AASHO Road Test Principal Relationships- Performance with

AASHO Road Test Principal Relationships-Performance with Stress, Rigid Pavements

W. R. HUDSON' and F . H. SCRIVNER-Respectively, Assistant Chief, Rigid Pavement Branch, and Chief,

Rigid Pavement Branch, AASHO Road Test

This paper presents a summary of the strain measurements taken on the Portland cement concrete pavements at the AASHO Road Test. Stress conversions and analyses of these data are discussed. The edge stresses masured under routine traffic on the test loops and the critical stresses measured under a simulated load on the non-traffic loop are compared with the Road Test Performance Equations. Additional research and analyses are suggested.

The load stresses in the rigid pavements at the AASHO Road Test were highly correlated with performance. The critical load stresses measured under dynamic load on a special set of pavements provided the highest correlation with pavement performance. A different correlation exists for single-axle loads than for tandem-axle loads. This may be due to the location of critical load stresses under the tandem axles.

Further analysis of the Road Test basic performance data and stress data is definitely warranted. Such an analysis would allow summarization of the differences between performance predicted from stresses and observed performance. (The present analysis compares predicted performance with stress.)

Additional experiments should be initiated to study these stress-performance relationships for other concrete pavements having different materials and thus different physical properties.

• When the AASHO Road Test was originally conceived, it was decided to include so-called capability studies in the testing program. The importance of such studies in making comparisons with other pavements was recognized. In addition, it was desired that the Road Test facilities should be used to the fullest extent possible to expand knowledge of pavement behavior. The reasons for including strains and other measurements were, "to develop engineering facts and criteria for use in design and in the preservation or betterment of existing pavements and to evaluate the load carrying capabilities of existing highways," and also to "study physical properties of concrete m-place and the rate of deterioration of these properties under load-deflection in relation to fatigue."

The Road Test provided a chance to study pavement strains under moving loads that is unparalleled in engineering history . The AASHO Road Test contained a factorial experiment for Portland cement concrete pavements

'Presently, Senior Design Engineei, Texas Highway Department

'Presently, Research Engineei, Texas Transportation Institute.

(HRB Special Report 61E). This factorial was orthogonal within each loop and included variables for slab thickness, subbase thickness, and surface reinforcement. The load variable was studied across loops and lanes.

In addition to this main factorial, a small factorial was provided on Loop 1 for special study. No routine traffic was applied to this factorial since it was used only for special tests. With these factorials available, two major strain experiments were undertaken: the measurement of edge strains on the main factorial loops under routine traffic, and the measurement of surface strains in the corner area under a vibratory load induced by a heavy eccentric load device on Loop 1. These two experiments are referred to as the Main Loop Strain Experiment and the Loop 1 Strain Experiment, respectively. The complete details of the measurements programs involved in these experiments are reported in AASHO Road Test Report 5, Chapter 3 (HRB Special Report 61E).

The results of both of these strain experiments are compared with performance in an effort to obtain the true relationships of performance with stress and thus fulfill one of the objectives of the Road Test.

227

228 C O N F E R E N C E ON T H E AASHO ROAD T E S T

PERFORMANCE Several choices of performance data are

available for use in this study. The basic performance data f rom the Road Test, cracking which is the result of overstress, or the performance equations developed through analysis of Road Test data and reported previously could be used. Considering the vast amount of time spent in analyzing these data and obtaining the performance equations, i t was decided that the equations represented the best estimate available of the true performance of all the Road Test rigid pavements. (At such time as more refined analysis techniques are developed a complete re-analysis of basic strain data versus basic performance data can be performed i f this study appears to jus t i fy the additional work.) Specifically the number of axle applications predicted for each section to a PSI of 2.5 is used as a measure of pavement performance for the comparisons made in this paper. I t is issumed that these applications are distributed normally across the pavement lane and not that they all stress the pavement in the same way as the vehicles at the placements fixed for measurement.

MEASUREMENTS OF STRAIN A l l concrete strains were measured with

etched foi l strain gages (Fig. 1) manufactured for the Road Test by Baldwin-Lima-Hamilton Corporation. The gage, as received f rom the manufacturer, consisted of a thin plastic strip on which was etched a fo i l resistant element. The effective gage length was 6 in. and the nominal gage resistance was 750 ohms. When used in conjunction with the project's specially developed equipment, the sensitivity of the gages was about ± 1 jx in. per in. of strain. The gages were covered with a thin layer of epoxy and encapsulated in brass shim stock to protect them f rom weather and traffic (Fig. 2 ) . Before installing the gages, the concrete pavement surface was ground smooth and cleaned thoroughly wi th carbon tetrachloride, acetone, and soapy water. The cleaned surface was dried for 2 to 6 hours with infrared heat lamps. The encapsulated gages were cemented to the prepared pavement immediately with a strong, durable epoxy resin. The gages were then covered with a layer of oily wax and a heavy bees-

r p - r n f T p , T j i p j 11 l yn , | . ( r p f . | T p r | i p y q ^IJTJTJTJTJJJI

1

n 1 1

1 t, • 5"---

Figure 1. Strain gage as received from factory.

