Excerpt

## Table of Contents

Abstract

Acknowledgment

Table of Contents

LIST OF FIGURES

LIST OF TABLES

LIST OF ABBREVIATIONS

1. INTRODUCTION

1.1 Statement of the problem

1.2. Objective

1.2.1 General Objective

1.2.2 Specific Objectives

1.3 Significance of the study

1.4 Research questions

1.5 Scope of the study

1.6 Research Design

2. LITERATURE REVIEW

2.1 Previously Developed Temperature Prediction Algorithms & Models

2.2 Effect of Environmental Factors on Flexible Pavement Performance

2.3 Relationship between Maximum Air Temperature & Pavement Surface Temperature

2.4 Marshall Mix Design

2.4.2 Procedures

2.4.3 Preparation of test specimens

2.4.4 Density & Void analysis

2.5 Statistical Modeling

2.5.1 Regression analysis

2.5.1.1 Multivariate regression

2.5.1.2 Testing the Significance of R

2.5.1.3 Adjusted R

2.5.1.4 Cross validation

3. RESEARCH METHODOLOGY

3.1 Study Area and Study Period

3.2 Historical Air Temperature and Latitude of the Study Areas

3.2.1 Berha/ Desert places of Ethiopia

3.2.2 Kola (tropical) places of Ethiopia

3.2.3 Sub-tropical (Weina-dega) places of Ethiopia

3.2.4 Temperate & alpine (Dega& Kur) Places of Ethiopia

3.3 Research Materials

3.4 Data Collection and Sampling Techniques

3.4.1 Determining Normality

3.4.1.1 Pearson`s Index of Skewness

3.4.1.2 Frequency distribution

3.4.2 Sample Size Determination

3.5 Model Development

3.5.1 Model Selection

3.5.2 Collinearity

3.5.3 Model Development

3.5.4 Model Validation

3.5.5 Cross validation

3.6 Laboratory Experiment (case study for Samara town)

3.6.1 Marshall Mixture Design Procedures

3.6.1.1 Aggregate Evaluation

3.6.1.2 Asphalt Cement Evaluation

3.6.1.4 Marshall Stability & flow test

4 Result Analysis and Discussion

4.1 Result Analysis

4.1.1 Analysis to develop the Model

4.1.1.1 Normality test and Confidence interval determination

4.1.1.2 Model selection

4.1.2 Analyzing Laboratory Test Results

4.1.2.1 Aggregate Evaluation Results

Aggregate Blending Results

4.1.2.2 Asphalt cement evaluation results

4.1.3.3 Marshall Specimen heating at 750C

4.2 Result Discussion

4.2.1 Result discussion related to the model

4.2.2 Implication of laboratory Test results

4.2.2.1 Implication of Aggregate test results

4.2.2.2 Implication of Bitumen test results

4.2.2.3 Comparison between the two Marshall Specimen heating temperatures (600C and 750C)

4.2.3 Options to determine maximum pavement surface temperature

5. Conclusion and Recommendation

5.1 Conclusion

5.2 Recommendation

References

Appendix I: Laboratory test results

Appendix II: On site measurement pictures

Appendix III: t-Distribution

Appendix IV: Model development for each fold (STATA Output)

Appendix V: Scatter Plot for Model Selection

Appendix VI: Tabular Presentation for K-th fold Cross validation

## Abstract

Marshall Mix design was developed for the hottest pavement surface temperature of USA, which is 60-degree Celsius. This design mechanism is very dominant in our country. It was directly adopted without any modification. The research aims to develop a prediction model which will be employed to modify Marshall Mix design method for Ethiopian climate and incorporate maximum pavement surface temperature.

In order to do so, ten years historical air temperature of Ethiopia, taken from National Metrology Agency which was used to determine the hottest month for onsite measurement of 24 towns. For each town actual maximum pavement surface temperature was measured from August 2016- February 2018, using Nano sensor/ radiator thermometer. The countries climate was classified in to four climatic regions for the purpose of this research. For each region, a representative town is incorporated on the study.

Based on site measurement and maximum air temperature with the associated latitude, Multivariate Regression Model was selected. To select the model R-squared value method, excel analysis of scatter plots and collinearity of the explanatory variables was checked. All the inputs were provided to STATA SE-13 statistical software and model developed. After the model was developed by all the 24 towns’ data, it was validated and cross validated by dividing the data in to 5 folds in order to make it applicable for all scenarios. The model was further elaborated in laboratory case study, for hottest town of Samara, Afar region capital. Mix design was prepared at 60 , which is the standard specimen heating temperature and at 75 which is the actual maximum pavement surface temperature of Samara town. The mix that was prepared at 60 , found to fulfill all the criteria’s of Marshall Mix design outlined by Asphalt Institute for heavy Traffics. Whereas, at the 75 , fails to do so.

Therefore, mix design should be conducted at the place maximum pavement surface Temperature rather than conducting at the standard 60degree Celsius.

## Acknowledgment

Foremost, I would like to thank Almighty God for bringing me this far & giving all the strength, the courage & the wisdom.

I would like to express my sincere gratitude to my advisor Dr. Habamu Melese for the continuous support of my thesis, for his patience, motivation, enthusiasm, and immense knowledge.

My sincere thanks goes to Dr. Alemgena Alene. Even though, it was hardly possible to work with him because of his extra loaded busy schedules, the valuable comments he gave me during the contact hours at the begging of this research guided me all the way.

Numerous were also sources of help and inspiration in the creation of this document and throughout the research process. God brought the people into the process that needed to be there when I needed them for this to be a success.

One of these people include Ato Meles, laboratory technician in AACRA Laboratory, it was impossible to achieve the goals of this research without his cooperation. My special thanks goes to him; thank you for your time & support.

The support & collaboration of Addis Ababa city Roads Authority Laboratory is precious. The Nano sensor for actual on site measurement, the material from Fanuel quarry site; it was all possible because of your good willingness and corporation. Thank you all.

My deep gratitude also goes to Ethiopian Construction Works Corporation (ECWC) especially for Awash –Mille project staffs. Your contribution is a lot for the success of this research & I am very grateful for all of you.

No words can express my gratitude to National Metrology Agency of Ethiopia (NMA), who provide all the necessary ten years data for free, TCD (transport Construction Company) laboratory, and of Core Consulting Engineers plc. Thank you for your positive attitude and collaboration.

Without the support of my wife, Genet Hailu, it was very difficult to pass these sleepless nights, restless weekends. You are a woman of valor and iconoclast- Thank you for everything.

