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Coordinating, Developing, and Delivering Highway Transportation Innovations

 
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This report is an archived publication and may contain dated technical, contact, and link information
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Publication Number:  FHWA-HRT-15-074     Date:  September 2016
Publication Number: FHWA-HRT-15-074
Date: September 2016

 

Pavement Structural Evaluation at the Network Level: Final Report

 

CHAPTER 8. DEFLECTION BASIN INDICES

8.1. Introduction

This chapter presents details concerning the analytical investigation undertaken to explore relationships between load-induced structural-related responses of a pavement system and the corresponding surface deflection basin-related indices. This investigation and associated results were considered an important effort toward the development of methodologies for incorporating TSDD measurements into network-level PMS applications.

Pavement failure (or structural capacity), in terms of fatigue or rutting can be estimated from performance prediction equations.(27,57) These equations relate load-induced pavement responses to the following two important pavement distresses: (1) certain level of AC fatigue cracking and (2) rutting failure in the subgrade. The critical load-induced pavement responses that relate to the two referenced distresses are the maximum tensile horizontal strain (also known as fatigue strain) at the bottom of the AC layer and the vertical compressive strain on top of the subgrade, respectively. In addition, there are studies that postulate the existence of reliable correlations between deflection basin- related indices and load-induced pavement structural responses, which suggest it is possible to correlate deflection basin indices to structural capacity (or distress).(62,63,21)

Specific TSDD deflection basin measurements depend on the device under consideration. For example, the TSD device measures surface vertical velocity at as many as nine locations within the deflection bowl, and subsequently, the surface vertical deflection basin is determined based on a certain assumption for the shape of the defection basin. Conversely, only two surface measurements within the deflection bowl are taken by the RWD. In turn, this means that the selection of deflection basin indices for correlation to structural capacity (or distress) must take into consideration the capabilities of the specific TSDD.

Chapter 7 of this report detailed the validation of the 3D-Move program, for the purposes of the project in question, using a variety of independent pavement responses that included surface deflection bowls (measured using project sensors) as well as horizontal strains at the bottom of the AC layers and vertical stresses at the top of the subgrade (measured using MnROAD sensors). Accordingly, the program was ready for the evaluation of the critical pavement responses and corresponding deflection-based indices, thus enabling the investigation of correlations between the two. Because 3D-Move uses a dynamic moving load model, important factors such as viscoelastic properties and vehicle speed can be accounted for in the evaluation of pavement response time histories.

A number of previous studies have proposed many surface vertical deflection-based indices, and they have also postulated that these indices relate to the structural capacity of pavements.(62,63,21) However, for the purposes of this project, it was important to identify those indices that best relate to the two critical pavement responses. The identification of the appropriate indices was undertaken using the following three-step procedure:

  1. Step 1: Identified the surface deflection indices that correlated well with the critical pavement responses using the 3D-Move simulation results presented in chapter 7, which were based on the TSDD field trials carried out at the MnROAD facility.

  2. Step 2: Used a set of 36 pavement structures (different combinations of layer thicknesses and moduli) and vehicle speed combinations (hereafter referred to as combinations) as input to 3D-Move to perform a sensitivity analysis of the correlations associated with various deflection indices (not limited to those indices identified in step 1).

  3. Step 3: Used the JULEA layered elastic program to further explore the robustness of the correlations identified in the first two steps by considering a much larger database (approximately 15,000 different pavement combinations) of pavements.(26) There were limitations (e.g., stationary, static, and elastic) associated with JULEA relative to realistic modeling of pavement response. However, if narrowly constrained correlations irrespective of pavement material properties were found through the use of the large JULEA database, then the impact of these limitations may not have been significant.

These three steps used to identify the most appropriate indices are described in greater detail in the following subsections.

8.2 Step 1: Using Existing 3D-Move Simulation Results

As a part of the calibration process described in chapter 7, pavement responses using 3D-Move were computed for three MnROAD accuracy cells with the TSDDs travelling at various vehicle speeds. By trial and error, three pavement case scenarios were identified for each of the accuracy cells, which bracketed the vertical surface deflection bowls computed by 3D-Move with those measured by the project sensors. In all, 42 datasets of pavement responses and corresponding vertical surface deflections datasets were generated using 3D-Move.

Defining Response Points in 3D-Move Runs

The 3D-Move program can output many response time histories (e.g., stresses, strains, displacements, and velocities) as a vehicle travels on at any specified location of the pavement surface. The TSDDs measured (or estimated) vertical surface deflections at many predetermined locations in the longitudinal direction along the midline between the rear tires (see figure 166). From the vertical displacement time history computed by 3D-Move at a point (observation point) on the midline between the tires, it was possible to determine the displacements at various individual locations along the midline using time space superposition. The 3D-Move output includes the time of the maximum displacement (tmax) and also the time (to) at which the instantaneous deflection at the midpoint between tires (D0) reached the point of observation (see figure 167). Since 3D-Move modeled the damping characteristics of the pavement layers, there was an offset between tmax and to. The location Dr refers to a point at a distance r in inches in front of D0. The maximum displacement that occurred at the location Dmax and other displacements at many locations shown along the midline between the tires in figure 166 could be readily determined using time-space superposition.

Figure 166. Illustration. Predetermined locations for estimation of vertical surface deflections in TSDDs. This illustration shows specified locations of the pavement surface as response points in traffic speed deflection devices (TSDDs) 3D-Move software. These points were located on the midline between two tires. The location D subscript r refers to a point at a distance, r, in inches in back or front of D subscript 0. The location includes D subscript -7.25, D subscript 0, D subscript -7.75, D subscript 8, D subscript 12, D subscript 18, D subscript 24, D subscript 36, D subscript 48, and D subscript 60.

Figure 166. Illustration. Predetermined locations for estimation of vertical surface deflections in TSDDs.

Figure 167. Illustration. Surface displacement from 3D-Move displacement time history. The graph shows a typical 3D-Move response history at any given response point. The y-axis shows surface vertical displacement, and the x-axis can be time or distance. The bell-shaped curve includes the time of the maximum displacement or t subscript max and also t subscript 0, which the mid-point between the tires reaches the point of observation behind t subscript max.

Figure 167. Illustration. Surface displacement from 3D-Move displacement time history.

Conversely, when other 3D-Move pavement responses (e.g., maximum AC tensile strain) were considered, it was necessary to select multiple transverse locations (the depth was fixed) in the computations. This is because the location of the maximum value of the response was not known a priori. After computing responses at many multiple transverse locations, the maximum response value could be determined.

Though the focus of this project was on the horizontal (or fatigue) strains at the bottom the AC and to a lesser extent on the vertical strains at the top of subgrade, a larger database of pavement responses was assembled from the 3D-Move runs. The list of the locations and corresponding responses and the distress mode includes the following (see figure 168):

Figure 168. Illustration. Selection of response points when using 3D-Move. This illustration shows the locations of response points defined in 3D-Move runs to capture pavement distress and relate it to surface displacements. The pavement structure includes three layers: asphalt concrete (AC), base, and subgrade. Rear tires and response point in midpoint between them and transverse responses in various depths are shown. Transverse responses include seven points in each depth which start from the midpoint between the tires. Transverse responses include: tensile strains at 0.5 inch (12.52 mm) from surface of AC for top-down cracking, vertical strain/stress at 2 inches (50.8 mm) from AC surface for AC rutting, tensile strain at the bottom of the AC for bottom-up fatigue cracking, vertical strain/stress at midpoint of base for base rutting, and vertical strain/stress at top of the subgrade surface for subgrade rutting.

1 inch = 25.4 mm

Figure 168. Illustration. Selection of response points when using 3D-Move.

Pavement Properties and Loading in 3D-Move Runs

The initial focus of the simulations was on the three MnROAD cells (cells 3, 19, and 34), where project sensor measurements were taken during the TSDD field trials. A sketch of the pavement structures at these three cells was presented earlier in figure 141 (see chapter 7). Since the AC thickness varied from 3 to 5 inches (76.2 to 127 mm) along these cells, the sections could be categorized as pavements with relatively thin AC. Other pavement layer thicknesses and moduli are also shown in this figure. To compare the 3D-Move results to measured data from the MnROAD and project sensors, the AC moduli corresponding to the temperatures at the time of the TSDD field trials were required. The procedure to get the AC layer modulus versus frequency relation at any given temperature based on FWD backcalculated layer moduli was described in chapter 7. Figure 138 and figure 139 in chapter 7 showed the axle configuration and loads for the TSD and RWD. These two cases of loading (tire loads, pressure, and spacing) could be used to determine the role of loading conditions on the correlations between surface deflection indices and pavement responses as described later in this chapter.

Selection of Deflection Basin Indices

A number of deflection basin-related indices have been proposed by researchers and are perceived as strong predictors of the critical structural-related responses and structural conditions (or capacity) of the pavements. Experimental and analytical studies have reported strong correlations between some deflection basin indices and pavement responses.(62,63,21) Horak proposed two different equations for R referred as R1 and R2 as in Figure 8 and Figure 9.(63,64)

As noted previously, the 3D-Move deflection basin parameters were computed based on surface vertical displacement along the midline between the two rear tires, while the maximum pavement responses were determined by considering many transverse response locations. The 3D-Move runs initially used both the TSD and RWD loadings individually, and then the combined dataset were used when exploring the correlations. A power curve generally described the data better than a linear fit, as judged by improved correlation coefficients (R2).

SCI is typically defined as the difference in displacements between D0 and Dr. D0 is the reference displacement; however, the locations D0 and Dmax were not the same due to viscous lag of the response due to the moving load. Accordingly, it was important to determine whether a better correlation existed if Dmax was used as the reference displacement. Parameter SCIm is defined by using Dmax instead of D0 as the reference displacement in the calculations of the indices. Since both TSD and RWD did not directly measure deflection at D0, another observation made during the investigation was the need to also consider D4, D-7.25, and D8 (i.e., displacements at 4, -7.25, and 8 inches (101.6, -184.15, and 203.2 mm), respectively) as reference displacement locations. In the case of the TSD, because of its capacity to measure multiple deflection points, a theoretical algorithm was used to compute D0. However, to minimize additional computations and associated errors, the possibility of utilizing direct TSD measurements at D4 and D8 were proposed. More specifically, a new index called Deflection Slope Index (DSI) was proposed based on reference at D4, D8, D12, D18, and D24. DSI is the difference between the deflection at reference location and Dr. In addition, indices representing deflection slope at a given location defined as Tangent Slope (TS) was also considered.

Table 44 shows these indices. A total of 75 individual indices are listed in this table. The deflection basin indices included in table 44 correlated with the two pavement structural-related responses presented earlier in this chapter. The deflection basin parameters that did not yield strong correlations to the structural-related responses were not considered further under the third step.

Table 44. Deflection basin indices used in the evaluation.
Parameter and Number of Indices Indices for Evaluation
R1 (7) R18
R112
R118
R124
R136
R148
R160
R2 (7) R28
R212
R218
R224
R236
R248
R260
Surface displacement (2) D0
D60
Area (1) A
Shape factors (2) F1
F2
SCI (7) SCI8
SCI12
SCI18
SCI24
SCI36
SCI48
SCI60
D-7.25 - D7.75 (for RWD)
BCI (1) BCI
BDI (1) BDI
AUPP (1) AUPP
SD (7) SD8
SD12
SD18
SD24
SD36
SD48
SD60
TS (8) TS4*
TS8*
TS12*
TS18
TS24*
TS36*
TS48
TS60*
SCIm (7) SCIm8
SCIm12
SCIm18
SCIm24
SCIm36
SCIm48
SCIm60
DSI4-r (7) DSI4 - 8
DSI4 - 12
DSI4 - 18
DSI4 - 24
DSI4 - 36
DSI4 - 48
DSI4 - 60
DSI8 - r (6) DSI8 - 12
DSI8 - 18
DSI8 - 24
DSI8 - 36
DSI8 - 48
DSI8 - 60
DSI12 - r (4) DSI12 - 18
DSI12 - 24 (same as BDI)
DSI12 - 36
DSI12 - 48
DSI12 - 60
DSI18 - r (4) DSI18 - 24
DSI18 - 36
DSI18 - 48
DSI18 - 60
DSI24 - r (2) DSI24 - 36 (same as BCI)
DSI24 - 48
DSI24 - 60

*TSD sensor location.

Note: Numbers within parentheses in left column indicate the number of indices for each deflection basin parameter.

The goodness of the correlations between the indices and pavement responses were categorized into three classes. Class 1 indices had an R2 greater than 0.9 and were considered the most appropriate indices. Class 2 indices were those with an R2 between 0.7 and 0.9, and class 3 indices were those with an R2 less than 0.7.

Two options were used when horizontal strains at the bottom AC were considered: (1) maximum tensile strains in transverse and longitudinal direction of vehicle travel and (2) maximum tensile strains at a location directly below the midpoint between the rear tires. For the purpose of brevity, only the following tables and figures that showed the highest (and therefore the most appropriate) correlations are included in this chapter:

The equations with R2 values more than 0.90 are presented bold. The example tables and figures provide results for TSD loadings only and also for the combined TSD and RWD loadings. There are 17 data points available for the TSD loadings and 43 for the combined dataset. Similar tables and figures looking at the fatigue strain relationship were developed for every index in table 44, but they are not included in the report, as they do not provide further insights. The data used to generate these tables and figures can be obtained directly from FHWA.

Based on the information presented in table 45 through table 52 and the review of the correlations for other indices, it was concluded that indices based on maximum horizontal strains were better than horizontal strains at the location directly below the midpoint between the tires. It was also concluded that the role of the difference in load characteristics (TSD versus RWD) on the relationships were minimal. However, SCIm, which used Dmax as the reference displacement, had a slightly better correlation. It also appears that using D4 instead of D0 to calculate SCI yielded better correlations.

Table 45. Relationships between R1 and horizontal strains at bottom of AC with TSD loading data.
Index Relation with Midline Horizontal Strain* Relation with Maximum Horizontal Strain*
Equation R2 Equation R2
R18 y = 3.3238x-1.02 0.75 y = 1.2327x-0.896 0.88
R112 y = 1.3707x-0.912 0.85 y = 0.4438x-0.775 0.94
R118 y = 0.5819x-0.791 0.88 y = 0.1802x-0.655 0.92
R124 y = 0.4157x-0.73 0.88 y = 0.1241x-0.595 0.89
R136 y = 0.397x-0.684 0.87 y = 0.1115x-0.551 0.86
R148 y = 0.5396x-0.682 0.87 y = 0.1395x-0.547 0.85
R160 y = 0.7837x-0.69 0.87 y = 0.1866x-0.553 0.85

*At the bottom of AC layer.

y = Horizontal strain.

x = Index.

Note: There were 17 TSD loading data points. Bold cells indicate indices in class 1.

Table 46. Relationship between R1 and horizontal strains at bottom of AC with all loading data.
Index Relation with Midline Horizontal Strain* Relation with Maximum Horizontal Strain*
Equation R2 Equation R2
R18 y = 6.2386x-1.091 0.74 y = 1.2078x-0.895 0.88
R112 y = 2.2986x-0.968 0.87 y = 0.3945x-0.763 0.95
R118 y = 0.9436x-0.843 0.91 y = 0.1584x-0.643 0.93
R124 y = 0.6542x-0.778 0.91 y = 0.1079x-0.583 0.90
R136 y = 0.6504x-0.733 0.90 y = 0.0994x-0.542 0.87
R148 y = 0.9188x-0.732 0.89 y = 0.125x-0.539 0.85
R160 y = 1.3733x-0.742 0.89 y = 0.1666x-0.545 0.85

*At the bottom of AC layer.

y = Horizontal strain.

x = Index.

Note: There were 43 data points from both TSD and RWD loading. Bold cells indicate indices in class 1.

Figure 169. Graph. Relationship between R112 and horizontal strains at bottom of AC with TSD loading data. This graph shows the relationship between radius of curvature at 12 inches (305 mm) from the center of the load (R1 subscript 12) and maximum horizontal strains at the bottom of the asphalt concrete (AC) with Traffic Speed Deflectometer (TSD) loading data. The y-axis shows maximum horizontal strain at bottom of AC from 0 to 0.0006 strain, and the x-axis shows R1 subscript 12 from 0 to 30,000 inches (0 to 762,000 mm). In general, maximum horizontal strain reduces with increase in R1 subscript 12. The best fitted curve is an inverse power curve with the equation y equals 0.4438 times x raised to the power of -0.775. The R square value is 0.94.

1 inch = 25.4 mm

Figure 169. Graph. Relationship between R112 and horizontal strains at bottom of AC with TSD loading data.

