Effect of Tunnel Shape and Support System on Stability of a Tunnel in a Deep Coal Mine in China

Stability level of tunnels that exist in an underground mine has a great influence on the safety, production and economic performance of the mine. Ensuring of stability for soft-rock tunnels is an important task for deep coal mines located in high in situ stress conditions. The aim of this study is to investigate the effect of tunnel shape and support pattern on the deformation, failure zone and stability around a tunnel located in a coal rock mass in China and to select an appropriate tunnel shape and a support pattern to provide a stable stress-deformation condition around the tunnel. Using the available information on stratigraphy, geological structures, in situ stress measurements and geo-mechanical properties of intact rock and discontinuity interfaces, a three-dimensional numerical model was built using the FLAC software to simulate the stress conditions around the tunnel in the coal rock mass. Analyses were conducted for several tunnel shapes and rock support patterns. Results obtained for the distribution of failed zones, and stress and displacement fields around the tunnel were compared to select the best tunnel shape and support pattern to achieve the optimum stability conditions. Also, a comparison is given between the numerical predictions and field deformation monitoring results.     

Estimation of crack opening from a two‐dimensional continuum‐based finite element computation

Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one‐dimensional approach for estimating a crack opening from a continuum‐based finite element calculation to two‐dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post‐treatment procedure. The original one‐dimensional problem devised in Dufour et al. [4] is recovered as profiles of deformation orthogonal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing finite element deformation profiles and theoretical profiles corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the profiles are assumed to be equal; in the weak approach, the integrals of each profile are set equal. Two‐dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, defined as the distance between the numerical and theoretical profiles, are less than a few percentages. In the case of a three‐point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack (> 40µm). Copyright © 2011 John Wiley & Sons, Ltd.     

Fast multipole displacement discontinuity method (FM‐DDM) for geomechanics reservoir simulations

The displacement discontinuity method (DDM) is frequently used in geothermal and petroleum applications for modeling the behavior of fractures in linear‐elastic rocks. The DDM requires O(N²) memory and O(N³) floating point operations (where N is the number of unknowns) to construct the coefficient matrix and solve the linear system of equations by direct methods. Therefore, the conventional implementation of the DDM is not computationally efficient for very large systems of cracks, often limiting its application to small‐scale problems. This work presents an approach for solving large‐scale fracture problems using the fast multipole method (FMM). The approach uses both the DDM and a kernel‐independent version of the FMM along with a preconditioned generalized minimal residual algorithm to accelerate the solution of linear systems of equations using desktop computers. Using the fundamental solutions for constant displacement discontinuity in a two‐dimensional elastic medium, several numerical examples involving fracture networks representing fractured reservoirs are treated. Numerical results show good agreement with analytical solutions and demonstrate the efficiency of the FMM implementation of the DDM for large‐scale simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Response of a tunnel deeply embedded in a viscoelastic medium

This paper presents a three‐dimensional energy‐based solution for the time‐dependent response of a deeply embedded and unsupported semi‐infinite tunnel of circular cross‐section. The tunnel is taken to be excavated quasi‐instantaneously from an infinite rock body that initially exhibits an isotropic stress state and that is made up of a homogeneous, isotropic and viscoelastic material. The viscoelastic behaviour is modelled by means of Burger's model, and the rock is taken to behave volumetrically linear elastic and to exhibit exclusively deviatoric creep. This viscoelastic problem is transformed into the Laplace domain, where it represents a quasi‐elastic problem. The displacement fields in the new solution are taken to be the products of independent functions that vary in the radial and longitudinal directions. The differential equations governing the displacements of the system and appropriate boundary conditions are obtained using the principle of minimum potential energy. The solutions for these governing equations in the Laplace domain are then obtained analytically and numerically using a one‐dimensional finite difference technique. The results are then transformed back into the time domain using an efficient numerical scheme. The accuracy of the new solution is comparable with that of a finite element analysis but requires much less computation effort. Copyright © 2011 John Wiley & Sons, Ltd.     