## LIST OF FIGURES

Figure 1- 1: presentation of Latitude & Longitude on Glob (www.quora.com, 2017)

Figure 1- 2 Research Design

Figure 2- 1 Factors influencing pavement performance (Gupta Ankit et al., 2006)..12

Figure 2- 2 main climatic aspects in a coupled soil-climate that exert significant impact on the performance of flexible pavements (Gupta Ankit et al., 2006)

Figure 2- 3 Frequency distribution of the data

Figure 3- 1 Sample study area, Axum23

Figure 3- 2 Average annual Maximum Temperature of samara Town

Figure 3- 3 on-site measurement at Extra dosed Type Hidase Bridge

Figure 3- 4 Average Annual Yearly Maximum Temperature of Arba-Minch from 2006 to

Figure 3- 5 Average Annual Maximum Temperature of Dire-Dawa from 2006 to

Figure 3- 6 Average Annual Maximum Temperature of Metehara for the past 10 years

Figure 3- 7 Average Annual Maximum Temperature of Konso from 2006 to

Figure 3- 8 Average Annual Maximum Precipitation of Addis Ababa from 2006 to

Figure 3- 9 Average Annual Maximum Temperature for Wolaita Sodo for the past eleven years 3- 10 Average Annual Maximum Temperature of Kombolcha for the past 10 years

Figure 3- 11 Average Annual Maximum Temperature of Hagere Mariam for the past eleven years

Figure 3- 12 Average Annual Maximum Temperature of Addis Ababa from 2006 to

Figure 3- 13 Average Annual Maximum Temperature of Bale Robe for the past ten years

Figure 3- 14 Radiation Thermometer (Sensor) used in this thesis to measure actual pavement surface temperature and air temperature

Figure 3- 15 Procedures of cross validation

Figure 3- 16 A (Sieve analysis) & B (specimen preparation for bitumen) in laboratory

Figure 3- 17 Water bath boiled at 60 (A) and Marshall testing head (B)

Figure 4- 1 Gradation of the Aggregate

Figure 4- 2 Theoretical maximum specific gravity vs. binder Contents

Figure 4- 3 Bulk Specific gravity for different bitumen contents

Figure 4- 4 Test Property curves for void analysis by the Marshall method, Air void vs. Binder content (a) VMA vs. Binder content (b) VFA vs. Binder content (c) Bulk unit weight vs. Binder content (d)

Figure 4- 5 Stability (a) and flow (b) curves for hot mix design data by the Marshall method

Figure 4- 6 Acceptable Narrow range of bitumen content

Figure 4- 7 Stability (a) and Flow (b) Comparison between the two heating temperatures

Figure Appendix V- 1: Linear function for the correlation b/n Ta &Ts

Figure Appendix V- 2: Logarithmic function for the correlation b/n Ta &Ts

Figure Appendix V- 3: Exponential function for the correlation b/n Ts & Ta

Figure Appendix V- 4 Power function for the correlation b/n Ts & Ta

Figure Appendix V- 5 Polynomial of degree three function for the correlation b/n Ts & Ta

Figure Appendix V- 6 Polynomial of degree four function for the correlation b/n Ts & Ta

Figure Appendix V- 7Polynomial of degree five function for the correlation b/n Ts & Ta

Figure Appendix V- 8 Polynomial of degree six function for the correlation b/n Ts & Ta

Figure Appendix V- 9: Exponential function for the correlation b/n Ts & Lat

Figure Appendix V- 10: Logarithmic function for the correlation b/n Ts & Lat

Figure Appendix V- 11: Power function for the correlation b/n Ts & Lat

Figure Appendix V- 12: Linear function for the correlation b/n Ts & Lat

Figure Appendix V- 13 Polynomial of degree Two function for the correlation b/n Ts & Lat

Figure Appendix V- 14 Polynomial of degree Three function for the correlation b/n Ts & Lat

Figure Appendix V- 15: Polynomial of degree Four function for the correlation /n Ts & Lat

Figure Appendix V- 16 : Polynomial of degree Five function for the correlation /n Ts & Lat

Figure Appendix V- 17: Polynomial of degree six function for the correlation /n Ts & Lat

## LIST OF TABLES

Table 3- 1 Scientific and Traditional classification of Climatic regions of Ethiopia (Ethiopian Atlas, 2018)

Table 3- 2 Upper and lower class determination

Table 3- 3 Model selection

Table 3- 4 R2-Value for combined effect

Table 3- 5 sample data to show non-collinearity between the two parameters

Table 3- 6 Input data for STATA (SE/13) analysis

Table 3- 7 Statistical Analysis, ANOVA test of the model

Table 3- 8 five-folds for the data

Table 3- 9 Model developed after cross validation

Table 3- 10 Cross validation estimate of test error

Table 3- 11 Requirements for penetration Grade Bitumen (ERA, 2013)

Table 4- 1 Seven days’ air temperature of Samara town

Table 4- 2 Summary of Aggregate test results with acceptable standards and test methods

Table 4-3 Aggregate Gradation

Table 4- 4 Asphalt evaluation Result, criteria and Method

Table 4- 5 Summary of the result

Table 4- 6 summarized result of Aggregate & Bitumen (40/50) for Asphalt Concrete Mix specimens heated at 750C

## LIST OF ABBREVIATIONS

Abbildung in dieser Leseprobe nicht enthalten

## 1. INTRODUCTION

Temperature variations have an important influence on the pavement thermal state. Depending on the temperature variation, stresses are induced in the overlay in two different ways, which need to be distinguished: through restrained shrinkage of the overlay and through the existing movements of slabs, due to the thermal shrinking phenomenon.

The time variation of pavement thermal state is controlled by climatic conditions, thermal diffusivity of the materials, thermal conductivity, specific heat, density and the depth below the surface *(Sousa et al., 2002).*

The temperature distribution in a pavement structure can be obtained through field measurements, using temperature-recording equipment (Data logger associated with thermocouples) or estimated by using mathematical models. The option of using the field measurement is desirable because actual temperature can be reliably measured and used in stress calculation models. However, this method is relatively slow and only provides information about temperatures in the observed period. On the other hand, a temperature theoretical model will give a temperature distribution quickly and can be used to predict temperature distributions under a wide range of conditions, including any unusual or extreme conditions.

The angular distance on a plane perpendicular to the plane of the equator is known as the latitude. This is used as one of the two coordinates for a location on earth. In the physical sense, it gives the north-south position of the location considered. The line at which the latitude is constant runs parallel to the equator around the globe.

Taken together with longitude, latitude can be used to specifically locate a position on earth. The equator is considered as the zero latitude (i.e. 0°). The North Pole has the latitude +90° and the South Pole has -90°. There are specially defined latitudes, such as Arctic circle and Tropic of Cancer in the northern hemisphere and Antarctic circle and Tropic of Capricorn in the southern hemisphere.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1- 1: presentation of Latitude & Longitude on Glob (www.quora.com, 2017).

