Thermal effect of mass concrete structures in the tropics: Experimental, modelling and parametric studies

This paper is an experimental investigation and analytical simulation of thermal effects on mass concrete structures in the tropics. A study of the temperature rise of a 1.1 m × 1.1 m × 1.1 m experimental mass concrete block, well instrumented with thermocouples to monitor the temperatures distribution was performed. A validated finite element model was used to predict the temperature development of the hydrating experimental mass concrete block. Thermal stress analysis was performed to give an estimate of stresses induced by the thermal gradient of the concrete block section and the crack index was used to quantify the probability of thermal cracking. A parametric study on the effect of the surface area to volume ratio (SVR) of mass concrete was performed to quantify the maximum allowable thermal gradient as well as the induced thermal stresses that may cause thermal cracks. For SVR less than 0.36, thermal cracks may occur at early ages of concrete strength development in the tropics. *Corresponding Author: Stephen Agyeman, Department of Civil Engineering, Sunyani Technical University, Box 206, Sunyani, Ghana E-mail: agyengo44@gmail.com Reviewing editor: Raja Rizwan Hussain, King Saud University, Saudi Arabia Additional information is available at the end of the article ABOUT THE AUTHORS Ing. Herbert Abeka obtained his Master’s degree in Development Planning and Policy, and MPhil Structural Engineering from the Kwame Nkrumah University of Science and Technology (KNUST). He is a Member of the Ghana Institution of Engineers (GhIE) and currently lecturing at civil engineering department of Sunyani Technical University. His research interests includes urban planning and settlements, structural simulations and animations. Engr. Stephen Agyeman obtained his Master’s degree in Road and Transportation Engineering from the KNUST. He is a Member of the Institution of Engineering and Technology (IET), Ghana and currently lecturing at civil engineering department of Sunyani Technical University. His research interest includes building permits, public transportation, traffic simulations and animations, and road traffic accidents analysis. Prof. Mark Adom-Asamoah obtained his PhD in Civil Engineering from Bristol University. He is a lecturer and Provost for the College of Engineering, KNUST. His research interest includes structural design, structural analysis and earthquake engineering. PUBLIC INTEREST STATEMENT Albeit the effects of thermal gradients on mass concrete is well known in developed countries, the maximum allowable temperature differential published value of 20°C (35°F) between the centre of a mass concrete element and its surface is being hotly debated among researchers. However, the application of the fixed temperature differential value by many agencies has been based on time and location where such massive concrete projects have taken place. The novelty of this work is the developed finite element analysis model that can be used by agencies to predict the temperature distribution and the associated stress development in massive concrete structures in the tropics. We conclude that in the tropics, mass concrete structures with SVR less than 0.36 are expected to cause thermal cracking at early ages of cement hydration and a minimum of 5 days are required for de-shuttering of the formwork to prevent the occurrence of thermal shock. Received: 09 June 2016 Accepted: 29 December 2016 First Published: 04 January 2017 Page 1 of 18 Herbert Abeka © 2017 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license.

Ing. Herbert Abeka obtained his Master's degree in Development Planning and Policy, and MPhil Structural Engineering from the Kwame Nkrumah University of Science and Technology (KNUST). He is a Member of the Ghana Institution of Engineers (GhIE) and currently lecturing at civil engineering department of Sunyani Technical University. His research interests includes urban planning and settlements, structural simulations and animations.
Engr. Stephen Agyeman obtained his Master's degree in Road and Transportation Engineering from the KNUST. He is a Member of the Institution of Engineering and Technology (IET), Ghana and currently lecturing at civil engineering department of Sunyani Technical University. His research interest includes building permits, public transportation, traffic simulations and animations, and road traffic accidents analysis.
Prof. Mark Adom-Asamoah obtained his PhD in Civil Engineering from Bristol University. He is a lecturer and Provost for the College of Engineering, KNUST. His research interest includes structural design, structural analysis and earthquake engineering.

PUBLIC INTEREST STATEMENT
Albeit the effects of thermal gradients on mass concrete is well known in developed countries, the maximum allowable temperature differential published value of 20°C (35°F) between the centre of a mass concrete element and its surface is being hotly debated among researchers. However, the application of the fixed temperature differential value by many agencies has been based on time and location where such massive concrete projects have taken place. The novelty of this work is the developed finite element analysis model that can be used by agencies to predict the temperature distribution and the associated stress development in massive concrete structures in the tropics. We conclude that in the tropics, mass concrete structures with SVR less than 0.36 are expected to cause thermal cracking at early ages of cement hydration and a minimum of 5 days are required for de-shuttering of the formwork to prevent the occurrence of thermal shock.

