The critical normalized roughness (Rcr) serves as a pivotal metric for distinguishing the roughness of the soil-- structure interface. The accurate determination of Rcr is highly important in both research and engineering applications related to the mechanical properties of the interface. However, research on methods for determining Rcr are scare, and the theoretical methods are especially rare. This paper aims to establish a theoretical calculation method of critical normalized roughness Rcr. Using tribology theory, the existence of Rcr was corroborated through the analysis of both single-particle sliding and whole-soil sliding mechanisms. A theoretical formula was subsequently established for the computation of Rcr. A comparison between the theoretical calculations and experimental results revealed that the proposed formula is applicable to both scenarios involving particle breakage and scenarios lacking particle breakage at the interface. Compared with scenarios without particle breakage, the theoretical formula exhibits a superior predictive capacity for cases involving particle breakage. The proposed theoretical calculation method in this paper provides a novel approach and perspective for determining the critical normalized roughness Rcr.