开挖卸荷条件下深部圆形洞室各向同性围岩分区破裂化机理

论文提出了一种静水压力条件下动态开挖卸荷对深埋圆形洞室各向同性围岩分区破裂化影响的力学模型,获得了动态开挖卸荷条件下深埋圆形洞室围岩的弹性应力场,确定了卸荷速率和岩体动态力学参数对深埋洞室各向同性围岩分区破裂化现象的影响.利用动态Hoek-Brown准则,获得了围岩破裂区和非破裂区的数量和宽度.数值计算结果表明卸荷速率和岩体动态力学参数对破裂区与非破裂区的数量和宽度有较大影响.     

深部岩体损伤对分区破裂化效应的影响

深部岩体是一种具有初始损伤的非连续介质,其内部存在着大量节理和裂隙。深部岩体分区破裂化效应与节理、裂隙的扩展、连接和汇合密切相关。由于节理、裂隙的扩展、连接和汇合可能会导致深部岩体的内部空间由欧氏几何空间向非欧几何空间转化。本文利用损伤变量表示含节理和裂隙岩体的损伤,根据非欧几何模型,获得了静水压力和非静水压力情况下深部圆形洞室损伤围岩的应力场,确定了损伤变量对圆形洞室围岩的应力场和分区破裂化效应的影响。采用Hoek-Brown准则,获得了静水压力和非静水压力情况下损伤围岩的破裂区与非破裂区的分布规律。本文的研究结果为理解深部岩体分区破裂模式提供了有价值的参考。     

Zonal disintegration of surrounding rock mass around the diversion tunnels in Jinping II Hydropower Station, Southwestern China

By means of numerical simulation, the special phenomenon of zonal disintegration of surrounding rock mass around the diversion tunnels of Jinping II Hydropower Station is analyzed in this paper. In order to model the growth and coalescence of cracks within rock mass in Jinping II Hydropower Station, the weak-element is adopted. When cracks coalesce, failure of deep crack-weakened rock masses occurs and fractured zone is formed. The present result is different from the one obtained by the traditional elasto-plastic theory. The numerical results show that the slip-line zonal fracture is created within rock mass around the diversion tunnels in Jinping II Hydropower Station. Meanwhile, the magnitude and distributions of fractured zones are determined by numerical simulation. It is shown that the present results are in good agreement with the one observed by model tests. Through sensitivity analysis, the effects of stress condition, cohesion and the angle of internal friction on the phenomenon of zonal disintegration is determined.     

Zonal disintegration of deep crack-weakened rock masses: A non-Euclidean model

Rock masses are characterized by the existence of distributed joints and fractures. One of behaviors of the deep rock masses is high in situ stresses. The internal space of rock-like materials subjected to high in situ stresses after deformation is treated as a non-Euclidean one. The incompatible deformation of the deep rock masses is induced by high in situ stresses within the framework of non-Euclidean geometric space. A non-Euclidean model in which effects of cracks on zonal disintegration phenomenon of the deep crack-weakened rock masses is taken into account is established. Based on the non-Euclidean model, the elastic stress-field distribution of the deep surrounding rock masses induced by compatible deformation of non-fractured zones and incompatible deformation of fractured zones is determined. The stress intensity factors at the tips of cracks is given out. The strain energy density factor is applied to investigate the occurrence of disintegration zones. It is observed from the numerical results that the magnitude and site of fractured zones depend on the value of in situ stress, mesomechanical parameters and non-Euclidean parameters.     

ZONAL DISINTEGRATION MECHANISM OF DEEP CRACK-WEAKENED ROCK MASSES UNDER DYNAMIC UNLOADING

Size and quantity of fractured zone and non-fractured zone are controlled by cracks contained in deep rock masses. Zonal disintegration mechanism is strongly dependent on the interaction among cracks. The strong interaction among cracks is investigated using stress superposition principle and the Chebyshev polynomials expansion of the pseudo-traction. It is found from numerical results that crack nucleation, growth and coalescence lead to failure of deep crack- weakened rock masses. The stress redistribution around the surrounding rock mass induced by unloading excavation is studied. The effect of the excavation time on nucleation, growth, interaction and coalescence of cracks was analyzed. Moreover, the influence of the excavation time on the size and quantity of fractured zone and non-fractured zone was given. When the excavation time is short, zonal disintegration phenomenon may occur in deep rock masses. It is shown from numerical results that the size and quantity of fractured zone increase with decreasing excavation time, and the size and quantity of fractured zone increase with the increasing value of in-situ geostress.     

