Chapter 10, Problem 10.18P

### 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

# 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.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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