Figure 2. Strain gage being encapsulated in brass shim stock.

wax-consistency petroleum product. A l l gages were connected by shielded wires under the shoulder to a junction box at the outer edge of the shoulder. Recording equipment was plugged into these junction boxes whenever readings were desired.

In order to use the strain measurements to best advantage the gage readings were converted to principal strains, major and minor. These principal strains were converted to stresses by elastic theory. Appendix E of Special Report 61E gives the development and formulas. In these conversions Young's modulus (E) was taken equal to 6.25 X 10" psi, the dynamic modulus for concrete pavement at the Road Test. Poisson's ratio (fx) was taken as 0.28, the average "measured for the Road Test pavements.

LOOP ONE STRESSES

Strain Measurements Between October 9, 1959, and November 2,

1960, a series of eight experiments, designed to furnish information regarding the distribution of load stress in the surface of concrete slabs, was conducted on the sections comprising the experiment design (Table 1).

A rapidly oscillating load was applied to the pavement through two wooden pads on 6-ft centers, each approximately the loaded area of a typical dual-tire assembly used in Loop 4 (Fig. 3) . This dynamic loading was intended to simulate that of a typical single-axle vehicle used in the main loop experiments.

The vibrating loader was mounted on a truck (Fig. 4) . The essential parts were two adjustable weights rotating in opposite directions in a vertical plane in such a manner that all dynamic force components except those in a verti-

P A V E M E N T P E R F O R M A N C E 229

T A B L E 1

EXPERIMENT DESIGN FOR SPECIAL STUDIES OF LOAD STRESSES I N SURFACE OF CONCRETE SLABS

Number of Sections

Subbase 5.0-In. 9.5-In. 12.5-In. Thickness Slab' Slab' Slab'

(in.) (12,000^) (22,000^) (30,0002)

N R N R N R

0 2 1 1 2 2 1 6 2 1 1 2 2 1

' N = nonreinforced; R = reinforced. ' Nominal test load.

Loaded

Area

nsverse Joint

Figure 3. Numbered points show the several load positions used in special strain studies.

cal direction were balanced by equal and opposite components. The dead weight necessary to prevent the upward components f rom l i f t ing the truck f rom the pavement was pro

vided in the form of concrete blocks resting on a platform located directly above the rotating weights. The load was transmitted through inverted A-fi-ames which could be folded upward against the side of the vehicle when not in use. Contact with the pavement being loaded was solely through the wooden pads mentioned previously.

During each of the eight experiments (rounds), the simulated single-axle load was applied at three or more of the positions indicated in Figure 3. Data f rom round 7, taken in September 1960 during the early morning hours when panel corners were curled upward and the strains were among the highest observed, were selected for complete analysis and are presented in the Road Test i-eport and used herein. Other data are available in Road Test file, DS 5205.

Strains were measured by means of 33 electrical resistance strain gages installed as previously described. The gages were layed out over the corner 6 f t square area of the slab in each section (Figs. 5 and 6) .

The use of delta rosettes at the nine interior points permitted the computation of the magnitude and direction of the principal strains at those points. Only single, gages were required along the edge and transverse joint, i t being assumed that the strain perpendicular to the edge or joint could be calculated by use of Poisson's ratio for the concrete. No gages were required at the intersection of joint and edge as the strain there was assumed to be zero.

Load cells for measuring the vibratory loads were developed at the project and were calibrated on the project's electronic scales. A continuous record of loading was made while the strain gage output was being recorded.

In normal operation the load was varied sinusoidally wi th time, at a frequency of 6 cps, f rom a minimum value of about 500 lb on each contact area to a maximum value which depended upon the tliickness of the pavement being tested (Table 1). The measured strain

1 ^ '""""" • "t ic

4^ »

Figure 4. Truck-mounted vibrating loader ready to apply load to pavement.

230 C O N F E R E N C E ON T H E AASHO ROAD T E S T

A A

-Single Gage Rosette Goge

A A A

Dowelled Transverse J o i n f - ^ 2' 2' »)« 2'

6'

Figure 5. Typical gage layout, Loop 1 strain experiment.

Figure 6. Typical installation of strain gages for a section in the Loop 1 experiment.

also varied sinusoidally with time, very nearly in phase with the load, and of course, at the same frequency. From examination of simultaneous traces of the load wave and strain wave i t was possible to determine the amplitude of each as well as the nature (tension or compression) of the strain.

Field Procedures and Data Processing

Field Procedures.—Data were taken on the test sections in random order within the experiment. A l l load positions selected for a particular round were completed on a section before measurements were made on the next section.

P A V E M E N T P E R F O R M A N C E 231

6RID POINTS

DOWELLED T R A N S V E R S E JOINT

Figure 7. In analysis of Loop 1 strain data, measurements at gages (Fig. 5) were assumed to apply at

points shown.

