A brief introduction is given in this paper of some of recent researches in rock mechanics in mining both at home and abroad. To provide information of fundamental importance explanation is given of stresses and strains in homogeneous elastic ground and also in anisotropically elastic ground, of the theory of brittle fracture of rock, of the meaning of shear stress, of the comparison of static and dynamic properties of rock, the barodynamic tests, and of the model test of underground cavities. For technical purposes introduction is given to the instrument used for civil engineering and mining purposes to measure accurately the travel time of elastic waves, to the crack coefficient and ground soundness, to the use of sonic techniques to explore cracks and fracture, and to the techniques of measuring the earth's pressure. Concerning the rock fracture, explanation is given of Griffith's theory of brittle fracture and the modified theory accounting for the effects of closure of the Griffith cracks in compression. Equation (7) is the Griffith's fracture criterion, that is the relationship between the major principal stress σ1 (Fig. 1) at fracture, the principal stress ratio k1 and the uniaxial tensile strength of the material σt. The resulting fracture criterion for a brittle material in which crack closure has occurred is given by equation (8). By measuring the principal stress changes and the direction (p, q and θ) with respect to the original principal stresses (σ1, σ2), the final principal stresses and the direction (σ1', σ2' and α) can be calculated by using equation (11). The relationship between the stresses on rock (principal stresses, S and T) and the deformation (U1, U2, U3, 60°respectively) of a borehole diameter (d) is given by equation (12). Therefore, we can calculate the absolute principal stresses (S and T) in rock by measuring the deformation (U1, U2, U3) of a borehole diameter (d) accompanied by the relaxation method.
In the field of civil engineering in Japan particular attention has hitherto been paid to rock mechanics mainly in relation to the problems on dam foundation. In 1960, the first study group on rock mechanics was organized, and its 1st symposium was held in 1962 at which the engineers concerned, including tunnel and soil engineers attended. The 2nd symposium was held in 1963 under the auspices of the above mentioned study group and was reorganized into a“Committee for Rock Mechanics of the Japan Society of Civil Engineering, ”with about 50 members concerned. This committee is currently divided into five divisions where valuable and zealous discussions and presentation of study achievements are made once a month. This paper explains briefly the methods actually used and the recent representative studies concerning rock mechanics in the field of civil engineering in Japan, which covers extremely diversified problems such as on combination of applied geology with rock mechanics, on various observations in situ and their interpretation, on analytical and model studies, on foundation treatment of real structures, on water movement in fissured rocks, and so on.
The study of mechanical properties of rocks enables us to understand properly the conditions under which earth's phenomena such as earthquakes, volcanism, orogenesis and tectogenesis take place. These phenomena are believed to occur due to physical processes such as mechanical and thermodynamical as well as physico-chemical processes in the earth. It is very important therefore to elucidate the mechanical properties of the constituent material of the earth, that is, rocks. Stresses set up in the earth are mostly based on the body forces, arising from the gravitational field, and they appear through the processes of deformation of rocks. The study of mechanical properties of rocks in earth sciences is based on the solution of the broad problems associated with the earth's phenomena as mentioned above. In a wider sense, it is the aim of the study to obtain the characteristic features of rocks counteracting the stresses. These characteristic features appear in elasticity, viscosity, plasticity, creep deformation, fluidity, yield strength, and fracture. The present paper deals with an outline of the recent developments in this mechanistic investigation in connection with the field of earth sciences. Rock is the aggregate of various kinds of minerals, and its properties depend not only on the properties of minerals themselves, but on the aggregate state of the minerals, namely, the properties of mineral boundary and rock mass structure. Consequently, these properties are considered to change according to the physical condition of the rock mass or the experimental methods. In earth sciences, however, the various results achieved by the experimental methods which are adequate to the solution of the present problems are synthesized through discussion. The study is in progress so as to use these results for a quantitative understanding of the conditions under which physical processes may occur in the earth. As a matter of cource, it is necessary to investigate the irreversible processes such as melting, recrystallization, or chemical change in the earth as well as the physical properties as mentioned above for full understanding of the earth's phenomena. The present paper is divided into four sections. Section 1 is introductory, and in Section 2 is given the present state of experimental conditions for rock deformation. In Section 3 are described the rock deformation under the low stresses of short period, the elasticity and attenuation of elastic waves. The velocity of elastic waves in rocks under high pressure and the anisotropy of rocks based on the wave propagation are discussed in connection with the estimation of the rock type below a Moho-discontinuity. In Section 4 are discussed rock deformation under the stresses of long period, the general deformation, creep, ductility, strength, fracture, and viscosity. The occurrence of earthquake is especially discussed not only on the basis of the fracture of rocks, but also from the point of view of transition from brittle to ductile in rocks. The hypotheses of earthquakes are also described. Rocks are structurally and chemically complicated, heterogeneous, anisotropic, and deformable, involving various elements affecting their properties. Regarding the conditions of rocks inside the earth, the temperature range is in the order from near zero to 103 degrees, and pressures from a small fraction of a bar to 106bar, and strain rates from 103sec to 10-15sec. It is not possible to make experiment of all these cases to investigate the state of rocks with such variables in broad band and their behaviors in the field of their aggregation. Accordingly, in order to obtain the quantitative, rather than phenomenological, understanding of the earth's phenomena
