CLOSURE OF UNDERGROUND OPENINGS IN JOINTED ROCKS

Abstract

Analysis of closure of underground openings in jointed rock mass is an important aspect in designing underground structures and support systems. Rock masses are often subjected to far field in-situ stresses and at any point in the mass there exists an equilibrium of stresses. As soon as an opening is created, the initial stress equilibrium is disturbed and redistribution of stresses takes place. As a consequence differential stresses occur in the rock mass at the boundary of the opening resulting in the closure of opening. The magnitude of differential stresses depends on in-situ stress state. The rock mass at the boundary may or may not fail depending on whether the rock mass strength is exceeded or not by the resulting stresses after excavation. If the rock mass does not fail, it may be treated to be elastic and closure of the opening may be assessed by using theory of elasticity provided a correct assessment of the modulus of deformation of the mass is possible. If the stresses after excavation exceed the strength of rock mass, the mass fails and a plastic zone develops around the opening. The plastic zone extends to a certain radial distance beyond which the rock mass remains in elastic state. Elastoplastic theories are used to get the closure of the opening in this case. Development of plastic zone or determination of extent of plastic zone (if it develops) depends on the strength of the rock mass. The strength of rock mass is determined through a strength criterion. Most of the approaches in vogue use triaxial strength criteria and ignore the effect of intermediate principal stress on the strength of the rock mass. It is now well established that intermediate principal stress does have significant influence on the strength and should be given due consideration. A polyaxial criterion iii has therefore been suggested in this study. The input parameters of the criterion can be easily obtained from field by using classification approach. A closed form solution for analyzing circular opening subjected to hydrostatic stress field has also been suggested. If plastic zone does not develop, the rock mass is treated to be elastic and closed form solutions based on theory of elasticity are used to assess the closure. The difficulty is however faced in accurate assessment of modulus of deformation Em which is an important input parameter in elastic analysis. The rocks in the field are jointed and anisotropic in nature and assessment of a representative isotropic value of modulus is a big challenge before geotechnical engineers. Moreover the modulus has also been reported to be pressure dependent by some researchers. Few experimental studies are available in literature on deformational behaviour of jointed rocks but these studies pertain to loading of rocks under uniaxial and triaxial conditions. Failure mechanism of rock mass at the boundary of opening is entirely different as the mass acts under constrained dilatency. The modulus of deformation obtained from uniaxial or triaxial tests as such is not directly applicable in analyses of closure behaviour of an underground opening. An experimental study was therefore planned through physical model tests, in which closure and corresponding internal pressure on the opening were monitored to get ground response curves. Specimens of jointed rock mass were prepared. A model material having weak- rock-like properties was used to simulate rock. Small elemental blocks of model material were assembled in a certain fashion to form the specimen of the mass. Prepared specimen of the mass consisted three joint sets orthogonal to each other. Various orientations of joints were used in tests. A small opening was created in the mass while preparing specimens. Arrangements were made to measure closure and internal pressure at the roof and walls of the opening. Far field IV in-situ stresses were applied through hydraulic jacks. The stresses were kept low so that the anisotropy induced due to joint orientation is not suppressed. Incremental closures were allowed in walls and roof and the corresponding internal pressures were recorded. The results have been analyzed and a procedure has been suggested to estimate modulus of rock mass based on mapping of joints in the field and simple laboratory tests. The modulus has been found to be pressure dependent. An empirical expression has also been suggested to incorporate pressure dependency in the modulus. The proposed elasto-plastic solution for squeezing ground condition, which incorporates a non-linear polyaxial strength criterion, has been applied to eleven case histories of tunnels in squeezing ground. Step by step procedure, to obtain the strength and deformation parameters of rock mass from classification approach, has been presented. The case histories have been analyzed by using the proposed solution as well as by an elasto-plastic solution using Mohr-Coulomb triaxial strength criterion. The closures predicted by incorporating polyaxial strength criterion have been found to be closer to those observed in the field. The proposed elasto-plastic solution is therefore recommended for design of support system in the squeezing ground conditions, as Mohr-Coulombs theory gives too conservative support pressures.