Abstract
In this study, a constitutive rule for the stress-strain relation in which the grain crushing of normally consolidated sand under one-dimensional compression was developed based on the behavior of the soil structure of sand grains. The constitutive rule is based on the phenomenological hypothesis that the logarithmic void strain gradient Δεes/Δσ (Area I), which corresponds to the elasto-plastic components of the soil structure, and the logarithmic void strain gradient Δεc/Δσ (Area II), which corresponds to of the failure component attributed to grain crushing, both follow the power law with respect to the compressive stress σ. Furthermore, we developed an evolution rule for the strain, considering the degradation of soil structure associated with failure due to grain crushing (Area III) along with the strain in the soil structure during failure due to grain crushing εc as an internal variable. The proposed constitutive rule that describes Areas I, II, and III in a unified manner was validated through verification against actual measurements. This constitutive rule is considered to be significant for improving the expressive capabilities of existing numerical models because it describes an extensive strain area.
