Root Reinforcement Models Research Articles

Comparing physical and statistical landslide susceptibility models at the scale of individual trees

Physically or statistically based approaches are widely used to quantify shallow landslide susceptibility. Despite the underlying data, methods, and assumptions being significantly different, there has been little quantitative work to evaluate the differences in model outcomes. Therefore, we compare a previously developed physical and a statistical shallow landslide susceptibility model for a study area in New Zealand's silvopastoral hill country. Both models include individual tree effects on slope stability. To identify individual trees for both models, we use convolutional neural networks to delineate tree crowns and classify species at the scale of individual trees with regional aerial photography. SlideforMAP, a physically based probabilistic model that includes both lateral and basal root reinforcement, is adapted for application in silvopastoral landscapes. Root reinforcement models for physical modelling are subsequently developed for the most abundant tree classes based on allometric relationships to remotely sensed, above-ground metrics. In contrast, the statistical landslide susceptibility model uses binary logistic regression, including empirically derived individual tree influence models alongside topographic and lithological explanatory variables. Binary logistic regression displays a better performance (AUC of 0.911 and 0.936 vs. 0.871 and 0.826) for our study area, resulting from the model being trained and tested on an inventory of past shallow landslide observations, whereas SlideforMAP makes predictions largely independent of past slope failures. SlideforMAP has the advantage of computing shallow landslide susceptibility for different rainfall scenarios coupled with specific return periods. The two predictions of landslide susceptibility within the study area were > 70 % in agreement. Differences in the model predictions are due to the different assumptions and datasets used by the models. Important considerations for land management include recognizing the advantages and limitations of both approaches in relation to erosion control objectives. We argue that the contrast afforded by the two different approaches to slope stability modelling in terms of assumptions, methods, and spatial predictions can increase process understanding, since – while being different – both approaches are geomorphologically plausible. However, to increase performance of erosion and sediment mitigation, we suggest land managers prioritize tree planting in areas where the statistical and physical approach agree within the “high” susceptibility classification (8 % of the study area). Comparing shallow landslide susceptibility scenarios based on potential trees and a treeless baseline can further improve targeted planting.

A Novel Integrated Design Methodology for Nature-Based Solutions and Soil and Water Bioengineering Interventions: The Tardio&Mickovski Methodology

A methodology for designing nature-based solutions (NBS) and soil and water bioengineering (SWB) works is proposed which includes the main particularities of this type of intervention. The dynamic nature of NBS/SWB works, their most important changes and possible critical scenarios are reflected in the proposed methodology. A clear and practical time framework for design checks is also defined. Existing structural design routines and plant root reinforcement models are integrated into the proposed time staged scheme. Likewise, the connections with the monitoring stage and the possibilities of continuous improvement are incorporated as an essential characteristic of the approach of this type of intervention. The proposed methodology is validated by means of a practical case study example embracing the whole service life of an SWB/NBS intervention. The obtained results are in good agreement with both the accumulated experience within the European SWB sector and the existing data collected in SWB monitoring works. The proposed methodology can be readily implemented in a wide range of nature restoration projects and works.

Vegetation-induced soil stabilization in coastal area: An example from a natural mangrove forest