Ethiopia is both a highland/mountainous (with elevation greater than 1500 m) and lowland (with elevation less than 1500 m) country. It is composed of nine major river basins, the drainage systems of which originate from the centrally situated highlands and make their way down to the peripheral or outlying low-lands *(Enyew BD, 2014).*

The climate in Ethiopia is geographically quite diverse, due to its equatorial positioning and varied topography. Three general temperature zones are apparent–cool, temperate, and hot–categorized predominantly by elevation. The cool zone incorporates parts of the north-western plateau, at elevations above 2,400 meters; the temperate zone lies between 1,500 and 2,400 meters, and supports most of the population. The hot zone, at elevations below 1,500 meters, constitutes much of the eastern and southern portions of the country, as well as the tropical valleys in the west and north (Enyew BD, 2014).

Precipitation patterns vary widely throughout the country due to elevation, atmospheric pressure patterns, and local features. In the lowlands, rainfall is typically quite meager, whereas the southwest, central and northwest regions receive quite appreciable quantities, but in varying patterns. In the southwest, a relatively even month-to month distribution may be observed, while the dominant pattern in the northwest and western regions, containing the Blue Nile basin, is generally associated with tropical monsoon-type behavior, delivering significant June-September rainfall. Other regions throughout the country, not necessarily adjacent, demonstrate a distinct bimodal pattern.

Pavement temperatures are affected by air temperatures as well as precipitation, wind speed, and solar radiation. The response of a pavement system is highly influenced by the temperature of the surface layers and moisture content of the unbound soils. Annual, seasonal, and daily variations in temperature and precipitation have large influences on pavement service life *(A. Ongel, 2004).*

Ethiopia has a total of 101,359 km of federal and regional roads, of asphaltic or gravel construction *(ERA, 2013)*. The major roads in Ethiopia are shown in the following figure. From these roads, 17.3% are paved roads. Almost all of the paved roads are flexible pavements with thin layer of upper bituminous surface. Ethiopia experiences two main climate seasons -a dry season and a rainy season. However, differences in altitude tend to add a number of variations, both in terms of temperatures and rainfall *(<http://www.world-guides.com/africa/east-africa/ethiopia/ethiopia_weather.html>)*. The maximum and minimum average yearly annual air temperature of each year is presented in table 1-1. However, the air temperature varies from place to place and from season to seasons.

Table 1- 1 Average Annual maximum & minimum Temperature of Ethiopia (world-guides.com, 2018)

Abbildung in dieser Leseprobe nicht enthalten

For the purpose of this thesis Ethiopian pavement surface temperature zones will be classified as Berha (Deseret) & Tropical (Kolla) pavements, Wiena Dega (Sub-Tropical), Temperate (Dega) & Alpine (Kur) pavements based on elevation of the selected sites. The actual pavement surface temperature & maximum air temperature and latitude of 24 towns will be incorporated to reach the objective.

The proposed regression model in this thesis will use maximum monthly air temperature and maximum hourly air temperature to measure the maximum pavement surface temperature on field for sites of the same latitude at a time based on 10 years’ data of National Metrology Agency (NMA) to fit the model.

### 1.1 Statement of the problem

One of the factors that affect the performance and life span of a pavement is the effect of temperature, this contribute to certain common types of asphalt pavement distresses such as permanent deformation or rutting (typically associated with high temperature environments), bleeding, and thermal cracking (associated with low temperature environments).

Marshall Mix design method is widely used throughout Ethiopia for HMA design. One of the draw backs of this method is the standard 60 [0]C temperature at which the test is conducted; which is derived from the maximum pavement surface temperature during the summer season in USA. As part of tropical regions, Ethiopian maximum pavement surface temperature is expected to deviate from 60[0]C.

Majority of the paved roads in Ethiopia are HMA, which suffer from different distress types directly & indirectly related to the mix design problems. Therefore, this thesis is aimed at, predicting the maximum pavement surface temperature in order to be used as an input for improving Marshal Mix design method.

### 1.2. Objective

#### 1.2.1 General Objective

To develop a prediction model relating maximum pavement surface temperature for Ethiopia using maximum air temperature and latitude

#### 1.2.2 Specific Objectives

- To divide Ethiopia in to different climatic zone of pavement surface

- To calibrate Huber`s equation

- To show the difference when the actual pavement surface temperature deviate from 60[0]C

### 1.3 Significance of the study

Nowadays excavators are busy scraping earth, making way for roads that will finally connect the far reaches of this largely rural country to its urban centers. According to ERA from these roads, 17.3% are paved roads. These paved roads suffer from different problems starting from in appropriate mix design to different performance failures during the service life of the road. This research is aimed to pave the way to reduce one of the problems that is in appropriate asphalt concrete mix design by providing a better testing mechanism related to maximum pavement surface temperature.

### 1.4 Research questions

- Which model best fit maximum air temperature & latitude with maximum pavement surface temperature?

- What is the relation between air temperature, latitude and maximum surface temperature?

- Which month & hour is appropriate to measure maximum pavement surface of each town?

### 1.5 Scope of the study

The research reported herein was focused on providing the most accurate pavement surface temperature prediction model related to the towns in Ethiopia. The study was carried out in 24 different towns. For each town based on the historical air temperature data the month in which the maximum air temperature will be recorded was determined and the result was implemented to measure the maximum pavement surface temperature of the towns.

The onsite measured data and air temperature data was used to establish the model using STATA-SE/13 statistical software. After the model was developed & validated laboratory test was conducted to demonstrate the difference in flow and stability of the actual and that of the standard 60[0]C at AACRA and Core Consulting Engineers laboratory.

### 1.6 Research Design

Abbildung in dieser Leseprobe nicht enthalten

Figure 1- 2 Research Design

## 2. LITERATURE REVIEW

The Strategic Highway Research Program (SHRP) established the Long Term Pavement Monitoring Program (LTPP) in 1987 to support a broad range of pavement performance analyses leading to improved engineering tools to design, construct, and manage pavements *(Diefenderfer etal, 2002 ).*

The statistics-based regression formulae are usually developed based on large databases of climatic, meteorological and geographical factors, such as air temperature, wind speed, solar radiation and latitude etc, as well as the measured field pavement temperatures. *(Rumney, 1969)* approximated temperature at the surface and at a 2-inch depth based on air temperature and hourly solar radiation. *(Lukanen et al., 1998*) predicted the seven-day average high pavement temperature using seven-day average high air temperature. More recently, *(Diefenderfer etal, 2002 ))* calculated the maximum and minimum temperature at any depth by using air temperature, daily solar radiation and depth within the pavement. Empirical formulae are usually applied to rapidly predict certain extreme temperatures within a pavement system or a specific temperature at a given pavement depth. However, the disadvantage of these types of formulae is that they give reasonable prediction for the input data included within the original sample database, but do not guarantee the accuracy of prediction for the input data outside the original sample database.

