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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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Suggested Citation:"Chapter 3 - Findings." National Academies of Sciences, Engineering, and Medicine. 2010. LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures. Washington, DC: The National Academies Press. doi: 10.17226/14381.
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57 3.1 Design and Construction State of Practice 3.1.1 Questionnaire and Interviews Code development requires examining the state of practice in design and construction in order to address the needs, research the performance, and examine alternatives. The identification of current design and construction methodologies was carried out via a questionnaire. A six-page questionnaire concerning the design and construction practices of highway departments was developed and distributed in June 2007 to 161 state high- way officials, TRB representatives, state and FHWA bridge engineers, and bridge engineers from Canadian Provinces. Appendix C provides a copy of the questionnaire. 3.1.2 Summary of the Questionnaire Response A total of 40 surveys was returned and analyzed (39 states and 1 Canadian province, see Table C-1 in Appendix C). The survey elicited information concerning foundation alternatives and shallow foundation design. The questionnaire was fol- lowed by telephone interviews with geotechnical engineers of selected states determined based on information gathered in the responses. Appendix C provides a summary of the responses obtained for the questionnaire in the form of two summary tables and a summary of the responses. The original form was used as a basis for the summary encompassing all responses. The percent (%) values provided relate to the arithmetic aver- age of the responding states and province (Alberta, Canada) for the specific item. 3.1.3 Summary of Major Findings— Foundation Alternatives Among survey respondents, the use of foundations by type was the following: shallow foundations were used by 17%, driven piles were used by 59%, and drilled foundations were used by 24%. The use of shallow foundations was not changed overall relative to the last survey (conducted under NCHRP Project 12-66). There is a consistent trend, however, in the decrease of the use of driven piles—75%, 62%, and 59% for 1999, 2004, and 2007, respectively—and the increase of the use of drilled foundations—11%, 21%, and 24% for 1999, 2004, and 2007, respectively (1999 data from Paikowsky et al., 2004; 2004 data from NCHRP Project 12-66). There is some dis- crepancy between the total foundation use and the percent- age of use specifically addressing piers and abutments. Some of this discrepancy can be attributed to the fact that all foun- dations include non-bridge structures like buildings, posts, and sound barriers. The average use presented above changes significantly across the country as shown in Table C-2 that relates to bridge foundations only (with average use of 17.7% for abutments and piers). The use of shallow foundations in the Northeast exceeds by far the use of shallow foundations in all other regions of the United States—40% in New York, New Jersey, and Maine; 47% in New Hampshire; 50% in Vermont; 53% in Massachusetts; 65% in Pennsylvania; and 67% in Connecticut. Other “heavy users” are Tennessee (63%), Washington (30%), Nevada (25%), and Idaho (20%). In contrast, out of the 39 responding states, 6 states do not use shallow foundations for bridges at all, and an additional 8 states use shallow foundations in 5% or less of highway bridge foundations. 3.1.4 Summary of Findings—Subsurface Conditions for Shallow Foundations The summary provided in Appendix C indicates that 55.8% of shallow foundations are built on rock (average of piers and abutments) with an additional 16.8% on Intermediate Geomaterial (IGM); hence, 72.6% of foundations are built on rock or cemented soils and only 27.4% are built on soils (24.2% are built on granular soils and 3.2% are built on clay C H A P T E R 3 Findings

or silt). A further breakdown is presented in Table C-2, allow- ing clarification of the practices of the different states. For example, Michigan indicated that 50% of its shallow foun- dations at the piers’ location are built on fine-grained soils; however, Michigan is using only 5% of its pier foundations on shallow foundations; hence, only 2.5% of the pier foundations are built on clay or silt. Examining all the states this way sug- gests that the state leading in building bridge foundations on clay is Washington (6%) followed by Vermont (5%), Idaho (4%), and Michigan and Nevada (3.75%) each. Further exam- ination of these facts (in a telephone interview) revealed that Washington’s use of foundations on silt and clay refers to highly densified glacial soils with SPT N values exceeding 30 for silts and between 40 to 100 for the clays. Twenty-eight states (out of 39) do not build shallow foun- dations for bridges on cohesive soils at all; hence, only 0.8% of all bridge shallow foundations are built on clay or silt (including Washington), in comparison to 16.9% on rock, 5.4% on IGM, and 12.2% on frictional soils. The survey also suggests that only about 60% of the foundations on clay were built without ground improvement measures; hence, only about 0.48% of the bridges were actually built on shallow foundations on cohesive soils, practically a marginal number considering the state of these soils as described by Washington State Department of Transportation (WSDOT). 3.1.5 Summary of Findings— Design Considerations 3.1.5.1 Foundations on Rock Findings for foundations on rock are the following: 1. About 90% of the states using foundations on rock obtain rock cores, evaluate RQD, and conduct uniaxial (unconfined) compressive strength tests. 2. About 19% of the states using foundations on rock use presumptive values alone, 22% use engineering analyses alone, and 59% use both when evaluating bearing capacity. 3. Fifty-three percent (53%) of the states use AASHTO’s pre- sumptive values. Other states use or consult the Canadian Foundation Engineering Manual (2006), NY Building Code (International Code Council, 2008), or NAVFAC (1986), or base their capacity values on local experience (e.g., South Dakota, Wisconsin, Oregon, Kansas, Iowa, and Arkansas). 4. Seventy percent (70%) of the responding states would like to see a specific analytical method presented for the eval- uation of the bearing capacity of foundations on rock. Twenty-five percent (25%) use the Kulhawy and Goodman (1987) analytical method and 33% use the Carter and Kulhawy (1988) semi-empirical design method. Others use Kulhawy and Goodman (1980), Hoek-Brown (1997), and Hoek and Marinos (2000). Two states commented on using GSI instead of RMR. 5. Sixty percent (60%) evaluate failure by sliding for footings on rock. Seven states do not evaluate sliding because of a requirement to “wedge” the foundation into the rock either by a key (Alabama—1 to 2 ft, Alaska—1.5 to 2.0 ft, North Carolina) or some other method (Iowa—notched in rock, Minnesota—using dowels, Pennsylvania—footings embedded 1 ft below top of rock, and Maryland—“seat” footings in the rock). Those that evaluate sliding use various methods and margins of safety (φ): Idaho—φ = 0.5, Ohio and Indiana—factor of safety = 1.5, New Hampshire— F.S. = 1.5 and φ = 0.8, Washington—F.S. = 1.5 and φ = 0.67, Alberta Canada—φ = 0.8 (friction) and φ = 0.6 (cohesion). Maine specified that sliding for Strength I is done by using minimum vertical load and maximum horizontal load and φ = 0.8 (based on footings on sand). Nevada specified that they use the limit equilibrium method per FHWA “Rock Slopes” with superimposed foundation loading. F.S. = 1.5 for static conditions and F.S. = 1.1 for seismic. 6. Seventy percent (70%) of the states do not analyze lateral displacement of shallow foundations on rock because they use limiting measures (key way, dowling, etc.) as described above. New York specifies geologic inspection during con- struction to ensure rock quality, and key way or dowelling is ordered if necessary. 7. Seventy-five percent (75%) of the responding states limit the eccentricity of footings on rock. Most of the states follow AASHTO recommendations for e/B ≤ 3⁄8. Some (Idaho, Iowa, Michigan, North Carolina, Ohio, Wisconsin, and Massachusetts) use e/B ≤ 1⁄4 based on the FHWA “Soils and Foundations Manual” that also meets the AASHTO standards specification. Wyoming, South Dakota, and Alberta (Canada) use e/B ≤ 1⁄6, with Alberta specifying that either eccentricity is maintained within limits or an effec- tive foundation size is used in which the dimensions are reduced by twice the eccentricity (e.g., B′ = B − 2e). 8. Seventy percent (70%) of the states do not analyze settlement of footings on rock as it is not seen as an issue of importance and the settlement is limited to 0.5 in. Twenty-eight percent (28%) use AASHTO procedures for broken/jointed rock, with Nevada also using Kulhawy and Goodman (1987) and the Army EM 110-1-2908 (1994). 3.1.5.2 Foundations on Soil Findings for foundations on soil are the following: 1. All states using shallow foundations on soils follow either AASHTO’s LRFD or ASD guidelines. Only a small number of responders use presumptive values. Fifty-eight per- cent (58%) use the theoretical general bearing capacity equation. 58

2. Fifty-three percent (53%) of the responders find it reason- able to omit the load inclination factors and 63% limit the eccentricity of the footing mostly with e/B ≤ 1⁄6 to 1⁄4 (standard specifications e/B = 1⁄6, LRFD specifications e/B = 1⁄4). Massachusetts responded that load inclination factors must be used in the final design of the footing. Pennsylvania commented that when inclination factors were considered together with factored loads, it resulted in an increased footing size; hence, unfactored loads are used. 3. Forty-five percent (45%) do not decrease the soil’s strength parameters considering punching shear, while 23% do so. Seven states commented that punching shear is not a viable option as foundations are not built on loose soil conditions or, alternatively, settlement criteria prevail, especially under such conditions. 4. Fifty-eight (58%) use the AASHTO procedures presented for footings on a slope. Nevada, Idaho, and Michigan commented that the charts are not clear and need to be improved. Washington and North Carolina commented on the use of Meyerhoff’s method, also presented by the Navy Design Manual (NAVFAC, 1986), essentially iden- tical to the AASHTO presentation. Oregon commented that the provided foundations on slope analysis result in a reasonable approach (somewhat conservative) while Pennsylvania commented that experience shows that sometimes this analysis results in a drastically larger footing. 5. Thirty percent (30%) of the responding states do not use the AASHTO procedures for footings on a layered soil, while 38% of the responders do use these procedures. Eighteen states commented on the procedures. Idaho, Michigan, Vermont, and Wisconsin commented that they calculate the bearing capacity for the layer with the lower strength. Iowa and Oregon commented that under such conditions alternative foundation solutions are examined. 6. Only 28% (with 40% responding “No”) of the respon- ders use the semi-empirical procedures described in Sec- tion 10.6.3.1.3 of AASHTO’s LRFD Bridge Specifications for evaluation of bearing capacity. The majority of the states that commented on the procedure expressed the opinion that the method is used for a rough evaluation, only as an initial estimation and/or in comparison to other methods. Oregon commented that the SPT method usually yields higher capacity and settlement controls the design. 7. Nineteen states responded when asked for comments about the currently existing resistance factors being all about the same value. Some states stated that they don’t have enough experience with LRFD to judge the resistance factor values. North Carolina and New Hampshire sug- gested combining all resistance factors to be 0.45, while Oregon, Pennsylvania, Vermont, and Washington com- mented that the resistance factors are in line with the factor of safety range (2.5 to 3.0) used in the ASD method- ology and hence result in a design similar to that obtained using ASD. 8. Seventy percent (70%) evaluate failure by sliding, with about half (33%) using the full foundation area and 30% using the effective foundation area. 9. Only 13% consider passive resistance for the lateral resist- ance of the shallow foundations and all utilize a limited value due to a limited displacement. Many responding states expressed concern with a long-term reliance on a passive resistance. Washington commented that it is rarely used to meet the sliding criterion of extreme events, and Minnesota commented it is used in front of shear keys only. 10. Traditionally no safety margin is provided to settlement analysis although it typically controls the size of shallow foundations. When asked about it, 35% answered that the issue should not be of concern and 25% answered that it should. Of those who responded, some recognized that safety margin needs to be researched (Connecticut, Michigan, and Tennessee) while others hold the notion that a safety margin on bearing capacity already addresses the issue (Hawaii, Maine, New Jersey, North Carolina, and Washington) or that settlement calculations are conserva- tive to begin with (New Hampshire and North Carolina). 11. Only two states stated that they conduct plate load tests: one state (Connecticut) referred to tests from over 20 years ago, and the other state referred to three recent tests (Massachusetts). 12. When asked to comment on any related subject, 13 states responded. A major concern expressed by Michigan was written by a bridge designer referring to the difficulties in using effective width for bearing capacity calculations as it requires iterations for each load case for service and strength. Moreover, the division of responsibilities between the geotechnical section (providing allowable pressure) and structural section (examining the final design iteratively) is a source for problems. The engineer proposes allowable contact stresses for service and strength based on gross footing width and eccentricity limited to B/6. (The issue of “allowable” to ULS is not so clear and the engineer was contacted.) 3.1.6 Telephone Interviews 3.1.6.1 Overview Engineers of seven states were interviewed to obtain com- plementary information and enhance understanding of the state of practice of shallow foundation design and construction. All the interviewed states were selected due to their exten- sive use of shallow foundations and/or specific usage that 59

required further investigation. Six of the interviews are sum- marized below. 3.1.6.2 Connecticut—Interview with Leo Fontaine, Transportation Principal Engineer Connecticut is the leading state among the responding states (39) in the use of shallow foundations (66% of bridge foundations). This fact was attributed by Transportation Prin- cipal Engineer, Leo Fontaine, to the longstanding high-quality engineering traditions established by Phillip Keene and Lyle Moulton that, along with sound economics, lead to the pre- vailing use of shallow foundations. Connecticut design practice for foundations on rock include unconfined rock testing, RQD evaluation, and bearing capacity calculations followed by the use of predominantly presumptive values (typically 5 to 6 tsf), mostly due to lack of confidence in the rock variability. Hence, Fontaine sees a great need for the calibration of the design methods based on a database. Connecticut’s design practice for foundations on soil refers mostly to frictional soils as the construction schedule prevents building foundations on soft soils using the conventional approach (e.g., preloading), and the use of ground improve- ment techniques was found to be less attractive than the use of deep foundations in such cases. The design process of the shallow foundations mostly includes SPT, internal friction angle, bearing capacity analysis without inclination factors, and then settlement evaluation that controls the foundation size. The procedure is completed by checking bearing capacity again with the foundation size dictated by the settlement analysis. For settlement analysis, service load is used without a safety margin, and based on past performance, Connecticut feels comfortable with the process. 3.1.6.3 Massachusetts—Interview with Nabil Hourani, Chief Geotechnical Engineer Massachusetts is one of three states using the highest portion of shallow foundations in bridge structures (53%), along with Connecticut (66%) and Pennsylvania (65%). When design- ing foundations on rock, Massachusetts uses Goodman’s method, which according to the accumulated experience, cor- relates well with both test results, unconfined and point load tests. Massachusetts does not use presumptive values and would like to see the uncertainty of the design methodology (i.e., Goodman) evaluated and calibrated for LRFD. Foundation design follows the AASHTO recommendations for the range of eccentricity limitation. The values, according to Nabil Hourani, Chief Geotechnical Engineer, were obtained from the load factor design methodology as presented in NCHRP Report 343 (Barker et al., 1991, Part 3 [Kim et al., 1991], Chapter 5, Figures 5.2 to 5.4). No settlement on rock is eval- uated; anchors and dowels are being used but not keys. 3.1.6.4 Pennsylvania—Interview with Beverly Miller, Bureau of Design The extensive use of shallow foundations in Pennsylvania (65%) is attributed to the combination of subsurface conditions (rock or stiff soil at a shallow depth) and economic competitive- ness. The design is commonly based on an in-house design manual (Pennsylvania DOT, Publication Number 15M, April 2000 edition, Part 4, Volume 1 of 2) and a software package (ABLRFD by PDT and Ibsen & Assoc., Inc.). About 60% of shallow foundations are built into rock, embedded 1 ft into the rock. As a result, it is not required that sliding be checked. About 33% of the foundations are built on granular material with no shallow foundations being built on cohesive soils. Cohesive soils would be either excavated (approximate depth of up to 10 ft) or penetrated by piles. The bearing capacity of foundations on rock is calculated utilizing Goodman (1989) and Carter & Kulhawy (1988) with φ = 0.55, relying on good past experience with both methods. Pennsylvania, according to Beverly Miller at the Bureau of Design, would very much like to see the methods being cali- brated. Presumptive values are rarely used and only used for comparison. Inclination factors are not used, and the design is based on unfactored loads because the use of factored loads resulted in unreasonably large foundations compared to past experience. Pennsylvania makes use of shallow foundations in water using protective measures. Abutments are built below construction scour, and piers are built below construction scour and use rip rap to mitigate for half of the local scour. 3.1.6.5 Tennessee—Interview with Edward Wasserman (Director of Structures Division), Len Oliver, and Vanessa Bateman (Soils and Foundations) A large portion of Tennessee has relatively shallow soil depth to rock. Similar to Pennsylvania, the practice in Tennessee is to excavate foundations to a depth of about 10 ft and use end bearing piles for soil depths exceeding 12 ft. The practice in Tennessee is to use capacity analysis on rock based on AASHTO’s Standard Specifications for Highway Bridges (1997), utilizing unconfined test results and being sensitive to the large variation in limestone strength and possible karst phenomena. Presumptive values are used in locations where good data are not available (e.g., drilling is not possible) or the tests are inconclusive. The Navy Design Manual (NAVAC, 1986) values are then used, being overall similar to AASHTO’s values. When the rock is highly fractured such that it controls the strength, shallow foundations are not 60

