Collapse mechanism of deep tunnels with three-centered arch cross section

The possible collapse of different circumstances is derived with the help of the limit analysis theory.Analytical equations related to collapsing mechanisms in deep tunnel with smooth three-centered arc cross sections are derived on the basis of Hoek-Brown failure criterion and upper bound limit analysis.The pore water pressure is considered in the analysis,as a work rate of external force.Numerical results about the shape of detaching curve and the weight of collapsing block per unit length corresponding to different parameters are obtained with the help of mathematical software.The shapes of collapsing block are drawn with respected to different parameters.Furthermore,the effects of different parameters on the shape of detaching curve and the weight of the collapsing block are discussed.     

Upper bound analysis for deep tunnel face with joined failure mechanism of translation and rotation

A joined failure mechanism of translation and rotation was proposed for the stability analysis of deep tunnel face, and the upper bound solution of supporting force of deep tunnel was calculated under pore water pressure. The calculations were based on limit analysis method of upper bound theory, with the employment of non-associated Mohr-Coulomb flow rule. Nonlinear failure criterion was adopted. Optimized analysis was conducted for the effects of the tunnel depth, pore water pressure coefficient, the initial cohesive force and nonlinear coefficient on supporting force. The upper bound solutions are obtained by optimum method. Results are listed and compared with the previously published solutions for the verification of correctness and effectiveness. The failure shapes are presented, and results are discussed for different pore water pressure coefficients and nonlinear coefficients of tunnel face.     

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.     

Influence of pore water pressure on upper bound analysis of collapse shape for square tunnel in Hoek-Brown media

To investigate the effective shape of collapsing block in square tunnel subjected to pore water pressure, the analytical solution of detaching curve was derived using upper bound theorem of limit analysis with Hoek-Brown failure criterion. The work rate of pore water pressure, which was regarded as an external rate of work, was taken into account in the framework of limit analysis. Taking advantages of variational calculation, the objective function with respect to detaching curve was optimized to obtain the effective shape of collapsing block for square tunnel. According to the numerical results, it is found that the varying pore water pressure coefficient only affects the height and width of the collapsing block, whereas the shape of collapsing block remains unchanged.     

Minimum safe thickness of rock plug in karst tunnel according to upper bound theorem

High pressure and water-bearing caverns ahead of a karst tunnel face tend to cause geological disasters, such as water and mud bursts. So, the determination of safe thickness of the reserved rock plug is a key technical problem to be solved for karst tunnel construction. Based on the Hoek-Brown nonlinear failure criterion, the minimum safe thickness of rock plug was investigated in the light of the limit analysis theory. On the basis of the proposed failure mode, the expression of the minimum thickness for rock plug was obtained by means of upper bound theorem in combination with variational principle. The calculation results show the influence of each parameter on safe thickness and reveal the damage range of rock plug. The proposed method is verified by comparing the results with those of the drain cavern of Maluqing Tunnel. The research shows that with the increase of compressive strength and tensile strength as well as constant A of Hoek-Brown criterion, the safe thickness decreases, whereas with the increase of cavern pressure, tunnel diameter, and constant B from Hoek-Brown criterion, the safe thickness increases. Besides, the tensile strength, or constants A and B affect the shear failure angle of rock plug structure, but other parameters do not. In conclusion, the proposed method can predict the minimum safe thickness of rock plug, and is useful for water burst study and prevention measures of tunnels constructed in high-risk karst regions.     

Energy analysis of stability of twin shallow tunnels based on nonlinear failure criterion

