   Chapter 13, Problem 13.18P Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939

Solutions

Chapter
Section 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.  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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