## 1 Introduction
Based on the modified M-B model, [PERSON] [25], [PERSON] [26] and [PERSON] [27] derived the relationship between the contact area of a single asperity and its normal deformation. [PERSON] [28] thought that the contact area of a single asperity increases with the increment of its normal deformation, and when the contact area is less than the critical contact area the deformation is plastic, otherwise it is elastic, which is consistent with the deformation mechanism of the M-B model. [PERSON] [29] and [PERSON] [30] proposed using the opening size of asperity's base to express the contour curve. They defined the index \(n\) of asperities at different levels to describe the deformation of asperity, and pointed out that under certain contact loads, the high-level asperity will transform to a low level. [PERSON] [31] combined fractal theory with a finite element model to study the contact characteristics of three-dimensional rough surface under thermal-mechanical coupling. By deducing the W-M function in the spherical coordinate system and conducting numerical simulation, [PERSON] [32] obtained the profile of rough spherical surface, established the fractal rough spherical contact model and analyzed the influence of fractal parameters on the relationship between contact load and contact area on rough spherical surface. According to the contact mechanism of spherical surface, [PERSON] [33] established the contact model of rough spherical surface, derived the analytical expression of real contact area and contact load, and obtained the contact pressure distribution of rough spherical contact area at different deformation stages. In the study of contact mechanics of rough surfaces based on fractal theory, fractal parameters are used to describe rough surfaces, it can overcome the influence of measuring instrument resolution and sampling length. However, the conclusion that \"asperity appears plastic, elastic-plastic and elastic deformation in turn\" is against reality. [PERSON] [34] fully considered the influence of surface roughness and analyzed the contact characteristics of rough surface when establishing the contact model. [PERSON] [35] established a loading-unloading contact analytical model between two cylindrical rough surfaces based on fractal theory and investigated the effect of parameters in the model on the loading-unloading contact performance. In addition, some scholars use the shoulder-shoulder contact model [36; 37; 38; 39] rather than top-top contact model when studying the contact force, contact stiffness and friction heat of two surfaces. However, these models do not have explicit applications for shoulder-shoulder contact, and do not specifically study the fractal machined surface that conforms to the W-M function. Therefore, the research on the contact mechanics for rough surfaces, especially the shoulder-shoulder contact, needs in-depth investigation. In the present paper, the contact state and porosity of rough sealing surfaces are analyzed; the geometric model for asperity and contact mechanics model for rough surfaces are established; and the deformation of asperity, the real contact area and contact load of rough sealing surfaces are discussed. Based on these, the effects of contact pressure and surface topography parameters (fractal dimension \(D\) and fractal roughness \(G\)) on the porosity and contact area of sealing surface are studied.