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Assign_4_2011_solution - University of California Davis...

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1 University of California, Davis Department of Civil and Environmental Engineering ECI-173 Foundation Design MEMORANDUM TO: ECI-173 Students Date: February 7, 2011 FR: Jason DeJong SUBJECT: Assignment No. 4 (Due by 4 pm Friday, February 18) Question 1: A square footing will need to support a vertical dead plus live load of 1.4 MN with a factor of safety against bearing failure of 3.0. The footing base will be placed 1.0 m below the ground surface in a deep deposit of sand. The water table is near the base of the footing. The soil's total unit weight above the water table is 17.5 kN/m 3 and below the water table is 19 kN/m 3 . Prepare a spreadsheet that computes the minimum footing width (B) required to provide adequate safety against bearing failure, and plot B versus the effective friction angle ( φ′ ) of the sand (for φ′ values of 30 ° to 45 ° ). Use the shape factors by Brinch Hansen (1970) and neglect depth factors. Solution: The attached spreadsheet performs the bearing capacity calculations for the specified range of effective friction angles, and includes a plot of minimum required footing width for a factor of safety (FS) of 3.0. The water table is at the base of the footing so we use effective unit weight for the calculation of bearing capacity. The footing length L is set equal to B. We may all get slightly different solutions depending on some minor details; e.g., the choice of approximation for N γ (the two equations given in the textbook produce small differences). There are different approaches that can be used to solve for the minimum footing width. One approach is to manually iterate by changing the footing width B until the required FS is obtained. A second approach is to use "goal seek" in Excel; You specify that the FS should be set equal to 3.0 by changing the footing width, B, and then "goal seek" performs the iterations for you. A third approach is to set up the iteration using a circular reference. The minimum footing width varies from about 2.7 m if the sand has an effective friction angle of only 30 degrees (i.e., loose) to as small as 0.95 m if the sand has an effective friction angle of 45 degrees (i.e., dense). Question 2: A strip footing of width B is embedded 2.5 feet into a deep deposit of medium-dense sand having an effective friction angle of 39 degrees. The water table is at a depth of 2.5 feet, and the unit weight of the sand is about 115 pcf above the water table and 125 pcf below the water table.
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