Barber was among the first researchers to discuss the calculation of maximum pavement temperatures based on weather reports. He observed that the changes in pavement temperature measured in Hybla Valley (Virginia, USA) roughly followed a sine curve with a period of one day. The analyses showed that when solar radiation and air temperature was included, the sine approximation provided reasonable estimates of surface temperatures. However, his model incorporates a total daily radiation factor instead of a more accurate measure such as hourly radiation and he proposed a model to correlate pavement surface temperatures and temperatures at 3.5 in. depth with weather station information.

Solaimanian developed a quadratic model that determines the maximum and minimum surface pavement temperature based on the latitude of the location of the pavement.

A computer simulation model that predicts summertime pavement temperatures based on the theoretical heat transfer models given *(Lukanen etal, 1998*) developed an empirical prediction model based on regression analysis and data from the Long -Term Pavement Performance Program to estimate the seven -day average maximum pavement temperature using the seven –day average maximum air temperature and also presented an analytical approach to predict pavement temperatures by employing heat and energy transfer theory.

Pavements are complex. Conditions that affect pavement temperature include: dirtying and wearing a way of a surface due to daily foot and vehicle traffic, affecting pavement surface, convection due to traffic movement over the pavement and shading caused by people, cars, vegetation and neighboring structures and buildings *(Bruce F., 2005) .*

Due to the weathering and the accumulation of dirt, the solar reflectance of conventional asphalt and concrete tend to change over time. Asphalt consists largely of petroleum derivatives as a binder mixed with sand or stone aggregate. Asphalt tends to lighten as the binder oxidizes and more aggregate is exposed through wear. Concrete also uses sand and stone aggregate, but in contrast to asphalt, typically uses Portland cement as a binder. Foot and vehicle traffic generally dirty the cement causing it to darken over time *(Bruce F., 2005).*

*(William et al., 2008)* developed a model for predicting temperature time series for dry and wet land surfaces. Surface heat transfer processes on impervious and pervious land surfaces were investigated for both dry and wet weather periods. The surface heat transfer equations were combined with a numerical approximation of the 1-D unsteady heat diffusion equation to calculate pavement and soil temperature profiles to a depth of 10 m. Equations to predict the magnitude of the radioactive, convective, conductive and evaporative heat fluxes at a dry or wet surface, using standard climate data as input, were developed.

A model for the effect of plant canopies on surface heat transfer was included for vegetated land surfaces. Given suitable climate data, the model can simulate the land surface and sub-surface temperatures continuously throughout a six month time period or for a single rainfall event. Land surface temperatures have been successfully simulated for pavements, bare soil, short and tall grass, a forest, and two agricultural crops (corn and soybeans). The simulations were run for three different locations in US, and different years as imposed by the availability of measured soil temperature and climate data *(William R. Herb, 2008).*

Astudy conducted by *(Stempihar et al., 2011)* showed that a comparison of different pavement layer thicknesses, the surface temperature generally decreases as the pavement thickness increases.

*(Manzouri, 2013)* analyzed the influence of pavement materials on the near surface air temperature. In order to accomplish this effort, test sections consisting of Hot Mix Asphalt (HMA), Porous Hot Mix asphalt (PHMA), Portland Cement Concrete (PCC), Pervious Portland Cement Concrete (PPCC), artificial turf, and landscape gravels were constructed in the Phoenix, Arizona area. Air temperature, albedo, wind speed, solar radiation, and wind direction were recorded, analyzed and compared above each pavement material type.

The results showed that there was no significant difference in the air temperature at 3-feet and above, regardless of the type of the pavement. Near surface pavement temperatures were also measured and modeled. The results indicated that for the Urban Heat Island analysis, it is important to consider the interaction between pavement structure, material properties, and environmental factors.

### 2.1 Previously Developed Temperature Prediction Algorithms & Models

*(Kennedy et al., 1994)* temperature predictions algorithms, as contained in Super pave, and the algorithms developed for temperature prediction in the South African climate by (*Viljoen, 2001*) are presented.

The maximum asphalt surface temperature predictions equations in Super pave *(Kennedy et al., 1994)* and by (*Viljoen, 2001*) are quite uncomplicated in their final form. They are based however, on the energy balance concept, and calibration of the equations involves identifying the best fit of values for the asphalt surface absorptivity, the transmission coefficient of air, the emissivity of air, the emissivity of the asphalt surface, the asphalt surface heat transfer coefficient and the conductivity of the asphalt material.

Viljoen (2001), equation will be presented by Equation 1 and *(Kennedy et al., 1994)* equation by equation 1 as follows:

Abbildung in dieser Leseprobe nicht enthalten

Where,

T s (max) is the daily maximum asphalt surface temperature in 0C

T air (max) is the daily maximum air temperature in 0C

Zn is zenith angle at midday

Zn is zenith angle at midday

C is cloud cover index

With: C=1.1 if T air (max) >30 [0]C

With: C=1.1 if T air (max) >30 0C

C=0.25 if < T air (max) < monthly mean air temperature

The Zenith angle is a function of the solar declination as shown in equation 2 below:

COS (Zn) = sin (latitude) sin (declination) +cos (latitude) cos (declination)

The equation recommended in super pave to determine the maximum surface temperature is:

Abbildung in dieser Leseprobe nicht enthalten

*(E. Denman, 2005)* approximate the solar declination using thermal PAD software in South Africa. The equation is presented as follows:

Abbildung in dieser Leseprobe nicht enthalten

*(Bentz, 2000)* Developed a computer model to predict the pavement surface temperature and time of wetness of concrete pavements and bridge decks. In this work the model is based on a one dimensional finite difference scheme and includes heat transfer by conduction, convection and radiation.

*(Wang etal, 2007)* provides an innovative method to derive the theoretical solution of an axisymmetric temperature field in a multi-layered pavement system. The multi-layered pavement system was modeled as a two-dimensional heat transfer problem. The temperature at any location kel integral transform with respect to the radial coordinate is utilized in the derivation of the solution. The interpolator y trigonometric polynomials based on discrete Fourier transform are used to fit the measured air temperatures and solar radiation intensities during a day, which are essential components in the boundary condition for the underlying heat transfer problem. A FORTRAN program was coded to implement the analytical solution. Measured field temperature results from a rigid pavement system demonstrate that the derived analytical solution generates reasonable temperature profiles in the concrete slab *(Dong Wang, 2007)*.

### 2.2 Effect of Environmental Factors on Flexible Pavement Performance

According to AASHTO, pavement performance is the ability of a pavement to satisfactorily serve traffic over time. It further defines the serviceability of a pavement as the ability to serve the traffic for which it was designed. Integration of both definitions will yield a new understanding of the performance, which can be interpreted as the integration of the serviceability over time *(AASHTO T307-99, 2003)*.

