🎓 Lesson 12
D4
Working Stress Design vs. LRFD: When to Use Which?
Working Stress Design (WSD) checks if stresses in a foundation stay safely below material limits, while Load and Resistance Factor Design (LRFD) uses separate safety factors for loads and strength to better account for real-world uncertainties.
🎯 Learning Objectives
- ✓ Explain the fundamental philosophical difference between WSD and LRFD using load–capacity interaction diagrams
- ✓ Calculate factored load combinations and factored bearing capacity for a shallow foundation using AASHTO LRFD 2023 provisions
- ✓ Analyze and compare safety margins (FS vs. reliability index β) for identical foundation geometries under WSD and LRFD
- ✓ Apply resistance factors (φ) for soil bearing capacity based on site investigation quality and testing method
- ✓ Design a square spread footing using both WSD and LRFD approaches and justify which is appropriate for a given project risk profile
📖 Why This Matters
Choosing between WSD and LRFD isn’t just academic—it affects cost, schedule, safety, and regulatory compliance. In mining infrastructure (e.g., crusher pad foundations, conveyor tower footings), misapplying WSD where LRFD is required can lead to non-compliance with MSHA or state DOT standards—and worse, unrecognized vulnerability to extreme loading (e.g., seismic aftershocks or saturated clay swelling). Conversely, overusing LRFD on small, low-risk exploration drill pads adds unnecessary complexity and cost. This lesson equips you to select the right design philosophy *before* you calculate the first bearing pressure.
📘 Core Principles
WSD assumes linear-elastic behavior and treats all uncertainties with one conservative factor—e.g., allowable bearing pressure q_allow = q_ult / FS, where FS = 2.5–3.0 for shallow foundations. It’s intuitive and widely used in legacy mine site designs, but doesn’t differentiate between uncertainty in dead load (low variability) and live or blast-induced dynamic loads (high variability). LRFD separates these: γ_D × D + γ_L × L ≤ φ × R_n, where γ_D ≈ 1.25, γ_L ≈ 1.75, and φ for cohesionless soil bearing capacity ranges from 0.45 (SPT-only) to 0.65 (high-quality CPT + load test). This reflects statistical calibration—LRFD targets a target reliability index (β ≈ 3.5) equivalent to ~99.98% confidence against failure, whereas WSD’s FS = 3.0 implies only ~95% confidence in many geotechnical contexts.
📐 Factored Bearing Capacity Check (LRFD)
The governing limit state equation for ultimate bearing capacity under LRFD requires that the factored load effect does not exceed the factored resistance: Σ(γ_i × Q_i) ≤ φ × q_ult,n. Here, q_ult,n is the nominal ultimate bearing capacity computed via Terzaghi or Vesic, and φ depends on soil type, test method, and data quality.
💡 Worked Example
Problem: A square spread footing (B = 2.5 m) on dense sand (ϕ' = 36°, γ = 18.5 kN/m³, c' = 0) supports a column with nominal dead load D = 850 kN and nominal live load L = 320 kN. Use AASHTO LRFD 2023: γ_D = 1.25, γ_L = 1.75, φ = 0.55 (SPT-based). Compute nominal q_ult,n using Vesic (N_q = 56.3, N_γ = 62.8) and verify the design.
1.
Step 1: Compute nominal ultimate bearing capacity: q_ult,n = c'N_c s_c d_c i_c + qN_q s_q d_q i_q + 0.5γBN_γ s_γ d_γ i_γ. With c'=0, q = γ×D_f = 18.5×0.8 = 14.8 kPa (assume D_f = 0.8 m), s_q = s_γ = 1.0, d_q = d_γ = 1.0, i_q = i_γ = 1.0 → q_ult,n = 14.8×56.3 + 0.5×18.5×2.5×62.8 = 833.2 + 1450.0 = 2283.2 kPa.
2.
Step 2: Apply resistance factor: φ×q_ult,n = 0.55×2283.2 = 1255.8 kPa.
3.
Step 3: Compute factored load per unit area: Σ(γ_iQ_i)/A = (1.25×850 + 1.75×320) / (2.5²) = (1062.5 + 560) / 6.25 = 1622.5 / 6.25 = 259.6 kPa.
4.
Step 4: Compare: 259.6 kPa ≤ 1255.8 kPa → OK (ratio = 0.21, ample margin).
Answer:
The factored bearing pressure (259.6 kPa) is well below the factored capacity (1255.8 kPa), satisfying AASHTO LRFD. The design margin is conservative due to high φ and moderate loads—but critical for blast-vibration–sensitive equipment foundations.
🏗️ Real-World Application
At the Stillwater Platinum Mine (Montana), LRFD was mandated for the new primary crusher foundation after a 2018 incident where a WSD-designed auxiliary feed hopper settled >25 mm during blasting—exceeding operational tolerance. Geotechnical review revealed the original WSD used FS = 2.75 on SPT-derived q_ult, but probabilistic back-analysis showed actual reliability index β = 2.1 (< target 3.5). Switching to LRFD with φ = 0.48 (for SPT + correlation to CPT) and γ_blast = 1.9 (per MSHA blast-load guidance) increased footing size by 18%, but eliminated post-blast settlement issues and satisfied MSHA Part 46 structural integrity requirements.