Mangrove forests provide essential ecosystem services in tropical and semitropical regions by supporting their natural regeneration and other biosystem processes, offering livelihood for local communities, and contributing significantly to the natural resources. Systematic analyses on the protective role of mangrove forests and their effects on reducing coastal erosion have been carried out rarely. Mangroves form a complex ecosystem that increases substrate stabilization and dissipates wave energy favouring the deposition of fine material. This study focuses on assessing the role of white mangrove (Avicennia marina (Forssk.) Vierh.) roots in stabilizing the coastline. In a study site located in Southern Iran, a series of field and laboratory measurements were conducted on root systems that were collected from transects perpendicular to the coastline. Root samples were collected from soil cores at fixed distances from tree stems in three layers at seaward and landward positions. Moreover, Root tensile tests were conducted to estimate their biomechanical characteristics which provided the data of parameters of root reinforcement models. Also, the spatial distribution of root reinforcement and the intrinsic-variability of stabilizing components in relation to horizontal and vertical distances from the tree stem were calculated. Three models of Wu & Waldron (W&W), Fiber Bundle (FBM), and Root Bundle Weibull (RBMw) were applied. results showed that the Root Volume Ratio (RVR) and the Number of Roots (NoR) decreased with distance from the tree stem. Root tensile forces increased with root diameter. Finally, calculated root reinforcements at 0.75 m distance associated with the highest value while the lowest value was observed at 1.50 m from the tree stem. The differences between seaward and landward positions were minor. Soil detachment ratio (SDR) was approximately 10% higher at landwards positions than seaward, due to different geomorphological conditions that affected the soil detachment process. The similartity of root reinforcement values among root systems at seaward and landward positions suggest that stem density may not be an important parameter in managing mangrove forests as a coastal protection measure. Yet, RVR at different distances and NoR increasing significantly with soil depth and being different at seaward and landward positions, could improve their potential role as a nature-based solution for shoreline protection.

Root reinforcement models: classification, criticism and perspectives

Root reinforcement models: classification, criticism and perspectives

Root reinforcement: continuum framework for constitutive modelling

The mechanical contribution of plant roots to soil strength has typically been studied at the ultimate limit state only. Since many geotechnical problems are related to serviceability, such as deformation of infrastructure, a new constitutive modelling framework is introduced. The rooted soil is treated as a composite material with separate constitutive relationships for soil and roots, and a comprehensive stress–strain relationship for the root constituent is presented. The model is compared to direct shear experiments on field soil reinforced with gorse, grass and willow roots, as well as an existing root reinforcement model based on the Winkler-spring supported beam theory. The results show that both the newly developed model and the beam-type model yield good predictions for the evolution of root-reinforced shear strength as a function of increasing shear displacements. Both successfully capture the large deformations required to reach peak reinforcement, the reduction in reinforcement due to root breakage and the presence of significant reinforcement even after very large deformations, associated with root slippage. Since both fibre and beam models only require physically meaningful input parameters, they can be useful tools to study the mobilisation of rooted soil strength and simulate the response of rooted soil in continuum-based numerical simulations.

Tensile strength of a compacted vegetated soil: Laboratory results and reinforcement interpretation

So far, root reinforcement on soil has been primarily evaluated through direct shear and roots pull-out tests, while the effect of other stress paths and the behaviour at the soil–root​ interface are still poorly investigated. In this regard, an apparatus with the facility to test soil and roots jointly under uniaxial extension is presented in the paper, together with its first results.Vegetated samples with Cynodon dactilon were tested after one and three months of growth. Soil exhibited a ductile response when close to saturation and a brittle one at drier states within the field capacity domain. The presence of roots increased the material’s tensile strength and enhanced its post-peak ductility. Measurements of matric suction and degree of saturation allowed interpreting the results in terms of constitutive stresses within a shear strength failure criterion for partially saturated soils. Even if plant roots critically impacted soil hydraulics, a positive strengthening effect was noticed on its mechanical behaviour.Roots mechanical and morphological features were characterised after tests. Two well-established root reinforcement models in the literature were used to interpret the results at the phenomenological scale while considering the hydro-mechanical behaviour at the soil–root interface, different root’s reinforcement mechanisms and the effect of soil’s hydro-mechanical states.

