Subcritical Crack Growth In Rock Research Articles

Subcritical crack growth in sandstone in aqueous environment with different calcium ion concentration

Investigating the time-dependent fracturing in sandstone is crucial to consider the long-term integrity of a sedimentary rock mass surrounding structures. Subcritical crack growth is one of the main causes of the time-dependent fracturing in rock materials. For the long-term integrity, it is essential to investigate subcritical crack growth in rock, which is influenced by the surrounding environmental conditions. Numerous cementitious materials are used to construct various structures such as underground repositories for radioactive waste, underground power plants, etc. In these cases, the calcium ion concentration in the ground water in a rock mass surrounding these structures is high. Therefore, investigation on the subcritical crack growth in rock in water with a high calcium ion concentration is essential. In this study, subcritical crack growth in sandstone is measured in distilled water and calcium hydroxide solution (Ca(OH)2) to investigate the influence of calcium ions on the time-dependent fracturing in rock. Berea sandstone was used as a rock sample. The load-relaxation method of the double-torsion test was used to measure the crack velocity and the stress intensity factor. All measurements have been carried out under controlled temperature and relative humidity. It was shown that the crack velocity in a calcium hydroxide solution is lower than that in distilled water even though the pH was high. In previous researches, it has been considered that the crack velocity in rock increased when the pH was high from the measurements in water and sodium hydroxide solution (NaOH). Therefore, it is considered that calcium ion affects the decrease of the crack velocity. It is concluded that a water environment with a high calcium ion concentration is suitable for the long-term integrity of a sedimentary rock mass.

Evaluating long-term strength of rock under changing environments from air to water

It is important to understand time-dependent deformation and fracturing in rock to evaluate its long-term strength (LTS); subcritical crack growth (SCG) provides insight into the weathering of a rock mass over the long term. The LTS of rock is commonly evaluated under the same environmental conditions. However, in practice, the environment is constantly changing and must be accounted for in evaluating the LTS of rock. In this study, we developed a method to evaluate LTS under changing environmental conditions, with a focus on the influence of water on the LTS of rock. LTS decreased rapidly when the environmental conditions changed from air to water. In a case where the environmental conditions changed repeatedly from air to water at various duration intervals, the value of the LTS was similar to that in a continuous water environment. Because a dramatic decrease in the LTS occurred when the environmental conditions changed from air to water, we conclude that the effect of water on the acceleration of SCG in rock should be considered in the long-term use of rock structures.

Mass-Transport Process in Subcritical Crack Growth in Carrara Marble

Information of subcritical crack growth in rock is essential to ensure the long-term integrity of a rock mass surrounding various structures and various architectures made of rock materials. In this study, using Carrara marble as a rock sample, subcritical crack growth was investigated experimentally. Especially, the load relaxation method of the double-torsion test was used for all measurement under controlled temperature and relative humidity. It was shown that the crack velocity in air increased with increasing temperature. The crack velocity increased with increasing the stress intensity factor. However, we found a region where the increase of the crack velocity with stress intensity factor was not significant. It is also found that the crack velocity in this region increased with temperature. This is similar to Region II of subcritical crack growth observed in glass in air. The Region II in glass is controlled by the mass-transport to the crack tip. In the case of rock, the transport of water to crack tip is important. In general, Region II is not observed for subcritical crack growth in rock materials, because rocks contain water. Since the porosity of Carrara marble is very low, the contained amount of water is also very small. Therefore, it is considered that Region II is observed in Carrara marble. Since the crack velocity increased in the environment with higher temperature, it is concluded that the condition with low temperature in air is desirable for the long-term integrity of a carbonate rock mass. Additionally, it is concluded that mass-transport is an important process for subcritical crack growth in rock with low porosity.

Influences of electrolyte concentration on subcritical crack growth in sandstone in water

Information on subcritical crack growth in rock is essential to ensure the long-term stability of structures in a rock mass. Subcritical crack growth in rock is known to be affected by its surrounding environment. In most cases, rock found underground is saturated by water. The underground water can be fresh water or salt water with variable electrolyte concentrations. However, the influence of electrolyte concentration on subcritical crack growth in rock has not been fully elucidated. In this study, subcritical crack growth in Berea sandstone and Shirahama sandstone was measured when saturated with distilled water and with sodium chloride solutions of differing concentrations. Crack velocity in Berea sandstone changed very little with different electrolyte concentrations. By contrast, in the Shirahama sandstone, crack velocity became lower with increased electrolyte concentrations up to 1.0mol/l. With increasing electrolyte concentration, the width of the electric double layer on the surface of mineral grains decreased, which caused a decrease in the repulsive force acting on the crack surface, leading to a decrease in crack velocity up to concentrations of 1.0mol/l. However, when the electrolyte concentration was higher than 1.0mol/l, crack velocity increased due to the nucleation of microscopic defects on the boundary between clays and stiff mineral grains. Thus, electrolyte concentration affects subcritical crack growth by decreasing the width of the electric double layer and the condensation of clay minerals.

