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Active Wedge Behind A Gravity Retaining Wall Complete 2011
 

Active Wedge Behind A Gravity Retaining Wall Complete 2011

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    Active Wedge Behind A Gravity Retaining Wall Complete 2011 Active Wedge Behind A Gravity Retaining Wall Complete 2011 Presentation Transcript

    • 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 Active Wedge
      • 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
      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?
      • What are its effects on the failure criteria?
      • To what degree?
      Rankine stress distribution behind a gravity retaining wall.
      University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
      2
    • 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
    • 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.
      • 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.
      • Eccentricity
      • Maximum stress, qMAX underneath the foundation.
      University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
      4
    • Example Retaining Wall: Case 1
      University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
      5
      γ1 = 117 pcfγconc = 150 pcf
      φ1’ = 34⁰
      δ’ = 18⁰
      Ca = 800 psf
      Assume firm underlying soil
    • 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
      6
    • 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
      7
    • 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
    • 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
      9
    • Failure Analysis: H/Wh = 1.0
      |e| ≤𝑏6 4.46 ft
       
      University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
      10
      +58%
    • 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
    • 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
    • Is it worth consideration?
      University of Massachusetts Lowell 14.531 Advanced Soil Mechanics
      13
      Yes
    • 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®