ISSN 10618309, Russian Journal of Nondestructive Testing, 2012, Vol. 48, No. 12, pp. 712–717. © Pleiades Publishing, Ltd., 2012. Original Russian Text © V.T. Belikov, D.G. Ryvkin, 2012, published in Defektoskopiya, 2012, Vol. 48, No. 12, pp. 74–81.

GENERAL PROBLEMS OF NONDESTRUCTIVE TESTING

Reconstructing the Temporal Changes in the Structural– Petrophysical Characteristics of a Disintegrating Massif of Rocks V. T. Belikov* and D. G. Ryvkin** Institute of Geophysics, Ural Branch, Russian Academy of Sciences, ul. Amundsena 100, Yekaterinburg, 620219 Russia * email: [email protected] ** email: [email protected] Received May 10, 2012

Abstract—Using the proposed algorithm as a basis, we performed the quantitative interpretation of experimental data on several temporally successive highamplitude radon anomalies. As a result, the relative changes in the open porosity, the specific internal surface, and the pressure of a deteriorating massif of rocks were restored. Keywords: massif of rocks, destruction, radon, porosity, specific internal surface, pressure DOI: 10.1134/S1061830912120029

INTRODUCTION The remote monitoring of the state and continuity of a massif of rocks, as well as changes in its struc tural–petrophysical characteristics, may be performed on the basis of the analysis of experimental data on such indicators of destruction processes as temporal highamplitude anomalies in the concentration of radon. The quantitative interpretation of corresponding experimental data must be based on physico mathematical models, which allows us to establish the relationship between the observed parameters of an anomaly and the structural and dynamic characteristics of a deteriorating massif of rocks. It is known that highamplitude radon anomalies that frequently precede disastrous events are pro duced by tectonophysical phenomena in a geomedium [11–13]. Being genetically related to destruction processes, they carry information on the temporal changes in the structural–petrophysical characteristics of rocks. The results of the quantitative interpretation of the experimental material on radon concentra tion variations allow one to study the character of destructive processes in more detail and the causes and conditions that predetermine a particular mode of their development. Moreover, the data on the temporal changes in the structural–petrophysical and dynamic characteristics of a porouscracked medium (PCM) will allow us to predict the scenarios of destruction processes and determine the conditions of their real ization. In [3, 5–8], a quantitative physical model was developed, a system of equations for describing the migration of radon in a deteriorating PCM was constructed, and the mechanism of the formation of high amplitude anomalies in its concentration was proposed. Using these results, the quantitative interpreta tion of experimental material on the temporal variations in the concentration of radon before rock bumps in mines was performed [3, 5–7]. The relative changes in the open porosity and the specific internal sur face (SIS) were studied, and the spatial–temporal characteristics of a destruction nucleus were deter mined. The data on relative SIS changes were further used to study the temporal variations in the free strain energy and the stressed state of a deteriorating massif of rocks [9]. In [10], an improved method and algorithm of the quantitative interpretation of highamplitude anom alies in the concentration of radon were proposed to study the relative temporal changes in the open porosity, SIS, and the stressed state during the process of destruction and tested with the use of the exper imental material on radon concentration variations under natural conditions [13]. It should be noted that the above algorithms of quantitative interpretation with the purpose of studying the temporal changes in the structural–petrophysical characteristics of a medium were developed for an individual radon anomaly with a single pronounced maximum (monomodal). Meanwhile, more complex anomalies representing an ensemble of several successive temporally overlapping highamplitude radon anomalies can frequently be observed during the monitoring of radon. A characteristic feature of such objects consists in the fact that, on the whole, they form a polymodal anomaly with a single major highamplitude maximum (global, 712

RECONSTRUCTING THE TEMPORAL CHANGES IN THE STRUCTURAL

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Fig. 1. Comparison of observed (triangles) and (1) theoretically calculated temporal variations in the activity of radon and 0

(2) the relative change in the open porosity ϕop/ ϕ op .

