Gravity-driven Free-surface Flows Research Articles

Initial stages of gravity-driven flow of two fluids of equal depth

Short-time behavior of gravity-driven free surface flow of two fluids of equal depth and different densities is studied. Initially, the fluids are at rest and separated with a vertical rigid plate of negligible thickness. Then, the plate disappears suddenly and a gravity-driven flow of the fluids starts. The flow in an early stage is described by the potential theory. The initial flow in the leading order is described by a linear problem, which is solved by the Fourier series method. The motions of the interface between the fluids and their free surfaces are investigated. The singular behaviors of the velocity field at the bottom point, where the interface meets the rigid bottom, and the top point, where the interface meets both free surfaces, are analyzed in detail. The flow velocity is shown to be log-singular at the bottom point. The leading-order inner asymptotic solution is constructed in a small vicinity of this point. It is shown that the flow close to the bottom point is self-similar. The motion of the interface is independent of any parameters, including the density ratio, of the problem in specially stretched variables. In the limiting case of negligible density of one of the fluids, the results of the classical dam break problem are recovered. The Lagrangian representation is employed to capture the behavior of the interface and the free surfaces at the top, where the fluid interface meets the free surfaces. The shapes of the free surfaces and the interface in the leading order computed by using the Lagrangian variables show a jump discontinuity of the free surface near the top point where the free surfaces and the interface meet. Inner region formulation is derived near the top point.

Initial stages of a three dimensional dam break flow

Short time behavior of a three dimensional, gravity-driven free surface flow is studied analytically and numerically. Initially the fluid is at rest, held by a vertical wall. A rectangular section of the wall suddenly disappears and the gravity driven three-dimensional flow starts. In order to describe the flow in the early stage, the potential theory is employed. Viscous effects are ignored for small times. The leading order problem is solved by using the Fourier series method and an integral equation method. Local analysis of the flow field close to the side edges of the rectangular section reveals a square root singularity. The flow velocity is also log-singular at the bottom edge of the rectangular section. In the limiting case, as the width of the rectangular section approaches infinity, the results of the classical two-dimensional dam break flow are recovered. Three dimensional effects become important closer to the side edges of the rectangular section.

Stability of gravity-driven free-surface flow past a deformable solid: The role of depth-dependent modulus.

The linear stability of a Newtonian liquid layer flowing down an inclined plane lined with a deformable linear elastic solid characterized by a continuously varying modulus is analyzed in this study. A low-wave-number asymptotic analysis is performed to obtain an analytical expression for the complex wavespeed which shows striking similarity with the earlier results of Sahu and Shankar [Sahu and Shankar, Phys. Rev. E 94, 013111 (2016)10.1103/PhysRevE.94.013111] for gravity-driven flow of Newtonian fluid past a solid bilayer having constant shear modulus (in each layer) lined on a rigid inclined plane. This shows that a deformable solid layer having a continuously varying shear modulus can be treated as a generalization of a system having multiple solid layers of constant shear modulus. Also, in the low-wave-number limit, we show that the stability of the free surface is governed by the value of effective shear modulus G_{eff}, and not by the detailed spatial variation of the modulus. Here the effective shear modulus (H/G_{eff}=∫_{1}^{1+H}1/[E_{0}+E[over ¯](z)]dz, where [E_{0}+E[over ¯](z)] represents the modulus gradient function) characterizes the overall modulus of the elastic solid, which is obtained by treating the continuous variation to be the limit of the arrangement of solid layers of infinitesimal thickness (each having a constant shear modulus) in a series. At finite wave numbers, we show that the free-surface and the liquid-solid interface become unstable as we increase the value of Γ, where Γ indicates the ratio of viscous stresses in the fluid to elastic stresses in the solid. When the system is analysed for different types of spatial modulus variations, we find results similar to those of Gkanis and Kumar [Gkanis and Kumar, Phys. Rev. E 73, 026307 (2006)10.1103/PhysRevE.73.026307], i.e., when we have two different configurations of the shear modulus function that have the same spatially averaged modulus, but have different values at the interface, the system is more stable for the configuration having higher shear modulus at the liquid-solid interface. In a similar manner, when we examined systems having the same shear modulus at the liquid-solid interface and same average modulus, the more stable case is the one which has a higher value of shear modulus just below the interface. Thus the use of deformable solids with a depth-dependent modulus potentially offers more control in the passive manipulation of the instabilities.

