Practice Problems: Foundation Design
Question 1
A geotechnical engineer is designing a square spread footing for an office building column. The column transmits a dead load of 250 kips and a live load of 180 kips. The site investigation reveals dense sand with an allowable bearing capacity of 6,000 psf. The footing will be placed at a depth of 4 feet below grade. Assuming a footing weight and soil surcharge of 15% of the column loads, what is the required footing dimension?
(a) 9.0 ft
(b) 9.5 ft
(c) 10.0 ft
(d) 10.5 ft
Question 2
A foundation engineer is evaluating the bearing capacity of a continuous strip footing that is 6 feet wide and will be placed at a depth of 5 feet in a sandy soil. The soil has a unit weight of 120 pcf and an angle of internal friction of 35°. Using Terzaghi's bearing capacity equation with bearing capacity factors Nc = 57.8, Nq = 41.4, and Nγ = 42.4, what is the ultimate bearing capacity?
(a) 15,200 psf
(b) 17,800 psf
(c) 18,500 psf
(d) 20,300 psf
Question 3
A structural engineer is designing a mat foundation for a 10-story building. The total column loads sum to 18,000 kips distributed over a footprint area of 120 ft × 80 ft. The soil has an allowable bearing capacity of 4,500 psf. The mat thickness is 3 feet with concrete weighing 150 pcf. What is the net bearing pressure on the soil?
(a) 1,410 psf
(b) 1,680 psf
(c) 1,930 psf
(d) 2,330 psf
Question 4
A geotechnical consultant is analyzing a drilled shaft foundation in clay soil. The shaft has a diameter of 4 feet and an embedment depth of 40 feet. The undrained shear strength of the clay is 1,800 psf, and the adhesion factor is 0.65. Neglecting end bearing, what is the allowable uplift capacity using a factor of safety of 3?
(a) 196 kips
(b) 245 kips
(c) 294 kips
(d) 588 kips
Question 5
A civil engineer is designing a rectangular spread footing (8 ft × 12 ft) for a bridge pier. The footing will be placed at 6 feet depth in layered soil. The effective unit weight of soil is 115 pcf. The footing is subjected to a vertical load of 400 kips and a moment of 240 kip-ft about the short axis. What is the maximum bearing pressure under the footing?
(a) 5,420 psf
(b) 6,170 psf
(c) 6,670 psf
(d) 7,080 psf
Question 6
A foundation designer is evaluating settlement of a square footing (10 ft × 10 ft) on clay. The footing applies a net pressure increase of 3,000 psf at a depth of 4 feet. The clay layer is 20 feet thick with a compression index of 0.32, initial void ratio of 0.85, and an effective overburden pressure at mid-depth of 1,800 psf. What is the estimated primary consolidation settlement?
(a) 3.2 inches
(b) 4.1 inches
(c) 4.8 inches
(d) 5.5 inches
Question 7
An engineer is designing a driven pile foundation for a waterfront structure. A 14-inch square concrete pile will be driven 50 feet into dense sand with an SPT N-value averaging 35 blows/ft. Using the Meyerhof method where allowable capacity = (N × pile perimeter × embedment depth)/50, what is the allowable pile capacity?
(a) 98 kips
(b) 130 kips
(c) 163 kips
(d) 196 kips
Question 8
A geotechnical engineer is evaluating a group of 16 friction piles arranged in a 4 × 4 configuration with 3-foot spacing (center-to-center). Each pile has a diameter of 12 inches and an allowable capacity of 75 kips. The group efficiency using the Converse-Labarre formula is 0.72. What is the allowable capacity of the pile group?
(a) 864 kips
(b) 950 kips
(c) 1,050 kips
(d) 1,200 kips
Question 9
A structural engineer is designing a combined footing for two columns spaced 18 feet apart. Column A carries 300 kips and Column B carries 200 kips. To locate the centroid of the footing at the resultant of loads, what distance should be measured from Column A to the centroid of the footing?
(a) 6.8 ft
(b) 7.2 ft
(c) 8.4 ft
(d) 9.0 ft
Question 10
A foundation engineer is analyzing lateral capacity of a single pile in soft clay. The pile diameter is 18 inches and it extends 30 feet into clay with an undrained shear strength of 600 psf. Using the Broms method for short rigid piles, if the ultimate lateral resistance is 9Su × D², what is the ultimate lateral load capacity at ground surface?
