Small and large strain monitoring of unsaturated soil behavior by means of multiaxial testing and shear wave propagation

m unsaturated clayey silt specimens show a small variation of the S-wave travel time with applied vertical stress. This behavior may indicate the effect of suction on stiffness for the clayey silt specimens, where a stronger effect is expected than in sand specimens. In general the unsaturated clayey silt specimens with higher suctions show higher S- wave velocities. The effect of suction is also observed in the reduction of hysterisis on S-wave velocity during application and removal of vertical stresses as the matric suctions are increased. This 131 phenomenon is caused by decreased susceptibility of the material to changes in stiffness with variation of applied effective stress. The use of the power law model to approximate the relationship between S-wave velocity and effective stresses on the plane of shear wave polarization seems appropriate in this study. Results from the modified true triaxial device, however suggest that the effective stresses parallel and perpendicular to the wave propagation should use a different exponent. 7.2. Multiaxial Testing Results With respect to the evaluation of small strain behavior of these particulate materials, the bender elements used to monitor the small strain stiffness during the stress paths applied, efficiently sense variations of stress on the direction of shear wave polarization on the test conducted on the modified true triaxial device. This is repeatedly observed in hydrostatic compression stages: the velocity of S-waves increases with increasing confinement for both vertically and horizontally polarized S-waves. In most cases, the S-wave velocity increases with the applied stress on the direction of S-wave polarization during shearing stages. The effect of suction on the small strain stiffness of the particulate media is seen only on the silty soil. The S-wave velocity of sand specimens in this study is not influenced by the induced matric suction. This may be explained because the relatively big and uniform pore sizes of the sand (compared to the silty soil) are not capable to sustain the matric suction values induced. Because of its uniformity, the majority of the pores drain at a given level of matric suction leaving the soil without the beneficial effect of the menisci water on suction, and thus in stiffness. Large strain analysis of the test results unsurprisingly shows that the shear strength of the particulate materials increases with confinement. The effect of suction on shear strength invariably shows that at low confinements the specimens with higher induced matric suctions present the higher values on shear strength. An intriguing result is observed on the silt specimen with no induced suction at high confinement. At high confinement this specimen with the lowest suction presents the biggest shear strength although at low confinement it has the lowest strength. 