Accounting of Strain Cycles Sustained by Airfield Rigid Pavements

Anastasios M. Ioannides1, J. Andrew Harrison2, Carlos R. Gonzalez3, and Peter G. Bly4

ABSTRACTThe so-called 72-in. rule, employed in U.S. Department of Defense rigid pavement design in establishing the number of strain cycles arising under a pass of any aircraft on a particular pavement system, is re-examined using mechanistic tools, particularly layer elastic theory and dimensional analysis. Field data collected at Denver International Airport are reproduced using analytical simulations, which permit the generation of analogous synthetic results pertaining to different pavement systems and aircraft gear configurations. The analysis affirms the expectation that the criterion for establishing the number of strain cycles cannot be simply a fixed value, defined by the tandem wheel spacing. Rather, the dual wheel spacing and the radius of each tire-print must also be taken into consideration. In addition, the radius of relative stiffness of the pavement system needs to be accounted for. In this study, these variables are accommodated in the form of three dimensionless independent input parameters. The single dependent variable is the ratio (trough strain ÷ maximum strain), denoted herein as υ. A process is formulated to ascertain whether υ is positive or negative: if υ>0, then one strain cycle may be expected; if υ<0, then two strain cycles may be expected. Comparisons of the process outcomes to those from the 72-in. rule show excellent agreement for the Denver conditions, testifying to the admirable simplicity and laudable wisdom of the latter. The process may be further refined for application to more complex gear configurations, e.g., tridems.

1. INTRODUCTIONThe current design procedures formulated by the U.S. Department of Defense (DOD) for Rigid Pavement Design are described in the Unified Facilities Criteria (UFC) 3-260-023-260-02: Pavement Design for Airfields, last updated on 30 June 2001 (UFC, #2001). More specifically, rigid pavement design is detailed in Chapters 12 and 19, the first according to plate-on-dense liquid (DL) analysis (Westergaard, #1948) and the second according to layer-on-elastic solid (ES) formulation (Burmister, #1943). The current software implementation of DOD procedures is under the umbrella of the Pavement-Transportation Computer Assisted Structural Engineering (PCASE) computer program, version PCASE 2.09.05, released on 21 May 2015 (PCASE, #2015). All DOD pavement designs account for fatigue phenomena through the pass-to-coverage (P/C) ratio concept, a term coined during the Service Behavior Tests on flexible pavements at Barksdale Field, Shreveport, LA, conducted in 1944 and described by Hansen (#1950). The concept eventually evolved to be a crucial part of the design methodologies adopted by the DOD for both flexible and rigid airfield pavements, having been significantly modified and expanded

1 Engineering Consultant, P.E., Ph.D., 9378 Hunters Creek Drive, Cincinnati, OH 45242, USA. ioanniam@yahoo.com.2 Senior Research Civil Engineer, P.E., U.S. Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180 USA. andrew.harrison@usace.army.mil.3 Senior Research Civil Engineer, P.E., Ph.D., U.S. Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180 USA. carlos.r.gonzalez@ usace.army.mil.4 Research Civil Engineer, P.E. U.S. Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180 USA. peter.g.bly@usace.army.mil. PhD Candidate, University of Minnesota, Department of Civil and Environmental Engineering.

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in the three decades that followed (Brown and Ahlvin, #1961; Ahlvin, et al. #1971; Brown and Thompson, #1973).

Following observations by Harrison (#1997) at the Denver International Airport (DIA), the PCASE routine that calculates the P/C ratio for concrete pavements has been modified, in order to distinguish between tandem gear configurations applying a single strain cycle from those that apply more than one such cycle per aircraft pass. The dividing line between these two gear groups is established in reference to the tandem spacing of the tires, and is currently set at 72 in., on account of the experience at DIA; this practice is referred to herein as the “rule of 72-in.”.

