![Reliability (ZR, S0)
X = Probability distribution of stress
(e.g., from loading, environment, etc.)
Y = Probability distribution of strength
(variations in construction, material, etc.)
Probability
Stress/Strength
Reliability = P [Y > X] dx
dy
y
f
x
f
X
Y
P
x
y
x
](https://image.slidesharecdn.com/04aashto1993flexiblepavdesignguide-241115194236-ce4ff233/85/04_aashto1993_flexible_pav_design_guide-ppt-29-320.jpg)
04_aashto1993_flexible_pav_design_guide.ppt
- 1. Date goes here AASHTO 1993 Flexible Pavement Design Equation
- 2. Outline 1. AASHO Road Test 2. Present Serviceability Index (PSI) 3. Equation and terms 4. Example
- 3. AASHO Road Test (1) 1958 - 1961 AASHO Road Test Picture from: Highway Research Board Special Report 61A-G
- 4. AASHO Road Test (2) • Construction: August 1956 - September 1958 • Test Traffic: October 1958 - November 1960 • Special Studies: Spring and early summer 1961 AASHO Road Test
- 5. Test Loops (1) Picture from: Highway Research Board Special Report 61A-G AASHO Road Test
- 6. Test Loops (2) AASHO Road Test Picture from: Highway Research Board Special Report 61A-G
- 7. Environment • Mean Temperature (July) 76°F • Mean Temperature (January) 27°F • Annual Average Rainfall 34 inches • Average Frost Depth 28 inches (for fine-grained soil) AASHO Road Test
- 8. Flexible Materials • HMA – Dense-graded – 85-100 pen asphalt • Base Course – Crushed limestone – 10% passing No. 200 – Average CBR = 107.7 • Subbase Course – Sand/gravel mixture – 6.5% passing No. 200 – CBR = 28 – 51 • Subgrade – A-6 soil (silt/clay) – 82% passing No. 200 – Average CBR = 2.9 – Optimum wc = 13% AASHO Road Test
- 9. Flexible Sections • HMA – 1 to 6 inches thick • Base Course – 0 to 9 inches thick • Subbase Course – 0 to 16 inches thick • Thickest section – 6 inches HMA – 9 inches base – 16 inches subbase – Used for heavy loads – 2.6 to 3.6 PSI at test end • Thinnest section – 1 inch HMA – Used for light loads – 8 to 25 ESALs to failure AASHO Road Test
- 10. Flexible Performance • Majority failed • Even thickest sections sustained appreciable damage • Most failed during spring thaw – Frost action was a major contributor – Thicker base & subbase helped to mitigate frost action AASHO Road Test
- 11. Rigid Materials • Cement – Type I – 564 lb/yd3 • Portland Cement Concrete – Maximum w/c = 0.47 – 14-day compressive strength = 3500 psi – 14-day flexural strength = 550 psi (1/3 point) – Slump = 1.5 to 2.5 inches – Maximum aggregate size = 1.5 and 2.5 inches • Subbase and subgrade were the same as flexible sections AASHO Road Test
- 12. Rigid Sections • Slabs – 2.5 to 12.5 inches thick • Subbase Course – 0 to 9 inches thick • Dowel Bars – All had dowel bars – Sizes varied • Thickest section – 12.5 inch slab – 9 inches subbase – Used for heavy loads – 4.2 to 4.5 PSI at test end • Thinnest section – 2.5 inch slab – Used for light loads – 4.2 to 4.4 PSI at end AASHO Road Test
- 13. Rigid Performance • Majority did not fail • Most sections PSI at the test end was around 3.8 to 4.4 AASHO Road Test
- 14. Trucks AASHO Road Test Picture from: Highway Research Board Special Report 61A-G
- 15. Subgrade Support Variation AASHO Road Test Picture from: Highway Research Board Special Report 61A-G
- 16. Test Tracks Today NCAT Test Track
- 17. Present Serviceability Rating (PSR) Definition: "The judgment of an observer as to the current ability of a pavement to serve the traffic it is meant to serve"
- 18. Present Serviceability Rating (PSR) AASHO Road Test Picture from: Highway Research Board Special Report 61A-G
- 19. Present Serviceability Rating (PSR) AASHO Road Test Picture from: Highway Research Board Special Report 61A-G
- 20. Present Serviceability Index (PSI) • Calculated value to match PSR P C SV PSI 9 . 0 1 log 80 . 1 41 . 5 SV = mean of the slope variance in the two wheelpaths (measured with the CHLOE profilometer or BPR Roughometer) C, P = measures of cracking and patching in the pavement surface C = total linear feet of Class 3 and Class 4 cracks per 1000 ft2 of pavement area. A Class 3 crack is defined as opened or spalled (at the surface) to a width of 0.25 in. or more over a distance equal to at least one-half the crack length. A Class 4 is defined as any crack which has been sealed. P = expressed in terms of ft2 per 1000 ft2 of pavement surfacing.
- 21. Basic Idea Time Serviceability (PSI) p0 pt p0 - pt Basic Equations
- 22. Basic Relationship and depend on pavement structure (thickness and stiffness) and loading determines the shape of the graph is the number of loads at which p = 1.5 W p p p p t o 0 Basic Equations
- 23. Basic Equation 07 . 8 log 32 . 2 1 1094 40 . 0 5 . 1 2 . 4 log 20 . 0 ) 1 log( 36 . 9 log 19 . 5 0 18 R R M SN PSI SN S Z W Basic Equations • Choose these values – Reliability (ZR and S0) – p0, pt ΔPSI • Measure MR
- 24. Explanation of Terms 07 . 8 log 32 . 2 1 1094 40 . 0 5 . 1 2 . 4 log 20 . 0 ) 1 log( 36 . 9 log 19 . 5 0 18 R R M SN PSI SN S Z W W18 Base 10 logarithm of the predicted number of ESALs over the lifetime of the pavement. The logarithm is taken based on the original empirical equation form from the AASHO Road Test.
