Mechanical behaviors of conjugate-flawed rocks subjected to coupled static–dynamic compression

Conjugate flaws widely exist in rock masses and play a significant role in their deformation and strength properties. Understanding the mechanical behaviors of rock masses containing conjugate flaws is conducive to rock engineering stability assessment and the related supporting design. This study experimentally investigates the mechanical properties of conjugate-flawed sandstone specimens under coupled static–dynamic compression, thereby providing insight into how conjugate fractures interact to produce tracing tensional joints. Results indicate that the coupled compressive strength and the dynamic elastic modulus of conjugate-flawed rock specimens show remarkable loading rate dependence. For a fixed strain rate, the specimen with a static pre-stress equal to 60% of its uniaxial compressive strength has the highest coupled strength. Besides, both higher static pre-stress and strain rate can induce smaller mean fragment size and greater fractal dimension of the specimen, corresponding to a more uniform distribution of the broken fragments with smaller sizes. When the static pre-stress is lower than 80%UCS, the flawed specimen under a higher strain rate is characterized by higher absorbed energy. However, when the pre-stress equals 80%UCS, the value of the energy absorbed by the specimen in the dynamic loading process is negative due to the release of the preexisting considerable elastic strain energy input from the static pre-loading. As for the failure modes, cracks always penetrate the preexisting ipsilateral flaw tips to form anti-wing cracks. Under dynamic loading, the conjugate-flawed specimen generally shows tensile failure at a low strain rate, while the shear failure dominates at a high strain rate. In addition, based on progressive failure processes of the conjugate-flawed rock specimens, the evolution of tracing tensional joints in the field is discussed.

     

不同围压下岩石抗压强度与变形参数尺寸效应的数值模拟

岩石抗压强度和变形参数是岩石工程设计的重要指标。由于岩石是典型的非均质材料,其强度和变形特性随样品尺 寸的变化而不同。本文采用PFC2D程序模拟了不同围压下不同尺寸岩样的压缩试验。结果表明（1） 岩样具有明显的尺寸效 应。同一围压下,尺寸越大,岩石强度、峰值应变和压缩模量越小,尺寸的变化对岩样的破坏模式影响较小;（2） 岩样具 有明显的围压效应。同一尺寸的岩样,随着围压的增大,岩石强度、峰值应变和压缩模量均增加,其中强度和峰值应变随 围压的增加呈线性增加。同时,随着围压的增大,岩石破裂模式由轴向劈裂破坏向剪切破坏变化;（3） 围压的存在会影响 岩样的尺寸效应。不同尺寸岩样的强度和峰值应变在相同围压区间内的增量基本相同,同时随着围压的增大,其强度和峰 值应变增加,进而使岩石强度和峰值应变的尺寸效应弱化;而不同尺寸岩样的压缩模量在相同围压区间内的增长率大致相 同,因而造成围压对压缩模量尺寸效应的影响较小     

节理岩体动态破坏的SHPB相似材料试验研究

采用相似材料模型试验对不同节理倾角、节理贯通度、节理条数、载荷应变率、节理充填物厚度、节理充填物类型及试件长径比等7种工况下的节理岩体动态强度及破坏模式进行了分离式Hopkinson压杆(SHPB)试验研究。结果表明：节理岩体动态破坏模式及强度与节理构造形态密切相关。对于单节理岩体,其强度及破坏特征在很大程度上受节理倾角控制,节理倾角0°、90°试件动强度分别为完整试件的90%和71%,且其破坏形式均为张拉破坏;倾角60°试件动强度几乎为0;倾角30°、45°试件的动强度分别为完整试件的50%和18%,且其破坏以剪切破坏为主,兼有张拉破坏。中心1/4、1/2、4/5及全贯通节理试件的峰值强度分别为完整试件的95%、74% 、28%和17%,即随节理贯通度增加,试件动强度逐渐降低。含1~3条节理的试件动强度分别为完整试件的54%、23%和10%,即随节理条数增加,试件动强度随之有较大幅度降低,但节理条数的增加并没有改变其破坏模式。随着节理充填物厚度增加及节理充填物强度降低,试件强度依次递减,但破坏模式并没有改变。完整试件和节理试件的动强度均随着载荷应变率的增加而变大,且前者对载荷应变率的敏感性要远远高于后者,相应地试件的破坏模式也变得更加复杂。两类试件的动强度均随着试件长径比的增加先增大后减小,即存在一个最佳长径比。     