2. RESEARCH SIGNIFICANCEIt is apparent that expressing the distinguishing criterion as a dimensional quantity, reflecting exclusively the tandem wheel spacing, may not apply universally to all airports, since this may be sensitive to the radius of relative stiffness of the pavement present at any other site, as well as to other gear configuration parameters of every aircraft. Recognizing that it would be infeasible and prohibitively expensive to repeat the DIA experiment at airports around the country, this paper pursues analytical simulation of various pavement cross-sections using layer elastic theory in order to quantify the factors responsible for the strain cycle signature of any aircraft applied at any airport. The principles of dimensional analysis are employed in order to limit the volume of data required for the analysis. The goals of this effort are: (a) to reproduce the slab response information available from DIA; and (b) to generate additional information applicable to other airport locations and aircraft, in order to verify the validity of the 72-in. rule. Accomplishing these objectives requires initially careful material characterization for the DIA pavements, so that the recorded strain signatures of selected aircraft may be reproduced with acceptable precision. Subsequently, using short factorials of analytical simulations, key variables that influence the pavement’s response are identified and used to develop a process to ascertain the number of strain cycles associated with each traffic pass, depending on the gear configuration and pavement structure considered.

3. THE DIA INSTRUMENTED PAVEMENT EXPERIMENTIn April 1992, the Federal Aviation Administration (FAA) initiated a rigid airfield pavement instrumentation research project at DIA, located approximately 37 km (23 miles) northeast of downtown Denver, CO. The pavements at DIA were designed based on traffic projections for the year 2035, i.e., for a design life of 40 years. Both the then current FAA and the Portland Cement Association design procedures were used to design the rigid pavements. The basic design for the runway pavements consisted of 432 mm (17 inches) of concrete, a bond breaker (emulsified asphalt with nonwoven geotextile), 203 mm (8 inches) of cement-stabilized base, and 305 mm (12 inches) of lime-stabilized subbase over approximately 1.5 m (5 feet) of compacted clay fill. On account of the possible presence of swelling soils, subsurface drains were provided at the edge of the taxiway shoulder.

The U.S. Army Corps of Engineers (USACE) Waterways Experiment Station (WES) was tasked with the design, installation and initial operation of the instrumentation system. The anticipated primary departure runway 16L-34R was instrumented to monitor pavement response to aircraft loads. The instrumented area was located 73.2 m (240 feet) north of the south end (34R) threshold, and consisted of 16 concrete slabs all on the west side of the runway centerline.

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Extensive field and laboratory tests were conducted to identify material properties. In situ measurements indicated that the average thickness at the instrumentation location was 17.81 in. with a coefficient of variation of 1.88%; the strain gages were located 1 in. from the bottom of the slab.

The instrumentation system began collecting pavement response data in June 1993. With the support of DIA, WES personnel were allowed to conduct controlled tests using an F-15 load cart in July 1993. In October 1993, Air Mobility Command (AMC) of the U.S. Air Force provided four military aircraft: the C-130, C-141, KC-10 and KC-135. In February 1995, DIA was officially opened for public use; data analysis, however, was delayed until September 1995, when WES was tasked by AMC to conduct the analysis of the military aircraft pavement response data collected and, additionally, to collect and analyze pavement response data from two additional military cargo aircraft, the C-5A and C-17. Pavement response data were collected with the C-5A and C-17 aircraft in February 1996. The data analysis is conveniently presented in summary by Harrison (#1997), who served as the Principal Investigator for the WES contract from the FAA.

4. FIELD MEASUREMENTS FROM THE DIA INSTRUMENTED SITEReproduced below are data from Harrison (#1997) for three military aircraft types included in the experiment: C-141, C-17 and C-5A. The configuration of one main landing gear from each is shown in Fig. 1.

Reviewing longitudinal strain data from one pass by each of these aircraft, Harrison (#1997) identified 1 strain cycle for the C-141, 2 strain cycles for the C-17, and 4 strain cycles for the C-5A. The corresponding Figures presented by Harrison (#1997) are reproduced in Fig. 2 (tension is positive). A strain cycle consists of both positive and negative strains and includes two strain reversals, i.e., two crossings the zero-strain line.

The questions that arise then are “What is the number of strain cycles produced by a given configuration?” and “What does this number depend on?” As a first attempt to answer these questions, WES engineers (reportedly, Don R. Alexander and Walter G. Barker, c. 1998) established the so-called “72-in. rule” for the tandem spacing, above which multiple strain cycles may be expected to result. The data, however, do not appear to support the value of 72 in. (rather, 65 in. might have been chosen), nor the number of strain cycles produced (the C-5A is an exception to the rule established).

