Effects of loading rate on rock fracture: fracture characteristics and energy partitioning

By means of the Scanning Electron Microscope (SEM), an examination was performed of the fracture surfaces (including their vertical sections) of both Fangshan gabbro and Fangshan marble specimens fractured at the loading rates MPa m^1/2 s⁻¹. The results showed that one or more branching cracks near the fracture surfaces of dynamic rock specimens were clear and the cracks increased with increasing loading rates. However, such branching cracks were rarely seen near the static fracture surfaces. In addition, with the aid of the Split Hopkinson Pressure Bar (SHPB) testing system and a high-speed framing camera, the energy partitioning in the dynamic fracture process of a short rod (SR) rock specimen was analysed quantitatively. The total energy W_L absorbed by an SR specimen in the dynamic fracture process mainly consisted of the fracture and damage energy W_FD and the kinetic energy W_K of flying fragments. The energies W_L and W_K could be quantitatively calculated through stress wave measurement and high-speed photography in the SHPB testing system. Thus, the fracture and damage energy W_FD could be obtained. The results showed that: (1) the energy W_K increased with an increase in the impact speed of the striker bar or the loading rate; (2) the energy W_FD for dynamic rock fracture was markedly greater than that for static rock fracture, and the W_FD increased with an increase in the impact speed of the striker bar or the loading rate; and (3) the value W_L/W_B (W_B is the energy input into the loading system) in the case of dynamic fracture is much lower than that in the case of static fracture. In addition, the ratio decreases with an increase in the loading rate or the impact speed of the striker bar. This means that the energy utilisation decreases when the loading rate or the impact speed of the striker bar rises. Finally, some application problems are discussed in the paper.     

加载速率对岩石动态断裂韧度影响的实验研究

为了获得岩石在高加载速率作用下的动态断裂韧度值并分析加载速率的影响,由分离式霍普金森压杆入射杆杆端附加劈尖及其基座对边切槽圆盘试样施加动态劈裂载荷。把应变片粘贴在裂纹尖端附近获得裂纹扩展时间;将劈裂载荷时间历程及裂纹扩展时间输入有限元计算模型,获得试样的起裂动态断裂韧度值。结果表明,在加载速率18.85×104MPa.m1/2s-1以下,大理岩的动态断裂韧度值随着加载速率的增大而上升,但上升趋势逐渐减弱。断裂韧度数值在高加载速率下呈现出明显的离散性。     

压缩条件下岩石断裂模式与断裂判据的研究

针对岩石类材料压缩断裂中可能发生的Ⅰ型张拉断裂和Ⅱ型剪切断裂的现象 ,依据裂纹尖端应力集中引发的微裂纹损伤性质 ,提出了主裂纹尖端“微裂纹单元应力模型”的概念。通过对不同方位微裂纹尖端Ⅰ、Ⅱ型应力强度因子变化规律的研究 ,以比应力强度因子和比断裂韧度作为表征参数函数方程 ,提出了压缩条件下岩石类材料复合型裂纹断裂模式与断裂破坏的判据。该判据既可以预测岩石内部斜裂纹在压应力下的Ⅰ型扩展 ,也可以预测它的Ⅱ型扩展。由此判据 ,还给出了Ⅱ型断裂出现的条件 ,讨论了不同的影响因素。其结果较好地说明了实验现象     

Effects of high temperatures on dynamic rock fracture

The dynamic fracture toughness of Fangshan gabbro and Fangshan marble subjected to high temperature was measured by means of the split Hopkinson pressure bar (SHPB) system. The specimens for measuring the fracture toughness were manufactured according to the requirements for the Short Rod (SR) specimen suggested by ISRM. Two cases were investigated: (1) the SR specimens of the gabbro and marble were fractured at high temperature (100–330°C), and (2) the specimens of the rocks were first pre-heat-treated at 200°C for the marble and 600°C for the gabbro, and then fractured at room temperature. The experimental results showed that under dynamic loading the fracture toughness of both the gabbro and the marble tested in the above-mentioned cases increased with increasing loading rates. The relationship between the fracture toughness and the loading rates in the two cases is similar to that obtained in the room temperature environment, i.e., without high temperature. (This is defined as the third case.) It can be concluded that temperature variation affects the dynamic fracture toughness of the two rocks to a limited extent within the temperature ranges tested. This is different from the results obtained under the static loading condition. Furthermore, by means of the scanning electronic microscope (SEM), the vertical sections of the fracture surfaces for some gabbro specimens were examined. In addition, the fractal dimensions of the fracture surfaces of some specimens were measured by means of fractal geometry. The results showed that under dynamic loading: (1) macro-crack branching near the fracture surfaces was universal; (2) the fractal dimensions increased with increasing loading rates; (3) in the sections of the specimens tested at high temperature there were many micro-cracks that were probably induced by thermal cracking. On the basis of the above macro- and micro-experimental investigation, an energy analysis of the process of dynamic rock fracture was performed. The results showed that the energy utilisation in dynamic fracture was much lower than that in static fracture.     

