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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 8.0 m.

The depth H1 of sand is 3.0 m.

The unit weight γ1 of the sand is 13kN/m3.

The sand friction angle ϕ1 is 30°.

The saturated sand friction angle ϕ2 is 30°.

The cohesion c1  of sand is 0.

The surcharge pressure (q) is 16kN/m2.

The depth H2 of saturated sand is 4.0 ft.

The saturated unit weight γ2 of the sand is 18.8kN/m3.

The cohesion c2 of saturated sand is 0.

Calculation:

Determine the active earth pressure coefficient Ka using the formula.

Ka=tan2(45ϕ2)

Substitute 30° for ϕ.

Ka=tan2(4530°2)=tan2(4515)=tan2(30)=0.333

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

σo=q

Substitute 16kN/m2 for q.

σo=16kN/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 16kN/m2 for σo and 0.39 for Ka.

σa=16(0.333)=5.32kN/m2

Determine the total stress σo at 3 m depth using the relation.

σo=q+γ1×H1

Substitute 16kN/m2 for q, 13kN/m3 γ1, and 3.0 m for H1.

σo=16+13×3.0=55kN/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 σa at 3.0 m depth using the relation.

σa=σoKa

Substitute 55kN/m2 for σo and 0.333 for Ka.

σa=55(0.333)=18.31kN/m2

Determine the total stress σo at 8 m depth using the relation.

σo=q+γ1×H1+(γ2γw)×H2

Substitute 16kN/m2 for q, 13kN/m3 γ1, 3.0 m for H1, 18.8kN/m3 γ2, 9.81kN/m3 for γw, and 5.0 m for H2.

σo=16+13×3+(18.89.81)×5=99.95kN/m2

Determine the pore water pressure at 8 m depth using the relation.

u=γw×h

Substitute 9.81kN/m3 for γw and 5.0 m for h.

u=9.81×5=49.05kN/m2

Determine the effective active earth pressure σa at 8 m depth using the relation

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