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Principles of Geotechnical Enginee...

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

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BuyFindarrow_forward

Principles of Geotechnical Enginee...

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

Refer to figure 11.48. A square foundation, 2.5 × 2.5 m in size, supports a column load of 478 kN. The soil characteristics are given in the figure. Field monitoring indicated that the foundation settlement was 46 mm at the end of 2 years.

  1. a. Estimate the average stress increase in the clay layer due to the applied load.
  2. b. Estimate the primary consolidation settlement.
  3. c. What is the degree of consolidation after 2 years?
  4. d. Estimate the coefficient of consolidation for the pressure range.
  5. e. Estimate the settlement in 3 years.

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(a)

To determine

Calculate the average stress increase in the clay layer due to the applied load.

Explanation

Given information:

The foundation load (P) is 478kN.

The length of the foundation (L) is 2.5m.

The breadth of the foundation (B) is 2.5m.

The depth of foundation (Df) is 1.5m.

The height of the clay layer 1 (H1) is 3.25m.

The height of the clay layer 2 (H2) is 3.5m.

The dry unit weight of sand (γd) is 16kN/m3.

The saturated unit weight (γsat) is 18.8kN/m3.

The liquid limit (LL) is 37.

Calculation:

Consider the unit weight of water (γw) is 9.81kN/m3.

Calculate the distributed load (q) as shown below.

q=PBL

Substitute 478kN for P, 2.5m for B, and 2.5m for L.

q=4782.5×2.5=4786.25=76.48kN/m2

Calculate the increase in vertical stress (Δσz) below the center of a rectangular area using the relation as follows.

Δσz=qI4 (1)

  Here, I4 is the influence factor and as a function of m1 and n1.

For the depth (z) of 1.75m:

Calculate the width (b) as shown below.

b=B2

Substitute 2.5m for B.

b=2.52=1.25m

Calculate the ratio (m1) as shown below.

m1=LB

Substitute 2.5m for L and 2.5m for B.

m1=2.52.5=1

Calculate the ratio (n1) as shown below.

n1=zb

Substitute 1.25m for b and 1.75m for z.

n1=1.751.25=1

(b)

To determine

Calculate the primary consolidation settlement.

(c)

To determine

Calculate the degree of consolidation after 2 years.

(d)

To determine

Calculate the coefficient of consolidation for the pressure range.

(e)

To determine

Calculate the settlement in 3 years.

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