Extending the Shields criterion to erosion of weakly cemented granular soils

United States

The present contribution tackles the issue of incipient conditions for initiation of erosion by a fluid flow at the surface of cohesive materials. To this end, a typical assessment procedure consists in subjecting a soil sample to progressive hydrodynamic stresses induced by a submerged impinging jet flow whose injection velocity is gradually increased. This paper presents the results of an extensive use of this protocol both in experiments and numerical simulations, the latter being based on a coupled DEM and LBM approach. Here we consider the specific case of weakly cemented soils, either made experimentally of glass beads bonded by solid bridges or modelled numerically by a solid bond rheology with a parabolic yield condition involving the micromechanical traction, shearing and bending of the bonds. The results show that, as expected, the hydrodynamic stress for erosion onset substantially increases with solid cohesion as compared to cohesion-less cases but can, however, be satisfactorily predicted by a simple extension of the usual Shields criterion that only applies for cohesion-less granular sediments. This extension includes a cohesion number, the granular Bond number, with a simple definition based on tensile yield values.

Powders &amp; Grains 2021

[EPJ Web of Conferences, Volume 249 (2021)](https://www.epj-conferences.org/articles/epjconf/abs/2021/03/contents/contents.html)

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Powders & Grains 2021

Powders & Grains 2021 will be held in Buenos Aires (Argentina, VIRTUAL) July 5, 13, 21, 29 and Aug 6, 2021. The aim of the conference is to give an up-to-date picture of the broad research field of granular media, powders and grains. Contributions from experts around the world will focus on research topics that cover a wide range of open problems in the field.

poster

Three-dimensional simulations of cone penetration tests (CPT) in cemented sandstone have been investigated using the Discrete Element Method (DEM). We generated the realistic grain size distribution of sandstone in the numerical simulations using the Ustyurt-Buzachi Sedimentary Basin samples. Numbers of numerical CPT tests at different bond strength values were performed with the penetrometer vertically moved down at a constant rate. The results of the real-world particle size distribution show that the cone penetration resistance and side friction increase with increasing depths; and with increase in bond strength the cone resistance and side friction decrease, while the friction ratio increases. The result of numerical CPT tests in cemented sandstone was found to be in good agreement with the Soil Behaviour Type (SBT) classification system from CPT data.

Numerical simulations of cone penetration in cemented sandstone

We investigate the avalanches of spherical and non-spherical granular particles inside half-filled rotating drums. The time series of the center of gravity of the particle assemblies are obtained via image analysis and their single-sided amplitude (SSA) spectra are analyzed. The spectra features of this new indicator turn out to be characteristic for the avalanches, in terms of the existence of peaks in the low-frequency range and the decay rate of high frequency components. The SSA spectrum has a peak for the packings of non-spherical particles but not for the spherical particles. The high frequency part is characterized by a power law decay { $1/f^a \ (a>0)$ }. A $1/f$-decay is found only for the spherical particles. For the packings of cornered particles, the exponents significantly deviate from $a=1$. As $1/f$ spectra are often associated with self-organized criticality and therefore a scale invariance of the dynamics, we may conclude that there is no scale-invariant structure for granular avalanches. Considering the small number of particles and the regularity of convex particle shapes being used, the spectral features revealed in this study could be utilized for validating particle simulations.

Experimental study of particle shape dependence of avalanches inside a rotating drum

The formation of shear bands is one of the most remarkable phenomena in the dynamics of granular matter. Several parameters have been so far identified to influence the behavior of the shear bands. We carried out experiments to investigate the evolution of the shear bands in the split-bottom Couette cell in the presence of confining pressure. We employed the Particle Image Velocimetry (PIV) to characterize the shear band both in the absence and presence of external pressure. Our results show that the location and width of the shear band are affected by both the confining pressure and the filling height. The shear zone evolves towards the middle of the cylinder and expands to a broader region with increasing applied pressure or filling height; also the angular velocity decreases relative to the rotation rate of the bottom disk. Our findings are consistent with prior empirical observations on the formation of wide shear bands at free surfaces.

Shearing of granular materials in a confined split-bottom Couette cell

The unknown particle scale mechanics of slow granular flows have hindered our understanding of its features, such as rate independence. The DEM simulations unveil the signatures of stick-slip pattern during flow. Furthermore, we analyzed the time evolution of contact networks and constructed a cascade failure mechanism - from the isostatic criterion - which demonstrates the emergence of stick-slip motion. This insight into micromechanics provides phenomenological reasoning for rate independence and large fluctuations in stress.

