4.1. Fresh and Hardened Properties of Concrete
Table 4 shows the results obtained from the tests on the concrete slump, temperature, and air content in all mix proportions. In both concrete proportions, similar results were obtained. The fresh concrete properties were measured to check their suitability for casting and finishing purposes. It was observed that the obtained results were within the suitable properties required in the precast concrete factory [
7]. The concrete temperatures in this study were used as one of the input values in the 3D FEM thermal stress analysis.
Setting time test results obtained are shown in
Table 5. There was an increase in the setting time in both concrete mix proportions in relation to the general time concrete made with N cement. There is generally retardation in the setting time observed when mineral admixtures such as BFS cement are added to concrete [
40]. In this study, initial setting time was used as a starting point for the measurement of autogenous shrinkage.
All compressive strength results obtained in the experiments are shown in
Table 6 for both accelerated cured concrete at 1 day, 7 days, and 14 days; and 28 days compressive strength for water cured concrete specimens. It was observed that the addition of LSP and F.GYP improved strength from 1 to 14 days and at 28 days for the water cured concrete as well. Despite the addition of LSP and F.GYP to the concrete, it was observed that even the control mix containing only N and BFS cement attained the minimum demolding compressive strengths [
41].
4.4. Heat of Cement Hydration of the Concrete—Semi Adiabatic Condition
Thermal cracking may occur in concrete members due to a rise in concrete temperature as a result of cement hydration. The rise in concrete temperature can be determined by subjecting concrete to adiabatic or semi-adiabatic condition. In this study, temperature rise due to heat of cement hydration was determined in semi-adiabatic condition to check the effect of limestone powder and fine gypsum. The observed results are shown in
Figure 9a,b. The predicted adiabatic temperature rise of concrete was determined using results obtained in semi-adiabatic condition and Equation (1). This equation is based on the relationship between semi-adiabatic temperature rise and adiabatic temperature rise as proposed from the past research work on a simple thermal insulation test [
43]:
where
: density of the sample specimen (kg/m
3),
C: specific heat capacity of concrete taken as (1.05 KJ/kg °C),
V: volume of the sample specimen (m
3),
S: surface area of the sample specimen (m
2),
h: heat transfer coefficient (W/m
2 °C),
T: temperature gradient existing between the sample specimen and ambient room temperature,
: adiabatic temperature state.
Thereafter, the parameters obtained from Equation (1) were used to generate constants in the JCI model in Equation (2) and graphs which were obtained are also shown in
Figure 9a,b [
42]. The derived constants from Equation (2) are indicated in
Table 7. The obtained results showed that the addition of limestone powder and fine gypsum enhanced the rate of the predicted adiabatic temperature rise and increased the ultimate temperature rise [
44]:
where
t: age in days,
Q(
t): adiabatic temperature rise at t (°C),
: ultimate adiabatic temperature rise (°C),
: parameters representing rate of adiabatic temperature rise,
age at starting of temperature rise.
4.5. Thermal Stress and Cracking Index Analysis by 3D FEM Method
Temperature change in concrete members due to external temperature change, cement hydration, and autogenous shrinkage may cause stress development within a structure. The extent of stress increase is due to internal restraint caused by non-uniform temperature across the section of a member and may lead to crack development (JCI, 2016) [
42]. Using a 3D FEM analysis method, which is based on the truss network model, a region with a high cracking tendency can be identified [
42,
45]. The 3D FEM analysis method quantitatively computes thermal stress and thermal cracking index by considering various conditions of the cast concrete such as structural dimensions, construction procedures, temperature histories, mechanical properties, etc. [
42]. In this analysis, the thermal cracking index is determined as the ratio of tensile strength to maximum principle stresses. When the thermal cracking index is low, the probability of cracking is high (low cracking resistance) and vice versa. Equation (3) was used to calculate the thermal cracking index [
42]:
where
ICR: thermal cracking index,
: splitting tensile strength,
: principal stress, and
: temperature adjusted age (day).
Thermal cracking index at all the positions of a member is calculated throughout the valuated period. Then, thermal cracking tendency of the member can be estimated based on the minimum cracking index. The time and the position of cracking can be also estimated. For example, if the minimum thermal cracking index is 1.0, the probability of cracking is estimated as 50% according to JCI guidelines for crack control of mass concrete structures. Note that the target thermal cracking index depends on the purpose of the structure [
42].
In this study, the influence of adding LSP and F.GYP in concrete mix proportions on cracking tendency was investigated. Two concrete mix proportions used include N + BFS and N + BFS + LSP +F.GYP. A typical concrete precast box culvert model member was used for the analysis as shown in
Figure 9 [
46]. Note that haunches were not included in the 3D FEM model as shown in
Figure 10.
Concrete mechanical properties used as input parameters in the 3D FEM include compressive strength, splitting tensile strength, and modulus of elasticity. In this study, compressive strength was experimentally obtained whilst splitting tensile strength and modulus of elasticity in Equations (4) and (5) were derived using the obtained compressive strength and constants as provided for in the JCI guidelines [
42]:
where
: splitting tensile strength of concrete at
(N/mm
2),
: compressive strength of concrete at
(N/mm
2),
: temperature adjusted age (days),
:
where
: modulus of elasticity of concrete at
(N/mm
2),
: compressive strength of concrete at
(N/mm
2),
.
The influence of creep of concrete was evaluated by using effective Young’s modulus, which was obtained by multiplying Young’s modulus by a reduction coefficient using Equation (6). To take large creep in the hardening process of concrete into account, the reduction constant was taken to be 0.42 before the age when the concrete temperature reaches the maximum temperature and 0.65 at later ages, which are recommended by JCI guidelines [
42]:
where
: effective modulus of elasticity of concrete at
,
reduction coefficient for modulus of elasticity due to creep,
: modulus of elasticity of concrete at
.
Table 8 shows some of the other input values thermal and stress analysis. For the purpose of analysis, the casting temperature for both mix proportions was taken to be 18.5 °C.
Thermal analysis and stress analysis were conducted in 3D FEM analysis. In the thermal analysis, heat transfer analysis was carried out using the adiabatic temperature rise of each mixture. In stress analysis, the coefficient of thermal expansion of concrete was taken to be 10 × 10
−6/°C and autogenous shrinkage under accelerated condition also taken into account.
Figure 10,
Figure 11 and
Figure 12 further provide location and temperature profile at the region with a low thermal cracking index observed in the center of the precast model member. It can be seen that the difference in concrete temperatures between the surface and internal concrete as shown in
Figure 13 generated tensile stresses. Similar high thermal stresses were observed at 1 day in both concrete mixtures that showed thermal cracking index values of 0.69 in N + BFS and 0.76 in N + BFS + LSP + F.GYP. The observed values may lead to surface cracking of the precast concrete model specimen at demolding time.
An input option to check the effect of covering precast concrete molds during accelerated curing was then introduced in 3D FEM analysis. All the outside surfaces were covered using curing sheets with 6 W/m
2 °C heat transfer coefficient [
42]. This type of curing sheet provides more resistance to heat transfer that may reduce the temperature difference between the surface and internal concrete. Then, the optimum time for covering the molds was investigated. There was a reduction in thermal stresses in both concrete mixtures covered 6 h before demolding as shown in
Figure 14. This resulted in a reduced temperature gradient in concrete that improved the thermal cracking index. The change in the thermal cracking index before and after the introduction of curing sheets is provided in
Figure 15 and
Table 9.