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University of Southern QueenslandFaculty of Engineering and SurveyingComprehensive Design Charts for theFooting on Slope ProblemA dissertation submitted byNathan Ross LyleIn fulfilment of the requirements ofCourses ENG4111 and ENG4112 Research Projecttowards the degree ofBachelor of Engineering (CIVIL)Submitted: November, 2009

AbstractThe problem of a rigid foundation resting near a slope or cut is a problem commonlyexperienced in engineering practice. Some of the major examples of this problem includemobile phone towers, bridge abutments and basement construction of high--rise buildings.This project illustrates the use of explicit finite difference software (FLAC) to analyse thebehaviour exhibited by the slope due to loading. The purpose of this research was to createa comprehensive set of design charts for the footing on slope problem. These design chartsuse nondimensional axes in order to allow the practising engineer to better visualise trendsthat exist due to the various dimensions of the problem.The FLAC model used to obtain results for use in the design charts was validated againsta number of available solutions. These included Upper Bound--Lower Bound, and physicalmodel solutions. Extensive parametric studies were conducted into the effect of the H/B,D/B, Strength, Surcharge and Stability Number Ratios.A number of illustrated examples were prepared to enable easy use of the design chartscreated for this project. These allow the user to learn the skills necessary to obtain thebearing capacity of a given footing on slope using the design charts. These examplesincrease the value of the design charts to practicing engineers greatly.In addition to the studies conducted for the smooth foundation case, used for creating thedesign charts, analysis into the case of a rough soil--footing interface was conducted. Theresults from this analysis were that the smooth soil--foundation interface case isconservative and provides a lower bearing capacity than the rough soil--interface case.Abstractii

University of Southern QueenslandFaculty of Engineering and SurveyingENG4111 & ENG4112 Research ProjectLimitations of UseThe Council of the University of Southern Queensland, its Faculty of Engineering andSurveying, and the staff of the University of Southern Queensland, do not accept anyresponsibility for the truth, accuracy or completeness of material contained within orassociated with this dissertation.Persons using all or any part of this material do so at their own risk, and not at the risk ofthe Council of the University of Southern Queensland, its Faculty of Engineering andSurveying or the staff of the University of Southern Queensland.This dissertation reports an educational exercise and has no purpose or validity beyond thisexercise. The sole purpose of the course ”Project and Dissertation” is to contribute to theoverall education within the student’s chosen degree programme. This document, theassociated hardware, software, drawings, and other material set out in the associatedappendices should not be used for any other purpose: if they are so used, it is entirely atthe risk of the user.Prof Frank BullenDeanFaculty of Engineering and SurveyingLimitations of Useiii

CertificationI certify that the ideas, designs and experimental work, results, analyses and conclusionsset out in this dessertation are entirely my own effort, exept where otherwise indicated andacknowledged.I further certify that the work is original and has not been previously submitted forassessment in any other course of institution, except where specifically stated.Nathan Ross LyleStudent Number: 0050056673SignatureDateCertificationiv

AcknowledgementsI would like to thank Dr. Jim Shiau for his guidance with this project. His constant help hasallowed me to achieve all of my goals for this research project.I also would like to thank my family and friends for their support through the last four years.Special thanks go to Emily for her encouragement and guidance in the past year.Acknowledgementsv

Table of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iiLimitations of Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iiiCertification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iiiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .viList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xviiNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1--11.1 Outline of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1--11.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1--21.2.1 Stresses Due to Soil Mass and Foundation Loading . . . . . . . .1.2.2 Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.3 Shallow Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.4 Foundation Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1--31--41--41--51.3 Failure Modes of Pad Footings . . . . . . . . . . . . . . . . . . . . . . . . . . . 1--61.3.1 General Shear Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.3.2 Local Shear Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.3.3 Punching Shear Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1--61--71--81.4 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1--101.5 Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1--101.6 Overview of Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1--101.6.1 Chapter 11.6.2 Chapter 21.6.3 Chapter 31.6.4 Chapter 41.6.5 Chapter 51.6.6 Chapter 61.6.7 Chapter 71.6.8 Chapter 81.6.9 Chapter 9----------Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . .Introduction to FLAC Analysis and MethodologyValidation of FLAC Analysis Model . . . . . . . . . . . .Parametric Studies . . . . . . . . . . . . . . . . . . . . . . . . .Design Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Examples of Chart Usage . . . . . . . . . . . . . . . . . . . .Interface Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . .Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1--101--111--111--111--111--111--121--121--121.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1--4Table of Contentsvi

2Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2--12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2--12.2 Footing on Slope Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2--22.2.1 Terzaghi’s Bearing Capacity Theory . . . . . . . . . . . . . . . . . . . . . .2.2.2 Meyerhof (1963) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2.3 Slope Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2.4 Meyerhof (1953) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.3 Kusakabe et. al (1981) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.3.1 Narita and Yamagughi (1990) . . . . . . . . . . . . . . . . . . . . . . . . . . .2.3.2 Shiau et. al (2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2--22--32--32--42--42--42--52.4 Catherine Smith (2006) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2--52.5 Josh Watson (2008) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2--52.6 Project Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2--62.6.1 Fast Langrangian Analysis of Continua . . . . . . . . . . . . . . . . . . .2.6.2 Quick Search and Replace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.6.3 AutoHotKey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.6.4 Broadvison Quicksilver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2--62--62--62--72.7 Project Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2--72.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2--83Introduction to FLAC Analysis and Methodology . . . . . . 3--13.1 Introduction to FLAC Software Package . . . . . . . . . . . . . . . . . . . 3--13.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.1.2 Fast Lagrangian Analysis of Continua . . . . . . . . . . . . . . . . . . . .3--13--23.2 Explanation of FLAC Models Used in Analysis . . . . . . . . . . . . . . 3--23.3 Comparison of Versions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3--53.4 Methodology Used in Obtaining Data . . . . . . . . . . . . . . . . . . . . . . 3--63.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3--64Validation of FLAC Analysis Model . . . . . . . . . . . . . . . . . . . . 4--14.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4--14.2 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4--14.3 FLAC Model Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4--24.4 Effect of Applied Velocity and Number of Iterations Used . . . . . 4--74.5 Effect of Element Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4--94.6 Effect of Model Extents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4--114.7 Effect of Mesh Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4--124.8 Comparison with Upper Bound-Lower Bound Results . . . . . . . 4--134.9 Comparison with Physical Model Results . . . . . . . . . . . . . . . . . . 4--16Table of Contentsvii

4.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4--165Parametric Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5--15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5--15.2 Effect of Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5--25.2.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5--75.3 Effect of D B Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5--75.3.1 30 Degree Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5--85.3.2 60 Degree Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5--105.3.3 90 Degree Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5--125.3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5--145.4 Effect of H B Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5--145.4.1 30 Degree Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4.2 60 Degree Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4.3 90 Degree Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5--155--175--195--215.5 Effect of Strength Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5--215.5.1 30 Degree Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.5.2 60 Degree Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.5.3 90 Degree Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5--225--235--245--265.6 Surcharge Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5--275.6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5--315.7 Effect of Stability Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5--325.7.1 30 Degree Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.7.2 60 Degree Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.7.3 90 Degree Slope Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.7.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65--325--335--345--34Design Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6--16.1 General Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6--16.2 Using Taylors Chart to Determine the Safety Factor of a Slope6.2.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2.3 Example 3