Microsoft Word - numero_63_art_02_3665.docx L. Nazarova et alii, Frattura ed Integrità Strutturale, 63 (2023) 13-25; DOI: 10.3221/IGF-ESIS.63.02 13 Method for locating weak zones at coal-bed–host rock interface in the context of outburst hazard: Theory and laboratory experiment Larisa Nazarova, Leonid Nazarov Chinakal Institute of Mining of the Siberian Branch of the RAS, Novosibirsk, Russia larisa.a.nazarova@mail.ru, http://orcid.org/0000-0002-3712-2939 mining1957@mail.ru, http://orcid.org/0000-0002-9857-295X ABSTRACT. Within the framework of a geomechanical model that describes deformation of rock mass during extraction of subhorizontal coal beds, the outburst hazard mechanism is substantiated: the approach of a working face to a weak zone at the coal-bed–host rock interface initiates tensile stress areas, which creates the prerequisites for the face spalling and loss of coal with methane. The inverse problem of determining conditions at the horizontal boundaries of a coal bed is formulated and solved using tomography data (patterns of P-wave velocity V) and the empirical dependence of V on the mean normal stress σ. Lab-scale test results on stepwise compression of parallelepipeds made of artificial geomaterials are presented. Tomography of the specimens was performed by acoustic sounding data, and the pattern of velocities V* was obtained. Using the pre-found empirical dependence V(σ) for geomaterial, the distribution σ*=V-1(V*) in the specimen was calculated, which served as the input data for the inverse problem on the shear stresses σxy at the specimen– press plate interface. The inversion of the lab data confirmed the possibility of identifying weak zones at the boundaries where σxy0. These zones are associated with probable sources of failure and outbursts. KEYWORDS. Coal and rock mass, Lab test, Tomography, Geomaterial, Inverse problem, Outburst. Citation: Nazarova, L., Nazarov, L., Method for locating weak zones location at coal-bed– host rock interface in the context of outburst hazard: Theory and laboratory experiment, Frattura ed Integrità Strutturale, 63 (2023) 13- 25. Received: 10.07.2022 Accepted: 02.10.2022 Online first: 16.10.2022 Published: 01.01.2023 Copyright: © 2023 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. INTRODUCTION he rate of the face advance in longwall mining can reach 20–30 m per day [1, 2], consequently, rock mass experiences rapid changes in geomechanical fields, which can induce rock fracture and hazardous dynamic phenomena (rock bursts, outbursts) [3–5]. The current condition of coal and rock mass is estimated using the data of air/gas ratio control, and microseismic and electromagnetic emission monitoring [6–8], which are recorded by mine control equipment (MMS [9], MineARC [10]). The interpretation of these data towards a short-term forecast of dynamic events includes: —semi-empirical models (for example, damage accumulation [11]) and statistical space–time analysis of long time series of informative parameters of geodynamic processes (in particular, seismic energy density in the study area) [12–17]; T https://youtu.be/wci0O86rQxo L. Nazarova et alii, Frattura ed Integrità Strutturale, 63 (2023) 13-25; DOI: 10.3221/IGF-ESIS.63.02 14 —identification of signs of a dynamic event the initiation mechanism of which is, as a rule, determined from a geomechanical model [18–21]. Seismic tomography [22–24] is recently often used in assessment of rock mass condition; in this case, areas of increased elastic wave velocities are associated with the stress concentration zones which are potential sources of dynamic events. A method for quantifying the external field stresses based on passive tomography data was proposed [25]. The passive methods are disadvantageous in monitoring induced seismicity parameters as they are deficient even for a medium-term forecast to be made or for detecting areas of concern located outside the illuminated domain in the object under study. In ore mining [26] and in extraction of coal [27, 28], most of the dynamic events are associated with discontinuities (faults, dikes) which disturb the stress state of the rock mass. The interfaces of coal beds and host rocks play the same role. Some sites of these interfaces represent thin interburdens of carbonaceous rocks or high-ash clayey