Mechanical Behaviors of Anchorage Interfaces in Layered Rocks with Fractures under Axial Loads

Rock bolts are widely employed as an effective and efficient reinforcement method in geotechnical engineering.Sandwich composite structures formed by hard rock and weak rock are often encountered in practical projects.Furthermore,the spatial structure of the rock mass has a direct influence on the effect of the anchorage support.To investigate the impact of rock mass structure on the mechanical characteristics of anchorage interfaces,pull-out tests on reinforced specimens with different mudstone thicknesses and fracture dip angles are conducted.The experimental results indicate that the percentage of mudstone content and fracture dip angle have a significant influence on the pullout load of the samples.A weaker surrounding rock results in a lower peak load and a longer critical anchorage length,and vice versa.The results also show that 70%mudstone content can be considered a critical condition for impacting the peak load.Specifically,the percentage of mudstone content has a limited influence on the variation in the peak load when it exceeds 70%.Optical fiber deformation results show that compared to the rock mass with fracture dip angles of 0°and 60°,the rock mass with a fracture dip angle of 30°has a more uniformly distributed force at the anchorage interface.When the fracture dip angle exceeds 60°,the dip angle is no longer a key indicator of peak load.The accuracy of the experimentally obtained load-displacement curves is further verified although numerical simulation using the discrete element method.

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.

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.

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.

Kinematic analysis of shallow tunnel in layered strata considering joined effects of settlement and seepage

The purpose of this work is to predict the state of collapse in shallow tunnel in layered strata by using a new curved failure mechanism within the framework of upper bound theorem.Particular emphasis is first given to consider the effects of seepage forces and surface settlement.Furthermore,the Hoek-Brown nonlinear failure criterion is adopted to analyze the influence of different factors on the collapsing shape.Two different curve functions which describe two different rock layers are obtained by virtual work equations under the variational principle.According to the numerical results,the parameter B in Hoek-Brown failure criterion and the unit weights in different rock layers have a positive relationship with the size of collapsing block while pore pressure coefficient and the parameter A in Hoek-Brown failure criterion present a reverse tend.

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.

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.

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.

Three-Dimensional Collapse Analysis for a Shallow Cavity in Layered Strata Based on Upper Bound Theorem

Layered rock strata are observed to be common during the excavation of tunnels or cavities,and may significantly affect the deformation and failure characteristics of surrounding rock masses due to various complex forms and mechanical properties.In this paper,we propose a three-dimensional axisymmetric velocity field for roof collapse of shallow cavities in multi rock layers,by considering the influences of roof cross-section shapes,supporting pressure,ground overload,etc.The internal energy dissipation rate and work rates of external forces corresponding to the velocity field are computed by employing the Hoek-Brown strength criterion and its associated flow rule.Further,the equations of the collapse surfaces and the corresponding weight of collapsing rock masses are derived on the basis of upper bound theorem.Furthermore,we validate the proposed method by comparing the results of numerical calculations and existing research findings.The change laws of the collapse range under varying parameters are obtained for the presence of rectangular and spherical cavities.We also find that the three-dimensional mechanism is relatively safer for engineering designing actually,compared with the traditional two-dimensional mechanism.All these conclusions may provide workable guidelines for the support design of shallow cavities in layered rock strata practically.

The formation of orthogonal joint systems and cuboidal blocks:New insights gained from flat-lying limestone beds in the region of Havre-Saint-Pierre(Quebec,Canada)

Vertical orthogonal joints are a common feature in shallow crustal rocks.There are several competing theories for their formation despite the ubiquity.We examined the exceptional exposures of orthogonal joints in flat-lying Ordovician limestone beds from the Havre-Saint-Pierre Region in Quebec,Canada(north shore of Saint-Lawrence River)to test conceptual models of joint formation in a natural setting.In the region,the spacing of cross-joints is consistently larger than the spacing of systematic joints by a factor of 1.5 approximately.The joint-spacing-to-bed-thickness ratios(s/t)are much larger in these beds(s/t=4.3 for systematic joints,and 6.4 for cross-joints)than those in higher strained strata along the south shore of the Saint-Lawrence River(s/t=1),highlighting the effect of tectonic strain in decreasing fracture spacing and block size.The high values of s/t indicate that cross-joint formation was unlikely caused by a switch from compression to tension once a critical s/t ratio for systematic joints was reached(as hypothesized in previous studies).We proposed a new model for the formation of orthogonal joint systems where the principal stress axes locally switch during the formation of systematic fractures.The presence of ladder-shaped orthogonal joints suggests a state of effective stress withσ_(1)^(∗)≫0>σ_(2)^(∗)>σ_(3)^(∗)and whereσ_(2)^(∗)-σ_(3)^(∗)is within the range of fracture strength variability at the time of fracture.This research provides a new mechanical model for the formation of orthogonal joint systems and cuboidal blocks.

