Cumulative Fatigue Damage Analysis of Concrete Pevement

1

CUMULATIVE FATIGUE DAMAGE ANALYSIS OF CONCRETE PAVEMENT USING ACCELERATED PAVEMENT TESTING RESULTS

SHREENATH RAO – UNIVERSITY OF ILLINOIS, URBANA-CHAMPAIGN

205 N. MATHEWS AVE., URBANA, IL 61801 PHONE: (314)772-1731 EMAIL: [email protected]

JEFFERY R. ROESLER - UNIVERSITY OF ILLINOIS, URBANA-CHAMPAIGN

205 N. MATHEWS AVE., URBANA, IL 61801 PHONE: (217)265-0218, FAX: (217)333-1924

EMAIL: [email protected]

ABSTRACT Mechanistic-empirical design procedures for concrete pavements use a cumulative damage analysis process to predict fatigue cracking in slabs. Application of traffic load results in fatigue damage, which is calculated as the ratio of actual number of load applications to allowable number of load applications for a given set of conditions. According to Miner's hypothesis, concrete should fracture when the cumulated fatigue damage equals unity. In mechanistic-empirical design procedures, this value corresponds to 50 percent chance of fatigue failure (50 percent cracked slabs).

The goal of this paper is to use Accelerated Pavement Testing (APT) of field slabs in order to examine Miner’s hypothesis along with various fatigue damage models for concrete pavements. Several test sections in Palmdale, California, consisting of combinations of joint spacings, shoulder type, dowelled joints, and widened lanes, were constructed and evaluated using the Heavy Vehicle Simulator (HVS). These instrumented slabs were loaded with dual wheel and aircraft wheel loads ranging from 40 kN (9,000 lb) to 150 kN (33,750 lb) with no wander, and were monitored past the concrete fatigue failure. Results indicate test slabs cracked at cumulative damage levels significantly different from unity for all fatigue damage models, and in most cases, by several orders of magnitude. The use of Miner’s hypothesis to characterize the cumulative fatigue damage in the concrete, did not accurately predict the fatigue failure of the concrete slabs. As such, alternative methods for incremental failure prediction should be explored.

Key Words: concrete pavement, accelerated load test, cumulative fatigue damage, Miner’s hypothesis

Cumulative Fatigue Damage Analysis of Concrete Pavement Using Accelerated Testing Results 2

INTRODUCTION

Fatigue cracking in concrete pavements is a key failure mechanism, and is the result of repeated applications of load at stress levels less than the flexural strength of the concrete slab (1). Under environmental loading conditions (no traffic loading), the magnitude and sign (tension versus compression) of the slab stresses change with the horizontal and vertical location in the slab, resulting in a stress field that depends on the following factors:

• Climatic conditions – temperature and moisture gradients in the slab • Built-in curl – effective built-in temperature difference (EBITD) resulting from a combination of built-in

temperature gradients and irreversible moisture gradients • Slab dimensions – length, width, and thickness • Layer properties – elastic modulus, Poisson’s ratio, unit weight, coefficient of thermal expansion, bond

between layers, etc. • Subgrade support – modulus of subgrade reaction • Other factors – adjacent slab properties, shoulder type and properties, load transfer, etc.

With the application of a moving traffic load, the new stress field is a function of the load location(s),

magnitude(s), contact pressure(s), and axle type configuration, in addition to all of the above factors. The removal of the traffic load resets the slab stresses back to their latent or residual state. The effect of these stress changes at any particular slab location is damage or microcracking in that portion of the concrete slab. After repeated load applications, damage (or more accurately, microcracks) accumulates and propagates in the concrete. The crack eventually extends and propagates to the surface (or to the bottom), resulting in transverse cracks, longitudinal cracks, and/or corner breaks.

Mechanistic-empirical design procedures (2,3,4) use cumulative damage at locations of critical stress to assess probability of slab cracking and failure. Since slab stress states change depending on the conditions and factors listed above, a means of combining the damage over time and slab position is needed for structural analysis and design. The fatigue damage concept, published by Miner (5), has been widely used for this purpose in pavement design and evaluation. Miner's fatigue damage accumulation hypothesis, which assumes that damage accumulates linearly is empirically based and is given as follows:

∑=i

i

NnDamageFatigue (1)

where, ni = Number of actual load applications under conditions represented by i. Ni = Number of allowable load applications until failure under conditions represented by i.

Miner’s hypothesis allows the summation of fatigue damage from loads of varying magnitudes and under a multitude of environmental conditions. According to Miner's hypothesis, materials should fracture when the fatigue damage equals 1, although under a calibrated system with reliability, this damage sum does not necessarily have to be unity (6).