used. Very often the foundation size is restricted by the strength of the concrete, which is a limiting value (10 to 15 tsf) compared with the rock’s strength. Inclination factors are not used because no load details are available from the structures group at the time of the design. When designing foundations for retaining wall, the maximum eccentricity is assumed. 3.1.6.6 Washington—Interview with Jim Cuthbertson, Chief Foundations Engineer Washington’s questionnaire response indicated a relatively common use of shallow foundations on silts and clay (6%), the highest of all responders. It was clarified that those soils are glacier, compacted, highly densified soils, with silts hav- ing SPT N values of 30 to 40 and clays having SPT N values of 40 to 100. These materials are in some ways IGMs and, hence, skew the statistics presented of foundations on silt/clay. When calculating bearing capacity, cohesion is neglected and only a frictional component is assumed. Foundations on rock and IGM are common (about 30%) and the use of the classical bearing capacity analysis leads to unrealistically high values, which are then limited to about 80 tsf ultimate capacity based on experience. Similar to the problem presented by Tennessee, in Washing- ton the geotechnical analysis is carried out before eccentricity values are available. This is resolved by providing foundation dimensions (width and length) that are required to be main- tained as effective foundation sizes. When the final design accounts for eccentricity, it results in foundation sizes that, after being reduced for eccentricity, end with the originally provided effective foundation sizes. This effective foundation width is used for settlement analysis calculations and sliding resistance. As the foundations are cast on grade, a full mobi- lization of the friction angle is assumed. 3.1.6.7 Maine—Interview with Laura Krusinski, Senior Geotechnical Engineer The extensive use of shallow foundations in Maine can be attributed to rock close to the ground surface (especially in coastal areas) and economic considerations. The foundations are sized first based on presumptive values and then are checked against the factored resistance. Maine is making an effort to obtain the references mentioned in the code and study them as no details are provided in the specifications. Laura Krusinski, Senior Geotechnical Engineer, finds it useful to provide details of recommended design methods and calibrate them against a database. As with other states, in Maine the foundation design is carried out before loading details are available; hence, eccentricity is assumed not to exist. However, the foundation is later checked as part of the structural design. Krusinski also sees a need for guidelines for footing embedment in 100-year and 500-year scour events. 3.1.7 Major Conclusions Major conclusions are the following: 1. In many states, the geotechnical aspects of the founda- tion design (bearing capacity, settlement, and sliding) are being evaluated before all the loading details are avail- able. As such, load inclination and/or eccentricity cannot be directly accounted for. Several approaches are taken to resolve the situation including (1) providing effective foundation sizes so that final design sizes will include the eccentricity effect (i.e., B = B′ + 2e); (2) assuming highest eccentricity; and (3) providing unit bearing values, nomi- nal and factored. 2. The vast majority of the shallow foundations used to sup- port bridges are founded on rock. Only various references are currently available in the specification. A need for specific, detailed methodology and its calibration was advocated by most states and all those interviewed. 3. Although most states do not use inclination factors in design, they examine the resistance to sliding, and once the final foundation size is established (after settlement consideration), they check again for bearing capacity with or without inclination factor (depending on the state). 4. New foundations on soft, cohesive soils are rarely being constructed. Some of the statistics in that regard were skewed due to referencing highly compacted cohesive soils (which border on being IGM) as regular cohesive soils. 3.2 Assembled Databases 3.2.1 Overview Section 2.1 presents the research plan for establishing data- bases for shallow foundation load tests. Two major databases were established: • UML-GTR ShalFound07, which incorporates Databases I and II. This database is based on a database originally assem- bled for NCHRP Project 12-66 and in its current scope contains 549 case histories of which 409 would conform to what is described as Database I and 140 case histories would conform to Database II. UML-GTR ShalFound07 will be discussed in Section 3.2.2. • UML-GTR RockFound07, which is presented as Database III and contains 122 case histories, 119 of which were used in the calibration. UML-GTR RockFound07 will be discussed in Section 3.2.3. A summary of the major attributes of each database is pre- sented below. Additional statistics are presented for relevant analyses (e.g., see Section 3.5 for centric vertical loading on shallow foundations in/on granular materials). 61

3.2.2 UML-GTR ShalFound07 The UML-GTR ShalFound07 database was expanded from its original format of 329 cases (developed for NCHRP Project 12-66) to contain 549 load test cases for shallow founda- tions, mostly on granular soils, and concentrating on load tests to failure and/or loading other than centric vertical loads. The database was constructed in Microsoft Access 2003 format. The bulk of the cases was collected and assembled from four sources: (1) ShalDB Ver5.1 (updated version of Briaud and Gibbens, 1997), (2) Settlement of Shallow Foundations on Gran- ular Soils, a report to the Massachusetts Highway Department by Lutenegger and DeGroot (1995), (3) a German test database compiled by DEGEBO (Deutsche Forschungsgesellschaft für Bodenmechanik) in a set of volumes, and (4) tests carried out at or compiled by the University of Duisburg-Essen, Germany. Table 22 lists the countries in which the tests were carried out and the number of related cases. The majority of cases were tests carried out in Germany, the United States, France, and Italy. Table 23 summarizes the database by classification based on the foundation type, predominant soil type below the footing base, and country. The foundation type was classified based on the footing width, which follows the convention utilized by Lutenegger and DeGroot (1995). The tests on footing widths less than or equal to 1 m (3.3 ft) were classified as plate load tests, widths between 1 m and 3 m (9.8 ft) were classified as small footings, widths between 3 m and 6 m (19.7 ft) were classified as large footings, and widths greater than 6 m were classified as rafts and mats. “Mixed” refers to soil containing alternating layers of sand or gravel and clay or silt. “Others” refers to cases with either unknown soil type or with materials like loamy scoria. The majority of the tests in the database are plate load tests on granular soils. A detailed list of input parameters in the database is presented in Appendix D (see Table D-1). See Figure 47 for the site con- dition (e.g., a footing tested in an excavation or a footing on a slope, etc.) and Figure 48 for the conventions of footing dimen- sions and loading. Figures D-1 through D-13 in Appendix D contain screen images of the UML-GTR ShalFound07 data- base in Microsoft Access. SearchModify, listed under Forms, allows the user to easily search/modify a footing case in the database. 62 Country No. of cases Australia 1 Brazil 19 Colombia 1 Croatia 1 France 60 Germ any 254 India 6 Italy 56 Jamaica 1 Japan 9 Kuwait 10 Nigeria 3 Northern Ireland 1 Portugal 6 South Africa 1 Sweden 11 UK 14 USA 84 Others 11 Total 549 Table 22. Countries in which tests were conducted and number of test cases conducted in each country. Predominant soil type Country Foundation type Sand Gravel Cohesive Mixed Others Total Germany Others Plate load tests B ≤3.3 ft (1m) 346 46 -- 2 72 466 253 213 Small footings 3.3 ft < B ≤9.8 ft (3m) 26 2 -- 4 1 33 -- 33 Large footings 9.8 ft< B ≤19.7 ft (6m) 30 -- -- 1 -- 31 -- 31 Rafts & Mats B > 19.7 ft 13 -- -- 5 1 19 1 18 Total 415 48 0 12 74 549 254 295 Note: “Mixed” are cases with alternating layers of sand or gravel and clay or silt “Others” are cases with either unknown soil types or with other granular materials like Loamy Scoria 1m ≈ 3.3 ft Table 23. Summary of UML-GTR ShalFound07 database.

63 SiteConditionID 40103 SiteConditionID 40104 SiteConditionID 40101 SiteConditionID 40102 SiteConditionID 40105 Figure 47. Footing dimensions and site details along with the associated SiteConditionID employed in database UML-GTR ShalFound07.

3.2.3 UML-GTR RockFound07 A database consisting of rock loading by small size inden- tation, shallow foundations, and drilled shafts (for which the tip load-displacement relations were measured) was assembled. The database is composed of a total of 122 case histories from 10 different countries. Thirty-nine of the cases were obtained from a study by Zhang and Einstein (1998), and 31 cases were obtained from a study by Prakoso (2002) whereas the re- maining cases were searched for and found in the literature. In a final review, three of the footing cases were found to be tested over a rock that contained a clay seam and, hence, were excluded from the statistics used in the calibrations. The database developed for the study included footing field load tests conducted in pseudo rock, hardpan, fine-grained sedi- mentary and igneous or volcanic rocks. The shallow foundation case histories were subcategorized according to their embed- ment, differentiating between embedded (embedment depth D > 0) and non-embedded (D = 0) footings with circular and/or square shapes. A majority of the circular footings are plates. All the rock sockets in the database are circular for which the end bearing capacity (tip resistance) could be isolated, sep- arating it from the shaft resistance of the rock sockets. Figures 49 to 52 present the distributions of the foundation sizes for all cases—non-embedded and embedded footings and rock sockets, respectively. Table 24 presents a summary of the database cases used for the determination of the uncer- tainty of the bearing capacity analyses of foundations on rock. Appendix E presents in detail the references that were used to build the rock foundation database along with the rock details and the foundation type. All 122 original cases are presented in Appendix E with the three foundations omitted clearly marked. The database has 30 non-embedded shallow foundations, 28 embedded shallow foundations, and 61 rock sockets. Only four of the shallow foundations have square shapes; the others are circular. All 61 rock sockets are circular. The width or diameter (B) of the shallow foundations range from 0.07 to 23 ft with an average (Bavg) of 1.98 ft. The Rock Sockets have a 64 (a) (b) d = thickness b = len gth 2 b = width3 x = x 2 x = z1 x = y3 Di-xx Ro-zz Ro-xx Ro-yy Se-zz Di-yy edge A edge D edge C edge B b = width3 x = z1 x = y3 b = len gth 2 x = x 2 d = thicklessFzSL MxxSL MzzSL MyySLFxSL FySL edge A edge D edge C edge B thickness Figure 48. Conventions for footing dimensions (a) and applied loads (b).

65 0 2 4 6 8 10 12 14 16 18 20 22 24 Footing width, B (ft) 0 10 20 30 40 N o. o f o bs er va tio ns 0 0.05 0.1 0.15 0.2 0.25 0.3 Fr eq ue nc y 119 Rock sockets and Footing cases Mean B = 2.58 ft COV = 1.594 Figure 49. Distribution of B (ft) for 119 case histories in database UML-GTR RockFound07. 0 2 4 6 8 10 N o. o f o bs er va tio ns 0 0.05 0.1 0.15 0.2 0.25 0.3 Fr eq ue nc y 30 Footing cases with D=0 Mean B = 4.20 ft COV = 1.799 0 2 4 6 8 10 12 14 16 18 20 22 24 Footing width, B (ft) Figure 50. Distribution of B (ft) for 30 non-embedded footing case histories in database UML-GTR RockFound07. 0 1 2 3 4 5 Footing width, B (ft) 0 5 10 15 20 25 N o. o f o bs er va tio ns 0 0.2 0.4 0.6 0.8 Fr eq ue nc y 28 Footing cases with D>0 Mean B = 1.18 ft COV = 0.926 Figure 51. Distribution of B (ft) for 28 embedded footing case histories in database UML-GTR RockFound07. 0 62 84 1210 Footing width, B (ft) 0 4 8 12 N o. o f o bs er va tio ns 0 0.05 0.1 0.15 Fr eq ue nc y 61 Rock socket cases Mean B = 2.47 ft COV = 0.739 Figure 52. Distribution of B (ft) for 61 rock socket case histories in database UML-GTR RockFound07.

diameter (B) ranging from 0.33 ft to 9 ft with an average (Bavg) of 2.59 ft. Table 24 presents a summary of the database case histories breakdown based on foundation type, embedment, sites, size and country. It can be inferred from Table 24 that most of the shallow foundation and rock socket data were obtained from load tests carried out in Australia and the United States, respectively. 3.3 Determination of the Measured Strength Limit State for Foundations Under Vertical-Centric Loading 3.3.1 Overview The strength limit state of a foundation may address two kinds of failure: (1) structural failure of the foundation material itself and (2) bearing capacity failure of the supporting soils. While both need to be examined, this research addresses the ULSs of the soil’s failure. The ULS consists of exceeding the load-carrying capacity of the ground supporting the founda- tion, sliding, uplift, overturning, and loss of overall stability. In order to quantify the uncertainty of an analysis, one needs to find the ratio of the measured (“actual”) capacity to the cal- culated capacity for a given case history. The measured strength limit state (i.e., the capacity) of each case needs, therefore, to be identified. Depending on the footing displacements, one may define (1) allowable bearing stress, (2) bearing capacity, (3) bearing stress causing local shear failure, and (4) ultimate bearing capacity (Lambe and Whitman, 1969). Allowable bearing stress is the contact pressure for which the footing movements are within the permissible limits for safety against instability and functionality, hence defined by SLS. Bearing capacity is that contact pressure at which settlements become very large and unpredictable because of shear failure. Bearing stress causing local shear failure is the stress at which the first major non- linearity appears in a load-settlement curve, and generally the bearing capacity is taken as equal to this stress. Ultimate bearing capacity is the stress at which sudden catastrophic settlement of a foundation occurs. Bearing capacity and ultimate bear- ing capacity define the ULS and differ only in the foundation response to load. Appendix F presents a review of foundation modes of failure and suggests that the terms “bearing capacity” and “ultimate bearing capacity” should be used interchangeably to define the maximum loading (capacity) of the ground, depending on the mode of failure. 3.3.2 Failure (Ultimate Load) Criteria 3.3.2.1 Overview—Shallow Foundations on Soils The strength limit state is a “failure” load or the ultimate capacity of the foundation. The bearing capacity (failure) can be estimated from the curve of vertical displacement of the footing against the applied load. A clear failure, known as a general failure, is indicated by an abrupt increase in settle- ment under a very small additional load. Most often, however (other than for small scale plate load tests in dense soils), test load-settlement curves do not show clear indications of bear- ing capacity failures. Depending on the mode of failure, a clear peak or an asymptote value may not exist at all, and the failure or ultimate load capacity of the footing has to be interpreted. Appendix F provides categorization of failure modes fol- lowed by common failure criteria. The interpretation of the failure or ultimate load from a load test is made more complex by the fact that the soil type or state alone does not determine the mode of failure (Vesic´, 1975). For example, a footing on very dense sand can also fail in punching shear if the foot- ing is placed at a greater depth, or if loaded by a transient, dynamic load. The same footing will fail in punching shear if the very dense sand is underlain by a compressible stratum such as loose sand or soft clay. It is clear from the above dis- cussion that the failure load of a footing is clearly defined only for the case of general shear; for cases of local and punching shear, it is often difficult to establish a unique failure load. 66 Location Foundation type No. of cases No. of sites No. of rock types Shape Size range (ft) USA Canada Italy UK Australia Taiwan Japan Singapore Russia SouthAfrica Shallow Foundations (D = 0) 331 22 10 Square 4 Circular 29 0.07 < B < 23 Bavg = 2.76 2 1 1 3 13 0 1 0 1 0 Shallow Foundations (D > 0) 28 8 2 Circular28 0.23 < B < 3 Bavg = 1.18 0 0 0 8 0 0 0 0 0 0 Rock Sockets 61 49 14 Circular 61 0.33 < B < 9 Bavg = 2.59 19 4 1 0 21 1 0 1 0 2 1Three (3) cases had been omitted in the final statistics due to a clay seam in the rock. Table 24. Summary of database UML-GTR RockFound07 cases used for foundation capacity evaluation.

