A ground reaction curve based upon block theory

Summary Discontinuities in a rock mass can intersect an excavation surface to form discrete blocks (keyblocks) which can be unstable. Once a potentially unstable block is identified, initial normal and shear stresses on each block face are calculated using elastic theory, and are then modified by discontinuity deformations as the keyblock displaces. The modified stresses are summed into resultant forces to evaluate block stability. Since the resultant forces change with displacement, successive increments of block movement are examined to see whether the block ultimately becomes stable or fails. Calculated keyblock stability increases with larger in situ stress magnitudes, larger lateral stress ratios, and larger shear strengths. Discontinuity stiffness controls block displacement more strongly than it does stability itself. Large keyblocks are less stable than small ones, and stability increases as blocks become more slender.     

非规则砂岩节理剪切变形本构关系试验研究

岩石节理剪切变形对岩体工程的安全性和稳定性具有重要影响。为研究常法向应力下岩石节理剪切变形本构关系,采用RDS-200型岩石直剪仪对非规则砂岩节理进行了不同法向应力下的直剪试验。根据岩石节理剪切应力?位移全程曲线形状特征,将其依次划分为峰前压密阶段、线性阶段、屈服阶段和峰后软化阶段;根据剪切应力在峰后软化阶段降低幅度和速率大小,将岩石节理剪切应力?位移曲线划分为3种类型：峰后平台型、峰后缓降型和峰后跌落型。基于岩石节理剪切应力?位移曲线各阶段剪切变形特征,采用分段函数建立了岩石节理剪切变形本构模型。与其他模型相比,新提出的岩石节理剪切变形本构模型对试验数据拟合精度更高,更好地描述了岩石节理剪切应力?位移全程曲线。另外,在通过岩石节理直剪试验由经验公式确定模型参数之后,所提出本构模型可在不同法向应力下实现对不同粗糙度岩石节理剪切应力?位移曲线的预测。研究结果对岩石节理剪切变形的数值模拟和工程估计具有一定的实用价值。     

土石混合体的剪应力波动和跌落行为机制

土石混合体在剪切过程中存在剪应力跌落的现象,基于该现象,本文采用大型直剪试验的方式,考虑不同含石量(0%、30%、50%、70%)、上覆垂直压力(50,200,300,400 kPa)、块石尺寸(9.5～19.0 mm、19.0～31.5 mm、31.5～53.0 mm) 3个主要控制因素,进行室内剪切变形试验,研究直剪过程中发生的剪应力跌落现象。同时,通过在试样内部钻孔、埋置细铝丝与干灰的方法获取剪切带变形厚度,结合其大小理解剪应力的脆性跌落特征和剪切带块石变形特征。基于试验分析表明,具备骨架结构且所含块石尺寸大于剪切带厚度的土石混合体试样在高垂直应力下的剪切过程中易出现块石应力集中,形成锁固体块石,该类块石往往控制着试样一定时空下的整体剪切强度,其受剪切作用翻滚、滑移甚至咬合棱角破碎是导致剪应力瞬间大幅度跌落的直接原因。高含石量、大尺寸块石、高垂直应力是形成块石应力锁固体的必要条件。低含石量状态(<50%),剪切带块石多顺剪切方向翻滚,越靠近剪切面边缘,变形越明显,块石相对空间位置变化较小。高含石量状态(>70%),剪切带块石可见相互滑移、攀爬,块石相对空间位置变化明显。块石尺寸小于剪切带厚度时,剪应力多呈现波动特征,而块石尺寸接近剪切带厚度时,剪应力波动加剧,出现明显的应力跌落,对应垂直位移出现突变。满足含石量高于70%、块石尺寸大于剪切带厚度的试样在相对较大的上覆垂直应力作用下易形成块石应力锁固体。     