Shallow landslides and vegetation at the catchment scale: A perspective

Shallow, rainfall-triggered landslides are an important catchment process that affect the rate and calibre of sediment within river networks and create a significant hazard, particularly when shallow landslides transform into rapidly moving debris flows. Forests and trees modify the magnitude and rate of shallow landsliding and have been used by land managers for centuries to mitigate their effects. We understand that at the tree and slope scale root reinforcement provides a significant role in stabilising slopes, but at the catchment scale root reinforcement models only partially explain where shallow landslides are likely to occur due to the complexity of subsurface material properties and hydrology. The challenge of scaling from slopes to catchments (from 1-D to 2-D) reflects the scale gap between geomorphic process understanding and modelling, and temporal evolution of material properties. Hence, our understanding does not, as yet, provide the necessary tools to allow vegetation to be targeted most effectively for landslide reduction. This paper aims to provide a perspective on the science underpinning the challenges land and catchment managers face in trying to reduce shallow landslide hazard, manage catchment sediment budgets, and develop tools for catchment targeting of vegetation. We use our understanding of rainfall-triggered shallow landslides in New Zealand and how vegetation has been used as a tool to reduce their incidence to demonstrate key points.

Quantifying the influence of individual trees on slope stability at landscape scale

Silvopastoralism in New Zealand's highly erodible hill country is an important form of erosion and sediment control. Yet, there has been little quantitative work to establish the effectiveness of space-planted trees in reducing shallow landslide erosion. We propose a method to provide high-resolution spatially explicit individual tree influence models at landscape scale for the dominant species in pastoral hill country. The combined hydrological and mechanical influence of trees on slopes is inferred through the spatial relationship between trees and landslide erosion. First, we delineate individual tree crowns and classify these into four dominant species classes found in New Zealand's pastoral hill country. This is the first species classification of individual trees at landscape scale in New Zealand using freely accessible data, achieving an overall accuracy of 92.6%. Second, we develop tree influence models for each species class by means of inductive inference. The inferred empirical tree influence models largely agree with the shape and distribution of existing physical root reinforcement models. Of exotic species that were planted for erosion and sediment control, poplars (Populus spp.) and willows (Salix spp.) make up 51% (109,000 trees) in pastoral hill country at a mean density of 3.2 trees/ha. In line with previous studies, poplars and willows have the greatest contribution to slope stability with an average maximum effective distance of 20 m. Yet, native kānuka (Kunzea spp.) is the most abundant woody vegetation species in pastoral hill country within the study area, with an average of 24.1 stems per ha (sph), providing an important soil conservation function. A large proportion (56% or 212.5 km2) of pastoral hill-country in the study area remains untreated. The tree influence models presented in this study can be integrated into landslide susceptibility modelling in silvopastoral landscapes to both quantify the reduction in landslide susceptibility achieved and support targeted erosion and sediment mitigation plans.

How roots of Picea abies and Fraxinus excelsior plantations contribute to soil strength and slope stability: evidence from a study case in the Hyrcanian Forest, Iran

Although the effects of different vegetation cover on soil reinforcement due to their roots have been addressed in the literature, there remains a lack of assessment and comparison of root biomechanical properties of hardwood and softwood plantations for similar site conditions. To address this gap, two adjacent hillslopes with similar site conditions but different forest plantations, a Picea abies (softwood) and a Fraxinus excelsior (hardwood), were selected to assess and compare their effectiveness in protecting sloping soils. The profile trench method was used to obtain root distribution from both upslope and downslope sides of tree samples and on each side at two horizontal distances from the tree stems. Root tensile strength of live root samples was measured using a standard Instron Universal Testing Machine. A modified Wu and Waldron root reinforcement model was used to calculate root cohesion for the two plantations. The root tensile strength for was significantly greater for softwood than for hardwood trees (19.31 ± 2.64 vs 16.98 ± 1.01 MPa). Interestingly, the number of roots, root area ratio values, and the root tensile strength of the two species did not significantly differ between the upslope and downslope sides of trees. The results also showed a higher root cohesion for the softwood than the hardwood species (1.56 ± 0.34 vs 1.03 ± 0.21 kPa). In addition, softwood trees extended their contribution to soil protection to a larger horizontal distance compared with hardwood. However, our findings generally revealed that the values of root cohesion of both studied plantations were surprisingly lower than those found in earlier reports.

