Principles of Foundation Engineering (MindTap Course List)
Principles of Foundation Engineering (MindTap Course List)
9th Edition
ISBN: 9781337705028
Author: Braja M. Das, Nagaratnam Sivakugan
Publisher: Cengage Learning
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Chapter 6, Problem 6.1P

For the following cases, determine the allowable gross vertical load-bearing capacity of the foundation. Use Terzaghi’s equation and assume general shear failure in soil. Use FS = 4.

Parameters for Problem 6.1

Chapter 6, Problem 6.1P, For the following cases, determine the allowable gross vertical load-bearing capacity of the

a)

Expert Solution
Check Mark
To determine

Find the allowable gross vertical load-bearing capacity of the continuous foundation.

Answer to Problem 6.1P

The allowable gross vertical load-bearing capacity of the continuous foundation is 5,195.45lb/ft2_.

Explanation of Solution

Given information;

The width (B) of the foundation is 3 ft.

The depth (Df) of the foundation is 3 ft.

The angle of friction ϕ of soil is 28°.

The cohesion c of the soil is 400lb/ft2.

The specific weight γ of soil is 110lb/ft3.

The factor of safety is (FS) is 4.0.

Calculation:

Refer Table (6.1), “Terzaghi’s bearing capacity factors” in the text book.

For ϕ=28°

Take the value of NC as 31.61.

Take the value of Nq as 17.81.

Take the value of Nγ as 13.70.

Determine the ultimate load bearing capacity qu of the foundation using the formula;

qu=cNC+qNq+12γBNγ=cNC+(γ×Df)Nq+12γBNγ=400×31.61+(110×3)17.81+12×110×3×13.70=20,781.8lb/ft2

Determine the allowable gross vertical load-bearing capacity qall using the formula;

qall=quFS=20,781.8lb/ft24=5,195.45lb/ft2

Hence, the allowable gross vertical load-bearing capacity qall of the continuous foundation is 5,195.45lb/ft2_.

b)

Expert Solution
Check Mark
To determine

Find the allowable gross vertical load-bearing capacity of the continuous foundation.

Answer to Problem 6.1P

The allowable gross vertical load-bearing capacity of the continuous foundation is 372.8kN/m2_.

Explanation of Solution

Given information;

The width (B) of the foundation is 1.5 m.

The depth (Df) of the foundation is 1.2 m.

The angle of friction ϕ of soil is 35°.

The cohesion c of the soil is zero.

The specific weight γ of soil is 17.8kN/m3.

The factor of safety is (FS) is 4.0.

Calculation:

Refer Table (6.1), “Terzaghi’s bearing capacity factors” in the text book.

For ϕ=35°

Take the value of NC as 57.75.

Take the value of Nq as 41.44.

Take the value of Nγ as 45.41.

Determine the ultimate load bearing capacity qu of the foundation using the formula;

qu=cNC+qNq+12γBNγ=cNC+(γ×Df)Nq+12γBNγ=0×57.75+(17.8×1.2)41.44+12×17.8×1.5×45.41=1,491.38kN/m2

Determine the allowable gross vertical load-bearing capacity qall using the formula;

qall=quFS=1,491.38kN/m24=372.8kN/m2

Hence, the allowable gross vertical load-bearing capacity qall of the foundation is 372.8kN/m2_.

c)

Expert Solution
Check Mark
To determine

Find the allowable gross vertical load-bearing capacity of the square foundation.

Answer to Problem 6.1P

The allowable gross vertical load-bearing capacity of the square foundation is 280.0kN/m2_.

Explanation of Solution

Given information;

The width (B) of the foundation is 3.0 m.

The depth (Df) of the foundation is 2.0 m.

The angle of friction ϕ of soil is 30°.

The cohesion c of the soil is zero.

The specific weight γ of soil is 16.5kN/m3.

The factor of safety is (FS) is 4.0.

Calculation:

Refer Table (6.1), “Terzaghi’s bearing capacity factors” in the text book.

For ϕ=30°

Take the value of NC as 37.16.

Take the value of Nq as 22.46.

Take the value of Nγ as 19.13.

Determine the ultimate load bearing capacity qu using the formula;

qu=1.3cNC+qNq+0.4γBNγ=1.3cNC+(γ×Df)Nq+0.4γBNγ=1.3(0)37.16+(16.5×2)22.46+0.4×16.5×3×19.13=1,119.95kN/m2

Determine the allowable gross vertical load-bearing capacity qall using the formula;

qall=quFS=1,119.95kN/m24280.0kN/m2

Hence, the allowable gross vertical load-bearing capacity qall of the square foundation is 280.0kN/m2_.

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