Based on nonlinear Mohr-Coulomb failure criterion, the analytical solutions of stability number and supporting force on twin shallow tunnels were derived using upper bound theorem of limit analysis. The optimized solutions were obtained by the technique of sequential quadratic programming. When nonlinear coefficient equals 1 and internal friction angle equals 0, the nonlinear Mohr-Coulomb failure criterion degenerates into linear failure criterion. The calculated results of stability number in this work were compared with previous results, and the agreement verifies the effectiveness of the present method. Under the condition of nonlinear Mohr-Coulomb failure criterion, the results show that the supporting force on twin shallow tunnels obviously increases when the nonlinear coefficient, burial depth, ground load or pore water pressure coefficients increase. When the clear distance is 0.5to 1.0 times the diameter of tunnel, the supporting force of twin shallow tunnels reaches its maximum value, which means that the tunnels are the easiest to collapse. While the clear distance increases to 3.5 times the diameter of tunnel, the calculation for twin shallow tunnels can be carried out by the method for independent single shallow tunnel. Therefore, 3.5 times the diameter of tunnel serves as a critical value to determine whether twin shallow tunnels influence each other. In designing twin shallow tunnels,appropriate clear distance value must be selected according to its change rules and actual topographic conditions, meanwhile, the influences of nonlinear failure criterion of soil materials and pore water must be completely considered. During the excavation process, supporting system should be intensified at the positions of larger burial depth or ground load to avoid collapses.     

Kinematical analysis of highway tunnel collapse using nonlinear failure criterion简

For different kinds of rocks, the collapse range of tunnel was studied in the previously published literature. However, some tunnels were buried in soils, and test data showed that the strength envelopes of the soils followed power-law failure criterion. In this work, deep buried highway tunnel with large section was taken as objective, and the basic expressions of collapse shape and region were deduced for the highway tunnels in soils, based on kinematical approach and power-law failure criterion. In order to see the effectiveness of the proposed expressions, the solutions presented in this work agree well with previous results if the nonlinear failure criterion is reduced to a linear Mohr-Coulomb failure criterion. The present results are compared with practical projects and tunnel design code. The numerical results show that the height and width of tunnel collapse are greatly affected by the nonlinear criterion for the tunnel in soil.     

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.     

Stability analysis for natural slope by kinematical approach

The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was constructed. The stability factor formulation by the upper bound theorem leads to a classical nonlinear programming problem, when the external work rate and internal energy dissipation were solved, and the constraint condition of the programming problem was given. The upper bound optimization problem can be solved efficiently by applying a nonlinear SQP algorithm, and stability factor was obtained, which agrees well with previous achievements.     

含黏粒砂土地层浅埋盾构隧道开挖渗流稳定性试验

针对含黏粒砂土地层浅埋盾构隧道开挖渗流稳定性问题,设计制作了主要由模型箱、水循环系统、盾构隧道与开挖面模型、饱和地层模型和量测系统组成的试验装置。通过模型试验,量测开挖面逐渐失稳过程中的地层沉降和开挖面饱和土压力以及前方地层孔隙水压力。结果表明:渗流条件下,开挖面前方地层孔隙水压力,会因地层黏-砂比的增大而增大,且会随开挖面体积损失的增大而增大;渗流会使开挖面极限有效土压力明显增大,开挖面极限有效土压力与地层黏-砂比基本上呈线性增加关系;地层极限失稳范围主要取决于开挖面前方和后方以及横向的破裂角,其中,后方破裂角受地层黏土含量和渗流的影响不大;无渗流时,地层极限失稳范围会因黏-砂比的增大而增大,而有渗流时,地层极限失稳范围会因黏-砂比的增大而减小。研究成果改进了对含黏粒砂土地层浅埋盾构隧道开挖渗流稳定性的认识,可以为实际工程以及有关的稳定性极限分析提供参考。     

Reliability analysis of supporting pressure in tunnels based on three-dimensional failure mechanism

Based on nonlinear failure criterion,a three-dimensional failure mechanism of the possible collapse of deep tunnel is presented with limit analysis theory.Support pressure is taken into consideration in the virtual work equation performed under the upper bound theorem.It is necessary to point out that the properties of surrounding rock mass plays a vital role in the shape of collapsing rock mass.The first order reliability method and Monte Carlo simulation method are then employed to analyze the stability of presented mechanism.Different rock parameters are considered random variables to value the corresponding reliability index with an increasing applied support pressure.The reliability indexes calculated by two methods are in good agreement.Sensitivity analysis was performed and the influence of coefficient variation of rock parameters was discussed.It is shown that the tensile strength plays a much more important role in reliability index than dimensionless parameter,and that small changes occurring in the coefficient of variation would make great influence of reliability index.Thus,significant attention should be paid to the properties of surrounding rock mass and the applied support pressure to maintain the stability of tunnel can be determined for a given reliability index.     

