It is well known that electromagnetic phenomena are often observed preceding earthquakes. However, the mechanism by which these electromagnetic waves are generated during the fracture and deformation of rocks has not been fully identified. Therefore, in order to examine the relationship between the electromagnetic phenomena and the mechanical properties of rocks, uniaxial compression and three-point bending tests for two kinds of rocks with different quartz content, granite and gabbro, have been carried out at quasi-static and dynamic rates. Especially, in the bending tests, pre-cracked specimens of granite were also tested. Using a split Hopkinson pressure bar and a ferrite-core antenna in close proximity to the specimens, both the stress–strain (load–displacement) curve and simultaneous electromagnetic wave magnitude were measured. It was found that the dynamic compressive and bending strengths and the stress increase slope of both rocks were higher than those observed in static tests; therefore, there is a strain-rate dependence in their strength and stress increase rate. It was found from the tests using the pre-cracked bending specimens that the intensity of electromagnetic waves measured during crack extension increased almost proportionally to the increase of the maximum stress intensity factor of specimens. This tendency was observed in both the dynamic and quasi-static three-point bending tests for granite.
Electromagnetic waves generated during the fracture of rocks have been studied across various fields for many years . Electromagnetic wave emission has various potential geophysical applications, such as research into the electromagnetic phenomena associated with earthquakes [2–9], investigation of the Earth's crust, monitoring cracks in rock deformation experiments [10,11] and so on. In order to elucidate the electromagnetic phenomena during fracture of several rocks, including granite and andesite, quasi-static compression tests were carried out and acoustic emission was also measured [12–16]. The majority of previous works concerning electromagnetic phenomena during the deformation and fracture of rocks have been performed under ‘static’ and ‘compressive’ loading. However, there are many mechanisms that may result in the electromagnetic phenomena generated from the dynamic or impact fracture of rocks. Examples of such fracture occurrences include earthquakes, volcanic eruptions  and the collision of a meteorite with the Earth. Therefore, it is quite important to investigate the electromagnetic emission induced by the dynamic or impact deformation of rocks.
At present, there are several physical models proposed to explain the universal features of electromagnetic wave generation. These models include the piezoelectric effect , e.g. quartz [19,20], electrification due to the scraping of crack surfaces , emission of electrons and charged particles from the fracture surfaces , movement of electric charges and so on. However, a complete theoretical explanation has not yet been given for the generation mechanism of electromagnetic phenomena. Recently, a series of uniaxial compression tests for three kinds of rock, i.e. quartziferous rock, sandstone and marble, were carried out under quasi-static and dynamic strain rates. It was found that clear transients in the electromagnetic waves were accompanied by rapid stress drop during compressive deformation and fracture, except for marble specimens, and the amplitude of the electromagnetic wave increased with the increase of the loading rate .
In order to examine the relationship between the mechanical properties of rocks and their electromagnetic phenomena, a series of uniaxial compression and three-point bending tests for two kinds of rocks with different quartz content, i.e. granite and gabbro, were performed. These tests were carried out not only at quasi-static but also at dynamic rates. During these tests, the stress–strain curves, load–displacement curves and the magnitude of electromagnetic waves from fracturing rocks were measured by using a split Hopkinson pressure bar apparatus and a ferrite-core antenna located close to the specimens. The mechanism of electromagnetic wave generation associated with the deformation and fracture of rocks was also considered.
(a) Materials and specimen
The materials used in this study are ‘biotite granite’ and ‘hypersthene-augite gabbro’, denoted ‘granite’ and ‘gabbro’, respectively. Polarizing microscope photographs of these rocks are shown in figures 1 and 2, respectively. The principal contents of both rocks are shown in table 1, which were estimated from the mode average of measurements of 400 points at 0.5 mm intervals in the x and y directions. As seen in table 1, the content of quartz in granite is about 18 times greater than that of gabbro.