Introduction
Whenever large volume of fresh concrete is poured during the construction of large homogeneous structures such as dams, bridges, water retaining structures and foundations, consideration is always given to the amount of heat that will be generated (Gajda, 2007;Klemczak, 2014). The concrete hydration is an exothermic reaction that can produce high amounts of heat during curing, especially in the first few days or weeks after casting (ACI Committee 318, 2005;Lawrence, 2009). This heat production can produce high temperatures at the centre of the mass concrete due to the insulating effect of the concrete. Since the concrete surface temperatures are lower due to the heat dissipated into the ambient environment, temperature gradients are formed (Khan, Cook, & Mitchell, 1998;Lachemi & Aïtcin, 1997;Lawrence, 2009;Pofale, Tayade, & Deshpande, 2013). These changes in temperature create volumetric changes, i.e. expansion from heating and contraction from cooling in the concrete (Lin & Chen, 2015;Tia, Lawrence, Ferraro, Do, & Chen, 2013). When these volumetric changes are restrained by the supports and the more mature interior concrete, tensile stresses are formed on the concrete's surface (Riding, Poole, Folliard, Juenger, & Schinder, 2012). If the surface tensile stresses become higher than overall tensile strength of the concrete, cracking normally occurs (de Borst & van den Boogaard, 1994;Kim, 2010;Lawrence, 2009). The cracking is even magnified in early age concrete that is still developing its full strength (Cervera, Faria, Oliver, & Prato, 2002;Lee & Kim, 2009).
Past research works on the creation of numerical models for the prediction of temperature distribution in mass concrete mainly focused on using basic heat generation functions for the calculation of adiabatic temperature rise (Ballim, 2004;Chini & Parham, 2005;De Schutter, 2002;De Schutter, Yuan, Liu, & Jiang, 2014;Ilc, Turk, Kavčič, & Trtnik, 2009;Tanabe, Kawasumi, & Yamashita, 1986;van Breugel, 1991). The used of real measured heat of hydration results from calorimetry testing of the cement paste is mostly uncommon in Africa, especially Ghana due to the initial cost in acquiring the instruments (Kim, 2010;Milestone & Rogers, 1981). However, available literature reviews that numerous labs in North America and Europe have calorimeter(s) for measuring the real heat of hydration (Cao, Zavaterri, Youngblood, Moon, & Weiss, 2014). Instead, attempts at modelling hydrating mass concrete have treated the heat generated by the reacting cement as being uniform throughout the concrete mass. Whereas, in reality, the heat generation is a function of the temperature and time history of the concrete at individual locations in the concrete mass (Lawrence, 2009;Radovanovic, 1998).
Although the effects of thermal gradients on mass concrete is well known in developed countries, there is no agreed maximum allowable temperature differential value between the centre of a mass concrete element and its surface. Bobko, Edwards, Seracino, and Zia (2015), have modelled the thermal behaviour of hydrating mass concrete with some degree of success and have fixed the temperature differential at 20°C (35°F). However, in the country where this temperature differential value was developed, a several agencies have established their own guidelines to regulate and control the adverse effect of thermal cracking in mass concrete depending on the time and location where such massive concrete projects are taking place (Edwards, 2013;Lawrence, Tia, Ferraro, & Bergin, 2012;Lawrence, 2009). This confirms the fact that heat generation in mass concrete structures varies for the tropics and the temperate zones for the same type of cement (Do, Lawrence, Tia, & Bergin, 2015). But in the tropics, specifically Ghana, these values do not even exist. This paper therefore formulated a finite element model, taking into consideration the non-homogeneity of heat generation within the mass concrete, the resulting thermal gradients, the associated thermal stresses and strains, and how to accurately predict the distribution of temperature in a hydrating concrete mass in the tropics. Novelty of this work is the developed finite element analysis model that can be used by agencies to predict the temperature distribution and the associated stress development in massive concrete structures in the tropics.

