## 6 Conclusions  
1. To decouple the effects of the water content state and compaction state and to facilitate engineering applications, the shear deformation characteristics of the unsaturated soils can be simulated based on the mass water content, thereby simplifying and clarifying the problem handling process;  
Figure 14: Comparison between the measured and computed results of the triaxial shear tests for the different confining pressures and water content of the unsaturated soil, (**a**) \(w=4\%\), \(\sigma_{3}=25\) kPa; (**b**) \(w=16\%\), \(\sigma_{3}=100\) kPa; (**c**) \(w=36\%\), \(\sigma_{3}=50\) kPa.  
2. During the shearing process of unsaturated compacted soil under a low confining pressure, obvious dilatancy characteristics can be observed. The soil shows volume shrinkage in the beginning, and then transitions to dilatancy; after passing the peak stress, it displays softening until the shearing stabilises;
3. The influence of the water content on the shear deformation characteristics of the unsaturated soils is analysed. The dilatancy characteristics show a unimodal changing pattern with the water content decreasing from saturation. As the water decreases, the soil particles disperse, agglomerate, and then deagglomerate; the dilatancy characteristics macroscopically first move upwards and then downwards;
4. The stress-dilatancy relationship and the prediction equation of the minimum dilatancy rate of the unsaturated soil with different confining pressures and water contents are provided. From two aspects of the peak state point and the whole shear process, it is confirmed that the water content state alters the slope of the change, and the compaction state only affects the amplitude of the dilatancy in the effective stress ratio-dilatancy rate relationship. The minimum dilatancy rate can be directly predicted by the corresponding compaction state and water content state;
5. By selecting the mass water content as the state variable, a constitutive model that is applicable to the dilatancy characteristics of the unsaturated soils is established. The methods for determining the model parameters based on the mass water content are analysed. Considering the stage where the parameter (or dilatancy) increases with the decrease in the water content, which is also the most concerned part of current engineering practice and academic research, the dilatancy parameters can be fitted with a relatively simple linear relationship. Based on the comparison between the triaxial shear test results and the calculation results under different confining pressures and different water contents, the applicability of the established model is verified.  
[PERSON] conceived and designed the experiments; [PERSON], [PERSON] and [PERSON] performed the experiments; [PERSON], [PERSON] and [PERSON] analysed the data; [PERSON] and [PERSON] did the analysis and discussion; [PERSON], [PERSON] and [PERSON] did the modelling and wrote the paper. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the National Natural Science Foundation of China (grant number U2034204, 52078031, U1834206), Natural Science Foundation of Beijing (grant number 8202038), and Scientific Foundation of Shanxi Transportation Committee (grant number 2017-1-6).  
Not applicable.  
The authors declare no conflict of interest.