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PT P %MG PMG Nw Pw Aw a t t/a Strain cycles page

C-141 238.3 195 94.4 224.955 8 28.119 144.20 6.7750 48 7.0848 1 78

C-17 422.9 150 92 389.068 12 32.422 216.15 8.2948 97 11.6942 2 82

C-5a 508.1 130 94.2 478.630 24 19.943 153.41 6.9879 65 9.3018 4 80

Figure 1. Main Gear Configurations

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Figure 2. Recorded Strain Data: (a) C-141; (b) C-5A; (c) C-17 (from Harrison, #1997)

5. REPRODUCTION OF C-141 STRAIN DATABecause of the relative simplicity of the C-141 gear, the strain data pertaining to it and recorded in Fig. 2a, were selected for further study. To begin with, this figure was digitized using the WebPlot Digitizer software. The accompanying remarks by Harrison (#1997) are enlightening:

“Tensile stress [or] strain is considered to be the best predictive indicator of pavement performance. Of the aircraft being evaluated in this analysis, C-141 aircraft is the most common aircraft used for design of rigid airport pavements. Therefore, it is desirable to compare the strain response due to the C-141 with the response of the C-5 and C-17. Figure [2a] provides the C-141 response data for an interior longitudinal strain gage. For this pass of the aircraft it is seen that maximum tensile strain is 21 micro-inches/inch and the maximum compressive strain is 6.5 micro-inches/inch for a total strain cycle of 27.5 micro-inches/inch. For design, only the computed tensile strain is used, thus the total strain reversal is not considered. For this gear it is seen [that] there is only one cycle (positive value under gear) of strain. [p. 78] Pavement response data were collected in October 1993 using the C-141 military cargo aircraft. Aircraft characteristics for these aircraft were provided by the

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USAF Mobility Center. The maximum aircraft load during testing, [and] the operating tire pressure for [this] aircraft are [238.3 kips and 195 psi, respectively; 94.4% of the load is carried by the main gear]. Tests were conducted with [this] aircraft over a two-day period only during the day light hours (7:00 am - 6:00 pm). Tests were conducted by positioning the aircraft main gear to run along the test lanes. Passes were made in both the north and south directions. The aircraft speed during testing was approximately 10 knots. Approximately 26 passes were made over the instrumented section with [this] aircraft. [p. 27]The longitudinal gear offset represents data from a single pass of the aircraft. As an aircraft made a pass, data are recorded at a timed interval. To obtain the longitudinal offset plots, the speed of the aircraft [are] determined and used to convert the time base line to a distance base. Data from selected aircraft passes were used for comparison with the computed response. [p. 54]”

The digitization of Fig. 2a resulted in minimum and maximum strain values of -6.003 and 20.657 με, respectively; these strain values agree fairly well with the corresponding rounded values quoted by Harrison (#1997) as -6.5 and 21 με, respectively. The trough between the two positive peaks is at 8.355 με, or υ = 40.45%, where υ denotes the ratio (trough strain ÷ maximum strain), in percent. The first positive peak is at 17.767 με; the corresponding υ-value is 47.03% of the first peak value.

Now, the speed of the aircraft producing Fig. 2a may be inferred from the time difference between the two positive strain peaks, which are observed to occur at 12.935 and 13.437 sec., respectively; thus, their time difference is 0.503 sec. This time difference may be expected to correspond to the tandem spacing, t, for the C-141, which was 48 in. The speed of the aircraft is, therefore, computed as 7.957 fps (or 4.714 knots). This speed is considerably slower than the approximate speed of 10 knots quoted by Harrison (#1997); the validity of its acceptance will be verified by comparison to theoretically calculated strain distributions.