The compression specimen is a cubic solid specimen with an edge length of h=12 mm and cross-sectional area A0=144 mm2, as shown in figure 3a. These samples were fabricated by wire cutting. The bending specimen is a rectangular solid specimen of length l=60 mm and with a square cross-section of an edge length h=12 mm (see figure 3b). Because the deformation of brittle materials is generally small, the two sides facing each other on which compressive or bending load is applied must be as parallel as possible. Opposing faces loaded during compression and bending tests were verified to be parallel within 1/1200 with respect to the feature size (e.g. a 10 mm-edged face may be canted by 1/120 mm relative to the distance defining the position from the opposing face). Bending specimens with a groove introduced into the centre by a diamond-bladed micro-cutter, as shown in figure 3b, were also prepared. The rocks usually involve many micro-cracks; therefore, we adopted the length of the groove as the pre-crack length, a0.
(b) Experimental set-up
To obtain larger electromagnetic signals, a slender antenna with a ferrite core, as shown in figure 4a, was located as close to the specimens as possible. The antenna consists of a ferrite bar of 180 mm length and wound approximately 200 times with 0.4 mm diameter enamelled wire. The tip of the antenna was installed a distance of 10 mm from the specimens’ side in compression tests and 3 mm in bending tests, as shown in figure 4b,c.
As shown in figure 4b, the upper and lower solid cylindrical anvils with 30 mm diameter were used for compression tests. For three-point bending tests, a bending jig with span L=50 mm was connected to the testing machine by screw (see figure 4c). In the case that a jig is made of a paramagnetic substance, its vibration induced by rapid unloading due to breakage of the specimen emits electromagnetic noise. Therefore, all jigs were made of non-magnetic stainless steel, SUS310.
Because the output from the antenna is extremely small in general, it is necessary to control the noise from the surroundings. Thus, a shield box was assembled using polymer boards with Permalloy sheets (thickness 0.1 mm) and tested by encasing the antenna and a specimen. A bandpass filter with a frequency band of 284–1000 kHz was used to eliminate high- and low-frequency noise after amplifying the output from the antenna to 100–1000 times by a differential amplifier. The reason for the choice of the frequency band, i.e. 284–1000 kHz, was that the band contained relatively less noise in our laboratory and has already been used for similar measurements in previous work .
(c) Quasi-static experiment
For the quasi-static compression tests, a hydraulic fatigue testing machine (Shimazu Servo-Pulser, 100 kN) was used. Its crosshead speed was 1.2×10−5 m s−1. Parallelism of the upper and lower compressive anvils attached to the testing machine was examined by using pressure-sensitive paper. For the quasi-static bending tests, a screw-gear-type testing machine (Shimazu Autograph, 5 kN) was used because the maximum load expected was not too large. The crosshead speed for static tests was 1.7×10−6 m s−1.
(d) Dynamic experiment
For dynamic compression tests and dynamic bending tests, the split Hopkinson bar apparatus as shown in figure 5 was used. The compression and bending jigs used in the quasi-static tests were also attached to the ends of the input and output bars for dynamic tests, as shown in figure 5b,c. The striker, input bar and output bar are made of SUS304 stainless steel whose lengths are, respectively, 400, 1470 and 970 mm. To measure the stress pulses, strain gauges were located at 862 mm from the impact surface of the input bar and 278 mm from the specimen bar interface on the output bar. The signals from the strain gauges were passed through bridge boxes and low-noise differential amplifiers (NF Co., 5305) and were finally recorded by a 12-bit digital storage oscilloscope (Yokogawa, DL850 V). To obtain a ramp pulse in the input bar, the impact surface of the striker bar was shaped into a slightly curved surface and thick paper with thickness of 0.5 mm was placed on the impact surface of the input bar.
