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2. 2. Traffic Loading andVolumeChapter 6.1 & 6.2Dr. Professor Christopher BarnesEneja Mushi M.Sc.Pavement Analysis and Management
3. 3. 6.1 Design Procedures• Traffic is the most important factor in pavementdesign.• When designing one should consider:1. Load Magnitude2. Configuration of load3. Load repetitions• Three different procedures for consideringvehicular and traffic effects in pavement design:1. Fixed traffic2. Fixed vehicle3. Variable traffic
4. 4. 6.1.1 Fixed Traffic• In fixed traffic, the thickness of pavement isgoverned by a single-wheel load• Number of load repetitions is not consideredas a variable.– If pavement is subjected to multiple wheels, theymust be converted to an equivalent single-wheelload so that design method based on single wheelcan be applied.Method used in: Airport pavement, Highwaypavement, no longer in use.
5. 5. 6.1.2 Fixed Vehicle• The thickness pavement is governed by numberof repetitions of a standard vehicle or axleload, usually 18kip single-axle load (SAL)• IF more than one axle, convert to SAL by anEquivalent Axle Load Factor (EALF)• # of repetitions of SAL or MAL must bemultiplied by its EALF to obtain the equivalenteffect SAL.• The summation of equivalent effects of all axleloads = equivalent single-axle load
6. 6. 6.1.3 Variable trafficand Vehicle• Traffic and Vehicles are considered individually, noneed to assign an equivalent factor for each axelload.• Load can be divided into # of groups, stresses,strains & deflections of each group candetermined separately and used in design.• Best fit for mechanistic methods of design, wherepavement responses can be evaluated by using acomputer.
7. 7. 6.2 Equivalent Single-Wheel Load• History: During WWII introduction of B-29 with DualWheel, up till then design was based on singlewheel aircraft.• New criteria need to be develop, time and moneyworked against it.• As a result, relating theoretically the new loadingconditions to an equivalent single wheel load sothat the existing theory would work.
8. 8. 6.2 EQUIVALENT SINGLE-WHEEL LOAD• ESWL depends on the criterion selected to compare SWL withMWL• Studies were conducted In 1969 by Huang and 1970 byGerrard and Harrison on single, dual and dual tandem wheelsassuming that all wheels have the same radii.1. Was found that use of different criteria, (stress, strain,deflection) is important in determining ESWL2. ESWL increases as pavement thickness increases and modulusration increases or multiple-wheel spacing decreases• ESWL can be calculated theoretically or experimentallymeasured stress, strain or deflection, or can be determinedfrom pavement distress and performance conducted byWASHO and AASHO road test
9. 9. 6.2.1 Equal Vertical StressCriterion• In 1959 Boyd and Foster presented asemirational method for determine ESWL
10. 10. 6.2.1 Equal Vertical StressCriterion• ESWL varies with pavement thickness• For thickness smaller than ½ the clearance betweentires, ESWL = ½ of total load• For thickness greater that 200 % of c-c oftires, ESWL= Total Load• Assuming a straight-line relationship betweenpavement thickness and wheel load on logarithmicscales the ESWL for any intermediate thickness canbe determined as follows.
11. 11. 6.2.1 Equal Vertical StressCriterionPd = load on one of the dual tiresz = pavement thicknessd = clerarance between dual tiresSd = center to center spacing between dualtires
12. 12. 6.2.1 Equal Vertical StressCriterion• Vertical stress factor σz/q shown in the figure belowcan be used to find ESWL based on Boussinesq’stheory
13. 13. 6.2.1 Equal Vertical StressCriterion• Fig. below shows pavement of thickness z undersingle and dual wheels that have the same contactradius a.
14. 14. 6.2.1 Equal Vertical StressCriterionIn the above fig. the maximum subgrade stress undersingle wheel occurs at point A with a stress factor σz/qsqs =contact pressure under single wheelLocation of max. stress under dual wheels is not knownand can be determined by comparing the stresses atpoint 1 2 3.The stress factor at each point can be obtained bysuperposition of the 2 wheels.Maximum stress factor = σz/qdqd = contact pressure under dual wheels.
15. 15. 6.2.1 Equal Vertical StressCriterionFollowing the above statements the formula definingthe single and dual wheel stress factor is:For the same contact radius, contact pressure isproportional to wheel load:Ps = single wheel load, Pd = load on each of the duals
16. 16. 6.2.2 Equal Vertical DeflectionCriterion• Time showed that Boyd and Foster’s method wasnot safe.• 1959 Foster and Ahlvin developed new method• Pavement system is considered as a homogeneoushalf-space and the vertical deflection at a depthequal to the thickness of the pavement can beobtained from Boussinesq solutions• A SWL that has the same contact radius as the oneof dual wheels and results in a maximum deflectionequal to that caused by the dual wheels in theESWL (equal single wheel load)
17. 17. 6.2.2 Equal Vertical DeflectionCriterion• Deflection Factor F can be used to determine ESWL.