Figure 170. Graph. Relationship between R112 and horizontal strains at bottom of AC with all loading data. This graph shows the relationship between the radius of curvature at 12 inches (305 mm) from the center of the load (R1 subscript 12) and horizontal strains at the bottom of the asphalt concrete (AC) with all loading data. The y-axis shows maximum horizontal strain at the bottom of AC from 0 to 0.0006 strain, and the x-axis shows R1subscript 12 from 0 to 30,000 inches (0 to 762,000 mm). In general, maximum horizontal strain reduces with an increase in R1 subscript 12. The best fitted curve is a power curve with the equation y equals 0.3945 times x raised to the power of -0.763. The R square value is 0.95.

1 inch = 25.4 mm

Figure 170. Graph. Relationship between R112 and horizontal strains at bottom of AC with all loading data.

Table 47. Relationship between SCI and horizontal strains at bottom of AC with TSD loading data.
Index Relation with Midline Horizontal Strain* Relation with Maximum Horizontal Strain*
Equation R2 Equation R2
SCI8 y = 0.0969x1.0201 0.75 y = 0.0553x0.8958 0.88
SCI12 y = 0.0277x0.9119 0.85 y = 0.0161x0.775 0.94
SCI18 y = 0.0104x0.7911 0.88 y = 0.0064x0.6547 0.92
SCI24 y = 0.0067x0.73 0.88 y = 0.0043x0.5948 0.89
SCI36 y = 0.0047x0.6841 0.87 y = 0.0031x0.551 0.86
SCI48 y = 0.0044x0.6817 0.87 y = 0.003x0.547 0.85

*At the bottom of AC layer.

y = Horizontal strain.

x = Index.

Note: There were 17 TSD loading data points. Bold cells indicate indices in class 1.

Table 48. Relationship between SCI and horizontal strains at bottom of AC with all loading data.
Index Relation with Midline Horizontal Strain* Relation with Maximum Horizontal Strain*
Equation R2 Equation R2
SCI8 y = 0.142x1.0914 0.74 y = 0.0543x0.8949 0.88
SCI12 y = 0.0365x0.9684 0.87 y = 0.0151x0.7626 0.95
SCI18 y = 0.0129x0.8432 0.91 y = 0.006x0.6427 0.93
SCI24 y = 0.008x0.778 0.91 y = 0.004x0.5827 0.90
SCI36 y = 0.0056x0.7335 0.90 y = 0.003x0.5422 0.86
SCI48 y = 0.0053x0.7324 0.89 y = 0.0028x0.5392 0.85

*At the bottom of AC layer.

y = Horizontal strain.

x = Index.

Note: There were 43 data points from both TSD and RWD loading. Bold cells indicate indices in class 1.

Figure 171. Graph. Relationship between SCI12 and horizontal strains at bottom of AC with TSD loading data. This graph shows the relationship between Surface Curvature Index at 12 inches (305 mm) (SCI subscript 12) and horizontal strains at the bottom of the asphalt concrete (AC) with Traffic Speed Deflectometer (TSD) loading data. The y-axis shows maximum horizontal strain at the bottom of AC from 0 to 0.0006 strain, and the x-axis shows SCI subscript 12 from 0 to 0.015 inches (0 to 0.381 mm). In general, maximum horizontal strain increases with an increase in SCI subscript 12. The best fitted curve is a power curve with an equation of y equals 0.0161 times x raised to the power of 0.775. The R square value is 0.94.

1 inch = 25.4 mm

Figure 171. Graph. Relationship between SCI12 and horizontal strains at bottom of AC with TSD loading data.

Figure 172. Graph. Relationship between SCI12 and horizontal strains at bottom of AC with all loading data. This graph shows the relationship between Surface Curvature Index at 12 inches (305 mm) (SCI subscript 12) and horizontal strains at the bottom of the asphalt concrete (AC) with all loading data. The y-axis shows maximum horizontal strain at the bottom of AC from 0 to 0.0006 strain, and the x-axis shows SCI subscript 12 from 0 to 0.015 inches (0 to 0.381 mm). In general, maximum horizontal strain increases with an increase in SCI subscript 12. The best fitted curve is a power curve with an equation of y equals 0.0151 times x raised to the power of 0.7626. The R square value is 0.95.

1 inch = 25.4 mm

Figure 172. Graph. Relationship between SCI12 and horizontal strains at bottom of AC with all loading data.

Table 49. Relationship between SCIm and horizontal strains at bottom of AC with TSD loading data.
Index Relation with Midline Horizontal Strain* Relation with Maximum Horizontal Strain*
Equation R2 Equation R2
SCIm8 y = 0.0713x0.9751 0.76 y = 0.0417x0.854 0.89
SCIm12 y = 0.0234x0.883 0.84 y = 0.014x0.7505 0.92
SCIm18 y = 0.0096x0.7774 0.88 y = 0.0061x0.6437 0.92
SCIm24 y = 0.0063x0.7211 0.87 y = 0.0041x0.5879 0.89
SCIm36 y = 0.0046x0.6782 0.87 y = 0.0031x0.5465 0.86
SCIm48 y = 0.0043x0.6763 0.86 y = 0.0029x0.5429 0.85

*At the bottom of AC layer.

y = Horizontal strain.

x = Index.

Note: There were 17 TSD loading data points. Bold cells indicate indices in class 1.

Table 50. Relationship between SCIm and horizontal strains at bottom of AC with all loading data.
Index Relation with Midline Horizontal Strain* Relation with Maximum Horizontal Strain*
Equation R2 Equation R2
SCIm8 y = 0.1022x1.0439 0.77 y = 0.0407x0.8526 0.91
SCIm12 y = 0.0306x0.9386 0.87 y = 0.0131x0.739 0.95
SCIm18 y = 0.012x0.8292 0.91 y = 0.0057x0.6323 0.93
SCIm24 y = 0.0076x0.7689 0.91 y = 0.0038x0.5763 0.89
SCIm36 y = 0.0055x0.7274 0.90 y = 0.0029x0.538 0.86
SCIm48 y = 0.0051x0.7268 0.89 y = 0.0027x0.5354 0.85

*At the bottom of AC layer.

y = Horizontal strain.

x = Index.

Note: There were 43 data points from both TSD and RWD loading. Bold cells indicate indices in class 1.

Figure 173. Graph. Relationship between SCIm12 and horizontal strains at bottom of AC with TSD loading data. This graph shows the relationship between Surface Curvature Index using maximum deflection at 12 inches (305 mm) (SCIm subscript 12) and horizontal strains at the bottom of the asphalt concrete (AC) with Traffic Speed Deflectometer (TSD) loading data. The y-axis shows maximum horizontal strain at bottom of AC from 0 to 0.0006 strain, and the x-axis shows SCIm subscript 12 from 0 to 0.015 inches (0 to 0.381 mm). In general, maximum horizontal strain increases with increase in SCIm subscript 12. The best fitted curve is a power curve with an equation of y equals 0.014 times x raised to the power of 0.7505. The R square value is 0.92.

1 inch = 25.4 mm

Figure 173. Graph. Relationship between SCIm12 and horizontal strains at bottom of AC with TSD loading data.

Figure 174. Graph. Relationship between SCIm12 and horizontal strains at bottom of AC with all loading data. This graph shows the relationship between Surface Curvature Index using maximum deflection at 12 inches (305 mm) (SCIm subscript 12) and horizontal strains at the bottom of the asphalt concrete (AC) with all loading data. The y-axis shows maximum horizontal strain at bottom of AC from 0 to 0.0006 strain, and the x-axis shows SCIm subscript 12 from 0 to 0.015 inches (0 to 0.381 mm). In general, maximum horizontal strain increases with increase in SCIm subscript 12. The best fitted curve is a power curve with an equation of y equals 0.0131 times x raised to the power of 0.739. The R square value is 0.95.

1 inch = 25.4 mm

Figure 174. Graph. Relationship between SCIm12 and horizontal strains at bottom of AC with all loading data.

Table 51. Relationship between DSI4 - r and horizontal strains at bottom of AC with TSD loading data.
Index Relation with Midline Horizontal Strain* Relation with Maximum Horizontal Strain*
Equation R2 Equation R2
DSI4 - 8 y = 0.0641x0.9153 0.79 y = 0.0357x0.7917 0.90
DSI4 - 12 y = 0.0201x0.8324 0.84 y = 0.0119x0.7019 0.91
DSI4 - 18 y = 0.0086x0.7386 0.87 y = 0.0054x0.6079 0.90
DSI4 - 24 y = 0.0057x0.6872 0.87 y = 0.0037x0.5573 0.87

*At the bottom of AC layer.

y = Horizontal strain.

x = Index.

Note: There were 17 TSD loading data points. Bold cells indicate indices in class 1.

Table 52. Relationship between DSI4 - r and horizontal strains at bottom of AC with all loading data.
Index Relation with Midline Horizontal Strain* Relation with Maximum Horizontal Strain*
Equation R2 Equation R2
DSI4 - 8 y = 0.0891x0.9776 0.82 y = 0.0337x0.7862 0.93
DSI4 - 12 y = 0.0257x0.8833 0.88 y = 0.0111x0.6886 0.94
DSI4 - 18 y = 0.0104x0.7857 0.91 y = 0.005x0.5947 0.91
DSI4 - 24 y = 0.0067x0.7313 0.90 y = 0.0035x0.5445 0.88

*At the bottom of AC layer.

y = Horizontal strain.

x = Index.

Note: There were 43 data points from both TSD and RWD loading. Bold cells indicate indices in class 1.

Figure 175. Graph. Relationship between DSI4 - 8 and horizontal strains at bottom of AC with TSD loading data. This graph shows the relationship between Deflection Slope Index based on deflection at 4 and 8 inches (101.6 and 203.2 mm) (DSI subscript 4 - 8) and horizontal strains at the bottom of the asphalt concrete (AC) with Traffic Speed Deflectometer (TSD) loading data. The y-axis shows maximum horizontal strain at bottom of AC from 0 to 0.0006 strain, and the x-axis shows DSI subscript 4 - 8 from 0 to 0.006 inch (0 to 0.152 mm). In general maximum horizontal strain increases with increase in DSI subscript 4 - 8. The best fitted curve is a power curve with an equation of y equals 0.0357 times x raised to the power of 0.7917. The R square value is 0.90.

1 inch = 25.4 mm

Figure 175. Graph. Relationship between DSI4 - 8 and horizontal strains at bottom of AC with TSD loading data.

Figure 176. Graph. Relationship between DSI4 - 8 and horizontal strains at bottom of AC with all loading data. This graph shows the relationship between Deflection Slope Index based on deflection at 4 and 8 inches (101.6 and 203.2 mm) (DSI subscript 4 - 8) and horizontal strains at the bottom of the asphalt concrete (AC) with all loading data. The y-axis shows maximum horizontal strain at bottom of AC from 0 to 0.0006 strain, and the x-axis shows DSI subscript  4 - 8 from 0 to 0.006 inch (0 to 0.152 mm). In general, maximum horizontal strain increases with increase in DSI subscript 4 - 8. The best fitted curve is a power curve with an equation of y equals 0.0337 times x raised to the power of 0.7862. The R square value is 0.93.

1 inch = 25.4 mm

Figure 176. Graph. Relationship between DSI4 - 8 and horizontal strains at bottom of AC with all loading data.

Because vertical strain at the top of the subgrade is an important response that relates to subgrade rutting, the deflection basin indices considered were also correlated with those strains.

Table 53, table 54, figure 177, and figure 178 show the relationships between SCI and vertical strain at the top of the subgrade. While SCI (e.g., SCI12) was one of the most appropriate indices related to maximum horizontal strain at the bottom of AC, it cannot be used to relate to subgrade strain because of poor correlation.

Table 53. Relationship between SCI and maximum vertical strains on top of the subgrade with TSD loading data.
Index Relation with Maximum Vertical Strain*
Equation R2
SCI8 y = 1E+07x1.7785 0.38
SCI12 y = 6E+06x1.904 0.62
SCI18 y = 2E+06x1.7981 0.76
SCI24 y = 815968x1.7374 0.84
SCI36 y = 447767x1.6776 0.88
SCI48 y = 402727x1.6869 0.89
SCI60 y = 414955x1.7136 0.89

*On top of subgrade.

y = Vertical strain.

x = Index.

Note: There were 17 TSD loading data points.

Table 54. Relationship between SCI and maximum vertical strains on top of the subgrade with all loading data.
Index Relation with Maximum Vertical Strain*
Equation R2
SCI8 y = 9E+06x1.752 0.39
SCI12 y = 4E+06x1.8178 0.62
SCI18 y = 1E+06x1.7333 0.78
SCI24 y = 621344x1.6678 0.84
SCI36 y = 360860x1.6188 0.88
SCI48 y = 328608x1.63 0.89
SCI60 y = 335884x1.654 0.90

*On top of subgrade.

y = Vertical strain.

x = Index.

Note: There were 43 data points from both TSD and RWD loading. Bold cells indicate indices in class 1.

Figure 177. Graph. Relationship between SCI60 and maximum vertical strain on top of the subgrade with TSD loading data. This graph shows the relationship between Surface Curvature Index at 60 inches (1,524 mm) (SCI subscript 60) and maximum vertical strains on top of the subgrade with Traffic Speed Deflectometer (TSD) loading data. The y-axis shows maximum vertical strain on top of the subgrade from 0 to 1,400 microstrain, and the x-axis shows SCI subscript 60 from 0 to 0.04 inch (0 to 1.016 mm). In general, maximum horizontal strain increases with increase in SCI subscript 60. The best fitted curve is a power curve with an equation of y equals 414,955 times x raised to the power of 1.7136. The R square value is 0.89.

1 inch = 25.4 mm

Figure 177. Graph. Relationship between SCI60 and maximum vertical strain on top of the subgrade with TSD loading data.

Figure 178. Graph. Relationship between SCI60 and maximum vertical strain on top of the subgrade with all loading data. This graph shows the relationship between Surface Curvature Index at 60 inches (1,524 mm) (SCI subscript 60) and maximum vertical strains on top of the subgrade with all loading data. The y-axis shows maximum vertical strain on top of subgrade from 0 to 1,600 microstrain, and the x-axis shows SCI subscript 60 is from 0 to 0.04 inch (0 to 1.016 mm). In general, maximum horizontal strain increases with increase in SCI subscript 60. The best fitted curve is a power curve with an equation of y equals 335,884 times x raised to the power of 1.654. The R square value is 0.8973.

1 inch = 25.4 mm

Figure 178. Graph. Relationship between SCI60 and maximum vertical strain on top of the subgrade with all loading data.

Table 55, table 56, figure 179, and figure 180 show the relationships between DSI24 - r and vertical strain at the top of the subgrade. DSI24 - 36, which is also known as BCI, had a good correlation, indicated by class 1 classification. Moreover, it was observed that those indices based on displacements at far away locations from the loaded area were better related to vertical strain at the top of the subgrade. This is because these indices reflect the influence of the lower portion of the pavement system.(62,63) Similar tables and figures looking at the rutting strain relationship were developed for every index in table 44, but they are not included in this report as they do not provide further insights. The data used to generate these tables and figures can be obtained directly from FHWA.

Table 55. Relationship between DSI24 - r and maximum vertical strain on top of the subgrade with TSD loading data.
Index Relation with Maximum Vertical Strain*
Equation R2
DSI24 - 36 y = 937463x1.3155 0.97
DSI24 - 48 y = 994720x1.4238 0.97
DSI24 - 60 y = 1E+06x1.5332 0.97

*On top of subgrade.

y = Vertical strain.

x = Index.

Note: There were 17 TSD loading data points. Bold cells indicate indices in class 1.

Table 56. Relationship between DSI24 - r and maximum vertical strain on top of the subgrade with all loading data.
Index Relation with Maximum Vertical Strain*
Equation R2
DSI24 - 36 y = 880697x1.3031 0.98
DSI24 - 48 y = 936915x1.4106 0.97
DSI24 - 60 y = 1E+06x1.5125 0.97

*On top of subgrade.

y = Vertical strain.

x = Index.

Note: There were 43 data points from both TSD and RWD loading. Bold cells indicate indices in class 1.

Figure 179. Graph. Relationship between DSI24 - 36 and maximum vertical strain on top of the subgrade with TSD loading data. This graph shows the relationship between Deflection Slope Index based on deflection at 24 and 36 inches (609.6 and 914.4 mm) (DSI subscript 
24 - 36) and maximum vertical strains on top of the subgrade with Traffic Speed Deflectometer (TSD) loading data. The y-axis shows maximum vertical strain on top of subgrade from 0 to 1,400 microstrain, and the x-axis shows DSI subscript 24 - 36 from 0 to 0.008 inch (0 to  0.203 mm). In general, maximum horizontal strain increases with increase in DSI subscript  24 - 36. The best fitted curve is a power curve with an equation of y equals 937,463 times x raised to the power of 1.3155. The R square value is 0.97.