Criteria proposed by different authors for the failure load interpretation are presented in Appendix F, while only the selected criterion is presented in the following section. Such interpretation requires that the load test be carried to very large displacements, which constrains the availability of test data, in particular for larger footing sizes. 3.3.2.2 Minimum Slope Failure (Ultimate) Load Criteria, Vesic´ (1963) Based on the load-settlement curves, a versatile ultimate load criterion is recommended to define the ultimate load at the point where the slope of the load-settlement curve first reaches zero or a steady, minimum value. The interpreted ultimate loads for different tests are shown as black dots in Figure 53 for soils with different relative densities, Dr. For footings on the surface of, or embedded in, soils with higher relative densities, there is a higher possibility of failure in general shear mode, and the failure load can be clearly identified for Test Number 61 in Figure 53. For footings in soils with lower relative densities, however, the failure mode could be local shear or punching shear, with the identified failure location being arbitrary at times (e.g., see Test Number 64). A semi-log scale plot with the base pressure (or load) in logarithmic scale can be used as an al- ternative to the linear scale plot if it facilitates the identification of the starting of minimum slope and hence the failure load. 3.3.2.3 The Uncertainty in the Minimum Slope Failure Criterion Interpretation In order to examine the uncertainty in the method selected for defining the bearing capacity of shallow foundations on soils, the following failure criteria (described in detail in Appendix F) were used to interpret the failure load from the load-settlement curves of footings subjected to centric vertical loading on granular soils (measured capacity): (a) minimum slope cri- terion (Vesic´, 1963), (b) limited settlement criterion of 0.1B (Vesic´, 1975), (c) log-log failure criterion (De Beer, 1967), and (d) two-slope criterion (shape of curve). Examples F1 and F2 in Appendix F demonstrate the application of the four examined criteria to the database UML-GTR ShalFound07. The measured bearing capacity could be interpreted for 196 cases using the minimum slope criterion (Vesic´, 1963) and 119 cases using the log-log failure criterion (De Beer, 1967). Most of the footings failed before reaching a settlement of 10% of footing width (the limited settlement criterion of 0.1B [Vesic´, 1975] could therefore only be applied to 19 cases). A single “representative” value of the relevant measured capacity was then assigned to each footing case. This was done by taking an average of the measured capacities interpreted using the minimum slope criterion, the limited settlement criterion of 0.1B (Vesic´, 1975), the log-log fail- ure criterion, and the two-slope criterion (shape of curve). 67 Figure 53. Ultimate load criterion based on minimum slope of load-settlement curve (Vesic´ , 1963).

The statistics of the ratios of this representative value over the interpreted capacity using the minimum slope criterion and the log-log failure criterion were comparable with the mean of the ratio for the minimum slope criterion being 0.98 versus that for the limited settlement criterion being 0.99. Due to the simplicity and versatility of its application, the minimum slope criterion was selected as the failure inter- pretation criterion to be used for all cases of footing, includ- ing those with combined loadings. Figure 54 shows the histo- gram for the ratio of the representative measured capacity to the interpreted capacity using the minimum slope criterion. Figure 54 presents the uncertainty associated with the use of the selected criterion, suggesting that the measured capacity interpreted using the minimum slope criterion has a slight overprediction. 3.3.3 Failure Criterion for Footings on Rock The bearing capacity interpretation of loaded rock can become complex due to the presence of discontinuities in the rock mass. In a rock mass with vertical open discontinuities, where the discontinuity spacing is less than or equal to the footing width, the likely failure mode is uniaxial compression of rock columns (Sowers, 1979). For a rock mass with closely spaced, closed discontinuities, the likely failure mode is the general wedge occurring when the rock is normally intact. For a mass with vertical open discontinuities spaced wider than the footing width, the likely failure mode is splitting of the rock mass and is followed by a general shear failure. For the inter- pretation of ultimate load capacities from the load-settlement curves, the L1-L2 method proposed by Hirany and Kulhawy (1988) was adopted. A typical load-displacement curve for foundations on rock is presented in Figure 55. Initially, linear elastic load-displacement relations take place; the load defining the end of this region is interpreted as QL1. If a unique peak or asymptote in the curve exists, this asymptote or peak value is defined as QL2. There is a nonlinear transition between loads QL1 and QL2. If a linear region exists after the transition, as in Figure 55, the load at the start of the final linear region is defined as QL2. In either case, QL2 is the interpreted failure load. This criterion is similar to the aforementioned minimum slope failure proposed by Vesic´ for foundations in soil. The selection of the ultimate load using this criterion is demonstrated in Example F3 of Appendix F using a case history from the UML-GTR RockFound07 data- base. It can be noted that the axes aspect ratios (scales of axes relative to each other) in the plot of the load-settlement curve changes the curve shape, and thus could affect the inter- pretation of the ultimate load capacity. However, unlike the interpretation of ultimate capacity from pile load tests, which utilizes the elastic compression line of the pile, there is no generalization of what the scales of the axes should be relative to each other for the shallow foundation load tests. It can only be said that depending on the shape of the load-settlement curve, a “favorable” axes aspect ratio needs to be fixed. This should be done on a case-by-case basis, using judgment, so that the region of interest (e.g., if the minimum slope criterion is used, the region where the change in the curve slope occurs) is clear. The L1-L2 method was applied to all cases for which 68 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 Ratio of "representative" capacity to the capacity interpreted using minimum slope criterion 0 20 40 60 80 100 120 N o. o f f oo tin g ca se s 0 10 20 30 40 50 60 R el at iv e fre qu en cy (% ) no. of data = 196 mean = 0.978 COV = 0.053 Figure 54. Histogram for the ratio of representative measured capacity to interpreted capacity using the minimum slope criterion for 196 footing cases in granular soils under centric vertical loading. Figure 55. Example of L1-L2 method for capacity of foundations on rocks showing the regions of the load-displacement curve and interpreted limited loads (Hirany and Kulhawy, 1988).

the load-settlement curve was available with sufficient detail and extent to be employed. For all other cases, the reported failure was adopted as the foundation’s capacity. 3.4 Determination of the Calculated Strength Limit States for the Case Histories (Foundations on Soils) 3.4.1 Equations for Bearing Capacity (Resistance) Estimation The bearing capacity equation specified in AASHTO (2008) with minimal necessary adjustment has been used to calculate the bearing capacity of a footing (qn) of length L and width B′ and supported by a soil with cohesion, c, average friction angle, φf, and average unit weights, γ1 and γ2, above and below the footing base, respectively. The format presented in Equation 95 is based on the general bearing capacity formulation used by Vesic´ (1975) as presented in Section 1.5.3 (see Equation 34). The numbering in parentheses represents the proposed num- bering for the modified AASHTO specifications. in which: where c = cohesion, taken as undrained shear strength cu in total stress analysis or as cohesion c′ in effective stress analysis (ksf); Nc = cohesion term bearing capacity factor as specified in Tables 25 and 26 (dim.); Nq = surcharge (embedment) term bearing capacity factor as specified in Tables 25 and 26 (dim.); N N s d im y y y yγ = −( . . . . ) ( )10 6 3 1 3 4 98a N N s d iqm q q q q= −( . . . . ) ( )10 6 3 1 3 3 97a N N s d icm c c c c= −( . . . . ) ( )10 6 3 1 3 2 96a q c N D N B Nn cm f qm m= + +i i i i i iγ γ γ1 20 5 10 6 3 1 3 . ( . . . . a −1 95) ( ) Nγ = unit weight (footing width) term bearing capacity factor as specified in Tables 25 and 26 (dim.); γ1 = moist or submerged unit weight of soil above the bearing depth of the footing (kcf); γ2 = moist or submerged unit weight of soil below the bearing depth of the footing (kcf); Df = footing embedment depth (ft); B = footing width (ft), equal to the physical footing width (B) in the case of centric loading or effective footing width (B′) in the case of eccentric loading; sc, sγ, sq = footing shape correction factors as specified in Table 27 (dim.); dc, dγ, dq = depth correction factors to account for the shear- ing resistance along the failure surface passing through the soil above the bearing elevation as specified in Table 28 (dim.); and ic, iγ, iq = load inclination factors as specified in Table 29 (dim.). The effective vertical stress calculated at the base of the footing should be used (where γi and Di are effective unit weight and depth to the ith layer up to a depth of Df) or alternatively, an average weighted soil unit weight (γ1) should be used above the base. Below the base an average soil unit weight (γ2) should be used within a zone of 1.5B. The high- est anticipated groundwater level should be used in design. In Tables 27 through 29, B and L are the physical footing dimensions (in the case of centric loading), or they have to be substituted with the effective footing dimensions, B′ and L′ (in the case of eccentric loading). In Table 29, H and V are the unfactored horizontal and vertical loads (kips), respectively. The angle θ is the projected direction of load in the plane of the footing, measured from the side of the footing length, L (deg.). Figure 17 (similar to AASHTO Figure 10.6.3.1.3a-1) shows the conventions for determining θ. The parameter n is defined according to Equation 99: n L B L B B L B = + ′ ′( ) + ′ ′( ) ⎡ ⎣⎢ ⎤ ⎦⎥ + + ′ ′( ) + ′ ′ 2 1 2 1 2cos θ L( ) ⎡ ⎣⎢ ⎤ ⎦⎥ − sin a 2 10 6 3 1 3 5 99 θ ( . . . . ) ( ) γ i i i D D D f + −( )∑ 1 0 69 Factor Cohesion term (Nc) Unit weight term (Nγ) Surcharge term (Nq) π φ 1.0 BearingCapacity Factors Nc, N , Nq Friction angle f = 0 φ φf > 0 φ 2 + π (Nq 1)⋅cot f φ 0.0 2⋅(Nq + 1)⋅tan f 245tantanexp f2 f⋅ ⋅ + φ Table 25. Bearing capacity factors Nc (Prandtl, 1921), Nq (Reissner, 1924), and N (Vesic, 1975) (AASHTO Table 10.6.3.1.3a-1).

f Nc Nq N f Nc Nq N 0 5.14 1.0 0.0 23 18.1 8.7 8.2 1 5.4 1.1 0.1 24 19.3 9.6 9.4 2 5.6 1.2 0.2 25 20.7 10.7 10.9 3 5.9 1.3 0.2 26 22.3 11.9 12.5 4 6.2 1.4 0.3 27 23.9 13.2 14.5 5 6.5 1.6 0.5 28 25.8 14.7 16.7 6 6.8 1.7 0.6 29 27.9 16.4 19.3 7 7.2 1.9 0.7 30 30.1 18.4 22.4 8 7.5 2.1 0.9 31 32.7 20.6 26.0 9 7.9 2.3 1.0 32 35.5 23.2 30.2 10 8.4 2.5 1.2 33 38.6 26.1 35.2 11 8.8 2.7 1.4 34 42.2 29.4 41.1 12 9.3 3.0 1.7 35 46.1 33.3 48.0 13 9.8 3.3 2.0 36 50.6 37.8 56.3 14 10.4 3.6 2.3 37 55.6 42.9 66.2 15 11.0 3.9 2.7 38 61.4 48.9 78.0 16 11.6 4.3 3.1 39 67.9 56.0 92.3 17 12.3 4.8 3.5 40 75.3 64.2 109.4 18 13.1 5.3 4.1 41 83.9 73.9 130.2 19 13.9 5.8 4.7 42 93.7 85.4 155.6 20 14.8 6.4 5.4 43 105.1 99.0 186.5 21 15.8 7.1 6.2 44 118.4 115.3 224.6 22 16.9 7.8 7.1 45 133.9 134.9 271.8 Table 26. Bearing capacity factors Nc (Prandtl, 1921), Nq (Reissner, 1924), and N (Vesic, 1975) (AASHTO Table 10.6.3.1.3a-2). Factor Friction angle Cohesion term (sc) Unit weight term (s ) Surcharge term (sq) f = 0 L B2.01 1.0 1.0 Shape Factors s c, s , sq f > 0 c q N N L B1 L B4.01 ftanL B1 Table 27. Shape correction factors sc, s, sq (Vesic´, 1975) (AASHTO Table 10.6.3.1.3a-3). Factor Friction angle Cohesion term (d c ) Unit weight term (d ) Surcharge term (dq) f = 0 for Df B: B D4.01 f for Df > B: B D arctan4.01 f 1.0 1.0 Depth Correction Factors d c, d , dq f > 0 1N d1 d q q q 1.0 for Df B: B D sin1tan21 f2ff for Df > B: B D arctansin1tan21 f2ff Table 28. Depth correction factors dc, d, dq (Brinch Hansen, 1970) (AASHTO Table 10.6.3.1.3a-4). Factor Friction angle Cohesion term (ic) Unit weight term (i ) Surcharge term (iq) f = 0 cNLBc Hn1 1.0 1.0 Load Inclination Factors i c, i , iq f > 0 1N i1 i q q q 1n fcotLBcV H1 n fcotLBcV H1 Table 29. Load inclination factors ic, i, iq (Vesic´, 1975) (AASHTO Table 10.6.3.1.3a-5).

The depth correction factor should be used only when the soils above the footing bearing elevation are competent and there is no danger of their removal over the foundation’s lifetime; otherwise, the depth correction factor should be taken as 1.0, or Df should be reduced to include the competent, secured depth only. The depth correction factors presented in Table 28 refer, when applicable, to the effective foundation width B′. Some de- sign practices use the physical footing width (B) for evaluating the depth factors under eccentric loading as well. The calibra- tion presented in this study was conducted using B′. The use of B in the depth factor expressions results in a more conservative evaluation as discussed by Paikowsky et al. (2009a). 3.4.2 Estimation of Soil Parameters Based on Correlations 3.4.2.1 Correlations Between Internal Friction Angle (φf) and SPT N Table 30 summarizes various correlations between SPT N and the soil’s internal friction angle (see Equations 100 to 105). 71 Reference Correlation equation Equation no. Peck, Hanson, and Thornburn (PHT) (1974) as mentioned in Kulhawy and Mayne (1990) 1 6054 27.6034 exp 0.014f N (100) Hatanaka and Uchida (1996) 1 60 1 60 20 20 for 3.5 30 f N N (101) PHT (1974) as mentioned by Wolff (1989) 21 160 6027.1 0.3 0.00054f N N (102) Mayne et al. (2001) based on data from Hatanaka and Uchida (1996) 1 6015.4 20f N (103) Specifications for Highway Bridges (SHB) Japan, JRA (1996) 1 60 1 60 15 15 for 5 and 45 f f N N (104) Note: pa is the atmospheric pressure and σ′v is effective overburden pressure in the same units. For English units, pa = 1 and σ′v is expressed in tsf at the depth N60 is observed. (N1)60 is the corrected SPT N value corrected using the correction given by Liao and Whitman (1986): (N1)60 = pa σ′v N60 (105) Table 30. Summary of equations correlating internal friction angle (f) to corrected SPT N value (N1)60. 0 10 20 30 40 50 60 70 Corrected SPT count, (N1)60 25 30 35 40 45 So il fri ct io n an gl e, φ f (de g) (PHT 1974) (Wolff 1989) (PHT 1974) (Kulhawy & Mayne, 1990) (Hatanaka & Uchida 1996) (Hatanaka & Uchida 1996) (Mayne et al. 2001) (JRA 1996) Figure 56. Comparison of various correlations between granular soil friction angle and corrected SPT blow counts using the overburden correction proposed by Liao and Whitman (1986).