复杂地层超大断面隧道施工围岩力学特征模型试验

以京沪高速济南连接线港沟隧道穿越断裂破碎带区域为依托工程,研究了复杂地层超大断面隧道施工情况下围岩力学响应特征。研发了大型可拼装式地质力学模型试验系统,搭建了以静态数据采集为基础的应力–应变场监测系统和以光栅测距为基础的位移场监测系统,开展了复杂地层超大断面隧道施工过程力学模型试验研究。通过对试验开挖过程中位移变形和围岩应力变化的实时监测,揭示了超大断面隧道穿越断裂破碎带施工过程的力学演化规律。监测数据表明：位移变形大致可分为“缓慢增加-急剧增大-稳定状态”3个过程,水平收敛位移要早于拱顶沉降进入急剧增大阶段;应力变化也可分为“应力积聚－应力释放－稳定状态”3个阶段。形成的试验方法技术以及结论对类似工程研究具有重要的指导和借鉴意义。     

Blast‐induced rock fracture near a tunnel

Damage in the form of cracks is predicted to assess the susceptibility of a tunnel to failure due to a blast. The material‐point method is used in conjunction with a decohesive failure model as the basis for the numerical simulations. The assumption of a cylindrical charge as the source for the blast allows the restriction of plane strain and two‐dimensional analyses. In the simulation, a further restriction of a single pressure pulse is used as the source of stress waves that are reflected and refracted after reaching the free surface of the tunnel wall. Three critical zones of significant cracking in the vicinity of a tunnel are identified as potential contributors to tunnel failure. Copyright © 2014 John Wiley & Sons, Ltd.     

A stress and displacement discontinuity element method for elastic transversely anisotropic rock

The paper presents closed‐form solutions for stress and displacement influence functions for stress discontinuity (SD) and displacement discontinuity (DD) elements, for a two‐dimensional plane‐strain elastic, transversely anisotropic medium. The solutions for SD elements are based on Kelvin's problem and for DD elements on the concept of dipoles. Stress and displacement influence functions are derived for the following elements: constant SD, linear SD, constant DD, linear DD, square root DD, parabolic DD, constant DD surface, and linear DD surface elements. The formulations are incorporated into FROCK, a hybridized boundary element method code, and are validated by providing comparisons between the results from FROCK and the finite element code ABAQUS. A limited parametric analysis shows the effects of slight anisotropy on the stress field around the tip of a crack and of the orientation of the crack with respect to the axes of elastic symmetry. Copyright © 2014 John Wiley & Sons, Ltd.     

复杂条件下隧道开挖循环进尺优化方法研究

复杂条件下如何选择合理的开挖进尺一直是隧道施工的难题之一。在已有的研究成果基础上,提出了圆形或近圆形隧道开挖过程的时空关系表达式,并给出基于现场位移监测数据的参数计算方法。结合关角隧道9#工区二郎洞断层破碎带现场施工情况及监测资料,建立了该断层破碎带开挖过程的时空效应关系式,结果表明,该关系式能够反映开挖过程中洞周位移的时空的变化。在此基础上提出了断层破碎带软岩开挖过程的时空效应分析及进尺优化的方法,对关角隧道9#工区几条较大断层破碎带隧道开挖的进尺进行了优化,优化后的开挖进尺是可行的,也解释了断层破碎带围岩隧道开挖“短进尺”的合理性。同时文中也分析了该方法的优点及适用范围。     

大断面海底隧道CRD法绝对位移控制基准建立及应用研究

隧道位移控制基准的建立是确保隧道安全施工的一项重要内容。以厦门－翔安海底隧道陆域浅埋暗挖段CRD法施工为工程背景,陆域浅埋段总长约2 525 m,主要穿越全、强风化花岗岩地带,含水率高、自稳能力差。依据全站仪非接触量测获得初期支护三维绝对位移分布规律,确定三维绝对位移基准控制指标,同时对86个围岩位移监测断面的监测数据进行变形正常断面和变形异常或险情断面的位移量统计分析,最终确定CRD法（center cross diaphragm method,交叉中隔壁法）三维绝对位移控制基准。研究结果表明,将CRD1、CRD3部拱顶竖直位移和上中隔墙、下中隔墙水平位移作为CRD法位移控制指标;CRD1部和CRD3部拱顶下沉极限位移分别为200 mm和130 mm;CRD3部拱顶竖直位移约为CRD1部的0.5～1倍;上中隔墙水平极限位移约为100 mm,下中隔墙水平极限位移约为15 mm。通过现场97个断面应用,共发现58次异常和险情,由于发现及时,处置有力,保证了施工安全。     

