The deformation modulus of rock masses is an important input for the calculation by analytical and/or numerical methods of stresses and deformations around underground works (like tunnels, chambers), and surface works (like dams, foundations, slopes). As it cannot be derived from laboratory tests, the current practice is to estimate it according several empirical formulations based in geomechanical classifications. After Bieniawski's (1978) first proposal, Serafim & Pereira and Barton (using data from Rocha, 1964) gave more specific formulations in a Lisbon Symposium (1983). Afterwards Boyd (1993), Barton (1995), Hoek & Brown (1997) and Hoek, Carranza-Torres & Corkum (2002) have all, presented contributions to the question. This paper reviews the proposed formulations, compares them and suggests some guidelines for the estimation of the deformation modulus to be used in design.


An appraisal of the deformability of the rock mass is needed in order to calculate stresses, strains and deformations in dams, foundations and tunnels. Determination of the elastic deformation modulus (Young modulus) of the rock masses has always been a problem not solved by theory. The classical approach has been in situ testing, but in practice this method is only feasible for big works. Hence, empirical correlations between geomechanical classifications and deformation modulus of the rock mass have always been very popular. The first one of these correlations was proposed by Bieniawski (1978), and afterwards several authors have introduced modifications to improve it. Most of these correlations fail to consider two very important aspects: anisotropy of rock mass and water effect. The elastic deformation modulus of the rock mass Em depends on very different factors. At the first stressing Em has a reduced value, which increases with the subsequent steps of dressing and distressing. Furthermore the Em modulus can have very different values depending on the direction of the principal stress. In stratified rock mass and/or with a governing joint orientation, the equivalent elastic modulus of deformation is the weighted arithmetic mean of the deformation modulus of the different strata (when the stress direction is parallel to the governing joints), and the weighted harmonic mean (when the stress direction is perpendicular to governing joints). The difference between both of them gets wider as anisotropy of the rock mass increases. Water also reduces both the strength and the equivalent deformation modulus when the this mass is saturated, a very important effect in dam foundations. The first papers neglected water effect. The introduction of GSI included a very simple way to consider the water effect: to evaluate RMR as if the rock mass were fully dry and to introduce water pore pressure in computations (see Bieniawski 2000). But that doesn't take account of the reduction of strength and deformability of the rock when saturated. Figure 1 (Pells, 1993) shows a Deere-Miller diagram containing data from compression tests (failure strength and deformation modulus at 50% of failure strength) in dry and saturated Hawkesbury sandstone. Saturation implies a reduction almost proportional in both parameters, but the relationship between them would remain approximately constant.

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