Fluid-Induced Material Transport: A Volume Averaged Approach to Modelling in SPH

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1 Fluid-Induced Material Transport: A Volume Averaged Approach to Modelling in SPH Vinay Kumar SPH Workshop, , Karlsruhe

2 Outline Motivation Model concept Groundwater model SPH formulation Soil model SPH formulation What next? Seite 2

3 Motivation: Physics River bed as a saturated system with free water standing above System can be driven out of equilibrium by two processes Change in hydraulic conditions Change in mechanical conditions Rapid drawdown changes boundary conditions of the groundwater system Affects the stress-state of soil Seite 3

4 The Model Concept Turbulent Flow Armour stones (simplified) Model 1 Exchange Darcy Flow Model 2 Seite 4

5 Groundwater System Pore spaces considered at a macroscopic level New properties arise consequently for fluid-flow Pore volume, geometry Porosity, permeability Pore velocity specific discharge Pore-fluid composition saturation New equations at this scale es.gif Seite 5

6 Transient Groundwater Flow Follows diffusion equation. Pore pressure is the diffused quantity Can be formulated with pressure or hydrostatic head The Diffusion coefficient lumps together the permeability, viscosity, porosity and the compressibilites of water and the soil skeleton. Seite 6

7 Transient Groundwater Flow Steady state to steady state time determined by relaxation time Soils with low permeability dissipate excess pore pressure slower Significant factor for stability Seite 7

8 Conduction in a slab t = 0s t = 10s Model dimension (1x0.2)m Cp = K = 1 Density = 1000kg/m^3 Kernel: Cubic Spline Time Integration: Verlet Seite 8

9 Heat conduction in a slab DualSPHysics Cleary et. al (1999) t = 10s t = 10s Seite 9

10 K 1e-4 (m/s) K 1e-5 (m/s) K 1e-6 (m/s) T 50s T 500s Seite 10

11 Evolution of P now known Rapid Drawdown Change in water level reduces the total overburden of soil According to, effective stress is reduced. Porewater pressure equilibrates slower (relaxation time) Seite 11

12 Soil Model Starting point, Hooke s law Pore pressure coupled to volumetric strain Seite 12

13 Soil Model in SPH Cauchy momentum equation in SPH Strain tensor in SPH Seite 13

14 Coupling concept Exchange Quelle: Lenaerts et al, 2009 Model 2 Tranport of mass from one region to another by creation and deletion of particles. Should obey conservation Quelle: Issa, 2004 Model 1 Seite 14

15 Summary The system is complex and dynamic Ultimately forseen to be used with periodically varying boundaries (e.g. movement of ships over a day) Diffusion equation approach allows simulation of larger dimension models This elasticity model is only the beginning! Seite 15

16 Thank you! Questions? Seite 16

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