exceeding the background by more than an order of magnitude) and also several local maxima on descent, and the amplitude of the latter tends to decrease with time (see Fig. 1). Such a morphology of temporal variations in the concentration of radon shows that the development mode of destruction processes differs from the mode that leads to the appearance of a monomodal anomaly. It should be expected that the char acter of temporal changes in the structural–petrophysical and dynamic characteristics of deteriorating rocks will also be different in this case. Hence, the problem of the quantitative interpretation of experimental data on several temporally successive highamplitude anomalies for the purpose of studying the specific features of the development of destruction processes that caused such a morphology of radon concentration variations is currently topical. The objective of our study is to develop and test an algorithm for the quantitative interpretation of experimental material on polyextremal highamplitude radon anomalies for the purpose of studying the relative temporal changes in the open porosity, SIS, and the stressed state of a medium during the process of destruction. The proposed algorithm was tested using the experimental data on radon concentration variations from [13]. PROBLEM FORMULATION Quantitative analysis and observation data show that destruction is the dominant factor in the appear ance of highamplitude radon anomalies that exceed its background value by ten or more times [3, 5, 11]. As destruction develops, isolated radoncontaining pores, cracks, and their groups in the rock massif regions (blocks) that were isolated before destruction are involved in the connected (open) porous cracked space, from which gas samples are taken for analysis. Moreover, the destruction of a rock may open its isolated fragments (grains) that have an increased ability to generate radon [10]. In this case, it is important to note that its equilibrium concentration in pores and blocks that were isolated before destruc tion, as well as in opened grains, may considerably exceed its value for open pores [8]. The character of the development of destruction processes in different zones of a region that is acces sible for radon monitoring may be different. It should be noted that, as a rule, the results of the mode observations of radon concentration variations, at a single point do not allow us to study the specific fea tures of destruction processes in separate parts of a massif of rocks. The sources that are associated with spatially different destruction zones (nuclei), in which destructive processes develop simultaneously, may make their own contribution to the formation of a given radon anomaly. In this case, we have no way of estimating the effect of each source separately on the morphology of an anomaly and studying the feature of changes in the structural characteristics of a medium in corresponding destruction zones using the cur rently existing experimental data. RUSSIAN JOURNAL OF NONDESTRUCTIVE TESTING

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To estimate the quantity of registered radon, it is sufficient to know the value of its flow on the surface of a cavity (enclosure), where observations are performed. Its value will carry information on all the sources in the region that is accessible to radon monitoring. For this reason, such a flow will be averaged over space and we may restrict our consideration to the onedimensional formulation of the problem. On the other hand, the currently available results of radon observations do not allow us to study the spatial dependence of the porosity and SIS. They only allow us to restore the temporal changes in the mentioned parameters averaged over a radon sampling area. A physicomathematical model for describing the migration of a radiogenic gas in a deteriorating PCM on the basis of the relationships of heat and mass transfer in heterogeneous multicomponent media [1, 2, 4] was proposed in [10]. It takes into consideration the following phases: (1) The matrix of a rock; (2) The open porous space (open phase), a fluid from which is analyzed for radon; and (3) An isolated phase that incorporates closed (isolated) pores and cracks that are involved in the con nected open porous space during the process of destruction, as well as the blocks of rocks with their own system of pores and cracks, the radon from which is inaccessible for analysis before destruction. The system of equations that describe the change in the structural–petrophysical characteristics of a massif upon the appearance of a radon anomaly incorporates the relationship for the balance of radon in the open porous space and also the equations for the volume fraction occupied by the open phase ϕop and for the open pore SIS Ω. The values γ and υ (will further be called the structural characteristics of destruc tion) that describe the rate of relative temporal changes in ϕop and Ω, respectively, are included into this system as parameters. Using the results of solving the mentioned system of equations in the inverse prob lem with the involvement of the observation data on radon concentration variations, we can restore the temporal changes in the structural–petrophysical characteristics of destruction (γ, υ) and, thereupon, the corresponding relative changes (with respect to an initial value) in ϕop and Ω [10]. NUMERICAL CALCULATIONS AND DISCUSSION OF RESULTS In this work, the results of observations on radon concentration variations from [13] were used as initial experimental material (see Fig. 1). The temporal changes in the structural characteristics of destruction were restored via the comparison of experimental and theoretical values of the relative (with respect to the background) activity of radon. When selecting temporal dependences γ(t) and υ(t), we considered the multimodality of a studied radon anomaly. The temporal dependence accepted for the parameter γ rea soning from its morphology may be characterized as follows: at t0 < t < t1, no destruction processes occur (γ = 0). At a time moment t1 (the beginning of an increase in the concentration of radon), they arise, and ϕ

ϕ

γ abruptly grows to γ = γ1, remaining constant during the time period t1 < t < t 2 ( t 2 is the moment of the ϕ

