------------------ | -------- | ------------- | ---------------------------------------------- | | Retained height | H | ft / m | Height from top of stem to top of footing | | Stem thickness (top) | t_top | in / mm | Horizontal thickness of the stem at the top | | Stem thickness (base) | t_base | in / mm | Horizontal thickness of the stem at the base | | Base width | B | ft / m | Total width of the footing from toe to heel | | Toe length | L_toe | ft / m | Projection of footing in front of the stem | | Base thickness | t_base_f | in / mm | Vertical thickness of the footing | | Friction angle | phi | degrees | Internal friction angle of soil | | Cohesion | c | psf / kPa | Soil cohesion (typically 0 for granular soils) | | Soil unit weight | gamma | pcf / kN/m3 | Unit weight of retained and foundation soil | | Surcharge | q | psf / kPa | Uniform surcharge load at the surface | | Seismic coefficient | kh | dimensionless | Horizontal seismic acceleration / g | | Water table depth | z_w | ft / m | Depth to water table below ground surface |

Design methodology

Rankine Active Earth Pressure

For a vertical wall with horizontal backfill, the active pressure coefficient is:

Ka = (1 - sin(phi)) / (1 + sin(phi)) = tan^2(45 - phi/2)

The total active thrust per unit length of wall:

Pa = (1/2) x Ka x gamma x H^2

The resultant acts at H/3 above the base for a triangular pressure distribution. For a uniform surcharge q, the additional horizontal pressure is Ka x q acting uniformly over the full height.

Mononobe-Okabe Seismic Earth Pressure

For seismic conditions, the pseudo-static active thrust coefficient Kae incorporates the horizontal acceleration kh:

Kae = cos^2(phi - theta) / [cos(theta) x cos^2(delta + theta) x F]
where theta = arctan(kh) and F accounts for wall friction and soil properties

The incremental seismic thrust delta_Pae = Pae - Pa acts at approximately 0.6H above the base.

Overturning Check

The factor of safety against overturning about the toe:

FS_overturning = sum(M_stabilizing) / sum(M_overturning)

Stabilizing moments include the wall stem weight, footing weight, and soil weight on the heel. Overturning moments come from the active thrust and surcharge. Minimum FS = 2.0 for static conditions.

Sliding Check

The factor of safety against sliding:

FS_sliding = (sum(V) x tan(phi_f) + c_f x B + 0.5 x Pp) / Pa_horizontal

where sum(V) is the total vertical force, phi_f and c_f are the foundation soil properties, and Pp is the passive resistance at the toe (reduced by factor 0.5). Minimum FS = 1.5 for static conditions.

Bearing Pressure Check

The eccentricity of the resultant vertical force:

e = B/2 - (sum(M_stabilizing) - sum(M_overturning)) / sum(V)

Eccentricity must satisfy e <= B/6 (middle-third rule). The maximum bearing pressure:

q_max = (sum(V)/B) x (1 + 6e/B)  for e <= B/6
q_toe = (2 x sum(V)) / (3 x (B/2 - e))  for e > B/6

Maximum bearing pressure must not exceed the allowable soil bearing capacity.

Passive Earth Pressure at Toe

The passive pressure coefficient:

Kp = (1 + sin(phi)) / (1 - sin(phi)) = tan^2(45 + phi/2)

Passive thrust per unit width:

Pp = (1/2) x Kp x gamma x Df^2 + 2 x c x sqrt(Kp) x Df

where Df is the embedment depth at the toe. Only 50% of Pp is credited in sliding resistance to account for the large deformation required to mobilize full passive pressure.

Typical Retaining Wall Proportions

These are preliminary proportions for gravity and cantilever walls on competent soil. All dimensions must be verified by full stability and structural checks.

