Seismic Earth Pressure on a Retaining Wall Step by Step - Mononobe-Okabe, Sloped Backfill (IBC 2024)

Intro

0:00Retaining wall design. An eight-foot concrete wall under a sloping hillside, in Seismic Design Category D, designed step by step in StructSuite.

The project: a wall under a 3:1 slope

0:10Here is the project. A house is built into a hillside, and the slope behind it is cut back seven feet. Above the wall, the hill keeps rising at three horizontal to one vertical. This time there is a soils report: it gives the lateral pressure for the sloping backfill, the friction, passive, and bearing values, and the seismic coefficient. The site is in Seismic Design Category D, with an S D S of one point zero. And the wall is poured with the building's sand-lightweight concrete.

What you will get

0:38Here is what you will get by the end of this video. The static and seismic pressures, with the bearing under the footing. And the reinforcement detail, with its shear key. Now let's build it, input by input.

Design basis: seismic earth pressure

0:53The codes: the IBC 2024, ASCE 7-22, and ACI 318-25. In Seismic Design Category D, a wall retaining more than six feet must add the seismic earth pressure. The static checks keep their safety factor of one and a half. Under the earthquake, the IBC accepts one point one. And the seismic increment itself comes from one of three methods; the slope decides which ones work.

Step 1 — Geometry & backfill slope

1:19Step one, the geometry, per foot of wall. The stem is eight feet tall and retains eight feet: the seven-foot cut, plus one foot of soil over the toe. A reinforced concrete stem, twelve inches thick, on an eighteen-inch footing.

1:34Trial one: a two-and-a-half-foot toe and a five-foot heel, the usual proportions for a level backfill. But this backfill is not level. The hillside above the wall rises at three horizontal to one vertical. The slope is entered as an angle: the arctangent of one third, eighteen point four three degrees. The book icon shows how to measure it, from the horizontal. A sloped backfill pushes harder, and adds the soil wedge over the heel.

Step 2 — Soils report values

2:04Step two. This time there is a soils report, so the lateral load comes from it: choose equivalent fluid pressure from the geotechnical report. The report gives fifty-five pounds per cubic foot, active, for a three-to-one sloping backfill. The IBC table values are for level backfill, so with a slope, a report value is what you want. From the same report: a soil unit weight of one hundred twenty-five, a friction coefficient of zero point three five, no cohesion for this sand, passive pressure of three hundred psf per foot, and an allowable bearing of two thousand five hundred psf.

Step 3 — Seismic: method, S_DS, k_h

2:39Step three. This site is in Seismic Design Category D, and the wall retains eight feet, more than six. So IBC section 1807.2.2 requires the seismic earth pressure. Answer include. Three ways to get the seismic increment: the geotechnical report's own pressure, Seed-Whitman, or Mononobe-Okabe. Start with Mononobe-Okabe. S D S, from the site's seismic analysis, is one point zero g. A cantilever wall can move, so it is a yielding wall, and the app takes k h as S D S over two point five: zero point four.

3:14Mononobe-Okabe needs the backfill friction angle: thirty-two degrees, from the report. Leave the wall friction blank, which means zero, the conservative choice. And the slope comes from Step one. Include the wall's own inertia: the stem and footing shake too. And the report allows a one-third increase in bearing for seismic loads, so the factor is one point three three.

Step 4 — Sand-lightweight concrete & bars

3:34Step four. This wall is poured with the same sand-lightweight mix as the building: four thousand psi. Pick sand-lightweight, and lambda becomes zero point eight five: less shear strength, and longer development lengths. It weighs only one hundred fifteen pounds per cubic foot, so it also holds the wall down less. Covers of two, three, and two inches. Stem bars, number six at eight. Horizontal, number four at nine. Heel, number six at twelve, straight.

3:58Toe, number five at nine, with a ninety-degree hook. And number four at twelve along the footing.

Mononobe-Okabe vs Seed-Whitman vs report k_h

4:37Now look at Step five: blocked. With k h of zero point four, the seismic angle is twenty-one point eight degrees. Thirty-two, minus twenty-one point eight, minus the slope, is negative. Mononobe-Okabe simply has no answer for a slope this steep with shaking this strong. Try Seed-Whitman. Also blocked: the resource paper behind it says it is not applicable to sloping ground above the wall. So, back to Mononobe-Okabe, with the soils report's own k h.

5:05S D S over two and a half is a practice default; the report gives a site-specific value, zero point two g, and it takes precedence. Enter it here.

Step 5 — Trial 1 fails: static & seismic sliding

5:14Step five now has two sets of stability checks: static, with a safety factor of one and a half, and seismic, where IBC section 1807.2.3 accepts one point one. Trial one slides. Static sliding is one point one one, under one point five. Seismic sliding is zero point seven one, under one point one. Open the seismic earth pressure row. With the report's k h, the seismic angle psi is eleven point three degrees.

5:41Thirty-two, minus eleven point three, minus eighteen point four three, leaves two point two six degrees. Positive, so Mononobe-Okabe has a solution, but only just. The seismic coefficient, K A E, is zero point six eight eight. Less the static coefficient, the increment is zero point three zero. That is a seismic thrust of over two thousand three hundred pounds per foot, acting at six tenths of the height. Large: a sloped backfill and strong shaking add up.

6:07Open seismic sliding. The static push, plus seventy percent of the seismic thrust, plus seventy percent of the wall's own inertia: five point four kips per foot, against three point eight of resistance. Zero point seven one.

Revision: wider footing, key, heel bars

6:21Revision one, in Step one. A wider footing: a three-foot toe and a seven-foot heel, for more weight and friction. And a shear key, twelve inches wide and twenty-four deep, under the stem front face, for a deeper passive block.

6:45Stability passes now. But a longer heel, under more soil, bends more: heel flexure is at one point five five. The bars must grow. Revision two, in Step four: heel bars, number seven at eight inches.

Step 5 — Final design passes

7:06Run the checks. Everything passes. Static overturning, five point zero three. Static sliding, one point eight three. Seismic overturning, two point six two. Seismic sliding, one point one five: it governs, and it passes the one point one. And the heel, with its number seven bars: zero point seven eight. Open seismic bearing. The allowable, two thousand five hundred, times the report's one point three three, is three thousand three hundred twenty-five psf.

7:34The seismic bearing pressure is one thousand eight hundred seventy-three.

Step 6 — Static & seismic diagrams

7:38Step six draws the wall. The load cases now include the seismic ones. Pick the seismic stability case. Seventy percent of the seismic thrust, one point eight four kips per foot, sits on top of the static pressure. And the bearing pressure rises to one thousand eight hundred seventy-three psf. Switch to resultants and lever arms, to see each force and where it acts.

8:05And the reinforcement detail, to scale: the sloped backfill, the stem bars and hooked dowels, the number seven heel mat, the hooked toe bars, and the shear key. Close the step. All six summaries are blue, and the wall prints as a complete calculation package.

Recap

8:21To recap. An eight-foot wall under a three-to-one slope, in category D. Mononobe-Okabe failed with the default k h, Seed-Whitman does not allow a slope, and the report's k h made it work. Trial one slid. A wider footing and a shear key fixed sliding, and bigger heel bars fixed the heel. Design your own wall, free, at StructSuite dot com.