___________________________________________________________________________
Acoustic Method for Structural and Stress Changes
Prognosis in Rock Mass
Gennadiy G. Pivnyak1), O.O. Sdvizkhova1), Roman O. Dychkovskyi1), Yu.N.Golovko1)
1)
National Mining University, Dnipropetrovsk, Ukraine dichre@yahoo.com
Abstract
The nature of dynamic manifestations of the rock pressure in deep mines is expressed. An occasional coincidence of the majority of affecting factors drives geomechanic system “rock mass-output” with maximal accumulated potential energy. The slightest disturbance of such system leads to the loss of its stability, which is accompanied by emission of potential energy in the form of dynamic manifestation of the rock pressure (impact). At the same time, the excess of potential energy continues the destruction of the part of rock mass and the outflow of the rock. Acoustic method of prediction of dynamic phenomena in deep mines is proposed as one of physically justified methods. It is based on the analysis of the structure of man-made generated signal coming through the limit stressed rock mass. Amplitude-frequency characteristics of the signal will reflect the presence of hazard situation, and scanning the rock mass from several sources of acoustic fluctuations will allow detecting location of assumed place of crash. A criterion of crack initiation is developed based on space-time approach to solid fracture description. Numerical relation between the critical crack length, a quasi-static stress, the amplitude and frequency of elastic vibrations is determined. The critical crack length is particularly sensitive to vibration amplitude at certain frequencies. The range of such frequencies has been determined. For example, in case of sandstone increasing the amplitude of elastic vibrations 2 times at the frequency of 1145 Hz reduces the critical length of initiated crack by 2-3 times. Numerical results are correlated with the experimental data regarding the acoustic prediction of dynamic phenomena in the rock mass.
Key words: cracks, rock impact, numerical modelling, loss of stability, acoustic scanning,
stress, amplitude, acoustic method, elastic vibrations
Akustyczna metoda prognozowania zmian strukturalnych
i naprężeń w górotworze
Streszczenie
Przedstawiony został charakter dynamicznych przejawów naprężeń w skałach w kopalniach głębokich. Przypadkowa zbieżność większości czynników oddziałujących, uwalnia układ geomechaniczny "moc górotworu" z maksymalną nagromadzoną energią potencjalną. Najmniejsze zakłócenia w takim układzie prowadzą do utraty stabilności, czemu towarzyszy emisja energii potencjalnej w postaci manifestacji dynamicznych naprężeń skalnych (udar). Jednocześnie, nadmiar energii potencjalnej kontynuuje zniszczenie części górotworu oraz wyrzucenie skał. Jako jedną z uzasadnionych fizycznie metod, proponuje się metodę akustycznego przewidywania zjawisk dynamicznych w kopalniach głębokich. Opiera się ona na analizie struktury sztucznie wygenerowanego sygnału, przechodzącego przez naprężony górotwór. Charakterystyka amplitudy - częstotliwości sygnału odzwierciedla obecność niebezpiecznych sytuacji, a skanowanie górotworu w różnych miejscach wahań, pozwoli
wykryć lokalizację przewidywanego miejsca katastrofy. Kryterium inicjowania pęknięć opracowane jest na podstawie podejścia czasoprzestrzennego do opisu pękania ciał stałych. Wyznaczany jest związek numeryczny pomiędzy długością pęknięcia krytycznego, naprężę-niem pseudostatycznym, amplitudą oraz częstotliwością drgań elastycznych. Długość pęknięcia krytycznego jest szczególnie podatna na amplitudę drgań o pewnych częstotli-wościach. Wyznaczony został zakres tego typu częstotliwości. Na przykład, w przypadku piaskowca, dwukrotne zwiększenie amplitudy drgań elastycznych o częstotliwości 1145 Hz, ogranicza długość krytyczną zainicjowanego pęknięcia 2 - 3 krotnie. Wyniki numeryczne skorelowane są z danymi eksperymentalnymi dotyczącymi predykcji akustycznej dynamicz-nego zjawiska w górotworze.
Słowa kluczowe: pęknięcia, udar skał, modelowanie numeryczne, utrata stabilności,
skanowanie akustyczne, naprężenia, amplituda, metoda akustyczna, drgania elastyczne
Introduction
Rock mass is essentially nonhomogeneous medium where complex mechanical processes take place under the influence of mining. They result in such negative dynamic phenomena as rock bumps, sudden coal bursts and pressure bumps in terms of certain combinations of influential factors. Extremely fast destruction of rock is their common feature.
