Masonry retaining wall

A cantilever concrete masonry wall on a reinforced concrete footing, per foot of wall. The stem is by strength design or allowable stress design to TMS 402-22, stability by service loads, the footing by ACI 318-19 strength design either way. A concrete stem is the cantilever retaining wall calculation.

The LRFD / ASD switch sets the stem only. Allowable stress takes the service moment on a cracked section with the axial load left out, conservative for a wall with little of it, axial stress with its slenderness factor and shear, Chapter 8; there is no second-order term. It rests on TMS 402-13 Chapter 8, not 402-22; section numbers are marked to verify, and a calculation saved with ASD before this option is now designed by allowable stress. Stability is by service loads whichever way the stem is designed, which is why the allowable stress example below still verifies it.

Edition. The design basis is TMS 402-22 / TMS 602-22. The text of the 2022 code is not on hand. Section numbers come from TMS's cross-reference, the changes from the TMS handouts of 2022, the second-order equation from the free sample of the Masonry Designers' Guide 2022, and the wording was read in TMS 402-13. Only Eq. 9-28 is a confirmed 402-22 equation number here.

Inputs of the masonry retaining wall #

• Wall and footing: stem height, height above the backfill, footing thickness, toe, heel, key.
• Masonry stem: thickness, grouting, wall weight (an input: it counts in stability and in the axial load), f'm, mortar, one layer of bars with its distance from the earth face, the lap on the dowels. The dowels are taken as the size of the stem bars. TEK 15-07B's tables use d of 5, 7 and 9 in., which is 2.625 in. from the face.
• Earth pressure: Rankine, Coulomb, at rest or an equivalent fluid density entered from the geotechnical report. Water table, surcharge as live or dead. A live surcharge over the heel does not resist sliding or overturning.
• Lateral resistance: friction coefficient and lateral bearing per foot of depth (IBC Table 1806.2, up to 15 times the value at depth), top depth neglected. The factors of safety are inputs, 1.5 prefilled (IBC 1807.2.3).
• Bearing pressure as soil depth over the key: off by default. TEK 15-07B turns the average bearing pressure under the footing into an equivalent soil depth at the top of the key, which raises its resistance a good deal. Off, the key sees only its depth below grade. Whether the extra is reliable is your judgment.
• Deflection limit: 0.007 of the retained height prefilled. TMS 402 9.3.4.5 is written for walls between supports; a limit for a cantilever is your input.
• Load factor on H: 1.6 prefilled, ASCE 7-22 2.3.

Auto-design (editor toolbar) varies wall thickness, heel, toe, footing thickness, stem bars, lap and footing bars. Objective: the lowest cost index. The height, key, soil, wall weight and loads are kept, so a thicker wall gets no credit for its extra weight until you enter it.

Checks performed #

The drawings are the wall section with bars and lateral pressure, and the service bearing pressure under it.

Limitations #

• Allowable stress of the stem by hand and by a reading of TEK 15-07B Table 1 (No. 5 at 16 in. carries 45 pcf at 8 ft in a 12 in. wall, No. 4 does not): no free worked stem in full. Axial load does not reduce the moment on this path.
• Seismic earth pressure, compaction pressure, global stability and the key's own strength are not checked. Enter their effects separately where they apply.
• One thickness and one layer of bars up the stem; bars are not cut off. Horizontal bars, bond beams, drains and waterproofing are not designed.
• Spacing above six times the thickness leaves masonry spanning between bars; the compressed width is limited but that span is not checked (TEK 15-07B Table 1 note c).
• Concrete masonry only. Prescriptive seismic reinforcement (7.3, 7.4) is not checked (to confirm against the code text).
• 6.1.7.1.2 and the modulus of rupture are 402-13 wording under the 402-22 numbers (to confirm against the code text).

Verification examples #

Verification status: 49 values compared in 8 examples (3 published, 5 hand calculations from the cited equations): 39 within tolerance, 10 recorded deviations. Code basis: written from an older edition, with the differences noted. Not yet compared line by line with the target edition.

Published: CMHA TEK 15-07B, pp. 2-3 (allowable stress era, IBC 2003): earth pressure, overturning moment, weights, friction and lateral bearing, sliding factor of safety, average pressure; the earth and footing moments agree. Its masonry lever arm does not: the note puts the masonry at the footing centre (2.67 ft) where its own drawing gives 2.15 ft, so its resisting moment, resultant and toe and heel pressures differ. It also uses 14,670 for its own sum of 16,194. Its key leaves out the key's own weight. All of these are recorded on the Verification page, not fitted.

Masonry Designers' Guide 2022, Example 17.2-5 (sample; 402-22; GFRP bars): pressure, forces, moments, section properties, Mcr. Only the equation for the second-order moment transfers to steel bars. Its printed 22,710 lb-in./ft drops the 5 from the denominator of its own equation; the equation as printed gives 21,464. Recorded on the Verification page.

A read of TEK 15-07B Table 2 (a sanity check, not a verification): at 8.7 ft and 45 pcf, No. 5 at 16 in. passes and No. 4 does not, as the table says. Its 60 pcf column gives the same No. 5 at 16 in., which falls short here; the table's basis isn't given, so this is an open question.

Hand calculations: stem strength and shear with no axial load, stability of the default wall, surcharge moments, lap. No free published example of a steel-reinforced masonry retaining stem written to 402-22 exists; the Guide's other examples are paid.