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Assessment of rockburst hazard by quantifying the consequence with plastic strain work and released energy in numerical models
International Journal of Mining Science and Technology 29 (2019) 93–97
Contents lists available at ScienceDirect
International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst
Assessment of rockburst hazard by quantifying the consequence with plastic strain work and released energy in numerical models F. Wang ⇑, R. Kaunda Mining Engineering Department, Colorado School of Mines, Golden, CO 80401, USA
a r t i c l e
i n f o
Article history: Received 15 June 2018 Received in revised form 29 July 2018 Accepted 26 August 2018 Available online 5 December 2018 Keywords: Unstable rock failure Rock burst Energy mechanism Numerical modeling Released energy
a b s t r a c t Quantifying the rockburst consequence is of critical importance to reduce the hazards with preventative measures in underground mines and deep tunnels. Contours of energy components within a pillar model are plotted at different rockmass damage stages, and plastic strain work and released energy are proposed as indicators of rockmass damage consequence. One pillar model under different loading stiffness is simulated to assess indicators of pillar burst and the resulting damages. The results show the rockmass damage under soft loading stiffness has larger magnitude of plastic strain work and released energy than that which is under stiff loading stiffness, indicating the rockburst consequence can be quantified with plastic strain work and released energy in numerical models. With the quantified rockburst consequence, preventative measures can be taken to avoid severe hazards to mine safety. Ó 2018 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction With the increasing demand of mineral resources and depletion of near-surface ores, the depths of underground mines have made the mining activities one of mankind’s most dangerous types of work [1,2]. The Mine Safety and Health Administration (MSHA) defines rockburst as ‘‘a sudden and violent failure of overstressed rock resulting in the instantaneous release of large amounts of accumulated energy”. The types of rockburst can be classified into three types: (1) strain burst, (2) pillar burst, and (3) fault slip [3]. Strain burst is the most common type of unstable rock failure in underground openings, where the intensity and scale are usually smaller than pillar burst and fault slip [1,4,5]. The cause of strain burst can range from shattering of rock under high-stress concentration to buckling of discontinuities parallel to underground openings. The occurrence of pillar burst also depends on the stress and discontinuity conditions in the rockmass, but pillar burst usually involves the rapid loss of strength in the core or foundation of a pillar [6–9]. Fault slip or slip burst can be either slip along pre-existing discontinuities or shear failure in the rockmass, when the shear stress is larger than shear strength in the fault [10–12]. The consequence of fault slip can vary from very small rockmass damage to consequential rockmass damage, but large seismic magnitude does not always result in large rockmass damage [13–15]. ⇑ Corresponding author. E-mail address: [email protected] (F. Wang).
Cook and Salamon revealed that, when the stiffness of a loading system is larger than the post-peak stiffness of the failed rock, the rock will fail in a violent and unstable manner [17,18]. The stiffness of the loading system could be the surrounding rockmass of the target rock. A relatively soft loading system can store more elastic strain energy than a stiff loading system at the same peak strength of the target rock. The post-peak stiffness of a rock is interpreted as the slope of the post-peak stress-strain behavior, which affects the amount of required energy for failure. In theory, when the stored elastic strain energy in the loading system provides more energy than the required energy for the target rock failure, the rock will fail in an unstable mode [7–13,16–19]. By integrating the equations of different energy components into UDEC software, the stored or released energy in each zone at each time step can be tracked and analyzed [20]. The energy components to be discussed in this study include total strain energy, elastic strain energy, plastic strain work, and instantaneous kinetic energy. Elastic strain energy results from the reversible deformation in rockmass, but if non-reversible plastic deformation or damage occurs in the rockmass, some stored elastic strain energy or loading work will become plastic strain work [21–23]. Total strain energy is defined as the sum of elastic strain energy and plastic strain work, which is the amount of strain energy stored in both reversible and non-reversible deformation in the rockmass. Elastic strain energy is usually dissipated in plastic strain work and released energy (kinetic energy) in the rockmass, and the magnitude of released energy depends on the surplus of elastic strain energy for plastic strain work [24–26].
https://doi.org/10.1016/j.ijmst.2018.11.023 2095-2686/Ó 2018 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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Rockmass failure in compression or slip along discontinuities can trigger seismicity, but mining-induced movements and seismicity in wall rock does not necessarily cause localized rockmass damage [4,27]. Seismicity cannot be used to reflect the degree of local rockmass damage caused by rockbursting [4]. Quantifying of rockmass damage will play a significant role in assessing the rockburst consequence and analyzing the mechanisms of rockburst, so some methods, such as measuring displacement, counting the number of plastic zones, and recording microseismic events, have been put forwards to quantify the rockmass damage [28]. With the predicted rockburst damage, preventative measures can be taken to avoid severe hazards to the mine safety in advance. In this study, a theoretical underground rock pillar is used as an example to study the rockburst consequence by quantifying the damage with plastic strain work and released energy.