Research on the influence of rock fracture toughness of layered formations on the hydraulic fracture propagation at the initial stage

Deep underground rocks exhibit significant layered heterogeneity due to geological evolution and sedimentation.Rock fracture toughness, as one of the important indicators of hydraulic crack propagation, also exhibits heterogeneous distribution. In order to investigate the influence of non-uniform fracture toughness of layered rockson hydraulic crack propagation, this paper establishes a planar three-dimensional hydraulic crack propagationmodel. The model is numerically solved using the 3D displacement discontinuity method (3D-DDM) and the finitedifference method. The calculation results indicate that when the distribution of the fracture toughness of layeredrocks changes from uniform to non-uniform, the fracture morphology develops from a standard circular crack toan elliptical crack. When the difference of the rock fracture toughness between adjacent rock layers and themiddle rock layer (pay zone) is large enough, the fracture morphology will develop towards a rectangular shape.In addition, when the fracture toughness of rock layers is non-uniformly distributed, the hydraulic crack not onlyrapidly expand in the softening layer (rock layer with lower fracture toughness), but also slowly propagate in thestrong layer (rock layer with higher fracture toughness). However, the propagation speed in the softening layer ismuch faster than that in the strong layer. The results indicate that the heterogeneity of rock fracture toughness hasan important impact on the morphology, propagation speed, and direction of hydraulic fractures.

Catastrophe analysis of deep tunnel above water-filled caves

To explore the influence of karst cavity pressure on the failure mechanisms of rock layers above water-filled caves, novel blow-out and collapse mechanisms are put forward in this study. The proposed method uses the nonlinear optimization to obtain the failure profiles of surrounding layered rock with water-filled cave at the bottom of the tunnel. By referring to the functional catastrophe theory, stability analysis with different properties in different rock layers is implemented with considering the incorporation of seepage forces since the groundwater cannot be ignored in the catastrophe analysis of deep tunnel bottom. Also the parametric analysis is implemented to discuss the influences of different rock strength factors on the failure profiles. In order to offer a good guide of design for the excavation of deep tunnels above the water-filled caves, the proposed method is applied to design of the minimum effective height for rock layer. The results obtained by this work agree well with the existing published ones.

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.

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.

Study on rock deformation monitoring using fiber Bragg grating in simulation experiment

Presented the fiber Bragg grating （FBG） sensors for rock strain monitoring in the 1.2 m long plane stress model of the simulation experiment. In the past, for the lack of appropriate technique to measure the deformation of rock structures, the measurement of deflection was restricted to just a few discrete points along rock, and the measuring points were limited to the location installed with displacement transducers. We developed a method to monitor the deformation of rock structures using fiber optical Bragg grating strain sensors. The sensors were embedded in rock layers of simulation experiment before the materials were put in. These sensors were then used to monitor the experienced strain with different face advancing distance. The test results indicate that, if properly installed, FBG sensors can survive under severe conditions associated with embedment process and yield accurate measurements of strains response. At the same time, we make comparisons of the data obtained by FBG sensors with those by centesimal gauge. The interest in FBG sensors was motivated by the potential advantages that they can offer more than existing sensing technologies.

Kernel broken smooth particle hydrodynamics method for crack propagation simulation applied in layered rock cells and tunnels

Understanding the cracking process of layered tunnels requires a high-fidelity method.Improved smooth particle hydrodynamics(SPH),termed kernel broken SPH(KBSPH),was implemented to simulate the crack propagation and deformation of layered rock cells and field layered tunnels with dip angles of 0°–90°,and the results were compared with those of the laboratory tests.Three attempts,including the bedding angle,interlayer distance,and lateral pressure coefficient,were made to investigate the crack propagation and deformation of layered tunnels.Finally,the pros and cons of the KBSPH method applied in the rock field were compared with those of other methods.The results indicate that the KBSPH can explicitly reproduce crack propagation by improving the kernel function with a totally damaged symbol,and the deformation responses have been captured reasonably.We infer that this method is effective and rapid in crack propagation and large deformation simulation for other types of rock tunnels.

Crack evolution of soft–hard composite layered rock-like specimens with two fissures under uniaxial compression

Acoustic emission and digital image correlation were used to study the spatiotemporal evolution characteristics of crack extension of soft and hard composite laminated rock masses(SHCLRM)containing double fissures under uniaxial compression.The effects of different rock combination methods and prefabricated fissures with different orientations on mechanical properties and crack coalescence patterns were analyzed.The characteristics of the acoustic emission source location distribution,and frequency changes of the crack evolution process were also investigated.The test results show that the damage mode of SHCLRM is related to the combination mode of rock layers and the orientation of fractures.Hard layers predominantly produce tensile cracks;soft layers produce shear cracks.The first crack always sprouts at the tip or middle of prefabricated fractures in hard layers.The acoustic emission signal of SHCLRM with double fractures has clear stage characteristics,and the state of crack development can be inferred from this signal to provide early warning for rock fracture instability.This study can provide a reference for the assessment of the fracture development status between adjacent roadways in SHCLRM in underground mines,as well as in roadway layout and support.