Hydro-Mechanical Properties of an Unsaturated Frictional Material

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172CHAPTER 8. NEW SWCC MODEL FOR SAND INCLUDING SCANNING CURVES 8.2 Soil-Water Characteristic Curve Model Following the steps of model building given in detail in Chapter 3 a soil-water characteristic curve model, that considers imbibition scanning curves is built. Based on the experimental results (several drainage processes) derived in the transient state column tests I the model is constructed. To provide a single model for all drainage processes, observed experimental data from initial drainage, 1 st drainage and 2 nd drainage process from loose specimen (all results derived from dense specimen are given in Appendix E in Figs E.1 to E.9) are considered. The experimental results were already presented in Chap- ter 6 but are once more given in Fig 8.1, where the volumetric water content is plotted versus suction. Whereas usually the axis of suction is plotted in logarithmic form here the non-logarithmic form is used, to observe the true shape of the suction-water content curves measured in the several depths along the column. From the experimental procedure it is known, that the sensor pair in the upper part (TDR/T 450) of the column remains through- out the whole experiment in the saturated zone. Thus these measurements are excluded from the model building. It is also important to repeat, that no significant influence of applied flow rate was observed and hence a dynamic effect does not be taken into account when choosing an appropriate model. When selecting a model a plot of the experimental data, process knowledge and process assumptions about the process are used for its suggestion. Plots of the soil-water characteristic curve are given in Fig. 8.1 for Hostun sand. As already mentioned before the main features of the suction water content relationship are the saturated volumetric water content, the air-entry value as well as the residual suction. Following the shape of the curves it is assumed that the volumetric water content is equal to the saturated volumetric water content before reaching the air-entry value. When passing this point the volumetric water content is decreasing (less steep for clay and most steep for sand). After the residual suction the curve is slanted. The curve show that a non-linear function is needed for the prediction. It is suggested that an exponential function might be appropriate for a model function. In Fig. 8.2 (see Fig. E.2 in Appendix E results of transformation derived from dense data) exemplary results of transformation procedure are given for initial drainage, 1 st drainage as well as 2 nd drainage results for loose specimen derived from the transient sand column test I (see Fig. 8.1). Based on these plots it is decided to fit the model with double logarithm in the response variable ln ln(θ) and with logarithm in the predictor variable ln(ψ), that give the best linear transformation: ln ln(θ) = β0 + β1 ln ln(ψ) (8.1) where: θ is the volumetric water content, ψ is the suction as well as β0 and β1 are parameters. The linear model given in Eq. 8.1 is proposed to relate the volumetric water content to the suction. Because drainage and imbibition processes are similar in shape, it is assumed that
8.2. SOIL-WATER CHARACTERISTIC CURVE MODEL 173 Volumetric water content (%) Volumetric water content (%) Volumetric water content (%) 50 40 state column test I Loose specimen Initial void ratio = 0.89 Initial drainage Transient 10 30 20 TDR/T 70 mm TDR/T mm 160 Flow rate ≈ 30 ml/min TDR/T 260 mm TDR/T 360 mm TDR/T 450 mm 50 5 4 3 2 1 0 0 40 Suction (kPa) drainage Flow rate ≈ 30 ml/min 1st 10 20 30 0 1 2 3 4 5 0 50 40 30 20 10 0 Suction (kPa) drainage Flow rate ≈ 100 ml/min 2nd 0 1 2 3 4 5 Suction (kPa) Figure 8.1: Experimental data (initial drainage, 1 st drainage, 2 nd drainage) from drainage transient state column tests used for model building (loose specimen) this equation also can be used for fitting of imbibition suction-water content relation. Based on the appropriate transformation found in the previous step finally the corresponding non- linear model is proposed: θ(ψ) = β0 + β3 exp(− ψβ1 ) (8.2) β2
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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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12 CHAPTER 2. STATE OF THE ART the
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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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30 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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80 CHAPTER 4. EXPERIMENTAL SETUPS D
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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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Page 240 and 241: 214 APPENDIX A. DETAILS ZOU’S MOD
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222 APPENDIX B. SOIL-WATER CHARACTE
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230 APPENDIX C. COLLAPSE POTENTIAL
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232 Vertical strain (-) Vertical st
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234 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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