Retaining Wall Earth Pressure Calculator: Rankine and Coulomb Active Pressure, Force and Moment
Work out the active pressure, force and overturning moment of a soil backfill on a retaining wall.
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How this calculator works
Enter the unit weight of the backfill, the wall height, the soil friction angle, the friction angle between the wall and the soil, and any surcharge on the surface.
The calculator finds the Rankine coefficient Ka = (1 - sin phi) / (1 + sin phi) and the force one half gamma h squared Ka, acting one third up from the base. Then the Coulomb coefficient with wall friction and its force.
It gives the horizontal and vertical parts of the Coulomb force, the overturning moments about the base, the difference between them, and the at-rest force for comparison.
Formulas used
- K_a = \frac{1 - \sin\phi}{1 + \sin\phi}
- P_a = \tfrac12\gamma h^2 K_a
- K_a = \frac{\cos^2\phi}{\cos\delta\left[1 + \sqrt{\frac{\sin(\phi+\delta)\sin\phi}{\cos\delta}}\right]^2}
- \bar{y} = h/3
Worked example
With the default numbers in the calculator above:
- Rankine active coefficient (smooth wall): 0.33
- Active force on the smooth wall, from the soil: 93.00 kN per metre length of wall
- Height of the resultant above the base: 2.00 m (33.33 percent of the height)
- Overturning moment about the base (smooth wall): 186.00 kN m per metre of wall
- Coulomb active coefficient (with friction between wall and soil): 0.30
- Active force with wall friction (it acts at the friction angle to the normal of the wall): 84.10 kN per metre length of wall
- Horizontal and vertical parts of that force: 81.23 kN/m horizontal, 21.77 kN/m vertical (down on the wall)
- Moment about the base, taking the whole force at its height: 168.19 kN m per metre of wall
- Overturning moment of the horizontal part alone: 162.46 kN m per metre of wall
- Difference in the moment, smooth wall minus wall with friction: 17.81 kN m per metre of wall
- For comparison: at-rest coefficient and force (a wall that cannot move at all): K0 = 0.50 gives 139.50 kN/m
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
What is the active condition?
The soil has moved enough away from the wall for its full strength to be used. The pressure on the wall is then at its lowest.
What is the difference between Rankine and Coulomb?
Rankine ignores friction between the wall and the soil. Coulomb includes it, which makes the force lower and slanted.
Where does the force act?
One third of the height above the base for a triangular pressure, and half the height for a uniform surcharge.
Does this include water?
No. Water behind the wall can double the load, so the backfill must be drained. Add the water pressure separately.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Das, Principles of Foundation Engineering; AS 4678 Earth-retaining structures; Craig, Soil Mechanics.
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