Figure 56 presents a comparison of the different correlations listed in Table 30. The graph in Figure 56 suggests that in the range of about (N1)60 = 27 to 70, the Peck, Hanson, and Thornburn (PHT) (1974) correlation (modified by Kulhawy and Mayne, 1990, see Equation 100) provides the most conser- vative yet realistic estimate of the soil’s friction angle. The use of Equations 100 and 101 is examined in Figure 57, where the bias (measured over calculated bearing capacity) when using both equations is presented. The use of Equation 100 resulted in the increase of the bias mean from 0.32 to 0.97 and COV improved from 0.454 to 0.362 compared to that when using Equation 101. Using Equation 101, the bias mean was 0.32 and the COV was 0.454; however, using Equation 100, the bias mean increased to 0.97 and the COV improved, becom- ing 0.32. For example, for the footing cases with Footing IDs (FOTIDs) of #46, #49, and #77, the friction angles obtained using Equation 101 are 41.0°, 33.9°, and 35.9°, and those using Equation 100 are 33.75°, 29.8°, and 32.3°. The resulting biases were found to be 0.41, 0.39, and 0.77, in the previous case, and 1.20, 0.69, and 1.30 in the latter, respectively. The correlation proposed by PHT (1974) as modified by Kulhawy and Mayne (1990) was adopted for the friction angle evaluation. The PHT (1974) correlation has been found to give more reasonable soil friction angles based on SPT N counts than other correlations. The same correlation was also used in NCHRP Project 24-17 (published as NCHRP Report 507: Load and Resistance Factor Design (LRFD) for Deep Foundations) and NCHRP Project 12-66 “AASHTO LRFD Specifications for Serviceability in the Design of Bridge Foundations.” The friction angle of the soils for the footings for which SPT N was available (typically field tests, categorized in later sections as “natural soil condition” cases) was therefore evaluated using the Equation 100 relationship. 3.4.2.2 Correlations Between γ and SPT N The following equation was established by Paikowsky et al. (1995) for estimation of the unit weight of granular soils from SPT blow counts: The unit weights for the footing cases (for which soil unit weight was not specified and SPT blow counts are available) have been estimated through an iteration process, as shown in the flowchart presented in Figure 58. For an ith layer of thickness (Di+1 − Di), as shown, the unit weight of soil is esti- mated through an iteration until a precision of a small error (ε) is obtained. 3.4.2.3 Correlation Between φf and γ For the unique set of tests conducted at the University of Duisburg-Essen (UDE), soil friction angles were estimated using locally developed correlation with soil bulk density. The soil friction angle used in these laboratory tests was exten- sively tested, and Figure 59 shows the results of 52 direct shear tests carried out on dry Essen sand with a dry unit weight in the range of 15.46 ≤ γ ≤ 17.54 kN/m3 (98.5 ≤ γ ≤ 111.75 pcf ). The tests were carried out with normal stresses between 50 ≤ σ ≤ 200 kPa (0.52 ≤ σ ≤ 2.09 tsf). Essen sand is a medium-to- coarse, sharp-edged silica sand. The sand has a specific gravity of Gs ≈ 2.693 ± 0.004 and minimum and maximum porosities of nmin ≈ 0.330 ± 0.012 and nmax ≈ 0.443 ± 0.006, respectively. The correlation was revised after identifying outlier(s). The best fit lines are as shown in Figure 59. Perau (1995) used all 52 test data. The revised correlation is the best fit line obtained from linear regression on 51 samples, with the circled test result considered as an outlier. The correlation given by Perau (1995) is the following: The revised correlation is the following: It was found that the difference between the ultimate bearing capacities obtained for a square footing (1.0 m2) using the friction angles obtained from the original correla- tion, Equation 107 (Perau, 1995), and the revised correlation (Equation 108) is 10% to 18% for the range of friction angles between 40° and 47°. φ γf n R= − = =( )3 824 21 527 51 0 804 1082. . , . ( ) φ γf n R= − = =( )3 9482 23 492 52 0 771 1072. . , . ( ) γ γ= ( ) + ( ) ≤0 88 99 146 1061 60. ( )N pcf for pcf 72 0 0.4 0.8 1.2 1.6 2 Bias using Peck, Hanson and Thornburn (1974) as mentioned in Kulhawy and Mayne (1990) 0 0.2 0.4 0.6 0.8 1 B ia s u sin g H at an ak a an d U ch id a (19 96 ) n = 15 Mean bias Figure 57. Comparison of biases for the cases in natural soil conditions when using Equations 100 and 101.

3.5 Uncertainty in the Bearing Capacity of Footings in/on Granular Soils Subjected to Vertical-Centric Loading 3.5.1 Scope of Case Histories In 172 load test cases of the UML-GTR ShalFound07 database, the foundations were subjected to vertical-centric loadings, and the load test results could be interpreted employ- ing the minimum slope failure criterion. The soil friction angles for these cases ranged from 30.5°(±0.5) to 45° (±0.5). 3.5.2 Summary of Mean Bias Statistics Of the 172 cases, 14 foundations were tested in natural soil conditions and the remaining 158 in controlled soil conditions. The cases for which SPT N blow count observations are available have been categorized as the cases in natural soil 73 a GWT4.62 1 )1(1 i iviiavi D DD calculate (N1)60i using Equation 105 viaii pNN 60601 b 99)(88.0 601 ib N ?ba ?146a GWT Di Di+1 Di+2N60(i+1) N60i N60(i-1) i i+1 (i = layer number) ba ba No Yes 146 a Yes Final ai No Initial guess = 114.5pcf calculate using Equation 106 Figure 58. Flow chart showing iteration for the estimation of soil unit weight. 32 36 40 44 48 Test results (n = 52) Perau, 1995 Revised correlation 15 15.5 16 16.5 17 17.5 18 100 105 110 Bulk density, γ (kN/m3) So il fr ic tio n an gl e, φ f (d eg ) Bulk density, γ (lb/ft3) Figure 59. Revised correlation for angle of internal friction and dry unit weight of Essen sand.

conditions, while those tested in laboratories using soils of known particle size and controlled compaction have been categorized as the cases in controlled soil conditions. Each of the cases was analyzed to obtain the measured failure from the load-settlement curve and the calculated bearing capacity following the equations and correlations presented in Section 3.4. The relation of the two (i.e., measured failure over calculated capacity) constitutes the bias of the case. Appendix G presents examples for bias calculations for the case histories. Section G.1 presents the bias calculations for footing ID (FOTID) #35 of database UML-GTR ShalFound07 related to vertical-centric loading. Figure 60 presents a flow- chart summary of the mean bias for vertical-centric load- ing cases grouped by soil conditions and footing widths. Figures 61 to 63 present the bias histograms and probability density functions as well as measured versus calculated bear- ing capacity relations for all the cases and the subcategoriza- tion of natural versus controlled soil conditions. The data in Figures 60 to 63 represent all available cases without giving consideration to outliers, which will be addressed in Chapter 4. The mean bias value for the footings in natural soil conditions was found to be around 1.0, regardless of the footing sizes (the largest footing tested was about 10 ft wide). In contrast, for the footings in controlled soil conditions the mean bias value changed from about 1.5 for larger footings to 1.7 for smaller footings. The variation in the mean bias with the footing width is further discussed in Chapter 4. Compared to the biases for the tests in controlled soil conditions, the biases for the tests in natural soil conditions have higher variation, even when the number of sites is comparable. One may con- clude that as the controlled soil conditions more correctly represent the accurate soil parameters, the higher mean bias reflects conservatism (under-prediction) in the calculation model (i.e., the bearing capacity equation). The layer variation in soil conditions and the integrated parameters from the SPT 74 Vertical-Centric Loading n = 173; mean bias = 1.59, COV = 0.291 Natural soil conditions (φf from SPT-N counts) n = 14; no. of sites = 8 mean = 1.00 COV = 0.329 Controlled soil conditions (Dr ≥ 35%) n = 159; no. of sites = 7 mean = 1.64 COV = 0.267 B > 1.0m n = 6 no. of sites = 3 mean = 1.01 COV = 0.228 0.1 < B ≤ 1.0m n = 8 no. of sites = 7 mean = 0.99 COV = 0.407 B ≤ 0.1m n = 138 no. of sites = 5 mean = 1.67 COV = 0.245 0.1 < B ≤ 1.0m n = 21 no. of sites = 3 mean = 1.48 COV = 0.391 Figure 60. Summary of bias (measured over calculated bearing capacity) for vertical-centric loading cases (Database I) (0.1 m = 3.94 in, 1 m = 3.28 ft). (a) 0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 Bias, λ = qu,meas / qu,calc 0 10 20 30 40 N um be r o f o bs er va tio ns 0 0.1 0.2 Vertical-centric loading n = 173 mean = 1.59 COV = 0.291 lognormal distribution normal distribution Fr eq ue nc y 0.1 1 10 100 Calculated bearing capacity, qu,calc (Vesic, 1975 and modified AASHTO) (ksf) 0.1 1 10 100 In te rp re te d be ar in g ca pa ci ty , q u , m ea s u sin g M in im um S lo pe c rit er io n (V esi c, 19 63 ) (ks f) Vertical-centric loading Data (n = 173) Data best fit line No bias line (b) Figure 61. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of shallow foundations under vertical-centric loading.

75 (a) 0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 0 10 20 30 40 N um be r o f o bs er va tio ns 0 0.1 0.2 0.3 Fr eq ue nc y Controlled soil conditions n = 159 mean = 1.64 COV = 0.267 lognormal distribution normal distribution Bias, λ = qu,meas / qu,calc (b) Calculated bearing capacity, qu,calc (Vesic, 1975 and modified AASHTO) (ksf) In te rp re te d be ar in g ca pa ci ty , q u , m ea s u sin g M in im um S lo pe c rit er io n (V esi c, 19 63 ) (ks f) Controlled soil conditions Data (n = 159) Data best fit line No bias line 0.1 1 10 100 0.1 1 10 100 Figure 62. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for vertical, centrically loaded shallow foundations on controlled soil conditions. 1 10 100 Calculated bearing capacity, qu,calc (Vesic, 1975 and modified AASHTO) (ksf) 1 10 100 In te rp re te d be ar in g ca pa ci ty , q u , m ea s u sin g M in im um S lo pe c rit er io n (V esi c, 19 63 ) (ks f) Natural soil conditions Data (n = 14) Data best fit line No bias line (b) (a) 0.2 0.6 1 1.4 1.8 2.2 2.6 3.4 3.8 0 1 2 3 4 5 6 N um be r o f o bs er va tio ns 0 0.1 0.2 0.3 0.4 Fr eq ue nc y Natural soil conditions n = 14 mean = 1.00 COV = 0.329 lognormal distribution normal distribution Bias, λ = qu,meas / qu,calc 3 Figure 63. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for vertical, centrically loaded shallow foundations on natural soil conditions.

when analyzing data for natural soil deposits result in layer variation (as expressed by the COV) and reduction in the mean bias. Further investigation as to the source of the obtained bias is presented in Section 4.4. 3.6 Uncertainty in the Bearing Capacity of Footings in/on Granular Soils Subjected to Vertical-Eccentric, Inclined-Centric, and Inclined-Eccentric Loading 3.6.1 Scope and Loading Procedures of the Case Histories The analysis of failure under vertical-eccentric, inclined- centric, and inclined-eccentric loading is based on test results from DEGEBO, Perau (1995), Montrasio (1994), and Gottardi (1992). The test conditions of the various data sources are summarized in Table 31. The following analysis is based on the loading convention shown in Figure 64(a). The application of loadings in the tests varied. In the tests with radial load paths, both the vertical and the horizontal loads were increased up to failure, maintaining a constant ratio of F3/F1 during the test, i.e., the load inclination (δ) was constant (see Figure 64(b)). The same applies to the tests with eccentric loading; the eccentricity, e = M2/F1, was main- tained constant during the test, because the vertical load was applied eccentrically at one location. On the other hand, in the tests with step-like load paths, the vertical load was increased up to a certain level and then kept constant while the hori- zontal load was increased up to failure (see Figure 64(c)). This means that the load inclination was no longer constant during the test but varied from zero up to the maximum load inclination at failure, δult. The step-like load paths were applied in tests under inclined-centric and inclined-eccentric loadings only. 3.6.2 Determination of the Measured Strength Limit State for Foundations Under Inclined Loading The procedure to determine the failure loads from the model tests depends on the load paths applied in the tests. The analysis shows that in the case of a test with a radial load path it is sufficient to consider only the vertical load versus vertical displacement curve. This curve already includes the unfavorable effect that a horizontal load or a bending moment has on the bearing capacity of a shallow foundation, leading to smaller vertical failure loads compared to the case of centric vertical loading. Figure 65 provides an example using test results with inclined loading performed by Montrasio (1994) under different load inclination angles. Both vertical load/vertical displacement and horizontal load/horizontal displacement curves are shown for each test with inclined load. The load displacement relation- ship in Figure 65 indicates that the vertical failure load, F1,ult, decreases with the increase of the load inclination. Applying the minimum slope criterion to the centric vertical load test results (δ = 0°, MoA2.1) provides the fail- ure load F10,ult = 0.956 kip (4.25kN). The failure loads for the tests with inclined loading decrease to F1,ult = 0.738kip (3.28kN) for a load inclination angle of δ = 3° (MoD2.1) and F1,ult = 0.677 kip (3.01kN) for δ = 8° (MoD2.2) and further 76 Source Soil conditions Footing size ft2 (m²) Footing base Loading 1 Load application1 Eccentric radial load path Inclined radial load path DEGEBO Fine to medium sand, loose to medium dense, dense; gravel, medium dense, dense 1.6 6.6 (0.5 2.0) 3.3 3.3 (1.0 1.0) 3.3 9.8 (1.0 3.0) 2.0 6.9 (0.6 2.09) medium rough (prefabricated) Inclined- eccentric radial load path Eccentric radial load path Inclined step-like load path Perau (1995) Medium to coarse sand, dense to very dense 0.3 0.3 (0.09 0.09) 0.2 0.2 (0.05 0.15) rough (base glued with sand) Inclined- eccentric F1-M2: radial load path F1-F3: step-like load path Eccentric radial load path Inclined radial load path Montrasio (1994) Medium to coarse sand (Ticino Sand), dense 0.3 0.3 (0.08 0.08) 0.5 0.3 (0.16 0.08) 0.8 0.3 (0.24 0.08) rough (base glued with sand) Inclined- eccentric F1-F3: step-like load path F3-M2: radial load path Eccentric radial load path Inclined radial or step-like load pathGottardi (1992) Medium to coarse sand (Adige Sand), dense 1.6 0.3 (0.5 0.1) rough (base glued with sand) Inclined- eccentric F1-M2: radial load path F1-F3: radial or step-like load path 1 See Figure 64 for details Table 31. Test data used for failure analysis.

77 3b 1x 2F 3M 1M 2M1 F 2x 3F 2b D 3x γ, φfg (a) Loading convention F1 F3 δ = constant F1 M2 arctan e = constant (b) Radial load path (c) Step-like load path F1 F3 1,const. increasing δ F Figure 64. Loading convention and load paths used during tests. 0 1 2 3 4 Vertical load, F1, F10 (kN) 8 6 4 2 0 V er tic al d isp la ce m en t, u 1 (m m) 0 0.2 0.4 0.6 0.8 1 F1 (kips) 0.3 0.2 0.1 0 u 1 (in ) MoD2.1 δ = 3° MoD2.2 δ = 8° MoD2.3 δ = 14° MoA2.1 δ = 0°(F10) (a) 0 0.2 0.4 0.6 0.8 1 1.2 Horizontal load, F3 (kN) 6 4 2 0 H o riz o n ta l d is pl ac em en t, u 3 (m m) 0 0.05 0.1 0.15 0.2 0.25 F3 (kips) 0.2 0.1 0 u 3 (in ) MoD2.1 δ = 3° MoD2.2 δ = 8° MoD2.3 δ = 14° (b) Figure 65. Load–displacement curves for model tests conducted by Montrasio (1994) with varying load inclination: (a) vertical load versus vertical displacement and (b) horizontal load versus horizontal displacement.

