WAZIPOINT Engineering Science & Technology: Calculation of Surface Load Transferred to a Specific Depth

To calculate how much of a surface load is transferred to a specific depth, soil mechanics uses stress distribution theories like Boussinesq’s equation and Newmark’s charts. The key idea is that stress diminishes with depth because the load spreads laterally through the soil mass.

General Formula (Point Load – Boussinesq)

For a point load $Q$ applied at the surface:

σz=3Q2πz2⋅1[1+(rz)2]5/2

$Q$ = applied load
$z$ = depth below surface
$r$ = radial distance from load axis
$σ_{z}$ = vertical stress at depth

Directly below the load ( $r = 0$ ):

σz=3Q2πz2

Example-1

If I apply a 100kG load per square foot on the surface of the land, how much load will be felt at a depth of 6 feet?

When you apply a 100 kG/ft² surface load, the stress felt at a depth of 6 feet depends on how the load is distributed (point load vs. large area). Using Boussinesq’s theory, the vertical stress beneath a point load decreases rapidly with depth because the load spreads laterally.

Directly Below the Load (r = 0)

If the load is concentrated over 1 ft²:

σz=3Q2πz2

For $Q = 100 kG$ , $z = 6 ft$ :

σz=3⋅1002π⋅36≈1.33 kG/ft2

At 6 ft depth, the stress is only about 1.3% of the surface intensity for a point load.

For Large Continuous Loads

If the load is applied over a wide mat or slab, the stress at depth remains close to the surface load because the soil beneath is compressed uniformly.
At 6 ft depth under a large area, stress could still be 80–100 kG/ft².
At 6 ft depth under a small footing, stress drops to just a few kG/ft².

Summary

Point load (1 ft²) → ~1.3 kG/ft² at 6 ft depth
Wide area load → ~80–100 kG/ft² at 6 ft depth

What happens to a 16 Wheel Truck on the road surface and point Load to a Specific Depth?

Truck Carrying 30-40 tons
Truck Wheel number 16
Each wheel loads 2000 kg
Point load feeling at 6 feet depth, 26 Kg

A 16‑wheel truck exerts enormous stresses on the road surface, but the way those stresses travel into the soil depends on tyre contact area and depth. Let’s break it down:

Load Transfer from a 16‑Wheel Truck

Axle load: A heavy truck may carry 30–40 tons. With 16 wheels, each tyre supports ~2–2.5 tons.
Tyre contact area: Each tyre footprint is small (≈40–60 in² at 100 psi). This means very high surface pressure.
Road surface stress: Pavement must resist concentrated stresses. Asphalt and concrete distribute load laterally to avoid rutting and cracking.

Stress at Depth (Point Load – Boussinesq)

For a point load $Q$ applied at the surface:

σz=3Q2πz2⋅1[1+(rz)2]5/2

Directly below the tyre ( $r = 0$ ):

σz=3Q2πz2

Example: If one tyre carries 2,000 kgf and depth $z = 6 ft$ :

σz=3⋅20002π⋅36≈26.5 kgf/ft2

That’s only a fraction of the surface stress, showing how quickly stress diminishes with depth.

Combined Effect of 16 Wheels

Near surface (road pavement): Each tyre footprint creates a high local stress zone.
At depth (soil subgrade): Stress bulbs from each tyre overlap. The deeper you go, the more uniform the stress distribution becomes.
Engineering implication: Pavement design uses layered systems (asphalt, base, sub‑base) to spread these concentrated tyre loads so that at 6–10 ft depth, stresses are low and uniform.

Tyre Size for a Truck

What is the Tyre Contact Area in a Truck

Photo Credit: Tensar U.K

The tyre contact area in a truck is the patch of ground over which each tyre transfers its load. It depends mainly on the tyre inflation pressure and the axle load: higher pressure reduces the contact area, while heavier loads increase it. For typical commercial trucks, tyre inflation pressures can exceed 700 kPa (≈100 psi), which means the contact area is relatively small compared to the load carried.

Key Concepts

Tyre contact area: The actual footprint of the tyre on the road surface.
Load transfer: Vehicle load is transmitted through tyres; stress on the ground = load ÷ contact area.
Tyre pressure effect: Higher inflation pressure → smaller contact area → higher stress. Lower pressure → larger contact area → lower stress.
Surface deformation: On unpaved roads, the tyre sinks into the soil, increasing contact area until the soil bearing capacity balances tyre pressure.

Typical Values for Trucks

Factor	Effect on Contact Area	Example
Tyre inflation pressure	Higher pressure reduces the contact area	At 100 psi, the contact area may be ~40–60 in² per tyre
Axle load	A heavier load increases the contact area	A 10-ton axle may give ~400–600 in² total contact area
Road type	Soft/unpaved surfaces increase contact area	Tyres sink, spreading the load
Tyre design	Wide, low-pressure tyres increase the area	Off-road trucks use oversized tyres to reduce stress

Tuesday, June 16, 2026

Calculation of Surface Load Transferred to a Specific Depth