132 7.3 Recommendations for Future Work Whenever possible, the use of parallel bender elements should be preferred over the series type to reduce the distortion produced by cross-taking and near field effects on the received traces. Their higher cost is compensated with the save in time that it takes to prepare the series bender elements to diminish such effects. Another alternative for avoiding the problems caused by the exposure of bender elements to humid environments might be the use of another device capable of generating shear waves such as flat shear plates. In view of the difficulties encountered on this investigation for the fragile nature of bender elements, it would be worthy to investigate the feasibility of using other options. A better assessment of the effect of suction on the stiffness of soils in the modified triaxial device might be to perform multistage testing varying the matric suction on the same specimen. That way, the changes of suction belong to the same soil-water characteristic curve, and they are not individual points from different curves as in the case of using different specimens. The issue of the non-changing travel time arrivals in the unsaturated silt specimens tested on the oedometer cell needs to be investigated. This phenomenon occurred in repeated specimens in which measurements of matric suction were also being recorded with a tensiometer porous cup. Although using a tensiometer to make direct measurements of matric suction is relatively simple, it is limited to measurement of matric suctions of up to about 90 kPa (-90 kPa of water tension) because of cavitation of water at tensions approaching -101 kpa. 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Denver, CO. pp. 84-121. 141 Appendix A Travel Time Data: Clayey Silt Figure A.1: Travel time data for vertically polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 0 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). 0 0.001 0.002 Time (s) 0 0.001 0.002 Time (s) 25 kPa 30 kPa 70 kPa 38 kPa 42 kPa 46 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σ2=σo-∆σ/2 σ3=σo-∆σ/2 σ1=σo+∆σ TC Test Soil: Silt Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 0 kPa ∆σ=0 kPa 7 kPa 18 kPa 30 kPa 39 kPa 51 kPa 57 kPa 45 kPa 30 kPa 9 kPa 0 kPa ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 75 kPa 90 kPa 105 kPa 120 kPa 135 kPa 120 kPa 45 kPa 0 kPa Net Pressure σo-ua= 25 kPa (a) (c) ∆σ=0 kPa 3 kPa 6 kPa 9 kPa 12 kPa 15 kPa 18 kPa 21 kPa 15 kPa 9 kPa 3 kPa 0 kPa σo-ua= 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] Net Pressure σo-ua= 100 kPa 0 0.0005 0.001 0.0015 0.002 0.0025 Time [s] (b) Net Pressure σo-ua= 50 kPa 142 Figure A.2: Travel time data for horizontally polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 0 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). σ2=σo-∆σ/2 σ3=σo-∆σ/2 σ1=σo+∆σ TC Test Soil: Silt Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 0 kPa Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa (a) (c) ∆σ=0 kPa 3 kPa 6 kPa 9 kPa 12 kPa 15 kPa 18 kPa 21 kPa 15 kPa 9 kPa 3 kPa 0 kPa ∆σ=0 kPa 7 kPa 18 kPa 30 kPa 39 kPa 51 kPa 57 kPa 45 kPa 30 kPa 9 kPa 0 kPa ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 75 kPa 90 kPa 105 kPa 120 kPa 135 kPa 120 kPa 45 kPa 0 kPa 25 kPa 30 kPa 70 kPa 38 kPa 42 kPa 46 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] Net Pressure σo-ua= 100 kPa 0 0.0005 0.001 0.0015 0.002 0.0025 Time [s] σo-ua= (b) 143 Figure A.3: Travel time data for vertically polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 25 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). 