Roof collapse mechanism of weak surrounding rock for deep-buried tunnels under high geostress conditions

High geostress,a typical attribute of tunnels located at significant depths,is crucial in causing stress-induced failure and influencing the stability of the tunnel crown.This study developed an analytical method for the failure mechanism that occurs in deep-buried tunnel roofs,taking into account the influence of geostress.The limit analysis theory was utilized for deriving analytical solutions about the geometry of the collapsing surface and the limit supporting pressure.The collapsing surface obtained by the analytical solution was validated by the findings of the physical model test,which shows a high level of agreement with the actual one.An extensive investigation was done to explore the effects of the lateral pressure coefficients,the tunnel buried depth,the geological conditions of the surrounding rock,the long-short axis ratio,and the size of the tunnel profile.The findings indicate that an increase in the lateral pressure coefficient from 0.5 to 1.5 results in a reduction in the height of the collapsing zone by 2.08 m and the width of the collapsing zone by 1.15 m,while simultaneously increases the limit supporting pressure by 18.9%.The proposed upper bound method accurately determines the limit supporting pressure and the geometry of the collapsing surface,which aligns well with the results acquired through numerical modelling and on-site monitoring in actual engineering applications.The proposed analytical method can serve as a reference for similar crown failure issues of deep-buried tunnels.

Analytical solution for steady seepage into a circular deep-buried mountain tunnel with grouted zone in anisotropic strata

Due to the existence of a large number of discontinuous fractures and interfaces in tunnel surrounding rocks,the groundwater inflow into tunnel generally presents significant anisotropy.Therefore,it is of great significance to consider the anisotropic permeability when dealing with water gushing-induced engineering accidents in water-rich mountain tunnels with large burial depth.In this study,based on the complex variable method and the seepage flow theory,a theoretical model of water inflow into a deep-buried circular tunnel in a fully saturated,anisotropic and semi-infinite aquifer is developed.The influence of grouted zone,initial support and secondary lining is fully considered.By comparison to the existing analytical methods and numerical results,the reliability of this proposed analytical solution is well validated.It is indicated from the parametric study that the groundwater inflow into tunnel presents an upward trend with an increasing value of the strata permeability in the vertical direction.Moreover,the water inflow rate and the total water head decrease with the growth of the thickness of grouting circle.It is suggested that reasonable grouting thickness and permeability should be controlled to enhance the grouting effect.This study provides a practical method for estimating the water inflow into a deep-buried,grouted and lined mountain tunnel considering the anisotropic strata permeability.

Fisher discriminant analysis model and its application for prediction of classification of rockburst in deep-buried long tunnel

A Fisher discriminant analysis （FDA） model for the prediction of classification of rockburst in deep-buried long tunnel was established based on the Fisher discriminant theory and the actual characteristics of the project. First, the major factors of rockburst, such as the maximum tangential stress of the cavern wall σθ, uniaxial compressive strength σc, uniaxial tensile strength or, and the elastic energy index of rock Wet, were taken into account in the analysis. Three factors, Stress coefficient σθ/σc, rock brittleness coefficient σc/σt, and elastic energy index Wet, were defined as the criterion indices for rockburst prediction in the proposed model. After training and testing of 12 sets of measured data, the discriminant functions of FDA were solved, and the ratio of misdiscrimina- tion is zero. Moreover, the proposed model was used to predict rockbursts of Qinling tunnel along Xi＇an-Ankang railway. The results show that three forecast results are identical with the actual situation. Therefore, the prediction accuracy of the FDA model is acceptable.

