🎓 Lesson 21
D5
Diagnosing Overturning vs. Sliding Failures
Overturning failure happens when a retaining wall tips over like a seesaw, while sliding failure occurs when it slides sideways along its base—like pushing a book across a table.
🎯 Learning Objectives
- ✓ Calculate the factor of safety against overturning using moment equilibrium
- ✓ Analyze the factor of safety against sliding using Coulomb’s base resistance model
- ✓ Explain how wall geometry, backfill properties, and foundation conditions differentially influence overturning vs. sliding susceptibility
- ✓ Apply surcharge and water pressure corrections to both stability calculations
- ✓ Design a minimum base width to satisfy both FS ≥ 1.5 for overturning and FS ≥ 1.3 for sliding per ASCE 7-22
📖 Why This Matters
In mining infrastructure—such as waste rock berms, tailings dam abutments, or highwall support walls—a misdiagnosis of failure mode can lead to catastrophic under-design. Overdesigning for sliding while ignoring overturning risks toppling during seismic loading; conversely, over-reinforcing against overturning may neglect drainage-induced base weakening that triggers sliding. Accurate forensic distinction saves lives, avoids regulatory penalties, and prevents $10M+ remediation costs—making this not just academic, but operational criticality.
📘 Core Principles
Stability analysis hinges on comparing driving and resisting actions. For overturning, we evaluate moments about the toe: resisting moment comes from wall weight (W), heel backfill weight, and any passive resistance at the toe; driving moment arises from active earth pressure (P_a), surcharges, and hydrostatic pressure. For sliding, we compare horizontal driving forces (P_a + surcharge component + water thrust) to base resistance: R = W·tan(δ) + c_b·B, where δ is base friction angle, c_b is base cohesion, and B is base width. Crucially, overturning governs in tall, narrow walls with low base friction; sliding dominates in shallow, saturated, or smooth-foundation scenarios—even if the wall appears stocky. Interface degradation (e.g., clay smear, frost heave, or geosynthetic slippage) disproportionately reduces sliding resistance, whereas overturning is more sensitive to eccentricity and moment arm length.
📐 Key Calculations: FS_overturning & FS_sliding
Two independent factors of safety must be computed: one for rotation about the toe, one for translation along the base. Both require consistent load modeling—including effective stress for submerged conditions and appropriate earth pressure coefficients (K_a, K_p).
Factor of Safety Against Overturning
FS_{ov} = \frac{\sum M_{resisting}}{\sum M_{driving}}Ratio of stabilizing moments about the toe to destabilizing moments about the toe.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| M_{resisting} | Resisting moment | kN·m/m | Sum of moments from wall self-weight, heel backfill, and passive resistance (if applicable) |
| M_{driving} | Driving moment | kN·m/m | Sum of moments from active earth pressure, surcharge, hydrostatic pressure, and seismic forces |
Typical Ranges:
Static design (mining berms): 1.5 – 2.5
Seismic design (Mw ≥ 6.0): 1.1 – 1.3
💡 Worked Example
Problem: A cantilever concrete retaining wall (γ_conc = 24 kN/m³) has H = 6 m height, base width B = 2.8 m, stem thickness = 0.4 m, heel length = 2.0 m, toe length = 0.4 m. Backfill: γ_soil = 18 kN/m³, φ' = 32°, c' = 0. Groundwater is at grade. Calculate FS_overturning and FS_sliding.
1.
Step 1: Compute K_a = tan²(45° − φ'/2) = tan²(45 − 16) = 0.307
2.
Step 2: Active force P_a = 0.5·K_a·γ_soil·H² = 0.5 × 0.307 × 18 × 6² = 99.5 kN/m, acting at H/3 = 2 m above base.
3.
Step 3: Wall weight components: stem = 24 × 0.4 × 6 = 57.6 kN/m; heel slab = 24 × 2.0 × 0.6 = 28.8 kN/m; backfill over heel = 18 × 2.0 × 6 = 216 kN/m → total W = 302.4 kN/m. Resisting moment = Σ(W_i × x_i) = (57.6×0.2) + (28.8×1.2) + (216×1.8) = 432.5 kN·m/m.
4.
Step 4: Driving moment = P_a × (H/3) = 99.5 × 2 = 199.0 kN·m/m → FS_ov = 432.5 / 199.0 = 2.17.
5.
Step 5: For sliding: base resistance R = W·tan(δ) + c_b·B. Assume δ = 2/3φ' = 21.3°, c_b = 0 → R = 302.4 × tan(21.3°) = 117.5 kN/m. FS_sl = R / P_a = 117.5 / 99.5 = 1.18 < 1.3 → FAILS sliding check.
Answer:
FS_overturning = 2.17 (>1.5 OK); FS_sliding = 1.18 (<1.3 NOT OK). Design requires either keying, toe reinforcement, or drainage to reduce P_a.
🏗️ Real-World Application
At the Mount Polley Mine tailings storage facility (British Columbia, 2014), post-failure forensic analysis revealed that the breach initiated as a sliding failure along a weak, saturated glaciolacustrine clay layer beneath the north embankment—not overturning. Despite adequate global overturning FS (>2.0), undrained base cohesion was overestimated and pore pressures underestimated. The slide occurred at low mobilized friction (δ ≈ 8°), triggering rapid lateral displacement. This case is now cited in CDA Bulletin 2015-1 and underscores why sliding checks must use *measured* interface parameters—not assumed values—and why piezometer data is non-negotiable in forensic stability review.
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Catastrophic collapse of 8.5 m cantilever wall after 100-year flood event