Chapter 13, Problem 13.1CTP

### 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

# Figure 13.14 provides a generalized case for Rankine active pressure on a frictionless retaining wall with inclined back and a sloping granular backfill. You are required to develop some compaction guidelines for the backfill soil when θ =10° and α = 0°, 10°, and 20°. Laboratory direct shear tests on the granular soil revealed that the effective friction angle varies with the dry unit weight as follows:The data show that the soil friction angle increases as the compacted unit weight increases. You already know from Chapter 12 that higher friction angle means better shear strength and stability. However, according to Eq. (13.38), higher unit weight also means higher active force Pa on the wall, which is not desirable. To further investigate if higher friction angle indeed has a beneficial effect, prepare a design chart by plotting the variations of Pa/0.5H2 (which is equal to Ka(R)γ) for various values of the backfill slope α and the friction angle ϕ'. Explain how this chart may aid a geotechnical engineer in developing guidelines for backfill construction for a given height (H) of the retaining wall.

To determine

Prepare a design chart by plotting the variations of Pa/0.5H2 for various values of the backfill slope α and the friction angle ϕ.

Explanation

Given information:

The angle θ value is 10°.

The backfill slope angle α is 0°, 10°, and 20°.

The dry unit weight of the soil γd is 16.5kN/m3, 18.7kN/m3, and 19.5kN/m3.

To soil friction angle ϕ is 28°, 32° , and 36°.

Calculation:

For θ=10°, α=0°, and ϕ=28°:

Determine the value of ψa using the formula.

ψa=sin1(sinαsinϕ)α+2θ

Substitute 0° for α, 28° for ϕ, and 10° for θ.

ψa=sin1(sin0sin28°)0+2(10°).=20°

Similarly, calculate and tabulate the values of ψa for the remaining values of soil friction angle as in Table 1.

Determine the Rankine active earth-pressure coefficient Ka(R) for generalized case using the formula.

Ka(R)=cos(αθ)1+sin2ϕ2sinϕcosψacos2θ(cosα+sin2ϕsin2α)

Substitute 0° for α, 10° for θ, 28° for ϕ, and 20° for ψa.

Ka(R)=cos(010°)1+sin228°2sin28°cos20°cos210°(cos0°+sin228°sin20°)=(0.984)0.5810.969(1.469)=0.402

Similarly, calculate and tabulate the values of Rankine active earth-pressure coefficient for the remaining values of soil friction angle as in Table (1).

Determine the value Ka(R)γd:

Substitute 0.402 for Ka(R) and 16.5kN/m3 for γd.

Ka(R)γ=0.402×16.5=6.633kN/m3

Similarly, calculate and tabulate the value of Ka(R)γ for the remaining dry unit weight of the soil as in Table (1).

For θ=10°, α=10°, and ϕ=28°:

Determine the value of ψa using the formula.

ψa=sin1(sinαsinϕ)α+2θ

Substitute 10° for α, 28° for ϕ, and 10° for θ.

ψa=sin1(sin10°sin28°)10°+2(10°)=31.42°

Similarly, calculate and tabulate the values of ψa for the remaining values of soil friction angle as in Table (1).

Determine the Rankine active earth-pressure coefficient Ka(R) for generalized case using the formula.

Ka(R)=cos(αθ)1+sin2ϕ2sinϕcosψacos2θ(cosα+sin2ϕsin2α)

Substitute 10° for α, 10° for θ, 28° for ϕ, and 31.42° for ψa.

Ka(R)=cos(10°10°)1+sin228°2sin28°cos31

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