Katsunori Fukui

Complete stress-strain curves for various rock types in uniaxial tension

Abstract A simple testing method in uniaxial tension was developed, and uniaxial tension tests of nine Japanese rocks were conducted together with uniaxial compression tests. A closed-loop servo-controlled testing machine was controlled by a method in which a linear combination of stress and strain was used as the feedback signal. It was found that the proposed testing method can be applicable for not only Class I, but also Class II mode failure in tension. Two interesting results were obtained in uniaxial tension: (1) A large amount of residual strength characterises the post-failure region; and (2) the shape of the complete stress-strain curve in tension is similar to that in compression.

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.

Three-dimensional Time-dependent Analysis of Rock by Finite Element Method.

A constitutive equation formerly proposed by Okubo et al for one- and two-dimensional analysis was extended to the three-dimensional. The constitutive equation was developed on the basis of the non-linear visco-elastic theory, and it was successfully applied to one- and two-dimensional problems such as long-term stability of circular tunnel. In the three-dimensional analysis, a constant volume-modulus was assumed, and analogy with equations by Levy-Mises and Prantl-Reuss was discussed theoretically. Comprehensive FEM analysis simulating constant-strain compression tests was carried out with tetrahedron, prism or brick elements changing number of elements, confinement of specimen ends, coefficient of variation of strength for each element and loading rate. The simulation was performed beyond the peak strength and the complete stress-strain curves were obtained for all cases. The three-dimensional results were analogous to the two-dimensional and conformed to the experimental results. For example, the peak and residual strengths were found to increase with loading rate.

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.

Large-scale penetration test using a drop hammer

In the present study, large-scale penetration tests using a wedge-type drop hammer were performed. The primary objective was to determine the penetration curve in a large-scale test. The force-penetration curve is well known to be approximately linear in small-scale tests. The secondary objective was to investigate the effect of hammer size on the force-penetration curve. Laboratory tests have shown that the strength of a rock sample decreases with its size. Thus, the apparent rock strength during a drop-hammer test likely decreases in relation to the size of the hammer.

Rheological Behaviour and Model for Porous Rocks Under Air-Dried and Water-Saturated Conditions

Most rocks exhibit viscoelastic properties or time-dependent behavior during deformation. For example, peak strength and Youngs modulus increase with loading rate in uniaxial compression tests. In the creep test, strain increases over time even though stress is maintained at a predetermined value. Such viscoelastic behavior is especially notable in porous rocks such as tuff and weathered rocks. In this study, we first present a brief review of the viscoelastic properties of porous rocks, and then propose a new rheological model based on constitutive equations previously proposed by the authors. The model consists of a spring and a dashpot. We assume that the constitutive equation described in a previous study can be applied to the spring. The viscosity of the dashpot is low prior to loading, and increases gradually with progressive loading. In creep testing at low stress levels, strain of the dashpot corresponds to creep strain because the spring constant does not decrease significantly at low stress levels. Experimental analysis of muddy sandstone, Oya tuff, Tage tuff and Kawazu tuff is compared with theoretical predictions. The measured and theoretical stress-strain curves are in good agreement. The increase in peak strength and Youngs modulus with loading rate is well simulated by the model. The most important result of this study is that even at low stress conditions, strain of the dashpot is considerably larger than considered in previous studies. Our model provides a sound simulation of the difference in Youngs moduli between air-dried and water-saturated conditions, where the difference is assumed to reflect the partitioning of strain into the dashpot. In water-saturated conditions, strain of the dashpot increases more rapidly than in air-dried conditions, and Youngs modulus is consequently relatively small.

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.

Size and Shape of TBM Debris Estimated by the Nishimatsu's Cutting- Resistance Equation

Information concerning the size and shape of tunnel boring machine (TBM) debris is essential for designing efficient loading, hauling and dumping systems for TBM excavation. It is also very important in deciding how to recycle the TBM debris. However, only very limited information is available at present, and theoretical or calculation methods to estimate the size and shape are still open to discussion. In this paper, the size and shape of TBM debris are estimated by the well-known Nishimatsus equation that is usually applied to roadheaders or shield-type machines with chisel bits. In this study, the equation was applied to the case of TBM excavation with disc cutters in which the shear failure or plane extends from a new groove to an adjacent pre-existing one. The estimated size and shape of TBM debris were found to be consistent with the measured results. Side forces applied to a disc cutter and the resultant stress on the cutter were considered. The maximum debris size encountered in tunnel excavation was also discussed assuming that it followed the Gumbel distribution. The results suggest that the proposed approach based on Nishimatsus equation shows potential for future study.