Hydro-Mechanical Properties of an Unsaturated Frictional Material

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186 CHAPTER 9. NUMERICAL SIMULATION OF COLUMN TEST BY FEM 9.2 Model used for Numerical Investigation Based on the suction-water content model developed by Parker & Lenhard (1987) numerical investigation are carried out. The model is an empirical scaling hysteresis approach that can produce a realistic representation of scanning curves and hysteresis loops. For prediction of main drainage and main imbibition curve Parker & Lenhard (1987) used the suction-water content model by van Genuchten (1980). Their concept introduces an apparent saturation in order to account for the effect of residual trapped non-wetting phase saturation. Thus they distinguish between the effective and the apparent wetting phase saturation. The effective saturation ¯ Sw is considered as the mobile part of the phase. The apparent saturation ¯ Sw is the sum of the effective saturation ¯ Sw and the trapped effective saturation ¯ Snt of the non- wetting phase (see Fig. 9.1). If there is non-wetting phase entrapment ( ¯ S nr(i)), the soil-water characteristic curve for drainage and imbibition do not form closed loops. The formation of closed loops is possible by substitution of the effective by the apparent saturation (Fig. 9.1), that also accounts for fluid entrapment. Consequently, hysteresis is formed by scaling the apparent saturation. For example, saturation at point ζ that lies on an imbibition scanning curve (see Fig. 9.1, right) can be scaled as follows: ¯Sw(ζ) = ¯S7 − ¯ S6 ¯S5 − ¯ · ( S6 ¯ S4 − ¯ S3) + ¯ S3. (9.1) For simulation of flow in unsaturated porous media and considering hysteresis effect in these simulations the model by Parker & Lenhard (1987) was implemented into MUFTE- UG by Sheta (1999) and Papafotiou (2008). Capillary Pressure i S w(i) j S nt(ij) S w(j) S w(j) S nr S nr(i) Effective Saturation Apparent Saturation 1 Figure 9.1: Hysteresis and phase entrapment properties of the soil-water characteristic curve Capillary Pressure 5 7 2 6 4 ζ ξ 3
9.3. SETUP OF NUMERICAL SIMULATIONS 187 9.3 Setup of Numerical Simulations For the numerical simulation, a regular rectangular FE mesh is used. The spacing of the grid is 5 mm along the z-axis (direction of gravity). The width of the finite elements on the x-axis is chosen such that the bottom area of the discretized model domain corresponds to the bottom area of the cylindrical sand column described in the previous section. In the numerical simulation, although the problem is one-dimensional, the model domain has a depth of 1.0 m. Thus, the width of the domain in the numerical model is chosen to be 0.073062 m (see Fig. 9.2). A timestep of 4 s is chosen. The initial and boundary conditions in the numerical simulation correspond to those of the experiment. The primary variables are the water pressure uw and the air saturation Sn. The specimen is initially saturated and thus the effective saturation of water in the model domain is equal to 1.0. A hydrostatic distribution is given for the water pressure. At the top boundary, a Dirichlet boundary condition is applied for the water and the air phase. This boundary condition defines directly a water pressure value equal to −3400 Pa at the top of the column. This water pressure is equal to the maximum value of matric suction measured during the sand column test I experiment. In combination with the Dirichlet boundary value 1.0 for the air saturation, the definition of phase pressure difference (ψ = ua − uw) delivers that the pressure of air at the top boundary is equal to zero (atmospheric condition). The applied Dirichlet boundary condition at the top of the numerical model does not avoid water to flow through this boundary and therefore might introduce an error in the mass balance. To prevent any mass of water from leaving the domain through the top boundary, the wetting phase relative permeability at the finite elements of the upper layer is explicitly set to zero. Outflow mass (kg) 12 10 8 6 4 2 0 0 20000 40000 60000 80000 100000 Time (s) Figure 9.2: Domain and boundary conditions (left) and water outflow and inflow (right) in the numerical simulation
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Hydro-Mechanical Properties of Part
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Acknowledgement The present dissert
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3.2 Steps of Model Building . . . .