There is widespread acceptance of Miner’s Hypothesis in pavement engineering for thickness design and failure analysis. Throughout the use of cumulative damage theory for concrete fatigue, researchers have found that the linear summation of damage is not necessarily valid, especially for variable amplitude loading conducted in the laboratory (7-12). The application of cumulative damage theory coupled with field calibration has given reasonable thickness design solutions for highway and airfield concrete pavements. However, the calibration phase tends to force the damage sum to match the observed cracking levels, and does not adequately explain the progressive failure of the concrete pavement. With the calibration procedure currently used, the fatigue transfer function chosen has a limited effect on the results.

The application of Miner’s Hypothesis for predicting concrete pavement fatigue failure is widely accepted as a valid approach, even though substantiation of the validity of Miner’s Hypothesis under full-scale, field-testing of concrete pavements has not been found in the literature. This paper will analyze the failure of full-scale, field concrete pavement sections using Miner’s Hypothesis for known wheel loadings, climatic conditions, and pavement material properties. Miner’s Hypothesis must work under the controlled loading and environmental conditions if it is to be extrapolated with confidence to cases where there is more uncertainty in the design inputs.


BACKGROUND

Stress Ratio

The stress ratio experienced by a concrete pavement has been related to the logarithm of the number of load applications required to produce fatigue-related failure, where the stress ratio, SR, is the ratio of the total tensile bending stress experienced by the concrete slab, to the concrete modulus of rupture.

MR

SR σ= (2)

where, σ = Total tensile stress due to traffic and environmental load at critical location. MR = Modulus of rupture (PCC strength).

The concrete modulus of rupture is typically obtained from the third-point loading configuration of beams, after 28 days of curing. Roesler (1) observed that the flexural strength of concrete is different if tested in a beam configuration versus a slab configuration, by as much as 30 percent. More recently, Roesler et al. (13) and Littleton (14) have found that the ratio of the slab flexural strength to beam flexural strength depends on the slab geometric properties, material properties, support conditions, and boundary conditions, and that the slab flexural strength can be twice as high as the beam flexural strength.

Fatigue Models

Several fatigue curves for concrete pavement have been developed using field and laboratory data that relate the stress ratio to the number of loads until failure. These include:

• Zero-Maintenance Design Beam Fatigue Model (15,16) ― Developed using concrete beams, with failure defined as complete beam fracture. Load stresses were calculated at the bottom of the beam using the bending beam equation.

log N = 17.61 – 17.61 SR (3)

where, N = Number of stress applications to failure for the given stress ratio SR.

• Calibrated Mechanistic Design Field Fatigue Model (17) ― Developed using Corp of Engineers (COE) field aircraft data and American Association of State Highway Officials (AASHO) Road Test data, with failure defined as 50 percent slab cracking. Load and temperature curling stresses were calculated at the slab edge using the finite element program, ILLI-SLAB.

2276.0367.5

0032.0)P1log(SRNlog

−−=−

(4)

where, P = Cracking probability.

• ERES/COE Field Fatigue Model (18) ― Developed using Corp of Engineers (COE) field aircraft data, with failure defined as 50 percent slab cracking. Load stresses were calculated at the slab edge using the influence chart software, H-51, and reduced by a factor of 0.75 to account for load transfer and support conditions.


log N = 2.13 SR-1.2 (5)

• Foxworthy Field Fatigue Model (19) ― Developed using Corp of Engineers (COE) field aircraft data, with failure defined as 50 percent slab cracking. Load stresses were calculated at the slab edge using the finite element program, ILLI-SLAB.

588.01323.1log +

=

SRN (6)

• PCA Beam Fatigue Model (20) ― Developed using concrete beams, with failure defined as complete beam fracture. Load stresses were calculated at the bottom of the beam using the bending beam equation.

log N = 11.737 - 12.077 SR for SR ≥ 0.55 (7)

268.3

4325.0SR2577.4N

−= for 0.45 < SR < 0.55 (8)

N = unlimited for SR ≤ 0.45 (9)

FIELD PROJECT

As part of the California Department of Transportation's (CALTRANS) Long Life Pavement Rehabilitation Strategies (LLPRS), a high early-strength hydraulic cement concrete pavement section was field-tested using the Heavy Vehicle Simulator, illustrated in Figure 1 (21). This fast-setting hydraulic cement concrete (FSHCC) was designed to gain enough strength to allow it to be opened to traffic within 4 hours of placement. The objective of the HVS tests was to evaluate the performance of this concrete under the combined effect of environmental and accelerated traffic loading.

Two 210 m (700 ft) FSHCC pavement strips, one on the North Tangent and another on the South Tangent, were constructed on State Route 14 about 8 km (5 mi) south of Palmdale, California. The North Tangent sections had 200 mm (8 in) nominal thickness concrete over 100 mm (4 in) nominal thickness cement-treated base, with various design considerations (no dowels + asphalt concrete shoulders, dowels + PCC shoulders, dowels + widened lanes). Design details of these sections are outlined in Roesler et al. (22) and in du Plessis (23).

