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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

13.17 through 13.19 A retaining wall is shown in Figure 13.41. For each problem, determine the Rankine active force, Pa, per unit length of the wall and the location of the resultant.

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Figure 13.41

To determine

Find the Rankine active force Pa per unit length of the wall and the location z¯ of the resultant force.

Explanation

Given information:

The height (H) of the retaining wall is 12 m.

The depth H1 of sand is 4.0 m.

The unit weight γ1 of the sand is 17kN/m3.

The sand friction angle ϕ1 is 36°.

The cohesion c1 of sand is 0.

The surcharge pressure (q) is 25kN/m2.

The depth H2 of saturated sand is 12 m.

The saturated unit weight γ2 of the sand is 23.2kN/m3.

The saturated sand friction angle ϕ2 is 42°.

The cohesion c2 of saturated sand is 0.

Calculation:

For sand:

Determine the active earth pressure coefficient Ka using the formula.

Ka=tan2(45ϕ2)

Substitute 36° for ϕ.

Ka=tan2(4536°2)=tan2(4518)=tan2(27)=0.259

For saturated sand:

Determine the active earth pressure coefficient Ka using the formula.

Ka=tan2(45ϕ2)

Substitute 42° for ϕ.

Ka=tan2(4542°2)=tan2(4521)=tan2(24)=0.198

Determine the total stress σo at 0 m depth using the relation.

σo=q

Substitute 25kN/m2 for q.

σo=25kN/m2

Determine the pore water pressure at 0 m depth using the relation.

u=γw×h

Here, γw is the unit weight of the water.

Take the unit weight of the water as 9.81kN/m3.

Substitute 9.81kN/m3 for γw and 0 m for h.

u=9.81×0=0

Determine the effective active earth pressure σa at 0 m depth using the relation.

σa=σoKa

Substitute 25kN/m2 for σo and 0.259 for Ka.

σa=25(0.259)=6.47kN/m2

Determine the total stress (sand) σo at 4 m depth using the relation.

σo=q+γ1×H1

Substitute 25kN/m2 for q, 17kN/m3 γ1, and 4.0 m for H1.

σo=25+17×4.0=93kN/m2

Determine the total stress (saturated sand) σo at 4 m depth using the relation.

σo=q+γ2×H2

Substitute 25kN/m2 for q, 17kN/m3 γ2, and 4.0 m for H2.

σo=25+17×4.0=93kN/m2

Determine the pore water pressure at 3.0 m depth using the relation.

u=γw×h

Substitute 9.81kN/m3 for γw and 0 m for h.

u=9.81×0=0

Determine the effective active earth pressure (sand) σa at 3.0 m depth using the relation.

σa=σoKa

Substitute 93kN/m2 for σo and 0.259 for Ka.

σa=93(0.259)=24.08kN/m2

Determine the effective active earth pressure (saturated sand) σa at 3.0 m depth using the relation.

σa=σoKa

Substitute 93kN/m2 for σo and 0.198 for Ka.

σa=93(0.198)=18.41kN/m2

Determine the total stress σo at 12 m depth using the relation.

σo=γ1×H1+(γ2γw)×H2

Substitute 17kN/m3 γ1, 4

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