ORIGINAL PAPER Development of a new equation for joint roughness coefficient (JRC) with fractal dimension: a case study of Bakhtiary Dam site in Iran Manouchehr Sanei & Lohrasb Faramarzi & Sareh Goli & Ahmad Fahimifar & Asghar Rahmati & Abolfazl Mehinrad Received: 3 June 2013 /Accepted: 26 September 2013 # Saudi Society for Geosciences 2013 Abstract The joint roughness has a significant effect on the shear behavior of rough joints, which control the shear strength of jointed rock mass. This index plays an important role in the mechanical and hydraulic proper- ties of rock masses. There have been extensive studies in last a few decades. Joint roughness coefficient (JRC) and fractal dimension D are two well-studied and adopted parameters used in estimating the surface roughness of rock joints. This study proposed a new relation between JRC and D , and compared this relation with the previous studies by applying it on JRC pro- files. This relation was also introduced into Barton’ s empirical equation to assess the shear strength of rock joints, and its performance was estimated by applying it to more than 30 laboratory direct shear tests on natural rock joints from Bakhtiary Dam site. The advantage of this study, when compared to the previous works done by others, is using the results of more than 30 direct shear tests on natural rock joints for the evaluation of reli- ability of the proposed equation. Therefore, the new obtained relationship between JRC and D seems to capture well the roughness coefficient of natural rock joints. Keywords Direct shear tests . Fractal dimension . Joint roughness . Natural rock joints Introduction The engineering properties of rock masses are controlled by the characteristics of the discontinuities (Zadhesh et al. 2013). It is a known fact that the discontinuities have significant effect on mechanical behavior of rock masses which reduce their strength (Sharifzadeh et al. 2011; Ghazvinian et al. 2012). It has wider application in the rock excavation engi- neering, e.g., caverns, tunnels, slope stability, dams, and rock foundations (Verma and Singh 2009; Salari-Rad et al. 2012). The most important properties of the discontinuities are ori- entation, extent, planarity, asperities, roughness, and strength of wall rock. Strength, deformability, and fluid flow properties of rock joints depend on the surface roughness of joints. Roughness effects on the friction angle, dilatancy, and peak shear strength were evaluated (Patton 1966; Goodman 1975). Therefore, the accurate value of roughness is important in modeling strength, deformability, and fluid flow. The rough- ness, represented by the joint roughness coefficient (JRC), varies from 0 (smooth) to 20 (rough). To assign a value of JRC to the joint, the roughness profile is compared with standard roughness profile. However, it is well understood that JRC determined by visual comparison is subjective and sometimes erratic (Barton and Choubey 1977). Many researchers have thus attempted to estimate the JRC value for a surface from the profile geometry such as fractal analysis (Den Outer et al. 1995; Huang et al. 1992; Muralha 1995) or statistics (Wu and Ali 1978; Krahn and Morgenstern 1979; Reeves 1985). The JRC value was recommended by ISRM (Brown 1981), and it has been widely used in engi- neering practices. Over the years, some statistical parameters having correlations with JRC have been developed (Dight and M. Sanei (*) : L. Faramarzi : A. Rahmati Department of Mining Engineering, Isfahan University of Technology, Isfahan, Iran e-mail: manouchehr.sanei@gmail.com S. Goli Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran A. Fahimifar Department of Civil Engineering, Amirkabir University of Technology, Tehran, Iran A. Mehinrad Project Management Team, Bakhtiary Joint Venture Consultants (BJVC), Tehran, Iran Arab J Geosci DOI 10.1007/s12517-013-1147-3