# Energy Dissipation and Storage in Underground Mining Operations

- 352 Downloads

## Abstract

In this paper, we focus on the energy alteration during longwall mining in an attempt to mimic the conditions of a coal mine in Western Turkey. We verify the proposed model using existing analytical and numerical solutions in terms of stress components. Based on the verified numerical model, the energy balance during longwall retreat is studied rigorously. It is found that excavation-induced increment of external work increases linearly with time, while the stored strain energy increment is quadratic. Meanwhile, the strain energy increment rate gradually decreases with longwall progress because of excavation-induced higher stored energy within the adjacent coal block. The energy dissipation process during lonwall mining, corresponding to crack propagation, is divided into four stages, namely initiation stage, steady growth stage, sharp increment stage, and stabilisation stage. Our results provide new insights into energy evolution during longwall mining both from the reversible and irreversible points of view. The current paper shows, for the first time, that the extended finite element method is suitable to describe the crack propagation during longwall mining. The excavation induced crack propagation in the roof strata predicted by the model is in agreement with the “arch-shaped” patterns obtained using laboratory tests and Discrete Element numerical simulations.

## Keywords

Longwall mining Energy dissipation XFEM approach Crack propagation## List of symbols

- \(\sigma ^p_y\)
Vertical stress at the plastic zone

- \(\sigma ^e_y\)
Vertical stress at the elastic zone

*M*Height of the coal seam

- \(\varphi\)
Friction angle

- \(\widehat{\sigma }\)
Peak value of concentration stress

- \(\sigma _{\text {cm}}\)
Uniaxial compressive strength of coal seam

*H*Depth of coal seam

*W*Width of extraction

- \(\varvec{u}\)
Displacement field

- \(\varvec{e}\)
Strain field

- \(\varvec{t^*}\)
Boundary traction field

- \(\varvec{b^*}\)
Body force field

- \(\Omega _{\text {I}}\)
Excavated block region

- \(\Omega _{\text {II}}\)
Remaining rock mass region

- \(U_{[{\text {e}}]}\)
Stored strain energy

- \(W_{[{\text {u}}]}\)
External work

- \(\widetilde{W}\)
Extra external work after excavation

- \(\widetilde{U}\)
Increased strain energy after excavation

- \(W_{\text {r}}\)
Released energy due to excavation

- \(N_{\text {I}}(x)\)
Conventional nodal shape function

*H*(*x*)Discontinuous jump function across the crack surfaces

- \(F_{\alpha }(x)\)
Elastic asymptotic crack-tip function \(N_{\text {I}}(x)\)

- \(\varvec{u_{\text {I}}}\)
Usual nodal displacement vector of function

- \(\varvec{a_{\text {I}}}\)
Nodal enriched degree of freedom vector of function

*H*(*x*)- \(\varvec{b_{\text {I}}^{\alpha }}\)
Nodal enriched degree of freedom vector of function \(F_{\alpha }(x)\)

- \(G_{\text {C}}\)
Quasi-static fracture energy

- \(K_{\text {IC}}\)
Fracture toughness

- \(Y_I(S/R)\)
The mode-I geometry factor

- \(P_{\text {max}}\)
The peak applied load

*B*The thickness of the specimen

*R*The specimen radius

*E*Elastic modulus

- \(\nu\)
Poisson’s ratio

- \(h_{\text {f}}\)
Height of fracture zone

- \(\gamma\)
Unit weight of roof strata

- \(A_{\text {m}}\)
Cross section of excavated panel

- \(\sigma _{\text {v}}\)
Initial vertical stress

- \(\sigma _{\text {c}}\)
Uniaxial compressive strength of roof strata

- \(A_{\text {d}}\)
Unit surface of destressed zone

*k*Bulking factor of caved materials

- MPS
Maximum principal stress

## Notes

### Acknowledgements

The first author would like to acknowledge the financial support provided by the China Scholarship Council (CSC) under Grant Number 201606420056. The authors would like to thank the anonymous reviewers for their considerable effort in improving the paper.

