🎓 Lesson 2
D2
Triaxial & Direct Shear Lab Interpretation
Triaxial and direct shear tests measure how much force it takes to make soil or rock slide along a plane when squeezed from different directions.
🎯 Learning Objectives
- ✓ Explain the physical meaning and engineering significance of Mohr-Coulomb failure envelope parameters (c′ and φ′)
- ✓ Analyze triaxial test results to calculate effective cohesion and friction angle using graphical or regression methods
- ✓ Compare direct shear and triaxial test outputs to select the appropriate test method for specific geotechnical conditions
- ✓ Apply shear strength parameters to assess factor of safety in simple infinite slope models
📖 Why This Matters
In open-pit mines and waste dumps, slope failures can halt production, endanger lives, and trigger environmental disasters. Understanding *how much* shear stress soil or weak rock can resist — not just its weight — is what separates stable designs from catastrophic slides. Triaxial and direct shear tests provide the foundational strength data used in every slope stability model, from hand calculations to 3D numerical simulations. Without accurate c′ and φ′, your design is guesswork — not engineering.
📘 Core Principles
Soil and rock fail when shear stress on a plane exceeds their shear strength — a function of normal stress acting on that plane. The Mohr-Coulomb model expresses this as τ_f = c′ + σ′_n tan φ′, where τ_f is shear strength, σ′_n is effective normal stress, c′ is effective cohesion, and φ′ is effective friction angle. Triaxial testing controls both confining (lateral) and deviatoric (axial) stresses, simulating in-situ stress states and allowing full stress path analysis — including pore water pressure measurement for saturated conditions. Direct shear testing fixes the failure plane and is simpler/faster but imposes artificial boundary constraints, often overestimating φ′ and underestimating c′ for cohesive soils. For blasting-adjacent slopes (e.g., pit walls, berms), triaxial data is preferred because blast-induced pore pressure changes and stress redistribution demand effective stress analysis.
📐 Mohr-Coulomb Failure Envelope (from Triaxial Data)
The effective stress shear strength parameters c′ and φ′ are derived by plotting Mohr’s circles at failure for ≥3 triaxial tests at different confining pressures (σ′₃), then drawing the common tangent — the failure envelope. Its intercept is c′; its slope is tan φ′.
💡 Worked Example
Problem: Three consolidated-drained (CD) triaxial tests on weathered shale yield: Test 1: σ′₃ = 50 kPa, σ′₁ = 182 kPa; Test 2: σ′₃ = 100 kPa, σ′₁ = 294 kPa; Test 3: σ′₃ = 200 kPa, σ′₁ = 518 kPa. Calculate c′ and φ′.
1.
Step 1: Compute principal stresses: σ′₁ and σ′₃ are given; compute center (C) and radius (R) of each Mohr circle: C = (σ′₁ + σ′₃)/2, R = (σ′₁ − σ′₃)/2.
2.
Step 2: Determine coordinates of failure points (σ′_n, τ_f): σ′_n = C + R·cos(2θ), τ_f = R·sin(2θ), where θ = 45° + φ′/2 — but instead, use the standard method: τ_f = (σ′₁ − σ′₃)/2, σ′_n = (σ′₁ + σ′₃)/2.
3.
Step 3: Plot (σ′_n, τ_f) points: (116, 66), (197, 97), (359, 159); perform linear regression → τ_f = 0.577σ′_n + 12.3 → c′ = 12.3 kPa, φ′ = arctan(0.577) ≈ 30°.
Answer:
The result is c′ = 12.3 kPa and φ′ = 30°, which falls within the typical range for weathered shale (c′ = 5–25 kPa; φ′ = 25°–35°).
🏗️ Real-World Application
At the Bingham Canyon Mine (Utah), slope stability analyses for the northeast wall relied on triaxial CD and CU test data from interbedded shales and siltstones. When monitoring revealed accelerating creep displacement, engineers re-evaluated c′ and φ′ using back-analysis of historic slide events — revealing that φ′ dropped from 32° to 27° under sustained high pore pressures. This 5° reduction reduced calculated factor of safety from 1.32 to 1.09, triggering immediate bench reinforcement and dewatering — preventing a potential 20-million-ton landslide. Direct shear tests had previously overestimated φ′ by 4–6° due to forced planar failure, underscoring why triaxial data was mandated for final design.
🔧 Interactive Calculator
🔧 Open Slope Stability & Landslide Risk Calculator📋 Case Connection
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Multiple deep-seated rockslides blocking critical transport corridor; unstable toe conditions and high pore pressures
📋 Tailings Storage Facility (TSF) Slope Reinforcement — Pilbara, Australia
Existing FoS < 1.1 under Mw 6.5 scenario; limited space for buttressing; strict environmental containment requirements
📋 Historic Landslide Reactivation Mitigation — Portuguese Riviera
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