Effects of substrate loading rate on biofilm structure

The effects of substrate surface loading rate on biofilm growth and structure were investigated by chemical, biochemical and microscopic methods. Three tubular reactors were operated at equal C:N ratio of 0.1, with substrate loading rates of 1.2, 0.6 and 0.3g-C/m(2)/day. Substrate loading positively influenced the biofilm growth rate. Denser biofilms with lower porosities were formed at higher substrate loading. Slowly growing biofilms having porous structures were found to have higher specific activities. Nitrification was suppressed under the higher substrate loading conditions even at the equal C:N ratio of 0.1, thus proving that the spatial competition between nitrifiers and heterotrophs as one limiting criteria for stable nitrification. The spatial organization of the ammonia oxidizers was biofilm structure related. The strain variability of ammonia oxidizers was substrate loading dependent. These findings suggest that substrate loading is a key parameter in determining biofilm structure and function.     

单轴受载下岩体破裂演化特征的声发射CT成像

 岩石受载下的内部破裂演化特征对于研究岩石破坏机制具有重要意义。将声发射(AE)与CT成像技术相结合,对3种不同加载速率下的泥岩试样进行声发射CT反演计算,分析各加载阶段波速分布特征,探究波速演化与岩样宏、微观破裂的关系。研究结果表明：(1) 在加载初期,岩样内部波速范围变化较小,波速异常区面积较小且分布较为零散;随着载荷增加,波速范围不断增加,同时波速异常区面积也在不断扩大;临近破坏阶段,波速范围进一步增加,其低波速区也逐渐形成大面积贯通。(2) 岩样实际宏观破裂位置与低波速区及波速异常丰富区位置吻合,说明临近破坏阶段,岩样内部微裂隙的大量萌生发育使低波速区快速扩展贯通,同时微裂隙周围的岩石颗粒因受挤压而呈现出高波速状态。(3) 受载初期,岩样内初始微裂隙发育萌生位置与低波速区大致吻合;随载荷增加,大量微裂隙开始在低波速区与波速异常丰富区聚集、延伸;在临近破坏阶段,微破裂密集区扩展贯通,其所处区域与岩样破裂位置大体一致。(4) 反演计算调整前后的AE事件整体分布特征保持一致,证明了初始AE事件定位的准确性及声发射CT成像的可靠性。     

Effects of water saturation and loading rate on direct shear tests of andesite

For estimating the long-term stability of underground framework, it is vital to learn the mechanical and rheological characteristics of rock in multiple water saturation conditions. However, the majority of previous studies explored the rheological properties of rock in air-dried and water saturated conditions, as well as the water effects on compressive and tensile strengths. In this study, andesite was subjected to direct shear tests under five water saturation conditions, which were controlled by varying the wetting and drying time. The tests were conducted at alternating displacement rates under three vertical stresses. The results reveal that the shear strength decreases exponentially as water saturation increases, and that the increase in shear strength with a tenfold increase in displacement rate is nearly constant for each of the vertical stresses. Based on the findings of the shear tests in this study and the compression and tension tests in previous studies, the influences of both water saturation and loading rate on the Hoek-Brown failure criterion for the andesite was examined. These results indicate that the brittleness index of the andesite, which is defined as the ratio of uniaxial compressive strength to tensile strength, is independent of both water saturation and loading rate and that the influences of the water saturation dependence and the loading rate dependence of the failure criterion can be converted between each other.     

A new testing method for investigating the loading rate dependency of peak and residual rock strength

One of the important methods for investigating viscoelasticity is to measure the loading-rate dependency of peak strength; however, no experimental method has been established for accurately measuring the loading-rate dependency of peak strength from a small number of samples. In this study we propose such a method. A single sample is loaded at alternating strain rates to obtain stress–strain curves for both strain rates. The loading-rate dependency of peak strength obtained via this method was compared with the findings of conventional methods. The loading-rate dependency indicated for Tage tuff, Sanjome andesite and Akiyoshi marble was nearly identical to previous results obtained using conventional methods, including results obtained under confining pressure. The loading-rate dependency of peak strength in these experiments shows a close relation with the creep stress-dependency of creep life. We also investigated the loading-rate dependency of the stress–strain curve for the post-failure region for which few results have been published. Under confining pressure, the corrected stress–strain curve, obtained by multiplying the stress of the complete stress–strain curve obtained at the fast strain rate by a constant determined by the ratio between the fast strain rate and slow strain rate, is nearly coincident with the stress–strain curve for the slow strain rate. This is an interesting result and represents new knowledge that may help elucidate failure mechanisms in the post-failure region. The loading-rate dependency of stress in the alternating strain rate experiment proposed here was most clearly observed when the stress–strain curve becomes flat, parallel to the strain axis. Some improvements to the proposed method are required to enable accurate investigations of loading-rate dependency during low stresses immediately after initiation of loading or during the abrupt decreases in stress that occur following peak strength.     