## References

- Abdollahipour A, Marji MF, Bafghi AY, Gholamnejad J (2016) DEM simulation of confining pressure effects on crack opening displacement in hydraulic fracturing. Int J Min Sci Technol 26(4):557–561Google Scholar
- Areias P, Belytschko T (2005) Analysis of three-dimensional crack initiation and propagation using the extended finite element method. Int J Numer Methods Eng 63(5):760–788Google Scholar
- Atkinson BK (1987) Fracture mechanics of rock. Academic Press, LondonGoogle Scholar
- Bańka P, Chmiela A, Fernández MM, Muñiz ZF, Sanchez AB (2017) Predicting changes in induced seismicity on the basis of estimated rock mass energy states. Int J Rock Mech Min Sci 95:79–86Google Scholar
- Barton N (2011) From empiricism, through theory, to problem solving in rock engineering. In: 6th Leopold Müller Lecture, Beijing, ISRM CongressGoogle Scholar
- Basarir H, Oge IF, Aydin O (2015) Prediction of the stresses around main and tail gates during top coal caving by 3D numerical analysis. Int J Rock Mech Min Sci 76:88–97Google Scholar
- Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5):601–620Google Scholar
- Belytschko T, Gracie R, Ventura G (2009) A review of extended/generalized finite element methods for material modeling. Modell Simul Mater Sci Eng 17(4):043,001Google Scholar
- Bieniawski ZT (1967) Mechanism of brittle fracture of rock: part I–theory of the fracture process. Int J Rock Mech Min Sci Geomech Abstr 4(4):395–404
**(IN11–IN12, 405–406)**Google Scholar - Brady BH, Brown ET (2013) Rock mechanics: for underground mining. 2nd edn. Chapman and Hall, London, p 588Google Scholar
- Cai M, Kaiser P (2014) In-situ rock spalling strength near excavation boundaries. Rock Mech Rock Eng 47(2):659–675Google Scholar
- Cai M, Kaiser P, Tasaka Y, Maejima T, Morioka H, Minami M (2004a) Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations. Int J Rock Mech Min Sci 41(5):833–847Google Scholar
- Cai M, Kaiser P, Uno H, Tasaka Y, Minami M (2004b) Estimation of rock mass deformation modulus and strength of jointed hard rock masses using the gsi system. Int J Rock Mech Min Sci 41(1):3–19Google Scholar
- Cai M, Kaiser P, Tasaka Y, Minami M (2007) Determination of residual strength parameters of jointed rock masses using the GSI system. Int J Rock Mech Min Sci 44(2):247–265Google Scholar
- Cao J, Li W (2017) Numerical simulation of gas migration into mining-induced fracture network in the goaf. Int J Min Sci Technol 27(4):681–685Google Scholar
- Comi C, Mariani S, Perego U (2007) An extended fe strategy for transition from continuum damage to mode I cohesive crack propagation. Int J Numer Anal Methods Geomech 31(2):213–238Google Scholar
- Cook N (1963) The basic mechanics of rockbursts. J South Afr Inst Min Metall 64(3):71–81Google Scholar
- Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150Google Scholar
- Dolbow J, Moës N, Belytschko T (2000) Discontinuous enrichment in finite elements with a partition of unity method. Finite Elem Anal Des 36(3):235–260Google Scholar
- Dong X, Karrech A, Basarir H, Elchalakani M, Qi C (2018) Analytical solution of energy redistribution in rectangular openings upon in-situ rock mass alteration. Int J Rock Mech Min Sci 106:74–83Google Scholar
- Eberhardt E, Stead D, Stimpson B, Read R (1998) Identifying crack initiation and propagation thresholds in brittle rock. Can Geotech J 35(2):222–233Google Scholar
- Fan Y, Lu W, Yan P, Chen M, Zhang Y (2015) Transient characters of energy changes induced by blasting excavation of deep-buried tunnels. Tunn Undergr Space Technol 49:9–17Google Scholar
- Fang X, Jin F, Wang J (2007) Simulation of mixed-mode fracture of concrete using extended finite element method (In Chinese). Eng Mech 24:46–52Google Scholar
- Fei K, Zhang J (2010) The application of ABAQUS in geotechnical engineering. China Water Power Press, BeijingGoogle Scholar
- Fosdick R, Truskinovsky L (2003) About Clapeyron’s theorem in linear elasticity. J Elast 72:145–172Google Scholar
- Gao F, Stead D, Coggan J (2014) Evaluation of coal longwall caving characteristics using an innovative udec trigon approach. Comput Geotech 55:448–460Google Scholar