ϕ

ϕ

ϕ

ϕ

end of an intensive destruction process). Within the intervals t 2 < t < t 3 , t 3 < t < t 4 , and t 4 < t < tend, where tend is the moment of the end of a destruction process and coincides with the end of an anomaly, γ = γ2, γ = γ3, and γ = γ4, respectively, and γ2 < γ1, γ3 < γ1, and γ4 < γ1. At t > tend, destruction stops (γ = 0). When speaking about the change in the open porous space SIS during the processes of destruction, we should note that at a certain stage of their development an increase in Ω may switch to its decrease (for example, in the growth of cracks) and, otherwise, an decrease in SIS may switch to the period of its increase upon the activation of destruction processes. The character of both increase and decrease with time may be different. The selected temporal dependence of the parameter υ may be described as follows. At t = t1, when destruction processes begin, υ abruptly grows to the value υ = υ1 > 0, remaining constant Ω

Ω

during the time period t1 < t < t 2 , where t 2 is the first inversion moment, when an increase in Ω switches Ω

ϕ

Ω

Ω

to its decrease (t1 < t 2 < t 3 ). Within the interval t 2 < t < t 3 , the parameter υ accepts a constant value υ = Ω

–υ2, υ2 > 0, where t 3 is the time moment at which repeated inversion occurs and an decrease in Ω Ω

Ω

Ω

switches to its increase. At t 3 < t < t 4 , υ = υ3 > 0, where t 4 is the third inversion moment, when an increase in Ω switches to the period of its decrease. The rate of a decrease in Ω is characterized by the value Ω Ω υ = –υ4, υ4 > 0, within the interval t 4 < t < t 5 and by the value υ = –υ5, υ5 > 0 at t > tend, υ = 0 within the Ω

interval t 5 < t < tend. RUSSIAN JOURNAL OF NONDESTRUCTIVE TESTING

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Relative changes in pressure

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RECONSTRUCTING THE TEMPORAL CHANGES IN THE STRUCTURAL

Fig. 2. Relative changes in the pressure p/p0 (solid lines) and SIS of open pores Ω/Ω0 (dashed line) in a rock massif during the process of destruction. The numbers on the pressure change curves are the values of the parameter A0.

It should be noted that the abovementioned times are the moments of possible inversion depending on Ω(t). For example, if it proves that υ2 = 0 as a result of solving the inverse problem, the character of the Ω

variation in SIS will not be changed at t = t 2 . It is important to emphasize that the shape of a radon anom aly itself carries the objective information on the times describing the character of the change in γ and υ. For this reason, owing to fact that the number of determined parameters in the inverse problem is rather high, all the mentioned times were selected in correspondence with the morphology of a radon concen tration anomaly. Their numerical values were selected with the involvement of physical reasoning corre sponding to the proposed model. The time moment accepted to be initial is t0 = 14.4 days. The time of the beginning of destruction pro cesses (the beginning of an increase in the concentration of radon) is t1 = 23.0 days. The time of the end of intensive destruction processes corresponding to the highest amplitude (global maximum) of a radon ϕ ϕ anomaly is t 2 = 27.6 days. The time moment t 3 = 34.9 days characterizes the first anomaly’s minimum ϕ

following the global maximum. The time t 4 = 46.2 days corresponds to the next minimum in the curves of radonconcentration variations. The time moment at which destruction processes stop is tend = 65.7 days. The Ω

ϕ

time t 2 = t 2 = 27.6 days corresponds to the first inversion in the change of Ω, when its increase switches Ω

ϕ

to a decrease. The time moment t 3 = t 3 = 34.9 days determines the second inversion in the character of ϕ

the change in Ω, when it begins to grow after the period of descent. At t 4 = 42.0 days, the third inversion Ω

ϕ

occurs and an increase in Ω switches to its decrease. At the time moment t 5 = t 4 = 51.7 days, the rate of a decrease in Ω is changed. All the times were counted from March 1, 1996, 12:00 AM. The parameters γ1, γ2, γ3, γ4, υ1, υ2, υ3, υ4, and υ5 were determined by minimizing the functional representing the sum of the squared deviations between theoretical and experimental radon activities. The interpreted part of the observed curve of tem poral variations in the concentration of radon from [13] is plotted in Fig. 1 in comparison with the theo 0 0 retical curve fitted via the procedure of optimization. The temporal changes in ϕop/ ϕ op , where ϕ op = 0

ϕ op (t0) is the volume fraction occupied by the open phase before the beginning of destruction, are plotted in the same figure. From the curves that are plotted in Fig. 1 it can be seen that the relative change in the open porosity has a monotonical character. It constantly grows during the formation of an anomaly and finally increases by 4.8 times. The rate of its growth is maximal at the stage of intensive destruction from t1 = 23.0 days to ϕ

t 2 = 27.6 days. It should be noted that the open porosity grows at the expense of both the isolated phase RUSSIAN JOURNAL OF NONDESTRUCTIVE TESTING

