Static and Dynamic Flexural Strength Anisotropy of Barre Granite

Granite exhibits anisotropy due to pre-existing microcracks under tectonic loadings; and the mechanical property anisotropy such as flexural/tensile strength is vital to many rock engineering applications. In this paper, Barre Granite is studied to understand the flexural strength anisotropy under a wide range of loading rates using newly proposed semi-circular bend tests. Static tests are conducted with a MTS hydraulic servo-control testing machine and dynamic tests with a split Hopkinson pressure bar (SHPB) system. Six samples groups are fabricated with respect to the three principle directions of Barre granite. Pulse shaping technique is used in all dynamic SHPB tests to facilitate dynamic stress equilibrium. Finite element method is utilized to build up equations calculating the flexural tensile strength. For samples in the same orientation group, a loading rate dependence of the flexural tensile strength is observed. The measured flexural tensile strength is higher than the tensile strength measured using Brazilian disc method at given loading rate and this scenario has been rationalized using a non-local failure theory. The flexural tensile strength anisotropy features obvious dependence on the loading rates, the higher the loading rate, the less the anisotropy and this phenomenon may be explained considering the interaction of the preferentially oriented microcracks.     

Investigation of the anisotropy of black shale in dynamic tensile strength

Shale usually exhibits strong anisotropy due to depositional environment and pre-existed microcracks caused by geological loading for a long time. Characterizing mechanical anisotropy properties of shale, especially the tensile strength anisotropy, plays an important role in the successful exploitation of shale gas. In this work, static and dynamic tests with semi-circular bending (SCB) specimen are conducted using hydraulic servo-control machine and modified split Hopkinson pressure bar (SHPB) system, respectively. To survey the tensile strength anisotropy of shale induced by stratification, samples are cored and cut into half by diametrical cutting along different angles relative to the stratification (0°, 30°, 45°, 60°, 90°, C0°). For dynamic tests, the utilization of pulse shaping technique ensures that the samples obtain dynamic equilibrium. The tensile strength values exhibit clear anisotropy under both static and dynamic loading conditions and show typical loading rate dependence at a given angle. An anisotropic index named α_k is defined to describe the tensile strength anisotropy at a certain loading rate. The outcomes illustrate that the anisotropic index decreases as the loading rate increases. In addition, failure pattern owns different characteristic under different loading angles with respect to the stratification. These phenomena may be explained by the pre-existing microcracks, and cracks interaction during dynamic loading conditions.     

岩石在动载作用下的破坏与强度

研究岩石的动载性能,在凿岩爆破上有重要意义。分段式霍布金生杆已应用于研究岩石对波动载荷的效应。作者使用改型的霍布金生杆法对岩石试件在动载下的破坏强度作了试验研究。冲击试验台配合微处理机作高速数据显示与处理,借助应力波在弹性杆中的一维理论对数据进行解释。测定了多种岩石静载与动载的强度,并对岩石试件尺寸及加载速率的影响也作了试验。     

黄土高边坡的三维动力稳定性分析——以固原九龙山边坡为例

针对高烈度区九龙山黄土高边坡的动力稳定性问题,调查分析了该边坡的工程地质条件和场地所在区域构造活动与分布特征。在考察动荷载循环、往复作用下黄土反应敏感性及动强度参数,以及沿坡高确定地震惯性力反应地震作用大小的基础上,将强度参数折减与有限差分方法结合,从而形成了边坡的拟静力强度折减有限差分分析方法。通过九龙山土边坡拟静力强度折减三维有限差分法计算分析,得到了强度折减条件下边坡的位移场和应力场,边坡关键点位移与折减系数之间的关系,以及黄土高边坡的动力稳定性安全系数。其分析结果与传统的二维极限平衡分析方法确定的结果基本一致,验证了边坡拟静力强度折减有限差分方法的合理性。     