1 inch = 25.4 mm

Figure 179. Graph. Relationship between DSI24 - 36 and maximum vertical strain on top of the subgrade with TSD loading data.

Figure 180. Graph. Relationship between DSI24 - 36 and maximum vertical strain on top of the subgrade with all loading data. This graph shows the relationship between Deflection Slope Index based on deflection at 24 and 36 inches (609.6 and 914.4 mm) (DSI subscript 24 - 36) and maximum vertical strains on top of the subgrade with all loading data. The y-axis shows maximum vertical strain on top of subgrade from 0 to 1,400 microstrain, and the x-axis shows DSI subscript 24 - 36 from 0 to 0.008 inch (0 to 0.203 mm). In general, maximum horizontal strain increases with increase in DSI subscript 24 - 36. The best fitted curve is a power curve with an equation of y equals 880,697 times x raised to the power of 1.3031. The R square value is 0.9768.

1 inch = 25.4 mm

Figure 180. Graph. Relationship between DSI24 - 36 and maximum vertical strain on top of the subgrade with all loading data.

Summary of Evaluation of Indices

Table 57 through table 60 summarize the most appropriate indices for TSD and for the combined data (TSD and RWD) against maximum horizontal strain at the bottom of the AC and maximum vertical strain on the top of subgrade, respectively. Some of the most significant observations from these tables are as follows (see table 44 for definitions of indices):

While SCI12 was found to be one of the most appropriate indices for maximum horizontal strain at the bottom of the AC (R2 = 0.95), it was not a good index for subgrade vertical strain (R2 = 0.62).

Table 57. Most appropriate indices using TSD data related to maximum horizontal strain at bottom of AC layer.
Best Indices with TSD Loading
(Relationship with Maximum Horizontal Strain)
Index R2
R1 R112 0.94
R118 0.92
R2 R218 0.92
R224 0.94
R236 0.90
SCI SCI12 0.94
SCI18 0.92
SCIm12 0.92
SCIm18 0.91
DSI DSI4 - 8 0.90
DSI4 - 12 0.91
DSI4 - 18 0.90
SD SD12 0.93
SD18 0.92
TS TS8 0.93
TS24 0.91
AUPP Am 0.90
Table 58. Most appropriate indices using all data related to maximum horizontal strain at bottom of AC layer.
Best Indices with All Data
(Relationship with Maximum Horizontal Strain)
Index R2
R1 R112 0.95
R118 0.93
R2 R218 0.95
R224 0.94
SCI SCI12 0.95
SCI18 0.93
SCIm8 0.91
SCIm12 0.95
SCIm18 0.93
DSI DSI4 - 8 0.93
DSI4 - 12 0.94
DSI4 - 18 0.91
DSI8 - 12 0.92
SD SD12 0.95
SD18 0.93
TS TS8 0.94
AUPP Am 0.91
Table 59. Most appropriate indices using TSD data related to maximum vertical strain at top of subgrade.
Best Indices with TSD Loading
(Relationship with Maximum Vertical Strain at Top of Subgrade)
Index R2
R2 R260 0.92
DSI DSI4 - 48 0.90
DSI4 - 60 0.90
DSI8 - 36 0.92
DSI8 - 48 0.93
DSI8 - 60 0.93
DSI12 - 18 0.90
DSI12 - 24* 0.94
DSI12 - 36 0.95
DSI12 - 48 0.95
DSI12 - 60 0.95
DSI18 - 24 0.97
DSI18 - 36 0.97
DSI18 - 48 0.97
DSI18 - 60 0.97
DSI24 - 36** 0.97
DSI24 - 48 0.97
DSI24 - 60 0.97
TS TS12 0.90
TS18 0.92
TS36 0.95
  Shape factor F2 0.91

*Indicates BDI.

**Indicates BCI.

Table 60. Most appropriate indices using all data related to maximum vertical strain at top of subgrade.
Best Indices with All Data
(Relationship with Maximum Vertical Strain at Top of Subgrade)
Index R2
R2 R248 0.90
R260 0.93
DSI DSI4 - 48 0.91
DSI4 - 60 0.91
DSI8 - 24 0.91
DSI8 - 36 0.93
DSI8 - 48 0.94
DSI8 - 60 0.94
DSI12 - 18 0.92
DSI12 - 24* 0.95
DSI12 - 36 0.96
DSI12 - 48 0.96
DSI12 - 60 0.96
DSI18 - 24 0.97
DSI18 - 36 0.98
DSI18 - 48 0.97
DSI18 - 60 0.97
DSI24 - 36** 0.98
DSI24 - 48 0.97
DSI24 - 60 0.97
TS TS18 0.91
TS24 0.91
TS36 0.94

*Indicates BDI.

**Indicates BCI.

Evaluating Indices Using MnROAD Measured Data

During the September 2013 TSDD field trials, pavement response data were collected using both project and MnROAD sensors. The project sensors collected surface displacements, while pavement responses (longitudinal AC strain and vertical stresses at the top of the subgrade) were collected by the MnROAD sensors.

The correlations between deflection indices and pavement responses can also be explored based solely on the measured data. From project sensors embedded at the pavement surface, the surface displacements along the midline of the tires in the longitudinal direction can be estimated. However, adjustments should be made to account for the time lag that exists between Dmax and D0. In addition, as pointed out in chapter 7, the lateral wheel wander can also affect the estimation of the midline deflections.

MnROAD sensors collected responses at interior pavement locations (see table 41), and they were also affected by the lateral wheel wander. In other words, the maximum responses given by the MnROAD sensors may not have been the actual maxima for the responses in question. Also, because MnROAD sensors that measured vertical stresses were considered unreliable (section 7.6), only the measured data from the longitudinal AC strain gauges were correlated.

Table 61 shows the best correlated indices from 3D-Move computed displacement bowls with respect to 3D-Move computed maximum AC strains and the measured maximum horizontal AC strains. R2 values of the correlations with computed displacements and maximum strains (i.e., both 3D-Move derived) are higher. It should be noted R2 values that are shown in the table correspond to the respective best curve-fit equations obtained for the relationship.

Table 61. Comparison of most appropriate indices with respect to maximum horizontal strain: 3D-Move results and MnROAD measured data.
Best Indices with All Data
(Relationship with Maximum Horizontal Strain for 3D-Move and Measured Strain)
Index R2 from 3D-Move Relationships R2 from Measured Relationships
R1 R112 0.95 0.86
R118 0.93 0.87
R2 R218 0.95 0.88
R224 0.94 0.89
SCI SCI12 0.95 0.86
SCI18 0.93 0.87
SCIm8 0.91 0.83
SCIm12 0.95 0.88
SCIm18 0.93 0.90
DSI DSI4 - 8 0.93 0.83
DSI4 - 12 0.94 0.85
DSI4 - 18 0.91 0.86
DSI8 - 12 0.92 0.85
SD SD12 0.95 0.86
SD18 0.93 0.87
TS TS8 0.94 0.91
AUPP Am 0.91 0.87

Evaluation of RWD Sensor Location from Project Sensor Measurements

As noted previously, the RWD used two sensors within the deflection bowl to characterize the deflected pavement surface. The sensors were located 7.25 inches (184.15 mm) behind the rear wheels and 7.75 inches (196.85 mm) in front of the rear wheels, as shown in figure 19 in chapter 4. In addition to the accuracy evaluation of RWD laser sensor presented in chapter 6, a deflection basin measured from the project sensor was used to evaluate the effectiveness of positioning the sensor 7.25 inches (184.15 mm) behind the wheels in capturing the maximum deflection. The response lag between the time that the rear tire crosses over the sensor and the time when the maximum response occurred in the project sensor signal is reproduced in table 62 for RWD testing. Table 62 also shows the percent difference between the deflections measured 7.25 inches (184.15 mm) behind the rear axle (D-7.25) and Dmax. Response lag is a function of pavement stiffness and vehicle speed. Cell 3, which was the stiffest of the three cells tested, had the least response lag and percent difference. Also, as expected, response lag decreased as vehicle speed increased. In summary, for stiffer pavements, the maximum deflection occurred closer to the center of the tire when tested at 60 mi/h (96.9 km/h). The hypothesis that maximum deflection occurs 7.25 inches (184.15 mm) behind the tire is valid only for less stiff pavements tested at relatively lower traffic speeds and may not be valid for stiff pavements tested at 60mi/h (96.9 km/h).

As noted, a number of previous studies have concluded that curvature indices, which are evaluated based on the difference in surface deflection at two points, reflect the characteristics of the AC layer.(62,63,21) The only possible curvature index from RWD, D-7.25D7.75 was evaluated further in this study. Table 62 also summarizes the percent difference between the computed index (D-7.25D7.75) and SCI15 as computed from the deflection basin measured in project sensor. SCI15 is the difference between maximum deflection and the deflection 15 inches (381 mm) in front of maximum deflection. When the response lag was less than 7.25 inches (184.15 mm) as in stiff pavements, the two deflection measurements D-7.25 and D7.75 were made on either side of the deflection basin, thus increasing the difference between the actual and computed index. The accuracy of the index computed from RWD deflection was hampered by the measurement location, especially in stiff pavements. In order to improve the compatibility of the RWD device to wider pavement sections, it is suggested that the location of the sensor be positioned in front of the rear axle.

Table 62. Effect of RWD laser position on deflection and computed index.
Cell Speed (mi/h) RWD Response Lag (inches) Percent Difference Between Deflection at D-7.25 and Dmax Percent Difference Between Index (D-7.25 – D7.75) and SCI15
34 30 7.3 0.04 0.15 -0.49 -0.11
45 6.9 0.25 0.27
19 30 4.5 3.42 4.04 22.11 28.75
45 3.4 5.33 32.98
60 4 3.38 31.17
3 30 4.3 3.47 6.84 28.95 41.91
45 2.5 5.80 42.30
60 1.6 11.26 54.49

1 mi/h = 1.6 km/h

1 inch = 25.4 mm

8.3 Step 2: Correlating Deflection Basin Indices using 3D-Move Analysis of Simulated Pavement Sections

In the previous section, 3D-Move runs for the MnROAD accuracy cells were used to find the surface deflection indices that correlated best with pavement responses. However, the pavements for the MnROAD accuracy cells were relatively thin, with AC layer thicknesses varying between 3 and 5 inches (76.2 and 127 mm). Factors such as AC layer thickness, modulus and vehicle speed can and do influence the deflection correlations. Accordingly, in this section, the details of the 3D-Move-based correlation investigation that used a variety of pavement structures with differing properties (thickness and modulus) and vehicle speeds are presented.

Simulated Pavements for 3D-Move Based Correlations

Figure 181 shows a generic pavement structure used in the analyses. For the AC layer, three thickness (3, 6, and 12 inches (76.2, 152.4, 304.8 mm)) and three moduli (200, 500, and 800 ksi (1.37, 3.44, and 5.51 GPa)) were considered. The base layer thickness and modulus were fixed at 12 inches (304.8 mm) and 60 ksi (0.41 GPa), respectively. Moduli of 10 and 20 ksi (0.07 and 0.14 GPa) were used for the subgrade layer. In addition, vehicle speeds of 30 and 60 mi/h (48.3 and 96.6 km/h) were used in the 3D-Move runs. This resulted in 36 combinations of pavement structures and vehicle speeds, as shown in table 63.

Figure 181. Illustration. Pavement structures used with 3D-Move analyses. This illustration shows a generic pavement structure used in the analyses. For the asphalt concrete layer, three thicknesses (3, 6, and 12 inches (76.2, 152.4, and 304.8 mm)) and three moduli (200, 500, and 800 ksi (1,378, 3,445, and 5,512 MPa) were considered. The base layer thickness and modulus are fixed at 12 inches (304.8 mm) and 60 ksi (413.4 MPa), respectively. Moduli of 10 and 20 ksi (68.9 to 137.8 MPa) are used for the subgrade layer. In addition, vehicle speeds of 30 and 60 mi/h (48.3 and 96.6 km/h) are used in the 3D-Move runs.

1 mi/h = 1.61 km/h

1 inch = 25.4 mm

1 ksi = 6.89 MPa

Figure 181. Illustration. Pavement structures used with 3D-Move analyses.

Table 63. Pavement considered in 3D-Move analyses and corresponding identification key.
Identification Key AC Modulus at 30 Hz (ksi) AC Thickness (inches) Subgrade Modulus (ksi) Vehicle Speed (mi/h)
B200-3-10-30 200 3 10 30
B200-3-10-60 200 3 10 60
B200-3-20-30 200 3 20 30
B200-3-20-60 200 3 20 60
B200-6-10-30 200 6 10 30
B200-6-10-60 200 6 10 60
B200-6-20-30 200 6 20 30
B200-6-20-60 200 6 20 60
B200-12-10-30 200 12 10 30
B200-12-10-60 200 12 10 60
B200-12-20-30 200 12 20 30
B200-12-20-60 200 12 20 60
B500-3-10-30 500 3 10 30
B500-3-10-60 500 3 10 60
B500-3-20-30 500 3 20 30
B500-3-20-60 500 3 20 60
B500-6-10-30 500 6 10 30
B500-6-10-60 500 6 10 60
B500-6-20-30 500 6 20 30
B500-6-20-60 500 6 20 60
B500-12-10-30 500 12 10 30
B500-12-10-60 500 12 10 60
B500-12-20-30 500 12 20 30
B500-12-20-60 500 12 20 60
B800-3-10-30 800 3 10 30
B800-3-10-60 800 3 10 60
B800-3-20-30 800 3 20 30
B800-3-20-60 800 3 20 60
B800-6-10-30 800 6 10 30
B800-6-10-60 800 6 10 60
B800-6-20-30 800 6 20 30
B800-6-20-60 800 6 20 60
B800-12-10-30 800 12 10 30
B800-12-10-60 800 12 10 60
B800-12-20-30 800 12 20 30
B800-12-20-60 800 12 20 60

1 ksi = 6.89 MPa

1 inch = 25.4 mm

1 mi/h = 1.61 km/h

The impact of pavement temperature was reflected in the AC modulus; therefore, it was not considered an independent parameter. The AC modulus as a function of frequency (a master curve) needs to be specified as input when the viscoelastic material characteristics are considered in 3D-Move. The procedure to build a master curve from AC mix properties is explained in chapter 7. The AC modulus given in table 63 was considered appropriate for a frequency of 30 Hz when estimating the AC moduli as a function of frequency. Table 64 shows the AC mix properties used to develop the master curve for the effort in question.

Table 64. AC mix properties used with 3D-Move analysis.
Variable Value
Air Voids (percent) 7
Effective binder content (percent) 11
Void filled with asphalt (percent) 61
Percent retained for 0.75 inch 11.62
Percent retained for 0.375 inch 35.3
Percent retained #4 sieve 52.64
Percent passing #200 sieve 7.28
PG grade 58-28
Binder—regression intercept 11.01
Binder—VTS -3.701

1 inch = 25.4 mm

3D-Move Results and Sensitivity Analysis

The 75 indices listed in table 44 were reevaluated using the 3D-Move results from the 36 pavement structure and vehicle speed combinations detailed in the previous section. The sensitivity of those indices was investigated with respect to the following parameters: AC thickness and modulus, subgrade modulus, and vehicle speed. A major objective of this analysis was to isolate the parameters that most affect the indices. Once identified, those parameters could be used as a starting point in categorizing the pavements in the next step using JULEA.(26)

For the purpose of brevity, only selected figures showing notable conclusions are presented in this chapter. Similar figures to those presented in this chapter were developed for other deflection indices, but they are not included in this report, as they do not provide further insights. The data used to generate these figures can be obtained directly from FHWA.

Figure 182 shows the variation of SCI12 for the pavement combinations considered. The x-axis shows the key that can be used to identify easily a specific pavement combination (see table 63). In this graph, nine categories are shown with different fill patterns. For each category, the AC surface layer properties (AC thickness and AC modulus) remained constant. As shown, SCI12, which has been often viewed as an indicator of the influence of the AC layer, is strongly influenced by the AC thickness and modulus.

