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Modeling of the Active Wedge behind a Gravity Retaining Wall<br />By: Rex Radloff<br />14.531 Advanced Soil Mechanics<br /...
Rankine Active Wedge<br /><ul><li>Wall friction is neglected
Active force acts 1/3H from the base
Front face angle (θ) is 90⁰
Overburden slope (β) is 0⁰
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...
What are its effects on the failure criteria?
To what degree?</li></ul>Rankine stress distribution behind a gravity retaining wall.<br />University of Massachusetts Low...
Active Wedge with Reactions<br />W<br />Note:<br />The weight and centroid of the active wedge is a function of H, Wh, WBs...
Modeling the Active Wedge<br />Known<br />Wall dimensions and materials.<br />Soil and wall shear strength parameters.<br ...
Angle α of the back face of the active wedge.
Active force, Pa, that is produced by the active wedge.
The location of the Pa resultant.
FS against overturning and sliding.
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Active Wedge Behind A Gravity Retaining Wall Complete 2011

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Transcript of "Active Wedge Behind A Gravity Retaining Wall Complete 2011"

  1. 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. 2. Rankine Active Wedge<br /><ul><li>Wall friction is neglected
  3. 3. Active force acts 1/3H from the base
  4. 4. Front face angle (θ) is 90⁰
  5. 5. Overburden slope (β) is 0⁰
  6. 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. 7. What are its effects on the failure criteria?
  8. 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. 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. 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. 11. Angle α of the back face of the active wedge.
  12. 12. Active force, Pa, that is produced by the active wedge.
  13. 13. The location of the Pa resultant.
  14. 14. FS against overturning and sliding.
  15. 15. Eccentricity
  16. 16. Maximum stress, qMAX underneath the foundation.</li></ul>University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />4<br />
  17. 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. 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. 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. 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. 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. 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. 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. 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. 25. Is it worth consideration?<br />University of Massachusetts Lowell 14.531 Advanced Soil Mechanics<br />13<br />Yes<br />
  26. 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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