Prior to fatigue testing, the North Tangent slabs were monitored over a 24-hour cycle without any applied load, and over a 24-hour cycle under a slow-moving 40-kN (9,000-lb) dual-wheel rolling load. These sections were also loaded from 20 kN (4,500 lb) to 80 kN (18,000 lb), in increments of 10 kN (2,250 lb) using the HVS dual-wheel rolling load. This data was used in a recent paper by Rao and Roesler (24) to estimate the effective built-in temperature difference (EBITD) in the slab for each of the test sections.

Fatigue testing data collected at two-hour intervals included visual distress surveys, vertical temperature profiles measured using thermocouples, midslab edge and corner surface deflections measured using Joint Deflection Measuring Devices (JDMDs), and vertical deflections (interior slab location) at multiple depths of the pavement structure measured using Multi-Depth Deflectometers (MDDs). Type K thermocouples were taped and spaced on wooden dowels at 0, 100 mm (4 in), and 200 mm (8 in), in order to measure the temperature profile in the concrete slab. Thermocouple stacks were placed at the four locations on each test section: in the sun, in the shade, in the temperature control box, and near the traffic barrier. The JDMDs and MDDs consisted of Linear Variable Displacement Transducers (LVDTs), and were used to measure vertical displacements under combined rolling wheel and temperature loadings. A typical instrumentation layout along with an illustration of the plan view of the HVS on a test section is shown in Figure 2. Details of the data acquisition system and instrumentation of each section are included in Roesler et al. (22), du Plessis (23), and du Plessis et al. (25).

The loads were applied through a dual or aircraft wheel configuration at low speeds (6 mi/hr [10 km/hr]), and without any wander. A brief summary of the sections used in the analysis, along with the estimated left and right slab corner EBITD, is shown in Table 1 (18). Since curling of a concrete slab in the field is restrained by many factors such as the slab’s self-weight, load transfer with adjacent slabs and shoulder, and non-uniform friction


between the base layer and concrete slab, this restraint can vary from one location of the slab to another, resulting in asymmetric curling of the slab, as seen in Table 1.

DATA ANALYSIS

Influence Charts

A finite element program, ISLAB2000 (26), was used to compute slab responses due to the combined effects of traffic and environmental loading. For each test section, stresses were computed at multiple slab locations for a range of effective linear temperature differences. The HVS moving load was modeled every 150 mm (6 in) along the length of the slab. This is illustrated in Figures 3 and 4, which show the influence chart for a moving HVS load applied at the edge of the slab for the undowelled section 535FD, and the dowelled widened lane section 540FD. An influence chart is a graphic representation of a response (in this case, stress) at a fixed point, due to placement of a static load at several different points on a straight line, thus simulating the effect of a moving load. Both figures show stress reversals from tension to compression and back to tension, for critical locations at the lane-shoulder joint. The critical location at the transverse joint is always in tension with the peak stress occurring when the load is at the slab corner.

For each test section, influence charts were developed for several slab locations along the transverse joint edge and the longitudinal lane-shoulder joint edge, for a range of total effective linear temperature differences. The results of the influence chart analysis for two critical locations on section 535FD using a 90kN (20,250lb) dual-wheel load are summarized in Tables 2 and 3. The differences between the two tables show the contrasting effect on stresses on a transverse joint versus stresses on a longitudinal free edge resulting from a moving dual-wheel load.

Concrete Strength

The North Tangent sections were constructed between 6/16/1998 and 6/18/1998. The FSHCC used for the Palmdale test site construction was an 80/20 blend of Ultimax® to PCC. Two of these trucks were selected at random to cast beams for 8 hour, 7-day, and 90-day flexural strength tests. The details of the flexural strength analysis for all of the sections are included in Roesler et al. (21). Strength tests were also performed on slabs 575 days after construction. The average strength gain chart for the FSHCC is shown in Figure 5. The FSHCC gained strength rapidly with very little change in strength after 90-days. The North Tangent sections 535FD to 541FD were tested between 03/29/00 and 01/18/01, which was more than one and half years after initial construction. Therefore, the average 575-day strength of 5.2 MPa and a coefficient of variation of 15 percent were used in the analysis.

Damage Accumulation

Results from the influence charts were used to calculate peak tensile stresses, minimum stresses, and unloaded slab stresses for each two-hour time increment, in order to account for temperature differences in the slab. The ratio of the calculated stress to the concrete strength is the stress ratio corresponding to the time increment. This stress ratio is used to calculate the allowable number of load applications to failure for that time increment using the aforementioned fatigue models. The ratio of the actual number of HVS applications within the time increment to the calculated allowable number of load applications is the damage for that time increment. The damage for all time increments to failure is cumulated at each of the stress locations. The results of the cumulative damage analysis are summarized in Tables 4 and 5 for sections 535FD and 537FD, for both mean concrete strength and the 95 percentile strength. Similar results were obtained for the other sections in the study, 538FD, 539FD, 540FD, and 541FD. The cracking pattern for section 537FD consequent to repeated load application is shown in Figure 6.

