Abstract
In this study, a time-dependent constitutive model of a coal pillar was developed using the Hoek–Brown strain-softening model, which is useful for studying the strength deterioration of a coal pillar over time. A database of 32 failed cases of coal pillars of different ages from the Witbank Coalfield has been utilized to deduce the strength parameters of the coal seam through back analysis. A three-dimensional finite-difference method (FDM) has been chosen to simulate the failed cases. The simulation results have been obtained in terms of pillar strength and FOS of the pillar concerning time. Based on the simulation results the life of the pillar is considered when FOS is nearly equal to 1. The appropriate strength parameters have been derived as peak strength parameters: \(m_{i} = 1.47\) and \(s_{i} = 0.01\); residual parameters: \(m_{r} = 0.125\) and \(s_{r} = 0.00001\); strength-reduction parameters: \(\alpha = 0.04\), \(\beta = 200\) for a coal mass. 39 stable cases from the same coalfields (Witbank) have been considered to validate the strength parameters. The simulation results of all the stable cases were showing FOS > 1. The proposed constitutive model is suitable for assessing a pillar’s time-dependent strength deterioration and creep behavior. The deterioration/yielding of the pillar is observed to be initiated from the skin/side, extending deeper into the pillar’s core with time and ultimately forming an hourglass shape. It is also observed that the FOS of the pillar decreases with time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
No datasets were generated or analysed during the current study.
References
Adhikary, D.P., Shen, B., Fama, M.E.D.: A study of highwall mining panel stability. Int. J. Rock Mech. Min. Sci. 39, 643–659 (2002). https://doi.org/10.1016/S1365-1609(02)00062-X
Aristorenas, G.V.: Time-dependent behavior of tunnels excavated in shale (1992)
Aydan, O., Sakamoto, A.: The characteristics of soft rocks and their effect on the long term stability of abandoned room and pillar lignite mines (2005)
Barla, G., Debernardi, D., Sterpi, D.: Time-dependent modeling of tunnels in squeezing conditions. Int. J. Geomech. 12, 697–710 (2012). https://doi.org/10.1061/(ASCE)GM.1943-5622.0000163
Bhattacharya, S., Singh, M.M., Huck, P.J.: The Time Relationship of Mine Subsidence and Its Impications on Subsidence Legislation (1986)
Bieniawski, Z.T.: In situ strength and deformation characteristics of coal. Eng. Geol. 2, 325–340 (1968). https://doi.org/10.1016/0013-7952(68)90011-2
Bublik, F.P., Ivanov, G.A.: Long-term strength of nonuniform pillars. Sov. Min. Sci. 6, 613–620 (1970). https://doi.org/10.1007/BF02507553
Chugh, Y.P., Missavage, R.A.: Effects of moisture on strata control in coal mines. Eng. Geol. 17, 241–255 (1981). https://doi.org/10.1016/0013-7952(81)90001-6
Duncan Fama, M.E., Trueman, R., Craig, M.S.: Two- and three-dimensional elasto-plastic analysis for coal pillar design and its application to highwall mining. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 32, 215–225 (1995). https://doi.org/10.1016/0148-9062(94)00045-5
Gadepaka, P.R., Jaiswal, A.: A novel approach for the assessment of caving behaviour in a bord and pillar depillaring panel by using continuum modelling. Int. J. Rock Mech. Min. Sci. 170, 105476 (2023). https://doi.org/10.1016/J.IJRMMS.2023.105476
Grgic, D., Giraud, A., Auvray, C.: Impact of chemical weathering on micro/macro-mechanical properties of oolithic iron ore. Int. J. Rock Mech. Min. Sci. 64, 236–245 (2013). https://doi.org/10.1016/J.IJRMMS.2013.09.005
Hill, D.: Coal pillar design criteria for surface protection. Resour. Oper. Conf. (2005)
Hoek, E., Brown, E.T.: Empirical strength criterion for rock masses. J. Geotech. Eng. Div. 106, 1013–1035 (1980). https://doi.org/10.1061/AJGEB6.0001029
Holland, C.T.: The strength of coal in mine pillar. In: 6th US Symposium on Rock Mechanics Univ. MO, Rolla, MO, pp. 450–466 (1964)
Inst, J.S.A., Metal, M., Van Der Merwe, J.N.: Revised strength factor for coal in the Vaal Basin. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 31, A9 (1994). https://doi.org/10.1016/0148-9062(94)92386-8
Jaiswal, A., Shrivastva, B.K.: Numerical simulation of coal pillar strength. Int. J. Rock Mech. Min. Sci. 46, 779–788 (2009). https://doi.org/10.1016/j.ijrmms.2008.11.003
Lane, W.L., Yanske, T., Roberts, D.: Pillar extraction and rock mechanics at the Doe Run Company in Missouri 1991 to 1999. (1999)
Leonard, O., Duvall, W.I.: Rock Mechanics and the Design of Structures in Rock. Wiley, New York (1967)
Lo, K.Y., Yuen, C.M.K.: Design of tunnel lining in rock for long term time effects. Can. Geotech. J. 18, 24–39 (2011). https://doi.org/10.1139/T81-004
Mathey, M.: Investigation into the Mechanism of Strength and Failure in Squat Coal Pillars in South Africa (2015)
Medhurst, T.P.: Estimation of the in situ strength and deformability of coal for engineering design (1997). https://doi.org/10.14264/333706
