单轴压缩下横观各向同性岩石破裂过程的数值模拟

采用基于细观损伤力学基础上开发的RFPA2D数值模拟软件,用2种不同的岩石材料来组成7个不同岩层倾角的横观各向同性的岩石试件,通过单轴加载数值模拟试验,模拟横观各向同性岩石渐进破裂的整个过程,分析了岩层与最大主应力之间的倾角和强度之间的关系,讨论了不同岩层倾角的横观各向同性岩体的不同破裂模式及其破坏准则。     

各向异性岩体中利用测井资料反演地应力的方法

地应力场分析在钻井工程中具有重要意义,现代声、电扫描测井技术通过提取井下人工诱导裂缝信息为地应力反演提供了新的技术手段。钻井工程常遇含层理、结构面的岩体,而常规井壁崩落法反演地应力将岩体假设为各向同性与实际情况不符。为考虑井壁围岩的各向异性特征,引入层理弱化面概念建立了利用片壁坍塌崩落资料预测最大水平主应力的模型。计算结果表明:岩体中软弱面方位对井壁坍塌裂缝的位置和规模产生重要影响;随着大小水平主应力比值的增大,井壁坍塌区域产状及位置会发生规律性地变化;通过测井资料提取坍塌裂缝产状及位置信息可较为精确地限定水平最大主应力的取值区间。     

横观各向同性岩体中圆形巷道反分析的惟一性

惟一性研究是位移反分析的基础工作之一。推导了横观各向同性岩体中圆形巷道的位移解析解,利用参数可辨识条件对横观各向同性岩体中圆形巷道位移反分析的惟一性进行了探讨。结果表明,无论量测多少个点的位移也不能惟一地反演出所有6个参数;必须至少已知3个参数时,才有可能惟一地反演其他参数;2个地应力分量是否相等对反分析结果有明显的影响;2个地应力分量的可辨识性最好,各向同性面上的弹性模量和泊松比次之,垂直各向同性面方向的弹性模量和泊松比最差。     

淮南矿区地应力场特征

利用空心包体地应力测量方法对淮南矿区的地应力进行了实测,获得了矿区的地应力场分布特征。研究表明,所有测点的两个主应力近水平,一个主应力近垂直。垂直主应力与上覆岩体的重力具有良好的相关性;水平主应力随深度的增加而增加,不同区域增加的梯度不同;最大水平主应力与最小水平主应力的比值与测点深度没有明显的关系,50%以上测点的水平主应力差异显著;最大水平主应力作用方位为北东向,局部受构造等影响,水平主应力发生变化。总体上,淮南矿区受北东向的挤压应力作用。根据3个主应力量值的关系,确定淮南矿区地应力场类型属大地动力场型和准静水应力场型。地应力场的以上特征对淮南矿区煤与瓦斯突出的发生具有重要作用,提出了在进行瓦斯抽放钻孔参数设计时应考虑地应力场特征的建议。      

天然地应力作用下不同产状岩体裂隙渗流特性研究

为了研究天然地应力作用下裂隙产状等因素对深部岩体裂隙渗流特性的影响,基于单裂隙面渗透性服从负指数变化规律,建立了三维应力作用下不同产状裂隙的渗透系数计算公式,利用Lagrange乘子法分析裂隙面产状变化对其渗透性的影响,并分析了岩体裂隙有、无充填物对其渗透性的影响及敏感性;然后,以我国大陆地区地应力统计规律为例,分析了地表以下5 000 m范围内在天然地应力作用下裂隙渗透性随深度、产状的变化规律。结果表明：裂隙产状的变化对其渗流特性有明显影响,对于浅层岩体,在大主应力大致呈水平方向分布时,随着裂隙面倾角的增加,裂隙渗透系数逐渐降低;但随着深度的增加,在裂隙深度超过约200 m和裂隙面走向与大或中主应力方向大致一致时,裂隙渗透性反而会随着裂隙面倾角的增加逐渐增加,在裂隙面走向与小主应力方向垂直时增加最为明显;对于深部岩体,裂隙的渗透性很小,裂隙面产状的变化对其渗透性影响很弱;对于有充填物裂隙,岩块与充填物的弹模比和充填物泊松比的变化对裂隙渗透性的影响很小。研究结果可为深入研究我国深部岩体渗透特性变化规律提供借鉴意义。     

