It is obvious that surface irregularities of a rock joint play a dominant role in its closure behavior. Therefore, special attention should be paid for the study of surface irregularities consisting of asperities in different scales. The laboratory tests of model joints are mainly conducted on the 2D joint profile because of producing the 3D joint surface is inconvenient. In this paper, a new technology called Laminated Object Manufacturing (LOM) is used to create the 3D surface geometry of joint models. It is proved that using the first five harmonics of Fourier transform will cause the first order asperities to be modeled and summing up higher order components lead the second order asperities to be also modeled. In this way, the effect of asperity order and scale is investigated on the joint closure. Hertz contact theory proposed for metal surfaces is employed to calculate the closure behavior of joint surfaces.
Patton[1] categorized asperity into first-order (waviness) and second-order (unevenness) categories. Hoek and Bray[2] stated that at low normal stress levels the second-order asperity (with highest-angle) controls the shearing process. As the normal stress increases, the second-order asperity is sheared off and the firstorder asperity (with a longer base length and lower-angle) takes over as the controlling factor [3]. In 3D joint surface modeling, a depicted mother mold is usually cast from a natural rock surface using silicon material. Then, the multiple replicas cast from the mother mold with identical surface geometry are reproduced [4]. It is difficult to generate another artificial surface from a typical surface. Especially, it is the urgent need in the field of scale effect using similar surfaces in different sizes. The key factor is the difficult of automatically generating a 3D rough joint surface. This paper proposes a method to generate the 3D joint surface using Laminated Object Manufacturing (LOM) technology [5]. This method can produce a 3D mother surface with a given surface geometry. The ability of generating two joint surfaces with the same primary roughness but different in micro scale is also possible. This method is helpful to study the effect of the primary and secondary asperity on the joint closure behavior, either. The present mathematical approaches for calculating the closure behavior or contact area is based on the stochastic concept [6]. Some statistical parameters for averaging the irregular joint surfaces must be obtained. They found that estimating the geometrical features seem to play the essential part for calculating the contact closure. Recently, several researchers [7] had been successfully adopted the Fourier transform concept to characterize the irregular joint surfaces. Superimposing several periodic functions can ideally approximate the irregular joint profile. In this paper, superimposing twenty components of sine functions that have different wavelengths, amplitudes and phases approximates the joint profile under a normal load [8]. Each component, a regular sine-shaped sub-profile, is subjected to a normal load and then progressively closures.
