One-Dimensional Compression Fractal Theory and Experimental Verification of Coarse-Grained Soil

Abstract Coarse-grained soil particles are suspectible to breakage under high-stress conditions, with particle breakage being the main reason for the compression of samples. The compression coefficient λ in the e–log σ′ curve is closely related to the degree of particle breakage. In this paper, a term representing surface energy caused by particle breakage was added to the energy conservation equation. The variation of surface area per unit volume of sample was described by fractal dimension, and then the relationship between fractal dimension and vertical stress was established. Finally, the theoretical formula of the compression coefficient was obtained, and the fractal theoretical model of one-dimensional compression deformation of coarse-grained soil was established. The compression coefficient is related to surface free energy, internal friction angle, shape factor, and initial particle size. In addition, calcareous sand and gypsum were selected for one-dimensional compression tests at high stress. With the increase of initial particle size, the compression coefficient increases. According to the relationship between fractal dimension and vertical stress, the theoretical value of the compression coefficient was obtained. The theoretical value is very close to the experimental value, which proves that the fractal theory of one-dimensional compression deformation of coarse-grained soil is correct.