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。     

加载速率对岩石单轴压缩试验影响的数值模拟研究

在单轴压缩数值模拟试验中，加载速率由每次边界条件变化幅度和边界条件变化后的平衡计算时间这两个因素共同控 制。同样的加载速率，两个因素的不同组合也会对加载效果有很大的影响。因此，探究以上两因素对岩石单轴压缩数值模拟 试验的影响机制，可对高效进行高精度的各加载速率下的数值模拟试验起到积极作用。本文使用MatDEM软件，基于软件自 动设定的加载区间以及标准平衡迭代，设置不同的应力施加步数Nd与平衡迭代比率Rb，进行不同加载速率下的数值模拟试 验。模拟结果表明：（1）单步加载后平衡迭代次数越多（Rb越大），该步中应力波传播与动能衰减越充分。在最优阻尼条件下， 当单步加载后平衡迭代次数等于40次（Rb等于0.8）时，每步加载中动能充分平衡，可以最低计算量取得准静态模拟结果； （2）单步加载应力增量越小（Nd越大），数值模拟试验精度越高；（3）当加载速率一定即计算量相同时，为保证更高的模拟试验 精度，应采用低单步应力增量与低单步加载后平衡迭代次数（Nd大、Rb小）的加载方案。本文为定量研究岩石加载速率问题和 相关数值模拟提供了参考。     

加载速率对岩石单轴压缩试验影响的数值模拟研究

在单轴压缩数值模拟试验中,加载速率由每次边界条件变化幅度和边界条件变化后的平衡计算时间这两个因素共同控 制。同样的加载速率,两个因素的不同组合也会对加载效果有很大的影响。因此,探究以上两因素对岩石单轴压缩数值模拟 试验的影响机制,可对高效进行高精度的各加载速率下的数值模拟试验起到积极作用。本文使用MatDEM软件,基于软件自 动设定的加载区间以及标准平衡迭代,设置不同的应力施加步数Nd与平衡迭代比率Rb,进行不同加载速率下的数值模拟试 验。模拟结果表明：（1）单步加载后平衡迭代次数越多（Rb越大）,该步中应力波传播与动能衰减越充分。在最优阻尼条件下, 当单步加载后平衡迭代次数等于40次（Rb等于0.8）时,每步加载中动能充分平衡,可以最低计算量取得准静态模拟结果; （2）单步加载应力增量越小（Nd越大）,数值模拟试验精度越高;（3）当加载速率一定即计算量相同时,为保证更高的模拟试验 精度,应采用低单步应力增量与低单步加载后平衡迭代次数（Nd大、Rb小）的加载方案。本文为定量研究岩石加载速率问题和 相关数值模拟提供了参考。     

DEM investigation on fracture mechanism of the CCNSCB specimen under intermediate dynamic loading

The cracked chevron notched semi-circular bending (CCNSCB) method falls into a significant testing category of chevron notched specimens for measuring the mode I fracture toughness, of which the progressive fracture mechanism deserves to be further assessed under intermediate dynamic loading rate (IDLR). In this study, the discrete element method (DEM) is adopted to depict the three-dimensional fracture processes of the CCNSCB specimens subjected to different IDLRs considering different supporting spans. The results demonstrate that the crack front of the CCNSCB specimen with any loading condition is prominently curved, which violates the straight-through crack propagation assumption and may induce some errors in the fracture toughness measurements. For each IDLR, the peak force of the CCNSCB specimen evidently increases with decreased supporting span, and the effect of loading rate on this parameter is more prominent for a smaller supporting span. For a relatively large span, the crack grows restrictively in the notched ligament, which conforms to the ideal assumption of the fracture process and contributes to an accurate measurement of the mode I fracture toughness. Thus, a large supporting span is suggested for the semi-circular bend tests. Additionally, the critical crack length and peak force are found dependent on the loading rate, and they are larger for the higher loading rate. Thus, the critical crack length determined under quasi-static conditions is not strictly suitable for the specimens under different IDLRs, especially for the much higher IDLR. This study calls for more attention on how to accurately determine the fracture toughness via chevron notched samples.     

