Chapter 11, Problem 11.1P

### 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 vertical column load, P = 600 kN, is applied to a rigid concrete foundation with dimensions B = 1 m and L = 2 m, as shown in Figure 11.45. The foundation rests at a depth Df = 0.75 m on a uniform dense sand with the following properties: average modulus of elasticity, Es = 20,600 kN/m2, and Poisson’s ratio, μs = 0.3. Estimate the elastic settlement due to the net applied pressure, Δσ, on the foundation. Given: H = 5 m.Figure 11.45

To determine

Calculate the elastic settlement due to the net applied pressure on the foundation.

The elastic settlement due to the net applied pressure (Se,rigid) is 12.1mm_.

Explanation

Given information:

The vertical column load (P) is 600kN.

The length of the foundation (L) is 2m.

The breadth of the foundation (B) is 1m.

The depth of foundation (Df) is 0.75m.

The average modulus of elasticity (Es) is 20,600kN/m2.

The Poisson’s ratio (μs) is 0.3.

The depth below the foundation (H) is 5m.

Calculation:

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

Se,flexible=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, Is is the shape factor, and If is the depth factor.

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

Δσ=PL×B

Substitute 600kN for P, 2m for L, and 1m for B.

Δσ=6002×1=300kN/m2

For the center of the foundation:

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

Calculate B as shown below.

B=B2

Substitute 1m for B.

B=12=0.5m

Calculate the ratio (m) as shown below.

m=LB

Substitute 2m for L and 1m for B.

m=21=2

Calculate the ratio (n) as shown below.

n=HB2

Substitute 5m for H and 1m for B.

n=512=10

Calculate the shape factor (Is) using the relation.

Is=F1+12μs1μsF2 (2)

Here, F1 and F2 are the factors and a function of m and n.

Calculate the factor (F1) as follows.

Refer Table 11.1 “Variation of F1 with m and n” in the Text Book.

Take the value of F1 as 0.641, for the values m of 2 and n of 10.

Calculate the factor (F2) as follows.

Refer Table 11.2 “Variation of F2 with m and n” in the Text Book.

Take the value of F2 as 0.031, for the values m of 2 and n of 10.

Calculate the shape factor (Is) as shown below.

Substitute 0.641 for F1, 0.031 for F2, and 0.3 for μs in Equation (2).

Is=0.641+(12×0.310.3)×0.031=0.641+0.018=0.659

Calculate the ratio DfB as shown below.

Substitute 0.75m for Df and 1m for B.

DfB=0.751=0.75

Calculate the ratio LB as shown below.

Substitute 2m for L and 1m for B.

LB=21=2

Calculate the depth factor (If) as follows.

Refer Table 11.3 “Variation of If with LB and DfB” in the Text Book.

Take the value of If as 0.75, for the values LB of 2, DfB of 0.75, and μs of 0.3.

Calculate the elastic settlement for the perfectly flexible foundation (Se,flexible) as shown below.

Substitute 300kN/m2 for Δσ, 4 for α, 0.5m for B, 0.3 for μs, 20,600kN/m2 for Es, 0.659 for Is, and 0.75 for If.

Se,flexible=300×4×0.5(10.3220,600)×0.659×0.75=296.55×4.417×105=0.013m

Calculate the elastic settlement for the rigid foundation (Se,rigid) as shown below.

Se,rigid=0.93Se,flexible

Substitute 0.013m for Se,flexible.

Se,rigid=0.93×0.013=0.01209m×1,000mm1m=12.1mm

Therefore, the elastic settlement due to the net applied pressure (Se,rigid) is 12.1mm_.

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