   Chapter 14, Problem 14.11P 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

A retaining wall located in an earthquake zone has a vertical back face and a horizontal backfill (Figure 14.8). The wall is also subjected to a surcharge loading of magnitude, q = 95 kN/m2. Determine the magnitude and location of the passive force, Ppe, due to earthquake conditions. Given: γ = 18 kN/m3, ϕ' = 40°, δ' = 20°, c' = 30 kN/m2, c ′ a = 0 , H = 7 m, and kv = kh = 0.2. To determine

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

Explanation

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

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