DISCUSSION OF RESULTS

The stress ratios calculated using peak stresses were small and of the order of 0.25 to 0.35 or less (for the dowelled slabs) and of the order of 0.50 for the undowelled slab. For low stress ratios such as these, the slab is expected to carry millions of load applications. However, failure occurred much earlier than expected, with calculated cumulative damage values significantly lower than 1.0 by several orders of magnitude. This result is especially troublesome since full-scale test sections for APT have more accurate and detailed information on mechanical load levels and position on the slab, environmental loading parameters, pavement layer geometric and material


properties, and the time of concrete fatigue failure relative to field test sections. The inaccuracy of Miner’s hypothesis as it applies to APT results can be attributed to several reasons described below.

Concrete Fatigue Models

The differences in the allowable number of load repetitions between the presented fatigue models resulted in significant differences in the calculated cumulative damage. In general, the lowest amount of damage at cracking was predicted by the Zero-Maintenance Design model, the Calibrated Mechanistic Design model, and the PCA model, in most cases by several orders of magnitude. The damage at cracking predicted by the Foxworthy model was higher and typically within a few orders of magnitude from unity. Fatigue models have been developed and calibrated based on different data sources, failure definitions, stress computations, and stress components (27). Further complicating matters are the concrete slab size and geometry, which are not directly considered in any of the existing fatigue models, despite the fact that they have been shown to be a significant factor in the fatigue resistance of concrete (14).

Strength Variability

The fatigue models were developed for 50 percent of slab cracking (given a large section with number of slabs) corresponding to cumulative damage of unity. In the above analysis, fatigue damage was calculated for a single slab for six test sections. Because of the loading configuration used with the HVS, several slab locations had stress states similar to that of the critical location used in the analysis. The high variability in FSHCC properties results in greater damage at slab locations with flexural strength lower than the mean, which is analogous to the weakest link in a chain. This is seen in Tables 4 and 5, where using a 95 percentile strength value to account for strength variability within a given slab results in a lower number of allowable repetitions and a higher cumulative damage at failure.

Miner’s Hypothesis ― Limiting Assumptions

Miner’s hypothesis has been used extensively in concrete and asphalt fatigue analysis to account for variable stress states over time. However, its mechanistic validity has been questioned over time by key researchers (7-12). Tables 4 and 5 show for any given fatigue model, Miner’s sum does not predict fatigue failure with any accuracy for both fixed load and variable temperature loading, and variable load and temperature (sections 535 and 537, respectively). Instead, its ease of application in pavement design has prolonged its life. The main limitation of S-N curves coupled with Miner’s hypothesis lies in a phenomenological explanation of fatigue failure of concrete through the stress ratio. The stress ratio approach assumes that the stress state in the concrete is constant over the entire concrete fatigue life, thus disregarding incremental damage (or more accurately, crack propagation). Since the previous load cycles damage the concrete, which in turn increases the proceeding stress states in the concrete material, this is not a valid assumption. For this reason, Miner’s hypothesis is not sustainable, and should not be expected to provide an intrinsic explanation of concrete fatigue failure. Furthermore, the following factors are known to affect the fatigue life of concrete, and yet cannot be accurately accounted for in a stress ratio / Miner’s hypothesis approach:

• Rest periods - Hilsdorf and Kesler (8). • Homogenous material, endurance limit, variable amplitude, stress history - Hildsdorf and Kesler (8),

Holmen (9), Oh (10). • Loading rate- Raithby and Galloway (11). • Stress reversals - Tepfers (12).

Another deficiency present in using Miner’s hypothesis with fatigue damage models is that for new

pavements, an initial damage of zero is assumed. Weak zones in the concrete resulting from factors such as drying shrinkage, poor mix characteristics, etc. are not considered. Load transfer between a slab and adjacent slab or shoulder, slab-base friction, slab weight, etc., restrain drying shrinkage, and can result in early-age stresses and microcracking on the surface of the slab. Although the test slabs did not have visual cracks prior to fatigue testing, several of the longer slabs on the test strip cracked prior to any load application. To account for this microscopic damage at the slab surface, a non-zero initial damage or a slab strength reduction needs to be incorporated.


A new method for characterizing concrete fatigue failure is needed to address the mechanistic shortcomings of Miner’s hypothesis. An intermediate step using limit state approach has merit, since it theoretically gives the same answers as the cumulative damage approach, without the complex analysis. A future approach that can account for crack propagation, sequenced loading, and size and geometric effects, is the application of fracture mechanic principles.