Thermal stresses
The thermal stresses that occur during the hardening of mass concrete are extremely complex and difficult to measure. This is due to several factors, chief among which is the complex distribution of temperature changes throughout the volume of the mass concrete. The central region of the mass concrete at early age experiences high but uniform temperatures while the temperature in the outer region decreases as we move closer to the surface (Folliard et al., 2008). Since the maturity of concrete and strength are functions of temperature, the central region of the mass concrete structure will be matured and stronger than the outer region. As the concrete hydrates faster in the middle, large thermal gradients are produced, and strength and maturity are decreased moving outwards towards the surface. Restraint against this contraction will cause tensile stresses and strains to develop, creating the possibility for cracks to occur at or close to the surface of the concrete (Atrushi, 2003;Yuan & Wan, 2002). These cracks are initiated when the tensile stresses exceed the low tensile strength at the surface. The magnitude of the tensile stresses are dependent on the difference in the mass concrete, creep or relaxation of the concrete, the coefficient of thermal expansion, the degree of restraint in the concrete and elastic modulus. The development of cracks will affect the ability of the concrete structure to withstand its design load, and further allow the infiltration of lethal materials which will undermine the integrity and durability of the mass concrete structure (De Schutter et al., 2014;Lawrence, 2009;Lawrence et al., 2012).
The causes of early age thermal cracking may include either internal or external restraint (ACI Committee 207, 2005a;Kim, 2010). Internal restraint is brought about by strain gradients within the material while exterior restraint is brought about by externally applied loads. This degree of restraint varies between 0 and 100% depending on the physical boundary conditions and on the geometry of the structure (Muhammad, 2009). To accurately predict these thermal cracks, thermal properties that need to be modelled include the specific heat, the coefficient of thermal expansion, thermal diffusivity and heat production. Mechanical properties that need to be quantified, in order to simulate a finite element model of the experimental block include the tensile strength, tensile strain and elastic modulus (Atrushi, 2003;Gawin, Pesavento, & Schrefler, 2006a, 2006bUlm & Coussy, 1995).
According to de Borst and van den Boogaard (1994), Ishikawa (1991), Jaafar (2007), Lawrence et al. (2012), Noorzaei, Bayagoob, Thanoon, and Jaafar (2006), and Tang, Millard, and Beattie (2015), Finite Element Method (FEM) which is a numerical modelling method is seen as the best predictor of thermal cracks in concrete. It offers a step-by-step approach in solving the problem though it has its own limitations of been costly and impossibly used at site to quickly determine the maximum heat of hydration of concrete (De Freitas, Cuong, Faria, & Azenha, 2013;Tatro & Schrader, 1992;Zhai, Wang, & Wang, 2015).

Concrete mix design (sample preparation)
The two concrete mixes used in this study had a water to cement ratio of 0.42 to allow for complete hydration. Both concrete mixes had 100% Type I Portland cement concrete. The concrete mix designs evaluated in this paper were prepared manually by mixing Type I Portland cement concrete, water, sand (quarry dust) and 20 mm machine crushed aggregates to obtain mixes 1 and 2 using design mix ratios in Table 1. Equipment used were strain gauges, loading fame, signal conditioning unit, data logger thermocouples and two computers (one for strain and the other for load cell acquisition). Concrete mix 2 was assumed to be fully adiabatic while mix 1 was assumed to be semi adiabatic. The semi adiabatic mix actually simulates the existing field practises in the tropics as achieving fully adiabatic is not possible under the prevailing working conditions. The raw materials information is also found in Table 1.
Two mass concrete blocks of dimensions 1.1 m × 1.1 m × 1.1 m were built ( Figure 1) using 150 mm × 150 mm × 600 mm beam moulds. Also, a 24 mm thick plywood with a 1 mm layer of polystyrene sheet was used as insulating material for one of the blocks. These blocks were setup to measure the thermal behaviour of concrete under semi adiabatic conditions. However, in an effort to simulate a full adiabatic process a 50 mm thick sand was added to the top surface of the already placed concrete. Figures 2 and 3 are the individual blocks after the concrete had been poured with and without the formwork respectively.

Instrumentation for data collection
Data logger thermocouples were instrumented at critical positions in the two experimental concrete blocks to monitor the temperature distribution with time. The layout of the thermocouples are presented in Figure 4. The thermocouples data were recorded at various times in order to calibrate the proposed finite element model to be used to estimate the potential for crack-growth in early age mass concrete.

