Seisuke Okubo

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.

A study of the class II behaviour of rock

SummaryFirst, Class II behaviour of rock is discussed with a spring model. The model is characterized by non-uniform failure, which agrees qualitatively with common experimental observation, and shows not only class I but also class II behaviour depending on strength variation of springs.Focusing on the difference between class I and class II behaviour in actual rocks, unloading-reloading tests were conducted in the post-failure region. From the test results, it was found that for both class I and class II rocks, the elastic strain tends to decrease in the post-failure region as the loadbearing capacity deteriorates. The results also show that a remarkable difference between class I and class II categories is the magnitude of non-elastic strain. That is, if non-elastic strain increases faster that elastic strain decreases, then rock shows class I behaviour, and in the opposite case class II behaviour. In general, the non-elastic strain increases with confining pressure and in some cases, rock behaviour changes from class II to class 1 at higher confining pressure.

Control performance of servo-controlled testing machines in compression and creep tests

Abstract Control performance of a closed-loop servo-controlled testing machine is discussed analytically and numerically. A simple model of the servo-controlled testing machine is proposed and the performance for a compression test is discussed. The control variable in this case is strain or a linear combination of stress and strain. Numerical simulation is also carried out assuming a non-linear rheological model which reproduces the post-failure behaviour of rock; this applies not only to Class I but also to Class II characteristics. The approximate required condition for stability of the system can be expressed by t 0 >1000· T v where t 0 and T v are the loading time to the strength failure point and the time constant of the servo-valve, respectively. Control performance in a creep test is also discussed analytically and numerically. via analytical discussion, it is found that the system is stable in the primary and the secondary creep regions, and unstable in the tertiary creep region. In the tertiary creep region, the stress or the force decreases with an increase in strain rate towards the final failure. Deviation from the true creep curve which can be obtained under perfectly constant load is calculated by computer simulation. The error is negligible if the residual life, that is, the time remaining to final failure, is larger than about 10 x T v .

Application of Weibull's theory to estimating in situ maximum stress σH by hydrofracturing

Abstract Hydrofracturing is a widely used and established method for rock stress measurement and is especially valuable at great depths. In conventional hydrofracturing (Haimson, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 15 (1978) 167), dealing with an axi-parallel fracture, the horizontal minimum stress σ h is obtained as the shut-in pressure and the maximum stress σ H is calculated from the breakdown pressure or reopening pressure. It has been pointed out, however, that σ H is not as reliable as σ h . This paper therefore presents a new approach for estimating σ H . In this approach the probabilistic aspects of tensile failure are considered as new sources of information, because the probability density of fracture direction may provide valuable information concerning the stress difference σ H − σ h . As the basic theory to describe the tensile failure of rock, we adopted the Weibull’s weakest link theory. The applicability of the theory is first verified via tensile tests on rock specimens of different shape and size, then the probabilistic approach is applied to hydrofracturing to give the probability function of breakdown and the probability density function for the fracture direction. The applicability of the proposed method is presented through numerical calculations and an example in which σ H − σ h is estimated from the probabilistic variability of the fracture direction.

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.

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.

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.

Simulation of Time-dependent Deformation of Visco-elastic Rock Mass around Mine Tunnel being induced by Face Advance.

Simulation of Time-dependent Deformation of Visco-elastic Rock Mass around Mine Tunnel being induced by Face Advance by Yoshihiro OGATA 1, Tsutomu YAMAGUCHI 1, Michio KURIYAGAWA 1, Seisuke OKUBO 2 and Yuichi NISHIMATSU 3 1. National Institute for Resources and Environmet, Onogawa, Tsukuba 305 2. Faculty of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113 3. Professer Emeritus, The University of Tokyo

CONSIDERATIONS ON THE CONSTITUTIVE EQUATION OF ROCKS

ABSTRACT Two types of constitutive equations can be used to simulate the time dependent behaviour of rocks. One of these is proposed supposing that the plastic strain increases, and another that the compliance increases. By either type of constitutive equations, time dependent behaviour where strain is monotonicaly increased or decreased can be well simulated. However, if load is once increased and then decreased, the calculated results are different between the two. In this paper, the time dependent behaviour such as loading rate dependency of strength is summarized and the fundamental requirements for a constitutive equation of rocks are given. Then, both types of constitutive equations are critically discussed.