Numerical and Laboratory Analysis of Relaxation Tests for Determining Time-Dependent Properties of Rock

Roof falls in coal mines may occur within a few months to a few years after excavation. In this paper, we proposed the use of relaxation tests as a substitute for time-dependent tests. The relation between creep behavior and relaxation behavior was numerically investigated and demonstrates that the material assigned with creep model can show relaxation behavior. Then the relaxation model was developed by modifying the Burgers creep model. Numerical simulation of a relaxation test on a simulated rock model in 3DEC yielded results that were similar to theoretical prediction. A relaxation test was performed on two groups of specimens under varying load conditions. Results from the laboratory tests validated the approach of using relaxation test to determine time-dependent properties. Finally, time-dependent properties were investigated by performing relaxation tests at different stages of a complete stress–strain curve. The relaxation test during strain-softening was unsuccessful; however, the relaxation behavior at residual stage in post-failure region was more significant than that in pre-failure region and the sudden drop in stress indicated there was strength deterioration due to the accumulation of viscous strain.     

Estimation of the Specific Energy of TBM Using the Strain Energy of Rock Mass,Case Study: Amir-Kabir Water Transferring Tunnel of Iran

The specific energy (SE) is the most important parameter to estimate the energy consumption in tunnel boring machines (TBMs). It is defined as the amount of required energy to excavate a unit volume of rock mass which used to predict the performance of TBMs. Several models are used to estimate the SE based on different parameters such as the rock mass properties, disc cutter dimensions and cutting geometry. The aim of this work is to propose new relations between the SE and the strain energy of rock mass (W) using the geological mappings of rock mass and TBM operational parameters from Amir-Kabir Water Transferring Tunnel of Iran. W is an appropriate criterion to estimate SE because it is a function of different parameters such as rock mass behavior, pre and post failure properties and peak and residual strains. In this study, to increase the correlation coefficient of relation between the mentioned parameters, the rock mass is classified in two methods, in the first method according to the geological strength index (GSI) all data is classified in three classes such as weak, fair and good and in the second method using the drop to deformation modulus ratio (η) the classification of data is performed in three classes such as η < 0.05, 0.05 ≤ η < 10 and η ≥ 10. The results show that there are direct relations between both parameters. It is suggested to estimate SE in all rock mass classes using the proposed relations based on GSI classification.     

Mechanical Behaviour of Cyclically Heated Fine Grained Rock

Summary The most vital difference between rock and rock mass are fractures and fissures. They affect the behaviour and strength of rock masses. According to their origin, size, and shape, rock mass contains several types of weakness planes varying from microfissure to faults. Other parameters such as underground water, temperature, time and stress state affect the rock's behaviour in its natural environment. The frequency of discontinuities in fractured rock is one of the basic parameters for reducing its strength. However it is generally difficult to test undisturbed fractured rock in a laboratory environment. In this study it was tried to open and loosen the grain boundaries of fine-grained rock specimens by cyclical heating and cooling. This should serve as a physical simulation of fractures in the rock mass and enables a discussion of the changes in mechanical behaviour of fractured rock. For this reason, laboratory test specimens of Carrara marble and Buchberger sandstone were used. The heating cycles were varied from 0 to 16. From the results of uniaxial compression, Brazilian and “Continuous Failure State” triaxial tests, it was pointed out that all of the mechanical parameters decreased gradually with an increasing number of heating cycles. Uniaxial compressive strength was reduced to about 50%, while the tensile strength decreased to about 60% for both types of rock. It was also observed that the variations of strength parameters were higher after the first heating cycles. As a result of cyclical heating, the slopes of pre-failure and post-failure curves in the stress-strain plane changed similarly, but the variations of modulus of elasticity were higher than the slopes of the post-failure curves for sandstone. The ratio between compressive and indirect tensile strength rose to a value of 98 after the last heating cycle. For unheated specimens of Carrara marble this ratio is 20. The axial strain at the failure point increased suddenly after the first heating cycle and the failure developed entirely intergranular in cyclically heated specimens.     