The main task for a pavement engineer is not only to design and construct a pavement but also to monitor the performance of the pavement in service to schedule the maintenance and rehabilitation works. The factors that are found affecting the performance of the pavements are presented in Figure 2-1(Gupta Ankit et al., 2006) *.*

The primary distresses associated with flexible pavements are fatigue cracking, thermal cracking, and rutting. In addition to these, reflection cracking is a major distress associated with asphalt overlays of flexible pavements.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2- 1 Factors influencing pavement performance (Gupta Ankit et al., 2006)

Environmental conditions have been found to exert significant impact on the performance of flexible pavements. External factors such as precipitation, temperature, humidity, freeze-thaw cycles, and depth of water table are the main environmental factors that have exerted major influences on the pavement performance. The internal factors, such as the susceptibility of the pavement materials to moisture and freeze-thaw damage, infiltration potential of the pavement, control the extent to which the pavement will react to the applied external environmental conditions.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2- 2 main climatic aspects in a coupled soil-climate that exert significant impact on the performance of flexible pavements (Gupta Ankit et al., 2006)

In order to incorporate the seasonal variation of moisture and temperature into the pavement design process, the seasonal changes in the moduli of various pavement layers must be determined. In other words, there is a need to quantify the effect of moisture variations on the moduli of unbound materials and the effect of temperature variations on the modulus of the asphalt concrete layer. This may be accomplished by studying the factors that affect the modulus for both layers and predicting the modulus from these factors.

Air temperatures as well as precipitation, wind speed, and solar radiation affect pavement temperatures. The response of a pavement system is highly influenced by the temperature of the surface layers and moisture content of the unbound soils. Annual, seasonal, and daily variations in temperature and precipitation have large influences on pavement service life. Therefore, the variability associated with climatic factors should be included in pavement design reliability analysis to help ensure desired performance.

For flexible pavements, temperature has an effect on the stiffness of the bituminous layers. Asphalt concrete becomes stiffer at lower temperatures and softer at higher temperatures and exhibits different material characteristics at different temperatures. The stiffnesses and shear strengths of unbound soil layers often vary seasonally with changes in moisture content and suction.

According to (Gupta Ankit et al., 2006) for flexible pavements, three major environmental effects are of particular interest:

- Temperature variations for the asphalt concrete. The dynamic modulus of asphalt concrete mixtures is very sensitive to temperature. Temperature distributions in asphalt concrete layers are predicted and then used to define the stiffness of the mixture throughout the sub-layers. Temperature distributions are also used as inputs for the thermal cracking prediction model.

- Moisture variation for sub-grade and unbound materials. The resilient modulus input of un bound materials is defined as being at optimum density and moisture content. A correction factor is defined to adjust the resilient modulus based on predicted moisture content.

- Freezing and thawing for sub-grade and unbound materials. The resilient modulus of unbound materials, located within the freezing zone, increases during freezing period sand decrease during thawing periods.

The 2002 Design Procedure produced by the National Cooperative Highway Research Program (NCHRP) takes into account climatic effects along with traffic and structural data in pavement design and rehabilitation *(NCHRP, 2002)*.While this design procedure allows the user to choose the climate region for the pavement, climate data available in the software for design spans only 5 years.

The study conducted by *(Pomerantz, 2000)* showed that albedo or its solar reflectivity has a significant effect on pavement temperatures of a given pavement surface. The solar absorptivity value changes according to pavement type and pavement age. For rigid pavements, this value increases as the concrete ages and darkens while for the flexible pavements it decreases with time as the pavement lightens in color. Therefore, solar absorptivity was assumed to be 0.65 for new rigid pavements and 0.8 for old rigid pavements while it was assumed to be 0.90 or 0.95 for new flexible pavements and 0.80 for old flexible pavements. These solar absorptivity values are based on field studies conducted by the Lawrence Berkeley National Laboratory *(Pomerantz, 2000).*

### 2.3 Relationship between Maximum Air Temperature & Pavement Surface Temperature

The SUPERPAVE TM software contains an equation relating design air temperature to design pavement temperature for both high and low design air temperatures. High design pavement temperature is determined 20 mm below the pavement surface. Low design pavement temperature is determined at the pavement surface(Huber, 1994) *.*

*Pavement surface temperature is based upon net heat flow at the pavement surface:*

*Net heat flow =*

*[Direct solar radiation] + [diffuse radiation] [convection] [conduction] – [black body radiation](Huber, 1994).*

Energy balance at the pavement surface is a transient phenomenon, continually changing with changing climatic conditions. For the purpose of calculating pavement surface temperature during the hottest 7-day period of the year, solar absorption, radiation transmission through air, atmospheric radiation and wind speed were set at the typical values in super pave TM software.

A deterministic equation was developed relating temperature difference between surface and air to latitude:

Abbildung in dieser Leseprobe nicht enthalten

(Huber, 1994)

Where,

Ts –surface temperature

Ta –air temperature

Lat –latitude in degrees

Below the pavement surface, the temperature is predicted using heat flow models contained in the Federal Highway Administration's Environmental Effects Model. During the hottest 7-day period in the heat of the day, pavement surface temperature is increasing and heat flows downward into the pavement. Using data from the temperature databases, an equation was developed that expresses the change in temperature with depth:

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Where, Td and Tf are in °F and the depth (d), is in inches.

Converting to SI units and calculating the temperature at a depth of 20 mm by substituting equation 6 in to equation 8 it becomes:

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Where T20mm and T air are in °C and the latitude is expressed in degrees.

### 2.4 Marshall Mix Design

Bituminous mixes are used in the surface layer of road and airfield pavements. The mix is composed usually of aggregate and asphalt cements. Some types of bituminous mixes are also used in base coarse. The design of asphalt paving mix, as with the design of other engineering materials is largely a matter of selecting and proportioning constituent materials to obtain the desired properties in the finished pavement structure.

The desirable properties of Asphalt mixes are:

- Resistance to permanent deformation: The mix should not distort or be displaced when subjected to traffic loads. The resistance to permanent deformation is more important at high temperatures.

- Fatigue resistance: the mix should not crack when subjected to repeated loads over a period of time.

- Resistance to low temperature cracking. This mix property is important in cold regions.

- Durability: the mix should contain sufficient asphalt cement to ensure an adequate film thickness around the aggregate particles. The compacted mix should not have very high air voids, which accelerates the aging process.

- Resistance to moisture-induced damage.

- Skid resistance.

- Workability: the mix must be capable of being placed and compacted with reasonable effort.

- Low noise and good drainage properties: If the mix is to be used for the surface (wearing) layer of the pavement structure.

Marshall Stability test is largely used for the routine testing in our country, Ethiopia. Criteria for the suitable mix design have been specified by the Asphalt Institute and Ethiopian Roads Authority.

