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- 1. Modeling of the Active Wedge behind a Gravity Retaining Wall<br />By: Rex Radloff<br />14.531 Advanced Soil Mechanics<br />University of Massachusetts Lowell<br />Department of Civil Engineering<br />
- 2. Rankine Active Wedge<br /><ul><li>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</li></ul>φw<br />Rankine wedge behind a gravity retaining wall.<br />What if the above was not held constant? <br /><ul><li>How would the magnitude and location of Pa change?
- 7. What are its effects on the failure criteria?
- 8. To what degree?</li></ul>Rankine stress distribution behind a gravity retaining wall.<br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />2<br />
- 9. Active Wedge with Reactions<br />W<br />Note:<br />The weight and centroid of the active wedge is a function of H, Wh, WBs, γ, α, θ, and β<br />The weight and centroid of the backfill is a function of H, WBs, Wh, γ, θ, and β<br />Active wedge with consideration towards θ, β, and φw<br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />3<br />
- 10. Modeling the Active Wedge<br />Known<br />Wall dimensions and materials.<br />Soil and wall shear strength parameters.<br />Grade of overburden soil.<br />Solve for<br /><ul><li>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.</li></ul>University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />4<br />
- 17. Example Retaining Wall: Case 1<br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />5<br />γ1 = 117 pcfγconc = 150 pcf<br />φ1’ = 34⁰<br />δ’ = 18⁰<br />Ca = 800 psf<br />Assume firm underlying soil<br />
- 18. γ= 117 pcf, Cs = 0 psf, Cw = 0 psf, H = 20.75 ft., Wh = 6.00 ft., φ = 34⁰, β = 0⁰<br />θ = 90⁰, φw = 34⁰ Pa = 6.51 Kips, α = 56.8⁰ <br />θ = 90⁰, φw = 0⁰ Pa = 7.12 Kips, α = 62.0⁰ (45 + φw/2)<br />θ = 71⁰, φw = 34⁰ Pa = 11.24 Kips, α =61.2⁰ <br />θ = 71⁰, φw = 0⁰ Pa = 10.84 Kips, α = 71.2⁰ <br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />6<br />
- 19. Failure Analysis: H/Wh = 3.4 <br />|e| ≤𝑏6 2.08 ft<br /> <br />The increase in Pa lead to a below acceptable FS for overturning.<br />The greater distance between the Pa vector and pt.O led to a below acceptable eccentricity. <br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />7<br />
- 20. Example Retaining Wall: Case 2<br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />8<br />γ1 = 117 pcfγconc = 150 pcf<br />φ1’ = 34⁰<br />δ’ = 18⁰<br />Ca = 800 psf<br />Assume firm underlying soil<br />
- 21. γ= 117 pcf, Cs = 0 psf, Cw = 0 psf, H = 20.75 ft., Wh = 20.75 ft., φ = 34⁰, β = 0⁰<br />θ = 90⁰, φw = 34⁰ Pa = 6.51 Kips, α = 56.8⁰ <br />θ = 90⁰, φw = 0⁰ Pa = 7.12 Kips, α = 62.0⁰ (45 + φw/2)<br />θ = 45⁰, φw = 34⁰ Pa = 29.03 Kips, α =57.2⁰ <br />θ = 45⁰, φw = 0⁰ Pa = 21.41 Kips, α = 84.50⁰ <br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />9<br />
- 22. Failure Analysis: H/Wh = 1.0<br />|e| ≤𝑏6 4.46 ft<br /> <br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />10<br />+58%<br />
- 23. Pa vs. α vs. θ<br />φw = 34⁰<br />Line of intersection<br />φw = 0⁰<br />Produced using Mathematica<br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />11<br />
- 24. Conclusion<br />The active force (Pa) depends on the angles θ, α, and φw found among the active wedge.<br />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.<br />As the angle θ decreases, the Pa will increase as well as the variance between the Pa calculated with and without wall friction.<br />Hard to openly predict the influence on the failure criteria<br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />12<br />
- 25. Is it worth consideration?<br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />13<br />Yes<br />
- 26. References<br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />14<br />Das, B.M., (2006). “Principles of Geotechnical Engineering – Sixth Edition”<br />Lambe, T.W., and R.V. Whitman, (1969). “Series in Soil Engineering - Soil Mechanics”<br />Mangano, Sal, (2010). “Mathematica Cookbook”<br />AutoCAD 2011® <br />Wolfram Mathematica®<br />

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