5.3

LRFD Spread Footings

5.3.1 LRFD and ASD Spread Footing Analyses – An Overview

Geotechnical LRFD analyses of spread footings are basically analyses of ultimate bearing capacity for the strength limit state and footing settlement for the service limit state. As we discussed earlier in Section 5.2, three primary loading conditions need to be analyzed to satisfy life-cycle loading analyses: service loadings for every day conditions, strength loadings for unlikely, but possible, overloading conditions that may result in structural failure, and extreme loadings representing once in a life-time events.

Current spread footing design practice is a mixture of both allowable stress design (ASD) and strength design (LRFD). Structural engineers estimate a range of wall and column loadings and give these loadings to the geotechnical engineer in the document requesting a geotechnical investigation. If building or bridge loadings are not given in the request for services document, the geotechnical engineer calls the structural engineer and asks for them. Many geotechnical engineers don't seem to be aware that the loadings received from structural engineers are service loadings. If the structural engineer is a young rather inexperienced engineer, he or she often gives the geotechnical engineer factored loadings when requested to provide building loadings. Using factored loadings to analyse footings and then applying a factor of safety (ASD) to the design, results in designing a footing with compounded conservatism.

I recall many times in the past asking my young geotechnical engineers whether they received service loadings or factored loadings from the structural engineer and they did not know. Upon investigation by calling a senior structural engineer at the structural firm, I often find that the young structural engineer gave my young geotechnical engineer factored loadings.

Continuing with the current footing design method description, by some established methods using soil information from field and laboratory testing and service loadings provided by the structural engineer, the geotechnical engineer calculates an allowable bearing pressure that results in reasonably sized footings. If the estimated footing sizes are about 10-feet wide or greater, the geotechnical engineer calls the structural engineer and discusses the possibility of using piles or drilled shafts for building support. Assuming the probable footing sizes are reasonable, the geotechnical engineer calculates estimated footing settlements using the probable footing sizes and allowable bearing pressure. If the predicted footing settlements are all less than 1 inch or the predicted differential settlements are less than about ¾ inch, the geotechnical engineer is satisfied that the recommended spread footing allowable bearing pressure is suitable and gives his results and recommendations to the structural engineer in the geotechnical report. Whether the geotechnical engineer is aware of it or not, everything that he or she has done to this point is part of an allowable stress design (ASD) because he or she has essentially analyzed service loadings for settlement.

Upon receipt of the geotechnical report, the structural engineer looks up the recommended allowable bearing pressure and if it is reasonable, he or she can start spread footing design as soon as column and wall loadings are available. If the geotechnical engineer's recommended allowable bearing pressure is not reasonable to the structural engineer, he or she often calls the geotechnical engineer to complain about their conservatism and many times they convince the geotechnical engineer to “up their recommendation.”

Using service loadings and the recommended allowable bearing pressure the structural engineer calculates the required area for column footings and footing width for wall footings. Up to this point in the design and sizing of spread footings, the structural engineer is also participating in allowable stress design (ASD). Next the structural engineer takes his factored loadings and the calculated spread footing size and computes a factored bearing pressure for use in his or her spread footing concrete design. At the point where the structural engineer calculates a factored soil bearing pressure, they have transitioned into strength design to be compatible with LRFD concrete design procedures. From this point forward in structural design all of the analyses are done in the LRFD format.

Given this explanation, you can see why I say that the current spread footing design process is a mixture of ASD and LRFD design procedures. Assuming that service loadings are used in geotechnical analyses and factored spread footing bearing pressures are used in concrete footing designs, current practice is a mixture of ASD and LRFD, whether the participating engineers are aware of it or not.

