Chapter 7 List the three types of bearing capacity failures

Chap. 7 Spread Footings: Geotechnical Ultimate Limit States

7.1 List the three types of bearing capacity failures and explain the differences between them.

Solution

General shear failure – It occurs in soils that are relatively incompressible and reasonably strong,

in rock, and in saturated, normally consolidated clays that are loaded rapidly enough that the

Chap. 7 Spread Footings: Geotechnical Ultimate Limit States

7.2 A 1.2-m square, 0.4-m deep spread footing is underlain by a soil with the following properties: γ

= 19.2 kN/m3, cʹ= 5 kPa,

φ

ʹ= 30°. The groundwater table is at a great depth.

(a) Compute the nominal unit bearing capacity using Terzaghi’s method.

(b) Compute the nominal unit bearing capacity using Vesić’s method.

Solution

Terzaghi’s method

Determine bearing capacity factors from Table 7.1 with

φ

ʹ = 30º

Vesić’s method

Determine bearing capacity factors from Table 7.1 with

φ

ʹ = 30º

No change in σʹzD = 7.68 kPa

Compute shape and depth factors from Equations 7.14 – 7.19

7.3 A 5 ft wide, 8 ft long, 2 ft deep spread footing is underlain by a soil with the following properties:

γ= 120 lb/ft3, cʹ=100 lb/ft2,

φ

ʹ= 28°. The groundwater table is at a great depth. Using Vesić’s

method, compute the column load required to cause a bearing capacity failure.

Solution

Determine shape and depth factors for Equation 7.13

Compute nominal unit bearing capacity using equation 7.13

Chap. 7 Spread Footings: Geotechnical Ultimate Limit States

7.4 A column carrying a vertical downward unfactored load of 270 k is to be supported on a 3-ft

deep square spread footing. The soil beneath this footing is an undrained clay with su= 3000

lb/ft2 and γ = 117 lb/ft3. The groundwater table is below the bottom of the footing. Using the

ASD method, compute the width B required to obtain a factor of safety of 3 against a bearing

capacity failure.

Solution

Use Terzaghi’s method

Compute nominal unit bearing capacity with Equation 7.4

Compute required footing width, B

7.5 A column carrying a vertical downward ultimate factored load of 1500 kN is to be supported on

a 1m deep square spread footing. The soil beneath this footing is an undrained clay with su= 150

kPa and γ = 18.1 kN/m3. The groundwater table is below the bottom of the footing. Using the

LRFD method, compute the required width B. Assume the geotechnical resistance factor is 0.5.

Solution

This is a cohesive soil that is being evaluated using the undrained strength, so we must substitute

Chap. 7 Spread Footings: Geotechnical Ultimate Limit States

7.6 A 120-ft diameter cylindrical tank with an empty weight of 1,900,000 lb is to be built on top on a

2-ft thick compacted gravel fill with a unit weight of 130 lb/ft3. The fill will be roughly the same

diameter as the tank. This tank is to be filled with water. The underlying soil is an undrained

clay with su=1000 lb/ft2 and γ = 118 lb/ft3, and the groundwater table is at a depth of 5 ft. Using

Terzaghi’s equations, compute the maximum allowable depth of the water in the tank that will

maintain a factor of safety of 3.0 against a bearing capacity failure. Include the weight of the

gravel fill in your computations and assume the weight of the water and tank is spread uniformly

across the bottom of the tank.

Solution

This is a cohesive soil that is being evaluated using the undrained strength, so we must substitute

For circular foundation

Chap. 7 Spread Footings: Geotechnical Ultimate Limit States

7.7 A 1.5-m wide, 2.5-m long, 0.5-m deep spread footing is underlain by a soil with cʹ = 10 kPa,

φ

ʹ = 32°, γ = 18.8 kN/m3. The groundwater table is at a great depth. Using ASD compute the

maximum unfactored load this footing can support while maintaining a factor of safety of 2.5

against a bearing capacity failure.

