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22. The following figure represents a cross-section through a concrete coffer dam. The dam is underlain by a semi-permeable soil layer which in turn is underlain by bedrock. The upstream side of the dam has 18 m of water depth and on the downstream side, the water table is coincident with the ground surface. The objective of this exercise is to solve for the head and flow beneath the coffer dam via the finite difference method in an Excel spreadsheet.
The finite difference grid we will use to solve this problem has cells measuring 7m X 7m. We will model both sides of the dam. The grid is a mesh-centered grid with the following layout:
The following spreadsheet is set up to solve this problem. Each of the cells in the spreadsheet represents one of the cell corners (blue dots) in the figure.
Click here to download a copy of the spreadsheet. Then complete the following steps:
Click here to download a copy of the solution.
a. (2 pts) Enter values for the appropriate cells representing the specified head boundary conditions. Use the bottom of the grid as the datum (h=0).
b. (10 pts) Enter the formulas for the remaining variable head cells. The spreadsheet is already set for manual calculations. You will need to press the F9 key repeatedly to solve the equations.
c. (1.5 pts) The cells on the bottom right are designed for computing the flowrate out of the upper right portion of the grid. Enter a set of equations in row 22 to compute dh (the change in head from the second row to the top row).
d. (1.5 pts) Enter a set of equations in row 23 to compute the hydraulic gradient (dh/dy).
e. (1.5 pts) Enter a set of equations in row 24 to compute the flow areas per unit thickness (Ai) for each cell. Reference the cell width-height value in cell N23.
f. (1.5 pts) Enter a set of equations in row 25 to compute the individual flowrates (Qi) using Darcy's law.
g. (1.5 pts) Compute the total flowrate (Qtotal) in cell S27.
(be sure to press F9 again after entering the equations for the flow)
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