Distributional parameter inferences on the mechanical properties of roots for E. nutans based on Bayesian analysis

Mechanical properties are the essential parameters to assess the contribution rates of roots in the soil strength, the slope stability, and the prevention of soil erosion. Therefore, an accurate and rapid measurement is required to determine the role of vegetation roots in the soil cohesion, and the slope stability. However, the commonly-used uniaxial tension tests cannot fully meet the large-scale measurement at present, due to the labor-consuming and time-costing. It is very necessary for the high precision on the biomechanical properties of roots. In this study, the distribution parameters were assessed on the biomechanical properties of roots using Bayesian analysis. The research object was selected as Elymus nutans from the landfill dumps in the Jiangcang coal mining, Tianjun County, Qinghai Province, China. The reason was the excellent adaptability and performance of the plant in the long cold climate condition of soil and water preservation. Subsequently, the uniaxial tension test was carried out to measure the biomechanical properties (such as the root diameter, tensile resistance, tensile strength, and tensile strain at crack and Young’s modulus). 28 datasets of roots were randomly collected with the mean values and variance as the prior information. The control group was treated as the sampling information for this herb. The prior mean of properties and sampling information were followed the Normal distribution, while the variance was the Inverse Gamma distribution. The posterior distribution (named Normal-Inverse Gamma distribution) was then established to calculate the hyper- and distributional parameters using the maximum likelihood method or moment estimation. The results show that the more comprehensive information was achieved in the Bayesian estimation, considering both prior and sampling information. Among the prior information, there was the small variable coefficient of the mean values in the biomechanical properties, except for tensile strain at crack. The geometric shape of posterior information was similar to that of the sampling one after the Kolmogorov-Smirov test. The size of sampling and the discreteness of prior information were determined as the mean value of the posterior that weighted by the mean between the prior and sampling information. The sizes of sampling and prior information were 28 and 63, respectively, indicating the relatively high sampling information. Therefore, the mean values of posterior information were adjusted, where the diameter from 0.331 3 to 0.330 4 mm, the tensile resistance from 2.639 to 2.575 5 N, tensile strength from 32.098 to 31.280 MPa, tensile strain at crack from 8.413% to 9.520 6%, and Young’s modulus from 107.24 to 98.634 6 MPa. Similarly, the variances of posterior information were adjusted, where the diameter from 0.010 8 to 0.018 6, tensile resistance from 3.019 to 5.412 4 N, tensile strength from 308.214 to 566.004 MPa, tensile strain at crack from 14.106 to 188.655 9, and Young’s modulus from 3 392.55 to 6 805.60. Both the size and discreteness should be considered in both prior and sampling information in the future. The biomechanical properties of vegetation roots can be expected to accurately estimate for the shear strength of rooted soil.