Crack is produced by dissolving powdered cocaine in a mixture of water and ammonia or sodium bicarbonate (baking soda). The mixture is boiled until a solid substance forms. The solid is removed from the liquid, dried, and then broken into the chunks (rocks) that are sold as crack cocaine.
Based on the theoretical relationship between microscopic crack growth and macroscopic deformation failure in brittle rocks, and from the angle of crack growth and propagation, this paper attempts to explain the mechanism of crack growth in brittle rocks under the effect of loading rate.
The propagation and growth of cracks in brittle rocks are the main factors leading to their damage, instability and failure14,15,16,17. By summarizing a large number of existing research results, Hoek and Martin17 pointed out that in the macroscopic continuous deformation stage, i.e., in the subcritical growth stage of the microscopic crack, it can be considered that the microscopic crack in the brittle rock mainly extends by the shear sliding mode and tensile failure modes, as shown in Fig. 1. However, regardless of the microcrack propagation pattern, the failure mode of the crack tip was tensile failure in this stage. According to the theory of Griffith18, when subjected to compressive stress, cracks in rock will expand along the direction of maximum principal stress under the action of load, while the cracks will expand perpendicular to the direction of minimum principal stress under the action of tensile stress.
When the sandstone specimen obtains in the natural state and subjected to non-load, the energy in the rock is relatively dispersed, and the energy field is approximately evenly distributed. Meanwhile, considering the heterogeneity and internal friction characteristics of rock, the internal energy of rock under compression will preferentially accumulate in the area with weak mechanical properties, resulting in uneven distribution of energy field. Before reaching the peak strength, energy is continuously input into the rock system through axial loading. Most of the energy is accumulated in the form of elastic energy, and only a small part of energy is used in the form of dissipative energy for the closure of the original micro-cracks in the rock and the formation of new cracks at the yield stage. As shown in Fig. 9, by combining with the strain evolution cloud diagram of sandstone at different times under the loading of 0.1 mm/min, it can be found that the deformation localization zone of rock begins to incubate from the left side of the top of the specimen, and the deformation localization zone is approximately parallel to the axis of the specimen. Before reaching the peak strength, there is no obvious macroscopic penetrating crack on the rock surface. When the peak strength is exceeded, as the load continues to increase, energy transfer to the area below and accumulation, leading to micro cracks on the surface of the specimen gradually expanded. When energy reaches the energy storage limit of rock, macro cracks are formed and eventually run through the whole specimen, resulting in the overall failure of rock. The macro failure of specimen is accompanied by the release of energy. The accumulation and release of energy is the essence of the destruction of rocks and other materials. According to the analysis, more energy is accumulated in the pre-peak stage, while in the post-peak stage, more energy is released, which drives the coalescence of cracks in the rock and leads to the instability failure of rock materials.
Numerical simulation can be used to study the properties of fractured rock masses from multiple angles, at low cost, and throughout the process. Several numerical simulations were carried out by UDEC. Vergara et al. explored how parallel non-persistent joints affected the mechanical behaviour of the rock mass10. The results showed that a change in joint orientation will lead to a large anisotropy in the strength of the rock mass. Through uniaxial compression of blocks with multiple non-persistent joints, their mechanical behaviour was investigated using PFC3D by Fan et al.11. They also investigated how particle size, stiffness and joint strength parameters affected the deformability and damaged patterns of the specimens. By developing a smooth nodular model, Potyondy and Cundall had this new approach to study nodular rocks12. The model reproduced many features of rock behavior, including elasticity, fracturing, acoustic emission, damage accumulation producing material anisotropy, hysteresis, dilation and post-peak softening. By extending the smooth joint model, Ivars et al. studied the strength of jointed rock masses13. Carpinteri et al. proposed an analytical/numerical model which was called overlapping crack model for the analysis of the mechanical behaviour of concrete in compression14. The overlapping crack model was introduced into the finite element method. Numerical simulations of eccentric compression tests were carried out and compared with the test results. The influence of the size-scale, the specimen slenderness and the degree of load eccentricity were investigated. The influence of each parameter on the ductility characteristics of the rock mass was quantified.
