Retaining Walls

Retaining walls hold back soil where ground levels change. Learn wall types, lateral earth pressure (at-rest, active, passive), Rankine and Coulomb theories, surcharge and water pressure, and stability checks for overturning, sliding and bearing.

Roads cut into hillsides, basements, bridge abutments and terraced gardens all need walls that resist the sideways push of soil. That lateral pressure grows with depth — and doubles or triples if water builds up behind the wall.

Designing a retaining wall means estimating the earth pressure, then making sure the wall doesn't overturn, slide or overload its foundation.

An analogy

Leaning a board against a pile of sand: the sand pushes the board outward, harder at the bottom. If you let the board move slightly, the push decreases (active); if you shove the board into the sand, resistance increases (passive).

Wall types

Gravity (mass concrete, masonry, gabions), cantilever RC (L or inverted-T), counterfort, reinforced soil (geogrid/strip-reinforced), sheet piles, embedded contiguous/secant pile and diaphragm walls (basements), and anchored walls.

Earth pressure states

At rest (no movement) K₀; active (wall moves away slightly, ~0.1 % of height) K_a — minimum; passive (wall pushed into soil) K_p — maximum. For φ = 30°: K_a = 1/3, K₀ = 0.5, K_p = 3.

Water and drainage

Water behind a wall adds full hydrostatic pressure (γ_w = 9.81) and reduces effective soil pressure only slightly — total thrust can double. Weep holes, drainage blankets and perforated pipes are essential; many wall failures are drainage failures.

Coulomb, seismic and global stability

Coulomb's wedge theory includes wall friction and sloping backfill. Mononobe–Okabe adds seismic thrust. Besides overturning, sliding and bearing, check global (deep-seated) stability of the whole slope and structural design of stem and base (bending, shear).

Formulas

• Rankine coefficients: K_a = (1 − sin φ)/(1 + sin φ), K_p = 1/K_a, K₀ ≈ 1 − sin φ
• Active thrust: P_a = ½ K_a γ H² (at H/3) + K_a q H (at H/2)
• Overturning: FS_o = ΣM_resisting / ΣM_overturning ≥ 2
• Sliding: FS_s = μ ΣV (+ passive) / ΣH ≥ 1.5
• Base pressure: q = (ΣV/B)(1 ± 6e/B)

Worked example: Active thrust

Given: H = 5 m, γ = 18 kN/m³, φ = 30°, dry; Surcharge 10 kPa

Find: K_a and thrust components.

• K_a = (1 − 0.5)/(1 + 0.5) = 1/3
• Soil: ½ × ⅓ × 18 × 25 = 75 kN/m at 1.67 m
• Surcharge: ⅓ × 10 × 5 = 16.7 kN/m at 2.5 m

Answer: 91.7 kN/m total

Worked example: Stability of a gravity wall

Given: Soil thrust 75 kN/m at 1.67 m; Wall weight 200 kN/m acting 1.5 m from toe; μ = 0.5

Find: FS against sliding and overturning.

• FS_s = 0.5 × 200/75 = 1.33 < 1.5 ✗
• FS_o = 200 × 1.5/(75 × 1.667) = 2.4 ✓

Answer: Sliding fails — add a shear key or widen the base

Common mistakes

• Wrong: Omitting drainage behind the wall. — Right: Provide free-draining backfill and weep holes, or design for full water pressure.
• Wrong: Using active pressure for walls that can't move (basements, propped). — Right: Use at-rest K₀ for rigid, restrained walls.

Applications

• Highways & railways: Cutting and embankment walls, reinforced-earth abutments.
• Basements: Diaphragm and secant pile walls propped by floors.
• Landscaping & ports: Gabions, crib walls and quay walls.

Key takeaways

• K_a < K₀ < K_p; Rankine for simple cases.
• P_a = ½K_aγH² at H/3 (+ surcharge K_aqH).
• Check overturning (≥ 2), sliding (≥ 1.5), bearing.
• Drainage is critical.

Going further

• Reinforced soil: Geogrids create a composite gravity mass — economical for tall walls and abutments.
• Anchored & propped walls: Ground anchors or struts allow thin embedded walls for deep excavations.
• Seismic earth pressure: Mononobe–Okabe increases active thrust by horizontal and vertical seismic coefficients.