The Influence of Construction Parameters on the Temperature Field of Rock-Filled Concrete

Abstract

This paper investigates the distribution characteristics and variation rules of the temperature field of rock-filled concrete during pouring. Based on the thermal model accounting for the hydration rate, it uses ANSYS software to study the influence rules of construction parameters, such as the rock-filled ratio, time between pours, pouring thickness at the peak value of rising temperature, temperature difference in the core and surface, and the position of the peak value of rising temperature during the construction of rock-filled concrete. The results indicate that, under varied rock-filled ratios, time between pours, and pouring thicknesses, the variation rules of the peak value of rising temperature, temperature difference in the core and surface, and the position of the peak value of rising temperature are the same. As the rock-filled ratio increases, the peak value of rising temperature and the temperature difference in the core and surface decrease, and the variation range of the position of the peak value of rising temperature enlarges as the number of pouring layers increases. When the time between pours is extended, both the peak value of rising temperature and the temperature difference in the core and surface decrease, and the fluctuation amplitude of the position of the peak value of rising temperature increases with the number of pouring layers. With the increase in the pouring thickness, the peak value of rising temperature and the temperature difference in the core and surface increase, and the position of the peak value of rising temperature does not change significantly with an increase in pouring layers. The maximums of the peak value of rising temperature and temperature difference in the core and surface are 15.56 °C and 14.54 °C, respectively, which meet the requirements of the specifications. The peak value of rising temperature has a linear relationship with the pouring layers. Therefore, constructing a hundred-meter-high dam is possible by controlling construction parameters, such as the rock-filled ratio, time between pours, and time between pours without taking temperature control measures.

1. Introduction

Rock-filled concrete is mass concrete constructed by pouring self-compacting concrete into a rock-filled body with a particle size greater than 300 mm [1,2,3,4] as shown in Figure 1. Because of the low amount of cementitious materials in rock-filled concrete, the heat of hydration is reduced [5]. The adiabatic temperature rise generally does not exceed 15 °C, lower than those of normal and roller-compacted concretes [6,7]. Generally, no or meager temperature control measures are required during construction [8]. For rock-filled concrete dams, construction parameters (such as 2 m-thick layer pouring [9] and 7-day inter-layer time between pours [7]) and temperature-controlled measures (such as external surface water flow and controlled placing temperature) are generally adopted. This mainly stems from similar engineering experience [10] and considering concrete’s heat dissipation. However, rock-filled concrete is developing towards a new type of rock-filled concrete dam with a high dam body, no transverse joints, and integral pouring [11]. The one-time pouring volume is large. If the pouring layer is relatively thick, the high temperature inside the dam will last for a long time, stabilizing the dam body temperature. If the thickness of the pouring layer is thin, in the high temperature season, the heat will be transferred from the outside to the inside of the concrete [12]. In addition, a thin pouring layer presupposes more pouring layers, and the bonding surfaces between layers are also unfavorable for the seepage prevention and shear resistance of the dam. Moreover, a long intermittent pouring time suggests that the next layer is poured long after the previous layer is poured. This situation affects the construction period, causing a large difference in elastic modulus between the upper and lower layers; hence, cracking may occur. Therefore, carefully selecting the pouring layer thickness and the inter-layer time between pours (i.e., the construction parameters of rock-filled concrete) under various working conditions is crucial to constructing high rock-filled concrete dams and mitigating against temperature-controlled cracking [13].

At present, several simulation studies have been carried out on the influence of construction parameters, such as pouring layer thickness and inter-layer time between pours, on the cracking of roller-compacted and ordinary concretes. The studies show that the safety of concrete is ensured by controlling construction measures, such as pouring layer thickness and inter-layer time between pours. Pang et al. [14] studied the influence of different times between pours on the temperature field of roller-compacted concrete dams. They found that increasing the time between pours can effectively reduce the temperature difference between the interior and the surface and the maximum temperature. Studying the influence of different pouring thicknesses on the internal temperature of pile caps, He [15] found that reducing the pouring thickness can significantly reduce concrete’s maximum internal temperature. Elsewhere, the influence and variation of different pouring schemes and temperature control measures on the temperature field and stress field of roller-compacted concrete dams have been studied [16,17]. Wang [18] showed that higher-requirement, temperature-controlled measures must be taken to construct thick pouring layers to ensure structural safety.

