Hydro-Mechanical Properties of an Unsaturated Frictional Material

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162 CHAPTER 7. ANALYSIS AND INTERPRETATION OF THE EXPERIMENTAL RESULTS m (-) Stiffness modulus (10³ kPa) 1.0 0.8 0.6 0.4 0.2 0.0 ratio = 0.59 (Schanz 1998) Void ratio = 0.66 Void 0.5 0.6 0.7 0.8 0.9 Void ratio = 0.89 Void ratio = 0.92 (Schanz 1998) 40 1.0 =100 kPa σref 30 20 10 0 Void ratio (-) 0.5 0.6 0.7 0.8 0.9 1.0 Void ratio (-) Figure 7.20: Calculated parameter ˆm and stiffness modulus for dry specimens with different void ratios The results of the stiffness moduli, that were derived from the experimental results are given in Tab. 7.3. This table summarizes stress dependent stiffness moduli, that were es- timated for a low vertical net stress (σ = 12 kPa) as well as a high vertical net stress (σ = 100 kPa) to see the development of this value. For all calculations a reference stress of σref = 100 kPa was used. For the stiffness modulus Eoed an increase with increasing suction (up to 20 kPa) is observed for σ = 12 kPa and σ = 100 kPa. With further increase in suction the stiffness modulus is decreasing again. For the parameter ˆm, values between ˆm = 0.62 to 0.81 for dense and ˆm = 0.58 to 0.76 for loose specimens were derived during loading path. For the un-/reloading path constant ˆm = 0.97 for dense specimen and ˆm = 0.93 for loose specimen was calculated. In Fig. 7.20 parameters ˆm calculated from oedometer test results are given for dry specimens and compared to results derived by Schanz (1998) for Hostun sand. According to ˆm the author found stiffness moduli of Eoed = 17.000 kPa (loose specimen) and Eoed = 35.000 kPa (dense specimen) for vertical net stress σref = 100 kPa. As can be seen in Fig. 7.20 the results of parameter ˆm and the stiffness modulus from the present study fit well to the results given in literature.
7.5. VOLUMETRIC BEHAVIOR 163 For description of one dimensional unloading and reloading test results of cohesive soils the stress dependent stiffness is calculated by using the following equation, that also was proposed by Schanz (1998). This equation is similar to Eq. 2.24: Eur = E ref ur � � ˆm σ + c · cot φ σref + c · cot φ (7.1) where: Eur is the stress dependent stiffness modulus for un-/reloading path, E ref ur is the normalized stiffness modulus, σref is the reference stress, σ the vertical net stress and ˆm a parameter. In this equation additionally the cohesion c and the influence of the friction angle φ are considered. In the present investigation it is suggested to replace in Eq. 7.1 the cohesion by the suction value ψ to take into account its influence on the stiffness behavior of unsaturated sand. The equation for determination of stress dependent stiffness modulus for initial loading Eoed becomes to: Eoed = E ref � � ˆm σ + ψ · cot φ oed σref + ψ · cot φ (7.2) where: ψ is the suction in the investigated sand. Experimental results performed under constant suction and appropriate results using Eq. 7.2 are given in Fig. 7.21 for loose as well Stiffness modulus (kPa) Stiffness modulus (kPa) 70000 60000 50000 40000 30000 20000 10000 0 Stiffness modulus (kPa) 70000 60000 50000 40000 30000 20000 10000 Applied suction: ψ=1.5 kPa Loose specimen Initial void ratio = 0.89 Assumption: ϕ=39° Model results Experimental 0 50 100 150 200 0 50 100 150 200 70000 70000 Vertical net stress (kPa) Vertical net stress (kPa) 60000 60000 ψ=20.0 kPa suction: Applied kPa ψ=50.0 suction: Applied 50000 40000 30000 20000 10000 0 Stiffness modulus (kPa) 0 50000 40000 30000 20000 10000 0 50 100 150 200 Vertical net stress (kPa) 0 Applied suction: ψ=3.0 kPa 0 50 100 150 200 Vertical net stress (kPa) Figure 7.21: Comparison of experimental results and predicted results (loose specimen)
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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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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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212 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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