**Open Access**-
**Authors :**Mahmoud Fathy Abdel-Maksoud Khamis , Asharf Elshahat Mohammed Elsaid -
**Paper ID :**IJERTV8IS110275 -
**Volume & Issue :**Volume 08, Issue 11 (November 2019) -
**Published (First Online):**27-11-2019 -
**ISSN (Online) :**2278-0181 -
**Publisher Name :**IJERT -
**License:**This work is licensed under a Creative Commons Attribution 4.0 International License

#### Optimum Sample Size for Pavement Condition Evaluation

Asharf Elshahat Mohammed Elsaid

Assistant Professor, Construction Engineering Dept., Faculty of Engineering,Zagazig University,

Zagazig, Sharkia, Egypt.

Abstract-The evaluation of the pavement condition is a necessary issue for any pavement management system. This evaluation depends on real field measurements on the road such as pavement surface distress and roughness. Sample size should clarify the condition of pavement of each section. Sample size determination is a significant issue because samples that are too large may waste money, resources and time, while samples that are too small may lead to incorrect results. The main objective of this study is to determine the optimum sample size required for pavement condition evaluation. To achieve this objective, some highways were selected randomly. These highways include desert and agricultural links. A complete survey of the selected highways was performed. The results of survey of each 100 meter were collected in a separate form paper. The total length of selected highways was 69 kilometer. Pavement condition index method was used in this study. For results analysis, a pavement condition index 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and100% sample size was calculated for each one kilometer of each link. A comparison of the results of pavement condition index of the selected sample sizes was made. Also, the percent of error of the average of results of pavement condition index of the selected sample sizes and complete survey of each one kilometer was calculated. The study revealed that, a sample size of 30 to 40% is the optimum sample size for pavement condition evaluation which gives the smallest value of error percent comparing to the pavement condition index of 100% sample size. Also, a correction factors was concluded for each selected sample size to obtain the pavement condition index value at 100% sample size.

Keywords-Flexible pavement; pavement condition evaluation; pavement survey; sample size; PCI.

INTRODUCTION

Pavement condition evaluation is a step of pavement management system. This evaluation relies on real field measurements such as pavement surface distress, skid resistance and roughness [1]. The method used for pavement condition evaluation, by any agency, depends on the permitted budget [2]. Data obtained from pavement condition evaluation have been used in the development of programs of rehabilitation and maintenance of pavement [3].

Sample size determination is a significant issue because samples that are too large may waste money, resources and time, while samples that are too small may lead to incorrect results. Sample size which can be selected from a population uses one of the two categories. The first category is a specified percentage of the population; while the second category is a

Mahmoud Fathy Abdel-Maksoud Khamis Assistant Professor, Construction Engineering Dept., Faculty of Engineering,Zagazig University,

Zagazig, Sharkia, Egypt.

statistically determined sample based on required precision and a specified level of confidence. Many studies have been performed to determine the suitable sample size for pavement condition evaluation. Schmitt et al found that a sample size of 10 to 15% is used if the target is to predict the distribution of condition of pavement network [4]. Templeton et al concluded that a sample size of 30 to 35% is adequate if the aim is to predict the cost for repairing poor links [5]. Also, a study performed by transportation department of Texas, and reported in the AASHTO pavement management guide, concluded that a sample size of 2 to 5% would be sufficient to evaluate the pavement condition of the network of highways [6]. Bishnu found that 13% sample unit is needed for surface distress index (SDI) method and 21% for pavement condition index (PCI) method [7]. Shahin suggested the following equation for determining the sample size to be surveyed [8]:

n = [(N * S2) / (e2 / (4 (N – 1) + S2))]

Where:

n = sample size to be surveyed;

N = total number of sample units in the pavement section;

E = allowable error in the estimate of the section`s PCI (a value of 5 points is recommended); and

S = standard deviation of the PCI between sample units in the section.

STUDY OBJECTIVES

The main objective of this study is to determine the optimum sample size required for pavement condition evaluation and to obtain the correction factors for each selected sample size to obtain condition index value at 100% sample size.

STUDY METHODOLGY

Eight highways were selected randomly. The characteristics of these highways are shown in Table (1) [9]. Data collection includes two parts. The first part is data collection from field. The second part is data from calculations. With respect to data collected from field, a complete survey of the selected highways was performed using pavement condition index (PCI) method. The results of survey of each 100 meter were collected in a separate form paper. The total length of selected highways was 69 kilometer. The total number of 100 meter sections was 690. With respect to data collection from calculations, pavement condition index method was used in this study.

Table (1): Characteristics of the studied highways [9]

Highway Character.

