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 contractors option, to be removed from the analysis for thickness determination. (Based on the above example.)

 

Given: T = 7.0

N = 10 - 1 removed = 9

 

Contractors 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