An incident pulse σi caused by the collision of the striker, accelerated by compressed air, travels in the input bar and reaches the specimen. Part of the incident pulse passes through the specimen and propagates in the output bar as a transmitted pulse σt, and the remainder reflects and travels again in the input bar as a reflected pulse σr. When the force is balanced at both sides of the specimen during a compression test, the nominal stress σ, nominal strain rate and nominal strain ε can be calculated from the following equations: 2.1 where t is time and A, C and ρ are, respectively, the cross-sectional area, the velocity of the elastic wave and the density of the input and output bars. In a dynamic three-point bending test, the load P, the deflection rate and the bending deflection δ can be calculated from the following equations: 2.2 The numerical values used for this study are the elastic modulus E=1.97×102 GPa, ρ=8.03×103 kg m−3 and .
Typical applied stress waves observed in the input and output bars during a dynamic compression test are shown in figure 6a. From this figure, we can see that a controlled incident wave with gentle rising slope is obtained by the thick paper sandwiched as mentioned above. We can also expect that this controlled incident wave may avoid the higher mode of dynamic bending deformation in the specimen. The stresses at both sides of the specimen were obtained from the sum of the incident and reflected waves, σi+σr, and the transmitted wave, σt, as shown in figure 6b. These stresses coincide well; therefore, the forces applied on both sides of the specimen were evenly balanced during the test. From this, we can confirm the validity of using equations (2.1) and (2.2) for their respective tests.
3. Experimental results and discussion
(a) Stress–strain curves in compression tests
Typical stress–strain curves obtained from the quasi-static ( and dynamic (–3.3×102 s−1) compression tests for granite and gabbro are shown in figure 7a,b, respectively. In static data, the broken line just after the peak stress presents the jump of displacement record caused by the sudden release of strain energy absorbed in the testing machine when the specimen broke; therefore, the displacement could not be measured properly after the peak load. As the initial gradual increase in stress depends on the contact geometry between the jig and specimen surfaces, it is relatively difficult to decide clearly the starting point of deformation. Thus, the slope of stress in the initial deformation was extrapolated to the base level as shown in the inset in figure 7a. In all cases, the compressive stress increases almost linearly and the stress reaches a peak value while gradually reducing the rate of increase. This is because micro-failure may occur in the specimen. It is also found that the linearly increasing rate of stress observed in dynamic tests is much greater than that observed in static tests . This is also caused by the generation of micro-cracks in the rock. The strain-rate dependence of the increasing rate of stress was observed in a series of quasi-static compression tests for several rocks at various strain rates of 10−7–10−3 s−1 by Okubo et al . From our results, we can say that there is a strain-rate dependence of the increasing rate of stress even in the dynamic range of strain rate.
(b) Load–displacement curves in three-point bending tests
Typical load–deflection curves obtained from the quasi-static ( and dynamic (–1.6 m s−1) three-point bending tests are shown in figure 8a,b, respectively. A similar trend in the results of compressive tests can be seen, i.e. the slope of the load–deflection curves in the early stage of bending deformation increases with the increase of loading speed and the slope gradually reduces as it approaches the maximum load. The generation of micro-cracks may affect the application of increasing rate of load.
(c) Compressive and bending strengths
The compressive and bending strengths σcomp and σbend, respectively, are shown in figure 9. The height of the column represents an average value, and the two edges of the error bar indicate the maximum and minimum values obtained from three to seven specimens for each test. For simplicity, σbend was obtained from the following equation, which corresponds to the stress at the bottom of the central cross-section of the bending specimen in the elastic region: 3.3 where I is the moment of inertia of the cross-sectional area and Pmax is the maximum load from the bending tests. From the observation that the fracture surface of all specimens appears almost at the centre of the specimen, and that an incident wave with gentle rising slope was used for dynamic bending tests, the bending deformation from the first-order mode may be achieved. Therefore, the evaluation of the bending strength using equation (3.3) is quite reasonable.
From these figures, it can be seen that for both rocks, i.e. granite and gabbro, the dynamic compressive strength is about 1.1–1.3 times greater than that observed in quasi-static tests and that the dynamic bending strength is also greater than the static data. The bending strength is much smaller than the compressive strength; thus, the energy required for bending fracture is extremely small compared with that for compressive fracture.