25 kPa 30 kPa 90 kPa 36 kPa 45 kPa 50 kPa 50 kPa 62 kPa 72 kPa 80 kPa 100 kPa σ2=σo-∆σ/2 σ3=σo-∆σ/2 σ1=σo+∆σ TC Test Soil: Silt Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 25 kPa Net Pressure σo-ua= 25 kPa (a) (c) ∆σ=0 kPa 7 kPa 15 kPa 30 kPa 38 kPa 20 kPa 7 kPa 0 kPa ∆σ=0 kPa 21 kPa 30 kPa 45 kPa 60 kPa 42 kPa 27 kPa 12 kPa 0 kPa ∆σ=0 kPa 22 kPa 45 kPa 67 kPa 82 kPa 97 kPa 52 kPa 30 kPa 0 kPa 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] Net Pressure σo-ua= 50 kPa 0 0.0005 0.001 0.0015 0.002 0.0025 Time [s] (b) σo-ua= Net Pressure σo-ua= 100 kPa 144 Figure A.4. Travel time data for horizontally polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 25 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). σ2=σo-∆σ/2 σ3=σo-∆σ/2 σ1=σo+∆σ TC Test Soil: Silt Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 25 kPa Net Pressure σo-ua= 25 kPa (a) 25 kPa 30 kPa 90 kPa 36 kPa 45 kPa 50 kPa 50 kPa 62 kPa 72 kPa 80 kPa 100 kPa ∆σ=0 kPa 7 kPa 15 kPa 30 kPa 38 kPa 20 kPa 7 kPa 0 kPa ∆σ=0 kPa 21 kPa 30 kPa 45 kPa 60 kPa 42 kPa 27 kPa 12 kPa 0 kPa ∆σ=0 kPa 22 kPa 45 kPa 67 kPa 82 kPa 97 kPa 52 kPa 30 kPa 0 kPa 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] 0 0.0005 0.001 0.0015 0.002 0.0025 Time [s] σo-ua= (b) (c) Net Pressure σo-ua= 100 kPa Net Pressure σo-ua= 50 kPa 145 Figure A.5. Travel time data for vertically polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 50 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). 4 4 25 kPa 30 kPa 80 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 64 kPa 70 kPa 94 kPa 100 kPa σ2=σo-∆σ/2 σ3=σo-∆σ/2 σ1=σo+∆σ TC Test Soil: Silt Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 50 kPa Net Pressure σo-ua= 25 kPa (a) (c) ∆σ=0 kPa 7 kPa 15 kPa 22 kPa 30 kPa 37 kPa 30 kPa 22 kPa 15 kPa 7 kPa 0 kPa ∆σ=0 kPa 9 kPa 21 kPa 39 kPa 60 kPa 39 kPa 21 kPa 9 kPa 0 kPa ∆σ=0 kPa 15 kPa 33 kPa 54 kPa 66 kPa 78 kPa 90 kPa 105 kPa 90 kPa 75 kPa 60 kPa 45 kPa 30 kPa 15 kPa σo-ua= 0 0.0005 0.001 0.0015 0.002 0.0025 Time [s] (b) 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] Net Pressure σo-ua= 100 kPa 0 0.001 0.002 0.003 Time [s] Net Pressure σo-ua= 50 kPa 146 Figure A.6. Travel time data for horizontally polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 50 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). σ2=σo-∆σ/2 σ3=σo-∆σ/2 σ1=σo+∆σ TC Test Soil: Silt Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 50 kPa Net Pressure σo-ua= 25 kPa (a) (c) 25 kPa 30 kPa 80 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 64 kPa 70 kPa 94 kPa 100 kPa ∆σ=0 kPa 7 kPa 15 kPa 22 kPa 30 kPa 37 kPa 30 kPa 22 kPa 15 kPa 7 kPa 0 kPa ∆σ=0 kPa 9 kPa 21 kPa 39 kPa 60 kPa 39 kPa 21 kPa 9 kPa 0 kPa ∆σ=0 kPa 15 kPa 33 kPa 54 kPa 66 kPa 78 kPa 90 kPa 105 kPa 90 kPa 75 kPa 60 kPa 45 kPa 30 kPa 15 kPa σo-ua= 0 0.0005 0.001 0.0015 0.002 0.0025 Time [s] (b) 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] Net Pressure σo-ua= 100 kPa Net Pressure σo-ua= 50 kPa 147 Figure A.7. Travel time data for vertically polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 0 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). σ2=σo σ3=σo σ1=σo+∆σ CTC Test Soil: Silt Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 0 kPa Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa Net Pressure σo-ua= 100 kPa (a) 0 0.0005 0.001 0.0015 0.002 0.0025 Time [s] (b) 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] (c) 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= ∆σ=0 kPa 10 kPa 15 kPa 20 kPa 25 kPa 30 kPa 35 kPa 30 kPa 25 kPa 15 kPa 0 kPa ∆σ=0 kPa 20 kPa 40 kPa 54 kPa 70 kPa 85 kPa 74 kPa 65 kPa 36 kPa 18 kPa 0 kPa ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 76 kPa 96 kPa 120 kPa 