Table 2 Strain-softening parameters applied to the rock model. Plastic shear strain
Cohesion yield stress (MPa)
0 0.001 0.02 0.08 0.15 0.25
37.5 37 32.5 25 15 0.1
2. Numerical simulation of unstable pillar failure 2.1. Physical behaviors of a theoretical rock pillar A rock pillar (6 m 4 m) with a mesh size of 0.2 m was developed in UDEC and loaded quasi-statically through two elastic beams (10 m in width) on either side (Fig. 1). To create different pillar burst consequences, the length of the two elastic beams increased from 5 to 30 m with a step of 5 m in the vertical direction, so that the beams had different magnitudes of stiffness. The roller boundaries were assigned to the sides of the beam, but the top and bottom surface of the model was loaded with a very small constant velocity (1.0 10 8 m/step) to eliminate the dynamic effects of loading. The mechanical properties of granite presented by Zhao and Cai was used as the starting point for the rock properties in the pillar (Table 1) [29]. Post-peak behavior of the rock plays a significant role in the mode of rock failure, but post-peak stress-strain curves of the granite were not obtained from the laboratory. Therefore, the post-peak stress-strain behavior of the granite is assumed in this study, which is similar to the assumed results by Manouchehrian and Cai [30]. Table 2 is the calibrated parameters of the strainsoftening behavior for the rock pillar in the model.
Fig. 2. Change of vertical stress with strain (left) and loading time (right) in the pillar.
The rock pillar has a peak strength of 340 MPa, and vertical stress-strain curves of the pillar between the different length of beams are plotted in Fig. 2a. Before the failure, the pillar has very similar stress-strain behavior, but the pillar between longer beams has larger vertical stress at the same magnitude of vertical strain after the pillar peak strength. This post-peak stress-strain deviation of the pillar has been recognized as an indicator of unstable rock failure by some researchers, and a larger deviation represents a more violent and unstable rock failure [16,30,31]. The plot of vertical stress with loading time shows rapid stress reduction within the pillar after the pillar peak strength (Fig. 2b). Since the boundary loading velocity is the same for all the six models, it takes longer time for the pillar to reach peak strength when the pillar is between longer loading beams. After the peak strength, the magnitude of stress reduction within the pillar increases with the lengths of loading beams, where the stress reduction ranges from 120 to 300 MPa during the short rock failure period. This rapid stress reduction after pillar peak strength can be used as an indicator of pillar burst [7,16]. 2.2. Influence of loading system stiffness on pillar burst consequence
Fig. 1. Geometry, mesh, and boundary conditions of the theoretical pillar model and part of beams in UDEC.
Table 1 Physical and mechanical properties of the granite specimen (granite data after the study by Zhao et al. [29,30]). Parameter
Granite
Density (kg/m3) Young’s modulus (GPa) Poisson’s ratio Friction angle (°) UCS (MPa)
2650 51 0.27 40 160
The change of energy components, including the total strain energy, elastic strain energy, and plastic strain work, is tracked during the quasi-statically loading process in numerical models. Since the length of loading beams vary from 5 to 30 m, the influence of loading system stiffness on pillar failure can be analyzed by comparing the change of energy in the models (Fig. 3). Before the pillar peak strength, a large amount of elastic strain energy and plastic strain work has been stored and created in the models, respectively. A rapid decrement in elastic strain energy and increment in plastic strain work can be observed in all the six models. In all the six models, elastic strain energy in the model is released in the form of plastic strain work and kinetic energy, which explains why the decrement in elastic strain energy is always larger than the increment in plastic strain work. Since part of elastic strain energy can be dissipated into kinetic energy, the decrement in total strain energy can be observed in all six models. After the pillar burst, the energy components continue to change due to the constant loading work from the top and bottom surface of the loading beams.
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Fig. 3. Energy transfer between energy components under the different length of beams.