A dimensional analysis to quantify the thermal budget around lithospheric‐scale shear zones

The thermal evolution around shear zones is controlled by three major thermal processes: diffusion, advection and shear heating. We present a dimensional analysis to quantify, to first‐order, the relative contributions of these three processes to the thermal evolution around lithospheric‐scale shear zones. We consider 11 parameters that control the kinematics, the three‐dimensional (3‐D) geometry, the initial thermal structure and the average strength of the shear zone. Three dimensionless parameters are presented to quantify the relative contributions of the three thermal processes. We validate the dimensional analysis with 2‐D thermo‐kinematic numerical models. The applicability of the dimensional analysis to any kind of shear zone (i.e. thrust, normal‐slip and strike‐slip shear zones) makes it a useful tool that is complementary to previous numerical and analytical studies. Finally, thrust‐type shear zones are used to illustrate how the three thermal processes control the thermal evolution.     

基于激光测量和FKM聚类算法的隧洞岩体结构面的模糊群聚分析

岩体隧洞结构面的数量、产状和发育情况是评价隧洞透水性和稳定性的重要指标。采用三维激光测量技术可以快速获取隧洞周围岩体激光点云数据和结构面的几何信息。提出了基于柱面投影和Delaunay生长算法的激光点云的三角网重构技术,利用构建的三角网平面方程的法向向量计算出单个三角网平面的产状,并应用FKM聚类算法进行隧洞岩体结构面产状的模糊群聚分类。该方法可以快速得到不同组的优势产状,且分类结果可用不同颜色进行空间显示。最后运用自主研发的FSS软件对某隧洞的岩体结构面优势产状进行了研究,研究结果表明：1）基于柱面投影和Delaunay生长法的点云构网方法特别适合于隧洞工程,构网速度快、效率高,重构得到的三角网表面与被采样的岩体表面拓扑差别最小;2）FKM模糊群聚方法对隧洞岩体结构面的群聚分类结果可靠、合理,具有较强的通用性和推广性。     

Weak discontinuity in porous media: an enriched EFG method for fully coupled layered porous media

In this paper, a series of multimaterial benchmark problems in saturated and partially saturated two‐phase and three‐phase deforming porous media are addressed. To solve the process of fluid flow in partially saturated porous media, a fully coupled three‐phase formulation is developed on the basis of available experimental relations for updating saturation and permeabilities during the analysis. The well‐known element free Galerkin mesh‐free method is adopted. The partition of unity property of MLS shape functions allows for the field variables to be extrinsically enriched by appropriate functions that introduce existing discontinuities in the solution field. Enrichment of the main unknowns including solid displacement, water phase pressure, and gas phase pressure are accounted for, and a suitable enrichment strategy for different discontinuity types are discussed. In the case of weak discontinuity, the enrichment technique previously used by Krongauz and Belytschko [Int. J. Numer. Meth. Engng., 1998; 41:1215–1233] is selected. As these functions possess discontinuity in their first derivatives, they can be used for modeling material interfaces, generating only minor oscillations in derivative fields (strain and pressure gradients for multiphase porous media), as opposed to unenriched and constrained mesh‐free methods. Different problems of multimaterial poro‐elasticity including fully saturated, partially saturated one, and two‐phase flows under the assumption of fully coupled extended formulation of Biot are examined. As a further development, problems involved with both material interface and impermeable discontinuities, where no fluid exchange is permitted across the discontinuity, are considered and numerically discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of piles subjected to lateral soil movements using a three‐dimensional displacement approach

