Hydro-Mechanical Properties of an Unsaturated Frictional Material

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138 Observed values (-) Observed values (-) Observed values (-) Observed values (-) 50 40 30 20 10 0 CHAPTER 7. ANALYSIS AND INTERPRETATION OF THE EXPERIMENTAL RESULTS 0 10 20 30 40 50 50 Statistical results Predicted - drainage values (-) van Genuchten (1980), m=1-1/n 40 R2= 0.993 30 20 10 0 50 40 30 20 10 0 0 10 20 30 40 50 Statistical results Predicted - drainage values (-) van Genuchten (1980) 0 50 10 20 30 Statistical results Predicted - drainage values (-) 40 50 40 30 Fredlund and Xing (1994) R2= 0.993 20 10 0 Statistical results - drainage Brooks and Corey (1959) R2= 0.966 R2= 0.993 0 10 20 30 40 50 Predicted values (-) a) b) c) Residuals (-) Residuals (-) Residuals (-) Residuals (-) 8 6 4 2 0 -2 -4 -6 -8 8 6 4 2 0 -2 -4 -6 -8 0 10 20 30 40 50 Predicted values (-) 0 10 20 30 40 50 8 Predicted values (-) 6 4 2 0 -2 -4 -6 -8 8 6 4 2 0 -2 -4 0 10 20 30 40 50 Predicted values (-) -6 d) h) -8 0 10 20 30 40 50 Predicted values (-) Figure 7.2: Statistical assessment of best fit results using several suction-water content models for imbibition process from modified pressure plate apparatus (loose specimens, steady state test) e) f) g)
7.2. SOIL-WATER CHARACTERISTIC CURVE 139 In Fig. 7.1 a) to d) the overall impression is that the points are close to the bisection line in the diagrams of observed and predicted values. As closer the points to the bisection line f(x) = x in the diagrams of observed versus predicted values as better the result of the curve fit. Using Brooks and Corey’s (1964) power-law relationship saturated volumetric water contents are not considered in the best-fit procedure and statistical analysis. This equation is not valid in the saturated zone and is only applicable for suctions larger than air-entry value (ψ > ψaev), that corresponds to volumetric water contents smaller than saturated volumetric water content (θ < θs). Due to sudden increase in volumetric water content after reaching the air-entry value up to the residual water content, points are concentrated mainly at low values (see Fig 7.1 a) to d)) as well as high values (see Fig 7.1 b) to d)) that corresponds to volumetric water contents in the residual zone and respectively to saturated volumetric water contents. For low volumetric water contents good agreement between observed and predicted values was found for all model functions. At larger volumetric water contents between θ = 7% to 20% for the most results the observed values are overestimated by the predicted values when using Brooks and Corey’s (1964) model function and van Genuchten’s (1980) model including m = 1 − 1/n. Except two points that are far underestimated by all model functions. Best agreement in the range of θ = 7% to 20% was found for van Genuchten’s (1980) and Fredlund and Xing’s (1994) model. Using Brooks and Corey’s (1964) equation for volumetric water content between θ = 20% to 46 the most experimental values are underestimated by the predicted values. Even the points are closer to the bisection line in Fig 7.1 this trend can be observed also when using van Genuchten’s (1980) equation considering m = 1 − 1/n. In this range best agreement between observed and predicted values was found for van Genuchtens (1980) as well as Fredlund and Xing’s (1994) model function. At all the results are closest to the bisection line using Fredlund and Xing’s (1994) model, which means that the observed values are similar to predicted values. This is also expressed by the coefficient of regression determination R 2 = 0.996. The plot of residuals versus predicted values should be randomly distributed above and below the line of f(x) = 0. The diagrams are given in Fig. 7.1 e) to h) respectively. The diagrams in Fig. 7.1 e) to h) show that for low volumetric water contents θ = 0% to θ = 10% the points are best scattered, when using Brooks and Corey’s (1964) and Fredlund and Xing’s (1994) model for fitting procedure. Mainly when using both van Genuchten’s (1980) equations vertical orientation of points was found in the residual zone. In the range of θ = 10% to θ = 46% the results are randomly distributed. Results derived from statistical analysis of fitting procedure from imbibition data (see Fig 7.2) show that observed and predicted values are in good agreement for fitting procedure using both van Genuchten’s (1980) and Fredlund and Xing’s (1994) model functions. This is also reflected in the coefficient of regression determination R 2 = 0.993. Results are randomly distributed in the plot of residual versus predicted values for all model functions. But for volumetric water contents θ = 20% to 46% most points are located above the line of f(x) = 0 when using Brooks and Corey’s (1964) function. This is also reflected in the underestima-
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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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Page 190 and 191: 164 Stiffness modulus (kPa) Stiffne
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188 CHAPTER 9. NUMERICAL SIMULATION
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CHAPTER 10. BEARING CAPACITY OF A S
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204 CHAPTER 10. BEARING CAPACITY OF
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206 CHAPTER 11. SUMMARY AND OUTLOOK
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214 APPENDIX A. DETAILS ZOU’S MOD
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216 APPENDIX A. DETAILS ZOU’S MOD
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218 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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