18. 18. 6.2.2 Equal Vertical DeflectionCriterion• Deflection of single and dual wheels, ws and wd =Fs = deflection factor (of single wheel)at point AFd = deflection factor (of dual wheels) at point 1, 2, 3To obtain deflection factor (Fd) is obtained bysuperposition of the duals
19. 19. 6.2.2 Equal Vertical DeflectionCriterion• To obtain the same deflection ws = wd or• For the same contact radius, contact pressureis proportional to wheel load:
20. 20. 6.2.2 Equal Vertical DeflectionCriterion• Although Foster and Ahlvin method is superior toBoyd and Foster, their homogeneous half-spaceinstead of a layered system is not logical from atheoretical viewpoint.• Foster-Ahlvin method is still unsafe because,some of the pavements with thickness greaterthan those obtained by the method wereconsidered inadequate or on the borderline,because ESWL for layered systems is greater thanthat for a homogeneous half-space.
21. 21. 6.2.2 Equal Vertical DeflectionCriterion• 1968 Huang suggested the use of layered theoryand presented a chart for determining ESWL basedon the interface deflection of the two layeredsystems as shown in the next slid.a = contact radius Load factorh1 = pavement thicknessE1/E2 = modulus ratioSd = dual spacing
22. 22. 6.2.2 Equal Vertical DeflectionCriterion
23. 23. 6.2.2 Equal Vertical DeflectionCriterionComparing eq. 6.6 and 6.7b we get eq. 6.8
24. 24. 6.2.2 Equal Vertical DeflectionCriterion• ESWL can be determined from the deflectionfactors presented in the figure below
25. 25. 6.2.2 Equal Vertical DeflectionCriterion• But the use of the chart shown in Figure 6.4 is muchquicker. The chart is based on a dual spacing Sd of 48in(1.22m).• If actual spacing is different it must be changed to 48 inand the values of a and h1 have to be changedproportionally.• As long as Sd/a and h1/a remain the same, the loadfactor will be the same.• The upper chart is for a contact radius of 6 in and thelower chart is for a contact radius of 16 in.• The load factor for any other contact radius can beobtained by a straight-line interpolation
26. 26. 6.2.2 Equal Vertical DeflectionCriterion• You can determine a` and h`1 from Sd h1 and a• Using h’1 as the pavement thickness find loadfactors L1 and L2 from the chart
27. 27. 6.2.3 Equal Tensile StrainCriterion• Conversion factors presented in figures below canbe used to determine ESWL
28. 28. 6.2.3 Equal Tension StrainCriterion• Tensile strain e at the bottom of layer 1 under asingle-wheel load is:• qs = contact pressure of a single wheel
29. 29. 6.2.3 Equal Tension StrainCriterion• The tensile strain under dual or dual-tandemwheels isqd = contact pressure of dual or dual-tandemwheels
30. 30. 6.2.4 Criterion Based onEqual Contact Pressure• The above analysis of ESWL are based on:Assumption 1: Single wheel has the same contactradius as each of the dual wheelAssumption 2: Single wheel has a different contactradius but the same contact pressure as the dualwheels. In this case solution is much morecomplicated.
31. 31. 6.2.4 Criterion Based onEqual Contact Pressure• To obtain equal deflection ws = wd orBecauseAnd
32. 32. 6.2.4 Criterion Based onEqual Contact Pressure• For equal contact radius, contact pressure isproportional to the wheel loadIf Pd and q are given, ad can be computed
33. 33. 6.2.4 Criterion Based anEqual Contact PressureIn 1968 Huang compared the ESWL based on =radius with that based on equal contactpressure for a variety of case.Found that: Unless the pavement is extremelythin and the modulus ratio close to unity, thedifference between the two methods are notsignificant
34. 34. 6.2.4 Criterion Based anEqual Contact Pressure• Two-layer interface deflections base on =contact pressure were also used by theAsphalt institute to compute the ESWL for full-depth asphalt pavement.• This procedure is applicable for small aircrafts.
35. 35. 6.2.5 Criterion Based onEquivalent Contact Radius• The 2 methods studied up till now were:– Equal contact radius– Equal contact pressure• In 1993 Ioannides and Khazanovich proposedthe use of an equivalent contact radius todetermin the load equivalency (equivalentsingle axle radius ESAR),
36. 36. 6.2.5 Criterion Based onEquivalent Contact Radius• The basic concept is to: Determine a single wheelload with an equivalent radius that would give thesame response as dual-wheel assembly.• They found (though statistical regressiontechniques) that the maximum bending stress dueto dual tires in the interior of a concrete slab wouldbe the same as a single tire with the equivalentradius
37. 37. 6.2.5 Criterion Based onEquivalent Contact Radius• aeq = equivalent tire contact pressure• a = contact radius of each of the dual tires• S = c-c spacing between the dual