||Theory of Poroelasticity for Consolidation in Saturated Soils
with Gravity Effect under Cyclic Loading
||Department of Hydraulics & Ocean Engineering
saturated porous media
gravitational body forces
Only few studies have used the popular theory of linear poroelasticity to conduct quantitative research on the effect of gravity on consolidation. In this thesis, the theory of poroelasticity is generalized to account for gravitational body forces. Two coupled partial differential equations are derived that together govern the three-dimensional consolidation of saturated porous media. The governing equations are adapted to the one-dimensional compression of a homogeneous saturated clay layer. For this example, an instantaneous undrained response is taken as the initial condition. Additionally, boundary conditions are defined in a way that allows us to incorporate cyclic loading and the following three drainage scenarios: top drained, bottom drained, and top and bottom drained. Subsequently, the consolidation problem was solved numerically using a finite difference scheme. The obtained results show that the effect of body forces on pore water pressure increases with depth to a maximum after one day of 0:9 % and 1:3 % under cyclic and constant loading conditions, respectively. It is also shown that pore pressures become highly variable over depth after 1 hour after the start of cyclic loading. Lastly, we demonstrate that total settlement over time is significantly lower when a cyclic load is imposed instead of a constant load and that the manner of loading and the type of drainage condition have no effect on the relative difference in total settlement resulting from the gravity effect.
Table of Contents
Table of Contents iii
List of Tables iv
List of Figures v
Chapter 1.Introduction 1
Chapter 2.Porelasticity theory 3
Chapter 3.Methods 7
3.1.Governing equations ...........7
3.2.Initial and boundary conditions ........8
3.3.Discretization and numerical solutions ........11
3.4.Numerical analyses ..........14
Chapter 4.Results and discussion 17
4.1.Numerical model validation ..........17
4.2.Pore water pressure comparisons .........19
4.2.1.Pore water pressure ranges ........19
4.2.2.Absolute pore water pressure differences .....21
4.2.3.Relative pore water pressure differences .....28
4.3.Settlement comparisons ..........32
4.3.1.Absolute settlement ..........32
4.3.2.Relative settlement ..........32
4.4.Future recommendations .........35
Chapter 5.Conclusion 36
Appendix A.Exact solution 39
A.1.Exact solutions ............39
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