受载煤岩组合体破坏前能量分布规律

为研究引发冲击地压的能量在煤岩系统中的分布规律,理论分析了二元、三元组合模型峰前能量分布计算公式,并对自主构建的不同比例的二元、三元组合体开展了轴向加载试验。试验结果表明：随着煤岩高度比增大,组合体峰前总能量也逐渐增大,但增幅逐渐减小;相同煤岩高度比的组合体,岩石组分越硬,组合体峰前总能量越小;无论何种组合体,煤组分能量占比最大,均大于50%;随着煤岩高度比的增大,煤组分能量占比逐渐增大,岩石组分能量占比逐渐减小;煤岩高度比相同的组合体,岩石组分越硬,煤组分能量占比越大。组合体峰前能量主要分布在煤组分中,其次为粗砂岩,细砂岩积聚能量最少。由此表明：煤岩系统中的能量主要分布在软弱煤岩层中,岩层弹性模量越大,积聚能量越少。据此提出了直接释能和间接释能两种冲击地压防控理念,对现场冲击地压的防治具有指导意义。     

Numerical studies on the failure process and associated microseismicity in rock under triaxial compression

In this paper, firstly the mesoscopic elemental mechanical model for elastic damage is developed and implemented into the rock and tool interaction code (R-T^2D). Then the failure processes of a heterogeneous rock specimen subjected to a wide variety of confining pressures (0–80 MPa) are numerically investigated using the R-T^2D code. According to the simulated results, on the one hand, the numerical simulation reproduced some of the well-known phenomena observed by previous researchers in triaxial tests. Under uniaxial compression, rock failure is caused by a combination of axial splitting and shearing. Dilatancy and a post-failure stage with a descending load bearing capacity are the prominent characteristics of the failure. As the confining pressure increases, the extension of the failed sites is suppressed, but the individual failure sites become dense and link with each other to form a shear fracture plane. Correspondingly, the peak strength, the residual strength and the shear fracture plane angle increase, but the brittleness decreases. When the confining pressure is high enough, the specimen behaves in a plastic manner and a narrow shear fracture plane leads to its failure. The prominent characteristics are volume condensation, ductile cataclastic failure, and a constant load bearing capacity with increasing strain. On the other hand, the numerical simulation revealed some new phenomena. The highest microseismicity events occur in the post-failure stage instead of the maximal stress, and most of the microseismicity energies are released in the failure localization process. As the confining pressure increases, the microseismicity events in the non-linear deformation stage increase dramatically and the ratio between the energies dissipated at the non-linear deformation stage and those dissipated in the whole loading process increases correspondingly. Therefore, it is concluded that the developed mesoscopic elemental mechanical model for elastic damage is able to reproduce accurately the failure characteristics in loading rock specimens under triaxial conditions, and the numerical modelling can furthermore obtain some new clarifications of the rock fracture process.     

饱水和天然状态下页岩滞后效应及阻尼特性研究

运用RLW-2000型微机伺服岩石三轴试验机,对饱水状态和天然状态页岩在不同围压下进行三轴循环加卸载试验,分析了两种含水状态页岩的力学特性和滞后效应,并基于能量原理讨论了阻尼比演化规律。试验结果表明：随循环次数增加,累积残余应变逐渐增加,相对残余应变先降低,后趋于稳定区域,直至破坏前急剧增加;饱水页岩的加卸载变形模量均比天然页岩小,加载变形模量整体比卸载变形模量小;在加载和卸载阶段,均出现应变始终滞后于应力的现象;饱水页岩的滞后效应比天然页岩更明显。提出了考虑滞后效应的能量计算方法,较以往能量计算的误差更小。最后基于能量原理对阻尼比的计算公式进行修正,发现饱水页岩的阻尼比比天然页岩大。阻尼比的变化较好地反映了页岩损伤机制,可作为预判页岩失稳破坏的重要指标。     

Karrat Fjord (Greenland) tsunamigenic landslide of 17 June 2017: initial 3D observations

On 17 June 2017, a landslide-generated tsunami reached the village of Nuugaatsiaq, Greenland, leaving four persons missing and presumed dead. Here, we present a preliminary high-resolution analysis of the tsunamigenic landslide scar based on three-dimensional (3D) reconstructions of oblique aerial photographs taken during a post-failure reconnaissance helicopter overflight. Through a 3D quantitative comparison with pre-failure topography, we estimate that approximately 58 million m³ of rock and colluvium (talus) was mobilized during the landslide, 45 million m³ of which reached the fjord, resulting in a destructive tsunami. We classify this event as a “tsunamigenic extremely rapid rock avalanche,” which likely released along a pre-existing metamorphic fabric, bounded laterally by slope-scale faults. Further analysis is required to properly characterize this landslide and adjacent unstable slopes, and to better understand the tsunami generation.     