In this method, the resistance to plastic deformation of a compacted cylindrical specimen of bituminous mixture is measured when the specimen is loaded diametrically at a deformation rate. There are two major features of the Marshall method of mix design. (i) density-voids analysis and (ii) stability flow tests. The Marshall stability of the mix is defined as the maximum load carried by the specimen at a standard test temperature of 60°C. The flow value is the deformation that the test specimen undergoes during loading up to the maximum load. Flow is measured in mm units(Freddy L.Roberts, 1996).

#### 2.4.2 Procedures

In the Marshall Test method of mix design, three compacted samples are prepared for each binder content. At least four binder contents are to be tested to get the optimum binder content. Specimens are subject to the following tests:

- Bulk density determination.

- Marshall Stability and flow test.

- Density and voids analysis.

#### 2.4.3 Preparation of test specimens

The coarse aggregate, fine aggregate, and the filler material should be proportioned so as to fulfill the requirements of the ERA standard. The required quantity of the mix is taken so as to produce compacted bituminous mix specimens of thickness 63.5 mm approximately. 1200 gm. of aggregates and filler are required to produce the desired thickness. The aggregates are heated to a temperature of 175° to 190°C the compaction mold assembly and rammer are cleaned and kept pre-heated to a temperature of 100°C to 145°C. The bitumen is heated to a temperature of 121°C to 138°C and the required amount of first trial of bitumen is added to the heated aggregate and thoroughly mixed. The mix is placed in a mold and compacted with number of blows specified. The sample is taken out of the mold after few minutes using sample extractor.

#### 2.4.4 Density & Void analysis

The bulk density of the sample is usually determined by weighting the sample in air and in water. It may be necessary to coat samples with paraffin before determining density. The specific gravity Gbcm of the specimen is given by:-

For each specimen using the bulk specific gravity & the rice specific gravity to calculate the % voids or (VTM)

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Where; VTM is Void in the total mix, Gmb is specific gravity and Gmm rice specific gravity

Calculate the VFA (void filled with asphalt) for each Marshall specimen using the VTM & VMA as follows

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Where; VMA is Void in the mineral aggregate, Gmb is specific gravity and Gsb bulk specific gravity

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Where; VFA is void filled with asphalt, VMA is void filled with asphalt and VTM is Percent of Voids.

### 2.5 Statistical Modeling

A statistical model is a mathematical model that embodies asset of statistical assumptions concerning the generation of some sample data and similar data from large population *(Wikipedia, 2018)*. There are different types of regression the most common are *(vidhya, 2018)*:-

- Linear Regression

- Polynomial Regression

- Logistic Regression

- Lasso Regression

- Elastic Net Regression

#### 2.5.1 Regression analysis

Regression analysis is a form of predictive modeling technique which investigates the relationship between a dependent (target) and independent (predicator) *(vidhya, 2018)*. It is an important tool for modeling and analyzing data *(vidhya, 2018)*. The benefits if using regression analysis are:-

- It indicates the Significant relationships between dependent variables and independent variables

- It indicated the strength of impact of multiple independent variables on a dependent variable

##### 2.5.1.1 Multivariate regression

Linear regression is a statistical tool for evaluating the relationship of one or more independent variables (x) to single continuous dependent variables (y). Regression analysis characterizes the relationship between the dependent and independent variables by looking determining the extent, direction and strength of the association *(Charles Jumbe et al., 2014) .*

The goal of linear regression is to find if change in one variable x causes change in another variable y, holding all other relevant factors fixed. Correlation is rarely enough to conclude. Therefore, need to hold other factors constant *(Charles Jumbe et al., 2014) .*

The population model is linear parameter

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The dependent variable (y) is linear and continuous. The error term has mean of zero, i.e. The differences between the estimated dependent variable (yhat) and the observed (actual) dependent variable (y) sums to zero (Σ(yhat-y) = 0). The independent variables are not correlated with each other (no multi co linearity). The independent variable is exogenous, i.e. they are not themselves dependent variables *(Charles Jumbe et al., 2014) .*

Multiple linear regression model is a model that associates one continuous dependent variable to two or more independent variables *(Charles Jumbe et al., 2014) .*

In multiple regression the strength of the relationship between the independent variables and the dependent variable is measured by a correlation coefficient. This multiple correlation coefficient is symbolized by *R.* The value of *R* can range from 0 to +1; *R* can never be negative. The closer to +1, the stronger the relationship; the closer to 0, the weaker the relationship *(G.Bluman, 2009)*.

As with simple regression, R[2] is the coefficient of multiple determination, and it is the amount of variation explained by the regression model. The expression 1 - R[2] represents the amount of unexplained variation, called the error or residual variation(G.Bluman, 2009) *.*

##### 2.5.1.2 Testing the Significance of R

An F test is used to test the significance of R. The F- test, used to compare two variances. This technique is called analysis of variance, or ANOVA. It is used to test claims involving three or more means

The hypotheses are:-

- The null hypothesis (NH) for the test will be i.e. that the coefficients are equal to zero implying that there is no relationship between the dependent variable and the independent variables.

- The alternate hypothesis (AH): , i.e. none of the coefficients is equal to zero.

If the NH is accepted, it implies that there is no relation between the dependent and independent variables even if the coefficients are not zero.

If the NH is rejected, i.e. the F-statistic is valid, then the overall model is valid and we can go ahead and check the other two tests (R[2] and t-statistic)

With the F test, two different estimates of the population variance are made. The first estimate is called the between-group variance, and it involves finding the variance of the means. The second estimate, the within-group variance, is made by computing the variance using all the data and is not affected by differences in the means. These two variances are sometimes called mean squares, denoted by MSB (mean square between) and MSW (mean square within) *(G.Bluman, 2009)*.

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(G.Bluman, 2009)

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*(G.Bluman, 2009)*

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(G.Bluman, 2009)

Where:-

SSB = sum of squares between groups

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SSW = sum of squares within groups (sum of squares for the error or residual)

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= Average of the means

The degrees of freedom for this F- test are d.f.N. = k -1, where k is the number of groups, and d.f.D. = N - k, where N is the sum of the sample sizes of the groups N = n1 + n2 + **….** + nk. The sample sizes need not be equal. The F test to compare means is always right-tailed *(G.Bluman, 2009)*.

##### 2.5.1.3 Adjusted R[2]

Since the value of *R* [2] is dependent on *n* (the number of data pairs) and *k* (the number of Variables), statisticians also calculate what is called an denoted by *R* [2]adj. This s based on the number of degrees of freedom.

