Evaluation of the Stress State in Two Adjacent Backfilled Stopes Within an Elasto-Plastic Rock Mass

Original paper


Backfill is used in the mining industry to improve the stability of underground openings and reduce the environmental impact due to the surface disposal of mine wastes. A critical issue for the design of backfilled stopes is the determination of the stress state in the backfill and surrounding rock mass. In recent years, much work has been conducted to assess the stresses in isolated backfilled stopes. Recent work performed by the authors indicates that the stress distribution in a backfilled stope may also be affected by the excavation of an adjacent opening. So far however, simulations of neighbouring stopes have been based on an elastic behavior for the rock mass, which may not reflect its actual response (especially under large stresses). This paper presents key results obtained from numerical simulations of two backfilled stopes excavated in sequence in an elasto-plastic rock mass. The simulations results illustrate the effects of the non-linear rock mass response and of other characteristics including stopes geometry (size and spacing) and depth, natural stress state, and backfill properties. These results indicate that, although arching effects tend to develop in all narrow stopes, the stress distribution in adjacent openings can be quite different for elastic or elasto-plastic rock mass behavior. The results presented here also illustrate the similarities and differences between the behavior of a single backfilled stope and of two adjacent stopes, depending on the rock mass properties and overall characteristics of the system.


Adjacent stopes Mine backfill Rock mass Stresses Numerical modelling Elastic Elasto-plastic behavior 

List of symbols


Stope width (m)


Cohesion of backfill (kPa)


Cohesion of rock (kPa)


Distance between stopes (or pillar width) (m)


Backfill modulus (MPa)


Rock mass elastic modulus (GPa)


Rock mass deformation modulus (GPa)


Depth (m) in the backfill


Stope height (m)


Earth pressure coefficient in the backfill (-)


Rankine’s active earth pressure coefficient


Earth pressure coefficient at rest


Earth pressure coefficient for the natural stresses in the rock mass


Depth at the base of the stope (m)


Maximum difference between the horizontal displacements (cm)


Maximum difference between the horizontal stresses (kPa)


Maximum difference between the vertical stresses (kPa)


Unit weight of backfill (kN/m3)


Unit weight of rock (kN/m3)


Unit weight of rock mass (kN/m3)


Horizontal displacement of rock walls (m)


Horizontal strain of backfill (%)


Poisson’s ratio of rock mass


Backfill Poisson’s ratio


Horizontal stress at backfill and in situ horizontal stress (kPa)


Vertical stress at backfill and in situ vertical stress (kPa)


Internal friction angle (°) of backfill


Internal friction angle (°) of rock mass


Dilatancy angle of backfill (°)



The authors acknowledge the financial support from NSERC and from the partners of the Industrial NSERC Polytechnique-UQAT Chair on Environment and Mine Wastes Management (2006–2012) and of the Research Institute on Mines and the Environment (RIME UQAT-Polytechnique; http://rime-irme.ca/).


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Civil, Geological and Mining EngineeringPolytechnique MontrealMontrealCanada

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