Numerical investigation of k<sub>σ</sub> at high confining pressures under field drainage conditions

Ali, Heba
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Dobry, Ricardo
Zeghal, Mourad
Bennett, Victoria
Ziotopoulou, Katerina
Abdoun, Tarek
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Civil engineering
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This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute (RPI), Troy, NY. Copyright of original work retained by author.
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The State of Practice (SoP) for assessing liquefaction triggering of cohesionless soils at high confining pressures extrapolates the SoP liquefaction triggering charts using the overburden correction factor (K<sub>σ</sub>). The SoP liquefaction triggering charts are calibrated using earthquake case histories at relatively shallow elevations with vertical effective stresses less than 2 atm, while the SoP overburden correction factor relationships are either based on undrained cyclic laboratory tests or low-confining pressure liquefaction field case histories (< 2atm). The reliance of the SoP liquefaction evaluation at high confining pressures on undrained laboratory tests or field case histories with low confining pressures lacks actual representation of the effect of high confining pressure in the field. Additionally, the preliminary findingsfrom the centrifuge experiments conducted by Dr. Min Ni, in her Ph.D. dissertation, on Ottawa F-65 sand at low and high confining pressures under some plausible field drainage conditions yielded K<sub>σ</sub> values greater than 1.0, much greater than those from the SoP relationships. With these experiments being representative of some possible field conditions at high confining pressures, further research is needed to explore the behavior of K<sub>σ</sub> at high confining pressure under different scenarios, which can be practically achieved using numerical simulations and parametric studies. The work presented herein calibrates the numerical program FLAC and the constitutive model PM4Sand to the 45-1 and 45-6 single-drainage centrifuge experiments by Dr. Min Ni at the system level, and extends these experimental results via a parametric study to study the effect of varying the sand layer permeability and thickness on the pore water pressureresponse and K<sub>σ</sub>. The results from the numerical calibration are found to be generally in very good agreement with the centrifuge experiments at both confining pressures, with an excellent agreement in the excess pore water pressure ratio and the shear stress time histories. In addition, the K<sub>σ</sub> from the numerical model is found to be 1.29, which is greater than 1 and very similar to the 1.28 value from the centrifuge experiments. The calibrated models are then prepared for a three-part parametric study. Part I studied the effect of varying the Ottawa sand permeability on the soil response when exposed to the same earthquake. This revealed the need of not restricting the location where K<sub>σ</sub> is calculated to the bottom of the soil, since the elevation where the maximum excess pore water pressure ratio reaches 0.8 changes as the permeability changes. This led to re-evaluation of the calibrated runs to determine the exact r<sub>umax</sub> = 0.8 location, with corresponding recomputation of K<sub>σ</sub>, which increased from about 1.3 to 1.51. Part II of the parametric study evaluated the effect of varying the permeability of the Ottawa sand layer on K<sub>σ</sub> with scaling up or down of the input motion in each case to reach a target maximum excess pore water pressure ratio of 0.8 in the whole sand layer. The study showed an undrained K<sub>σ</sub> greater than 1.0 (= 1.27), in contradiction with the cyclic undrained triaxial results on Ottawa sand from Dr. Min Ni’s dissertation and the cyclic undrained results on sands from the literature. However, the study provided an increasing K<sub>σ</sub> versus permeability trend that further supports the results from the centrifuge tests by Dr. Min Ni. K<sub>σ</sub> is found to increase with permeability until an approximate permeability of 0.001 cm/sec, where K<sub>σ</sub> levels off at around 1.50. Additionally, the location where the maximum excess pore water pressure ratio occurs is found to move downwards in the soil profiles as the permeability increases, for both confining pressures of 1 and 6 atm. Part III of the parametric study focused on the effect of varying the thickness of the Ottawa sand layer on K<sub>σ</sub>. It revealed that K<sub>σ</sub> decreases as the soil thickness increases, down to an approximate thickness of 5 m, and then levels off at an approximate value of K<sub>σ</sub> = 1.50, which is the same value at which K<sub>σ</sub> leveled off for a thickness of 5 m when increasing the permeability from zero to 0.012 cm/sec. Moreover, the location where the maximum excess pore water pressure ratio occurs is found to move upward in the soil profile as the soil thickness increases, regardless of confining pressure, which is the opposite to the behavior noticed when the soil permeability increases.
School of Engineering
Dept. of Civil and Environmental Engineering
Rensselaer Polytechnic Institute, Troy, NY
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