疲劳载荷对岩石物理力学性质的影响

在MTS上进行了疲劳加载实验 ,取得了南京砂岩的模量、泊松比、波速都随频率的增高呈非线性增大 ,强度具有明显的各向异性。饱和大理岩具有显著的应力振幅效应和频率效应以及各向异性。应力振幅对大理岩物性的影响大于频率对大理岩物性的影响     

气液复合加载的岩爆模型试验研究

 针对现有岩爆模型试验设备及方法存在的不足,采用自主研发的气液复合型岩爆模型试验装置,进行不同应力梯度下的大尺寸岩爆模型试验。通过对试件宏观破坏现象、内部变形规律及声发射特征参数的分析,研究岩爆发生、发展过程及破坏机制。结果表明：岩爆的发生与荷载梯度、能量的集聚程度和破坏时能量的释放速率密切相关,模型荷载梯度差值不一导致局部应力集中程度不同,影响试件破坏前期能量的耗散与集聚及岩爆时刻能量的释放速率,竖向破坏荷载梯度差值越大,局部应力集中程度越高,能量释放速率越快,转化为动能的能量越多,岩爆现象越易发生。模型试件破坏时,顶部竖向最大荷载值 处于与单轴抗压强度 比值为0.5～0.7范围,梯度荷载条件下,动静组合加载是试件破坏荷载降低的主要原因,其试验方法符合工程岩体的实际受荷。     

Multifractal characterization of rock fracture surfaces

The multifractal behavior of rock fracture surfaces is studied taking into account fractal heterogeneity and anisotropy of surface structures. A projective covering method (PCM) is proposed and used to estimate directly the fractal dimension D_s[2, 3) of a fracture surface. The study indicates that the multifractal spectrum of the fracture surfaces provide much additional information on the fracture mechanism and the distribution of asperity concentration on the surface. The fracture surfaces induced in rocks under different failure mechanisms display distinct multifractal behavior.     

岩体裂隙面粗糙度对其渗流特性的影响研究

为了研究岩体裂隙面的粗糙程度与渗流机制间的相互关系,将裂隙沿长度方向均匀分割成若干段,通过设置每一段末端的随机高度,生成两侧对称的粗糙裂隙面。基于格子Boltzmann方法,采用不可压缩流体的D2G9模型,验证了经典的Poiseuille流,计算了不同相对粗糙度岩体裂隙的渗流特性,讨论了裂隙面粗糙度对渗流流态的影响。研究结果表明:裂隙结构壁面对流体的阻碍作用,使得流体在壁面附近的流动产生急剧调整,同时随着裂隙相对粗糙度的增加,在裂隙隙宽急剧变化的部位,局部伴随着旋涡的形成,导致流体内部摩擦阻力作用增大。在单位时间截面渗流流量及每一段平均隙宽相等的条件下,将本数值解与多平行板理论解进行了对比,对于相对粗糙度δ=0.01674的裂隙方案,由于多平行板理论解忽略了粗糙裂隙隙宽变化而引起的局部压降,其裂隙中线处压降产生的最大误差达到15.2%。当相对粗糙度较小时,裂隙中线处的压力与光滑平板流相类似,近似呈线性变化。随着裂隙相对粗糙度增大,压力变化偏离直线方向,且在断面由窄突然变宽的部位,压力变化偏离线性尤为显著。     

岩石中断裂力学的研究

在断裂力学的基础上,研究了岩石破坏类型和受压裂缝的扩展,并对微裂缝演化进行了探讨,提出利用断裂力学中的裂纹尖端应力和应变场的分布情况,可以预测和制止岩体的失稳。基于能量平衡建立岩石裂纹的扩展条件,进而导出断裂稳定性准则。指出岩石断裂力学中存在的一些问题,并对研究要点进行了总结,为岩石断裂问题研究提供了理论依据。     

Effects of shear stress and substrate loading rate on Pseudomonas aeruginosa biofilm thickness and density

Thickness, roughness, and density data were obtained from monopopulation Pseudomonas aeruginosa biofilms grown in an annular reactor under different substrate loading rates and shear stresses. Biofilm thickness showed significant increases, up to approx. 30 μm, with increasing substrate loading rate. Shear stress had no significant effect on thickness. Biofilm roughness, as measured by the standard deviation of the thickness, increased with increasing thickness. Areal mass density significantly increased with substrate loading rate and was not significantly affected by shear stress. Substrate loading and shear stress did not significantly affect volumetric mass density. A numerical expression that describes changes volumetric density as a function of biofilm depth is presented.     

Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses

fracture systems have strong influence on the overall mechanical behavior of fractured rock masses due to their relatively lower stiffness and shear strength than those of the rock matrix.Understanding the effects of fracture geometrical distribution,such as length,spacing,persistence and orientation,is important for quantifying the mechanical behavior of fractured rock masses.The relation between fracture geometry and the mechanical characteristics of the fractured rock mass is complicated due to the fact that the fracture geometry and mechanical behaviors of fractured rock mass are strongly dependent on the length scale.In this paper,a comprehensive study was conducted to determine the effects of fracture distribution on the equivalent continuum elastic compliance of fractured rock masses over a wide range of fracture lengths.To account for the stochastic nature of fracture distributions,three different simulation techniques involving Oda's elastic compliance tensor,Monte Carlo simulation(MCS),and suitable probability density functions(PDFs) were employed to represent the elastic compliance of fractured rock masses.To yield geologically realistic results,parameters for defining fracture distributions were obtained from different geological fields.The influence of the key fracture parameters and their relations to the overall elastic behavior of the fractured rock mass were studied and discussed.A detailed study was also carried out to investigate the validity of the use of a representative element volume(REV) in the equivalent continuum representation of fractured rock masses.A criterion was also proposed to determine the appropriate REV given the fracture distribution of the rock mass.     

岩扇贝幼贝滤食率的基础研究

为了解岩扇贝Crassadoma gigantea幼贝的摄食率,采用静水法研究了在不同温度(6、10、14、18、22℃)、体质量(小、中、大3种规格)、饵料(新月菱形藻Nitzschia closterium、湛江等边金藻Isochrysis zhanjiangensis、亚心形扁藻Platymonas subcordiformis、小球藻Chlorella vulgaris)和饵料浓度(15×10~4、30×10~4、45×10~4、60×10~4、75×10~4 cells/mL)条件下岩扇贝的滤食率及其昼夜节律。结果表明:温度、体质量、饵料种类和饵料浓度对岩扇贝幼贝滤食率有显著或极显著影响(P<0.05或P<0.01);在试验温度和体质量范围内,幼贝单位体质量的滤食率均随温度和体质量的增加而增大;幼贝对4种单胞藻的滤食率依次为新月菱形藻>湛江等边金藻>亚心形扁藻>小球藻,且对4种单胞藻的滤食率有显著性或极显著性差异(P<0.05或P<0.01);当新月菱形藻浓度为30×10~4 cells/mL时,幼贝的滤食率达到最大,极显著高于其他饵料浓度组(P<0.01);幼贝的滤食率存在显著的昼夜变化(P<0.05),一天中存在一个滤食高峰时段,即17:00~21:00[40.161×10~8 cells/(g.h)],且显著高于其他时段(P<0.05),存在两个低峰时段,即9:00~13:00[32.496×10~8 cells/(g.h)]和1:00~5:00[29.934×10~8 cells/(g·h)],均显著低于其他时段(P<0.05)。研究表明,岩扇贝的适温范围及对饵料的适应性较广,可作为中国重要扇贝引进品种加以培养。     

