Principles of Geotechnical Engineering (MindTap Course List)
Principles of Geotechnical Engineering (MindTap Course List)
9th Edition
ISBN: 9781305970939
Author: Braja M. Das, Khaled Sobhan
Publisher: Cengage Learning
Question
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Chapter 14, Problem 14.11P
To determine

Find the magnitude and location of the passive force Ppe due to earthquake conditions.

Expert Solution & Answer
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Answer to Problem 14.11P

The magnitude of the passive force Ppe due to earthquake conditions is 9,823kN/m_.

The location of the resultant measured from the bottom of the wall is 3.12m_.

Explanation of Solution

Given information:

The magnitude of surcharge loading (q) is 95kN/m2.

The unit weight γ of the backfill is 18kN/m3.

The height (H) of the retaining wall is 7.0 m.

The soil friction angle ϕ is 40°.

The angle of wall friction δ is 20°.

The cohesion c of the soil is 30kN/m2.

The soil-wall interfall adhesion ca is 0.

The horizontal inertial kh force is 0.2.

The vertical inertial kv force is 0.2.

Calculation:

Determine the ratio of angle of wall friction to the soil friction angle.

δϕ=20°40°=0.5

Determine the ratio of soil-wall interfall adhesion to the cohesion.

cac=030=0

Determine the magnitude of the passive force due to earthquake conditions using the formula.

Ppe=[12γH2Kpγ(e)+qHKpq(e)+2cHKpc(e)]1cosδ (1)

Here, Kpγ(e), Kpq(e), and Kpc(e) are the passive earth-pressure coefficients in the normal direction.

Refer Figure (14.9b) “Variation of Kpγ(e) (a) δϕ=1; (b)” in the text book.

For δϕ=0.5;

Take the value of Kpγ(e) as 6.75.

Refer Figure (14.10b) “Variation of Kpγ(e) (a) δϕ=1; (b)” in the text book.

For δϕ=0.5;

Take the value of Kpq(e) as 6.67.

Refer Table (14.7) “Variation of Kpc(e)” in the text book.

For the ratio of angle of wall friction to the soil friction angle is 0.5.

The value of Kpc(e) is 4.33

Substitute 18kN/m3 for γ, 7.0 m for H, 6.75 for Kpγ(e), 95kN/m2 for q, 6.67 for Kpq(e), 30kN/m2 for c, 4.33 for Kpc(e), and 20° for δ in Equation (1).

Ppe=[12(18)(72)(6.75)+95(7)(6.67)+2(30)(7)(4.33)]1cos20°=9,823kN/m

Thus, the magnitude of the passive force Ppe due to earthquake conditions is 9,823kN/m_.

Determine the unit weight of the passive force Ppe using the formula.

UnitweightofPpe=1cosδ[12γH2Kpγ(e)]

Substitute 20° for δ, 18kN/m3 for γ, 7.0 m for H, and 6.75 for Kpγ(e).

UnitweightofPpe=1cos20°[12(18)(7)2(6.75)]=3,168kN/m

Determine the distance of passive earth force acting above the bottom of the wall using the relation.

Distance=H3

Substitute 7.0 m for H.

Distance=7.03=2.33m

Determine the weight of surcharge component using the formula.

Unitweightofsurcharge=1cosδ[qHKpq(e)]

Substitute 20° for δ, 95kN/m2 for q, 7.0 m for H, and 6.67 for Kpq(e).

Unitweightofsurcharge=1cos20°[95(7.0)(6.67)]=4,720kN/m

Determine the distance of surcharge component acting above the bottom of the wall using the relation.

Distance=H2

Substitute 7.0 m for H.

Distance=7.02=3.5m

Determine the unit weight of the cohesion component using the formula.

Unitweightofcohesioncomponent=1cosδ[2cHKpc(e)]

Substitute 20° for δ, 30kN/m2 for c, 7.0 m for H, and 4.33 for Kpc(e).

Unitweightofcohesioncomponent=1cos20°[2(30)(7)(4.33)]=1,935kN/m

Determine the distance of cohesion component acting above the bottom of the wall using the relation.

Distance=H2

Substitute 7.0 m for H.

Distance=7.02=3.5m

Determine the location of the resultant measured from the bottom of the wall using the formula.

z¯=UnitweightofPpe×Distance+(Unitweightofsurcharge+cohesion)(distance)Ppe

Substitute 3,168kN/m for unit weight of Ppe, 2.33 m for distance, 4,720kN/m for unit weight of surcharge, for unit weight of cohesion, 3.5 m for distance, and 9,823kN/m for Ppe.

z¯=3,168×2.33+(4,720+1,935)(3.5)9,823=3.12m

Thus, the location of the resultant measured from the bottom of the wall is 3.12m_.

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