If you are interested in reviewing the procedures used by structural engineers to design concrete spread footings, I am aware of two good references published by the Portland Cement Association (PCA). The first one is Notes on ACI 318-05 Building Code Requirements for Structural Concrete with Design Applications (Kamara and Rabbat, 2005). Chapter 22 of this book discusses design of footings and gives detailed examples of the concrete footing design process, including a clear description of calculating factored soil bearing pressure for use in LRFD concrete design. I might add that the older I get the more I turn into an editor. On the bottom of page 22–25 in this reference when describing the area A2, the text should read 2 vertical to 1 horizontal not 1 vertical to 2 horizontal.

The second book from PCA that clearly describes the factoring of allowable soil bearing pressure for concrete footing design is titled Simplified Design: Reinforced Concrete Buildings of Moderate Size and Height (Alsamsam and Kamara, 2004). I told you that design was becoming more and more complex as time goes on, and structural engineers like the rest of us are always on the outlook for references and methods that “simplify” their lives. Chapter 7 of this book is devoted to simplified design of footings. I expect that geotechnical engineers reading the footing design description in Chapter 7 will bristle at the material included in Section 7.3 which suggests that structural engineers may simplify footing design by foregoing geotechnical investigations and using local building code values for allowable soil pressures. Forgoing a geotechnical investigation may make footing design simpler, but it will also fatten the wallets of attorneys suing structural engineers for failed structures built over undetected waste dump sites!

5.3.2 A Spread Footing LRFD Design Approach

Requirements for geotechnical LRFD spread footing analyses are included in the 2010 AASHTO Bridge Design Specifications Section 10.6. When describing LRFD design of spread footings, the 2010 AASHTO manual states, “Spread footings shall be proportioned and designed such that the supporting soil or rock provides adequate nominal resistance, considering both the potential for adequate bearing strength and the potential for settlement, under all applicable limit states in accordance with the provisions of this Section” (i.e., Section 10.6). I'm tempted to do some editing of my own on this wordy, run-on sentence, but then it is a quote from a government document!

AASHTO requires, and as a practicing geotechnical engineer I prefer using an effective footing area to account for overturning moments and eccentrically applied foundation loadings in accordance with the Meyerhof method. When using the effective footing area, B′ wide by L′ long, the applied loadings are assumed to act at the centroid of the reduced effective area. Recall from Section 4.2, Equation 4.2.2 that the reduced footing dimensions are defined as:

(5.3.1)

where,
eB = eccentricity in the B direction
eL = eccentricity in the L direction.

When calculating footing settlements for service limit states and bearing resistance for strength limit states, the reduced footing area based on B′ and L′ is used.

AASHTO commentary 10.6.2.1 suggests that spread footing design is frequently controlled by service limit state settlements. They also suggest that it is “advantageous” to size footings for service limit states and then check the strength and extreme limit states. I agree. This approach of checking service loadings roughly follows the footing design approach previously followed by geotechnical and structural engineers for decades, as described above in Section 5.3.1.

As I have mentioned before and will mention again, geotechnical and structural engineers must work together to assure that both geotechnical and structural footing design concerns are resolved.

Starting with the service loading analyses first, the geotechnical engineer should develop load versus settlement charts for service loadings for a range of footing sizes. These charts are used by the structural engineer to size footings for each column, wall, abutment, and so on. With the preliminary footing sizes based on service loadings and settlement limitations, the structural engineer calculates factored loadings for each applicable strength limit state and calculates the footing bearing pressure for each case. Given the preliminary footing sizes and factored bearing pressures for strength limit states, the geotechnical engineer calculates the nominal and factored bearing pressure resistance. Comparing the factored loading footing bearing pressure with the factored bearing pressure resistance, the preliminary sizes of footings are checked to see if the footings are large enough to satisfy strength limit state loading cases. If the footings are large enough so that their factored bearing resistances are greater than the factored bearing pressures, footing concrete and reinforcing are designed and the footings are checked for extreme loading cases.