CONCLUSIONS

Miner’s law for accumulation of damage and applicability of several concrete fatigue transfer functions was tested against the full-scale results from heavy vehicle simulator testing. Field data was collected using instrumented test slabs, and visual distress surveys were performed in order to identify slab cracking. For each test section, responses due to the moving wheel load were modeled with a finite element program for a range of temperature differences, using influence line plots. These plots were generated for several critical locations on the transverse and longitudinal joints. The influence line plots were used to estimate peak tensile stresses, unloaded slab stresses, and minimum stresses at the critical locations. These stresses were used to calculate cumulative damage with various fatigue models.

The results of the damage accumulation analysis showed that although it is possible to predict the location of the failure crack based on rolling wheel analysis and slab stresses, Miner’s approach cannot be used to predict the timing or number of load repetitions corresponding to slab cracking with any level of accuracy. This was found for full-scale fatigue testing with a fixed load and varying temperature, and for varying loading and temperature. Typical fatigue models, described in the paper, are based on a given set of data, stress calculations, and failure definitions, and cannot be extrapolated accurately to another loading condition without a “calibration” phase.

In addition, it is unclear what value of stress (peak tensile stress, maximum stress change, maximum tensile stress change) and even what value of strength (full strength, reduced strength, increased strength) should be used in the analysis. An alternative approach to Miner’s Hypothesis is greatly needed to account for the material’s fracture resistance, size effect, and the various loading effects experienced on concrete pavements.

ACKNOWLEDGEMENTS

The research results included in this paper were conducted under a grant from the University of California at Berkeley Pavement Research Center and the support of the California Department of Transportation. The financial assistance received from UC-Berkeley and Caltrans is greatly appreciated.


REFERENCES

(1) Roesler, J. R. Fatigue of Concrete Beams and Slabs. Ph. D. Dissertation, University of Illinois, Urbana, IL, 1998.

(2) Barenberg, E.J., and M.R. Thompson. Calibrated Mechanistic Design Procedure for Pavements, Phase 2 NCHRP 1-26. National Cooperative Highway Research Program/Transportation Research Board, National Research Council, Washington, D.C., 1992.

(3) Darter, M., L. Khazanovich, M. Snyder, S. Rao, and J. Hallin. Development and Calibration of a Mechanistic Design Procedure for Jointed Plain Concrete Pavements. Proceedings, 7th International Conference on Concrete Pavements, Orlando, FL, 2001.

(4) Hiller, J. E. and J. R. Roesler. Transverse Joint Analysis for use in Mechanistic-Empirical Design of Rigid Pavements. In Journal of Transportation Research Board 1809, TRB, National Research Council, Washington, D.C., 2002, pp. 42–51.

(5) Miner, M. A. Cumulative Damage in Fatigue. Transactions, American Society of Mechanical Engineer, Vol. 67, pp. A159–A164.

(6) Zollinger, D. G. and E. J. Barenberg. Proposed Mechanistic Based Design Procedure for Jointed Concrete Pavements. IHR-518, Illinois Cooperative Research Program, University of Illinois, Urbana, IL, 1989.

(7) Ioannides, A. M. Fracture Mechanics Applications in Pavement Engineering: A Literature Review. Contract No. DACA39-94-C-0121, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS, 1995.

(8) Hilsdorf, H. and C. E. Kesler. Fatigue Strength of Concrete under Varying Flexural Stresses. Proceedings, American Concrete Institute, Vol. 63, 1966, pp. 1059–1075.

(9) Holmen, J. O. Fatigue of Concrete by Constant and Variable Amplitude Loading. Bulletin No. 79-1, Division of Concrete Structures, NTH, Trondheim, 1979.

(10) Oh, B. H. Cumulative Damage Theory of Concrete under Variable-Amplitude Fatigue Loadings. ACI Materials Journal, Vol. 88, No. 1, 1991, pp. 41–48.

(11) Raithby, K. D. and J. W. Galloway. Effects of Moisture Condition, Age, and Rate of Loading on Fatigue of Plain Concrete. Abeles Symposium, Fatigue of Concrete, ACI Publication SP-41, 1974, pp. 15–34.

(12) Tepfers, R. Fatigue of Plain Concrete Subjected to Stress Reversals. ACI Publication SP-75, 1982, pp. 195–217.

(13) Roesler, J. R., D. Lange, and G. Ulreich. Fracture Behavior of Full-Scale, Fiber-Reinforced Concrete Slabs. Final Report for W.R. Grace, Inc., University of Illinois, Urbana, IL, 2003.

(14) Littleton, P. C. Effect of Stress State on Concrete Slab Fatigue Resistance. Master’s Thesis, University of Illinois, Urbana, IL, 2003.

(15) Darter, M. I., and E. J. Barenberg. Design of Zero-Maintenance Plain Jointed Concrete Pavement, Volume 1—Development of Design Procedures. Report FHWA-RD-77-111. FHWA, U.S. Department of Transportation, 1977.

