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# Active Wedge Behind A Gravity Retaining Wall Complete 2011

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• 1. Modeling of the Active Wedge behind a Gravity Retaining Wall
By: Rex Radloff
14.531 Advanced Soil Mechanics
University of Massachusetts Lowell
Department of Civil Engineering
• 2. Rankine Active Wedge
• Wall friction is neglected
• 3. Active force acts 1/3H from the base
• 4. Front face angle (θ) is 90⁰
• 5. Overburden slope (β) is 0⁰
• 6. Back face angle (α) is 45 + φ/2
φw
Rankine wedge behind a gravity retaining wall.
What if the above was not held constant?
• How would the magnitude and location of Pa change?
• 7. What are its effects on the failure criteria?
• 8. To what degree?
Rankine stress distribution behind a gravity retaining wall.
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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• 9. Active Wedge with Reactions
W
Note:
The weight and centroid of the active wedge is a function of H, Wh, WBs, γ, α, θ, and β
The weight and centroid of the backfill is a function of H, WBs, Wh, γ, θ, and β
Active wedge with consideration towards θ, β, and φw
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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• 10. Modeling the Active Wedge
Known
Wall dimensions and materials.
Soil and wall shear strength parameters.
Grade of overburden soil.
Solve for
• Angle θ of the front face of the active wedge.
• 11. Angle α of the back face of the active wedge.
• 12. Active force, Pa, that is produced by the active wedge.
• 13. The location of the Pa resultant.
• 14. FS against overturning and sliding.
• 15. Eccentricity
• 16. Maximum stress, qMAX underneath the foundation.
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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• 17. Example Retaining Wall: Case 1
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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γ1 = 117 pcfγconc = 150 pcf
φ1’ = 34⁰
δ’ = 18⁰
Ca = 800 psf
Assume firm underlying soil
• 18. γ= 117 pcf, Cs = 0 psf, Cw = 0 psf, H = 20.75 ft., Wh = 6.00 ft., φ = 34⁰, β = 0⁰
θ = 90⁰, φw = 34⁰  Pa = 6.51 Kips, α = 56.8⁰
θ = 90⁰, φw = 0⁰  Pa = 7.12 Kips, α = 62.0⁰  (45 + φw/2)
θ = 71⁰, φw = 34⁰  Pa = 11.24 Kips, α =61.2⁰
θ = 71⁰, φw = 0⁰  Pa = 10.84 Kips, α = 71.2⁰
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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• 19. Failure Analysis: H/Wh = 3.4
|e| ≤𝑏6 2.08 ft

The increase in Pa lead to a below acceptable FS for overturning.
The greater distance between the Pa vector and pt.O led to a below acceptable eccentricity.
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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• 20. Example Retaining Wall: Case 2
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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γ1 = 117 pcfγconc = 150 pcf
φ1’ = 34⁰
δ’ = 18⁰
Ca = 800 psf
Assume firm underlying soil
• 21. γ= 117 pcf, Cs = 0 psf, Cw = 0 psf, H = 20.75 ft., Wh = 20.75 ft., φ = 34⁰, β = 0⁰
θ = 90⁰, φw = 34⁰  Pa = 6.51 Kips, α = 56.8⁰
θ = 90⁰, φw = 0⁰  Pa = 7.12 Kips, α = 62.0⁰  (45 + φw/2)
θ = 45⁰, φw = 34⁰  Pa = 29.03 Kips, α =57.2⁰
θ = 45⁰, φw = 0⁰  Pa = 21.41 Kips, α = 84.50⁰
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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• 22. Failure Analysis: H/Wh = 1.0
|e| ≤𝑏6 4.46 ft

University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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+58%
• 23. Pa vs. α vs. θ
φw = 34⁰
Line of intersection
φw = 0⁰
Produced using Mathematica
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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• 24. Conclusion
The active force (Pa) depends on the angles θ, α, and φw found among the active wedge.
Any deviation between the calculated active force behind the same retaining wall depends on the combining effects of θ, α, and φw found among the active wedge.
As the angle θ decreases, the Pa will increase as well as the variance between the Pa calculated with and without wall friction.
Hard to openly predict the influence on the failure criteria
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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• 25. Is it worth consideration?
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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Yes
• 26. References
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
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Das, B.M., (2006). “Principles of Geotechnical Engineering – Sixth Edition”
Lambe, T.W., and R.V. Whitman, (1969). “Series in Soil Engineering - Soil Mechanics”
Mangano, Sal, (2010). “Mathematica Cookbook”
AutoCAD 2011®
Wolfram Mathematica®