the first two tend to be more significant.

Groundwater monitoring of an open-pit limestone quarry:Water-rock interaction and mixing estimation within the rock layers by geochemical and statistical analyses

Water-rock interaction and groundwater mixing are important phenomena in understanding hydrogeological systems and the stability of rock slopes especially those consisting largely of moderately watersoluble minerals like calcite. In this study, the hydrogeological and geochemical evolutions of groundwater in a limestone quarry composed of three strata: limestone layer(covering), interbedded layer under the covering layer, and slaty greenstone layer(basement) were investigated. Water-rock interaction in the open-pit limestone quarry was evaluated using PHREEQC, while hierarchical cluster analysis(HCA)and principal component analysis(PCA) were used to classify and identify water sources responsible for possible groundwater mixing within rock layers. In addition, Geochemist's Workbench was applied to estimate the mixing fractions to clarify sensitive zones that may affect rock slope stability. The results showed that the changes in Ca2+and HCO3àconcentrations of several groundwater samples along the interbedded layer could be attributed to mixing groundwater from the limestone layer and that from slaty greenstone layer. Based on the HCA and PCA results, groundwaters were classified into several types depending on their origin:(1) groundwater from the limestone layer(LO),(2) mixed groundwater flowing along the interbedded layer(e.g., groundwater samples L-7, L-11, S-3 and S-4), and(3) groundwater originating from the slaty greenstone layer(SO). The mixing fractions of 41% LO: 59% SO, 64% LO: 36% SO, 43%LO: 57% SOand 25% LO: 75% SOon the normal days corresponded to groundwaters L-7, L-11, S-3 and S-4,respectively, while the mixing fractions of groundwaters L-7 and L-11(61% LO: 39% SOand 93% LO: 7% SO,respectively) on rainy days became the majority of groundwater originating from the limestone layer.These indicate that groundwater along the interbedded layer significantly affected the stability of rock slopes by enlarging multi-breaking zones in the layer through calcite dissolution and inducing high water pressure, tension cracks and potential sliding plane along this layer particularly during intense rainfall episodes.

Modification of rock mass rating system:Interbedding of strong and weak rock layers

Rock mass classification systems are the very important part for underground projects and rock mass rating(RMR) is one of the most commonly applied classification systems in numerous civil and mining projects. The type of rock mass consisting of an interbedding of strong and weak layers poses difficulties and uncertainties for determining the RMR. For this, the present paper uses the concept of rock bolt supporting factor(RSF) for modification of RMR system to be used in such rock mass types. The proposed method also demonstrates the importance of rock bolting practice in such rock masses. The geological parameters of the Shemshak Formation of the Alborz Tunnel in Iran are used as case examples for development of the theoretical approach.

Dynamic compression characteristics of layered rock mass of significant strength changes in adjacent layers

Layered rock mass of significant strength changes for adjacent layers is frequently observed in underground excavation,and dynamic loading is a prevalent scenario generated during excavation.In order to improve the driving efficiency and reduce engineering accidents,dynamic compression characteristics of this kind of rock mass should be understood.The dynamic properties of a layered composite rock mass are investigated through a series of rock tests and numerical simulations.The rock mass is artificially made of various proportions of sand,cement and water to control the distinct strength variations at various composite layers separated by parallel bedding planes.All rock specimens are prefabricated in a specially designed mould and then cut into 50 mm in diameter and 50 mm in height for split Hopkinson pressure bar(SHPB)dynamic compression testing.The test results reveal that increasing strain rate causes the increases of peak strength,σ_p,and the corresponding failure strain,ε_p,while the dynamic elastic modulus,E_d,remains almost unchanged.Interestingly,under the same strain rates,Ed of the composite rock specimen is found to decline first and then increase as the dip angle of bedding plane increases.The obtained rock failure patterns due to various dip angles lead to failure modes that could be classified into four categories from our dynamic tests.Also,a series of counterpart numerical simulations has been undertaken,showing that dynamic responses are in good agreement with those obtained from the SHPB tests.The numerical analysis enables us to Iook into the dynamic characteristics of the composite rock mass subjected to a broader range of strain rates and dip angles than these being tested.