decreases to F1,ult = 0.425kip (1.89kN) when the load inclination increases to δ = 14° (MoD2.3). Consequently, the correspond- ing horizontal component of the failure load, F3,ult, increases with the increase in the load inclination. Overall, the horizontal loads are significantly smaller than the vertical failure loads due to limited soil-foundation frictional resistance. This pro- cedure results in vertical failure loads (F1,ult) that can be directly related to the theoretical failure loads determined by the calcu- lation model for the relevant load inclination, hence making it possible to obtain the bias of the model for the bearing capacity of foundations under inclined loads. In the case of a step-like load path, a different procedure has to be applied. In these tests, the vertical load was kept constant up to failure, hence the vertical load/vertical displacement curves are not meaningful. The failure is analyzed on the basis of the horizontal load/horizontal displacement curves result- ing in horizontal failure loads, F3,ult. The vertical failure loads, F1,ult, are the ones corresponding to the horizontal failure loads, F3,ult, and coincide with the constant vertical load in each test. As the load inclination is increased during the test, the maximum load inclination reached is the load inclination at failure, tan δult = F3,ult/F1,ult. The theoretical (vertical) failure load is then calculated for the load inclination at failure, δult, and compared to the measured vertical failure load, F1,ult, to determine the bias. Additionally, the theoretical horizontal failure loads are calculated using the respective load inclina- tion at failure and the theoretical vertical failure loads. It can be shown that the resulting biases of the horizontal failure loads coincide with the biases of the vertical failure loads and confirm this procedure. In both procedures, the minimum slope criterion and the two-slope criterion were examined for the failure load inter- pretation. In most cases, the results were found to be com- parable. However, in some cases, the two-slope criterion was not applicable (FOTIDs #251 and #266, DEGEBO tests on eccentric loading, FOTIDs #301 and #317, and DEGEBO tests on inclined loading) while the minimum slope criterion could always be used and therefore seemed to have a distinct advantage. 3.6.3 Summary of Mean Bias Statistics for Vertical-Eccentric Loading Table 32 presents a summary of the statistics of the bias for the footings under vertical-eccentric loading. Section G.2 in Appendix G presents the details of the bias calculation for a single relevant case history (ID #471) of database UML-GTR ShalFound07. The total number of cases under vertical- eccentric loading from all sources was 43, including all outliers to be addressed in Chapter 4. Seventeen cases from DEGEBO, 14 cases from Montrasio (1994) and Gottardi (1992) and 12 cases from Perau (1995) could be analyzed. Figure 66 pres- ents a histogram and a PDF of the bias as well as the relation- ship between measured and calculated bearing capacities for all vertical, eccentrically loaded foundation cases summarized in Table 32. DEGEBO results show the highest mean and COV of the bias when using any of the failure criteria. Table 33 summarizes the statistics of the bias associated with bearing capacity calculations when using the full geometrical size of the foundation width (B). Table 33 was added in order to gain perspective on the bias in cases where the influence of the effective width is neglected. Comparing Tables 32 and 33, it can be seen that the mean bias of the ultimate strength estimation decreases and the COV of the bias increases when full footing geometry (B) is used instead of the effective footing dimensions (B′). This is an expected outcome considering the larger B would result in a higher bearing capacity (and hence decreased bias) while the methodology is incorrect, contributing to the increased uncertainty (being represented by the COV). The decreased bias and increased COV would necessitate a significant increase in the resistance to ensure a specified safety, i.e., utilizing lower resistance factors. For example, considering all cases, the resistance factor obtained is 0.60 when B′ is used and 0.30 78 Minimum slope criterion Two-slope criterion Tests No. of cases Mean Std. dev. COV Mean Std. dev. COV DEGEBO – radial load path 17 (15)1 2.22 0.754 0.340 2.04 0.668 0.328 Montrasio (1994)/Gottardi (1992) – radial load path 14 1.71 0.399 0.234 1.52 0.478 0.313 Perau (1995)– radial load path 12 1.43 0.337 0.263 1.19 0.470 0.396 All cases 43(41)1 1.83 0.644 0.351 1.61 0.645 0.400 1 Number of cases for two-slope criterion Table 32. Summary of the statistics for biases of the test results for vertical-eccentric loading when using effective foundation width (B′).

when B is used. Thus, Tables 32 and 33 indicate that the bear- ing capacity obtained using the full footing width (B) is unsafe when compared to the bearing capacity obtained when using the effective width (B′). 3.6.4 Summary of Mean Bias Statistics for Inclined-Centric Loading The mean and standard deviation of the calculated biases in the case of inclined loading are summarized in Table 34 for the two failure criteria. Section G.3 of Appendix G presents the details of the bias calculations for a single relevant case history (ID #547) of database UML-GTR ShalFound07. Figure 67 presents a histogram and PDF of the bias as well as the relation- ship between measured and calculated bearing capacity for all inclined, centrically loaded shallow foundations. There are no differences in the biases obtained from the two-slope and the minimum slope failure criteria for the cases of step-like load paths. Gottardi’s tests with radial load paths sometimes seem to result in smaller biases than the other tests, but overall, no significant differences exist in the biases of the step-like and radial load path tests. The biases determined for the DEGEBO tests are also in the same order of magnitude as the ones from the small-scale model tests although they were carried out on foundations significantly larger in size. DEGEBO tests were carried out on foundations of 1.6 ft × 3.3 ft 79 0.4 1.2 2 2.8 3.6 Bias, λ = qu,meas / qu,calc 0 2 4 6 8 10 12 N um be r o f o bs er va tio ns 0 0.05 0.1 0.15 0.2 0.25 Fr eq ue nc y Vertical-eccentric loading n = 43 mean = 1.83 COV = 0.351 lognormal distribution normal distribution (a) 0.1 1 10 100 Calculated bearing capacity, qu,calc (Vesic, 1975 and modified AASHTO) (ksf) 0.1 1 10 100 1000 In te rp re te d be ar in g ca pa ci ty , q u , m ea s u sin g M in im um S lo pe c rit er io n (V esi c, 19 63 ) (ks f) Vertical-eccentric loading Data (n = 43) Data best fit line No bias line (b) Figure 66. (a) Histogram and probability density function of the bias and (b) relationship between measured and calculated bearing capacity for all vertical, eccentrically loaded shallow foundations. Minimum slope criterion Two-slope criterion Tests No. of cases Mean Std. dev. COV Mean Std. dev. COV DEGEBO – radial load path 17 (15)1 1.30 0.464 0.358 1.20 0.425 0.355 Montrasio (1994)/Gottardi (1992) – radial load path 14 0.97 0.369 0.380 0.86 0.339 0.396 Perau (1995) – radial load path 12 0.79 0.302 0.383 0.64 0.296 0.465 All cases 43(41)1 1.05 0.441 0.420 0.92 0.423 0.461 1 Number of cases for two-slope criterion Table 33. Summary of the statistics for biases of the test results for vertical-eccentric loading when using the full foundation width (B).

(0.5 m × 1.0 m) to 3.3 ft × 9.8 ft (1 m × 3 m) versus the small scale models having foundation sizes of 2 in. × 6 in. (5 cm × 15 cm) to 4 in. × 20 in. (10 cm × 50 cm). 3.6.5 Summary of Mean Bias Statistics for Inclined-Eccentric Loading Table 35 presents a summary of the statistics of the bias for footings subjected to inclined-eccentric loadings, with both radial and step-like load paths and including the effective foundation width, B′. Figure 68 presents a histogram and PDF of the bias as well as the relationship between measured and calculated bearing capacity for all inclined, eccentrically loaded shallow foundation cases. As in the inclined-centric loading cases, there is no significant difference in the tests results between the radial and the step-like load paths. The bearing capacity calculations of these case histories were noticeably affected by using the effective foundation width (B′) versus the geometrical actual foundation width (B). Table 36 sum- marizes the statistics associated with the bearing capacity calculations using the full geometrical foundation width (B) in order to gain perspective on the bias in cases where the influ- ence of the effective width is neglected. The biases presented in Table 36 indicate that for the examined case histories the calculated bearing capacity using the effective width resulted in a bias about two times larger (i.e., a bearing capacity two times 80 Minimum slope criterion Two-slope criterion Tests No. of cases Mean Std. dev. COV Mean Std. dev. COV DEGEBO/ Montrasio (1994)/Gottardi (1992) – radial load path 26 (24)1 1.56 0.346 0.222 1.35 0.452 0.334 Perau (1995)/Gottardi (1992) – step-like load path 13 1.17 0.537 0.459 1.17 0.537 0.459 All cases 39 (37)1 1.43 0.422 0.295 1.29 0.455 0.353 1 Number of cases for two-slope criterion Table 34. Summary of the statistics for biases of the test results for inclined-centric loading when using foundation width (B). 0.2 0.6 1 1.4 1.8 2.2 2.6 Bias, λ = qu,meas / qu,calc 0 4 8 12 N um be r o f o bs er va tio ns 0 0.1 0.2 0.3 Fr eq ue nc y Inclined-centric loading n = 39 mean = 1.43 COV = 0.295 lognormal distribution normal distribution (a) (b) 0.1 10 100 Calculated bearing capacity, qu,calc (Vesic, 1975 and modified AASHTO) (ksf) 0.1 1 10 100 In te rp re te d be ar in g ca pa ci ty , q u , m ea s u sin g M in im um S lo pe c rit er io n (V esi c, 19 63 ) (ks f) Inclined-centric loading Data (n = 39) Data best fit line No bias line 1 Figure 67. (a) Histogram and probability density function of the bias and (b) relationship between measured and calculated bearing capacity for all inclined, centrically loaded shallow foundations.

Minimum slope criterion Two-slope criterion Tests No. of cases Mean Std. dev. COV Mean Std. dev. COV DEGEBO/Gottardi (1992) – radial load path 8 2.06 0.813 0.394 1.78 0.552 0. 310 Montrasio (1994)/ Gottardi (1992) 6 2.13 0.496 0.234 2.12 0.495 0.233 Perau (1995) – positive eccentricity 8 2.16 1.092 0.506 2.15 1.073 0.500 Perau (1995) – negative eccentricity 7 3.43 1.792 0.523 3.39 1.739 0.513 Step-like load path All step-like load cases 21 2.57 1.352 0.526 2.56 1.319 0.516 All cases 29 2.43 1.234 0.508 2.34 1.201 0.513 Table 35. Summary of the statistics for biases of the test results for inclined-eccentric loading when using effective foundation width (B′). (a) 1.2 1.8 2.4 3.6 4.2 4.8 5.4 6.6 7.2 Bias, λ = qu,meas / qu,calc 0 1 2 3 4 5 6 7 8 9 N um be r o f o bs er va tio ns 0 0.05 0.1 0.15 0.2 0.25 0.3 Fr eq ue nc y Inclined-eccentric loading n = 29 mean = 2.43 COV = 0.508 lognormal distribution normal distribution 3 6 (b) 0.1 Calculated bearing capacity, qu,calc (Vesic, 1975 and modified AASHTO) (ksf) 0.1 1 10 100 In te rp re te d be ar in g ca pa ci ty , q u , m ea s u sin g M in im um S lo pe c rit er io n (V esi c, 19 63 ) (ks f) Inclined-eccentric loading Data (n = 29) Data best fit line No bias line 100101 Figure 68. (a) Histogram and probability density function of the bias and (b) relationship between measured and calculated bearing capacity for all inclined, eccentrically loaded shallow foundations. Minimum slope criterion Two-slope criterion Tests No. of cases Mean Std. dev. COV Mean Std. dev. COV DEGEBO/Gottardi (1992) – radial load path 8 1.07 0.448 0.417 0.94 0.365 0. 387 Montrasio (1994)/ Gottardi (1992) 6 1.18 0.126 0.106 1.18 0.125 0.106 Perau (1995)– positive eccentricity 8 0.70 0.136 0.194 0.70 0.135 0.194 Perau (1995) – negative eccentricity 7 1.09 0.208 0.191 1.08 0.208 0.193 Step-like load path All step-like load cases 21 0.97 0.267 0.276 0.96 0.267 0.277 All cases 29 1.00 0.322 0.323 0.96 0.290 0.303 Table 36. Summary of the statistics for biases of the test results for inclined-eccentric loading when using foundation width (B).

smaller) than that obtained using the full geometrical width of the foundation. The ramifications of these findings are relevant to design practices in which the loading details are not known at the time of the design. This issue was touched upon in Section 3.1.7 and will be further discussed in Chapter 4. The change in variability between the two cases as well as the mean bias are greatly affected by a few outliers and will be further discussed in Chapter 4. The effects of the moment direction (or load eccentricity) with respect to the horizontal load, noted in Tables 35 and 36 as positive and negative moments for tests conducted by Perau (1995), are discussed in the following sections. 3.7 Loading Direction Effect for Inclined-Eccentric Loading The loading direction in the case of inclined-eccentric load- ing affects the failure loads. Figure 69 presents the definitions established for the loading direction along the footing width (a) and along the footing length (b) (see also Butterfield et al., 1996) depending on the eccentricity direction in relation to the direction of the applied lateral load. The footing in the upper part of Figure 69 (a) and (b) is loaded by a horizontal load and an eccentric vertical load with “negative” eccentricity. The resultant moment, which is negative in case of loading eccen- tricity along footing width b3 (a) and positive in case of loading eccentricity along footing length b2 (b)(refer to Figure 69 for sign conventions), then acts in the opposite direction to the horizontal load. The induced rotations counteract the dis- placements forced by the horizontal load, leading to a higher resistance of the footing compared with the inclined-centric load case and, thus, to higher failure loads. In contrast, the footing in the lower part of Figure 69 is loaded by an eccentric vertical load with “positive” eccentricity. This leads to a pos- itive moment in the case of loading eccentricity along footing width b3 (a), and a negative moment in the case of loading eccentricity along footing length b2 (b), which acts in the same direction as the horizontal load. The induced rotations enforce the horizontal displacements; hence, the footing resistance is smaller than in the case of inclined-centric loading, leading to smaller failure loads. In a different approach, when the moment is in the “opposite” direction, it induces higher contact stresses between the foun- dation and the soil in the “front” of the foundation where the lateral load is applied. As the foundation-soil friction is pro- gressive, the higher contact stress results in a higher friction resistance and, hence, the overall layer capacity. In contrast, when the moment acts in the “same” direction, the contact stress at the “front” of the footing decreases, thereby reducing the friction and resulting in a decrease in the total foundation resistance (bearing capacity). The effect of the loading direction expressed in Tables 35 and 36 is demonstrated in a graphical format in Figures 70 and 71. Figures 70 and 71 present a his- togram and PDF of the bias as well as the relationship between measured and calculated bearing capacity for inclined-eccentric loading under positive and negative moments, respectively. A comparison of Figures 70 and 71 shows an increase of the bias for the negative moment cases. The effect of loading direction is further demonstrated by the results of two tests carried out by Gottardi (1992) and shown in Figure 72. The failure loads in the case of loading in the same direction (positive loading eccentricity) are significantly smaller than the failure loads in the case of opposite loading direction (negative loading direction). The influence on the bias is substantial—0.37 versus 0.64 for the two-slope criterion and 0.37 versus 0.66 for the minimum slope criterion. Hence, it appears that this difference cannot be neglected and needs to be considered. Figure 73 shows the load-displacement curves for two double tests (positive and negative loading eccentricity) con- ducted by Perau (1995) and one double test by Montrasio (1994), applying different loading directions at the same level of vertical loading. The results of Perau’s and Montrasio’s tests show a similar trend. Montrasio’s test leads to a bias of 1.86 versus 1.97 (positive versus negative loading eccentricity), 82 e3 F1 b3 F3 M2 F1 F3 e3 F1 b3 F3 M2 F1 F3 Moment acting in the same direction as the lateral loading – positive eccentricity Moment acting in direction opposite to the lateral loading – negative eccentricity b3 b3 e3 F1 b3 F3 M2 F1 F3 e3 F1 b3 F3 M2 F1 F3 Moment acting in the same direction as the lateral loading – positive eccentricity Moment acting in direction opposite to the lateral loading – negative eccentricity b3 b3 Figure 69. Loading directions for the case of inclined-eccentric loadings: (a) along footing width and (b) along footing length.

83 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 Bias, λ = qu,meas / qu,calc 0 1 2 3 N um be r o f o bs er va tio ns 0 0.1 0.2 0.3 0.4 Fr eq ue nc y Inclined-eccentric loading Positive eccentricity n = 8 mean = 2.16 COV = 1.092 lognormal distribution normal distribution (a) 0.1 1 10 Calculated bearing capacity, qu,calc (Vesic, 1975 and modified AASHTO) (ksf) 0.1 1 10 In te rp re te d be ar in g ca pa ci ty , q u , m ea s u sin g M in im um S lo pe c rit er io n (V esi c, 19 63 ) (ks f) Inclined-eccentric loading Positive eccentricity Data (n = 8) Data best fit line No bias line (b) Figure 70. (a) Histogram and probability density function of the bias and (b) relationship between measured and calculated bearing capacity for all inclined, eccentrically loaded shallow foundations under positive moment. 1.2 1.8 2.4 3 3.6 4.2 4.8 5.4 6 6.6 7.2 Bias, λ = qu,meas / qu,calc 0 1 2 3 N um be r o f o bs er va tio ns 0 0.1 0.2 0.3 0.4 0.5 Fr eq ue nc y Inclined-eccentric loading Negative eccentricity n = 7 mean = 3.43 COV = 0.523 normal distribution lognormal distribution (a) 0.1 1 10 Calculated bearing capacity, qu,calc (Vesic, 1975 and modified AASHTO) (ksf) 0.1 1 10 In te rp re te d be ar in g ca pa ci ty , q u , m ea s u sin g M in im um S lo pe c rit er io n (V esi c, 19 63 ) (ks f) Inclined-eccentric loading Negative eccentricity Data (n = 7) Data best fit line No bias line (b) Figure 71. (a) Histogram and probability density function of the bias and (b) relationship between measured and calculated bearing capacity for all inclined, eccentrically loaded shallow foundations under negative moment.