Figure 182. Graph. Variation of SCI12 calculated with 3D-Move in simulated pavement combinations. This bar graph shows Surface Curvature Index at 12 inches (304.8 mm) (SCI subscript 12) in simulated pavement combinations. The y-axis shows SCI subscript 12 from 0 to 0.006 inch (0 to 0.1524 mm), and the x-axis includes 36 simulated pavement combinations. These combinations includes three asphalt concrete (AC) thicknesses (3, 6, and 12 inches (76.2, 152.4, and 304.8 mm)) with three moduli (200, 500, and 800 ksi (1,378, 3,445, and 5,512 MPa)), two subgrade moduli (10 and 20 ksi (68.9 and 137.8 MPa)), and two speeds (30 and 60 mi/h (48.3 and 96.6 km/h)). The combinations can be categorized in nine categories. For each category, the AC surface layer properties (AC thickness and AC modulus) were constant. For example, pavement structure with AC thickness of 3 inches (76.2 mm) and modulus of 200 ksi (1,378 MPa) in two subgrade moduli of 10 and 20 ksi (68.9 and 137.8 MPa) and two speeds of 30 and 60 mi/h (48.3 and 96.6 km/h) are placed in the first category, which represents the softest AC. Pavement structure with AC thickness of 12 inches (304.8 mm) and modulus of 800 ksi (5,512 MPa ) in two subgrade moduli of 10 and 20 ksi (68.9 and 137.8 MPa) and two speeds of 30 and 60 mi/h (48.3 and 96.6 km/h) are placed in the last category, which represents the stiffest AC.  SCI subscript 12 varies from about 0.005 inch (0.127 mm) for the first category to about 0.0002 inch (0.005 mm) for the last category. For the combinations in each category, SCI subscript 12 is almost the same, so it can be concluded this index is strongly influenced by the AC thickness and modulus.

1 inch = 25.4 mm

Figure 182. Graph. Variation of SCI12 calculated with 3D-Move in simulated pavement combinations.

TS is potentially considered an important index because it is measured directly by the TSD, and thus uncertainties associated with algorithms needed to convert the measured deflection velocities to surface deflections are avoided. In general, TS showed high sensitivity to changes in the pavement layer properties (stiffness and thickness). In particular, TS48 and TS60 seemed to be mostly affected by subgrade modulus. For example, TS60 is clearly influenced by subgrade modulus (see figure 183). As is shown later in this chapter, TS4 and TS8 are better correlated with the maximum horizontal strain at the bottom of thin and thick AC layers, respectively.

Figure 183. Graph. Variation of TS60 calculated with 3D-Move in simulated pavement combinations. This bar graph shows tangent slope at 60 inches (1524 mm) (TS subscript 60) in simulated pavement combinations. The y-axis shows TS subscript 60 from 0 to 0.00014, and the x-axis includes 36 simulated pavement combinations. These combinations includes three asphalt concrete thicknesses (3, 6, and 12 inches (76.2, 152.4, and 304.8 mm)) with three moduli (200, 500, and 800 ksi (1,378, 3,445 and 5,512 MPa)), two subgrade moduli (10 and 20 ksi (68.9 and 137.8 MPa)), and two speeds (30 and 60 mi/h (48.3 and 96.6 km/h)). In the combinations with the same subgrade moduli, the variations of TS subscript 60 are minimal. TS subscript 60 for the combinations with subgrade moduli of 10 ksi (68.9 MPa) varies from 0.000085 to 0.000115. TS subscript 60 for the combinations with subgrade moduli of 20 ksi (137.8 MPa) is about 0.00005 for all combinations. It is concluded this index is influenced by subgrade modulus.

Figure 183. Graph. Variation of TS60 calculated with 3D-Move in simulated pavement combinations.

R as defined by Horak was significantly affected by the properties of the surface AC layer and slightly affected by the stiffness of the subgrade.(62,63) Figure 184 shows the variation in R60 for the pavement combinations considered.

Figure 184. Graph. Variation of R60 calculated with 3D-Move in simulated pavement combinations. This bar graph shows radius of curvature at 60 inches (1524 mm) (R subscript 60) in simulated pavement combinations. The y-axis shows R subscript 60 from 0 to 140,000, and the x-axis includes 36 simulated pavement combinations. These combinations includes three asphalt concrete (AC) thicknesses (3, 6, and 12 inches (76.2, 152.4, and 304.8 mm)) with three moduli (200, 500, and 800 ksi (1,378, 3,445 and 5,512 MPa)), two subgrade moduli (10 and 20 ksi (68.9 and 137.8 MPa)), and two speeds (30 and 60 mi/h (48.3 and 96.6 km/h)). R subscript 60 varies from about 13,000 to 16,000 for the combinations with AC thickness of 
3 inches (76.2 mm). R subscript 60 varies from about 20,000 to 33,000 for the combinations with AC thickness of 6 inches (152.4 mm), and it varies from about 42,000 to 120,000 for the combinations with AC thickness of 12 inches (304.8 mm). It is concluded that this index is only slightly affected by the subgrade modulus.

1 inch = 25.4 mm

Figure 184. Graph. Variation of R60 calculated with 3D-Move in simulated pavement combinations.

D60 seemed to be the most promising parameter for estimating the subgrade modulus, as shown in figure 185. This parameter seemed to be only affected by the subgrade modulus; other material properties did not have a noticeable influence.

Figure 185. Graph. Variation of D60 calculated with 3D-Move in simulated pavement combinations. This bar graph shows deflection at 60 inches (1524 mm) (D subscript 60) in simulated pavement combinations. The y-axis shows D subscript 60 from 0 to 0.003 inch (0 to 0.0762 mm), and the x-axis includes 36 simulated pavement combinations. These combinations includes three asphalt concrete thicknesses (3, 6, and 12 inches (76.2, 152.4, and 304.8 mm)) with three moduli (200, 500, and 800 ksi (1,378, 3,445, and 5,512 MPa)), two subgrade moduli (10 and 20 ksi (68.9 and 137.8 MPa), and two speeds (30 and 60 mi/h (48.3 and 96.6 km/h)). In the combinations with the same subgrade moduli, the variations of D subscript 60 is minimal. D subscript 60 for the combinations with subgrade moduli of 10 ksi (68.9 MPa) varies from 0.0022 to 0.0025 inch (0.056 to 0.0635 mm), and D subscript 60 for the combinations with subgrade moduli of 20 ksi (137.8 MPa) varies from 0.0011 to 0.0013 inch (0.028 to 0.033 mm). It is concluded this index is influenced by subgrade modulus.

1 inch = 25.4 mm

Figure 185. Graph. Variation of D60 calculated with 3D-Move in simulated pavement combinations.

Figure 186 shows the variation in maximum horizontal strain at the bottom of the AC layer for various pavement combinations considered. Table 65 summarizes the response trends as a few of pavement-related parameters are increased one at a time. As shown in the referenced figure and table, increasing subgrade modulus affected the thin and thick pavements differently. For thin pavements, increasing the subgrade stiffness resulted in an increase in the horizontal strains at the bottom of the AC layer, while the opposite trend was observed for thick pavements (i.e., the strains decreased).

Click for description.

Figure 186. Graph. Variation of maximum horizontal strain at bottom of AC layer in simulated pavement combinations.

Table 65. Effects of an increase in selected pavement parameters on maximum horizontal strain at bottom of AC layer.
Increase in Parameter Maximum Horizontal Strain at
Bottom of AC Layer
AC modulus Decreased
AC thickness Decreased
Speed Decreased
Subgrade modulus Thin AC (3 inches) increased;
thick AC (12 inches) decreased

1 inch = 25.4 mm

Figure 187 through figure 206 show the variability of the correlations of some of the indices to the maximum horizontal strain at the bottom of the AC layer. In all figures, the numbers within parentheses in the legends indicate the number of data points. One of the important interpretations from these figures is that the AC thickness impacted the strengths of the relationships as judged by the R2 values. Many indices did not consistently relate well with the maximum horizontal strain for thin (3 inches (76.2 mm)) AC pavements. Other material properties, such as the subgrade and AC moduli, also influenced the strengths of the relationships for thin pavements. Conversely, thick (12 inches (304.8 mm)) AC pavements were less sensitive to those parameters.

Click for description

1 inch = 25.4 mm

Figure 187. Graph. Variability of relationships of R1 with maximum horizontal strain at bottom of AC layer for various AC thicknesses.

Figure 188. Graph. Variability of relationships of R1 with maximum horizontal strain at bottom of AC layer for various subgrade moduli. This bar graph shows the variability of relationships of radius of curvature (R1) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various subgrade moduli. The y-axis shows the R square value from 0 to 1, and the x-axis shows the R1 indices, which include R1 subscript 8, R1 subscript 12, R1 subscript 18, R1 subscript 24, R1 subscript 36, R1 subscript 48, and R1 subscript 60. The R square value for the R1 indices is shown for three datasets: all data points with 36 data points, subgrade modulus of 10 ksi (68.9 MPa) with 18 data points, and subgrade modulus of 20 ksi (137.8 MPa) with 18 data points. For all data points, the R square value varies from 0.87 to 0.96, and all indices except R1 subscript 60 have an R square value greater than 0.9; however, no value is shown for R1 subscript 8. For subgrade modulus of 10 ksi (68.9 MPa), The R square value is almost 0.97 for all indices; however, no value is shown for R1 subscript 8. For subgrade modulus of 20 ksi (137.8 MPa), the R square value varies from 0.81 to 0.97, and all indices except R1 subscript 8 have an R square value greater than 0.9.

1 ksi = 6.89 MPa

Figure 188. Graph. Variability of relationships of R1 with maximum horizontal strain at bottom of AC layer for various subgrade moduli.

Figure 189. Graph. Variability of relationships of R1 with maximum horizontal strain at bottom of AC layer for various AC moduli. This bar graph shows the variability of relationships of radius of curvature (R1) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various AC moduli. The y-axis shows the R square value from 0 to 1, and the x-axis shows the R1 indices, which include R1 subscript 8, R1 subscript 12, R1 subscript 18, R1 subscript 24, R1 subscript 36, R1 subscript 48, and R1 subscript 60. The R square value for the R1 indices is shown for four datasets: all data points which include 36 data points, AC modulus of 200 ksi (1,378 MPa) with 12 data points, AC modulus of 500 ksi (3,445 MPa) with 12 data points, and AC modulus of 800 ksi (5,512 MPa) with 12 data points. For all data points, the R square value varies from 0.87 to 0.96, and all indices except R1 subscript 60 have an R square value greater than 0.9; however, no value is shown for R1 subscript 8. For AC modulus of 200 ksi (1,378 MPa), the R square value varies from 0.74 to 0.98, and four indices (R1 subscript 8, R1 subscript 12, R1 subscript 18, and R1 subscript 24) have an R square value greater than 0.9. For AC modulus of 500 ksi (3,445 MPa), the R square value varies from 0.9 to 0.99. Finally for modulus of 800 ksi (5,512 MPa), the R square value varies from 0.93 to 0.99; however, no value is shown for R1 subscript 8.

1 ksi = 6.89 MPa

Figure 189. Graph. Variability of relationships of R1 with maximum horizontal strain at bottom of AC layer for various AC moduli.

Figure 190. Graph. Variability of relationships of R1 with maximum horizontal strain at bottom of AC layer for various vehicle speeds. This bar graph shows the variability of relationships of radius of curvature (R1) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various vehicle speeds. The y-axis shows the R square value from 0 to 1, and the x-axis shows the R1 indices, which include R1 subscript 8, R1 subscript 12, R1 subscript 18, R1 subscript 24, R1 subscript 36, R1 subscript 48, and R1 subscript 60. The R square value for the R1 indices is shown for three datasets: all data points which include 36 data points, vehicle speed of 30 mi/h (48.3 km/h) with 18 data points, and vehicle speed of 60 mi/h (96.6 km/h) with 18 data points. For all data points, the R square value varies from 0.87 to 0.96, and all indices except R1 subscript 60 have an R square value greater than 0.9. No value is shown for R1 subscript 8. For vehicle speed of 30 mi/h (48.3 km/h), the R square value varies from 0.86 to 0.96, and all indices except R1 subscript 48 and R1 subscript 60 have R square value greater than 0.9. No value is shown for R1 subscript 8. For vehicle speed of 60 mi/h (96.6 km/h), the R square value varies from 0.87 to 0.96, and all indices except R1 subscript 60 have an R square value greater than 0.9. No value is shown for R1 subscript 8.

1 mi/h = 1.61 km/h

Figure 190. Graph. Variability of relationships of R1 with maximum horizontal strain at bottom of AC layer for various vehicle speeds.

Figure 191. Graph. Variability of relationships of R2 with maximum horizontal strain at bottom of AC layer for various AC thicknesses. This bar graph shows the variability of relationships of radius of curvature (R2) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various AC thicknesses. The y-axis shows the R square value from 0 to 1, and the x-axis shows the R2 indices, which include R2 subscript 8, R2 subscript 12, R2 subscript 18, R2 subscript 24, R2 subscript 36, R2 subscript 48, and R2 subscript 60. The R square value for the R2 indices is shown for four datasets: all data points which include 36 data points, AC thickness of 3 inches (76.2 mm) with 12 data points, AC thickness of 6 inches (152.4 mm) with 12 data points, and AC thickness of 12 inches (304.8 mm) with 12 data points. For all data points, the R square value is almost 0.96 for all indices; however, no value is shown for R2 subscript 8. For AC thickness of 3 inches (76.2 mm), the R square value varies from 0.61 to 0.99. For AC thickness of 6 inches (152.4 mm), the R square value varies from 0.91 to 0.98. Finally for AC thickness of 12 inches (304.8 mm), the R square value varies from 0.90 to 0.94; however, no value is shown for R2 subscript 8.

1 inch = 25.4 mm

Figure 191. Graph. Variability of relationships of R2 with maximum horizontal strain at bottom of AC layer for various AC thicknesses.

Figure 192. Graph. Variability of relationships of R2 with maximum horizontal strain at bottom of AC layer for various subgrade moduli. This bar graph shows the variability of relationships of radius of curvature (R2) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various subgrade moduli. The y-axis shows the R square value from 0 to 1, and the x-axis shows the R2 indices, which include R2 subscript 8, R2 subscript 12, R2 subscript 18, R2 subscript 24, R2 subscript 36, R2 subscript 48, and R2 subscript 60. The R square value for the R2 indices is shown for three datasets: all data points which include 36 data points, subgrade modulus of 10 ksi (68.9 MPa) with 18 data points, and subgrade modulus of 20 ksi (137.8 MPa) with 18 data points. For all data points, the R square value is almost 0.96 for all indices; however, no value is shown for R2 subscript 8. For subgrade modulus of 10 ksi 
(68.9 MPa), the R square value is almost 0.97 for all indices; however, no value is shown for R2 subscript 8. For subgrade modulus of 20 ksi (137.8 MPa), the R square value varies from 0.83 to 0.97, and all indices except R2 subscript 8 have R square value greater than 0.9.

1 ksi = 6.89 MPa

Figure 192. Graph. Variability of relationships of R2 with maximum horizontal strain at bottom of AC layer for various subgrade moduli.

Figure 193. Graph. Variability of relationships of R2 with maximum horizontal strain at bottom of AC layer for various AC moduli. This bar graph shows the variability of relationships of radius of curvature (R2) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various AC moduli. The y-axis shows the R square value from 0 to 1, and the x-axis shows the R2 indices, which include R2 subscript 8, R2 subscript 12, R2 subscript 18, R2 subscript 24, R2 subscript 36, R2 subscript 48, and R2 subscript 60. The R square value for the R2 indices is shown for four datasets: all data points which include 36 data points, AC modulus of 200 ksi (1,378 MPa) with 12 data points, AC modulus of 500 ksi (3,445 MPa) with 12 data points, and AC modulus of 800 ksi (5,512 MPa) with 12 data points. For all data points, the R square value is almost 0.96 for all indices; however, no value is shown for R2 subscript 8. For AC modulus of 200 ksi (1,378 MPa), the R square value is almost 0.98 for all indices. For AC modulus of 500 ksi (3,445 MPa), the R square value varies from 0.95 to 0.99. Finally for modulus of 800 ksi (5,512 MPa), the R square value is almost 0.99; however, no value is shown for R2 subscript 8.

1 ksi = 6.89 MPa

Figure 193. Graph. Variability of relationships of R2 with maximum horizontal strain at bottom of AC layer for various AC moduli.

Figure 194. Graph. Variability of relationships of R2 with maximum horizontal strain at bottom of AC layer for various vehicle speeds. This bar graph shows the variability of relationships of radius of curvature (R2) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various vehicle speeds. The y-axis shows the R square value from 0 to 1, and the x-axis shows the R2 indices, which include R28 subscript, R2 subscript 12, R2 subscript 18, R2 subscript 24, R2 subscript 36, R2 subscript 48, and R2 subscript 60. The R square value for the R2 indices is shown for three datasets: all data points which include 36 data points, vehicle speed of 30 mi/h (48.3 km/h) with 18 data points, and vehicle speed of 60 mi/h (96.6 km/h) with 18 data points. For all data points, the R square value is almost 0.96 for all indices; however, no value is shown for R2 subscript 8. For vehicle speeds of 30 and 60 mi/h (48.3 and 96.6 km/h), the R square value is almost 0.96 and all indices; however, no value is shown for R2 subscript 8.

