Understanding Road Wear and its Causes Philip A. Viton February 5, 2014 Road Wear February 5, 2014 1 / 41
Introduction Introduction Even though congestion is near the forefront of the public s perception of urban transportation problems, that is not where most of the transportation planner s effort is focussed. That effort is focussed on road maintenance and repair keeping the existing road network usable. So we turn now to a consideration of the issues that road maintenance raises for planners. Road Wear February 5, 2014 2 / 41
Introduction The Interstate Puzzle The Interstates were built in the 1950s and 1960s. At that time, transportation engineers predicted that the new roads would last about 40 years before needing rehab. So we should have begun to see maintenance on interstates beginning in about 1990. Clearly this didn t happen: the interstates began to wear out much sooner. Why did the engineers get it so wrong? Road Wear February 5, 2014 3 / 41
Introduction The Issues We study the question of major road maintenance: a process called resurfacing. Resurfacing takes up (removes) the existing road surface and replaces it with a new one. There are other forms of maintenance, like patching cracks, but they are less important for transportation planners. Given this, we need to understand: How can we measure road condition? (This will enable us to decide when a road needs resurfacing). What determines how resistant a road is to wear? How do different vehicles cause damage to roads? Road Wear February 5, 2014 4 / 41
Introduction Strategy As before, our approach has two components: 1. We study some engineering concepts underlying road wear and maintenance. 2. We then use these concepts to address the planner s concerns: what should we be doing here? There is a nice visual explanation of measuring road condition by Man Tia (Univ. of Florida) available at http://nersp.nerdc.ufl.edu/~tia/5837-2.pdf. Road Wear February 5, 2014 5 / 41
This and the next color images are taken from Tia s notes. Road Wear February 5, 2014 6 / 41 Road Condition (I) Engineering Background A road with extensive cracking, but the ride quality is not too bad.
Road Condition (II) Engineering Background Also extensive cracking, but ride is probably much worse. Road Wear February 5, 2014 7 / 41
Engineering Background Measuring Road Condition (I) Engineers measure road condition by the Present [Pavement] Serviceability Index, PSI. The PSI is observable via surveys (profilometers, etc). Two important values: Newly resurfaced road (π 0 ): PSI 4.2. Trigger value (π f ): road needs resurfacing. PSI 2.5 (primary roads (freeways, major arterials)). PSI 2.0 (secondary roads). Note that these are to a certain extent subjective, especially the trigger values. Road Wear February 5, 2014 8 / 41
Engineering Background Measuring Road Condition (II) The PSI standard has been the one most commonly used in the US. However, there has recently been developed another standard: this is the International Roughness Index (IRI). USDOT now uses this measurement. It is supposed to be somewhat more objective than the PSI. It is said to be possible to do approximate conversions between the two (based on empirical regressions). ( ) PSI = ae b IRI hence IRI = b 1 ln PSI a Estimates: Paterson (1986): a = 5 b = 0.18 Al-Omari & Darter (1992): a = 5 b = 0.26 Note that PSI and IRI values go in opposite directions: high values of PSI are good, while higher values of IRI indicate greater road roughness, ie bad condition. Road Wear February 5, 2014 9 / 41
Engineering Background Measuring Road Condition (III) A modern auto-mounted laser profiler Road Wear February 5, 2014 10 / 41
Engineering Background Mesuring Road Condition (IV) Road Wear February 5, 2014 11 / 41
Engineering Background Roughness of US Roads Data is percent of mileage in the given IRI roughness category. Road 1993 2008 Urban Interstate Roughness > 220 2.5 1.4 Roughness < 60 8.5 19.2 Other Urban Expressway Roughness > 220 3.8 1.4 Roughness < 60 3.5 10.3 Urban Principal Arterial Roughness > 220 9.2 11.6 Roughness < 60 3.3 15.7 Rural Interstate Roughness > 220 1.0 0.3 Roughness < 60 8.3 31.4 Road Wear February 5, 2014 12 / 41
