1. A mat foundation is used to support a building with dimensions 75 ft by 45 ft and a total load of 5400 tons. The mat is at a depth of 7.5 ft below ground surface. The soil beneath the mat has a density of 115 lbf/ft^3 and an average SPT N-value of 18.
a) Find the allowable bearing capacity.
b) Find the factor of safety against bearing capacity.
2. A 2.5 m by 2.5 m square spread footing is designed to support an axial column load of 650 kN and a moment of 155 kN*m. The footing is place 1m into a sandy soil with a density of 2050 kg/m^3 and an angle of internal friction of 30°.
a) Find the eccentricity of the resultant load.
b) Find the equivalent width that should be used for the footing design.
c) Use the Meyerhoff theory, what is the value of the bearing capacity factor Ny to be used in calculating bearing capacity?
d) Use the Meyerhoff theory, what is the value of the bearing capacity factor Nq to be used in calculating bearing capacity?
e) Use the Meyerhoff theory, what is the value of the shape factor for Ny to be used in calculating bearing capacity?
f) What is the value of the net bearing capacity?
g) What is the value of the allowable bearing capacity?
h) What is the total allowable load?
i) What is the maximum soil pressure on the bottom of the footing?
j) What is the factor of safety against bearing capacity?
3. A 12 ft x 12 ft footing exerts a pressure of 4000 lbf/ft^2 on the soil below it. What is the increase in vertical soil stress 8 ft below and 6 feet from center of the footing?
4. A 2:1 (horizontal :vertical) sloped cut is made in homogeneous saturated clay. The clay's specific weight is 110 lbf/ft^3 and ultimate shear strength is 1050 lbf/ft^2. The cut is 45 ft deep. The clay extends 12 ft below the toe of the cut to the rock layer. What is the cohesive factor of safety of this cut?
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