Calculation Procedures

 

 

 

 

Stem design material is limited to concrete or concrete block masonry. Design strength of concrete and masonry may be specified.

 

Conventional "heel" and "toe" terminology is used, whereby the "heel" side of the wall supports the retained earth. In this program, the "heel" distance is measured from the front face of the stem.

 

Concrete design for stem and footing is based upon ultimate strength design (SD) using factored loads. Factors for various building codes will be displayed on the Criteria > Load Factors page, and may be edited. Since they are editable, be sure to check them before starting a design since you may have changed them.

 

Masonry design is based upon the Allowable Stress Method (ASD) or LRFD, as selected.

 

A geotechnical engineer will have determined design criteria (equivalent fluid pressure, soil bearing, sliding coefficient, etc.). If this is not the case, the designer should exercise special care in selecting these values appropriate to the site conditions. Optionally, you can enter the angle of internal friction for the soil, and the program will compute the corresponding active pressure, using the Rankine or Coulomb formulas based upon the soil density and backfill slope you have specified. If either the Rankine or Coulomb method is chosen, passive pressure and toe active pressure will be based upon the Rankine Formula, assuming a level toe-side backfill. Global stability is not checked and should be provided by the geotechnical engineer if conditions suggest.

 

The factor of safety against sliding and overturning should be at least 1.5:1, and the program displays warning messages when this condition is not satisfied.

Where stem thickness varies, it is assumed that the front face (toe side) of the stem is flush, and the change in thickness occurs on the heel side.

 

Weight of concrete block masonry can be lightweight, medium weight, or normal weight, per the table in this User's Manual. These weights can be modified using the Criteria > Materials screen. Refer to Appendix C.

 

Horizontal temperature/shrinkage reinforcing is at the discretion of the designer and is not computed by the program. Minimum for concrete is 0.0020 times the area of the wall, and 0.0007 for masonry. Some designers may add a layer of reinforcing on the front face of the wall. Two layers of reinforcing is required by code for walls over 10 inches thick; however, some codes exempt “basement walls”, and presumably retaining walls since they too are in contact with earth. For horizontal temperature and shrinkage reinforcing for various stems see Appendix A. Some engineers consider a stem wall like a slab-on-grade and use a lesser percentage of horizontal reinforcing.

 

Toe and heel footing reinforcing may not be required if the footing extends only a short distance beyond the face of the stem. In these cases, shear and bending can be resisted by plain concrete (flexural tension and shear). The program calculates whether flexural tension is adequate by computing the section modulus of the footing (deducting 2" from the bottom of the footing per ACI recommendation) and allowable flexural tension. If this is the case the program indicates that no reinforcing is required, however, the designer may want to include it.

 

Axial loads may be applied to the top of the stem but it is recommended that they do not exceed about 3,000 lbs to avoid reversal of heel bending moment. Slenderness interaction reductions for cantilevered walls are not calculated since h/t ratios are typically less than about 12. Only "positive" eccentricities from the centerline of the top stem are accepted (i.e. toward the toe), since negative eccentricity could lead to unconservative results.

 

Excessively high axial loads are not anticipated by the program and should not be applied if they would cause tension in the bottom of the footing heel – the program assumes typical retaining wall conditions where the heel moment causes tension at the top of the footing. If a design requires a very high axial load, say, over 3 kips/lf, suggest using a footing design software or hand calculations.

 

A vertical component of active pressure, Pv  can be assumed to act along a vertical plane at the back of the footing and the program (Options screen) did allow choices of whether it is used to affect soil pressure, overturning resistance, or sliding resistance. Since some texts and our consultants recommend not using it except for overtturnign resistnace, and only when therer is a sloped backfill, you have only the choice to use it to resist overturning.

 

Surcharge can be composed of either dead load, live load, or both. For the design of the footing and stem sections it is factored per the Load Factor criteria selected.

 

Concrete block thickness’ of 6", 8", 10", 12", 14", and 16" are allowed in the program.

 

Stem reinforcing may be #4 through #10 bars. Soft Metric sizes are shown in parenthesis alongside.

 

Critical section for bending and shear in the footing is at the face of the stem for concrete and 1/4 nominal thickness within the wall for masonry stems, for bending. For shear, for both concrete and masonry stems, the critical section is a distance "d" from the face of the stem toward the toe, and at the face of the stem for the heel. The program does not calculate toe or heel bar development lengths inward from the face of the stem (where the moment is maximum). When selecting and detailing the arrangement of toe and heel bars this should be considered. Refer to Appendix B for development lengths in concrete, which can be adjusted for the stress level.

 

The program designs key reinforcing but flexural and shear stresses for plain concrete are generally adequate, particularly if the depth to width ratio of the key is less than about 1.5:1. The program calculates the bending in the key and determines whether reinforcing is required. For determining section modulus, 3" is deducted from the key width per ACI recommendation. If so, a message will appear. You can then change the key dimensions until the message disappears, or use the rebar suggestions displayed. The key moment and shear is produced by the passive resisting pressure acting against the key.

 

Bond stress masonry for masonry stems. Flexural bond is a slipping (grip) stress between reinforcing and grout, resulting from the incremental change in moment from one point to another, and is a function of the total shear at the section. The program does not specifically check bond stress, but does use the formula μ = M / (j d π db), and compares this with the allowable development length. The formula for bond, relating to shear, is: μ = V / (Σo j d), where Σo is the perimeter of the bar(s) per linear foot. “j” and “d” are the familiar terms. This can be re-written to be approximately:   μ = 0.35 V s / db j d, where “s” is the bar spacing in feet and db is the bar diameter, if the designer wishes to check to the bond.

