ISSN (Online), Volume 5, Issue 7, July (2014), pp IAEME AND TECHNOLOGY (IJCIET) MODELING OF SOIL EROSION BY WATER

Transcription

1 INTERNATIONAL Intnational Journal of Civil Engineing JOURNAL and Technology OF CIVIL (IJCIET), ENGINEERING ISSN (Print), AND TECHNOLOGY (IJCIET) ISSN (Print) ISSN (Online) Volume 5, Issue 7, July (2014), pp IAEME: Journal Impact Factor (2014): (Calculated by GISI) IJCIET IAEME MODELING OF SOIL EROSION BY WATER Kissi Benaissa *1, El Haouzi Ahmed 1 1 National School of Arts and Trades of Casablanca (ENSAM-Casablanca), Univsity Hassan II. Avenue Hassan II.B.P: 145, Mohammedia Morocco ABSTRACT Many dam ruptures events have occurred throughout the world, Then main cause was piping phenomenon that occurred in the foundation soil or in the dam structure. Sviceability of hydraulic infrastructures needs considing vulnability of soil to intnal osion und the action of a seepage flow. Undstanding the undlying mechanisms and quantifying the effects of ptinent variables that affect this phenomenon is of great importance in ord to prevent such catastrophes. Erosion due to liquid flow discharge can be modeled by diffent. In this work, the wat osion is modeled in the wat/soil intface during the hole osion test (HET). The Hole Erosion Test is commonly used to quantify the rate of piping osion. The aim of this work is to predict the osion of soil in the wat/soil intface by using the Fluent package and three dimensional modeling.this modelling makes it possible describing the effect of the flow on osion in the intface wat/soil by using the k turbulence model equations, and predicts a non uniform osion along the hole length unlike the usual one dimensional models. In particular, the flow velocity is found to increase noticeably the osion rate. Effects on the wall-shear stress resulting from varying flow velocity and applied hydraulic gradient are analyzed. Keywords: Piping, Soil Erosion, Turbulence, k Model, Near-Wall Boundary, Hole Erosion Test. 1. INTRODUCTION Soil osion is a complex phenomenon which yields at its final stage insidious fluid leakages und the hydraulic infrastructures known as piping and which provokes their rupture. Many dam ruptures events have occurred throughout the world, some of them we reported by Fost and al. [1]. (Fig.1) 123

2 Then main cause was piping phenomenon that occurred in the foundation soil or in the dam structure. Sviceability of hydraulic infrastructures needs considing vulnability of soil to intnal osion und the action of a seepage flow, [2, 3]. A simplified one-dimensional model for intpreting the Hole Erosion Test (HET) with a constant pressure drop was developed by Bonelli and Brivois [4, 5]. This model yielded a charactistic osion time which was found to be depending on the initial hydraulic gradient and the soil coefficient of osion. Fig.1: TETON Dam Failure, USA 1976 We can consid various measures to reduce the risk of formation of wat osion. In particular (Figure.2: a) and b)): - Decrease the value of the hydraulic gradient (to envisage an impmeable carpet in the side upstream of an earth dam ) - To inst piezomets of discharge. - To charge the soil and to emge a matial which can play the part of filt to change its granulometry. a) b) Fig.2: Example of anti-wat osion an earth dam A three-dimensional modeling of fluid flow taking place in the hole inside the hole osion test sample test was pformed by means of enhanced CFD software package. The hole wall had been assumed to be rigid and to have ideal circular cylindrical geometry. Unlike the early models which are essentially one-dimensional, the two-dimensional modeling had shown that the wall-shear stress is not uniform along the hole wall [6]. 124

3 For instance, the inlet side of the sample hole undgoes genally much more osion than the outlet side. But, one-dimensional modeling of this test could not predict this oded shape since it yields uniform osion at the whole fluid/soil intface inside the soil sample hole. The aim of this study is to describe the biphasic turbulent flow at the origin of osion taking place inside the porous soil sample by considing the influence of variation of the flow velocity on rate osion. A Computational Fluid Dynamics (CFD) approach is used to investigate the shear stress that develops at the wat/soil intface and which represents the main mechanical action that causes surface osion. When the shear stress is calculated by means of Fluent, the classical linear osion law is used to estimate osion rate. This law gives osion rate, consided to be the amount of mass departure due to osion p unit time and by unit surface area, by & = c ( τ τ cr ) whe c and τ cr are constants depending on the consided soil matial. For a cylindrical hole, the rate & can be related to time variation of local radius by & = ρ d dr / dt whe ρ d is the dry density of soil and R is hole radius. The osion law yields that & is proportional to the amount of shear exceeding the critical shear τ cr for which osion begins. The standard HET is such that, the fluid domain which is assumed to be axisymmetric extends ov 117 mm in the axial z-direction and 3 mm in the radial r-direction (Figure 2). Fig.2: Geometry of the HET tube 2. THREE-DIMENSIONAL MODELING APPROACH OF THE HET The turbulence modelling is achieved by means of Fluent software package. Fluent is a genal purpose Computational Fluid Dynamics (CFD) code that has been applied to various problems in the fields of fluid mechanics and heat transf. This code has been validated through numous investigations. Fluent is especially appropriate for the complex physics involved in heat and mass transf and consids mixtures by modeling each fluid species independently or as a homogenized medium, [7]. Flow taking place inside the hole is turbulent. To pform realistic simulation of turbulence, the exact instantaneous Navi-Stokes govning equations are habitually time-avaged or ensemble-avaged. The obtained avaged equations contain furth unknown variables, and turbulence models are introduced to detmine them in tms of known quantities. Various turbulence models have been proposed in the litature; howev the is no single turbulence model which could be univsally applied for all classes of problems. The choice of a ptinent model for a 125

