I-96 Case Study: Jointed Concrete Pavement Curling and Warp Presented in the Context of Pavement Asset Management

Transcription

1 I-96 Case Study: Jointed Concrete Pavement Curling and Warp Presented in the Context of Pavement Asset Management Christopher R. Byrum, PhD, PE

2 PAVEMENT ANALYSIS: Soil-Structure Interaction Engineering 3-D Analyses: M x = Eh ( 1 µ ) 2 x z 2 2-D Analyses: M = 2 EI d z dx 2

3 PAVEMENT PROFILE: A 2-D view of a 3-D Engineering Solution LWP RWP

4 Elevation, mm GPS3 Site ± mm LWP RWP R Curved Way Up Distance, m NOTES: 1. Highest IRI of all GPS3 pavements less than 1 years old. 2. High faulting at an early age. 3. Sandy clay subgrade (PI=14.5, w%=13), sand and gravel with 11% P2 base. 4. Built in 1984, 3-35 KESAL/yr, 22 mm PCC, no dowels. Profile Date: 6/19/1992 ProfileTime: * High Level 3:51:44 PM of Locked-In Warp and Faulting. Profile Date: June 19, 1992 Profile Time: 15:51:44 * Thermally Curved-Down at this time of day.

5 Split Profile into 2 Sub-Matrices Raw Profile X1 L1 R1 X2 L2 R2 X3 L3 R Discontinuities (cracks, joints...) = + Continuous Slab Segments Xn Ln Rn

6 What is the Curvature of This? Elevation, feet GPS Structurally Continuous WARPED SLAB Distance, feet See TRB Paper# 9261: Measuring Curvature in Concrete Slabs and Connecting the Data to Slab Modeling Theory

7 Elevation, feet All Have Same Average Curvature But Different Statistics: std. deviation, median, max., min.. Slope = SINE-WAVE PERTUBATION Distance, feet Slope = κ mean L z''( x) dx z'( L) = = L L z'()

8 κ AVG concept not valid through a working/hinging joint or crack Discontinuity Elevation Slope = Zero Slope = Zero Average Curvature Over These Spans = Zero

9 Elevation, mm Slope, l/l z = f(x) Elevation Distance, m dz dx Discrete Slope Distance, m LWP RWP Upward Translation = Rocking See TRB Paper No For how to evaluate slab tilt and pumping from profile slope data Curvature, 1/m x d z dx 2 Discrete Curvature Moment Hinge Distance, m

10 z 1/κ = R, Radius of Curvature Second Derivative x CURVATURE of f(x) = d 2 z κ 2 dx 1 R

11 Average Slab Curvature, 1/ft Comparing to National Database I-96 Site : AM 5: AM 7: AM 9: AM 11: AM 1: PM 3: PM 5: PM 7: PM 9: PM Time of Testing Search IPRF Joint Load Transfer for Final Report describing airfield test sites shown 1-AC18(22)-a 1-AC18(22)-b 2-AC17-a 2-AC17-b 3-CT16 4-AC18-a 4-AC18-b 5-AGG18 6-CT16 7-AGG17 8-AGG15 9-AGG14 1-AGG14 11-CT14 LTPP GPS3 RWP Howell I-96

12 Average Slab Curvature, 1/ft Comparing to National Database Trying to Measure 1-AC18(22)-a Curl/Warp includes the 1-AC18(22)-b difficult task of 2-AC17-a trying to 2-AC17-b measure or verify a 3-CT16 ZERO value : AM 5: AM 7: AM 9: AM 11: AM 1: PM 3: PM 5: PM 7: PM 9: PM Time of Testing 4-AC18-a 4-AC18-b 5-AGG18 6-CT16 7-AGG17 8-AGG15 9-AGG14 1-AGG14 11-CT14 LTPP GPS3 RWP Howell I-96

13 OK, Zero +/- How Much???? How precise is your method? Precision mostly related to texture size

14 For a single 18-ft slab we get: Arc lengths = # of arcs = Arc Values = 216 Arc Values from 18-ft Slab LWP 2 Wheel Paths = 432 arcs, 32 end slopes, 16 κ-strings Report: Curvature Frequency Distribution Number of Arcs Standard Deviation of Arc Curvatures Median, Avg, Max, Min Curvature Average Continuous Segment Length Fault Sizes...many other indices

15 The Central Limit Theorem- For any large population having finite standard deviation, the mean of sample size, n, approaches the mean of the population as n becomes large. Standard Error for Predicted Mean Curvature = σ κ n

16 Avg. Curvature Std. Error, ft Single Slab 5-ft Sample 9,-ft uniform section Number of Slabs Standard error values are most related to the size of pavement surface texture and surface finishing/flaw features.

17 Curvature analysis summary output table. Software calculates the curvature statistics for the raw data arcs, and then does the same arc calculations on cubic splines fit at 2.5-ft intervals through the raw data. Standard error is reduced using a spline fitting technique..72/sqrt(18) =.17? Site: R1 Middle Lane, 55-6 Profile Date: 1/23/15 Curvature Summary ProfileTime: 8:11 AM Avg. hinge spacing = 11.9 Curvature Index Value Sample Size StdDev Std Error of Mean Leave Slab Arcs Approach Slab Arcs " Arcs " Arcs " Arcs " Arcs " Arcs " Arcs " Arcs " Arcs " Spline Arcs " Spline Arcs " Spline Arcs " Spline Arcs " Spline Arcs " Spline Arcs " Spline Arcs " Spline Arcs All Arc Average All Arc Mean All Arc Median Spline Average Spline Trim Mean Spline Median Leave Slab Splines Approach Slab Splines Short Slab Index Old Byrum CI (1999) Current Byrum CI Curvature Units = ft -1 x 1