Zagazig – Abohmad

Belbais – Alaasher

Zagazig – Belbais

Zagazig – Mniaelkamh

Tanta – Almahalla

Tanta Kotour

Type

Divided

Divided

Divided

Divided

Divided

Undivided

Area

Agriculture

Desert

Agriculture

Agriculture

Agriculture

Agriculture

Length, km

20

16

25

24

22

10

Date of last maintenance

2014

2015

2008

2013

2007

2012

Traffic, vpd

16064

7939

25621

9106

28964

8898

Thickness of Surface, cm Thickness of Binder, cm Thickness of Base, cm

5

5

5

5

5

5

6

5

5

5

5

5

30

25

25

35

30

25

As mentioned before, pavement condition (PCI) method was used in this study to evaluate the pavement condition of selected highways. In this method, deduct values were obtained based on the type, density, and severity of observed distresses in the studied section. Then this deduct value subtracted from 100 to give the pavement condition index (PCI) and the rate of pavement [10].

Figure (1) shows the formation of different percentage sample units. Each kilometer divided into ten units of 10% sample units. These units were recorded by 1, 2, 3, 4, 9, and 10. The first and the second units of 10% sample units constitute the second sample unit of 20% sample. Also, the second and the third units 10% sample units constitute the second sample unit of 20% sample. Also, th third and the fourth units of 10% sample units constitute one sample unit of 20% sample and so on. For each kilometer, the number of sample units of 10% is ten sample units. While the number of sample units of 20% is nine sample units. The number of sample units of 30% is eight sample units. While the number of sample units of 40% is seven sample units and so on. So, the total number of sample units used in this study was 3795 unit. Determination of PCI values for different percentages of sample units were calculated.

Fig. (1): Formation of different sample unit percentage

The analysis of the results divided into three parts. The first part is a comparison of the average of PCI values of each selected percentage (10%, 20%, 30%, 90%, and 100%) for selected links. The second part is calculation of sensitivity analysis of using different sample units rather than complete survey of each kilometer. Sensitivity can be expressed by two expressions, first, as absolute value, and second as a percent change value. Sensitivity as used here is expressed as a percent value. The change in PCI value of using different sample units rather than complete survey of each kilometer is calculated as:

EPCI = [((PCIi PCI100%)/(PCI100%)) x 100%]

Where:

EPCI = Percent error in pavement condition index value.

PCI100% = Pavement condition index value of complete survey of complete survey of one kilometer.

PCIi = Pavement condition index value computed using different percentage sample units 10%, 20%, 30%,

. etc).

The third part of analysis is a calculation of correction factors for using different sample units rather than complete survey of each kilometer.

RESULTS AND ANALYSIS

For results and analysis, a pavement condition index of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 100%

sample units was calculated for each one kilometer of each link. The total number of sample units is 3795 unit.

Comparison of the average PCI Values

Figures (2 to 9) show comparison of PCI values of using different percentages of sample units with PCI value of complete survey of link for selected links. Value of PCI at 10% is the average value of PCI`s values of 10% sample units of over the length of each link. The trend is the same for other percentage of sample units i.e. for 20%, 30%, 40%, 80%, 90%. A comparison of PCI values of using different percentages of sample units with PCI value of complete survey of link for Zagazig Abohamad is shown in Figure (2). It can be noticed that values of PCI at 90%, 20%, 30%, and 10%, respectively, are greater than PCI at 100%. Also, values of PCI at 40%, 80%, 70%, 60%, and 50%, respectively, are smaller than PCI at 100%. PCI at 10% is the greatest value while PCI at 50% is the smallest value. The most closest PCI value to PCI at 100% is PCI at 40% while the most farthest PCI value to PCI at 100% is PCI at 10%.

Fig. (2): Average PCI values of using different percentages sample units for Zagazig Abohamad highway

Figure (3) shows the comparison of PCI values of using different percentages of sample units with PCI value of

complete survey of link for Abohamad zagazig. It can be noticed that values of PCI at 30%, 20%, and 10%, respectively, are greater than PCI at 100%. Also, values of PCI at 40%, 60%, 90%, 50%, 70%, and 80%respectively, are smaller than PCI at 100%. PCI at 10% is the greatest value while PCI at 80% is the smallest value. The most closest PCI value to PCI at 100% is PCI at 40% while the most farthest PCI value to PCI at 100% is PCI at 10%.

Fig. (3): Average PCI values of using different percentages sample units for Abohamad – Zagazig highway

A comparison of PCI values of using different percentages of sample units with PCI value of complete survey of link for Belbais Alaasher is shown in Figure (4). It can be noticed that values of PCI at 30%, 20%, and 10%, respectively, are greater than PCI at 100%. Also, values of PCI at 80%, 40%, 70%, 60%, 50%, and 90%, respectively, are smaller than PCI at 100%. PCI at 10% is the greatest value while PCI at 90% is the smallest value. The most closest PCI value to PCI at 100% is PCI at 30% while the most farthest PCI value to PCI at 100% is PCI at 10%.