Temperature profiles
The location of the temperature sensors in the blocks was strategically chosen to capture the differences in temperature between the centre of the block and the exposed surface. The ambient temperature was also monitored to determine if it would contribute to thermal cracking of the concrete. The temperature sensors at the side and bottom of the block were also placed to validate the effectiveness of the insulation, and to also assess the boundary conditions used in the proposed finite element model (Do, Lawrence, Tia, & Bergin, 2014).

Mechanical properties of concrete
In order to accurately model early-age stress development in concrete members, it was necessary to determine the mechanical properties (Atrushi, 2003;Bernard, Ulm, & Lemarchand, 2003). Many forms of equations have been developed to relate the compressive strength to the maturity development. Two commonly used equations according to Viviani (2005), are given as Equations (1) and (2): where, f C is the compressive strength value (MPa), a is a fit parameter which is usually negative (MPa), b is a fit parameter (MPa/°C/h), f Cult. is the ultimate compressive strength parameter fit from the compressive strength tests (MPa), τ s is a fit parameter (h), T e is equivalent age at the reference Figure 3. Early age concrete block without formwork.

Figure 4. Thermocouple locations in Block 1 and Block 2.
Note: All dimensions in mm.
curing temperature (h), β s is a fit parameter, M(t) is the maturity or temperature-time factor at age t, tc is average concrete temperature during the time interval, t is time For thermal stress analysis, Equation (2) was preferred since is not discontinuous at setting and this functional form is similar to hydration models. The fit parameters f Cult. , τ s and β s were found to be 27.4, 12.35 and 1.52 respectively with an R 2 of 0.98.
In terms of concrete tensile strength, values used for the study were estimated from their respective compressive strengths (Folliard et al., 2008). Most current method for calculating the splitting tensile strength, Equation (3) assumes a power type function based on the compressive strength according to Raphael (1984): where, f Ct is the concrete splitting tensile strength value, a and b are fit parameters, and f C is the concrete compressive strength. Fit parameters a and b were found to be 0.06 and 1.09, respectively with an R 2 of 0.99.
Moreover, for accurately modelling of the thermal behaviour (stresses) of mass, it is important to consider the changes in the mechanical properties (elastic modulus) with time of the concrete (De Schutter, 2002;Lawrence et al., 2012). The elastic modulus is also commonly calculated from the concrete's compressive strength. Most models of this type follow a form of Equation (4): where, E is the elastic modulus, f C is the compressive strength (MPa), and k and n are model parameters.
Equation (4) was used in calculating the elastic modulus from the compressive strengths developed because most engineers are familiar with it from prior experience in structural design, and readily accept its use.

Finite element thermal modelling
The Fourier heat transfer equation is the underline mathematical model can be used to compute the temperature for an elemental volume at a particular instance of time. The generalized governing Equation (5) expressed in the Cartesian coordinate system, was used in the three dimensional heat flow analysis.
where, c p is the specific heat capacity, ρ is the density of the concrete, t is the time, k is the thermal conductivity, T is the temperature and Q H , the rate of internal heat evolution, x, y, z are the coordinates at a particular point in the structure. This finite element model that was used to simulate the thermal behaviour in mass concrete was verified or calibrated so that its temperature distribution for the entire volume closely match with that of the experimental block. The main modelling parameters utilized in the thermal analysis were: • Convection coefficient.
• Internal heat generation rate of concrete.

Input parameters for thermal analysis
The input parameters were either modelled as deterministic or stochastic based on the type of analysis, the type of element and the reference temperature, the heat generation function etc. A nonlinear formulation of the transient thermal analysis was adopted to account for the variations of boundary and loading conditions with time. Also, at the element level in the finite element analysis, a utilization of solid elements capable of providing reliable estimates of the thermal quantities were simulated using an eight-node isoparametric element having a single degree of freedom at each node. Under, the ANSYS platform, the PLANE 70-3D thermal solid element type was chosen from the library of constitutive material elements. The main output parameters that were of interest are the maximum in-place temperature and the thermal gradient. We defined thermal gradient as the change in temperature with respect to change in distance across a section of the concrete. Since the thermal properties for an elemental volume changed with time, coupled with convection at the surface above the formwork, an initial boundary temperature referred to as the reference temperature was chosen as the placing temperature. This parameter needed to be defined so that the timestepping algorithm be initiated in the analysis.

Poisson's ratio
According to Mehta and Monteiro (2013), Poisson's ratio has no consistent relationship with the curing age of the concrete. A value of 0.18 was used, which was within the universally accepted range of 0.15 and 0.20 for concrete.