18 9,-ft length Uniformly Behaving Section 18 separate 5-ft analysis samples POB POE

19

20 R1 Middle Lane, Oct-15 8:11:.3 Elevation LWP RWP.2 Elevation, in Distance, ft. Slope, in/ft texture Curved Slabs Un-Faulted Joint Faulted Joint Slope-of-slope in slabs.75/14(12) =.45 ft -1

21 R2 Right Lane, Oct-15 6:29: Elevation, in. Elevation LWP RWP Distance, ft. Pumping/tilted slabs.1.5 Tilted Patches, approach-side uplift = 6 (.5) =.3-inch (7.6 mm) uplift Mid-slab cracks Slope, in/ft Original curved slab segments Faulted Joint, size.5(.3)25.4 = 3.8 mm

22 IRI trends per 5-ft segment 13 EB I-96 Howell 22 profiles obtained 5AM to 1PM Average IRI. in/mi Uniform Segment Average Behavior 7 6 5: 6: 7: 8: 9: 1: 11: 12: 13: 14: average 4th Order Fit to Average

23 Average Fault Size 1 EB I-96 Howell 9 Avg. Fault/Hinge Elevation Difference, mm : 6: 7: 8: 9: 1: 11: 12: 13: 14: average 4th Order Fit to Average

24 Slab Curvature Index, CI.4 EB I-96 Howell 22 profiles obtained 5AM to 1PM Median Wheelpath Curvature (1/ft x 1) Approx. Locked-In Curvature (Warp) Values = zero-temperature-gradient-moment/bending 5: 6: 7: 8: 9: 1: 11: 12: 13: 14: average 4th Order Fit to Average

25 Site-Specific Curling vs. IRI trend: Sites with longer slabs would likely have steeper sloped trends Site Data IRI, in/mi y = x R² = Average Slab Curvature, 1/ft x 1

26 Median Wheelpath Curvature, (1/ft x 1) EB I-96 East of Latson Road Slab Curvature Middle Lane 1-ft to 3-ft arc data Middle Lane 1-ft to 8-ft arc data Right Lane 1-ft to 3-ft arc data Approx. Air Temp. Howell, MI 5: 6: 7: 8: 9: 1: 11: 12: 13: 14: Time of Day Air Temp. 3 5: 6: 7: 8: 9: 1: 11: 12: 13: 14:

27 5-ft averages Slab Warp 2 d z dx dz Slab Tilting/Pumping dx 2 Approx. Locked-in Warp Slab Curvature, 1/ft x to Slab Slope Index; Pumped Volume, cft/lane/mile to Sum of Fault Sizes, mm/5 ft 1 Discontinuities Ride Quality Index 2 to IRI, in/mi to

28 Measured IRI, in/mi ft samples IRI Prediction from profile shape parameters: simple linear regression Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 396 ANOVA df SS MS F Significance F Regression E-189 Residual Total Predicted IRI, in/mi IRI breakdown data from a single uniformly behaving section Coefficients Standard Error t Stat P-value Intercept E-8 CI_median E-34 12StdevCI StdevCI E-15 Avg Flt Size E-5 #Faults ToTFlt, mm

29 I-96 Howell Regression Model IRI, in/mi Site avg. Warp Stdev Curv Faulting All IRI breakdown data from a single uniformly behaving section

30 Predicted IRI, m/km The LTPP GPS3 Profile Data Adjusted R 2 =.93 # Data Points = Measured IRI, m/km IRI breakdown data from many different pavement sections from the LTPP GPS3

31 5 4.5 Sensitivity Analysis for the IRI Regression Model IRI breakdown data from many different pavement sections -LTPP GPS3 All High IRI, m/km High High None Very Very Curved Flat Flat Avg. GPS3 JPC "Average" LTPP GPS3 Profile High High Low Faulting Avg. Slab Curvature Stdev Curvature All Parameters Low All Low 115 in/mi

32 Curling = Average Slab Curvature Change.16 ft -1 change for a total change in air temperature of about 2 degrees Fahrenheit over a 5-hour period 8AM (min. temp) to 1PM (max. temp) for testing in October. Warping = Average Slab Curvature at/near Zero-Gradient Time +.2 ft -1, with apparent locked-in warp curvatures in the 5-ft samples ranging between about +.26 and +.7 ft -1 Middle Lane IRI 85 to 115 in/mi average of about 1 in/mi (not failed at 21 yr) Truck Lane IRI = 165 to 3 in/mi average of about 2 in/mi (near terminal at 21 yr) IRI Change = 25 in/mi change for a slab curvature change (curling) of about.16 ft -1 TEST SITE SUMMARY LTPP GPS3 = 7 in/mi change for about.5 ft -1 range in CI

33 Average Slab Curvature, 1/ft Slab Comparing Curvature to National Noticeable Database by Drivers at >.15 ft -1 Perception threshold Perception threshold : AM 5: AM 7: AM 9: AM 11: AM 1: PM 3: PM 5: PM 7: PM 9: PM Time of Testing 1-AC18(22)-a 1-AC18(22)-b 2-AC17-a 2-AC17-b 3-CT16 4-AC18-a 4-AC18-b 5-AGG18 6-CT16 7-AGG17 8-AGG15 9-AGG14 1-AGG14 11-CT14 LTPP GPS3 RWP Howell I-96