The formula for the adjusted *R* [2] is: *(G.Bluman, 2009)*

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The adjusted *R* [2] is smaller than *R* [2] and takes into account the fact that when *n* and *k* are approximately equal, the value of *R* may be artificially high, due to sampling error rather than a true relationship among the variables. This occurs because the chance variations of all the variables are used in conjunction with each other to derive the regression equation. Even if the individual correlation coefficients for each independent variable and the dependent variable were all zero, the multiple correlation coefficient due to sampling error could be higher than zero. Hence, both *R* [2] and *R* [2]adj are usually reported in a multiple regression analysis.

##### 2.5.1.4 Cross validation

Model evaluation is an integral part of model development process. It helps to find the best model that represents the data and how well the chosen model will work in the future. Evaluating model performance with the data used for training is not acceptable in data mining because it can easily generate overoptimistic and over fitted models. One of the methods to minimize over fitted or overoptimistic models in data mining is cross validation.

When only a limited amount of data is available, to achieve an unbiased estimate of the model performance we use k-fold cross validation. In k-fold cross validation, the data is divided into k-subsets of equal size. The model is built k-times, each time leaving out one of the subsets from training and use it as the test set.

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= standard error of CV estimate

Where, CVk- test error on Kth fold

CV-estimate of test error, MSE-mean square of the error

CV- Estimate of the error

For the validation, data can be divided in to single test set. However this process is a little fragile because the presence or absence of a single outlier can vastly change our out of error is messy. A better approach than training task split is using multiple test set and averaging out of sample error which gives a more precise estimate of the true out of sample error. One of the most common approaches for multiple test set is cross validation in which we spit the data in to k-fold (train-test) split. We create the folds in such a way that each point in our data set occurs in exactly one test set. This provides k-test set so that every single point the data set occur exactly once. Rows are assigned randomly to avoid any kind of systematic biases in the data. This is one of the best way to estimate out of sample for predictive model. One important note after doing cross validation all the resemble models will be thrown away. Cross validation is only used to estimate out of sample error for the model and then re fix the model on the full training data set.

## 3. RESEARCH METHODOLOGY

### 3.1 Study Area and Study Period

The study areas of this research are 24 towns of Ethiopia located in North, South, East, West and central Ethiopia.

The areas incorporated in this study were Addis Ababa, Abay Berha, Arbaminch, Ambo, Axum, Bahirdar, Bale Robe, Batu/Ziway, Bishoftu, Bulehora, Deberebirehan, Dejen, Diredawa, Gonder, Hawassa, Jimma, Kombolcha, konso, Mekele, Meki, Methara, Nekemte, Semera and Wolayita sodo.

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Figure 3- 1 Sample study area, Axum

Onsite air temperature and pavement surface temperature measurement was conducted from August 2016- February 2018. The total study period was from August 2016 to August 2018. Due to some political turbulence in the country, climate change and financial problems the study period was expanded unexpectedly to two years.

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Table 3- 1 Scientific and Traditional classification of Climatic regions of Ethiopia (Ethiopian Atlas, 2018)

### 3.2 Historical Air Temperature and Latitude of the Study Areas

Ethiopian Roads are continuously and intensively influenced by climatic factors. The scientific and traditional classification of climatic regions of Ethiopia is presented as below.

The towns were selected based on the availability Meteorology station. From the meteorology stations, the average annual maximum temperature & latitude of the selected towns and the warmest months determined.

#### 3.2.1 Berha/ Desert places of Ethiopia

According to the Ethiopian Atlas, this region is less than 800m above sea level. For this thesis, the region is represented with Samara town and Abay Berha.

**Samara** is a town located in North- East Ethiopia, which is part of Awash Aseb high way. Samara is a new built town to replace the former Afar region capital Assaita. The latitude is 11.76 and altitude 590m above sea level.

Data collected from NMA (National Meteorology Agency of Ethiopia) for average maximum air temperature, minimum temperature and maximum precipitation for the past eleven years of Samara will be tabulated & presented on figures from 3-2.

Figure 3-2 shows data collected from NMA (National Meteorology Agency) of Ethiopia. According to the data, the average annual maximum temperature of Samara town for the past nine years was found to be 46.5 , which was collected at 12:00 am (mid-day). The warmest months of Samara town were June 2006.

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Figure 3- 2 Average annual Maximum Temperature of samara Town

**Abay Berha** is a collective name given for areas of Blue Nile river basin. According to the Central statistics, agency of Ethiopia 8 bridges had been constructed on the basin; the one, which is selected for this thesis, is the bridge that was constructed in 2008 to connect Goha Tsion with Degen.

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Figure 3- 3 on-site measurement at Extra dosed Type Hidase Bridge

It was hardly possible to find particular information concerning latitude & longitude including its altitude with average annual temperature of the Abay Berha/ Abay Deseret. The maximum air temperature & pavement surface temperature for further investigation will be used from onsite measurement as presented above on Figure 3-3.

#### 3.2.2 Kola (tropical) places of Ethiopia

The tropical places in Ethiopia are places with altitude less than 1500 m. Some of these places are part of the great east African rift valley. The Ethiopian lowlands stretch North-South along the border with Sudan & include the lower valley of the Blue Nile, Tekeze and Baro rivers. Ethiopian rift valley has two distinct sections. The first section is the north east which is relatively flat and being the lowest at Afar Region Denakil plain (Dallol), which drops as low as 116m. The other section is the southwest section. This section contains Ethiopia`s lake region, an internal drainage basin of many small rivers.

Latitude, precipitation and maximum & minimum temperature of four representative cities in the country for the past ten years will be presented as below: Arba-Minchi, Dire-Dawa, Metehara & Konso.

**Arba-Minch** is a town located in southern Ethiopia in Gamo Gofa zone &500km away from Addis Ababa. The latitude is 6 and altitude 1207m above sea level.

Data collected from NMA (National Meteorology Agency of Ethiopia) for average maximum air temperature, for the past ten years of Arba- Minch will be tabulated & presented on figures from 3-4.

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Figure 3- 4 Average Annual Yearly Maximum Temperature of Arba-Minch from 2006 to 2015

According to NMA (National Meteorology Agency) of Ethiopia the average annual maximum temperature of Arba-Minch for the past ten years was 37.7 , which was collected at 12:00 am (mid-day). The average maximum temperature was recorded in February 2015.

The average annual minimum temperature was found to be 10.98 . The data was collected at 9:00 am (morning). According to this data the calmest month vary from December to February.

The other parameter the average annual maximum precipitation was found to be 64.39mm, which was collected at 9: 00 am. The rainy season of this town vary from May to October. For the years 2010, 2011, 2014&2015 the town received heavy rainfall on May and on 2009&2013 the town received heavy rain on October. The other years maximum rainfall lie in between these two months.

**Diredawa** is a town located in the eastern edge of the great African rift valley with latitude 9 and altitude 1180m above sea level.

Data collected from NMA (National Meteorology Agency of Ethiopia) for average maximum air temperature for the past ten years of Dire-Dawa will be tabulated & presented on figures from 3-5.