- Griffith A (1924) The theory of rupture. In: Proceedings of the first international congress applied mechanics, pp 55–63Google Scholar
- He BG, Zelig R, Hatzor YH, Feng XT (2016) Rockburst generation in discontinuous rock masses. Rock Mech Rock Eng 49(10):4103–4124Google Scholar
- Hu XY, Liu ZL, Zhuang Z (2017) XFEM study of crack propagation in logs after growth stress relaxation and drying stress accumulation. Wood Sci Technol 51(6):1447–1468Google Scholar
- Jing L, Hudson J (2002) Numerical methods in rock mechanics. Int J Rock Mech Min Sci 39(4):409–427Google Scholar
- Kachanov LM (1986) Introduction to continuum damage mechanics. Martinus Nijhoff Publishers, BostonGoogle Scholar
- Kaiser PK, Cai M (2012) Design of rock support system under rockburst condition. J Rock Mech Geotech Eng 4(3):215–227Google Scholar
- Karrech A, Duhamel D, Bonnet G, Roux J, Chevoir F, Canou J, Dupla J, Sab K (2007) A computational procedure for the prediction of settlement in granular materials under cyclic loading. Comp Meth Appl Mech Eng 197(1–4):80–94Google Scholar
- Karrech A, Duhamel D, Bonnet G, Chevoir F, Roux JN, Canou J, Dupla JC (2008) A discrete element study of settlement in vibrated granular layers: role of contact loss and acceleration. Granul Matter 10(5):369–375Google Scholar
- Karrech A, Regenauer-Lieb K, Poulet T (2009) A damaged visco-plasticity model for pressure and temperature sensitive geomaterials. Int J Eng Sci 49:1141–1150Google Scholar
- Karrech A, Regenauer-Lieb K, Poulet T (2011) Continuum damage mechanics for the lithosphere. J Geophys Res Solid Earth 116(B04):205Google Scholar
- Karrech A, Regenauer-Lieb K, Poulet T (2012) A limit analysis approach to derive a thermodynamic damage potential for non-linear geomaterials. Philos Mag 92(28–30):3439–3450Google Scholar
- Karrech A, Schrank C, Freij-Ayoub R, Regenauer-Lieb K (2014) A multi-scaling approach to predict hydraulic damage of poromaterials. Int J Mech Sci 78:1–7Google Scholar
- Karrech A, Abbassi F, Basarir H, Attar M (2017) Self-consistent fractal damage of natural geo-materials in finite strain. Mech Mater 104:107–120Google Scholar
- Klepaczko J, Bassim M, Hsu T (1984) Fracture toughness of coal under quasi-static and impact loading. Eng Fract Mech 19(2):305–316Google Scholar
- Lemaitre J, Chaboche J (2001) Mécanique des matériaux solides. Duond, ParisGoogle Scholar
- Lim I, Johnston I, Choi S (1993) Stress intensity factors for semi-circular specimens under three-point bending. Eng Fract Mech 44(3):363–382Google Scholar
- Lisjak A, Figi D, Grasselli G (2014) Fracture development around deep underground excavations: insights from FDEM modelling. J Rock Mech Geotech Eng 6(6):493–505Google Scholar
- Liu P, Zheng J (2010) Recent developments on damage modeling and finite element analysis for composite laminates: a review. Mater Des 31(8):3825–3834Google Scholar
- Liu T (1981) Surface movements, overburden failure and its application. Coal Industry, BeijingGoogle Scholar
- Lockner D, Byerlee J, Kuksenko V, Ponomarev A, Sidorin A (1991) Quasi-static fault growth and shear fracture energy in granite. Nature 350(6313):39–42Google Scholar
- Manouchehrian A, Cai M (2015) Simulation of unstable rock failure under unloading conditions. Can Geotech J 53(1):22–34Google Scholar
- Melenk JM, Babuška I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139(1–4):289–314Google Scholar
- Meng Z, Shi X, Li G (2016) Deformation, failure and permeability of coal-bearing strata during longwall mining. Eng Geol 208:69–80Google Scholar
- Miao X, Cui X, Wang J, Xu J (2011) The height of fractured water-conducting zone in undermined rock strata. Eng Geol 120(1):32–39Google Scholar
- Mohammadnejad T, Andrade J (2016) Numerical modeling of hydraulic fracture propagation, closure and reopening using xfem with application to in-situ stress estimation. Int J Numer Anal Methods Geomech 40(15):2033–2060Google Scholar
- Moon T, Nakagawa M, Berger J (2007) Measurement of fracture toughness using the distinct element method. Int J Rock Mech Min Sci 44(3):449–456Google Scholar
