🎓 Lesson 19
D5
Crack Formation Mechanisms & Width Prediction Models
Cracks in concrete are tiny breaks that form when the material stretches too much or shrinks as it dries, and engineers predict how wide they’ll get to keep structures safe and usable.
🎯 Learning Objectives
- ✓ Calculate crack widths in flexural members using the Gergely–Lutz and Eurocode 2 models
- ✓ Analyze the influence of reinforcement spacing, cover depth, and bar diameter on crack width
- ✓ Explain the physical mechanisms driving early-age shrinkage versus load-induced cracking
- ✓ Apply ACI 224R-16 guidelines to evaluate whether predicted crack widths comply with exposure-based serviceability limits
- ✓ Design minimum reinforcement spacing and cover to satisfy maximum allowable crack width for aggressive environments
📖 Why This Matters
In reinforced concrete infrastructure—from tunnels and mine headframes to processing plant foundations—excessive cracking compromises durability by allowing water, chlorides, and sulfates to reach the steel. In mining contexts, this accelerates corrosion in wet, acidic, or saline environments (e.g., heap leach pads, tailings dams), leading to premature failure. Predicting crack width isn’t about strength—it’s about longevity: a 0.3 mm crack may be acceptable in dry office buildings but violates strict 0.15 mm limits for concrete exposed to sulfate-rich groundwater in underground mines.
📘 Core Principles
Crack formation occurs in three interdependent phases: (1) initiation—when local tensile strain exceeds concrete’s tensile capacity (~0.6√f′c MPa); (2) propagation—governed by bond-slip behavior and crack spacing governed by reinforcement distribution; and (3) stabilization—where crack width reaches equilibrium under sustained service load. Key drivers include restrained autogenous and drying shrinkage (up to 800 µε in high-strength mixes), thermal contraction, and flexural tension. Crucially, crack width is not determined by total strain—but by the *difference* in strain between steel and concrete at the crack location, amplified by the distance from the neutral axis and mitigated by reinforcement density and bond quality.
📐 Gergely–Lutz Empirical Model (ACI 224R-16)
The Gergely–Lutz model remains widely used for rapid serviceability checks. It relates crack width to steel stress, bar diameter, effective concrete area, and member geometry—emphasizing practical field variables over complex mechanics.
💡 Worked Example
Problem: A mine ventilation shaft wall (250 mm thick) uses Grade 420 MPa deformed bars (20 mm diameter) at 150 mm center-to-center spacing. Concrete cover = 40 mm. Service moment induces σₛ = 240 MPa in tension steel. f′c = 35 MPa. Calculate predicted crack width.
1.
Step 1: Compute effective depth d = thickness − cover − (bar dia/2) = 250 − 40 − 10 = 200 mm.
2.
Step 2: Compute effective tension area Aₑ = 2 × (cover + bar spacing/2) × thickness = 2 × (40 + 75) × 250 = 57,500 mm².
3.
Step 3: Apply Gergely–Lutz: w = (0.076 × β × σₛ × d × √(Aₑ / Nₛ)) / (fₛ × 10⁶), where β = 1.2 (one-way slab), Nₛ = number of bars per meter = 1000/150 ≈ 6.67, so Aₑ/Nₛ = 57,500/6.67 ≈ 8620 mm². Then w = (0.076 × 1.2 × 240 × 200 × √8620) / 10⁶ ≈ 0.21 mm.
4.
Step 4: Compare to ACI 224R-16 exposure class 'Severe' limit: 0.15 mm — result exceeds limit, requiring design revision (e.g., reduce spacing to 125 mm or use smaller-diameter bars).
Answer:
The predicted crack width is 0.21 mm, which exceeds the ACI-recommended 0.15 mm limit for severe exposure (e.g., underground mine environments with moisture and sulfates).
🏗️ Real-World Application
At the Red Chris Mine (British Columbia), a reinforced concrete launders system experienced accelerated corrosion after 3 years of operation. Forensic analysis revealed average crack widths of 0.28 mm—well above the 0.15 mm limit specified in CAN/CSA A23.3-19 for sulfate-exposed elements. Root cause was over-reliance on high-strength (f′c = 55 MPa) low-water-cement-ratio concrete without compensating for increased autogenous shrinkage—and insufficient confinement reinforcement. Post-remediation, designers adopted Eurocode 2’s ‘effective modulus’ approach with crack spacing control (sₘₐₓ ≤ 250 mm) and increased distribution steel (ϕ12@100 mm), reducing measured widths to <0.12 mm in pilot sections.