Temperature effects on the failure of deep circular tunnel under true-triaxial compression

The failure characteristics of thermal treated surrounding rocks should be studied to evaluate the stability and safety of deep ground engineering under high-ground-temperature and high-ground-stress conditions.The failure process of the inner walls of fine-grained granite specimens at different temperatures(25–600℃)was analyzed using a true-triaxial test system.The failure process,peak intensity,overall morphology(characteristics after failure),rock fragment characteristics,and acoustic emission(AE)characteristics were analyzed.The results showed that for the aforementioned type of granite specimens,the trend of the failure stress conditions changed with respect to the critical temperature(200℃).When the temperature was less than 200℃,the initial failure stress increased,final failure stress increased,and failure severity decreased.When the temperature exceeded 200℃,the initial failure stress decreased,final failure stress decreased,and failure severity increased.When the temperature was 600℃,the initial and final failure stresses of the specimens decreased by 60.93%and 19.77%compared with those at 200℃,respectively.The numerical results obtained with the software RFPA3D-Thermal were used to analyze the effect of temperature on the specimen and reveal the mechanism of the failure process in the deep tunnel surrounding rock.

Impact of surface-reflected seismic waves on the seismic isolation performance of circular tunnel isolation layers

Seismic isolation is an effective strategy to mitigate the risk of seismic damage in tunnels.However,the impact of surface-reflected seismic waves on the effectiveness of tunnel isolation layers remains under explored.In this study,we employ the wave function expansion method to provide analytical solutions for the dynamic responses of linings in an elastic half-space and an infinite elastic space.By comparing the results of the two models,we investigate the seismic isolation effect of tunnel isolation layers induced by reflected seismic waves.Our findings reveal significant differences in the dynamic responses of the lining in the elastic half-space and the infinitely elastic space.Specifically,the dynamic stress concentration factor(DSCF)of the lining in the elastic half-space exhibits periodic fluctuations,influenced by the incident wave frequency and tunnel depth,while the DSCF in the infinitely elastic space remain stable.Overall,the seismic isolation application of the tunnel isolation layer is found to be less affected by surface-reflected seismic waves.Our results provide valuable insights for the design and assessment of the seismic isolation effect of tunnel isolation layers.

Experimental study on similarity materials for soft rock of deep-buried tunnels

When every parameter is properly scaled down in accordance with some similarity coefficients, it is possible to study the physical-mechanical properties of rock mass with a scale model. To identify the key mechanisms of soft rock in deep buried tunnels, the proper sand, binder and ratio were selected. During the process, the model manufacture technology was introduced and typical tests were done and the results were presented. The physical and meehanieal properties effects caused by each composition were discussed. It is shown that the physical and mechanical properties of chosen ratio material such as uniaxial compressive strength tests, elasticity modulus, tensile strength, internal frictional angle, and Poisson＇s ratio meet with similarity relationship well. The physical and mechanical properties of deep soft rock are simulated successfully.

Stress wave propagation and incompatible deformation mechanisms in rock discontinuity interfaces in deep-buried tunnels

Complex weak structural planes and fault zones induce significant heterogeneity,discontinuity,and nonlinear characteristics of a rock mass.When an earthquake occurs,these characteristics lead to extremely complex seismic wave propagation and vibrational behaviors and thus pose a huge threat to the safety and stability of deep buried tunnels.To investigate the wave propagation in a rock mass with different structural planes and fault zones,this study first introduced the theory of elastic wave propagation and elastodynamic principles and used the Zoeppritz equation to describe wave field decomposition and develop a seismic wave response model accordingly.Then,a physical wave propagation model was constructed to investigate seismic waves passing through a fault,and dynamic damage was analyzed by using shaking table tests.Finally,stress wave attenuation and dynamic incompatible deformation mechanisms in a rock mass with fault zones were explored.The results indicate that under the action of weak structural planes,stress waves appear as a complex wave field decomposition phenomenon.When a stress wave spreads to a weak structural plane,its scattering may transform into a tensile wave,generating tensile stress and destabilizing the rock mass;wave dynamic energy is absorbed by a low-strength rock through wave scattering,which significantly weakens the seismic load.Wave propagation accelerates the initiation and expansion of internal defects in the rock mass and leads to a dynamic incompatible deformation.This is one of the main causes for large deformation and even instability within rock masses.These findings provide an important reference and guide with respect to stability analysis of rock mass with weak structural planes and fault zones.

Experimental simulation investigation of influence of depth on spalling characteristics in circular hard rock tunnel

A series of true-triaxial compression tests were performed on red sandstone cubic specimens with a circular hole to investigate the influence of depth on induced spalling in tunnels.The failure process of the hole sidewalls was monitored and recorded in real-time by a micro-video monitoring equipment.The general failure evolution processes of the hole sidewall at different initial depths(500 m,1000 m and 1500 m)during the adjustment of vertical stress were obtained.The results show that the hole sidewall all formed spalling before resulting in strain rockburst,and ultimately forming a V-shaped notch.The far-field principal stress for the initial failure of the tunnel shows a good positive linear correlation with the depth.As the depth increases,the stress required for the initial failure of the tunnels clearly increased,the spalling became more intense;the size and mass of the rock fragments and depth and width of the V-shaped notches increased,and the range of the failure zone extends along the hole sidewall from the local area to the entire area.Therefore,as the depth increases,the support area around the tunnel should be increased accordingly to prevent spalling.

Numerical Simulation of Rock Burst in Circular Tunnels Under Unloading Conditions

Rock burst in a circular tunnel under high in-situ stress conditions was investigated with a numerical method coupled the rock failure process theory (RFPA) and discontinuous deformation theory (DDA). Some numerical tests were carraied out to investigate the failuer patterns of circular tunnel under unloading conditions. Compared the results under loading conditions,the shapes of failure zones are more regular under the unloading conditions. The failure pat-terns in the same type of rock mass are clearly different because of non-homogeneity of the rock material. The extension of cracks shows some predictability with an increasing of in-situ stress. When the homogeneity index of rocks (m) is ei-ther relatively high or low and lateral pressure coefficients (λ) is high,the number of regular shear slide cracks decreases and the probability of a rock burst also becomes lower. Our numerical simulation results show that the stability of sur-face rock and the natural bedding stratification of rock material greatly affect rock bursts. Installing bolts with due dili-gence and suitably can effectively prevent rock bursts. However,it is not effective to control rock bursts by releasing the strain energy with normal pre-boreholes.

Experimental investigation on influence of loading rate on rockburst in deep circular tunnel under true-triaxial stress condition

To investigate the influence of loading rate on rockburst in a circular tunnel under three-dimensional stress conditions,the true-triaxial tests were conducted on 100 mm×100 mm×100 mm cubic sandstone specimens with d50 mm circular perforated holes,and the failure process of hole sidewall was monitored and recorded in real-time by the microcamera.The loading rates were 0.02,0.10,and 0.50 MPa/s.The test results show that the rockburst process of hole sidewall experienced calm period,pellet ejection period,rock fragment exfoliation period and finally formed the V-shaped notch.The rockburst has a time lag and vertical stress is high when the rockburst occurs.The vertical stress at the initial failure of the hole sidewall increases with loading rate.During the same period after initial failure,the rockburst severity of hole sidewalls increased significantly with increasing loading rate.When the vertical stress is constant and maintains a high stress level,the rockburst of hole sidewall under low loading rate is more serious than that under high loading rate.With increasing loading rate,the quality of rock fragments produced by the rockburst decreases,and the fractal dimension of rock fragments increases.

Elasto-plastic analysis of the surrounding rock mass in circular tunnel based on the generalized nonlinear unified strength theory

The present paper aims to establish a versatile strength theory suitable for elasto-plastic analysis of underground tunnel surrounding rock. In order to analyze the effects of intermediate principal stress and the rock properties on its deformation and failure of rock mass, the generalized nonlinear unified strength theory and elasto-plastic mechanics are used to deduce analytic solution of the radius and stress of tunnel plastic zone and the periphery displacement of tunnel under uniform ground stress field. The results show that: intermediate principal stress coefficient b has significant effect on the plastic range,the magnitude of stress and surrounding rock pressure. Then, the results are compared with the unified strength criterion solution and Mohr–Coulomb criterion solution, and concluded that the generalized nonlinear unified strength criterion is more applicable to elasto-plastic analysis of underground tunnel surrounding rock.

Rockburst process and strength-weakening effect of the high-stress circular tunnel under internal unloading

To investigate the influence of unloading effect of a circular tunnel face on rockburst process,by innovatively combining rock drilling unloading devices and triaxial systems,the strain rockburst simulation under the entire stress path of“high initial stressþinternal unloadingþstress adjustment”(HUS test)was realized for the intact cubic red sandstone samples(100 mm×100 mm×100 mm).Comparative tests were conducted on cubic red sandstone samples with prefabricated circular holes(425 mm)under the stress path of“prefabricated circular hole+þhigh initial stress+stress adjustment”(PHS test),thereby highlighting the influence of internal unloading on rockburst failure.The test results revealed that with an increase in vertical stress,the sidewalls in both the HUS and PHS tests suffered strain rockburst failure.Compared with the PHS test,the initial failure stress in the HUS test is lower,and it is easier to induce sidewall rockbursts.This indicates that the internal unloading influences the sidewall failure,causing an obvious strength-weakening effect,which becomes more significant with an increase in buried depth.The strain rockburst failure was more severe in the HUS test owing to the influence of internal unloading.V-shaped rockburst pits were formed in the HUS tests,whereas in the PHS test,arcshaped rockburst pits were produced.It was also found that strain rockburst failure may occur only when the rock has a certain degree of rockburst proneness.

Elasto-plastic Analysis of Circular Tunnels in Jointed Rock Masses Satisfy the Hoek-Brown Failure Criterion

The relationship between the Hoek-Brown parameters and the mechanical response of circular tunnels is il-lustrated. Closed-form and approximate solutions are given for the extent of the plastic zone and the stress and dis-placement fields under axisymmetrical and asymmetric stress conditions. For the same rock masses and under axisym-metrical stress conditions,the radius of the plastic zone in terms of Hoek-Brown criterion is generally an approximation of the radius in terms of the Mohr-Coulomb criterion. The radius in terms of the Hoek-Brown criterion is larger under low stress conditions. For poor quality rock masses (GSI<25),measures (such as grouting,setting rock bolts,etc.) that improve the GSI of rock masses are effective in improving the stability of tunnels. It is not advisable to improve the sta-bility of the tunnels by providing a small support resistance p through shotcrete,except for very poor quality jointed rock masses. Without reference to the quality of the rock mass,the disturbance factor D should not less than 0.5. Meas-ures which disturb rock masses during tunnel construction should be taken carefully when the tunnel depth increases.

Failure process and characteristics of three-dimensional high-stress circular tunnel under saturated water content

True-triaxial compression tests were carried out on cubic granite samples with a circular through hole using a true-triaxial testing system to investigate the influence of saturated water content(SWC) on the failure process and characteristics of a circular tunnel of surrounding rocks. The spalling failure under SWC can be divided into four periods: calm period, buckling deformation period, period of rock fragment gradual buckling and exfoliation, and period of formation of symmetrical V-shaped notches. When the horizontal axial and vertical stresses were constant, the spalling failure severity was reduced with the increase in lateral stress. Under natural water content, a strong rockburst with dynamic failure characteristics occurred on the circular hole sidewall. Under SWC, the failure severity was reduced and the circular hole sidewall experienced spalling failure, exhibiting progressive static failure characteristics.Therefore, water can reduce the failure severity of surrounding rocks in deep underground engineering, which has a certain guiding significance for the prevention and control of rockbursts.

MECHANISM AND CATASTROPHE THEORY ANALYSIS OF CIRCULAR TUNNEL ROCKBURST

Mechanism of circular tunnel rockburst is that, when the carrying capacity of the centralized zone of plastic deformation in limiting state reduces, the comparatively intact part in rock mass unloads by way of elasticity; rockburst occurs immediately when the elastic energy released by the comparatively intact part exceeds the energy dissipated by plastic deformation. The equivalent strain was taken as a state variable to establish a catastrophe model of tunnel rockburst, and the computation expression of the earthquake energy released by tunnel rockburst was given. The analysis shows that, the conditions of rockburst occurrence are relative to rock＇s ratio of elastic modulus to descendent modulus and crack growth degree of rocks; to rock mass with specific rockburst tendency, there exists a corresponding critical depth of softened zone, and rockburst occurs when the depth of softened zone reaches.