周辺環境の変化を考慮した岩石のサブクリティカルき裂進展に基づく長期強度の評価

It is important to evaluate the long-term stability of rock materials for the purpose of ensuring the long-term integrity of structures in a rock mass. In this study, we showed an evaluation method of the long-term strength of rock considering the change of the surrounding environmental conditions. It was shown that the long-term strength of rock decreased remarkably when the environmental condition changed from air to water condition and from low temperature to high temperature condition. This is due to the acceleration of subcritical crack growth in rock, because the relationship between the crack velocity and the stress intensity factor for subcritical crack growth is dependent on the temperature and existence of water. It is also recognized that the values of long-term strength of rock are affected significantly by the highest temperature and water if the rock can be surrounded by water. It is concluded that the long-term strength of rock under water environment with high temperature is important for ensuring the long-term integrity of structures in a rock mass.

Effects of relative humidity and temperature on subcritical crack growth in rock

In order to ensure long-term stability of structures in a rock mass, the study of time-dependent fracturing is essential. We have therefore investigated the effects of relative humidity and temperature on subcritical crack growth in rock experimentally on samples of Kumamoto andesite, Oshima granite, Berea sandstone, Shirahama sandstone and Kushiro sandstone using the Double Torsion method. All experiments were conducted in moist air. Our results show that, in experiments conducted under the same relative humidity, crack velocity in igneous rocks increased with increasing temperature, in agreement with previous studies. On the other hand, the change of the crack velocity in sandstones at a given stress intensity factor was unclear when the temperature increased under a constant relative humidity in air. Our results also show that, in experiments conducted at the same temperature, crack velocity increased dramatically with increasing relative humidity. This increase is much larger than that expected from the conventional concept based on the theory of stress corrosion. The increase of the crack velocity was larger for sandstone which contained larger amount of clays. We conclude that subcritical crack growth in rock in air is affected remarkably by the relative humidity and the existence of clays.

Subcritical crack growth in rocks under shear loading

[1] In this study, the subcritical crack growth parameters for Coconino sandstone under modes II and III loading were determined experimentally by using the constant stress rate test. We extend the constant stress rate test technique to modes II and III subcritical crack growth in rocks. The experimental results of the modes II and III tests, combined with mode I results published elsewhere, show that the values of the modes I, II, and III subcritical crack growth parameters are very similar to each other regardless of the loading configuration and the specimen geometries. The main reason for this is thought to be that subcritical crack growth is environmentally induced crack growth rather than the mechanical rupture of bonds. The effect of confining stress, specimen size, and water saturation on subcritical crack growth under mode II loading has also been investigated. The parameter n linearly increases with increasing confining stress and the parameter A exponentially decreases with increasing confining stress. Increasing the specimen size results in a linear increase in the subcritical crack growth parameter A. But, the parameter n is independent of the specimen size. The parameter n is almost constant regardless of water saturation, and the parameter A is found to increase slightly when the specimen is fully saturated. These results suggest that the subcritical crack growth parameter n can be considered a material constant for a given rock type.

Subcritical crack growth in rocks in an aqueous environment

Subcritical crack growth is one of the main causes of time-dependent fracturing in rock. In the present study, we investigated subcritical crack growth in rock in distilled water (pH = 5–7) and in an aqueous solution of sodium hydroxide (NaOHaq, pH = 12), comparing the results to those in air. We also investigated the effect of the pH in an aqueous environment. We used andesite and granite for all our tests. We determined the relationship between the crack velocity and the stress intensity factor using the double-torsion test under conditions of controlled temperature. We showed that crack velocities in water were higher than those in air, in agreement with other research results indicating that crack velocity increases in water. When we compared our results for NaOHaq with those for water, however, we found that the crack velocity at the same stress intensity factor did not change even though the pH of the surrounding environment was different. This result does not agree with the accepted understanding that hydroxide ions accelerate subcritical crack growth in rocks. We concluded that the pH at the crack tip influences subcritical crack growth, and not the bulk pH, which has little effect.