THE EFFECTS OF THREE-DIMENSIONAL PENNY-SHAPED CRACKS ON ZONAL DISINTEGRATION OF THE SURROUNDING ROCK MASSES AROUND A DEEP CIRCULAR TUNNEL

In this study, it was assumed that three-dimensional penny-shaped cracks existed in deep rock masses. A new non-Euclidean model was established, in which the effects of pennyshaped cracks and axial in-situ stress on zonal disintegration of deep rock masses were taken into account. Based on the non-Euclidean model, the stress intensity factors at tips of the pennyshaped cracks were determined. The strain energy density factor was applied to investigate the occurrence of fractured zones. It was observed from the numerical results that the magnitude and location of fractured zones were sensitive to micro- and macro-mechanical parameters, as well as the value of in-situ stress. The numerical results were in good agreement with the experimental data.     

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。     

2021-07期目录

在陈宗基院士关于地下硐室长期稳定性力学问题研究的基础上,采用Sadovsky院士关于复杂地质岩体的等级构造学说,围绕深部岩体非均匀构造与封闭应力固有的统计力学属性,研究了岩体非均匀变形与封闭应力特性,以及深部硐室围岩的长期稳定性等两个力学问题。给出了岩体非均匀构造与封闭应力的数学表征;根据质量守恒定律得到了计算深部硐室围岩长期变形的一般公式;得到了围岩变形中劈裂扩容变形占主要部分的结论,并且阐明了深部围岩卸荷时更易出现劈裂破坏的原因。给出了劈裂破坏形态的演进序列与扩容位移的计算方法。将围岩松动圈范围、破裂区位置和边壁位移的计算结果与锦屏一级电站厂房现有监测数据进行了对比,两者相当吻合。     

Zonal fracturing mechanism in deep crack-weakened rock masses

The mechanical behaviors of deep crack-weakened rock masses are different from those of shallow crack-weakened rock masses. The surrounding rock in shallow crack-weakened rock mass engineering is classified into loose zone, plastic zone and elastic zone, while the surrounding rock in deep crack-weakened rock mass engineering is classified into fractured zone and non-fractured zone, which occur alternatively. It is assumed that the deep rock masses contain one joint set, in which the probability density function describing the distribution of sizes is assumed to follow the Rayleigh distribution, and the probability density function describing the distribution of spacing is assumed to follow the Weibull distribution. On the basis of strength criterion of deep rock mass, the near-field stress redistribution around circular opening induced by excavation is determined. The strong interaction among cracks is investigated by using the dislocation model. The nucleation, growth, interaction and coalescence of cracks were analyzed based on the strain energy density factor theory. When cracks coalesce, failure of deep crack-weakened rock masses occurs, fractured zone is formed. Then, size and quantity of fractured zone and non-fractured zone are given out. The size and quantity of fractured zone increase with decreasing strength of rock mass. The size and quantity of fractured zone increase with increasing in situ stress. Zonal fracturing phenomenon occurs once value of in situ stress is larger than the unaxial compressive strength of rock masses. The size and quantity of fractured zone decrease with increasing λ when p₂ > p₁. The size and quantity of fractured zone increase with increasing λ when p₂ < p₁.     

Rock burst of deep circular tunnels surrounded by weakened rock mass with cracks

Rock masses containing pre-existing cracks are considered as non-homogeneous geomaterials. During excavation of tunnels, pre-existing cracks may nucleate, grow and propagate through rock matrix, then secondary cracks may appear. The stress concentration at the tips of secondary cracks is comparatively large, which may lead to the unstable growth and coalescence of secondary cracks, and consequently the occurrence of fractured zones. For brittle rocks, the dissipative energy of slip and growth of pre-existing cracks and secondary crack growth is small, but the elastic strain energy storing in rock masses may be larger than the dissipative energy of slip and growth of pre-existing macrocracks and secondary crack growth. The sudden release of the residual elastic strain energy may lead to rock burst in crack-weakened rock masses. Based on this understanding, the criteria of rock burst in crack-weakened rock masses are established. The influences of the in situ stresses, micromechanical parameters and physico-mechanical parameters on the distribution of rock burst zones and area of rock burst zones are investigated in detail.     

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。     

Irreversible dilatancy or compressibility of viscoplastic rock-like materials and some applications

An elastic/viscoplastic constitutive equation for rock-like materials which is able to describe, besides creep, an irreversible compressibility and/or dilatancy of the volume is formulated. Mathematical definitions are used for the concepts of dilatancy, compressibility, compressibility/dilatancy boundary, and failure. Two examples of such constitutive equations are given for a hard rock and a softer rock.Two applications of this constitutive equation are presented. First the creep dilatancy and/or compressibility of the rocks surrounding an oil well or a pressure shaft are studied for various initial primary stresses. The location and the conditions under which the rock surrounding the well may become dilatant are then shown. The same problem is studied for the case of horizontal tunnels. Various depths and primary stresses are considered and it is shown where possible failure may occur. For both applications numerical examples are given.     