(d) Electromagnetic waves observed
In figures 10 and 11, the electromagnetic wave–time curve and the stress–time curve observed in quasi-static and dynamic compression tests for granite are shown. In static tests, a relatively large signal received by the antenna was observed just before the drop in stress due to crushing of the specimen. In dynamic tests, the electromagnetic wave was initially observed in the reduced slope region of the stress–strain curve following the initial linear region, which resulted from the generation of micro-cracks in granite. Then, a relatively large signal received by the antenna appears during the decrease region of stress after crushing. From this, we can say that the generation of electromagnetic waves relates closely to the generation of micro- or major cracks. When comparing the two figures, it is found that the electromagnetic waves are mainly produced when catastrophic failure of rocks occurs, and a greater amplitude of the electromagnetic wave, i.e. the signal received from the antenna, is observed in dynamic tests than in static tests.
In order to examine the effect of quartz content on the generation of electromagnetic waves, the comparison of granite data with gabbro data is necessary. It should be noted that granite contains much more quartz by volume than gabbro, as shown in table 1. Figure 12 shows the electromagnetic wave–time curve observed in dynamic compression tests for gabbro with the stress–time curve simultaneously measured. Similar generation behaviour of electromagnetic waves to the results shown in figure 11 can be seen, although the magnitude of the received signal by the antenna is less than half those observed from granite. This means that the effect of quartz content is remarkable, i.e. a larger quartz content can be expected to generate electromagnetic waves of greater strength.
As mentioned previously, many explanations have been proposed for the generation of electromagnetic waves observed during the fracture of rocks. The theory of a piezoelectric effect of quartz [18–20] seems to be one of the most convincing theories, which our results of figures 11 and 12 support. It has also been proposed that the electromagnetic emission is caused by the electrification due to friction between crack surfaces contacting each other . The bending test is one of several suitable methods to investigate the accuracy of this theory. If this theory does model the behaviour as predicted, little or no emission should occur in three-point bending because bending fracture is basically mode-I fracture. That is, no friction between crack surfaces happens in idealized bending fracture. However, the crack path is usually a zigzag path instead of a straight line in rock fracture. Therefore, we cannot say definitively that three-point bending fracture does not include some rubbing of crack surfaces. Figures 13 and 14 show the results of dynamic three-point bending tests for granite and gabbro, respectively. Even in three-point bending tests, a relatively large signal received by the antenna can be observed. Electromagnetic emission of large amplitude appears in the unloading region after the maximum load. These figures show that the theory of a piezoelectric effect in quartz may be more reasonable and predominant than the frictional electrification theory. In addition, because it was previously demonstrated that electromagnetic emission could not be observed in the fracture of marble [12,23] and the intensity of electromagnetic emission depends on the content of quartz, as shown in figures 11–14, we can say that the theory of the piezoelectric effect of quartz is one of the most reasonable mechanisms for the electromagnetic emission generated in the fracture of granite and gabbro. Of course, several other mechanisms can still be considered in various different situations.
(e) Three-point bending test using granite specimen with pre-crack
From all the experiments presented above, it was found that the electromagnetic wave produced during the fracture of rocks, especially of large amplitude, was observed during unloading due to severe crack generation. Therefore, the unloading behaviour, i.e. crack growth during bending fracture, probably relates significantly to the generation of electromagnetic waves. This means that it is quite meaningful to clarify the relation between the occurrence of electromagnetic waves and the parameters of fracture mechanics, such as stress intensity factor or crack extension rate, because the manner of crack extension can be represented well by these parameters.
For this purpose, applying the compliance method to the results of three-point bending tests may be useful. In three-point bending with L/h=4 (L, span; h, height of specimen), the stress intensity factor K is given by 3.4 and 3.5 The error of these equations is less than 0.2% when ξ≤0.6. If we assume a plane stress state, the relation between the compliance λ and crack length a can be derived as follows: 3.6 If we assume that any points on the load–deflection curve obtained from three-point bending tests give the corresponding compliance λ, the corresponding crack length a can be obtained by using equation (3.6), although there is some complexity in the calculation.