However, there are relatively few studies on the influence of construction parameters on the temperature field of rock-filled concrete. Pan et al. [9] used the finite element method to study the influence of construction parameters, such as varied pouring temperatures on the temperature field to take appropriate temperature control measures. Similarly, Gao [19] used finite element software to study the influence of various construction parameters such as time between pours and transverse joint settings on the temperature of rock-filled concrete. Here, they ensured structural safety by controlling its maximum pouring temperature. Also, Xu et al. [20] used the finite element method to perform heterogeneous simulation calculations on the rock-filled concrete dam of the Shibahe Reservoir. The research found that the equivalent homogeneous model can reflect the internal temperature field of rock-filled concrete. The above-mentioned studies mainly focused on the temperature field research of pouring temperature, transverse joint settings, etc. However, it did not conduct systematic research on the construction parameters, such as pouring thickness and time between pours, frequently used in engineering. Moreover, the adiabatic temperature rise models used in previous simulation studies did not consider the influence of the temperature rise rate, while the actual concrete temperature rise and rate influence each other [21,22], and the influence law is still not clearly understood.

Based on this, this paper focuses on the safety issues of the temperature control and crack prevention of rock-filled concrete dams by relying on the rock-filled concrete dam projects in the northwest region of China [23,24,25]. Using finite element software and a hydration heat release model that considers the hydration rate [26,27,28], we study the influence laws of construction parameters, such as different rock-filled ratios, time between pours, and pouring thicknesses on the temperature field during the construction process of rock-filled concrete in the high-temperature (summer) season. Through the indicators of peak temperature rise, temperature difference between the interior and the surface, and peak temperature rise position in rock-filled concrete, we study the changes in the temperature field of rock-filled concrete under different construction parameters, which is beneficial for adopting appropriate construction plans during the construction process of rock-filled concrete, to provide a theoretical basis and engineering significance for developing rock-filled concrete for constructing high dams.

2. Finite Element Simulation

2.1. Heat Conduction Governing Equation

The temperature field of rock-filled concrete with a rock-filled particle size of less than 1 m is uniform and isotropic and there are no moisture migrations or external temperature influences in the adiabatic model [20]. After pouring, the heat conduction equation [29] can be expressed as

$${\displaystyle \frac{\partial T}{\partial \tau }}=\alpha \left({\displaystyle \frac{{\partial }^{2}T}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}T}{\partial y^2}}+{\displaystyle \frac{{\partial }^{2}T}{\partial z^2}}\right)+{\displaystyle \frac{Q}{c\rho }}$$

(1)

where $\alpha$ is the material’s ability to conduct heat relative to its capacity to store heat (m²/h), and $Q$ represents the heat released per unit volume per unit time because of cement hydration (kJ/(kg·h)), which is directly associated with the hydration reaction rate. This rate changes over time and is also affected by temperature, $c$ is the specific heat of concrete (kJ/(kg·°C)), and $\rho$ is the density of concrete (kg/m³).

Under concrete hydration, the rising speed of concrete temperature under adiabatic conditions [30] is given as follows:

$${\displaystyle \frac{\partial \theta }{\partial \tau }}={\displaystyle \frac{Q}{c\rho }}={\displaystyle \frac{W{q}_c}{c\rho }}$$

(2)

where $\theta$ is the adiabatic temperature rise in concrete (°C); $W$ is the cement dosage (kg/m³); $q_c$ is the heat of hydration released by unit cement per unit time (kJ/(kg·h)).

Then, the three-dimensional heat conduction equation considering the adiabatic temperature rise in concrete can be simplified as follows:

$${\displaystyle \frac{\partial T}{\partial \tau }}=\mathsf{\alpha }\left({\displaystyle \frac{{\partial }^{2}T}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}T}{\partial y^2}}+{\displaystyle \frac{{\partial }^{2}T}{\partial z^2}}\right)+{\displaystyle \frac{\partial \theta }{\partial \tau }}$$

(3)

2.2. Hydration Heat Release and Thermal Parameters

(1)

Thermal source

The heat release from cement hydration is the main cause of heat generation, and the heat release rate of cement hydration and temperature influence each other bidirectionally. The heat source adopts an adiabatic temperature rise model considering the hydration rate [22], as shown in Equation (4).

$$\phi \left(t\right)=\rho \times c\times q\left(t\right)$$

(4)

where $\phi \left(t\right)$ is the heat generation rate per unit volume of concrete within time $t$, $\rho$ is the density of concrete (kg/m³), $c$ is the specific heat of concrete (J), and $q\left(t\right)$ represents the concrete’s adiabatic temperature rise rate at time t (°C/h). Here, $q\left(t\right)$ is derived as follows:

$$q\left(t\right)={\displaystyle \frac{m{t}^a}{{(t-d)}^2+b}}$$

(5)

where a, b, d, and m are constants.

