🎓 Lesson 28
D5
Post-Tensioning Fundamentals: Bonded vs Unbonded Systems
Post-tensioning is a method of strengthening concrete by pulling steel tendons tight after the concrete has hardened, like tightening ropes inside a solid block to hold it together under load.
🎯 Learning Objectives
- ✓ Explain the mechanical differences between bonded and unbonded post-tensioning systems using stress-transfer mechanisms
- ✓ Analyze tendon layout and anchorage configurations to identify failure modes (e.g., bond loss, anchorage pullout, duct corrosion)
- ✓ Design minimum grout fill and duct size for a bonded system per ACI 423.1 requirements
- ✓ Calculate effective prestress force loss due to friction and anchorage set for an unbonded tendon using the AASHTO LRFD equation
📖 Why This Matters
In underground mine infrastructure—such as shaft linings, stopes, and portal structures—post-tensioned concrete resists high ground pressures, seismic loading, and long-term creep. Choosing between bonded and unbonded systems directly impacts durability in aggressive, wet, sulfide-rich environments; a single corrosion-induced tendon failure can compromise structural integrity without warning. Understanding this distinction isn’t academic—it’s critical for life-cycle safety and inspection planning.
📘 Core Principles
Prestress is introduced via hydraulic jacks applying force to tendons anchored at ends or within the member. In bonded systems, grout bonds tendons to concrete, enabling load redistribution, crack control, and redundancy—if one tendon fails, adjacent tendons share the load. Unbonded systems rely solely on end-anchorage; tendons act independently, simplifying installation and field adjustments but eliminating composite action and increasing vulnerability to localized anchor damage. Key distinctions include: (1) load transfer mechanism (bond vs. anchorage), (2) behavior under fire/corrosion (bonded offers thermal protection and passive corrosion resistance via grout alkalinity; unbonded requires robust sheathing integrity), and (3) code-mandated redundancy—ACI 423.1 requires ≥3 bonded tendons per zone for critical structures, whereas unbonded systems require full anchorage redundancy per tendon.
📐 Friction Loss in Unbonded Tendons
Friction loss (Δfₚₜ) reduces effective prestress along the tendon length due to curvature and wobble. It’s calculated using the AASHTO LRFD ‘wobble + curvature’ model, essential for verifying minimum jacking force and residual stress at critical sections.
AASHTO LRFD Friction Loss
Δfₚₜ = fₛₑ [1 − e^(−(μθ + kL))]Calculates prestress loss due to duct friction during stressing of unbonded tendons.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| Δfₚₜ | Friction-induced prestress loss | MPa | Reduction in tendon stress from friction along duct length |
| fₛₑ | Initial jacking stress | MPa | Stress applied at jack before losses |
| μ | Curvature friction coefficient | rad⁻¹ | Depends on tendon/sheath interface (0.15–0.25 for greased HDPE) |
| θ | Total angular deviation | radians | Sum of all duct curvature angles along tendon path |
| k | Wobble coefficient | m⁻¹ | Accounts for unintentional duct misalignment (0.0015–0.0035 /m) |
| L | Tendon length | m | Length over which friction acts |
Typical Ranges:
Underground mine shaft lining: 0.0020 – 0.0030 /m
HDPE-sheathed monostrand: 0.15 – 0.20 rad⁻¹
💡 Worked Example
Problem: An unbonded tendon is stressed through a 25 m curved duct with 3.5° total deviation (0.0611 rad) and a wobble coefficient k = 0.0025 /m. Initial jacking stress fₛₑ = 1,300 MPa. Calculate friction loss Δfₚₜ.
1.
Step 1: Identify parameters — μ = 0.18 (typical greased tendon in HDPE sheath), k = 0.0025 /m, θ = 0.0611 rad, L = 25 m
2.
Step 2: Apply formula Δfₚₜ = fₛₑ [1 − e^(−(μθ + kL))] = 1300 × [1 − e^(−(0.18×0.0611 + 0.0025×25))]
3.
Step 3: Compute exponent: (0.0110 + 0.0625) = 0.0735 → e^(−0.0735) = 0.929 → Δfₚₜ = 1300 × (1 − 0.929) = 92.3 MPa
Answer:
The friction loss is 92.3 MPa, representing a 7.1% reduction — within acceptable limits (<10%) per ACI 423.1 Section 6.4.2.
🏗️ Real-World Application
At the Boliden Garpenberg Mine (Sweden), a 42-m-deep ventilation shaft lining used bonded post-tensioning with 12.7 mm strand tendons in 70 mm diameter galvanized ducts, grouted with ASTM C1157 Type GU cementitious grout (water-cement ratio = 0.38). Grout fill was verified via ultrasonic pulse velocity (UPV) testing (>4,200 m/s), confirming 98% void-free fill. In contrast, the Rio Tinto Yandi ore pass collar used unbonded monostrand tendons with polyethylene-sheathed, lithium-greased 15.2 mm strands — chosen for rapid installation in confined space and ease of future re-stressing during operational life extension.