Thermal conductivity
A characteristic value of thermal conductivity of concrete is in the range 9 to 10.5 kJ/mh°C per the Korean standards and in the range 7.1 to 10.6 kJ/mh°C per the American Standards (ACI Committee 207, 2005b). A constant thermal conductivity value of 9 kJ/mh°C was adopted in this study per the assumption that it will not vary with location across a section, and time during the analysis.

Specific heat of concrete
A typical value of specific heat capacity for concrete ranges from 1.13 to 1.3 kJ/kg°C according to JCI, and 0.92-1.00 kJ/kg°C according to ACI Committee 207 (2005b). The specific heat values chosen in this study are 0.9 kJ/kg°C

Coefficient of thermal expansion
The coefficient of thermal expansion used in this thermal stress analysis was 2 × 10 −6 /°C.

Initial boundary conditions consideration
Boundary heat transfer conditions, which are time or temperature dependent, are important for solving the Fourier differential equations. The four major boundary heat transfer mechanisms are conduction, convention, solar absorption, and irradiation. Each point of a concrete element has a different rate of heat of hydration due to the effects of the environment. We considered the overall convection heat transfer caused by air motion using Newton's law of cooling (Equation (6)).
where, Q is heat flow (kJ/h), h is mean convection heat transfer coefficient (kJ/m 2 h°C), A is surface area (m 2 ), T S is surface temperature (°C), T a is air temperature (°C).
The combined heat transfer coefficient used to account for convection as well as irradiation throughout the thermal analysis was 29.3 kJ/m 2 h°C.

Modelling of heat of hydration from cementitious material
The discrete time-dependent temperature profile at the core of the experimental block was used to predict a continuous heat of cement hydration in the modelling. Due to the nature of the heat curve, the adiabatic hydration model that is usually defined by exponential function has been proposed by a number of researchers. The empirical adiabatic hydration model proposed by Suzuki, Tsuji, Maekawa, and Okamura (1990) was used to relate the rate of heat evolution of the cementitious material. Equation (7) was used to compute internal heat evolution to define the temperature rise curve.
where, T ∞ is the ultimate temperature rise, T a (t) is the Adiabatic temperature rise at t days after casting, α is the coefficient of temperature rise (reaction rate), t is time in days.

Modelling of heat generating rate
The time-dependent temperature distribution at the core of the concrete block was used to simulate adiabatic temperature rise. These temperature were then normalized by subtracting the initial placing temperature. Suzuki's model was adopted, by which a univariate nonlinear regression analysis was performed to establish the temperature-time relationship. The software package MATLAB was used to perform this analysis. Upon comparing the predicted model with experimentally determined results at a 95% confidence interval, R 2 Value of 0.988 was obtained. The proposed model quantified the volumetric for the thermal analysis using Equation (8): where, q(t) is the heat generation per unit volume in t days, t is time in days.