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Figure 3- 5 Average Annual Maximum Temperature of Dire-Dawa from 2006 to 2015

According to NMA (National Meteorology Agency) of Ethiopia the average annual maximum temperature of Dire-Dawa for the past ten years was 39.80 , which was collected at 12:00 am (mid-day). The average annual maximum temperature of Dire town was recorded in August 2008.

The average annual minimum temperature was found to be 10.44 . The data was collected at 9:00 am (morning). According to this data the calmest month vary from December to February. The other parameter the average annual maximum precipitation was found to be 64.39mm, which was collected at 9: 00 am.

The rainy season of this town vary from April to November. For the years 2006-2008 & 2014, the town received heavy rainfall on April and for the year 2011-2012 &2015 the town received heavy rain on May while on 2009&2010 on September & October respectively.

**Metehara** is a town located in Central Ethiopia Misrak Shewa Zone of Oromia region. The latitude is 8.85 and altitude 944m above sea level. Data collected from NMA (National Meteorology Agency of Ethiopia) for average maximum air temperature, minimum temperature and maximum precipitation for the past ten years of Methara will be tabulated & presented on figures from 3-6.

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Figure 3- 6 Average Annual Maximum Temperature of Metehara for the past 10 years

The average annual maximum temperature was 41 , which was collected at 12:00 am (mid-day). The maximum of this town was June 2009. The average annual minimum temperature was found to be 6.37 . The data was collected at 9:00 am (morning). According to this data, the calmest months vary from December & January. For the years 2006, 2012 &2015 the calmest month were January. For all the remaining years except in 2009, when the calmest temperature was recorded in March the calmest month was December.

**Konso** is a town on the Sagan River located in South West Ethiopia in Southern Nations Nationalities and people’s region. The latitude & longitude is 5.33 and altitude 1431 m above sea level. Data collected from NMA (National Meteorology Agency of Ethiopia) for average maximum air temperature for the past eleven years of Konso will be tabulated & presented on figures from 3-7.

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Figure 3- 7 Average Annual Maximum Temperature of Konso from 2006 to 2016

According to NMA (National Meteorology Agency) of Ethiopia the average annual maximum temperature of Konso town for the past eleven years was 35 , which was collected at 12:00 am (mid-day). The warmest months of Konso town was March for all the past years except for 2006, 2010 &2014 which was February.

The average annual minimum temperature was found to be 13.62 . The data was collected at 9:00 am (morning). According to this data the calmest months vary from December & August. For the years 2007, 2008 & 2009 the calmest month were July. For 2010, 2011 &2016 the calmest month was August. December, September & April were the calmest months of the years 2013 & 2014 and 2012 respectively.

#### 3.2.3 Sub-tropical (Weina-dega) places of Ethiopia

According to Ethiopian national atlas these places are places with elevation greater than 1500m and below 2300 m. Some representative places of this climatic region are presented in this section.

**Ambo** is a city located in central Ethiopia West Shewa zone of Oromia region. The latitude is 8.98 and altitude 2068 m above sea level.

Data collected from NMA (National Meteorology Agency of Ethiopia) for average maximum air temperature, minimum temperature and maximum precipitation for the past ten years of Ambo will be tabulated & presented on figures from 3-8.

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Figure 3- 8 Average Annual Maximum Precipitation of Addis Ababa from 2006 to 2016

According to NMA (National Meteorology Agency) of Ethiopia the average annual maximum temperature of Ambo town for the past ten years was 35.6 , which was collected at 12:00 am (mid-day). The warmest month of all the past ten years for Ambo town was February 2011.

The average annual minimum temperature was found to be 6.63 . The data was collected at 9:00 am (morning). According to this data the calmest months vary from December & January. For the years 2006& 2016 the calmest month were December. For 2008, 2009&2014 the calmest month was November. January was the calmest month of the years 2010 & 2015.

**Wolaita Sodo** is a town and separate Woreda in south-central Ethiopia. It administrative zone of south nations &nationalities of Ethiopia. It has a latitude & longitude of 6.81 with altitude of 1854 m above sea level. Data collected from NMA (National Meteorology Agency of Ethiopia) for average maximum air temperature for the past eleven years of Wolaita Sodo will be tabulated & presented on figure 3-9.

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Figure 3- 9 Average Annual Maximum Temperature for Wolaita Sodo for the past eleven years

According to NMA (National Meteorology Agency) of Ethiopia the average annual maximum temperature of Wolaita Sodo town for the past six years was 32.5 , which was collected at 12:00 am (mid-day). The warmest months of Wolaita Sodo town were March, October & February. For the year 2007, 2008, 2009, 2011, 2012, 2014, 2015 &2016 was March. For 2010 & 2013 the warmest month was February. For the year 2006 the warmest month was October. However, the maximum temperature for all the past years was recorded in March 2009.

The average annual minimum temperature was found to be 9.8 . The data was collected at 9:00 am (morning). According to this data, the calmest months vary from November to January. For the years 2007, 2010, 2011 & 2012 the calmest month were December. For 2009, 2014 &2015 the calmest month was January. November & February were the calmest months of the years 2006 & 2008 respectively.

**Kombolcha** is a city and woreda located in North Central Ethiopia Debub wollo zone of Amhara region. The latitude is 11.83 and altitude 1857m above sea level.

Data collected from NMA (National Meteorology Agency of Ethiopia) for average maximum air temperature presented on figures from 3-10.

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3- 10 Average Annual Maximum Temperature of Kombolcha for the past 10 years

According to NMA (National Meteorology Agency) of Ethiopia the average annual maximum temperature of Kombolcha town for the past six years was 34 , which was collected at 12:00 am (mid-day). The warmest months of Kombolcha town were March, October & February. However, the maximum temperature of all the past years was recorded in June 2009. For the year 2007, 2008, 2009, 2011, 2012, 2014, 2015 &2016 was March. For 2010 & 2013 the warmest month was February. For the year 2006 the warmest month was October.

The average annual minimum temperature was found to be 9.8 . The data was collected at 9:00 am (morning). According to this data the calmest months vary from November to January. For the years 2007, 2010, 2011 & 2012 the calmest month were December. For 2009, 2014 &2015 the calmest month was January.

**Hagere-Mariam** is a town located in South Ethiopia 382 km away from the capital. It located in the Borena Zone of Oromia region with latitude of 5.65 and altitude 1861m above sea level.

Data collected from NMA (National Meteorology Agency of Ethiopia) for average maximum air temperature on figure 3-11.

**[...]**

- Quote paper
- Debela Daba (Author), 2019, Prediction of Maximum Pavement Surface Temperature Using Maximum Air Temperature and Latitude, Munich, GRIN Verlag, https://www.grin.com/document/489870

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