5.3.3 Development of Spread Footing Load-Settlement Curves

I would like to give my friends at the Arizona Department of Transportation's Geotechnical Design Section a tip of the hat. They have issued an LRFD design policy document SF-1 (ADOT, 2010a) for design of spread footings that is very helpful in showing consulting geotechnical engineers how to prepare LRFD foundation design charts for use by bridge designers. I highly recommend that you go on the internet and find a copy of this document or contact the Geotechnical Design Section at ADOT and request a copy. I might add that they have several design policy documents for spread footings and for drilled-shaft LRFD designs that illustrate how geotechnical engineers can report the results of their analyses in formats that are beneficial to bridge design engineers. Figure 5.3.1 is a copy of the example “Factored Bearing Resistance Chart” for spread footing design from ADOT's Geotechnical Design Policy SF-1.

Figure 5.3.1 Spread footing factored bearing resistance chart example (ADOT, LRFD Geotechnical Design Policy Document SF-1, 2010)

Figure 5.3.1 includes a lot of information in one small package. The horizontal axis is effective footing width in feet, applying the Meyerhof method, as given above in Equation 5.3.1. The vertical axis is factored net bearing resistance in kips per square foot. By net bearing resistance, we mean that the nominal bearing resistance has been reduced by subtracting the overburden stress at the base of footing level. The factored net bearing resistance is the net bearing resistance times the appropriate resistance factor φbearing.

The rising bold dashed line in the upper left corner of Figure 5.3.1 is the factored net bearing resistance for the strength limit state using a resistance factor φb of 0.45 because this example is for SPT data in sandy soil. The family of falling curves running from the upper left to the lower right side of Figure 5.3.1 represents the service limit state where the factored nominal net bearing resistance is given for selected settlements. In this example the service load settlements range from 0.25 to 2.0 inches. I might add that these factored nominal net bearing resistances for service loadings equal their nominal net bearing resistances because the resistance factor for the spread footing service limit state, φb equals 1.0.

You might now be asking yourself, how can we plot strength and service loading cases on the same plot in Figure 5.3.1? The strength and service limit states are different, but we can benefit by plotting them on the same figure so that service and strength cases can be checked by the project structural engineer at the same time.

Settlement values given for the family of curves shown in Figure 5.3.1 are immediate settlements. How do we calculate settlement values used to plot service limit state curves like those shown in Figure 5.3.1? This is where difficulties and complexities start to enter the spread footing analysis process.

We know from earlier discussions that footing settlements may develop as immediate/elastic settlements, consolidation settlements, or secondary compression (i.e., creep) settlements. To decide what settlements to compute, you need to have an idea of when in the life of a structure footing settlements are important to structural function. If settlements don't cause structural distress, and if people don't see them, who cares? Oh, you would be surprised who cares.

After you have determined what types of settlements are important, you need to roughly determine how accurately you need to estimate footing settlements.

5.3.4 Development of a Spread Footing Service and Strength Resistance Chart

To develop a spread footing service limit state chart like that given in Figure 5.3.1, you first have to decide what calculation method to use in estimating footing settlements. After you decide on a settlement calculation method, you have to solve the settlement equations backwards, in other words, you select a settlement for a given footing width, and back calculate the bearing pressure that is required to generate the selected settlement. Doesn't that sound relatively simple?

AASHTO 2010 manual section 10.6.2.4.2 indicates that you can calculate immediate settlements in sands by use of elastic theory or by an empirical method proposed by Hough (Hough, 1959). I expect that many engineers would pick one of these two methods and go with it. Why not? These methods are specified by AASHTO so their use is in compliance with government requirements. You might believe that this use of AASHTO-specified methods of calculating spread footing settlements is prescriptive design requiring compliance by the geotechnical engineer, but it is not.

Both AASHTO 2010 and FHWA 2006 (Samtani and Nowatzki, 2006) suggest that empirical methods such as the Hough method may over-estimate spread footing settlements by a factor of two or more, resulting in use of costly deep foundations when spread footings may have performed satisfactorily. First AASHTO 2010 specifies a settlement calculation method to be used, and then they tell you that it is likely too conservative. What is this all about? To explain, let me first share ADOT's approach to the conservatism issue, then let me point out the small print in AASHTO 2010.