Specifically, d is the age at which the peak point of the adiabatic temperature rise rate occurs. When there are multiple peak points or the peak point is not obvious in the adiabatic temperature rise rate curve, d can be taken as the middle moment of the peak width of the adiabatic temperature rise rate. Here, 0 < a < 1 is used to adjust the developmental trend of the decline period of the adiabatic temperature rise rate curve, whereas b determines the peak width of the temperature rise rate, that is, to represent the total duration of the acceleration and the deceleration periods of the adiabatic temperature rise rate. The m value adjusts the magnitude of the peak point of the temperature rise rate. Although t has a definite practical physical meaning, it is not independent and is correlated with a, b, and d [31], the relevant parameters are shown in

Table 1. Temperature rise rate parameters.

Rock-Filled Ratio (%)	m	a	b	d
30	13.415	0.816	10.998	−5.339
40	27.003	0.689	10.428	−10.349
50	83.605	0.325	1175.967	19.568

. Under different rock-filled ratios, the temperature rise rate is shown in Figure 2.

(2)

Air temperature function

The average monthly air temperature in the northwest region throughout the year is 13.7 °C. The highest and lowest air temperatures occur in July and January, respectively. A cosine function is used to fit the daily average air temperature change within the year to obtain Equation (6), and the fitting correlation coefficient is 0.99.

$$T_a=13.7-11.03\mathrm{c}\mathrm{o}\mathrm{s}\left[{\displaystyle \frac{\pi }{6}}\right(\tau -0.94\left)\right]$$

(6)

where τ is time; when τ = 0, it is 0 o’clock on 1 January.

(3)

Thermal parameters

The thermal parameters of concrete materials are obtained through laboratory tests and references [21,32]. Those of the rock-filled concrete and bedrock materials are listed in

Table 2. Material parameters of rock-filled concrete and bedrock materials in this study.

Material	Thermal Conductivity Coefficient (kJ/(m·h·°C))	Specific Heat (kJ/(kg·°C))	Density (kg/m3)
Rock-filled concrete	12.56	0.8545	2516
Bedrock	14.53	0.7490	2630

.

2.3. Geometric Model

The model takes the downstream direction as the positive direction of the X-axis, the right bank direction of the dam body as the positive direction of the Y-axis, and the upward direction of the dam body as the positive direction of the Z-axis, as shown in Figure 3. The dam model has five layers; the height of each dam layer is 2–4 m, the length of the dam section is 5 m, and the width of the dam bottom is 30 m. The upstream and downstream of the dam body and the depth of the foundation are taken as 1.5 times the dam height. The model adopts an eight-node hexahedral element, and the meshing unit is selected as 0.5 m [20]. The number of model units is 20,520, the number of nodes is 23,960, and the solid70 unit is used for the temperature field calculation. The finite element model is shown in Figure 1. The bottom surface of the model is a constant temperature boundary of 20 °C, the two cross-sections along the dam axis are adiabatic boundaries, and all other boundaries except these aforementioned ones are surface heat dissipation boundaries.

2.4. Simulation Scheme

The simulation schemes are shown in

Table 3. Simulation calculation number.

Calculation Number	Rock-Filled Ratio (%)	Pouring Thicknesses (m)	Time Between Pours (day)
50-2-3	50	2	3
50-2-5	50	2	5
50-2-7	50	2	7
50-3-7	50	3	7
50-4-7	50	4	7
40-2-7	40	2	7
30-2-7	30	2	7

. According to the Technical Guidelines for Rock-Filled Concrete Dam Construction (NB/T1007-2018) [10,33], construction parameters such as rock-filled ratio, time between pours, and pouring layer thickness are selected. The rock-filled ratios are 30%, 40%, and 50%, the times between pours are 3, 5, and 7 days, and the pouring layer thicknesses are 2, 3, and 4 m.

The high-temperature summer season is selected as the pouring season. At this time, the temperature difference between the concrete and the environment is small, and the peak temperature rise is the largest compared with pouring in other seasons. Therefore, pouring starts in June, and 25 °C is the selected initial pouring temperature, considering the average temperature of the month. Here, the construction stage is simulated. The model is poured in five layers. The first layer starts in mid-June, and all are poured by mid-July. No temperature control measures are taken throughout the construction.

2.5. Model Validation

The measured adiabatic temperature rise process curve of the rock-filled concrete with 50% rock-fill proportion was subjected to a comparative analysis against the outcomes of the numerical simulation computations. Refer to Figure 4. The temperature rise curves of the simulated values and the experimental values exhibit consistency, being capable of portraying the development tendency of the adiabatic temperature rise in the rock-filled concrete. The disparity between the maximum adiabatic temperature rise value computed through numerical simulation over a 504 h period and the measured value is 1.05 °C, which implies that the model is correct.