With the load in one of the selected positions, the recording equipment was switched to each of the 33 pavement gages in succession. The output of each pavement gage was recorded on paper tape, along with the record from the load gages. The over-all time required to complete the measurements associated with one load position on one section, including the time required to set up the vibrating loader, was about 30 min, of which about 5 min were spent in recording the strains.

Data Processing.—The first requirement for each experiment was to derive by statistical techniques a pair of empirical equations for each load position, of the following general forms:

Major principal strain = a function of pavement design, load and the coordinates of the gage point. (1)

Minor principal strain = a function of pavement design, load and the coordinates of the gage point. (2)

The coordinate system used was that shown in Figure 7.

The second requirement was to compute from Eqs. 1 and 2 and the appropriate plane stress equations linking stress and strain—the estimated value of major and minor principal stresses at closely spaced points in the pavement surface within the 36 sq ft area of observation.

Examination of the data indicated that variations in the strain observed on sections at the same level of slab thickness but at different levels of reinforcing and/or subbase thickness were small and apparently random in nature. Therefore, within each round and for the same load position, the readings of gages with the same coordinates x and y installed on panels of the same slab thickness (irrespective of sub-base thickness and reinforcing) were averaged to obtain a set of data representing that round, load position and slab thickness combination.

Thus, for one load position within an experiment, the processing described above resulted in three sets of data corresponding to the three levels of slab thickness (5.0, 9.5 and 12.5 in.) with each set consisting of 33 averaged strain gage readings. As the third step in processing, each such set was converted from strain gage readings to magnitude and direction of major and minor principal strains at the 15 gage points on a panel employing standard techniques based on elastic theory (see Appendix E , HRB Special Report 61E).

As the fourth and final step prior to analysis each principal strain was divided by the corresponding load in accordance with experimental evidence that strain is directly proportional to load. Thus, as a result of the four-step processing of the data, the only remaining independent variables to be considered in the analysis of strain were the coordinates x and i/ of a gage point and the thickness, D,, of the slab.

Typical Stress Distributions Analysis of Strains.—The three sets of data

corresponding to each round and load position combination were analyzed using statistical procedures. The strain data were represented by a linear model whose 48 terms (3 slab thicknesses by 16 combinations of x and y) were mutually orthogonal polynomials in x, y, and Di. As a result of the elimination of reinforcing and subbase thickness as independent variables, there were six sections within each round, load position and slab thickness combination whose variation in strain furnished a measure of residual effects. The residual effects, in turn, were used to determine the statistical significance of each coefficient (DS 5211). Of the 48 original coefficients only those that were found to be significant at the 1 percent level were used in the calculations to be described.

Distribution of Principal Stresses.—As indicated, the analyses of data from load positions 1, 2, 3, and 4 of round 7 were selected for complete study. The analyses of these data resulted in four pairs of equations (one for each load position) like Eqs. 1 and 2. Principal strains predicted from these equations were converted to principal stresses in accordance with the formulas from elastic theory using values of Young's modulus and Poisson's ratio for the

232 CONFKRENCE ON T H E AASHO ROAD TEST

6 KIPS

0 10

DOWELLEO TRANSVERSE JOIN

- ,11.2 KIPS.. - , • -T -1

DOWELLEO TRANSVERSE JOINT

IS KIPS

DOWELLED TRANSVERSE JOINT 6

SLAB O THICKNESS u

W ft

9.5 INCHES

12 S INCHES

SKIPS

DOWELLED TRANSVERSE JOINT

II2KIPS

- - I 0 0

DOWELLED TRANSVERSE JOINT G

IS KIPS 15 KIPS

-120

DOWELLED TRANSVERSE JOINT S

MAJOR PRINCimL STRESS, psi MINOR PRINCIPAL STRESS, psi

Figure 8. Contours of major and minor principal stresses for the critical load position at each thickness level (Loop 1 experiment).

PAVEMENT PERFORMANCE 288

concrete as determined in the Road Test laboratory. The stresses so determined were used in plotting the contours of equal principal stress (Fig. 8). In these plots all stresses are recorded in pounds per square inch, with the usual sign convention—^tensile stresses positive, compressive stresses negative.

Critical Stresses.—Maximum values of tensile stresses and maximum values of compressive stresses for the edge load positions studied were taken from Figure 8 and listed in Table 2. Figure 8 shows the load position and the stress distribution when these critical stresses occurred.

In accordance with an assumption commonly made in the application of elastic theory to a slab resting on an elastic foundation, the stresses at points on a vertical line through the slab are equal but opposite in sign at the slab surfaces and exceed, in absolute value, the stress at any other point on the line. I f this assumption is made in the present instance, then each stress marked with an asterisk in Table 2 is equivalent, in absolute value, to the critical tensile stress for the indicated slab thickness and load position. These stresses occur along the pavement edge with the center of the outer loaded area at the distance of 1 ft from the edge and 4 to 6 ft from the nearest transverse joint.