ADOT spread footing LRFD design guidance outlined in SF-1 repeats the wording included in FHWA 2006 about conservatism of the Hough method, and then they propose using the Schmertmann method for calculating immediate settlements of spread footings as outlined in Section 8.5.1 of FHWA 2006. Schmertmann's method is generally considered to be more precise than the Hough SPT chart method, although as I mentioned earlier even the Schmertmann method has significant limitations when correlated CPT values are used (among other limitations). Schmertmann originally proposed his method of calculating settlements of spread footings on sands in 1970. In 1978 Schmertmann revised his method to increase the soil modulus calculated from cone penetration data. ADOT recommends using the 1978 Schmertmann method as described in FHWA 2006, although they recommend using SPT-correlated values of soil modulus. In Section 3.2 above I have given you a rather detailed description of the 1978 Schmertmann method for calculating settlements in sandy soils.

Although I am aware that CPT equipment is rather scarce in many parts of the United States and that SPT equipment is commonly used in geotechnical investigation work, I still believe that you should use CPT equipment whenever possible to achieve better settlement estimates with the Schmertmann method.

I might also add that for LRFD service loading cases FHWA 2006 recommends that you limit use of the time factor to 0.1 year for immediate settlements and 1.0 year for secondary compression or creep settlements. They also recommend that you use a time factor C2 equal to 1.0 if you are also calculating consolidation settlements.

Based on my review of FHWA 2006 and ADOT LRFD spread footing design guidance, it is apparent that they suggest a refinement of spread footing settlement calculations for bridge structures over the Hough method to improve accuracy of spread footing settlement estimates. They suggest that the Hough method may be more suitable for calculating embankment fill immediate settlements.

In AASHTO 2010 LRFD manual Section C10.6.2.4.2, they mention that refined settlement calculations may be required, and they give several additional references for other settlement calculation methods. AASHTO 2010 also recommends in Section 10.4.6.3 that “where evaluation of elastic settlements is critical to the design of the foundation … in-situ methods such as PMT (i.e., the pressuremeter test) or DMT (i.e., the dilatometer test) for evaluating the modulus of the stratum should be used.” The only reason that I can imagine for performing pressuremeter or dilatometer tests is to obtain improved estimates of soil moduli to improve calculated spread footing settlements.

Again when considering methods of computing spread footing settlements, we are presented with an application of the graded approach. If empirical methods provide suitable prediction accuracy for our design purposes they are appropriate to use. If advanced tests and analysis procedures are required to fulfill our design purposes then they are more appropriate to use.

5.3.4.1 Calculation of the Strength Limit State for Spread Footings

To plot a strength limit state line on the factored bearing resistance chart shown in Figure 5.3.1, you have to calculate the nominal bearing resistance for a series of footing widths. Calculation of the strength limit state for spread footings requires an equation for calculating of the nominal bearing resistance (what we used to call the ultimate bearing capacity). Like we have done for decades, the nominal bearing resistance of spread footings is calculated using the bearing capacity equation (what some folks call the 3 Ns equation), see Equation 5.3.2 below.

(5.3.2)

where,
c = cohesion or undrained shear strength (kips per square foot, ksf)
Nc = cohesive bearing capacity factor (dimensionless)
Nq = surcharge bearing capacity factor (dimensionless)
Nγ = unit weight (of soil below footing) bearing capacity factor (dimensionless)
q = γDf, q is the surcharge pressure of soil above the bearing surface of the footing, if there is no applicable surcharge loading on the ground surface, then q is calculated from γ the moist unit weight of soil (kips per cubic foot) above the bearing level times Df the depth of footing in feet (q is expressed in units, ksf)
γ = total moist unit weight of soil below the footing bearing surface in the third term of the bearing capacity equation (kips per cubic foot, kcf)
B = footing width (feet)
C = Cwq and Cwγ ground water table correction factors (dimensionless)
s = sc, sq, and sγ are shape correction factors, since the bearing capacity equation was originally formulated for strip footings not square or rectangular footings (dimensionless)
dq = depth correction factor since the shearing resistance of the soil between the bottom of footing and ground surface was not originally included in the bearing capacity equation (dimensionless)
I = ic, iq, and iγ are inclination factors to correct for loadings that are not vertically oriented or do not act perpendicular to the footing bearing surface (dimensionless).

