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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 10.48. If R = 4 m and hw = height of water = 5 m, determine the vertical stress increases 2 m below the loaded area at radial distances where r = 0, 2, 4, 6, and 8 m.

images

Circular contact area of radius R on the ground surface

Figure 10.48

To determine

Calculate the increase in vertical stress 2m below the loaded area.

Explanation

Given information:

The radius of the storage tank (R) is 4m.

The maximum height of water (hw) is 5m.

The depth (z) is 2m.

The radial distances (r) are 0m,2m,4m,6m, and 8m.

Calculation:

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

Calculate the intensity of pressure (q) on the circular area as shown below.

q=γwhw

Substitute 9.81kN/m3 for γw and 5m for hw.

q=9.81×5=49.05kN/m2

Calculate the increase in vertical stress (Δσz) using the relation as follows.

Δσz=q(A+B) (1)

Here, A and B are the factors and a functions of zR and rR.

Calculate the depth to radius ratio (zR) as shown below.

Substitute 2m for z and 4m for R.

zR=24=0.5

For the radial distance (r) of 2m:

Calculate the ratio (rR) as shown below.

Substitute 2m for r and 4m for R.

rR=24=0.5

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

Calculate the value of A as shown below.

Refer Table 10.8 “Variation of A with zR and rR” in the Text Book.

Take the value of A as 0.51622, for the values zR of 0.5 and rR of 0.4.

Take the value of A as 0.46448, for the values zR of 0.5 and rR of 0.6.

Calculate the value of A for the values zR of 0.5 and rR of 0

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