Influence of inclination angles and confining pressures on mechanical behavior of rock materials containing a preexisting crack

To deeply understand the cracking mechanical behavior of brittle rock materials, numerical simulations of a rock specimen containing a single preexisting crack were carried out by the expanded distinct element method (EDEM). Based on the analysis of crack tips and a comparison between stress- and strain-based methods, the strain strength criterion was adopted in the numerical models to simulate the crack initiation and propagation processes under uniaxial and biaxial compression. The simulation results indicated that the crack inclination angle and confining pressure had a great influence on the tensile and shear properties, peak strength, and failure behaviors, which also showed a good agreement with the experimental results. If the specimen was under uniaxial compression, it was found that the initiation stress and peak strength first decreased and then increased with an increasing inclination angle α. Regardless of the size of α, tensile cracks initiated prior to shear cracks. If α was small (such as α ≤ 30°), the tensile cracks dominated the specimen failure, the wing cracks propagated towards the direction of uniaxial compression, and the propagation of shear cracks was inhibited by the high concentration of tensile stress. In contrast, if α was large (such as α ≥ 45°), mixed cracks dominated the specimen failure, and the external loading favored the further propagation of shear cracks. Analyzing the numerical results of the specimen with a 45° inclination angle under biaxial compression, it was revealed that lateral confinement had a significant influence on the initiation sequence and the mechanical properties of new cracks.     

基于DIC技术的3D打印节理试件破裂机制研究

为了准确表征不同角度预制节理岩石在单轴压缩下的变形破坏模式,基于3D打印技术制作了节理模型用于模拟岩体中的结构面,通过水泥砂浆的浇筑得到含不同角度预制节理的岩石试件并进行单轴压缩试验,同时采用数字图像相关技术（DIC）观测、分析试验过程中试件裂纹产生、扩展以及贯通过程。结果表明：随着预制节理从0°增加到90°,试件强度与峰值应变均呈现先降低后升高的变化趋势,0°和45°试件弹性模量相对于完整试件有所降低。基于DIC检测结果,0°、30°、45°及60°试件裂纹皆从预制节理尖端部位起裂,各角度试件的起裂应力与试件强度变化规律一致。各角度试样起裂时在剪应力控制下以剪切翼型裂纹形式起裂,0°与45°试件裂纹在扩展过程由剪切发展为张拉型裂纹,30°和60°试件以剪切裂纹形式贯穿始终,90°试件从底部起裂并最终表现为张拉破坏。研究还发现,下翼起裂角θ2和上翼起裂角θ1之间存在明显的线性正相关关系,关系式为θ2 =0.828 6θ1 +12.185,且起裂应力大小变化与峰值应力变化一致,皆随节理角度的增加先减小后增大。     

Numerical simulation on the cracking and failure law of compacted clay lining in landfill closure cover system

According to the mass conservation equation of solid phase, water transport, air migration and enthalpy balance equations in a deformable and unsaturated porous medium, and the mechanics model, a thermal‐hydro‐mechanical (THM) coupling mathematical model is developed in order to accurately predict the crack propagation of the compacted clay lining (CCL) in a landfill closure cover system. Numerical simulation analysis of the cracking and failure of the CCL in a landfill closure cover system under complex conditions (landfill gas pressure, variation of soil surface temperature, moisture loss of coverage soil, and uneven settlement of landfilled MSW (municipal solid waste)) is performed. The results show that the cracks are discovered firstly on the soil surface and then extend to the deeper cover system and became bigger. The cracks had broken through the closure cover system at 30 days. Over the depth range of 0.06 m, the change rate of settlement is found to be the highest because of the strong influence of temperature. The rise of temperature around the cracks is fast when the CCL is broken through by the cracks. There is a hollow area near the cracks over the depth range from 0.15 to 0.7 m, and the temperature stabilize at around 11°C without any obvious reduction. Under the condition of evaporation, the main crack in the CCL is similar to a pumping well, which causes more rapid moisture content reduction around the cracks. Vertical deformation increases linearly with depth in the process of deformation and cracking of CCL induced by uneven settlement of landfilled MSW. Copyright © 2014 John Wiley & Sons, Ltd.     