The states of stress and deformation of foundations rock and of tunnels as well as the stability of rock slopes have been studied extensively in rock mechanics in these days. The study of rock mechanics includes at present the investigation not only of the mechanical behaviours of rock cores but also of rock masses and of rock structures. The experimental investigations in rock mechanics require the core tests and the model tests in the laboratory and the rock tests in-situ. The model tests have until recently been carried out extensively by using various materials and by application of various measuring techniques, and in consequence of improvements so far made both in the line of the material and in the line of the technique the photoelastic methods have come to play an important role in rock mechanics. The main subjects of investigations by the photoelastic method have been the rupture phenomena of rock cores, the stress states in the foundation rock, the elastic and plastic states of stress and the propagation of rupture zone around the tunnel or the adit, and the mechanism of progression of crack. The photoelastic method has been in practice in-situ in field measurements, and its new applications are under consideration. The photoelastic method developed in this way makes it possible to know better about the mechanical properties of the foundation rock and the earth pressure phenomena, and it renders greater help to planning wiser design of rock structures. From this point of view, the recent photoelastic investigations in rock mechanics according to the corresponding techniques are summarized here under. The photoelastic investigations in rock mechanics explained herein are conveniently divided in two, the study in the laboratory and the study in the site. The techniques in the former contain (1) the two-dimensional method by using transparent models, (2) the stress freezing method, (3) the centrifugal photoelastic method, (4) the method by using soft photoelastic materials, (5) the method for orthotropic models, (6) the photoelastic coating method and (7) the method for pulverulent models. In the latter, the bodies to be measured, such as the concrete linings and the rock of the tunnels or the adits and the steel supports, get the photoelastic pieces embedded in them or glued on their surfaces.
Although surfacial rocks appear brittle, the earth's crust the large aggregate of rocks is supposed to be very viscous. In the realm of rock mechanics, however, the aspect of plasticity cannot be overlooked. Rock deformations that accompany any kind of failures or fractures are declaredly plastic. Fine slips and incipient failures of rocks may take places where locally concentrated stresses satisfy the yielding condition, while the apparent general stresses are consistently below the elastic limits. The crypto-plastic flow as a result of such minor slips in the geological materials throw many problems not yet settled. In a polycrystalline rock, boundary surfaces of grains are obstructive for moving inside dislocations and apt to concentrate local stresses matchable to the yield values. Similar concentration processes may occur in the matrices of sedimentary rocks regardless whether the cementing substance is a solid mineral or adhesive water. Brittle tensile fractures created in homogeneous fine-grained rocks exhibit uneven surfaces with special patterns of (1) concentric undulations-conchoidal fractures, (2) radial striatures at right angles with the conchoidal waves-plumose fracture and (3) columnar fringes. Tension cracks under the high confining pressures show none of such figures. The so-called angle of internal friction is merely expressing increase in strength with increasing lithostatic pressure. The effect of pore fluid pressure upon the fracturing of rock is revised on the basis of plasticity theory. The lithostatic pressure or the grain to grain average rock pressure has been neglected hitherto. Reduced effective stresses are given in that the deviatoric stress minus the pore fluid pressures. The Berea Sandstone under the total given hydrostatic pressure-lithostatic pressure plus pore water pressure=2kbar-is perfectly plastic with a material constant k0=2.2kbar, but the rock yields at k*=k0-pore water pressure. The value of k0 increases with increasing total pressures. If all the principal values of reduced effective stress are tensile, the porosity increases contrary to the triaxial compression. Strain hardening is revealed at higher confining pressures than that corresponding the fixed value of pressure, while thixotropy is evident below. Most of the subconsolidate sedimentary rocks that are indurated by means of adhesive water are perfectly plastic even at very low confining pressure. In a simple compression test of a clay cake as a model of a large sedimentary body, there will appear a symmetrical pair of stationary surfaces dividing a central plastic region and two non-plastic prisms at the both ends. The stationary dividing surface is named ∏ surface. The intercalary plastic region between the two opposite ∏ surfaces are by no means entirely plastic during the initial stages of loading, but only certain outside parts in the test piece behave plastically. The plastic parts grow rapidly under increasing load. The moving surfaces of these parts named Σ are plastic wave surfaces, over which not all of jumps of the first derivatives of velocity and stress vanish. Plastic shock wave front Σ* as well as Σ propagates with the speed same as that of elastic shear waves. Seismic effects of such plastic waves are themes of paramount interest. Γ surfaces are another set of singular and characteristic surfaces. If the slip discontinuity across ∏ tends to infinity, the surface develops into a fault. The miscellaneous descriptions and statements given in the above lines automatically suggest many items to be worked out.