Length of standing jumps along granular flows down smooth inclines

Predicting the flows of dense granular media is still a challenging issue. Here, numerical discrete element method simulations are used to investigate the diversity of patterns within granular jumps that accompany height, velocity, and density discontinuities in gravity-driven free-surface flows. It is demonstrated that standing granular jumps can serve as a useful gauge for evaluating the dissipation mechanisms that govern the flowability of granular media.

Asymmetric concentration dependence of segregation fluxes in granular flows

We characterize the local concentration dependence of segregation velocity and segregation flux in both size and density bidisperse gravity-driven free-surface granular flows as a function of the particle size ratio and density ratio, respectively, using discrete element method (DEM) simulations. For a range of particle size ratios and inlet volume flow rates in size-bidisperse flows, the maximum segregation flux occurs at a small particle concentration less than 0.5, which decreases with increasing particle size ratio. The segregation flux increases up to a size ratio of 2.4 but plateaus from there to a size ratio of 3. In density bidisperse flows, the segregation flux is greatest at a heavy particle concentration less than 0.5 which decreases with increasing particle density ratio. The segregation flux increases with increasing density ratio for the extent of density ratios studied, up to 10. We further demonstrate that the simulation results for size driven segregation are in accord with the predictions of the kinetic sieving segregation model of Savage and Lun.

Stability of gravity-driven free surface flow of surfactant-laden liquid film flowing down a flexible inclined plane

We examined the linear stability of gravity-driven creeping flow of a liquid film flowing down an inclined plane when the inclined plane is coated with a deformable solid layer and the gas-liquid interface is contaminated with a monolayer of insoluble surfactant. The contaminated liquid film flowing down a rigid incline admits gas-liquid (GL) interfacial mode and surfactant-induced Marangoni mode, both of which remain stable in the creeping flow limit. The primary aim of this study is to explore the effect of the presence of a deformable wall, in place of a rigid inclined wall, on the stability behavior of Marangoni mode which originates because of the transport of surfactant at the GL interface. In presence of a deformable solid layer, two additional parameters namely, shear modulus and thickness of deformable solid layer also affects the stability behavior of falling film configuration. Our long-wave asymptotic analysis and results at finite and arbitrary wavenumbers demonstrated the destabilization of Marangoni mode solely due to the presence of deformable solid layer. Specifically, we have shown that for a given solid thickness, the Marangoni mode becomes unstable when the shear modulus of solid layer decreases below a critical value (i.e. the solid layer becomes sufficiently soft). The effect of increasing solid thickness is found to be destabilizing. The LS interfacial mode also becomes unstable at high wavenumbers below a threshold value of shear modulus, however, this value is much smaller than that required to trigger Marangoni mode instability. This implies that as the solid coating becomes more and more deformable, the Marangoni mode becomes unstable first followed by the LS interfacial mode. The GL mode was always found to be stable in creeping flow limit. Further, our long-wave analysis shows that the solid deformability has an additional stabilizing effect on GL mode. The neutral stability curves in nondimensional solid deformability parameter (or equivalently shear modulus) vs. wavenumber plane clearly depicts that the Marangoni mode is the dominant unstable mode in the creeping flow limit. Thus, the present study shows the destabilization of Marangoni mode solely due to presence of deformable solid layer and this we believe is the first example of the case where the instability of the Marangoni mode is observed when the fluid-fluid interface (here, GL interface) remains stress-free in the basic state.

Free surface flow characteristics of multi-phase viscoplastic fluids on inclined flumes and planes

Laboratory experiments were conducted to understand the dynamics of gravity-driven free surface flow of multi-phase viscoplastic fluids. Foam and sand–foam mixtures were employed to represent multi-phase yield stress fluids. Two different foam–water ratios of 0.1 and 0.2 were used and a wide range of sand concentrations from 0 to 0.82 were selected. A series of flume tests were conducted to model the two-dimensional flow of sand–foam mixtures for two slopes of 10° and 15°. Effects of sand concentration co on the dynamics of free surface flow were investigated. Three-dimensional spreading tests were carried out using an inclined plane with four bed slopes of α = 10°, 12°, 15° and 18. Single and multi-discontinuity were observed in the spreading of foam mixtures. It was found that the number of discontinuities can be correlated with the bed slope and multi-discontinuity occurred for α ≥ 12°. Flow heights and frontal velocities were measured for different experimental conditions (slope angle, rheological parameter). The results of spreading tests were properly scaled using a non-dimensional time scale and Froude number. Experimental results were used to predict the rheological characteristics of sand–foam mixtures based on the Herschel–Bulkley constitutive law. Predictions were compared with independent measurements of the rheological parameter. The inclined plane test results showed that the shear stress predictions were independent of the bed slope and the uncertainty of the predictions was slightly higher than the rheometery results from the literature.