Untangling the influence of soil moisture on root pullout property of alfafa plant

Root pullout property of plants was of key importance to the soil reinforcement and the improvement of slope stability. To investigate the influence of soil moisture on root pullout resistance and failure modes in soil reinforcement process, we conducted pullout tests on alfalfa (Medicago sativa L.) roots at five levels (40, 30, 20, 10 and 6 kPa) of soil matric suction, corresponding to respectively 7.84%, 9.66%, 13.02%, 19.35% and 27.06% gravimetric soil moisture contents. Results showed that the maximal root pullout force of M. sativa decreased in a power function with increasing soil moisture content from 7.84% to 27.06%. Root slippage rate increased and breakage rate decreased with increasing soil moisture content. At 9.66% soil moisture content, root slippage rate and breakage rate was 56.41% and 43.58%, respectively. The threshold value of soil moisture content was about 9.00% for alfalfa roots in the loess soil. The maximal pullout force of M. sativa increased with root diameter in a power function. The threshold value of root diameter was 1.15 mm, because root slipping force was greater than root breaking force when diameter >1.15 mm, while diameter ≤1.15 mm, root slipping force tended to be less than root breaking force. No significant difference in pullout forces was observed between slipping roots and breaking roots when they had similar diameters. More easily obtained root tensile force (strength) is suggested to be used in root reinforcement models under the condition that the effect of root diameter is excluded as the pullout force of breaking roots measured in pullout tests is similar to the root tensile force obtained by tensile tests.

Modeling bio-engineering traits of Jatropha curcas L.

The wide distribution of Jatropha curcas L. in tropical areas provides the opportunity to use this plant for improving slope stability and controlling erosion. To determine the effectiveness of Jatropha curcas L. as a bio-engineering plant we measured stem diameter and height of 1, 3, 5, 6, 18, and 36 month-old plants, and root distribution at 6, 18, and 36 months by full excavation of the root system. We also measured in the laboratory the elastic modulus and maximum tensile force of 50 roots. These data were used to calibrate a weighted log-likelihood root distribution model and a root reinforcement model. Models were coupled to estimate root reinforcement at stand scale over a three year period as a function of the plantation's tree density. Our results of root distribution indicate a rapid decrease of root diameter along the root length leading to rapidly decreasing root reinforcement with distance from the stem. Minimal root reinforcements at 0.5m from the stem is about 1 and 11kPa for 18 and 36-month old plants, respectively. At 1m from the stem only 36-month old plants provide any significant root reinforcement.Despite its relatively low root reinforcement relative to other larger tree species Jatropha curcas L. is a suitable bio-engineering plant because it easily propagates, grows fast, and is resilient. Root reinforcement in the first stage of growth needs high density plantation of up to 40,000 plants per hectare. This should then be followed by thinning down to 10,000 plants per hectare to optimize root reinforcement at 3 years age.

Reduced testing and modelling of the bearing capacity of rooted soil for wheeled forestry machines

The next generation of forestry machines must be developed to be gentler to soil and to the root mat than present machines, especially in thinning operations. The bearing capacity of the soil is a key property for determining the terrain trafficability and machine mobility. This asks for better and more general terramechanics models that can be used to predict the interaction between different machine concepts and real and complex forest soil.This paper presents results from terramechanics experiments of rooted soil with a new and small-scale testing device. The force–deflection results are analyzed and compared with analytical root reinforcement models found in literature. The presented study indicates that rooted soil properties obtained with the new laboratory test device can be used to create an augmented soil model that can be used to predict the bearing capacity of rooted soil and also to be used in dynamic machine–soil interaction simulations.

