Download miễn phí Luận văn A volume-Mass constitutive model for unsaturated soils
TABLE OF CONTENT
COPYRIGHT.i
ABSTRACT.ii
ACKNOWLEDGEMENT.iv
TABLE OF CONTENT.v
LIST OF TABLES.xi
LIST OF FIGURES.xii
LIST OF NOTATIONS AND SYMBOLS.xxvii
CHAPTER 1: INTRODUCTION
1.1 BACKGROUND.1
1.2 OBJECTIVES AND SCOPE.7
1.3 SUMMARY OFCHAPTERS.8
CHAPTER 2: LITERATURE REVIEW
2.1 GENERAL.10
2.2 VOLUME-MASS STATE VARIABLES.11
2.2.1 StressState Variables.12
2.2.2 State Variables.16
2.3 BASIC VOLUME-MASS CONSTITUTIVE RELATIONS.17
2.3.1 Volume-Mass Constitutive Relations on the Zero Soil Suction Plane.18
2.3.2 Volume-MassConstitutive Relationshipson Non-Zero Soil Suction Planes.24
2.3.3 Volume-Mass constitutive Relations on Zero Net Mean StressPlane.32
2.3.4 Volume-Mass constitutive Relations on the Non-Zero Net Mean Stress Planes.46
2.3.5 Water Content andSoil Volume Relationship.50
2.4 VOLUME-MASS CONSTITUTIVE SURFACES FOR UNSATURATEDSOILS.53
2.4.1 General.53
2.4.2 Prediction or Estimation of the Volume-Mass Constitutive Surfaces.55
2.4.3 Uniqueness of the Volume-Mass Constitutive Surfaces.59
2.5 VOLUME-MASS CONSTITUTIVE MODELS FOR UNSATURATED SOILS.61
2.5.1 General.61
2.5.2 Physically-Based Elastic Constitutive Models.61
2.5.3 Surface Fitting ConstitutiveModels.65
2.5.4 Elasto-PlasticModels.70
2.6 MODELING THE EFFECT OF SHEAR STRESS TO THE VOLUME-MASS
CONSTITUTIVE RELATIONS.79
2.7 MEASUREMENT OF THE VOLUME-MASS CONSTITUTIVE SURFACES.81
2.7.1 Testing Equipment.81
2.7.2 Materialsand Preparation.87
2.7.3 Common Testing Programsin the Literature.87
2.8 APPLICATIONS OF THE VOLUME-MASS CONSTITUTIVE RELATIONSHIPS IN THE
PREDICTION OF SOIL PROPERTIES.91
2.8.1 Prediction of Shear Strength Function.91
2.8.2 Prediction of HydraulicConductivity Function.92
2.9 CHAPTER SUMMARY.95
CHAPTER 3: THEORY
3.1 GENERAL.97
3.2 TERMINOLOGY FOR THE PROPOSED MODEL.98
3.2.1 State Variables:.99
3.2.2 Pore-Size Distribution Curve.101
3.2.3 Development of the Proposed Volume-Mass Constitutive Model.104
3.3 ASSUMPTIONS, SYMBOLS AND NOTATIONS.107
3.3.1 Assumptions.107
3.3.2 Notationsand Symbols.115
3.4 STRESS-STRAIN RELATIONSHIPFOR THE SOIL STRUCTURE SURROUNDING A
PORE.117
3.4.1 Drying-Wetting Processes under Zero Net Mean Stress.117
3.4.2 Drying Process undera Constant Net Mean Stress.119
3.4.3 Wetting Process under a Constant Net Mean Stress.128
3.4.4 Loading-Unloading Processes at a Constant Soil Suction.136
3.4.5 Summary Stress-Strain Relationshipfor the Soil Structure Surrounding a Pore.136
3.5 YIELD STRESS INDUCED FROM SEVERAL SINGLE STRESS PATHS.137
3.5.1 Drying and Wetting Processes under Zero Net Mean Stress.137
3.5.2 Loading-Unloading Processes at Zero Soil Suction.138
3.5.3 Drying and Wetting Processes at a Constant Net Mean Stress.140
3.5.4 Loading-Unloading Processes at a Constant Soil Suction.142
3.5.5 Compression Curve of a Soil at a ConstantSoil Suction.144
3.6 MODELSFORTHESOIL-WATER CHARACTERISTIC CURVE OF VOLUME CHANGE
SOILS.146
3.6.1 An Equation with Independent Properties.147
3.6.2 A Simple Equation.150
3.7 DETERMINATION OF THE COMPRESSION INDICES OF A WATER-FILLED PORE.151
3.7.1 An Equation for Volume Change along the Initial Drying Process.151
3.7.2 Volume Change of Collapsible and Non-Collapsible Pores.157
3.7.3 Summary of the Compression Indices of a Water-Filled Pore.160
3.8 A MODEL FOR HYSTERETIC SOIL-WATERCHARACTERISTIC CURVES.162
3.8.1 A Model for the Three Key Hysteretic Soil-Water Characteristics Curves.162
3.8.2 Scanning HystereticSoil-Water Characteristics Curves.167
3.8.3 Hysteresis Model in the Context of the Pore-Size Distribution.169
3.9 ANALYTICAL SOLUTION FOR THE VOLUME-MASS CONSTITUTIVE RELATIONSHIPS .171
3.9.1 Yield Stresses.174
3.9.2 Prediction of the Water ContentSurface.176