Model geometry
A 1.1 m × 1.1 m × 1.1 m finite element model of the experimental block was constructed in the software package, ANSYS. A mass concrete block was then used to measure the effect of the heat evolution rate on the temperature development with time and location. A discretization scheme of 50 mm along each edge of the block was chosen while a temperature based convergence criteria was set to give reliable estimates of the temperature distribution. The element type concrete 65 was used to represent the element definition to produce 10,648 elements and nodes that were meshed in other to solve the problem. Figure 5 shows the ANSYS model block and Table 2 shows the summarised input parameters values used in the analysis. The transient thermal analysis model was implemented in the commercial finite element program, ANSYS, a general purpose program capable of numerical simulation of a variety of physical problems. For concrete structures with surface area to volume ratio (S v ) being less than 2, it can be classified as massive and as such the thermal effect should be considered (Flaga, 2011). Thus, we simulated analytically the specified heat generation rate, mechanical and thermal properties of the experimental block of concrete having geometric configuration of 1.1 m × 1.1 m × 1.1 m and S v of 0.91. The parameters that were treated mainly as random variables were the ambient temperature, the hydration rate of the cementitious material as well as the heat transfer coefficient for the different surfaces of the mass concrete block. The ambient temperature and the heat evolution from the hydrating cement played major roles in the temperature rise in mass concrete (Ayotte, Massicote, Houde, & Gocevski, 1997;Truman, Petruska, Ferhi, & Fehl, 1991). Though these variables were random in nature, the temperature distribution at that particular time was assumed to emanate from a stochastic process. Also, because strength properties of concrete increased with time, coupled with the large thermal gradient between the core and surface of a mass concrete section, the damaging effect of the thermal behaviour of the hydrating cement was considered critical at early age. We defined early age of mass concrete as the first 6 days after placing of concrete. Therefore, the transient thermal analysis was estimated for 6 days. In order to monitor the temperature distribution with respect to time, the experimental concrete block was well instrumented with thermocouples at specific location ( Figure 4). Measurements were then taken at discrete time steps of 2, 12, 18, 24, 48, 72, 96, 120 and 144 h. Figure 6 shows the analytical output of the temperature variation at the centre of the concrete block. Spline interpolation was adopted in order to obtain a continuous function of the time-temperature development. Figure 7 shows comparatively results of the observed temperature distribution and the simulated analytical results at the core of the concrete. A 75.4°C temperature rise at 24 h was observed at the core of the mass concrete section considered, with a gradual decline to 40.36°C at 144 h after placing of concrete. A temperature rise of 75.4°C meant that there was Delayed Ettringite Formation (DEF) which led to massive cracking of the experimental blocks (Gajda & Vangeem, 2002). Other contributing factors of the DEF development may include; temperature, alkalis in the cement, SO 3 and C 3 A contents of the cement, aggregate mineralogy, and high humidity conditions (Loïc, 2003). The value of 75.4°C is comparable to temperature rise within 24 h of concrete placement value of 74.32°C obtained by Prasanna and Subhashini (2010), and the range of 79 to 42°C obtained by Bartojay (2012). A maximum temperature differential at a particular instant of time was 22.9°C throughout the analysis period (observed at the core and surface of the concrete block). This difference is attributed to the fact that hydrating concrete at the surface loses heat to the atmosphere at a higher rate than the core element of concrete.

Thermal stress analysis
The temperature distribution and the thermal gradient are primarily the thermal quantities that were of interest in our transient thermal analysis model (Khan et al., 1998;Waller, D'Aloıä, Cussigh, & Lecrux, 2004). However, to actually ascertain the potential for cracking due to this external state of loading, a stress analysis was required to assess whether the limiting state of stress has been exceeded. The limit state condition occurred when the thermally induced stresses were greater than the tensile strength of concrete at a given age. Internal restraints caused the maximum temperature differential, the uneven expansion and the contraction of the two extremes for a given section, thereby producing cracks at the upper surfaces (Khan et al., 1998;Lachemi & Aïtcin, 1997). The procedure adopted for the stress analysis is similar to that of the thermal model. Definitions of element type, analysis type and quantification of the variations in mechanical properties and boundary conditions were made. The temperature distribution over the entire concrete block was applied as load in this model at every time step.  Figure 8 presents the results of thermal stress analysis for the analytical model. The maximum tensile stress in all the orthogonal directions, due to thermal distribution was found to occur around the surface. The maximum thermal stresses coincided with the time corresponding to the peak temperature distribution. For the validated analytical model, it occurred at 24 h after placing concrete. Beyond this time, there was a gradual decline in the thermal stress because the corresponding temperature development was also decreasing. Due to this phenomenon, the temperature at early age was key in estimating the occurrence of cracks in mass concrete. The crack index, defined as the ratio of tensile strength of concrete to the induced thermal stress at early ages, was used to measure the probability of cracks developing in the mass concrete structure. For crack index values less than unity, thermal crack is expected to occur. The validated analytical model yielded a crack index value of 2.1 signifying that stress induced by the temperature development were not large enough to cause thermal cracks.