地应力与岩体模量关系的理论及试验研究

岩体模量（弹性模量及变形模量）是工程岩体力学特性的基础参数之一,研究地应力状态与岩体模量之间的关系具有重要意义.基于静弹性热力学模型原理,结合弹性理论,推导了水平主应力与岩体性质参数的定量关系,并对地应力与岩体模量的关系进行了探讨.在此基础上,以赣龙铁路梅花山隧道为依托,开展了围岩应力及岩体模量参数的现场测试工作,并将实测成果与理论分析进行对比.结果表明：当埋深影响较小时,花岗岩中的水平主应力与岩体模量呈线性正相关关系;当埋深相差较大时,深度对地应力及岩体模量的影响均不可忽略,水平主应力与岩体模量一般呈非线性关系,需要进一步研究;对花岗岩中的岩体弹性模量和变形模量与水平主应力之间的相关性进行对比发现,岩体变形模量与水平主应力的相关性更好.研究成果可为工程岩体力学参数取值及评价提供借鉴.     

中国西南深切峡谷岸坡地应力场基本特征

基于西南地区10个大型水电工程95点空间应力测试数据与50点硐壁应力恢复法测试数据,统计分析了边坡地应力场随垂向、水平向深度变化规律,根据主应力量级、倾角变化规律分析边坡浅表部地应力场特征,探讨了西南深切峡谷地区边坡地应力场分布规律。研究表明,（1）边坡应力场在宏观上可划分为浅表部区(0～300 m)与深部区(>300 m);（2）浅表部区主应力量级、倾角波动较为剧烈,而深部区主应力量级、倾角较为稳定,其最大主应力介于15～30 MPa,中间主应力介于10～20 MPa,最小主应力介于5～12 MPa,最大、最小主应力倾角介于0°～30°,最大主应力约为最小主应力的1.5～3.5倍;（3）浅表部区地应力场具有由主应力较小、最大主应力倾角与坡角近平行转变为主应力急剧增高、最大主应力倾角变化不明显,继而转变为主应力量级、最大主应力倾角剧烈波动,最后逐渐转变与深部应力场近于一致的特征。     

开滦矿区地应力场特征及其研究意义

地应力是影响矿井突水的重要因素之一,是存在于地壳中的重要能量场条件。采用现场应力解除法对开滦矿区多个矿井进行了地应力测试,分析了研究区现今地应力分布规律,在此基础上,建立了煤层底板突水危险性与岩石力学性质及地应力之间的相关关系和模型,对范各庄矿12煤层底板和东欢坨矿12-2煤层底板突水危险性进行了评价。研究结果表明,本区地壳浅部现代地应力作用较强,整体处于近东西向挤压应力场中,在挤压应力作用下,煤岩层应力状态主要表现为水平主应力大于垂直主应力,原岩应力主要由构造应力和自重应力场构成。煤层底板突水危险性受岩石力学条件和地应力所控制,当岩石破裂压力大于水压（Pf〉Pw）,则不产生突水;若岩石破裂压力小于水压时,则有可能突水。当承压水的水压（Pw）小于最小水平主应力（σhmin）时,不会产生突水。只有当承压水的水压（Pw）大于最小水平主应力（σhmin）时,存在突水危险性。范各庄矿12煤层底板和东欢坨矿12-2煤层底板破裂压力（Pf）和最小主应力（σhmin）均大于其底板岩体承受的水压（Pw）,本区在无构造破坏卸压条件下是不会发生底板突水的。     

我国某地下油库预可行性研究地应力测量及其应用分析

本文运用水压致裂地应力测量方法,对我国某地下油库预可行性研究工程场区两个钻孔进行了地应力测量。测量结果表明:最大和最小水平主应力(S_H,S_h)都远大于对应深度处的垂向应力(S_v),三向主应力的关系为:S_H > S_h > S_v,应力大小在该深度范围属中等偏大级别;工程场区最大水平主应力方向近EW方向,与测点外围确定的区域最大水平主应力总体方向较为一致;建议未来地下硐库长轴按近EW分布,地应力状态、岩体结构构造、岩石强度等基本保证了其岩体稳定性。      

甘肃某水电站的水压致裂三维地应力测量

本文详细介绍了常规水压致裂方法的测量程序以及三孔交汇法三维地应力测量的原理。同时为查明某水电站的三维地应力状态,在厂房附近的交通洞内开展了两个测点的三维地应力测量。测量结果表明:三个主应力的大小表现为S_HS_hS_v,有利于逆断层的活动,这与测孔附近发育的逆断层相符合。最大水平主应力S_H方向为NE31°和NE33°,这与区域应力场NE向或NNE向相一致;三维应力计算结果显示,两向水平主应力接近水平,垂直应力倾角大于70°。虽然洞轴线的布线方向与最大主应力夹角过大,由于工程区为非高应力区,因此不影响洞室的稳定性。     

