基于岩石蠕变及D-P准则的深部巷道围岩弹塑性分析

为深入分析岩石蠕变及中间主应力对深部高应力软岩巷道围岩稳定性及分区变形特性的影响机理, 通过剖析长期荷载作用下深部巷道围岩的变形特征, 揭示了基于围岩蠕变特性的深部巷道围岩四分区变形机理, 并依据Druck-Prager准则及关联性流动法则考虑了中间主应力、岩体扩容及应变软化的影响, 推导出巷道围岩各分区应力、变形和半径解析解. 结合工程算例, 通过对现场监测数据以及不同力学模型的计算结果进行对比分析, 论证了本文理论的科学性, 并揭示了不同强度准则和围岩参数对深部巷道围岩各分区形态的影响规律. 结果表明, 忽视深部巷道围岩的蠕变特性将导致初始黏聚力的取值大于实际值, 从而造成围岩的理论承载能力大于实际承载能力; 在[0, 0.7]区间内提高中间主应力系数可有效控制围岩塑性区及破碎区范围的扩展; 当初始黏聚力及内摩擦角减小时, 中间主应力系数对围岩塑性区、破碎区范围及巷道变形的影响力显著提高. 研究成果可为地下工程支护设计及围岩稳定性评估提供理论参考.      

深部岩体圆形巷道围岩松动圈形成机理数值试验研究

采用损伤力学和统计理论的单元本构模型,探讨深部岩体巷道围岩破坏规律, 利用岩石破裂过程分析软件RFPA$^{\rm 2D}$, 对深部 岩体中的圆形巷道的变形及非线性渐进破坏特征、巷道周边关键部位的位移和应力变化进行 了分析,研究了圆形巷道围岩松动圈的形成机理. 研究表明：巷道开挖后,其周边形成应力 集中带,随着围岩压力的持续作用,巷道周边产生塑性变形区,并沿径向形成裂纹;随着裂 纹的不断扩展,巷道周边出现松动破裂区,即松动圈. 产生破裂区后,应力集中程度减弱, 应力高峰点向远处转移.     

SOLUTION AND ANALYSIS OF CIRCULAR TUNNEL FOR THE STRAIN-SOFTENING ROCK MASSES CONSIDERING THE AXIAL IN SITU STRESS AND SEEPAGE FORCE

为了研究轴向应力和渗透力共同作用下软化围岩的应力与位移的变化及分布规律. 基于摩尔-库伦屈服准则及应力-应变软化模型并考虑轴向应力和渗透力的共同作用,将整个塑性区分为有限个同心圆环,以弹塑性交界面处的应力、应变为初始值,并采用微小径向应力增量逐步求出各个圆环上的应力应变及塑性区半径,据此重构了考虑渗透力和轴向力共同作用下软化围岩应力应变特性的逐步求解方法. 利用该方法,推导出软化围岩应力应变的解. 计算结果表明：在考虑轴向应力作用下,塑性区半径和隧道围岩位移都随着渗透力的增加而有所减小;当轴向应力为最小主应力时,渗透力的影响更为显著. 这说明渗透力的存在对于隧道围岩的应力应变分布以及塑性半径和围岩的位移有不可忽略的影响.     

考虑轴向力和渗透力时软化围岩隧道解析

为了研究轴向应力和渗透力共同作用下软化围岩的应力与位移的变化及分布规律. 基于摩尔-库伦屈服准则及应力-应变软化模型并考虑轴向应力和渗透力的共同作用,将整个塑性区分为有限个同心圆环,以弹塑性交界面处的应力、应变为初始值,并采用微小径向应力增量逐步求出各个圆环上的应力应变及塑性区半径,据此重构了考虑渗透力和轴向力共同作用下软化围岩应力应变特性的逐步求解方法. 利用该方法,推导出软化围岩应力应变的解. 计算结果表明:在考虑轴向应力作用下,塑性区半径和隧道围岩位移都随着渗透力的增加而有所减小;当轴向应力为最小主应力时,渗透力的影响更为显著. 这说明渗透力的存在对于隧道围岩的应力应变分布以及塑性半径和围岩的位移有不可忽略的影响.      