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and the matrix of a rock. The above estimate of the relative increase in ϕop is correct under the assumption that the volume fraction occupied by the open phase is considerably smaller than the volume fraction occupied by the other phases of PCM at an initial time moment and throughout the entire period of a destruction process. The data of radon measurements do not allow us to perform any quantitative estima tion of the changes in the total porosity of a massif [10]. At the same time, the character of the relative change in SIS (Ω/Ω0, where Ω0 = Ω(t0) is the open porous space SIS before the beginning of destruction processes) is appreciably nonmonotonical. The curve of its relative variations in Fig. 2 has two sharply pro nounced maxima observed at time moments 27.6 and 42.0 days, when SIS grows in comparison with its initial value by nearly 10.2 and 9.8 times, respectively. Between these maxima, we can observe a minimum, when Ω/Ω0 is equal to 2. After the second maxima, SIS begins to decrease down to a level at which it is nearly two times lower than its initial value. The obtained data on the temporal dependence of Ω/Ω0 allow us to restore the relative temporal changes of the pressure in a massif of rocks under the assumption that a medium is in the state of uniform triaxial compression and the development mode of destruction processes is evolutional. For this purpose, we used equation [9, 10] 1

2 p Ω  = 1 – A 0 ⎛  – 1⎞ , ⎝ Ω0 ⎠ p0

(1)

where p and p0 are the pressures in the matrix of a rock at current and initial time moments, respectively, and A0 is a parameter that characterizes the initial ratio between the free surface and strain energies [9]. The results of our calculations are plotted in Fig. 2. The parameter A0 was taken as equal to 1/20 and 1/25. Analyzing one of the plotted curves (for A0 = 1/20), we may note that as a destruction process devel ops there first occurs a decrease of pressure (unloading) in a massif (before the first maximum on the Ω/Ω0 curve) down to the value p = 0.73p0 at the first minimum. As SIS decreases, the pressure in a medium grows (massif loading), attaining a maximum at p = 0.98p0. The pressure in a deteriorating massif then decreases with increasing SIS, attaining the second minimum at p = 0.75p0. Further, the pressure in a deteriorating massif grows again (reloading) with decreasing SIS, attaining the value p = 1.01p0 by the end of an anomaly. The obtained results show that the appearance of a multimodal radon anomaly is caused by the tem porally repeated periods of the activation of destruction processes. Each following stage of their activation may begin when the rearrangement of a medium in correspondence with the previous stage has not yet been finished. Such a character of the development of destruction processes means that the pressure in a massif also periodically changes. In other words, the appearance of a multimodal anomaly in the nearly evolutional development mode of destruction processes [9] indicates that the pressure changes nonmono tonically. Periods of its decrease that correspond to the growth of the freesurface energy and SIS alternate with the stage of an increase in the pressure, when SIS decreases owing to the growth of cracks and the compression of a massif. The growth of pressure then switches to the period of its decrease, which corre sponds to the next stage of the activation of destruction processes. Finally, a decrease in SIS produces the reloading of a massif and, as a consequence, an increase in the pressure. It has been mentioned above that individual maxima of a radon anomaly may be considered as associ ated with different destruction nuclei. For example, the maximum at t = 42.0 days that follows the global maximum may be genetically related to the other source (nucleus), which differs from the source that pro duces the global maximum on the curve of radon concentration variations. At this moment, the destruc tion processes in the nucleus associated with the global maximum have already passed the active stage and the medium in this area of a massif is relaxing to a new equilibrium state, while the active stage that leads to an increase in the open porosity and SIS begins at t = 42.0 days in the source that are responsible for the local maximum. The latter reflects upon an increase in these parameters, on the average, throughout the entire region accessible for radon monitoring. The following maxima of an anomaly (at least, some of them) may also be associated with other destruction nuclei. At the same time, we may not exclude the vari ant in which some of the successive maxima of an anomaly occur owing to the activation of destruction processes in the massif regions that caused the preceding maxima. CONCLUSIONS The application of the proposed algorithm for the quantitative interpretation of experimental data on polyextremal highamplitude radon anomalies allowed us to study the relative temporal changes in the RUSSIAN JOURNAL OF NONDESTRUCTIVE TESTING