(a) 10.1 kips
(b) 13.5 kips
(c) 16.9 kips
(d) 20.3 kips
Question 11
A civil engineer is designing an isolated square footing for a column supporting a factored load of 520 kips. The concrete has a compressive strength of 4,000 psi and the soil bearing capacity is 8 ksf. The footing thickness is 24 inches. What minimum footing dimension is required based on bearing capacity?
(a) 8.0 ft
(b) 8.5 ft
(c) 9.0 ft
(d) 9.5 ft
Question 12
A geotechnical consultant is performing a plate load test using a 1-foot square plate. The test shows a settlement of 0.5 inches at a pressure of 4,000 psf. Using the relationship that settlement of a full-size footing is proportional to its width, what settlement would be expected for an 8-foot square footing at the same bearing pressure?
(a) 2.0 inches
(b) 3.0 inches
(c) 4.0 inches
(d) 5.0 inches
Question 13
An engineer is evaluating the factor of safety against sliding for a retaining wall footing. The vertical load is 45 kips per foot of wall length, the horizontal thrust is 12 kips per foot, and the coefficient of friction between concrete and soil is 0.55. What is the factor of safety against sliding?
(a) 1.8
(b) 2.1
(c) 2.4
(d) 2.7
Question 14
A foundation designer is analyzing punching shear for a square column (18 inches × 18 inches) supported by a square footing (9 ft × 9 ft × 30 inches thick). The factored column load is 650 kips and concrete strength is 4,000 psi. The critical perimeter is at d/2 from column face where d = 24 inches. What is the punching shear stress?
(a) 152 psi
(b) 168 psi
(c) 184 psi
(d) 201 psi
Question 15
A geotechnical engineer is designing a deep foundation in layered soil. A drilled shaft with 3-foot diameter extends through 15 feet of sand (φ = 32°, γ = 120 pcf) and 25 feet into clay (Su = 1,200 psf). Using α = 0.6 for clay adhesion and β = 0.25 for sand friction, what is the total skin friction capacity?
(a) 485 kips
(b) 545 kips
(c) 612 kips
(d) 678 kips
Question 16
A structural engineer is proportioning a wall footing for a 12-inch thick concrete wall carrying a service load of 18 kips per linear foot. The allowable soil pressure is 3,500 psf. The footing depth is 18 inches with an assumed weight of 150 pcf for concrete and 120 pcf for soil. What is the minimum required footing width?
(a) 5.5 ft
(b) 6.0 ft
(c) 6.5 ft
(d) 7.0 ft
Question 17
A foundation engineer is analyzing negative skin friction on a pile driven through 30 feet of recently placed fill (γ = 110 pcf, K = 0.5, δ = 22°). The pile has a perimeter of 4 feet. What is the total downdrag force on the pile from the fill layer?
(a) 45 kips
(b) 52 kips
(c) 59 kips
(d) 66 kips
Question 18
A civil engineer is designing a shallow foundation on sand where the groundwater table is initially at 12 feet below ground surface. Due to seasonal variation, the water table can rise to 3 feet below ground. The footing is 8 ft × 8 ft at 4 feet depth. If the saturated unit weight is 125 pcf and dry unit weight is 110 pcf, what is the reduction in bearing capacity due to water table rise?
(a) 22%
(b) 28%
(c) 34%
(d) 40%
Question 19
A geotechnical consultant is evaluating elastic settlement of a circular footing with diameter 12 feet on dense sand. The net applied pressure is 4,500 psf, elastic modulus of soil is 3,500 psi, and Poisson's ratio is 0.3. Using the equation Se = qB(1-ν²)Iₛ/Eₛ where Iₛ = 0.85 for circular footings, what is the immediate settlement?
(a) 0.52 inches
(b) 0.68 inches
(c) 0.84 inches
(d) 1.02 inches
Question 20
A foundation designer is evaluating overturning stability of a 6-foot wide strip footing subjected to a vertical load of 30 kips/ft at the center and a horizontal load of 8 kips/ft at 2 feet above the base. What is the factor of safety against overturning about the toe?
(a) 3.8
(b) 4.5
(c) 5.6
(d) 6.2