Strain-softening behaviour of sand in strain path testing under plane-strain conditions

Experimental data are presented in this paper to study the strain-softening behaviour of sand under plane-strain conditions. K ₀ consolidated strain path tests were conducted using a new plane-strain apparatus. The stress–strain behaviour of medium dense sand under plane-strain conditions was characterized. The test results show that the occurrence of pre-failure strain softening under plane-strain conditions is affected by the void ratio, the strain increment ratio and the initial effective confining stress. This is consistent with previous findings established under axisymmetric conditions. However, a pre-failure strain-softening behaviour in plane-strain tests conducted under high-confining stresses may consist of three stages, namely, material softening, banding softening, and ultimate state. This observation is different from that in triaxial tests where banding softening does not normally occur.     

一种基于弹性应变能的裂隙岩体等效弹性模量评价方法

基于线弹性断裂力学裂隙面张开位移及剪切位移理论公式,考虑裂隙存在常法向和常切向刚度情况,研究了含单个裂隙岩体加载过程中由于裂隙存在而附加的弹性应变能。基于应变能等效方法并假设两种裂隙变形模型--非均匀变形模型和均匀变形模型,研究了二维非贯通裂隙岩体的等效杨氏模量和等效剪切模量解析表达式。研究结果表明,对于贯通裂隙规则分布情况,均匀变形模型得到的解析解与Amadei等的结果一致;对于非贯通裂隙正态分布情况,考虑裂隙相互作用的非均匀变形模型解明显低估裂隙岩体的等效杨氏模量和等效剪切模量,而考虑裂隙相互作用的均匀变形模型解与有限元数值解的偏差在10%以内。得到的解析表达式在一定条件下可以作为裂隙岩体等效弹性模量评价方法之一。     

Strains and stresses in the rock around and unlined hot water cavern

Summary Hot water stored in an unlined rock cavern is an efficient energy storage. A research program has been carried out with a test plant at the city of Avesta, Sweden. The plant consists of a rock cavern, the volume of which is 15000 m³, which serves as an energy buffer in the district heating system of the city. The water is heated from a garbage incinerator located close to the cavern.During the first test period the temperature of the stored water has varied between 40°C and 95°C. The heating of the rock causes strains and stresses in the rock. The measurements show that the state in the rock does mainly respond to the average temperature and not to the fluctuations. The maximum thermal stress is 9 MPa occurring at the wall of the cavern. The heave of the ground is less than 5 mm.The development of stress and strain will continue after the first test period since thermal equilibrium was not reached during this period.     

开挖卸荷对砂岩力学特性影响试验研究

卸荷作用广泛存在于人类的工程活动和地质作用过程中,岩体在卸荷条件下的力学特性研究一直是工程界探讨的热点问题之一。根据实际边坡工程开挖后应力变化状态确定试验方案,进行了砂岩三轴卸荷破坏试验,研究了卸荷状态下岩体的应力应变特征、破坏特征及力学参数变化规律,并与加载破坏试验数据进行了对比分析。试验结果表明,卸荷破坏时岩样变形模量随着卸荷量的增加可降低5%～42%左右,二者之间的关系可用指数函数拟合;卸荷破坏时岩体的峰值应变随围压线性增长,残余应变与围压无明显关系;相比于加载破坏,卸荷破坏时岩体凝聚力c值降低了4%左右,内摩擦角? 增加了12%左右;卸荷速率对岩样强度和变形参数有较大影响;卸荷条件下岩体破坏具有沿卸荷方向强烈扩容特征,主要表现为张剪破坏,并伴随有环向裂纹,初始围压越高,卸荷程度越强烈,岩体的破碎程度越高。     

The Effect of the Stress Path on Squeezing Behavior in Tunneling

Summary  The interplay between support systems and the rock when tunneling under squeezing conditions is normally studied by means of two-dimensional analyses. The present paper shows that the underlying plane strain assumption involved in a two-dimensional analysis may lead, under certain conditions, to ground pressure and deformation values that are considerably lower than those produced by stress analyses that take into account spatial effects in the vicinity of the tunnel face. The differences are due to the stress path dependency in the elasto-plastic behavior of the ground and, more specifically, to the inability of the plane strain model to map the actual radial stress history, which involves a complete radial unloading (and, later, a re-loading) of the tunnel boundary over the unsupported span. This inherent weakness of any plane strain analysis is relevant from the design standpoint, particularly for heavily squeezing conditions that require a yielding support. For the majority of tunneling conditions and methods, however, involving as they do the completion of a stiff support within a few meters of the face, the errors introduced by the plane strain assumption are not important from a practical point of view.     

