Wheel Load — Shallow Cover
For shallow burial depths where h < 2.67(Do−t)/12, the surface wheel load concentrates on the pipe. This equation accounts for diameter, wall thickness, impact factor, and cover depth.
Wl = 0.48 Pl If (Do−t)² / (12² × 2.67h³) × (2.67h/((Do−t)/12) − 0.5)
Wheel Load — Deep Cover
For deeper burial (h ≥ 2.67(Do−t)/12), the load distributes more widely through the soil and the simpler equation applies. Increasing cover depth significantly reduces the load reaching the pipe.
Wl = 0.64 × Pl × If / h
Pressure from Wheel Load
Converts a wheel load per linear foot into a pressure acting on the pipe crown by dividing by the outside diameter.
Pw = 12 × Wl / Do
Pressure — Fill Greater than 2 ft
For fill depths greater than approximately 2 feet, this simplified Boussinesq-based equation estimates the live-load pressure on the pipe from the surface wheel load and cover height.
Pw = Pl / (1.75 × h)²
How It Works
Surface vehicle loads spread through the soil at an angle. Shallow pipes (less fill) see a concentrated load, while deeper pipes benefit from greater load distribution. Two separate equations handle fill depths above and below a threshold. The wheel load per linear foot can then be converted to a pressure using the pipe diameter.
Example Problem
An H-20 truck wheel load of 16,000 lb acts on a pipe with 3 ft of cover and an impact factor of 1.5. Use the deep-cover equation.
- Identify the known values: surface wheel load Pₗ = 16,000 lb, impact factor I = 1.5, cover height h = 3 ft.
- Since h = 3 ft exceeds the shallow-cover threshold for most pipe sizes, use the deep-cover equation: Wₗ = 0.64 × Pₗ × I / h.
- Substitute the values: Wₗ = 0.64 × 16,000 × 1.5 / 3.
- Multiply the numerator: 0.64 × 16,000 × 1.5 = 15,360.
- Divide by the cover height: 15,360 / 3 = 5,120.
- The wheel load on the pipe is 5,120 lb/ft. Increasing cover to 4 ft would reduce this to 3,840 lb/ft.
When to Use Each Variable
- Solve for Shallow Wheel Load — when the pipe has shallow cover (less than the threshold depth), e.g., checking a utility crossing under a parking lot with minimal fill.
- Solve for Deep Wheel Load — when the pipe has deep cover and the simplified Boussinesq formula applies, e.g., analyzing a trunk sewer under a highway.
- Solve for Pressure from Load — when converting a wheel load per linear foot into a pressure on the pipe crown, e.g., combining with soil pressure for total load analysis.
- Solve for Pressure (Deep Fill) — when the fill depth exceeds about 2 ft and you want a direct pressure estimate from the Boussinesq method.
Key Concepts
Surface wheel loads spread through soil at an angle, so deeper pipes see less concentrated loading. Two regimes apply: shallow cover (concentrated load, dependent on pipe diameter and wall thickness) and deep cover (simplified Boussinesq distribution). The impact factor accounts for dynamic amplification from moving vehicles — typically 1.5 for highway traffic.
Applications
- Road crossings: verifying buried utilities can withstand highway truck loads (H-20, HL-93)
- Airport taxiways: checking pipe strength under heavy aircraft wheel loads with shallow cover
- Construction sites: evaluating temporary loading from heavy equipment crossing buried pipelines
- Parking lot design: ensuring storm drains under pavement can handle expected vehicle traffic
Common Mistakes
- Using the deep-cover equation when the pipe is actually at shallow depth — the threshold depends on pipe diameter and cover height; using the wrong equation can underestimate loads by 50% or more
- Ignoring the impact factor for moving loads — a static wheel load must be multiplied by 1.5 (or more) for dynamic highway loading; omitting this factor underestimates the actual force
- Neglecting to combine wheel load with soil and hydrostatic pressures — the pipe must resist all simultaneous loads, not just the largest one
Frequently Asked Questions
How deep does a buried pipe need to be to handle truck traffic?
Most jurisdictions require a minimum cover of 3 to 4 feet for pipes under roads carrying H-20 truck loads. Shallower cover concentrates the load on the pipe and may require concrete encasement or a steel casing for protection.
What is the H-20 highway loading standard?
H-20 is an AASHTO standard representing a 20-ton (40,000 lb) truck with a maximum single-wheel load of 16,000 lb. It is the baseline design load for buried utilities under public roads. Heavier standards like HL-93 combine a truck with a lane load.