155 kPa 190 kPa 148 Figure A.8. Travel time data for horizontally polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 0 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). σ2=σo σ3=σo σ1=σo+∆σ CTC Test Soil: Silt Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 0 kPa Net Pressure σo-ua= 25 kPa (a) ∆σ=0 kPa 20 kPa 40 kPa 54 kPa 70 kPa 85 kPa 74 kPa 65 kPa 36 kPa 18 kPa 0 kPa 0 0.0005 0.001 0.0015 0.002 0.0025 Time [s] (b) 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] Net Pressure σo-ua= 50 kPa (c) Net Pressure σo-ua= 100 kPa 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= ∆σ=0 kPa 10 kPa 15 kPa 20 kPa 25 kPa 30 kPa 35 kPa 30 kPa 25 kPa 15 kPa 0 kPa ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 76 kPa 96 kPa 120 kPa 155 kPa 190 kPa 149 Figure A.9. Travel time data for vertically polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 25 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). 0 0.001 0.002 Time (s) 0 5 .10 4 0.001 0.0015 0.002 0.0025 Time (s) 0 5 .10 4 0.001 0.0015 0.002 0.0025 Time (s) 0 5 .10 4 0.001 0.0015 0.002 0.0025 Time (s) σ2=σo σ3=σo σ1=σo+∆σ CTC Test Soil: Silt Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 25 kPa Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa Net Pressure σo-ua= 100 kPa (a) (c) ∆σ=0 kPa 6 kPa 10 kPa 15 kPa 25 kPa 35 kPa 45 kPa 35 kPa 27 kPa 20 kPa 10 kPa 0 kPa ∆σ=0 kPa 6 kPa 12 kPa 20 kPa 28 kPa 35 kPa 45 kPa 55 kPa 65 kPa 60 kPa 50 kPa 40 kPa 30 kPa 16 kPa 0 kPa ∆σ=0 kPa 10 kPa 25 kPa 36 kPa 50 kPa 65 kPa 80 kPa 100 kPa 78 kPa 64 kPa 50 kPa 38 kPa 24 kPa 10 kPa 0 kPa 0 0.0005 0.001 0.0015 0.002 0.0025 Time [s] (b) 0 0.001 0.002 0.003 Time [s] .001 . 02 0.003 Time [s] .001 .002 0.003 Time [s] σo-ua= 15 kPa 18 kPa 50 kPa 22 kPa 25 kPa 25 kPa 32 kPa 36 kPa 42 kPa 50 kPa 60 kPa 70 kPa 80 kPa 100 kPa 90 kPa 150 Figure A.10. Travel time data for horizontally polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 25 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). 0 0.001 0.002 Time (s) 0 5 .10 4 0.001 0.0015 0.002 0.0025 Time (s) 0 5 .10 4 0.001 0.0015 0.002 0.0025 Time (s) σ2=σo σ3=σo σ1=σo+∆σ CTC Test Soil: Silt Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 25 kPa Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa (a) ∆σ=0 kPa 6 kPa 12 kPa 20 kPa 28 kPa 35 kPa 45 kPa 55 kPa 65 kPa 60 kPa 50 kPa 40 kPa 30 kPa 16 kPa 0 kPa ∆σ=0 kPa 10 kPa 25 kPa 36 kPa 50 kPa 65 kPa 80 kPa 100 kPa 78 kPa 64 kPa 50 kPa 38 kPa 24 kPa 10 kPa 0 kPa ∆σ=0 kPa 6 kPa 10 kPa 15 kPa 25 kPa 35 kPa 45 kPa 35 kPa 27 kPa 20 kPa 10 kPa 0 kPa 0 0.0005 0.001 0.0015 0.002 0.0025 Time [s] (b) .001 0. 02 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] 0 . 01 0. 02 0.003 Time [s] Net Pressure σo-ua= 100 kPa (c) σo-ua= 15 kPa 18 kPa 50 kPa 22 kPa 25 kPa 25 kPa 32 kPa 36 kPa 42 kPa 50 kPa 60 kPa 70 kPa 80 kPa 100 kPa 90 kPa 151 Figure A.11. Travel time data for vertically polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 50 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). 0 5 .10 4 0.001 0.0015 0.002 0.0025 Time (s) 0 5 .10 4 0.001 0.0015 0.002 0.0025 Time (s) 0 5 .10 4 0.001 0.0015 0.002 0.0025 Time (s) 0 5 .10 4 0.001 0.0015 0.002 0.0025 Time (s) σ2=σo σ3=σo σ1=σo+∆σ CTC Test Soil: Silt Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 50 kPa Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa (a) ∆σ=0 kPa 5 kPa 10 kPa 15 kPa 25 kPa 35 kPa 41 kPa 30 kPa 20 kPa 10 kPa 0 kPa ∆σ=0 kPa 10 kPa 24 kPa 30 kPa 44 kPa 50 kPa 60 kPa 48 kPa 35 kPa 20 kPa 0 kPa 0 kPa 15 kPa 46 kPa 20 kPa 25 kPa 25 kPa 30 kPa 36 kPa 42 kPa 50 kPa 60 kPa 70 kPa 82 kPa 100 kPa 90 kPa ∆σ=0 kPa 10 kPa 20 kPa 30 kPa 40 kPa 50 kPa 58 kPa 75 kPa 90 kPa 100 kPa 90 kPa 78 kPa 55 kPa 25 kPa 0 kPa 0 0.0005 0.001 0.0015 0.002 0.0025 Time [s] (b) .001 0. 