Commenting on the recorded responses, especially the observed difference in the height of the two positive strain peaks in Fig. 2a, Harrison (#1997) notes:

“One interesting aspect of the measured data is the difference in the approach and departure pavement response. [p. 56] It is noted that there is a rebounding lag as the aircraft departs which is not considered in the analytical model. [p. 62] The fact that the pavement is still rebounding from the first loading may contribute the greater [response] due to the second loading. [p. 74] It is also noted that the slab appears to [respond] more slowly as the aircraft approaches than the slab rebounds as the aircraft departs. [p. 76] The computed pavement response is symmetrical whereas the measured response shows a lag in the rebound after the load departs. The computed response matched better on the approach side. [p. 56]”

6. LAYER ELASTIC ANALYSISIn view of the DIA pavement system’s multi-layered cross-section, layer elastic analysis (LEA) was pursued, using computer code WINLEA, which is the current Windows implementation of program JULEA (#Uzan, c. 1991), prepared c. 2001 by Carlos R. Gonzalez (personal

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communication: July, 2019) at Engineering Research and Development Center (ERDC), Vicksburg, MS. Harrison (#1997) provides the following information about his own analytical studies [pp. 51-53]:

“Pavement Characterization: For the Westergaard theory only the concrete properties, pavement thickness and subgrade k need to be defined for the pavement model. From laboratory tests conducted on concrete samples, the modulus of elasticity and Poisson's ratio were estimated to be 4.7 × 106 psi and 0.2, respectively. Field tests provided a k value of 185 psi per inch for the k at the top of the lime stabilized [subbase], [and led to the] estimate an effective k for the top of the stabilized base of 220 psi per inch. The layered elastic model was used to compute strains and displacements to compare with the measured strains and displacements. Characterization for the layer elastic theory required a modulus of elasticity, Poisson's ratio and thickness for each layer plus an interface bond parameter to define the condition of bond between the layers. The DIA pavement consisted of an 18-inch PCC slab, an 8-inch cement stabilized base, and a 12-inch lime stabilized [subbase] over the compacted clay subgrade. The PCC properties were the same as those used in the Westergaard model. The 8-inch cement stabilized base was modeled as a layer having an E value of 1.0 × 106 psi and a Poisson's ratio of 0.2. The selection of these values was based strictly on literature review of similar materials. Laboratory resilient modulus tests provided data for the selection of the modulus of elasticity and Poisson's ratio for the lime stabilized [subbase] and the compacted subgrade. For the lime stabilized [subbase], 60,000 psi was selected for E and 0.4 was selected for Poisson's ratio. For the compacted subgrade, the E and Poisson's ratio were 20,000 psi and 0.5, respectively. The thickness of [the PCC slab was] given by the design as 17 inches but was determined by field measurements to be [closer to] 18 inches. In past studies it has been [found] unrealistic to model the subgrade as having infinite thickness, thus a finite thickness is selected. Below the subgrade layer, a cutoff layer is used to limit computed deflections. The cutoff layer has normally been placed at a 20-foot depth and, since some of the deflection gages were anchored at the 20-foot depth, this is the depth at which the cutoff layer was initially placed. After comparing the computed deflections with the measured deflections, a cutoff layer was also used at a 10-foot depth to compare the gages that were anchored at the 10- foot depth. The cutoff layer was modeled with an E value of 1.0 × 106 psi and a Poisson's ratio of 0.5. The interfaces between all layers, excluding the interface beneath the concrete slab, [were] considered as fully bonded. Since the pavement was constructed with a bond breaker under the concrete slab, the interface between the concrete slab and the cement stabilized layer was initially modeled as being frictionless. Analyzing the response of the pavement indicated that at times the interface behaved as if the interface was bonded. Thus, for some of the modeling, the interface was modeled as being fully bonded.”

7. PAVEMENT CHARACTERIZATION BY BACKCALCULATION

7.1 Using Synthetic Deflections

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Adopting values per Harrison (#1997) for a baseline 5-layer system (Table 1a), WINLEA was run for a Falling Weight Deflectometer (FWD) load of 75 kips, resulting in the following displacements for 7 sensors, 0 to 72 in. at 12 in. spacing:

Displacement (mils): 8.5373; 8.3542; 7.3884; 6.4002; 5.4133; 4.4697; 3.5965.