加锚岩石力学性质及破坏特征试验研究

采用煤矿煤层顶板岩石作为加锚基体,用钢丝模拟锚杆,对由二者组成的加锚岩石进行了巴西劈裂、单轴压缩和压剪试验研究。结果表明,当加锚试件岩石基体出现塑性屈服裂纹开始扩展后,锚杆逐渐取代岩石基体成为外荷载的承载主体,试件的破坏特征由脆性向延性转变。加锚试件劈裂过程中,圆盘中心出现裂缝后,部分试件仍具有一定的承载能力,其抗拉强度提高了51.1%;另有部份试件则表现为迅速破坏并丧失承载能力,其抗拉强度提高了91.6%。单轴压缩试验中,加锚试件的破坏形式可分为两类:一类为裂纹平行锚杆轴向发展;另一类为裂纹垂直锚杆轴向发展,加锚试件的抗压强度提高了34.6%。加锚试件剪切过程中,其承载能力出现了明显的二次劣化现象,回归试验结果可得加锚试件的内摩擦角基本不变,而凝聚力提高了22.9%。     

基于3D-DIC的砂岩裂纹扩展及损伤监测试验研究

裂纹监测对岩石损伤演化的认识至关重要。为研究岩石裂纹扩展及损伤变形特性,开展了含不同倾角（0°～90°）预制裂隙的标准细黄砂岩样的单轴压缩试验。利用三维数字图像相关技术（3D-DIC）获取岩样三维空间坐标下的应变分布,并结合声发射从光学与声学的角度监测了裂纹的扩展演化。由此提出了一种裂纹主应变的计算方法,定量表征岩石劣化的损伤变量D值。最后,探讨了由声发射与损伤变量D值确定岩样特征强度的影响因素。结论如下：（1）裂纹主应变反映了岩样受荷过程中同源裂纹在时间上的变化速率与空间上的扩展趋势,能较好地表征岩石的开裂行为;（2）声发射适用于确定岩样的起裂应力,不适用于损伤应力的确定,损伤变量D值所确定的起裂应力滞后于声发射,但适用于损伤应力特征值的确定;（3）结合声发射与DIC技术确定的归一化起裂应力范围为0.63～0.94、归一化损伤应力的范围为0.83～0.99;（4）预有裂隙会影响岩石的材料力学性能。随着倾角的增加,岩石的起裂应力、损伤应力及峰值应力呈增长的趋势,由于难以形成局部应变场聚集,裂纹的萌生与起裂更加困难。结果表明,3D-DIC技术的利用可以提高对岩石开裂行为的理解,对岩石的损伤监测与判识更有重要的意义。     

压缩荷载下泥岩裂缝演化规律的CT试验研究

裂缝的演化与空间展布规律是影响泥岩盖层密闭效果的关键因素。为研究泥岩失稳破坏过程中裂纹的萌生、扩展和汇集贯通等演化规律,针对龙马溪组泥岩进行了单轴压缩下的同步CT扫描试验,通过裂纹面积的变化特征及裂纹结构的分形特性,探讨了不同加载水平下裂纹的演化规律,从细观尺度揭示了泥岩裂纹演化与宏观变形特性的关系。研究结果表明：泥岩CT图像灰度频率及裂纹面积的变化均可反映裂纹的演化特征。荷载水平（即当前荷载与峰值荷载之比）为0～20%时,裂纹面积迅速增加,裂纹开始萌生,但由于受到闭合效应的抑制,相对并不活跃;荷载水平（当前荷载与峰值荷载之比）为20%～65%时,裂纹面积变化不大,裂纹萌生效应和闭合效应同时进行,且作用大致相抵,泥岩进入稳定承压阶段;荷载水平为65%～85%时,裂纹面积陡然增加,裂纹进入扩展及汇集贯通阶段,而荷载水平为65%时的突然跳跃,表明裂纹从萌生闭合到扩展过渡具有突发性和瞬时性。随着荷载的继续增加,泥岩内部结构呈复杂化、混乱化的变化趋势,且裂纹从外向内逐渐贯通。裂纹分形维数呈现的增长―下降―再增长―再下降的波状变化规律,是裂纹萌生、闭合、扩展和归并等相互转化的结果。     

Cracking Processes in Rock-Like Material Containing a Single Flaw Under Uniaxial Compression: A Numerical Study Based on Parallel Bonded-Particle Model Approach