02 0.003 Time [s] (c) 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] Net Pressure σo-ua= 100 kPa σo-ua= 152 Figure A.12. Travel time data for horizontally polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 50 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). 0 5 .10 4 0.001 0.0015 0.002 0.0025 Time (s) 0 5 .10 4 0.001 0.0015 0.002 0.0025 Time (s) 0 5 .10 4 0.001 0.0015 0.002 0.0025 Time (s) 0 5.10 4 0.001 0.0015 0.002 0.0025 Time (s) σ2=σo σ3=σo σ1=σo+∆σ CTC Test Soil: Silt Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 50 kPa Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa (a) 0 kPa 15 kPa 46 kPa 20 kPa 25 kPa 25 kPa 30 kPa 36 kPa 42 kPa 50 kPa 60 kPa 70 kPa 82 kPa 100 kPa 90 kPa ∆σ=0 kPa 5 kPa 10 kPa 15 kPa 25 kPa 35 kPa 41 kPa 30 kPa 20 kPa 10 kPa 0 kPa ∆σ=0 kPa 10 kPa 24 kPa 30 kPa 44 kPa 50 kPa 60 kPa 48 kPa 35 kPa 20 kPa 0 kPa ∆σ=0 kPa 10 kPa 20 kPa 30 kPa 40 kPa 50 kPa 58 kPa 75 kPa 90 kPa 100 kPa 90 kPa 78 kPa 55 kPa 25 kPa 0 kPa 0 0.0005 0.001 0.0015 0.002 0.0025 Time [s] 0.001 . 02 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] 0 0.001 0.002 0.003 Time [s] Net Pressure σo-ua= 100 kPa (c)(b) σo-ua= 153 Appendix B Travel Time Data: Silica Sand Figure B.1: Travel time data for vertically polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 0 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa Net Pressure σo-ua= 100 kPa ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 75 kPa 60 kPa 45 kPa 30 kPa 15 kPa 0 kPa 0 0.0005 0.001 0.0015 Time [s] (b) 0 0.0005 0.001 0.0015 Time [s] (c) 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] σ1=σo+∆σ TC Test Soil: Sand Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 0 kPa (a) σ2=σo-∆σ/2 σ3=σo-∆σ/2 ∆σ=0 kPa 7 kPa 15 kPa 22 kPa 30 kPa 22 kPa 15 kPa 7 kPa 0 kPa ∆σ=0 kPa 30 kPa 60 kPa 90 kPa 120 kPa 90 kPa 60 kPa 30 kPa 0 kPa 154 Figure B.2: Travel time data for horizontally polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 0 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). Net Pressure σo-ua= 25 kPa (b) Net Pressure σo-ua= 50 kPa (c) Net Pressure σo-ua= 100 kPa 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] σ1=σo+∆σ TC Test Soil: Sand Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 0 kPa (a) σ2=σo-∆σ/2 σ3=σo-∆σ/2 ∆σ=0 kPa 7 kPa 15 kPa 22 kPa 30 kPa 22 kPa 15 kPa 7 kPa 0 kPa ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 75 kPa 60 kPa 45 kPa 30 kPa 15 kPa 0 kPa ∆σ=0 kPa 30 kPa 60 kPa 90 kPa 120 kPa 90 kPa 60 kPa 30 kPa 0 kPa 155 Figure B.3: Travel time data for vertically polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 25 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa Net Pressure σo-ua= 100 kPa (c)(b) 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] σ1=σo+∆σ TC Test Soil: Sand Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 25 kPa (a) σ2=σo-∆σ/2 σ3=σo-∆σ/2 ∆σ=0 kPa 30 kPa 60 kPa 90 kPa 120 kPa 90 kPa 60 kPa 30 kPa 0 kPa ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 75 kPa 60 kPa 45 kPa 30 kPa 15 kPa 0 kPa ∆σ=0 kPa 7 kPa 15 kPa 22 kPa 30 kPa 22 kPa 15 kPa 7 kPa 0 kPa 156 Figure B.4: Travel time data for horizontally polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 25 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). σ1=σo+∆σ TC Test Soil: Sand Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 25 kPa Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa (a) (b) Net Pressure σo-ua= 100 kPa (c) 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] σ2=σo-∆σ/2 σ3=σo-∆σ/2 ∆σ=0 kPa 30 kPa 60 kPa 90 kPa 120 kPa 90 kPa 60 kPa 30 kPa 0 kPa ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 75 kPa 60 kPa 45 kPa 30 kPa 15 kPa 0 kPa ∆σ=0 kPa 7 kPa 15 kPa 22 kPa 30 kPa 22 kPa 15 kPa 7 kPa 0 kPa 157 Figure B.5: Travel time data for vertically polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 50 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa (b) (c) Net Pressure σo-ua= 100 kPa 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] σ1=σo+∆σ TC Test Soil: Sand Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 50 kPa (a) σ2=σo-∆σ/2 σ3=σo-∆σ/2 ∆σ=0 kPa 30 kPa 60 kPa 90 kPa 120 kPa 90 kPa 60 kPa 30 kPa 0 kPa ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 75 kPa 60 kPa 45 kPa 30 kPa 15 kPa 0 kPa ∆σ=0 kPa 7 kPa 15 kPa 22 kPa 30 kPa 22 kPa 15 kPa 7 kPa 0 kPa 158 Figure B.6: Travel time data for horizontally polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 50 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa Net Pressure σo-ua= 100 kPa (c)(b) 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] σ1=σo+∆σ TC Test Soil: Sand Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 50 kPa (a) σ2=σo-∆σ/2 σ3=σo-∆σ/2 ∆σ=0 kPa 30 kPa 60 kPa 90 kPa 120 kPa 90 kPa 60 kPa 30 kPa 0 kPa ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 75 kPa 60 kPa 45 kPa 30 kPa 15 kPa 0 kPa ∆σ=0 kPa 7 kPa 15 kPa 22 kPa 30 kPa 22 kPa 15 kPa 7 kPa 0 kPa 159 Figure B.7: Travel time data for vertically polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 0 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). σ2=σo σ3=σo σ1=σo+∆σ CTC Test Soil: Sand Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 0 kPa Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa Net Pressure σo-ua= 100 kPa (a) ∆σ=0 kPa 20 kPa 40 kPa 60 kPa 80 kPa 100 kPa 80 kPa 60 kPa 40 kPa 20 kPa 0 kPa 0 0.0005 0.001 0.0015 Time [s] (b) 0 0.0005 0.001 0.0015 Time [s] (c) 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 kPa ∆σ=0 kPa 30 kPa 60 kPa 90 kPa 120 kPa 150 kPa 120 kPa 90 kPa 60 kPa 30 kPa ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 45 kPa 30 kPa 15 kPa 0 kPa 160 Figure B.8: Travel time data for horizontally polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 0 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). σ2=σo σ3=σo σ1=σo+∆σ CTC Test Soil: Sand Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 0 kPa Net Pressure σo-ua= 25 kPa (a) (b) Net Pressure σo-ua= 50 kPa (c) Net Pressure σo-ua= 100 kPa 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= ∆σ=0 kPa 20 kPa 40 kPa 60 kPa 80 kPa 100 kPa 80 kPa 60 kPa 40 kPa 20 kPa 0 kPa 0 kPa ∆σ=0 kPa 30 kPa 60 kPa 90 kPa 120 kPa 150 kPa 120 kPa 90 kPa 60 kPa 30 kPa 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 45 kPa 30 kPa 15 kPa 0 kPa 161 Figure B.9: Travel time data for vertically polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 25 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). σ2=σo σ3=σo σ1=σo+∆σ CTC Test Soil: Sand Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 25 