When the length of beams increases from 5 to 30 m, more and more elastic strain energy is stored in the model at the pillar peak strength, but after pillar burst, less and less elastic strain energy is left in the numerical models. However, the plastic strain work is the same at the pillar peak strength in all models, but the pillar between longer beams has a larger magnitude of increment in plastic strain work during pillar burst. During a pillar burst event, elastic strain energy becomes plastic strain work and kinetic energy, so the decrement in elastic strain work is larger than the increment in plastic strain work, resulting in a decrement in total strain energy in the model. A rapid change of elastic strain energy, plastic strain work, and total strain energy also can be used as indicators of rockburst. With the decreasing of loading system stiffness in the models, more elastic strain energy can be stored at the pillar peak strength, so a large magnitude of plastic strain work and released energy is expected for pillar burst under soft loading systems. 2.3. Quantification of rockburst consequence The rapid decrement in total strain energy and plastic strain work can be used as not only indicators of rockburst but also as potential indicators of rockburst intensity and consequence. When the pillar fails under different stiffness of loading systems, different magnitudes of increment in plastic strain work and decrement in total strain energy can be observed during the pillar failure process. Since plastic strain work is a parameter that quantifies the amount of work of creating non-reversible deformation in the rockmass, the magnitude can stand for the degree of plastic deformation in the rockmass. The plot of plastic strain work within the pillar shows that all six models have the same plastic strain work before the pillar failure, but the magnitude increases with the length of the loading beams after the pillar burst (Fig. 4). The quantification of rockmass damage with plastic strain work not only provides us an estimation of the rock burst consequence but is also an indicator to compare the rockburst consequence in different scenarios. It is clear that the pillars between longer beams
Fig. 4. Change of plastic strain work in the model with both loading time.
will have larger increment in plastic strain work during the pillar burst, which confirms the soft loading system is a contributing factor to the occurrence of rockburst. Total strain energy is defined as the sum of elastic strain energy and plastic strain work, so a decrement in total strain energy means the decrement in elastic strain energy is larger than the increment in plastic strain work during the pillar burst. Most of the elastic strain energy is dissipated into plastic strain work in the models, but a surplus of elastic strain energy will be dissipated into kinetic energy [19,23]. Therefore, the decrement of total strain energy equals the released energy in the form of kinetic energy. The released energy (the decrement in total strain energy) after the pillar peak strength can be observed in all six models, and a pillar between longer beams has a larger magnitude of released energy (see Fig. 5). Because this released energy is the energy source of instantaneous kinetic energy during the pillar burst process, the magnitude is directly related to the intensity and violence of pillar burst. Since the maximum instantaneous kinetic energy is timedependent and time-sensitive, it cannot be used to indicate the rockburst intensity with high accuracy, making the released energy as a better indicator of rock failure intensity. For example, the decrement in total strain energy is 1 and 42 MJ for the pillar
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3. Energy states within zones of the numerical model
Fig. 5. Change of total strain energy in the model with loading time.
Fig. 6. Change of instantaneous kinetic energy in the model with loading time.
between the beam length of 10 and 20 m, respectively, while the maximum kinetic energy for these two cases is 0.2 and 0.23 MJ (Figs. 5 and 6). Current numerical modeling results show that the maximum instantaneous kinetic energy can be influenced by the elastic strain energy density in the models, whose detail is beyond the scope of this paper.
The energy distribution in each zone of the model can be plotted to show the energy state before and after the pillar burst. In this study, the pillar between the beam length of 25 m is chosen as an example to demonstrate the change of strain energy during pillar burst. This pillar has a big decrement in elastic strain energy, increment in plastic strain work, and decrement in total strain energy when it fails, so failure can be regarded as a typical pillar burst. The loading times of 13.5 and 13.6 s correspond to the moments just before pillar burst and just after pillar burst, respectively. A great change of total strain energy distribution within the pillar can be observed before and after the pillar burst because a large amount of elastic strain energy from the loading system is transferred into plastic strain work in the pillar (see Figs. 3 and 7). Before the pillar burst, a larger amount of total strain energy lies in the core and two sides of the pillar. However, the total strain energy in the middle of the pillar disappears after the pillar burst, and most of the total strain energy is concentrated on the core of the pillar after the pillar burst. After the pillar burst, the magnitude of total strain energy in some zones can be as much as four times of that before pillar burst. The distribution of elastic strain energy within each zone of the pillar and part of the beams is plotted in Fig. 8. Before the pillar burst, a large amount of elastic strain energy is concentrated in the middle of the pillar, but very little elastic strain energy is in the two sides of the pillar, potentially caused by the wedge failure in the pillar. After the pillar burst, the elastic strain energy decreases to a very small magnitude, so the pillar has lost the strength and the elastic strain energy has become other forms of energy. The plastic strain work distribution within the pillar before and after the pillar burst is plotted in Fig. 9. Before the pillar burst, the plastic strain work mainly centers around the shear zones on both sides of the pillar, and the shear failure zones can explain why there is nearly no elastic strain energy on two sides of the pillar
Fig. 7. Distribution of the total strain energy within zones of the pillar before and after pillar burst.