An analytical approach using the three‐dimensional displacement of a soil is investigated to provide analytical solutions of the horizontal response of a circular pile subjected to lateral soil movements in nonhomogeneous soil. The lateral stiffness coefficient of the pile shaft in nonhomogeneous soil is derived from the rocking stiffness coefficient that is obtained from the analytical solution, taking into account the three‐dimensional displacement represented in terms of scalar potentials in the elastic three‐dimensional analysis. The relationship between horizontal displacement, rotation, moment, and shear force of a pile subjected to lateral soil movements in nonhomogeneous soil is obtainable in the form of the recurrence equation. For the relationship between the lateral pressure and the horizontal displacement, it is assumed that the behavior is linear elastic up to lateral soil yield, and the lateral pressure is constant under the lateral soil yield. The interaction factors between piles subjected to both lateral load and moment are calculated, taking into account the lateral soil movement. The formulation of the lateral displacement and rotation of the pile base subjected to lateral loads in nonhomogeneous soils is presented by taking into account the Mindlin equation and the equivalent thickness for soil layers in the equivalent elastic method. For lateral movement, lateral pressure, bending moment, and interaction factors, there are small differences between results obtained from the 1‐D and the 3‐D displacement methods except a very flexible pile. Copyright © 2015 John Wiley & Sons, Ltd.     

小三峡岩溶隧道围岩防突层安全厚度有限元分析

针对小三峡隧道岩溶发育的工程地质特征,采用有限元方法建立典型隧道断面数值计算模型,分析充水溶洞位于隧道不同方位、不同距离时隧道围岩位移和塑性区变化规律,并结合围岩的位移变化情况和塑性区分布情况作为评价隧道围岩突水的判据,得出防止隧道围岩突水的岩层最小安全厚度。研究结果表明:在岩溶水压力作用下,当洞径比一定时,随着溶洞逐渐远离隧道,溶洞对隧道的影响在逐渐减弱;当间径比一定时,溶洞直径越大对隧道的影响越明显;同时根据围岩的位移和塑性区计算结果得到了隧道围岩最小防突厚度。研究成果可为小三峡隧道安全施工提供技术支撑。      

Vertical dynamic response of pile in a radially heterogeneous soil layer

An analysis of a pile vertical response considering soil inhomogeneity in the radial direction under dynamic loads is presented. The solution technique is based on a three‐dimensional axisymmetric model, which includes the consideration of the vertical displacement of the soil. The soil domain is subdivided into a number of annular vertical zones, and the continuity of the displacements and stresses are imposed at both the interface of pile–soil and the interfaces of adjacent soil zones to establish the dynamic equilibrium equations of the pile–soil interaction. Then, the equations of each soil zone and of the pile are solved one by one to obtain the analytical and semi‐analytical dynamic responses at the top of the pile in the frequency domain and time domain. Parametric studies have been performed to examine the influence of soil parameters' variations in the radial direction caused by the construction effect on the dynamic responses of pile. The results of the studies have been summarized and presented in figures to illustrate the influences of the soil parameters as they change radially. The effect of the radius of the disturbed soil zone caused by construction is also studied in this paper. Copyright © 2008 John Wiley & Sons, Ltd.     

高应力深部洞室模型试验分区破裂现象机制的初步研究

以经典的芬纳公式为手段,以观察到分区破裂现象的模型试验为背景,通过对简化后的圆形巷道围岩应变场和能量场的分析,发现极限平衡区边界存在径向应变的不连续性和弹性变形能的聚集性。认为与开挖洞室呈同心圆的环状断裂的形成,是极限平衡区在边界上由于应变场的不协调而导致的与弹性区的断裂分离。而分区破裂的产生,则是这种断裂分离形成后极限平衡区向深处发展的结果。解释了分区破裂产生时洞周围岩应变和位移随距离洞室增加呈波浪形变化的非单调性规律,给出了分区破裂形成后各破裂区半径的表达式,关系式表明各破裂区之间存在等比关系,比值与地应力状态及围岩力学参数有关。将分区破裂模型试验的参数代入该式,可得,n =1.1左右,与实验完成后剖开模型的各破裂区分布特征基本相符。     

Modelling of coupled fluid‐mechanical problems in fractured geological media using enriched finite elements

