Table Of Contents

1.0 Objectives.1

2.0 Computations.1

2.1. Pore Pressure.1

2.1.1. Single Top Drainage

2.1.2. Single Bottom Drainage

2.1.3. Double Drainage

2.2. average degree of consolidation.2

2.3. STABILITY FACTOR, R..2

Table of Figures

FigureTitlePage

Graph 1Showing R = 0.51 for Single Top Drainage2

Graph 2Showing R = 0.51 for Single Bottom Drainage3

Graph 3Showing R = 0.51 for Double Drainage3

812003734Aaron RampersadCVNG 3006 CW#1

1.0 ObjectivesTo develop a computer solution in Excel and MATLAB to implement the numerical finite difference solution for a 1-D Consolidation equation.

2.0 Computations

2.1. Pore PressureThe numerical programs are entitled Finite_Difference_1DConsol.m which is the MATLAB program and Aaron_Finite_Difference_1DConsol.xls which is the Excel program. Both of which are initially computed for a stability value, R = 0.5.

2.1.1. Single Top DrainageUsing the following governing equations: For z=0, pore pressure = 0 kN/m2 For z=16m, pore pressure is obtainable by applying the boundary conditions:

For all other Nodes:

2.1.2. Single Bottom DrainageUsing the following governing equations: For z=0, pore pressure is obtained by applying the boundary conditions:

For z=16m, pore pressure = 0 kN/m2 For all other Nodes:

2.1.3. Double Drainage For z=0 and z=6, pore pressure, For all other Nodes:

2.2. average degree of consolidation Since z=0.2, then the area of each segment can be obtained by the trapezoidal rule:

To find D.O.C. at that particular time step we can use the following equation:

Where U0= fully consolidated area of soil i.e. (16m x 100kN/m2)

2.3. Stability Factor, RIn the both aforementioned programs, R, the stability factor can be changed to yield different stabilities of the finite difference computations. For values of R = 0.25, 0.35, 0.45 and 0.5, the stability remained relatively stable with no abnormal values. However when changed to 0.51, abnormalities were observed throughout the entire finite difference computation which can be seen below in the graphs (which can also be obtained from the program). This shows that there is a limiting factor of stability.Graph 1.0 Showing R = 0.51 for Single Top Drainage

Graph 2.0 Showing R = 0.51 for Single Bottom Drainage

Graph 3.0 Showing R = 0.51 for Double Drainage

3 | Page