Methodology / Analysis & Design Assumptions

GENERAL:

For cantilever walls the stem is fixed to the footing, the footing is free to rotate on the supporting soil, and no lateral restraint can exist at or near the top of the wall (otherwise it is not a cantilevered wall).

For restrained ("basement" or "tie-back") walls, the program assumes either 100% fixity at the base, or pinned (zero rotational fixity). Lateral support is at or near the top, and moment/shears are computed at the base, maximum positive, and at the upper support. The program does not check flexural stress reduction for axial loads (the unity interaction formula) since in most cases of basement walls the h/t ratio is below about 10 for masonry walls and somewhat higher for concrete, and axial stresses are low. If axial stresses are considered significant (say over 1000 lbs. per ft. length of wall), the interaction should be checked at the point of maximum positive moment.

For restrained walls, the program assumes that the restraint at or near the top is provided by a continuous line of restraint, such as could be provided by continuous connection to a slab or other diaphragm. If the connection between the retaining wall and the restraining diaphragm occurs only at discrete points, the horizontal span of the wall between those tieback points may become a design consideration. This potential failure mode would have to be checked by supplemental hand calculations, as the program does not consider this type of behavior.

References used for the development of this program are listed in Appendix E.

Stem design material is limited to concrete or concrete 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 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 Design (ASD) or Strength Design (SD), as selected.

A geotechnical engineer will typically have determined design criteria (equivalent fluid pressure, allowable soil bearing pressure, sliding coefficient, etc.). If this is not the case, you can enter the angle of internal friction for the soil, and the program will compute the corresponding active pressure, using the Coulomb formulas based upon the soil density and backfill slope you have specified. If the Coulomb method is chosen, passive pressure will be based upon the Rankine Formula, assuming a level toe-side backfill.

Global stability is not checked.

Weight of concrete block masonry can be lightweight, medium weight, or normal weight, per the table in this User's Manual. Refer to Appendix C.

Horizontal temperature/shrinkage reinforcing is at the discretion of the designer. For horizontal temperature and shrinkage reinforcing for various stems see Appendix A.

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, it is suggested to use footing design software or hand calculations.

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

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.

Stem reinforcing may be #4 through #10 bars.

Critical section for bending in the footing is at the face of the stem for concrete and 1/4 nominal thickness within the wall for masonry stems. 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 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 reinforcing is required, 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.

Slab restraint at the base can be specified on the Footing > Key Design & Sliding Options tab. The program only allows this restraint to occur at the top of the footing – not higher.

RESTRAINED WALLS:

A vertical component of active pressure is not activated, whether or not it is checked on the General tab, since the top of the wall is assumed not to deflect and thereby not activate such force. Overturning moment is not applicable, and is therefore not displayed, since overturning stability is by restraint at or near the top of the wall.

When 100% Fixity @ Base is selected soil pressures are assumed to be completely uniform.

When 100% Fixity @ Base is not selected, and if slab restrains sliding, the soil pressures are calculated considering the following effects:

•Moment on soil due to eccentricity of vertical loads.

When 100% Fixity @ Base is not selected, and if no slab restrains sliding, the soil pressures are calculated considering the following effects:

•Moment on soil due to shear times the footing thickness.

•Moment on soil due to eccentricity of vertical loads.

Shear at base of stem is computed based on the summation of all lateral force above that point.