Research on the closure and creep mechanism of circular tunnels

A numerical code called Rock Failure Process Analysis (RFPA2D) was em- ployed to investigate the closure,damage and failure behavior of the horizontal tunnels.In this code the time-dependent deformation was described in terms of evolution of meso- scopic structure,leading to progressive degradation of elastic modulus and failure strength of material.In terms of material degradation,a series of numerical simulations were per- formed to study the convergence and subsequent failure in circular tunnels.The numerical results provide a complete illumination for the closure,damage and failure behavior with different loading conditions.It is shown that the depth and the ratio of far field stresses play an important role in the creep behavior of tunnels.Creep failure is expected to occur in the direction of the smallest far field stress component,which means that rheological failure of tunnels is influenced not only by the rock characteristic around the tunnels but also by the orientation and distribution of far field stress on a global scale.

Axisymmetric alternating direction explicit scheme for efficient coupled simulation of hydro-mechanical interaction in geotechnical engineering-Application to circular footing and deep tunnel in saturated ground

Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit(ADE)scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in nonuniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourthorder finite difference(FD) approximation to the spatial derivatives of the axisymmetric fluid-diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps,giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua(FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%-50% that of FLAC’s basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%-1.8%.

Transient response of a concrete tunnel in an elastic rock with imperfect contact

The two-dimensional transient response of an imperfect bonded circular lined pipeline lying in an elastic infinite medium is investigated.Imperfect boundary conditions between the surrounding elastic rock and the tunnel are modelled with a two-linear-spring design.The novelty of the manuscript consists in studying at the same time transient regimes and imperfect bonded interfaces for simulating the dynamic response of a tunnel embedded in an elastic infinite rock.Wave propagation fields in tunnel and rock are expressed in terms of infinite Bessel and Hankel series.To solve the transient problem,the Laplace transform and the associated Durbin’s algorithm are performed.To exhibit the dynamic responses,influences of various parameters such as the quality of the interface conditions and the thickness of the lining are presented.The dynamic hoop stresses and the solid displacements of both the tunnel and the rock are also proposed.

Shear testing on rock tunnel models under constant normal stress conditions

Large shear deformation problems are frequently encountered in geotechnical engineering.To expose the shear failure mechanism of rock tunnels,compression-shear tests for rock models with circular tunnel were carried out,including single tunnel and adjacent double tunnels.The failure process is recorded by the external video and miniature cameras around the tunnel,accompanied by real-time acoustic emission monitoring.The experiments indicate that the shearing processes of rock tunnel can be divided into four steps:(i)cracks appeared around tunnels,(ii)shear cracks and spalling ejection developed,(iii)floor warping occurred,and(iv)shear cracks ran through the tunnel model.Besides,the roughness of the sheared fracture surface decreased with the increase in normal stress.Corresponding numerical simulation indicates that there are tensile stress concentrations and compressive stress concentrations around the tunnel during the shearing process,while the compressive stress concentration areas are under high risk of failure and the existence of adjacent tunnels will increase the degree of stress concentration.

Limit analysis of supporting pressure in tunnels with regard to surface settlement

The proliferation of Hoek-Brown nonlinear failure criterion and upper bound theorem makes it possible to evaluate the stability of circular tunnels with an original curved collapsing mechanism. The arch effect of shallow circle tunnel is not taken into consideration so that the mechanical characteristics can be easily described. Based on the mechanism, the upper bound solution of supporting pressure of tunnels under the condition of surface settlements and overloads on the ground surface is derived. The objective function is formed from virtual work equations under the variational principle, and solutions are presented by the optimum theory. Comparisons with previous works are made. The numerical results of the present method show great agreement with those of existing ones. With regard to the surface settlement and overloads, the influence of different rock parameters on the collapsing shape is analyzed.