84 0 4 8 12 F1 [kN] 8 6 4 2 0 u1 [mm] 6 4 2u3 [mm] 0.4 0.8 1.2 1.6 F3 [kN] GoE6.1, e=-0.0167 GoE6.2, e=+0.0167 0 0.1 0.2 0.3 [kip] 0.3 0.2 0.1 [in] 0.2 0.15 0.1 0.05 0u3 [in] 1 2 3 F1 [kip] Figure 72. Load–displacement curves for inclined-eccentric loading with different loading directions utilizing data from Gottardi (1992). indicating a minor effect of the loading direction. However, this effect is more significant in Perau’s tests, where the evaluation of the failure loads leads to a mean bias of 1.79 (COV 0.206) for a horizontal load and moment acting in the same direc- tion (positive loading eccentricity) and 2.76 (COV 0.152) for a moment in an opposite loading direction (negative loading eccentricity). In general, it can be stated that the effect of the loading direction is less pronounced if the vertical load (F1) is relatively high (i.e., the load inclination is relatively small) because this effect is predominantly determined by the load inclination and not by the load eccentricity. The level of the vertical load (F1) can properly be expressed by relating it to the failure load for centric vertical loading (F10). The notation F10 has been adopted in order to differentiate the failure load of vertical- centric loading from the vertical component F1 of the inclined failure loads (refer to Figure 65 and Section 3.6.2). In this context, small load inclinations coincide with relatively high vertical load levels. Figure 74 shows an evaluation of the bear- ing capacity in the F2/F10 − M3/(F10 • b2) plane performed by Lesny (2001) using Perau’s (1995) test results. In reference to Figure 64, F2 is the horizontal component of the inclined load and b2 is the footing length in the same direction. Different loading directions and different load levels have been ana- lyzed in Figure 74, resulting in distorted trend lines due to the existence of a higher capacity if horizontal load and moment act in the opposite direction (i.e., both load components are positive and the loading eccentricity is negative). However,

the analysis also reveals that the gain of capacity is relatively small, and, for vertical load levels greater than or equal to 0.3, the effect of loading direction is negligible. 3.8 Uncertainty in the Bearing Capacity of Footings in/on Rock 3.8.1 Overview The ratio of the measured/interpreted bearing capacity to the calculated shallow foundation bearing capacity (the bias λ) was used to assess the uncertainty of the selected design methods for the 119 case histories of database GTR-UML RockFound07. Section 1.7 details the methods of analysis selected for the bearing capacity calculations. Appendix G provides detailed examples for the calculations performed for each analysis. Sections G.5 and G.6 relate to the utilization of Goodman’s (1989) method, and Section G.7 relates to the utilization of Carter and Kulhawy’s (1988) method in the traditional way (i.e., using Equation 82a). This section sum- marizes the results of the analyses for the examined methods: the semi-empirical mass parameters procedure developed by Carter and Kulhawy (1988) and the analytical method pro- posed by Goodman (1989). The consistency of the rocks in the database, the types of foundation, and the level of knowledge of the rock were categorized, when applicable, while examining their influ- ence on the bias. In addition, histograms and PDFs of the bias obtained by the different methods are presented and discussed. 85 0 0.2 0.4 0.6 F1 [kN] 1.6 1.2 0.8 0.4 0 u1 [mm] 4 3 2 1u3 [mm] 0.04 0.08 0.12 0.16 F3 [kN] PeE1.2 - e3=-0.0225m PeE1.4 - e3=0.0225m PeE1.3 - e3=-0.0225m PeE1.5 - e3=0.0225m MoE1.4 - e3=0.01m MoE1.1 - e3=-0.01m 0 0.01 0.02 0.03 [kip] 0.06 0.04 0.02 [in] 0.12 0.08 0.04 0u3 [in] 0.04 0.08 0.12 F1 [kip] PeE - steplike MoE - radial Figure 73. Load–displacement curves for inclined-eccentric loading with different loading directions utilizing data from Perau (1995) and Montrasio (1994).

3.8.2 Carter and Kulhawy’s (1988) Semi-Empirical Bearing Capacity Method 3.8.2.1 Presentation of Findings Carter and Kulhawy’s (1988) method is described in Sec- tion 1.7.6 and its application is demonstrated in Section G.7 in Appendix G. Table E-2 of Appendix E presents the calculated bearing capacity values and the associated bias for each of the 119 case histories of database UML-GTR RockFound07 (Table E-2 includes all 122 original cases and the excluded 3 cases as noted). The relationships between the bearing capacities (qult) calculated using the two Carter and Kulhawy (1988) semi-empirical procedures (Equation 82a and the revised relations given by Equation 82b) and the interpreted bearing capacity (qL2) are presented in Figure 75. Equation 109a provides the best fit line generated using regression analysis of all data using Equation 82a and results in a coefficient of determination (R2) of 0.921. Equation 109b represents the best fit line generated using regression analysis of all data using Equation 82b for calculating the bearing capacity and results in a coefficient of determination (R2) of 0.917. 86 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 M3/(F10•b2) 0 0.02 0.04 0.06 0.08 0.1 0.12 F 2 / F 10 F /F = 0.08 F /F = 0.13 F /F = 0.145 F /F = 0.26 F /F = 0.33 F /F = 0.41 F /F = 0.55 F /F = 0.08 F /F = 0.13 F /F = 0.15 F /F = 0.26 F /F = 0.33 F /F 10 10 10 10 10 10 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 1 1 1 1 10= 0.5 Figure 74. Influence of loading direction on capacity in the case of inclined-eccentric loading (Lesny, 2001). 0.01 0.1 1 10 100 1000 10000 100000 Carter and Kulhawy (1988) Bearing Capacity qult (ksf) 1 10 100 1000 10000 100000 In te rp re te d Fo un da tio n C ap ac ity q L2 (k sf) 58 Footing cases 61 Rock Socket cases 119 All cases with revised equation qL2 = 16.14 qult)( 0.619 (n = 119; R2 = 0.921) qL2 = 36.51 qult)( 0.600 (Revised) (n = 119; R2 = 0.917) qL2 = qult Figure 75. Relationship between calculated bearing capacity (qult) using two versions of Carter and Kulhawy (1988) and interpreted bearing capacity (qL2).

It can be observed in Figure 75 (and in Equations 109a and 109b) that the revised expression provided by Equation 82b gives systematically higher resistance biases than those biases obtained using Equation 82a. The bias mean and COV obtained using Equation 82b for all data (n = 119) are found to be 30.29 and 1.322, respectively, versus 8.00 and 1.240, respectively, obtained using Equation 82a. Both relations provide close to parallel lines when compared to the measured capacities. Equa- tions 109a and 109b suggest that Equation 82b roughly predicts half the capacity of Equation 82a as its multiplier to match the measured capacity is about double. As the relations pro- vided by Equation 82a are already consistently conservative, Equation 82a is preferred over Equation 82b, and the results processed and analyzed are those obtained using Equation 82a. Statistical analyses were performed to investigate the effect of the joint or discontinuity spacing (s′) either measured or determined based on AASHTO (2008) tables (see Section 1.8.3) and the effect of the friction angle (φf) of the rock on the calculated bearing capacity. Statistics for the ratio of the bias q qL2 0 600 36 51 109= ( ). ( ).ult b q qL2 0 619 16 14 109= ( ). ( ).ult a (measured bearing capacity, qL2, to calculated bearing capacity, qult) using Carter and Kulhawy’s (1988) semi-empirical method are summarized in Table 37. In Table 37, the statistics are categorized according to the joint spacing and the source of the data (i.e., measured discontinuity spacing versus spacing assumed based on the specifications). In Table 38, the data are subcategorized according to type of foundation (footings versus rock sockets) and the source of the joint spacing data. Table 39 is a summary of the statistics for the ratio of the measured bearing capacity (qL2) to calculated bearing capacity (qult) categorized according to foundation type and rock quality ranges for each type and all types combined. The distribution of the ratio of the interpreted bearing capac- ity to the calculated bearing capacity (the bias λ) for the 119 case histories (detailed in Table E-2 of Appendix E) is presented in Figure 76. The distribution of the bias λ has a mean (mλ) of 8.00 and a COVλ of 1.240 and resembles a lognormal random vari- able. The distribution of the bias λ for foundations on fractured rock only (20 cases) is presented in Figure 77 and has an mλ of 4.05 and a COVλ of 0.596. The distribution of the bias λ for the foundations on fractured rock resembles a lognormal random variable and has less scatter, reflected by the smaller COV when compared with the distribution of λ for all 119 case histories. 87 Cases n No. of sites m COV All (m easured q u ) 119 78 8.00 9.92 1.240 Measured discontinuity spacing (s′) 83 48 8.03 10.27 1.279 Fractured with measured discontinuity spacing (s′) 20 9 4.05 2.42 0.596 All non-fractured 99 60 8.80 1066 1.211 Non-fractured with m easured discontinuity spacing (s′) 63 39 9.29 11.44 1.232 Non-fractured with s′ based on AASHTO (2007) 36 21 7.94 9.22 1.161 n = number of case histories, mλ = mean of biases, σλ = standard deviation, COV = coefficient of variation Calculated capacity based on Equation 82a Table 37. Summary of the statistics for the ratio of measured (qL2) to calculated bearing capacity (qult) for all foundations on rock using the Carter and Kulhawy (1988) method. Cases n No. of sites m COV All rock sockets 61 49 4.29 3.08 0.716 All rock sockets on fractured rock 11 6 5.26 1.54 0.294 All rock sockets on non-fractured rock 50 43 4.08 3.29 0.807 Rock sockets on non-fractured rock with measured discontinuity spacing (s′) 34 14 3.95 3.75 0.949 Rock sockets on non-fractured rock with s′ based on AASHTO (2007) 16 13 4.36 2.09 0.480 All footings 58 29 11.90 12.794 1.075 All footings on fractured rock 9 3 2.58 2.54 0.985 All footings on non-fractured rock 49 26 13.62 13.19 0.969 Footings on non-fractured rock with m easured discontinuity spacing (s′) 29 11 15.55 14.08 0.905 Footings on non-fractured rock with s′ based on AASHTO (2007) 20 11 10.81 11.56 1.069 n = number of case histories, mλ = mean of biases, σλ = standard deviation, COV = coefficient of variation Calculated capacity based on Equation 82a Table 38. Summary of the statistics for the ratio of measured (qL2) to calculated bearing capacity (qult) of rock sockets and footings on rock using the Carter and Kulhawy (1988) method.

3.8.2.2 Observations The presented findings of Carter and Kulhawy’s (1988) methods for the prediction of bearing capacity suggest the following: 1. The bias of the estimated bearing resistances obtained using the revised equation (Equation 82b) are systematically higher than those obtained using Equation 82a, with very similar COVs. As both equations are by and large conser- vative, only the traditional equation (Equation 82a) was used for further analysis and method evaluation. 2. The method (Equation 82a) substantially underpredicts (on the safe side) for the range of capacities typically lower than 700 ksf. The bias increases as the bearing capacity decreases. This provides a logical trend in which founda- 88 Foundation Type Cases n No. of sites m COV RMR > 85 23 23 2.93 1.908 0.651 65 < RMR < 85 57 36 3.78 1.749 0.463 44 < RMR < 65 17 10 8.83 5.744 0.651 All 3 < RMR < 44 22 9 23.62 13.550 0.574 RMR > 85 16 16 3.42 1.893 0.554 65 < RMR < 85 35 24 3.93 1.769 0.451 44 < RMR < 65 9 8 6.82 6.285 0.921 Rock Sockets 3 < RMR < 44 1 1 8.39 -- -- RMR > 85 7 7 1.81 1.509 0.835 65 < RMR < 85 22 13 3.54 1.732 0.489 44 < RMR < 65 8 5 11.09 4.391 0.396 Footings 3 < RMR < 44 21 8 24.34 13.440 0.552 n = number of case histories, mλ = mean of biases, σλ = standard deviation, COV = coefficient of variation Calculated capacity based on Equation 82a Table 39. Summary of the statistics for the ratio of measured (qL2) to calculated bearing capacity (qult) using the Carter and Kulhawy (1988) method categorized by the rock quality and foundation type. 0 8 12 16 20 24 28 32 36 40 44 48 52 Bias, λ = qu,meas / qu,calc 0 4 8 12 16 N um be r o f o bs er va tio ns 0 0.05 0.1 0.15 Fr eq ue nc y 119 Rock sockets and Footing cases Carter and Kulhawy (1988) mean = 8.00 COV = 1.240 lognormal distribution normal distribution 4 Figure 76. Distribution of the ratio of the interpreted bearing capacity (qL2) to the bearing capacity (qult) calculated using Carter and Kulhawy’s (1988) method (Equation 82a) for the rock sockets and footings in database UML-GTR RockFound07. 0 1 2 3 4 5 6 7 8 9 10 Bias, λ = qu,meas / qu,calc 0 1 2 3 4 5 N um be r o f o bs er va tio ns 0 0.05 0.1 0.15 0.2 0.25 Fr eq ue nc y 20 Foundation cases on Fractured Rocks Carter and Kulhawy (1988) mean = 4.05 COV = 0.596 lognormal distribution normal distribution Figure 77. Distribution of the ratio of the interpreted bearing capacity (qL2) to the bearing capacity (qult ) calculated using Carter and Kulhawy’s (1988) method (Equation 82a) for foundations on fractured rock in database UML-GTR RockFound07.

tions on lower bearing capacity materials are provided with a higher margin of safety while for foundations on harder rock with higher bearing capacities, the bias is smaller than one (1.0) (i.e., measured capacities are lower than calculated capacities). The bearing capacity values on the higher capacity sides are controlled by the strength of the foun- dation material (i.e., concrete), and, therefore, the results in that range are not necessarily translated into unsafe practice. 3. Comparison of the statistics obtained for shallow foun- dations (n = 58, mλ = 11.90, COVλ = 1.075 and number of sites = 29) with the statistics obtained for rock sockets (n = 61, mλ = 4.29, COVλ = 0.716 and number of sites = 49) may suggest that the method better predicts the capacity of rock sockets than the capacity of footings. This obser- vation might also suggest that the use of load-displacement relations for the tip of a loaded rock socket is not analogous to the use of load-displacement relations for a shallow foundation constructed below surface; hence, the data related to the tip of a rock socket should not be employed for shallow foundation analyses. This observation must be re-examined in light of the varied bias of the method with the rock strength, as is evident in Figure 75 and detailed in Table 39. The varying bias of the method, as observed in Figure 75 and described in Number 2 above, results in a relatively high scatter (COV = 1.240 for all cases). When the evaluation is categorized based on rock quality, the scatter (COV) systematically decreases to be between about 0.5 to 0.6, as detailed in Table 39. However, the changes in the mean of the bias with rock quality for the footings are much more pronounced than the changes for the rock sockets because most of the footings were tested on rock that was of lower quality than the rock existing at the tip of the rock sockets. For example, of the 22 cases of the lowest rock quality (3 ≤ RMR < 44), 21 cases involved a shallow foundation and 1 case involved a rock socket. In contrast, of the 23 cases of the highest quality rock (RMR ≥ 85), only 7 cases involve footings and 16 cases involve rock sockets. The conclusion, therefore, is that the variation in the method application is more associated with the rock type/strength and its influence on the method’s predic- tion than the foundation type. This conclusion is further confirmed by examination of the Goodman (1989) method, in which the bias is not affected by rock quality and, hence, similar statistics are obtained for the rock socket and the footing cases. 4. No significant differences exist between the cases for which discontinuity spacing (s′) was measured in the field and the cases for which the spacing was deter- mined based on generic tables utilizing rock description (Tables 37 and 38). 3.8.3 Goodman’s (1989) Analytical Bearing Capacity 3.8.3.1 Presentation of Findings Goodman’s (1989) method is described in Section 1.7.5 and its application is demonstrated in Sections G.5 and G.6 of Appendix G. Table E-3 of Appendix E presents the calculated bearing capacity values for each of the 119 case histories. The relationship between the bearing capacity calculated using Goodman’s (1989) analytical procedure (qult) and the inter- preted bearing capacity (qL2) is presented in Figure 78. Equa- tion 110 represents the best fit line that was generated using regression analysis and resulted in a coefficient of determination (R2) of 0.897. Statistical analyses were performed to investigate the effect of the measured and AASHTO-based joint (2007) or dis- continuity spacing (s′) and friction angle (φf) of the rock on the bearing capacity calculations. Table 40 summarizes the statistics for the ratio of the measured bearing capacity (qL2) to calculated bearing capacity (qult) using Goodman’s (1989) analytical method for the entire database. Table 41 provides the statistics for subcategorization based on foundation type and available information. Table 42 is a summary of the statistics for the ratio of the measured bearing capacity (qL2) to the calculated bearing capacity (qult) categorized according to foundation type and rock quality ranges for each type. q qL2 0 824 2 63 110= ( ). ( ).ult 89 1 10 100 1000 10000 100000 Goodman (1989) Bearing Capacity qult (ksf) 1 10 100 1000 10000 100000 In te rp re te d Fo un da tio n C ap ac ity q L2 (k sf) 58 Footing cases 61 Rock Socket cases qL2 = 2.16 qult)( 0.868 (n = 119; R2 = 0.897) qL2 = qult × Figure 78. Relationship between Goodman’s (1989) calculated bearing capacity (qult) and the interpreted bearing capacity (qL2)