1 mi/h = 1.61 km/h

Figure 194. Graph. Variability of relationships of R2 with maximum horizontal strain at bottom of AC layer for various vehicle speeds.

Figure 195. Graph. Variability of relationships of SCI with maximum horizontal strain at bottom of AC layer for various AC thicknesses. This bar graph shows the variability of relationships of Structural Condition Index (SCI) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various AC thicknesses. The y-axis shows the R square value from 0 to 1, and the x-axis shows SCI indices, which include SCI subscript 8, SCI subscript 12, SCI subscript 18, SCI subscript 24, SCI subscript 36, SCI subscript 48, and SCI subscript 60. The R square value for the SCI indices is shown for four datasets: all data points which include 36 data points, AC thickness of 3 inches (76.2 mm) with 12 data points, AC thickness of 6 inches (152.4 mm) with 12 data points, and AC thickness of 12 inches (304.8 mm) with 12 data points. For all data points, the R square value varies from 0.87 to 0.96 for all indices except SCI subscript 60 has an R square value greater than 0.9. No value is shown for SCI subscript 8. For AC thickness of 3 inches (76.2 mm), the R square value varies from 0.21 to 0.93, and the values are available only for three indices (SCI subscript 8, SCI subscript 12, and SCI subscript 18). For AC thickness of 6 inches (152.4 mm), the R square value varies from 0.36 to 0.98, and four indices (SCI subscript 8, SCI subscript 12, SCI subscript 18, and SCI subscript 24) have an R square value greater than 0.9. Finally for AC thickness of 12 inches (304.8 mm), the R square value varies from 0.90 to 0.99; however, no value is shown for SCI subscript 8.

1 inch = 25.4 mm

Figure 195. Graph. Variability of relationships of SCI with maximum horizontal strain at bottom of AC layer for various AC thicknesses.

Figure 196. Graph. Variability of relationships of SCI with maximum horizontal strain at bottom of AC layer for various subgrade moduli. This bar graph shows the variability of relationships of Structural Condition Index (SCI) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various subgrade moduli. The y-axis shows the R square value from 0 to 1, and the x-axis shows SCI indices, which include SCI subscript 8, SCI subscript 12, SCI subscript 18, SCI subscript 24, SCI subscript 36, SCI subscript 48, and SCI subscript 60. The R square value for the SCI indices is shown for three datasets: all data points which include 36 data points, subgrade modulus of 10 ksi (68.9 MPa) with 18 data points, and subgrade modulus of 20 ksi (137.8 MPa) with 18 data points. For all data points, the R square value varies from 0.87 to 0.96, and all indices except SCI subscript 60 have an R square value greater than 0.9. No value is shown for SCI subscript 8. For subgrade modulus of 10 ksi (68.9 MPa), the R square value is almost 0.97 for all indices; however, no value is shown for SCI subscript 8. For subgrade modulus of 20 ksi (137.8 MPa), the R square value varies from 0.81 to 0.97, and all indices except SCI subscript 8 have R square value greater than 0.9.

1 ksi = 6.89 MPa

Figure 196. Graph. Variability of relationships of SCI with maximum horizontal strain at bottom of AC layer for various subgrade moduli.

Figure 197. Graph. Variability of relationships of SCI with maximum horizontal strain at bottom of AC layer for various AC moduli. This bar graph shows the variability of relationships of Structural Condition Index (SCI) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various AC moduli. The y-axis shows the R square value from 0 to 1, and the x-axis shows SCI indices, which include SCI subscript 8, SCI subscript 12, SCI subscript 18, SCI subscript 24, SCI subscript 36, SCI subscript 48, and SCI subscript 60. The R square value for the SCI indices is shown for four datasets: all data points with 36 data points, AC modulus of 200 ksi (1,378 MPa) with 12 data points, AC modulus of 500 ksi (3,445 MPa) with 12 data points, and AC modulus of 800 ksi (5,512 MPa) with 12 data points. For all data points, the R square value varies from 0.87 to 0.96, and all indices except SCI subscript 60 have an R square value greater than 0.9. No value is shown for SCI subscript 8. For AC modulus of 200 ksi (1,378 MPa), the R square value varies from 0.74 to 0.98, and four indices (SCI subscript 8, SCI subscript 12, SCI subscript 18, and SCI subscript 24) have an R square value greater than 0.9. For AC modulus of 500 ksi (3,445MPa), the R square value varies from 0.9 to 0.99. Finally, for modulus of 800 ksi (5,512 MPa), the R square value varies from 0.93 to 0.99; however, no value is shown for SCI subscript 8.

1 ksi = 6.89 MPa

Figure 197. Graph. Variability of relationships of SCI with maximum horizontal strain at bottom of AC layer for various AC moduli.

Figure 198. Graph. Variability of relationships of SCI with maximum horizontal strain at bottom of AC layer for various vehicle speeds. This bar graph shows the variability of relationships of Structural Condition Index (SCI) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various vehicle speeds. The y-axis which shows R square value from 0 to 1, and the x-axis show SCI indices, which include SCI subscript 8, SCI subscript 12, SCI subscript 18, SCI subscript 24, SCI subscript 36, SCI subscript 48, and SCI subscript 60. The R square value for the SCI indices is shown for three datasets: all data points with 36 data points, vehicle speed of 30 mi/h (48.3 km/h) with 18 data points, and vehicle speed of 60 mi/h (96.6 km/h) with 18 data points. For all data points, the R square value varies from 0.87 to 0.96, and all indices except SCI subscript 60 have an R square value greater than 0.9. No value is shown for SCI subscript 8. For vehicle speed of 30 mi/h (48.3 km/h), the R square value varies from 0.86 to 0.96, and all indices except SCI subscript 48 and SCI subscript 60 have an R square value greater than 0.9. No value is shown for SCI subscript 8. For vehicle speed of 60 mi/h (96.6 km/h), the R square value varies from 0.87 to 0.96, and all indices except SCI subscript 60 have an R square value greater than 0.9. No value is shown for SCI subscript 8.

1 mi/h = 1.61 km/h

Figure 198. Graph. Variability of relationships of SCI with maximum horizontal strain at bottom of AC layer for various vehicle speeds.

Figure 199. Graph. Variability of relationships of SCIm with maximum horizontal strain at bottom of AC layer for various AC thicknesses. This bar graph shows the variability of relationships of Structural Condition Index with maximum deflection (SCIm) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various AC thicknesses. The y-axis shows the R square value from 0 to 1, and the x-axis shows SCIm indices, which include SCIm subscript 8, SCIm subscript 12, SCIm subscript 18, SCIm subscript 24, SCIm subscript 36, SCIm subscript 48, and SCIm subscript 60. The R square value for the SCIm indices is shown for four datasets: all data points with 36 data points, AC thickness of 3 inches (76.2 mm) with 12 data points, AC thickness of 6 inches (152.4 mm) with 12 data points, and AC thickness of 12 inches (304.8 mm) with 12 data points. For all data points, the R square value varies from 0.86 to 0.97, and all indices except SCIm subscript 48 and SCIm subscript 60 have an R square value greater than 0.9. For AC thickness of 3 inches (76.2 mm), the R square value varies from 0.18 to 0.92, and the values are available only for three indices (SCIm subscript 8, SCIm subscript 12, and SCIm subscript 18). For AC thickness of 6 inches (152.4 mm), the R square value varies from 0.35 to 0.99, and three indices (SCIm subscript 8, SCIm subscript 12, and SCIm subscript 18) have an R square value greater than 0.9. Finally for AC thickness of 12 inches (304.8 mm), the R square value varies from 0.91 to 0.99.

1 inch = 25.4 mm

Figure 199. Graph. Variability of relationships of SCIm with maximum horizontal strain at bottom of AC layer for various AC thicknesses.

Figure 200. Graph. Variability of relationships of SCIm with maximum horizontal strain at bottom of AC layer for various subgrade moduli. This bar graph shows the variability of relationships of Structural Condition Index with maximum deflection (SCIm) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various subgrade moduli. The y-axis shows R square value from 0 to 1, and the x-axis shows SCIm indices, which include SCIm subscript 8, SCIm subscript 12, SCIm subscript 18, SCIm subscript 24, SCIm subscript 36, SCIm subscript 48, and SCIm subscript 60. The R square value for the SCIm indices is shown for three datasets: all data points with 36 data points, subgrade modulus of 10 ksi (68.9 MPa) with 18 data points, and subgrade modulus of 20 ksi (137.8 MPa) with 18 data points. For all data points, the R square value varies from 0.86 to 0.97, and all indices except SCIm subscript 48 and SCIm subscript 60 have an R square value greater than 0.9. For subgrade moduli of 10 and 20 ksi (68.9 to 137.8 MPa), the R square value is almost 0.97 for all indices.

1 ksi = 6.89 MPa

Figure 200. Graph. Variability of relationships of SCIm with maximum horizontal strain at bottom of AC layer for various subgrade moduli.

Figure 201. Graph. Variability of relationships of SCIm with maximum horizontal strain at bottom of AC layer for various AC moduli. This bar graph shows the variability of relationships of Structural Condition Index with maximum deflection (SCIm) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various AC moduli. The y-axis shows the R square value from 0 to 1, and the x-axis shows SCIm indices, which include SCIm subscript 8, SCIm subscript 12, SCIm subscript 18, SCIm subscript 24, SCIm subscript 36, SCIm subscript 48, and SCIm subscript 60. The R square value for the SCIm indices is shown for four datasets: all data points with 36 data points, AC modulus of 200 ksi (1,378 MPa) with 12 data points, AC modulus of 500 ksi (3,445 MPa) with 12 data points, and AC modulus of 
800 ksi (5,512 MPa) with 12 data points. For all data points, the R square value varies from 0.86 to 0.97, and all indices except SCIm subscript 48 and SCIm subscript 60 have an R square value greater than 0.9. For AC modulus of 200 ksi (1,378 MPa), the R square value varies from 0.73 to 0.98, and four indices (SCIm subscript 8, SCIm subscript 12, SCIm subscript 18, and SCIm subscript 24) have an R square value greater than 0.9. For AC modulus of 500 ksi (3,445 MPa), the R square value varies from 0.9 to 0.99. Finally for modulus of 800 ksi (5,512 MPa), the R square value varies from 0.93 to 0.99.

1 ksi = 6.89 MPa

Figure 201. Graph. Variability of relationships of SCIm with maximum horizontal strain at bottom of AC layer for various AC moduli.

Figure 202. Graph. Variability of relationships of SCIm with maximum horizontal strain at bottom of AC layer for various vehicle speeds. This bar graph shows the variability of relationships of Structural Condition Index with maximum deflection (SCIm) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various vehicle speeds. The y-axis shows the R square value from 0 to 1, and the x-axis shows SCIm indices, which include SCIm subscript 8, SCIm subscript 12, SCIm subscript 18, SCIm subscript 24, SCIm subscript 36, SCIm subscript 48, and SCIm subscript 60. The R square value for the SCIm indices is shown for three datasets: all data points with 36 data points, vehicle speed of 30 mi/h (48.3 km/h) with 18 data points, and vehicle speed of 60 mi/h (96.6 km/h) with 18 data points. For all data points, the R square value varies from 0.86 to 0.97, and all indices except SCIm subscript 48 and SCIm subscript 60 have an R square value greater than 0.9. For vehicle speed of 30 mi/h (48.3 km/h), the R square value varies from 0.84 to 0.97, and all indices except SCIm subscript 60 have an R square value greater than 0.9. For vehicle speed of 60 mi/h (96.6 km/h), the R square value varies from 0.87 to 0.97, and all indices except SCIm subscript 60 have an R square value greater than 0.9.

1 mi/h = 1.61 km/h

Figure 202. Graph. Variability of relationships of SCIm with maximum horizontal strain at bottom of AC layer for various vehicle speeds.

Figure 203. Graph. Variability of relationships of DSI4  -  r with maximum horizontal strain at bottom of AC layer for various AC thicknesses. This bar graph shows the variability of relationships of Deflection Slope Index based on deflection at 4 inches (101.6 mm) and r inches from the center of the load (DSI subscript 4  -  r) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various AC thicknesses. The y-axis shows the R square value from 0 to 1, and the x-axis shows DSI subscript 4  -  r  indices, which include DSI subscript 4  -  8, DSI subscript 4  -  12, DSI subscript 4  -  18, DSI subscript 4  -  24, DSI subscript 4  -  36, DSI subscript 4  -  48, and DSI subscript 4  -  60. The R square value for the DSI subscript 4  -  r indices is shown for four datasets: all data points with 36 data points, AC thickness of 3 inches (76.2 mm) with 12 data points, AC thickness of 6 inches (152.4) with 12 data points, and AC thickness of 12 inches (304.8 mm) with 12 data points. For all data points, the R square value varies from 0.84 to 0.96, and all indices except DSI subscript 4  -  48 and DSI subscript 4  -  60 have an R square value greater than 0.9. For AC thickness of 3 inches (76.2 mm), the R square value varies from 0.26 to 0.78, and the values are available only for two indices (DSI subscript 4  -  8 and DSI subscript 4  -  12). For AC thickness of 6 inches (152.4 mm), the R square value varies from 0.29 to 0.99, and three indices (DSI subscript 4  -  8, DSI subscript 4  -  12, and DSI subscript 4  -  18) have an R square value greater than 0.9. Finally for AC thickness of 12 inches (304.8 mm), the R square value varies from 0.90 to 0.99.

1 inch = 25.4 mm

Figure 203. Graph. Variability of relationships of DSI4 - r with maximum horizontal strain at bottom of AC layer for various AC thicknesses.

Figure 204. Graph. Variability of relationships of DSI4  -  r with maximum horizontal strain at bottom of AC layer for various subgrade moduli. This bar graph shows the variability of relationships of Deflection Slope Index based on deflection at 4 inches (101.6 mm) and r inches from the center of the load (DSI subscript 4  -  r) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various subgrade moduli. The y-axis shows the R square value from 0 to 1, and the x-axis shows DSI subscript 4  -  r indices, which include DSI subscript 4  -  8, DSI subscript 4  -  12, DSI subscript 4  -  18, DSI subscript 4  -  24, DSI subscript 4  -  36, DSI subscript 4  -  48, and DSI subscript 4  -  60. The R square value for the DSI subscript 4  -  r indices is shown for three datasets: all data points with 36 data points, subgrade modulus of 10 ksi (68.9 MPa) with 18 data points, and subgrade modulus of 20 ksi (137.8 MPa) with 18 data points. For all data points, the R square value varies from 0.84 to 0.96, and all indices except DSI subscript 4  -  48 and DSI subscript 4  -  60 have R square value greater than 0.9. For subgrade modulus of 10 ksi (68.9 MPa), the R square value is almost 0.97 for all indices. For subgrade modulus of 20 ksi (137.8 MPa), the R square value varies from 0.95 to 0.97.

1 ksi = 6.89 MPa

Figure 204. Graph. Variability of relationships of DSI4 - r with maximum horizontal strain at bottom of AC layer for various subgrade moduli.

Figure 205. Graph. Variability of relationships of DSI4  -  r with maximum horizontal strain at bottom of AC layer for various AC moduli. This bar graph shows the variability of relationships of Deflection Slope Index based on deflection at 4 inches (101.6 mm) and r inches from the center of the load (DSI subscript 4  -  r) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various AC moduli. The y-axis shows the R square value from 0 to 1, and the x-axis shows DSI subscript 4  -  r indices, which include DSI subscript 4  -  8, DSI subscript 4  -  12, DSI subscript 4  -  18, DSI subscript 4  -  24, DSI subscript 4  -  36, DSI subscript 4  -  48, and DSI subscript 4  -  60. The R square value for the DSI subscript 4  -  r indices is shown for four datasets: all data points with 36 data points, AC modulus of 200 ksi (1,378 MPa) with 12 data points, AC modulus of 500 ksi (3,445 MPa) with 12 data points, and AC modulus of 800 ksi (5,512 MPa) with 12 data points. For all data points, the R square value varies from 0.84 to 0.96, and all indices except DSI subscript 4  -  48 and DSI subscript 4  -  60 have an R square value greater than 0.9. For AC modulus of 200 ksi (1,378 MPa), the R square value varies from 0.67 to 0.98, and four indices (DSI subscript 4  -  8, DSI subscript 4  -  12, DSI subscript 4  -  18, and DSI subscript 4  -  24) have an R square value greater than 0.9. For AC modulus of 500 ksi (3,445 MPa), the R square value varies from 0.87 to 0.99, and all indices except DSI subscript 4  -  60 have R square value greater than 0.9. Finally for modulus of 800 ksi (5,512 MPa), the R square value varies from 0.92 to 0.99.

