Figure 8.32 shows the general design equations given by AASHTO for MSE walls with a horizontal backslope and a traffic surcharge. Included is the calculation of safety factors for overturning and sliding, and the maximum base pressure. Inclusion of a traffic surcharge is required only in those instances where traffic loadings will actually surcharge the wall. Separate surcharge diagrams are applied for the two conditions shown. For stability of the mass, the traffic surcharge should act at the end of the reinforced zone so as to eliminate the “stabilizing” effect of this loading. However, for purposes of determining horizontal stresses, which are increased as a result of this surcharge, the loading is
Assumed for bearing capacity and overall (global) stability comps.
Assumed for overturning and sliding resistance comps.
FACTOR OF SAFETY AGAINST OVERTURNING (MOMENTS ABOUT POINT 0):
= S moments resisting (Mr) = V1 (L/2) 2 0
OT moments overturning (Mo) F1 (H/3) + F2 (H/2) _ .
FACTOR OF SAFETY AGAINST SLIDING:
Fs = S horizontal resisting force(s) = V1 (tan p or tan ф)* ___ 15 SL horizontal driving force(s) F1 + F2 _ ‘
ф = friction angle of reinforced backfill or foundation, whichever is lowest
where q = traffic live load
*tan p is for continuous soil reinforcement (e. g., grids and sheets).
For discontinuous soil reinforcements (e. g., strips) use tan ф. p is the soil/ reinforcement interface friction angle. Use the lower of tan at the base of the wall or tan p at the lowest reinforcement layer for continuous reinforcements.
Note: For relatively thick facing elements (e. g., segmental concrete facing blocks), it may be desirable to include the facing dimensions and weight in sliding and overturning calculations (i. e., use B in lieu of L).
FIGURE 8.32 General design requirements for MSE walls with horizontal backfill and traffic surcharge. (From Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials, Washington, D. C., 2002, with permission)
deemed to apply over the entire surface of the wall backfill. Figure 8.33a and b shows the AASHTO equations for the sloping backfill case and the broken backfill case.
While the conventional analysis of a mechanically stabilized earth wall assumes a rigid body, field evaluation has shown that the variation and magnitude of the foundation loading exerted by the wall on the underlying soil differ from the traditional trapezoidal
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FACTOR OF SAFETY AGAINST OVERTURNING (MOMENTS ABOUT POINT 0): |
Fg = X moments resisting (Mr) = V1 (L/2) + V2 (2L/3) + Fv (L) ^ ^
OT moments overturning (Mo) FH (h/3)
FACTOR OF SAFETY AGAINST SLIDING:
Fs = X horizontal resisting force(s) (V1 + V2 + Fv) (tan p or tan ф)*^
SL horizontal driving force(s) FH _ ‘
ф = friction angle of reinforced backfill or foundation, whichever is lowest
*tan p is for continuous soil reinforcements (e. g., grids and sheets).
For discontinuous soil reinforcements (e. g., strips) use tan ф. p is the soil/ reinforcement interface friction angle. Use the lower of tan at the base of the wall or tan p at the lowest reinforcement layer for continuous reinforcements.
Note: For relatively thick facing elements (e. g., segmental concrete facing blocks), it may be desirable to include the facing dimensions and weight in sliding and overturning calculations (i. e., use B in lieu of L).
FIGURE 8.33a General design requirements for MSE walls with sloping backfill.
(From Standard Specifications for Highway Bridges, 2002, American Association of State Highway and Transportation Officials, Washington, D. C., with permission)
Fv = Ft cos ( I )
For infinite slope I = p Ka for retained fill using 8 = p = I: sin2 (0 + ф’)
FACTOR OF SAFETY AGAINST OVERTURNING (MOMENTS ABOUT POINT 0): Fg 2 moments resisting (Mr) = V1 (L/2) + V2 (2L/3) + Fv (L) ^ 20
OT moments overturning (Mo) Fh (h/3)
FACTOR OF SAFETY AGAINST SLIDING:
Fs £ horizontal resisting force(s) = (V1 + V2 + Fv) (tan p or tan Ф)*^ 1 5 SL horizontal driving force(s) Fh _ ‘
ф = friction angle of reinforced backfill or foundation, whichever is lowest
*tan p is for continuous soil reinforcements (e. g., grids and sheets).
For discontinuous soil reinforcements (e. g., strips) use tan ф. p is the soil/ reinforcement interface friction angle. Use the lower of tan ф at the base of the wall or tan p at the lowest reinforcement layer for continuous reinforcements.
Note: For relatively thick facing elements (e. g., segmental concrete facing blocks), it may be desirable to include the facing dimensions and weight in sliding and overturning calculations (i. e., use B in lieu of L).
FIGURE 8.33b General requirements for MSE walls with broken backfill.
(From Standard Specifications for Highway Bridges, 2002, American Association of State Highway Officials, Washington, D. C., with permission)
pressure distribution assumed under reinforced-concrete cantilever walls. Tests were performed by placing pressure cells under the base of an MSE wall. The wall was the Fremersdorf wall constructed in Germany, which is depicted in Fig. 8.34 along with the bearing pressure recorded from the pressure cells. Tests on that structure demonstrated that loading is greater toward the front of the structure because of earth pressure imposed
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FIGURE 8.34 Fremersdorf MSE wall with foundation pressures from pressure cell readings. (From the Reinforced Earth Co., with permission) |
by the retained fill behind the wall. In addition, the total load was slightly greater than the total weight of the wall, indicating that the thrust behind the structure was inclined. The difference between total loading and weight, and the location of the resultant, made it possible to compute the thrust angle p.
The bearing pressure distribution from the Fremersdorf wall is idealized in the AASHTO equation for soil pressure (cv) shown in Fig. 8.35. A uniform pressure (Meyerhof distribution) is calculated over a width equal to the length of the soil reinforcement elements minus 2 times the eccentricity of the vertical force.