MY准则解析复合型裂尖塑性区

首次以MY(平均屈服)准则对I-II复合型裂纹在小范围屈服下的裂尖塑性区进行了分析,分别获得了平面应力和平面应变状态下塑性区尺寸的解析解。这两解表明,塑性区尺寸是材料屈服强度、应力强度因子、极角θ的函数。与Tresca准则、TSS屈服准则获得的解以及Mises解比较表明:Tresca准则预测塑性区上限,TSS屈服准则预测塑性区下限,MY准则预测的塑性区居于Tresca与TSS塑性区之间,逼近Mises解。另外,文中讨论了平面应力和平面应变状态下裂纹尖端的开裂问题,结果表明:当裂纹角β=π4时,平面应力状态下裂纹沿0-θ=0.2952π方向开裂;平面应变状态下裂纹沿0-θ=0.3188π方向开裂。     

深部回采巷道围岩零应变交界圈现象的模型试验研究

以淮南矿区口孜东矿深部回采巷道为工程背景,采用真三轴模型试验装置模拟了从浅埋静水压力、深埋静水压力、初掘采动应力(K=1.5为1.5倍900m埋深静水压力,后同)到回采动压(K=2~3)等不同应力条件下,大、小两种尺寸的直墙拱形回采巷道围岩应变状态,获得了浅埋条件下巷道围岩浅部拉应变、深部零应变,以及深埋静水压力及初掘采动应力下,巷道围岩出现"零应变交界圈"现象及深埋回采高应力下非线性大应变的围岩应变特征。应变监测结果反映了深部回采巷道围岩变形破坏的动态演化过程,为巷道的稳定性控制提供了一定的思考。     

基于实测地应力深埋巷道塑性区定量分析

深埋巷道大变形、强流变的破坏特征源于其高地应力的作用,准确分析已开掘巷道塑性区分布对巷道围岩变形影响、开掘方案选择及后续类似条件巷道布置意义深远。在围岩力学参数测试、地应力场测试的基础上,采用弹塑性理论、M-C准则、修正的“当量半径”理论简化计算了直墙半圆拱形断面布置下深埋巷道的围岩塑性区大小,分析了巷道围岩塑性区受采动应力、侧压系数单独及耦合作用影响规律。在侧压系数为0.5、垂直压力为35MPa时底板塑性区最大,其值为2.65m,建议加强巷道底板的支护与维护,并给出了塑性区控制方案。研究结果可为后续类似条件下巷道开掘方案优选、支护设计及围岩稳定性判定提供一定的借鉴。     

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针对红透山深部断层下巷道围岩破坏诱发的涌水现象,以该矿水文地质条件 为基础,建立了岩体水力学模型,应用岩石破裂过程渗流-应力耦合分析系统 (RFPA$^{\rm 2D}$-Flow)模拟研究了深部断层下巷道围岩破坏过程：裂隙形成、扩展到突水通 道最终贯通形成涌水的全过程. 通过对损伤区分布、应力场和渗流场的演化规律进行分析, 揭示了巷道应力重新分布诱发损伤及渗流涌水规律,对涌水通道进行模拟定位,为红透山铜 矿深部巷道支护防渗设计提供了科学依据.     

高应力回采巷道围岩破裂机理及控制研究

为了研究巷道围岩破裂的危险性与工程地质的相关性, 借助弹塑性力学 的复变函数方法求解了巷道围岩的应力函数, 然后深入研究了高应力回采巷道围岩破裂机理, 提出以危险函数来评价巷道围岩破裂的危险性和确定巷道破裂时的滑移面分布特征的方法, 得到回采巷道的实用控制技术, 此法具有使用性广、计算简便的优点.     

对《粘弹-塑性介质中围岩与衬砌的应力状态》一文的讨论和补充

由于采用解析的方法求解在粘弹一塑性状态下围岩与衬砌的应力状态,在大型工程中可提供衬砌围岩体系的应力、应变状态的定性认识,对实际中的大量中小工程,在目前采用高精度的计算既无必要的条件,而经济上也不合理的情况下,可提供概略的计算结果.所以解析解的求取,对解决实际问题仍具有一定的重要意义.“粘弹一塑性介质中围岩与衬砌的应力状态”一文(载于力学学报1981年1期),就其轴对称情况求出了解答.现对一些问题提出讨论,并做了若干更正及补充.     