Method for synchronisation of soil and root behaviour for assessment of stability of vegetated slopes

A new methodology to incorporate the mechanical root anchorage effects in both short- and long-term slope stability analysis is proposed based on observed and assumed behaviour of rooted soil during shear failure.The main focus of the present work is the stress–strain range comparison for both soil and roots and development of a stability model that would incorporate relevant root and soil characteristics based on the fact that available soil–root composite shear resistance depends on the magnitude of the shear strain. This new approach, combining stress–strain analysis, continuum mechanics, and limit equilibrium stability assessment, allows for a more realistic simulation of the rooted soil composite whereby the stabilising effect of the rooted soil is incorporated in the slope stability calculations by means of the synchronisation of root and soil mechanical behaviour during failure.The stability of vegetated terraces in a study area in Spain is used as a case study to demonstrate the proposed methodology and to compare the results with the traditional use of the perpendicular root reinforcement model. The results of the study show that as the shear displacement (strain) increases, the stress is transferred from the soil that provides most of the resistance at low strains onto the roots that provide the most of the resistance to shear at high strains. Including this behaviour in the overall resistance to failure of the root–soil continuum resulted in a more conservative and realistic assessment of the stability of a vegetated slope immediately after a precipitation event when a progressive failure is most likely to be triggered.

Effects of root tensile force and diameter distribution variability on root reinforcement in the Swiss and Italian Alps

Root reinforcement is considered to be one of the most important factors contributing to the stability of vegetated hillslopes; however, its estimation is still challenging because of the spatial variability of root distribution and root mechanical properties. This work uses the root bundle model to assess the sensitivity of root-reinforcement estimation to the variability in both root mechanical properties and root distribution. We used a large data set of root tensile tests and root distributions of an important alpine species, Picea abies (L.) Karst., collected in a wide range of altitudinal and climatic ranges on both north and south sides of the alpine mountain range. The results demonstrate that the site-specific characterization of mechanical properties and root distribution is fundamental for the quantification of root reinforcement at the stand scale. Root diameter distribution plays a dominant role in influencing the root-reinforcement model’s output; however, in contrast with results from other works, differences in root diameter–force functions are significant and cannot be ignored. Model results also show that coarse roots contribute significantly more to the reinforcement of soil than fine roots, underlying the need of additional data for roots with diameters larger than 5 mm.

Evaluation of root reinforcement models using numerical modelling approaches

The root reinforcement (RR) models commonly used in slope stability modelling can be simply explained as a single soil additional cohesion parameter estimated with simple analytical functions of root traits. We have simulated 3D direct shear tests using the standard implicit Finite Element Method (FEM) and the Discrete Element Method (DEM), aiming to (i) evaluate the RR models and (ii) compare the two numerical approaches. In homogeneous soil with low cohesion, 36 straight, non-branched and thin root models were implanted in three parallel lines. Root traits, including orientation relative to the shear direction (45°, 90° and −45°), longitudinal modulus of elasticity (10 MPa and 100 MPa), and bending and compressive behaviours (beam, truss and cable) were investigated. Compared to the FEM, the DEM achieved consistent results and avoided convergence problems, but required longer computation time and used parameters potentially difficult to identify. Root reinforcement did not occur until significant plastic deformation of soil. The RR values estimated by the shear tests were much lower than those estimated by the usual RR models and were significantly dependent upon root traits. Ignoring the effect of root traits in RR models might lead to an important bias when using slope stability models.

Effect of spatial variation of tree root characteristics on slope stability. A case study on Black Locust (Robinia pseudoacacia) and Arborvitae (Platycladus orientalis) stands on the Loess Plateau, China