3.9.3 Prediction of the Void Ratio Surface.179
3.10 NUMERICAL SOLUTION FOR VOLUME-MASSCONSTITUTIVE RELATIONSHIPS.186
3.11 CONVERSION FOR ONE-DIMENSIONAL (K0) LOADING CONDITION.191
3.12 DETERMINATION OF THE MODEL PARAMETERS.193
3.13 CHAPTER SUMMARY.195
CHAPTER 4: VISUALIZATION
4.1 GENERAL.197
4.2 MATERIALS.198
4.3 APPLICATION OF THE VOLUME-MASS CONSTITUTIVE EQUATIONS.199
4.4 VISUALIZATION OF THE VOLUME-MASS CONSTITUTIVE SURFACES.207
4.4.1 StressPaths.207
4.4.2 Volume-Mass Constitutive Surfaces for the Three ArtificialSoils.209
4.4.3 Discussions.219
4.5 VISUALIZATION OF THE UNSATURATED SOIL PROPERTYSURFACES.220
4.5.1 Shear Strength Surfaces.222
4.5.2 Hydraulic Conductivity Surfaces.224
CHAPTER 5: LABORATORY TESTING PROGRAM
5.1 GENERAL.227
5.2 OBJECTIVES OF THE TESTING PROGRAM.227
5.3 MATERIALS AND PREPARATIONS:.228
5.3.1 Materials.228
5.3.2 Specimen Preparations.230
5.4 EQUIPMENT:.231
5.4.1 U. of S.Pressure Plate Cell.232
5.4.2 GCTS Pressure Plate Apparatuses.234
5.5 CALIBRATION OF THE EQUIPMENT.238
5.5.1 Calibration of the Oedometer Systems.238
5.5.2 Calibrations of the U.of S. PressurePlate Cell.239
5.5.3 Calibrations of GCTS Pressure Plate Apparatus.240
5.6 DETAILSOF THE TESTING PROGRAM:.241
5.6.1 Testing Phase #1:.244
5.6.2 Testing Phase #2:.245
5.6.3 Testing Phase #3:.250
5.6.4 Testing Phase #4:.252
CHAPTER 6: PRESENTATION OF THE EXPERIMENTALRESULTS
6.5 GENERAL.256
6.6 TEST RESULTS FOR TESTING PHASE #1:.256
6.7 TEST RESULTS FOR TESTING PHASE #3:.258
6.8 TEST RESULTS FOR TESTING PHASE #3:.268
6.9 TEST RESULTS FOR TESTING PHASE #4:.271
6.9.1 Test Resultsfor Processed Silt.274
6.9.2 Test Results for Indian Head Till.280
CHAPTER 7: DISCUSSION AND INTERPRETATION OF THE TEST RESULTS
7.1 GENERAL.287
7.2 FUNCTIONALITY AND ACCURACYOFTHE GCTS PRESSURE PLATE.288
7.3 SOIL-WATER CHARACTERISTIC CURVES.290
7.3.1 Shape of the Soil-Water Characteristic Curve ofa SlurrySoil.290
7.3.2 Effects of the Pre-ConsolidationStress onthe Soil-Water Characteristic Curve of a Soil .292
7.3.3 Entrapped Air and the Actual Boundary Wetting Curve.301
7.4 VOLUMEAND WATER CONTENTALONG LOADING ANDUNLOADING PROCESSES
AT CONSTANT SOIL SUCTIONS.304
7.4.1 Compression Indices of the Soil Tested in the Laboratory Testing Program.304
7.4.2 Determination of K0Parameters.305
7.4.3 Volume and Water Content Change Along Loading-Unloading Processes .307
7.5 UNIQUENESS OF THE VOLUME-MASS CONSTITUTIVE SURFACES.324
7.5.1 Verification of the Stress PathDependence Involved witha Drying Process.324
7.5.2 Verification of the Stress PathIndependence Involving only Wetting Processes.326
7.6 CHAPTER SUMMARY.332
CHAPTER 8: VERIFICATION OF THE PROPOSED MODEL
8.2 GENERAL.334
8.3 VERIFICATION USING THE DATA COLLECTEDFROM THE RESEARCH LITERATURE..334
8.3.1 Verification Using Regina Clay (Fredlund, 1964).336
8.3.2 Verification Using Saskatchewan Silt(Huang,1994).339
8.3.3 Verification Using Jossigny Silt (Fleureau et al., 1995).341
8.3.4 Verification Using Kaolinite (Fleureau et al., 2004).343
8.4 VERIFICATION USING THE DATA MEASUREDFROM THE LABORATORY TESTING
PROGRAM.347
8.4.1 Prediction Results for Beaver Creek Sand.347
8.4.2 Prediction Results for Saskatchewan Silty Sand.349
8.4.3 Prediction Results for Processed Silt.351
8.4.4 Prediction Results for Indian Head Till.365
8.5 CHAPTER SUMMARY.379
CHAPTER 9: CONCLUSIONS AND RECOMMENDATIONS
9.1 SUMMARY.381
9.2 CONCLUSIONS.372
9.2.1 Equipment:.383
9.2.2 Laboratory Studies:.383
9.2.3 Theoretical Studies.386
9.3 RECOMMENDATION FOR FUTURE RESEARCH.389
9.3.1 Equipment.389
9.3.2 FutureResearch Studies.389
REFERENCES.391
APPENDICES A, B, C AND D
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g
P
Lo soil suction (k a)
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0.25
0.4
0.4
0.55