椭圆形溶洞对邻近深埋圆形隧洞的影响分析

将深埋溶洞-隧洞所处的地下空间转换为平面应变情况下的弹性半空间,溶洞为似椭圆形;由于圆形断面隧洞埋深与孔径相比比较大从而不考虑重力梯度影响,考虑隧洞衬砌法向支撑力的影响,且考虑溶洞先于隧洞形成等因素,利用复变函数中的柯西积分法结合Schwarz交替法求解出弹性半空间内椭圆形溶洞及圆形隧洞周边任意一点处的应力值和位移值解析解的具体显式表达式。采用有限元分析对理论推导的椭圆形溶洞-圆形隧洞体系的解析解进行验证。     

A semi-analytical elastic solution for stress field of lined non-circular tunnels at great depth using complex variable method

In this paper, a semi-analytical elastic plane strain solution was provided for stress field around a lined non-circular tunnel subjected to uniform ground load. Concrete lining and the surrounding rock mass were assumed as linearly elastic materials. Due to complexity of the problem for non-circular geometric configurations, complex variable method introduced by Muskhelishvili and conformal mapping functions were used to determine stress components within concrete lining and the surrounding rock mass. Finally, the solution was validated by ABAQUS finite element software through an example. Very good agreement was demonstrated between semi-analytical and numerical solution although some discrepancies were found at tunnel corners where large curvature existed. It was demonstrated that the solution predicted stress components more accurately around the tunnels, especially the corners with large stress concentration. Practical significance of the solution was placed in the fact that it could be used as a quick-solver with high accuracy.     

Stress concentration around a nano-scale spherical cavity in elastic media: effect of surface stress

Influence of surface effect on stress concentration around a spherical cavity in a linearly isotropic elastic medium is studied on the basis of continuum surface elasticity. Following Goodier's work, a close form solution of the elastic field created by biaxial uniform load is presented. The stress concentration factors under different load combinations are obtained. It is concluded that consideration of surface effect leads to dependence of stress concentration factors on cavity size. Besides, numerical result indicates that stress concentration factors around the cavity are mainly affected by residual surface tension. The result is significant in the understanding of relevant mechanical phenomena in solids with nano-sized cavities.     

基于Hoek-Brown准则的破裂围岩应力分析

深部煤矿巷道在高围压的作用下,围岩普遍出现破裂,而且围岩破裂范围在扩大的同时,往往出现继续破坏的现象,并形成不同的分区.论文针对长的圆形巷道,将围岩分成破裂、塑性和弹性三个区域,采用Hoek-Brown准则,进行非关联弹塑性分析,获得了其应力和变形的封闭解析解,并说明该解析解是不唯一的.通过利用在弹塑交界处应力连续的条件、以及在破裂和塑性交界处径向应变连续的条件,获得了确定围岩破裂区和塑性区半径的解析算式.最后,通过算例并分析了破裂区和塑性区应力和应变的分布特点、以及破裂区范围的影响.利用所获得的结果,可以为巷道的稳定性分析以及支护设计提供理论依据.     

Hoek–Brown criterion applied to circular tunnel using elastoplasticity and in situ axial stress

Based on the nonlinear Hoek–Brown failure criterion, elastoplastic analytical solutions are developed for the elastoplastic stresses, strains and plastic zones around a circular tunnel subjected to different value of the axial in situ stress. Effects of the transverse in situ stress, the axial in situ stress and the strength parameters of rock masses on the elastoplastic stresses, strains and plastic zones in the surrounding rock masses are investigated. It is found from the numerical results that the stresses, strains, and plastic zones in the surrounding rock depend not only on the transverse in situ stress but also on the axial in situ stress as well as the mechanical parameters of rock masses.     

基于统一强度理论的非静水压圆形隧道塑性区半径的脆塑性摄动解

基于统一强度理论和弹?脆?塑性模型, 综合考虑围岩强度的中间主应力效应和脆性软化, 采用摄动法建立了非静水压圆形隧道塑性区半径的解析解, 继而探讨所得解析解的适用范围, 并与文献复变函数法、摄动法、数值模拟和总荷载不变法进行对比, 最后分析各因素对隧道塑性区形状和大小的影响规律. 研究结果表明: 所建立的圆形隧道塑性区半径摄动解析解为反映中间主应力效应不同程度的系列解答, 可退化为理想弹塑性模型解答且得到文献中4种方法的正确性和合理性验证, 适用于塑性区完全包围隧道的情况, 对应的隧道塑性区为双轴对称的类椭圆, 具有广泛的理论意义和工程应用价值; 摄动参数对隧道类椭圆形塑性区的大小和长/短轴变化都有明显影响; 隧道塑性区范围随中间主应力效应、围岩峰后强度参数的增加均显著减小, 说明不考虑中间主应力效应的Mohr?Coulomb强度准则解答偏保守, 弹?脆?塑性模型相比理想弹塑性模型更适合隧道塑性分析.      

偏压隧道二次应力场分析及应用

详细分析了倾斜地表下岩体的应力状态,通过分解叠加的等效原则解出一般条件下围岩的二次应力解析解,并探讨该应力场的特性,结合黄土岭隘道工程,将解析值与实测数据进行对比分析,理论分析与实测结果符合良好。