These deflections were analyzed with ILLI-BACK 3.0 (Ioannides, #1994), yielding:

h = 17.81 in.; AREA = 53.54 in.; k = 463 psi/in.; Es = 75.12 ksi; Ec = 5.29 Mpsi for DL and 4.02 Mpsi for ES.

7.2 Using Field Data from ReportA Data Report, dated July 2000 (ERDC, #2000) includes a table of FWD tests conducted on June 5, 2000, from which Stations 210, 270, 330, and 370 were selected, as evenly spaced along runway 34R-16L, on both sides of the instrumented area. From each of these stations, ILLI-BACK 3.0 was used to analyze the third drop. Results are presented in Table 1b.

7.3 Using File Data from FAA DatabaseTo provide a third source of information, FWD data were download en masse from the FAA website (https://www.airporttech.tc.faa.gov/Products/Databases/Denver-Instrumentation/Browse-Database/FWD; last accessed 8/22/19), and ILLI-BACK 3.0 batch backcalculation with 7 sensors (Configuration 2) was employed. There were 3936 cases, of which 2728 were retained as nominally reliable: 48 cases were eliminated since the AREA was below 16.223 in., a limit of ILLI-BACK 3.0 applicability; 14 cases were eliminated since the AREA was higher than 72 in., the theoretical maximum value for 7 sensors at 12-in. spacing; 997 cases were eliminated since the coefficient of variation (COV) for DL is outside the range of reliability, set at 5 to 30%; and 149 cases were eliminated since k was below 200 psi/in., considered to be the lower limit of reasonableness given the pavement cross-section and the ILLI-BACK 3.0 results, above. The backcalculation results from the remainder 2728 cases are shown in Table 1c. These values agree quite well with those from the briefer studies above, and are considered to constitute a solid foundation for the investigation to follow.

8. PAVEMENT SYSTEM REDUCTION TO LAYER-ON-ELASTIC SOLID

8.1 Comparison between 5-Layer Section and Layer-On-Elastic Solid (4 Loads; t=48 in.)Retaining the pavement layer properties values per Harrison (#1997) used above for the FWD simulation (Table 1a), WINLEA was executed again with 5 layers, but this time the 4 C-141 loads as specified in Fig. 1 were applied to provide the baseline responses, as follows:

Max. εy = 22.929 με at 1 in., i.e., a bit higher than the max in Fig. 2a of 20.657 με. The trough occurs at 24 in. and is 12.749 με or υ = 55.6%. The second peak occurs at 47 in. and is 22.929 με.

The digitized data from Fig. 2a established the range for the peak as 18 to 21 με; the target range for υ is 40-47%. The WINLEA results above are slightly too high in both instances, but are considered gratifyingly good as an initial effort to reproduce the data recorded by Harrison (#1997), in the manner probably followed in establishing the 72-in. rule.

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Adopting the slab-on-elastic solid (ES) backcalculated values (17.81 in.; 4.02 Mpsi and 75.12 ksi), WINLEA was executed for the four C-141 loads, and resulted in max. εy = 22.328 με at 1 in., i.e., a bit higher than the max in Fig. 2a of 20.657 με. The trough occurs at 24 in. and is 8.564 με or υ = 38.48%. The second peak occurs at 47 in. and is 22.328 με. Note that in this case, the subgrade is assumed to be an infinite one (eliminating the rigid bottom). Such a subgrade is simulated in WINLEA by dividing it into two fully bonded layers of the same properties; the upper one is set to 12 in., and the lower one to 0 in., i.e., semi-infinite. The layer-on-ES results are also gratifyingly similar to the digitized data and to the WINLEA 5-layer values, closing the loop, so to speak. It is noted that υ is very sensitive and difficult to pin down: 5-layers produced 55.6%, and layer-on-ES yielded υ = 38.4%, whereas the expected range from the digitized data is υ = 40 to 47%.

