Rock Mechanics and Rock Engineering

, Volume 52, Issue 1, pp 229–245 | Cite as

Energy Dissipation and Storage in Underground Mining Operations

  • Xiangjian Dong
  • Ali KarrechEmail author
  • Hakan Basarir
  • Mohamed Elchalakani
  • Abdennour Seibi
Original Paper


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.


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


Height of the coal seam


Friction angle

\(\widehat{\sigma }\)

Peak value of concentration stress

\(\sigma _{\text {cm}}\)

Uniaxial compressive strength of coal seam


Depth of coal seam


Width of extraction


Displacement field


Strain field


Boundary traction field


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


Extra external work after excavation


Increased strain energy after excavation

\(W_{\text {r}}\)

Released energy due to excavation

\(N_{\text {I}}(x)\)

Conventional nodal shape function


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


The mode-I geometry factor

\(P_{\text {max}}\)

The peak applied load


The thickness of the specimen


The specimen radius


Elastic modulus


Poisson’s ratio

\(h_{\text {f}}\)

Height of fracture zone


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


Bulking factor of caved materials


Maximum principal stress



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.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • Xiangjian Dong
    • 1
  • Ali Karrech
    • 1
    Email author
  • Hakan Basarir
    • 1
  • Mohamed Elchalakani
    • 1
  • Abdennour Seibi
    • 2
  1. 1.School of Civil, Environmental and Mining EngineeringThe University of Western AustraliaCrawleyAustralia
  2. 2.Petroleum Engineering DepartmentUniversity of Louisiana at LafayetteLafayetteUSA

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