Friction law for dense granular flows: 
application to the motion of a mass down a 
rough inclined plane

Pouliquen, Olivier; Forterre, Yoël

doi:10.1017/s0022112001006796

Cited by 398 publications

(650 citation statements)

References 40 publications

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“…Let us assume that a i is greater than the residual friction angle /, which is consistent with the experimental observations of dry granular flows [30]. The normal stress P i is zero in the critical state of triggering the flow since the flow velocity is almost null at that time point.…”

Section: Introductionsupporting

confidence: 65%

A hypoplastic constitutive model for debris materials

Guo¹,

Peng²,

Wu³

et al. 2016

Acta Geotech.

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Debris flow is a very common and destructive natural hazard in mountainous regions. Pore water pressure is the major triggering factor in the initiation of debris flow. Excessive pore water pressure is also observed during the runout and deposition of debris flow. Debris materials are normally treated as solid particle-viscous fluid mixture in the constitutive modeling. A suitable constitutive model which can capture the solid-like and fluid-like behavior of solid-fluid mixture should have the capability to describe the developing of pore water pressure (or effective stresses) in the initiation stage and determine the residual effective stresses exactly. In this paper, a constitutive model of debris materials is developed based on a framework where a static portion for the frictional behavior and a dynamic portion for the viscous behavior are combined. The frictional behavior is described by a hypoplastic model with critical state for granular materials. The model performance is demonstrated by simulating undrained simple shear tests of saturated sand, which are particularly relevant for the initiation of debris flows. The partial and full liquefaction of saturated granular material under undrained condition is reproduced by the hypoplastic model. The viscous behavior is described by the tensor form of a modified Bagnold's theory for solid-fluid suspension, in which the drag force of the interstitial fluid and the particle collisions are considered. The complete model by combining the static and dynamic parts is used to simulate two annular shear tests. The predicted residual strength in the quasi-static stage combined with the stresses in the flowing stage agrees well with the experimental data. The non-quadratic dependence between the stresses and the shear rate in the slow shear stage for the relatively dense specimens is captured.

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Section: Introductionsupporting

confidence: 65%

A hypoplastic constitutive model for debris materials

Guo¹,

Peng²,

Wu³

et al. 2016

Acta Geotech.

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“…The depth-averaged equations, introduced by [49] and recently revisited [29,50] in the context of shallow granular flows down an inclined plane, allow us to estimate the effective friction coefficient µ * . The acceleration is balanced by the gravity parallel to the plane, the tangential stress between the fixed bottom and the flowing layer, and a pressure force related to the thickness gradient [29,49,50]. The momentum balance is reduced to the following equation in steady 2D flow conditions:…”

Section: Control Flows Without An Obstaclementioning

confidence: 99%

“…It can be calculated provided an assumption on the shape of the velocity profile: β = 4/3 for linear velocity profiles and β = 5/4 for Bagnold velocity profiles [51]. The k factor, in the thickness gradient term, is the ratio of the normal stress σ xx to the normal stress σ yy , classically introduced for dense granular flows [49,50].…”

Section: Control Flows Without An Obstaclementioning

confidence: 99%

“…The force P 0 due to the intersitial fluid (air) at the free surface of the flow are ignored: P 0 ∼ 0. The pressure force P 1 due to the incoming fluid on section (S 1 ) is parallel to the bottom: P 1x = 1 2 kρ 1 gh 1 cos θ (P 1y = 0), where k is the earth pressure coefficient classically introduced for dense granular flows [49,50]. The pressure force P 2 resulting from the outgoing fluid on section (S 2 ) is assumed to be negligible (P 2 ≈ 0).…”

Section: Control Flows Without An Obstaclementioning

confidence: 99%

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Mean steady granular force on a wall overflowed by free-surface gravity-driven dense flows

Faug¹,

Beguin²,

Chanut³

2009

Phys. Rev. E

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We studied free-surface gravity-driven recirculating flows of cohesionless granular materials down a rough inclined plane and overflowing a wall normal to the incoming flow and to the bottom. We performed 2D spherical particle discrete element simulations using a linear damped spring law between particles with a Coulomb failure criterion. High-frequency force fluctuations were observed. This paper focuses on the mean steady force exerted by the flow on the obstacle versus the macroscopic inertial number of the incoming flow, where the inertial number measures the ratio between a macroscopic deformation timescale and an inertial timescale. A triangular stagnant zone is formed upstream of the obstacle and sharply increases the mean force at low incoming inertial numbers. A simple hydrodynamic model based on depth-averaged momentum conservation isproposed. This analytical model predicts the numerical data fairly well and allows us to quantify the different contributions to the mean force on the wall. Beyond this model, our study provides an example of the ability of simple hydrodynamic approaches to describe the macroscopic behavior of an assembly of discrete particles, not only in terms of kinematics, but also in terms of forces.

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“…They found that the volume fraction Φ of the sample is also a function of I but varies only slightly in the dense regime. The inertial number, which is the square root of the Savage number 20 or of the Coulomb number 21 17,22 , it can be shown that the friction coefficient µ(I ) has the shape given in Fig. 1.…”

mentioning

confidence: 99%