Medhurst, T.P., Brown, E.T.: A study of the mechanical behaviour of coal for pillar design. Int. J. Rock Mech. Min. Sci. 35, 1087–1105 (1998). https://doi.org/10.1016/S0148-9062(98)00168-5
Mohammad, R., Abbas, M., Mohammad, F.H., Iraj, N.: Study of the roof behavior in longwall gob in long-term condition. J. Geol. Min. Res. 10, 15–27 (2018). https://doi.org/10.5897/jgmr2017.0284
Murali Mohan, G., Sheorey, P.R., Kushwaha, A.: Numerical estimation of pillar strength in coal mines. Int. J. Rock Mech. Min. Sci. 38, 1185–1192 (2001). https://doi.org/10.1016/S1365-1609(01)00071-5
NB, A.: The time factor on subsidence. In: Proceedings of the First Conference on Ground Control Problems in the Illinois Coal Basin, pp. 260–267. Southern lllinois University at Carbondale, Carbondale (1980)
Okubo, S., Fukui, K.: An analytical investigation of a variable-compliance-type constitutive equation. Rock Mech. Rock Eng. 39, 233–253 (2006). https://doi.org/10.1007/S00603-005-0070-7/METRICS
Paraskevopoulou, C., Diederichs, M.: Analysis of time-dependent deformation in tunnels using the convergence-confinement method. Tunn. Undergr. Space Technol. 71, 62–80 (2018). https://doi.org/10.1016/j.tust.2017.07.001
Rezaei, M.: Long-term stability analysis of goaf area in longwall mining using minimum potential energy theory. J. Min. Environ. 9, 169–182 (2018). https://doi.org/10.22044/jme.2017.5950.1408
Rezaei, M., Hossaini, M.F., Majdi, A.: Development of a time-dependent energy model to calculate the mining-induced stress over gates and pillars. J. Rock Mech. Geotech. Eng. 7, 306–317 (2015a). https://doi.org/10.1016/j.jrmge.2015.01.001
Rezaei, M., Hossaini, M.F., Majdi, A.: A time-independent energy model to determine the height of destressed zone above the mined panel in longwall coal mining. Tunn. Undergr. Space Technol. 47, 81–92 (2015b). https://doi.org/10.1016/J.TUST.2015.01.001
Sainoki, A., Mitri, H.S.: Numerical investigation into pillar failure induced by time-dependent skin degradation. Int. J. Min. Sci. Technol. 27, 591–597 (2017). https://doi.org/10.1016/j.ijmst.2017.05.002
Salam, M.D.G.: A Study of the Strength of Coal Pillars, vol. 55 (1967). https://doi.org/10.10520/AJA0038223X_3918
Salamon, M.D.G., Munro, A.H.: A study of the strength of coal pillars. J. S. Afr. Inst. Min. Metall. 68, 55–67 (1967)
Salmi, E.F., Nazem, M., Karakus, M.: The effect of rock mass gradual deterioration on the mechanism of post-mining subsidence over shallow abandoned coal mines. Int. J. Rock Mech. Min. Sci. 91, 59–71 (2017). https://doi.org/10.1016/j.ijrmms.2016.11.012
Sheorey, P.R.: Pillar strength considering in situ stresses – IR@CIMFR. Minetech 21, 45–49 (2000)
Sheorey, P.R., Das, M.N., Barat, D., Prasad, R.K., Singh, B.: Coal pillar strength estimation from failed and stable cases. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 24, 347–355 (1987). https://doi.org/10.1016/0148-9062(87)92256-X
Taylor, R.K.: Coal measures mudrocks: composition, classification and weathering processes (UK). Q. J. Eng. Geol. 21, 85–99 (1988). https://doi.org/10.1144/gsl.qjeg.1988.021.01.06
Taylor, J.A., Fowell, R.J.: Mining Instability and the Misuse of the 10-times-seam Thickness Rule (2007)
Van der Merwe, J.N.: Predicting coal pillar life in South Africa. J. S. Afr. Inst. Min. Metall. 103, 293–301 (2003)
Van Der Merwe, J.N.: Review of coal pillar lifespan prediction for the Witbank and Highveld coal seams. J. S. Afr. Inst. Min. Metall. 116, 1083–1090 (2016). https://doi.org/10.17159/2411-9717/2016/v116n11a11
Van Der Merwe, J.N.: Coal pillar strength analysis based on size at the time of failure. J. S. Afr. Inst. Min. Metall. 119, 681–692 (2019). https://doi.org/10.17159/2411-9717/566/2019
Van Der Merwe, J.N., Mathey, M.: Update of coal pillar database for South African coal mining. J. S. Afr. Inst. Min. Metall. 113, 825–840 (2013)
Vásárhelyi, B.: Statistical analysis of the influence of water content on the strength of the miocene limestone. Rock Mech. Rock Eng. 38, 69–76 (2005). https://doi.org/10.1007/S00603-004-0034-3
Vyalov, S.S.: Creep in rock. Hydrotech. Constr. 6, 228–234 (1972). https://doi.org/10.1007/BF02377485
York, G., Canbulat, I., Jack, B.W.: Coal pillar design procedures (2000)
Author information
Authors and Affiliations
Contributions
Prudhvi Raju Gadepaka prepared the entire computation and numerical simulation with support from Dr. Ashok Jaiswal. Prudhvi Raju Gadepaka wrote the manuscript with support from Dr. Ashok Jaiswal. Sonu Saran reviewed and edited the manuscript. All authors discussed the results and contributed to the final manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Gadepaka, P.R., Sonu & Jaiswal, A. Assessment of the strength deterioration of a coal pillar using a strain-softening time-dependent constitutive model. Mech Time-Depend Mater (2024). https://doi.org/10.1007/s11043-024-09692-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11043-024-09692-6