Capturing the complete stress–strain behaviour of jointed rock using a numerical approach

This paper presents the results of a series of numerical experiments using the synthetic rock mass (SRM) approach to quantify the behaviour of jointed rock masses. Field data from a massive sulphide rock mass, at the Brunswick mine, were used to develop a discrete fracture network (DFN). The constructed DFN model was subsequently subjected to random sampling whereby 40 cubic samples, of height to width ratio of two, and of varying widths (0.05 to 10 m) were isolated. The discrete fracture samples were linked to 3D bonded particle models to generate representative SRM models for each sample size. This approach simulated the jointed rock mass as an assembly of fractures embedded into the rock matrix. The SRM samples were submitted to uniaxial loading, and the complete stress–strain behaviour of each specimen was recorded. This approach provided a way to determine the complex constitutive behaviour of large‐scale rock mass samples. This is often difficult or not possible to achieve in the laboratory. The numerical experiments suggested that higher post‐peak modulus values were obtained for smaller samples and lower values for larger sample sizes. Furthermore, the observed deviation of the recorded post‐peak modulus values decreased with sample size. The ratio of residual strength of rock mass samples per uniaxial compressive strength intact increases moderately with sample size. Consequently, for the investigated massive sulphide rock mass, the pre‐peak and post‐peak representative elemental volume size was found to be the same (7 × 7 × 14 m). Copyright © 2015 John Wiley & Sons, Ltd.     

Prediction of Rock Mass Squeezing of T4 Tunnel in Iran

One of the most important steps in designing underground structures is the evaluation of ground conditions in terms of squeezing potential and behavior of the geological structures. Generally, constructing a tunnel in the squeezing condition is a very slow and difficult task. Therefore, recognition and evaluation of the squeezing potential is very important in selecting a suitable excavation method and support, especially in weak rocks. This research is concerned with the assessment of squeezing potential along tunnel T4 of water conveyance system from Azad dam to Ravansar plain with the length of 11,380 m, located between Kurdistan and Kermanshah provinces, west of Iran. This tunnel is in an almost NS direction and flows through the contact zone of Iran and Arabic plates. According to the engineering geological investigations, the squeezing potential has been recognized as the most important difficulty in the excavation of tunnel T4. This conclusion can be explained by the several indicators including lithology, high disintegration of rock masses, alteration of rocks on the border of Iran and Arabic plates’ contact zone, low rock mass quality, high overburden, and highly jointed rock masses in a shuffle tectonic condition. This paper deals with the engineering geological and geomechanical properties of rock masses. Then, it evaluates squeezing intensity using empirical, semi-empirical, and analytical properties methods. The analysis conducted in these work shows that the tunnel excavation would encounter squeezing problems, which is most severe in region 2 due to the effects of the major young Zagros fault.     

Singular value decomposition of the compliance response matrix for the triaxial stress condition

Performance-based design demands accurate prediction of soil deformation under a working load condition. The nonlinear stress–strain behavior needs to be analyzed quantitatively to advance the understanding of complex soil behavior in the pre-failure condition. The singular value decomposition technique is introduced to quantitatively analyze the compliance matrix representing the strain response envelope (SRE). The rotation of the ellipse of the SRE relates to the anisotropic response of the soil deformation. The off-centered SRE provides evidence of the kinematic hardening plasticity. Quantitative data on the movement of SREs provide us with crucial information to investigate the effect of stress history and the evolution of stiffness anisotropy in soil deformation.     