Forecast of the dynamic phenomena is the most important factor in the system of measures to ensure the industrial safety. A range of forecasting techniques is based on the recording and analysis of acoustic vibrations occurring in the rock [1]. The risk criteria applied in these techniques are empirical having no scientific background. Taking into account that forecasting dynamic manifestations of rock pressure can be more simply interpreted as the forecast of sudden destruction of rock, it is more expedient to study the influence of vibration processes on the cracks in stress-strained environment.
Acoustic vibrations in rock are generated by internal and external sources. External acoustic impulses in a solid body are generated by the violations of its integrity (e.g. dislocation and cracks). A number of scientific papers [2] consider the issues of elastic impulse generation under the development of cracks. It is assumed that the cracks in their nature are places of acoustic activity of rocks. The source of energy for the development of a crack breaking internal bonds in the structure of a solid body is the energy of stress-strained medium in the vicinity of the crack. The crack being the press concentrator, under the stress exceeding a certain value, grows thus releasing the excess of elastic energy in the rock mass; in this case the abrupt change of stresses surrounding the cracks generates the impulse, which in its turn, effects other cracks. Under the stress causing brittle failure of the material, external elastic waves can accelerate the process of crack growth [3].
Different rock destruction mechanisms are also the sources of external vibrations in underground workings. In any case, the cracks that were initially available in the rock, are under the effect of both slowly changing stress-strained state, and under the effect of significantly faster changing stresses (vibrations) generated by some external source. In this case the dimensions of cracks may increase. Determining the conditions necessary for such increase of crack dimensions is essential theoretical step to increase the reliability of forecasting techniques for dynamic phenomena on the basis of analyzing the acoustic signals recorded in the rock mass.
Analytical researches
A single crack is considered in unlimited space located in nonstationary stress field. It is necessary to determine the loading conditions under which the dimensions of a given crack may increase.
As is known, a crack is the discontinuity of environment resulting in the stress concentration in the area adjacent to its top point. The value of stress in the top point of the crack can exceed the breaking strength of the material, which results in the increase of a crack, developing conditions for crack formation and, as a consequence, the destruction of certain volume of material. Several approaches to the determination of criteria defining the conditions of destruction under stresses changing in time and space are available.
The authors [4] offer the most popular criterion based on space-time approach to describe destruction:
x
t
dt
dx
cd
t r t x d x 1 1 0 0 0 0,
τ
1
(1)
Where σ1(x,t) is primary stress; σ1c is breaking strength;
τ
is time parameter characterizing the delay of response of the broken material at a considered structural level; d is length; х is axial coordinate perpendicular to primary stress; t is time; x0,t0 are coordinates of a point and time moment of destruction.In the vicinity of the top point of a disc crack with characteristic dimension of 1, force field is uniquely defined by the value of primary stress σ1(t) and stress intensity
connected by the following relation
x
t
K
t
x
2
)
(
,
11
. If the length parameter israther formally defined as
2 1 1
2
c cK
d
,the destruction criterion (1) can be written as
l
к
к
dt
t
c t t 0 0
1 1τ
1
(2) Here is that critical value of intensity coefficient called crack resistance factor in the theory of rupture.
Expression (2) defines the conditions of the start of crack movement under the action of stresses.
In general, not only stresses act in the rock mass in terms of mining. Their changes in space and time are caused by underground workings and stoping, as well as rapidly changing alternate stresses in elastic waves originating under impact action on the mass and generated inside the mass under its brittle failure. In this context, in a certain point of the mass, under simultaneous action of stresses and
elastic wave, the stress in the vicinity of the crack is represented by the sum of stresses and stress in the wave.
Then at the moment of crack initiation, the primary stress will look as follows:
]
)
(
2
cos[
)
(
)
(
0 0 0 0 1
t
K
t
t
a
t
t
(3) Here is stress component unrelated to vibrations, is tensile stress, is component developing on the time-dependent stress change while mining; а, υ, φ0 are amplitude, frequency and phase at the time moment of the crack initiation.
