Gravity Retaining Wall Calculator
Check a plain concrete gravity retaining wall: enter the height of soil it holds back, the stem's top and bottom widths and the footing, and the soil, and see whether it overturns, slides, overloads the soil or cracks. If it fails, the calculator suggests a wall that works. Pro adds a PDF report.
The wall works, using 94% of what it can take (limited by sliding).
The wall in section, to scale: the soil pressure behind it and the plain concrete stem and footing.
Stability
| OverturningSafety factor 3.41, at least 1.5 | 44% PASS |
| SlidingSafety factor 1.60, at least 1.5: 0.35 × 2,648 lb + 225 lb in front against 720 lb | 94% PASS |
| Soil bearing1,327 psf under the toe, 1,500 psf allowed | 88% PASS |
| The resultant in the middle third5 in off center, 7 in allowed (a sixth of the footing) | 75% PASS |
Active soil pressure coefficient 0.333 (Rankine, friction angle 30°), the same as 40 pcf of fluid pressure: 720 lb per ft of wall. The wall, the footing and the soil on them weigh 2,648 lb per ft.
Stem
Plain concrete, no bars: checked at 12 levels down the stem for tension, compression and shear.
| Stem tension5 psi on the back face at the base of the stem (0.9D + 1.6H); 150 psi allowed | 3% PASS |
| Stem compressionat the base of the stem (1.2D + 1.6H) | 1% PASS |
| Stem shear2 psi at the base of the stem; 40 psi allowed | 6% PASS |
Footing
| Toe bending13 psi tension in the bottom at the stem, taking the footing as 10 in thick; 150 psi allowed | 9% PASS |
| Toe shear7 psi at the stem; 40 psi allowed | 18% PASS |
| Heel bending5 psi tension in the top at the stem, taking the footing as 10 in thick; 150 psi allowed | 3% PASS |
| Heel shear3 psi at the stem; 40 psi allowed | 7% PASS |
- Keep water from building up behind the wall: gravel backfill against the back and a drain at the footing, or weep holes. This calculator assumes drained soil.
Safety factor 1.5 against overturning and sliding (IBC 1807.2.3); passive pressure 150 pcf on the front of the footing, leaving out the top 1 ft. 2,500 psi plain concrete to ACI 318-19 Chapter 14, with the soil pressure factored by 1.6.
Gravity retaining wall sizes by height
The least concrete that works for each height of level backfill with no surcharge: a 12 in top, a 0′ 6″ toe and heel, and the stem's back sloping out to the bottom width. Sand weighing 120 pcf with a 30° friction angle, 0.35 sliding friction, 150 pcf passive pressure and 2,000 psf allowable bearing (IBC Table 1806.2), the footing 1′ below the ground in front, and 2,500 psi concrete.
| Retained height | Stem top | Stem bottom | Footing | Width | Toe | Heel |
|---|---|---|---|---|---|---|
| 2′ | 12 in | 1′ 3″ | 12 in | 2′ 3″ | 0′ 6″ | 0′ 6″ |
| 3′ | 12 in | 1′ 9″ | 12 in | 2′ 9″ | 0′ 6″ | 0′ 6″ |
| 4′ | 12 in | 2′ 6″ | 12 in | 3′ 6″ | 0′ 6″ | 0′ 6″ |
| 5′ | 12 in | 3′ 3″ | 12 in | 4′ 3″ | 0′ 6″ | 0′ 6″ |
| 6′ | 12 in | 4′ | 12 in | 5′ | 0′ 6″ | 0′ 6″ |
| 7′ | 12 in | 4′ 6″ | 12 in | 5′ 6″ | 0′ 6″ | 0′ 6″ |
| 8′ | 12 in | 6′ 3″ | 12 in | 7′ 3″ | 0′ 6″ | 0′ 6″ |
Keeping the resultant in the middle third or stopping the wall sliding sets the width up to 6 ft, and the soil's bearing above that; on clay, at 1,500 psf, walls over 5 ft come out much wider. Check your own wall above; soils vary more than these walls do.
How the calculator checks a gravity wall
A gravity wall holds the soil back by its own weight. It's plain concrete, with no bars, so it has to be wide enough that the soil can't tip or slide it, and thick enough that the concrete never has to take more than a small tension. The front face is upright and the back slopes out toward the bottom, so the soil resting on the slope adds to the weight. Per foot of wall:
- Soil pressure: Rankine's active pressure for the soil's friction angle and the backfill slope (or the equivalent fluid pressure from a soils report), on a vertical plane through the end of the heel, from the bottom of the footing to the ground. The soil between that plane and the wall counts as weight.
- Overturning: the weight of the wall, the footing and the soil on them, turning the wall back about the toe, must be at least 1.5 times the soil pressure turning it over (IBC 1807.2.3).
- Sliding: friction under the footing plus the passive pressure of the soil in front of it, leaving out the top 1 ft, must be at least 1.5 times the push.
- Bearing: the soil pressure at the toe or heel must be no more than the allowable, and the resultant must fall in the middle third of the footing, so the whole footing presses on the soil.
- Water and earthquakes: as in the cantilever wall calculator: water pressure, lighter soil below the water and uplift under the footing; with SDS entered, Seed and Whitman's added soil pressure and the wall shaking, with a safety factor of 1.1.
- Stem: checked at twelve levels from the top down, as plain concrete by ACI 318-19 Chapter 14. The soil pressure above each level (times 1.6) bends the stem; the weight of the concrete and soil above it (times 0.9 and, separately, 1.2) presses it together. The tension on either face may be at most φ 5 √f′c (150 psi for 2,500 psi concrete, φ = 0.60) and the shear φ 4/3 √f′c (40 psi).
- Toe and heel: each bends as a plain concrete cantilever off the stem, taken 2 in thinner than built because it's cast against the soil (ACI 14.5.1.7). Keep them short, about as long as the footing is thick, or the footing needs bars.
Not checked: settlement, the slope of the ground as a whole, and walls of stacked block or stone, whose joints take no tension. A wall over 4 ft from the bottom of the footing to the top, or one holding up a surcharge like a driveway, needs a building permit (IBC 105.2), and often an engineer's stamp.
Gravity retaining wall questions
What is a gravity retaining wall?
A wall that holds back soil by its own weight, with no bars. It's usually plain concrete, stone or large blocks, wide at the bottom and narrower at the top. A cantilever retaining wall instead uses a thinner reinforced stem on a wide footing, and the soil on the footing's heel holds it down.
How wide should a gravity retaining wall be?
The bottom is usually about half to two thirds of the wall's full height, from the bottom of the footing to the top, and the top at least 12 in. Sloped backfill, a surcharge, water or soft soil push it wider. The table above gives sizes for good soil.
How tall can a gravity wall be?
Concrete gravity walls are common up to about 6 to 8 ft of retained soil. Above that the concrete adds up quickly, and a cantilever wall uses much less of it. This calculator goes to 10 ft.
Why slope the back instead of the front?
With the back sloping, the soil resting on it adds weight behind the middle of the wall, which helps against overturning and sliding. An upright front face is also easier to form and looks plumb. Walls are also built with the front leaning back into the soil (a batter), which this calculator doesn't model.
Does a gravity wall need drainage?
Yes. Water behind a wall can double the pressure on it. Put free-draining gravel against the back of the wall with a perforated drain along the footing, or weep holes through the wall, so the soil stays drained. If water can rise behind the wall anyway, enter its level and the calculator counts it.