Loads Part II — Other Loads

Comprehensive coverage of gravity, accidental, seismic, and fatigue loads, plus load combination strategies aligned with API RP 2A and ISO 19902.

1. Gravity Loads (Permanent and Variable)

Dead Load (Permanent Gravity)

Dead load comprises the self-weight of the structure and permanent installations:

• Structural Steel: Jacket legs, braces, deck frame, subsea templates. Typically 500–2,500 tonnes for a conventional shallow-water platform.
• Topside Equipment: Drilling rigs, separators, compressors, piping, instrumentation. Often 5,000–15,000 tonnes for a production platform.
• Fixed Facilities: Accommodations, utilities, power generation systems, water/waste treatment.
• Hydrostatic Added Mass: Virtual mass effect of water accelerating with the structure in dynamic analyses; typically 40–60% of structural mass for large-diameter cylinders.

Dead load is modeled as gravity acting downward at the center of mass of each component. Accurate weight estimates require detailed design and 3D CAD models. Industry practice uses CAD-extracted weights during detailed design phases; preliminary estimates use parametric equations based on deck area and drilling capability.

Live Loads (Variable Gravity)

Live loads represent temporary, operational loads:

• Drilling Fluid (Mud): Active mud system in tanks and risers; typical density 1.3–2.0 tonne/m³. A single well can hold 300–800 cubic meters of fluid.
• Produced Hydrocarbons: Oil stored in tanks (floating structures use hull ballast compartments); 5,000–50,000 cubic meters typical.
• Personnel and Consumables: 100–300 personnel on a manned platform; food, spare parts, drilling supplies. Typically 500–1,000 tonnes.
• Crane and Lifting Operations: Heavy-lift cranes introduce dynamic load amplification during hook-down; factor typically 1.5–2.0× the lifted load weight.

Live loads are case-dependent and must be explicitly defined for design scenarios. API RP 2A requires designers to specify maximum mud weight, hydrocarbon inventory, and operational constraints. Load reduction factors for non-coincident live loads are codified in design standards but are typically not applied to critical loads (e.g., full mud weight simultaneous with full lifting operation is rarely credible but is sometimes assumed for conservative design).

2. Buoyancy and Hydrostatic Pressure

Archimedes' Principle

For submerged or partially submerged structures, buoyancy acts upward at the center of buoyancy (centroid of displaced volume):

For fixed platforms (jackets, GBS), buoyancy is typically small relative to weight. For floating units (FPSO, Spar, Semi-sub), buoyancy exactly equals weight at equilibrium draft; any overweight causes sinking, and under-buoyancy causes sinking or heel.

Hydrostatic Pressure Distribution

Hydrostatic pressure increases linearly with depth: p(z) = ρ·g·z (gauge pressure, z measured downward from free surface). For closed members (caissons, columns), internal atmospheric pressure may be maintained, creating a net inward pressure. Modern codes require explicit hydrostatic load checks for:

• Member Buckling: External pressure can reduce axial buckling capacity; API RP 2A Eq. 6-35 and ISO 19902 Section 11 provide combined loading unity checks.
• Wall Thickness Adequacy: Thick-walled cylinders are less sensitive; thin shells require careful buckling analysis.
• Flooding Scenarios: If a member is breached, internal water fills the void; designers must assess whether structural strength remains sufficient.

3. Accidental Loads

Dropped Object Impact

A heavy object falling from the deck (pipe, equipment, crane block) impacts a structural member with kinetic energy E_k = 0.5·m·v². The impact is typically modeled as an inelastic collision, converting kinetic energy to local deformation and permanent damage:

• Low-Energy Impact: Denting of deck plating or bracing members; typically repaired with local strengthening.
• High-Energy Impact: Fracture of welds or shearing of bracing members; can compromise structural integrity and trigger progressive collapse.

Modern platforms employ rigorous "dropped object" prevention programs: all equipment lifted must be tagged, certified, and tracked. Deck layouts minimize objects over critical load paths. Many regulatory authorities now require quantitative risk assessment for dropped objects, estimating frequency and consequence.

Vessel Collision

Floating vessels (supply ships, emergency response vessels) may collide with a platform in fog, storms, or navigation errors. Typical collision scenarios include:

• Bow Impact: High-speed impact to platform jacket or floatation. Energy absorbed by vessel deformation and structural crushing.
• Side Swipe: Glancing impact along a leg or riser; lower energy but can sever critical systems.

Collision energy is estimated from vessel mass (3,000–20,000 tonnes for supply vessels) and speed (2–5 m/s in operational scenarios, higher in loss-of-control scenarios). Modern designs include:

• Protective dolphins (energy-absorbing structures surrounding the platform)
• Increased jacket leg wall thickness in collision zones
• Redundancy in critical systems (dual umbilicals, multiple risers)

Explosion and Fire

Explosive atmosphere (gas cloud) and ignition sources can lead to overpressure and thermal loads. API RP 2A Section 5.11 and ISO 19902 Appendix G address explosion-resistant design. Key points:

• Blast Overpressure: Transient pressure spike (rise time 1–10 ms). Typical design pressures: 30–200 kPa depending on inventory and ventilation.
• Structural Response: Large-area elements (decks, bulkheads) undergo transient deformation; ductile plastic hinges dissipate energy.
• Thermal Stress: Fire can reduce material strength by 20–50% at elevated temperatures. Modern codes require fire-proofing (passive or active cooling) of critical members.

