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Energy-based fibre bundle model algorithms to predict soil reinforcement by roots

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Abstract

Background and aims

Modelling and predicting soil reinforcement by roots is a central quest in eco-engineering to assess the effectiveness of vegetation in landslide or erosion mitigation. Several fibre bundle model algorithms (FBMs) have been successfully introduced for soil reinforcement estimation and have achieved satisfactory results. However, FBMs yield variable reinforcement estimates due to their different hypotheses on the progressive root failure mode in soil (e.g., failure driven by load, strength or strain of roots); thus, they lack consensus in mechanism and application. Herein, we proposed three new FBMs, namely, FBMs-W, in which the root failure mode is driven by energy (i.e., work), and compared them with others using ground truth data. These FBMs-W allow, to some extent, reconciliation of the previous assumptions in conflicts because both load and displacement of roots affect in root failure procedures.

Methods

To measure soil reinforcement, we conducted in situ direct shear tests under both rooted and bare soil conditions and two soil moisture levels using living roots from four common tree or shrubby species (Robinia pseudoacacia  L., Pinus tabulaeformis Carr., Syringa oblate Lindl., and Vitex negundo L. var. heterophylla (Franch.) Rehd.) on the Loess Plateau, China. The observed soil reinforcement was then compared with predicted ones using different FBMs for model assessment.

Results

All the FBMs overestimated the soil reinforcement compared with the observed values. Among the FBMs, the three FBMs-W showed fairly conservative predictions of root cohesion (cr) that were close to each other. FBMs-W gave the most stable soil reinforcement estimates with the smallest standard deviations. The above results were consistent among the four species.

Conclusion

Our findings highlight the high disparities in soil reinforcement estimates and bias from the observed values due to the choice of model algorithms. Due to the conservativeness and stability of the soil reinforcement estimates and good coherence with the observed root failure order, we recommend that FBMs-W should be good candidates to choose by future modellers and practitioners when evaluating the likelihood of the stability of a vegetated slope.

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Abbreviations

ANOVA:

Analysis of variation

ANCOVA:

Analysis of covariance

WWM:

Wu and Waldron’s model

RWWM:

Revised Wu and Waldron’s model

FBM:

Fibre bundle model

FBMs-F:

Group of force-driven fibre bundle models

FBM-N:

Fibre bundle model of force evenly distributed according to root number

FBM-Dia:

Fibre bundle model of force distributed according to root diameter

FBM-S:

Fibre bundle model of force distributed according to root cross-sectional area

FBM-Dis:

Fiber bundle model of imposing successive displacement to a bundle of n parallel roots

FBMs-W:

Group of work-driven fibre bundle models

FBM-WN:

Fibre bundle model of work evenly distributed according to root number

FBM-WDia:

Fibre bundle model of work distributed according to root diameter

FBM-WS:

Fibre bundle model of work distributed according to root cross-sectional area

U (a, b):

Uniform distribution for random choice of root diameter values, where a and b are the two diameter class cut-offs

c r :

Soil additional cohesion from roots (kPa)

c r, alg :

Additional cohesion determined by a soil reinforcement model algorithm (alg), which can be a WWM or an FBM (kPa)

c :

Bare soil effective cohesion (kPa)

σ :

Confining pressure acting on the shear plane (kPa)

ϕ :

Soil internal friction angle (°)

θ :

Angle of root deviation relative to soil shear surface (°)

T r :

Root tensile strength (MPa)

A r :

Root cross-sectional area (mm2)

A :

Soil shear surface area (m2)

d :

Root diameter (mm)

N :

Total number of root diameter classes

n :

Root number in a given bundle

i :

In the WWM, the subscript i refers to root diameter class; in the FBM, i refers to root number

W r :

Root fracture energy to breakage in tension (J/mm2), which refers to the resistance of root to tensile breakage in terms of energy

f :

Tensile load applied to a root in a tensile test (N)

F r :

Maximum tensile force (N)

L 0 :

Initial gauge length in a tensile test (mm)

l :

Root tensile displacement (mm)

L max :

Maximum displacement of root (mm)

j :

Sequence number of a step of increment of FBM-W

f i,j :

Real load of root i under the jth increment (N)

F j :

Global load of whole root bundle at the jth iteration (N)

W j :

Energy increment under the jth iteration (J)

w :

Soil moisture content (%)

m w :

Soil wet mass (g)

m d :

Soil dry mass (g)

ε :

Root tensile strain (dimensionless)

ε r :

Root critical tensile strain at root failure (dimensionless)

Δτ :

Observed soil reinforcement measured in a direct shear test (kPa)

τ :

Shear stress of in situ shear test (kPa)

τmax (σn , wm , root):

Maximum shear stress of the root permeated soil under specific normal stress σn and moisture content wm (kPa)

−τmax (σn , wm , bare):

Maximum shear stress of the bare soil under specific normal stress σn and moisture content wm (kPa)

E r :

Root Young’s modulus (GPa)

k SR :

Ratio between soil reinforcement estimation and measurement (dimensionless)

c r_var :

Root cohesion under shifted root mechanical trait values in uncertainty analysis (kPa)

c r_init :

Root cohesion under initial root mechanical trait values in uncertainty analysis (kPa)

k UA :

Ratio between cr_var and cr_init for uncertainty analysis (dimensionless)

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Acknowledgements

This work was jointly financed by the Subsequent Project of Chinese National Scientific and Technical Innovation Research of the 12th Five Year Planning (2015BAD07B030303, ZQZ), the National Natural Science Foundation of China (31400616, JNJ) and the French INRA meta-programme EcoServ project OPUS VI (No.° 291 – MP-P10691, ZM). We gratefully acknowledge the Beijing Municipal Education Commission for their financial support through Innovative Transdisciplinary Program 'Ecological Restoration Engineering'. We are grateful to Dr. Thierry Fourcaud (CIRAD, UMR AMAP, France) and Dr. Lihua Chen (Beijing Forestry University, China) for their inspiring suggestions to this work, as well as Mr. Yuebin Li for the help with the field site experiments and Mr. Weibo Ling and Mr. Wenji Du for the help with coding and computation. We also express our thanks to the reviewer Dr. Tristram C. Hales and the other two anonymous reviewers whose comments have greatly improved our manuscript.

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Authors and Affiliations

  1. College of Soil and Water Conservation, Beijing Forestry University, Jixian National Forest Ecosystem Research Network Station, CNERN, Qinghua East Road 35#, Haidian District, Beijing, 100083, China

    Jinnan Ji, Wenbin Qu & Zhiqiang Zhang

  2. AMAP, INRA, CNRS, IRD, CIRAD, University of Montpellier, Boulevard de la Lironde, 34398, Montpellier Cedex 5, France

    Zhun Mao

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  1. Jinnan Ji
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Correspondence to Zhiqiang Zhang.

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Ji, J., Mao, Z., Qu, W. et al. Energy-based fibre bundle model algorithms to predict soil reinforcement by roots. Plant Soil 446, 307–329 (2020). https://doi.org/10.1007/s11104-019-04327-z

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