Cartilage surface roughness has significant implications on joint lubrication. However, the effects of the variability in surface roughness in different directions (especially in horizontal direction) in mixed-mode lubrication have not been fully investigated and relevant research work in this field is limited. This study presents a probabilistic numerical approach to investigate the influence of variability and uncertainty of Root-Mean-Square (RMS) roughness heights (vertical roughness) and roughness correlation lengths (horizontal roughness) on cartilage lubrication.The synthetic surface topographies with typical ranges of vertical and horizontal roughness characteristics were firstly input to a coupled cartilage contact model. A response surface was then constructed using the input roughness parameters and the output coefficient of friction (CoF). Finally, a large number of independent or correlated roughness samples were generated for computing the probability of mixed-mode lubrication failure (PoF), which was defined as CoF0.27 (corresponding to a 90% loss of fluid support in the contact interface).Both independent RMS roughness heights and correlation lengths are correlated positively with CoF. This indicates that the increase of the vertical surface roughness could exacerbate cartilage wear, whereas increasing surface roughness in horizontal direction (i.e., reducing correlation lengths) could retain gap fluid that aids mixed-mode lubrication. Importantly, it shows that CoF is dominant by RMS roughness height. The uncertainty in the independent correlation lengths may lead to the underestimation of PoF. By simulating osteoarthritic surface roughness with a strong correlation between RMS roughness heights and correlation lengths, the value of PoF could reach 70-99%.This study highlights the significance of incorporating the mutual relations between the surface roughness in vertical and horizontal directions into research, and the findings could potentially contribute to the design of biomimetic cartilage surfaces for the treatment of osteoarthritis.
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