The critical state of structural loess is related to its initial void ratio

which causes the non-unique critical state line that can be described by an index “spacing ratio”. However

Modified Cam-clay model and its enhanced models show unique critical state line

which make it unable to capture the critical state and strain-softening of intact loess. To solve the issue

this paper conducts the investigation for the spacing ratio of intact loess and model prediction for the mechanical behaviors of intact loess. Firstly

the calculation method of the spacing ratio is given

and the values of the spacing ratio corresponding to different void ratios are calculated from triaxial undrained compression test results on intact loess. It was found that there exists an inversely proportional relationship between the spacing ratio and the void ratio. The physical meaning of the spacing ratio is also clarified. Secondly

a modified model is obtained by introducing a hardening parameter into a framework of structure bounding surface plasticity model considering spacing ratio. In the modified model

the various values of spacing ratio represent non-unique critical state line

and the structural decay of intact loess is accomplished by coupling the effect of plastic deviatoric strain and plastic volumetric strain. The modified model well predicts the critical state

strain-softening

stress paths

and pore pressure of intact loess. The above results show that the physical meaning of the spacing ratio is clear

and its role in predicting critical state is reliable. If the spacing ratio is considered in a constitutive model

it can well capture the critical state of intact loess. The conclusions have theoretical and practical meanings for numerical analysis of geotechnical engineering in loess area.