Earth load is soil density times 9.81 to turn kilograms into newtons: 0.6 m of soil at 1,500-2,000 kg/m³ presses 8.8-11.8 kPa on a roof, which on a 5 x 5 m roof is 22.5-30 tonnes of mass and 221-294 kN of force. Soil also pushes sideways, and a saturated backfill 2.5 m deep presses on a wall with about 2.27 times the thrust of dry backfill, almost all of the extra coming from the water.
Earth load calculation turns soil density, depth and groundwater into the vertical force on a roof and the sideways thrust on a wall, with the units carried through every step.
Kilograms Are Not Newtons, So Convert Before Comparing
Mass is measured in kilograms and force in newtons. A mass of 1 kg at rest on the ground presses down with 9.81 N. Writing “2,500 kg” where the calculation gave a force of 2,500 N overstates it about tenfold, because 2,500 N is the weight of only 2,500 / 9.81 = 255 kg. In this article every step keeps its unit, so a reader can see where each number came from.
- 1 N = 1 newton. 1 kN = 1,000 N, the weight of about 102 kg (1,000 / 9.81 = 101.9).
- 1 kPa = 1 kN/m², a pressure.
What You Need
- Soil density in kg/m³. The parent article gives 1,500-2,000.
- Geometry: cover depth, roof area, wall height.
- A soil friction angle for the sideways calculation. The value used below, 30°, is an assumed example, not a measurement of your soil; find yours from tests or from local experience.
- A water assumption: drained, or fully saturated with no drainage.
Method: Roof Load, Then Wall Thrust
Step 1: Unit weight. Multiply density by 9.81 m/s².
Step 2: Vertical pressure. Multiply unit weight by cover depth.
Step 3: Roof force. Multiply pressure by roof area. Add the parent article’s allowance of about 25% for saturated soil.
Step 4: Lateral coefficient. For soil that can move a little as the wall yields, the Rankine active coefficient is Ka = (1 - sin φ) / (1 + sin φ). For a wall held rigid, as a buried box with a roof tied to it is, the at-rest coefficient K0 = 1 - sin φ (Jaky) is the safer assumption.
Step 5: Thrust per metre of wall. Pressure grows linearly with depth, so the thrust is the area of the triangle: P = ½ K γ H², acting H/3 above the base.
Step 6: Add water and surcharge, below.
Worked Example
A. The roof
- Unit weight: 1,500 kg/m³ x 9.81 m/s² = 14,715 N/m³ = 14.7 kN/m³. At 2,000 kg/m³: 19,620 N/m³ = 19.6 kN/m³.
- Pressure at 0.6 m: 14.7 kN/m³ x 0.6 m = 8.8 kPa. At 2,000 kg/m³: 19.6 x 0.6 = 11.8 kPa.
- Roof area: 5 m x 5 m = 25 m². Volume: 0.6 m x 25 m² = 15 m³.
- Mass: 15 m³ x 1,500 kg/m³ = 22,500 kg = 22.5 t. At 2,000: 30,000 kg = 30 t.
- Force: 8.83 kPa x 25 m² = 220.7 kN (about 221 kN), equal to 22,500 kg x 9.81 = 220,725 N. At 2,000 kg/m³: 11.77 x 25 = 294.3 kN (about 294 kN).
- Saturated, x 1.25: 220.7 x 1.25 = 276 kN and 294.3 x 1.25 = 368 kN, which corresponds to 28.1-37.5 t of mass.
The parent article quotes 25-40 tonnes for this roof and, separately, 25% extra for saturation. The dry range from these inputs is 22.5-30 t and the saturated range 28.1-37.5 t, so the 25-40 t figure is best read as the overall envelope. Do not add 25% on top of it.
B. The wall, drained
Assumed inputs: wall height H = 2.5 m, soil unit weight γ = 17 kN/m³ (1,733 kg/m³, inside the parent range), φ = 30°.
- Ka = (1 - 0.5) / (1 + 0.5) = 0.5 / 1.5 = 0.333. K0 = 1 - 0.5 = 0.5.
- Pressure at the base, active: 0.333 x 17 kN/m³ x 2.5 m = 14.2 kPa.
- Thrust, active: ½ x 0.333 x 17 x 2.5² = 17.7 kN per metre of wall. In weight terms, 17.7 / 9.81 = 1.8 tonnes pressing along every metre.
- Overturning moment about the base: 17.7 kN x (2.5 / 3) m = 14.8 kN·m per metre.
- At-rest thrust: ½ x 0.5 x 17 x 2.5² = 26.6 kN per metre.
C. The wall, saturated with no drainage
Assumed saturated unit weight 19 kN/m³, so the submerged unit weight is γ’ = 19 - 9.81 = 9.19 kN/m³.
- Pressure at the base: Ka γ’ H + γw H = 0.333 x 9.19 x 2.5 + 9.81 x 2.5 = 7.66 + 24.53 = 32.2 kPa.
- Thrust: ½ x 32.2 x 2.5 = 40.2 kN per metre, which is 40.2 / 17.7 = 2.27 times the drained active thrust.
- Water alone supplies ½ x 9.81 x 2.5² = 30.7 kN per metre, about three quarters of the total.
D. A surcharge
A pile of spoil 0.6 m high is a uniform surcharge q = 17 kN/m³ x 0.6 m = 10.2 kPa; use 10 kPa. It adds a uniform pressure Ka q = 0.333 x 10 = 3.3 kPa over the whole wall height, a thrust of 3.3 x 2.5 = 8.3 kN per metre acting at mid-height (1.25 m). This is why spoil is kept back from walls and pit edges.
What This Does And Does Not Establish
The formulas are standard textbook earth-pressure theory: Rankine (1857) for the active case and Jaky (1944) for the at-rest coefficient, as set out in any soil mechanics text such as Das, Principles of Geotechnical Engineering. They assume level ground behind a smooth vertical wall. The friction angle, unit weights and wall height above are assumed examples. The results show orders of magnitude and the effect of water; they are not a substitute for judging your own soil and wall. Compare also Dead Loads and Load Analysis.
Common Mistakes
- Calling newtons kilograms, or the reverse.
- Ignoring water. It is the largest single term in example C.
- Using the active coefficient for a rigid, roof-tied box. The at-rest value is higher and safer.
- Forgetting surcharge from spoil, vehicles or a neighbouring slope.
Safety
These numbers are a check, not a licence
Earth structures fail without warning and kill people under them. Use the parent article’s three-times margin on the roof, drain every wall, keep spoil and traffic away from walls and pit edges, and have a second person re-do the arithmetic before anything is built.
What’s Next
- Learn next: Retaining Wall Design — using the thrust to check a wall
- Combine with: Roof Structures for Earth Loading — carrying the roof force