Vegetation is widely used for controlling shallow landslides. The mechanisms by which roots increase apparent soil cohesion is well documented and many values of root additional cohesion are available in the literature for different plant species. However, less information is given about the spatial variation of soil reinforcement by roots at a slope scale and its influence on slope stability, in particular in forest areas. The goal of this paper is to describe the spatial variability of root additional cohesion on two monospecific 17-y-old stands of Robinia pseudoacacia and Platycladus orientalis grown on slopes in the semiarid Loess Plateau of China, and to analyze numerically the effect of this variability on slopes stability. For this purpose, vertical trenches were dug at different distance and directions around trees situated at three different slope locations, i.e. up-, mid- and down-slope. Grids with a 10×10 cm mesh were placed on vertical walls. Roots were counted within each grid cell and split according to their diameter class. Root area ratio (RAR) was estimated and compared among different positions around the trees and at three different locations along the slope. Roots tensile strength was determined with laboratory mechanical tests. RAR and root tensile strength were used as inputs in six different root reinforcement models to calculate root additional cohesion. A 2D finite element model of slope stability was developed and used to calculate the increase in factor of safety (FoS) due to root additional cohesion on rectilinear and terraced slopes. Results showed that both root tensile strength and Young's modulus of R. pseudoacacia was about two times higher than tensile strength of P. orientalis. RAR distribution had a strong relationship with local soil moisture content measured in July during the raining season, and was significantly different with regards to tree location on the slope. The six theoretical models used to estimate the root additional cohesion gave different vertical profiles of root reinforcement distribution according to the underlying hypothesis on how forces are transferred to the roots. Theoretical analyses of slope stability showed that terraced slopes were 20% more stable than rectilinear slopes, disregarding the differences in hydrological regimes between these two terrain morphologies. Numerical sensitivity analyses also showed that the FoS reached an asymptotic value when increasing root additional cohesion. Actual additional cohesions of the two studied sites corresponded to FoS that were already close to this asymptotic values. Consequently variations of these actual root cohesions would not much affect slope stability. However it was showed that more attention should be given to the reinforcement of the bottom part of the actual slopes, where roots have a larger positive impact on the FoS

Centrifuge modelling of soil slopes containing model plant roots

A series of centrifuge model tests were conducted to investigate the contribution of root reinforcement to slope stability. A compacted sandy clay slope, inclined at 45°, was reinforced with model roots. The model roots were varied in material, architecture, and numbers. They had stiffness values corresponding to upper and lower values found for plant roots. The architecture included taproots and branched roots. Slope collapse was triggered by raising the water table while soil displacements, pore-water pressures, and root strains were measured. The mode of failure was changed by the presence of roots from a progressive block failure to translational failure. The tests revealed how axial strains and bending strains were mobilized in the roots and how the roots influenced the slope failure mechanism. Different limit equilibrium slope stability calculations were performed at slope failure conditions to quantify the amount of reinforcement provided by different root types. These measured root reinforcement contributions were compared with those predicted according to common root reinforcement models. A reinforcement calculation method allowing for root pull-out was found to give the best agreement.

Root tensile strength of 3 typical plant species and their contribution to soil shear strength; a case study: Sasumua Backslope, Nyandarua District, Kenya

The effect of root reinforcement depends on the morphological characteristics of the root system, the tensile strength of individual roots, the soil-root cohesive strength, and the distribution of the root system in the soil. This research looks into Sasumua Backslope in Kenya, where a great deal of erosion is responsible for large soil losses. Shallow mass movements are evident throughout the slope. Root reinforcement effect of nine typical species was assessed, using Wu et al. (1979) model. The plant species comprised of shrubs (Atriplex halimus), grasses (Pennisetum clandistenum and Themeda triandra), and tree ferns (Asparagus species). Physical counting of roots per depth class was conducted to obtain root area ratio (RAR) values of the individual species. For each species, single root specimens were sampled and tested for tensile tests in the laboratory using the Hounsfield Tensometer apparatus. Maximum RAR values were located within 0.1 m for all the species, with maximum rooting depth of 0.7 m for fern tree. Shrubs species showed high RAR values between 0.1 – 0.3 m depth. Tensile force increases with diameter. Generally shrubs break at high tensile force (160 N maximum), followed by tree ferns (maximum 90 N) and lastly grass (maximum 75 N). Root tensile strength decreases with increasing root diameter, and follows a power law equation of the form . Generally, tensile strength can be well predicted by root diameter. The maximum root tensile strength values recorded was 39 N/mm2 for grass. The results presented in this paper contribute to expanding the knowledge on root resistance behavior and on root density distribution within the soil. The studied location has allowed the implementation of soil–root reinforcement models initially used by Wu et al. (1979) and the evaluation of the vegetation contribution to soil stability.

