Critical state behaviors of a coarse granular soil under generalized stress conditions

Critical state line (CSL) is the central concept in soil mechanics. A series of true triaxial compression tests under the constant-\({p}'\) and constant-b loading condition were carried out to investigate the CSL of a coarse granular soil. It was observed that the intermediate principal stress ratio (i.e., the b-value) greatly influenced the CSLs in both \(q{-}{p}'\) and \(e{-}{p}'\) spaces. The CSL slope in the \(q{-}{p}'\) space decreased with an increase in b-value. The intercept and gradient of the CSL in the \(e{-}{p}'\) space decreased with increasing b-value. CSLs incorporating the effects of the b-value in \(q{-}{p}'\) and \(e{-}{p}'\) spaces were extended to three-dimensional critical state surfaces (TCSSs) in \(q{-}{p}'{-}b\) and \(e{-}{p}'{-}b\) spaces. Two empirical equations were proposed for the two TCSSs in \(q{-}{p}'{-}b\) and \(e{-}{p}'{-}b\) spaces, respectively. The predictions by the two equations were in good agreement with the corresponding experimental data. The relationship between the excess friction angle (the difference between the peak state and critical state friction angles) and initial state parameter was influenced by the b-value. However, the relationship between the maximum dilatancy and initial state parameter was independent of the b-value.