1 — Design inputs

Axle load = 200 kN (rear axle)  |  4 wheels (2 dual pairs) → P = 100 kN per contact

Tyre pressure p = 620 kPa  |  Traffic N = 10,000 passes

Subgrade: firm clay, c_u = 40 kPa (summer)  |  FoS = 1.5 (CIRIA C769, temp. works)

Fill: 6F5 granular, SHW Cl. 804 compaction, ≤150 mm layers

2 — Hand calculation

Step 1 — Equivalent circular contact radius

r = √(P / (π × p)) = √(100000 / (π × 620000)) = 0.2266 m

q_applied = P / (πr²) = 620 kPa ✓ consistent with tyre pressure

Step 2 — Required static fill depth (1H:2V spread)

Loaded radius at depth h: r + h/2

Set spread stress = q_allow = N_c·c_u / FS

Geogrid (N_c = 5.71):

q_allow = 5.71 × 40 / 1.5 = 152.3 kPa

h = 2[√(P·FS / (π·N_c·c_u)) − r]

   = 2[√(100×1.5 / (π×5.71×40)) − 0.2266]

   = 2[0.4572 − 0.2266] = 0.4613 m

Unreinforced (N_c = 3.14):

q_allow = 3.14 × 40 / 1.5 = 83.7 kPa

h = 2[√(150 / (π×3.14×40)) − 0.2266] = 0.7800 m

Step 3 — Traffic factor (k = 0.12 empiricism)

TF = 1 + 0.12·log₁₀(10000) = 1.48

Geogrid: h = 0.4613 × 1.48 = 0.683 m → use directly

← >600 mm single-layer cap; use 3 geogrid layers ↓

Multilayer (13%/layer, 2 extra layers): h = 0.6827 / (1 + 0.13×2)

   = 0.6827 / 1.26 = 0.5418 m → round to 25 mm → h_design = 0.550 m ✓

Unreinforced: 0.7800 × 1.48 = 1.154 m → round → h_design = 1.175 m ✓

3 — Engine vs. hand summary

r = 0.2266 m  |  q_allow (geogrid) = 152.3 kPa  |  h_static = 0.4613 m

h_design geogrid (3 layers) = 0.550 m  |  h_design unreinforced = 1.175 m

All quantities: Δ = 0.0% VERDICT: ✓ ALL MATCH

Note: k=0.12 & 13%/layer are empiricisms, not codified. Full Giroud & Han (2004) recommended as upgrade — H-01/H-04/H-05