强冲击荷载下岩石材料断裂及破碎机制研究

脆性材料如岩石、混凝土和陶瓷等在冲击荷载作用下的动态力学特征及破碎机制研究涉及力学,物理学,航空航天,能源开采和防护工程等多个领域。具体问题如同震作用中的断层泥形成及非对称粉碎化,行星撞击产生的陨石坑,飞行器对空间站的超高速撞击与防护,采矿过程中的矿石破碎尺寸控制,工程爆破过程中的破岩效率提高和灾害防治,炮弹壳体的破碎以及超高速弹穿甲等。岩石材料的静态,动态及动静组合下的力学响应研究已经取得了丰硕成果,相比之下,岩石材料在冲击荷载下的细观断裂机制和破碎特征方面研究还颇为不足。脆性材料在宽应变率尺度上是否存在统一的归一化强度形式?材料的动态力学特性与过渡性破碎现象的内在联系是什么?如何理解缺陷材料在冲击过程中的裂纹成核、发展及交汇对破碎成形的影响?这些问题已经严重地阻碍了我们对脆性材料在极限荷载作用下的认识。针对上述问题,在国家自然科学基金重点项目和国家建设高水平大学公派研究生项目的资助下,(1)研究材料在冲击荷载作用下的力学特征;(2)了解脆性材料的冲击破碎机制两个方面工作为基础,采用室内试验,理论模型和数值模拟开展了强冲击荷载下岩石材料的强度,断裂和破碎特性方面的研究。在力学试验方面,采用霍普金森压杆装置研究了花岗岩石在冲击劈裂下的试验条件和力学特征,提出了动抗拉强度因子在高应变率范围存在Ⅰ,Ⅱ和Ⅲ个区域,结合高速摄像系统和DIC方法验证了圆盘中心起裂条件;解释了由边界失效引起的Ⅲ区强度异常的原因。通过数字图像处理技术获得连续尺寸范围内的碎块尺寸;对比了传统电测应变法和DIC法测量精度的差异,研究了冲击劈裂试验中的残余动能和能量分布,提出了劈裂→劈裂+压裂→非对称压裂→边界失效冲击破碎演变形式。同时,得到了花岗岩在冲击压缩中存在的Ⅰ,Ⅱ类破坏模式,从断裂强度与应变率、残余应变与断裂应变、耗散能量与应变率的关系讨论了临界应变率的确定方法。结合自主开发的数字图像碎片分析系统研究了不同应变率下的碎片分布和特征尺寸,基于有限长三维柱状模型建立了多重破碎能量模型,成功解释了高应变率下材料灾难性破碎的成因。进一步地采用三轴霍普金森压杆装置研究了不同围压条件下岩石的强度特征和破坏准则。发现当围压一定时,材料的破坏强度随应变率增加逐渐增加,对于不同围压条件,应变率效应基本一致。强度随应变率的变化关系可以近似为线性,归一化强度因子随应变率呈线性增加,同时也随围压增加而增加。在相同应变率范围内的强度随围压的变化关系可以用Hoek-Brown准则解释。结合CT和SEM扫描技术研究了围压状态下岩石的细观破坏现象及三维损伤特征,重构结果显示低围压下的试样破坏主要以平行于最大主应力方向的拉伸裂纹扩展为主,而围压的提高一定程度上增加了剪切滑移的可能性,同时伴随大范围的晶体破碎。在理论模型方面,通过建立压应力状态下岩石动断裂滑移模型研究了脆性材料由于微裂纹扩展引起的非线性应变细观机制及对宏观本构关系的影响;通过提出过渡性压剪裂纹模型修正了传统模型在近端场的误差,结合Freund逼近解提出了统一的幂数型裂纹动态扩展准则,基于Catigiano能量平衡原理推导了矩阵形式的非线性应变计算公式。分析了微裂纹在压剪过程中的闭合、线性滑移、自相似扩展以及翼裂纹弯折等阶段的力学机制和影响因素。进一步拓展至考虑裂纹相互作用的裂隙岩体模型,讨论了归一化无量纲应变率模型和特征参量的物理意义。在数值模拟方面,考虑到试验技术和理论分析对研究多尺度非均质岩石冲击损伤行为问题的不足,提出基于岩石真实细观结构建模的多尺度离散元方法,通过建立不同断裂模型考虑了晶体边界的弱化作用,同时借助FPZ模型描述了晶体内部的穿晶破坏形式。考虑晶体破坏特征的GBM更能真实反应岩石的微观力学特征,在应力应变行为和微破裂方面很好地模拟了花岗岩试验结果。创新性地结合纳米压痕技术获得不同矿物成分的细观力学参数,提出了推荐性离散元标定方法,简化了GBM的标定程序,很大程度上提高了GBM的适用范围。最后将其应用于研究岩石率效应机制、动态破碎及多尺度损伤研究。发现岩石裂纹起裂和损伤应力阈值在裂纹体应变变化和声发射破裂等行为上表现出相似性。动载荷作用下的损伤演化与静载荷作用下的损伤演化有明显的不同。在动载荷作用下,Weibull分布表现出较宽的形状尺寸和较大的平均尺度。微裂纹从晶间断裂向穿晶断裂的转变导致了不同的宏观破坏特征。单个断裂或轻微碎裂的试样是由断裂面与以晶间断裂为主的分支裂纹共同形成。相反,粉碎状破裂的岩石是穿晶裂纹聚集在裂缝表面周围的结果,进而形成大范围剪切带。细观尺度上的沿晶破裂向穿晶破裂转换被认为是应变率效应机制和冲击粉碎化破碎的根本原因。