# Modified Equation of Shear Strength with Respect to Saturation
## 6 Conclusions  
In geotechnical engineering, the measurement of saturation degree is relatively simple through laboratory tests, however, the measurement of matric suction is expensive, time-consuming, and difficult. Therefore, in this paper, a new shear strength model was developed, applied, and tested for applications in engineering problems related to unsaturated soil. Test results indicate that this model is of good quality to be used in engineering to predict the relationship between the degree of saturation and shear strength with a wide range of soils. The new shear strength model describing the degree of saturation is expressed as a multiple parameter equation. Based on [PERSON]'s shear strength theory and the van Genuchten model for the soil-water characteristic curve, the proposed model can be expressed as a function of saturation, residual degree of saturation, effective shear strength indices (effective cohesion and internal friction angle), net normal stress, and five characterization parameters (\(\xi_{2}\), \(\xi_{3}\), \(\xi_{4}\), \(m\), \(S_{rw}\)); \(S_{rw}\) is the residual saturation, \(\xi_{2}\) and \(\xi_{3}\) are fitting parameters, \(\xi_{4}\) is related to the air entry value \(\left(\xi_{4}=\xi_{1}\cdot P_{0}\right)\), and \(m\) is related to the material characteristic. In addition, the expression of the effective stress parameter is described as a Sigmoid function. Comparing the result of shear strength under the variation of one parameter, we found that this model was much more sensitive regarding the parameter m, which is related to the material characteristic. The validation of this proposed model was based on laboratory tests for the determination of the soil-water characteristic curve and the triaxial shear strength tests of silty sand. The predicted results were close to the experimental points and the maximum discrepancy was less than 7%. Furthermore, the calculated results acquired from the proposed model were compared with the experimental points of the previously published data including the clayed-silty sand and Ankara clay. The comparison between the theoretical prediction and experimental points is promising; this also shows the adaptability of the proposed model to a wide range of soils. This model can also be incorporated into analytical solutions and the numerical simulation of slope stability in unsaturated soils. The degree of saturation can be considered in the unsaturated soil shear strength directly and shear strength can be predicted by using a simple method to test the degree of saturation after obtaining the soil sample by using a cutting ring to avoid the complex measurement of the matric suction. Therefore, knowing the degree of saturation, the shear strength can be determined using Equation (5) without the knowledge of the matric suction. This could also give guidance to practical engineering applications such as slope stability. Simultaneously, there are further effects to be added, and a multiple parameter and complex coupling model that considers temperature will be explored in the immediate future. Figure 25: Comparison for sensitivity of the four parameters. **Author Contributions:** [PERSON] and [PERSON] conceived of the idea. [PERSON] developed the new shear strength model and performed the experiments. [PERSON] and [PERSON] verified the analytical methods. [PERSON] helped to conduct the sensitivity analysis part in Section 5. [PERSON] helped to modify this paper. All authors discussed the results and contributed to the final manuscript. We would like to thank [PERSON], [PERSON], [PERSON] and [PERSON] for their valuable comments on this manuscript. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported by the Geotechnical Laboratory at Ghent University. The first author would like to acknowledge the financial support received from the China Scholarship Council (No. 201908420298). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.