Keywords: rockburst, finite element method, instability, brittle plasticity, underground openings, infinite media.

A finite element model is proposed to predict the occurrence of rockburst [1] in underground openings. It is assumed that rockburst results due to instability of rock mass and the analysis is based on a perturbation technique. The rock mass is considered to be elastic-brittle-plastic. A novel method of elastic supports is used to simulate the effects of unbounded rock mass.

A rockburst is a sudden and violent expulsion of rock from the surrounding rock mass. Possible effects of rockbursts include injuries and fatal accidents, damage to equipment, construction and production delays, and higher cost of construction and operation. There is a need for the development of suitable computational methods for the prediction and control of rockbursts particularly for a safe and economical underground excavation for construction or mining in burst-prone ground.

The finite element method is considered to be the most suitable method for the analysis of such complex problems. However, in the application of this method to problems in geomechanics, a computational difficulty arises due to the infinitely large extent of the geomaterial. Recently, a novel method of elastic supports [2]] was developed to eliminate the disadvantages associated with infinite elements and the coupled finite element boundary element methods. The method is based on the use of multi-directional elastic supports with spatially varying stiffnesses along the truncation boundary of the finite element model to simulate the effects of unbounded extent of geomaterial. The method was successfully applied to the elastoplastic analysis of fracture [3] and elastic-brittle-plastic analysis of underground openings [4]. In this paper, this method is applied to the instability analysis of rock mass.

The present analysis is for the situation when rockburst results due to underground excavation and not due to the presence of faults, dykes, etc. Very little work has been done in the past on the application of the finite element method for the instability analysis of rockburst. Bardet used the finite element method to analyze rockburst as a surface buckling problem [5]. The computational technique was based on the eigenvalue approach. However, he assumed the rock mass to be hypo-elastic and applied the technique to the wedge-test problem. As mentioned earlier, the instability analysis proposed in this paper is based on a perturbation approach. In this approach, it is assumed that there is a potential of rockburst occurrence when a loading stiffness parameter approaches a zero value [1].

In the present analysis, the underground opening is considered to have an arbitrary geometry and as mentioned earlier, the rock mass is considered to be elastic-brittle-plastic. Mohr-Coulomb and Hoek-Brown failure criteria are used and both associated and non-associated plasticity are considered. The far field is assumed to be homogeneous, linearly elastic and extending to infinity. A commercially available finite element software is used to implement the proposed method and plane strain axisymmetric analyses of underground openings are conducted.

The effectiveness and efficiency of the proposed numerical technique are demonstrated by comparing finite element results with analytical solutions for 'deep' circular openings. Highly accurate results are produced even if the finite element truncation boundary is located very close to the yielded zone. Some example problems are presented to demonstrate the potential occurrence of rockburst.

1

J.C. Jaeger, N.G.W. Cook, "Fundamentals of Rock Mechanics", Chapman & Hall, London, 1979.

2

S.K. Sharan, "Viscoplastic plane-strain analysis of infinite solids using elastic supports", International Journal for Numerical Methods in Engineering, 45(3), 355-369, 1999. doi:10.1002/(SICI)1097-0207(19990530)45:3<355::AID-NME594>3.3.CO;2-R

3

S.K. Sharan, "Elasto-plastic finite element analysis of a crack in an infinite plate", International Journal of Fracture, 103(2), 163-176, 2000. doi:10.1023/A:1007698426810

4

S.K. Sharan, "Elastic-brittle-plastic analysis of circular openings in Hoek-Brown media", International Journal of Rock Mechanics and Mining Sciences, 40, 817-824, 2003. doi:10.1016/S1365-1609(03)00040-6

5

J.P. Bardet, "Finite element analysis of rockburst as surface instability", Computers and Geotechnics, 8, 177-193, 1989. doi:10.1016/0266-352X(89)90042-6

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