The distribution of the ratio of the interpreted measured bearing capacity to the calculated bearing capacity (λ) for the 119 case histories in Table E-3 of database UML-GTR RockFound07 is presented in Figure 79. The distribution of λ has a mean (mλ) of 1.35 and a COVλ of 0.535 and resembles a lognormal random variable. The distribution of λ for only the foundations on fractured rock is presented in Figure 80 and has an mλ of 1.24 and a COVλ of 0.276. 3.8.3.2 Observations The presented findings of Goodman’s (1989) method for the prediction of bearing capacity suggest the following: 1. The method is systematically accurate, as demonstrated by the proximity of the best fit line to the perfect match line (measured qL2 = predicted qu) presented in Figure 78 90 Cases n No. of sites m COV All 119 78 1.35 0.72 0.535 Measured discontinuity spacing (s′) and friction angle ( f ) 67 43 1.51 0.69 0.459 Measured discontinuity spacing (s′) 83 48 1.43 0.66 0.461 Measured friction angle ( f ) 98 71 1.41 0.76 0.541 Fractured 20 9 1.24 0.34 0.276 Fractured with measured friction angle ( f ) 12 7 1.33 0.25 0.189 Non-fractured 99 60 1.37 0.77 0.565 Non-fractured with m easured s′ and measured f 55 37 1.55 0.75 0.485 Non-fractured with m easured discontinuity spacing (s′) 63 39 1.49 0.72 0.485 Non-fractured with measured friction angle ( f ) 86 64 1.42 0.81 0.569 Spacing s′ and f , both based on AASHTO (2007) 5 3 0.89 0.33 0.368 Discontinuity spacing (s′) based on AASHTO (2007) 36 21 1.16 0.83 0.712 Friction angle ( f ) based on AASHTO (2007) 21 7 1.06 0.37 0.346 n = number of case histories, mλ = mean of biases, σλ = standard deviation, COV = coefficient of variation Table 40. Summary of the statistics for the ratio of measured (qL2) to calculated bearing capacity (qult) of rock sockets and footings on rock subcategorized by data quality using the Goodman (1989) method. Cases n No. of sites m COV All rock sockets 61 49 1.52 0.82 0.541 Rock sockets with m easured friction angle ( f ) 46 48 1.64 0.90 0.547 All rock sockets on fractured rock 11 6 1.29 0.26 0.202 Rock sockets on fractured rock with m easured friction angle ( f ) 7 5 1.23 0.18 0.144 All rock sockets on non-fractured rock 50 43 1.58 0.90 0.569 Rock sockets on non-fractured rock with measured s′ and measured f 26 26 1.58 0.79 0.497 Rock sockets on non-fractured rock with measured discontinuity spacing (s′) 34 14 1.49 0.71 0.477 Rock sockets on non-fractured rock with measured friction angle ( f ) 39 43 1. 72 0.96 0.557 Rock sockets on non-fractured rock with discontinuity spacing (s′) based on AASHTO (2007) and measured friction angle ( f ) 13 12 1.99 1.22 0.614 Rock sockets on non-fractured rock with measured discontinuity spacing (s′) and friction angle ( f ) based on AASHTO (2007) 8 3 1.19 0.21 0.176 Rock sockets on non-fractured rock with discontinuity spacing (s′) based on AASHTO (2007) and friction angle ( f ) based on AASHTO (2007) 3 2 0.75 0.36 0.483 All footings 58 29 1.23 0.66 0.539 Footings with measured friction angle ( f ) 52 23 1.27 0.69 0.542 All footings on fractured rock 9 3 1.18 0.43 0.366 Footings on fractured rock with m easured friction angle ( f ) 5 2 1.47 0.29 0.200 All footings on non-fractured rock 49 26 1.24 0.70 0.565 Footings on non-fractured rock with measured s′ and measured f 29 11 1.51 0.73 0.481 Footings on non-fractured rock with m easured discontinuity spacing (s′) 29 11 1.51 073 0.481 Footings on non-fractured rock with measured friction angle ( f ) 47 21 1.25 0.72 0.573 Footings on non-fractured rock with discontinuity spacing (s′) based on AASHTO (2007) and me asured friction angle ( f ) 18 10 0.82 0.45 0.543 Footings on non-fractured rock with discontinuity spacing (s′) based on AASHTO (2007) and friction angle ( f ) based on AASHTO (2007) 2 1 1.10 0.13 0.115 n = number of case histories, mλ = mean of biases, σλ = standard deviation, COV = coefficient of variation Table 41. Summary of the statistics for the ratio of measured (qL2) to calculated bearing capacity (qult) of rock sockets and footings on rock subcategorized by foundation type and data quality using the Goodman (1989) method.

and the bias of about 1.2 to 1.5 for all types of major subcategorization. 2. The consistently reliable performance of the method for all ranges of rock strength (and hence RMR) provides a COV of 0.535 for all cases. The variation of the bias mean and COV with rock quality is essentially absent, as can be observed in Table 42. This is in contrast to the perform- ance of Carter and Kulhawy’s (1988) method, in which the variation of bias with rock strength resulted in a similar COV only when each range of rock strength was examined separately. This observation enforces the notion of incor- porating rock quality categorization (e.g., RMR) within the bearing capacity predictive methodology when necessary. 3. Similar statistics were obtained for shallow foundations (n = 58, mλ = 1.23, COVλ = 0.539) and rock sockets (n = 61, mλ = 1. 52, COVλ = 0.541). These observations suggest that 91 Foundation type Cases n No. of sites m COV RMR > 85 23 23 1.55 0.679 0.438 65 < RMR < 85 57 36 1.33 0.791 0.595 44 < RMR < 65 17 10 1.27 0.746 0.586 All 3 < RMR < 44 22 9 1.24 0.529 0.426 RMR > 85 16 16 1.59 0.809 0.509 65 < RMR < 85 35 24 1.40 0.722 0.515 44 < RMR < 65 9 8 1.47 0.916 0.624 Rock Sockets 3 < RMR < 44 1 1 1.27 -- -- RMR > 85 7 7 1.46 0.204 0.140 65 < RMR < 85 22 13 1.22 0.896 0.738 44 < RMR < 65 8 5 1.06 0.461 0.437 Footings 3 < RMR < 44 21 8 1.24 0.542 0.437 n = number of case histories, mλ = mean of biases, σλ = standard deviation, COV = coefficient of variation Table 42. Summary of the statistics for the ratio of measured (qL2) to calculated bearing capacity (qult) using the Goodman (1989) method categorized by rock quality and foundation type. 0 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 Bias, λ = qu,meas / qu,calc 0 10 20 30 40 N um be r o f o bs er va tio ns 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Fr eq ue nc y 119 Rock sockets and Footing cases Goodman (1989) mean = 1.35 COV = 0.535 lognormal distribution normal distribution Figure 79. Distribution of the ratio of the interpreted bearing capacity (qL2) to the bearing capacity (qult) calculated using Goodman’s (1989) method for the rock sockets and footings in database UML-GTR RockFound07. 0 0.4 0.8 1.2 1.6 2.4 2.8 3.2 Bias, λ = qu,meas / qu,calc 0 2 4 6 8 10 12 N um be r o f o bs er va tio ns 0 0.1 0.2 0.3 0.4 0.5 0.6 Fr eq ue nc y 20 Foundation cases on Fractured Rocks Goodman (1989) mean = 1.24 COV = 0.276 lognormal distribution normal distribution 2 Figure 80. Distribution of the ratio of the interpreted bearing capacity (qL2) to the bearing capacity (qult) calculated using Goodman’s (1989) method for foundations on fractured rock in database UML-GTR RockFound07.

the use of load-displacement relations for the tip of a loaded rock socket is analogous to the load-displacement relations of a shallow foundation constructed below surface. 4. The scatter of the method is significantly improved when measured discontinuity spacing (s′) is applied to the analysis. A COV value of 0.461 for 83 cases is obtained when the spacing is known. A COV value of 0.712 for 36 cases was exhibited by the analyses when using a discontinuity spacing (s′) based on the generic rock description provided by LRFD Bridge Design Specifications Section 10: Foundations (AASHTO 2007). 5. A significant reduction in the mean and the bias was systematically observed for foundations (both footings and rock sockets) on fractured rock. This observation is limited, however, to a small number of cases—20 for 9 sites as compared to 99 for 60 sites for all other cases. 3.9 Uncertainties in the Friction Along the Soil-Structure Interface 3.9.1 Overview The solid-soil interfacial friction is an important factor affecting soil-structure interaction. In the context of the ULS of shallow foundation design, one needs to address the possibility of shallow foundation sliding when subjected to lateral loading, often encountered in bridge abutments. The issue of foundation-rock sliding was not investigated as the state of practice suggested common use of keys and dowels and therefore the subject is more related in design to rock or concrete controlled strength. The issue of footings resting on granular soil is mostly confined to the possibili- ties of prefabricated versus cast-in-place foundations on soil. A general discussion of the soil-structure interfacial friction is presented. The uncertainties in the interfacial friction angle of solid-structure interfaces of various “roughness” subjected to inclined loads have been evaluated based on three sources of data: • Results of research using a dual interface apparatus to estab- lish mechanisms and provide a framework (Paikowsky et al., 1995), • Results of tests on foundations cast on soil (Horn, 1970), and • Results of tests on precast foundations (Vollpracht and Weiss, 1975). Additional sources are used to examine the data listed above including friction limits under inclined loads. A practical summary and appropriate resistance factors are further dis- cussed and presented in Chapter 4. 3.9.2 Experimental Results Using a Dual Interface Apparatus (DIA) 3.9.2.1 Background Paikowsky et al. (1995) developed a dual interface shear apparatus to evaluate the distribution and magnitude of friction between granular materials and solid inextensible surfaces. The dual interface apparatus (DIA) facilitates the evalua- tion of boundary conditions (effects) and interfacial shearing modes including unrestricted interfacial shear unaffected by the boundaries. Such measurements allow comparisons to test results from a modified direct shear (MDS) box commonly used for measuring soil-solid interfacial friction (by replacing the lower part of the shear box with a solid surface). Ideal and natural granular materials were sheared along controlled and random solid surface interfaces and compared to direct shear test results. The tests are designed based on a micro-mechanical model approach describing the interface friction mechanism (Paikowsky, 1989) and making use of the term “normalized roughness” (Rn) as defined by Uesugi and Kishida (1986) and illustrated in Figure 81: where Rmax is the maximum surface roughness measured along a distance L equal to the mean grain size of the soil particle D50. Three zones of Rn associated with the interfacial shear mech- anism reflecting different shear strength levels were identified and presented (see Figure 82): Zone I for a “smooth” inter- face, Zone II for an “intermediate” interface roughness and Zone III for a “rough” interface, respectively. In Zone I, shear failure occurs by sliding particles along the soil-solid body R R L D D n = =( )max ( ) 50 50 111 92 particle R max Figure 81. Solid surface topography representation through normalized roughness.

interface for all granular materials, while in Zone III shear failure occurs within the granular mass, mobilizing its full shear strength. In Zone II, the interaction between the solid surface and the soil allows only partial mobilization of the soil’s shear strength, depending on normalized roughness and several other factors, primarily the granular material particle shape. The data in Figure 82 relate to tests with glass beads varying in size from fine to coarse (related to sand) and uniform grain shape (round). The use of natural sand sheared along an inter- face results in the same three-zone characterization, differenti- ated only by the absolute magnitude of the friction angles. 3.9.2.2 Experimental Results Using DIA Soil-solid body interfaces with different normalized rough- ness and round particles have been tested. The interface friction angles along the unrestricted zone at the center of the solid surfaces, δcenter, were obtained as follows, expressed as the mean (±1 standard deviation): • Zone I—Smooth interface (14 test results): 6.0 (±0.8°) • Zone II—Intermediate interface roughness: δcenter increases from about 8° to 25° with an increase in the logarithm of the normalized roughness (Rn) • Zone III—Rough interface (6 test results): 28.7 (±1.3°) The friction angle of the granular materials used in the experiments was established to be residual φf = 31.6 (±1.0)° from the direct shear tests of 17 samples. As a result, the ratio of the friction coefficients, tan(δcenter)/tan(φf), were obtained as 0.171 for Zone I, 0.890 for Zone III, and therefore 0.171 to 0.890 (increasing with Rn) for Zone II. 3.9.2.3 DIA Results versus MDS Results Figure 83 presents the relationship between the unrestricted friction angles (δcenter) to friction angles measured using a direct shear box modified for interfacial testing with a solid surface of the same roughness (δMDS). The observations of the results obtained from the DIA and the MDS tests indicate that if the shearing mechanism takes place along the soil-solid surface interface, the test results are markedly influenced by the resist- ing stresses developing on the boundary walls of the direct shear box (for detailed measurements on the boundary walls, see Paikowsky and Hajduk, 1997; Paikowsky et al., 1996). The shearing resistances measured over the center interfacial area in the DIA tests, which is related to δcenter, represent unrestricted friction conditions since this location is not within the bound- aries’ zone of influence in the shear box. Paikowsky et al. (1995) found that the ratios of δMDS to δcenter for sand and glass beads in different zones of interface roughness are the following: • Zone I—1.50, • Zone II—1.20, and • Zone III—1.10. These results clearly indicate the inadequacy of the small- size direct shear box for interfacial friction measurements and 93 ce n te r 10-4 10-3 10-2 10-1 100 101 Normalized Roughness (Rn = Rmax/D50) 0 5 10 15 20 25 30 35 40 45 δ°δ° centerδ° 5 10 15 30 45 60 90 4mm glass beads 1mm glass beads #1922 glass beads (washed and sorted) #2429 glass beads (washed) ZONE I "SMOOTH" "ROUGH" ZONE II "INTERMEDIATE" ZONE III ds Roughness Angle - α° Figure 82. Interfacial characterization according to zones identified through the relations existing between average unrestricted interfacial friction angles (measured along the central section) of glass beads and normalized roughness (Paikowsky et al., 1995).

