Among the constitutive models for rock fractures developed over the years, Barton’s empirical model has been widely used because it is easy to apply and includes several important factors associated with fracture characteristics. Anisotropic behavior of rock joints were investigated experimentally by different researchers. They proposed models that can deal with the strength, deformability, or dilatancy of rock fractures. These models include several parameters and they are much more complicated than Barton’s model. Experimental data found in the literature are used in this paper to formulate a method to simulate anisotropic behavior of rock fractures in accordance with Barton’s model. The shear strength, shear stiffness, and dilation displacement of rock fractures subjected to shearing in all directions can be predicted using the proposed model applied on Barton’s failure criterion parameters.
The mechanical behavior of jointed rock masses is strongly affected by the behavior of fractures. Several empirical and theoretical constitutive models [1-19] were developed to simulate the behavior of rock fractures. Many researchers [20-24] have attempted to predict the shear strength of non-planar rock fractures based on their dilatant behavior. The prediction of the dilatancy phenomenon of regular or irregular fractures subjected to direct shear loading has been addressed by numerous researchers [1, 2, 7, 19, 25-30]. Among these models, Barton’s empirical model has widely been used because it is easy to apply and includes several important factors of fracture properties .
The shearing strength of rock fractures is composed of two components: (1) the base friction angle, fb, resulting from two sawed surfaces sliding over each other, which is equal for all shearing directions; and (2) the resistance to sliding and/or shearing of the fracture asperities, which is a geometrical parameter. Consequently, the shear strength of rock fratures will be anisotropic as long as the surface is uneven and displays anisotropy in its geometric property .
Huang and Doong  conducted an experimental study on the anisotropy in shear strength of fractures by shearing silicon rubber replicas of rock fractures in different directions. They found that: (1) the shear strength of the joints with the same surface morphology might be different when sheared in reverse direction; (2) the effect of anisotropy decreases with increasing normal stress. Their results show that the shear direction changes the shear strength of replicas. They adopted Barton’s failure criterion  together with Tse and Cruden’s equation  relating the joint roughness coefficient, JRC, with the root mean square, RMS, of the asperity angle. However, they had no specific solution for including the shear direction in the shear strength of rock fractures.
Jing et al. [34, 35], through their experimental study, found that the distribution of the total friction angles, fp , on the nominal plane of the fracture surface (lower block), may be generalized as follows: (1) fp varies with both the shear direction and magnitude of normal stress; (2) the degree of the directional variation of fp decreases with increasing normal stress.