An empirical equation fitted to the three pairs of values of D2 and critical stress given in Table 2 is the following:

I6OL1 (3)

where

?i = the critical stress as determined on Loop 1, in psi;

Li = a single-axle load, in kips; and Z>z = slab thickness, in in.

Eq. 3 predicts the three critical stresses denoted by asterisks in Table 2 with an error of

T A B L E 2

M A X I M U M T E N S I L E AND COMPRESSIVE S T R E S S E S PGR A 1-Kip S I N G L E - A X L E L O A D

(Data from Design 1, Loop 1, Lane 2)

Maximum Stress (psi)

Load Position

Tensile Compressive Load Position

5.0-In. Slab

9.5-In. 12.5-In. 5.0-In. 9.5-In. 12.5-In. Slab Slab Slab Slab Slab

1 2 3 4

12 47 9 39 8 58 6 94

4.21 2 63 3 78 1 61 1 12 3 27 2 05 17 97 7 41 4 71 2 85 1 38 18 82* 7 82 4 89 2 60 1 52 17 57 8 10* 5 57*

* Maximum for indicated slab thickness.

Figure 9. Maximum compressive stresses for a 1-kip single-axle load, outer wheel near edge of pavement.

less than 2 percent. Figure 9 is a graph of the equation. The critical load stress for any single-axle load, pavement-thickness combination, within the range observed, presumably may be estimated from Eq. 3. Additional stresses that may be present as the result of temperature or moisture fluctuations, of course, are not included in the stress estimated from this curve or from the contours in Figure 8. It is also probable that stresses arising from static loads would be greater than those estimated from the strains measured in this study.

Performance vs Loop 1 Stress It was assumed at this point that the stresses

calculated using Eq. 3 are representative of the critical stresses which were induced in the main factorial test sections by the test loads. Several studies were performed on the main loop pavements where the strains induced by the normal test load were found to be substantially equal to the strains induced by the vibration load of the same magnitude (Fig. 10).

The concrete pavement in Loop 1 was constructed at the same time as that in the main loops and out of the same materials. It is likely that it would also perform the same within the limits of error of the Road Test performance equations.

With these facts in mind, it seems logical that the Loop 1 critical stresses can be assumed to be representative of the critical stresses induced in the main factorial pavements by the respective test loads.

The critical stresses computed from Eq. 8 are given in Table 3 for the various combinations of surface thickness and load which reached a serviceability level oi p = 2.5 during the life of the Road Test or whose performance could be extrapolated reasonably from the Road Test equation. The calculated number of applications of the test load required for each sec-

234 CONFERENCE ON T H E AASHO ROAD TEST

S30

P t r f t e t C Ltnt .

orrt lotion

y •

•

•

Each poinl 0(10 pove reprasentt monl

10 ta 30 strain Mloiurad Undar Normgl 30^ Singia A>l« Lsod

Figure 10. Correlation of strains under normal loads at 30 mph and under vibrator loads at 6 cps.

T A B L E 3

D A T A U S E D I N L O O P 1 STRBSS-PE!BPOKMANCB STUDY

Axle Load, L .

(kips)

Slab Thickness,

(in.)

Axle Load Applications,*

(lOOO's)

Loop 1 Stress,

(psi)

6 2 5 777 283 12 3 5 303 362 12 5 0 2,054 225 12 6 5 • 9,421 158 18 3 5 65 542 18 5 0 425 337 18 6.5 1,847 237 22 4 5 0 170 419 22.4 6 5 786 295 22 4 8 0 2,584 224 30 5 0 47 561 30 6 5 236 396 30 8 0 811 300 30 9 5 2,218 239

* From equations in Section 3.2.2.1, H R B Special Report 61E.

tion to reach a serviceability of 2.5 is also given.

A regression analysis was made in order to correlate these data (Fig. 11).

10^ (4)

3,000|

2,000

T> 1,000 N » io

CM

800

600

400

80

i o ' " °

r 2=0 996

std dev004Z

Critical Stress, Loop I Pavements - p s i ( 0 ; )

= 0.996; std. dev. of log , = 0.042

Figure 11. Relationship of performance to Loop 1 critical stress equation.

in which

W^is = predicted number of applications toi a serviceability of 2.5.

= critical stress as predicted for Loop 1 in psi.

= correlation coefficient. Eqs. 3 and 4 are correlated extremely well. The total errors involved in predicting performance from stress, however, must also include those errors for the original equations as described in HRB Special Report 61E.