Cracking processes have been extensively studied in brittle rock and rock-like materials. Due to the experimental limitations and the complexity of rock texture, details of the cracking processes could not always be observed and assessed comprehensively. To contribute to this field of research, a numerical approach based on the particle element model was used in present study. It would give us insights into what is happening to crack initiation, propagation and coalescence. Parallel bond model, a type of bonded-particle model, was used to numerically simulate the cracking process in rock-like material containing a single flaw under uniaxial vertical compression. The single flaw’s inclinations varied from 0° to 75° measured from the horizontal. As the uniaxial compression load was increased, multiple new microcracks initiated in the rock, which later propagated and eventually coalesced into longer macrocracks. The inclination of the pre-existing flaw was found to have a strong influence on the crack initiation and propagation patterns. The simulations replicated most of the phenomena observed in the physical experiments, such as the type, the initiation location and the initiate angle of the first cracks, as well as the development of hair-line cracks, which later evolved to macrocracks. Analyses of the parallel bond forces and displacement fields revealed some important mechanisms of the cracking processes. The first cracks typically initiated from the tensile stress concentration regions, in which the tensile stress was partially released after their initiation. The tensile stress concentration regions subsequently shifted outwards close to the propagating tips of the first cracks. The initiation and propagation of the first cracks would not significantly influence the compressive stress singularity at the flaw tips, which was the driving force of the initiation of secondary cracks. The initiation of microcracking zone consisting almost exclusively of micro-tensile cracks, and that of microcracking zone consisting of micro-tensile cracks and mixed micro-tensile and shear cracks, were found to be correlated with two distinct types of displacement fields, namely type I (DF_I) and type II (DF_II), respectively.     

单轴压缩条件下裂隙岩样冻融损伤破坏模式分析

以寒区裂隙岩体为研究对象,采用水泥砂浆类岩石材料制作具有不同几何特征的裂隙岩样,对预制的不同裂隙岩样进行冻融循环试验和单轴压缩试验,研究裂隙长度、裂隙倾角、裂隙数目以及冻融循环次数对试件贯通模式的影响。试验表明：裂隙岩体的几何特征以及冻融循环作用对岩体损伤破坏模式有较大影响。随着冻融循环次数的增加,岩样破裂面的破裂程度越来越严重,破坏模式也越来越复杂;裂隙倾角为30°的裂隙岩样,主要发生拉伸破坏,而裂隙倾角为60°的裂隙岩样,则表现为拉剪贯通,且双裂隙岩样岩桥间多出现压剪裂纹,对于裂隙倾角为90°的岩样,裂隙数目以及裂隙长度对其影响不大,均为劈裂破坏,且破坏面不一定为裂隙面;预制裂隙长度越大,越容易产生除了主拉裂纹以外的支裂纹（压裂纹）。研究结果可为寒区岩体工程建设及运营提供科学的参考。     

Influence of single flaw on the failure process and energy mechanics of rock-like material

This paper investigates the influence of a flaw on crack initiation, the failure mode, deformation field and energy mechanism of the rock-like material under uniaxial compression. The results of laboratory test and numerical simulation demonstrate the flaw inclination effect can be classified into three groups: 0–30°, 30–60° and 75–90°. The characteristic stresses increase as the flaw angle increases. The tensile cracks initiate from gentle flaws (α ⩽ 30°) and shear cracks appear at tips of steep flaws (α ⩾ 45°). The input energy, strain energy and dissipation energy of a specimen show approximate increasing trends as the flaw angle increases.     

双向压缩条件下闭合裂隙岩体断裂破坏机制及渗透压环境判定准则

在研究双向压缩条件下压剪复合型裂纹应力分布特征及断裂破坏机制基础上,考虑渗透压对初始裂隙面上有效正应力的影响,提出高低渗透压环境的判定准则,并基于滑动裂纹模型理论及最大周向拉应力破坏准则,得到不同渗透压环境下初始裂隙尖端微裂纹起裂特征与规律。研究结果表明：压剪复合应力条件下,初始裂隙尖端发育微裂纹的最优倾角与裂隙面摩擦系数直接相关,随裂隙面摩擦系数的增大,最优初始裂隙倾角由45°起逐渐增大;低渗透压条件下,渗流场的存在使裂纹面摩擦系数发生弱化,进而使得最优初始裂隙倾角向45°靠近,而渗透压直接降低裂隙面上有效正应力且与裂隙倾角无关,其仅仅影响裂隙体材料的初裂强度;高渗透压条件下,初始裂隙面由压剪复合应力状态转化为拉剪复合应力状态,并在拉剪复合应力场作用下,尖端微裂纹起裂角随KI/KII的不断增大,由70.5°逐渐趋近于0°。     

Experimental investigations on the elastic parameters and uniaxial compressive strength of slate under freeze–thaw cycles