Inverse rheometry and basal properties inference for pseudoplastic geophysical flows

The present work addresses the question of performing inverse rheometry and basal properties inference for pseudoplastic gravity-driven free-surface flows at low Reynolds’ number. The modeling of these flows involves several parameters, such as the rheological ones or the state of the basal boundary (modeling an interface between the base and the fluid). The issues of inverse rheometry are addressed in a general laboratory flow context using surface velocity data. The inverse characterization of the basal boundary is proposed in a geophysical flow context where the parameters involved in the empirical effective sliding law are particularly difficult to estimate. Using an accurate direct and inverse model based on the adjoint method combined with an original efficient solver, sensitivity analyses and parameter identification are performed for a wide range of flow regimes, defined by the degree of slip and the non-linearity of the viscous sliding law considered at the bottom.The first result is the numerical assessment of the passive aspect of the viscosity singularity inherent to a power-law pseudoplastic (shear-thinning) description in terms of surface velocities. From this result, identification of the two parameters of the constitutive law, namely the power-law exponent and the consistency, are performed. These numerical experiments provide, on the one hand, a very robust identification of the power-law exponent, even for very noisy surface velocity observations and on the other hand, a strong equifinality problem on the identification of the consistency. This parameter has a minor influence on the flow, in terms of surface velocities. Typically for temperature-dependent geophysical fluids, a law describing a priori its spatial variability is then sufficient (e.g. based on a temperature vertical profile).This study then focuses on the basal properties interacting with the fluid rheology. An accurate joint identification of the scalar valued triple (n,m;β) (respectively the rheological exponent, the non linear friction exponent and the friction coefficient) is achieved for any degree of slip, allowing to completely infer the flow regime. Next, in a geophysical flow context, identifications of a spatially varying friction coefficient are performed for various perturbed bedrock topography. The (2D-vertical) results demonstrate a severely ill-posed problem that allows to compute a given set of surface velocity data with different topography/friction pairs.

A NEW MODEL FOR SHALLOW VISCOELASTIC FLUIDS

We propose a new reduced model for gravity-driven free-surface flows of shallow viscoelastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for viscoelastic fluids. The viscosity is assumed small (of order epsilon, the aspect ratio of the thin layer of fluid), but the relaxation time is kept finite. In addition to the classical layer depth and velocity in shallow models, our system describes also the evolution of two components of the stress. It has an intrinsic energy equation. The mathematical properties of the model are established, an important feature being the non-convexity of the physically relevant energy with respect to conservative variables, but the convexity with respect to the physically relevant pseudo-conservative variables. Numerical illustrations are given, based on a suitable well-balanced finite-volume discretization involving an approximate Riemann solver.

Gravity-driven granular free-surface flow around a circular cylinder

AbstractSnow avalanches and other hazardous geophysical granular flows, such as debris flows, lahars and pyroclastic flows, often impact on obstacles as they flow down a slope, generating rapid changes in the flow height and velocity in their vicinity. It is important to understand how a granular material flows around such obstacles to improve the design of deflecting and catching dams, and to correctly interpret field observations. In this paper small-scale experiments and numerical simulations are used to investigate the supercritical gravity-driven free-surface flow of a granular avalanche around a circular cylinder. Our experiments show that a very sharp bow shock wave and a stagnation point are generated in front of the cylinder. The shock standoff distance is accurately reproduced by shock-capturing numerical simulations and is approximately equal to the reciprocal of the Froude number, consistent with previous approximate results for shallow-water flows. As the grains move around the cylinder the flow expands and the pressure gradients rapidly accelerate the particles up to supercritical speeds again. The internal pressure is not strong enough to immediately push the grains into the space behind the cylinder and instead a grain-free region, or granular vacuum, forms on the lee side. For moderate upstream Froude numbers and slope inclinations, the granular vacuum closes up rapidly to form a triangular region, but on steeper slopes both experiments and numerical simulations show that the pinch-off distance moves far downstream.

