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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 elevation and plan of a bracing system for an open cut in sand are shown in Figure 14.21. Using Peck’s empirical pressure diagrams, determine the design strut loads. Given: γsand = 18 kN/m3, ϕ' = 38°, x = 3 m, z = 1.25 m, and s = 3 m.

images

To determine

Find the design strut loads by using the Peck’s empirical pressure.

Explanation

Given information:

The unit weight γsand of the sand is 18kN/m3.

The soil friction angle ϕ is 38°.

The depth z is 1.25 m.

The depth x is 3.0 m.

The depth s is 3.0 m.

Calculation:

Determine the height (H) of the bracing system using the relation.

H=z+x+x+x+s

Substitute 1.25 m for z, 3.0 m for x, and 3.0 m for s.

H=1.25+3.0+3.0+3.0+3.0=13.25m

Determine the maximum pressure intensity σa using the formula.

σa=0.65γHtan2(45ϕ2)

Substitute 18kN/m3 for γ, 13.25 m for H, and 38° for ϕ.

σa=0.65(18)(13.25)tan2(4538°2)=36.9kN/m2

Draw the diagram of level A to B as in Figure 1.

Refer Figure 1.

Determine the reaction at level A by taking moment about level B.

MB1=0A=(13)[(σa×(x+z)((x+z)2))]

Substitute 36.9kN/m2 for σa, 3.0 m for x, and 1.25 m for z.

A=(13)[(36.9×(3+1.25)((3+1.25)2))]=111.08kN/m

Draw the sketch of level B to C as in Figure 2.

Refer Figure 2.

Determine the reaction at level B1 using the relation.

B1=σa(x+z)A

Substitute 36.9kN/m2 for σa, 3.0 m for x, 1.25 m for z, and 111.08kN/m for A.

B1=36.9(3+1.25)111.08=45.75kN/m

Determine the reaction B2 or C1 using the relation.

B2=C1=σa(x)2

Substitute 36.9kN/m2 for σa and 3.0 m for x.

B2=C1=36.9(3.0)2=55.35kN/m

Draw the sketch of level C to D as in Figure 3.

Refer Figure 3.

Determine the reaction at level D by taking moment about level C.

MC2=0D=(13)[σA×(x+s)(x+s2)]

Substitute 36

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