D. Cohen

Root-soil mechanical interactions during pullout and failure of root bundles

[1] Roots play a major role in reinforcing and stabilizing steep hillslopes. Most studies in slope stability implement root reinforcement as an apparent cohesion by upscaling the behavior of static individual roots. Recent studies, however, have shown that much better predictions of slope stability can be made if the progressive failure of bundles of roots are considered. The characteristics of progressive failure depend on interactions between soil deformation and root bundle geometric and mechanical properties. We present a detailed model for the quantitative description of the mechanical behavior of a bundle of roots under strain‐controlled mechanical forcing. The Root Bundle Model explicitly considers typical values of root‐size spatial distribution (number and dimension of roots), geometric factors (diameter‐length proportion, tortuosity, and branching characteristics), and mechanical characteristics (tensile strength and Young’s modulus) and interactions under various soil conditions (soil type, confining pressure, and soil moisture). We provide systematic analyses of the roles of these factors on the mechanical response of the bundle and explore the relative importance of various parameters to the macroscopic root‐soil mechanical response. We distinguish between increased strength imparted by small roots at small deformations and the resilience imparted by larger roots to the growth of large tensile cracks, showing that the maximal reinforcement of fine roots is reached within the first 5 cm of displacement whereas a root of 20 mm diameter may reach its maximal pullout force after 10 cm displacement. The model reproduces the gradual straining and ultimate residual failure behavior of root systems often observed in hillslopes, with progressive growth of tension cracks improving estimations of root reinforcement when considering the effects of root distribution and the variation of the pullout force as a function of displacement. These results enhance understanding of root reinforcement mechanisms and enable more realistic implementation of root reinforcement modeling for stability calculations of vegetated slopes and for guiding ongoing experimental efforts to gather critical root‐soil mechanical information.

Fiber bundle model for multiscale modeling of hydromechanical triggering of shallow landslides

[1]xa0Sudden and rapid mass movements associated with landslides and snow avalanches present a hazard to life and infrastructure, yet their predictions and triggering mechanisms remain poorly understood. Statistical methods and correlative studies have been used to produce landslide or avalanche susceptibility maps, often with limited physical basis. Mechanistic approaches based on factor-of-safety computation seldom represent the progressive transition from local failure events to a landslide and, in general, do not include heterogeneities associated with land cover or with subsurface material properties and hydrologic pathways. Focusing on rainfall-induced shallow landslides, we propose the use of the fiber bundle model (FBM), a generic yet powerful and adaptable model used in modeling fatigue and fracture of complex and disordered materials. The primary strength of the FBM is its ability to represent the progressive failure of cracks and shear zones and the ruptures of highly heterogeneous bonding elements that are present in soils at all scales. The model also provides a natural framework for interpretation of acoustic emission signatures from failing slopes, which may form the basis of a monitoring and warning system.

Pullout tests of root analogs and natural root bundles in soil: Experiments and modeling

[1]xa0Root-soil mechanical interactions are key to soil stability on steep hillslopes. Motivated by new advances and applications of the Root Bundle Model (RBM), we conducted a series of experiments in the laboratory and in the field to study the mechanical response of pulled roots. We systematically quantified the influence of different factors such as root geometry and configuration, soil type, and soil water content considering individual roots and root bundles. We developed a novel pullout apparatus for strain-controlled field and laboratory tests of up to 13 parallel roots measured individually and as a bundle. Results highlight the importance of root tortuosity and root branching points for prediction of individual root pullout behavior. Results also confirm the critical role of root diameter distribution for realistic prediction of global pullout behavior of a root bundle. Friction between root and soil matrix varied with soil type and water content and affected the force-displacement behavior. Friction in sand varied from 1 to 17 kPa, with low values obtained in wet sand at a confining pressure of 2 kPa and high values obtained in dry sand with 4.5 kPa confining pressure. In a silty soil matrix, friction ranged between 3 kPa under wet and low confining pressure (2 kPa) and 6 kPa in dry and higher confining pressure (4.5 kPa). Displacement at maximum pullout force increased with increasing root diameter and with tortuosity. Laboratory experiments were used to calibrate the RBM that was later validated using six field measurements with natural root bundles of Norway spruce (Picea abies L.). These tests demonstrate the progressive nature of root bundle failure under strain-controlled pullout force and provide new insights regarding force-displacement behavior of root reinforcement, highlighting the importance of considering displacement in slope stability models. Results show that the magnitude of maximum root pullout forces (1–5 kPa) are important for slope stability. The force-displacement relations characterized in this study are fundamental inputs for quantifying the resistive force redistribution on vegetated slopes and may provide explanation for abrupt loss of strength during landslide initiation and deformation.