In order to understand the underground earth pressure phenomena in competent rock, it will be essential to clarify the stress around the underground openings. This stress depends upon various conditions such as the original state of stress, the shape and size of openings, the mechanical properties of rock and so on. Therefore it may be hard to evaluate the stress under all possible conditions. A number of investigations have hitherto been carried out on the stress around the underground openings, but they have so long been undertaken on the premise that the ground is perfectly elastic and that the original state of stress was rather simple. Measurements of stress in the rock around the underground openings, show however, that the original stress was threedimensional and the principal stresses did not always take vertical and horizontal directions. Therefore the authors have attempted to analyze the stress under such an original state of stress. The theoretical study has shown that at least five kinds of photoelastic experiments are necessary to evaluate the stress around each opening, no matter what the original stress state may have been. Three of them may be two-dimensional photoelastic experiments, but the remaining two must be three-dimensional. When the direction of one of the principal stresses in the original ground coincides with the direction of the axis of a drift, we need only three kinds of two-dimensional photoelastic experiments. From each experiment we can determine a stress coefficient for any point in the model. The stress components at any point in the model can be expressed in terms of these stress coefficients whatever the original state of stress may have been. Necessary photoelastic experiments have been carried out to find stress coefficients at several points on the wall surface of drifts having several shapes of cross section. For drifts with three kinds of rectangular cross section, five stress coefficients have been determined at several points on the wall surface of each drift, and for drifts with other five kinds of cross section, three stress coefficients have been determined. They are all tabulated. As for the stress around a circular opening such as a circular shaft, drift or a bore hole, such strict analysis as had never been contemplated has been attempted, and the authors have succeeded in obtaining a general expression for each stress component. Meanwhile to succeed in maintaining the earth pressure control during the operation of mining massive deposits, it is required to estimate the stress concentration in the pillars. Since the shape and arrangement of the rooms and pillars are various, it is extremely difficult to establish any strict formulas for use to find the stress. The authors have, however, proposed approximate formulas on the basis of the results of photoelastic experiments carried out by themselves. All the results of investigation described above hold true, provided that the ground is perfectly elastic, that the stress induced around the openings is comparatively small and is therefore within the elastic limit of the rock. If, however, the stress exceeds this limit, the results of investigation must be duly corrected. Model experiments as well as theoretical investigations have been carried out to find on what condition fracture will appear in the rock around the underground openings. It has been found that tensile fracture will take place wherever half the tensile stress computed on the assumption that the rock is perfectly elastic reaches the tensile strength of the rock, whereas compressive fracture will take place wherever 0.95 times the compressive stress computed under the same assumption reaches the compressive strength of the rock.
