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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

The 5-m high retaining wall in Figure 13.40b is subjected to a surcharge line load of q = 44 kN/m on the ground surface. Determine the increase in lateral force per unit length of the wall due to the line load.

images

(b)

Figure 13.40

To determine

Find the increase in lateral earth pressure force σh per unit length of the wall due to the line load.

Explanation

Given information:

The surcharge line load (q) is 44kN/m.

The distance (x) of load acting from the retaining wall is 1 m.

The height (H) of the retaining wall is 5 m.

The distance measured from top of the retaining wall is 1, 2, 3, 4, and 5 m.

Calculation:

Determine the value of m using the formula.

m=xH

Substitute 1 m for x and 5 m for H.

m=15=0.2

The calculated value of m is less than 0.4, therefore, use Equation (13.21) to calculate the lateral earth pressure.

Determine the value of n when distance measured from top of the retaining wall is 1 m using the relation.

n=zH

Substitute 1 m for z and 5 m for H.

n=15=0.2

Similarly, calculate and tabulate the value of n for the remaining distance as in Table (1).

Determine the lateral earth pressure when the distance measured from top of the retaining wall is 0 m using the formula.

σh=0.203qHn(0.16+n2)2

Substitute 44kN/m for q, 5.0 m for H, and 0 for n.

σh=0.203(44)50(0.16+02)2=1.786(0)=0

Similarly, calculate and tabulate the lateral earth pressure for the remaining distances as in Table 1.

Show the n value and lateral earth pressure as in Table (1).

n=zHσh(kN/m2)
00.00
0.28.93
0.46.97
0.63.96
0.82.23
1.01.32

Show the plot between depth and lateral earth pressure as in Figure (1).

Refer Figure 1.

Determine the lateral force on the wall per unit length of area A1 using the formula.

A1=12×b×h

Here, b is the width and h is the height.

Substitute 1 m for b and 8.93kN/m2 for h.

A1=12×1.0×8.93=4.47kN/m

Determine the lateral force on the wall per unit length of area A2 using the formula.

A2=(l1+l22)h

Here, l is the length of respective sides and h is the height.

Substitute 8.93kN/m2 for l1, 6.97kN/m2 for l2, and 1.0 m for h.

A2=(8.93+6.972)(1.0)=7.95kN/m

Determine the lateral force on the wall per unit length of area A3 using the formula.

A3=(l1+l22)h

Substitute 6

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