块系岩体滑移失稳中低摩擦效应的理论与试验研究

深部岩体具有块状层次结构,深部动载造成岩块发生相互间的振动脱离产生低摩擦效应,从而极易诱发原先处于平衡状态的岩体的动力变形破坏。在前人研究基础上,将块系岩体振动简化为等效质量-黏弹性模型,引入岩石摩擦滑移速率弱化模式,最终得到块系岩体滑移失稳计算模型。通过计算分析块系岩体自身特性及外荷载特性对岩块间低摩擦效应的影响。理论计算表明：水平静力及外扰动保持不变,增大岩块间弹性系数或者减小黏性系数,更容易引发岩体低摩擦滑移。随着冲击扰动、水平拉力幅值的增加,岩块的水平残余位移量值增加,当它们幅值超过一临界值时,岩块发生自持续滑移失稳运动。冲击扰动诱发岩块间不可逆位移、动力滑移失稳的临界能量与剪切力水平密切相关,在较大的剪切内力条件下,极其微弱的动力扰动即可诱发较大的岩块间不可逆位移甚至岩块的动力滑移失稳,随着剪切内力的减小,诱发岩块滑移失稳的能量阈值不断增大,当剪切内力低于岩块动摩擦强度时,单次冲击扰动只能诱发岩块间的不可逆位移。初步开展扰动诱发含初应力紫砂岩块体滑移试验,试验结果与理论计算基本符合,证明该模型的可行性。     

岩石节理在固定法向压力刚度条件下的剪切理论研究

节理在固定法向压力刚度（CNS）条件下的剪切过程比较复杂,剪切中由于剪胀的存在使得法向压力增大,而法向压力的增加又限制了剪胀的发生。根据CNS剪切过程中某一瞬时状态下法向压应力大小,以节理在该法向压应力下法向剪胀位移与剪切位移的关系为基础,建立一个楔形物理模型。通过循环迭代求得CNS剪切过程中每一步的法向压应力值,进而得到整个过程的剪切应力值。通过该模型,讨论了节理各参数对CNS剪切过程的影响,结果表明,其剪切应力值受法向压应力刚度与节理法向变形参数共同协调控制（包括单轴压缩变形及剪胀角的磨损）,节理在剪切过程中越不易发生压缩变形,其剪切应力值越大。     

Shear deformation and strength of the interphase between the soil–rock mixture and the benched bedrock slope surface

A series of benched excavations were typically carried out on the bedrock slope surface to improve the stability of the soil–rock mixture (S–RM) fill slope. It is difficult to devise an in situ, large-scale direct shear test for the interphase between the S–RM fill and the benched bedrock slope surface. This study introduced a comprehensive approach to investigate the shear deformation and strength of the interphase. First the soil–rock distribution characteristics were analyzed by test pitting, image analysis, and sieve test. Then the PFC2D random structure models with different rock block size distributions were built, and large-scale numerical shear tests for the interphase were performed after calibrating model parameters through laboratory tests. The stress evolution, damage evolution and failure, deformation localization (based on a principle proposed in this paper), rotation of rock blocks, and shear strength were systematically investigated. It was found that as the rock block proportion and rock block size (rock block proportion of 50 %) increase, the fluctuations of the post-peak shear stress–displacement curves of the interphase become more obvious, and the shear band/localized failure path network becomes wider. Generally, smaller rock blocks are of greater rotation angles in the shear band. The peak shear stress and internal friction angle of the interphase increase, while the cohesion decreases with growth of the rock block proportion. However, all these three parameters increase as the rock block size (rock block proportion of 50 %) increases.     