Fig. 8. Distribution of elastic strain energy within the pillar and part of beams before and after pillar burst.
F. Wang, R. Kaunda / International Journal of Mining Science and Technology 29 (2019) 93–97
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Fig. 9. Distribution of plastic strain energy within the pillar and part of beams before and after pillar burst.
(Fig. 8). After the pillar burst, a great amount of plastic strain work is created in the core of the pillar, indicating that large plastic deformation or rock damage is induced in the middle section of the pillar. The distribution of plastic strain work also shows consistency with the pillar failure process, where the pillar failure is the loss of strength in the middle of the pillar. 4. Conclusions Tracking the energy components in numerical models, rapid decrement in elastic strain energy, increment in plastic strain work, and the decrement in total strain energy could be used as indicators to distinguish between stable rock failure and unstable rock failure. During a pillar burst, the decrement in elastic strain energy is always larger than the increment in plastic strain work, and the surplus of elastic strain energy is the energy source of kinetic energy in the models. A softer loading system can store more elastic strain energy before a pillar burst, which will increase the magnitude of plastic strain work and released energy during pillar burst. After a pillar burst, a larger magnitude of plastic strain work and released energy is observed for the pillar under soft loading systems, so these two energy components could be used to quantify the rockburst consequence in numerical models. Moreover, released kinetic energy is a better indicator of rockburst intensity than instantaneous kinetic energy. During a pillar burst, a large amount of elastic strain energy from the core of the pillar and loading beams was transferred into plastic strain work in the core of pillar, where little plastic strain work was created before the pillar burst. A wedge failure on both sides of the pillar was expected before pillar burst, which would greatly increase the elastic strain energy concentration in the core of the pillar. Acknowledgments The research conducted for this study was funded by the National Institute of Occupational Health and Science (NIOSH) under Grant Number 200-2016-90154. The authors would like to extend their sincere gratitude for this financial support. References [1] Ortlepp W. RaSiM comes of age—a review of the contribution to the understanding and control of mine rockbursts. In: Symp rockburst seism mines. p. 3–20. [2] Mark C. Coal bursts that occur during development: a rock mechanics enigma. Int J Min Sci Technol 2018;28(1):35–42. [3] Müller W. Numerical simulation of rock bursts. Min Sci Technol 1991;12 (1):27–42. [4] White B, Whyatt J. Role of fault slip on mechanisms of rock burst damage, Lucky Friday Mine, Idaho, USA. In: ARES 99 2nd South African Rock Eng Symp. p. 169–78.
[5] White B, Williams T, Whyatt J. Mechanics of a large, strain-type rock burst and design for prevention. Min Tunn Innov Oppor 2002:1095–100. [6] Whyatt TW, Blake JW. 60 years of rockbursting in the Coeur D’Alene District of Northern Idaho, USA: lessons learned and remaining issues. In: Proceedings of the 109th annual exhibit and meeting. Englewood, CO: Society for Mining, Metallurgy & Exploration. p. 10. [7] Kias E, Ozbay U. Modeling unstable failure of coal pillars in underground mining using the discrete element method. 47th US rock mech symp, 2013. [8] Khademian Z, Nakagawa M, Ozbay U. Modeling injection-induced seismicity through calculation of radiated seismic energy. Press J Nat Gas Sci Eng 2018;52 (February):582–90. [9] Sinha M, Walton G. Insight into hard rock pillar behavior from numerical simulation using a progressive S-shaped criterion. No. June, p. ARMA conference paper; 2017. [10] Constitutive Rice JR. Relations for fault slip and earthquake. Instabilities 1983;121(3). [11] Sainoki A, Mitri HS. Dynamic behaviour of mining-induced fault slip. Int J Rock Mech Min Sci 2014;66:19–29. [12] He MC, Nie W, Zhao ZY, Guo W. Experimental investigation of bedding plane orientation on the rockburst behavior of sandstone. Rock Mech Rock Eng 2012;45(3):311–26. [13] Hazzard JF, Collins DS, Pettitt WS, Young RP. Simulation of unstable fault slip in granite using a bonded-particle model. Pure Appl Geophys 2002;159 (1):221–45. [14] Sainoki A, Mitri HS. Back analysis of fault-slip in burst prone environment. J Appl Geophys 2016;134:159–71. [15] Whyatt TW, Blake JW. Lessons learned and remaining issues; 2002. [16] Gu R, Ozbay U. Distinct element analysis of unstable shear failure of rock discontinuities in underground mining conditions. Int J Rock Mech Min Sci 2014;68:44–54. [17] Linkov AM. Rockbursts and the instability of rock masses. Int J Rock Mech Min Sci Geomech 1996;33(7):727–32. [18] Cook NGW. A note on rockbursts considered as a problem of stability. Publ J 1965:437–46. [19] Salamon