Several instruments have hitherto been deviced for use to measure the stress in rock or concrete constructions. The authors have, however, attempted to develop a new instrument for the same purpose based on photoelasticity. This instrument has proved suitable for the measurement of stress variation over a long period of time, though it is not available for remote measurement. The principle to determine stress by this instrument is as follows: A glass gage is fixed tightly in a cavity on the surface of a body whose stress variation is to be measured. When there takes place any variance of stress state in the body, there appears some stress in the gage, which is determined by a polariscope. There is a definite relation between the stress variation in the body and the stress that occurred in the gage. Therefore we can determine the former from the latter. Three kinds of gages have been designed and subjected to test, and it has been found that a hollow cylindrical gage is best suited. The polariscope designed for use in this stress measurement is of portable reflection type, about 500gr in weight, furnished with a detachable compensator. For the light source, the white light from a miniature bulb is used. The stress state in a hollow cylindrical gage caused by the change in stress in the body has been analyzed by the theory of elasticity. Assume that a gage was fixed to a body which was then free of stress but now be in a two-dimensional stress state with p and q as the principal stresses, it will now be easy to realize that the gage is in a complicated state of stress. From the results of analysis, the contours of equal values of principal stress difference have been determined and illustrated in Fig. 4, assuming that the ratio of the outer to the inner radius of the gage be 6:1, the Young's moduli of the body and the gage be respectively 2.1×105 and 6.3×105kg/cm2 and the Poisson's ratios of both be 0.2. It is readily noticed from these figures that the stress pattern depends upon the ratio as well as the magnitudes of p and q. Further analysis has shown that the Poisson's ratio of the body affects a little of the stress in the gage. From these results of analysis the most convenient way to find p and q has been studied to obtain the following method: From the shape of stress pattern the directions as well as the ratio of p and q are determined by consulting with Figs. 5 and 6. The magnitude of q can be found from the color of the isochromatics which pass certain definite points. The determination of p and q can also be conducted by manipulating the compensator installed on the polariscope. At the end of analysis, assuming that a gage was fixed to a body which was already in a certain state of stress, the relation among the initial and final stress states and the measured stress has been discussed. Long experience in using this instrument for determining stress variation in rock has shown that it has several advantages, e.g. it is suitable for measurement over a long period of time; it enables us to determine p and q by observing only one gage; the elastic constants of the body have less influence upon the results and the record of measurement can be kept as a color photograph.
A report is made in the present study of the measurements that were made of the stress waves and the accompanying particle velocities of rock particles in the cylindrical rock specimen caused by the detonator's attack and also by the explosive's attack. First the results were analyzed mainly from the standpoint of the compressibility of rock under impulsive high pressure, and some examples of the Hugoniot equation of state of rocks under comparatively low and high pressure obtained by authors' experiments are shown together with those obtained by others. It has been concluded in consequence of the above mentioned analysis that the compressibility of rock under comparatively low pressure, such as in the case of detonator's attack, has generally the linear relationship with pressure but the compressibility of rock under high pressure, such as in the case of explosive's attack, does not always have such linear relationship with pressure, but shows peculiar characteristics according to the individual physical properties of the rock in question. Secondly, the maximum pressure produced at the boundary between explosive and rock by a collision of the detonation wave has been considered, and it has been shown how the magnitude of this maximum pressure can be affected by the dynamic characteristics of rock, especially by the compressibility of rock.
The mechanical behaviors of rocks under various loading-rates which ranged from 1×10-2kg/cm2/sec to 12×105kg/cm2/sec, have been investigated in this paper. The higher rates of loading have been obtained by the use of a drop-hammer testing machine, while the lower rates of loading have been obtained by the use of a hydraulic testing machine. In the case of the high-speed loading test, which is undertaken for the purpose of comparing it with the low-speed loading test, the shock waves should be eliminated perfectly, so as not to expose the rock specimens to impact loading. Or the rock specimens would only be definitely exposed to an elastic pressure. From the above consideration, a new drop-hammer testing machine has been designed. It consists of an anvil, a drop-hammer and a cylindrical dynamometer. The anvil weighs about 800kg and is mounted on four dampers. The drop-hammer weighs about 40kg, having a damper in its body. On the other hand, the dynamometer is equipped with eight resistance-type wire strain gauges. From the test, the following results were obtained, using sandstone, marble, or cementmortar. (1) The compressive strength of rocks increases with the loading-rate, sandstone at the rate of about 1.6 in respect of the ratio of the high-speed compressive strength to that of low-speed, marble at the rate of about 1.9, and cementmortar at the rate of about 1.5. In these cases, the average loading-rates of the high-speed test are about 3.0∼12×105kg/cm2/sec, and the average loading-rates of the low-speed test are about 9.5∼10×10-2kg/cm2/sec. Also, the values of the secant modulus of elasticity of rock increase with the loading-rate. Poisson's number of each rock decreases with the increase of the compressive load, but Poisson's number on the same compressive stress has a tendency to increase as the loading-rate. (2) The compressive strength of rocks increases with the strain-rate; for instance, the relation between the compressive strength and the strain-rate of marble is expressed by σd=730+26logvd/v0+2.6(logvd/v0)2.12 where σ0: strength in the low-speed loading test (kg/cm2) σd strength in the test of voluntary loading speed (kg/cm2) υ0: strain-rate in the low-speed loading test υd: strain-rate in the test of voluntary loading speed (3) The strength and the secant modulus of elasticity of rocks in the tension test increase with the loading-rate; for instance, the ratio of the high-speed tensile strength to the low-speed one is about 2.1, and the ratio of the modulus of elasticity in the high-speed test to that in the low-speed test is about 2.5 for marble. In these tests, the average loading-rates of the high-speed test are about 2.7×104kg/cm2/sec, and the average loading-rates of the low-speed test are about 9.9×10-3 kg/cm2/sec.