ABSTRACT

In this study, uniaxial compression experiments with seven different bedding angles and six numbers of freeze–thaw cycles were conducted to investigate the influences of freeze–thaw cycles on the elastic parameters and the uniaxial compressive strength of slate. The laws of the elastic parameters, uniaxial compressive strength and failure characteristics were analysed, and a new uniaxial compressive strength prediction model that considers the bedding angle and the number of freeze–thaw cycles as control variables was established and verified using the experimental data. The results showed that the uniaxial compressive strength, elastic modulus and shear modulus decreased exponentially with an increasing number of freeze–thaw cycles. However, the Poisson’s ratio increased linearly with an increasing number of freeze–thaw cycles. The uniaxial compressive strength initially decreased and then increased with increasing bedding angle. There are three forms of failure occurred during the tests: when the bedding angle was 0°≤β ≤ 26.6°, the splitting failure and shear failure occurred at the same time; when the bedding angle was 26.6°≤β ≤ 83.0°, sliding failure occurred along the bedding plane; and when the bedding angle was 83.0°≤β ≤ 90°, splitting failure occurred along the axial direction of sample.     

泥页岩单轴抗压破裂特征及UCS影响因素

正确认识泥页岩单轴抗压破裂特征及UCS影响因素对探究泥页岩破裂机制、钻完井设计、压裂评价、微裂缝预测、测井解释及地震响应等方面均具有重要参考价值。本文在对国内外近些年有关泥页岩单轴抗压及UCS研究系统调研及近期研究成果全面分析基础上,对泥页岩破裂特征及UCS影响因素进行了综合分析。研究结果表明,泥页岩单轴加载曲线的非弹性段变形机制受微裂缝的滑动、新微裂缝的产生、扩展及孔隙坍塌的综合影响。泥页岩单轴抗压破裂呈张性或张剪性,张性破裂易发生于刚度较高、固结程度较强的部位;而剪性破裂易发生于刚度较低、固结程度较弱的部位。S型破裂准则可以较为准确的描述泥页岩从单轴到三轴发生破裂时所对应的强度变化。从地质学角度,对影响泥页岩UCS的因素进行了归纳,分别为矿物组成、层理面角度、分选性、微组构、有机质含量及分布、孔隙度、水分、微裂缝8方面因素,详细分析了不同影响因素的影响机制。在这些影响因素中,微裂缝由于分布特征复杂,其对泥页岩单轴抗压破裂及UCS的影响机制研究尚不深入。因此建议未来应加强泥页岩微裂缝参数的定量化研究,从微观尺度研究微裂缝对泥页岩单轴抗压破裂的具体影响机制,该研究可以为页岩油气勘探、开发提供科学指导。     

单轴压缩条件下含三叉裂隙类岩石试样力学特性的细观研究

三叉裂隙是自然界普遍存在的一种岩体缺陷形式,其对岩体的力学特性有重要影响。对含预制三叉裂隙的水泥砂浆试样进行室内单轴压缩试验,配合使用摄像机拍摄裂纹的起裂、扩展、贯通过程,通过数字图像技术处理获取试样的应变场云图,并结合PFC2D程序研究不同?、? 条件下试样的强度特征、裂纹模式和裂纹演化扩展规律。研究表明：三叉裂隙对试样单轴抗压强度有明显的削弱作用。当? 恒定为120°时,试样在? = 30°时达到最大抗压强度;当? 恒定为90°时,随?增大,试样抗压强度呈先减小后增大的趋势,且当? = 45°时达到最大抗压强度。试样产生的裂纹可分为3类,分别是张拉型裂纹(Ⅰ型裂纹)、剪切型裂纹(Ⅱ型裂纹)、混合型裂纹(Ⅲ型裂纹)。这3类裂纹通常从裂隙尖端开始产生,并且Ⅰ型裂纹沿加载方向扩展,通常未扩展至试样边界;Ⅱ型和Ⅲ型裂纹通常与加载方向呈一定角度扩展至试样边界。通过对裂纹的几何形态和组成宏观裂纹的微裂纹成分的分析,得知导致含三叉裂隙试样在单轴压缩条件下失效的是张拉破坏。数字图像技术得到的应变云图表明,当载荷达到一定阶段,裂隙尖端出现应力集中,微破裂开始发育并聚集成微破裂区,微破裂区扩大产生宏观裂纹。通过对主应变和剪应变云图分析,发现导致试样失效的是张拉破坏,剪应变在裂纹扩展过程中的影响较小。     

