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Purpose The relationship between root tensile strengths and diameters is often fitted using power law curves. More accurate fitting methodologies were developed, investigating a) the validity of least-squares regression assumptions underlying existing methods, b) how to best quantify intra-diameter variation, and c) whether to fit in terms of tensile strength or tensile force at failure. Methods Regression and maximum likelihood estimation were used to fit various power law models. 6461 tensile strength measurements from 153 existing datasets, covering 103 different plant species, were used to compare models. Results The intra-diameter variation in root strength is proportional to the average strength at each diameter, and is best described using a gamma distribution. When using linear regression on log-transformed measurements, a mathematical correction must be used to avoid underestimating the actual strength (18% on average). Compared to fitting tensile strengths, fitting in terms of root forces at failure was less reliable; the extra emphasis this method places on the effect of large diameters roots was not appropriate because of the typical abundance of thin roots in the field relative to those tested in tension. Average power law fits were proposed for broadleaved trees, conifers, shrubs, grasses and forbs. Conclusion Power law curves should be fitted in terms of root strength rather than root forces at failure, using the newly developed fitting methods that simultaneously fit both the inter-diameter (power law) and intra-diameter variation and can account for fitting bias. This will increase the reliability of future root reinforcement predictions.
Purpose The relationship between root tensile strengths and diameters is often fitted using power law curves. More accurate fitting methodologies were developed, investigating a) the validity of least-squares regression assumptions underlying existing methods, b) how to best quantify intra-diameter variation, and c) whether to fit in terms of tensile strength or tensile force at failure. Methods Regression and maximum likelihood estimation were used to fit various power law models. 6461 tensile strength measurements from 153 existing datasets, covering 103 different plant species, were used to compare models. Results The intra-diameter variation in root strength is proportional to the average strength at each diameter, and is best described using a gamma distribution. When using linear regression on log-transformed measurements, a mathematical correction must be used to avoid underestimating the actual strength (18% on average). Compared to fitting tensile strengths, fitting in terms of root forces at failure was less reliable; the extra emphasis this method places on the effect of large diameters roots was not appropriate because of the typical abundance of thin roots in the field relative to those tested in tension. Average power law fits were proposed for broadleaved trees, conifers, shrubs, grasses and forbs. Conclusion Power law curves should be fitted in terms of root strength rather than root forces at failure, using the newly developed fitting methods that simultaneously fit both the inter-diameter (power law) and intra-diameter variation and can account for fitting bias. This will increase the reliability of future root reinforcement predictions.
The maximum shear modulus (G0(ij)) of rooted soils is crucial for assessing the deformation and liquefaction potential of vegetated infrastructures under seismic loading conditions. However, no data or theory is available to account for the anisotropy of G0(ij) of rooted soils. This study presents a new model that can predict G0(ij) anisotropy of rooted soils by incorporating the projection of the stress tensor on two independent tensors that describe soil fabric and root network. Bender element tests were conducted on bare and vegetated specimens under isotropic and anisotropic loading conditions. The presence of roots in the soil increased G0(VH) at all confining pressures (p′), as well as G0(HH) and G0(HV) at low p′. However, the trend was reversed at higher p′ because the roots reduced the effects of confinement on G0(ij) by replacing stronger soil–soil interfaces with weaker soil–root interfaces. Roots made the soil fabric and G0(ij) more anisotropic. The proposed model can effectively predict the observed anisotropy of G0(ij) under isotropic and anisotropic loading conditions. The new model also offers a new method for determining the fabric anisotropy of sand based on the anisotropy of shear modulus.
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