Fig. (4): Average PCI values of using different percentages sample units for Belbais – Alaasher highway

Figure (5) shows the comparison of PCI values of using different percentages of sample units with PCI value of complete survey of link for Zagazig – Belbais. It can be noticed that values of PCI at 90%, 40%, 30%, 20%, and 10%, respectively, are greater than PCI at 100%. While PCI at 80%, 50%, 70%, and 60% are smaller than PCI at 100%. PCI at 10% is the greatest value while PCI at 60% is the smallest value. The most closest PCI at 100% is PCI at 40% while the most farthest PCI value to PCI at 100% ia PCI at 10%.

Fig. (5): Average PCI values of using different percentages sample units for Zagazig Belbais highway

A comparison of PCI values of using different percentages of sample units with PCI value of complete survey of link for Belbais Zagazig is shown in Figure (6). It can be noticed that values of PCI at 40%, 30%, 20%, and 10%, respectively, are

greater than PCI at 100%. While PCI at 90%, 50%, 60%, 70%, and 80%, respectively, are smaller than PCI at 100%. PCI at 10% is the greatest value while PCI at 80% is the smallest value. The most closest PCI value to PCI at 100% is PCI at 40% while the mst farthest PCI value to PCI at 100% is PCI at 10%.

Fig. (6): Average PCI values of using different percentages sample units for Belbais – Zagazig highway

Figure (7) shows the comparison of PCI values of using different percentages of sample units with PCI value of complete survey of link for Zagazig – Mniaelkamh. It can be noticed that values of PCI at 30%, 70%, 90%, 80%, 20%, and 10%, respectively, are greater than PCI at 100%. While PCI at 60%, 50%, and 40%, respectively, are smaller than PCI at 100%. PCI at 10% is the greatest value while PCI at 40% is the most smallest value. The most closest PCI value to PCI at 100% is PCI at 30% while the most farthest PCI value to PCI at 100% is PCI at 10%.

Fig. (7): Average PCI values of using different percentages sample units for Zagazig Mniaelkamh highway

A comparison of PCI values of using different percentages of sample units with PCI value of complete survey of link for Tanta Almahalla is shown in Figure (8). It can be noticed that values of PCI at 60%, 80%, 30%, 20%, and 10%, respectively, are greater than PCI at 100%. Also, values of PCI at 70%, 40%, 50%, and 90%, respectively, are smaller than PCI at 100%. PCI at 10% is the greatest value while PCI at 90% is the smallest value. The most closest PCI value to PCI at 100% is PCI at 40% while the most farthest PCI value to PCI at 100% is PCI at 10%.

Fig. (8): Average PCI values of using different percentages sample units for Tanta Almahalla highway

Figure (9) shows the comparison of PCI values of using different percentages of sample units with PCI value of complete survey of link for Tanta – Kotour. It can be noticed that values of PCI at 30%, 20%, and 10%, respectively,are greater than PCI at 100%. Also, values of PCI at 90%, 80%, 40%, 70%. 50%, and 60%, respectively, are smaller than PCI at 100%. PCI at 10% is the greatest value while PCIat 60% is the smallest value. The most closest PCI value to PCI at 100% is PCI at 30% while the most farthest PCI value to PCI at 100% is PCI at 10%.

Fig. (9): Average PCI values of using different percentages sample units for Tanta Kotour highway

Sensitivity Analysis of Using Different Sample Units

Figures (10 to 17) show the sensitivity analysis of using different sample units rather than using complete survey of each kilometer for selected highways. The sensitivity analysis used in this study is expressed by error percent. The error percent of using different sample units rather than using 100% survey for Zagazig Abohamad highway isshown in Figure (10). It can be noticed that, zero error percent can be achieved at 39%. The maximum positive value of error percent occurred at 10% then at 30% with values 1.54% and 0.94% respectively, while the maximum negative value of error percent occurred at 50% then 60% with values – 1.43% and – 1.06% respectively.

Fig. (10): Error percent in PCI of using different percentages sample units for Zagazig – Abohamad highway

Figure (11) shows the error percent of using different sample units rather than using 100% survey for Abohamad Zagazig highway. It can be noticed that, zero error percent can be achieved at 38%. The maximum positive value of error percent occurred at 10% then at 20% with values 6.59% and 3.75% respectively, while the maximum negative value of error percent occurred at 80% then 70% with values 5.28% and 3.04% respectively.

Fig. (11): Error percent in PCI of using different percentages sample units for Abohamad – Zagazig highway

The error percent of using different sample units rather than using 100% survey for Belbais Alaasher highway is shown in Figure (12). It can be noticed that, zero error percent can be achieved at 30%. The maximum positive value of error percent occurred at 10% then at 20% with values 0.62% and 0.07% respectively, while the maximum negative value of error percent occurred at 90% then 50% with values – 0.39% and – 0.30% respectively.

