Critical State of Sand Matrix Soils

Table 1

Overall developments of CSSM with respect to soil liquefaction.

Year	Researchers	Developments
1940	Casagrande [11]	Introduced critical void ratio, the same void ratio where contracted loose soil and dilated dense soil approach after sheared to large strains
1956	Taylor [12]	Showed experimentally that dilatancy is stress dependent
1958	Roscoe et al. [13]	Defined critical state as the ultimate state at which a soil continues to deform at constant stress and constant void ratio
1968	Schofield and Wroth [4]	Brought together stress-dependent strength and dilatancy to introduce critical state soil mechanics with Cam-Clay model
1969	Castro [14]	Observed three different types of stress-strain behaviour (liquefaction, limited liquefaction, and dilation) in monotonic loading tests
1975	Casagrande [15]	Developed steady state line from both drained and undrained tests and noticed that dense sand can be liquefying under sufficient high load
1981	Poulos [16]	Formalised the concept of steady state of deformation (continually deformation under four constant conditions: volume, normal effective stress, shear stress, and velocity)
1985	Poulos et al. [17]	Recognised that steady-state line is useful for identifying the susceptibility of flow liquefaction
1985	Been and Jefferies [18]	Proposed state parameter, the void ratio difference between current state and critical state at same mean stress
1991	Been et al. [19]	Showed that critical state and steady state of sands are equivalent and independent of stress path, sample preparation method, and initial density