kPa Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa Net Pressure σo-ua= 100 kPa (a) (c) ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 45 kPa 30 kPa 15 kPa 0 kPa (b) 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= ∆σ=0 kPa 20 kPa 40 kPa 60 kPa 80 kPa 100 kPa 80 kPa 60 kPa 40 kPa 20 kPa 0 kPa 0 kPa ∆σ=0 kPa 30 kPa 60 kPa 90 kPa 120 kPa 150 kPa 120 kPa 90 kPa 60 kPa 30 kPa 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 162 Figure B.10: Travel time data for horizontally polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 25 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). σ2=σo σ3=σo σ1=σo+∆σ CTC Test Soil: Sand Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 25 kPa Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa (a) (b) Net Pressure σo-ua= 100 kPa (c) 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= ∆σ=0 kPa 15 kPa 30 kPa 45 kPa 60 kPa 45 kPa 30 kPa 15 kPa 0 kPa ∆σ=0 kPa 20 kPa 40 kPa 60 kPa 80 kPa 100 kPa 80 kPa 60 kPa 40 kPa 20 kPa 0 kPa 0 kPa ∆σ=0 kPa 30 kPa 60 kPa 90 kPa 120 kPa 150 kPa 120 kPa 90 kPa 60 kPa 30 kPa 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 163 Figure B.11: Travel time data for vertically polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 50 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). σ2=σo σ3=σo σ1=σo+∆σ CTC Test Soil: Sand Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 50 kPa Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa (a) (b) (c) Net Pressure σo-ua= 100 kPa 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= ∆σ=0 kPa 20 kPa 30 kPa 40 kPa 50 kPa 60 kPa 50 kPa 40 kPa 30 kPa 20 kPa 0 kPa ∆σ=0 kPa 20 kPa 40 kPa 60 kPa 80 kPa 100 kPa 80 kPa 60 kPa 40 kPa 20 kPa 0 kPa ∆σ=0 kPa 25 kPa 50 kPa 75 kPa 100 kPa 125 kPa 150 kPa 125 kPa 100 kPa 75 kPa 50 kPa 25 kPa 0 kPa 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 164 Figure B.12: Travel time data for horizontally polarized bender elements: (a) description of stress paths during testing (suction ua-uw = 50 kPa), (b) travel time data during isotropic consolidation, and (c) travel time data during shearing (loading and unloading). σ2=σo σ3=σo σ1=σo+∆σ CTC Test Soil: Sand Net Pressure: σo-ua= 25, 50, and 100 kPa Suction: ua-uw= 50 kPa Net Pressure σo-ua= 25 kPa Net Pressure σo-ua= 50 kPa (a) Net Pressure σo-ua= 100 kPa (c)(b) 25 kPa 30 kPa 70 kPa 35 kPa 40 kPa 45 kPa 50 kPa 50 kPa 60 kPa 80 kPa 90 kPa 100 kPa σo-ua= ∆σ=0 kPa 20 kPa 30 kPa 40 kPa 50 kPa 60 kPa 50 kPa 40 kPa 30 kPa 20 kPa 0 kPa ∆σ=0 kPa 20 kPa 40 kPa 60 kPa 80 kPa 100 kPa 80 kPa 60 kPa 40 kPa 20 kPa 0 kPa ∆σ=0 kPa 25 kPa 50 kPa 75 kPa 100 kPa 125 kPa 150 kPa 125 kPa 100 kPa 75 kPa 50 kPa 25 kPa 0 kPa 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 0 0.0005 0.001 0.0015 Time [s] 165 Vita 166 Oscar Fernando Porras Ortiz was born in Durango, Durango, Mexico, on May 25, 1963. He received his Bachelor of Science in Civil Engineering from Instituto Tecnológico de Durango, Mexico. After working on the construction industry and for Secretaría de Educación Pública for several years, he went to the United States to continue his education. He obtained a Master of Science in Civil Engineering degree in the area of asphalt technology from Louisiana State University in December 2000. Subsequently, he stayed at the same institution pursuing a doctoral degree where he expects to receive the degree of Doctor of Philosophy in civil engineering in December 2004.