Geological environments, such as petroleum reservoirs, normally exhibit physical discontinuities, for example, fractures and faults. Because of the reduced thickness of these discontinuities, finite element formulations with strong discontinuity have been applied to the numerical modelling of geological environments. Until now, two relevant characteristics of petroleum reservoirs have not been addressed by these formulations. The first is the pore pressure jump in the direction normal to a discontinuity in a fluid‐mechanical coupling condition, which is present primarily in sealing faults owing to the contrast of permeability with the porous medium. The absence of this jump can affect the prediction of the deformability of a physical discontinuity. Furthermore, reservoir models frequently use coarse meshes. Thus, the method used to evaluate the pore pressure in the discontinuity may exhibit a strong dependence relative to the mesh refinement. Based on these characteristics, in this study, a formulation of an enriched finite element for application to coupled fluid‐mechanical problems with pre‐existing physical discontinuities saturated by a single fluid is presented. The formulation employs discontinuous interpolation functions and enables the reproduction of jumps of displacement and pore pressure associated with a discontinuity inside the element without the need to discretise it. An approximation to estimate the pore pressure in the discontinuity was developed, one which seeks to minimise the influence of refinement. The element's response is verified by comparison with a one‐dimensional analytical solution and simple examples that are simulated using commercial software. Copyright © 2015 John Wiley & Sons, Ltd.     

偏压小间距公路隧道施工的三维数值模拟

以云南平年隧道为工程背景,采用MARC三维非线性有限元法程序,对新奥法修建的偏压、错台、浅埋小间距隧道模拟了先行隧道不同超前距离情况下的动态施工过程。掌子面距离的变化对洞室的横向位移的影响大于竖向位移,且对于左洞更为显著;随着左右洞掌子面距离的增大,洞周位移、中间岩柱位移均减小,但部分范围内地表沉降值有所增大,局部区域受力、变形恶化。     

A three‐dimensional displacement approach for analysis of laterally loaded piles in nonhomogeneous soil

An analytical approach using the three‐dimensional displacement of a soil is investigated to provide analytical solutions of the horizontal response of a circular pile subjected to lateral loads in nonhomogeneous soil. The rocking stiffness coefficient of the pile shaft in homogeneous soil is derived from the analytical solution taking into account the three‐dimensional displacement represented in terms of scalar potentials in the elastic three‐dimensional analysis. The lateral stiffness coefficient of the pile shaft in nonhomogeneous soil is derived from the rocking stiffness coefficient taking into account the rocking rotation of a rigid pile shaft. The relationship between horizontal displacement, rotation, moment, and shear force of a pile subjected to horizontal loads in nonhomogeneous soil is obtainable in the form of the recurrence equation. The formulation of the lateral displacement and rotation of the pile base subjected to lateral loads in nonhomogeneous soils is presented by taking into account Mindlin's equation and the equivalent thickness for soil layers in the equivalent elastic method. There is little difference between lateral, rocking, and couple stiffness coefficients each obtained from both the two‐dimensional and three‐dimensional methods except for the case of Poisson's ratio near 0.5. The comparison of results calculated by the current method for a pile subjected to lateral loads in homogeneous and nonhomogeneous soils has shown good agreement with those obtained from analytical and numerical methods. Copyright © 2017 John Wiley & Sons, Ltd.     

Exact solutions for one‐dimensional transient response of fluid‐saturated porous media

Based on the Biot theory, the exact solutions for one‐dimensional transient response of single layer of fluid‐saturated porous media and semi‐infinite media are developed, in which the fluid and solid particles are assumed to be compressible and the inertial, viscous and mechanical couplings are taken into account. First, the control equations in terms of the solid displacement u and a relative displacement w are expressed in matrix form. For problems of single layer under homogeneous boundary conditions, the eigen‐values and the eigen‐functions are obtained by means of the variable separation method, and the displacement vector u is put forward using the searching method. In the case of nonhomogeneous boundary conditions, the boundary conditions are first homogenized, and the displacement field is constructed basing upon the eigen‐functions. Making use of the orthogonality of eigen‐functions, a series of ordinary differential equations with respect to dimensionless time and their corresponding initial conditions are obtained. Those differential equations are solved by the state‐space method, and the series solutions for three typical nonhomogeneous boundary conditions are developed. For semi‐infinite media, the exact solutions in integral form for two kinds of nonhomogeneous boundary conditions are presented by applying the cosine and sine transforms to the basic equations. Finally, three examples are studied to illustrate the validity of the solutions, and to assess the influence of the dynamic permeability coefficient and the fluid inertia to the transient response of porous media. Copyright © 2010 John Wiley & Sons, Ltd.