1 ksi = 6.89 MPa

Figure 205. Graph. Variability of relationships of DSI4 - r with maximum horizontal strain at bottom of AC layer for various AC moduli.

Figure 206. Graph. Variability of relationships of DSI4  -  r with maximum horizontal strain at bottom of AC layer for various vehicle speeds. This bar graph shows the variability of relationships of Deflection Slope Index based on deflection at 4 inches (101.6 mm) and r inches from the center of the load (DSI subscript 4  -  r) with maximum horizontal strain at the bottom of the asphalt concrete (AC) layer for various vehicle speeds. The y-axis shows the R square value from 0 to 1, and the x-axis shows DSI subscript 4  -  r indices, which include DSI subscript 4  -  8, DSI subscript 4  -  12, DSI subscript 4  -  18, DSI subscript 4  -  24, DSI subscript 4  -  36, DSI subscript 4  -  48, and DSI subscript 4  -  60. The R square value for the DSI subscript 4  -  r indices is shown for three datasets: all data points with 36 data points, vehicle speed of 30 mi/h (48.3 km/h) with 18 data points, and vehicle speed of 60 mi/h (96.6 km/h) with 18 data points. For all data points, the R square value varies from 0.84 to 0.96, and all indices except DSI subscript 4  -  48 and DSI subscript 4  -  60 have R square value greater than 0.9. For vehicle speed of 30 mi/h (48.3 km/h), the R square value varies from 0.83 to 0.96, and all indices except DSI subscript 4  -  48 and DSI subscript 4  -  60 have an R square value greater than 0.9. For vehicle speed of 60 mi/h (96.6 km/h), the R square value varies from 0.84 to 0.96, and all indices except DSI subscript 4  -  48 and DSI subscript 4  -  60 have R square value greater than 0.9.

1 mi/h = 1.61 km/h

Figure 206. Graph. Variability of relationships of DSI4 - r with maximum horizontal strain at bottom of AC layer for various vehicle speeds.

Table 66 summarizes the goodness of fit for the relationships between each of the indices considered with the maximum horizontal strain at the bottom of the AC layer using a number of subsets. The subsets considered were AC thickness, subgrade modulus, AC modulus, and vehicle speed. Again, AC thickness was the most influential parameter. Subgrade modulus, AC modulus, and loading speed seemed to affect the most appropriate indices only marginally. However, further classifying the pavements based on subgrade modulus could improve the R2 of thin pavements.

Table 66. Variability of the relationships of the indices with maximum horizontal strain at bottom of AC with respect to AC thickness, subgrade modulus, AC modulus, and vehicle speed.
Relationship with Maximum Horizontal Strain Index R2 (All Data) (36 Cases) Sensitivity Analysis with Respect to AC Thickness Sensitivity Analysis with Respect to Subgrade Modulus Sensitivity Analysis with Respect to AC Modulus Sensitivity Analysis with Respect to Vehicle Speed
3 inches (12 Cases) 6 inches (12 Cases) 12 inches (12 Cases) 10 ksi (18 Cases) 20 ksi (18 Cases) 200 ksi (12 Cases) 500 ksi (12 Cases) 800 ksi (12 Cases) 30 mi/h (18 Cases) 60 mi/h (18 Cases)
R1 R18 N/A 0.9384 0.9777 N/A N/A 0.8131 0.9841 0.9453 N/A N/A N/A
R112 0.9556 0.6898 0.9931 0.9052 0.9686 0.9681 0.9853 0.9878 0.9784 0.9569 0.9548
R118 0.9584 0.2165 0.9757 0.9547 0.971 0.9642 0.9741 0.9896 0.988 0.9586 0.9586
R124 0.9528 Poor 0.9001 0.9775 0.9704 0.9612 0.9507 0.985 0.9871 0.9525 0.9535
R136 0.9334 Poor 0.6526 0.993 0.9719 0.962 0.8842 0.9654 0.9772 0.9316 0.9354
R148 0.904 Poor 0.4656 0.9692 0.9741 0.9653 0.8099 0.9343 0.9591 0.8999 0.9079
R160 0.8691 Poor 0.3587 0.9139 0.9761 0.9684 0.7411 0.8974 0.9348 0.8628 0.875
R2 R28 N/A 0.989 0.9724 N/A N/A 0.8301 0.9846 0.9492 N/A N/A N/A
R212 0.9614 0.9287 0.9815 0.8977 0.9731 0.9741 0.9898 0.9874 0.9795 0.9628 0.9603
R218 0.9641 0.7018 0.9741 0.9299 0.9742 0.9703 0.9912 0.9903 0.9876 0.9651 0.9634
R224 0.9622 0.6138 0.9581 0.9361 0.9729 0.9672 0.9898 0.9896 0.9881 0.9633 0.9614
R236 0.9602 0.6642 0.9268 0.9348 0.9725 0.9651 0.9866 0.9877 0.9863 0.9622 0.9587
R248 0.9599 0.7308 0.9103 0.9288 0.9732 0.9654 0.9844 0.9867 0.9848 0.9626 0.9578
R260 0.9606 0.7989 0.9108 0.9229 0.974 0.9667 0.9834 0.9863 0.9842 0.9638 0.9581
SCI SCI8 N/A 0.9384 0.9777 N/A N/A 0.8131 0.9841 0.9453 N/A N/A N/A
SCI12 0.9556 0.6898 0.9931 0.9052 0.9686 0.9681 0.9853 0.9878 0.9784 0.9569 0.9548
SCI18 0.9584 0.2165 0.9757 0.9547 0.971 0.9642 0.9741 0.9896 0.988 0.9586 0.9523
SCI24 0.9528 Poor 0.9001 0.9775 0.9704 0.9612 0.9507 0.985 0.9871 0.9525 0.951
SCI36 0.9334 Poor 0.6526 0.993 0.9719 0.962 0.8842 0.9654 0.9772 0.9316 0.9354
SCI48 0.904 Poor 0.4656 0.9692 0.9741 0.9653 0.8099 0.9343 0.9591 0.8999 0.9079
SCI60 0.8691 Poor 0.3587 0.9139 0.9761 0.9684 0.7411 0.8974 0.9348 0.8628 0.875
SCIm8 0.9668 0.9187 0.9904 0.9179 0.9778 0.9763 0.9804 0.9875 0.9845 0.9715 0.9669
SCIm12 0.9667 0.6377 0.994 0.9447 0.9766 0.972 0.9832 0.9921 0.9903 0.9699 0.967
SCIm18 0.9602 0.1804 0.9692 0.9666 0.9726 0.9647 0.9706 0.9908 0.9913 0.9621 0.9608
SCIm24 0.9522 Poor 0.8868 0.9825 0.9708 0.9608 0.945 0.9846 0.9882 0.9526 0.9533
SCIm36 0.9305 Poor 0.6355 0.9929 0.9717 0.9609 0.8746 0.9631 0.9762 0.9273 0.9329
SCIm48 0.8997 Poor 0.4518 0.9677 0.9738 0.9642 0.7975 0.9305 0.9568 0.9201 0.9041
SCIm60 0.8639 Poor 0.3479 0.913 0.9758 0.9673 0.727 0.8926 0.9317 0.8395 0.8703
DSI DSI4 - 8 0.9625 0.7765 0.9933 0.9238 0.9737 0.9713 0.9836 0.9898 0.9852 0.9622 0.9629
DSI4 - 12 0.9595 0.2574 0.991 0.9484 0.971 0.9642 0.9806 0.9918 0.9898 0.959 0.9604
DSI4 - 18 0.95 Poor 0.9518 0.969 0.966 0.954 0.9594 0.9872 0.9891 0.9417 0.9382
DSI4 - 24 0.9397 Poor 0.8447 0.984 0.9641 0.9488 0.9256 0.9781 0.9843 0.938 0.9417
DSI4 - 36 0.9138 Poor 0.5643 0.992 0.9658 0.9486 0.8397 0.9514 0.9694 0.9102 0.9174
DSI4 - 48 0.8781 Poor 0.3864 0.9632 0.9687 0.9524 0.7501 0.9134 0.9471 0.8719 0.884
DSI4 - 60 0.8374 Poor 0.2929 0.9046 0.9711 0.9561 0.6711 0.8702 0.919 0.8285 0.8457
DSI8 - 12 0.9446 Poor 0.9717 0.9629 0.9605 0.9463 0.9614 0.9876 0.9893 0.9432 0.9464
DSI8 - 18 0.9256 Poor 0.871 0.9788 0.9522 0.9285 0.9163 0.9731 0.9823 0.9256 0.9285
DSI8 - 24 0.9075 Poor 0.6725 0.9897 0.9502 0.9199 0.86 0.9543 0.971 0.9036 0.9117
DSI8 - 36 0.8655 Poor 0.3484 0.9848 0.9535 0.9186 0.7354 0.9091 0.9441 0.8584 0.8724
DSI8 - 48 0.812 Poor 0.2171 0.9358 0.9577 0.923 0.6203 0.8512 0.9092 0.6676 0.8222
DSI8 - 60 0.7544 Poor Poor 0.8565 0.961 0.9275 0.5277 0.7894 0.868 0.7399 0.7677
DSI12 - 18 0.8922 Poor 0.6672 0.9866 0.9387 0.8974 0.8412 0.9432 0.966 0.8872 0.8974
DSI12 - 24 (BDI) 0.8628 Poor 0.3825 0.9919 0.938 0.8861 0.7578 0.909 0.9438 0.8552 0.8703
DSI12 - 36 0.7951 Poor 0.147 0.9644 0.9439 0.8845 0.5987 0.8343 0.8961 0.7826 0.8068
DSI12 - 48 0.7153 Poor Poor 0.8829 0.9495 0.8896 0.4716 0.7465 0.8392 0.6979 0.5487
DSI12 - 60 0.636 Poor Poor 0.7749 0.9534 0.8945 0.3786 0.6604 0.7762 0.6153 0.5881
DSI18 - 24 0.7944 Poor Poor 0.9822 0.9324 0.8543 0.6157 0.8302 0.8887 0.7805 0.788
DSI18 - 36 0.6846 Poor Poor 0.9042 0.9409 0.8542 0.4414 0.7098 0.8048 0.6483 0.6895
DSI18 - 48 0.57 Poor Poor 0.766 0.9476 0.8603 0.3214 0.5832 0.7103 0.5463 0.5796
DSI18 - 60 0.4695 Poor Poor 0.6235 0.9519 0.8651 0.241 0.4749 0.6146 0.4447 0.4808
DSI24 - 36 (BCI) 0.5723 Poor Poor 0.7995 0.9448 0.8455 0.3289 0.5857 0.7055 0.2316 0.5947
DSI24 - 48 0.4356 Poor Poor 0.6131 0.9516 0.853 0.2232 0.4353 0.5747 0.4115 0.4587
DSI24 - 60 0.3295 Poor Poor 0.461 0.9558 0.857 0.1565 0.3238 0.4559 0.2184 0.3512
TS TS4 0.8724 0.9471 0.9807 0.6903 0.8938 0.9635 0.9787 0.9774 0.8763 0.9053 0.8624
TS8 0.9573 0.1228 0.9911 0.9484 0.9692 0.9612 0.9804 0.9918 0.99 0.9564 0.8925
TS12 0.9236 0.143 0.9096 0.9741 0.9486 0.9236 0.9199 0.9748 0.9836 0.9209 0.9264
TS18 0.8431 Poor 0.2844 0.991 0.931 0.8665 0.7226 0.8857 0.929 0.8335 0.8782
TS24 0.7211 Poor Poor 0.9486 0.9351 0.8423 0.4949 0.7499 0.8275 0.4878 0.7333
TS36 0.3756 Poor Poor 0.5418 0.9545 0.8559 0.1879 0.3685 0.5086 0.354 0.3894
TS48 0.121 Poor Poor 0.2052 0.9657 0.8309 Poor 0.1103 0.1754 0.1007 0.1268
TS60 Poor Poor Poor Poor 0.9631 0.2868 Poor Poor Poor Poor Poor
SD SD8 N/A 0.9384 0.9777 N/A N/A 0.8131 0.9841 0.9453 N/A N/A 0.9323
SD12 0.9556 0.6898 0.9931 0.9052 0.9686 0.9681 0.9853 0.9878 0.9784 0.9569 0.9548
SD18 0.9584 0.2165 0.9757 0.9547 0.971 0.9642 0.9741 0.9896 0.988 0.9586 0.9368
SD24 0.9528 Poor 0.9001 0.9775 0.9704 0.9612 0.9507 0.985 0.9871 0.9525 0.9558
SD36 0.9334 Poor 0.6526 0.993 0.9719 0.962 0.8842 0.9654 0.9772 0.93 0.9354
SD48 0.904 Poor 0.4656 0.9692 0.9741 0.9653 0.8099 0.9343 0.9591 0.8999 0.8665
SD60 0.8691 Poor 0.3587 0.9139 0.9761 0.9684 0.7411 0.8974 0.9348 0.8628 0.875
Shape factors F1 0.8367 Poor 0.3641 0.5875 0.9689 0.918 0.7359 0.8497 0.8789 0.793 0.7538
F2 0.6588 Poor Poor 0.4127 0.9193 0.885 0.4727 0.6782 0.7676 0.6447 0.1206
Area A 0.8063 Poor 0.3538 0.5841 0.9669 0.8978 0.7148 0.8219 0.8478 0.7462 0.7591
AUPP Am 0.9588 Poor 0.9075 0.9805 0.9745 0.926 0.9544 0.9879 0.9899 0.9354 0.9081
Midline surface deflection D0 0.7719 Poor 0.2321 0.7194 0.9797 0.9302 0.5954 0.7963 0.8559 0.7894 0.7605

1 inch = 25.4 mm

1 ksi = 6.89 MPa

N/A = No correlation exists.

A close examination of the correlations for pavements with AC thicknesses of 3 and 6 inches (76.2 and 152.4 mm) reveals that indices R18 ,R28, SCI8, SCIm8, TS4, and SD8 were best related with the maximum horizontal strain with insignificant influence from the AC layer thickness or modulus. Overall, R212 and SCIm8 appeared to be the most appropriate indices that were only minimally affected by the AC thickness and other factors studied.

It can also be concluded that increases in AC modulus resulted in an improvement in R2 for almost all indices. As explained earlier, TS, which is a direct TSD measurement, is an important index. As shown in table 66, TS4 had the highest correlations for pavements with AC layer thicknesses of 3 and 6 inches (76.2 and 127 mm), and TS8 was one of the most appropriate indices for thicker (AC of 12 inches (304.8 mm)) pavements.

Based on the results presented so far in this chapter, it was recommended that the pavements be divided into the following three groups for selecting indices that most appropriate correlate with the maximum horizontal strain at the bottom of the AC surface layer:

For pavements with AC surface layer thicknesses greater than 12 inches (304.8 mm), other pavement layer properties (moduli and thicknesses) did not play an important role. Alternatively, for thinner pavements, the most appropriate indices were affected by the subgrade and base moduli.

Most Appropriate Indices for Correlations with Maximum AC Horizontal Strain Using Available Data

In this subsection, the most appropriate indices using all available runs (43 from step 1 and 36 from step 2, as defined in section 8.1) were explored. The pavement sections for the MnROAD accuracy cells represented pavements that were relatively thin with AC thicknesses varying between 3 and 5 inches (76.2 and 127 mm). Conversely, the pavement combinations considered in step 2 included pavements with AC thicknesses between 6 and 12 inches (152.4 and 304.8 mm). Table 67 shows the reasonable indices (R2 > 0.9) when using the combined (steps 1 and 2) database. The total number of reasonable indices with the total database (79 cases) is greater than the number of reasonable indices in step 1 (MnROAD accuracy cells).

Table 67. Most appropriate correlated indices with maximum horizontal AC strain with total database (79 cases).
Best Indices
(with Respect to Maximum Horizontal Strain)
Index R2
R1 R112 0.94
R118 0.97
R124 0.95
R2 R212 0.92
R218 0.96
R224 0.97
R236 0.94
R248 0.90
SCI SCI12 0.94
SCI18 0.97
SCI24 0.95
SCIm8 0.92
SCIm12 0.96
SCIm18 0.97
SCIm24 0.94
DSI DSI4 - 8 0.94
DSI4 - 12 0.97
DSI4 - 18 0.95
DSI4 - 24 0.92
DSI8 - 12 0.96
DSI8 - 18 0.91
TS TS8 0.97
SD SD12 0.94
SD18 0.97
SD24 0.95
AUPP Am 0.95

Summary and Conclusions from 3D-Move Analyses

There are three datasets of 3D-Move runs: (1) MnROAD accuracy cell field trials (step 1); (2) sensitivity analyses with 36 simulated pavement combinations (step 2); and (3) combined data from steps 1 and 2, giving a total of 79 pavement combinations. Table 68 through table 70 presents the reasonable indices with R2 greater than 0.9 from step 1 as well as the 20 indices with the highest R2 from step 2 and for the combined database. The number of the reasonable indices (R2 > 0.9) from step 2 and from the combined database was greater than the reasonable indices from step 1. However, it is important to note that the step 1 pavements only considered AC thicknesses that varied between 3 and 5 inches (76.2 and 127 mm).

