Chapter 11, Problem 11.2P

### Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939

Chapter
Section

### Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939
Textbook Problem

# A rigid reinforced concrete foundation is subjected to a column load of 87,000 lbs. The foundation measures 8 ft × 8 ft in plan and rests on 21 ft of layered soil underlain by rock. The soil layers have the following characteristics:If the foundation depth Df = 4 ft and μs = 0.4 for all layers, estimate the elastic settlement of the foundation. Use Eq. (11.1)

To determine

Calculate the elastic settlement of the foundation.

Explanation

Given information:

The column load (P) is 87,000lbs.

The length of the foundation (L) is 8ft.

The breadth of the foundation (B) is 8ft.

The depth of foundation (Df) is 4ft.

The Poisson’s ratio (μs) is 0.4.

The depth below the foundation (H) is 21ft.

The characteristics of soil layers are given in Table.

 Layer type Thickness (ft) Es (lb/in.2) γd (lb/ft3) Loose sand 0−5 2,200 105 Medium clay 5−13 980 109 Dense sand 13−21 9,100 122

Calculation:

Calculate the elastic settlement for the perfectly flexible foundation (Se) using the relation.

Se=Δσ(αB)1μs2EsIsIf (1)

Here, Δσ is the net applied pressure on the foundation, α is the factor depends on the foundation where settlement is being calculated, B is B2 for center of foundation or B for corner of foundation, Es is the average modulus of elasticity of the soil under the foundation measured from z=0 to z=5B, Is is the shape factor, and If is the depth factor.

Calculate the net applied pressure (Δσ) as shown below.

Δσ=PL×B

Substitute 87,000lbs for P, 8ft for L, and 8ft for B.

Δσ=87,0008×8=1,359.375lb/ft2

Calculate the average modulus of elasticity of the soil under the foundation (Es) using the relation.

Es=Es(i)Δzz¯ (2)

Here, Es(i) is the soil modulus of elasticity within a depth Δz and z¯ is H or 5B, whichever is lesser.

Calculate z¯ as shown below.

z¯=Hor 5B

Substitute 21ft for H and 8ft for B.

z¯=21ft (or) 5×8=21ft (or) 40ft=21ft

Calculate the average modulus of elasticity of the soil under the foundation (Es) as shown below.

Rephrase Equation (2) for the foundation.

Es=Es(L)ΔzL+Es(M)ΔzL+Es(D)ΔzLz¯

Substitute 2,200lb/in.2 for Es(L), 980lb/in.2 for Es(M), 9,100lb/in.2 for Es(D), 5ft for ΔzL, 8ft for ΔzB, 8ft for ΔzD, and 21ft for z¯.

Es=2,200×5+980×8+9,100×821=91,64021=4,364lb/in.2×(12in1ft)2=628,416lb/ft2

For the center of the foundation:

The factor (α) is 4 at the center of the foundation

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