Engineering Background Engineering Background: Road Types Following engineering practice, we distinguish two types of roads: Rigid : surface is a slab of Portland cement concrete. Used in most freeways (interstates and other limited access roads). Flexible: bituminous surface (blacktop). Used for most non-freeways, and some more-lightly-used rural freeways. Road Wear February 5, 2014 13 / 41
Engineering Background Durability (I) A road s durability is a measure of its resistance to wear (damage). The measurement of durability differs by the type of road in question. Rigid Roads Durability D = inches of Portland cement concrete. US standard for heavily used interstates: D = 10 (inches of concrete). Road Wear February 5, 2014 14 / 41
Engineering Background Durability (II) Flexible Roads Durability is measured by the road s Structural Number (SN). This is a weighted average of three thicknesses (in inches). Component Weight Composition Surface, D 1 0.11 asphalt concrete Base D 2 0.44 crushed stone, gravel, sand Sub-base D 3 0.14 compacted soil SN =(0.11 D 1 ) + (0.44 D 2 ) + (0.14 D 3 ) Typical values: Freeway: 5.6 (but relatively few flexible-road freeways) Arterial 4.2 Collector: 3.2 Local road: 2.5 Road Wear February 5, 2014 15 / 41
Engineering Background Damage to Roads (I) Damage is done by cumulative vehicle passages: the cumulative impact of vehicles going over the road and tearing it up. The force exerted on the road by a given vehicle is related to the vehicle s weight (load) as transmitted through the vehicle s axles. Clearly, different types of vehicles (and different weights) will do different amounts of damage. So we need some way of standardizing these impacts. Engineering standard: ESAL = damage done by 18,000 lbs on a single axle. (18,000 lbs = 18 kips, kilo-pounds). Note that this is indirect it doesn t say that a vehicle tears up a certain volume of road surface. Nor does a 1-ESAL vehicle necessarily describe an actual vehicle: it s just a measure of the (relative) tendency to deteriorate a road surface. Road Wear February 5, 2014 16 / 41
Damage to Roads (II) Engineering Background Some representative ESAL values (assumes typical loads for commercial vehicles): Vehicle Type ESAL Value Passenger car 0.0008 Urban Transit Bus 0.6806 SU2 Truck 0.1890 SU3 Truck 0.1303 CS3 Truck 0.8646 CS4 Truck 0.6560 DS5 Truck 2.3187 TT5 Truck Trailer 0.5317 Key: SU = single unit; CS = conventional semi-trailer ; DS = Double Trailer. n = number of axles. (So SU2 = single-unit 2-axle truck). See Appendix for truck pictures. Road Wear February 5, 2014 17 / 41
Damage to Roads (III) Engineering Background Let s look at ESALs relative to passenger cars: Vehicle Type Urban Transit Bus 851 SU2 Truck 236 SU3 Truck 183 CS3 Truck 1081 CS4 Truck 820 DS5 Truck 2898 TT5 Truck Trailer 665 ESAL Value Key: SU = single unit; CS = conventional semi-trailer ; DS = Double Trailer. n = number of axles. (So SU2 = single-unit 2-axle truck). See Appendix for truck pictures. Road Wear February 5, 2014 18 / 41
Policy Implications, I Engineering Background When discussing road wear cars don t matter: road damage is effectively caused by trucks and buses Road Wear February 5, 2014 19 / 41
Engineering Background Putting It All Together We now understand: Road condition (measured by PSI or IRI). Road damage (caused by cumulative ESALs). Road durability (D, different units for rigid and flexible roads). How do these ideas fit together? How are they related to one another? Road Wear February 5, 2014 20 / 41
The AASHO Study The AASHO Study The AASHO Road Study was an influential attempt to relate these ideas. Conducted November 1958 November 1960. Controlled experiment. Stretch of road in Illinois (later incorporated into I-80). Test beds consisted of a series of rigid and flexible slabs of various thicknesses (D s). Trucks of determinate weights/axle configurations repeatedly traversed the road. Researchers recorded the number of passages at which the slabs failed (reached PSI trigger value). Road Wear February 5, 2014 21 / 41
The AASHO Study Location of the AASHO Study Road Wear February 5, 2014 22 / 41
An AASHO Test Track The AASHO Study Road Wear February 5, 2014 23 / 41
