Abstract: Under the action of compression and shear loads,only a small part of the steep asperities on the joint surface contacts and interacts with each other.In the past,when describing the roughness,the distribution characteristics of the asperities of the whole surface were considered,which made the roughness index weaken the effect of the steeper asperities and strengthen the effect of the gentler asperities on the shear strength (in fact,most of the gentler asperities did not contact during the shear process).Firstly,the area ratio of different apparent angles was studied based on the Grasselli apparent angle distribution function.The effect of the steeper contact asperities on joint shear strength was analyzed.For fully coupled joints without filling,when the joints are subjected to normal load,a small part of asperities will undergo elastic deformation,and the initial contact part will yield.As the normal stress continues to increase,more and more asperities will contact with each other and yield.This process will continue until the area of the contact asperities is large enough to withstand the given normal load.Therefore,the minimum dip angle of all contact asperities is the dip angle of the asperities which just yield under a certain load.Furthermore,the approximate expression of the actual contact area was obtained based on the contact theory.Considering the distribution characteristics of the actual contact part of the joint asperities,the average effective apparent angle of the actual contact joint asperities was obtained,and the reasonable 3D roughness index was obtained.The Brazilian splitting test was carried out to obtain the splitting joint surface instead of the natural joint surface to study the joint roughness,and the joint coordinate data was obtained through the scanning test of the joint morphology surface.The peak dilatation angle of joint reflects the actual shear process under a certain stress,and can accurately reflect the peak shear strength of joint.The results show that the new index of joint roughness can be well related to the peak shear strength of joints.