方解石多晶集合体的高速率简单剪切变形实验研究

本文介绍了方解石多晶集合体在高应变率(373S^-1到1507S^-1)下简单剪切变形实验,结果表明,破裂形式和应变率有关,随着应变率的增加,从晶间微破裂为主变为晶内微破裂和粉碎为主。     

试件形状对冻结粉土抗压强度影响的试验研究

在不同温度和应变率条件下,分别对圆柱体和正方体冻结粉土进行了单轴抗压强度试验,分析比较了二者的应力-应变关系、抗压强度及破坏应变.结果发现:单轴压缩下正方体与圆柱体冻结粉土的力学性质存在差异.正方体冻结粉土的应力-应变曲线有明显的弹性屈服点,屈服点后曲线呈线性硬化,而圆柱体冻结粉土的应力-应变曲线无明显弹性屈服,全应力-应变曲线呈抛物线型.相同温度和应变率条件下,圆柱体试样的应变软化程度比正方体试样大.相同试验条件下正方体冻结粉土的抗压强度及破坏应变大于圆柱体的抗压强度和破坏应变,二者抗压强度及破坏应变的差异程度与温度和应变率无关.研究结果可为冻结壁的设计提供重要依据和参考.     

Effects of size and strain rate on the mechanical behaviors of rock specimens under uniaxial compression

Size and strain rate are two key factors that dramatically influence the estimation of rock mechanical behaviors. To better understand the effects of size and strain rate on measured rocks, rock specimens with six different sizes were tested at six different strain rates under uniaxial compression using the MTS 815 Rock Mechanics Test System. Having determined that the size and strain rate significantly affect the peak strain, peak stress, elastic modulus, acoustic emission (AE), and failure pattern of the rock specimens, the relation was established between the strength and the size and strain rate of red sandstone. And the variation was revealed among the size and strain rate, the AE, and the failure pattern. It turned out that the peak stress was negatively correlated with the rock size and was positively correlated with the strain rate. When the length to diameter ratio (L/D) of the rock specimen was less than 2.0, the AE appeared mildly. The AE quantities gradually increased before the peak stress, and then sharply decreased after the peak stress. The failure pattern of the rock specimen was relatively complicated, with a fracture plane appearing along the axial direction. Conical failure type was also presented. When the L/D ratio of the specimen was greater than 2.0, the AE characteristics of red sandstone showed the radical model. There were relatively few AE rings before the peak stress. But the AE rings increased suddenly and dramatically during the peak stress. The rock specimens primarily failed with a single shear plane. Moreover, with an increase in the strain rate, the AE activities were enhanced and the AE quantities increased. When the strain rate of the rock specimen was less than 5.0?×?10^?4/s, the rock specimen failed with a shear or tensile-shear pattern. And when the strain rate was greater than 5.0?×?10^?4/s, the rock specimen tended to fail in a conical pattern.     

Nonlinear SEM numerical analyses of dry dense sand specimens under rapid and dynamic loading

The paper mainly concerns the mechanical response of 2D dry dense sand specimens under shock loading. The problem is numerically analysed by means of a SEM dynamic code, within which an already conceived non‐local viscoplastic constitutive model characterized by a non‐associated flow rule and by an anisotropic strain hardening has been implemented. In particular the strain localization and time dependency of the material mechanical response are taken into consideration. Both rapid/static loading and dynamic histories are numerically simulated. In the first case, the time dependency of the material mechanical response can be captured by neglecting inertial effects, while in the second one the two factors are superimposed and the propagation of the stress waves within the specimen is discussed. The interest of these analyses derives from the fact that the diffusion phenomenon takes place within a specimen already localized. Copyright © 2006 John Wiley & Sons, Ltd.     

