Abstract:
Tsunami loading can cause sediment instability, which can compromise the structural integrity of coastal buildings and infrastructure. To understand the process by which a tsunami can cause sediment instability, it is necessary to understand how the pore water pressure in the soil changes during tsunami loading. Tsunami run-up causes the pore water pressure in the soil bed to increase, then during tsunami draw-down, the pore water pressure in the soil bed decreases. This rise and fall leads to a gradient of excess pore water pressure, which results in upward seepage during tsunami draw-down. If the excess pore water pressure gradient becomes large enough, significant sediment instability may occur. Although simple models have been developed to estimate the pore water pressure in hypothetical soil beds during tsunami loading, current models are generally based on the solution to the diffusion equation. As a result, they cannot incorporate the changes in pore water pressure caused by both the weight of the overlying tsunami water and the seepage of infiltrating tsunami water. In addition, current models do not incorporate other physical phenomena, such as those that can be addressed by variation of the diffusion coefficient with depth, aired water (i.e., entrained air), zones of unsaturated soil, and varying impermeable layer depths.
Based on the changes in pore water pressure due to overlying water and seepage of infiltrating water during a tsunami, a deformation model was developed and coupled with a seepage model. The proposed seepage-deformation model is able to model the broad range of drainage conditions of a soil bed, from the fully undrained condition to the fully drained condition. A new formulation for the coefficient of consolidation as a function of Skempton's B value is also suggested. The coupled seepage-deformation model is formulated and implemented in MATLAB using the finite difference method for one-dimensional loading.
The coupled seepage-deformation model is used to perform numerical experimentation after a convergence study is performed. The convergence study is performed using two representative numerical experiments to select an appropriate grid size and time step. The numerical experimentation focuses on saturated and unsaturated soil conditions, linear and nonlinear soil constitutive models, different Skempton's B values, and de-aired and aired water for a constant depth to the impermeable layer of 10 m and using one hypothetical tsunami with a total duration of approximately 32 minutes and a maximum flow height of 5.5 m. The results of the numerical experimentation show that the excess pore water pressure head gradient induced by tsunami loading in the soil bed when de-aired water is the pore fluid is negligible and is much less compared with the tsunami-induced excess pore water pressure head gradient developed in the soil bed when aired water is the pore fluid. The results also show that the excess pore water pressure head gradient induced in a soil bed governed by a more realistic nonlinear soil constitutive model is larger when compared to corresponding excess pore water pressure head gradient estimates in soil beds governed by a linear model. The results also show that as Skempton's B value increases from zero to one, the maximum excess pore water pressure head gradient at the ground surface reduces linearly. In addition, studying the effect of depth to impermeable layer, the tsunami height, and the entire tsunami duration (i.e., run-up and draw-down) shows that the maximum excess pore water pressure head gradient at ground surface increases linearly with an increase of tsunami height, and reduces non-linearly with an increase of tsunami duration. The results show that excess pore water pressure head gradient generally increases with an increase of the impermeable layer depth, but only up to a certain depth. The effect of depth to impermeable layer is the same when multiple tsunami heights are investigated; however, the effect deviates when tsunamis with different durations are used. Results also show that the increase of hydraulic conductivity reduces the excess pore water pressure head gradient, as expected, and the maximum excess pore water pressure head gradient at the ground surface generally reduces with an increase of the soil bulk’s modulus for large bulk modulus. Furthermore, the results show that an increase of gas content also increases the excess pore water pressure head gradient.
At the end of the dissertation, the potential for tsunami-induced soil liquefaction based on two definitions of soil liquefaction is investigated using the coupled seepage-deformation model. More specifically, the effective stress definition of soil liquefaction, which is often used to describe earthquake-induced soil liquefaction, and the excess pore-water pressure gradient definition of soil liquefaction, which is more general and can explain tsunami-induced liquefaction, are investigated. Finally, the coupled seepage-deformation model is extended to two-dimensions. The results of the two-dimensional numerical experiments show that their one-dimensional counterparts likely underestimate the excess pore water pressure head gradient induced by tsunami loading. However, future work is needed to improve the two-dimensional implementation.