Table 68. Most appropriate indices for MnROAD accuracy runs (43 cases) with respect to maximum horizontal strain at bottom of AC.
Best Indices
(with Respect to Maximum Horizontal Strain)
Index R2
R1 R112 0.95
R118 0.93
R2 R218 0.95
R224 0.94
SCI SCI12 0.95
SCI18 0.93
SCIm8 0.91
SCIm12 0.95
SCIm18 0.93
DSI DSI4 - 8 0.93
DSI4 - 12 0.94
DSI4 - 18 0.91
DSI8 - 12 0.92
SD SD12 0.95
SD18 0.93
TS TS8 0.94
AUPP Am 0.91
Table 69. Most appropriate indices for sensitivity analyses (36 cases) with respect to maximum horizontal strain at bottom of AC.
Best Indices
(with Respect to Maximum Horizontal Strain)
Index R2
R1 R112 0.96
R118 0.96
R124 0.95
R2 R212 0.96
R218 0.96
R224 0.96
R236 0.96
R248 0.96
R260 0.96
SCI SCI12 0.96
SCI18 0.96
SCIm8 0.97
SCIm12 0.97
SCIm18 0.96
DSI DSI4 - 8 0.96
DSI4 - 12 0.96
SD SD12 0.96
SD18 0.96
TS TS8 0.96
AUPP Am 0.96
Table 70. Most appropriate indices for combined MnROAD accuracy and sensitivity analysis data (79 cases) with respect to maximum horizontal strain at bottom of AC.
Best Indices
(with Respect to Maximum Horizontal Strain)
Index R2
R1 R112 0.94
R118 0.97
R124 0.95
R2 R218 0.96
R224 0.97
R236 0.94
SCI SCI12 0.94
SCI18 0.97
SCI24 0.95
SCIm12 0.96
SCIm18 0.97
DSI DSI4 - 8 0.94
DSI4 - 12 0.97
DSI4 - 18 0.95
DSI8 - 12 0.96
SD SD12 0.94
SD18 0.97
SD24 0.94
TS TS8 0.97
AUPP Am 0.95

Based on the results from step 1, the following observations and conclusions were made (see table 44 for definitions of indices):

In looking at the combined results from steps 1 and 2, the following observations and conclusions were made:

Ultimately, it was recommended that pavements be divided into the following groupings when comparing indices for estimating maximum horizontal strains in the AC surface layer:

For AC thicknesses greater than 12 inches (304.8 mm), other pavement layer properties (e.g., moduli and thicknesses) did not play an important role, while for thinner pavements, the appropriate indices were affected by subgrade and base modulus.

8.4 Step 3: Determining Relationship between Index and Critical Responses from JULEA Analysis

In the previous sections, the 3D-Move analyses identified deflection indices that correlated well with maximum horizontal (or fatigue) strain at the bottom of the asphalt layer. These analyses showed that the correlation between the indices and fatigue strain was most sensitive to the AC thickness; pavements with AC thicknesses less than 3 inches (76.2 mm) were not considered. Also, the analyses identified the best index across the board in situations in which the AC thickness is unknown. Based on these results, the indices summarized in table 71 were considered for further evaluation and development of a deflection index-fatigue strain relationship.

Table 71. Best indices correlating maximum fatigue strain chosen from 3D-Move analyses.
AC Thickness of Pavement Section Chosen Index from 3D-Move Analysis
Between 3 and 6 inches R18, R212, R218, SCI8, SCI12, DSI4 - 8, DSI4 - 12, and TS4
Greater than 6 inches R212, R218, SCI12, SCI18, DSI4 - 8, DSI4 - 12, DSI4 - 18, DSI8 - 12, DSI8 - 18, TS4, TS8, TS12, and AUPP (Am)
Unknown R212, R218, SCI12, and DSI4 - 12

1 inch = 25.4 mm

As part of the evaluation, a wider range of pavement structures were analyzed using JULEA.(26) A database of 15,000 pavement structures was developed using a Monte Carlo simulation, considering a uniform distribution for the modulus and thickness ranges reported in table 72. The corresponding pavement responses (strain and deflections) were computed for each simulated pavement section using JULEA.(26) Additionally, a procedure similar to the one used in the 3D-Move analyses (see figure 168) was used to compute the maximum fatigue strain also using JULEA. Similarly, surface deflections at locations detailed in figure 166 were computed. A configuration consisting of 116-psi (799.24-kPa) tire pressure, 13.5-inch (342.9-mm) tire spacing, and 9,000-lb (4,086-kg) load dual tire typically used in TSDDs was used.

Table 72. Pavement property range used in generating database.
Pavement Parameter Minimum/ Maximum AC Layer Base Layer Subgrade Layer Stiff Layer
Modulus (psi) Minimum 100,000 20,000 5,000 2,000,000
Maximum 1,000,000 80,000 20,000
Thickness (inches) Minimum 2 4 24 Infinite
Maximum 16 20 240

1 psi = 6.89 kPa

1 inch = 25.4 mm

Sensitivity Analysis

An effective sensitivity analysis involves a simulation technique that can sample the input variables collectively based on their potential variability and evaluate their effect on a specific distress of a pavement structure. In section 8.3, the computation time involved in 3D-Move analysis limited its utility as a simulation-based sensitivity analysis. Accordingly, the comprehensive JULEA database referenced in the previous section was used to verify the results from 3D-Move sensitivity analyses.(26) The JULEA database was first used to identify the most sensitive pavement properties that affected the critical pavement responses. The identified properties were then used to limit the number of 3D-Move sensitivity analysis. The JULEA database was subsequently used to identify the most sensitive deflection indices, which correlated well with fatigue strains.

The Tornado plot was used to visualize the pavement properties (layer stiffness and thickness) that most significantly affected the fatigue strains.(65) The degree of correlation between fatigue strain and pavement properties was calculated using a rank order correlation coefficient, which is a non-parametric technique for quantifying the relationship between two parameters. The rank order correlation coefficient, r, is independent of the relationship between the input and output. As such, it is well suited for studies that involve analytical models to predict fatigue strain (as is the case here). Rank order correlation uses the position (rank) of a data point in an ordered list to compute its correlation coefficient. The rank order correlation coefficient known as Karl Spearman's r is calculated between the output and each dependent variable as follows:(65)

Figure 207. Equation. Rank order correlation coefficient. r equals 1 minus the quantity of open parenthesis 6 times the summation of open parenthesis delta R closed parenthesis, squared, end quantity, divided by the quantity n times the quantity of open parenthesis n squared minus 1, closed parenthesis end quantity closed parenthesis.

Figure 207. Equation. Rank order correlation coefficient.

Where:

r = Rank order correlation coefficient.

Δ R = Difference in the ranks between the input and the output values in the same data pair.

n = Number of simulations.

The magnitude of r identifies the extent of correlation between the input and output. The effect of the variable on the predicted response is high when the absolute value of r is close to 1. When r is close to 0, the effect of the variable on the predicted distress is minimal. A positive correlation value indicates that a low value from the input will lead to a low value in the output, and a negative correlation indicates a low value from the input will lead to a high value in the output.

Sensitivity of Pavement Properties on Fatigue Strain

Figure 208 shows the sensitivity of fatigue strain to various pavement properties using the rank-ordered correlation coefficient as determined from the JULEA database of 15,000 pavement structures.(26) As shown, AC layer thickness is the most sensitive parameter. Also, the negative correlation for all pavement properties indicates that the increase in each of the simulated pavement properties reduces the maximum fatigue strain. The subgrade stiffness and thickness, for example, had a negligible effect on the maximum fatigue strain.

Figure 208. Graph. Sensitivity of pavement properties on maximum fatigue strain. This bar graph shows the comparison of rank order correlation coefficient, r, for maximum fatigue strain with different pavement properties. The y-axis shows six pavement properties labeled (from top to bottom) asphalt concrete (AC) thickness, AC stiffness, base stiffness, base thickness, subgrade stiffness, and subgrade thickness. The x-axis shows the rank order coefficient from -1.0 to 1.0. The figure shows correlation is -0.87 for AC thickness and reduces in the order shown: AC stiffness r = -0.41, base stiffness r = -0.19, base thickness r = -0.07, subgrade stiffness r = -0.04, and subgrade thickness r = 0.01.

Figure 208. Graph. Sensitivity of pavement properties on maximum fatigue strain.

Sensitivity of Indices to Critical Pavement Design Responses

In section 8.3, it was recommended that pavements be divided into the following AC thickness groupings when comparing indices for estimating fatigue strain:

In this section, the JULEA database of 15,000 pavement structures was grouped based on AC thickness to verify the sensitivity between deflection indices and fatigue strain.(26)

Pavement Structures with AC Layer Less Than 3 Inches (76.2 mm) Thick

For pavement structures with an AC layer less than 3 inches (76.2 mm) thick, the stiffness of the base, AC, and subgrade layers as well as the thickness of the base layer significantly influenced the fatigue strain. Accordingly, a weak correlation between the deflection indices and fatigue strains was observed only when the AC thickness was considered. Similar trends were observed in the 3D-Move analyses.

It is hypothesized that the contribution of thin AC layers to the measured deflections is limited, and hence other factors must be taken into consideration to establish deflection index-fatigue strain correlations with a high degree of correlation. However, for network-level PMS applications, a relation involving multiple material properties is not practical, and hence such a relation was not pursued further.

Pavement Structures with AC Layer Between 3 and 6 Inches (76.2 and 152.4 mm) Thick

Figure 209 shows the relative sensitivity of maximum fatigue strain to selected deflection indices for pavement structures with an AC layer thickness between 3 and 6 inches (76.2 and 152.4 mm). As shown, all the indices presented in table 71 have relatively good correlation with maximum fatigue strain.

Figure 209. Graph. Sensitivity of curvature index on maximum fatigue strain in thin pavements. This bar graph shows the comparison of rank order correlation coefficient, r, for maximum fatigue strain with different indices. The y-axis shows nine curvature indexes: R1 subscript 8, SCI subscript 8, R2 subscript 12, DSI subscript 4  - 8, SCI subscript 12, TS subscript 4, R2 subscript 18, DSI subscript 4  - 12, and area under pavement profile (AUPP). The x-axis shows r from -1.0 to 1.0. The correlation is at its maximum at -0.965 with R1 subscript 8 and 0.965 with SCI subscript 8. The correlation with other indices are R2 subscript 12 = -0.962, DSI subscript 4  - 8 = 0.959, SCI subscript 12 = 0.949, TS subscript 4 = 0.946, R2 subscript 18 = -0.938, DSI subscript 4  - 12 = 0.937, and AUPP = 0.884.

Figure 209. Graph. Sensitivity of curvature index on maximum fatigue strain in thin pavements.

Pavement Structures with AC Layer Between 6 and 16 Inches (152.4 and 406.4 mm) Thick

Figure 210 shows the relative sensitivity of maximum fatigue strain to selected deflection indices for pavement structures with an AC layer thickness between 6 and 16 inches (152.4 and 406.4 mm). As shown, all the indices presented in table 71 had relatively good correlation with maximum fatigue strain.

Figure 210. Graph. Sensitivity of curvature index on maximum fatigue strain in thick pavements. This bar graph shows the comparison of rank order correlation coefficient, r, for maximum fatigue strain with different indices. The y-axis shows 13 curvature indexes: DSI subscript 8  -  12, DSI subscript 4  -  18, DSI subscript 8  -  18, SCI subscript 18, area under pavement profile (AUPP) (Am), DSI subscript 4  -  12, R2 subscript 18, SCI subscript 12, TS subscript 12, R2 subscript 12, DSI subscript 4  -  8, TS subscript 8, and TS subscript 4. The x-axis shows r from -1.0 to 1.0. The correlation with the indices are DSI subscript 8  -  12 = 0.99, DSI subscript 4  -  18 = 0.99, DSI subscript 8  -  18 = 0.99, SCI subscript 18 = 0.988, AUPP (Am) = 0.988, DSI subscript 4  -  12 = 0.988, R2 subscript 18 = -0.981, SCI subscript 12 = 0.98, TS subscript 12 = 0.98, R2 subscript 12 = -0.973, DSI subscript 4  -  8 = 0.972, TS subscript 8 = 0.971, and TS subscript 4 = 0.932.

Figure 210. Graph. Sensitivity of curvature index on maximum fatigue strain in thick pavements.

Pavement Structures with Unknown AC Layer Thickness

Figure 209 and figure 210 show that, unlike other indices, the R212 index appears to be a reasonable predictor of maximum fatigue strain for pavements with both thin and thick AC layers. Accordingly, when the AC thickness is not known, the R212 index can be used to estimate maximum fatigue strains based on measured TSDD deflections, as suggested by the 3D-Move sensitivity analyses.

Relationship between Indices and Critical Response

Incorporating TSDD measurements into network-level PMS applications requires an established relationship between the computed or measured indices and fatigue strain. In this section, the fatigue strain was related to the indices deemed sensitive in the previous section and also from the 3D-Move analysis. Table 73 presents the relationships developed for pavement structures with thin (3 to 6 inches (76.2 to 152.4 mm)) and thick (6 to 16 inches ((152.4 to 406.4 mm)) AC layers. The correlation coefficient associated with each relationship is also presented in the table. For thin AC layers, separate relationships were developed for those cases where the AC layer thickness (H1) is greater than the base layer thickness (H2) (i.e., H1/H2 > 1).

Table 73. Relationship between curvature indices and maximum fatigue strain.
AC Layer Thickness Pavement Sections Chosen Best Indices Relation R2
Thin (3 to 6 inches) All SCI8 (mil) 98.754 × SCI80.8915 0.93
(H1/H2) > 1 100.79 × SCI80.8958 0.96
Thick (6 to 16 inches) All SCI18 (mil) 40.224 × SCI180.9257 0.98
Unknown All R212 (inches) 337974 × R212-0.779 0.97

1 inch = 25.4 mm

Because the relations between the deflection indices and maximum fatigue strain can be sensitive to AC layer thickness, better predictions of the maximum fatigue strains are possible when the AC thickness is known or measured during the TSDD testing. The JULEA database was used to categorize the pavement structures according to AC layer thickness in 1-inch (25.4-mm) intervals.(26) Each group contained about 1,000 pavement structures within the pavement properties presented in table 72. Table 74 summarizes the relationships between the most sensitive deflection indices and the fatigue strain for each group. The correlation coefficient for each relationship is also presented in table 74.

Table 74. Relationship between curvature indices and critical pavement responses with known AC thickness.
AC Layer Thickness (inches) Unbound Layer Properties Chosen Index Range of Indices Value (mil) Maximum Fatigue Strain (microstrain) R2
3–4 Base 20–80 ksi and 4–12 inches;
subgrade 5–20 ksi and 24–240 inches
SCI8 1.59 to 8.55 83.958 x SCI80.9903 0.90
4–5 1.23 to 6.65 90.107 x SCI81.0049 0.95
5–6 0.96 to 4.83 98.847 x SCI80.9723 0.97
6–7 Base 20–80 ksi and 4–20 inches;
subgrade 5–20 ksi and 24–240 inches
SCI18 1.87 to 10.22 36.295 x SCI181.0096 0.92
7–8 1.58 to 11.07 37.106 x SCI181.0029 0.95
8–9 1.38 to 7.33 38.252 x SCI180.986 0.97
9–10 1.16 to 7.45 39.638 x SCI180.9611 0.98
10–11 1.02 to 6.89 40.933 x SCI180.9195 0.97
11–12 0.87 to 6.07 41.393 x SCI180.894 0.97
12–13 0.79 to 5.1 41.505 x SCI180.8672 0.96
13–14 0.69 to 4.68 41.301 x SCI180.8283 0.95
14–15 0.63 to 4.23 40.361 x SCI180.8313 0.96
15–16 0.59 to 4.27 39.278 x SCI180.7978 0.95

1 inch = 25.4 mm

ksi = 6.89 MPa

Effect of TSDD Loading Configuration

The RWD and TSD used in the MnROAD field trials had different loading configurations, as summarized in table 75. To study the effect of loading configuration on the relationship between deflection index and fatigue strain, a separate database of 50,000 pavement structures, each subjected to the TSD and RWD loading configurations, was simulated within the pavement properties presented in table 72.

