Contents lists available at ScienceDirect International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms Ultimate bearing capacity of rock masses based on modified Mohr-Coulomb strength criterion R.A. Galindo ⁎ , A. Serrano, C. Olalla Technical University of Madrid, Spain ARTICLE INFO Keywords: Bearing capacity Spread foundation Non-linear strength Criterion Characteristic method 1. Introduction Traditionally, the study of bearing capacity of rock shallow founda- tions has been addressed by empirical formulae and practical recom- mendations are generally based on rough correlations with unconfined compressive strength. Most likely, the most used criteria are those present in various Building Codes of different cities and countries, such as. 3–6 Depending on the document that is used, the results obtained differ considerably, even in one order of magnitude. Theoretical analysis of foundation bearing capacity in rock has been addressed very late mainly because rock masses have intrinsic char- acteristics as a result of discontinuities, anisotropy, non-linearity, etc. This means that a simple theoretical treatment of the ultimate bearing capacity, in the case of a homogeneous isotropic continuous medium with a linear failure criterion, would be unrealistic. There are cases in which a rock mass could be regarded as a homogeneous and isotropic continuous medium. This would be the case when the rock mass is so weak that its behaviour exerts a greater influence than the discontinuity factor, or when the rock mass is extremely fractured both homogeneously and isotropically. Thus, the proposed methodology is appropriate for homogeneous and isotropic rock media in a similar way to the one suggested by Hoek (1983), not only for solving stability problems but also the elastic-plastic behaviour in tunnel opening operations. This methodology depends on the number and spacing of discontinuities and on the real dimensions of the analysed problem (Fig. 1). The hypothetical case of a rock mass with few defects could also be taken into consideration when such defects are of little importance and when these types of rocks do not form continuous surfaces that are critical for stability. When the rock mass is highly fractured, even with regard to small foundations or changes from soil to rock 8 the stresses are not insignificant related to the resistance of the rock mass, and can bring about “plastification”. In this case, the rock behaviour can also be studied using the theories of plasticity with a suitable failure criterion. Both in large foundations with heavy loads and in many of the cases of small foundations, “plastification” of the rock mass may take place. Regarding the effect of the own weight of the rock mass on the stability, in the case of small foundations, only a small volume are affected and the stresses caused by their own weight are negligible when compared to the strength of the rock. Furthermore, it should be noted (as is discussed below) that the analysis of the boundary conditions of the problem of bearing capacity of foundations is limited to the case of soft slope (e.g., no more than 20º). The ultimate bearing capacity of foundations on rock masses has been studied in detail from a theoretical point view for the Hoek-Brown failure criterion 9 applied to shallow foundations 10–12 and deep foundations 13–15 ; extending the study to the Modified Hoek-Brown failure criterion 16,17 in both types of foundations . 18–20 The strength behaviour of the rocks is generally expressed by a failure criterion. A non-linear strength criterion for intact rocks was suggested by Singh et al. , 1,2 which is an extended form of the conventional Mohr–Coulomb criterion. An important advantage of the proposed criterion is that the conventional Mohr–Coulomb shear strength parameters are retained as such. In, 2 the criterion proposed for intact rock 1 is extended to jointed rocks, which are anisotropic in nature. This criterion was deduced from Barton’s concept of critical state in rocks. 21 Barton 21 states that ‘‘critical state for any intact rock is defined http://dx.doi.org/10.1016/j.ijrmms.2016.12.017 Received 14 March 2016; Received in revised form 20 August 2016; Accepted 30 December 2016 ⁎ Correspondence to: ETSI Caminos, C. y P., C/ Profesor Aranguren s/n, Madrid 28040, Spain. E-mail address: ragalindoa@hotmail.com (R.A. Galindo). International Journal of Rock Mechanics & Mining Sciences 93 (2017) 215–225 1365-1609/ © 2017 Elsevier Ltd. All rights reserved. MARK