Seeking a better fit to the digitized peaks (avg. εy = 19.12 με) and trough (εy = 8.355 με), several slightly modified WINLEA layer-on-ES runs with 4 loads were performed, among which the following was adopted: h = 17.81; Ec = 5M, μc = 0.2; Es = 74.5 ksi; μs = 0.5; and ℓe = 29.116 in. For this system, the first peak is εy = 19.262 με at 1 in.; the trough is εy = 8.350 με at 24 in. (υ = 43.30%); the second peak is εy = 19.262 με at 47 in. These responses are 100.26%, 99.94% and 99.68% of the corresponding digitized values. A comparison plot is presented in Fig. 3.

Figure 3. Data Fits for C-141 at DIA

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9. EFFECT OF DUAL SPACINGAdopting this layer-on-ES system, several WINLEA runs were performed with 4 loads at t = 48 in., in which the dual spacing, s, was varied from 12 to 576 in. The results are shown in Table 2a. Clearly, the effect of s cannot be ignored. If s is ignored (or as s tends to infinity), the resulting trough is about twice as deep as that for the DIA pavement and C-141.

10. EFFECT OF TANDEM SPACING

10.1 Dual Spacing, s = 32.5 in. (Four Loads)Adopting the layer-on-ES system under 4 loads (s = 32.5 in.), the tandem spacing, t, was varied, to study its effect on the trough. This system is identical to that in the previous paragraph, for s = 32.5 in. The results are shown in Table 2b, which when plotted produce Fig. 4.

Figure 4. Synthetic Strain Cycles for Tandem Gears

It is observed that in every case, the trough occurs half-way between peaks, as dictated by symmetry; the peaks are t-in. apart. The cross-over point (υ = 0) for this case occurs at t = 77.33 in., i.e., slightly higher than per the 72-in. rule.

10.2 Dual Spacing, s = infinite (Two Loads)Although the effect of s is significant, it is desirable at this point to eliminate this variable by reducing the number of loads to 2, so that the effect of t can be decoupled from that of s. The tire load may be increased at will, since the system is linearly elastic: adopting 40 k on each tire,

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results in a peak value approximately equal to that at DIA, i.e., about 20 με. The tandem spacing, t, was varied, to study its effect on the trough. The system analyzed is essentially identical to that for a previous case with s = 576 in., except for the scaling effect of increasing the applied load. The results are presented in Table 2c. In this case, the cross-over point (υ = 0) is 64.15 in., i.e., somewhat lower than per the 72-in. rule.

To establish a connection between results in Tables 2b and 2c, the data are plotted in Fig. 5, normalized as (t/s) and [υ at s = ∞ ‒ υ at any (t/s)]. For the case considered, t/s = 48/32.5 = 1.477, and the curve gives the υ-increment as 21.739. So, if υ at s = ∞ is known (= 21.610), then υ at (t/s) of 1.477 is (21.610+21.379) = 43.349%.

Figure 5. Correction Increment, Δυ, for the effect of (t/s)

11. EFFECT OF RADIUS OF RELATIVE STIFFNESSAdopting the layer-on-ES cross-section with two loads (t = 48 in.; s = ∞; Pw = 40 k; Aw = 144.2 in.2), analyses were conducted with WINLEA to see what happens to the trough as the radius of relative stiffness, ℓe, and other variables change. Aw denotes the area of the tire-print of each wheel. Initially, the concrete modulus, Ec, was varied, but subsequently the subgrade modulus, Es, concrete slab thickness, h, and Aw were also varied. The results are given in Table 3. Evidently, υ increases as ℓe increases.

To obtain a generalized relationship, the data for Ec may be plotted with (t/ℓe) as the independent variable and υ as the dependent variable (see Fig. 6).

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Figure 6. Effect of (t/ℓe)

The linear regression is obtained only for the positive values of υ, since any exaggeration of the negative values will have no practical significance for the purposes of this investigation. The cross-over point is around (t/ℓe) = 2.23, which for ℓe = 29.12 in. (per DIA) yields t = 65.0 in., a number quite close to the previously calculated value of 64.15 in.

The Es points align very well with the general trend. The h points show a small deviation, attributable to the fact that the strain calculation point was set at (16.81/17.81) × h, i.e., it was not a constant. Only the Aw points exhibit a significant deviation from the general trend, introducing yet another variable into the problem. Consequently, the Aw points are replotted in Fig. 7, as [υ at (a/ℓe) = 0.232686 − υ at any (a/ℓe)].