An analytical fiber bundle model for pullout mechanics of root bundles

[1]xa0Roots in soil contribute to the mechanical stability of slopes. Estimation of root reinforcement is challenging because roots form complex biological networks whose geometrical and mechanical characteristics are difficult to characterize. Here we describe an analytical model that builds on simple root descriptors to estimate root reinforcement. Root bundles are modeled as bundles of heterogeneous fibers pulled along their long axes neglecting root-soil friction. Analytical expressions for the pullout force as a function of displacement are derived. The maximum pullout force and corresponding critical displacement are either derived analytically or computed numerically. Key model inputs are a root diameter distribution (uniform, Weibull, or lognormal) and three empirical power law relations describing tensile strength, elastic modulus, and length of roots as functions of root diameter. When a root bundle with root tips anchored in the soil matrix is pulled by a rigid plate, a unique parameter, , that depends only on the exponents of the power law relations, dictates the order in which roots of different diameters break. If 1, large roots break first. When = 1, all fibers break simultaneously, and the maximum tensile force is simply the roots mean force times the number of roots in the bundle. Based on measurements of root geometry and mechanical properties, the value of is less than 1, usually ranging between 0 and 0.7. Thus, small roots always fail first. The model shows how geometrical and mechanical characteristics of roots and root diameter distribution affect the pullout force, its maximum and corresponding displacement. Comparing bundles of roots that have similar mean diameters, a bundle with a narrow variance in root diameter will result in a larger maximum force and a smaller displacement at maximum force than a bundle with a wide diameter distribution. Increasing the mean root diameter of a bundle without changing the distributions shape increases both the maximum force and corresponding displacement. Estimates of the maximum pullout forces for bundles of 100 roots with identical diameter distribution for different species range from less than 1 kN for barley (Hordeum vulgare) to almost 16 kN for pistachio (Pistacia lentiscus). The model explains why a commonly used assumption that all roots break simultaneously overpredicts the maximum pullout force by a factor of about 1.6–2. This ratio may exceed 3 for diameter distributions that have a large number of small roots like the exponential distribution.

Shear‐induced force fluctuations and acoustic emissions in granular material

[1]xa0We conducted a series of strain-controlled experiments to study the characteristics of a shear zone forming in dense flow of confined dry granular media. The primary objective was to link force fluctuations due to jamming and force network reformation with episodic release of elastic energy as passively monitored by acoustic emission sensors. Under constant deformation rate, the shear stress exhibits a characteristic sawtooth behavior reflecting the strong influence of micromechanical processes on the macroscopic stress-strain behavior. Measured shear stress jumps were highly correlated with low-frequency (<u200920u2009kHz) acoustic emission events. High-frequency (30u2009kHz–80u2009kHz) acoustic signals that were measured with different sensors appear to be directly linked to continual grain-scale interactions (e.g., friction, rolling). A conceptual mechanical fiber bundle model (FBM) was used to represent dynamics at the shear zone of large granular assemblies. The model was capable of reproducing the dynamics of stress jumps and associated elastic energy release events. The combination of acoustic emission (AE) measurements and FBM framework offers new insights into the behavior of shear failure and enhances capabilities for resolving grain-scale mechanical processes and for predicting rapid mass movement such as shallow landslides and debris flows.