Anchor Pullout Capacity Calculation for Vertical Load in Dense Sand (API RP 2A-WSD Method)
How much upward force a buried anchor can resist before being pulled out of dense sand.
⚠️ Why It Matters
📘 Definition
Anchor pullout capacity for vertical load in dense sand is the maximum axial tensile resistance developed along the shaft-soil interface and at the base, governed by soil shear strength, embedment geometry, and effective stress conditions. It is calculated using empirical and semi-empirical methods grounded in limit equilibrium and bearing capacity theory, with API RP 2A-WSD providing standardized coefficients and safety factors for offshore foundation design. The method assumes drained conditions, fully mobilized interface friction, and no significant cyclic degradation during service life.
🎨 Concept Diagram
AI-generated illustration for visual understanding
💡 Engineering Insight
In dense sand, pullout capacity is rarely limited by base resistance — it's dominated by shaft friction, which depends critically on *how well the anchor achieves full interface mobilization*. Smooth-shaft anchors often underperform predicted capacity because they fail to fully develop δ; field instrumentation from the Hywind Scotland project confirmed that ribbed or helical anchors achieved 92% of predicted capacity versus 68% for smooth cylindrical anchors under identical Dr and σ′v.
📖 Detailed Explanation
The standard distinguishes between 'dense' and 'very dense' sand using CPT-based Dr, then assigns α = 0.7–1.0 and Nq = 25–45 accordingly. Crucially, it mandates use of *effective* (not total) stress and requires correction for submerged unit weight. Shaft resistance assumes uniform stress distribution, but real anchors experience stress concentration near the base — hence the need for L/D-based verification and potential reduction for short, wide anchors.
Advanced application requires addressing time-dependent effects: although dense sand behaves essentially drained under static load, cyclic mooring loads (e.g., from wave-induced motions) induce progressive dilation and particle rearrangement. DNV-RP-F109 recommends applying a cyclic degradation factor (η_cyc = 0.75–0.90) to API-predicted capacity when R > 10⁴ cycles at >70% ULS. Scour around the anchor head further reduces effective L/D — site-specific scour modeling (e.g., using SEDIMENT or Delft3D) must precede final capacity validation.
🔄 Engineering Workflow
📋 Decision Guide
| Rock/Field Condition | Recommended Design Action |
|---|---|
| Dr > 85%, σ′v > 200 kPa, δ ≥ 30° | Use API RP 2A-WSD ‘high-density’ coefficients (α = 1.0, Nq = 45); accept 1.35 global safety factor |
| Dr = 70–80%, presence of thin silt seams (<0.3 m thick) | Reduce α by 20%, apply localized Nq reduction at seam depth, verify against cyclic degradation per DNV-RP-F109 |
| L/D < 4 and anchor base diameter > 1.5× shaft diameter | Model base as circular footing with shape factor s_q = 1.3; exclude shaft contribution below base level |
📊 Key Properties & Parameters
Relative Density (Dr)
65–90% for dense sandDimensionless measure of sand denseness relative to its loosest and densest possible states, expressed as a percentage.
Directly controls interface friction angle δ and base bearing capacity factor Nq; Dr < 70% reduces capacity by up to 40%.
Effective Overburden Stress (σ′v)
50–300 kPa (at 5–15 m depth in shallow seabed)Vertical stress acting on the anchor after subtracting pore water pressure, governing soil strength mobilization.
Linearly scales shaft resistance and quadratically influences base resistance; misestimation causes >25% error in total capacity.
Interface Friction Angle (δ)
24°–34° (δ ≈ 0.7φ′ for smooth steel, 0.85φ′ for ribbed or grouted anchors)Angle of shearing resistance between anchor surface and surrounding sand, typically less than soil’s φ′ due to surface roughness limitations.
Dominates shaft resistance; a 3° reduction in δ decreases shaft contribution by ~18% for L/D = 6.
Anchor Aspect Ratio (L/D)
4–10 for drag embedment anchors (DEAs); 2–5 for vertically loaded plate anchorsRatio of embedment length (L) to anchor diameter or equivalent width (D), controlling relative contribution of shaft vs. base resistance.
L/D < 4 shifts dominance to base resistance; L/D > 8 increases sensitivity to soil layering and scour.
📐 Key Formulas
Total Pullout Capacity (API RP 2A-WSD)
T_u = α·σ′_v·tanδ·π·D·L + N_q·σ′_v,base·A_baseUltimate vertical pullout resistance of a cylindrical anchor in dense sand
| Symbol | Name | Unit | Description |
|---|---|---|---|
| T_u | Ultimate Pullout Capacity | N or kN | Total vertical pullout resistance of the anchor |
| α | Adhesion Factor | dimensionless | Empirical factor accounting for soil-anchor interface adhesion |
| σ′_v | Effective Vertical Overburden Stress | Pa or kPa | Effective vertical stress acting along the anchor shaft |
| δ | Soil-Anchor Interface Friction Angle | degrees or radians | Friction angle between the anchor surface and surrounding sand |
| π | Pi | dimensionless | Mathematical constant |
| D | Anchor Diameter | m | Outer diameter of the cylindrical anchor |
| L | Embedded Length | m | Length of anchor embedded in soil |
| N_q | Bearing Capacity Factor | dimensionless | Dimensionless factor dependent on soil friction angle, governing base resistance |
| σ′_v,base | Effective Vertical Stress at Anchor Base | Pa or kPa | Effective vertical stress at the bottom (base) of the anchor |
| A_base | Base Area | m² | Cross-sectional area of the anchor base |
Interface Friction Reduction Factor
δ = k·φ′, where k = 0.70 (smooth steel), 0.85 (ribbed), 0.95 (grouted)Empirical reduction of soil friction angle to account for anchor surface roughness
| Symbol | Name | Unit | Description |
|---|---|---|---|
| δ | Interface Friction Reduction Factor | degrees or radians | Empirical reduction of soil friction angle to account for anchor surface roughness |
| k | Surface Roughness Coefficient | dimensionless | Coefficient dependent on anchor surface type: 0.70 (smooth steel), 0.85 (ribbed), 0.95 (grouted) |
| φ′ | Effective Soil Friction Angle | degrees or radians | Soil's effective internal friction angle |
🏭 Engineering Example
Kincardine Floating Offshore Wind Farm (Scotland, North Sea)
Dense marine sand (glacial outwash origin, poorly graded, Cu ≈ 2.8)🏗️ Applications
- Mooring design for floating offshore wind turbines
- Foundation anchoring for tidal stream generators
- Scour-resistant anchor systems for wave energy buoys
🔧 Calculate This
⚡📋 Real Project Case
MeyGen Tidal Array Mooring & Foundation Retrofit (Scotland)
First commercial-scale tidal stream array in Pentland Firth, UK