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Publication Number: FHWA-RD-02-088
Date: May 2003

Evaluation of Joint and Crack Load Transfer Final Report

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Mechanistic modeling of joints and cracks in PCC pavements using a finite element program requires input of certain parameters.  The most commonly used finite element programs for rigid pavement analysis usually require input of joint stiffness.  This chapter presents a procedure for backcalculation of joint stiffness for the LTPP rigid sections and assessment of the results.

Joint Stiffness Backcalculation Procedure

To backcalculate joint/crack stiffness, the following information must be available:

To calculate LTEs for cracks and joints, coefficients of subgrade reaction and radii of relative stiffness were downloaded during the summer of 2001 from the LTPP database table MON_DEFL_RGD_BAKCAL_SECT (June 2001 release).  This table provides representative k-values and radii of relative stiffness for rigid LTPP sections for different FWD passes. 

Representative joint stiffnesses were calculated using the following procedure:

Step 1.  Select LTE value

For each FWD pass, compare mean LTEs from leave and approach tests (tests J4 and J5 for JCP and C4 and C5 for CRCP) and select the lowest value.

Step 2.  Calculate nondimensional joint stiffness

Using the LTE value from step 1, calculate nondimensional joint stiffness using the following equation:

 Equation 22 The nondimensional joint stiffness equals the sum total of the total of 1 divided by the load transfer efficiency index, minus 0.01, divided by 0.012, all to the negative 1.17786 power.                                             (22)

where:

-          AGG* is  = nondimensional joint stiffness.

This equation is obtained by inverting Crovetti's equation (presented in equation 8).  Analysis of the ISLAB2000 deflection data presented in figure 69 shows that these equations adequately predict nondimensional joint stiffness for a wide range of values.

Figure 69. Predicted versus actual ISLAB2000 nondimensional joint stiffness. Predicted nondimensional joint stiffness, of 0.01 to 1000, is graphed on the horizontal axis. Actual nondimensional joint stiffness, of 0.01 to 1000, is graphed on the vertical axis. There is a slope increasing at a 45-degree angle. There are plots that positioned along the slope. The figure shows that the predicted nondimensional joint stiffness is accurate.

Figure 69.  Predicted versus actual ISLAB2000 nondimensional joint stiffness.

Step 3. Calculate joint stiffness

Using the following equation, calculate joint stiffness:

Equation 23 Joint stiffness equals the nondimensional joint stiffness times the coefficient of subgrade reaction times the radius of relative stiffness.                                                         (23)

where:

-          k a is  = the coefficient of subgrade reaction

-          Radius of relative stiffness is  = radius of relative stiffness

-          AGG is  = joint stiffness

This procedure cannot account for several effects discussed in chapters 4 and 5, such as possible load level -dependency and different behavior under loading on the leave and approach side of the joint.  However, an advantage of this procedure is that the resulting joint stiffness can be used for a forward analysis using a popular finite element program for rigid pavement analysis, such as ILLI-SLAB and J-SLAB.

Joint Stiffness Data Assessment

Joint stiffnesses were backcalculated for those LTPP sections and FWD visits for which the LTPP database table MON_DEFL_RGD_BAKCAL_SECT contained k-values and radii of relative stiffness.  This resulted in representative crack stiffness for 134 visits of 72 CRCP sections and 910 visits of 250 JCP sections.

Figure 70 presents a frequency distribution of crack stiffness for CRCP sections.  For more than two-thirds of the cases, the backcalculated CRCP crack stiffnesses ranged between 800 and 1600 MPa.  The mean crack stiffness value for all cases was 1240 MPa.

Frequency distributions of representative joint stiffness of joints of doweled and nondoweled JCP pavements are presented in figure 71.  Comparingson of these distributions show that nondoweled joints usually have much lower stiffness than doweled joints.  More than half of the backcalculated stiffness for nondoweled joints were less than 200 MPa, and the average value from all cases was 470 MPa.  In addition, more than 60 percent of doweled joints had stiffnesses greater than 600 MPa, with the average value equal to 730 MPa.

As stated above, LTE of cracks and joints varies with time, as do joint and crack stiffnesses.  Figure 72 presents a comparison of joint stiffnesses backcalculated from the FWD deflections obtained on the same day of testing, but from different FWD passes.  Significant variability exists for some joints, especially for those that exhibited lower stiffness at the time of the first FWD pass. 

Recommendation for Joint Stiffness Selection

Currently, very little guidance is available for selecting joint and crack stiffness parameters for analyses of rigid pavement using finite element programs like ILLI-SLAB or JSLAB.  This findings of this study have resulted in recommendations for the selection of joint stiffness values if they cannot be obtained from other sources.  These recommendations are summarized in table 17.  However, more research is needed to validate these recommendations.

Table 17.  Recommended joint/crack stiffnesses for different types of pavements.

Pavement Type

Recommended Ranges (MPa)

Non-doweled JCP

100 -500

Doweled JCP

400 -1000

CRCP

800 -1400

Figure 70. Frequency distribution of representative CRCP crack stiffness. Joint stiffness, from 0 to 3000 mega Pascal, is graphed on the horizontal axis. Percent of passes, from 0 to 30, is graphed on the vertical axis. The figure is a bar graph, starting at the lowest percent of passes (2) at 400 mega Pascal. The figure increases to the highest pass (27 percent) at 1200 mega Pascal and decreases to 3 percent at 3000 mega Pascal. For more than two-thirds of the cases, the continuously reinforced concrete pavement crack stiffness ranged between 800 to 1600 mega Pascal.

Figure 70.  Frequency distribution of representative CRCP crack stiffness.

Figure 71. Frequency distributions of representative joint stiffnesses for joints of doweled and nondoweled JCP. Joint stiffness, from 200 to 3000 mega Pascal, is graphed on the horizontal axis. Percent of passes of 0 to 60, is graphed on the vertical axis. The figure is a histogram with two sites. The sites are nondoweled and doweled joint concrete pavement. Nondoweled joint concrete pavement begins at the highest percent of passes (52) at 200 mega Pascal and decreases dramatically to the lowest percent of passes (2) at 3000 mega Pascal. Doweled joint concrete pavement begins at the highest percent of passes (19) at 200 mega Pascal and decreases gradually to the lowest percent of passes (2) at 2000 mega Pascal. A comparison of these distributions show that nondoweled joint usually have much lower stiffness than doweled joints. More than half of the backcalculated stiffnesses for nondoweled joints were less than 20 percent. More than 60 percent of doweled joints had stiffnesses greater than 600 mega Pascal.

Figure 71.  Frequency distributions of representative joint stiffnesses for joints of doweled and nondoweled JCP.

Figure 72. Comparison of backcalculated joint stiffness from two FWD passes on the same day of testing. Joint stiffness pass 1, from 0 to 3500 mega Pascal, is graphed on the horizontal axis. Joint stiffness pass 2, from 0 to 3500 mega Pascal, is graphed on the vertical axis. There is a slope increasing in a straight line at a 45-degree angle. The figure is a scatter plot with the plots clustered mostly below 1000 mega Pascal in both pass 1 and 2. As joint stiffness of pass 1 increases, joint stiffness of pass 2 increases. Comparison of backcalculated joint stiffness from falling weight deflectometers are significant, especially those that exhibited lower stiffness at the time of the first pass.

Figure 72. Comparison of backcalculated joint stiffness from two FWD passes on the same day of testing.

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