Boundary element analysis of transversely isotropic bi-material halfspaces with inclined planes of isotropy and interfaces

In this paper, a single-region boundary element method (BEM) is presented for the analysis of transversely isotropic bi-material halfspaces with arbitrarily inclined planes of isotropy and material interfaces. The proposed BEM uses the fundamental solution of a transversely isotropic bi-material fullspace and five boundary element techniques. Infinite boundary elements are introduced to consider the far-fields of a transversely isotropic bi-material halfspace. The effective integration methods are proposed for dealing with various integrals in the discretized boundary integral equation. The stresses at internal points are obtained using the coordinate transformation of kernel functions, and the stresses on the boundary surface are calculated using an improved traction recovered method. Numerical verifications of displacements and stresses for a benchmark problem are conducted, and excellent agreement with previously published results is obtained. Numerical examples are presented to illustrate the influence of non-horizontal or horizontal planes of isotropy in bi-material halfspaces on the displacements and stresses induced by the tractions on the horizontal boundary surface. Results reveal that the elastic fields vary clearly with the dip angle of the isotropic plane and the stresses across the bi-material interface are closely related to the ratios of the elastic parameters of the bi-material.     

Elastic solutions for a transversely isotropic half-space subjected to a point load

We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the effect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite different for the displacement and stress calculated from isotropic solutions. © 1998 John Wiley & Sons, Ltd.     

弹性矩形板下横观各向同性多层地基分析

利用弹性矩形板与多层地基表面的竖向位移协调条件与光滑接触条件,由横观各向同性多层地基应力与位移非耦合的传递矩阵解,推导出弹性矩形板下竖向应力和位移的解析解。在此基础上,编制了相应的程序,并进行了数值计算。计算结果表明：矩形板刚度对板底竖向位移及板中心下的竖向应力有着较为显著的影响;板底竖向位移及板中心下的竖向应力随着板刚度的增加而减小,相同荷载作用下横观各向同性地基与均匀各向同性地基模型的计算结果差异较大,实际工程中很有必要采用更符合土体性质的横观各向同性地基模型     

Elastic solutions for a transversely isotropic half-space subjected to buried asymmetric-loads

Elastic closed-form solutions for the displacements and stresses in a transversely isotropic half-space subjected to various buried loading types are presented. The loading types include finite line loads and asymmetric loads (such as uniform and linearly varying rectangular loads, or trapezoidal loads). The planes of transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are directly obtained from integrating the point load solutions in a transversely isotropic half-space, which were derived using the principle of superposition, Fourier and Hankel transformation techniques. The solutions for the displacements and stresses in transversely isotropic half-spaces subjected to linearly variable loads on a rectangular region are never mentioned in literature. These exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, and the degree and type of rock anisotropy. Two illustrative examples, a vertical uniform and a vertical linearly varying rectangular load acting on the surface of transversely isotropic rock masses, are presented to show the effect of various parameters on the vertical surface displacement and vertical stress. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different for those calculated from isotropic solutions. Copyright © 1999 John Wiley & Sons, Ltd.     

考虑剪应力作用时横观各向同性岩体中圆形巷道位移反分析的惟一性

推导了考虑剪应力作用时横观各向同性岩体中圆形巷道的位移解析解,利用参数可辨识条件对考虑剪应力作用时横观各向同性岩体中圆形巷道位移反分析的惟一性进行了探讨。结果表明,无论布置多少个测点也不能惟一地反分析出所有7个参数,必须至少已知3个参数,才有可能惟一地反分析出其他参数;水平与竖直地应力分量是否为 0 对反分析惟一性有一定影响;3个地应力分量的可辨识性最好,各向同性面上的弹性模量和泊松比次之,垂直于各向同性面方向的弹性模量和泊松比最差。与不考虑剪应力时位移反分析惟一性结果相比,考虑剪应力时参数的可辨识性顺序不变,但是条件惟一的比例降低,不惟一和绝对惟一的比例增加,说明考虑剪应力能够提高位移反分析的惟一性。工程实例计算表明,推导的位移解析解和反分析惟一性探讨结果能够很好地指导岩体参数反演计算。     