If you intend to determine the nominal bearing resistance of spread footings for bridge or transportation-related structures, I recommend that you refer to the AASHTO 2010 manual or to the FHWA 2001 shallow foundations manual (Munfakh et al., 2001). If you are designing a spread footing for a building using geotechnical LRFD, you are free to use whichever bearing capacity equation you deem fit. Personally I am partial to the Meyerhof version of the bearing capacity equation.

After you calculate an appropriate value for the nominal bearing resistance you need to select a resistance factor that is appropriate for the soil type, field testing type, laboratory testing, and the bearing capacity equation that you used. Current AASHTO 2010 guidance for selection of a spread footing strength resistance factor is given in their Table 10.5.5.2.2–1. In this AASHTO table for the spread footing strength limit state, they give resistance factors that range from 0.45 to 0.50. AASHTO also indicates that you can use a resistance factor of 0.55 when a plate load test is used to determine the bearing resistance. I wonder … what would the resistance factor be if you did a full-scale footing load test to failure? If we conducted, properly designed, monitored, full-scale footing load tests, I would lobby for an increased resistance factor similar to increased factors allowed when you perform full-scale pile or drilled-shaft load tests.

Of course AASHTO gives you guidance on selecting spread footing bearing resistance factors, φb, and that's fine, but I recommend that you periodically check geotechnical journals for current papers on this topic because a significant amount of research is currently ongoing in this field.

Wait a moment, what did I say in the first sentence two paragraphs above? “After you calculate an appropriate value of the nominal bearing resistance …” Are you going to let me get away with a comment like that? What “appropriate value” are we talking about? Very good question, I'm glad you asked.

The nominal bearing resistance or ultimate bearing capacity calculated by the 3 Ns bearing capacity equation, Equation 5.3.2, requires values of the soil cohesion, soil internal friction angle and soil moist unit weight. I hope you noticed that we have two values of the moist unit weight in play in this equation. The second term, called the surcharge term, uses the moist unit weight of soil above the footing's bearing elevation to calculate the surcharge q, and the third term, called the gamma term, uses the moist unit weight of soil below the footing's bearing elevation. Now what about the soil shear strength parameters c and ?

Standard practice indicates that for sandy, cohesionless soils, we should use effective stress or drained soil shear strength parameters in the bearing capacity equation. Laboratory tests that give drained shear strength parameters c′ and ′ would be the direct shear test and the CD (consolidated drained) triaxial test. There are also correlated effective stress values of friction angle reported for CPT and SPT tests that you might consider using to find ′.

For spread footings on clayey, cohesive soils, standard practice indicates that a total stress analysis with undrained shear strength parameters should be used in the bearing capacity equation. Tests used to find the undrained shear strength of clayey soils includes the unconfined compression test and the UU (unconsolidated undrained) triaxial test (i.e., su = cu = qu/2).

This is all fine, but please don't forget that the drainage condition and stress path of the state of stresses that you are analyzing controls the actual shear strength of your foundation soils. For example, if your foundation is supported by clayey soil and is loaded slowly enough to avoid generation of excess pore water pressures, you should use effective stress parameters c′ and ′ in your bearing capacity calculations. If on the other hand your foundation is supported on saturated silty, fine sand and the anticipated loading is an extremely quick dynamic loading, you should use undrained shear strength parameters in your bearing capacity calculations. One more case, what if your foundation soil is clay shale or stiff, fissured clay that looses strength with time due to wetting and dissipation of negative pore water pressures (i.e., loss of suction and dry strength)? For this case, you should use softened, effective shear strength parameters in your bearing capacity calculations, that is, soil shear strength parameters which model the soil's softened stress state at a future time. The three telescope spread footing foundations shown in Figure 5.3.2 bear on select compacted granular fill.