MAIN LOOP S T R E S S E S

Measurement of Strains During the life of the project 13 rounds of

main loop strain data were gathered. A "round" consisted of one set of measurements on the selected factorial experiment (Fig. 12). A given section was not visited again until all sections had been tested. Successive rounds were numbered consecutively. Some rounds were incomplete due to weather and were omitted from consideration. These strain measurements were made during an 8-hr workshift which always occurred during a regular driving schedule. The vehicle normally assigned to a given lane was used as the test load for that


RIGID PAVEMENT MAIN LOOP E X P E R I M E N T

2.5 3.5 5.0 6.5 8.0 9.5 II.O 12.5

% \ R N R N R N R N R N R N R N R N

12'^ S 3 X X 0 X X 0 X X

12'^ S 6 X X X 0 0 X X X 3

12'^ S 9 X X X X X X X X

u 3 X X 0 X X 0 X X 6 X X X 0 0 X X X 9 X X X X X X X X 3 X X 0 X X 0 X X 6 X X X 0 0 X X X

4 9 X X X X X X X X

4 If 3 X X 0 X X 0 X X 32 T 6 X X X 0 0 X X X

9 X X X X X X X X If 3 X X 0 X X 0 X X

224^5 6 X X X 0 0 X X X 9 X X X X X X X X 3 X X 0 X X 0 X X 6 X X X 0 0 X X X 9 X X X X X X X X 3 X X 0 X X 0 X X

30" S 6 X X X e 0 X X X

6 9 X X X X X X X X

6 l( 3 X X • X X 0 X X 6 X X X • • X X X 9 X X X X X X X X

X Denotes a Test Section • Denotes Replicate (2) Test Sections

Figure 12.

lane. The 8-hour work shifts were changed every round so that three rounds of measurements provided data from all times of day or night.

In this way, normal variation due to temperature could be studied and the average strains occurring at the point of measurement could be estimated.

No data from cracked slabs were included in the major study. Inspections were made to insure the uncracked condition of the slabs being tested throughout the life of the project. When a crack occurred in the slab selected for measurement, a new slab was chosen and the gages were relaid. When all slabs in a section cracked or a section was removed from the test, no further measurements were made on that section.

Installation of Gages Gages were installed at the outer edge of the

pavement on both sides of the center joint in a section (Fig. 13). Gages on 15-ft panels (nonreinforced sections) were placed at the center of the panel 7.5 ft from the joint. Gages on the 40-ft panels (reinforced sections) were placed 10 ft from the joint.

The manufacture and protection of the gages has previously been discussed.

Field Procedures A special trailer van (Fig. 14), equipped with

a large gasoline-powered generator, carried the electronic equipment necessary to energize the strain gages and to record their output continuously on paper tape as the test vehicle passed by. The trailer also carried special devices for maintaining the calibration of the equipment as well as an indicator for measuring the transverse placement of the test vehicle.

Dynamic measurements were accepted or rejected by the measurements crew on the basis of the transverse position of the outer dual wheel of the rear axle as it passed over the transverse joints separating the instrumented slabs. If the centroid of this wheel was 20 in. (—3 in. to +2 in.) from the pavement edge, the measurements were accepted; otherwise, they were rejected. (This biased tolerance was selected as the result of special studies of the distribution of the placement of vehicles whose operators were attempting to drive at the specified distance of 20 in. from edge.) The crew remained at each test section until at least three vehicles had succeeded in passing at the specified distance. The minimum of three measurements on each of two strain gages were averaged to obtain the section strain to be used in the analysis.


-<E. OF W E M E N T -

3 C D C

D C

' T R A N S V E R S E JOINT AT C E N T E R OF T E S T SECTION

INSTRUMENTS FOR DYNAMIC D E F L E C T I O N S

STRAW GAGE

UNDERGROUND C A B L E S

JUNCTION BOX

( • • w =1 1 K )

7X STRAIN GAGE

EDGE OF RWEMENT-

10'

EDGE OF SHOULDER-

ENLARGED VIEW OF STRAIN S A G E A S S E M B L Y

6" STRAIN G A G E -

-.001" B R A S S FOIL E N V E L O P E

Figure 13. Location of gages for main loop experiment.

- E D G E OF PAVEMENT

Figure 14. Instrument van to record strain readings.

Analysis of Data—Main Loops In early studies i t became apparent that sev

eral variables should be isolated in order to simplify the study of strain data. Two of these variables were load and temperature.

Load Effects.—Several load-strain studies conducted early in the Road Test indicated that for a given pavement at a given time strain varies linearly with load. This was substantiated many times. As a result of these studies the general mathematical model adopted for strains was:

Strain Axle Load

/ (design and other variables) (5)

Temperature Effects.—Strain measurements are affected by temperature. This was amply demonstrated early in the test. In order to isolate this variable several 24-hr studies were made during the spring and fal l seasons to take advantage of daily variation in ambient temperature. Numerous investigations of the data

(strains, air temperatures and internal slab temperature) indicated that a consistent variable for study was the temperature differential, top to bottom of a 6.5-in. thick PCC slab. These analyses led to the following model for best f i t .

Strain Axle Load

/ (design and random variables) ^ -^Qf (slab temp) (g)

General Strain Equation Dynamic edge strain data f rom rounds 4, 5,

8, and 9 (Table 4) gathered between Apr i l and August 1959 were selected for use in determining the most representative empirical relationship between edge strain, design, load and temperature. These rounds cover spring, summer and fa l l seasons when a large majority of the sections were still in good condition.