coals [29, 30] with low deformation characteristics and strength properties (for example, cohesion of 0.005–0.2 MPa [31, 32]). When the mining front approaches such sites, the stresses change abruptly and the dynamic events take place [27, 33, 34]. Early detection of such weak zones will enable preventive measures to be undertaken [35] to reduce the risk of the undesirable geodynamic phenomena. In this article, a method for detecting weak zones is proposed and tested on a laboratory scale. The method includes solution of the inverse boundary value problem for shear stresses at the coal-bed–host rock interface using the tomography data. Perhaps, this will allow us to see into one of the “rock mechanics enigma” [36]. GEOMECHANICAL MODEL OF THE OBJECT Longwall mining technology ongwall mining is one of the most effective methods for extracting coal beds of various thickness (from thin, up to 1 m to high coal, more than 5-6 m). First, a coal bed is divided into extraction panels (lateral dimensions about 1–2 km) which, in turn, are then cut into rectangular sub-panels (Fig. 1). The sub-panel dimensions can range widely (length lp from 20 to 200 m, width wp from 20 to 100 m) depending on the geological structure of the deposit and on the productivity of the coal cutter–loader [37]. With such dimensions, the stress state of the sub-panel in the vertical sections (dashed line in Fig. 1) can be described in terms of the plane strain state [38] model if the external stress field corresponds to the normal faulting geodynamic regime [39]. Figure 1: Longwall mining layout. Formulation of direct problem In the Cartesian coordinate system (x,y), we consider a vertical section (Fig. 1) of rock mass containing a horizontal coal bed with a thickness 2H occurring at a depth D, cut into sub-panels with a length 2L by the main galleries and panel entries (Fig. 2). As was stated earlier, we accepted the plane strain hypothesis. The coal bed has a uniform contact with host rock (displacements are continuous), except for four symmetrically located sites with a length 2l in the roof and floor, where there is no edge friction. Hereinafter, these sites are called weak zones (WZ). L L. Nazarova et alii, Frattura ed Integrità Strutturale, 63 (2023) 13-25; DOI: 10.3221/IGF-ESIS.63.02 15 Figure 2: Computational domain and boundary conditions (±b are the abscissas of the WZ midpoints). The stress-strain state in the computational domain G={|x|≤X, |y|≤Y} is described by the linear elasticity model including: the equilibrium equations  , 0ij j iyσ ρgδ ; (1) Hooke’s law   ( ) 2ij xx yy ij ijσ λ ε ε δ με (2) and the Cauchy relations for infinitesimal strains  , ,0.5( )ij i j j iε u u (3) where σij and εij are the components of the stress and strain tensors, respectively; ui are the displacements (i,j = x,y); δij is the Kronecker delta; λ, μ and ρ are the Lamé parameters and rock density; g is the acceleration due to gravity; summation is performed over repeated coefficients. The following boundary conditions are set at different segments of ∂G (Fig. 2):   ( , ) 0, ( , ) ( )xy yy Vσ x Y σ x Y σ D Y    ( , ) 0, ( , ) 0xy yσ x Y u x Y     ( , ) ( ), ( , ) 0xx V xyσ X y βσ D y σ X y   1 1 2 2 7 7 8 80 , ,xx xyσ σ on A B A B A B and A B (4)   1 2 1 2 7 8 7 80 , ,xy yyσ σ on A A B B A A and B B     2 7 2 70yyσ on A A and B B     2 3 2 3 4 5 4 5 6 7 6 70 , , , ,xyσ on A A B B A A B B A A and B B  3 4 3 4 5 6 5 50 , ,xyσ on A A B B A A and B B where σV(y)=ρgy is the lithostatic stress; β is the lateral pressure coefficient, the symbol [ ] means the jump. L. Nazarova et alii, Frattura ed Integrità Strutturale, 63 (2023) 13-25; DOI: 10.3221/IGF-ESIS.63.02 16 Implementation of system (1)–(4) used the finite element method on a square grid (xm, yn) (step of grid is 0.1 m) and an original code [40]. The preset values of the geometric parameters in the model were: L=10 m, H=2 m, l=1 m, D=500 m, X=100 m, Y=20 m. Most of the coal deposits in Kuzbass occur in the regions dominated by the normal faulting regime [41]; therefore, β=0.4 is assumed [38]. Tab. 1 gives the physical properties of rocks according to [42, 43]. Rock E, GPa ν λ, GPa μ, GPa ρ, kg/m3 σt, GPa Host rock 35 0.25 14 14 2000 5–20 Coal 6 0.21 1.67 2.5 1500 1.0–1.2 Table 1: Physical properties of rocks (E—Young modulus, ν—Poisson