4 given problem will depend on the actual physics of the flow, the degree of accuracy required and the computational cost tolated. Refence [8] gives a detailed discussion on how to pform at best the appropriate choice of a turbulence model. Among the various models, the standard k model which was proposed first by Laund and Spalding [9] has become the most popular when dealing with practical engineing flow calculations. This model relies on phenomenological considations and integrates empiricism to pform closure of equations. 3. STANDARD K-ΕPSILON MODEL The simplest "complete models'' of turbulence are two-equation models in which the solution of two separate transport equations allows the turbulent velocity and length scales to be independently detmined. The standard k- model in FLUENT falls within this class of turbulence model and has become the workhorse of practical engineing flow calculations in the time since it was proposed by Laund and Spalding [9]. Robustness, economy, and reasonable accuracy for a wide range of turbulent flows explain its popularity in industrial flow and heat transf simulations. It is a semi-empirical model, and the divation of the model equations relies on phenomenological considations and empiricism. As the strengths and weaknesses of the standard k- model have become known, improvements have been made to the model to improve its pformance. The standard k- model [9] is a semi-empirical model based on model transport equations for the turbulence kinetic engy (k) and its dissipation rate (). The model transport equation for k is dived from the exact equation, while the model transport equation for was obtained using physical reasoning and bears little resemblance to its mathematically exact countpart. In the divation of the k- model, the assumption is that the flow is fully turbulent, and the effects of molecular viscosity are negligible. The standard k- model is thefore valid only for fully turbulent flows. 4. TRANSPORT EQUATIONS FOR THE STANDARD K-ΕPSILON MODEL The turbulence kinetic engy, k, and its rate of dissipation,, are obtained from the following transport equations: µ t k ( ρk) + ( ρ ku ) = ( µ + ) + G + G ρ Y + S t xi xj σ k x j i k b M k (1) And µ ( ρ) + ( ρ u ) = ( µ + ) + C ( G + C G ) C ρ + S t xi xj x k k 2 t i 1 k 3 b 2 σ j (2) In these equations, Gk represents the genation of turbulence kinetic engy due to the mean velocity gradients. G b is the genation of turbulence kinetic engy due to buoyancy. Y M represents the contribution of the fluctuating dilatation in compressible turbulence to the ovall dissipation rate. C1, C2, and C3 are constants. σ k and σ are the turbulent Prandtl numbs for k and, respectively. S k and S are us-defined source tms. Although the default values of the model constants are the standard ones most widely accepted, you can change them (if needed) in the Viscous Model panel. 126

5 5. RESULTS AND DISCUSSIONS The analysis presented in this section focuses on the simulation of the turbulent fluid flow taking place inside a cylindrical pipe having a rigid wall that replicates the geometry of the hole in the HET. The fluid domain which is assumed to be axisymmetric extends 170 mm in the axial z- direction and 30 mm in the radial r-direction. The origin of the refence frame is placed at the entrance section. Modeling und fluent has been pformed by using wat density and dynamic viscosity at 3 the tempature 20 C for which ρ = 1000 kg / m and η = ρµ = Pa. s. The four values of flow consided are given in table 1: Table (1): Reynolds numb and velocity of flow consided in this study Reynolds Velocity ( m / s ) Debit ( m 3 / s ) T.I(%) The solution method chosen und Fluent is Volume Of Fluid (VOF). The viscous Model selected is the standard k model and the near-wall treatment is conforming to the enhanced wall treatment with pressure gradient effects. The boundary conditions that we used are: - Inlet at the left extremity of the domain with gauge pressure value specified and turbulence specification method corresponding to turbulence intensity T.I (%) and hydraulic diamet equal to 1/8 the radius R. turbulence intensity can be calculated as: T. I = 0.16 Re - Outlet at the right extremity of the domain with gauge pressure fixed at 0, turbulence specification method was used with turbulence intensity T.I (%) and hydraulic diamet equal to the radius R. - Symmetry type axis at the axis of symmetry which is the bottom side of the domain as presented in figure 1. - Wall at the top side of the domain, (figure 1), whe the enhanced near-wall treatment with pressure gradient effects option is selected. Default convgence statements we selected. They assure that continuity, velocities, turbulent kinetic engy and its dissipation rate are stationary within a relative tolance limit fixed at 10-6.The solution convges in approximately 300 itations. Figures 2 and 3 give the Profiles of Wall Shear Stress on wall as function of Reynolds numb. 127

