A generic form of fibre bundle models for root reinforcement of soil

G J Meijer

doi:10.1007/s11104-021-05039-z

Abstract

PurposeThe mechanical contribution of plant roots to the soil shear strength is commonly modelled using fibre bundle models (FBM), accounting for sequential breakage of roots. This study provides a generic framework, able to includes the many different existing approaches, to quantify the effect of various model assumptions.MethodsThe framework uses (1) a single model parameter determining how load is shared between all roots, (2) a continuous power-law distribution of root area ratio over a range of root diameters, and (3) power-law relationships between root diameters and biomechanical properties. A new load sharing parameter, closely resembling how roots mobilise strength under landslide conditions, is proposed. Exact analytical solutions were found for the peak root reinforcement, thus eliminating the current need for iterative algorithms. Model assumptions and results were validated against existing biomechanical and root reinforcement data.ResultsRoot reinforcements proved very sensitive to the user-defined load sharing parameter. It is shown that the current method of discretising all roots in discrete diameter classes prior to reinforcement calculations leads to significant overestimations of reinforcement. Addition of a probabilistic distribution of root failure by means of Weibull survival functions, thus adding a second source of sequential mobilisation, further reduced predicted reinforcements, but only when the reduction due to load sharing was limited.ConclusionThe presented solutions greatly simplify root reinforcement calculations while maintaining analytical exactness as well as clarity in the assumptions made. The proposed standardisation of fibre bundle-type models will greatly aid comparison and exchange of data.

Highlights

Plant roots reinforce shallow soil layers against mass movements through both extracting moisture and by mobilising their mechanical strength
The continuous root distribution (Eq 8) can be used to calculate the peak root reinforcement according to the Wu/Waldron solution (Eq 1) by integrating over all root diameters, rather than the usual summation over all root diameter classes: dr,max cr,u,W W Mc = k φr tr,u dx x=dr,min where cr,u,Wu/Waldron Model with continuous root diameter distributions (WWMc) is the peak reinforcement according to the WWM with continuous root diamemeter distributions (‘c’ for ‘continuous’)
This study showed that all existing root reinforcement calculation procedures that rely on a fibre bundle approach are part of the same ‘family’, with different assumptions for load sharing parameter βF, despite the different names used to identify these models

Summary

Introduction

Plant roots reinforce shallow soil layers against mass movements through both extracting moisture and by mobilising their mechanical strength. The latter effect is difficult to predict and many models have since been developed. I where tr,u,i is the tensile strength of root i (subscript ‘r’ for ‘root’ and ‘u’ for ‘ultimate’, i.e. at root peak strength), φr,i the root area ratio of root i (i.e. the fraction of the soil cross-section occupied by this root) and k an multiplication factor accounting the effect of root orientation at root failure, often assumed as k = 1.2 (Wu et al 1979)

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