材料缺陷对岩样变形局部化影响的数值模拟

在平面应变压缩条件下,采用拉格朗日元法研究了材料缺陷对岩样应变局部化及宏观力学行为的影响。在数值计算中,采用了莫尔-库仑与拉破坏复合的破坏准则,峰后岩石的本构关系为线性应变软化。对于理想岩样（不含任何缺陷）,从剪切应变率的等值线图及变形网格图发现,变形场相对试样垂直对称轴对称。在试样的边界上设置材料缺陷后,变形场的对称性被打破。材料缺陷附近是局部化现象启动的主要位置。与不含材料缺陷试样相比,含缺陷试样的局部化提前启动。当缺陷位于试样左边界中部附近时,试样内部出现多条剪切带,发生韧性剪切破坏,峰后应力-轴向应变曲线和应力-侧向应变曲线均倾向于韧性,岩样的稳定性增强;当缺陷位于试样上、下端面附近时,仅出现一条贯穿试样左右边界的剪切带,发生脆性剪切破坏,峰后两种曲线倾向于脆性,易发生失稳破坏。从数值结果中还观测到了剪切带的跳跃或迁移现象及剪切带的相互竞争、此消彼涨的现象。当岩样中不包含任何缺陷时,试样应力-变形曲线的峰值强度最高。随着缺陷的上移,峰值强度下降,直到峰值强度基本保持不变。缺陷越接近于岩样的下端,对岩样应力-变形曲线的峰值强度的影响越小。     

黏结强度对异质土界面强度与变形特性影响试验研究

我国黄土高原地区黄土沉积覆盖于新近系三趾马红土之上,形成具有胶结的异质土界面。为研究黏结强度对黄土–三趾马红土界面抗剪强度与变形特性影响,开展其剪切力学试验研究,探讨界面间黏结强度对界面破坏模式、界面变形与抗剪强度特性影响规律。结果表明:(1) 有无界面黏结导致异质土界面试样破坏模式不同,界面黏结增大了试样沿界面间的滑动阻力,试样剪切破坏更趋于剪断模式,剪断面损伤程度也越高;(2) 异质土界面剪应力–剪应变曲线均呈应变软化型,有无界面黏结导致界面试样剪切变形特征不同,有界面黏结试样剪切破坏位移大,峰值强度后剪应力降低幅值大,试样脆性剪断破坏特征越显著;(3) 剪切过程中异质土界面产生明显的竖向剪胀变形,有界面黏结试样竖向剪切位移小,且其随界面粗糙度、法向应力变化幅值小;(4) 异质土界面抗剪强度呈非线性变化,界面黏结存在显著提升了界面试样抗剪强度。当异质土界面间粗糙度较低时,黏结强度对界面试样抗剪强度提升幅度大;当异质土界面间粗糙度高时,黏结强度对界面试样抗剪强度的提升幅度下降,此时界面抗剪强度主要受控于界面两侧土体抗剪强度。      

动载作用下端锚锚固体力学响应特征研究

为研究动载作用下巷道围岩失稳破坏机制,基于SHPB试验系统,研究了不同冲击气压（0.2、0.3、0.4、0.5、0.6 MPa）下预应力端锚锚固体的应力波传播规律及层裂破坏特征,采用图解法计算了锚固体试件的层裂强度及应变率,建立了锚固体层裂损伤模型并采用高速摄像机进行了验证。结果表明：不同冲击气压下试件应力波峰值应变均呈指数形式衰减,且空间衰减幅值及衰减指数与冲击气压呈正相关关系;锚固体试件层裂首先发生在自由端附近,沿反射波传播方向层裂厚度逐渐增加,0.3 MPa冲击气压以上,试件每两处层裂面中间产生一道新层裂;在18～33 s⁻¹应变率范围内,应变率率效应占主导地位,层裂强度最高达69 MPa,而应变率为41 s⁻¹时,层裂强度降低至17 MPa;锚固体自由端在动载冲击后出现层裂闭合现象,但在锚固端由于锚固界面残余黏聚力作用,层裂位置未发生闭合现象。     