圆形硐室岩爆的折迭突变模型

均匀围压下圆形硐室岩爆是传统意义上的软化区内岩环经过塑性变形局部化阶段完成的。当处于极限状态的塑性变形集中区承载能力下降时, 岩环中相对完好部分以弹性方式卸载,当后者释放的弹性能超过前者塑性变形所耗散的能量时便发生岩爆。简捷地通过等效应力 和等效应变 关系建立突变模型对硐室岩爆进行了分析, 将状态变量 用软化区半径 来表示。分析表明: 岩爆发生条件与硐室岩体的升降模量比 和岩体裂隙发育程度 的乘积有关; 对于特定冲击倾性的岩体,存在对应的临界软化区深度 , 即软化区深度达到 时便发生岩爆;还给出硐室岩爆释放地震能等计算式,岩爆释放的地震能量级则与硐室软化区深入程度有关。     

Development of a Nonlinear Model for Soft Rock and its Applications

A phenomenological model has been developed for soft rock based on the results of a series of triaxial compression (TC) tests conducted on Kobe sandstone with a very high precision measurement. From the analysis and interpretation of the test results, it has been found that small strain Young’s modulus (E^e) was a function of the major principal stress. E^e for elastic strains of soft rock was assumed to be cross-anisotropic. A damage function has been used to derive the appropriate elastic Young’s modulus when subjected to shear loading. As the basic stress–strain relation, the relationship between the tangent modulus and the shear stress level was used. The differential form of which was subsequently integrated by a 4th order Runge–Kutta solver to obtain the stress–strain relation. The model of soft rock is based on an isotropic strain hardening elasto-plastic framework which takes into account the pressure sensitivity, cross-anisotropy, degradation of Young’s modulus with the degree of mobilized shear stress and the nonlinearity of the shear stress-shear strain relationship. Although the model was developed from the analysis of the TC tests results of Kobe sandstone, it was also applied to the other types of soft rock or stiff geomaterials. Plate loading tests were conducted at a level of 61 m below the ground level at the bottom of a large excavated shaft at four locations. Finally, the model was used to simulate the plate loading test results successfully. This model was successfully calibrated with Akashi sandstone and applied in the simulation for the settlement of Akashi-Kaikyo Bridge piers. The simulations were carried out for both drained and undrained condition by changing the Poisson’s ratio. The layering information beneath the foundations were used in the FEM simulation. The use of very accurate Young’s modulus from the field shear wave velocity test was the key to the successful simulation of the settlement under bridge pier foundations.     

The Taguchi approach to the evaluation of the influence of different testing conditions on the mechanical properties of rock

Laboratory testing is often used to derive the mechanical properties of rock. Testing conditions heavily influence the results of such laboratory experiments in which factors, including the water content, diameter of samples, slenderness of sample and strain (or loading) rates are of great importance. This paper evaluates the influences of four major test conditions: water content, strain rate, sample diameter and sample slenderness, on the peak uniaxial compressive strength (UCS) and modulus of elasticity (MoE) of sandstone. Following the Taguchi approach, an experimental study was conducted on cylindrical sandstone specimens, and the results were interpreted using signal-to-noise ratio (S/N) and analysis of variance (ANOVA). The results reveal that water content is the most influential test condition for peak UCS and the influence of sample diameter, slenderness and strain rate decreases in the cited order. MoE is greatly affected by sample slenderness, whereas the other three test conditions show an approximately similar and smaller influence. These characteristics were further verified by the ANOVA results. These behaviours are consistent with the results reported in the literature. Finally, the Taguchi approach, which is a very useful and versatile technique, which has not been effectively applied in rock mechanics and rock engineering, was successfully used to evaluate the influences of different test conditions on the peak UCS and MoE of laboratory rock samples.     

高静载条件下受频繁动力扰动时蛇纹岩动力学特性研究

基于改进的分离式霍普金森压杆（SHPB）岩石动静组合加载试验系统,进行了在不同静力轴压条件下受频繁动力扰动作用的动力学试验,研究蛇纹岩在高静载下受频繁冲击扰动过程中的动态变形特性、动态峰值应力和应变、能量变化规律和岩石破坏模式等动力学特性。研究结果表明：高静载条件下受频繁冲击扰动作用时,在动态峰值应力前,动态应力与应变呈正相关关系,而在动态峰值应力后,出现变形回弹和不回弹两种现象;随着动力扰动次数的增加,岩石动态峰值应力减小、动态峰值应变增大、动态变形模量减小、岩石由释放能量向吸收能量方向转化;随着预加静力轴压的增大,单次冲击过程中岩石损伤加剧,岩石破坏需要的扰动冲击次数减少,同时岩石由拉伸破坏模式向压剪破坏模式转变,破坏块度由小变大、均匀度降低。试验结果对揭示深部岩体承受高地应力和频繁开挖爆破等动力扰动作用下的破坏机制具有重要意义,同时为工程实际中通过调整围岩静应力状态和爆破以提高围岩长期稳定性的可行性提供了室内试验支持。