(16) Darter, M. I., and E. J. Barenberg. Zero-Maintenance Pavements: Results of Field Studies on the Performance Requirements and Capabilities of Conventional Pavement Systems. Report FHWA-RD-76-105. FHWA, U.S. Department of Transportation, 1976.

(17) Salsilli, R. A., E. J. Barenberg, and M. I. Darter. Calibrated Mechanistic Design Procedure to Prevent Transverse Cracking of Jointed Plain Concrete Pavements. Proceedings, 5th International Conference on Concrete Pavements, West LaFayette, IN, 1993.

(18) Darter, M. I. A Comparison Between Corps of Engineers and ERES Consultants, Inc. Rigid Pavement Design Procedures. Technical Report Prepared for the United States Air Force SAC Command. Savoy, IL, 1988.

(19) Foxworthy, P. T. Concepts for the Development of a Nondestructive Testing and Evaluation System for Rigid Airfield Pavements. Ph. D. Dissertation, University of Illinois, Urbana, IL, 1985.

(20) Packard, R. G. and S. D. Tayabji. Mechanistic Design of Concrete Pavements to Control Joint Faulting and Subbase Erosion. International Seminar on Drainage and Erodability at the Concrete Slab-Subbase-Shoulder Interfaces. Paris, France, 1983.

(21) Roesler, J. R., J. Harvey, D. Hung, L. du Plessis, and D. Bush. Evaluation of Longer-Life Concrete Pavements for California using Accelerated Pavement Testing. Proceedings - Accelerated Pavement Testing International Conference, Reno, NV, 1999.


(22) Roesler, J. R., C. W. Scheffy, A. Ali, and D. Bush. Construction, Instrumentation, and Testing of Fast-Setting Hydraulic Cement Concrete in Palmdale, California. Report prepared for California Department of Transportation, 2000.

(23) du Plessis, L. HVS Test Results on Fast-Setting Hydraulic Cement Concrete, Palmdale, California Test Sections, North Tangent. Draft Report prepared for California Department of Transportation, 2002.

(24) Rao, S. and J. Roesler. Characterizing Effective Built-In Curling from Field Concrete Pavement Measurements. Journal of Transportation Engineering, American Society of Civil Engineers, Reston, VA, submitted, manuscript number TE/2003/022937, June 2003.

(25) du Plessis, L., D. Bush, F. Jooste, D. Hung, C. Scheffy, J. Roesler, L. Popescu, and J. Harvey. HVS Test Results on Fast-Setting Hydraulic Cement Concrete, Palmdale, California Test Sections, South Tangent. Report Prepared for California Department of Transportation, 2002.

(26) Khazanovich, L., H. T. Yu, S. Rao, K. Galasova, E. Shats, and R. Jones. ISLAB2000 – Finite Element Program for Rigid and Composite Pavements, User’s Guide. ERES Consultants, Champaign, IL, 2000.

(27) Smith, K. and J. R. Roesler. Review of Fatigue Models for Concrete Airfield Pavement Design. ASCE Airfield Pavement Specialty Conference, Las Vegas, NV, September 21-24, 2003.


LIST OF TABLES

TABLE 1 Properties of sections included in cumulative damage analysis. TABLE 2 Influence chart analysis summary for critical transverse joint location (1.2 m from left slab corner) using half-axle 90kN load on section 535FD. TABLE 3 Influence chart analysis summary for critical longitudinal edge location (1.5 m from left slab corner) using half-axle 90kN load on section 535FD. TABLE 4 Cumulative damage at critical stress locations calculated using various fatigue models for undowelled section 535FD. TABLE 5 Cumulative damage at critical stress locations calculated using various fatigue models for doweled (with tied PCC shoulder) section 537FD.


LIST OF FIGURES

FIGURE 1 Diagram and specifications of HVS (21). FIGURE 2 Typical instrumentation layout, test section 535FD (23). FIGURE 3 Influence diagram showing effect of 90 kN half-axle moving load on stresses at two critical locations on the PCC slab (section 535FD, EBITD = -33.3 °C, ∆T = 0 °C). FIGURE 4 Influence diagram showing effect of half-axle 90kN and aircraft 150 kN moving load on stresses at two critical locations on the PCC slab (section 540FD, EBITD = -17.1 °C, ∆T = 0 °C). FIGURE 5 Average flexural strength gain curve. FIGURE 6 Crack pattern in slab (537FD) after fatigue damage load application.


FIGURE 1 Diagram and specifications of HVS (21).