6 Fig.3: Profiles of Wall Shear Stress on wall for Re=20000 Fig.4: Erosion rate as function of inlet velocity (Reynolds numb) (in Pascal) 4 Table 2 gives the osion rate (in 10 kg / s ) which corresponds to the amount of mass departure p unit time due to osion. This amount is obtained by integrating the osion law ov the whole length of the hole and by multiplying the result by the initial circumfence of the hole. 4 The classical linear osion law & = c ( τ τ s ) was used, with the osion constants c = s / m and τ s = 0.2 Pa as identified for a soil sample containing 50% kaolinit clay and 50% of sand that was tested in [10]. 4 TABLE (2): EROSION RATE IN 10 kg / s AS FUNCTION OF REYNOLDS NUMBER Re τ (Pa) & Re= Re= Figures 2 and 3 show that the wall-shear is not uniform along the whole hole length. The wall-shear stress at the inlet extremity can exceed multiple times its pmanent value in the plateau zone inside the hole. This is in contrast with the habitual hypothesis used to dive one-dimensional modeling of the HET. The obtained results, as shown in figure 4, indicate that osion rate increase with Reynolds numb and wit the axial coordinate. 128

7 The obtained results state clearly the three-dimensional charact of flow taking place inside the hole and show strong variations in comparison with two-dimensional and one-dimensional approaches. Predicting the osion in its initial stage can be done und the assumptions that the wall is rigid and that the linear osion law is valid. This was pformed and results are summarized in table 2 whe it could be obsved that the Reynolds numb has strong effect on the amount of osion rate. The osion rate increases as function the flow velocity with a maximum value at the inlet extremity. At the inlet extremity wall-shear stress is maximal and osion is maximal. 6. CONCLUSIONS A three-dimensional modeling of fluid flow taking place in the hole inside the hole osion test sample test was pformed by means of enhanced CFD software package. The hole wall had been assumed to be rigid and to have ideal circular cylindrical geometry. Unlike the early models which are essentially one-dimensional, the three-dimensional modeling had shown that the wallshear stress is not uniform along the hole wall (in the wat/soil intface). It was possible then through using a linear osion law to predict non uniform osion along the hole length. Studying the effect of Reynolds numb has shown that it has important effect on the wall-shear stress and thus would affect in its turn surface osion that develops at the fluid soil sample intface. This enabled qualitatively undstanding why the oded profile of the hole wall as obsved during expiment is not uniform. 7. REFERENCES [1] M.A. Fost, R. Fell, M. Spannangle. The statistics of embankment dam failures and accidents. Canadian geotechnical Journal 37 (2000) [2] Fjar E., Holt R.M., Horsrud P., Raaen A.M., Risnes R., Petroleum related rock mechanics, revised edition Elsevi, Amstdam, [3] Lachouette D. Golay F., Bonelli S. One dimensional modelling of piping flow osion. C. R. Mecanique 336 (2008) [4] D. Lachouette, F. Golay, S. Bonelli. One dimensional modelling of piping flow osion. Comptes Rendus de Mécanique 336 (2008), [5] S. Bonelli, O. Brivois. The scaling law in the hole osion test with a constant pressure Drop. Intnational Journal for Numical and Analytical Methods in Geomechanics, 32(2008) [6] Kissi Benaissa, Parron Va Miguel Angel, Rubio Cintas Maria Dlolores, Dubujet Philippe, Khamlichi Abdellatif, Bezzazi Mohammed, El Bakkali Larbi. Predicting initial osion during the Hole Erosion Test by using turbulent flow CFD Simulation. Applied Mathematical Modelling. 36 (2012) [7] A. Escue, J. Cui. Comparison of turbulence models in simulating swirling pipe flows. Applied Mathematical Modelling. (2010) doi: /j.apm [8] Fieldview refence Manual, Software Release Vsion 10, Intelligent Light, [9] Laund, B.E., Spalding, D.B. Lectures in Mathematical Models of Turbulence. Academic Press, London, England, [10] T.L. PHAM. Erosion et dispsion des sols argileux par un fluide. In French. Ph.D Thesis, Ord numb: D.U. ED: 430. Ecole Nationale des Ponts et Chaussées, Paris, France, [11] A. Rizk, A. Aldebky and N. Guirguis, Comparison Between Natural Cross and Hybrid Ventilation for Hot Climate by Using CFD Intnational Journal of Civil Engineing & Technology (IJCIET), Volume 5, Issue 2, 2014, pp , ISSN Print: , ISSN Online: