This paper superimposes twenty components of sine-shaped sub-profiles with different wavelengths, amplitudes and phases to approximate the irregular joint profile. Each component sub-profile is individually subjected to a normal load and then closed. A mathematical model based on the Hertz contact theory that usually applied on two contacting circular bodies is thus capable of employing for calculating the elastic deformation of irregular profile. The resulting closure deformation for an irregular joint profile can be summed up from the twenty regular sub-profiles. A preliminarily closure test on model joints is performed to evaluate the applicability of this mathematical model.


The shear behavior and flow conductivity of rough joints is primarily dominated by the contact of joint asperities. Two joint surfaces pressed together approach each other owing to the elastic deformation of the asperity on them. The actual contact area or joint aperture, however, is difficult to be estimated due to the randomness of joint irregularities. The contact condition of joints is primarily reflected on the closure behavior of asperities. Goodman (1976) had been presented an empirical relationship between the closure d and normal load P as: d = A +B ln P. Mated and unmated joints behave the same way but with different constants A and B. Goodman gave no physical interpretation of these two constants. The unmated joint shows more closure than the mated joints. A similar conclusion was also drawn from BandisÕs researches (1983). Numerous mathematical approaches for calculating the closure behavior or contact area are based the stochastic concept (Greenwood-Williamson, 1966; Swan, 1983; Brown et al. 1985). Some statistical parameters for averaging the irregular joint surfaces must be obtained first. They found that estimating the geometrical features seem to play the essential part for calculating the contact closure.

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