4. Seismic Loads

Seismic Zones and ISO 19901-2

Offshore platforms in seismic regions (California, Southeast Asia, Mediterranean, etc.) must be designed for earthquake-induced ground motion. ISO 19901-2 classifies regions into seismic zones based on historical activity and probabilistic seismic hazard assessment (PSHA):

• Zone 0: Negligible seismic risk; no specific design requirements.
• Zone 1: Low seismic risk; design acceleration 0.05–0.10g (5–10% gravity).
• Zone 2: Moderate risk; design acceleration 0.10–0.25g.
• Zone 3: High risk; design acceleration 0.25–0.40g+.

Deep-water floating platforms experience reduced seismic loading due to low natural frequencies (long periods > 20 seconds); shallow-water jackets with stiff structures (periods 3–8 seconds) are more excited by typical earthquake spectra (5–20 second period bands).

Equivalent Linear Elastic (ELE) and Acceleration-Led (ALE) Methods

Two primary design approaches:

• Equivalent Linear Elastic (ELE): Model structure as linear-elastic with equivalent damping to account for soil nonlinearity. Soil springs are iteratively updated based on shear strain levels. Simpler, less computer-intensive; widely used for jacket design.
• Acceleration-Led (ALE): Couple nonlinear soil-structure interaction (SSI) with nonlinear structural response (plasticity, buckling). More accurate but computationally expensive; used for high-consequence structures in high-seismic zones.

Modern practice typically uses ELE for routine designs and ALE for risk-critical projects. Both methods require site-specific geotechnical investigation and cone penetrometer (CPT) data to characterize soil profiles.

5. Fatigue Loads and Wave Scatter Diagrams

Cumulative Fatigue Damage

Unlike a single extreme load that must not exceed design capacity, fatigue damage accumulates from cyclic stress over many cycles. Miner's rule estimates total damage:

The S-N curve (stress amplitude vs. number of cycles to failure) is empirically derived from fatigue testing of welded steel joints. API RP 2A Table 9-1 provides curves for various weld details and material grades.

Wave Scatter Diagram

A scatter diagram tabulates the frequency of occurrence of sea states (wave height and period pairs) at a given site over a long period (typically 20+ years). Example for Gulf of Mexico:

Hs (m)	T ≤ 8s (%)	8s < T ≤ 12s (%)	T > 12s (%)	Total (%)
0–1	15.2	8.5	1.2	24.9
1–2	12.8	18.3	4.5	35.6
2–3	8.2	15.4	5.2	28.8
3–4	3.1	4.8	2.4	10.3
> 4	0.2	0.1	0.1	0.4

Fatigue analysis uses the scatter diagram to weight the contribution of each sea state to total damage. Sea states with Hs < 2 m, occurring 60% of the time, often contribute 40–60% of total fatigue damage due to frequency. The 100-year extreme (Hs ~ 14–16 m in GoM) contributes negligibly to fatigue.

6. Load Combinations and Safety Philosophy

Design Limit States

Modern codes differentiate between three limit states:

• Ultimate Limit State (ULS): Structure approaches collapse or significant permanent deformation. Single extreme load event (100-year wave, 100-year earthquake). Design criterion: demand/capacity ≤ allowable ratio (typically 0.9–1.0 depending on code).
• Serviceability Limit State (SLS): Structure remains functional but may experience excessive deformation, vibration, or fatigue damage. Operational sea states over design life (20–30 years). Design criterion: deflection limits, fatigue cumulative damage D ≤ 0.3–0.5.
• Accidental Limit State (ALS): Structure survives rare accidents (dropped objects, vessel collision) without loss of life or environmental release. Design criterion: post-accident structural integrity maintained.

Load Factors and In-Place Load Cases

API RP 2A prescribes load factors for different load types and design scenarios. Example in-place load combination (ULS):

The 1.5 factor on wave load reflects the largest uncertainty in load estimation; wind and current receive lower factors due to lower probability of simultaneous occurrence with design wave. Designers must check all critical members for this combination and select the governing case.

LRFD vs. ASD Philosophy

Load and Resistance Factor Design (LRFD) applies factors on loads and resistances:

Allowable Stress Design (ASD) applies a single safety factor to permissible stress:

API RP 2A-WSD uses ASD for in-place analysis; ISO 19902 increasingly emphasizes LRFD. Both approaches, if properly calibrated, yield equivalent safety; choice is often driven by regulatory authority.

7. Dynamic Amplification Factor (DAF)

Wave and wind loads applied quasi-statically overestimate peak stresses compared to true dynamic response. The Dynamic Amplification Factor (DAF) accounts for the structure's inertia and resonance:

API RP 2A Table 10-2 provides DAF values; ISO 19902 requires explicit dynamic analysis if the fundamental period exceeds 3 seconds. Very flexible structures (deepwater spars with periods > 20 s) experience minimal DAF because the wave loading frequency (0.05–0.15 Hz) is far below the structural frequency.