Cantilever RC Retaining Wall — Design & Independent Validation

What this spreadsheet does

This workbook is the complete structural design of a cantilever reinforced-concrete retaining wall for a site labelled “Thapar, Derabassi” (India). It runs the full workflow across three sheets:

1. STABILITY CHECKS — geometry, soil and material data; earth-pressure coefficients; self-weights; then the rigid-body checks for bearing pressure / eccentricity, overturning and sliding.
2. DESIGN STEM — the vertical wall as a cantilever: factored base moment, depth check, main flexural steel, distribution steel and outer-face steel.
3. DESIGN TOE & HEEL SLAB — the base slab (the toe length works out to zero, so this is effectively the heel slab), plus a supplementary under-reamed pile scheme in case the founding soil erodes.

Key inputs

• Retained height = 1.65 m; angle of repose φ = 30°; γ_soil = 18 kN/m³
• Safe bearing capacity = 170 kN/m²
• Concrete M25, steel Fe500
• Base 1.5 m wide × 0.275 m thick; stem 0.23 m; heel 1.27 m
• Load factor 1.5 on service moments

Codes of practice followed

• IS 456:2000 — limit-state RC design; stem uses the limiting-moment factor 0.138·f_ck·b·d² for Fe500, and 0.12% minimum steel for HYSD bars.
• SP-16 (Design Aids for RC to IS 456) — required steel percentages read from the tables.
• Rankine earth-pressure theory (sloped-surcharge form) — K_a = 0.333, K_p = 3.
• IS 2911 (Part 3) — under-reamed pile capacities (Table 1).

Independent validation

Every governing figure was recomputed from the raw inputs in an independent engine. All stored results reproduce exactly, with no formula errors (#REF/#VALUE) and a number chain that ties out end to end.

This proves the arithmetic and formula wiring are internally consistent and error-free. It does not by itself prove the engineering method is correct — the four points below are methodology observations for an engineer to confirm.

Engineering observations (not spreadsheet errors)

1. Overturning resisting moment. M_r is taken as W·(B−Z), but Z already contains the active-thrust overturning moment, so overturning is effectively subtracted from the resisting side. The pure resisting moment is 52.7 kNm, giving FoS ≈ 3.13 rather than 2.23. The result is conservative, so the “Pass” still holds, but it is not the textbook formula.
2. Stem moment credits passive pressure. The stem base moment subtracts a passive (K_p) term of about 2.2 kNm, which reduces the design moment (unconservative) and contradicts the stability sheet, which states that passive earth pressure is not considered.
3. Minimum steel. Stem main bars 10 mm @ 300 give ≈262 mm² against a 0.12% minimum of 276 mm²; stem distribution 8 mm @ 250 (≈201 mm²) is below the 276 mm² required. Both fall marginally short of the IS 456 minimums as written.
4. Toe length = 0. B − heel − stem = 1.5 − 1.27 − 0.23 = 0, so the wall has no toe projection and the “toe & heel” sheet is really just the heel. Worth confirming this is intended.

Summary: the workbook computes cleanly and passes all stability and design checks; the four items above are method choices worth an engineer’s review before issue.