Drainage Design Requirements

Common pitfalls

• Saturated backfill without drainage: Even a partially saturated backfill can double the lateral force on the wall. Always design and detail positive drainage.
• Over-reliance on passive resistance: Passive pressure at the toe requires large deformation. Crediting more than 50% of passive resistance in sliding checks is unconservative unless the toe is well-compacted and laterally constrained.
• Ignoring surcharge loads: Construction equipment, material stockpiles, and adjacent structures create surcharge loads. For walls near roadways, include a minimum 250 psf surcharge.
• Middle-third violation: When the resultant moves outside the middle third, a tension zone develops at the heel, the effective bearing width shrinks, and toe pressure spikes. This is a common cause of footing failure.
• Global stability not evaluated: Stability checks (overturning, sliding, bearing) are for the wall-base system only. The entire wall-soil assembly can rotate on a deep-seated failure surface, which requires separate slope stability analysis.

Frequently Asked Questions

What is the minimum factor of safety for retaining wall overturning and sliding? Under static loading, most codes and practice guidelines require a minimum factor of safety (FS) of 2.0 against overturning and 1.5 against sliding. The overturning FS is the ratio of stabilizing moments (wall self-weight plus soil weight on the heel) to overturning moments (active earth pressure resultant). Passive resistance at the toe is typically multiplied by a reduction factor of 0.5 because full passive pressure requires large soil deformation to mobilize. Under seismic or transient load cases, reduced factors of 1.1-1.2 may be acceptable with geotechnical engineer approval.

What is the difference between active, passive, and at-rest earth pressure? Active pressure (Ka) develops when the wall moves away from the retained soil enough to mobilize the full internal friction angle — typically a few millimeters of rotation at the top. At-rest pressure (K0) applies when the wall is restrained against movement, such as a basement wall braced by a floor slab; it is higher than active pressure, commonly K0 = 1 - sin(phi) for normally consolidated soils. Passive pressure (Kp) acts on the toe-side of the wall base and resists sliding; it requires much larger soil deformation to mobilize and is usually reduced before being credited in sliding checks.

How does a surcharge load increase lateral earth pressure on a retaining wall? A uniform surcharge q (force per unit area) applied at the surface behind the wall adds a constant horizontal pressure of Ka x q throughout the full height of the retained soil. This is equivalent to adding a fictitious soil layer of height q/gamma on top of the actual retained height. Strip loads or point loads produce non-uniform pressure distributions requiring more detailed analysis using elastic theory. Vehicle traffic near the wall is a common oversight — a standard minimum surcharge of 250 psf (12 kPa) is typically specified for walls adjacent to roadways.

Why is drainage behind a retaining wall critical to stability? Water pressure from a saturated backfill can equal or exceed the active earth pressure in magnitude, effectively doubling the total lateral force on the wall without any change in soil properties. Hydrostatic pressure acts uniformly at full depth and has no friction component, making it far more destabilizing than equivalent dry soil. Good drainage — through weep holes at 5 ft on center, a 4-inch perforated drain pipe at the base, and 12 inches of clean gravel drainage aggregate behind the wall — eliminates hydrostatic pressure buildup, which is the single most effective measure to improve retaining wall stability.

What does the middle-third rule mean for retaining wall bearing pressure? The middle-third rule states that the resultant vertical force must fall within the middle third of the footing base width (eccentricity e <= B/6). When the resultant is within the middle third, both toe and heel pressures are compressive. If the resultant moves outside the middle third, tension develops at the heel — concrete cannot sustain tension, the effective bearing area shrinks, and toe pressure spikes, potentially exceeding allowable soil bearing capacity. The eccentricity e = M/V is often the controlling check for cantilever wall proportions.

Related calculators

• Concrete footing calculator → — Isolated spread footing design
• Seismic load calculator → — ASCE 7 seismic base shear
• Load combinations → — ASCE 7-16 and IBC factored combinations
• Steel retaining wall → — Steel sheet pile and soldier pile walls
• Combined footing → — Combined and strap footing design
• Unit converter →
• All tools directory →
• All reference tables →

Code references

• ASCE 7-22 Section 3.2 — Lateral earth pressure and surcharge load provisions
• ACI 318-19 Chapter 11 — Plain concrete design for gravity walls
• ACI 318-19 Chapter 14 — Retaining wall design including stem, heel, and toe reinforcement
• IBC Section 1807 — Foundation walls and retaining walls — minimum design lateral loads
• FHWA NHI-10-024 — Earth Retaining Structures reference manual
• NAVFAC DM 7.02 — Foundations and earth structures

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