SAMPLE CALCULATIONS FOR DETERMINING PAVEMENT THICKNESS INDEX

The following is an example of the steps used to determine the thickness index for a section of pavement.

PART 1

This example is based on ten cores and a project let in English. Cores, from a metric project, measured in millimeters, would be evaluated by the same steps and in accordance with the metric pay schedule.

Given:       T = Design thickness of pavement = 7.0 in.

n = Number of Cores = 10     

Core lengths =  7.40, 7.10, 8.10, 7.60, 7.95, 8.25, 9.70, 7.90, 8.10, 8.00

STEP 1:    = mean thickness =

X = 7.40 + 7.10 + 8.10 + 7.60 + 7.95 + 8.25 + 9.70 + 7.90 + 8.10 + 8.00 = 80.1

 = 80.1  10 = 8.01                                                                               = 8.01

STEP 2:   

S = standard deviation of the sample

Core #                              

               1                         7.40 - 8.01  =   - 0.610                     - 0.610 x - 0.610   =   0.372

               2                         7.10 - 8.01  =   - 0.910                     - 0.910 x - 0.910   =   0.828

               3                         8.10 - 8.01  =    0.090                       0.090 x   0.090   =   0.008

               4                         7.60 - 8.01  =   - 0.410                     - 0.410 x - 0.410   =   0.168

               5                         7.95 - 8.01  =   - 0.060                     - 0.060 x - 0.060   =   0.004

               6                         8.25 - 8.01  =    0.240                       0.240 x   0.240   =   0.058

               7                         9.70 - 8.01  =    1.690                       1.690 x   1.690   =   2.856

               8                         7.90 - 8.01  =   - 0.110                       0.110 x - 0.110   =   0.012

               9                         8.10 - 8.01  =    0.090                       0.090 x   0.090   =   0.008

               10                       8.00 - 8.01  =   - 0.010                     - 0.010  x - 0.010   =   0.000

                                                                                                               =   Sum   =   4.314

S = 0.69

STEP 3:    TI = thickness index =  ( - S) - T

TI = (8.01 - 0.69) - 7.00

TI = 7.32 - 7.00 = 0.32                                                                             TI = 0.32

PART II

The following illustrates the procedures to follow when a thick core would qualify, at the contractor’s option, to be removed from the analysis for thickness determination.  (Based on the above example.)

      Given:       T  = 7.0

N  = 10 - 1 removed = 9

      Contractor’s Option:

S = 0.69 (from Part I)

Three standard deviations = 3 x S = 2.07

Core length at which contractor can choose to remove the

core from the TI (up to 10% of the total number of cores)

T + 3S = 7.0 + 2.07 = 9.07

The core that is 9.70 thick would qualify for removal.

STEP 1:    =

X = 7.40 + 7.10 + 8.10 + 7.60 + 7.95 + 8.25 + 7.90 + 8.10 + 8.00 = 70.4

        = 70.4 9 = 7.82 = 7.82

STEP 2:   

Core #                              

1                         7.40 - 7.82  =    -0.420                    -0.420  x   -0.420  =   0.176

2                         7.10 - 7.82  =    -0.720                    -0.720  x   -0.720  =   0.518

3                         8.10 - 7.82  =      0.280                     0.280  x    0.280  =   0.078

4                         7.60 - 7.82  =    -0.220                    -0.220  x   -0.220  =   0.048

5                         7.95 - 7.82  =      0.130                     0.130  x    0.130  =   0.017

6                         8.25 - 7.82  =      0.430                     0.430  x    0.430  =   0.185

7                         9.70 - 8.01  =      1.690                     1.690  x    1.690  =   2.856

               8                         7.90 - 7.82  =      0.080                     0.080  x    0.080  =  0.006

               9                         8.10 – 782  =      0.280                     0.280  x    0.280  =  0.078

               10                       8.00 - 7.82  =      0.180                     0.180  x    0.180  =  0.032

                                                                                                                  =  Sum =  1.138

S =0.38

STEP 3:    TI = ( - S) - T

TI - (7.82 - 0.38) - 7.00                                                                            TI = 0.44

TI - 7.44 - 7.00 = 0.44