Earth Pressure Acting on Basement Walls

1st Floor above Ground Level

The forces that keeps the basement wall in position - the force at the basement floor/slab and the force from the 1st floor joists above ground level - are indicated in the figure below.

The resultant force due to the earth pressure acting on a basement wall can be calculated as

F_a = 0.5 K γ h_s²                             (1a)

where

F_a = resultant force acting on the basement wall (kN/m)

h_s = height of backfill soil (m)

γ = specific weight of backfill soil (kN/m³)

K = coefficient of earth pressure at rest

Coefficient of earth pressure at rest can be calculated as

K = μ / (1 - μ)                      (1b)

where

μ = Poisson's ratio

Poisson's ratios for some typical backfill soils:

• clay: 0.41
• sand : 0.29
• sandy clay: 0.37
• sandy loam: 0.31

Specific weight can be calculated as

γ = ρ a_g                               (1c)

where

ρ = density of soil (kg/m³)

a_g = acceleration of gravity (9.81 m/s²)        

• Soil densities

Density for some typical backfill materials:

• clay, dry: 1600 kg/m³
• sand, dry: 1555 kg/m³

The acting position of the acting force can be calculated as

d_a = h_s / 3                           (1d)

where

d_a = distance from the bottom of the basement wall    (m)

The maximum bending moment acting in the basement wall can be calculated as

M_max = (F_a h_s / 3 ht) (h_s + (2 h_s / 3)(h_s / (3 h_t))^1/2)                            (1e)

where

M_max = maximum moment in the basement wall (Nm)

The position of the max moment in the basement wall can be calculated as

d_m = h_s (h_s / (3 h_t))^1/2                 (1f)

Note! - cracking of a basement wall is likely to occur where the moment is at the maximum. Due to tension reinforcement bars should be concentrated closer to the inside wall. 

• Reinforcing Bar - Metric

1st Floor at Ground Level

The forces that keeps the basement wall in position - the force at the basement floor/slab and the force from the 1. floor joists at ground level - are indicated in the figure below.

The resultant force due to the earth pressure acting on a basement wall can be calculated as

F_a = 0.5 K γ h_s²                             (2a)

The acting position of the acting force can be calculated as

d_a = h_s / 3                           (2b)

where

d_a = distance from the bottom of the basement wall    (m)

The maximum moment acting in the basement wall can be calculated as

M_max = 0.128 F_a h_s                                (2c)

where

M_max = maximum moment in the basement wall (Nm/m)

The position of the max. moment in the basement wall can be calculated as

d_m = 0.42 h_s                   (2e)

Example - Earth Pressure on Basement Wall

A basement wall with height 2.5 m is backfilled with sand.

The Poisson's ratio for sand is 0.29 and the coefficient of earth pressure can be calculated as

K = 0.29 / (1 - 0.29)

   = 0.41

The specific weight for the sand can be calculated as

γ = (1555 kg/m³) (9.81 m/s²)

  = 15255 N/m³

  = 15.3 kN/m³ 

The resultant force acting on the basement wall can be calculated as

F_a = 0.5 (0.41) (15.3 kN/m³) (2.5 m)²    

    = 19.6 kN/m

The acting position of the resultant force can be calculated as

d_a = (2.5 m) / 3

    = 0.83 m    

The maximum moment acting in the basement wall can be calculated as

M_max = 0.128 (19.6 kN) (2.5 m)

         = 6.3 kNm/m

The position of the max. moment in the basement wall can be calculated as

d_m = 0.42 (2.5 m)

     = 1.05 m