火成岩のサブクリティカルき裂進展に及ぼす湿度の影響

The effect of the humidity on subcritical crack growth in igneous rock in air was investigated experimentally. Rocks used in this study were Kumamoto andesite and Oshima granite. Double-Torsion method was used in this study to measure the crack velocity and the stress intensity factor. All experiments were conducted under the same temperature and different relative humidity to investigate the effect of the humidity.It was shown that the humidity affected the crack velocity strongly. The crack velocity increased with the increase of the humidity. The crack velocity increased by 1 ∼ 4 orders of magnitude when the humidity increased threefold or fourfold. This increase is larger than that estimated from the classical stress corrosion theory. It is concluded that the humidity has the strong effect on subcritical crack growth in rock and the control of the humidity is important to prevent the weakening of rock.

緩亀裂進展による圧縮破壊―岩盤内の均質化亀裂進展（第５報）―

Compressive fracture process of rock under the uni-axial compression is discussed, as a result of the sub-critical crack growth in it. A numerical procedure for the failure prediction is presented and discussed, basing upon the critical pressure-crack elongation curve (pc - a curve) for the pure mode I crack propagation (KII = 0, KI = KIC) in the homogenized joint model, which is analyzed by means of the Stress Compensation-Displacement Discontinuity Method (SC-DDM). The crack elongation rate (da/dt) is formulated by the empirical equation of the form of da/dt ∝ KIn, where n: the sub-critical crack growth index. The applied stress-crack elongation curve (p - a curve) in the uni-axial compression test is analyzed to clarify the strain rate dependency of the macroscopic compressive strength (Sc), and the time-crack elongation curve (t - a curve) in the creep test of the uni-axial compression is analyzed to evaluate the effect of applied stress upon the lifetime (tF). It is concretely shown that the non-linearity of stress-strain curves and time-strain curves is deeply associated with the sub-critical crack growth in rock. Moreover the significant influence of heterogeneity and in-homogeneity of rock is discussed by presenting a parallel plate model to assess the damage effect and so on.

岩石のサブクリティカル亀裂進展に関する既往の研究と新たな展開

A review of studies of subcritical crack growth in rock is presented. First, theoretical background of subcritical crack growth is presented. It has been considered that the main mechanism of subcritical crack growth in silicate materials is stress corrosion under low homologous temperature and pressure. Next, theoretical background of stress corrosion is presented. Especially, the theoretical relation between the crack velocity and the stress intensity factor is described. Then, progress of the study of subcritical crack growth in silicate materials is presented by reviewing previous studies for glass, quartz, and silicate rocks. It has been clarified that the reactive species of stress corrosion is water and hydroxyl ion. For anisotropic rock, the crack velocity was dependent on the propagation direction and opening direction even at the same stress intensity factor.Finally, recent results of subcritical crack growth in rock are presented. It was clarified that the relation between the crack velocity and the stress intensity factor was decided by the crack opening direction. The crack velocity was higher when the temperature and the humidity were higher. It was shown that the activation energy became smaller when the crack path was smooth from the observation of the crack path.

Study of subcritical crack growth in andesite using the Double Torsion test

Abstract Subcritical crack growth is one of the main causes of time-dependent behavior in rocks. Double torsion (DT) tests have often been used to study subcritical crack growth in rocks. There are three methods used for the DT test, each with different loading conditions: the constant load (CL) method, the constant displacement (CDR) method, and the load relaxation (RLX) method. The RLX method is convenient, because the wide range of data of subcritical crack growth can be obtained with a single experimental run. In this study, subcritical crack growth in andesite was investigated using RLX method of the DT test. To determine the appropriate shape for the guide groove in DT specimens, tests were performed using rectangular, semi-circular, and triangular section grooves. The level of reproducibility of the test results was highest for specimens with a rectangular groove. Hence, this is an appropriate guide groove shape for DT specimens. DT tests were also performed for different water vapor pressures to investigate the effects on subcritical crack growth. The results showed that crack growth was facilitated at higher water vapor pressures. Additionally, the activation energy for subcritical crack growth in andesite was determined from the experimental results, and the crack velocity values for various temperature, humidity, and stress conditions were calculated theoretically. The crack velocity can be predicted from theory for various environmental and stress conditions.