Effect of specimen size
The standard specimen size used in this study was a block size of 1.1 m × 1.1 m × 1.1 m. To study the effect of size on the behaviour of concrete, four additional block sizes were modelled. The sizes chosen were: 2 m × 2 m × 2 m, 3 m × 3 m × 3 m, 4 m × 4 m × 4 m and 5 m × 5 m × 5 m. A comparison of the temperature profiles at the centre of blocks containing concrete is shown in Figure 9. The surface area to volume ratio of each specimen was used as a parameter to evaluate the temperature distribution. It is evident that as the surface area to volume ratio decreased, there was a corresponding increase in temperatures with respect to time of each specimen. Also, Figure 9 shows the progression of the peak temperatures, as the surface area to volume ratio decreased (indirectly increased in block size). It has been observed that, mass concrete structures with peak temperatures higher than 70°C are expected to experience an undesirable phenomenon known as DEF (Kishi & Maekawa, 1995;Lawrence, 2009;Tim, 2014;Wang, Ge, Grove, Ruiz, & Rasmussen, 2006). From Figure 9, surface area to volume ratios for all the specimens under study yielded a maximum observed temperature rise exceeding 70°C. The effect of the surface area to volume ratio (indirectly the block size) on the maximum temperature differentials is presented in Figure 10. The maximum temperature differential between the centre and top surface edge increased from 22.9°C in the 1.1 m block to 70.1°C for the 5 m block. The temperature differentials and the thermal gradient (change in temperature with respect to distance) were the major parameters used to measure the degree of internal restraint caused by the temperature rise in mass concrete. The maximum temperature differential limiting value of 20°C was assumed between the surface and centre of mass concrete structure to achieved desirable strength characteristics with no thermal crack. From Figure 10, both the experimental and the analytical results produced temperatures higher than 20°C for all the specimens under study. A univariate regression analysis revealed Equation (9): where, T max is the maximum temperature differential, S v is the surface area to volume ratio. The relationship between the maximum induced stress and the increasing maximum temperature differential caused by increasing block size (decreasing surface area to volume ratio) is presented in Figure 11. For a given concrete mixture, the maximum induced stress increased with increasing maximum temperature differential (correlation coefficient of 0.99). Also, the maximum temperature difference and resulting stress in concrete elements were highly dependent on the type of concrete used. Figure 12 shows a propagation of maximum induced stress with respect to surface area to volume ratio. When these stresses are higher than the tensile strength, thermal crack may occur. Superimposed on Figure 12 is the tensile strength for the various specimen under study at times when the thermal stresses are expected to be maximum. It was revealed that at surface area to volume ratio roughly higher than 0.36, thermal crack may not be observed. A univariate nonlinear regression was done to provide a relation between both quantities as provided in Equations (10)  where, σ tensile is the tensile strength, σ thermal is the thermal stresses, S v is the SVR. Figure 13 relates the crack index to the surface area to volume ratio. It can be seen that these two parameters are highly correlative (R 2 value 0.992). For surface area to volume ratio less than 0.36, the crack index was less than 1, signifying that the induced thermal stresses have exceeded the tensile strength at that concrete age, therefore the probability of thermal cracks developing become certain. The regression analysis yielded Equation (12): where, I cr is the crack index, S v is the SVR.

Conclusions
Investigations were conducted on predicting early age thermal cracks in mass concrete structures at tropical atmospheric conditions using Ghana as the geographical scope for the research. The current state-of-the-art practice is to perform adiabatic calorimetry testing on concrete mixtures and use finite element analysis to predict temperature distribution during the time. The predicted temperature distribution is then used to quantify the induced thermal stresses. Given that the tensile strength at a particular age of concrete is less than the thermal stress, the probability of thermal cracks developing becomes certain. The research adopted both experimental and analytical modelling (Finite Element Model) scenarios to predict the early age thermal cracking in mass concrete structures in the tropics. The experimental program involved the construction of two mass concrete blocks of dimension 1.1 m × 1.1 m × 1.1 m that were intended to simulate both adiabatic and semi adiabatic conditions. The temperature distributions from these experimental blocks were used to calibrate and validate finite element models that were implemented in the commercial software ANSYS. A parametric study on the effect of the size on various concrete blocks were also investigated to help estimate the propagation of crack growth during the early ages of mass concrete structures. From the study, construction of mass concrete structures with SVR less than 0.36 is not adequate enough to prevent the occurrence of cracks. Also, the age of concrete at peak temperature was observed to increase with an increase in the size of the mass concrete block. The specific conclusions drawn were: (1) The widely accepted limiting temperature differential of 20°C that is likely to cause thermal cracking may not be valid in the tropics for mass concrete structures.
(2) In the tropics mass concrete structures with a SVR value less than 0.36 are expected to cause thermal cracking at early ages of cement hydration.
(3) As such to provide reliable estimate of the likelihood of cracking, this assertion should be supplemented by performing a finite element stress analysis.
(4) In the tropics, we recommend a minimum of 5 days for de-shuttering of the formwork to prevent the occurrence of thermal shock.