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。     

Simulation of earthquake‐induced slope deformation using SPH method

This paper presents the development, calibration, and validation of a smoothed particle hydrodynamics (SPH) model for the simulation of seismically induced slope deformation under undrained condition. A constitutive model that combines the isotropic strain softening viscoplasticity and the modified Kondner and Zelasko rule is developed and implemented into SPH formulations. The developed SPH model accounts for the effects of wave propagation in the sliding mass, cyclic nonlinear behavior of soil, and progressive reduction in shear strength during sliding, which are not explicitly considered in various Newmark‐type analyses widely used in the current research and practice in geotechnical earthquake engineering. Soil parameters needed for the developed model can be calibrated using typical laboratory shear strength tests, and experimental or empirical shear modulus reduction curve and damping curve. The strain‐rate effects on soil strength are considered. The developed SPH model is validated against a readily available and well‐documented model slope test on a shaking table. The model simulated slope failure mode, acceleration response spectra, and slope deformations are in excellent agreement with the experimental data. It is thus suggested that the developed SPH model may be utilized to reliably simulate earthquake‐induced slope deformations. This paper also indicates that if implemented with appropriate constitutive models, SPH method can be used to model large‐deformation problems with high fidelity. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical Investigation of the Dynamic Compressive Behaviour of Rock Materials at High Strain Rate

The dynamic compressive strength of rock materials increases with the strain rate. They are usually obtained by conducting laboratory tests such as split Hopkinson pressure bar (SHPB) test or drop-weight test. It is commonly agreed now that the dynamic increase factor (DIF) obtained from impact test is affected by lateral inertia confinement, friction confinement between the specimen and impact materials and the specimen sizes and geometries. Therefore, those derived directly from testing data do not necessarily reflect the true dynamic material properties. The influences of these parameters, however, are not straightforward to be quantified in laboratory tests. Therefore, the empirical DIF relations of rock materials obtained directly from impact tests consist of contributions from lateral inertia and end friction confinements, which need be eliminated to reflect the true dynamic material properties. Moreover, different rocks, such as granite, limestone and tuff have different material parameters, e.g., equation of state (EOS) and strength, which may also affect the DIF of materials but are not explicitly studied in the open literature. In the present study, numerical models of granite, limestone and tuff materials with different EOS and strength under impact loads are developed to simulate SHPB tests and to study the influences of EOS and strength, lateral inertia confinement and end friction confinement effects on their respective DIFs in the strain rate range between 1 and 1,000 s^?1. The commercial software AUTODYN with user-provided subroutines is used to perform the numerical simulations of SHPB tests. Numerical simulation results indicate that the lateral inertia confinement, friction confinement and specimen aspect (L/D) ratio significantly influence DIF obtained from impact tests and the inertia confinement effect is different for different rocks. Based on the numerical results, quantifications on the relative contributions from the lateral inertia confinement and the material strain rate effect on DIF of granite, limestone and tuff material compressive strength are made. The effects of friction coefficient, L/D ratio and rock type on DIF are discussed. Empirical relations of DIF with strain rate for the three rock materials representing the true material strain rate effect are also proposed.     

Numerical analysis on seepage failures of dike due to water level-up and rainfall using a water–soil-coupled smoothed particle hydrodynamics model

For seepage failures of dike due to water level-up and rainfall, surface infiltration and strength change induced by suction reduction are important factors; thus, numerical analysis should consider the coupling of water and soil, as well as the effect of saturation to obtain more precise failure mechanism. Based on the advanced smoothed particle hydrodynamics (SPH) method, this work proposed a two-phase-coupled SPH model in coordination with a novel constitutive model for unsaturated soils. Then, a triaxial compression test is simulated to check the applicability of the SPH method on the soil phase. After that, the failure test of a dike due to water level-up is discretized and simulated, from which the seepage process, the distribution of maximum shear strain, the slip surface, and pore water pressure are obtained. The two-phase-coupled SPH model is also applied to a slope failure test of heavy rainfall, and the results are compared to the model test. Finally, a dike failure test due to rainfall is analyzed using the proposed SPH model to reproduce the surface infiltration and suction reduction. The proposed SPH model provides several insights of seepage failures and can be a helpful tool for the analysis of dike failures induced by water level-up and rainfall.     

节理倾角对黄土力学特性影响试验研究

黄土节理种类多样、角度多变,是影响黄土力学性质的重要因素.为研究节理对黄土力学性质影响,开展含预制节理黄土试样单轴与三轴压缩强度试验,分析了非贯通节理对试样剪切破坏模式影响,探讨了节理倾角对黄土强度与变形特性影响规律.结果表明:节理试样剪切破坏均为压剪破坏,破坏模式可分为节理面与破裂面贯通型和节理面与破裂面斜交型,压力...     