The electromagnetic wave (i.e. the signal received by the antenna), the centre deflection of the specimen and the applied load obtained from a dynamic three-point bending test using a specimen with a pre-crack of 3.0 mm are shown in figure 15a–c, respectively. The deflection curve is smoothed by polynomial approximation because it is necessary to evaluate precisely the crack length by means of the compliance method. The electromagnetic wave starts to be generated just before the peak load and gradually increases in intensity, and then the maximum amplitude of the wave appears when the load drops dramatically. As the drop in the load corresponds to fracture in the rock, it can be considered that the generation of cracks may be one of the principal causes of electromagnetic wave radiation. By using equation (3.6) and the compliance obtained from the relation between load and deflection, the crack length during tests was estimated as shown in figure 15e. The crack starts to extend before the load reaches its peak and increases rapidly due to the large decrease of load. By substituting the crack length and load into equation (3.4), we can estimate the stress intensity factor K as shown in figure 15f. The shape is quite similar to the load–time curve of figure 15c, although the maximum stress intensity factor Kmax does not necessarily correspond to the peak load. The Kmax appears a little bit behind the peak load because of a larger crack length. The electromagnetic wave simultaneously observed, which is the same wave shown in figure 15a, is shown again in figure 15d to illustrate the relationship between the crack extension and the generation of electromagnetic waves. The period of the electromagnetic radiation corresponds well to the period of crack extension. From figure 15, it may be concluded comprehensively that the change in stress state around quartz in granite due to the crack extension in fracture causes the generation of the electromagnetic waves.
(f) Relation between electromagnetic waves and stress intensity factor
In order to obtain a quantitative relation between electromagnetic waves and stress intensity factor, quasi-static and dynamic three-point bending tests were carried out. The specimens used are the granite bending specimen shown in figure 3b, which has pre-cracks of 1, 2 and 3 mm in length at their central cross-section. Specimens without a pre-crack were also used. As shown in figure 15, the compliance method was applied to the results of the bending tests to determine the crack length a and the maximum stress intensity factor Kmax during tests. By assuming an infinitesimal initial crack, the crack length in the not pre-cracked specimen during tests was also calculated. The maximum amplitude of antenna output p* (see figure 15) was adopted as a value representing the intensity of electromagnetic waves. The data of p* and Kmax are plotted in figure 16. By using the least-squares method, a fitting curve was obtained. Although there is small scatter in the data, it appears to be that p* increases almost proportionally with the increase of Kmax over the range of the stress intensity factor from 2 to 6 MPa m1/2. From this figure, we can say that stronger electromagnetic waves are generated when fracture is accompanied by a larger stress intensity factor. This means that rock with large toughness radiates strong electromagnetic waves when it fractures.
In this study, a series of compression tests and three-point bending tests for two kinds of rocks with different contents of quartz, i.e. biotite granite and hypersthene-augite gabbro, were carried out at quasi-static and dynamic rates to examine the relation between their mechanical properties and electromagnetic phenomena. The principal results are as follows:
(i) The theory of the piezoelectric effect of quartz is the most likely explanation for the electromagnetic emissions observed in the fracture of granite and gabbro. However, minor contributions from other mechanisms might be considered, too.
(ii) The change of stress state around quartz in granite due to the extension of cracks may cause the generation of the electromagnetic waves.
(iii) Greater electromagnetic waves are generated during the fracture of rock that includes a relatively larger content of quartz.
(iv) The maximum amplitude p* of electromagnetic waves observed in dynamic tests is greater than that obtained from quasi-static tests.
(v) The p* of the electromagnetic waves caused by the fracture of granite is almost proportional to the maximum stress intensity factor Kmax in the granite specimen. Therefore, during the fracture of rock with large toughness, a strong electromagnetic wave is provably generated.
(vi) Granite and gabbro have strain-rate dependence in their strength and in the slope of the initial region of their stress–strain curves.
One contribution of 11 to a Theme Issue ‘Shock and blast: celebrating the centenary of Bertram Hopkinson's seminal paper of 1914 (Part 2)’.
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