浅埋隧道围岩应力场的解析解

隧道围岩应力和变形分析是隧道设计的重要内容。对深埋隧道的研究已取得了很多结果。但对于受地表边界和地面荷载的影响，浅埋隧道围岩分析在数学处理上仍存在一定的困难。一般采用边界元或有限元等数值方法，未见有解析解的报导。本文采用复变函数解法研究地面荷载作用下浅埋圆形隧道围岩的平面弹性问题，该解法利用复变函数保角变换将物理平面上的研究域映射到像平面上的圆环域内。将复势函数进行罗伦级数展开，通过边界条件得到罗伦级数展开式系数的递推公式，并由复势函数确定应力分量和位移分量。最后通过算例给出了围岩应力分布和沉降曲线。所得结果适用于任意分布荷载的情况，具有通用性。     

Deformation and the strip necking zone in a cracked steel sheet

When a tensile stress is applied to a thin cracked plate, a strip necking region results ahead of a crack tip. The relative opening displacement between the crack surfaces and between the upper and lower boundaries of the strip necking region were measured by the moiré method. The strains ahead of the strip necking region and the thickness reduction (therein) were also measured. The measured relative opening displacements were compared with the calculated values using the Dugdale strip necking model. The thickness reduction in the strip necking region is equal to the relative opening displacement.     

Effects of electric field on crack growth for a penny-shaped dielectric crack in a piezoelectric layer

The assumptions of impermeable and permeable cracks give rise to significant errors in determining electro-elastic behavior of a cracked piezoelectric material. The former simply imposes that the permittivity or electric displacement of the crack interior vanishes, and the latter neglects also the effects of the dielectric of an opening crack interior. Considering the presence of the dielectric of an opening crack interior and the permeability of the crack surfaces for electric field, this paper analyzes electro-elastic behavior induced by a penny-shaped dielectric crack in a piezoelectric ceramic layer. In the cases of prescribed displacement or prescribed stress at the layer surfaces, the Hankel transform technique is employed to reduce the problem to Fredholm integral equations with a parameter dependent nonlinearly on the unknown functions. For an infinite piezoelectric space, a closed-form solution can be derived explicitly, while for a piezoelectric layer, an iterative technique is suggested to solve the resulting nonlinear equations. Field intensity factors are obtained in terms of the solution of the equations. Numerical results of the crack opening displacement intensity factors are presented for a cracked PZT-5H layer and the effect of applied electric field on crack growth are examined for both cases. The results indicate that the fracture toughness of a piezoelectric ceramic is affected by the direction of applied electric fields, dependent on the elastic boundary conditions.     

A reexamination of plasticity-induced crack closure in fatigue crack propagation

The crack closure concept is often used to consider the R-ratio and overload effects on fatigue crack growth. The presumption is that when the crack is closed, the external load produces negligible fatigue damage in the cracked component. The current investigation provides a reassessment of the frequently used concept with an emphasis on the plasticity-induced crack closure. A center cracked specimen made of 1070 steel was investigated. The specimen was subjected to plane-stress mode I loading. An elastic–plastic stress analysis was conducted for the cracked specimens using the finite element method. By applying the commonly used one-node-per-cycle debonding scheme for the crack closure simulations, it was shown that the predicted crack opening load did not stabilize when the extended crack was less than four times of the plastic zone size. The predicted opening load was strongly influenced by the plasticity model used. When the elastic–perfectly plastic (EPP) stress–strain relationship was used together with the kinematic hardening plasticity theory, the predicted crack opening load was found to be critically dependent on the element size of the finite element mesh model. For R = 0, the predicted crack opening load was greatly reduced when the finite element size became very fine. The kinematic hardening rule with the bilinear (BL) stress–strain relationship predicted crack closure with less dependence on the element size. When a recently developed cyclic plasticity model was used, the element size effect on the predicted crack opening level was insignificant. While crack closure may occur, it was demonstrated that cyclic plasticity persisted in the material near the crack tip. The cyclic plasticity was reduced but not negligible when the crack was closed. The traditional approaches may have overestimated the effect of crack closure in fatigue crack growth predictions.     

<Emphasis Type="Italic">T</Emphasis>-stress analysis for a Griffith crack in a magnetoelectroelastic solid

T-stress as an important parameter characterizing the stress field around a cracked tip has attracted much attention. This paper concerns the T-stress near a cracked tip in a magnetoelectroelastic solid. By applying the Fourier transform, we solve the associated mixed boundary-value problem. Adopting crack-faces electromagnetic boundary conditions nonlinearly dependent on the crack opening displacement, coupled dual integral equations are derived. Then, the closed-form solution for the T-stress is obtained. A comparison of the T stresses for a cracked magnetoelectroelastic solid and for a cracked purely elastic material is made. Obtained results reveal that in addition to applied mechanical loading, the T-stress is dependent on electric and magnetic loadings for a vacuum crack.     

