MSE ramp: back-to-back reinforced soil walls calculator

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Worked example — results

• ✓ Sliding FS ≥ required at every station
• ✓ Eccentricity ≤ L/6
• ✓ Bearing FS ≥ required
• ✓ Pullout FS ≥ required in every layer
• ✓ Rupture: Tmax ≤ Ta in every layer
• ✓ Connection capacity adequate
• ✓ L ≥ 0.7H and ≥ minimum (or ≥ 0.6H when overlapped)

Method, formulas and assumptions

• Tallest wall height (ramp end) = 1.5+90*5/100 = 6 m
• Reinforcement length at tallest section = MAX(2.4,0.9*6) = 5.4 m
• Ka reinforced fill tan²(45 − φr/2) = TAN(RADIANS(45-34/2))^2 = 0.28271
• Ka retained fill = TAN(RADIANS(45-30/2))^2 = 0.33333
• Zinc life (15 µm/yr 2 yr, then 4 µm/yr) = IF(86<=30,86/15,2+(86-30)/4) = 16 yr
• Carbon steel loss per side (12 µm/yr after zinc) = MAX(0,100-16)*0.012 = 1.008 mm
• Bearing factor Nq = EXP(PI()*TAN(RADIANS(30)))*TAN(RADIANS(45+30/2))^2 = 18.401
• Bearing factor Nγ (Vesic) = 2*(18.401+1)*TAN(RADIANS(30)) = 22.402
• Allowable tensile capacity per element = CHOOSE(1,0.55*450*50*MAX(0,4-2*1.008)/1000,80/(1.15*1.6*1.1)/1.5,0.48*450*4*PI()*MAX(0,10-2*1.008)^2/4/1000) = 24.552 kN
• Minimum FS sliding along ramp = MIN([st.FSsl]) = 2.3733
• Max eccentricity / L = MAX([st.e])/5.4 = 0.056413
• Minimum FS bearing = MIN([st.FSbr]) = 7.2576
• Thrust factor at tallest section = MIN([st.tf]) = 0
• Layers at tallest section = COUNT([ly.z]) = 8
• Minimum FS pullout = MIN([ly.FSpo]) = 1.5004
• Max rupture utilisation = MAX([ly.Ur]) = 0.66192
• Max connection utilisation = MAX([ly.Uc]) = 0.66192
• Strip thickness at end of life = MAX(0,4-2*1.008) = 1.984 mm
• Reinforcement quantity per m of ramp (both walls) = 2*8*5.4*CHOOSE(1,1/0.5,1,1/0.5) = 172.8 m
• Global stability is not computed here: run a slip-circle analysis (e.g. the Bishop slope tool) through the reinforced mass and foundation, especially on soft ground.
• Back-to-back interaction (FHWA-NHI-10-024 §4.3.8): D = W − 2L. D ≥ H tan(45 − φb/2) → independent walls (full thrust); overlap ≥ 0.3H → no thrust from the core; between, thrust is interpolated linearly here (an interpretation, verify for the project).
• Steel strips: Kr/Ka 1.7 → 1.2 over 6 m; welded mesh 2.5 → 1.2; geogrid 1.0. Coherent-gravity active zone for inextensible reinforcement, Rankine for geogrid.
• Corrosion: FHWA rates (zinc 15 µm/yr for 2 yr then 4 µm/yr; carbon steel 12 µm/yr per side). Rupture ASD 0.55Fy (strips), 0.48Fy (mesh), geogrid Tult/ΠRF/1.5.

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