Two-dimensional natural element analysis of double-free surface flow under a radial gate

The gravity-driven free surface flow problems for which both the solid and free surface boundaries are highly curved are very difficult to solve. A computational scheme using a variable domain and a fixed domain natural element method (NEM) is developed in the present study for the computation of the free surface profile, velocity and pressure distributions, and the flow rate of a 2D gravity fluid flow through a conduit and under a radial gate. The problem involves two highly curved unknown free surfaces and arbitrary curved-shaped boundaries. These features make the problem more complicated than flow under a sluice gate or over a weir. The fluid is assumed to be inviscid and incompressible and the results obtained are confirmed by conducting a hydraulic model test. The results are in agreement with other flow solutions for free surface profiles and pressure distributions.

Pattern formation and mixing in three-dimensional film flow

The effect of inertia on gravity-driven free surface flow over different three-dimensional periodic corrugations is considered analytically, numerically and experimentally. In the case of high bottom amplitudes, compared to the film thickness, the results predict complex free surface structures especially in cases where the topography is not fully flooded by the liquid film. The investigation of the flow field shows a rich variety of pattern formation phenomena depending on the interplay between the geometry of the topography and the inertia of the film. Finally, we show how the complex topographical structure enhances the laminar mixing within the film.

The inverse problem in creeping film flows

We consider the inverse problem for gravity-driven free surface flows at vanishing Reynolds numbers. In contrast to the direct problem, where information about the underlying topographic structure is given and the steady free surface shape and the flow field are unknown, the inverse problem deals with the flow along unknown topographies. The bottom shape and the corresponding flow field are reconstructed from information at the steady free surface only. We discuss two different configurations for the inverse problem. In the first case, we assume a given free surface shape, and by simplifying the field equations, we find an analytical solution for the corresponding bottom topography, velocity field, wall shear stress, and pressure distribution. The analytical results are successfully compared with experimental data from the literature and with numerical data of the Navier–Stokes equations. In the second inverse problem, we prescribe a free surface velocity and then solve numerically for the full flow domain, i.e. the free surface shape, the topography and simultaneously the wall shear stress and the pressure field. The results are validated with the numerical solution of the corresponding direct problem.

Competing geometric and inertial effects on local flow structure in thick gravity-driven fluid films

The formation and presence of eddies within thick gravity-driven free-surface film flow over a corrugated substrate are considered, with the governing equations solved semianalytically using a complex variable method for Stokes flow and numerically via a full finite element formulation for the more general problem when inertia is significant. The effect of varying geometry (involving changes in the film thickness or the amplitude and wavelength of the substrate) and inertia is explored separately. For Stokes-like flow and varying geometry, excellent agreement is found between prediction and existing flow visualizations and measured eddy center locations associated with the switch from attached to locally detached flow. It is argued that an appropriate measure of the influence of inertia at the substrate is in terms of a local Reynolds number based on the characteristic corrugation length scale. Since, for small local Reynolds numbers, the local flow structure there becomes effectively decoupled from the inertia-dominated overlying film and immune from instabilities at the free-surface; the influence of inertia manifests itself as a skewing of the dividing streamline (separatrix). It is shown that the formation and presence of eddies can be manipulated in one of two ways. While an decrease/increase in the corrugation steepness leads to the disappearance/appearance of kinematically induced eddies, an increase/decrease in the inertia present in the system leads to the appearance/disappearance of inertially induced eddies. A critical corrugation steepness for a given film thickness is defined, demarking the transition from a kinematically to an inertially induced local eddy flow structure and vice versa.

Breaking size segregation waves and particle recirculation in granular avalanches

Particle-size segregation is a common feature of dense gravity-driven granular free-surface flows, where sliding and frictional grain–grain interactions dominate. Provided that the diameter ratio of the particles is not too large, the grains segregate by a process called kinetic sieving, which, on average, causes the large particles to rise to the surface and the small grains to sink to the base of the avalanche. When the flowing layer is brought to rest this stratification is often preserved in the deposit and is known by geologists as inverse grading. Idealized experiments with bi-disperse mixtures of differently sized grains have shown that inverse grading can be extremely sharp on rough beds at low inclination angles, and may be modelled as a concentration jump or shock. Several authors have developed hyperbolic conservation laws for segregation that naturally lead to a perfectly inversely graded state, with a pure phase of coarse particles separated from a pure phase of fines below, by a sharp concentration jump. A generic feature of these models is that monotonically decreasing sections of this concentration shock steepen and eventually break when the layer is sheared. In this paper, we investigate the structure of the subsequent breaking, which is important for large-particle recirculation at the bouldery margins of debris flows and for fingering instabilities of dry granular flows. We develop an exact quasi-steady travelling wave solution for the structure of the breaking/recirculation zone, which consists of two shocks and two expansion fans that are arranged in a ‘lens’-like structure. A high-resolution shock-capturing numerical scheme is used to investigate the temporal evolution of a linearly decreasing shock towards a steady-state lens, as well as the interaction of two recirculation zones that travel at different speeds and eventually coalesce to form a single zone. Movies are available with the online version of the paper.

