FLAC3D (FLAC3D, 2008) environment has been used to simulate MIS that was induced by moving longwall face. Length of the face was 240m and it moved by step increments. Size of the step was 40m that is six times less then the length of the panel. Every step cycled a number of iterations that provided rate of model continuum deformation that corresponds to the actual rate of rock mass strain. The actual rate has been adopted from data collected during strata movement monitoring in Zasiadko coal mine [3].
Immediate roof of the coal seam that has thickness 1.45m has been presented with argillite having thickness from 8m to 12m and uniaxial compression strength 40MPa. A competent thick sand-stone presents main roof. This rock layer is usually the main source of dynamic failures that induce MIS. Fragment of mine map depicted in Figure 1. A single isolated coal longwall face re-treated East panel in the direction that indicated by arrow. The face kept the rate of advance in diapason 5 - 7m per day. MIS has been monitored during retreating of East coal face [6].
Eighteenth panel was employed to collect difference of rock mass deformation due to variation of rate advance of the 18th coal face that deviated from 2m per day up to 7m per day. This face was idle during several days that provided wide diapason of the rate advance. Strata deformation was monitored in a vertical hole that had been drilled in the head entry. Position of the hole indicated by cross and numbered by 1 in Figure 1. The hole has been instrumented by five extensom-eters that were installed to the depth of 7m. The most deeper extensometers are #1 and #2. Distance between these extensometers were 2m. The experimental entry has been maintained behind the longwall face to provide direct ventilation of the face for safety reasons. This helped to collect sufficient data for assessment of impact of face rate retreat [5,6].
Figure 1. Fragment of mine map
Dynamic destruction of rock mass has not theoretical solution so far. Constitutive model of dy-namic failure should account either traditional parameters that are used for description of nonlinear behavior of rock mass and additional factors such as rate of loading and rate of relaxation first of all. We used empirical constitutive model that has been proposed by (Bialek et al. 2004) as a basis. They found good agreement between surface deformation index I and seismic energy that has been induced by longwall movement. Index I was calculated as product of subsidence to their derivative. From physical point of view, such empirical dependence describes rock mass dynamic failure properly because the more ground deformation and its rate or time derivative the more probable dynamic failure [1,2].
Polish investigators used surface subsidence because they are easy to measure in situ. However process of rock mass failure usually has been described using equivalent stress. In addition, dynamic failure has a less chance when rate of stress relaxation is big. That is why we proposed to use equivalent stress in place of subsidence and accounted the rate of relaxation. Finally we used next formula to calculate MIS:
where σe = equivalent stress, ε = relaxation strain, t = time.
Dimension of I can be presented as (J/m3)2 that means square of specific energy. Parameter ε˜ = dε/dt stands for a rate of potential energy dissipation. Volumetric strain rate that FLAC3D calculates substitutes ε˜.
Equivalent stress was calculated according formula (Shashenko e.al. 2003):
where σi = principal components of the stress, ψ = σt / σc where σt and σc denote tension and compression limits of rock mass strength respectively [3,5].
Constitutive low that has been described by equations (1) and (2) is empirical and has no strict theoretical basis. However it properly reflects main geomechanic behavior of rock mass under dynamic loading. This low simplifies algorithm of MIS calculation and saves efforts owing utilization existent tools and advantages that has been developed in FLAC3D so far.
A symmetric half of rock mass volume that surrounds the correspondent half of the East longwall face has been chosen as indicated by dotted rectangular in Figure 1. Bottom of the model was 200m and lateral boundaries of the model were at 200m from the goaf of East panel that provided sufficient distance to minimize boundary conditions in vicinity of the longwall where MIS causes real danger for miners. Normal displacements were restricted on all lateral and bottom boundaries of the model. Gravity and specific weight of the rock mass 2500kg/m3 generated ground pressure around the face that has been moved at the depth of 500m.
Figure 3 demonstrates grid of the model and MIS events distribution. First, elastic model had been assigned and stress equilibrium was reached in the intact model. Then model has been changed to Mohre-Colomb and five successive steps were employed to move the face during MIS problem solving. Therefore every next step used stress state that has been developed at the previous step of modeling [10].
Animation 1. Dynamics of seismic events at pushing of lava from position 160 meters in position 200 meters
This animation was done by means of the program GIF - animator, consists of six shots, delay between shots 2 seconds.
Figure 2. Distribution of MIS around the face after its advance to 200m
Deterioration of rock mass cohesion and mobilization of internal friction were simulated to imitate process of undermined strata caving. Contact of roof and floor has been accounted by shifting null zone to ubiquitous when sum of immediate roof subsidence and heave of immediate floor exceeded thickness of extracted coal seam. This procedure enhanced solution owing ac-counting of gob compaction effect [7,8].
Square of calculated MIS energy was by order 4.6e16 J2 that corresponds to experimental results of (Bialek et al. 2004) who registered amount of induced energy at order 1.6e8 J. As can bee seen in Figure 3, most MIS occur behind start room and in front of moving longwall face, where abutment zones developed. Sum of the MIS behind the start room was greater because abutment zone developed on the same place here that did not move. Abutment zone in front of the face moved as the face retreated. Therefore current MIS intensity is less here.
Approximately same MIS activity has been registered over the gob in undermined strata. Fig-ure 4 demonstrates actual MIS distribution for a fixed positions of the East longwall face. Fragment A in Figure 4 depicted a case when all MIS expressed behind the start room, whereas frag-ment B illustrates situation when MIS occurred both in front of the moving face and behind it in the zone of active subsidence [4].
Figure 3. MIS distributions monitored in Zasiadko coal mine
Histograms of actual and calculated energy of MIS depicted in Figure 5. Both histograms can be described by exponential distribution. The most frequent are low energetic seismic events whereas powerful dynamic failures of rock mass occur rarely. Histograms of actual data and cal-culated energy have no essential difference according Pierson test. Therefore developed algorithm may be used for prediction mining induced seismicity during longwall mining.
FLAC3D explicitly uses inertial terms as a numerical mean to reach equilibrium state. However force debalance occurs naturally during intensive deposit extraction. This debalance is propor-tional to the rate of longwall movement and can be simulated by selection of proper number of cycles during solving dynamic problem. Rate of longwall advance was calibrated using actual measurement of rock mass strain intensity with extensometers.
Figure 5. MIS energy histograms
Dynamic failure of rock mass due to intensive longwalling has been simulated on approach that exploits an idea that increase of the equivalent stress and of its rate builds up the potential energy of rock mass deformation and raises probability of dynamic failure as a result of potential energy transition to kinetic form if the rate of the energy dissipation is small.
Comparison of simulated and experimental seismic events distributions demonstrated good agreement. Space distribution of mining induced seismicity around moving longwall face in FLAC3D model and in situ demonstrated qualitative agreement. Histograms of seismic energy that have been collected on the basis of numeric simulation and actual measurement have no dif-ference according Pearson test. Therefore FLAC3D can be used to predict mining induced seis-micity during longwall retreat on different rate.
This abstract is unfinished. Full version master's work will be completed in December 2011.
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