Analysis of coupled axial and lateral deformation of roots in soil

Abstract

Summary Plant roots can help to stabilise slopes. Existing analytical models to predict their mechanical contribution are however limited: they typically focus on the ultimate limit state, employ various empirical factors, and ignore much of the underlying root‐soil interaction. A new model was developed based on large deflection Euler‐Bernoulli elastic beam theory that can be used to study the mobilisation of root strength under various loading conditions (direct shear and pull‐out). Both lateral and axial loading of the root by the soil were incorporated, based on existing methodologies for foundation piles (p‐y and t‐z curves). The model is able to take the key parameters into account (root biomechanical properties, root architectural properties, and soil properties) while remaining quick to solve using a numerical boundary value problem solver. The model was compared with experimental direct shear test data using various root analogues (rubber, plastic, and wood) in dry sand with various densities and effective stress levels and was able to accurately predict the measured shear force‐displacement behaviour. Comparison with experimentally measured pull‐out force‐displacement curves using rubber and wooden root analogues with various architectures in dry and partially saturated sands was also satisfactory. In the future, this model can aid with addressing long‐standing problems in the root‐reinforcement community: quantifying the effect of (sequential) mobilisation of root strength in direct shear, the effect of the angle at which the root crosses a shear plane, the effect of root topology on root‐reinforcement or the effect of root bending, and root shear shear forces on root‐reinforcement.

Root branching affects the mobilisation of root-reinforcement in direct shear

“…The methodology as set out by [6] was followed, describing the behaviour of the root using four coupled differential equations. The first equation accounts for axial deformations along the deformed root axis s:…”

“…The magnitude of axial and transverse resistances q a and q l depends on the relative soil-root displacement. Simplifying from [6], these relative deformations are taken as the relative displacements in the undeformed local root segment coordinate system:…”

“…where c is the soil cohesion. When the modelled root systems consists of multiple connected root segments, Equations 1, 2, 5 and 6 are simultaneously solved for all segments, taking into account appropriate boundary conditions where segments connect, see [6].…”

“…Euler-Bernoulli beam theory has been adopted previously to model thick, individual roots by various authors [4,5]. Recently, this concept was developed further by coupling axial and bending behaviour and taking into account large root deformations [6], thus making this approach suitable for both thick and thin roots for realistic slope deformations.…”

Understanding the mechanisms of root-reinforcement in soils: soil shear tests using X-ray computed tomography and digital volume correlation

“…direct shear, centrifugal and root tensile strength tests [2][3][4][5][6]. In addition, many models for soilroot interactions have also been developed [7,8].…”