横观各向同性饱和地基竖向振动的衰减特性

基于提出的横观各向同性饱和多孔介质Biot波动方程的一般解,研究了饱和半空间地基在竖向点源简谐激振荷载作用下地表振动的衰减特征,分析了激振频率以及横观各向同性饱和土介质的各向异性参数和孔隙渗透系数对地表振动特征的影响。计算结果表明,低频和高频激振时,地表位移衰减特性存在明显差异;在饱和土的各向异性参数中,纵向和水平方向动态渗透系数比值和刚度系数比值对地表位移衰减影响最大,这也说明采用各向同性饱和介质的动力学模型不能准确地描述具有明显各向异性特性的饱和土地基的动力特性。     

Elastic fields in two joined transversely isotropic media of infinite extent as a result of rectangular loading

This paper presents the closed‐form solutions for the elastic fields in two bonded rocks induced by rectangular loadings. Each of the two bonded rocks behaves as a transversely isotropic linear elastic solid of semi‐infinite extent. They are completely bonded together at a horizontal surface. The rectangular loadings are body forces along either vertical or horizontal directions and are uniformly applied on a rectangular area. The rectangular area is embedded in the two bonded rocks and is parallel to the horizontal interface. The classical integral transforms are used in the solution formulation, and the elastic solutions are expressed in the forms of elementary harmonic functions for the rectangular loadings. The stresses and displacements in the rocks induced by both the horizontal and vertical body forces are also presented. The numerical results illustrate the important effect of the anisotropic bimaterial properties on the stress and displacement fields. The solutions can be easily implemented for numerical calculations and applied to problems encountered in rock mechanics and engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

Response of multilayered transversely isotropic medium due to axisymmetric loads

A novel procedure associated with the precise integration method (PIM) and the technique of dual vector is proposed to effectively calculate the magnitude and distribution of deformations in a homogeneous multilayered transversely isotropic medium. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the soil system. The linearly elastic medium is subjected to four types of vertically acting axisymmetric loads prescribed either at the external surface or in the interior of the soil medium. There are no limits for the thicknesses and number of soil layers to be considered. By virtue of the governing equations of motion and the constitutive equations of the transversely isotropic elastic body, and based on the Hankel integral transform and a dual vector formulation in a cylindrical coordinate system, the partial differential motion equations can be converted into first‐order ordinary differential matrix equations. Applying the approach of PIM, it is convenient to obtain the solutions of ordinary differential matrix equations for the continuously homogeneous multilayered transversely isotropic elastic soil in the transformed domain. The PIM is a highly accurate algorithm to solve the sets of first‐order ordinary differential equations, which can ensure to achieve any desired accuracy of the solutions. What is more, all calculations are based on the standard method with the corresponding algebraic operations. Computational efforts can be reduced to a great extent. Finally, numerical examples are provided to illustrate the accuracy and effectiveness of the proposed approach. Some more cases are analyzed to evaluate the influences of the elastic parameters of the transversely isotropic media on the load‐displacement responses. Copyright © 2015 John Wiley & Sons, Ltd.     

Elastic solutions of displacements for a transversely isotropic full space with inclined planes of symmetry subjected to a point load

This work presents analytical solutions for displacements caused by three‐dimensional point loads in a transversely isotropic full space, in which transversely isotropic planes are inclined with respect to the horizontal loading surface. In the derivation, the triple Fourier transforms are employed toyield integral expressions of Green's displacement; then, the triple inverse Fourier transforms and residue calculus are performed to integrate the contours. The solutions herein indicate that the displacements are governed by (1) the rotation of the transversely isotropic planes (?), (2) the type and degree of material anisotropy (E/E′, ν/ν′, G/G′), (3) the geometric position (r, φ, ξ) and (4) the types of loading (P_x, P_y, P_z). The solutions are identical to those of Liao and Wang (Int. J. Numer. Anal. Methods Geomechanics 1998; 22 (6):425–447) if the full space is homogeneous and linearly elastic and the transversely isotropic planes are parallel to the horizontal surface. Additionally, a series of parametric study is conducted to demonstrate the presented solutions, and to elucidate the effect of the aforementioned factors on the displacements. The results demonstrate that the displacements in the infinite isotropic/transversely isotropic rocks, subjected to three‐dimensional point loads could be easily determined using the proposed solutions. Also, these solutions could realistically imitate the actual stratum of loading situations in numerous areas of engineering. Copyright © 2007 John Wiley & Sons, Ltd.