Plots of the data and preliminary analyses along with the load and temperature studies were helpful in selection of a model. The final analysis indicated that the design variables, re-


T A B L E 4

S C H E D U L E OP R O U T I N E DYNAMIC E D G E STRAIN AND DYNAMIC C O R N E R D E F L E C T I O N M E A S U R E M E N T S IN LOOPS 2 T H R O U G H 6

E X P E R I M E N T D E S I G N 1 (Data available in DS 5250)

Measurement Round Number

Mid-Date of Observation Period

Hours

From To Loops

Stram and deflection 1 Oct. 25 , 1958 1000 2400 2, 3, 4, 5, 6 Strain, ground frozen 2 Jan. 6, 1959 0700 2300 2, 3 , 4, 5, 6 Strain 4 Apr. 14, 1959 0900 2300 2, 3 , 4, 5, 6 Stram 5 May 16, 1959 1100 2300 2, 3, 4, 5, 6 Stram and deflection 6 June 6, 1959 2300 0600 2', 3 S 4', 5', 6 ' Strain and deflection 7 June 23, 1959 2300 0500 2S 3S 4', 5S 6' Stram 8 July 13, 1959 1100 2000 2, 3 , 4, 5, 6 Strain and deflection 9 Aug. 2 , 1959 2300 0600 2, 3», 4, 5, 6 Stram 10 Sept. 9, 1959 2300 0600 2 , Z\ 4, 5, 6 Strain 11 Oct. 1 3 , 1 9 5 9 2200 0600 2, 3», 4^ 5, 6 Strain 12 Nov. 18, 1959 2200 0500 31' 2 4.1.2 6 ' Strain 13 Dec. 4 , 1 9 5 9 2300 0400 31- 2 A.1'1 1 ^ 1 5» Strain 14 Dec. 14, 1959 2300 0500 5S 62

1 Only sections on 6-in. subbase were tested. ' Thinnest level not tested.

inforcing and subbase thickness, were not significant. The following equations resulted:

Tandem-axle loads:

Single-axle loads: B 20.54

L i 10" "o '' Tandem-axle loads:

3.814 J^^ IQO 00351- J)^0 8523

(7)

(8)

i in which: e = estimated edge strain at the surface of

the concrete slab; L i = nominal axle load of the test vehicle (a

single-axle or a tandem-axle set) ; Di = nominal thickness of the concrete slabs; T = the temperature (°F) at a point 14 in.

below the top surface of the 6.5-in. slab minus the temperature at a point V2 in. above the bottom surface, determined at the time the strain was measured (the statistic T may be referred to occasionally as the "the standard differential").

Residuals from the analyses that are less than the average root mean square residual determined in the two analyses correspond to observations that range from 83 to 120 percent of the predicted values.

Using the theory of elasticity given in Appendix E , Special Report 61E, Eqs. 7 and 8 were converted to the following stress equations.

Single-axle loads: I39.2L1

(9)

25.86L1 (10)

0 0 3 5 r J)^0 8523

in which aa = predicted stress under single-axle load. ffc = predicted stress under tandem-axle load.

Comparison of Loop 1 and Main Loop Stresses Setting T equal to zero for single-axle loads

the equation becomes:

I39.2L1 jrj 1 278

(11)

Eq. 11 gives stresses nearly equal in value to those computed from the Loop 1 critical stress equation (Eq. 3) as shown in Figure 15. When D is 11 or 12.5 in., the stresses are numerically equal. The differences between these two equations could be due to one or more of the following reasons, among others:

1. 5i are critical stresses and their location varies with slab thickness, whereas ffo is calculated for a fixed edge location.

2. The loads used to induce ff, were applied through a wooden contact area of fixed size. S„ were induced by normal tires and in general the contact area increased with slab thickness.

3. Both ffi and 5„ occurred near the pavement edge, however, the centroid of the loaded area was slightly closer to the location of ?i than to the location of 5a.

This close agreement between the stress equations supports the validity of using the Loop 1 equation in a performance study.


10

Mam Loop StrosMt Loop 1 Stressas Mam Loop StrosMt Loop 1 Stressas

\ \ \ \

\ \ \

<

N \ s \ \> S

VS. \ \

\ \

K

Figure 15. Comparison of main loop and Loop 1 stress equations.

Stresses-Performance In order to compare the stress-performance

relationship for single-axle loads with that of tandem-axle loads, two regression analyses of the type described in connection with Loop 1 data were performed on the data from the main loops. The data for these correlations are given in Tables 5 and 6, respectively.

