Kinetic energy and collapse of granular materials

Suffusion involves fine particles migration within the matrix of coarse fraction under seepage flow, which usually occurs in the gap-graded material of dams and levees. Key factors controlling the soil erodibility include confining pressure (p′) and fines content (F c), of which the coupling effect on suffusion still remains contradictory, as concluded from different studies considering narrow scope of these factors. For this reason, a systematical numerical simulation that considers a relative wide range of p′ and F c was performed with the coupled discrete element method and computational fluid dynamics approach. Two distinct macroresponses of soil suffusion to p′ were revealed, ie, for a given hydraulic gradient i = 2, an increase in p′ intensifies the suffusion of soil with fines overfilling the voids (eg, F c = 35%), but have negligible effects on the suffusion of gap-graded soil containing fines underfilling the voids (eg, F c = 20%). The micromechanical analyses, including force chain buckling and strain energy release, reveal that when the fines overfilled the voids between coarse particles (eg, F c = 35%) and participated heavily in load-bearing, the erosion of fines under high i could cause the collapse of the original force transmission structure. The release of higher strain energy within samples under higher p′ accelerated particle movement and intensified suffusion. Conversely, in the case where the fines underfilled the voids between coarse particles (eg, F c = 20%), the selective erosion of fines had little influence on the force network. High p′ in this case prevented suffusion.

Section: Strong Force Chain Bucklingmentioning

confidence: 99%

A coupled CFD‐DEM investigation of suffusion of gap graded soil: Coupling effect of confining pressure and fines content

Liu

Wang

Hong

et al. 2020

“…Following a certain loading history, the body is in a strained configuration C and occupies a volume V of boundary (Γ). Adopting a semi‐Lagrangian formulation (each material point

\overset{x}{true}

of the current configuration C corresponds (through bijective mapping) to a material point

\overset{X}{true}

of the initial configuration C 0 ), and ignoring gravity, the following equation establishes the relation between the kinetic energy of the system and the second‐order work():

\overset{E_{c}}{true} = I_{2} + W_{2}^{e x t} - W_{2}^{i n t},

where

\overset{E_{c}}{true}

is a second‐order time differentiation of system kinetic energy,

I_{2} = \int_{V_{0}} ρ_{o} \overset{\overset{u}{true}}{true}^{2} normald V_{0}

is an inertial term, and

ū false(\overset{X}{true} false)

is the Lagrangian displacement field.

W_{2}^{e x t}

is the external second‐order work, and

W_{2}^{i n t}

is the internal second‐order work.…”

Section: Second‐order Work Criterionmentioning

confidence: 99%

“…Following a certain loading history, the body is in a strained configuration C and occupies a volume V of boundary (Γ). Adopting a semi-Lagrangian formulation (each material pointx of the current configuration C corresponds (through bijective mapping) to a material pointX of the initial configuration C 0 ), and ignoring gravity, the following equation establishes the relation between the kinetic energy of the system and the second-order work 34,36 :…”

Section: Second-order Work Criterionmentioning

confidence: 99%

A multiscale work‐analysis approach for geotechnical structures

Xiong

Yin

Nicot

2019

Self Cite

Summary This paper presents a second‐order work analysis in application to geotechnical problems by using a novel effective multiscale approach. To abandon complicated equations involved in conventional phenomenological models, this multiscale approach employs a micromechanically‐based formulation, in which only four parameters are involved. The multiscale approach makes it possible a coupling of the finite element method (FEM) and the micromechanically‐based model. The FEM is used to solve the boundary value problem (BVP) while the micromechanically‐based model is utilized at the Gauss point of the FEM. Then, the multiscale approach is used to simulate a three‐dimensional triaxial test and a plain‐strain footing. On the basis of the simulations, material instabilities are analyzed at both mesoscale and global scale. The second‐order work criterion is then used to analyze the numerical results. It opens a road to interpret and understand the micromechanisms hiding behind the occurrence of failure in geotechnical issues.

“…10 are the unique result of an initial particle arrangement and the imposed boundary movements. One must remember, however, that the DEM simulates a dynamic system, and the particles' movements are produced by a continual condition of dis-equilibrium [23]. Internal instability can, in fact, be present, and should be expected.…”

Section: Example 3: Irregular Assembly Of 64 Disksmentioning

confidence: 99%

“…Combining Eqs. (9), (10), (13), (14), (23), (24), and (33)- (5), the stiffness matrix [H] in Eq. (10) is the sum of mechanical and geometric parts, the latter being the sum of four influences:…”

mentioning

confidence: 99%

Stiffness pathologies in discrete granular systems: Bifurcation, neutral equilibrium, and instability in the presence of kinematic constraints

Kuhn

Prunier

Daouadji

2019

Self Cite

Summary The paper develops the stiffness relationship between the movements and forces among a system of discrete interacting grains. The approach is similar to that used in structural analysis, but the stiffness matrix of granular material is inherently nonsymmetric because of the geometrics of particle interactions and of the frictional behavior of the contacts. Internal geometric constraints are imposed by the particles' shapes, in particular, by the surface curvatures of the particles at their points of contact. Moreover, the stiffness relationship is incrementally nonlinear, and even small assemblies require the analysis of multiple stiffness branches, with each branch region being a pointed convex cone in displacement space. These aspects of the particle‐level stiffness relationship give rise to three types of microscale failure: neutral equilibrium, bifurcation and path instability, and instability of equilibrium. These three pathologies are defined in the context of four types of displacement constraints, which can be readily analyzed with certain generalized inverses. That is, instability and nonuniqueness are investigated in the presence of kinematic constraints. Bifurcation paths can be either stable or unstable, as determined with the Hill–Bažant–Petryk criterion. Examples of simple granular systems of three, 16, and 64 disks are analyzed. With each system, multiple contacts were assumed to be at the friction limit. Even with these small systems, microscale failure is expressed in many different forms, with some systems having hundreds of microscale failure modes. The examples suggest that microscale failure is pervasive within granular materials, with particle arrangements being in a nearly continual state of instability.