LIST OF EQUATIONS
3. Chapter 3 Theoretical Methods for Modelling Pavement Deterioration Deterioration
3.2. Climate Change Model
Climate change can be seen in the form of increasing temperatures, snow and ice, extreme weather, precipitation and sea levels. The selection of the change in temperature due to the impact of climate change is based on the author’s interests, and other factors are not studied in the research. For the element of change in temperature, the following sections focus on the components used for determining the impact of the change in temperature with respect to pavement infrastructure.
3.2.1. Pavement Temperature Model
Temperature is a critical element in asphalt mixtures. It mainly affects the mechanical properties of asphalt mix materials. Temperature affects the strength or structural capacity of the asphaltic mix. Arangi and Jain (2015) emphasised the risk of heat. They stated that temperature could be a main cause of pavement distresses that lead to shortening the lifespan of a pavement. Matic et al. (2012) advised that pavement temperature be monitored accurately through the means of air temperatures, which will help the pavement engineer to calculate the resilient modulus and estimate pavement deflections.
Hot mix asphalt is classified as a viscoelastic material (viscous and elastic material), which means that pavement material will act as an elastic solid at low temperatures. Therefore, at low temperatures, permanent deformation is not likely to occur. However, at high temperatures, the pavement material will act as a viscous fluid. If the increase in temperature exceeds the design limit, strain will start to take place, leading to rutting (Asbahan and Vandenbossche 2011). Arangi and Jain (2015) also stated that, at a low temperature, the asphaltic mix could be hard, brittle and vulnerable, which eventually leads to cracking, and, at a high temperature, it becomes soft and susceptible to permanent deformation. Asbahan and Vandenbossche (2011) defined many factors that affect the temperature such as solar radiation, ambient temperature, wind speed and reflectance of the pavement.
Many scholars have broadly studied prediction of pavement temperature.
Barber (1957) was the first scholar who investigated the changes in pavement
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temperature. Dempsey and Thompson (1970) introduced nomographs to measure the pavement temperature at both the surface and at a depth of 50 mm. Khraibani et al.
(2010) developed a pavement temperature prediction model through computer simulation based on the theory of heat transfer. Arangi and Jain (2015) introduced a linear model for maximum pavement temperature which depended on asphalt binder type besides other factors. Al-Abdul Wahhab and Balghunaim (1994) conducted a study to quantify the pavement temperature in Saudi Arabia based on an annual measurement of pavement temperatures at various sections. Their findings showed that maximum pavement temperatures were recorded between 3°C and 72°C in an arid environment, while the temperature fluctuated between 4°C and 65°C in seaside zones. Moreover, Hassan et al. (2004) studied the pavement highest temperature at a depth of 20 mm below the ground surface for 445 days of collected data. The study took place in Oman, which is considered to have similar weather conditions to the UAE. Hassan et al. (2004) proposed a linear regression model by applying the highest air temperature as the independent variable and the highest 20 mm pavement temperature as a predictor, as per the equation 3-1 and Figure 3-2. (The equation achieved R2 of 0.847.)
𝑻𝟐𝟎𝒎𝒎=𝟑.𝟏𝟔𝟎+𝟏.𝟏𝟑𝟗×𝑻𝒂𝒊𝒓
Equation 3-1: Pavement temperature model developed by Hassan et al. (2004)
T20mm= Pavement temperature at 20 mm depth, ºC
Tair = Maximum air temperature, ºC.
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Figure 3-2: Pavement temperature measure developed by Hassan et al. (2004)
Hassan et al.'s (2004) experiment underwent similar weather conditions to UAE weather. Scoring a high value in the regression model provides more confidence in using such an equation. Hassan et al.'s (2004) model is used in this research to determine the maximum pavement temperature. Further explanation is provided in Chapter 5 section 5.11.
3.2.2. Thornthwaite Moisture Index model for pavements
Thornthwaite Moisture Index was first introduced in 1948 by C. W.
Thornthwaite. The primary purpose of the system was to provide a new climate model for a specific community. Sun (2015) highlighted that the Thornthwaite Moisture Index (TMI) is widely applied to estimating the variation of climate. The climatic parameter (TMI) is a dimensionless parameter that represents a climate condition for a specific location generated from a function of evaporation and rainfall. The TMI is a yearly index and its value will differ based on various equations, methods and study periods. It presents many climate types. Martin and Choummanivong (2010) stated that TMI “describes the aridity or humidity of the soil and climate of a region and is calculated from the collective effects of precipitation, evapotranspiration, soil water storage, moisture deficit, and runoff “. Taylor and Philp (2016) emphasised the importance of using the TMI. They added that it is broadly used in the area of highway engineering such as pavement deterioration model and maintenance and rehabilitation planning climate indicator. Sun (2015) added that the positive index of the TMI
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indicates a humid climate with soil that has a high moisture conten while the negative index indicates an arid climate with less moisture in the soil. TMI application is widely accepted in the engineering field because it is a simple method and more practical than others. Thornthwaite introduced the TMI equation in 1948. Sun (2015) stated that this equation has been recognised and widely accepted by many scholars and practitioners over the past several decades. However, there are limitations as the equation needs to be computed yearly with water-balance analysis and such a procedure requires enormous information and data recording. Moreover, some of these data have to be estimated because they do not exist, while others are difficult to obtain (Sun 2015). The following two equations were introduced by Mather (1974) and Witczak, Zapata and Houston (2006) respectively to overcome the shortage in Thornthwaite’s original equation in 1948:
𝑇𝑀𝐼 = 100 ( 𝑃
𝑃𝐸𝑇− 1)
Equation 3-2: Thornthwaite Moisture Index equation developed by Mather (1974) Where,
P = Annual precipitation,
PET = Adjusted potential evapotranspiration
𝑇𝑀𝐼 = 75 ( 𝑃
𝑃𝐸𝑇− 1) + 10
Equation 3-3: Thornthwaite Moisture Index equation developed by Witczak et al. (2006)
Where,
P = Annual precipitation,
PET = Adjusted potential evapotranspiration
Equations 3-2 and 3-3 are default equations proposed by Mather (1974) and Witczak, Zapata and Houston (2006). To build a new TMI value that matches UAE conditions, an assessment of UAE weather data is needed. The highlighted equations (3-2 and 3-3) are used to define the most reliable model for TMI that matches UAE weather. Further explanation is provided in Chapter 5 section 5.11.3.
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