Hard rocks on the earth's surface are frequently observed at places as severely deformed and folded without fractures. How much would rocks flow under how large external forces through how long period of time of their application? The present experiments have been intended to answer this question. As for the rocks of the test-piece materials, granite was employed that forms the upper layer of the crust under the continents. Two large test-pieces of granite from one block were shaped into straight beams of 215cm length with rectangular cross-sections of 12.3cm width and 6.8cm thickness. These two test-pieces are separately mounted freely on end supports of blunt knife-edges at a distance of 210cm, which are made of granite quite similar to the materials of the test-pieces. One of the two test-pieces called the unloaded beam bends under its own weight and the other called the center-loaded beam does under its own weight plus an extra center-load of 22.06kg. The maximum bending stress produced in the unloaded beam is 12.8kg/cm2 and that in the center-loaded 24.8kg/cm2. The experiments started on August 7, 1957. Since then, the experiments have been continued and until today (end of Feb., 1965) a time of seven and a half years has elapsed. Our experiments are the experiments that shall be carried on without end. For finding vertical displacements of 11 measuring points at the upper surface of each of the test-pieces on end supports that would continue its secular bending, a dial guage of 0.01mm/div is used to measure vertical coordinates of them which slides along a straight steel beam (SSB) of 103cm length which is horizontally placed in the middle portion of the upper surface of the test-piece with SSB's three legs at fixed points. When the measurements are not performed, SSB is removed from the test-piece. Prior to the commencement of these measurements, the test-piece was mounted horizontally on two supports specially positioned as shown in Fig. 4 to produce no appreciable elastic bendings and the initial values of the vertical coordinates of the measuring points were found. Influences upon the measurements of those vertical coordinates that should be produced from the circumstance that SSB might not be set constantly in each of the continuing experiments are obtained to get corrections, and also the corrections due to additional displacements of the measuring points by mounting SSB are likewise determined from a measurement by a level of a small inclination of the test-piece produced at its end by the mounting of SSB. This measurement of the small inclination of the test-piece enabled us to calculate instantaneous Young's modulus under a small stress of the test piece at the time of each experiment carried out on it. The results obtained for the first 7 years since the beginning of the experiments are as follows: (1) Since about 50 days after the beginning of the experiments, the upper surface of both test-pieces show very minute folds. They display gradual growth for the first 3 to 4 years since the beginning of the experiments and hereafter remain almost stationary until today. For both test-pieces the forms of the folds are unsymmetrical with respect to the central point P0, the wavelengths being much larger than the spacing of 10cm of the measuring points and the average amplitudes of the folds being in the order of 0.01mm. These folds may be seen as laboratory midget-models of synclinorium. The center-loaded beam shows stronger folds than the unloaded does. (2) Both test-pieces display very strange phenomena of sags that oscillate with time with periods differing from one year-temperature of the laboratory is kept constant within the range of±2°C but humidity is not done so and does annual changes. Analyses of these oscillating sags will be published in the next paper.
It happens occasionally that new slopes or tunnel walls fail due to swelling of mudstone or claystone in consequence of water sucked. In this paper, various mechanisms of such failures have been investigated, and their causes are classified into the following 3 main cases. (1) Deviatoric stress may have been generated in the mudstone or claystone due to the unisotropical expansion caused by the sucking of water. In order to examine the hypothesis stated above, some samples of mudstone from the deluvial layer situated about 180m beneath the surface of Osaka City and of claystone from Maibara Pass have been tested. In these tests, it has been shown that the swelling strain perpendicular to the bedding is larger than that parallel to the bedding. Accordingly, if the stress on the mudstone or claystone is decreased under a nearly confined state, the stress generated in the stone becomes unisotropical. If the deviatoric stress thus generated reaches the strength of the stone, failure takes place in the stone. This strain or stress due to the swelling increases with time, and the rate of increase can be estimated by applying the expansion coefficient of the rock. Moreover, the capability of sucking water of the mudstone or claystone has been measured by suction-measuring device. (2) The failure of the structure of the rock may have been caused by the local unequal expansion of the minerals contained and the fine seam of different materials. To observe the phenomena that have occurred in the rock when the rock has sucked water, micrometric expansive deformation will be measured by means of a microscope. (3) The failure of the stone may have occurred in consequence of ununiform swelling due to the unequal distribution of sucked water.