The AASHO Study The AASHO Study The AASHO study looked at the number of passages ( = times) a given vehicle (described by its weight and axle configuration) could go across a slab (of known durability) before deteriorating the slab from new to trigger value of PSI. Note that this number of passages is not the number of ESALs we ll convert the results to ESALs later. Road Wear February 5, 2014 24 / 41
The AASHO Study Results of the AASHO Study (I) The AASHO researchers assumed a functional form: where: N(D) = A 0 (D + 1) A 1 (L 1 + L 2 ) A 2 L A 3 2 N(D) = number of passages to reach trigger value, starting from new road condition. D = durability of slab (inches of concrete or structural number). L 1 = weight per axle in thousands of pounds. L 2 = 1 for a single-axle vehicle, 2 for tandem-axle vehicles. A s : parameters to be estimated. The equation is linear in logs, so we can write ln(n(d)) = ln A 0 + A 1 ln(d + 1) + A 2 ln(l 1 + L 2 ) + A 3 ln L 2 and estimate the A s using linear regression (though it isn t clear that this is what the AASHO researchers actually did). Road Wear February 5, 2014 25 / 41
The AASHO Study Results of the AASHO Study (II) The AASHO researchers published the following parameter estimates (no t-statistics or indications of goodness of fit) Estimate: Estimate: Parameter Rigid Road Flexible Road ln A 0 13.47 13.65 A 1 7.35 9.36 A 2 4.62 4.79 A 3 3.28 4.33 Road Wear February 5, 2014 26 / 41
The AASHO Study The Interstate Puzzle, redux (I) Let s try a calculation for rigid roads based on the AASHO study results. We ll take D = 10 (inches of concrete), and obtain results in ESALs by taking L 1 = 18 (thousand pounds) L 2 = 1 (on a single axle), which is the definition of an ESAL. So we compute: N(D) = A 0 (D + 1) A 1 (L 1 + L 2 ) A 2 L A 3 2 = e 13.47 (10 + 1) 7.35 (18 + 1) 4.62 1 3.28 = e 13.47 (11 7.35 )(19 4.62 ) = 3. 947 7 10 7 = 39.477 million ESALs Road Wear February 5, 2014 27 / 41
The AASHO Study The Interstate Puzzle, redux (II) Then: We know that a heavily-used interstate generates roughly 0.75 1.00 million ESALs per year. So the expected road lifetime (before needing resurfacing) is between 39 and 53 years. This explains the engineers original predictions of interstate lifetimes. Road Wear February 5, 2014 28 / 41
What Went Wrong? What Went Wrong? (I) Clearly these estimates are wildly over-optimistic. We ve already noted some reasons why roads might have worn out sooner than anticipated: Unanticipated economic growth. Unanticipated growth in road utilization. But these do not explain the magnitude of the over-estimate. Road Wear February 5, 2014 29 / 41
What Went Wrong? What Went Wrong? (II) The real answer is a bit more subtle. It lies in the way the AASHO researchers analyzed their data. By the time the researchers stopped the experiment, some of the thickest (most durable) slabs had not failed. But the researchers recorded the slabs as having failed at the maximum number of passages. That is, if the experiment was stopped after N passages, a slab that hadn t failed was recorded as if it had failed at N passages. There was thus no difference in the data between slabs (a) happened to fail at just N passages, and (b) slabs that hadn t yet failed when N was reached. This distorted the results. Road Wear February 5, 2014 30 / 41
What Went Wrong? An Alternative Statistical Model (I) If the experiment was stopped at N passages, we know that for a non-failing slab, the number N of passages to failure is greater than N, though the precise N for these slabs is unknown. On the other hand, for a failing slab we know exactly how many passages were needed to induce failure So we have two classes of slabs: those for which we actually know how many passages induced failure, and those for which we have only a lower bound. For the AASHO study, the number of non-failing slabs was 191 out of 264 (rigid slabs) and 45 of 284 (flexible slabs). Road Wear February 5, 2014 31 / 41
What Went Wrong? An Alternative Statistical Model (II) There is a statistical model for this phenomenon: the Tobit model. It assumes that the unobserved number of passages to failure for a non-failing slabs is normally distributed above N. This is a nonlinear regression model, and must be estimated by maximum-likelihood methods. Nowadays, most statistical packages contain built-in routines to estimate the Tobit model. Road Wear February 5, 2014 32 / 41