盾构施工与波浪荷载耦合作用后软土力学特性

针对波浪循环荷载作用和盾构穿越海堤过程中的施工扰动对下卧软黏土地基的弱化效应问题,研究了盾构施工与波浪荷载耦合作用后海洋软土的强度和刚度变化规律。通过逐步降围压的方式模拟盾构施工过程中的地层损失所引起的应力释放,循环加载3 000次模拟波浪荷载长期作用,开展了波浪和盾构施工耦合作用后的软土空心圆柱扭剪不排水剪切单元体试验。试验结果表明:(1) 在盾构施工与波浪荷载耦合作用下,软黏土的强度和刚度均随围压变大而增强,在同一围压下,二者均随波浪循环次数和土体损失率（δ）的增大而减小。(2) 在相同的波浪循环剪切次数下,软黏土初始切线模量随δ的增加而呈线性递减趋势,而软黏土黏聚力和内摩擦角随δ的增加而呈现非线性减小。波浪和盾构施工耦合作用后软黏土的强度和刚度均呈现不同程度的衰减,二者耦合扰动作用对软黏土的弱化效应在实际工程中应充分重视。此研究对探讨复杂扰动条件下海洋结构性软土力学特性规律,丰富和发展扰动状态下结构性软土的计算理论,以及对海岛基础设施建设具有重要的参考价值。     

An Example of Realistic Modelling of Rock Dynamics Problems: FEM/DEM Simulation of Dynamic Brazilian Test on Barre Granite

The scope of this study is to numerically simulate the behaviour of Brazilian disc specimens as observed in laboratory during dynamic, high-strain rate, indirect tensile tests using an innovative combined finite-discrete element method (FEM/DEM) research code. Laboratory experiments using a split Hopkinson pressure bar (SHPB) apparatus were conducted by the authors and the measured indirect tensile strength values were used to verify the FEM/DEM models. In the models the applied boundary conditions, related to the loading rate of the specimen, were matched with the experimental observations. The results of the numerical simulations, including tensile strength and failure time, are in agreement with the laboratory findings. The main failure mechanisms, i.e. tensile splitting along loading axis and shear failure close to loading platens are captured by the numerical model. A linear relationship between tensile strength and loading rate is found for the range of dynamic strain rates tested and simulated. The simulation results are in good agreement with laboratory observations and demonstrate the potential for using FEM/DEM to realistically model dynamic response of rocks.     

Dynamic Characterization of Orthogneiss Rock Subjected to Intermediate and High Strain Rates in Tension

The dynamic characterization of rocks under intermediate and high strain rates is fundamental to understand the material behavior in case of heavy earthquakes and dynamic events. The implementation of material constitutive laws is of capital importance for the numerical simulation of the dynamic processes as those caused by earthquakes. These data are necessary and require experimental techniques able to induce on the rock materials state of loading reproducing the actual dynamic condition. The dynamic characterization has been carried out by means of two special apparatus: the split Hopkinson tension bar and the hydro-pneumatic machine. These equipments are briefly described with a discussion on the results of dynamic tension tests at three different strain rates (0.1, 10, 100 strain/s) on Onsernone Orthogneiss for loading directions 0°, 45° and 90° with respect to the schistosity. Results of the tests show a significant strain rate sensitive behavior, exhibiting dynamic tensile strength increasing with strain rate, up to about two times with respect to the quasi-static conditions in the case of 0° and 45° orientation and more than three times in the case of 90° at high strain rates. Dynamic increase factors versus strain rate curves for tensile strength were also evaluated and discussed.     

循环荷载作用下单桩动力模型试验与桩−土界面特性研究

通过开展红黏土中单桩轴向循环振动模型试验,研究不同循环荷载比和加载频率对桩长期动力特性的影响,从桩侧土剪切刚度和侧阻退化两方面出发,对循环荷载作用下桩顶累积沉降机制进行分析。在FLAC3D中,实现能够反映剪切刚度疲劳退化的修正Hardin-Drnevich（H-D）模型,并对常法向刚度（CNS）循环剪切下侧阻退化进行数值模拟。试验发现,循环荷载幅值是桩顶累积沉降变化的重要影响因素;桩顶动刚度在加载初期要先经历一个迅速降低的短暂过渡阶段,之后则不随振次的增加而改变;桩身振动在桩周土中引起的超孔压较小,有效应力的降低不足于使侧阻力发生较大程度的退化;随着加载速度的增大,桩顶动刚度和加速度均随之增大。采用修正H-D模型得到的理论滞回曲线与数值结果基本吻合,验证了程序编制的正确性。     