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open porosity and SIS in the destruction of a massif of rocks. It was proven that their character consider ably differs from the character that is observed in a medium upon the appearance of monomodal anoma lies. In this case, periodicity is present in the development of a destruction process. Its active stage alter nates with a period of relaxation to a new equilibrium stage, thereupon the destruction processes in this (or another) region of a massif may become active again to begin a new cycle. If the open porosity grows monotonically, we can observe some periodicity in the character of the change in SIS. For the anomaly that was considered in this work, we can observe two sharply pronounced SIS change maxima separated by a minimum. Such a character of SIS temporal variations means that the dynamic conditions in a medium are also changed cyclically. As shown by the results of calculations on the resto ration of the relative temporal changes in the pressure, we can observe the following cycle in a deteriorat ing rock massif: loading, unloading, and reloading. By the end of an anomaly, the pressure in a massif reaches a level that nearly coincides with its value before the activation of destruction processes and the formation of a radon anomaly. The further improvement of the algorithms for the quantitative interpreta tion of experimental data on observed radon concentration variations from the viewpoint of their univer salization with respect to the morphology of an anomaly will allow us to obtain data on the temporal changes in the structural–petrophysical and dynamic characteristics of a deteriorating massif of rocks. ACKNOWLEDGMENTS This work was supported by the Program no. 4 of the Presidium of the Russian Academy of Sciences and by the Program no. 6 of the Department of Earth Sciences of the Russian Academy of Sciences. REFERENCES 1. Belikov, V.T., The Conditions for the Dissociation and Recombination of Water Vapor in a Fluid Flow, Geol. Geofiz., 1986, no. 3, pp. 110–113. 2. Belikov, V.T., The Quantitative Description of Heat and Mass Transfer Processes in the Lithosphere, Geol. Geofiz., 1991, no. 5, pp. 3–9. 3. Belikov, V.T. and Shestakov, A.F., Vliyanie protsessov razrusheniya na migratsiyu radona v treshchinnovatoporistoi srede (The Effect of Destruction Processes on the Migration of Radon in a PorousCracked Medium), Available from VINITI, 1996, Moscow, no. 2315V96. 4. Belikov, V.T., On the Thermodynamic Interpretation of an Empirical Relationship for the Longevity of Solids, Defektoskopiya, 1996, no. 1, pp. 96–101. 5. Belikov, V.T. and Shestakov, A.F., Determining the Structural Characteristics of a Geomedium from the Tem poral Variations in the Concentration of Radon. I., Defektoskopiya, 1997, no. 9, pp. 79–88. 6. Belikov, V.T. and Shestakov, A.F., Determining the Structural Characteristics of a Geomedium from the Tem poral Variations in the Concentration of Radon. II., Defektoskopiya, 1997, no. 9, pp. 89–97. 7. Belikov, V.T. and Shestakov, A.F., Use of Variations in Radon Concentration in Determining Spatial and Tem poral Characteristics of Destruction Zones, Rus. J. Nondestr. Test., 2000, vol. 36, no. 3, pp. 231–236. 8. Belikov, V.T. and Shestakov, A.F., SpaceTime Characteristics of a Fracture Region Determined from Long Term Anomalies of the Radon Concentration, Izv. Phys. Solid Earth, 2007, vol. 43, no. 5, pp. 412–418. 9. Belikov, V.T., and Shestakov, A.F., TimeDependent Stress Change during Failure of Rocks, Rus. Geol. Geophys., 2008, vol. 49, no. 5, pp. 350–356. 10. Belikov, V.T. and Ryvkin, D.G., Studying Changes in the Structural and Dynamic Characteristics of a Disinte grating Massif of Rocks Using Radon Concentration Variations, Rus. J. Nondestr. Test., 2011, vol. 47, no. 5, pp. 343–351. 11. Bulashevich, Yu.P., Utkin, V.I., Yurkov, A.K., and Nikolaev, V.V., The Change in the Concentration of Radon Due to Rock Bumps in Deep Mines, Dokl. Ross. Akad. Nauk, 1996, vol. 346, no. 1, pp. 245–248. 12. Gidrogeokhimicheskie predvestniki zemletryasenii (Hydrogeochemical Precursors of Earthquakes), Varshal, G.M., Ed., Moscow: Nauka, 1985. 13. Trique, M., Richon, P., Perrier, F., Avouac, J.P., and Sabroux, J.C., Radon Emanation and Electric Potential Variations Associated with Transient Deformation near Reservoir Lakes, Nature, 1999, vol. 399, no. 6732, pp. 137–141.

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