Retaining Wall Design Notes

Last updated June 29, 2023
By Ian Story

Code Basis

The building code is very vague on the specifics of how to calculate retaining walls. The code prescribes certain checks, but does not prescribe how those checks are to be carried out. For example:

2018 IBC 1807.2.2 specifies that retaining walls supporting more than 6 feet of backfill (note: this is total backfill, not unbalanced fill) must be designed for seismic lateral earth pressure, as determined by a geotechnical investigation. The code does not prescribe how the seismic lateral earth pressure should be determined, though the commentary does point to Section 7.5.1 of the 1997 NEHRP Provisions commentary for a discussion of the issue.

Seismic Calculation Methods

For walls free to yield sufficiently to develop active earth pressure conditions during ground shaking, the current state of the art appears to be the Mononobe-Okabe method. This method is widely used, even for conditions that don’t match the assumptions under which the method was developed (i.e. uniform fine sand backfill).

For walls that cannot yield (such as basement walls braced at the top), the Mononabe-Okabe method is unconservative. Wood’s method appears to be the current state of the art for nonyielding walls.

Seismic Parameters

The most common approaches to global stability (slope stability) checks during an earthquake are pseudo-static approaches. These methods essentially modify the strength and direction of gravity by adding a constant acceleration vector (with horizontal and vertical components) to the base gravitational pull. The system’s response is then calculated under this modified gravitational force and direction.

The acceleration vector is typically expressed as two values: K_h and K_v (horizontal and vertical acceleration), measured in g’s.

Mononobe-Okabe Method

Calculate an active seismic earth pressure coefficient, K_aE (this combines static active pressure and seismic earth pressure).

$K_a_E = \frac{cos^2(\phi+\omega-\theta)}{cos(\theta)cos^2(\omega)cos(\delta - \omega + \theta)\left[1+\sqrt{\frac{sin(\phi+\delta)sin(\phi-\beta-\theta)}{cos(\delta-\omega+\theta)cos(\omega+\beta)}}\right]^2}$

where:
$\phi=$ backfill internal friction angle (degrees)
$\omega=$ batter angle of back face of wall (degrees, positive = wall leaning into slope)
$\theta=tan^-^1(\frac{k_h}{1+k_v})$ (degrees)
$\k_h=$ horizontal seismic acceleration coefficient (g’s)
$\k_v=$ vertical seismic acceleration coefficient (g’s, positive accelerating upward)
$\delta=$ friction angle at wall-soil interface (degrees, commonly taken as $\frac{2}{3}\phi$ for a rough wall surface, consider reducing to $\frac{1}{2}\phi$ for smooth formed concrete)
$\beta=$ slope of backfill (degrees)

The total earth pressure under seismic conditions would be calculated as follows:

$P_a_E = \frac{1}{2}K_a_E(1+k_v)\gamma H^2$

where:
$\gamma =$ density of backfill (pcf)
$H =$ retained height of backfill (to bottom of footing, not unbalanced height) (feet)

Note the $(1+k_v)$ term. The vertical acceleration amplifies (or decreases, depending on direction) the effective weight of the backfill. Before we calculate the total force, however, we need to decompose the total dynamic force into two components representing the static earth pressure and the dynamic earth pressure surcharge due to seismic effects: