Chapter 10, Problem 10.7P

### 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

# Point loads of magnitude 125, 250, and 500 kN act at B, C, and D, respectively (Figure 10.40). Determine the increase in vertical stress at a depth of 10 m below the point A. Use Boussinesq’s equation.Figure 10.40

To determine

Calculate the increase in vertical stress at a depth of 10m below the point A by using Boussinesq’s equation.

Explanation

Given information:

The magnitude of load at B (PB) is 125kN.

The magnitude of load at C (PC) is 250kN.

The magnitude of load at D (PD) is 500kN.

The depth below point A (z) is 10m.

Calculation:

Calculate the distance (r) from A using the relation.

r=x2+y2 (1)

Here, x is the distance of a point from A along x axis and y is the distance of a point from A along y axis.

Show the location of points A, B, C, and D as in Figure 1.

Refer to Figure 1.

Calculate the distance (r) for point B from A as shown below.

Substitute 8m for x and 0 for y in Equation (1).

r=82+0=8m

Similarly, calculate the distance (r) of remaining points and tabulate as in Table 1.

Calculate the ratio rz as shown below.

For point B,

Substitute 8m for r and 10m for z.

rz=810=0.8

Similarly, calculate the ratio rz of remaining points and tabulate as in Table 1.

Calculate the value of influence factor (I1) as shown below.

Refer Table 10.1 “Variation of I1 for various values of rz” in the textbook.

Take the value of I1 as 0.1386 for the ratio rz of 0.8.

Similarly, take the value of I1 for the remaining points and tabulate as in Table 1.

Calculate the increase in vertical stress (Δσz) for any point using the relation.

Δσz=Pz2I1 (2)

Calculate the increase in vertical stress ((Δσz)B) for point B as shown below.

Substitute 125kN for P, 10m for z, and 0.1386 for I1 in Equation (2).

(Δσz)B=125102×0

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