Figure 2.

Theoretical evaluation of root penetration criterion in a linear regime. (a) Schematic diagram of the mechanical forces imposed on the foundation pile. (b) External force acting against the virtual displacement with lateral frictional force $f_s$ (blue) and penetration resistance force $f_t$ (red) as a function of displacement. (c) Resultant force acting against the virtual displacement for the foundation pile. (d) Schematic diagram of the mechanical forces imposed on the plant root. (e) External force acting against virtual displacement with lateral structures (lateral roots and root hairs) $f_s$ (blue) and penetration resistance force $f_t$ (red) as a function of displacement. (f) Resultant force acting against virtual displacement for the plant root. (g) Root penetration criterion in a linear regime. (h) Color plot of the time interval before root uplift $t_{\mathit{lift}}$.