循环荷载下兖石铁路路基膨胀土的动力特性试验研究

采用兖（州）至石（臼所）铁路路基膨胀土,借助GDS动三轴仪,研究了含水率、振动频率、动应力幅值对膨胀土累计塑性应变、动强度以及临界动应力的影响。试验结果表明:以轴向累计应变达到5%作为破坏标准时,循环次数与累计塑性应变曲线关系呈现出稳定型、临界型、破坏型3种状态;动强度与临界动应力均随含水率的增大而显著降低,饱和状态下的临界动应力只有40 kPa,低于列车实际动荷载;临界动应力与饱和度之间存在一条临界状态线,可以判断试样处于稳定、临界、还是破坏状态。振动频率对土体动力特性的影响:在f=0.5~2 Hz内,动强度随频率的增加而增大,当频率继续增大到5 Hz时,膨胀土动强度显著提高;在f=0.5~5 Hz范围内,临界动应力随频率的增加而增大,近似呈线性关系。相关研究结果对揭示动荷载下膨胀土的力学特性,确保膨胀土地区铁路线的安全运营具有重要意义。     

低温含水砂岩动态压缩力学性能试验研究

为研究砂岩动态压缩力学性能,采用SHPB装置对低温含水砂岩试样进行6种不同加载速率的冲击压缩试验。结果表明：-10℃时砂岩动态抗压强度和弹性模量明显大于-15℃时,动态抗压强度与应变率均呈乘幂关系增长;动态弹性模量与应变率呈正相关性,-10℃和-15℃时均呈多项式关系;动态应力-应变曲线分为4个阶段,应变软化阶段的应变范围随应变率的增加而增大;砂岩试样破坏模式随着应变率的增加,由块状劈裂结构、片状层裂结构的拉伸破坏,转变为锥形体结构的剪切破坏,最终呈现颗粒状粉碎破坏。     

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.     

板裂化模型试样失稳破坏及其裂隙扩展特征的试验研究

锦屏二级水电站深埋隧洞大量岩爆案例表明板裂化围岩的失稳破坏与岩爆之间具有很强的相关性。采用高强石膏配制满足板裂化围岩结构特征的硬脆性模型试样,通过一侧约束条件下的单轴压缩试验研究板裂化模型试样的失稳破坏过程、强度与变形特性及其裂纹扩展特征。研究表明,（1）板裂化模型试样失稳破坏过程表现出应变型岩爆的特征,其典型的破坏过程为预制裂隙尖端张拉裂纹的萌生与扩展-试样劈裂成板-岩板屈曲变形-岩板压折、岩片弹射;（2）与完整试样相比,含1条、2条、3条预制裂隙模型试样的峰值强度、弹性模量均呈现稳定下降的趋势,而峰值轴向应变则是先减小后增大;（3）试样预制裂隙尖端张拉裂纹的产生会造成：相邻预制裂隙尖端横向应变值的突变、试样侧向变形量的突增以及侧向变形速率的显著增大;（4）临空面附近的预制裂隙,其尖端产生的张拉裂纹在很短的时间内便会失稳扩展,并造成试样的失稳破坏。最后,分析试样变形破坏过程中的声发射特性。研究结果对于揭示深埋硬岩隧洞板裂化围岩的失稳破坏规律、岩爆的发生机制具有重要意义。     

高轴压和围压共同作用下矽卡岩受频繁动态扰动时的动力学特性

以冬瓜山铜矿深部出矿进路附近的矽卡岩为研究对象,采用改进的SHPB试验系统,进行高轴压和围压共同作用下受频繁动态扰动时深部矽卡岩动力学特性的研究。研究结果表明：预加载的高轴压和围压促使岩石内部微裂纹闭合,致使冲击荷载作用时动态应力-应变曲线初始阶段无下凹现象,即无压密阶段;峰值应力后,当岩样内部存储的弹性力大于卸荷时的冲击荷载时,出现应变减小的回弹现象,否则压缩应变一直增大至岩样破碎;累计扰动冲击次数随围压增大递增,随轴压增大递减,且增减率受围压、轴压大小的影响;动态变形模量、动态峰值应力随扰动冲击次数增加而减小,但最大应变及动态峰值应变增加;动态均值强度随轴压增大而减小,随围压增大先减小后增大;岩石动态变形过程中伴随着弹性变形,产生的回弹应变总体上随扰动冲击次数的增加呈先增大后减小的趋势发展。