Mapping the state of fracture around cavities

The state of stress around cavities is heterogeneous. Consequently, the state of fracture may also vary from point to point. Under compressive loading, cavity may be in one of four possible states: pre-fracture (pre-microfracture initiation), microfracture propagation (initiation to the onset of dilata dilatancy to failure) and post-failure. These four states are separated by the crack initiation stress, the crack damage stress and the failure stress. fracture events with confining pressure is examined with reference to three intact rocks: a brittle granite, a semi-brittle limestone and a ductile sal

The maximum principal stress (σ₁) at crack initiation, crack damage (onset of dilatancy), yielding and failure are established as a function stress (σ₃). For a single intact rock, all four fracture events can be represented using one function (the Rocker function) with a single fac various fracture states.

The proposed fracture criteria, based on the experimental data, are combined with the existing state of stress to prepare a fracture map around an elli intact Lac du Bonnet granite. The state of stability is expressed through a newly defined stability factor, the unconfined strength ratio (USR), wh to the traditional safety factor. In contrast to the conventional safety factor in rock mechanics (SFstrength/σ₁), which is σ₃ 3–σ₁, space of the stability diagram.     

Size and stress gradient effects on fracture around cavities

Summary The effect of hole size on fracture initiation around cavities in rock is examined through physical model tests on Tyndall limestone. Twenty five models, employing nine different hole sizes, ranging from 3.2 to 62 mm in diameter were tested in uniaxial compression. Strain gauges placed both on the face of the model block and inside the cylindrical cavity were used to record the state of fracture.Fracture initiation data for primary, remote and sidewall fractures were determined using the stress-strain curves from the respective strain gauge locations. For all three fracture types, the initiation stress decreases with increasing hole size and appears to approach a horizontal asymptote for large cavity sizes. The fracture mechanics formulations and the stress averaging method give the best fit to the primary fracture initiation except for very small cavity sizes. The stress averaging method also provides a very good fit to the sidewall fracture initiation data.     

3D numerical model for dynamic loading-induced multiple fracture zones around underground cavity faces

Three dimensional numerical modelling was used to examine the fracture responses around cavities in rock masses experiencing the stress of excavation. In addition to the primary fracture zone in the near-field, numerical modelling generated a second fracture zone in the far-field and an elastic non-fracture zone between the two fields, i.e., fracture and non-fracture zones occurred alternately around a deep cavity. Further research illustrated that the dynamic load and static stress gradient are two necessary precursors for a far-field fracture in the excavation process. Neither quasi-static loading nor homogeneous stress conditions could induce a far-field fracture. A simple theory is introduced, suggesting that multiple fracture zones occur during excavation due to both the initial stress gradient and the dynamic load. This finding indicates that it may be possible to induce continuous rock fractures in deep underground rock masses by employing optimal excavation methods to generate multiple contiguous fracture zones.     

Plasticity solutions for soil behaviour around contracting cavities and tunnels

The action of tunnel excavation reduces the in-situ stresses along the excavated circumference and can therefore be simulated by unloading of cavities from the in-situ stress state. Increasing evidence suggests that soil behavior in the plane perpendicular to the tunnel axis can be modelled reasonably by a contracting cylindrical cavity, while movements ahead of an advancing tunnel heading can be better predicted by spherical cavity contraction theory. In the past, solutions for unloading of cavities from in-situ stresses in cohesive-frictional soils have mainly concentrated on the small strain, cylindrical cavity model. Large strain spherical cavity contraction solutions with a non-associated Mohr–Coulomb model do not seem to be widely available for tunnel applications. Also, cavity unloading solutions in undrained clays have been developed only in terms of total stresses with a linear elastic-perfectly plastic soil model. The total stress analyses do not account for the effects of strain hardening/softening, variable soil stiffness, and soil stress history (OCR). The effect of these simplifying assumptions on the predicted soil behavior around tunnels is not known. In this paper, analytical and semi-analytical solutions are presented for unloading of both cylindrical and spherical cavities from in-situ state of stresses under both drained and undrained conditions. The non-associated Mohr-Coulomb model and various critical state theories are used respectively to describe the drained and undrained stress-strain behaviors of the soils. The analytical solutions presented in this paper are developed in terms of large strain formulations. These solutions can be used to serve two main purposes: (1) to provide models for predicting soil behavior around tunnels; (2) to provide valuable benchmark solutions for verifying various numerical methods involving both Mohr–Coulomb and critical state plasticity models. Copyright © 1999 John Wiley & Sons, Ltd.     