ratio, σt—tensile strength). Outburst mechanism Fig. 3 shows the minimum principal stress pattern     2 2 2 1 ( ) 4 2 xx yy xx yy xyσ σ + σ σ σ σ in the coal bed at different distances between WZ and the roadway: the positive values correspond to compression and the negative values—to tension. If there is no WZ (Fig. 3a), then a tensile stress area appears in the vicinity of the roadway, and σ2 in this area is much less than σt. A similar situation occurs in the coal bed if the roadway comes short of WZ (Fig. 3b, b=8 m). A qualitatively different picture is observed when the roadway crosses the weak zone (Fig. 3c, b=9 m): an area of tensile stresses appears in the vicinity of WZ, and the magnitude of these stresses exceeds the tensile strength of coal. Taking into account the presence of free gas in the coal bed, these areas are the most probable sources of outbursts [44], when separation failure occurs and coal bursts into the roadway. Early detection of WZ will enable preventive measures to be undertaken (for example, pre-drilling) to reduce the risk of dynamic events. Figure 3: Isolines of principal stress σ2 (MPa) in coal bed at different locations of WZ relative to roadway. Formulation and solution of inverse problem for detecting weak zones The velocity of elastic waves in rocks depends on stresses [45, 46]. Weak zones at the coal-bed–host rock interface perturb the stress field (Figs. 3b and 3c). These perturbations affect the wave velocities, thus, it is possible to use the acoustic tomography data of the coal bed to reconstruct the stress state and locate the WZ. The dependence of the P-wave velocity V in hard coal on the mean normal stress σ can be described by the empirical relation L. Nazarova et alii, Frattura ed Integrità Strutturale, 63 (2023) 13-25; DOI: 10.3221/IGF-ESIS.63.02 17   0 0( ) exp( )V σ A B ασ (5) where A0=2698 m/s, B0=484 m/s, α=0.0779 1/MPa [47]. Fig. 4 depicts the velocities V in the sub-panel at different distances between WZ and the roadway (solid lines—b=8 m, dashed lines—b=6 m), calculated by model (1)–(4) with regard to (5) and at the mean normal stress σ=(1+ν)(σxx+σyy)/3 as per the plane strain conditions. Apparently, the velocity fields in the vicinity of WZ have a noticeable difference detectable using seismic tomography if the first break times are determined with an absolute accuracy of no less than 0.1 ms (spatial resolution 0.2 m). Figure 4: Isolines of P- wave velocity V (m/s) in coal bed at different locations of WZ. We formulate the inverse boundary value as follows: at the known vertical stresses σyy(x,H)=Fy(x) in the coal bed roof, we find the shear stresses σxy(x,H)=Fx(x) if the distribution of P-wave velocities in the illuminated domain I (Fig. 3) is known at a given shooting scheme. The roof and floor sites where σxy(x,H)≈0 are associated with WZ. This formulation is allowable since the distribution of the abutment pressure in subhorizontal coal mining can be found a priori (based on the configuration of mined-out space and rock density), while the conditions at the coal-bed–host rock interface are usually unknown [5, 30, 48]. Let us generate input data for the inverse problem. For a certain value of b and the above parameters of model (1)–(4) in the region R={|x|≤L, |y|≤H} (Fig. 2), we calculate the stresses and then, using (5), the distribution of P-wave velocities V0(x,y). In the domain I={|x|≤L, 1≤ y ≤3}, we define a shooting scheme that includes five sources Sq (q=1,…,5) and receivers Tp (p=1,…,5) at the vertical boundaries of the sub-panel (red circles in Fig. 2). Based on V0(x,y), we calculate the first break times 0 pqt to be later on imposed with the multiplicative noise with the magnitude δ=0.1 ms  * 0(1 )pq pqt δξ t , where ξ is a random variable uniformly distributed over [-1,1]. Using the original code [49], we perform tomography by *{ }pqt , find the distribution of the velocities V*(x,y) in the illuminated domain I (Fig. 5) and, finally, from (5), obtain the input data   0 * 0 * 1 ( , ) ln ( , ) B σ x y α A V x y . (6) Figure 5: Synthesized P-wave velocity V* distribution. In the domain G of the finite element grid, we select a fragment corresponding to the extraction sub-panel R (Fig. 2). For each element of the set    1 1 21, , ..., }m m m{x L x x L , we set the conditions at ∂R for (1)–(3) L. Nazarova et alii, Frattura ed Integrità Strutturale, 63 (2023) 13-25; DOI: 10.3221/IGF-ESIS.63.02 18     ( , ) ( ), ( , ) ( )xy m yy yσ x H f x σ x H F x (7)    ( , ) ( , ) 0 ,xx xyσ L y σ L y where     1 ( ) . 0 m m m x x f x x x The set  1 2,...,( , )}m ij m m m{σ x y of solutions of system (1)–(3), (7) is discrete Green’s function for the boundary value problem:  ( , ) ( ), ( , ) ( )xy x yy yσ x H F x σ x H F x     ( , ) ( ), ( , ) ( )xy y yy yσ x H F x σ x H F x    ( , ) ( , ) 0xx xyσ L y σ L y We represent the function 𝐹 as a sum    2 1 ( ) ( ) m x m m m m F x C f x (8) with unknown coefficients Cm which are determined by the LS method from the condition of the cost function minimum             2 1 2 1 2 *( , ..., ) ( , ) ( , ) m m m m m m mI C C C σ x y σ x y dxdy min (9) where   ( , ) (1 )( )/ 3m m m xx yyσ x y ν σ σ . A system of linear equations with respect to Cm can be derived from (9)   2 1 m nm m n m m K C Q (10)     * 1 2( , ) ( , ) , ( , ) ( , ) , , ..., .m n n mn n I I K σ x y σ x y dxdy Q σ x y σ x y dxdy n m m Solution of (10) together with (8) gives the desired distribution of the shear stresses σxy(x,H)=Fx(x) at the boundary of the extraction sub-panel. The red dashed line (Fig. 6) shows the exact distribution of σxy(x,H) at b=7 m, and the blue solid line shows the result of the inverse problem solution using the described procedure—the reconstructed function Fx(x) which clearly indicates the existence of a weak zone in the section 6≤ x ≤8. L. Nazarova et alii, Frattura ed Integrità Strutturale, 63 (2023) 13-25; DOI: 10.3221/IGF-ESIS.63.02 19 Figure 6: Exact and reconstructed shear stresses at sub-panel boundary. LABORATORY EXPERIMENT o test the proposed approach to assessing shear stresses at the coal-bed–host rock interface using tomography, a laboratory experiment was carried out using non-standard specimens. Model geomaterial The main goal of the laboratory experiments was to test the usability of acoustic methods in detection of WZ on contact surfaces in high-stress coal and rock mass under conditions close to real life (the empirical dependence of velocities on stresses corresponds to coal). In this regard, the epoxy resin + mica composition was chosen as a model material. The percentage of mica was selected so that the acoustic and deformation characteristics of the manmade geomaterial corresponded to coal of medium hardness. Five cylindrical specimens (height 76 mm, diameter 38 mm) were manufactured, and the three specimens (without mica) were tested in uniaxial compression according to the standard procedure [50]. The P-wave velocity V was also determined by acoustic sounding. Tab. 2 offers the results obtained (mean values). E, GPa ν λ, GPa μ, GPa ρ, kg/m3 V, m/s 9.2 0.21 2.76 3.8 1600 2350 Table 2: Physical properties of epoxy resin. The other two specimens (with different mica contents) were subjected to stepwise axial loading, and the P-wave velocity V was determined by ultrasonic sounding at each stress σ1. The data obtained (Tab. 3) were approximated by the exponential function (5), the values of the empirical constants A0, B0 and α were found by the least square method, and σ =(1+ν)σ1/3. These values were used for the experimental data interpretation. Specimen σ1, MPa A0 m/s B0 m/s α 1/MPa 0 1 2 3 4 5 6 1 1710 1750 1790 1825 1860 1890 1910 2046 325 0.1263 2 1740 1790 1840 1875 1905 1925 1950 2091 342 0.1412 Table 3: Stress dependence of P-wave velocity V (m/s). Laboratory setup and experimental design For the main experiments, four specimens were manufactured in the form of a parallelepiped with dimensions: length L=100 mm, height H=140 mm, thickness 30 mm (Fig. 7). A specimen was placed in a loading machine (Instron 300DX, maximum force 300 kN), thin silicone plates (length l) were embedded between the specimen and plates P1 and P2 (Figs. T L. Nazarova et alii, Frattura ed Integrità Strutturale, 63 (2023) 13-25; DOI: 10.3221/IGF-ESIS.63.02 20 7, 8) in order to simulate WZ. Six piezoelectric transducers T1,…,T6, S1,…,S6 (operating frequency 60–70 kHz) were arranged on the vertical faces of the specimen to function as sources and receivers. Fig. 9 shows general view photo of the laboratory setup. Figure 7: Parallelepiped-shaped specimens of manmade geomaterial. Figure 8: Experimental design and shooting geometry (a); computational domain and boundary conditions for lab data inversion (b). The specimen was subjected to vertical incremental loading at a step of 3 MPa. Sounding was carried out at each loading stage k: one of the sources generated a pulse received by six transducers on the opposite face, and the absolute recording accuracy was 0.1 μs (ADC frequency is 10 MHz). By the first break, the P-wave travel time k pqt between the sensors Tp and Sq (p,q=1,…,6) was determined as an average value over ten soundings. The set { k pqt } is the input data for the specimen tomography. Two series of experiments included measurement of the wave travel times at the vertical stresses σ1=3 and 6 MPa if: the plates were rigidly connected with the specimen (l =0); at the specimen–plate interfaces, there were low friction areas (WZ) with the length l=25 mm (thick red lines in Fig. 8). By way of illustration, Tab. 4 gives the values of k pqt in the presence of WZ. L. Nazarova et alii, Frattura ed Integrità Strutturale, 63 (2023) 13-25; DOI: 10.3221/IGF-ESIS.63.02 21 Figure 9: General view of laboratory setup. σ1=3 MPa (k=1) σ1=6 MPa (k=2) T1 T2 T3 T4 T5 T6 T1 T2 T3 T4 T5 T6 S1 56.5 57.9 61.8 67.8 75.5 84.2 55.3 56.6 60.5 66.4 73.8 82.4 S2 57.9 56.6 58.0 61.9 67.9 75.4 56.6 55.3 56.7 60.5 66.4 73.8 S3 61.8 57.9 56.6 58.0 61.9 67.8 60.5 56.7 55.4 56.7 60.5 66.3 S4 67.8 61.8 57.9 56.6 58.0 61.8 66.3 60.5 56.7 55.4 56.7 60.4 S5 75.3 67.8 61.8 57.9 56.6 57.9 73.7 66.3 60.5 56.7 55.3 56.6 S6 84.1 75.3 67.8 61.8 57.9 56.5 82.2 73.7 66.3 60.5 56.6 55.3 Table 4: P-wave travel times k pqt (μs) between sensors. Experimental data interpretation The tomography of the specimens was carried out by the times k pqt using algorithm [49]. Fig. 10 presents the reconstructed field of the P-wave velocities V* in the illuminated domain (blue dash line rectangle in Fig. 8) with the selected observation system {Tp, Sq} at σ1=6 MPa and the weak zones at the interfaces of the specimen and loading plates. The main cause for the asymmetry of the V*(x,y) isolines is the random arrangement of the filler particles in the specimens (Fig. 7). For this reason, for example, the travel times 1 16t and 1 61t (Tab. 4) turn out to be different, although distances between the corresponding sensors are the same, and the loading is symmetrical about two axes x=0.5L and y=0.5H. To find the shear stresses σxy at the horizontal boundaries of the domain G={0≤ x ≤L, 0≤ y ≤H} (Fig. 8b), we formulate the boundary value problem for the system of Eqns. (1)–(3):   1( , ) ( ), ( , )xy x yyσ x H F x σ x H σ    1( ,0) ( ), ( ,0)xy x yyσ x F x σ x σ L. Nazarova et alii, Frattura ed Integrità Strutturale, 63 (2023) 13-25; DOI: 10.3221/IGF-ESIS.63.02 22    (0, ) (0, ) ( , ) ( , ) 0xx xy xx xyσ y σ y σ L y σ L y corresponding to the experimental conditions. The unknown function Fx is found using the procedure for solving the boundary inverse problem described in the previous section of the article. The input data are the mean normal stress distributions σ* in the illuminated domain, found from the reconstructed velocity fields V* (Fig. 9) with regard to (6) and the values A0, B0 and α (Tab. 3, line 1). Fig. 10 presents the calculated results which indicate that the curves Fx(x) clearly identify WZ—the boundary sites 0≤ x/L ≤0.25 and 0.75≤ x/L ≤1 where Fx(x)≈0. Figure 9: P-wave velocities V* (m/s) in specimen illuminated domain, restored from tomography by 2 pqt at σ1=6 MPa and l=25 mm. Figure 10: Shear stress σxy on the upper face of the specimen under different vertical loads (red line—σ1=3 MPa, blue line—σ1=6 MPa) found from solving inverse problem by tomography data k pqt . CONCLUSIONS he method for determining conditions at the coal-bed–host rock interface has been theoretically substantiated and experimentally validated. It relies on solving an inverse boundary value problem within the framework of a geomechanical model by seismic tomography data using empirical dependences of elastic wave velocity on stresses obtained in a laboratory setting. The method not only permits to reconstruct the stress state of rock mass in the course of mining, but also acts as an element of a system for predicting outbursts in extraction of subhorizontal bedded coal. T L. 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