复合地层盾构开挖面极限支护力上限分析

随着地下空间进一步的开发与利用,盾构施工面临的地质条件更加复杂多样。盾构在复合地层中掘进时,因地层间力学性质差异,易因开挖面支护力确定不当而造成失稳破坏,给工程带来负面影响。针对盾构隧道穿越复合地层时,由于上下地层间力学性质差异而导致开挖面支护压力较均质土体中难以确定问题,基于组合对数螺旋线破坏模式作为复合地层中盾构开挖面失稳模型,利用极限分析上限定理推导了复合地层盾构隧道开挖面极限支护力上限表达式,结合非线性优化技术求得极限支护力最优解答,并通过与现有文献进行对比,验证了采用组合对数螺旋破坏模式的合理性;同时讨论了不同参数对极限支护力及临界破坏模式的影响,给出了破坏时临界滑动面示意图。研究结果表明：当上部地层内摩擦角和黏聚力固定,极限支护力随下部地层内摩擦角和黏聚力的增大而降低;随着隧道直径的增大,极限支护力显著增大;定义深度系数为上层地层深度与隧道直径之比,深度系数越小,极限支护力对于地层抗剪强度参数变化越敏感,但对于单一地层,深度系数的变化对极限支护力没有影响。所得结论对实际工程具有一定的指导意义。     

Safe retaining pressures for pressurized tunnel face using nonlinear failure criterion and reliability theory

Based on the active failure mechanism and passive failure mechanism for a pressurized tunnel face, the analytical solutions of the minimum collapse pressure and maximum blowout pressure that could maintain the stability of pressurized tunnel faces were deduced using limit analysis in conjunction with nonlinear failure criterion under the condition of pore water pressure. Due to the objective existence of the parameter randomness of soil, the statistical properties of random variables were determined by the maximum entropy principle, and the Monte Carlo method was employed to calculate the failure probability of a pressurized tunnel. The results show that the randomness of soil parameters exerts great influence on the stability of a pressurized tunnel, which indicates that the research should be done on the topic of determination of statistical distribution for geotechnical parameters and the level of variability. For the failure probability of a pressurized tunnel under multiple failure modes, the corresponding safe retaining pressures and optimal range of safe retaining pressures are calculated by introducing allowable failure probability and minimum allowable failure probability. The results can provide practical use in the pressurized tunnel engineering.     

富水高压隧道掌子面涌突水稳定性研究

富水地层隧道掌子面在水力作用下,易发生失稳,造成安全事故,因此确保隧道掌子面稳定性是保障正常施工的关键。本文以豹狸岗隧道修建过程中遇到的富水裂隙密集带为背景展开研究,采用流固耦合理论结合数值分析方法,建立模型研究掌子面失稳模式;基于突水突泥地层掌子面稳定性分析力学模型,模拟掌子面渗透破坏以及失稳过程,提出掌子面稳定性评价方法,确定了保障掌子面稳定的极限防突体厚度（掌子面与断层破碎带之间的距离）,以此来判别掌子面掘进至断层破碎带附近的加固时机。     

Failure probability analysis of coal crushing induced by uncertainty of influential parameters under condition of in-situ reservoir

The uncertainties of some key influence factors on coal crushing, such as rock strength, pore pressure and magnitude and orientation of three principal stresses, can lead to the uncertainty of coal crushing and make it very difficult to predict coal crushing under the condition of in-situ reservoir. To account for the uncertainty involved in coal crushing, a deterministic prediction model of coal crushing under the condition of in-situ reservoir was established based on Hoek-Brown criterion. Through this model, key influence factors on coal crushing were selected as random variables and the corresponding probability density functions were determined by combining experiment data and Latin Hypercube method. Then, to analyze the uncertainty of coal crushing, the first- order second-moment method and the presented model were combined to address the failure probability involved in coal crushing analysis. Using the presented method, the failure probabilities of coal crushing were analyzed for WS5-5 well in Ningwu basin, China, and the relations between failure probability and the influence factors were furthermore discussed. The results show that the failure probabilities of WS5-5 CBM well vary from 0.6 to 1.0; moreover, for the coal seam section at depth of 784.3-785 m, the failure probabilities are equal to 1, which fit well with experiment results; the failure probability of coal crushing presents nonlinear growth relationships with the increase of principal stress difference and the decrease of uniaxial compressive strength.     

