Design of reinforced concrete cantilever retaining walls per Turkish standards: Rankine earth pressure theory, active and passive pressure coefficients, global stability checks (sliding, overturning, bearing capacity), reinforced concrete design of the stem and base slab per TS 500, drainage requirements, and seismic earth pressure per TSC 2018 §16 using the Mononobe-Okabe method. Complete worked example for a 3.5 m retaining wall.
Turkish practice for retaining wall design follows classical Rankine or Coulomb earth pressure theory as referenced in ZTA 2020 and consistent with TS EN 1997-1. For cantilever retaining walls of moderate height (H < 6–8 m), Rankine theory with a smooth wall assumption is standard. Coulomb theory with wall friction δ is used for gravity walls or when the wall-backfill interface angle significantly deviates from vertical.
Rankine active pressure acts on a vertical plane through the heel of the footing. The theoretical mechanism assumes the soil mass slides as a rigid block along a failure plane at angle (45° + φ/2) from horizontal.
| φ (°) | Ka | Kp | Typical Soil |
|---|---|---|---|
| 20° | 0.490 | 2.04 | Soft clay, loose fill |
| 25° | 0.406 | 2.46 | Silty sand, medium clay |
| 30° | 0.333 | 3.00 | Medium dense sand (typical) |
| 35° | 0.271 | 3.69 | Dense sand, gravel |
| 40° | 0.217 | 4.60 | Dense gravel |
All stability checks are carried out with characteristic (unfactored) loads per ZTA 2020 and compared against minimum factors of safety (FGS). Factored loads are used only for structural RC design.
Stabilizing moments: weight of wall stem (Ws), base slab (Wb), soil over heel (Wsoil), and surcharge over heel, each multiplied by their lever arm to the toe. Overturning moments: Pa·H/3 (triangular pressure resultant) + surcharge pressure × H/2 (uniform pressure), measured from the toe.
Where ΣV = total vertical force (wall + soil); tanδbase = friction coefficient at base = tanφ·(2/3) for concrete-on-soil ≈ 0.45–0.55; cbase = base adhesion ≈ c/2; Pp = passive resistance (use 50% as noted above). If FGS < 1.5, add a shear key under the footing base — the key forces the failure plane deeper into the soil where passive resistance is higher.
If e > B/6 (resultant outside kern), the Meyerhof reduced-base width B' = B − 2e applies and qmax = 2·ΣV/(3·(B/2 − e)). Avoid e > B/6 whenever possible — it indicates an unstable, rocking wall.
The stem acts as a vertical cantilever fixed at the base. The critical section for design moment is at the base of the stem (top of the footing). Factored pressures: the active earth pressure diagram is multiplied by load factor 1.6 for the earth pressure load (treated as a variable action per TS 498 loading combinations).
The required tension reinforcement is on the back face (soil side). Use the flexural design procedure from TS 500 §8 with fcd = fck/1.5 and fyd = fyk/1.15. The stem typically tapers: wider at base (tbase ≈ H/12 to H/10) narrowing to 200–250 mm at top. Shear is carried by concrete alone for typical wall heights; shear reinforcement only if Vd > Vcr = 0.65·fctd·b·d.
The toe and heel portions of the base slab are designed as cantilevers. The net upward pressure (soil reaction minus slab self-weight) is the factored load for the heel; the net downward pressure (soil weight over heel minus soil reaction) governs the toe.
Hydrostatic pressure behind a retaining wall can double or triple the total earth pressure force. Turkish building practice and ZTA 2020 §9.3 require adequate drainage of the retained soil mass for all permanent retaining walls.
TSC 2018 §16 adopts the Mononobe-Okabe (M-O) method for seismic earth pressure on retaining walls. The total active thrust (static + dynamic increment) replaces the static active thrust in stability checks under seismic loading combinations.
The factor r depends on the consequence class of the retaining structure (Table 16.7): r = 0.5 for walls that can undergo some outward movement without causing damage to structures above; r = 1.0 for critical walls (near buildings, on transportation routes) that must maintain displacement limits. For most freestanding retaining walls in Turkey, r = 0.5 is used unless there are structures close to the top of the wall.
The dynamic increment ΔPAE = PAE − PA (seismic total minus static) is assumed to act at 0.6H from the base (higher than the static resultant at H/3), reflecting the concentrated dynamic pressure near the top during earthquake shaking.
| Aspect | Turkey (ZTA 2020 / TS 500) | Eurocode (EN 1997-1) | US (ASCE 7 / LRFD) |
|---|---|---|---|
| Overturning FOS | 1.5 (static) | Moment equilibrium via partial factors (DA1/DA2) | FOS ≥ 1.5 (ASD) |
| Sliding FOS | 1.5 (static) | Resistance / Action ≥ 1.0 (DA1) | FOS ≥ 1.5 (ASD) |
| Passive resistance | 50% of Rankine Kp | Reduced by γφ = 1.25 on tanφ | 50% of Rankine (AASHTO) |
| Seismic method | Mononobe-Okabe (TSC §16) | EN 1998-5 Annex E (M-O) | Mononobe-Okabe (AASHTO) |
| Seismic kh | 0.4·r·SDS | S1·r from EN 1998-5 §7 | 0.5·PGA / g (AASHTO) |
| Drainage requirement | Explicit (ZTA §9.3) | Explicit (EN 1997 §9.4.3) | Explicit (AASHTO §11.6) |
| RC design code | TS 500 (LSD) | EN 1992-1-1 (LSD) | ACI 318 (LRFD) |
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