What is an impact factor and when should I change it?
The impact factor accounts for dynamic effects from moving vehicles. The standard value is 1.5 for highway traffic. Use 1.0 for static loads (parked equipment), and consider higher values (1.75–2.0) for poorly maintained roads or heavy construction equipment.
Why are there two equations for different depths?
At shallow depths, the load spreads through a smaller soil prism and depends on pipe diameter and wall thickness. At greater depths the load distributes more widely and a simpler inverse-distance formula gives accurate results.
Can this calculator handle aircraft loading at airports?
The equations apply to any surface wheel load. For aircraft, use the single-gear wheel load and adjust the impact factor. Aircraft like Boeing 737 have gear loads much higher than H-20 trucks, so deeper cover or stronger pipe may be needed.
How do I combine wheel load with soil pressure?
First calculate the wheel load pressure (Pw) using this calculator. Then calculate the soil pressure from the soil weight above the pipe (gamma × h). The total external load on the pipe is the sum of wheel load pressure and soil pressure.
Does the formula account for pavement thickness?
No. The cover height h should be measured from the ground surface to the pipe crown, not from the bottom of the pavement. Thick pavement distributes load better, but the formula conservatively ignores this benefit.
Reference: National Resources Conservation Service. National Engineering Handbook. 1995. USDA.
Pipe Wheel Loading Formulas
Two equations handle different burial depths. The deep-cover formula is the most commonly used:
Wₗ = 0.64 × Pₗ × I / h
Where:
- Wₗ — wheel load on the pipe (lb/ft)
- Pₗ — surface wheel load (lb), e.g., 16,000 lb for H-20
- I — impact factor (1.5 for highway traffic)
- h — cover height from surface to pipe crown (ft)
For shallow cover, a more complex formula accounts for the pipe diameter and wall thickness. The wheel load can then be converted to pressure using Pₘ = 12 × Wₗ / Dₒ.
Worked Examples
Road Crossings
What load does a water main see under a two-lane road?
A 24-inch water main crosses under a city street with 4 ft of cover. An H-20 truck (16,000 lb wheel) drives over it. Impact factor = 1.5.
- Wₗ = 0.64 × 16,000 × 1.5 / 4
- Wₗ = 15,360 / 4
- Wₗ = 3,840 lb/ft
At 4 ft of cover the load is manageable for most ductile iron and steel pipe. Shallower crossings may need a concrete cap or steel casing.
Airport Taxiway
How much load does a fuel line see under a taxiway?
A fuel transfer pipe runs under an airport taxiway with 5 ft of cover. A Boeing 737 main gear applies 45,000 lb per wheel. Impact factor = 1.3 (slow taxi speed).
- Wₗ = 0.64 × 45,000 × 1.3 / 5
- Wₗ = 37,440 / 5
- Wₗ = 7,488 lb/ft
Aircraft loading is significantly higher than highway trucks. Steel casing or concrete encasement is typically required for airport crossings.
Construction
Will a temporary haul road crush a shallow drainage pipe?
A corrugated pipe (Do = 18 in, wall t = 0.25 in) sits under 2 ft of gravel on a construction haul road. Dump trucks have 20,000 lb wheel loads. Impact factor = 1.75 for rough terrain. The fill threshold 2.67·(Do−t)/12 ≈ 3.95 ft means this is in the shallow-cover regime.
- Shallow formula (h < 3.95 ft) from Merritt: Wₗ ≈ 0.48·P·I·(D−t)² / (2.67·h³) · [2.67h/(D−t) − 0.5]
- Plug in D−t = 1.479 ft, h = 2 ft, P = 20,000 lb, I = 1.75
- Wₗ ≈ 5,350 lb/ft
Shallow-cover loads spread differently than deep-cover loads. At ~5,350 lb/ft with only 2 ft of cover and a heavy wheel, steel plates or additional fill are still typically required for haul-road crossings.
Related Calculators
- Pipe Soil Pressure Calculator — soil weight pressure and buoyancy.
- Buried Corrugated Pipe Calculator — combined design pressure and wall thrust.
- Pipe Hydrostatic Pressure Calculator — external water pressure on buried pipe.
- Pipe Vacuum Load Calculator — internal vacuum load on buried pipe.
- Pressure Unit Converter — convert wheel loading pressure between units.
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National Resources Conservation Service. National Engineering Handbook. 1995. USDA.