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31 4. Perform MEPDG computations for each uniform section factors corresponding to the types of dowel misalignment using the calculated mean equivalent dowel diameter for assumed in this example. the section. 3.5.1.1 Embedment Length Adjustment Factor If certain adjustment measures such as dowel retrofitting are performed, the effective dowel diameters of the retrofitted Since the embedment length is greater than 2 in. [51 mm] joints should be recalculated and the pavement performance and less than 6.9 in. [175 mm], the adjustment factor for the predictions computed. longitudinal translation and related reduction in embedment length is calculated using Equation 6 as follows: 3.5 Examples of Application remb = -0.010 (5 ) + 0.167 (5 ) + 0.324 = 0.909 2 of The Equivalency Concept 3.5.1 Example 1. Assessment of a Single Joint 3.5.1.2 Vertical Translation (Low Concrete Cover) Adjustment Factor The following example illustrates the calculation of the effect of dowel misalignment on joint performance for a joint The reference concrete cover and the actual concrete cover in an 11-in. thick pavement. The joint is assumed to contain (CC) are calculated using Equation 9, as follows: 12 dowels with 18 in. [457 mm] length and 1.5 in. [38 mm] diameter with the following features: 11 1.5 CCref = - - 0.5 = 4.25 in. 2 2 1. The saw cut is 4 in. [102 mm] away from the designed loca- 11 1.5 11 tion, resulting in 4 in. [102 mm] of longitudinal translation CC = - - - 4.75 = 4 in. 2 2 2 and 5 in. [127 mm] of embedment length for all dowels. 2. The dowel basket used for the placement was 0.75 in. [19 mm] taller than was required for the mid-depth dowel CCref is also limited to a maximum of three times the dowel placement, resulting in 0.75 in. [19 mm] vertical trans- diameter, or 4.5 in. [114 mm] in this example. Thus, the lational displacement towards the pavement surface and calculated value for CCref of 4.25 in. [108 mm] is used. The reduced concrete cover from 4.75 in. to 4 in. [121 mm to adjustment factor for the loss in concrete cover is calculated 102 mm] for all dowels. using Equation 12 as follows: 3. The dowels were placed with the rotational misalignment rcc = 1 - -153.3 ( 4.25 ) + 2503 ( 4.25 ) + 153.3 ( 4 ) 2 (vertical tilt and horizontal skew) given in Table 3.9. - 2503 ( 4 ) 9628 = 0.968 The procedure for determining the equivalent dowel diam- eter for this joint involves the calculation of four adjustment 3.5.1.3 Vertical Tilt Adjustment Factor Table 3.9. Assumed dowel For the vertical tilt values provided in Table 3.10, mean misalignments. vertical tilt of 0.2 in. [5 mm], standard deviation of the verti- cal tilt of 0.633 in. [16 mm], and wheel path dowel vertical tilt Dowel Bar Vertical tilt, Horiz. Skew, of 0.5 in. [13 mm] were calculated. The joint stiffness can be Number in./18 in. in./18 in. 1 -0.44 -0.26 calculated using Equation 14 as follows: 2 0.50 -0.32 3 -0.34 -0.32 JStiff = 10.8942 - 0.20623 ( 0.2 ) - 0.61796 ( 0.633) 4 -0.80 -0.38 5 -0.54 -0.48 - 0.86862 ( 0.5 ) = 10.03 6 1.46 -0.27 7 -0.54 -0.39 The LTE of the joint can be calculated using Equation 15 8 0.46 -0.33 as follows: 9 -0.54 -0.47 10 -0.54 -0.43 11 -0.54 -0.44 100 LTE = = 85.51% 1 + 1.2 (10.03) -0.849 12 -0.54 -0.42

