Table 1 List of definitions of all the parameters.
Variable/parameter | Definition |
|---|---|
\({f}_{s}\) | Lateral frictional force |
\({f}_{t}\) | Penetration resistance force |
\({f}_{s}+{f}_{t}\) | Resultant force of penetration and friction |
\({f}_{g}\) | Growing force of the root |
\({E}_{s}\) | Elastic coefficient associated with \({f}_{s}\) |
\({E}_{t}\) | Elastic coefficient associated with \({f}_{t}\) |
\(\varphi\) | Wall extensibility |
\({u}_{c}\) | Threshold of displacement for root to slip |
\({u}_{lift}\) | Threshold of displacement for root to lift up |
\(\delta u\) | Strain associated with the unit time scale |
\({t}_{lift}\) | Time for root to lift up |
\(u(+)\) | Virtual displacement of the root base |
\(u(-)\) | Virtual displacement of the root tip |
\({G}_{p}\) | Primary growth rate of the root |
\({G}_{s}\) | Secondary growth rate of the root |
\(L(t)\) | Length of the zone presenting root hairs |
\({L}_{0}\) | Initial length of the zone presenting root hairs |
\(t\) | Time variable |
\(u(\pm )\) | Virtual displacement \(\mathrm{u}(+)\) or \(\mathrm{u}(-)\) |
\(R(t)\) | Radius of the root |
\({R}_{0}\) | Initial radius of the root |
\({u}_{s}\) | Effective displacement of the frictional domain |
\({P}_{0}\) | Initial earth pressure |
\({P}_{p}\) | Preconsolidation stress |
\(P^{\prime}(={P}_{p}-{P}_{0})\) | Relative soil pressure |
\({P}_{t}\) | Current soil pressure |
\({e}_{0}\) | Initial void ratio |
\({e}_{t}\) | Current void ratio |
\(\uplambda\) | Normal consolidation coefficient |
\({V}_{0}\) | Initial void volume |
\({V}_{t}\) | Current void volume |
\({V}_{s}\) | Soil volume |
\({D}_{v}\) | Distance from the depth at which the soil does not move when the root grows |
\(S\) | Soil mechanical parameter |
\(\alpha\) | Non-dimensional parameter representing growth anisotropy of the root |
\(\beta\) | Non-dimensional parameter representing ratio between \({P}_{p}\) and \({E}_{s}\) |
\(\gamma\) | Non-dimensional parameter representing ratio between \(S\) and \({G}_{s}\) |
\(E\) | Young’s modulus of the soil |