12. APPLICATIONS AND CONCLUSIONThe purpose of the process developed in this investigation is to ascertain whether υ is positive or negative. This process may be summarized as follows:

1. For the pavement cross-section and aircraft gear configuration considered, assemble the required inputs: ℓe, t, s, and a;

2. For the given (t/ℓe ), use the following regression formula to obtain the first estimate of υ, which applies for s = ∞ and (a/ℓe) = 0.23269, the latter pertaining to the C-141 at DIA:

υ1 = -0.37582162 (t/ℓe) + 0.838963843. For the given (a/ℓe), adjust υ1 by adding the following increment:

Δυ1 = -0.48624124 (a/ℓe) + 0.10782633Thus, obtain the second estimate of υ, which applies for s = ∞ and the (a/ℓe) value of interest:

υ2 = υ1 + Δυ1

4. Finally, correct υ2 for the given (t/s) value of interest, by adding the following increment: Δυ2 = -13.4844 (t/s)5 + 110.3891 (t/s)4 - 334.4460 (t/s)3 + 443.0355 (t/s)2 - 227.2771 (t/s)

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+ 38.3750

Figure 7. Correction Increment, Δυ, for the effect of (a/ℓe)

Thus, obtain the third and final estimate of υ, which applies for the (t/s) and (a/ℓe) values of interest:

υ3 = υ2 + Δυ2

5. Reach the conclusion: If υ = υ3 > 0, then one strain cycle may be expected; if υ = υ3 < 0, then two strain cycles may be expected.

This process was applied to the case of C-141 at DIA and yielded υ = 44.06%, i.e., 101.75% of the corresponding value of 43.30%, predicted by LEA for the layer-on-ES system. Therefore, one strain cycle may be expected. For the C-17 at DIA, the process yields υ = -31.11%, and two strain cycles may be expected. For the C-5A, the process results in υ = 22.31%, and one strain cycle may be expected. The process also leads to positive υ-values for the C-130, KC-10 and KC-135, the other aircraft tested at DIA.

All of these results agree with the outcomes of the 72-in. rule, which emerges as admirable for its simplicity and laudable for its wisdom. Nonetheless, according to the data presented by Harrison (#1997), four strain cycles were observed under the C-5A, i.e., 2 strain cycles per set of tandems. Therefore, the process may be adjusted for such more complex gears, e.g., tridems, by introducing yet another variable, reflecting the spacing between the tandem sets, or the tridems. In the meantime, the threshold value of υ for these gears may be raised from 0 to 25%.

Permission to publish granted by Director, Geotechnical and Structures Laboratory.

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REFERENCES

Ahlvin, R.G., Ulery H.H., Hutchinson, R.L. and Rice, J.L. (1971), “Multiple-Wheel Heavy Gear Load Pavement Tests,” Technical Report S-71-17, Vol. I: Basic Report, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS, November.

Brown, D.N. and Ahlvin, R.G. (1961), “Revised Method of Thickness Design for Flexible Highway Pavements at Military Installations,” Technical Report No. 3-582, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS, August.

Brown, D.N. and Thompson, O.O. (1973), “Lateral Distribution of Aircraft Traffic,” Miscellaneous Paper S-73-56, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS, July.

Burmister, D.M. (1943), “The Theory of Stresses and Displacements in Layered Systems and Application to the Design of Airport Runways,” Proc. HRB, Vol. 23, 1943, pp. 126-144; Discussion, pp. 144-148.

ERDC (2000), “Data Collected at the FAA Denver Instrumentation Site, Denver International Airport,” Data Report, Engineering Research and Development Center, Vicksburg, MS, July.

Hansen, R. (1950), “Service Behavior Tests, Barksdale Field, Shreveport, LA,” in “Development of CBR Flexible Pavement Design Method for Airfields - A Symposium”, Transactions, ASCE, Vol. 115, pp. 495-505. Originally published in Proceedings, ASCE, January, 1949.

