How can the effect of particle surface roughness on the contact area be predicted?

This paper describes a systematic study of the effect of fractal rough surfaces on the contact area with the aim of advancing contact constitutive laws used in the Discrete Element Method. An in-house Boundary Element code is adopted to investigate the mechanical behaviour of computer-generated surface roughness. Surfaces are generated to have methodically controlled root mean square height (S_q), root mean square gradient (S_dq), short wavevector (q₀), large wavevector (q₁), Hurst exponent (H) and fractal dimension (D_f). The effect of each parameter on the contact area is investigated. Two recently proposed analytical solutions in tribology (i.e. Persson-Tosatti and Pastewka-Robbins) are applied to predict the real contact area. A parameter based on S_q, q₀, and H is proposed and its sensitivity for real contact area prediction is demonstrated. Surfaces of natural sand are simulated and their mechanical response shows similar trend as the computer-generated surfaces, albeit more complex.