Figure 5.3.2 Three large telescope spread footing foundations

5.3.5 Other Spread Footing LRFD Considerations – Eccentricity and Sliding

Although analyses of spread footing settlement and bearing resistance are of primary importance when doing LRFD design of spread footings, we still have to consider foundation stability, which includes considerations of overturning moments and lateral sliding forces.

5.3.5.1 Overturning Moments – Limiting Eccentricity

Back when allowable stress design was king, we used to have a rule of thumb that the resultant force on a footing should act within the middle third of the footing base. The middle third was defined as B/3 where B was equal to the footing width. The idea behind this middle third concept was simple. If the resultant force on a footing acted outside the middle third of its base, the edge of the footing would start to lift off the ground. Somewhere along the line, engineers in charge decided that use of the phrase “resultant in the middle-third” was confusing. In its place they declared that the eccentricity of the loading acting on a footing should not exceed B/6, where eccentricity was defined as the overturning moment acting on the footing divided by the vertical loading acting on the footing. I guess this was simple enough. They were just applying the rule of statics that says that two statically equivalent systems have the same forces and moments acting. But wait a moment, the allowable eccentricity B/6 acts on both sides of the center of the footing resulting in a width of permissible eccentricity of two times B/6 which is equal to B/3. Use of the eccentricity definition resulted in the same criterion as the earlier middle third rule.

So long as we were using ASD with service loadings, the middle third or the allowable eccentricity of B/6 was the limiting criterion for application of overturning moments (i.e., M/V ≤ B/6) to a spread footing. Now we are factoring applied footing loadings for the strength limit case in LRFD design, what limiting eccentricity do we use for factored loadings?

AASHTO 2010 in Section 10.6.3.3 says that the eccentricity of loading for the strength limit state with factored loads should not exceed B/4. Use of an eccentricity of B/4 would be the same thing as using the middle-half for earlier limiting eccentricity criteria. Physics hasn't changed; won't an eccentricity of B/4 result in footing edge lift. The answer is yes. This makes me wonder if AASHTO is anticipating a limited amount of footing edge lift or are they considering the limited probability that fully factored loadings will actually occur. In the commentary to AASHTO 2010 Section 10.6.3.3, they have the following statement, “A comprehensive parametric study was conducted for cantilevered retaining walls of various heights and soil conditions. The base widths obtained using the LRFD load factors and eccentricity of B/4 were comparable to those of ASD with an eccentricity of B/6.” I'm not sure. I have some doubts about this commentary statement. This sounds like an economic decision to me.

This B/4 versus B/6 eccentricity situation piqued my curiosity about what the Arizona Department of Transportation might be doing. Sure enough, ADOT has issued a geotechnical design policy document SF-2 titled “Limiting Eccentricity Criteria for Spread Footings based on Load and Resistance Factor Design (LRFD) Methodology.” ADOT took a look at AASHTO's B/4 eccentricity limitation and checked it against their retaining wall standards and concluded that the B/4 limitation would result in an increase in footing widths of about 15 to 20% for standard walls that previously met the ASD footing width limitations. I didn't call my friends at ADOT to hear their reasoning, but it doesn't take much imagination to see that increasing the footing width of all wall and bridge footings in the State of Arizona that had eccentric loadings by 20% would cost a lot of money.