Harrison, J.A. (1997), “Analysis of Rigid Pavement Response Data Induced by Military Aircraft at Denver International Airport,” M.S. Thesis, Mississippi State University, near Starkville, MS, December.

Ioannides, A. M. (1994), “Concrete Pavement Backcalculation Using ILLI-BACK 3.0,” Nondestructive Testing of Pavements and Backcalculation of Moduli (Second Volume), ASTM STP 1198, Harold L. von Quintus, Albert J. Bush, III, and Gilbert Y. Baladi, Eds., American Society for Testing and Materials, Philadelphia, 1994.

PCASE (2015), “Pavement-Transportation Computer Assisted Structural Engineering (PCASE) software program, version 2.09.05,” developed by ERDC Geotechnical and Structures Laboratory (GSL), Vicksburg, MS, downloadable from https://transportation.erdc.dren.mil/pcase/ accessed: 10/3/18; see also, https://www.erdc.usace.army.mil/Media/Fact-Sheets/Fact-Sheet-Article-View/ article/476785/the-pcase-program/

UFC (2001), “Unified Facilities Criteria: Pavement Design for Airfields,” UFC 3-20-02, 30 June 2001, US Army Corps of Engineers, Naval Facilities Engineering Command, Air Force Civil Engineer Support Agency, supersedes TM 5-818-2/AFM 88-6, Chap 4, dated January 1985; TM 5-822-2/AFM 887, Chap 5, dated July 1987; TM 5-822-13/AFJMAN 32-1018, dated October 1994; TM 5-822-5/ AFM 88-7, Chap 1, dated June 1992; TM 5-5-824-1/AFM 88-6, Chap 1,

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dated June 1987; TM 5825-2/AFM 88-6, Chap 2/DM 21.3, dated August 1978; TM 5-825-2-1/AFM 88-6, Chap 2, Sec A, dated November 1989; TM 5-825-3/AFM 88-6, Chap 3, dated August 1988; and TM 5-825-3-1/ AFM 8-6, Chap 3, Sec A, dated September 1988; Washington, DC.

Uzan, J. (c. 1991), “JULEA: Jacob Uzan Layered Elastic Analysis,” Technion University, Haifa, Israel.

Westergaard, H. M. (1948), “New Formulas for Stresses in Concrete Pavements of Airfields,” Transactions, ASCE, Vol. 113, pp. 425-439. Originally published in 1947, in Proceedings, ASCE. First submitted as Technical Memorandum, Navy Department, Bureau of Yards and Docks, Sept. 1945, under the title “New Formulas for Stresses and Deflections in Concrete Airfields.”

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Word CountAbstract: 240Introduction: 282Research Significance: 237Body (incl. Conclusions):

Text: 3798Figures: 7 @ 250 = 1750Tables: 3 @ 250 = 750

References: 422

Total: 7479

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TABLES

Table 1 – Backcalculation Results Using ILLI-BACK 3.0

(a) Baseline WINLEA 5-Layer Pavement System

(b) From Data Report (ERDC, 2000)

(c) From FAA DatabaseP D0 D1 D2 D3 AREA LK LE K ES EDL COV EES COV D0/D1 D1/

D0Min. 17791 1.9 1.8 1.7 1.5 40 29 18 200 27118 0.5 5.1 0.3 1.9 0.99 0.70Max

. 64371 27.9 22.0 19.0 16.1 60 68 50 712 98315 13 30 10.7 34.5 1.42 1.01

Avg. 44382 6.4 5.5 4.9 4.4 51 45 31 446 71568 4.394 15 3.280 9 1.16 0.86COV

% 26 42 42 41 39 7 15 18 20 15 46 36 50 38 5 5

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Table 2 – Influence of Gear Configuration Parameters

(a) Effect of Dual Spacing, s (t=48 in.)

(b) Effect of Tandem Spacing, t (s=32.5 in.)

(c) Effect of Tandem Spacing, t (s=∞)

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Table 3 - Influence of Radius of Relative Stiffness, ℓe

(a) Variation of Slab Modulus, Ec

(b) Variation of Slab Thickness, h, Subgrade Modulus, Es, and Contact Area of Wheel, Aw

□

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