Solution

Vesić’s Bearing Capacity Factors (Table 7.1)

Shape and depth factors

Compute nominal unit bearing capacity using Equation 7.13

n

Compute allowable column load

Chap. 7 Spread Footings: Geotechnical Ultimate Limit States

7.8 A 5–ft wide, 8-ft long, 2-ft deep spread footing is underlain by a soil with cʹ = 200 lb/ft2,

φ

ʹ = 37°,

γ = 121 lb/ft3. The groundwater table is at a great depth. Using LRFD with a resistance factor of

0.5 determine the ultimate factored load this footing can carry.

Solution

Vesić’s Bearing Capacity Factors (Table 7.1)

Shape and depth factors

Compute nominal unit bearing capacity using Equation 7.13 and then nominal column load.

Compute ultimate column load

Chap. 7 Spread Footings: Geotechnical Ultimate Limit States

7.9 A bearing wall carries a total unfactored load 220 kN/m. It is to be supported on a 400-mm deep

continuous footing. The underlying soils are medium sands with cʹ = 0,

φ

ʹ = 37°, γ = 19.2 kN/m3.

The groundwater table is at a great depth. Using ASD, compute the minimum footing width

required to maintain a factor of safety of at least 2 against a bearing capacity failure. Express

your answer to the nearest 100 mm.

Solution

Use Terzaghi’s method

Bearing capacity factors from Table 7.1

Compute nominal unit bearing capacity with Equation 7.5

Allowable bearing capacity is

Compute required footing width, B

Chap. 7 Spread Footings: Geotechnical Ultimate Limit States

7.10 A bearing wall carries a factored ultimate vertical load of 67 k/ft. After the footing in Problem

7.9 was built, the groundwater table rose to a depth of 0.5 m below the ground surface. Compute

the new factor of safety against a bearing capacity failure. Compare it with the original design

value of 2 and explain why it is different.

Solution

Bearing capacity factors and overburden stress do not change

Compute

γ

′

for ground water Case 2 conditions using Equation 7.34

Compute the nominal unit bearing capacity using γʹ and weight of the footing

Compute current factor of safety

Chap. 7 Spread Footings: Geotechnical Ultimate Limit States

7.11 A bearing wall carries a factored ultimate vertical load of 67 k/ft. It is to be supported on a 18-in

deep continuous footing. The underlying soils are medium sands with cʹ = 0,

φ

ʹ = 37°, γ = 124

lb/ft3. The groundwater table is at a great depth. Using LRFD, with a resistance factor 0.45,

compute the minimum footing width required. Express your answer to the nearest 4 inches.

Solution

Compute nominal bearing capacity using Terzaghi’s theory (Equation 7.5)

Compute required footing width

7.12 A 5–ft wide, 8-ft long, 3-ft deep footing supports a downward load of 200 k and a horizontal

shear load of 25 k. The shear load acts parallel to the 8–ft dimension. The underlying soils have

cʹ = 220 lb/ft2,

φ

ʹ = 28°, γ = 123 lb/ft3. Using a total stress analysis, compute the factor of safety

against a bearing capacity failure.

Solution

Because footing is rectangular, must use Vesić’s method.

Shape factors

Depth factors

Compute nominal bearing capacity with Equation 7.13

Chap. 7 Spread Footings: Geotechnical Ultimate Limit States

7.13 For the footing describe in Problem 7.12, determine the factor of safety against sliding. Is the

factor of safety adequate?

Solution

Inputs

Compute coefficient of friction and footing weight

Compute earth pressures

Chap. 7 Spread Footings: Geotechnical Ultimate Limit States

7.14 A spread footing supported on a sandy soil has been designed using ASD to support a certain

column load with a factor of safety of 2.5 against a bearing capacity failure. However, there is

some uncertainty in both the column load, P, and the friction angle,

φ

. Which would have the

greatest impact on the actual factor of safety: An actual P that is twice the design value, or

actual

φ

that is half the design value? Use bearing capacity computations with reasonable

assumed values to demonstrate the reason for your response.

Solution

For simplicity assume footing is at ground surface and sand is cohesionless. Terzaghi’s bearing