Upper bound solution for supporting pressure acting on shallow tunnel based on modified tangential technique

Based on the nonlinear failure criterion and the upper bound theorem, the modified tangential technique method was proposed to derive the expression of supporting pressure acting on shallow tunnel. Instead of the same stress state, different normal stresses on element boundaries were used. In order to investigate the influence of different factors on supporting pressures, the failure mechanism was established. The solution of supporting pressure, with different parameters, was obtained by optimization theory. The corresponding failure mechanism and numerical results were presented. In comparison with the results using the single tangential technique method, it is found that the proposed method is effective, and the good agreement shows that the present solution of supporting pressure is reliable.     

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.     

Mechanism of zonal disintegration phenomenon in enclosing rock mass around deep tunnels

In order to study the mechanism of the zonal disintegration phenomenon (ZDP), both experimental and theoretical investigations were carried out. Firstly, based on the similarity law, gypsum was chosen as equivalent material to simulate the deep rock mass, the excavation of deep tunnel was modeled by drilling a hole in the gypsum models, two circular cracked zones were measured in the model, and ZDP in the enclosing rock mass around deep tunnel was simulated in 3D gypsum model tests. Secondly, based on the elasto-plastic analysis of the stressed-strained state of the surrounding rock mass with the improved Hoek-Brown strength criterion and the bilinear constitutive model, the maximum stress zone occurred in vicinity of the elastic-plastic interface due to the excavation of the deep tunnel, rock material in maximum stress zone is in the approximate uniaxial loading state owing to the larger tangential force and smaller radial force, the mechanism of ZDP was explained, which lay in the creep instability failure of rock mass due to the development of plastic zone and transfer of the maximum stress zone within the rock mass. Thirdly, the analytical critical depth for the occurrence of ZDP was obtained, which depended on the mechanical indices and stress concentration coefficient of rock mass. Foundation item: Projects(50525825, 90815010) supported by the National Natural Science Foundation of China; Project(2009CB724608) supported by the Major state Basic Research Development Program of China     

Stability analysis of shallow tunnels subjected to seepage with strength reduction theory

Based on strength reduction theory, the stability numbers of shallow tunnels were investigated within the framework of upper and lower bound theorems of limit analysis. Stability solutions taking into account of water seepage were presented and compared with those without considering seepage. The comparisons indicate that the maximum difference does not exceed 3.7%, which proves the present method credible. The results show that stability numbers of shallow tunnels considering seepage are much less than those without considering seepage, and that the difference of stability numbers between considering seepage and without considering seepage increase with increasing the depth ratio. The stability numbers decrease with increasing permeability coefficient and groundwater depth. Seepage has significant effects on the stability numbers of shallow tunnels.     

Post-failure behavior of tunnel heading collapse by MPM simulation

Tunnel collapse presents a serious threat to the safety of urban construction. The traditional approach adopted to assess this risk is to evaluate the factor of safety against failure. However, this analysis only determines on whether the tunnel will collapse or not, and does not provide information on the magnitude of the post-failure behavior(for example, catastrophic or progressive) if the tunnel collapse occurs. In this study, a meshless method based on the material point method(MPM) was used to investigate the post-failure behavior of tunnel heading collapse in two-dimensional plane-strain conditions. The capability and accuracy of MPM were verified by comparing the elicited results to centrifuge test data and to analytical solutions obtained from limit state methods. MPM simulations were conducted at different soil conditions(clay or sand) and profiles(homogenous or linear increasing strength) as well as at different tunnel geometries(i.e. tunnel depth and unlined length). The differences in the post-failure behavior and mechanisms are examined and reported.