潜导水及其在地下工程洞体突水中的作用

本文提出了潜导水的概念,并通过对潜导水主要特征、潜导水压传递原理、潜导水压大小的分析,阐述了潜导水在地下工程洞体突水中的作用。     

A simple boundary equation technique for elastic stress analysis of underground cavities

Summary A boundary integral equation approach is illustrated which does not require the solution of singular integrals in order to compute the coefficients of the final system of linear equations. This characteristic allows the carrying out of all the necessary integrations by means of numerical techniques, leading to a rather simple and compact solution algorithm. In addition the approach permits the evaluation of a measure of the error affecting the numerical solution. The stability and the accuracy of the procedure, which is based on the minimization of the difference between known boundary tractions and corresponding numerically derived stresses, are discussed with reference to some rock engineering problems and it is shown that the approach is particularly suitable for stress analyses related to underground openings. To get some insight into the overall performance of the procedure, the results obtained in the analysis of a tunneling problem of practical interest are compared with those deriving from a standard Finite Element calculation.     

饱和土中弹性波在双椭圆孔洞周围的散射

利用复变函数法和多极坐标法,研究了饱和土中弹性波在双椭圆孔洞周围的散射及动应力集中的问题。首先通过引入位移势函数,将二维稳态条件下Biot波动方程解耦成势函数所满足的3个Helmholtz方程, 根据分离变量方法即可得Helmholtz方程在柱坐标下势函数的通解。利用土骨架和孔隙水的边界条件,确定波函数展开式中的未知系数,进而得到位移、应力和孔压的表达式。给出了弹性波对2个椭圆形孔洞的动应力集中系数的数值结果,并讨论了波数和孔距变化对动应力集中系数和孔压集中系数的影响。     

A case of the formation of underground cavities in loose silty sand deposits

A case of the formation of underground cavities to depths of some metres in loose sandy Quaternary sediments is described and the factors controlling their appearance and evolution are discussed. Special attention is given to the role of underground erosion, through the circulation of water, and to the importance of grain-size analysis of the sandy soil, as well as to the presence of slightly differentiated soil material (silty sand or clayey sand) distinguished in thin intercalations. This material, with only slightly increased cohesion, has the function of a roofing material in the mechanism of cavity formation.     

某水电站地下洞室群初始地应力场反演回归分析

采用三维弹塑性有限元法对某水电站地下洞室群三维初始地应力场进行了反演回归分析。计算结果表明,厂区初始地应力场分布规律合理,实测点处地应力计算值与实测值吻合较好,可以作为后续数值分析和地质力学模型试验的依据。     

地下空间逾渗与裂缝属性的关系分析

裂缝连通性评价是地下空间研究的重要内容。逾渗分析是研究裂缝网络连通性的一种有效手段。裂缝网络逾渗临界值多使用裂缝间接表征参数(如分形维数)来确定,但存在裂缝网络连通性不同却有相同间接表征参数的情况,这降低了预测的可靠性。为避免此类问题并更加准确快速地表征裂缝网络的连通性,文章在构建逾渗临界值方程时,摒弃了间接参数简化的方式,使用裂缝直接表征参数(如裂缝数量、长度等)进行非线性拟合。通过二维数值模拟建立不同参数的离散裂缝网络模型,分析逾渗低、中、高概率临界条件与裂缝直接表征参数的关系,建立逾渗临界条件预测方程,并对方程在不同尺度研究区的应用进行了讨论和验证。结果表明：预测方程可有效地预测不同概率的逾渗临界值。同时文章在预测方程的基础上,建立了裂缝网络连通性评价标准,这对于裂缝发育地区的地下空间评价工作具有一定的指导和借鉴意义。     

Elastoplastic deformation around underground openings under biaxial initial stress field

