Experimental evidences on a unique critical state line for coarse-grained soil with different gradations in light of skeleton void ratio

In the e-(p'/pa) plane, the critical state line (CSL) under different gradations exhibits translation and rotation, which increases the uncertainty of the state parameter. The constitutive model based on the state parameter faces challenges in predicting whether coarse-grained soil will exhibit dilatancy or contraction. The selection of the void ratio index is one of the important factors. This study conducts large-scale triaxial compression tests under different gradations, introduces the concept of skeleton void ratio, and compares the effect of gradation on CSL. The results show that the initial gradation significantly affects the critical void ratio of coarse-grained soils but has little effect on the critical stress ratio. Different gradations cause the CSL in the e-(p'/pa) plane to translation and rotate, whereas in the esk-(p'/pa) plane, the CSL converges to a single curve. A linear relationship exists between the parameter b of the skeleton void ratio and the fractal dimension D, and the parameters a = 0.13 and b = -1.5 are applicable to most coarse-grained soils. This finding will simplify the application of the skeleton void ratio. The unified CSL equation proposed in this study provides a good foundation for developing state-dependent constitutive models.