重庆武隆鸡尾山滑坡视向滑动机制分析

重庆武隆鸡尾山山体为典型的斜倾厚层灰岩山体,其破坏模式不同于常见侧向崩塌-堆积层滑坡,属于真倾向滑移变形转为视向整体滑动的特殊失稳模式。在现场地质调查的基础上,从地层岩性、岩体结构、岩溶及地下水作用、软弱夹层等影响因素分析重庆武隆鸡尾山滑坡形成原因;根据滑坡破坏机制,基于关键块体控制理论,对鸡尾山滑坡进行三维稳定性极限平衡分析;利用三维离散元软件模拟鸡尾山滑坡的初始变形破坏过程,分析了鸡尾山滑坡不同影响因素条件下的视向滑动形成机制和变形破坏特征,并探讨了节理化和溶蚀岩体的参数取值。结果分析认为,在重力的长期作用下,鸡尾山山体初始沿真倾向方向滑移,沿岩溶发育的陡倾节理裂隙逐渐产生后缘及侧向裂缝,形成块状后部驱动块体,由于地下水等因素使软弱夹层软化,驱动块体下滑力增大,前缘阻滑关键块体内部应力积累,并最终沿强度较低的岩溶发育带发生剪切破坏,从而导致整体滑动;在进行滑坡稳定性极限平衡分析时,考虑实际的滑坡机制,将滑体分为驱动块体和关键块体分别进行力的解析,并以关键块体的安全系数代表滑坡的安全系数更加合理。数值模拟显示,软弱夹层强度降低、岩溶发育带剪切破坏后,滑体进入大变形阶段,表明关键块体控制和阻滑作用明显,软弱夹层强度降低是滑坡发生的关键因素。采矿形成的采空区对山体的影响主要是使上覆岩体压应力增大,但对滑体的变形无影响。     

含二阶起伏体的模拟岩体节理试样剪切特性试验研究

利用规则的小尺寸锯齿构造二阶起伏体,对不同二阶起伏体高度的人工节理进行常法向应力下的直剪试验,研究了节理剪切力学特性。对节理的剪切强度、变形特征进行了分析,并对破坏特征做出解释。试验结果表明：二阶起伏体对节理剪切力学特性有重要影响,含二阶起伏体节理的剪切力学特性与只含有一阶起伏体节理的剪切力学特性不同,只含一阶起伏体的节理剪应力只有一个峰值,含二阶起伏体的节理会出现波浪状的剪胀曲线和多峰值剪应力,且峰值剪应力随剪切位移增大依次出现并逐个减小;随着二阶起伏体高度增大,节理峰值剪切强度增大,节理依次出现磨损破坏、多次性剪断破坏、一次性剪断破坏。     

Generalization of two-dimensional discontinuous deformation analysis for forward modelling

This paper provides the theoretical basis for a forward numerical model of rock block systems. This method was developed to compute stress, strain, sliding and opening of rock blocks; rigid body movement and deformation occur simultaneously. Input data consist of block geometry, loading forces, the deformability constants E and v, and the restraint or boundary conditions of the block system. Output data give the movements, deformations, stresses and strains of each block, and the sliding and detachment or rejoining of blocks. The forces acting on each block, from external loading or contact with other blocks, satisfy the equilibrium equations. Equilibrium is also achieved between external forces and the block stresses. Furthermore, this analysis fulfills constraints of no tension between blocks and no penetration of one block into another. To acheive equilibrium and satisfy these constraints, simultaneous equations are solved repeatdly with partial changes of the coefficients each time the contact constraints are chosen.     

松软煤层复合顶板条件下大跨度切眼支护技术研究

为了研究松软煤层复合顶板条件下大跨度切眼支护技术难题,采用数值模拟、理论分析、现场监测方法,分析了切眼巷道变形、位移、破坏特征,确定了围岩类别和支护参数,提出了左旋螺纹钢锚杆+金属网+金属梁+锚索的联合支护技术。研究表明:无支护条件下切眼巷道围岩出现"蝶形"破坏,顶板和两帮是支护的关键部位,支护后切眼巷道顶板和两帮位移大幅度减小,顶板应力释放区垂直应力明显减小,两帮应力集中区垂直应力增加,巷道顶、底角剪应力集中区范围减小。现场监测结果显示支护满足安全生产要求,为类似地质条件巷道支护提供借鉴。      

大型地下厂房块体稳定性简便分析方法

块体是结构控制型岩体中常见的潜在危险源之一。利用极限平衡法及强度折减法两种方法计算了某在建特大型水电站地下厂房开挖揭露的部分块体的安全系数,并根据计算结果提出一种利用块体几何及力学参数判断其稳定性的简便图解方法,经现场监测数据验证计算结果可靠性可满足工程要求。研究表明,对同一块体而言,极限平衡法和强度折减法得到的安全系数以及对其稳定性的总体判别结果并不一致。强度折减法受软件算法及网格尺寸影响,结果偏于保守。简单块体的安全系数计算应以极限平衡法为主,而复杂形态块体的安全系数用强度折减法计算较为方便。利用垂向地应力、块体体积、最大角点深度及结构面等效强度等4个指标并结合块体稳定性判别分区图,可满足快速判断块体稳定性的需要。对于判别为不稳定的块体,应及时支护并考虑加强支护。研究成果可用于类似工程块体稳定性的快速分析。     