基于颗粒离散元模型的不同加载速率下花岗岩数值试验研究

不同加载速率条件下岩石的力学特性,对于其动载下破裂内在机制的研究具有积极的意义。基于颗粒流理论,通过黏结颗粒模型（bonded particle model,简称BPM）虚拟实现不同加载速率0.001～0.500 m/s下花岗岩单轴压缩和巴西劈裂试验,定量分析加载速率对应力-应变、破裂形态、应变能率及声发射的影响。结果表明：单轴抗压强度和抗拉强度及其对应峰值应变随加载速率增加而非线性增长;单轴压缩作用下,随加载速率增加,试样由单一斜截面破坏向多斜截面破坏转变,且主控裂隙带宽度急剧增大,由裂纹数量及水平向高应变率区域变化规律可明显看出,试样破坏程度随着加载速率增加而逐渐加剧;巴西劈裂作用下试样从一条主控裂隙向多条主控裂隙转变,且裂纹向圆盘试样两侧边缘部分延伸,破坏程度加剧;单轴压缩和巴西劈裂作用下,声发射事件及应变能率均随加载速率增加而呈现出非线性增长趋势。     

地震作用下预应力锚索加固顺层岩坡极限分析

针对地震作用下预应力锚索加固顺层岩坡典型模型,提出了一种地震作用下预应力锚索加固顺层岩坡的极限分析改进方法,该方法考虑了边坡极限状态时锚索的受力变化。基于岩体刚性假设并考虑滑移过程锚索受力变化,结合极限平衡法推导出边坡加固预应力锚索的受力变化公式;地震作用仅考虑地震波传播至滑动面时产生的透射波对边坡稳定性的影响,从功率的角度出发,结合极限分析上限法与强度折减法,考虑预应力锚索受力变化,推导出地震作用下预应力锚索加固顺层岩坡的动安全系数计算理论公式;结合算例,采用考虑与不考虑滑移过程锚索受力变化两种计算方法,分析了在不同入射波波幅、入射角度及滑动面黏聚力、内摩擦角条件下两种方法计算结果的差异。算例结果表明：考虑与不考虑滑移过程锚索受力变化计算方法,计算得出的动安全系数变化规律一致,但考虑滑移过程锚索受力变化的改进计算方法得出的动安全系数动态变化幅度明显更小,反映了锚索的抗震作用效果,可为地震作用下该类型岩坡的预应力锚索加固设计分析提供参考。     

输电线路掏挖基础极限上拔承载力变分解法

针对输电线路掏挖基础极限上拔承载力问题,根据塑性极限平衡原理,假设基础周围土体发生整体剪切破坏并服从Mohr-Coulomb破坏准则,建立静力学平衡方程式,并结合变分法原理求解不同加载条件下基础的极限抗拔力。通过变参数计算,分析土体强度及基础埋深比对中心上拔、偏心上拔及倾斜上拔时基础极限上拔力的影响。经归一化处理,分别给出水平力和弯矩存在对基础抗拔力折减的影响系数。当归一化弯矩与上拔力比值Nm 0.4时,? m减小速度放缓。相对于内摩擦角,黏聚力变化对? m的影响更明显。水平力影响系数? h同时受到土体内摩擦角、黏聚力以及基础埋深比的共同影响,规范建议值较变分解法的计算结果偏大。通过与规范公式法计算结果及试验结果进行对比,验证了所提方法的合理性和准确性。研究结果为偏心上拔及高露头基础顶部作用水平荷载时基础抗拔承载力的计算提供参考。     

Some Fundamental Issues in Dynamic Compression and Tension Tests of Rocks Using Split Hopkinson Pressure Bar

