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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 the flexible loaded rectangular area shown in Figure 10.47. Using Eq. (10.36), determine the vertical stress increase below the center of the loaded area at depths z = 3, 6, 9, 12, and 15 m.

images

Figure 10.47

To determine

Calculate the increase in vertical stress below the center of the loaded area.

Explanation

Given information:

The uniformly distributed soil (q) is 330kN/m2.

The length of the rectangular cross section (L) is 18m.

The breadth of the rectangular cross section (B) is 9m.

The depths (z) are 3m,6m,9m,12m, and 15m.

Calculation:

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 3m:

Calculate the width (b) as shown below.

b=B2

Substitute 9m for B.

b=92=4.5m

Calculate the ratio (m1) as shown below.

m1=LB

Substitute 18m for L and 9m for B.

m1=189=2

Calculate the ratio (n1) as shown below.

n1=zb

Substitute 4.5m for b and 3m for z.

n1=34.5=0.67

Similarly calculate the remaining values and tabulate as in Table 1.

Refer Table 10.11 “Variation of I4 with m1 and n1” in the Text Book

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