MDG. Energy considerations in rock mechanics: fundamental results. J South African Inst Min Metall 1984;84(8):233–46. [20] Itasca Consulting Group.UDEC 6.0. Energy Calculation. Mannual; 2014. p. 1–28. [21] Kim BH, Larson MK. Evaluation of bumps-prone potential regarding the spatial characteristics of cleat in coal pillars under highly stressed ground conditions, vol. 17-0370; 2017. [22] Shlyannikov V, Boychenko N, Fernández-Canteli A, Muñiz-Calvente M. Elastic and plastic parts of strain energy density in critical distance determination. Eng Fract Mech 2015;147:100–18. [23] Gale WJ. A review of energy associated with coal bursts. Int J Min Sci Technol 2018:4–10. [24] Beck DA, Brady BHG. Evaluation and application and controlling parameters for seismic events in hard-rock mines. Int J Rock Mech Min Sci 2002;39 (5):633–42. [25] Levkovitch V, Beck D, Reusch F. Numerical simulation of the released energy in strain-softening rock materials and its application in estimating seismic hazards in mines. Sydney, Australia: Beck Engineering. p. 7. [26] He M, Ren F, Liu D. Rockburst mechanism research and its control. Int J Min Sci Technol 2018;28(5):829–37. [27] Urbancic TI, Trifu CI. Recent advances in seismic monitoring technology at Canadian mines. J Appl Geophys 2000;45(4):225–37. [28] Cai M, Kaiser PK, Martin CD. Quantification of rock mass damage in underground excavations from microseismic event monitoring. Int J Rock Mech Min Sci 2001;38(8):1135–45. [29] Zhao XG, Cai M. Influence of specimen height-to-width ratio on the strainburst characteristics of Tianhu granite under true-triaxial unloading conditions. Can Geotech J 2015;52(7):890–902. [30] Manouchehrian A, Cai M. Simulation of unstable rock failure under unloading conditions. Can Geotech J 2015;13(June):1–13. [31] Gu R, Ozbay U. Numerical investigation of unstable rock failure in underground mining condition. Comput Geotech 2015;63:171–82.
Contents lists available at ScienceDirect
International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst
Assessment of rockburst hazard by quantifying the consequence with plastic strain work and released energy in numerical models F. Wang ⇑, R. Kaunda Mining Engineering Department, Colorado School of Mines, Golden, CO 80401, USA
a r t i c l e
i n f o
Article history: Received 15 June 2018 Received in revised form 29 July 2018 Accepted 26 August 2018 Available online 5 December 2018 Keywords: Unstable rock failure Rock burst Energy mechanism Numerical modeling Released energy
a b s t r a c t Quantifying the rockburst consequence is of critical importance to reduce the hazards with preventative measures in underground mines and deep tunnels. Contours of energy components within a pillar model are plotted at different rockmass damage stages, and plastic strain work and released energy are proposed as indicators of rockmass damage consequence. One pillar model under different loading stiffness is simulated to assess indicators of pillar burst and the resulting damages. The results show the rockmass damage under soft loading stiffness has larger magnitude of plastic strain work and released energy than that which is under stiff loading stiffness, indicating the rockburst consequence can be quantified with plastic strain work and released energy in numerical models. With the quantified rockburst consequence, preventative measures can be taken to avoid severe hazards to mine safety. Ó 2018 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction With the increasing demand of mineral resources and depletion of near-surface ores, the depths of underground mines have made the mining activities one of mankind’s most dangerous types of work [1,2]. The Mine Safety and Health Administration (MSHA) defines rockburst as ‘‘a sudden and violent failure of overstressed rock resulting in the instantaneous release of large amounts of accumulated energy”. The types of rockburst can be classified into three types: (1) strain burst, (2) pillar burst, and (3) fault slip [3]. Strain burst is the most common type of unstable rock failure in underground openings, where the intensity and scale are usually smaller than pillar burst and fault slip [1,4,5]. The cause of strain burst can range from shattering of rock under high-stress concentration to buckling of discontinuities parallel to underground openings. The occurrence of pillar burst also depends on the stress and discontinuity conditions in the rockmass, but pillar burst usually involves the rapid loss of strength in the core or foundation of a pillar [6–9]. Fault slip or slip burst can be either slip along pre-existing discontinuities or shear failure in the rockmass, when the shear stress is larger than shear strength in the fault [10–12]. The consequence of fault slip can vary from very small rockmass damage to consequential rockmass damage, but large seismic magnitude does not always result in large rockmass damage [13–15]. ⇑ Corresponding author. E-mail address: [email protected] (F. Wang).