 

Bond stress in masonry retaining walls is of questionable significance since the bars are customarily cast in grout which by code must be at least 2,000 psi, therefore comparable to embedment in concrete. Furthermore, Amrein (see bibliography) quotes a research study concluding the bond stress could be 400 psi based upon experimental studies showing minimum achieved stresses of 1,000 psi, thereby giving the former value a safety factor of 2.5.

 

This is probably a moot issue since rarely would bond stresses govern over shear stresses, particularly if the stress level in the reinforcing is factored in. Additionally, development lengths for reinforcing in masonry, and code required lap lengths, are considered quite conservative.

 

A lap length dilemma occurs when a masonry stem extends above a concrete stem. To illustrate, consider this: A #7 bar in concrete must be lapped 5’-2” (assuming class B splices, fy = 60ksi, f’c = 3,000 psi) whereas the same bar in masonry must only be lapped 3’-6” (assuming Fy = 24,000 psi). Nevertheless, that is the code, and furthermore no reduction is permitted for under-stressed reinforcing. The designers dilemma is deciding how far up a concrete stem must extend before continuing in masonry. Using the #7 bar example, one would extend the concrete portion up about 5’-6”, then continue with masonry. In this case the bars in the masonry would need to lap below (into the concrete) 48 bar diameters (for Fy = 24,000 psi). Alternatively, and seemingly more logical, would be to extend the reinforcing in the concrete portion up into the masonry 48 bar diameters. But, in this case, how far up should the concrete portion extend? This is the designers’ dilemma, and there appears to be no published guidelines. The program skirts the issue by only giving you the code required “lap lengths if above / below” the section considered.

 

Slab restraint at the base can be specified on the Criteria > Options screen. The program only allows this restraint to occur at the top of the footing – not higher.

Supplementary specifications or notes for the construction of the retaining wall should always be provided, including provisions for draining backfill and other site conditions affecting the design.

RESTRAINED WALLS:

 

A vertical component of active pressure is not activated, whether or not it is check on the Options screen, since the top of the wall is assumed not to deflect and thereby not activate such force. Overturning moment is not applicable, and therefore not displayed, since lateral stability is by restraint at or near the top of the wall and at the base either by slab restraint or a combination of friction and passive resistance.

When floor slab restraint is specified on the Options screen, the point of lateral support is assumed to be at the top of the footing. This may not be strictly true but is considered a reasonable design assumption.

When 100% base fixity is selected, and floor slab restraint is provided, soil pressures are computed as for cantilevered walls, using the fixed moment at the base of the stem as the overturning moment. Bending in toe of footing neglects any stiffening effect of floor slab. For this case, passive and frictional resistances are not displayed, nor is sliding ratio, but total lateral force at base is shown for checking floor slab.

When 100% base fixity is selected, and no floor slab restraint, soil pressures are computed as for cantilevered walls but using the fixed moment at the base of the stem as the overturning moment, and sliding resistance based upon lateral reaction at the base of the footing-this is somewhat conservative since if passive resistance is available the point of lateral support is slightly above the bottom of the footing.

When “Fix Stem @ Base” is unchecked, the footing will not be designed to provide base-of-stem fixity. In this case, the total lateral reactions assume all lateral restraint at bottom occurs at bottom of footing (pin-connection) even if floor slab is present. This may be slightly conservative or unconservative depending upon whether floor slab is present, or if not, if passive resistance is available. Reaction at top restraint assumes pin-connection at bottom of footing.

Shear at base of stem is computed based upon lateral force above that point.

When base of stem is not “fixed” by footing, there will still be some moment at base of stem due to any eccentricity of resultant loads on the footing, and if slab restraint is not provided, an additional moment due to the lateral reaction at the bottom of the footing multiplied by the thickness of the footing. Since the bottom of the stem is assumed “pinned,” for analysis purposes, the resulting soil pressure will be trapezoidal; however, in actuality there will be some fixity at the stem-footing interface. If the Stem Base moment capacity (shown on Stem Screen) is greater than the Moment used for Soil Pressure (shown on Stability screen), then the soil pressure will be uniform over the footing width, and this is displayed

SEGMENTAL RETAINING WALLS:

Their design generally follows the guidelines in Design of Segmental Retaining Walls, 2nd Edition, and Segmental Retaining Walls – Seismic Design Manual, 1st. Edition, both published by the National Concrete Masonry Association (NCMA). Some assumptions have been made to simplify the program (as stated in the program), yet cover most construction practices and design requirements. The user has a choice of masonry block and geogrid vendors, and more will be added as requests are received.

WATER RETENTION PONDS:

Active pressure on the side retaining water (heel side in RetainPro) should be 64 pcf for water, and usually 30 pcf for soil on toe side.  Density on toe side should be soil weight (usually about 110 pcf) and use density of 64 pcf on heel side. Note that if water can seep under the footing there will be a buoyant effect and the weight of the footing (Material Data) would need to be changed. And since the heel pressure under the footing may equal the pressure on top, it would not be appropriate to use the weight of the water to resist overturning.  In this case you could enter, say, 1 pcf for density on the heel side (the program will not accept a zero value).