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0.7
0.7
0.85
0.85
1
1
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Log ne
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100000
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P
Log soil suction (k a)
0.25
0.25
0.4
0.4
0.55
0.55
0.7
0.7
0.85
0.85
1
1
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Log ne
t mean
stress
(kPa)1e+06
100000
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P
Log soil suction (k a)
0
0
0.05
0.05
0.1
0.1
0.15
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0.2
0.2
0.25
0.25
0.3
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0.35
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Log ne
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stress
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P
Log soil suction (k a)
0
0
0.05
0.05
0.1
0.1
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0.15
0.2
0.2
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c) Degree of saturation – stress paths #3 f) Degree of saturation – stress paths #4
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2000
1750
1500
1250
1000
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500
250
Figure 4-13. Volume-mass constitutive surfaces for the artificial clay at low ranges of
soil suction and net mean stress (followed by the series stress paths #1)
b) Void ratio
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Log ne
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Log soil suction (
a)
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1750
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P
Log soil suction (k a)
0.2
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a) Gravimetric water content
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Figure 4-14. Volume-mass constitutive surfaces for the artificial clay on wide ranges of
soil suction and net mean stress (followed by the series stress paths #1 and #2).
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Log ne
t mean
stress
(kPa)1e+06
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o
P
Log s il suction (k a)
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Log ne
t mean
stress
(kPa)1e+06
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Log soil suction (kPa)
0.5
0.5
1
1
1.5
1.5
2
2
2.5
2.5
3
3
3.5
3.5
10000
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Log ne
t mean
stress
(kPa)1e+06
100000
10000
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ct
P
Log soil su
ion (k a)
0
0
0.25
0.25
0.5
0.5
0.75
0.75
1
1
1.25
1.25
b) Void ratio – stress paths #1
c) Degree of saturation – stress paths #1 f) Degree of saturation – stress paths #2
a) Water content – stress paths #1
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Log ne
t mean
stress
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L g
Pa
o soil suction (k
)
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(kPa)1e+06
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L
c
P
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0.5
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2
2.5
2.5
3
3
3.5
3.5
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1e+06
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g
Log ne
t mean
stress
(kPa)
Lo soil suction (kPa)
0
0
0.25
0.25
0.5
0.5
0.75
0.75
1
1
1.25
1.25
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d) Water content – stress paths #2
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e) Void ratio – stress paths #2
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10000
1000
100
10
1
Figure 4-15. Volume-mass constitutive surfaces for the artificial clay on wide ranges of
soil suction and net mean stress (followed by the series stress paths #3 and #4).
Log ne
t mean
stress
(kPa)1e+06
100000
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1000
100
10
1
g
a)
Lo soil suction (kP
0
0
0.1
0.1
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0.5
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0.6
0.6
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Log ne
t mean
stress
(kPa)1e+06
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L
Pa
og soil suction (k
)
0.5
0.5
0.72
0.72
0.94
0.94
1.16
1.16
1.38
1.38
1.6
1.6
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100
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Log ne
t mean
stress
(kPa)1e+06
100000
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g
o
Lo s il suction (kPa)
0
0
0.1
0.1
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Log ne
t mean
stress
(kPa)1e+06
100000
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g
Lo
soil suction (kPa)
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0
0.1
0.1
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0.2
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0.3
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0.4
0.5
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0.9
0.9
1
1
b) Void ratio – stress paths #3
c) Degree of saturation – stress paths #3 f) Degree of saturation – stress paths #4
e) Void ratio – stress paths #4
a) Water content – stress paths #3
10000
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Log ne
t mean
stress
(kPa)1e+06
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L
n
og soil suctio (kPa)
0.5
0.5
0.72
0.72
0.94
0.94
1.16
1.16
1.38
1.38
1.6
1.6
d) Water content – stress paths #4
Log ne
t mean
stress
(kPa)1e+06
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o
Log s il suction (kPa)
0
0
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
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218
4.4.3 Discussions
Similar to the void ratio and water content constitutive surfaces predicted for the
artificial silt presented using the closed-form equations, the volume-mass constitutive
surfaces predicted for the three artificial soils at low soil suctions and net mean stresses
using the EPUS software program (Figures 4-7, 4-10 and 4-13) agree well with all the
postulates presented by Fredlund et al., (2000).
For the volume-mass constitutive relationships predicted following all four series
stress paths (i.e., #1, #2 , #3 and #4) for three artificial soils (Figures 4-8 to 4-15), the
compression curves of the soils at saturation and the soil-water characteristic curves of
the soils at zero net mean stress are reasonable. The volume-mass constitutive surfaces
obtained by following series stress paths #1 (i.e., Figures 4-8, 4-11 and 4-14) show that
at a higher soil suction or a higher net mean stress, both water content and void ratio are
lower. At soil suctions less than the air entry value (i.e., for drying surface) and less than
the water entry value (i.e., for wetting surface) all pores are filled with water and the soil
behaves exactly like that at saturation; Therefore, the volume-mass constitute
relationships are stress path independent (Figures 4-8 to 4-15). When all pores are filled
with water, all stress paths give the same predictions for both void ratio and water
content. The volume-mass constitutive surfaces starting from initially slurry seem to
have steeper slopes than that for starting from air-dried condition. These prediction
results appear to be reasonable.
The void ratio constitutive surfaces obtained by following stress paths #3 and #4
(Figures 4-9, 4-12 and 4-15) seem to be strange (i.e., at 106 kPa soil suction and 104 kPa
net mean stress, void ratio is higher than that at soil suction of 0.1 kPa and net mean
stress of 104). The shape of the surfaces is similar to that measured by Matyas and
Radhakrishna (1968). It shows that an unsaturated soil can either swell or collapse along
a wetting process depending on the magnitude of net mean stress. Explanations on
collapse and swell behaviors of an unsaturated soil have been presented by numerous
researchers (Clemence & Finbarr, 1981; Popescu, 1986; Lawton et al., 1991a, 1991b;
Gens and Alonso, 1992; Gens, 1995; Pereira, 1996).
219
In conclusion, the volume-mass constitutive surfaces plotted in Figures 4-8, to 4-
15 shows that the proposed volume-mass constitutive model is capable of:
1) Predicting the volume-mass constitutive surfaces exhibited stress path
dependence when examining a drying process;
2) Predicting volume-mass constitutive surfaces exhibited stress path
independence when the...