Accurate characterizations of rock strengths under higher loading rates are crucial in many rock engineering applications. The split Hopkinson pressure bar (SHPB) system has been used to quantify the dynamic compressive strength of rocks using the short cylindrical specimen and the dynamic tensile strength of rocks using the Brazilian disc (BD) specimen. However, SHPB is a standard tool that is suitable for metal testing; there are some fundamental issues that need to be carefully visited in applying SHPB to rock dynamic tests. This paper addresses several such critical issues, including the choice of slenderness ratio of the compressive specimen, the effect of friction between the sample and bars on the measured results of compressive strength, the necessity of dynamic force balance on the dynamic BD test, and the validity of using the standard BD equation in the data reduction. We show that with proper experimental designs that address these issues, the dynamic compressive strength and dynamic tensile strength of rocks measured using SHPB are valid and reliable.     

Numerical simulation on excavation-induced damage of rock under quasi-static unloading and dynamic disturbance

During the excavation of underground opening, the rock may experience a complex loading path that includes the highly confined compression before excavation, unloading of confining stress and further disturbance of dynamic loading after excavation. By using Rock Failure Process Analysis for Dynamics (RFPA-Dynamics), the failure of rock sequentially subjected to this complex loading path is numerically simulated, in order to examine the rock failure mechanism induced by excavation. The RFPA-Dynamics is firstly used to reproduce the failure of rock under confined compression, followed by unloading of confining pressure, and it is validated against with the existing experimental observation. Then, the failure characteristics of rock specimen sequentially subjected to the quasi-static triaxial loading, unloading of confining pressure and dynamic disturbance are numerically simulated, where the effect of magnitude of axial loading and confining pressure, and duration and amplitude of the dynamic disturbance on the final failure patterns of rock are examined. The numerical results indicate that the arc-shaped spalling damage zone is prone to develop with the increase in the axial pressure and lateral pressure coefficient. As for the effect of dynamic disturbance, the contribution of duration and amplitude of dynamic disturbance on the energy input are similar, where the area of damage zone increases with the energy input into the rock specimen. In this regard, the area of the damage zone is influenced by both the magnitude of in situ stress and waveform of dynamic disturbance. This study denotes that it is of great significance to trace the complex loading path induced by excavation in order to capture the rock failure mechanism induced by underground excavation.     

Fracturing and Failure Behavior of Carrara Marble in Quasistatic and Dynamic Brazilian Disc Tests

The tensile strength and fracturing behavior of Carrara marble subjected to the dynamic Brazilian disc test using the split Hopkinson pressure bar technique are determined and compared with those obtained by the conventional quasistatic Brazilian disc test. Detailed observation of the cracking processes is aided by high-speed video footage captured at a frame rate of 100,000 frames per second. The dynamic increase factor is computed, revealing a strong strain rate dependence of the Carrara marble when subjected to strain rates above 1 s^?1. Similar to the quasistatic loading tests, conspicuous white zones/patches commonly appear prior to the initiation of visible cracks in the dynamic loading tests. Identification of the white patch initiation and evolution is aided by image comparison software. Comparing the cracking and failure processes under quasistatic and dynamic loading, some distinct differences in the white patch geometry and initiation load are observed. In addition, the extent of the compressive failure zones around the contact points between the loading platens and specimens is found to increase with the strain rate.     

循环荷载下软黏土不排水强度弱化分析的动力有限元ABAQUS实现

在波浪循环荷载作用下饱和软黏土地基出现孔隙水压力升高,并导致不排水强度弱化,严重影响防波堤的承载性能。考虑静偏应力影响,基于最大孔隙水压力发展模型和正常固结软黏土不排水强度公式,推导出软黏土不排水强度随循环荷载作用次数和应力水平变化的动态折减规律。结合软黏土不排水强度动态折减规律和M-C屈服准则,在有限元软件ABAQUS上实现软黏土不排水强度循环弱化分析的数值开发和动力运算过程。运用该动力有限元方法对天津港防波堤地基软黏土的动、静三轴试验进行数值模拟运算。结果表明,最大孔隙水压力发展曲线以及循环荷载作用后不排水强度的数值预测结果与动三轴试验结果吻合良好。另外,动力有限元方法（DFEM）能够表示土体强度在循环荷载作用下的具体弱化过程。