In ADOT document SF-2 (ADOT, 2010b) they proposed their own limited eccentricity criteria based on calibration of past ASD wall design practice using LRFD load factors in Section 3 of AASHTO 2010. Again, I suggest that you obtain a copy of ADOT's document SF-2, but below I have included a sample of their proposed limiting eccentricity criteria:

“The eccentricity, e, of loading at the strength limit state, evaluated based on factored loads shall meet the following limits:

• For footings on soils: e ≤ B [(1/3) – (β/320)]
• For footings on rocks: e ≤ B [(3/7) – (β/500)]

where,
B = the footing dimension (width or length) in which the eccentricity is being evaluated,
β = the backslope inclination angle of the soil retained behind the wall in degrees with respect to the horizontal. The maximum limit on β is 26.56 degrees (i.e., 2H : 1V slope; H = Horizontal, V = Vertical). In addition, the slope shall satisfy the minimum slope stability requirements for the project.

The eccentricity, e, computed by the above equations has the same units as B.”

ADOT has several limitations on the application of their proposed eccentricity criteria, such as granular backfill only, active earth pressures only, and so on, which I will not list here, but again I suggest you look up their SF-2 document.

5.3.5.2 Spread Footing Sliding Failure

Failure of a footing by sliding in LRFD methodology is considered to be a strength limit case. Factored lateral loadings are compared with factored sliding resistances developed from sliding friction resistance and passive sliding resistance. As I mentioned earlier in Section 4.2 when discussing sliding resistance of gravity and cantilevered retaining walls, the passive soil resistance must be present throughout the life of the footing to be included in sliding resistance.

Apparently the reliability of base frictional resistance is considered to be much higher than passive soil resistance to sliding, because resistance factors given in AASHTO Table 10.5.5.2.2-1 range from 0.8 to 0.9 for frictional sliding resistance and are given as 0.5 for passive soil resistance. Passive resistance may not be highly reliable, but you also have to remember that large lateral deformations are required to mobilize full passive resistance, while relatively small lateral deformations are required to mobilize frictional resistance to sliding. Without doing strain-compatible calculations, I would expect a greater reduction in passive resistance when it is added to frictional resistance.

References

AASHTO (2010) AASHTO LRFD Bridge Design Specifications, 5th edn, 2 volumes, American Association of State Highway and Transportation Officials, Washington, D.C.

ADOT Geotechnical Design Section (2010a) Geotechnical Design Policy SF-1, LRFD, Development of Factored Bearing Resistance Chart by a Geotechnical Engineer for Use by a Bridge Engineer to Size Spread Footings on Soils based on Load and Resistance Factor Design (LRFD) Methodology, December 1, 2010, 15 pages including the cover letter.

ADOT Geotechnical Design Section (2010b) Geotechnical Design Policy SF-2, LRFD, Limiting Eccentricity Criteria for Spread Footings based on Load and Resistance Factor Design (LRFD) Methodology, December 1, 2010, 7 pages including the cover letter.

Alsamsam, I.M. and Kamara, M.E. (2004) Simplified Design, Reinforced Concrete Buildings of Moderate Size and Height, Chapter 7 Simplified Design for Footings, 3rd edn, Portland Cement Association, Skokie, Illinois, 19 pages.

Hough, B.K. (1959) Compressibility as the basis for soil bearing value, Paper No. 2135. Journal of the Soil Mechanics and Foundations Division, American Society of Civil Engineers, 85(SM4).

Kamara, M.E. and Rabbat, B.G. (2005) Notes on ACI 318-05 Building Code Requirements for Structural Concrete with Design Applications, Chapter 22 Footings, Portland Cement Association, Skokie, Illinois, 22 pages.

Munfakh, G., Arman, A., Collin, J.G., et al. (2001) Shallow Foundations Reference Manual, FHWA-NHI-01-023, Federal Highway Administration, United States Department of Transportation, Washington, D.C.

Samtani, N.C. and Nowatzki, E.A. (2006) Soils and Foundations Reference Manual, Volumes 1 and 2, FHWA-NHI–06-089, 2 volumes, National Highway Institute, Federal Highway Administration, Washington, D.C., 1056 pages.