模拟岩石中裂纹扩展连接的近场动力学方法

脆性岩石材料在压应力作用下常出现两类裂纹：翼型张拉裂纹和次生剪切裂纹。近场动力学是一种新型的无网格数值计算方法。在近场动力学理论中,采用积分形式的控制方程代替微分形式的控制方程使得该数值算法在断裂问题上具有独特的优势。将Mohr-Coulomb准则和最大主应力准则引入非普通“态”基近场动力学理论中,分别用于模拟材料常见的压剪和张拉破坏。这种扩展的非普通“态”基近场动力学可以有效地模拟脆性岩石材料在多种受力状态下的裂纹起裂、扩展和连接问题。通过5个不同的数值算例说明该数值算法在处理脆性岩石材料断裂问题的有效性和准确性。首先,通过模拟含圆孔的弹性板拉伸数值试验说明该数值算法的有效性和准确性。其次,数值模拟了简单三点弯曲试验以及不使用其他外部准则条件下动荷载作用下裂纹的分叉试验,所得结果与其他试验结果或数值结果相吻合,从而验证了该理论的有效性。然后,模拟了包含斜裂纹的巴西圆盘试验,裂纹扩展路径和计算所得的断裂韧度同样吻合于试验结果。最后,模拟了单轴压缩状态下,预制裂纹试样的裂纹扩展和连接问题。将该数值算法与试验结果对比表明,所提出的数值方法可以模拟和预测岩石类材料的张拉和压剪裂纹的起裂、扩展和连接行为。     

基于高密度电阻率法的土体干缩裂隙动态发育过程精细监测研究

土体在气候作用下发育干缩裂隙是一种常见的自然现象,裂隙的存在会极大弱化土体的工程性质,诱发许多岩土与地质工程问题。为了实时掌握黏性土中干缩裂隙网络的发展状态,提出了一套基于高密度电阻率层析成像技术（ERT）的土体干缩裂隙动态发展过程精细监测方法。分别开展模型试验及原位试验,利用自行研制的测定系统持续采集电流-电位差数据,随后利用自行开发的有限元法电阻率层析成像（FemERT）系统进行数据处理,获取了裂隙网络在不同发育阶段的空间分布特征。结果表明：（1）ERT可以实现土体裂隙发育过程的精细监测,具备监测三维裂隙网络几何形态的能力,裂隙宽度的识别精度达到毫米级,裂隙深度的识别精度达到厘米级;（2）ERT的感度分布特征解释了裂隙发育对于土体电阻率的影响规律,测定电阻值时程曲线因裂隙产生位置的不同而呈现不同的变化规律;（3）反演电阻率及其相对变化率（Rev）可以直观表征裂隙网络在不同阶段的空间几何形态,凸显裂隙动态发育过程对于土体导电性的影响。     

多节理岩体裂纹扩展及变形破坏试验研究

为了研究不同倾角下多节理岩体力学行为,采用10 MN微机控制电液伺服大型多功能动静力三轴仪,开展包含较多预制非贯通节理类岩石试件的单轴压缩试验,研究了多节理岩体裂纹的特征、贯通模式、破坏模式、应力-应变特征等与节理倾角之间的关系。试验结果表明,（1）多节理岩体的裂纹类型主要有翼裂纹和次生共面裂纹,翼裂纹的扩展路径与单个节理情况下的扩展路径差异较大,翼裂纹起裂后沿起裂方向存在较长的扩展长度,直接与相邻节理或翼裂纹形成贯通,并且裂纹的贯通表现出四种不同的模式;（2）多节理岩体的破坏模式归纳为3种类型：平面破坏、块体转动式破坏和台阶式破坏;（3）根据多节理岩体的应力-应变曲线在应变软化阶段所表现出的不同非线性变形行为特征,可以将曲线归纳为4种类型;（4）多节理岩体的强度和变形各向异性特征非常显著,强度和弹性模量均在节理倾角30°时最小,90°时最大。     