Quantifying the potential for flow to remove the emergent aquatic macrophyte Sparganium erectum from the margins of low-energy rivers

The emergent macrophyte species Sparganium erectum occurs commonly at the margins of low- to medium- energy river systems across the northern temperate zone. It is considered as an invasive species along low-energy water courses in many parts of the US and Australia. The life-cycle and biomechanical properties of this species make it very well adapted to such environments, allowing rapid growth and sediment trapping, such that encroachment into the channel occurs as the growing season progresses. The widespread growth of species such as S. erectum is therefore of particular concern, when considering the flood risk potential of many rivers. As such, the conditions required for survival or uprooting and scouring of this plant are of interest, as are the times of the year and processes by which these plants spread to increase the size of current stands, and to form new stands. It is known that S. erectum reproduces by several vegetative methods including rhizome growth, dispersal of detached rhizomes, and relocation of entire plants. However, the mechanisms and flow conditions necessary for uprooting or scouring of entire plants, and the separation of fragments of this species, at different times of the year, are largely unknown. The aim of this paper is to model the uprooting resistance of S. erectum plants as reported by Liffen et al. (in press), and to investigate the manner by which this species is adapted to proliferate in low-energy, low-gradient streams. The results presented here show that Monte Carlo simulations using the RipRoot root-reinforcement model can be used to accurately model plant pullout forces, rhizome interconnectivity and length changes for S. erectum plants throughout the growing season. Analysis presented here also suggests that plant uprooting forces are several orders of magnitude larger than potential drag forces that could act on the S. erectum plants at the River Blackwater site modeled, and even at sites with much higher channel slopes. This result suggests that the ability of these plants to thrive in low-energy rivers, but not in higher-energy river environments, is less related to driving forces causing drag on the plants, and more related to the energy conditions controlling erosion and deposition of the fine substrate materials these plants thrive in. The critical shear stress of the fine within-vegetation material was shown here to only be exceeded by the average boundary shear stress within the vegetation, during winter months when above-ground biomass and thus Manning's n values were at their lowest. For example, during March and April average boundary shear stress was predicted to exceed critical boundary shear stress for 6% of the time. Erodibility measurements from jet-tests conducted at the River Blackwater fieldsite suggested that this excess in boundary shear stress could result in potential vertical scour of up to 0.09 m in both March and April. During the majority of the growing season sediment trapping rather than erosion dominated, with enough deposition occurring over the summer to protect all but the shallowest, weakest and least interconnected rhizomes and plants from being scoured in the winter months. The balance between erosion and deposition within stands of S. erectum in these low-energy environments therefore allows for the maintenance of established stands of vegetation, whilst still allowing for scouring of weaker S. erectum plants that can establish previously un-colonized channel margins further downstream.

Mechanical Behavior of the Soil-Root System

The reinforcement of soil by vegetation depends on the biomechanics, length, and morphology of roots. Often, morphology and length are simplified in root reinforcement models by assuming symmetry above and below the shear plane. For many root systems, however, the presence of root collars and lateral rootlets could be greater beneath the shear plane. This is not taken into account in current models, so the current study derives a set of analytical equations to account for these effects and thereby provide a more realistic model of root reinforcement. To gain a better understanding of the mechanical behavior of the soil-root system, the resulting simulation was also compared with that of the data produced by the existing model in the literature (Waldron and Dakessian, 1981). This comparison shows that as root morphology and length are taken into account, the shear strength increment obtained with the new equations could reach values 1.4 times greater than that of previous models when the shear bond strength is small. In contrast, if the shear bond strength is greater, an increase in the root embedment length only produces a minor effect on the shear strength increment. In addition, we note that if the root system has the same constituents, the influence of roots on the shear strength increment decreases with an increase in the depth ofthe shear plane. The influence of rooted soils with smaller shear bond strength is found to be more significant than that of rooted soils with greater shear bond strength.