Kimihiro Hashiba

Effect of Water on the Deformation and Failure of Rock in Uniaxial Tension

To design and construct underground structures, it is essential to understand the mechanical properties of rock in not only compression but also tension. It is well known that water is one of the important factors affecting the deformation and failure of rock. In this study, laboratory tests and numerical simulations were conducted to understand the effect of water on rock properties in uniaxial tension. In the experiments, a testing machine previously used for uniaxial tension tests in dry conditions was modified for tests in wet conditions. Using this machine, complete stress–strain curves from the pre- to postpeak regions of water-saturated specimens in uniaxial tension were obtained. The results for granite, tuff, and two types of andesite showed that the stress–strain curves in wet conditions have a lower initial slope and lower strength than those in dry conditions, and they are strongly nonlinear in the prepeak region. Comparing the changes in the results for uniaxial tension versus compression due to water, it was found that the reduction rate of uniaxial tensile strength was greater than that of uniaxial compressive strength, while the ratio between the reduction rates was almost constant for various rocks. In numerical simulations, the stress–strain curves in the prepeak region under dry and wet conditions could be reproduced by crack extension models under uniaxial tensile stress. Numerical analyses indicated that the nonlinearity of the stress–strain curves is probably due to the longer crack extension in wet compared with dry conditions.

Index of Loading-Rate Dependency of Rock Strength

To estimate long-term deformation and stability of underground structures, knowledge of the time-dependent behavior of rock is essential. It is well known that rock strength increases with an increase in loading rate (loading-rate dependency), strain increases under constant stress (creep) and stress decreases under constant strain (relaxation). It has been reported that such time-dependent behaviors under different loading conditions are closely related to each other. The constant n, which represents slow crack growth due to stress corrosion, has been used to formulate the loading-rate dependency of strength (Sano et al. 1981) and the relation between creep stress and lifetime (Wilkins 1981). Lajtai et al. (1991) stated that rock strength is proportional to the 1/ (n ? 1)-th power of loading rate and that creep lifetime is inversely proportional to the n-th power of creep stress. Hashiba et al. (2006) presented the results of strength and creep tests which demonstrated the relation concerning n. Okubo et al. (2013) collected the values of n for some Japanese rocks and reported that the value for Sanjome andesite was consistent in uniaxial compression, uniaxial tension, Brazilian tension, three-point bending and direct shear tests in dry conditions. Quantitative comparison of the time-dependent behaviors of various rocks is essential but difficult to do using stress–strain relations or creep strain curves. The abovementioned expression for n represents the degree of time dependency and is suitable for the comparison of rocks or testing conditions. Furthermore, Hashiba and Fukui (2013) considered the value of n as an index of time dependency and proposed a rock mass classification incorporating this value. Okubo et al. (2013) reported the values of n for only nine Japanese rocks, one Japanese hardpan and one Chinese coal. In previous studies many other researchers have provided a large amount of information on the loading-rate dependency of rock strength. In this study, the values of n were calculated from the published data for many rocks and obtained from laboratory tests for three rocks. The degree of time dependency was compared between various rocks and the effects of the testing conditions were examined with the aid of the data. In the latter part of this paper, the relationship between the time dependency, variability and size effect on rock properties is discussed from a theoretical viewpoint considering the values of n and simple hypotheses.

Time-Dependent Behaviors of Granite: Loading-Rate Dependence, Creep, and Relaxation

To assess the long-term stability of underground structures, it is important to understand the time-dependent behaviors of rocks, such as their loading-rate dependence, creep, and relaxation. However, there have been fewer studies on crystalline rocks than on tuff, mudstone, and rock salt, because the high strength of crystalline rocks makes the detection of their time-dependent behaviors much more difficult. Moreover, studies on the relaxation, temporal change of stress and strain (TCSS) conditions, and relations between various time-dependent behaviors are scarce for not only granites, but also other rocks. In this study, previous reports on the time-dependent behaviors of granites were reviewed and various laboratory tests were conducted using Toki granite. These tests included an alternating-loading-rate test, creep test, relaxation test, and TCSS test. The results showed that the degree of time dependence of Toki granite is similar to other granites, and that the TCSS resembles the stress-relaxation curve and creep-strain curve. A viscoelastic constitutive model, proposed in a previous study, was modified to investigate the relations between the time-dependent behaviors in the pre- and post-peak regions. The modified model reproduced the stress–strain curve, creep, relaxation, and the results of the TCSS test. Based on a comparison of the results of the laboratory tests and numerical simulations, close relations between the time-dependent behaviors were revealed quantitatively.

Literature survey and experimental study on the direct tension test on rocks

Direct tension tests are indispensable for obtaining an accurate understanding of the deformation and failure characteristics of rocks in tension. For this technical note, the authors collected original papers published in international journals and surveyed the previously reported methods and results of direct tension tests on rocks. Some important factors affecting the strength and stress–strain curve are discussed, such as the shape, size, anisotropy, and water content of the specimen; the loading rate; and the confining pressure. The relationship between the results of the direct tension tests and those of other tests also is discussed. Although various types of testing apparatuses have been adopted in direct tension tests on rocks, the dependence of test results on the apparatuses has not been investigated. In this study, direct tension tests were conducted using various testing apparatuses in seven laboratories. The results of the direct tension tests showed that direct tensile strengths were not dependent on the type of test apparatus used or whether a flexible linkage system was used. The results of the tuff in this study showed that the coefficient of variation of the direct tensile strengths is smaller than that of the Brazilian tensile strengths. Moreover, the results revealed that the coefficient of variation of the direct tensile strengths is comparable to that of the uniaxial compressive strengths of the tuff. The authors noted that to obtain the stress–strain curve from the pre-failure region to the post-failure region, it is necessary to conduct a test with a high-stiffness machine and without a flexible linkage system. This technical note summarized the results of the standardization activity by the authors in the Japanese Geotechnical Society.

New Multi-Stage Triaxial Compression Test to Investigate the Loading-Rate Dependence of Rock Strength

Compression tests for investigating the time-dependence of rock under confining pressures are time consuming and require more specimens than do uniaxial compression tests. In this study, a new testing method combining multi-stage confining pressure and alternating loading rate is proposed to investigate the loading-rate dependence of triaxial compressive strength from a small amount of rock sample. In the test, a small-size rock specimen 10 mm in diameter and 20 mm in height was loaded under a strain rate alternating between slow and fast and under a confining pressure increased once just after reaching the peak strength. Strengths corresponding to two strain rates and two confining pressures could be obtained from one specimen. The cohesion, angle of internal friction, and loading-rate dependence of strength from the data were consistent with those from the commonly used triaxial compression tests under a constant strain rate or constant confining pressure. The proposed test with a small amount of rock sample can reduce not only the time and cost but also the environmental load of sampling in situ.