三峡永久船闸高边坡开挖三维离散元数值模拟

采用面－面接触的三维离散元刚性块体模型，从实测节现面中取出其中的三组，按照其倾向，倾角和节理间距将三峡永久船闸未开挖的区域划分为10^5个离散单元，通过施加力边界条件，给出了与实测初始地应力场接近的数值模拟结果；然后，分4步模拟了永久船闸的开挖过程。计算结果表明：开挖过程会引起节理面出现张开趋势，个别岩体还会沿着节理面滑移。岩体位移的不对称现象较为自然地说明了由节理引起的岩体各向异性特征。     

The Dimensioning of Dowels for the Stabilization of Potentially Unstable Rock Blocks on the Walls of Underground Chambers

The analysis of dowels (non pre-stressed passive reinforcements) for the stabilization of potentially unstable rock blocks due to sliding is one of the most interesting problems concerning the static of underground rock chambers. The stabilizing force produced by dowels is not in fact known a priori and it depends on the dowel–rock interaction. The parameters that influence the problem are not only the geometrical ones of the dowel, but also the mechanical characteristics of the rock and the orientation of the displacement vector of the block. A detailed study of the dowel–rock interaction has been carried out in this work. This analysis is able to lead to the evaluation of the axial and shear forces in the dowel in correspondence to the crossed discontinuity of the block. The vectorial composition of these two forces constitutes the stabilization force of the dowel. An extensive parametric analysis then made it possible to determine the great variability of the stabilization force of the dowel in function of the influential parameters of the problem. The graphics that were obtained can be considered a useful design instrument as they quickly allow the dimensioning of the dowels to be done to reach the required safety factor for the rock block.     

The elastic distortion problem with large rotation in discontinuous deformation analysis

Conventional discontinuous deformation analysis (DDA) results in a change of block volume, which is known as free expansion, during rotation calculations because of the use of a linear displacement function to simulate the behavior of a block with a rigid body and elastic behaviors. This study demonstrates that the linear displacement function also generates unsolved elastic distortion, especially when the block undergoes large rotation in each calculation step. The distortion disturbs the contact judgment in the open–close iteration and update calculations of vertex coordinates, stresses, velocities, etc. at the end of each calculation step. A new procedure follows the flow chart of the original DDA, but it adopts additional codes for the coordinate-transformation calculations in vertex coordinate, stress, and velocity updates. When the vertex coordinates are updated, vertex displacements caused by strains are calculated before involving the block-rotation term in the displacement function to mitigate the elastic distortion. In addition, new codes compile formulas to transform stresses and velocities with block rotation. The new DDA ensures the correctness of rotating elastic calculations to solve practical falling rock problems with a large rotational angle in each calculation step.     

峰前循环剪切作用下岩石节理剪切力学特性

微震、工程爆破等低应力循环剪切荷载作用对节理岩体工程失稳破坏具有重要影响。为研究峰前循环剪切加卸载作用下岩石节理剪切力学特性,采用RDS-200型岩石节理剪切试验系统对人工劈裂黄砂岩节理进行了峰前循环剪切下的直剪试验。通过与未进行峰前循环剪切加卸载时岩石节理力学参数预测值对比,得到峰前循环剪切加卸载作用对峰前剪切刚度、峰值剪切强度、峰值剪切位移与残余剪切强度的影响。结果表明：（1）峰前循环剪切加卸载后,当法向应力为2 MPa时,岩石节理峰前剪切刚度增大,当法向应力为4～10 MPa时,岩石节理峰前剪切刚度在循环剪切应力幅值范围内增大,在超出循环剪切应力幅值时减小;（2）峰前循环剪切加卸载后,峰值剪切强度降低了10%～20%,降低百分比随法向应力增大整体呈对数函数增大;峰值剪切位移增加了2%～40%,增加百分比随法向应力增大整体呈对数函数减小;（3）峰前循环剪切加卸载后,岩石节理残余剪切强度无明显变化,峰值剪切强度与残余剪切强度差值减小,峰后剪切应力做功损失百分比降低。     

