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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
Rankine stress distribution behind a gravity retaining wall. University of Massachusetts Lowell 14.531 Advanced Soil Mechanics 2
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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 3
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Modeling the Active Wedge Known Wall dimensions and materials. Soil and wall shear strength parameters. Grade of overburden soil. Solve for
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 7
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Example Retaining Wall: Case 2 University of Massachusetts Lowell 14.531 Advanced Soil Mechanics 8 γ1 = 117 pcfγconc = 150 pcf φ1’ = 34⁰ δ’ = 18⁰ Ca = 800 psf Assume firm underlying soil
University of Massachusetts Lowell 14.531 Advanced Soil Mechanics 10 +58%
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Pa vs. α vs. θ φw = 34⁰ Line of intersection φw = 0⁰ Produced using Mathematica University of Massachusetts Lowell 14.531 Advanced Soil Mechanics 11
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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 12
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Is it worth consideration? University of Massachusetts Lowell 14.531 Advanced Soil Mechanics 13 Yes
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References University of Massachusetts Lowell 14.531 Advanced Soil Mechanics 14 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®
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