Estimation of elastoplastic deformation around an underground opening induced by the excavation of it, especially displacement and strain field in plastic region, is presented in this paper, as well as the formulation for calculating the displacement and strain in the plastic region around the underground opening by the coupled Boundary Element Method - Characteristics Method (BEM-CM). In this method, the non-associated flow rule is adopted to calculate the displacement and strain field in the plastic region, which is determined by the integration of the displacement along characteristics lines under the boundary condition of the elastic displacement on an elastoplastic interface analysed. It is shown that this method is one of the accurate and effective methods for estimating not only the shape and extent of the plastic region but also the state of the displacement and strain in the plastic region around the underground opening, comparing the theoretical solution with numerical results by this method for a circular opening under hydrostatic initial stress condition. Furthermore, this method is applied to rectangular and horse-shoe shaped openings and the characteristics of the strain field in the plastic region are discussed. © 1997 by John Wiley & Sons, Ltd.     

循环动荷载下下伏空洞路面塌陷的模型试验研究

在循环动荷载作用下,地下空洞会逐步发展成为路面塌陷。针对此问题,本文建立了模拟路面塌陷发生发展全过程的模型试验。试验结果表明,随着动荷载值的减小,土体所能承受的极限振动循环次数呈指数型增加。而当地下存在一定尺寸的地下空洞时,即使动荷载值较小,在足够多次数的振动循环作用后,也有可能引发路面塌陷。最大粒径较大、不均匀系数较高土体的静力稳定性较强,体现在其能承受的极限静荷载较大;但其动力稳定性较弱,体现在其能承受的极限振动循环次数较少。反之,最大粒径较小、不均匀系数较小土体的静力稳定性较弱,而动力稳定性较强。地下空洞上覆土层厚度越大,则其静力、动力稳定性均较强。同时,循环动荷载作用下地表沉降与土体裂缝的发展呈现出三阶段规律。阶段1为初始固结沉降阶段,持续时间较短,土体受到振动压密作用,地表发生整体沉降,土体裂缝未见明显发展;阶段2为等速沉降阶段,持续时间较长,中心土体受到振动剪切作用,地表中心沉降与土体裂缝随时间呈等速发展;阶段3为加速沉降阶段,持续时间最短,中心土体受到振动破坏作用,地表中心沉降与土体裂缝快速发展直至发生塌陷。     

A BEM investigation on the influence of underground cavities on the seismic response of canyons

Two-dimensional site effects caused by cavities under topographical functions can considerably impact the seismic reaction of the ground surface. Due to the complexity of scattering issues by topographical features above subterranean cavity, few studies have been done in this field. In the present study, the seismic response of semi-sine-shaped canyons above a subterranean cavity (hole) of different dimensions, depths and locations is examined. The medium is assumed to have a linear elastic constitutive behavior exposed to vertically propagating incident SV and P waves. All calculations are performed using the direct boundary element technique in the time domain. It is observed that a cavity below a canyon can considerably change the ground response of the surface in different periodic bands. The seismic interaction between canyon and cavity with respect to various geometrical parameters will lead to different amplification patterns in the center and edge of the canyon. One of the most important results is the increase in amplification of long periods compared with the case of a canyon without cavity. Moreover, parametric research shows the fact that the cavity detail and canyon height, the ratio of cavity to the canyon size and cavity location impact on the seismic amplification of the canyon surface. Finally, spectral amplification coefficients of the canyon surface led by the cavity are reported for different cases of the canyon–cavity interaction.     

福建数字地下流体网对远处大震映震能力分析

本文收集、整理了2004年12月26日印尼苏门答腊西北近海8.7级地震和2005年印尼的8.5级和巴基斯坦的7.8级地震,我省地下流体数字化监测台网观测到的震时和震后效应。测点以永安-晋江断裂为界线,北边多数表现为水位上升,南边多数为下降。初步分析认为,这种现象可能与现代构造应力场有关。     

Determination of plastic regions around underground openings by a coupled boundary-element-characteristics method

A two-dimensional hybrid method for solving elastoplastic problems in engineering is presented by coupling two existing methods, namely, the boundary element method and the characteristics method. The formulation of this method is presented, as well as an excellent procedure for the determination of the boundary between elastic and plastic regions. It is shown not only that this method is a powerful and accurate method for evaluating the shape and extent of the plastic region around rock caverns, which is of prime importance for the construction of rock caverns, but also applicable to a given range of the initial stress field ratio where only compressive failure occurs. Then, some typical examples are solved in order to check the accuracy of the solution by this method. Furthermore, its successful applications are presented and discussed to determine the shape and the extent of the plastic regions around parallel, circular and rectangular openings.     