Weak, strong and detached oblique shocks in gravity-driven granular free-surface flows

Hazardous natural flows such as snow-slab avalanches, debris flows, pyroclastic flows and lahars are part of a much wider class of dense gravity-driven granular free-surface flows that frequently occur in industrial processes as well as in foodstuffs in our kitchens! This paper investigates the formation of oblique granular shocks, when the oncoming flow is deflected by a wall or obstacle in such a way as to cause a rapid change in the flow height and velocity. The theory for non-accelerative slopes is qualitatively similar to that of gasdynamics. For a given deflection angle there are three possibilities: a weak shock may form close to the wall; a strong shock may extend across the chute; or the shock may detach from the tip. Weak shocks have been observed in both dense granular free-surface flows and granular gases. This paper shows how strong shocks can be triggered in chute experiments by careful control of the downstream boundary conditions. The resulting downstream flow height is much thicker than that of weak shocks and there is a marked decrease in the downstream velocity. Strong shocks therefore dissipate much more energy than weak shocks. An exact solution for the angle at which the flow detaches from the wedge is derived and this is shown to be in excellent agreement with experiment. It therefore provides a very useful criterion for determining whether the flow will detach. In experimental, industrial and geophysical flows the avalanche is usually accelerated, or decelerated, by the net effect of the gravitational acceleration and basal sliding friction as the slope inclination angle changes. The presence of these source terms necessarily leads to gradual changes in the flow height and velocity away from the shocks, and this in turn modifies the local Froude number of the flow. A shock-capturing non-oscillating central method is used to compute numerical solutions to the full problem. This shows that the experiments can be matched very closely when the source terms are included and explains the deviations away from the classical oblique-shock theory. We show that weak shocks bend towards the wedge on accelerative slopes and away from it on decelerative slopes. In both cases the presence of the source terms leads to a gradual increase in the downstream flow thickness along the wedge, which suggests that defensive dams should increase in height further down the slope, contrary to current design criteria but in accordance with field observations of snow-avalanche deposits from a defensive dam in Northwestern Iceland. Movies are available with the online version of the paper.

Stability of gravity-driven free-surface flow past a deformable solid at zero and finite Reynolds number

The linear stability of Newtonian liquid flow down an inclined plane lined with a deformable elastic solid layer is analyzed at zero and finite Reynolds number. There are two qualitatively different interfacial modes in this composite system: the free-surface or gas-liquid (“GL”) mode which becomes unstable at low wave numbers and nonzero Reynolds number in flow down a rigid plane, and the liquid-solid (“LS”) mode which could become unstable even in the absence of inertia at finite wave numbers when the solid layer is deformable. The objectives of this work are to examine the effect of solid layer deformability on the GL and LS modes at zero and finite inertia, and to critically assess prior predictions concerning GL mode instability suppression at finite inertia obtained using the linear elastic model by comparison with the more rigorous neo-Hookean model for the solid. In the creeping-flow limit where the GL mode instability is absent in a rigid incline, we show that for both solid models, the GL and LS modes become unstable at finite wavelengths when the solid layer becomes sufficiently soft. At finite wavelengths, the labeling of the two interfacial modes as GL and LS becomes arbitrary because these two modes get “switched” when the solid layer becomes sufficiently deformable. The critical strain required for instability becomes independent of the solid thickness (at high enough values of thickness) for both GL and LS modes in the linear elastic solid, while it decreases with the thickness of the neo-Hookean solid. At finite Reynolds number, it is shown for both the solid models that the free-surface instability in flow down a rigid plane can be suppressed at all wavelengths by the deformability of the solid layer. The neutral curves associated with this instability suppression are identical for both linear elastic and neo-Hookean models. When the solid becomes even more deformable, both the GL and LS modes become unstable for finite wave numbers at nonzero inertia, but the corresponding neutral curves obtained from the two solid models differ significantly in detail. At finite inertia, for both the solid models, there is a significant window in the shear modulus of the solid for moderate values of solid thickness where both the GL and LS modes are stable at all wave numbers. Thus, using the neo-Hookean model, the present study reaffirms the prediction that soft elastomeric coatings offer a passive route to suppress and control interfacial instabilities.

