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. 2023 May 9;13:7473. doi: 10.1038/s41598-023-34025-x

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Theoretical evaluation of root penetration criterion in a nonlinear regime. (a-c) Schematic diagram of the growth anisotropy (a), static pressure and friction ratio (b) and dynamic pressure and friction ratio (c). (d) Color plot of the diffrent cases depending on the indices of α, β, and γ. (e–i) External force and resultant force as a function of the absolute value of the virtual displacement. Case 1: penetration only (P) (e). Case 2: uplifting only (U) (f). Case 3: P, then, U (g). Case 4: U, then P (h). Case 5: P, then, U, then P (i).