Physical model test and numerical simulation on the failure mechanism of the roadway in layered soft rocks

To explore the failure mechanism of roadway in layered soft rocks,a physical model with the physically finite elemental slab assemblage(PFESA)method was established.Infrared thermography and a video camera were employed to capture thermal responses and deformation.The model results showed that layered soft roadway suffered from large deformation.A three-dimensional distinct element code(3 DEC)model with tetrahedral blocks was built to capture the characteristics of roadway deformation,stress,and cracks.The results showed two failure patterns,layer bending fracture and layer slipping after excavation.The layer bending fracture occurred at positions where the normal direction of layers pointed to the inside of the roadway and the layer slipping occurred in the ribs.Six schemes were proposed to investigate the effects of layered soft rocks.The results showed that the deformation of ribs was obviously larger than that of the roof and floor when the roadway passed through three types of strata.When the roadway was completely in a coal seam,the change of deformation in ribs was not obvious,while the deformation in the roof and floor increased obviously.These results can provide guidance for excavation and support design of roadways in layered soft rocks.

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.

Lateral compression and energy absorption of foamed concrete-filled polyethylene circular pipe as yielding layer for high geo-stress soft rock tunnels

Foamed concrete as energy absorption material for high geo-stress soft rock tunnels has been proven to be feasible due to its high compressibility and lightweight.However,the lengthy curing and defoaming problems caused by the cast-in-place method of large-volume foamed concrete remain unsolved.In this study,we propose a novel energy absorber composed of foamed concrete-filled polyethylene(FC-PE)pipe and analyze its deformation and energy absorption capacity via quasi-static lateral compression experiments.Results show that FC-PE pipes exhibit typical three-stage deformation characteristics,comprising the elastic stage,the plastic plateau,and the densification stage.Furthermore,the plateau stress,energy absorption,and specific energy absorption of the specimens are 0.81–1.91 MPa,164–533 J,and 1.4–3.6 J/g,respectively.As the density of the foamed concrete increases,the plateau stress and energy absorption increase significantly.Conversely,the length of the plastic plateau and energy absorption efficiency decrease.Moreover,based on the vertical slice method,progressive compression of core material,and the 6 plastic hinges deformation mechanism of the pipe wall,a theoretical calculation method for effective energy absorption is established and achieves good agreement with experimental results,which is beneficial to the optimization of the composite structure.

Tomography of the dynamic stress coefficient for stress wave prediction in sedimentary rock layer under the mining additional stress

In this study,the tomography of dynamic stress coefficient(TDSC)was established based on a mechanical model of stress wave propagation in bedding planes and a mathematical model of the stress wave attenuation in rock masses.The reliability of the TDSC was verified by a linear bedding plane model and field monitoring.Generally,the TDSC in the dynamic stress propagation of bedding planes increases with the following conditions:(1)the increase of the normal stiffness of the bedding plane,(2)the increase of the incident angle of the stress wave,(3)the decrease of the incident frequency of the stress wave,or(4)the growth of three ratios(the ratios of rock densities,elastic moduli,and the Poisson’s ratios)of rocks on either side of bedding planes.The additional stress weakens TDSC linearly and slowly during the stress wave propagation in bedding planes,and the weakening effect increases with the growth of the three ratios.Besides,the TDSC decreases exponentially in the rock mass as propagation distance increases.In a field case,the TDSC decreases significantly as vertical and horizontal distances increase and its wave range increases as vertical distance increases in the sedimentary rock layers.

Time-dependent squeezing deformation mechanism of tunnels in layered soft-rock stratum under high geo-stress

Large squeezing deformation of layered soft rock tunnel under high geo-stress has a significant time-dependent deformation behavior.In this paper,we studied the deformation mechanism during the construction period of deep-buried softrock tunnel by means of a combination of field observations and a numerical method.First,a new classification criterion for large deformations based on the power exponent variation law between the deformation and the strength-stress ratio is proposed.Then,the initial damage tensor reflecting the bedding plane(joint)distribution and an equivalent damage evolution equation derived from the viscoplastic strain are introduced based on the geometric research method,i.e.,a new rheological damage model(RDL model)of layered soft rock is established consisting of elastic,viscous,viscoelastic,viscoplastic and plastic elements.A field test was conducted on the Maoxian tunnel in Sichuan province,southwestern China,which is in broken phyllite(layered soft rock)under high geo-stress.The tunnel has experienced large deformation due to serious squeezing pressure,thus we adopted double primary support method to overcome the supporting structure failure problems.The rheological parameters of phyllite in the Maoxian tunnel were recognized by using SA-PSO optimization,and the RDL model does a good job in describing the time-dependent deformation behavior of a layered soft-rock tunnel under high geo-stress.Thus,the RDL model was used to investigate the supporting effect and bearing mechanism of the double primary support method.Compared with the single primary support method,the surrounding rock pressure,secondary lining force,surrounding rock deformation,and the depth of the damage to the rock mass was reduced by 40%-60%after the double primary support method was used.