Single-axle loads: 10

(12)

= 0.990; std. dev. of log W,, = 0.051

Tandem-axle loads:

(13)

r' = 0.85; std. dev. of log W2 5 = 0.25

A further study of the tandem-axle data indicates that for a given axle load the correlation coefficient is much greater than the 0.85 for all loads. Table 7 shows the correlations for the four loads involved in the Road Test. The coefficients vary with axle load. This indicates that additional study of the load effect would be helpful in improving the over-all correlation.

Figure 16 shows the comparison of Eqs. 12 and 13. The correlations for each of these equations is good. The standard deviations are acceptably low. The total residuals involved in this analysis however include the residuals for the performance equation also. A study of

T A B L E 5

D A T A U S E D I N S I N G L E - A X L E M A I N L O O P S T R E S S vs PERFORMANCE STUDY

Axle Load, L l

(kips)

Slab Thickness,

D2 (m.)


W2 6

Main Loop Stress,

a

6 2 5 777 259 12 3 5 303 337 12 5 0 2,054 214 12 6 5 9,421 153 18 3 5 55 505 18 5 0 425 321 18 6 5 1,847 229 22 4 3 5 21 629 22 4 5 0 170 399 22 4 6 5 786 285 22 4 8 0 2,584 219 30 5 0 47 534 30 6 5 236 382 30 8 0 811 293 30 9 5 2,218 235


T A B L E 6

D A T A U S E D IN T A N D E M - A X L E M A I N L O O P S T R E S S vs PERFORMANCE STUDY

Tandem-Axle Load,

L I (kips)

Slab Thickness,

L>2 (in.)


W2 6 Stress,

24 3 5 124 213 24 5 0 918 158 24 '6 5 2,965 126 32 3 5 36 285 32 5 0 289 210 32 6 5 1,293 168 32 8 0 4,302 141 40 5 0 112 263 40 6 5 537 210 40 8 0 1,778 176 40 9 5 4,976 152 48 6 5 252 252 48 8 0 869 211 48 9 5 2,375 182 48 11.0 5,861 161


T A B L E 7

SUMMARY OF T A N D E M - A X L E STRESS-PERFORMANCE CORRELATIONS, B Y L O A D

Tandem-Axle Load

(kips) Std. Dev.

24 20 48 6 61 0 999 0 0098 32 21 21 6 78 1 00 0 0063 40 21 78 6 92 1 00 0 0085 48 22 36 7 07 1 00 0 0094

Avg. 21 46 6 85 1 00 0 0085

PAVEMENT PERFORMANCE 239 3 0 0 0

2 0 0 0

in Clj II a.

8 Q.

1000

8 0 0

6 0 0

5 0 0

4 0 0

3 0 0

2 0 0

a a. <

100

8 0

6 0

SO

4 0

3 0

roo

\ " \ • • \ \ *

X \

Single

V

Axle Stress

, . 1 0 ' "

Equation 2

34 \ *

X \ = 9 9 0

std dev ' 051

\ *

X \

X \ X \

\ * V

\ X

x \

\ * \ •

X \

\ ^

Tandem A xle Stress Equal i n Z ' « 6

ion \ r*= 85

std d e v ' 0 28

\ r*= 85

std d e v ' 0 28 X \ \ \ \ ISO 2 0 0 3 0 0 4 0 0 SOO 6 0 0 7 0 0

Compressive Edge Stress-psi(d')

Figure 16. Relationship of performance to main loop compressive edge stress equation.

these curves shows a wide difference in number of applications of a given stress level to failure depending on whether it is measured under a single- or tandem-axle load. This indicates that the compressive stress at the pavement edge may not provide a good absolute measure of pavement performance. Probably the location of the edge strain as measured is not near the critical strain for tandems as it was shown to be for single axles. Unfortunately it was not possible to conduct measurements on Loop 1 with simulated tandem-axle loads. Such studies might have shown the location of the critical strain and provided a better basis for correlation.

Since such data are not available, a cursory

examination was made of the maximum tensile strains recorded on the main loops under both single- and tandem-axle loads. These maximum tensile strains occurred when the drive axle was past the gage and the trailer axle was approaching the gage in all cases. Therefore, single and tandem axles might be expected to have the same general correlation. These data are scattered but a future more comprehensive study seems warranted.

It may also be possible to study this effect by the principle of superposition using two different load positions separated by the distance between normal tandem axles. Such a study was started at the Road Test. The work is available in the DS 5200-5211 series of files.


T A B L E 8

D A T A U S E D I N M A I N L O O P S I N G L E - R O U N D S T R E S S vs PERFORMANCE STUDY

Axle Load, L ,

(kips)

Slab Thickness,

(in.)


Avg. Stress Round 4,

12 3 5 303 353 12 5 0 2 , 0 5 4 231 12 6 5 9 , 4 2 1 183

18 5 0 425 332 18 6 5 1 ,847 251 18 8 0 6 ,316 190 22 4 6 5 786 285 22 4 8 0 2 , 5 4 8 224 22 4 9 5 7 , 4 3 7 190

30 8 0 811 305 30 9 5 2 , 2 1 8 244 30 11 0 5 , 4 8 4 203

* From equations in Section 3.2.2.1, H R B Special Report 6 1 E .

