Non-geometric hazards like sinkage and slipping, correlated to terrain categories, have an apparent effect on the locomotion of legged robots. Tactile-based terrain classification is a more accurate way to distinguish terrains in different properties than the vision, but selecting representative features instead of cumbersome ones in the complex foot-terrain interaction for efficient classification is still a challenge. In this letter, two specific leg motions are designed to inspect terrain bearing and friction properties, and manually designed features are extracted based on the foot-terrain interaction model for classification. These features are physics-informed, tidy and interpretable, and can be used with different classifiers under different foot configurations. Four classic classifiers with physics-informed features are trained for terrain classification and evaluated on our self-developed dataset. At the same time, the proposed method was compared with other two methods: an artificial feature extraction method and a CNN-based method. The results show that our proposed method reaches remarkable precision in terrain classification and can still guarantee a high accuracy under a small number of training samples.