Simulation of roof shear failure in coal mine roadways using an innovative UDEC Trigon approach

Shear failure is a common failure mechanism in underground coal mine roadways. This paper presents an innovative numerical approach to simulate shear failure of a coal mine roadway roof. The distinct element code, UDEC, incorporating a proposed Trigon logic is employed for the study. Using this approach, shear failure in the mine roof characterized by fractured initiation and propagation is successfully captured. The results suggest that shear failure of the roadway roof initiates at the roadway corners and then progressively propagates deeper into the roof, finally forming a large scale roof failure. The numerical results confirmed the time sequence of marked microseismic activity, significant stress changes and accelerated displacement during the process of a roof fall. The effect of rock bolting in the control of roof shear failure in a roadway is evaluated using the UDEC Trigon approach. It is found that the installation of rock bolts constrains rock dilation, reduces failure of rock bridges and maintains rock strength thereby leading to a significant decrease in roof sag.     

基于小波分析的岩石节理剪切特性研究

岩体工程中,节理面的轮廓特征是决定节理岩体剪切特性的重要因素,既往研究发现节理的表面轮廓可分解为一阶大起伏和二阶小凸起,且两者在剪切特性中发挥不同的作用。为了定量分析两阶表面特征对节理剪切强度的影响,本文通过小波分析法分解节理表面,并利用二维颗粒流数值模拟结合直剪试验验证,研究了具有不同起伏角(4°、8°、12°、16°、20°)波形节理面的细观破坏模式以及波面参数对剪切特性的影响规律。结果表明,波长对剪切强度影响较小,而起伏角是决定节理剪切强度的关键因素,随着起伏角增大剪切强度和摩擦角线性增大; 直剪切过程中裂纹数量随法向应力的增大而增加,以拉伸裂纹为主; 一阶大起伏与二阶小凸起的波形起伏角和摩擦角正相关。以上研究成果为预测节理岩体强度提供了理论支撑,对保障边坡、隧道等岩体工程的安全稳定性具有参考价值。     

A development of the discontinuous deformation analysis for rock fall analysis

Discontinuous deformation analysis (DDA), a discrete numerical analysis method, is used to simulate the behaviour of falling rock by applying a linear displacement function in the computations. However, when a block rotates, this linear function causes a change in block size called the free expansion phenomenon. In addition, this free expansion results in contact identification problems when the rotating blocks are close to each other. To solve this problem of misjudgment and to obtain a more precise simulation of the falling rock, a new method called Post‐Contact Adjustment Method has been developed and applied to the program. The basic procedure of this new method can be divided into three stages: using the linear displacement function to generate the global matrix, introducing the non‐linear displacement function to the contact identification, and applying it to update the co‐ordinates of block vertices. This new method can be easily applied to the original DDA program, demonstrating better contact identification and size conservation results for falling rock problems than the original program. Copyright © 2005 John Wiley & Sons, Ltd.     

Effects of Cyclic Loading on the Shear Behaviour of Infilled Rock Joints Under Constant Normal Stiffness Conditions

The variation of the shear strength of infilled rock joints under cyclic loading and constant normal stiffness conditions is studied. To simulate the joints, triangular asperities inclined at angles of 9.5° and 18.5° to the shear movement were cast using high-strength gypsum plaster and infilled with clayey sand. These joints were sheared cyclically under constant normal stiffness conditions. It was found that, for a particular normal stiffness, the shear strength is a function of the initial normal stress, initial asperity angle, joint surface friction angle, infill thickness, infill friction angle, loading direction and number of loading cycles. Based on the experimental results, a mathematical model is proposed to evaluate the shear strength of infilled rock joints in cyclic loading conditions. The proposed model takes into consideration different initial asperity angles, initial normal stresses and ratios of infill thickness to asperity height.