LISTADO DE VARIABLES QUE INFLUYEN EN EL FUTURO DE LA ORINOQUIA

Incropera and Dewitt[184] define the thermal conductivity of concrete as the quantity of heat that pass through concrete in a unit length (heat transfer rate) for a given temperature gradient. The thermal conductivity affects the temperature gradients and thermal stresses, which are developed inside the concrete. The thermal conductivity is measured in Watts per Kelvin per meter (W·K−1·m−1). The values of the thermal conductivity of ordinary concrete generally ranges between about 1.4 and 3.6 W/m K[12, 185].

Factors that affect the thermal conductivity of concrete are as follow:

 Moisture content of concrete

Kim et al[186] carried out a research to investigate factors, which influence on the thermal conductivity of concrete, mortar and cement paste. They reported that the

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aggregate volume fraction and the moisture condition of specimens were declared as the primary factors that affected the thermal conductivity of concrete. Meanwhile, type of admixtures and cementitious materials that were used in mortar or cement paste, strongly influenced the thermal conductivity of mortar and cement paste. Furthermore, Kim et al[186] reported that the thermal conductivity of concrete was also influenced by fine aggregate fraction, water- cement ratio and curing temperature.

Similar to Kim et al[186]’s work, Khan[187] who used the Campell-Allen and Thorne[188]’s model to evaluate the influence of aggregate type with various moisture contents. He found that the type and the moisture content of aggregate influenced the thermal conductivity of concrete.

In 1998, Khan et all[189] reported the effect different water-cement ratios for low, medium and high strength mixes at very early ages on the thermal conductivity of concrete. They found that for the normal strength concrete, the thermal conductivity of the maturing concrete was about 33% higher than that of hardened concrete, while the difference for the high strength concrete was only 2%. It is believed that the thermal conductivity decreases linearly to increased strength gain. They agreed with other researchers that the thermal conductivity of concrete, particularly at early ages was greatly affected by the moisture of the concrete. It is believed due to water has a considerably lower thermal conductivity than that of aggregates, which is estimated 70% of the total volume of concrete. The moisture content of concrete is directly related to the hydration degree of the concrete.

 Mix proportion of concrete

In 2006, Demirboga[190] observed the effect of cementitious materials, when they were used in concrete, on the thermal conductivity of concrete. He used silica fume, FA, GGBS and combination of them to evaluate their effect on the thermal conductivity of concrete. He found that the maximum thermal conductivity of 1.233 W/m.0K, which was obtained from the concrete mixture with Portland

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cement only. The thermal conductivity of concrete decreased with the increase of the percentage of cementitious materials in the concrete. Neville[12] reported that the thermal conductivity of rock aggregate depended on its crystallinity. The increase of the thermal conductivity of the rock aggregate will increase directly the thermal conductivity of concrete.

 Curing temperature of concrete

Neville[12] found that the effect of temperature on the thermal conductivity of concrete could be neglected when the concrete was cured within the room temperature limits. However, at the higher curing temperatures, the change of values of the thermal conductivity of concrete becomes more considerable and complex. An increase of the temperature up to a maximum at about 50 to 60 0C increases slowly the thermal conductivity of concrete. The thermal conductivity of concrete decreases sharply when the temperature increased up to 120 0C as the concrete loss of water/moisture, which was due to the high temperature. The thermal conductivity of concrete then tends to be a constant, at the temperature between 120 and 140 0C. At the temperature of 800 0C, the thermal conductivity of concrete is about 50% of that of concrete cured at temperature 20 0C.

Kim et al[186] demonstrated experimentally that the thermal conductivity of concrete at early age decreases as its temperature increases. It is due to heat released from the cement hydration. Similarly, Morabito[191] also reported that the thermal conductivity of concrete decreased with the increase of the concrete temperature.

 Age of concrete

Marshall[192] and Brown and Javaid[193] found that the thermal conductivity was affected by the age of concrete, however, it was only for the first few days. Brown and Javaid[193] measured the thermal properties of concrete with the water cement ratio of 0.65 from the first 6-hours to seven days. The results showed that the thermal conductivity of the concrete increased from the first 6-hours up to 1-day

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and then decreased at the following days until the age of 7-days. After the age, the thermal conductivity then appeared to remain constant. The thermal conductivity of concrete at 6 hours was measured to be 2176 W/m.oC and at the age of 7-day it had dropped by approximately 30% and was equal to 1.515 W/m.oC. It is appeared that the thermal conductivity decreases linearly to the moisture content and degree of hydration, similar to that was reported by De Schutter and Taerwe[194].

In contrast, Byfors[122] and Rilem Committee No. 42[195] reported that the effect of age on the thermal conductivity of concrete was not notable. Similarly, Kim et al[186] reported that in general, the age of concrete has a very small effect on its thermal conductivity with the exception of the time period 0 to 2 days.

The thermal conductivity of concrete can be determined from the thermal diffusivity relationship as follows:

Equation 2.106 The SI units for thermal diffusivity are metres square/hour (m2/h). Typical values for concrete diffusivity are in the range from 0.002 to 0.006 m2/h[12]. The thermal diffusivity describes the rate at which a temperature disturbance at one point in a body moves to another point.

The accurate estimation of the value of thermal conductivity is very important in a modelling the temperature of concrete during its hydration period, especially when the formwork of concrete is still used. The heat conduction and the associated temperature gradients within the concrete will generally develop the heat-transfer process within its matrix and greatly influence the development of its temperature profile. The sensitivity of the in-situ temperature of concrete to its thermal conductivity can be verified using heat transfer finite element modelling.

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Recently, some methods to measure the thermal conductivity of concrete has been introduced such as the prism method that estimates the thermal properties of concrete with reasonable accuracy[196].

Some values of the thermal conductivity of concrete found in the literatures are presented in Table 2.5 below.

Table 2.5: Thermal conductivity of concretein relation to ages Researcher Thermal conductivity k

(W/m.K)

Age (days)

Gibbon and Ballim[197] 0.6 - 2.6 0 - 4

Yoshida[197] 1.5 - 1.8 0 - 2

Rousan and Roy[198] 1 - 1.8 7 - 84

Davey[199] 0.8 - 2.3 not specified

ACI[200] 1.8 - 3.8 14

The typical value of the thermal conductivity of concrete in relation to the type of aggregate used in concrete is shown in the following table.

Table 2.6: Thermal conductivity of concrete in relation to the type of aggregate[186]

Type of aggregate Wet density of concrete (kg/m3) Thermal conductivity K (W/m.K) Quartzite 2440 3.5 Dolomite 2500 3.3 Limestone 2450 3.2 Sandstone 2400 2.9 Granite 2420 2.6 Basalt 2520 2 Barytes 3040 2 Expanded Shale 1590 0.85

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The thermal conductivity of concrete is an input parameter to simulate the temperature of concrete using Finite Element Modelling (FEM). It is difficult to estimate the thermal conductivity of concrete, as the concrete consists of different composite materials (non-homogeneous material). The differences of aggregate types used and moisture conditions of concrete give different values of the thermal conductivity of the concrete, as these are the primary factors influencing the value of the thermal conductivity. However, in respect to temperature variation in a concrete structural element, heat of hydration is the major thermal property of concrete. Therefore, in this study, the values of the thermal conductivity of concrete used are based on literature review values, is discussed further in section 7.3.