🎓 Lesson 5
D3
Sliding Resistance: Base Friction & Keys
Sliding resistance is how much force it takes to make a retaining wall slide sideways along its base or across internal joints called keys.
🎯 Learning Objectives
- ✓ Calculate base sliding resistance using effective normal force and interface friction angle
- ✓ Design shear keys to contribute ≥30% of total sliding resistance where base friction alone is insufficient
- ✓ Analyze combined resistance from base friction and keyed interfaces under drained and undrained conditions
- ✓ Explain how key geometry (depth, width, spacing) influences mobilized passive resistance
- ✓ Apply Eurocode 7 and ASTM D4767 test data to select appropriate interface friction angles for rock–concrete and soil–concrete contacts
📖 Why This Matters
In mining infrastructure—such as high-wall retaining structures for open-pit benches or tailings dam abutments—sliding failure can trigger catastrophic slope collapse, equipment loss, and environmental harm. Unlike overturning, sliding often occurs without warning and with minimal deformation. Understanding and quantifying sliding resistance isn’t just theoretical: it directly dictates whether a wall needs costly deep foundations, grouted shear keys, or revised geometry—impacting schedule, budget, and safety compliance.
📘 Core Principles
Sliding resistance arises from two primary mechanisms: (1) Coulomb base friction, governed by the effective normal stress and the interface friction angle (δ), and (2) passive resistance mobilized by shear keys—recessed projections that engage the backfill or foundation material. The interface friction angle δ is not equal to the soil’s or rock’s internal friction angle φ; it is typically reduced (e.g., δ = 0.67φ for granular soils, δ = 0.5φ for intact rock) due to surface roughness mismatch and stress-level dependency. Keys act like miniature retaining walls: their resistance depends on embedment depth, key width, and the passive pressure coefficient Kp of the surrounding material. Combined resistance must be evaluated under both service (working) and ultimate (factored) limit states per geotechnical design codes.
📐 Total Sliding Resistance
The total sliding resistance R_total combines base friction (R_base) and key contribution (R_key). Base resistance follows Coulomb’s law; key resistance uses Rankine passive theory modified for finite embedment and shape effects. Both are summed vectorially when keys are oriented perpendicular to potential sliding direction.
💡 Worked Example
Problem: A concrete gravity retaining wall (unit weight = 24 kN/m³) has a 4 m wide base, 8 m height, and uniform surcharge q = 20 kPa. Foundation is weathered granite (c′ = 0, φ′ = 38°). Interface friction angle δ = 26°. A single centered shear key, 0.8 m deep and 0.4 m wide, is cast into bedrock. Assume Kp = tan²(45° + φ′/2) ≈ 3.85 and γ_r = 26 kN/m³.
1.
Step 1: Compute vertical load (W) = (wall volume × unit weight) + (surcharge × base width) = (4×8×24) + (20×4) = 768 + 80 = 848 kN/m
2.
Step 2: R_base = W × tanδ = 848 × tan(26°) ≈ 848 × 0.488 = 414 kN/m
3.
Step 3: R_key = 0.5 × γ_r × Kp × d² + c′ × d × Kp^(0.5) (simplified for c′=0) = 0.5 × 26 × 3.85 × (0.8)² = 0.5 × 26 × 3.85 × 0.64 ≈ 322 kN/m
4.
Step 4: Total R_total = R_base + R_key = 414 + 322 = 736 kN/m. Horizontal driving force H_active = 0.5 × γ_soil × K_a × H² ≈ 295 kN/m → FS_sliding = 736 / 295 ≈ 2.5 > 1.5 → acceptable.
Answer:
The total sliding resistance is 736 kN/m, yielding a factor of safety of 2.5—well above the minimum required 1.5 per ASCE 7-22 and Eurocode 7.
🏗️ Real-World Application
At the Bingham Canyon Mine (Utah, USA), a 2018 stability review of the north wall access road retaining structure identified marginal sliding safety (FS = 1.32) during seismic loading. Field testing revealed interface friction δ between precast concrete panels and fractured porphyry was only 22° (vs. assumed 28°). Remediation included installing three 1.2 m deep, 0.6 m wide grouted shear keys spaced at 3 m intervals—increasing R_total by 41% and raising FS to 1.9. Post-construction inclinometer and load-cell monitoring confirmed <0.3 mm lateral movement over 3 years—validating the key design.