Uniaxial compression was used to study the fracturing, acoustic emission and mechanical properties of fractured material with different crack modes, different grain sizes and different crack lengths in this paper.
Figures 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59 and 60 show that fracturing specimens comprising various grain sizes first produced wing cracks that extended from the bottom of the specimen to the tip of the left crack. Other crack also started laterally and propagated towards the tip of the crack on the right side. They are anti-tensile fissures. Specimens with two ranges of grain sizes or a wide range of grain sizes produced stretching cracks that extended downward from the top of the fissure when they are compressed. At the same time, wing cracks that extended upward were produced, followed by anti-tensile cracks that extended downward. These cracks were initiated at different points and propagated in different directions.
Most probably, students recognize that in nature rocks exist in different sizes, from exposed mountain sides and plateaus to boulders to gravel to grains of sand. The processes by which rocks break down into smaller and smaller pieces, however, may be new to students. Begin the investigation by asking students about the various sizes of rocks they may have experienced or seen.
Ice wedging refers to the repeated freezing and melting of water within small cracks in rocks near the surface. The water in the cracks freezes as the temperature drops below freezing. As the water freezes, it expands. This expansion exerts tremendous pressure on the surrounding rock and acts like a wedge, making cracks wider. After repeated freezing and thawing of water, the rock breaks apart.
Plant roots can grow in cracks. As the plant grows, the root becomes larger. The pressure of a confined growing root can be substantial. These pressures make cracks in the rocks larger, and, as roots grow, they can break rocks apart.
where V0 is the volume of the rock specimen and the absorbed energy can be divided into three main groups: crack propagation and fracture and damage energy of micro-cracks in the sample, the kinetic energy of flying fragments, and other forms of consumption which can be neglected energy, such as heat and sound. The energy absorption rate can reflect the amount of energy absorbed by the rock sample during the dynamic loading process, while the energy absorption density represents the energy absorption of flawed rocks per unit volume.
Ks=ud/uk is defined based on the elastic strain energy storage law, and Ks is used to represent the stable state of the sandstone system under storage and dissipation. Figure 17 shows the changes in Ks with the loading rate, where Ks first increases and then decreases with the increasing loading rate, and the value of Ks is always less than 1, which indicates that most of the strain energy of the rock is transformed into elasticity under impact loading. The specimen generally absorbs the energy during the impact loading, which also verifies the conclusion that the rock sample absorbs energy when rock-burst occurs. With the increasing of Ks, the initiation and propagation of cracks are accompanied by the increasing of elastic strain energy. At this time, less plastic strain energy is generated and gradually released outward which reduces the ability of the rock to resist external loads. The system of the crack sample gradually changes from an unsteady state to a steady state, and the energy storage capacity also gradually weakens. The Ks of the 45° and 90° fracture specimens begin to decrease with the increasing loading rate when the loading rate increases to 2500 GPa/s, and a large amount of strain energy is used for the sliding friction of rock fracture, which indicates that the closure of pores and micro-cracks is gradually completed. However, the elastic strain energy continues to increase, the entire rock system still maintains a stable state, the reversible elastic strain energy in the rock system gradually accumulates, the energy behavior continues to be energy storage, and its ability to store energy is further enhanced. As Ks gradually decreases, the degree of steady state increases gradually while the stability increases gradually. Ks reaches the minimum value under the action of large impact loading, and ud/uk is also the minimum value at this time, while the energy storage capacity of the sample gradually increases. The turning point occurs when the loading rate is 2800 GPa/s for the specimens with a 0° flaw, which indicates that the 0° crack rock has stronger impact resistance and needs more external energy to break the rock with the increasing loading rate, but its Ks has the same variation law of specimens with the 45° and 90° rocks. 2b1af7f3a8