- 25. Explanation of Terms 07 . 8 log 32 . 2 1 1094 40 . 0 5 . 1 2 . 4 log 20 . 0 ) 1 log( 36 . 9 log 19 . 5 0 18 R R M SN PSI SN S Z W SN Structural number. An abstract number expressing the structural strength of a pavement required for given combinations of soil support (MR), total traffic (ESALs) and allowable change in serviceability over the pavement life (ΔPSI).
- 26. Structural Number • Converted to a layer depth using coefficients. – SN = a1D1 + a2D2m2 + a3D3m3 + … a = layer structural coefficient D = layer depth (inches) m = layer drainage coefficient
- 27. Structural Number Material a-value Surface course HMA (asphalt concrete) 0.44 Base course Crushed stone 0.14 Stabilized base material 0.30 – 0.40 Subbase course Crushed stone 0.11 Drainage Coefficient (m) Generally, quick draining layers that almost never saturate can have drainage coefficients as high as 1.4, while slow-draining layers that often saturate can have drainage coefficients as low as 0.40. Most often, the drainage coefficient is neglected (i.e. set as m = 1.0).
- 29. Reliability (ZR, S0) X = Probability distribution of stress (e.g., from loading, environment, etc.) Y = Probability distribution of strength (variations in construction, material, etc.) Probability Stress/Strength Reliability = P [Y > X] dx dy y f x f X Y P x y x
- 30. Reliability (ZR, S0) Reliability ZR 99.9 -3.090 99 -2.327 95 -1.645 90 -1.282 80 -0.841 75 -0.674 70 -0.524 50 0 S0 Typical values for flexible pavement are 0.40 to 0.50. S0 cannot be calculated from actual traffic or construction numbers so it is almost always assumed to be 0.50.
- 31. Solving the Equation • Iterative process – Both ESAL and structural equation have SN • Often solved assuming ESAL values
- 33. Date goes here 1993 AASHTO Structural Design Step-by-Step
- 34. Step 1: Traffic Calculation • Total ESALs – Buses + Trucks – 2.13 million + 1.33 million = 3.46 million
- 35. Step 2: Get MR Value • CBR tests along Kailua Road show: – CBR 8 ≈ • MR conversion psi CBR MR 000 , 12 8 1500 1500 psi CBR MR 669 , 9 8 2555 2555 64 . 0 64 . 0 AASHTO Conversion NCHRP 1-37A Conversion
- 36. Step 3: Choose Reliability • Arterial Road – AASHTO Recommendations Functional Classification Recommended Reliability Urban Rural Interstate/freeways 85 – 99.9 85 – 99.9 Principal arterials 80 – 99 75 – 95 Collectors 80 – 95 75 – 95 Local 50 – 80 50 – 80 WSDOT 95 85 75 75 Choose 85%
- 37. Step 3: Choose Reliability Reliability ZR 99.9 -3.090 99 -2.327 95 -1.645 90 -1.282 85 -1.037 80 -0.841 75 -0.674 70 -0.524 50 0 Choose S0 = 0.50
- 38. Step 4: Choose ΔPSI • Somewhat arbitrary – Typical p0 = 4.5 – Typical pt = 1.5 to 3.0 – Typical ΔPSI = 3.0 down to 1.5
- 39. Step 5: Calculate Design • Decide on basic structure • Note: AASHTO doesn’t differentiate between types of HMA and base but many agencies do – Differentiation may not based on any testing Resilient Modulus (psi) Layer a Typical Chosen HMA 0.44 500,000 at 70°F 500,000 ACB 0.44 500,000 at 70°F 500,000 UTB 0.13 20,000 to 30,000 25,000 Aggregate 0.13 20,000 to 30,000 25,000
- 40. Step 5: Calculate Design • Solve equation for 2 layers – HMA and ACB is one layer – UTB and aggregate is the other • Solve for each layer using the MR of the layer directly underneath • Divide up HMA and ACB • Divide up UTB and aggregate
- 41. Step 5: Calculate Design • Preliminary Results – Total Required SN = 3.995 – HMA/ACB • Required SN = 2.74 • Required depth = 6.5 inches – UTB and aggregate • Required SN = 1.13 • Required depth = 9 inches
- 42. Step 5: Calculate Design • Apply HDOT rules and common sense – HMA/ACB • Required depth = 6.5 inches • 2.5 inches Mix IV (½ inch Superpave) • 4 inches ACB (¾ inch Superpave) – UTB and aggregate • Required depth = 9 inches • Minimum depths = 6 inches each – 6 inches UTB – 6 inches aggregate subbase
- 43. Comparison Layer California AASHTO HMA Surface 2.5 inches 2.5 inches ACB 7.0 inches 4.0 inches UTB 6.0 inches 6.0 inches Aggregate subbase 6.0 inches 6.0 inches
Editor's Notes
- #3: As Joe said, the location was in Ottowa Illinois
- #5: -6 test tracks -different loads on each test track -Each track had PCC and HMA as well as bridges -When they were done, the tracks became part of I-80
- #6: Here’s a typical track showing the turn around loop
- #15: Subgrade deflection variation over the year Notice in the spring time it is VERY high indicating spring thaw Most HMA pavements failed in the springtime because of this thaw
- #18: PSR -5 point rating scale -show picture in WSDOT Guide
- #22: Draw graph