# Integrating Root Morphology Based on Whole-Pullout Test of Model Roots: A Case Study
## 4 Discussion  
The aforementioned study utilized orthogonal experiments and a range analysis to determine the sensitivity levels of various factors affecting the vertical pullout resistance of plant root systems. Obtained from references [29,40], the sensitivity index (\(I_{S}\)) was employed to validate and calculate the sensitivity of each factor. The formula for calculating the sensitivity index is as follows:  
\[I_{S}=\frac{p_{max}-p_{min}}{p_{max}} \tag{1}\]  
where \(p_{max}\) and \(p_{min}\) represent the maximum and minimum pullout resistance, respectively, corresponding to the levels of each factor. The pullout resistance is determined by taking  
Figure 5: Trend chart of average pullout resistance across factors: (**a**) average pullout resistance vs. the unit weight of soil around the root; (**b**) average pullout resistance vs. the number of lateral roots; (**c**) average pullout resistance vs. taproot length; (**d**) average pullout resistance vs. branching angle of the lateral root. the experimental indicator's average value (\(k_{i}\)). The results of the calculations are presented in Table 6.  
According to Table 6, the sensitivity index for the number of lateral roots was 0.612, making it the most sensitive factor affecting the vertical pullout resistance of plant root systems. This was followed by the taproot length and the unit weight of soil around the root, with sensitivity indices of 0.410 and 0.372, respectively. Lastly, the branching angle of the lateral root had the lowest sensitivity index, at 0.162. The order of sensitivity for each factor, as determined by the sensitivity index calculation, was consistent with the conclusions drawn from the range analysis results in Section 3.2. This study utilized PC plastic model roots to simulate plant root systems and investigated the impact of various morphological characteristics on the vertical pullout resistance of roots. Through a variance analysis, it was found that the number of lateral roots and the taproot length had significant effects on vertical pullout resistance. These findings were similar to those obtained by [PERSON] et al. [24], [PERSON] et al. [41], [PERSON] et al. [42], and [PERSON] et al. [10], who conducted in situ pullout and shear tests on actual plant root systems. This indicates that the employed method was feasible. The experimental results indicate that the branching angle of the lateral root had the least impact on the vertical pullout resistance of plant roots and exhibited the lowest level of significance. To explore the underlying reason for this phenomenon, reference [43] conducted a comprehensive \(\mu_{X}\) theoretical analysis method based on the whole root system pullout test to study the forces acting on root segments. In Figure 6, an arbitrary root segment d\(l\) at depth \(z\) beneath the soil surface was selected for a force analysis. Assuming that the soil density and the static friction coefficient of the root-soil interface are represented by \(\gamma\) and \(\mu\), respectively, the normal pressure per unit area and the maximum static frictional force on the root segment are \(\gamma z\) and \(\mu\gamma z\), respectively. Consequently, the resultant static frictional force d\(l\) on the root segment d\(l\) can be developed as follows:  
\[\mathrm{d}f=A(z)\cdot\mu\gamma z=2\pi\mu\gamma\cdot R(z)\cdot z\cdot\mathrm{d}l \tag{2}\]  
where \(R\) represents the radius of the root segment, which is a variable denoted as a function of depth \(z\): \(R(z)\). \(A(z)=2\pi R(z)\cdot\mathrm{d}l\) denotes the surface area of the root segment d\(l\).