Cook and Salamon revealed that, when the stiffness of a loading system is larger than the post-peak stiffness of the failed rock, the rock will fail in a violent and unstable manner [17,18]. The stiffness of the loading system could be the surrounding rockmass of the target rock. A relatively soft loading system can store more elastic strain energy than a stiff loading system at the same peak strength of the target rock. The post-peak stiffness of a rock is interpreted as the slope of the post-peak stress-strain behavior, which affects the amount of required energy for failure. In theory, when the stored elastic strain energy in the loading system provides more energy than the required energy for the target rock failure, the rock will fail in an unstable mode [7–13,16–19]. By integrating the equations of different energy components into UDEC software, the stored or released energy in each zone at each time step can be tracked and analyzed [20]. The energy components to be discussed in this study include total strain energy, elastic strain energy, plastic strain work, and instantaneous kinetic energy. Elastic strain energy results from the reversible deformation in rockmass, but if non-reversible plastic deformation or damage occurs in the rockmass, some stored elastic strain energy or loading work will become plastic strain work [21–23]. Total strain energy is defined as the sum of elastic strain energy and plastic strain work, which is the amount of strain energy stored in both reversible and non-reversible deformation in the rockmass. Elastic strain energy is usually dissipated in plastic strain work and released energy (kinetic energy) in the rockmass, and the magnitude of released energy depends on the surplus of elastic strain energy for plastic strain work [24–26].
https://doi.org/10.1016/j.ijmst.2018.11.023 2095-2686/Ó 2018 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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F. Wang, R. Kaunda / International Journal of Mining Science and Technology 29 (2019) 93–97
Rockmass failure in compression or slip along discontinuities can trigger seismicity, but mining-induced movements and seismicity in wall rock does not necessarily cause localized rockmass damage [4,27]. Seismicity cannot be used to reflect the degree of local rockmass damage caused by rockbursting [4]. Quantifying of rockmass damage will play a significant role in assessing the rockburst consequence and analyzing the mechanisms of rockburst, so some methods, such as measuring displacement, counting the number of plastic zones, and recording microseismic events, have been put forwards to quantify the rockmass damage [28]. With the predicted rockburst damage, preventative measures can be taken to avoid severe hazards to the mine safety in advance. In this study, a theoretical underground rock pillar is used as an example to study the rockburst consequence by quantifying the damage with plastic strain work and released energy.
Table 2 Strain-softening parameters applied to the rock model. Plastic shear strain
Cohesion yield stress (MPa)
0 0.001 0.02 0.08 0.15 0.25
37.5 37 32.5 25 15 0.1
2. Numerical simulation of unstable pillar failure 2.1. Physical behaviors of a theoretical rock pillar A rock pillar (6 m 4 m) with a mesh size of 0.2 m was developed in UDEC and loaded quasi-statically through two elastic beams (10 m in width) on either side (Fig. 1). To create different pillar burst consequences, the length of the two elastic beams increased from 5 to 30 m with a step of 5 m in the vertical direction, so that the beams had different magnitudes of stiffness. The roller boundaries were assigned to the sides of the beam, but the top and bottom surface of the model was loaded with a very small constant velocity (1.0 10 8 m/step) to eliminate the dynamic effects of loading. The mechanical properties of granite presented by Zhao and Cai was used as the starting point for the rock properties in the pillar (Table 1) [29]. Post-peak behavior of the rock plays a significant role in the mode of rock failure, but post-peak stress-strain curves of the granite were not obtained from the laboratory. Therefore, the post-peak stress-strain behavior of the granite is assumed in this study, which is similar to the assumed results by Manouchehrian and Cai [30]. Table 2 is the calibrated parameters of the strainsoftening behavior for the rock pillar in the model.
Fig. 2. Change of vertical stress with strain (left) and loading time (right) in the pillar.
The rock pillar has a peak strength of 340 MPa, and vertical stress-strain curves of the pillar between the different length of beams are plotted in Fig. 2a. Before the failure, the pillar has very similar stress-strain behavior, but the pillar between longer beams has larger vertical stress at the same magnitude of vertical strain after the pillar peak strength. This post-peak stress-strain deviation of the pillar has been recognized as an indicator of unstable rock failure by some researchers, and a larger deviation represents a more violent and unstable rock failure [16,30,31]. The plot of vertical stress with loading time shows rapid stress reduction within the pillar after the pillar peak strength (Fig. 2b). Since the boundary loading velocity is the same for all the six models, it takes longer time for the pillar to reach peak strength when the pillar is between longer loading beams. After the peak strength, the magnitude of stress reduction within the pillar increases with the lengths of loading beams, where the stress reduction ranges from 120 to 300 MPa during the short rock failure period. This rapid stress reduction after pillar peak strength can be used as an indicator of pillar burst [7,16]. 2.2. Influence of loading system stiffness on pillar burst consequence
Fig. 1. Geometry, mesh, and boundary conditions of the theoretical pillar model and part of beams in UDEC.