Hydrodynamic modelling of flow over a spillway using a two-dimensional finite volume-based numerical model

Spillway flow, a classical problem of hydraulics, is generally a gravity-driven free surface flow. Spillway flows are essentially rapidly varying flows near the crest with pronounced curvature of the streamlines in the vertical direction. Two processes simultaneously occur in the flow over the crest, that is, formation and gradual thickening of the turbulent boundary layer along the profile, and gradual increase in the velocity and decrease in the depth of main flow. Spillway hydrodynamics can be obtained through physical modelling or numerical modelling. Physical modelling of spillways is expensive, cumbersome and time-consuming. The main difficulties in solving the spillway problem numerically are: rapidly varying flow, existence of both subcritical and supercritical flows, development of turbulent boundary layers, unknown free surface and air entrainment. Numerical simulation of such flows over spillways in all flow regimes is a challenging task. This paper describes a numerical model and its application to a case study to investigate the hydraulic characteristics of flow over spillway crest profiles by simulating the velocity distribution, pressure distribution and discharge characteristics. Results of the numerical modelling are compared with those from the physical modelling and found to be satisfactory.

Particle-size segregation and diffusive remixing in shallow granular avalanches

Segregation and mixing of dissimilar grains is a problem in many industrial and pharmaceutical processes, as well as in hazardous geophysical flows, where the size-distribution can have a major impact on the local rheology and the overall run-out. In this paper, a simple binary mixture theory is used to formulate a model for particle-size segregation and diffusive remixing of large and small particles in shallow gravity-driven free-surface flows. This builds on a recent theory for the process of kinetic sieving, which is the dominant mechanism for segregation in granular avalanches provided the density-ratio and the size-ratio of the particles are not too large. The resulting nonlinear parabolic segregation–remixing equation reduces to a quasi-linear hyperbolic equation in the no-remixing limit. It assumes that the bulk velocity is incompressible and that the bulk pressure is lithostatic, making it compatible with most theories used to compute the motion of shallow granular free-surface flows. In steady-state, the segregation–remixing equation reduces to a logistic type equation and the ‘S’-shaped solutions are in very good agreement with existing particle dynamics simulations for both size and density segregation. Laterally uniform time-dependent solutions are constructed by mapping the segregation–remixing equation to Burgers equation and using the Cole–Hopf transformation to linearize the problem. It is then shown how solutions for arbitrary initial conditions can be constructed using standard methods. Three examples are investigated in which the initial concentration is (i) homogeneous, (ii) reverse graded with the coarse grains above the fines, and, (iii) normally graded with the fines above the coarse grains. Time-dependent two-dimensional solutions are also constructed for plug-flow in a semi-infinite chute.

The effect of the earth pressure coefficients on the runout of granular material

In the framework of a better territory risk assessment and decision making, numerical simulation can provide a useful tool for investigating the propagation phase of phenomena involving granular material, like rock avalanches, when realistic geological contexts are considered. Among continuum mechanics models, the numerical model SHWCIN uses the depth averaged Saint Venant approach, in which the avalanche thickness ( H) is very much smaller than its extent parallel to the bed ( L). The material is assumed to be incompressible and the mass and the momentum equations are written in a depth averaged form. The SHWCIN code, based on the hypothesis of isotropy of normal stresses ( σ xx = σ yy = σ zz ), has been modified (new code: RASH 3D) in order to allow for the assumption of anisotropy of normal stresses ( σ xx = Kσ zz ; σ yy = Kσ zz ). A comparison among the results obtained by assuming isotropy or anisotropy is given through the back analysis of a set of laboratory experiments [Gray, J.M.N.T., Wieland, M., Hutter, K., 1999. Gravity-driven free surface flow of granular avalanches over complex basal topography. Proceedings of the Royal Society of London, Series A 455(1841)] and of a case history of rock avalanche (Frank slide, Canada). The carried out simulations have also underlined the importance of using a different earth pressure coefficient value ( K) for directions of convergence and of divergence of the flux.