Table 75. Loading configuration of TSDD used in the field test.
TSDD Equipment Dual Tire Load (lb) Tire Pressure (psi) Dual Tire Spacing (inches)
TSD 11,150 116 13.5
RWD 9,500 100 14.5

1 lb = 0.454 kg

1 psi = 6.89 kPa

1 inch = 25.4 mm

Figure 211 and figure 212 show the relationships between SCI12 and fatigue strain for the RWD and TSD loading configurations, respectively. The similarity between the two confirms that the proposed relationships are not dependent on the loading configuration, as was also found during the 3D-Move analysis.

Figure 211. Graph. General relationship between maximum fatigue strain and SCI for RWD loading. This graph shows the relation between maximum fatigue strain and Surface Curvature Index (SCI) computed as the difference between deflection at center and 12 inches lateral from the center for Rolling Wheel Deflectometer (RWD) loading. The y-axis shows maximum fatigue strain from 0 to 800 microstrain, and the x-axis shows SCI (D subscript 0 minus D subscript 12) from 0 to 12 mil (0 to 0.3048 mm). The graph shows a minimal scatter in the relation, and equation of the power trend line fitted to the relation is y equals 63.899 times x raised to the power of 0.9004.

1 mil = 0.0254 mm

Figure 211. Graph. General relationship between maximum fatigue strain and SCI for RWD loading.

Figure 212. Graph. General relationship between maximum fatigue strain and SCI for TSD loading. This graph shows the relation between maximum fatigue strain and Surface Curvature Index (SCI) computed as the difference between deflection at center and 12 inches lateral from the center for Traffic Speed Deflectometer (TSD) loading. The y-axis shows maximum fatigue strain from 0 to 800 microstrain, and the x-axis shows SCI (D subscript 0 minus D subscript 12) from 0 to 15 mil (0 to 0.381 mm). There is a minimal scatter in the relation, and equation of the power trend line fitted to the relation is y equals 63.293 times x raised to the power of 0.8922.

1 mil = 0.0254 mm

Figure 212. Graph. General relationship between maximum fatigue strain and SCI for TSD loading.

8.5 Field Evaluation of Indices

So far, the focus of this chapter has been mostly on numerical analyses in order to recommend the most appropriate indices. In this section, the estimated TSD accuracies and precisions reported in chapter 6 were used to estimate the most practical and robust indices among those reported in previous sections. For this evaluation, the TSD new deflection algorithm discussed in chapter 5 was used since the old method did not provide enough data points for the analyses. Since the new TSD algorithm provides deflections at 4-inch (100.6-mm) intervals, including D0, only indices that conformed to this spacing were addressed. These values, along with the TS directly measured by the TSD, were used to evaluate the precision and accuracy of the most appropriate indices using the data collected during the MnROAD testing. The following subsections describe the process and the results obtained from such evaluation. It should be noted that the trends and recommendations in this section are based on the limited data collected during the MnROAD field testing and are subject to the uncertainties associated with the measurements and analyses enumerated for the accuracy and precision studies outlined in chapters 5 and 6.

Accuracy

For the accuracy evaluation, the selected indices from the TSD were compared with the same indices calculated from the deflection or velocity basins measured with geophone 3 at all cells. The accuracy was evaluated in terms of the percentage of difference as established in chapters 5 and 6 for the deflection slopes irrespective of the AC thickness recommendations for estimating the strains. Figure 213 presents the results from such evaluation. The error bars in the figure correspond to the 25th and 75th percentile ranges of the difference. A 15 percent threshold median difference, which was considered as a reasonable level of difference given the state of the technology, was also added to the plot shown in figure 213. The indices based on the deflection slopes yielded lower difference values as compared to the other indices. The indices based on R seem to be the least accurate.

Figure 213. Graph. Accuracy evaluation of indices. This column plot presents the median difference for individual indices. The y-axis shows the difference from 0 to 60 percent, and the x-axis shows the indices, which are grouped together by index type including Surface Curvature Index (SCI), the radius of curvature (R1 and R2), the Deflection Slope Index (DSI), the tangent slope (TS), and the area under the pavement profile (AUPP). The column plot includes 25 and 75 percentile error bars. The plot includes a 15 percent difference threshold marked as a continuous horizontal line. Four out of the five indices in the DSI group have a median difference below the 15 percent threshold.

Figure 213. Graph. Accuracy evaluation of indices.

Precision

As presented in section 6.3, the new TSD vertical deflection estimates were found to be less precise than the deflection slope measurements. For this evaluation, precision was incorporated using the same approach but with a slightly different presentation of results. As in chapter 6, the SEE values and ranges were estimated for each index and cell. The median COV, obtained from the ratio between the median SEE and the median range, was used to quantify the precision of each deflection index irrespective of the AC thickness recommendations for estimating the strains. Figure 214 shows the resulting median COVs as well 25th and 75th percentile ranges of the COVs. A 15 percent threshold median COV was also added to the plot as a reasonable precision. Most indices were under this 15 percent threshold COV. As shown, the indices based on the deflection slopes performed better than those based on the TSs by themselves. The three R indices performed the worst, with median COVs ranging from 29 to 40 percent.

Figure 214. Graph. Precision evaluation of indices. This column plot presents the median coefficient of variation (COV) for individual indices. The y-axis shows COV from 0 to 60 percent, and the x-axis shows the indices, which are grouped together by index type including the Surface Curvature Index (SCI), the radius of curvature (R1 and R2), the Deflection Slope Index (DSI), the tangent slope (TS), and the area under the pavement profile (AUPP). The column plot includes 25 and 75 percentile error bars. The plot includes a 15 percent COV threshold marked as a continuous horizontal line. The three indices on the radius of curvature group are the only ones over the 15 percent threshold.

Figure 214. Graph. Precision evaluation of indices.

Overall Field Results

To easily visualize the overall performance of these indices, figure 215 was developed by combining figure 213 and figure 214. This plot, which presents the precision results on the abscissa and the accuracy results on the ordinance, is segmented into four quadrants to further characterize the performance of the indices in question. As shown, the most robust indices are those in the lower left quadrant (marked in green) and include four DSIs, TS4, and AUPP. The indices in the upper left quadrant (TS and SCI) may also be considered as reasonably precise but not as accurate as those in the lower left quadrant. Based on this study, the three radii of curvature indices under consideration do not seem to yield accurate enough results since they all fall in the upper right-hand quadrant (i.e., quadrant with low accuracy and precision marked in red). DSI4 - 12 was found to be the most robust index based on the TSDD accuracy and precision analyses conducted in this study.

Figure 215. Graph. Overall field performance of indices. This scatter graph compares the median coefficient of variation (COV) and the median difference for the deflection indices discussed in the section. The y-axis shows median difference from 0 to 35 percent, and the x-axis shows median COV from 0 to 45 percent. The plot is divided into four quadrants using a 15 percent threshold for both axes. The lower left quadrant and the top right quadrant are colored green and red, respectively. Individual data points are labeled with the name of the indices. Green colored quadrant contains indices with the smaller COV and difference and include DSI subscript 4  -  12 and DSI subscript 8  -  12. Red colored quadrant contains indices with higher COV and difference and include three radius of curvature indices (R1 subscript 12, R1 subscript 8, and R2 subscript 12).

Figure 215. Graph. Overall field performance of indices.

The uncertainties of the modeled indices were evaluated by dividing the SEE in estimating the maximum fatigue strain by the median range of calculated strains for each of the indices for different AC thicknesses as described previously. The results from such analysis are presented in figure 216. This figure depicts the same 15 percent threshold as described in section 8.5. Most of the indices have a median COV below 15 percent except for the ones used to determine the strain for unknown pavement thickness.

Figure 216. Graph. Precision of modeled indices in different pavement thicknesses. This column plot presents the median coefficient of variation (COV) for individual indices defined by pavement thickness. COV is on the y-axis from 0 to 40 percent, and indices are on the x-axis, which include the Surface Curvature Index (SCI), the radius of curvature (R1 and R2), the Deflection Slope Index (DSI), tangent slope (TS), and the area under the pavement profile (AUPP). Three types of data are shown: 3 to 6 inches (76.2 to 152.4 mm) of asphalt concrete (AC), over 6 inches (152.4 mm) of AC, and unknown AC thickness. The column plot includes 25 and 75 percentile error bars. The plot includes a 15 percent difference threshold marked as a continuous horizontal line. The greatest errors correspond to the indices on the unknown pavement thickness group.

1 inch = 25.4 mm

Figure 216. Graph. Precision of modeled indices in different pavement thicknesses<

8.6 Summary

The overall performance of the selected indices was evaluated by combining the field and JULEA results.(26) The outcomes from figure 214 through figure 216 were combined into table 76. Indices were then ranked within their pavement thickness ranges according to a performance number (see table 77). The device precisions, device accuracies, and model uncertainties were assigned values of 1 (poor) when their COV values were greater than 20 percent, 3 (fair) when their values were between 10 and 20 percent, and 5 (good) for values less than 10 percent. Similarly, the R2 values were assigned 1 (poor) for values less than 0.90, 3 (fair) for values between 0.90 and 0.95, and 5 (good) for values above 0.95.

Table 76. Summary of performances of different indices.
AC Thickness of Pavement Section Index Units Precision COV (Percent) Accuracy (Percent Difference) Model COV (Percent) Model R2
Between 3 and 6 inches DSI4 - 12 mil 9 8 16 0.88
SCI12 mil 11 18 15 0.90
DSI4 - 8 mil 10 12 13 0.92
TS4 mil/inch 14 11 13 0.91
SCI8 mil 13 24 12 0.93
R18 inches 37 31 14 0.93
R212 inches 40 21 13 0.93
Greater than 6 inches DSI4 - 12 mil 9 8 13 0.97
DSI8 - 12 mil 9 7 12 0.98
SCI12 mil 11 18 14 0.96
DSI4 - 8 mil 10 12 17 0.95
TS8 mil/inch 9 15 17 0.94
TS12 mil/inch 10 21 17 0.96
AUPP mil 11 13 15 0.97
R212 inches 40 21 16 0.95
TS4 mil/inch 14 11 25 0.87
Unknown DSI4 - 12 mil 9 8 22 0.97
SCI12 mil 11 18 20 0.97
R212 inches 40 21 19 0.97
TS4 mil/inch 14 11 24 0.93

1 inch = 25.4 mm

1 mil = 0.0254 mm

1 mil/inch = 0.0001 mm/mm

Table 77. Ranking of different indices.
AC Thickness of Pavement Section Index Units Device Precision Device Accuracy Model Uncertainty Model R2 Overall Performance (1–5)
Between 3 and 6 inches DSI4 - 12 mil 5 5 3 1 3.5
SCI12 mil 3 3 3 3 3.0
DSI4 - 8 mil 3 3 3 3 3.0
TS4 mil/inch 3 3 3 3 3.0
SCI8 mil 3 1 3 3 2.5
R18 inches 1 1 3 3 2.0
R212 inches 1 1 3 3 2.0
Greater than 6 inches DSI4 - 12 mil 5 5 3 5 4.5
DSI8 - 12 mil 5 5 3 5 4.5
SCI12 mil 3 3 3 5 3.5
DSI4 - 8 mil 3 3 3 5 3.5
TS8 mil/inch 5 3 3 3 3.5
TS12 mil/inch 5 1 3 5 3.5
AUPP mil 3 3 3 5 3.5
R212 inches 1 1 3 5 2.5
TS4 mil/inch 3 3 1 1 2.0
Unknown DSI4 - 12 mil 5 5 1 5 4.0
SCI12 mil 3 3 1 5 3.0
R212 inches 1 1 3 5 2.5
TS4 mil/inch 3 3 1 3 2.5

1 inch = 25.4 mm

1 mil = 0.0254 mm

1 mil/inch = 0.0001 mm/mm

Note: A ranking of 1 indicates poor, a ranking of 3 indicates fair, and a ranking of 5 indicates good.

The overall performance was then determined by assigning a 25 percent importance to each of the four parameters (device precision, device accuracy, model uncertainty, and R2) and obtaining a weighted average of the four parameters. Indices that required a deflection parameter of 18 inches (457.2 mm) were not included in this table since TSD did not report a value at that distance. DSI4 - 12 appears first on the three different AC thicknesses categories. SCI12 also performed well in the three AC thickness categories with an overall performance of 3 or higher. It should be noted that device accuracy can be improved if the effectiveness of the deflection algorithm is improved. At a minimum, the TSD old deflection algorithm, which was identified in accuracy analysis (section 6.2) to be better than new deflection algorithm, can be modified to compute the deflections at the locations needed to determine the identified effective indices.

In considering the results and conclusions presented in this chapter, it is important to recognize that a limitation of the analyses is that the device precision and accuracy were obtained for pavements with a AC thickness of 5 inches (127 mm) or less if the full depth reclamation with engineered emulsion is not considered as AC. The most robust index, DSI4 - 12, is related to maximum fatigue strain using the JULEA database and is presented in table 78.

Table 78. Relationship between robust TSD index DSI4 - 12 and critical pavement responses with unknown and known AC thickness.
AC Layer Thickness (inches) Maximum Fatigue Strain (microstrain) R2
3–6 (thin AC) 69.1 x DSI4 - 120.9348 0.88
6–16 (thick AC) 76.22 x DSI4 - 120.8924 0.97
Unknown 76.24 x DSI4 - 120.8969 0.97
3–4 66.96 x DSI4 - 120.9351 0.77
4–5 62.567 x DSI4 - 121.0174 0.88
5–6 64.66 x DSI4 - 121.0379 0.94
6–7 71.646 x DSI4 - 121.0005 0.96
7–8 74.381 x DSI4 - 120.9757 0.97
8–9 76.458 x DSI4 - 120.9427 0.98
9–10 77.802 x DSI4 - 120.9107 0.97
10–11 77.868 x DSI4 - 120.8674 0.96
11–12 76.861 x DSI4 - 120.8395 0.95
12–13 75.154 x DSI4 - 120.8149 0.95
13–14 72.194 x DSI4 - 120.778 0.94
14–15 70.196 x DSI4 - 120.7824 0.94
15–16 66.402 x DSI4 - 120.7525 0.93

1 inch = 25.4 mm

8.7 Temperature Correction Procedure

The deflection parameter measured by the TSDD is a function of pavement temperature at the structural evaluation. Consistent evaluation and tracking of the index computed from deflection parameters over the pavement service period requires the maximum fatigue strains computed from the index to be corrected to a standard reference temperature. The recommended approach, developed as part of the project, is as follows:

  1. Compute temperature correction factor, Tc, as follows:


  2. Figure 217. Equation. Temperature correction factor. T subscript c equals 19.791 times exponential raised to the power of -0.043 times T subscript r minus the quantity 19.791 times exponential raised to the power of -0.043 times T subscript f.

    Figure 217. Equation. Temperature correction factor.

    * Modified November 21, 2016

    Where:

    Tf (°F) = Temperature at time of the TSDD field measurements.

    Tr (°F) = Reference temperature, which should be set to 70 °F (21.11°C).

  3. Compute dynamic modulus (Ef) based on computed strains and AC layer thickness using relations presented in table 79.

  4. Compute dynamic modulus at reference temperature, Er of 70 °F (21.11°C) as follows:

  5. Figure 218. Equation. Dynamic modulus at reference temperature. E subscript r equals the ratio of E subscript f and the quantity open parenthesis 1 minus T subscript c closed parenthesis.

    Figure 218. Equation. Dynamic modulus at reference temperature.

  6. Compute temperature corrected strains using the computed dynamic modulus at reference temperature (Er) and the inverse of the relations presented in table 79.

While the correlation coefficients for the relations in table 79 are not high, the error in the temperature corrections is expected to be minimal because the same relations are used to compute the AC dynamic modulus from the computed strains and then to re-compute the strains from the temperature corrected AC dynamic modulus.

Table 79. Relationship between maximum fatigue strain (ε) and AC modulus for temperature correction.
AC Layer Thickness (inches) Relation Between Maximum Fatigue Strain and AC Modulus R2
3–4 5.28E+08 x ε max-1.27 0.47
4–5 6.56E+08 x ε max -1.36 0.59
5–6 7.23E+08 x ε max-1.44 0.62
6–7 6.39E+08 x ε max-1.46 0.67
7–8 4.96E+08 x ε max-1.46 0.68
8–9 4.91E+08 x ε max-1.51 0.72
9–10 3.68E+08 x ε max-1.49 0.76
10–11 3.29E+08 x ε max-1.51 0.77
11–12 2.88E+08 x ε max-1.52 0.79
12–13 2.50E+08 x ε max-1.53 0.83
13–14 2.30E+08 x ε max-1.55 0.83
14–15 1.61E+08 x ε max-1.49 0.85
15–16 1.45E+08 x ε max-1.51 0.85

 

 

 

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