the need to be aware of the biased measurements. For the smooth and intermediate zones of normalized roughness, a significant bias exists when applying direct shear test results, namely 0.67 (Zone I) and 0.83 (Zone II). The ranges of the interface friction angles based on δcenter are presented in Table 43, along with the corresponding friction coefficient ratios obtained from the DIA tests. The ratio of δMDS to δcenter is represented by the multiplier m. The bias of the typical measured (by a direct shear box) interfacial friction angle (δMDS) is 1/m. The values of m are used to obtain the converted friction coefficient ratios, tan δ/tan φ, resulting in 0.25 for Zone I, 1.00 for Zone III, and increasing from 0.25 to 1.00 for Zone II. 3.9.3 Experimental Results of Footings Cast in Place (Horn, 1970) Horn (1970) presented experimental results of sliding resist- ance tests for 44 concrete footings of 3.3 ft × 3.3 ft × 1.6 ft (H) (1 m × 1 m × 0.5 m [H]) cast in place on sandy-gravel fill. The soil contained 15% gravel with stones greater than 2.5 in. (63 mm) and maximum stone size (dmax) of 7.9 in. (200 mm), porosity of 0.22, and material friction angle φf = 33.5° obtained from direct shear tests. Figure 84 presents the ratio of the interface friction coefficient (tan δs) and the soil’s internal friction coefficient (tan φf) as a function of the applied nor- mal stress on the foundation. Both friction angle values were corrected by Horn, applying the so-called energy correction proposed by Hvorslev (1937) as reported in Schofield and Wroth (1968).The mean and COV of the friction coefficient ratio, tan(δcenter)/tan(φf), of the 44 tests were found to be 0.99 and 0.091, respectively. The mean of the friction coefficient ratio and the corresponding range of interface friction angles of 33.3 ± 3.5° correspond to those for Zone III (rough interface) in Table 43. 3.9.4 Uncertainties in the Interface Friction Coefficient Ratio The uncertainties in the interface friction coefficient ratio (tan δs/tan φf) are directly related to the uncertainties in the interface friction and the soil friction angles. If the uncertainties in these angles are known, the statistics of the friction coefficient 94 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 Rn,ave - Average Normalized Roughness 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 SMOOTH (Rn ≤ 0.02) INTERMEDIATE (0.02 < Rn < 0.5) ROUGH (Rn ≥ 0.5) δ° δ° MDS center 5 10 15 30 45 60 90 α°- Roughness Angle 4mm glass beads 1mm glass beads Ottawa Sand #1922 glass beads (w/s) #2429 glass beads (w) Figure 83. The ratio of modified direct shear box to unrestricted (central section) interfacial friction angles versus average normalized roughness (Paikowsky et al., 1995). Roughness zone center Friction coefficient ratio from DIA Multiplier m (= MDS/ center) MDS (= center m) Converted friction coefficient ratio Zone I 6.0 0.8 0.17 1.50 9.0 0.25 Zone II 8.0 to 25.0 0.17 to 0.90 1.20 9.5 to 30.0 0.25 to 1.00 Zone III 28.7 0.90 1.10 31.5 1.00 Note: Material friction angle obtained from direct shear test = 31.6° (±1.0°) Table 43. Ranges of soil-solid body interface friction angles for different interface roughness zones, based on DIA tests (based on Paikowsky et al., 1995).

ratio can be computed as follows. If the distributions followed by both friction angles are normal, the corresponding friction coefficients and, thereby, the friction coefficient ratio, also follow normal distributions. For simplicity in notation, let the interface and material friction coefficients be X1 and X2, respectively. Hence, for mean mXi and standard deviation σXi, If the friction coefficient ratio is g, then where the mean and the variance of ln(Xi) are given by Then the mean and variance of g, mg and σg2 are given by m m m g g g g g g = +( ) = ( ) ( ) ( ) ( ) exp . exp ln ln ln 0 5 2 2 2 σ σ σ −( )1 112( ) m mXi Xi Xi Xi Xi ln ln ln ln . ln ( ) ( ) ( ) = ( )− = + 0 5 1 2 2 σ σ σ2 2mXi ⎛ ⎝⎜ ⎞ ⎠⎟ ⎛ ⎝⎜ ⎞ ⎠⎟ g X X g X X m mg X = ⇒ ( ) = ( ) − ( ) =( ) 1 2 1 2 1 ln ln ln ln lni.e., ( ) ( ) ( ) ( ) ( ) − = + m X g X X ln ln ln ln ,2 1 2 2 2 2 and σ σ σ X N m X N m X X X X 1 1 1 2 2 2 2 2 ∼ ∼ , , σ σ ( ) ( ) Table 44 presents the uncertainties in the estimation of the soil friction angle (based on Phoon et al., 1995; NCHRP Project 12-55, 2004). Hence, for a given soil friction angle, say 31.6°, obtained from correlations to SPT N counts, the standard deviation is 6.32°. Using Equation 112, the COV of the friction coefficient ratio is 0.444 for Zone I and 0.201 for Zone III. The friction coefficient ratio uncertainties in Zones I and III are presented in Table 45 for material friction angles obtained from various tests. Comparing the results for Zone III (rough interface) in Table 45 with the experimental results by Horn (1970), it can be seen that the COV of the friction coefficient ratio in Table 45 corresponds to that obtained by Horn for Zone III and φf from lab tests. It can thus be concluded that for a rough foundation base (e.g., resulting from a direct pour on the soil), the interface roughness in Zone III is rel- evant and, further, that the uncertainties in the sliding friction coefficient ratio (tan δs/tan φf) directly correspond to those existing in the method by which the soil friction angle is being defined (i.e., lab test, SPT, and so forth). Based on these observations, the uncertainties in the inter- face friction coefficient ratio to be used for calibration purposes can be recommended as presented in Table 46, 95 0 200 400 600 800 1000 1200 Normal Stress σn (kN/m2) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 ta n δ s, c o rr ec te d / t an φ f , c or re ct ed 0 10 15 20 25 ksf Horn (1970) 44 Tests mean = 0.99 s.d. = 0.091 5 Figure 84. Ratio of measured friction coefficients of cast-in-place footings (rough base) to the soil’s internal friction coefficient versus applied normal stress (Horn, 1970). f for Granular soils D’Appolonia & University of Michigan, 20041 Used for study f Obtained from Bias COV Bias COV SPT 1.00 to 1.20 0.15 to 0.20 1.00 0.20 CPT 1.00 to 1.15 0.10 to 0.15 1.00 0.15 Lab test 1.00 to 1.13 0.05 to 0.10 1.00 0.10 1Unpublished material based on Phoon et al., 1995. Table 44. Variations in the estimated soil friction angle (f). Friction coefficient ratio (tan s/tan f) Zone I (Smooth) Zone III (Rough) tan s/tan f = 0.25 tan s/tan f = 1.00 f Obtained from COV COV SPT 0.444 0.201 CPT 0.374 0.158 Lab test 0.312 0.109 Table 45. Uncertainties in friction coefficient ratio obtained using Equation 112, based on data in Tables 43 and 44.

where the bias of the friction coefficient ratio estimation is assumed to be that of the direct shear test interfacial testing (bias = 1/m) and that of Table 44 for the estimation of φf (bias = 1.0). The interpretation of smooth, intermediate, and rough interfaces has been illustrated in Table 47, based on friction angles provided by the NAVFAC (1986) for different dis- similar materials used in geotechnical construction. The COV to be used depends on the range of roughness (as defined in Table 47). The resistance factors associated with the un- certainties discussed above and a rationale for their use is discussed in Chapter 4. 96 Friction coefficient ratio (tan s/tan f) Smooth Intermediate Rough Bias = 0.67 Bias = 0.83 Bias = 0.91 f Obtained from COV COV COV SPT 0.45 0.45 to 0.20 0.20 CPT 0.38 0.38 to 0.15 0.15 Lab test 0.31 0.31 to 0.10 0.10 Table 46. Uncertainties in interface friction coefficient ratio according to interface roughness and the determination of the soil friction angle. Interface Materials ta n δ s Friction (degrees) Interface roughness Clean sound rock 0.70 35 Rough Clean gravel, gravel-sand mixtures, coarse sand 0.55 to 0.60 29 to 31 Inter med iate-Rough Clean fine to medium sand, silty medium to coarse sand, silty or clayey gravel 0.45 to 0.55 24 to 29 Inter med iate-Rough Clean fine sand, silty or clayey fine to me dium sand 0.35 to 0.45 19 to 24 Inter med iate Fine sandy silt, nonplastic silt 0.30 to 0.35 17 to 19 Inter med iate Very stiff and hard residual or preconsolidated clay 0.40 to 0.50 22 to 26 Inter med iate-Rough Mass concrete on the following foundation materials : Medium stiff and stiff clay and silty clay (Masonry on foundation ma terials has sam e friction factors.) 0.30 to 0.35 17 to 19 Inter med iate Clean gravel, gravel-sand mixtures, well-graded rock fill with spalls 0.40 22 Interm ediate Clean sand, silty sand-gravel mixture, single size hard rock fill 0.30 17 Interm ediate Silty sand, gravel or sand mixed with silt or clay 0.25 14 Interm ediate-Sm ooth Steel sheet piles against the following soils: Fine sandy silt, nonplastic silt 0.20 11 Interm ediate-Sm ooth Clean gravel, gravel-sand mixture, well-graded rock fill with spalls 0.40 to 0.50 22 to 26 Inter med iate-Rough Clean sand, silty sand-gravel mixture, single size hard rock fill 0.30 to 0.40 17 to 22 Inter med iate Silty sand, gravel or sand mixed with silt or clay 0.30 17 Interm ediate Formed concrete or concrete sheet piling against the following soils: Fine sandy silt, nonplastic silt 0.25 14 Interm ediate Dressed soft rock on dressed soft rock 0.70 35 Rough Dressed hard rock on dressed soft rock 0.65 33 Rough Masonry on masonry, igneous and metamorphic rocks: Dressed hard rock on dressed hard rock 0.55 29 Interm ediate-Rough Masonry on wood (cross grain) 0.50 26 Interm ediate-Rough Various structural materials : Steel on steel at sheet pile interlocks 0.30 17 Interm ediate Table 47. Friction coefficients (NAVFAC, 1986b) and interface roughness of dissimilar materials.

3.9.5 Experimental Results of Precast Footings (Vollpracht and Weiss, 1975) Vollpracht and Weiss (1975) presented experimental results of sliding resistance tests for 10 precast concrete footings of 1.6 ft × 6.6 ft × 2.6 ft (H) (0.5 m × 2.0 m × 0.8 m [H]) on sandy gravel fill. The soil interfacial friction angle was 39°, void ratio e was 0.395, and relative density was 61%. The mean soil- foundation interface friction angle of the 10 tests was found to be 23.2° (±4.08°). Figure 85 presents the ratio of the inter- face friction coefficient (tan δs) and the soil’s internal friction coefficient (tan φf) as a function of the applied normal stress on the foundation. The mean of the 10 tests was found to be 0.53±0.102 (± 1 standard deviation). This range clearly iden- tified the precast concrete–sand interfacial shear as having the intermediate roughness of Zone II. The scatter of the data can be attributed to the different ratios of horizontal to vertical loads, as will be further discussed below. 3.9.6 Summary of Relevant Results Table 48 summarizes the uncertainties in interface friction coefficient ratios according to type of foundation construction—cast-in-place or precast concrete—utilizing the aforementioned data. 3.9.7 Examination of Load Inclination and Other Factors Influencing Footings Interfacial Friction Different tests were carried out to examine the bearing capacity of foundations under inclined loading. These tests were analyzed in Sections 3.6 and 3.7 for bearing capacity purposes, and some tests are re-evaluated here for interfacial friction purposes. Tests were carried out by Foik (1984) on foundations under inclined loads ranging in size from 2.9 in. × 5.4 in. (7.4 cm × 13.7 cm) to 46 in. × 26 in. (117 cm × 65 cm). The foundations’ base had a rough contact surface made of glued coarse sand or fine gravel. Figure 86 presents the relationship between the soil’s unit weight and the internal friction angle. Figure 87 presents the relationship between the soil’s unit weight and the measured friction coefficient ratios of the footings. Figure 88 presents the relationship between the load inclination (expressed as inter- facial friction coefficient, tan δs) and the internal friction angle coefficient (expressed as internal friction coefficient, tan φf), and Figure 89 presents the relationship between the load 97 0 50 100 150 200 250 Normal Stress σn (kN/m2) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ta n δ s / t an φ f 0 1 2 3 4 5 ksf Vollpracht and Weiss (1975) 10 Tests mean = 0.53 s.d. = 0.102 Figure 85. Ratio of measured friction coefficients of precast footings to the soil’s internal friction coefficient versus applied normal stress (Vollpracht and Weiss, 1975). Friction coefficient ratio (tan s/tan f) Cast in place Prefabricated Bias = 0.91 Bias = 0.53 f Obtained from COV COV SPT 0.20 0.34 CPT 0.15 0.30 Lab test 0.10 0.26 Table 48. Uncertainties in interface friction coefficients of foundations on granular soils according to the foundation’s construction method and the determination of the soil friction angle. 16.6 16.8 17.0 17.2 17.4 Unit Weight of Soil γd (kN/m3) 32.0 36.0 40.0 44.0 48.0 In te rn al F ri ct io n A ng le φ f (o ) 106 107 108 109 110 lb/ft3 Foik (1984) 75 data points φf = 5.083 γd - 42.900 R2 = 0.997 Figure 86. Relationship of soil unit weight and the internal friction angle used by Foik (1984) in test results interpretation.

98 0.00 0.20 0.40 0.60 0.80 1.00 1.20 16.6 16.7 16.8 16.9 17 17.1 17.2 17.3 17.4 ta n δ s / t an φ f Unit Weight of Soil γd [kN/m3] tan phi tan delta (a/b = 12cm/8.6cm) tan delta (a/b = 12cm/8.3cm) tan delta (a/b = 8.3cm/12cm) tan delta (a/b = 13.7cm/7.4cm) tan delta (a/b = 7.4cm/13.7cm) tan delta (a/b = 9cm/16.4cm) tan delta (a/b = 20cm/5cm) tan delta (a/b = 26.5cm/6.5cm) tan delta (a/b = 5cm/20cm) tan delta (a/b = 63cm/35cm) tan delta (a/b = 50cm/150cm) tan delta (a/b = 117cm/65cm) Figure 87. Ratio of measured footing friction coefficient ratios to the soil’s internal friction coefficient versus soil unit weight (Foik, 1984). 0.88 0.90 0.92 0.94 0.96 0.98 1.00 Internal Friction Angle Coefficient (tan φf) 0.0 0.2 0.4 0.6 0.8 1.0 Lo ad In cl in at io n (ta n δ s) Foik (1984) 75 data points 99.6 ≤ area (cm2) ≤ 169 2205 ≤ area (cm2) ≤ 7605 Trendline for Large Foundations Figure 88. Load inclination (tan s) versus the internal friction angle coefficient (tan f) (Foik, 1984). 0 100 200 300 400 500 Vertical Applied Stress at time of Failure (kPa) 0.0 0.2 0.4 0.6 0.8 1.0 Lo ad In cl in at io n (ta n δ s) 0 10 20 30 40 50 60 70 psi Foik (1984) 75 data points 99.6 ≤ area (cm2) ≤ 169 2205 ≤ area (cm2) ≤ 7605 Trendline for Large Foundations Figure 89. Load inclination (tan s) versus vertical applied stress at the time of failure (VB /a  b) (Foik, 1984).

inclination (tan δs) and the vertical applied stress at the time of failure (VB/a × b). The data in Figures 86 to 89 suggest the following: 1. Large variation exists in the ratio of the foundation’s friction coefficient to the soil’s internal friction coefficient. The data in Figure 87 do not indicate on a clear factor that controls this variation, but in all cases tan δs < tan φf. 2. Figures 88 and 89, which show the interface friction coeffi- cient as a function of the soil’s internal friction coefficient and the vertical applied stress (respectively) suggest that the scatter in the data is significantly smaller for the larger foot- ing sizes. This may be explained by the physical difficulties of applying loads and conducting tests on small footings. 3. The interface friction coefficient (equal to the load inclina- tion at failure) is clearly affected by the size of the vertical load, as shown in Figure 89. The sliding of the footing under small vertical loads is eliminated and large loads can be applied, which, again, seems to be associated with the phys- ical limitations of conducting tests. 99

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LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures Get This Book
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TRB’s National Cooperative Highway Research Program (NCHRP) Report 651: LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures explores recommended changes to Section 10 of the American Association of State Highway and Transportation Officials’ Load Resistance Factor Design Bridge Design Specifications for the strength limit state design of shallow foundations.

Appendixes A through H for NCHRP Report 651 are available online.

Appendix A: Alternative Model Background

Appendix B: Findings—State of Practice, Serviceability and Databases

Appendix C: Questionnaire Summary

Appendix D: UML-GTR ShalFound07 Database

Appendix E: UML-GTR RockFound07 Database

Appendix F: Shallow Foundations Modes of Failure and Failure Criteria

Appendix G: Bias Calculation Examples

Appendix H: Design Examples

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