# Experimental Study of Influence of Plant Roots on Dynamic Characteristics of Clay
## 3 Experimental Results Analysis
### Reinforcement Mechanism of Roots  
The root systems of plants play a crucial role in fortifying the soil and augmenting its mechanical properties. In the field of mechanics, [PERSON] [40; 41] developed a soil mechanics model for evaluating the effectiveness of vertical root systems in slope protection based on the Mohr-Coulomb strength criteria. However, some scholars argue that the WU model overestimates the reinforcement effect of roots on soil. [PERSON] believes this is mainly because the WU model assumes the simultaneous fracture of all roots, with full tensile strength exerted at the fracture point [42], which is inconsistent with reality. In one study, [PERSON] applied the fiber bundle continuous fracture theory, widely used in the materials industry, proposed a progressive failure mode for roots, and subsequently developed the FBM (fiber-bundle model). However, during the actual failure process, factors such as soil properties, root diameter, root growth direction, and friction between roots and soil can influence the soil reinforcement effect of roots, and these factors are not considered in the FBM model. Therefore, to address these issues, [PERSON] et al. introduced the RBM (root bundle model) [43], which considers the total pull resistance of root bundles as a function of displacement, represented as the sum of the pull resistance of individual roots [43; 44]. \[F_{tot}(\Delta x)=\sum_{i=1}^{N}F_{i}(\Delta x)\cdot n_{i} \tag{9}\]  
where \(F_{i}(\Delta x)\) is the pullout force of a root belonging to diameter class \(i\), \(N\) is the number of diameter classes, and \(n\) is the number of roots present in the bundle of diameter class \(i\). \(F_{i}(\Delta x)\) is calculated for each root diameter class using the single root pullout model. The variation of the bundle pullout force as a function of the displacement can be expressed with the following differential equation:  
\[\frac{\partial F_{tot}(\Delta x)}{\partial\Delta x}=\sum_{i=1}^{N}F_{i}( \Delta x_{f})\cdot n_{i}-\sum_{i=1}^{N}F_{i}(\Delta x_{0})\cdot n_{i} \tag{10}\]  
where \(\Delta x_{f}\) and \(\Delta x_{0}\) are displacements at two different loads. Growing plant roots release thick substances like root mucilage with adhesive properties, effectively binding soil particles. The presence of polysaccharides and organic acids in root mucilage forms gel-like bonds, enhancing soil cohesion and shear resistance. Root activities lead to biological cementation, establishing a gel-like structure among soil particles \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\sigma_{c}\)(kPa) & **100** & **200** & **300** \\ \hline \(\rho_{g}\)/(g\(\cdot\)cm\({}^{-3}\)) & \(\lambda_{max}\)(\%) & \(\gamma_{r}\)(\(\times\)10\({}^{-4}\)) & \(\lambda_{max}\)(\%) & \(\gamma_{r}\)(\(\times\)10\({}^{-4}\)) & \(\lambda_{max}\)(\%) & \(\gamma_{r}\)(\(\times\)10\({}^{-4}\)) \\ \hline
0 & 5.36 & 6.58 & 4.76 & 4.03 & 4.46 & 3.63 \\
1\% Uniform & 5.06 & 5.71 & 4.47 & 3.15 & 4.39 & 3.32 \\
1\% Upper Distribution & 5.42 & 5.55 & 4.85 & 4.39 & 4.49 & 2.91 \\
1\% Lower Distribution & 4.85 & 5.31 & 4.43 & 3.68 & 4.24 & 3.20 \\
1.5\% Uniform & 4.92 & 4.18 & 4.52 & 3.08 & 4.36 & 3.06 \\ Distribution & 5.14 & 4.49 & 4.44 & 2.81 & 4.20 & 2.62 \\
2.5\% Uniform & 5.15 & 4.11 & 4.62 & 3.08 & 4.18 & 2.31 \\ Distribution & 5.39 & 4.20 & 4.82 & 3.04 & 4.27 & 2.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hardin–Dmreich hyperbolic model’s damping ratio fitting parameters. and fortifying cohesive forces within the soil. Other than bolstering the overall stability of the soil, this structural enhancement acts as a preventive measure against water and wind erosion. Plant root systems give rise to the development of a root network. Efficiently binding soil particles, this network enhances the soil's cohesion. During dynamic loading, this binding effect becomes more pronounced, resisting the relative displacement of soil particles induced by external vibrations. This elevation enhances the overall stiffness and strength of the soil.