Micromechanics of slow granular flows

In this study, we investigate the flow rate of model granular material in a silo under the influence of mechanical vibrations. Experimental measurements and discrete element simulations (DEM) are performed in a quasi-2D silo. The influence on the flow rate of the opening size and the vibration applied on the entire silo is studied. Two distinct regimes are evidenced, governed by the Froude number Fr and the relative frequency. In the first regime, a decreased flow rate is observed when increasing the vibration intensity. This behavior is explained by the presence of reorganizations induced by the vibration, leading to a more homogeneous but also slower flow. In the second regime, an increased flow rate is evidenced when increasing the vibration intensity. We find this behavior comes from the intermittent nature of the flow, where the flow rate is directly controlled by the propagation of shock waves all along the silo.

Discharge of a granular silo under mechanical vibrations

Wave velocity and attenuation are two of the most important attributes of geomaterials under seismic loads. To understand how they are influenced by particle and microstructural characteristics, Discrete Elements Method simulations are carried out to simulate the propagation of linear and nonlinear waves in isotropic, frictional granular packings. The focus is on the effects of confining pressure and source characteristics (i.e., input strain and frequency) on wave velocity and attenuation. Three different approaches are used to quantify the seismic quality factor Q or damping in time and frequency domain. Our simulation results verify previous findings on the scaling of wave velocity with respect to confining pressure and coordination number. Quality factors measured both in time and frequency domains increase with confining pressure and show an interesting non-monotonic behavior with input frequency. As expected, wave velocity and quality factor for S-waves decrease with an increasing input shear strain amplitude, while for P-waves they first decrease and then increase at input strain amplitude of 6×10-4. Change of participation number shows that the inhomogeneity of the system increases with the increase of the input strain.

Elastic wave velocity and attenuation in granular material

Numerical models of granular materials are useful in tribology, and can be used to predict wear and friction in contacts. DEM-like simulations are used to model particles of third-body, which are partly wear debris from rubbing bodies. It has been shown that the third-body particles can have different flow regimes, depending on their mechanical properties. Among the different characteristics of flow regimes, agglomerate size seems to be crucial. A method based on vortex analysis used in fluid mechanics allows characterizing this cluster size. The results show that different vortex sizes can be observed during the simulation. In particular, it is observed that some vortexes of a characteristic size persist over time, and could be representative of agglomerates. These results pave the way for a better characterisation of the different flow regimes.

Detecting vorticity in cohesive deformable granular material

We studied experimentally the effect of grain size and maximum load on the compaction and subsequent relaxation of a granular column when it is subjected to vertical uniaxial compression. The experiments were performed using two different types of grains: 1) solid glass beads, and 2) porous beads that consist of agglomerates of glass powder. We found that the compression force increases non-linearly with time, with sudden drops for the case of glass beads and periodic undulations for dust particles. Whereas the grain size effect is small in the average force load, the fluctuations become larger as the grain size increases. On the other hand, the relaxation process is well described by the Maxwell model with three different relaxation time scales.

Grain size effect on the compression and relaxation of a granular column: solid particles vs dust agglomerates

We analyse the different morphologies induced by an oscillating plate above an erodible bed. We present some data describing how the shape and the stiffness of the plate affect the main features of the generated heap. We investigate several configurations with different geometries, frequencies and the amplitudes. Some
preliminary results are available, in which the role of the flexibility of the plate is taken in account. Unlike the rigid plate in which a proper oscillation induces the formation of one heap, the morphology of the bed is now characterized by more than one heap due to a different pressure profile induced by a flexible plate.

Particles bed morphology under an oscillating stiff and flexible plates

This presentation shows the results of five triaxial compression tests performed on approximately 9000 oblate spheroids (lentils) with different initial orientations with respect to the loading axis (0º, 30°, 45º, 60º, and 90°). Typical stress-strain information is complemented with x-ray tomography scans every 1 % strain. Starting from an initial labelling of particles, a new technique is used to obtain unprecedented detail of tracking of all the particles through time. This rich dataset is analysed from the perspective of inter-particle contacts (building on previous metrological work on this subject) revealing that the mean contact orientation in both samples rotates towards the direction of σ1 at a rate depending on the initial orientation. Different trends are observed for the alignment of contact orientation. 


Extending the Shields criterion to erosion of weakly cemented granular soils

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Numerical simulations of cone penetration in cemented sandstone

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