Overall weight 59,646 kg

Load weight of the test wheel tire 20-100 kN with truck tire

20-200 kN with aircraft tire

Tire Pressure 690 kPa

Dimensions of tested area of pavement 1.5 m × 8 m maximum

Velocity of the test wheel 10 km/h maximum Maximum trafficking rate 1000 repetitions/hr Average trafficking rate 750 repetitions/hr Average daily repetitions 16,000 Engines: Hydraulic plant 10-cylinder diesel Electrical plant/hydraulic control 6-cylinder diesel Dimensions: Length 22.56 m Width, overall 3.73 m Height 3.7 m Wheel base 16.7m

Number of axles 3 (1 in rear, 2 in front)


MDDJDMD

Slab 33 (5.3m)Slab 32 (3.7m)Slab 31 (4.1m)

TC/Sun TC/Shade

TC/K-rail

TC/Box

Temperature Chamber

Slab

wid

th 3

.7m

8.0m

0.6mTest Section

HVS outline

5 4 3 2 1

6

ThermocoupleMDDJDMD

Slab 33 (5.3m)Slab 32 (3.7m)Slab 31 (4.1m)

TC/Sun TC/Shade

TC/K-rail

TC/Box

Temperature Chamber

Slab

wid

th 3

.7m

8.0m

0.6mTest Section

HVS outline

5 4 3 2 1

6

Thermocouple

FIGURE 2 Typical instrumentation layout, test section 535FD (23).


-4

-2

0

2

4

-2 0 2 4

Distance from left corner, m

Stre

ss, M

Pa

Location A

Location B

Test Slab90kN Load

Test Slab Legend

B

Top of Slab StressesTension - Positive

A

FIGURE 3 Influence diagram showing effect of 90 kN half-axle moving load on stresses at two critical locations on the PCC slab (section 535FD, EBITD = -33.3 °C, ∆T = 0 °C).


-4

-2

0

2

4

-2 0 2 4

Distance from left corner, m

Stre

ss, M

Pa

Location A - 90kNLocation B - 90kNLocation A - Aircraft 150kNLocation B - Aircraft 150kN

Test Slab

Test Slab Legend

B

Top of Slab StressesTension - Positive

A

FIGURE 4 Influence diagram showing effect of half-axle 90 kN and aircraft 150 kN moving load on stresses at two critical locations on the PCC slab (section 540FD, EBITD = -17.1 °C, ∆T = 0 °C).


0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 120 240 360 480 600

Age (days)

Flex

ural

Str

engt

h (M

Pa)

FIGURE 5 Average flexural strength gain curve.


Figure 4.6.1: 537FD Crack Patterns (After)

Note: Loading Sequence40 kN dry: 0 – 13 240 Reps

70 kN dry: 13 240 – 13 740 Reps90 kN dry: 13 740 – 333 740Reps

150 kN dry aircraft wheel:333 740 – 388 746Reps




43 740 Reps73 740 Reps83 740 Reps193 740 Reps

43 740 Reps73 740 Reps83 740 Reps

193 740 Reps

2.0 m

1.0 m

1.0 m

0.6 m

2.0 m

1.3 m

0.6 m

2.0 m

Crack at0 Reps

Figure 4.6.1: 537FD Crack Patterns (After)







43 740 Reps73 740 Reps83 740 Reps193 740 Reps

43 740 Reps73 740 Reps83 740 Reps

193 740 Reps

2.0 m

1.0 m

1.0 m

0.6 m

2.0 m

1.3 m

0.6 m

2.0 m

Crack at0 Reps

FIGURE 6 Crack pattern in slab (537FD) after fatigue damage load application.


TABLE 1 Properties of sections included in cumulative damage analysis.

Section ID Slab Thickness (mm)

Joint Spacing: Left Slab-Test Slab-Right Slab (m)

Dowels? Shoulder Type

Left Corner EBITD (°C)

Right Corner EBITD (°C)

535FD 219.5 4.11-3.71-5.35 No AC -33.3 -21.8

537FD 212.8 5.78-3.94-3.66 Yes Tied PCC >-5.0 -10.9

538FD 221.0 5.86-3.92-3.75 Yes Tied PCC -14.7 -18.5

539FD 203.0 5.86-3.85-3.71 Yes 600 mm

Widened lane w/AC

-10.8 -13.0

540FD 223.0 5.86-3.80-3.80 Yes 600 mm

Widened lane w/AC

-12.0 -17.1

541FD 243.5 5.91-3.89-3.67 Yes 600 mm

Widened lane w/AC

-5.5 -8.5


TABLE 2 Influence chart analysis summary for critical transverse joint location (1.2 m from left slab corner) using half-axle 90kN load on section 535FD.