- Mou Z, Dong L, Ni X (2010) Research on the influence of roof strata on rock burst risk. J China Univ Min Technol 39(1):40–44Google Scholar
- Paterson MS, Wong Tf (2005) Experimental rock deformation: the brittle field. 2nd edn. Springer-Verlag, BerlinGoogle Scholar
- Peng SS (2006) Longwall mining. West Virginia University, Department of Mining Engineering, Morgantown, WV (USA)Google Scholar
- Rezaei M, Hossaini MF, Majdi A (2015) A time-independent energy model to determine the height of destressed zone above the mined panel in longwall coal mining. Tunn Undergr Space Technol 47:81–92Google Scholar
- Salamon M (1984) Energy considerations in rock mechanics: fundamental results. J South Afr Inst Min Metall 84(8):233–246Google Scholar
- Song JH, Areias P, Belytschko T (2006) A method for dynamic crack and shear band propagation with phantom nodes. Int J Numer Methods Eng 67(6):868–893Google Scholar
- Vajragupta N, Uthaisangsuk V, Schmaling B, Münstermann S, Hartmaier A, Bleck W (2012) A micromechanical damage simulation of dual phase steels using XFEM. Comput Mater Sci 54:271–279Google Scholar
- Walsh JB (1977) Energy changes due to mining. Int J Rock Mech Min Sci Geomech Abstr 14(1):25–33Google Scholar
- Wang B, De Backer H, Chen A (2016a) An xfem based uncertainty study on crack growth in welded joints with defects. Theor Appl Fract Mech 86:125–142Google Scholar
- Wang G, Wu M, Wang R, Xu H, Song X (2017a) Height of the mining-induced fractured zone above a coal face. Eng Geol 216:140–152Google Scholar
- Wang J, Ning J, Jiang J, Bu T, Shi X (2017b) Research on the energy criterion for rockbursts induced by broken hard and thick rock strata and its application. Geotech Geol Eng 35(2):731–746Google Scholar
- Wang P, Jiang J, Zhang P, Wu Q (2016b) Breaking process and mining stress evolution characteristics of a high-position hard and thick stratum. Int J Min Sci Technol 26(4):563–569Google Scholar
- Wang S, Li X, Wang S (2017c) Separation and fracturing in overlying strata disturbed by longwall mining in a mineral deposit seam. Eng Geol 226:257–266Google Scholar
- Wells GN, Sluys L (2001) A new method for modelling cohesive cracks using finite elements. Int J Numer Methods Eng 50(12):2667–2682Google Scholar
- Wilson AH (1983) The stability of underground workings in the soft rocks of the coal measures. Int J Mining Eng 1(2):91–187Google Scholar
- Xie H, Li L, Peng R, Ju Y (2009) Energy analysis and criteria for structural failure of rocks. J Rock Mech Geotech Eng 1(1):11–20Google Scholar
- Xu N, Zhang J, Tian H, Mei G, Ge Q (2016) Discrete element modeling of strata and surface movement induced by mining under open-pit final slope. Int J Rock Mech Min Sci 88:61–76Google Scholar
- Zhang C, Canbulat I, Hebblewhite B, Ward CR (2017) Assessing coal burst phenomena in mining and insights into directions for future research. Int J Coal Geol 179:28–44Google Scholar
- Zhang Q, Zhao J (2014) Quasi-static and dynamic fracture behaviour of rock materials: phenomena and mechanisms. Int J Fract 189(1):1–32Google Scholar
- Zhang Z (2002) An empirical relation between mode I fracture toughness and the tensile strength of rock. Int J Rock Mech Min Sci 39(3):401–406Google Scholar
- Zhang Z, Kou S, Jiang L, Lindqvist PA (2000) Effects of loading rate on rock fracture: fracture characteristics and energy partitioning. Int J Rock Mech Min Sci 37(5):745–762Google Scholar
- Zhu H, Zhao Y (2017) Formation and development of underground engineering stable equilibrium theory. In: Zhu H, Chen M, Zhao Y, Niu F (eds) Stability assessment for underground excavations and key construction techniques, pp 3–32Google Scholar
- Zhu X, Wang J (2004) Introduction to partly soil models in abaqus software and their application to the geotechnical engineering. Rock Soil Mech 25(2):144–148Google Scholar
- Zhuang D, Tang C, Liang Z, Ma K, Wang S, Liang J (2017) Effects of excavation unloading on the energy-release patterns and stability of underground water-sealed oil storage caverns. Tunn Undergr Space Technol 61:122–133Google Scholar
- Zi G, Belytschko T (2003) New crack-tip elements for XFEM and applications to cohesive cracks. Int J Numer Methods Eng 57(15):2221–2240Google Scholar