Analysis of stress concentrations in plates with rectangular openings by a combined conformal mapping – Finite element approach

Plates with rectangular openings develop stress concentrations under bending. While these stresses can be determined using finite elements, in many problems this would be difficult because a high density mesh would be needed in the neighborhood of every opening corner. In this paper, it is shown how a complex-variable conformal mapping approach can be numerically coupled with the finite element method to analyze these corner stresses. This approach can be used even with relatively coarse meshes where the finite element results, by themselves, do not resolve the stress concentrations. In essence, the method relies on finite element analysis to obtain information on the stress field in a region surrounding the plate opening; this information is subsequently used to set up the parameters of the conformal mapping approach to obtain the near field stresses at the opening corners.     

The electro-mechanical response of highly compliant substrates and thin stiff films with periodic cracks

We present results that describe the mechanical response of highly compliant substrates coated with ultra-thin stiff films, with thickness and elastic moduli differences spanning four orders of magnitude. Dimensional analysis based on shear-lag models of cracked films is used to identify key parameters that control the effective elastic properties of the cracked multi-layer, crack opening displacements, and the steady-state energy release rate for channeling crack formation. Analytical forms that describe multi-layer response in terms of film properties and crack spacing are presented and corroborated with numerical models for linear elastic materials. A key result is that the energy release rate scales with 1/(1 − α), where α is one of the Dundurs’ parameters describing elastic mismatch. The results can also be used to evaluate the performance of electrostrictive actuators comprised of cracked blanket electrodes and elastomer dielectrics. In this scenario, an interesting result is that ultra-thin cracked films can continue to distribute charge, since crack openings may be small enough to allow breakdown in air at typical operating voltages.     

A NEW APPROACH TO FREE VIBRATION ANALYSIS OF A BEAM WITH A BREATHING CRACK BASED ON MECHANICAL ENERGY BALANCE METHOD

In this paper, a new approach to free vibration analysis of a cracked cantilever beam is proposed. By considering the effect of opening and closing the crack during the beam vibration, it is modeled as a fatigue crack. Also, local stiffness changes at the crack location are considered to be a nonlinear amplitude-dependent function and it is assumed that during one half a cycle, the frequencies and mode shapes of the beam vary continuously with time. In addition, by using the experimental tests, it is shown that the local stiffness at the crack location varies continuously between the two extreme values corresponding to the fully closed and the fully open cases of the crack. Then, by using the mechanical energy balance the dynamic response of the cracked beam is obtained at every time instant. The results show that for a specific crack depth, by approaching the crack location to the fixed end of the beam, more reduction in the fundamental frequency occurs. Furthermore, for a specific crack location, the fundamental frequency diminishes and the nonlinearity of the system increases by increasing the crack depth. In order to validate the results, the variations of the fundamental frequency ratio against the crack location are compared with experimental results.     

基于裂纹诱导弦挠度的梁开闭裂纹损伤识别

考虑裂纹缝隙效应,建立了Euler-Bernoulli梁中开闭裂纹位置、深度和初始张开角等损伤参数的识别方法．首先,基于梁中开闭裂纹的等效单向扭转弹簧模型,给出了开闭裂纹Euler-Bernoulli梁静力弯曲挠度的显式闭合解．在此基础上,证明了裂纹诱导弦挠度函数由分段三次多项式组成,并基于其构造特征,建立了基于测量挠度的梁中开闭裂纹位置、裂纹等效扭转弹簧柔度、裂纹初始张开角和裂纹上下侧属性等参数的数值识别方法．最后,通过数值实验考察了挠度测量误差和裂纹位置等对裂纹识别结果的影响,结果表明：裂纹位置、裂纹等效扭转弹簧柔度和裂纹初始张开角等的识别误差随挠度测量误差增大而增大,但裂纹识别结果具有较强的鲁棒性,在工程实际中具有一定的应用前景．     

THE ZONAL DISINTEGRATION MECHANISM OF SURROUNDING ROCK AROUND DEEP SPHERICAL TUNNELS UNDER HYDROSTATIC PRESSURE CONDITION: A NON-EUCLIDEAN CONTINUUM DAMAGE MODEL

A new non-Euclidean continuum damage model is proposed to investigate the zonal disintegration phenomenon of the surrounding rocks around deep spherical tunnels under hydrostatic pressure condition as well as the total elastic stress field distributions.The elastic stress fields of the surrounding rocks around deep spherical tunnels under hydrostatic pressure condition are obtained.If the elastic stresses of the surrounding rocks satisfy the strength criterion of the deep rock masses,the number,size and location of fractured and nonfractured zones are determined.The efect of physico-mechanical parameters of the surrounding rocks on the zonal disintegration phenomenon is studied and numerical computation is carried out.It is found from numerical results that the number,size and location of fractured and non-fractured zones are sensitive to the physico-mechanical parameters of the surrounding rocks.