<p>The roughness of fault surfaces as a function of measurement length recovers a consistent power–law relationship across multiple faults, suggesting the scaling arises from some fundamental physical process. We examine this relationship by deriving the distribution of elastic stress in triangular asperities under asymmetric loading and subject the asperities to tensile, plastic, and shear failure conditions. The power–law scaling of fault roughness implies a two-regime asymptotic scaling behaviour of strength. All failure modes predict power–law weakening at small scales but diverge on whether strength must increase or decrease at large scales. The power–law weakening behaviour is consistent with measurements on the size-dependence of strength. This analysis implies that material strength is the governing property behind the size-dependent roughness of faults surfaces at small scales, but some process other than material failure is responsible at large scales unless roughness becomes self-similar.</p>