岩石におけるサブクリティカル亀裂進展の組織・環境依存性

In order to make realize long-term stability of rock mass, it is necessary to study the time-dependent fracture problem in rocks.Subcritical crack growth due to stress corrosion is considered to be one of the key factors of the time-dependent behaviors in rocks. It is known that subcritical crack growth is affected by the environmental condition. Thus, it is important to research the dependence of subcritical crack growth in rocks on the environmental condition. Especially, water is known to be a corrosive agent of stress corrosion in rocks.In this study, Double Torsion (DT) test was carried out by using granite and andesite under various temperature and relative humidity, and the dependence of subcritical crack growth on water vapor pressure was investigated quantitatively.It was shown that subcritical crack growth in rocks was facilitated as water vapor pressure became large. For andesite, activation energy was estimated from the experimental results, and crack velocities under various temperature and water vapor pressure were calculated. The theoretical values of crack velocity agreed well with observed values.For granite, considering the dependence of subcritical crack growth on the crack density of pre-existing microcracks as well as the dependence of water vapor pressure, crack velocities were calculated theoretically. The theoretical values were consistent with observed values very well. It is concluded that crack velocity can be predicted by considering the environmental condition and the crack density of pre-existing microcracks.

花こう岩における応力腐食による亀裂進展現象の異方性および粒径依存性

Subcritical crack growth is considered to be a source of the time-dependent fracture in rocks. Thus, it is very important to know the nature of subcritical crack growth in rocks. Although rocks are generally anisotropic, rocks have been assumed as isotropic materials in many studies. Therefore, anisotropic properties of subcritical crack growth in rocks are not known well. In this study, Double-Torsion test was carried out using three kinds of granite to investigate the anisotropic properties and the grain-size dependency of subcritical crack growth. Double-Torsion specimens were prepared from each granitic rock with considering the propagation direction and the opening direction of the crack.It was shown experimentally that the subcritical crack growth behavior in granite was anisotropic. When the crack advanced parallel to RIFT plane, the stress level at the crack tip was the smallest in all granite used in this study. Additionally, the stress level at the same crack velocity was in good agreement when the opening direction of the crack was the same.It was also indicated that subcritical crack growth in granite was dependent on the grain size. For coarser grained granite, the stress level causing crack growth tended to be lower than that of fine-grained granite.It could be considered that anisotropy and grain-size dependency of subcritical crack growth in granite related to the preferred orientation and the density of pre-existing microcracks, because it was recognized that as the velocity of P-wave propagating in the opening direction of the crack was low, that is, as the crack density of granite was high, the stress level causing subcritical crack growth was low. It can be concluded that the subcritical crack growth behavior in granite is affected strongly by the orientation distribution of pre-existing microcracks.

Growth of geologic fractures into large-strain populations: review of nomenclature, subcritical crack growth, and some implications for rock engineering

Several aspects of fracture arrays are reviewed briefly and discussed. The terminology applied to progressive or multi-stage brittle deformation in rock masses is improved by noting fundamental mechanical differences in fracture type and the kinematic coupling between dilatant mixed-mode crack displacements and wing cracks developed at the fracture tips . An array of initially mixed-mode (I–II) cracks will evolve under remote tensile least principal stress and with increasing strain to a dilatant, mode-I crack array oriented approximately perpendicular to the remote tensile stress. This progressive fracture growth thus defeats predictions of fracture-set orientation and displacement based only on a Mohr circle estimate of initial elastic stress (valid in the rock mass only at the earliest stages of fracture nucleation). Slow, subcritical crack growth in rock is associated with distinctive changes in fracture population geometry, as shown by published numerical simulations of fracture–network evolution. An increase in the stress corrosion index promotes joint clustering and significant changes in joint length–frequency that may lead to characteristic differences in the statistics of large-strain fracture populations. These geometric clues can be used to refine estimates of strength and deformability of rock masses and to infer classes of physico-chemical processes acting at the fracture tips during the development of the fracture population.

Slow crack growth in minerals and rocks: Theory and experiments

Strength and mechanical behavior of rocks and minerals are modified by aqueous environments. This results in two effects: mechanical and chemical. The chemical effect is investigated from both a theoretical and an experimental point of view. It is shown that a thermodynamic approach leads to a satisfactory understanding of the chemical effect through an ‘extended griffith concept’. Predictions of the model have been tested using slow crack growth experiments. The experiments have been performed with a special Double Torsion apparatus which was built for this purpose. The good agreement observed between theory and experiments suggests that subcritical crack growth in rocks is controlled by adsorption onto the crack tip. This result was previously suggested by other authors (Dunning et al., 1984). However, the important consequences of the model are that (1) there should exist a threshold stress below which subcritical crack growth stops, and this threshold depends on the environment; (2) subcritical crack growth and time-dependent phenomena could take place in the crust in a stress interval which could be as high as 50% of the rupture stress.