Peak Tensile Stress, (MPa)

Minimum Stress, (MPa)

Unloaded Slab Stress, (MPa)

Max. Stress Change, (MPa)

Stress Change Relative to Unloaded Slab, (MPa)

Tensile Stress Change, (MPa)

Total Effective Linear Temp. Difference, (°C)

PTS MS USS (PTS-MS) (PTS-USS)

(PTS-MS) for MS > 0, else (PTS - 0.0)

-47.2 2.53 0.45 0.45 2.08 2.08 2.08

-41.7 2.50 0.44 0.44 2.06 2.06 2.06

-36.1 2.47 0.43 0.43 2.03 2.03 2.03

-30.6 2.42 0.42 0.42 2.00 2.00 2.00

-25.0 2.35 0.40 0.40 1.94 1.94 1.94

-19.4 2.26 0.38 0.38 1.88 1.88 1.88

-13.9 2.16 0.35 0.35 1.80 1.80 1.80

-8.3 2.02 0.30 0.30 1.72 1.72 1.72


TABLE 3 Influence chart analysis summary for critical longitudinal edge location (1.5 m from left slab corner) using half-axle 90kN load on section 535FD.

Peak Tensile Stress, (MPa)

Minimum Stress, (MPa)

Unloaded Slab Stress, (MPa)

Max. Stress Change, (MPa)

Stress Change Relative to Unloaded Slab, (MPa)

Tensile Stress Change, (MPa)

Total Effective Linear Temp. Difference, (°C)

PTS MS USS (PTS-MS) (PTS-USS)

(PTS-MS) for MS > 0, else (PTS - 0.0)

-47.2 2.80 -3.11 0.77 5.91 2.03 2.80

-41.7 2.75 -3.10 0.75 5.85 2.00 2.75

-36.1 2.68 -3.10 0.73 5.78 1.95 2.68

-30.6 2.57 -3.12 0.70 5.69 1.87 2.57

-25.0 2.43 -3.15 0.67 5.58 1.76 2.43

-19.4 2.25 -3.22 0.62 5.47 1.63 2.25

-13.9 2.03 -3.35 0.56 5.39 1.47 2.03

-8.3 1.77 -3.59 0.45 5.36 1.31 1.77


TABLE 4 Cumulative damage at critical stress locations calculated using various fatigue models for undowelled section 535FD.

Transverse Joint Location Lane-Shoulder Joint Location

Strength Fatigue Model Peak Tensile Stress-Damage

Maximum Stress Change-Damage*

Peak Tensile Stress-Damage

Maximum Stress Change-Damage**

Zero-Maintenance 3.0 × 10-5 1.1 × 10-6 1.2 × 10-4 n/a

Calibrated Mech. Design 5.6 × 10-3 7.9 × 10-5 0.020 220

ERES/COE 0.35 0.016 0.91 870

Foxworthy 27 6.8 41 1100

Mean Strength

PCA 0.012 0 0.098 n/a

Zero-Maintenance 0.016 2.0 × 10-4 0.092 n/a

Calibrated Mech. Design 0.67 0.033 1.7 1200

ERES/COE 12 1.3 23 3100

Foxworthy 130 48 180 2200

95 Percentile Strength (Mean

Strength – 1.65 Standard Deviations)

PCA 4.2 0.17 14 n/a

Slab cracked after 67,935 repetitions of 90 kN with corner break around left slab corner. * Always in tension – maximum stress change less than peak tensile stress. ** Tension through compression and back to tension – maximum stress change greater than peak tensile stress.


TABLE 5 Cumulative damage at critical stress locations calculated using various fatigue models for doweled (with tied PCC shoulder) section 537FD.

Transverse Joint Location Lane-Shoulder Joint Location

Strength Fatigue Model Peak Tensile Stress-Damage

Maximum Stress Change-Damage*

Peak Tensile Stress-Damage

Maximum Stress Change-Damage**

Zero-Maintenance 5.6 × 10-9 3.1 × 10-10 3.2 × 10-8 96

Calibrated Mech. Design 1.3 × 10-11 1.4 × 10-20 3.3 × 10-7 12

ERES/COE 2.1 × 10-7 6.8 × 10-14 1.8 × 10-4 83

Foxworthy 0.1 3.5 × 10-4 0.51 230

Mean Strength

PCA 0.0 0.0 0.0 1270

Zero-Maintenance 1.3 × 10-7 2.7 × 10-9 2.6 × 10-6 n/a

Calibrated Mech. Design 5.8 × 10-7 2.5 × 10-13 4.1 × 10-4 120

ERES/COE 4.9 × 10-4 1.2 × 10-8 0.036 460

Foxworthy 2.4 0.034 5.4 550

95 Percentile Strength (Mean

Strength – 1.65 Standard Deviations)

PCA 0.0 0.0 0.0 n/a

Slab cracked after 13,240 repetitions of 40 kN, 500 repetitions of 70 kN, and 30,000 repetitions of 90 kN with midslab transverse crack. Corner break extended to the transverse joint after 180,000 repetitions of 90 kN (figure 6). * Always in tension – maximum stress change less than peak tensile stress. ** Tension through compression and back to tension – maximum stress change greater than peak tensile stress.

Cumulative Fatigue Damage Analysis of Concrete Pevement

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