Average Stress and Performance A complete stress analysis such as that used

in the main correlations shown herein is not normally available to the engineer. An effort has therefore been made to correlate performance with stress calculations from one round of strain data (cFJ) . was obtained by converting the round 4 strain data to stress in the usual way. Such data could be considered to be equivalent to measurements obtainable on an average in-service highway by installing 2 to 4 strain gages and taking several readings on each gage in one day. As such, this correlation may be the most useful stress equation developed as far as making actual pavement performance predictions is concerned.

The data for this correlation are given in Table 8. The resulting equation is shown in Figure 17.

1 niS 27

r= = 0.985; std. dev. of log 5 = 0.58

These statistics are more nearly a measure of the error than for the correlations involving the stress equations because the actual strain data were used in lieu of an equation. The error associated with the performance equation, however, must still be included as part of the over-all correlation error.

DISCUSSION AND SUMMARY

Discussion of Results The stress-performance analyses reported

here are all basically well correlated. The best statistical fit involves the Loop 1 stress equation (ffi). This is to be expected since this was

5,000

0 9 8 5

Std d e v o o s a 4,000

3,000

2.000

1.000

ISO 200 300 _ ABO Average Compresstve Edge Stress-psitObI

Figure 17. Relationship of performance to main loop average compressive edge stress.

the most comprehensive stress study made at the Road Test.

Theory says that stresses in concrete slabs are influenced by many variables, including load, thickness, support, modulus of elasticity, Poisson's ratio and the contact area of the applied load. Excluding load and thickness, the other factors listed were held constant for the Road Test pavements (Tables 9 and 10), within the limits of measurement error. With these other factors held constant the stresses obtained from strain measurements for the study pavement proved to be reasonably good predictors of the performance which these pavements ultimately gave.

It is not known whether these same relationships between stress and performance would hold if the variations in stress were due to factors other than load or slab thickness, presumably they would. However, the factors and interactions involved in such a determination are so complicated as to require additional experimental evidence. Additional dynamic load-stress experiments are desirable in which several of the physical constants for the test pavements may be varied for study. The studies at the Road Test indicate that the vibratory loading device does an excellent job of simulating strains due to actual dynamic truck loading. This type of loading device would facilitate making these studies at a reasonable cost.

Information concerning critical load stresses under various axle configurations would be very helpful. This study indicates that edge stresses alone are not adequate to predict the performance of pavements since the stress-performance equations are different for single


T A B L E 9

CHARACTERISTICS OP P C C M A T E R I A L S

Design Characteristics 5-In. Pvt., 2J^-and3J^-Design Characteristics Greater In. Pvt.

Cement content', bags/cu yd 6 0 6 0 Water-cement ratio, gal/bag 4 8 4 9 Volume of sand, % total

agg. vol. 32 1 34 1 Air content, percent 3-6 3-6 Slump, in. Maximum aggregate slze^ in. Compressive strength, (psi): Maximum aggregate slze^ in. Compressive strength, (psi):

14 days 4,000 4,000 1 year 5,600 6,000

Flexural strength, (psi): 14 days 640 670 1 year 790 880

Static modulus of elasticity (10« psi) 5 25 5 25

Dynamic modulus of elasticity (10« psi) 6 25 5 87

' Type I cement. ' Uncrushed natural gravel.

T A B L E 10

CHARACTERISTICS OP S U B B A S E M A T E R I A L S

Aggregate gradation, % passing: I J ^ inch sieve 1 inch sieve % inch sieve J i inch sieve No. 4 sieve No. 40 sieve No. 200 sieve

PI , minus No. 40 material Max. dry density, pcf Field density, as percent compaction

100 100 96 90 71 25

7 N.P. 138 102

and tandem axles. Additional information concerning the type of loading would be necessary. This difference exists on any pavement serving mixed traffic and must be considered in any prediction for such pavements.

Summary 1. The load stresses in the Road Test rigid

pavement as indicated by strain measurements are excellent predictors of the performance which can be expected from these same pavements. The development of stress performance relationships for pavements with many combinations of physical variables or a general equation applicable regardless of the values of physical variables would be useful in evaluating existing pavements. Such an equation would also provide valuable information for continued design studies.

2. Additional experimentation is desirable to determine the location of critical load stresses for tandem-axle loading. Such studies would be useful in resolving the differences between the stress-performance equations under single and tandem axles.

3. A study of stress distributions under a range of normal traffic placement would be useful in completing the picture of stress-performance relationships.

4. It is desirable to continue efforts to study strains (and thus stresses) on the bottom of the slab since these appear to be critical. This could verify the assumption that a stress in the upper surface of a slab is opposed by stress of equal magnitude and opposite sign at the lower surface of the slab on the same vertical axis.

5. Continued study of tensile stresses from Road Test data is indicated.

Documents

AASHO Road Test Principal Relationships- Performance with