A novel binary effective medium model to describe the prepeak stress-strain relationship of combined bodies of rock-like material and rock

Combined bodies of rock-like material and rock are widely encountered in geotechnical engineering, such as tunnels and mines. The existing theoretical models describing the stress-strain relationship of a combined body lack a binary feature. Based on effective medium theory, this paper presents the governing equation of the “elastic modulus” for combined and single bodies under triaxial compressive tests. A binary effective medium model is then established. Based on the compressive experiment of concrete-granite combined bodies, the feasibility of determining the stress threshold based on crack axial strain is discussed, and the model is verified. The model is further extended to coal-rock combined bodies of more diverse types, and the variation laws of the compressive mechanical parameters are then discussed. The results show that the fitting accuracy of the model with the experimental curves of the concrete-granite combined bodies and various types of coal-rock combined bodies are over 95%. The crack axial strain method can replace the crack volumetric strain method, which clarifies the physical meanings of the model parameters. The variation laws of matrix parameters and crack parameters are discussed in depth and are expected to be more widely used in geotechnical engineering.