What Went Wrong? The Small Winston Re-Analysis Kenneth Small and Clifford Winston (American Economic Review, 1988, and Road Work, 1989) applied a Tobit model to the original AASHO data (which is publicly available). Findings: (asymptotic t-statistics in parentheses): Estimate: Estimate: Parameter Rigid Road Flexible Road ln A 0 13.505 (44.0) 12.0625 (50.9) A 1 5.041 (15.3) 7.761 (31.7) A 2 3.241 ( 12.5) 3.652 ( 24.8) A 3 2.27 (9.4) 3.238 9 (17.1) Road Wear February 5, 2014 33 / 41
What Went Wrong? The Interstate Puzzle, Resolved (I) To appreciate the significance of the new results, let s repeat our calculation with the revised estimates. As before, we take a rigid road, with D = 10, L 1 = 18, L 2 = 1. We have N(D) = A 0 (D + 1) A 1 (L 1 + L 2 ) A 2 L A 3 2 = e 13.505 (10 + 1) 5.041 (18 + 1) 3.241 1 2.27 = e 13.505 (11) 5.041 (19) 3.241 = 9. 340 4 10 6 = 9.3404 million ESALs Road Wear February 5, 2014 34 / 41
What Went Wrong? The Interstate Puzzle, Resolved (II) This is to be compared to 39 million ESALs expected under the original AASHO model. With 0.75 to 1.00 million ESALs per year, we now expect a heavily-used road to last between 9 and 12 years before needing re-surfacing. This is clearly much more reasonable in light of actual experience. So our primary answer to the interstate puzzle is that the original researchers used the wrong statistical model to analyze their data. This had important public policy consequences: it significantly over-estimated expected road lifetimes. Road Wear February 5, 2014 35 / 41
Road Lifetime Road Lifetime, GVW and Axles We have noted that road wear is related to vehicle weight (load) and its distribution over the vehicle s axles. Let s see how this plays out. Consider a truck of Gross Vehicle Weight G (thousand pounds) operating on L 1 axles, with L 2 indicating whether or not the axles are in tandem (L 2 = 2) or not (L 2 = 1). How many times (passages) can such a truck pass over a durability D road before it deteriorates from new (π 0 ) to needing re-surfacing (π f )? The answer is given by the AASHO functional form: N(D) = A 0 (D + 1) A 1 ((G /L 1 ) + L 2 ) A 2 L A 3 2 where G /L 1 is the weight per axle Road Wear February 5, 2014 36 / 41
Some Simulations Road Lifetime Take G = 55 (thousand pounds), D = 10, and assume a rigid road. Passages Axles Tandem (m) 2 1 2.51 2 2 10.83 4 1 21.22 4 2 82.75 8 1 162.20 8 2 531.0 Road Wear February 5, 2014 37 / 41
Some Simulations Road Lifetime We see: The number of passages rises steeply with the number of axles. Going from 2 to 4 single axles results in a factor-of-10 increase in road life (from 2.5 to 21 million passages). The effect is even more strong with tandem axles. Going from 2 single axles to 2 tandem axles quadruples life (from 2.5 to 11 million passages). Going from 2 single axles to 4 tandem axles is a factor-of-33 improvement (from 2.5 to 83 million passages). Road Wear February 5, 2014 38 / 41
Road Lifetime Policy Implications These considerations lead to important policy implications: Public policy should provide incentives for truckers to distribute their loads over as many axles as possible, and to use tandem axles. This minimizes forces on the road, and hence road wear. But most roads are operated in precisely the contrary manner: tolls increase with the number of axles (other things held constant). Existing policy encourages truckers to minimize the number of axles, which is completely wrongheaded. Road Wear February 5, 2014 39 / 41
Appendix - Truck Types Road Lifetime Road Wear February 5, 2014 40 / 41
Citations Road Lifetime B. Al-Omari and M. I. Darter, Relationships between IRI and PSR, Interim report UILU-ENG-92-2013, Illinois Department of Transportation, 1992. W. D. Paterson, International roughness index: Relationship to other measures of roughness and riding quality, Transportation Research Record, (1084), 1986. Kenneth A. Small and Clifford M. Winston, Optimal highway durability, American Economic Review, 78(3), pp. 560 69, 1988. Kenneth A. Small, Clifford M. Winston, and Carol Evans, Road Work, The Brookings Institution, Washington, D.C., 1989. Road Wear February 5, 2014 41 / 41