Fig. (12): Error percent in PCI of using different percentages sample units for Belbais- Alaasher highway

Figure (13) shows the error percent of using different sample units rather than using 100% survey for Zagazig – Belbais highway. It can be noticed that, zero error percent can be achieved at 35%. The maximum positive value of error percent occurred at 10% then at 20% with values 17.92% and

10.65% respectively, while the maximum negative value of error percent occurred at 90% then 70% with values 12.32% and 9.61% respectively.

Fig. (13): Error percent in PCI of using different percentages sample units for Zagazig – Belbais highway

The error percent of using different sample units rather than using 100% survey for Belbais Zagazig highway is shown in Figure (14). It can be noticed that, zero error percent can be achieved at 31%. The maximum positive value of error percent occurred at 10% then at 20% with values 8.95% and 3.28% respectively, while the maximum negative value of error percent occurred at 90% then 70% with values – 11.55% and – 7.63% respectively.

Fig. (14): Error percent in PCI of using different percentages sample units for Belbais – Zagazig highway

Figure (15) shows the error percent of using different sample units rather than using 100% survey for Zagazig – Mniaelkamh highway. It can be noticed that, zero error percent can be achieved at 31%. The maximum positive value of error percent occurred at 10% then at 20% with values 0.74% and 0.31% respectively, while the maximum negative value of error percent occurred at 50% then 60% with values 0.14% and 0.10% respectively.

Fig. (15): Error percent in PCI of using different percentages sample units for Zagazig Mniaelkamh highway

The error percent of using different sample units rather than using 100% survey for Tanta Almahalla highway is shown in Figure (16). It can be noticed that, zero error percent can be achieved at 37%. The maximum positive value of error percent occurred at 10% then at 20% with values 9.04% and 3.66% respectively, while the maximum negative value of error percent occurred at 90% then 50% with values – 2.64% and – 1.06% respectively.

Fig. (16): Error percent in PCI of using different percentages sample units for Tanta – Almahalla highway

Figure (17) shows the error percent of using different sample units rather than using 100% survey for Tanta – Kotour highway. It can be noticed that, zero error percent can be achieved at 36%. The maximum positive value of error percent occurred at 10% then at 20% with values 19.81% and 10.24% respectively, while the maximum negative value of error percent occurred at 60% then 50% with values 5.64% and 5.48% respectively.

Fig. (17): Error percent in PCI of using different percentages sample units for Tanta – Kotour highway

Calculation of Correction Factors

For any reason, such as fund and time constraints, any sample unit percent rather than complete survey can be used. A correction factor can be used to obtain the PCI value corresponding to complete survey of pavement link. Figure (18), the summation of figures (10 to 17), shows the sensitivity analysis of using different sample units rather than using 100% survey for selected highways. From this figure, it can be noticed that the range of zero percent error of PCI is 30 to 40% sample unit. Table (2) shows the average percent error of PCI for using different sample units rather than using 100% survey. The correction factor can be calculated from percent error equation as follows:

Correction Factor = [1/(1+Error Percent)]

PCI100% = Correction Factor x PCI at any sample unit

Fig. (18): Error percent in PCI for different used sample units for all studied highways.

Table (2): Correction factors and average error percent in PCI of using different sample units

Sample unit %

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Average Error of PCI, %

8.151

4.08

1.14

-0.85

-2.31

-2.86

-3.17

-2.8

-3.56

0

Correction factor

0.925

0.961

0.988

1.009

1.024

1.029

1.033

1.028

1.037

1

For example, if 10% sample unit is used and PCI is 63%. From Table (2), correction factor corresponding to 10% is 0.925. So, the PCI at 100% survey = 63 x 0.925 = 58.

CONCLUSIONS

Based on the results of this study, the following conclusions were drawn:

Using of 10% and 20%, which are the most common used percent, does not express the real value of PCI of any pavement section.

Using of a sample size of 30 to40% is the best to express the real value of PCI of any pavement section.

The error percent is positive for sample units less than the best sample unit while it is negative for sample units greater than the best sample unit.

Correction factors due to using different sample units, 10%,20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% and 100% are 0.925, 0.961, 0.988, 1.009, 1.024, 1.029, 1.033, 1.028, 1.037, and 1.00 respectively, to obtain the PCI value corresponding to complete survey of pavement link.

RECOMMENDATIONS

In view of the previous analysis and conclusions, it is recommended that:-

1 Using of a sample size of 30 to 40% is the optimum sample size for pavement condition evaluation.

2 Using of 0.925, 0.961, 0.988, 1.009, 1.024, 1.029,

, 1.028, 1.037, and 1.00 as a correction factors for using

sample units of 10%,20%, 30%, 40%, 50%, 60%, 70%, 80%,

90% and 100% respectively, to obtain the PCI value corresponding to complete survey of pavement link.

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