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32 The adjustment factor for vertical tilt can be obtained from should be treated as if it had dowels with a diameter of 1.31 in. Equation 17 as follows: [33 mm] (and not the actual 1.5-in. [38-mm] diameter). 0.0103 rvt = exp ( 0.0582 85.51) = 0.995 3.5.2 Example 2. Assessment of 1.5 a Pavement Section The following example illustrates the calculation of the 3.5.1.4 Horizontal Skew Adjustment Factor effect of dowel misalignment on the performance of a 540-ft. For horizontal skew values provided in Table 3.10, mean [165-m] pavement section with an 11 in. [279 mm] thickness. horizontal skew of 0.38 in. [10 mm], standard deviation of the The pavement section has 30 joints, each of which contains horizontal skew of 0.073 in. [1.9 mm], and maximum wheel 12 dowels with 18 in. [457 mm] length and 1.5 in. [38 mm] path dowel horizontal skew of 0.32 in. [8 mm] were calcu- diameter. The pavement was designed for the following per- lated. The joint stiffness can be calculated using Equation 14 formance criteria (after 20 years at 90 percent reliability): as follows: Transverse cracking not to exceed 12% of cracked slabs. JStiff = 10.8942 - 0.20623 ( 0.38 ) - 0.61796 ( 0.073) Mean joint faulting not to exceed 0.12 in. [3 mm] IRI not to exceed 190 in./mile [3.0 m/km]. - 0.86862 ( 0.32 ) = 10.49 The equivalent dowel diameters were calculated for each The LTE of the joint can be calculated using Equation 15 joint (results are shown in Table 3.10). Because the pavement as follows: section is less than 1000 ft [305 m], the mean equivalent dowel diameter was computed for the entire pavement section result- 100 ing in 1.41 in. [36 mm]. This equivalent dowel diameter was LTE = = 85.98 1 + 1.2 (10.49 ) -0.849 then used in an MEPDG simulation to predict faulting and IRI for the project. Figures 3.21. and 3.22 present the predicted The adjustment factor for horizontal skew can be obtained faulting and IRI, respectively, for the as-designed pavement from Equation 17 as follows: (dowel diameter of 1.50 in. [38 mm]) and for a similar pave- ment with 1.41 in. [36 mm] dowels. 0.0103 These results indicate that the predicted faulting and IRI of rhs = exp ( 0.0582 86.03) = 1.02 the project are within the specified acceptance thresholds. 1.5 However, analysis of the MEPDG run output files (not pre- Because the adjustment factor should not exceed 1, an sented here) showed that because of dowel misalignment the adjustment factor of 1.0 should be assumed. reliability of faulting and IRI not exceeding the performance threshold decreased from 96.7 to 91.9% and from 92.5 to 91.0%, respectively. 3.5.1.5 Assembly of Calculated Adjustment Factors The equivalent dowel diameter (deq) for the joint is obtained Table 3.10. Equivalent dowel diameter for each joint by multiplying the original dowel diameter (d0) by the adjust- in the pavement section. ment factors for concrete cover, embedment length, vertical tilt, and horizontal skew as follows: Equivalent Equivalent Equivalent Dowel Dowel Dowel Joint # Joint # Joint # Diameter Diameter Diameter deq = remb rcc rvt rhs d0 = 0.909 0.968 0.996 1 1.5 1 (in.) 1.31 11 (in.) 1.5 21 (in.) 1.21 2 1.5 12 1.22 22 1.5 = 1.31 in. 3 1.41 13 1.5 23 1.5 4 1.14 14 1.5 24 1.27 5 1.5 15 1.49 25 1.5 Since the concrete cover for each dowel was greater than 6 1.1 16 1.5 26 1.5 the minimum required concrete cover, no further reduction of 7 1.5 17 1.5 27 1.5 8 1.5 18 1.23 28 1.5 the equivalent dowel diameter is needed. Therefore, to account 9 1.5 19 1.05 29 1.37 for the effects of the misalignment in this joint, the pavement 10 1.5 20 1.5 30 1.5

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33 0.14 0.12 Performance Threshold 1.41 in. 0.10 1.5 in. 0.08 Faulting, in. 0.06 0.04 0.02 0.00 0 2 4 6 8 10 12 14 16 18 20 22 Pavement age, years Figure 3.21. Predicted faulting for the as-designed pavement project. 240 200 Performance Threshold 1.41 in. 1.5 in. 160 IRI, in. / mile 120 80 0 2 4 6 8 10 12 14 16 18 20 22 Pavement age, years Figure 3.22. Predicted IRI for the as-designed pavement project.