岛状多年冻土管道周围热-水-应力耦合数值模拟

考虑大气温度以及管内流动介质温度的影响,建立由多个土层构成的岛状冻土物理模型,研究塔河地区埋地输油管道周围热-水-应力（T-H-M）耦合作用,分析水-热-应力耦合作用下管道的受力情况并进行管道强度验算。采用多物理场耦合软件COMSOL Multiphysics进行数值模拟,计算在T-H-M三场耦合及非耦合两种工况下岛状多年冻土管道周围应力和沉降曲线等。分析比较表明,岛状多年冻土区的温度,冰水相变以及水分迁移对应力场存在较大的影响;水分场、温度场以及应力场三者之间耦合作用明显;岛状冻土随季节呈周期性冻融,管道周围出现较大应力集中和沉降现象,会对管道安全产生一定影响。     

地下洞室围岩脆性破坏时的应力特征研究

在高应力作用下,岩爆、钻孔崩落、片帮都是地下空间硬脆围岩中常见的破坏现象,这三类现象本质上均可归于完整岩体的脆性破坏,它们分别反映了高应力作用下完整岩体不同的破坏程度。通过对前人关于岩爆判据、钻孔崩落判据和片帮应力强度比判据研究成果的类比分析可知,这些脆性破坏现象在破坏时具备相同的应力背景条件。脆性破坏的应力条件可以用地下空间周边切向最大应力与岩石单轴抗压强度之比（ / ）或者工程区最大主应力与岩石单轴抗压强度之比（ / ）来描述,两种指标本质上反映了相同的应力背景条件。对于 / , / = 0.4 ± 0.1是发生脆性破坏的应力临界条件;对于 / , / = 0.15 ± 0.05是发生脆性破坏的应力临界条件。大量的工程实例和基于Hoek-Brown强度准则的力学分析也证明了这一背景条件的正确性。这里两种指标都取了一个范围,主要是由于不同的岩体分级、岩性和工程地质条件会对指标的界定产生较为显著的影响。     

Numerical modeling of three‐phase dissolution of underground cavities using a diffuse interface model

Natural evaporite dissolution in the subsurface can lead to cavities having critical dimensions in the sense of mechanical stability. Geomechanical effects may be significant for people and infrastructures because the underground dissolution may lead to subsidence or collapse (sinkholes). The knowledge of the cavity evolution in space and time is thus crucial in many cases. In this paper, we describe the use of a local nonequilibrium diffuse interface model for solving dissolution problems involving multimoving interfaces within three phases, that is, solid–liquid–gas as found in superficial aquifers and karsts. This paper generalizes developments achieved in the fluid–solid case, that is, the saturated case [1]. On one hand, a local nonequilibrium dissolution porous medium theory allows to describe the solid–liquid interface as a diffuse layer characterized by the evolution of a phase indicator (e.g., porosity). On the other hand, the liquid–gas interface evolution is computed using a classical porous medium two‐phase flow model involving a phase saturation, that is, generalized Darcy's laws. Such a diffuse interface model formulation is suitable for the implementation of a finite element or finite volume numerical model on a fixed grid without an explicit treatment of the interface movement. A numerical model has been implemented using a finite volume formulation with adaptive meshing (e.g., adaptive mesh refinement), which improves significantly the computational efficiency and accuracy because fine gridding may be attached to the dissolution front. Finally, some examples of three‐phase dissolution problems including density effects are also provided to illustrate the interest of the proposed theoretical and numerical framework. Copyright © 2014 John Wiley & Sons, Ltd.     

地下洞室群对地面运动影响问题的级数解答:SH波入射

采用波函数展开法给出平面SH波入射下半空间中洞室群对地面运动影响问题的一个级数解答，并分析了入射波频率和入射角以及两洞室之间距离等参数对地面运动的影响。数值结果表明，地下洞室群对沿线地面运动具有显著的放大作用：两个洞室情况地面运动可以达到单个洞室情况的1．6倍、无洞室情况的3．5倍以上。建议地铁等地下工程在设计和规划时应考虑工程建设后对沿线设计地震动的影响。