含预制单裂隙花岗岩的真三轴单面临空岩爆试验研究

通过开展含预制单裂隙花岗岩的真三轴单面临空岩爆试验,并利用高速摄像系统和声发射（acoustic emission,简称AE）系统监测岩爆过程,探究了不同产状裂隙岩石的破坏模式、强度变形和声发射演化特性,分析了裂隙产状与岩爆过程及弹射动能之间的关系,对比了含裂隙岩石岩爆发生机制与无裂隙完整岩石的差异。有关力学特性的分析表明,随着裂隙倾角的减小,岩样破坏模式大体呈现由“内剪外劈”向“Z型斜剪”变化的趋势,裂隙对岩石强度的削弱作用不断增大。当裂隙倾角小于30°时,岩石峰值应力普遍仅为完整岩样的一半左右;小倾角裂隙的长度越大,岩样岩板劈裂现象变得显著,形成岩爆坑略微变大,且强度折减幅度越大,峰值轴向应变相应变小;裂隙位置向临空面靠近会加剧岩板的劈裂效应,塑性阶段普遍会产生较大变形并萌生大量裂纹,当裂隙已出露且切断临空面将不易形成岩爆坑。有关岩爆过程及弹射动能的分析表明,随着裂隙倾角的减小,岩样弹射动能呈现先显著降低后小幅回升的变化规律,30°倾角为转变拐点;岩样内部裂隙距临空面越近,裂隙岩样的弹射动能越小;树脂填充裂隙使得岩样弹射动能极大提升,而水泥填充的则无明显提升。有关声发射特征的分析表...     

曲线翼型裂纹扩展路径理论分析及试验验证

采用数值和试验的方法对翼型裂纹的扩展路径进行分析,发现单轴下张开型裂纹的翼型裂纹的扩展路径逼近于过原主裂纹中心点、平行于最大主应力的一条直线。基于翼型裂纹路径这个特点,采用了双曲线参数方程近似表达真实翼型裂纹的扩展路径,通过翼型裂纹的起裂角、起裂点及翼型裂纹的渐近线方程求解了双曲线方程中的未知参数。采用双曲线翼型裂纹路径和试验中所得翼型裂纹路径进行了对比分析,二者吻合得很好,验证了采用双曲线近似表示真实存在的翼型裂纹模型的正确性。应用双曲线翼型裂纹模型对翼型裂纹的扩展和失稳进行分析,采用ABAQUS求解了双曲线翼型裂纹模型的应力强度因子,并与试验进行对比,发现双曲线翼型裂纹模型能很好地解释翼型裂纹的实际扩展规律,这表明了采用双曲线近似表示真实翼型裂纹路径的有效性。     

爆破开挖对岩体含水裂纹扩展的扰动机制

岩体裂纹的水力劈裂是岩体开裂渗漏甚至施工涌水的重要影响因素之一,也是岩土工程界的研究热点。从断裂力学角度分析了爆破开挖对岩体含水裂纹扩展的扰动作用,结果表明,爆破开挖扰动下,岩体含水裂纹的扩展,与爆炸应力波强度及其入射角、地应力的大小与方向、孔隙水压大小、裂纹的倾角及断裂韧度等因素相关;爆炸应力波的作用,相当于增大了岩体裂纹中的孔隙水压力,每1 cm/s的峰值振动速度相当于增大100 kPa的孔隙水压力,爆破振动速度越大,所产生的爆破扰动荷载越大;岩体开挖引起的岩体裂纹近区地应力及其孔隙水压力的变化,对裂纹的失稳与扩展具有较复杂的影响,可改变裂纹的失稳扩展模式。     

裂隙黄土边坡三维稳定性极限分析

黄土边坡中竖直裂隙的发育往往会对边坡稳定产生影响。相对于平面应变机制,建立三维破坏机制下边坡稳定性分析方法更能接近实际边坡失稳情况。基于塑性极限分析上限法,考虑预先存在竖直裂隙的三维黄土边坡不同破坏机制（坡面破坏、坡脚破坏和坡底破坏）,建立能量平衡方程及其无量纲临界高度值γH/c表达式,采用随机搜索法得到了临界高度的上限解。分析了约束宽度、边坡坡度、内摩擦角以及裂隙深度对三维竖直裂隙黄土边坡临界高度值的影响。结果表明：对于坡脚破坏机制,临界高度值随着裂隙深度的增加而减小,减小至临界裂隙深度 (δ /H)_min后,裂隙深度的增加不再影响临界高度值;临界裂隙深度随着坡度β 的增大而增大,随着内摩擦角φ 的增大而减小。当约束宽度B/H<0.8时,大多数破坏机制为坡面破坏。当约束宽度B/H=0.8、内摩擦角φ =10° 及约束宽度B/H=0.6、内摩擦角φ =15° 时,边坡的破坏从坡面破坏机制逐渐过渡到坡脚破坏机制。存在竖直裂隙的黄土边坡比完整边坡具有更小的临界高度,约束宽度及内摩擦角会对三维黄土边坡破坏机制产生影响。