Numerical simulation and experimental study on dissolving characteristics of layered salt rocks

Underground salt cavern reservoirs are ideal spaces for energy storage. China is rich in salt rock resources with layered lacustrine sedimentary structures. However, the dissolution mechanism of layered salt rocks remains poorly understood, resulting in significant differences between the actual measurements and the designed indices for the layered salt rock water-soluble cavity-making cycle and the cavity shape. In this work, the dissolution rates of 600 groups of layered salt rocks in China under different conditions were determined experimentally.Thus, the established artificial neural network prediction model was used to assess the effects of the contents of NaCl, Na2 SO4, and CaSO4 in the salt rocks, concentrations, dissolution angles, and flow rates on their dissolution rates by performing ANOVA and F-test. The results provide a theoretical basis for evaluating the dissolution rate of layered salt rocks under different conditions and for the numerical simulation of the layered salt rock water-soluble cavity-making process.

3D FEM analysis for layered rock considering anisotropy of shear strength

An empirical expression of cohesion （C） and friction angle （Ф） for layered rock was suggested. This expression was compared with a test result made by the former researchers. The constitutive relationship of a transversely isotropic medium and Mohr-Coulomb criterion in which C and Ф vary with directions were employed, and a relative 3D elasto-plastic FEM code was developed, in which the important thing was to adopt a search-trial method to find the orientation angle （p） of shear failure plane （or weakest shear plane） with respect to the major principal stress as well as the corresponding C and Ф Taking an underground opening as the calculation object, the numerical analyses were carried out by using the FEM code for two cases of transversely isotropic rock and isotropic rock, respectively, and the computation results were compared. The results show that when the rock is a transversely isotropic one, the distributions of displacements, plastic zones and stress contours in the surrounding rock will be non-axisymmetric along the tunnel＇s vertical axis, which is very different from that of isotropic rock. The stability of the tunnel in transversely isotropic rock is relatively low.

Forward prediction for tunnel geology and classification of surrounding rock based on seismic wave velocity layered tomography

Excavation under complex geological conditions requires effective and accurate geological forward-prospecting to detect the unfavorable geological structure and estimate the classification of surround-ing rock in front of the tunnel face.In this work,a forward-prediction method for tunnel geology and classification of surrounding rock is developed based on seismic wave velocity layered tomography.In particular,for the problem of strong multi-solution of wave velocity inversion caused by few ray paths in the narrow space of the tunnel,a layered inversion based on regularization is proposed.By reducing the inversion area of each iteration step and applying straight-line interface assumption,the convergence and accuracy of wave velocity inversion are effectively improved.Furthermore,a surrounding rock classification network based on autoencoder is constructed.The mapping relationship between wave velocity and classification of surrounding rock is established with density,Poisson’s ratio and elastic modulus as links.Two numerical examples with geological conditions similar to that in the field tunnel and a field case study in an urban subway tunnel verify the potential of the proposed method for practical application.

Integrated simulation and monitoring to analyze failure mechanism of the anti-dip layered slope with soft and hard rock interbedding

The significant difference between the mechanical properties of soft rock and hard rock results in the complexity of the failure mode of the anti-dip layered slope with soft and hard rock interbedding.In order to reveal the landslide mechanism,taking the north slope of Fushun West Open-pit Mine as an example,this paper analyzed the failure mechanism of different landslides with monitoring and field surveys,and simulated the evolution of landslides.The study indicated that when the green mudstone(hard rock)of the anti-dip slope contains siltized intercalations(soft rock),the existence of weak layers not only aggravates the toppling deformation of anti-dip layered slope with high dip,but also causes the shear failure of anti-dip layered slope with stable low dip.The shear failure including subsidence induced sliding and wedge failure mainly exists in the unloading zone of the slope.Its failure depth and failure time were far less than that of toppling failure.In terms of the development characteristics of deformation,toppling deformation has the long-term and progressive characteristics,but shear failure deformation has the abrupt and transient characteristics.This study has deepened the understanding of such slope landslide mechanism,and can provide reference for similar engineering.

Flow simulation considering adsorption boundary layer based on digital rock and finite element method

Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,comparatively fewer works have been devoted to study the effect of adsorption boundary layer(ABL)in throats based on the digital rock method.By considering an ABL,we investigate its effects on fluid flow.We build digital rock model based on computed tomography technology.Then,microscopic pore structures are extracted with watershed segmentation and pore geometries are meshed through Delaunay triangulation approach.Finally,using the meshed digital simulation model and finite element method,we investigate the effects of viscosity and thickness of ABL on microscale flow.Our results demonstrate that viscosity and thickness of ABL are major factors that significantly hinder fluid flow in throats.