Table 1 Physical and mechanical properties of the granite specimen (granite data after the study by Zhao et al. [29,30]). Parameter
Granite
Density (kg/m3) Young’s modulus (GPa) Poisson’s ratio Friction angle (°) UCS (MPa)
2650 51 0.27 40 160
The change of energy components, including the total strain energy, elastic strain energy, and plastic strain work, is tracked during the quasi-statically loading process in numerical models. Since the length of loading beams vary from 5 to 30 m, the influence of loading system stiffness on pillar failure can be analyzed by comparing the change of energy in the models (Fig. 3). Before the pillar peak strength, a large amount of elastic strain energy and plastic strain work has been stored and created in the models, respectively. A rapid decrement in elastic strain energy and increment in plastic strain work can be observed in all the six models. In all the six models, elastic strain energy in the model is released in the form of plastic strain work and kinetic energy, which explains why the decrement in elastic strain energy is always larger than the increment in plastic strain work. Since part of elastic strain energy can be dissipated into kinetic energy, the decrement in total strain energy can be observed in all six models. After the pillar burst, the energy components continue to change due to the constant loading work from the top and bottom surface of the loading beams.
F. Wang, R. Kaunda / International Journal of Mining Science and Technology 29 (2019) 93–97
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Fig. 3. Energy transfer between energy components under the different length of beams.
When the length of beams increases from 5 to 30 m, more and more elastic strain energy is stored in the model at the pillar peak strength, but after pillar burst, less and less elastic strain energy is left in the numerical models. However, the plastic strain work is the same at the pillar peak strength in all models, but the pillar between longer beams has a larger magnitude of increment in plastic strain work during pillar burst. During a pillar burst event, elastic strain energy becomes plastic strain work and kinetic energy, so the decrement in elastic strain work is larger than the increment in plastic strain work, resulting in a decrement in total strain energy in the model. A rapid change of elastic strain energy, plastic strain work, and total strain energy also can be used as indicators of rockburst. With the decreasing of loading system stiffness in the models, more elastic strain energy can be stored at the pillar peak strength, so a large magnitude of plastic strain work and released energy is expected for pillar burst under soft loading systems. 2.3. Quantification of rockburst consequence The rapid decrement in total strain energy and plastic strain work can be used as not only indicators of rockburst but also as potential indicators of rockburst intensity and consequence. When the pillar fails under different stiffness of loading systems, different magnitudes of increment in plastic strain work and decrement in total strain energy can be observed during the pillar failure process. Since plastic strain work is a parameter that quantifies the amount of work of creating non-reversible deformation in the rockmass, the magnitude can stand for the degree of plastic deformation in the rockmass. The plot of plastic strain work within the pillar shows that all six models have the same plastic strain work before the pillar failure, but the magnitude increases with the length of the loading beams after the pillar burst (Fig. 4). The quantification of rockmass damage with plastic strain work not only provides us an estimation of the rock burst consequence but is also an indicator to compare the rockburst consequence in different scenarios. It is clear that the pillars between longer beams
Fig. 4. Change of plastic strain work in the model with both loading time.
will have larger increment in plastic strain work during the pillar burst, which confirms the soft loading system is a contributing factor to the occurrence of rockburst. Total strain energy is defined as the sum of elastic strain energy and plastic strain work, so a decrement in total strain energy means the decrement in elastic strain energy is larger than the increment in plastic strain work during the pillar burst. Most of the elastic strain energy is dissipated into plastic strain work in the models, but a surplus of elastic strain energy will be dissipated into kinetic energy [19,23]. Therefore, the decrement of total strain energy equals the released energy in the form of kinetic energy. The released energy (the decrement in total strain energy) after the pillar peak strength can be observed in all six models, and a pillar between longer beams has a larger magnitude of released energy (see Fig. 5). Because this released energy is the energy source of instantaneous kinetic energy during the pillar burst process, the magnitude is directly related to the intensity and violence of pillar burst. Since the maximum instantaneous kinetic energy is timedependent and time-sensitive, it cannot be used to indicate the rockburst intensity with high accuracy, making the released energy as a better indicator of rock failure intensity. For example, the decrement in total strain energy is 1 and 42 MJ for the pillar
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3. Energy states within zones of the numerical model
Fig. 5. Change of total strain energy in the model with loading time.
