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Rock mass classification is important in preliminary design of geotechnical engineering projects. Using the columnar jointed basalt at the foundation of Baihetan Hydropower Station as an example, this paper presents a classification scheme of the columnar jointed rock. Unlike many common rock masses, an obvious characteristic of columnar jointed rock is that it is discontinuous in geometry while continuous in mechanics. Due to the inapplicability of existing rock mass classification systems, a classification scheme, combined with rock mass integrity, weak plane tightness, and permeability, is proposed. The new classification system has five grades with quantitative factors, which takes into account the features of columnar joints. As an easy-to-use scheme and case study, it would be helpful as a reference in the rock mass classification of similar problems.