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11 Summary and Outlook 205 11.1 Gen
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2.16 Influence of Brooks and Corey
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6.2 Experimental results of soil-wa
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7.17 Unsaturated hydraulic conducti
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B.6 Experimental results and best f
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8.3 Constitutive parameters for the
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E ref ur Oedometer reference stiffn
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ρ Density (g/cm 3 ) ρd ρs Dry de
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2 CHAPTER 1. INTRODUCTION Figure 1.
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4 CHAPTER 1. INTRODUCTION - Model b
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6 CHAPTER 1. INTRODUCTION
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8 CHAPTER 2. STATE OF THE ART condu
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10 CHAPTER 2. STATE OF THE ART soil
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14 CHAPTER 2. STATE OF THE ART Figu
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16 CHAPTER 2. STATE OF THE ART - Su
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18 CHAPTER 2. STATE OF THE ART - Re
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20 CHAPTER 2. STATE OF THE ART Volu
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22 CHAPTER 2. STATE OF THE ART Drai
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24 CHAPTER 2. STATE OF THE ART wher
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26 CHAPTER 2. STATE OF THE ART drai
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28 CHAPTER 2. STATE OF THE ART Tabl
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32 CHAPTER 2. STATE OF THE ART by W
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34 CHAPTER 2. STATE OF THE ART proc
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36 CHAPTER 2. STATE OF THE ART - Im
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38 CHAPTER 2. STATE OF THE ART auth
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40 CHAPTER 2. STATE OF THE ART 2.5.
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46 CHAPTER 2. STATE OF THE ART fitt
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48 CHAPTER 2. STATE OF THE ART Satu
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50 CHAPTER 2. STATE OF THE ART when
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52 CHAPTER 2. STATE OF THE ART Degr
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54 CHAPTER 2. STATE OF THE ART 1. T
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56 CHAPTER 2. STATE OF THE ART 0.2
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58 CHAPTER 2. STATE OF THE ART meth
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60 CHAPTER 2. STATE OF THE ART When
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62 CHAPTER 2. STATE OF THE ART Vert
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64 CHAPTER 2. STATE OF THE ART a) S
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66 CHAPTER 2. STATE OF THE ART - Ja
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68 CHAPTER 2. STATE OF THE ART
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70 CHAPTER 3. INTRODUCTION TO PROCE
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76 CHAPTER 4. EXPERIMENTAL SETUPS s
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78 CHAPTER 4. EXPERIMENTAL SETUPS 1
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82 CHAPTER 4. EXPERIMENTAL SETUPS d
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84 CHAPTER 4. EXPERIMENTAL SETUPS b
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86 CHAPTER 4. EXPERIMENTAL SETUPS t
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90 CHAPTER 4. EXPERIMENTAL SETUPS D
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94 CHAPTER 4. EXPERIMENTAL SETUPS T
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96 CHAPTER 5. MATERIAL USED AND EXP
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98 CHAPTER 5. MATERIAL USED AND EXP
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100 CHAPTER 5. MATERIAL USED AND EX
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116 CHAPTER 6. EXPERIMENTAL RESULTS
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236 APPENDIX E. NEW SWCC MODEL - DE
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238 APPENDIX E. NEW SWCC MODEL - DE
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240 40 50 30 APPENDIX E. NEW SWCC M
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242 Observed Values Number of obser
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244 BIBLIOGRAPHY Aubertin, M., Mbon
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246 BIBLIOGRAPHY Campbell, J. D. (1
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248 BIBLIOGRAPHY Davis, J. L. & Ann
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250 BIBLIOGRAPHY Ferré, P. A. & To
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252 BIBLIOGRAPHY Grozic, J. L. H.,
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254 BIBLIOGRAPHY Janbu, N. (1969),
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256 BIBLIOGRAPHY Lawton, E. C., Fra
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258 BIBLIOGRAPHY Mualem, Y. (1977),
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260 BIBLIOGRAPHY Phene, C. J., Hoff
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262 BIBLIOGRAPHY Rojas, J. C., Sali
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264 BIBLIOGRAPHY Stoimenova, E., Da
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266 BIBLIOGRAPHY Vanapalli, S. K. &
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268 BIBLIOGRAPHY Unsaturated Geotec
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Schriftenreihe des Lehrstuhls für
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Herausgeber: Th. Triantafyllidis 32
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Hydro-Mechanical Properties of an Unsaturated Frictional Material

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