Fig. 6. Change of instantaneous kinetic energy in the model with loading time.
between the beam length of 10 and 20 m, respectively, while the maximum kinetic energy for these two cases is 0.2 and 0.23 MJ (Figs. 5 and 6). Current numerical modeling results show that the maximum instantaneous kinetic energy can be influenced by the elastic strain energy density in the models, whose detail is beyond the scope of this paper.
The energy distribution in each zone of the model can be plotted to show the energy state before and after the pillar burst. In this study, the pillar between the beam length of 25 m is chosen as an example to demonstrate the change of strain energy during pillar burst. This pillar has a big decrement in elastic strain energy, increment in plastic strain work, and decrement in total strain energy when it fails, so failure can be regarded as a typical pillar burst. The loading times of 13.5 and 13.6 s correspond to the moments just before pillar burst and just after pillar burst, respectively. A great change of total strain energy distribution within the pillar can be observed before and after the pillar burst because a large amount of elastic strain energy from the loading system is transferred into plastic strain work in the pillar (see Figs. 3 and 7). Before the pillar burst, a larger amount of total strain energy lies in the core and two sides of the pillar. However, the total strain energy in the middle of the pillar disappears after the pillar burst, and most of the total strain energy is concentrated on the core of the pillar after the pillar burst. After the pillar burst, the magnitude of total strain energy in some zones can be as much as four times of that before pillar burst. The distribution of elastic strain energy within each zone of the pillar and part of the beams is plotted in Fig. 8. Before the pillar burst, a large amount of elastic strain energy is concentrated in the middle of the pillar, but very little elastic strain energy is in the two sides of the pillar, potentially caused by the wedge failure in the pillar. After the pillar burst, the elastic strain energy decreases to a very small magnitude, so the pillar has lost the strength and the elastic strain energy has become other forms of energy. The plastic strain work distribution within the pillar before and after the pillar burst is plotted in Fig. 9. Before the pillar burst, the plastic strain work mainly centers around the shear zones on both sides of the pillar, and the shear failure zones can explain why there is nearly no elastic strain energy on two sides of the pillar
Fig. 7. Distribution of the total strain energy within zones of the pillar before and after pillar burst.
Fig. 8. Distribution of elastic strain energy within the pillar and part of beams before and after pillar burst.
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Fig. 9. Distribution of plastic strain energy within the pillar and part of beams before and after pillar burst.
(Fig. 8). After the pillar burst, a great amount of plastic strain work is created in the core of the pillar, indicating that large plastic deformation or rock damage is induced in the middle section of the pillar. The distribution of plastic strain work also shows consistency with the pillar failure process, where the pillar failure is the loss of strength in the middle of the pillar. 4. Conclusions Tracking the energy components in numerical models, rapid decrement in elastic strain energy, increment in plastic strain work, and the decrement in total strain energy could be used as indicators to distinguish between stable rock failure and unstable rock failure. During a pillar burst, the decrement in elastic strain energy is always larger than the increment in plastic strain work, and the surplus of elastic strain energy is the energy source of kinetic energy in the models. A softer loading system can store more elastic strain energy before a pillar burst, which will increase the magnitude of plastic strain work and released energy during pillar burst. After a pillar burst, a larger magnitude of plastic strain work and released energy is observed for the pillar under soft loading systems, so these two energy components could be used to quantify the rockburst consequence in numerical models. Moreover, released kinetic energy is a better indicator of rockburst intensity than instantaneous kinetic energy. During a pillar burst, a large amount of elastic strain energy from the core of the pillar and loading beams was transferred into plastic strain work in the core of pillar, where little plastic strain work was created before the pillar burst. A wedge failure on both sides of the pillar was expected before pillar burst, which would greatly increase the elastic strain energy concentration in the core of the pillar. Acknowledgments The research conducted for this study was funded by the National Institute of Occupational Health and Science (NIOSH) under Grant Number 200-2016-90154. The authors would like to extend their sincere gratitude for this financial support. References [1] Ortlepp W. RaSiM comes of age—a review of the contribution to the understanding and control of mine rockbursts. In: Symp rockburst seism mines. p. 3–20. [2] Mark C. Coal bursts that occur during development: a rock mechanics enigma. Int J Min Sci Technol 2018;28(1):35–42. [3] Müller W. Numerical simulation of rock bursts. Min Sci Technol 1991;12 (1):27–42. [4] White B, Whyatt J. Role of fault slip on mechanisms of rock burst damage, Lucky Friday Mine, Idaho, USA. In: ARES 99 2nd South African Rock Eng Symp. p. 169–78.
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