Inserting (3) into (2), after transformations we obtain the condition observed at the moment of crack initiation with elastic vibration impact taken into account:
c
K
l
k
c
a
0 12
2
)
(
sin
,
(4)Incubation time τ is not uniquely defined parameter, and its value can be selected and interpreted in different ways [4]. In any case, τ should be considered as a parameter characterizing the response delay of the destructed material at the structural level under nonstationary loading. When criterion relation is expressed through compound stress, parameter τ is defined as a period of energy transfer between adjacent elemental discontinuity structures with the typical size of d. If only regular composition of stress is used, as in (3), it is possible to evaluate the response time on the basis of solving the problem on the drop of step-like expansion wave on the crack of finite length. Numerical value of such problem and its analysis [5] show that the stress intensity coefficient at the top point of the crack increases monotonically reaching its peak at the moment of Rayleigh wave incidence from the opposite top point, and then fluctuates around its stationary value. Based on this, assume: , where is the velocity of Rayleigh wave. Then, introducing the following non-dimensional quantities we write (4) as follows
Equation (5) finally defines the condition of the crack initiation.
If are invariables, relative parameters and also remain unchanged. Thus, the variables in criterion condition (5) are only half-length of wave and reduced amplitude of harmonic vibrations . Therefore, the crack initiation with the characteristic length of is defined only by vibration amplitude . (5)
Connection between the above values can be obtained as the solution of transcendental equation (5).
Numerical analysis of criterion ratio. The analysis of criterion ratio (5) explains that, under the values of the complex parameter close to 1, the increase of vibration amplitude causes abrupt drop of the length of cracks capable of starting motion (Fig. 1).
Fig. 1. Dependence of critical length of crack on relative amplitude of induced vibrations ( = 0)
This parameter is determined by the vibration frequency and rock crack resistance. Thus, under certain combination of rock properties and the frequency of vibrations generated in the rock mass, the start of “short” cracks with length comparable to outcrop dimensions is possible. If , then the duplication of dimensionless amplitude of vibrations (from 0.4 to 0.8) results in almost three-time decrease of the length of starting cracks.
For instance, according to the data [6, 7] for fine sandstone, the Rayleigh wave length is
c
R=2400 m/s and crack resistance coefficient is MPa .Assuming and tensile strength MPa, we obtain that the above effect has to be manifested in the form of abrupt drop of critical length of the crack (from 4m to 1.6m), and therefore, significant rise of hazard of catastrophic breakdown under vibration frequency of 1145 Hz.
Comparison with experimental data. Paper [8] demonstrates the results of experimental research of potential hazardous areas of rock mass by probing with an artificial acoustic signal generated in the coal seam by development machines. Using acoustic device AK-1, acoustic signal was recorded, and the components of amplitude-frequency spectrum were processed within the range of 0…300 Hz and 1250…4000 Hz.
Processing statistical information allowed establishing interrelation between amplitude-frequency characteristic of elastic vibrations propagating in the mass and the level of potential hazard of dynamic phenomenon. It is noted that the real
outburst zone of a coal seam is characterized by a large changeability of amplitude-frequency characteristic, including the migration of basic amplitude-frequency within the spectrum and manifestation of high-amplitude high frequency harmonics. The last factor has been recorded in all the registered cases of coal and gas outburst. That is why the duplication or triplication of the amplitude of recorded vibrations in the rock mass under mining at the frequencies of 1000 – 1300 Hz is considered as empirically established and standardized [1] sign of possible dynamic manifestation of rock pressure.
The results of the above theoretical results coincide with empirical data: duplication of amplitude of vibrations induced in the rock mass at the frequency level of 1445 Hz results in the start of motion of “short” cracks with the length of less than 2m, which can be considered as the possibility of abrupt release of potential energy in the rock stratum and development of dynamic phenomenon.
Conclusions
1. Destruction in a rock mass is oriented, and the plane of strata movement can be described geometrically. That determines the areas of their impact allowing the possibility to determine the level of impact depending on the stoping type. 2. On the basis of common space-time approach to the description of destruction
of solid bodies, the condition of the crack initiation under nonstationary loading has been defined; it is the sum of different components.
3. Numerical relations between stress, amplitude and vibration frequency have been determined as well as crack length when the start of its “motion” is possible.
4. Sandstone has been taken as an example to show that the duplication of elastic vibrations amplitude in the range of high frequencies (1145 Hz) cuts the critical length of the starting crack by 2 – 3 times.
5. Numerical results correlate with the experimental data showing that duplication or triplication of amplitude of recorded vibrations in the rock mass at frequencies of approximately the same value (1000 – 1300 Hz) is the marker of the rise of possible dynamic phenomena.
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