3. Calculation Results and Analysis of the Temperature Field

Figure 5, Figure 6 and Figure 7 show the results of the peak value of rising temperature, the temperature difference in the core and surface, and the position of the peak value of rising temperature in rock-filled concrete under various rock-filled ratios, different times between pours, and different pouring thicknesses. We observed that these factors/conditions are identical. They can be divided into two stages: during the construction period, as the concrete pouring progresses, the peak value of rising temperature rise, the temperature difference in the core and surface, and the position of the peak value of rising temperature increase. During the layer-by-layer intermittent pouring, the peak temperature rise, the temperature difference in the core and surface, and the position of the peak value of rising temperature fluctuate upward at first before falling. During curing, as the concrete pouring is completed, the peak temperature rise, the temperature difference between the interior and the surface, and the position of the peak value of rising temperature increase initially before decreasing. It is supposed that at the early hydration stage, the hydration rate is very fast, the heat accumulates inside the concrete, and the temperature rises sharply. However, after the internal temperature peaks, the hydration rate gradually reduces, the heat production rate of the concrete becomes less than the heat dissipation rate on the concrete surface, and the internal temperature of the concrete gradually decreases.

3.1. The Influence of Rock-Filled Ratio on the Temperature Field

Figure 5a,b illustrate that as the rock-filled ratio increases, the peak value of rising temperature and the temperature difference in the core and surface decrease. The decreasing range is small during construction but large during maintenance. Among them, the peak value of rising temperature and the temperature difference in the core and surface fluctuate increasingly with the increase in the number of pouring layers. The peak values of rising temperature for rock-filled ratios of 30%, 40%, and 50% are 15.56, 14.93, and 11.08 °C, respectively, occurring at 33, 47, and 50 days, respectively. The occurrence time is postponed as the rock-filled ratio increases. The temperature differences of the core and surface are 14.54, 13.77, and 10.65 °C, respectively. Compared with the 30% rock-filled ratio, the peak values of rising temperature of the rock-filled concrete with 40% and 50% rock-filled ratios are reduced by 0.63 °C (4.05%) and 4.49 °C (28.86%), respectively. The temperature differences of the core and surface are reduced by 0.77 °C (5.29%) and 3.89 °C (36.52%), respectively. For every 1% increase in the rock-filled ratio, its peak value of rising temperature and temperature difference in the core and surface between the interior and the surface decrease by 0.22 °C and 0.19 °C, respectively. Increasing the rock-filled ratio can significantly reduce the peak value of rising temperature and the temperature difference in the core and surface.

The temperature decrease is mainly due to the increase in the rock-filled ratio, lowering the amount of cementitious materials and the heat released by the hydration temperature rise. The reason why the temperature and temperature difference decrease less at the early stage than in the later stage is that the cementitious materials in the rock-filled concrete release heat while the rock absorbs heat [8,34], more in the early stage than later. Therefore, the peak value of rising temperature and the temperature difference in the core and surface can be reduced by increasing the rock-filled ratio, which is consistent with the research results elsewhere [23].

Figure 5c shows that as the rock-filled ratio increases, the position of the peak value of rising temperature that occurs during the construction remains unchanged, but increases during the curing. For the rock-filled ratios of 30% and 40%, the position of the peak value of rising temperature is at 1, 2.5, 4.5, and 4 m, respectively, as the pouring progresses. After pouring, the location peaks at 6 m, then decreases to 5.5 m. For the 50% rock-filled ratio, the position of the peak value of rising temperature is at 1, 2.5, 4.5, and 6.5 m, respectively, while the pouring is underway. After pouring, it reaches the highest position of 8.5 m before lowering to 5.5 m. This trend occurs because during construction, the hydration heat of the pouring layer is continuously released, and the peak location rises gradually. After the pouring, the hydration heat release reduces, at a rate lesser than the heat dissipation rate. The position of the peak value of rising temperature first increases before decreasing gradually towards the core of the dam body. As the rock-filled ratio decreases, the amount of cementitious materials used increases, the heat release cycle becomes long, the hydration heat release increases, the heat dissipation rate becomes less than the temperature rise rate, and the heat of the pouring layer cannot be dissipated in time; hence, the heat is accumulated in the core of the dam body. Notably, the result of the 50% rock-filled ratio is consistent with the literature [14], that is, the surface temperature of the dam body is distributed in layers during the construction, and the highest temperature at the same time occurs on the surface of the newly constructed layer.

3.2. The Influence of Time Between Pours on the Temperature Field

Figure 6a,b illustrate that as the time between pours decreases, the peak value of rising temperature and the temperature difference in the core and surface increase. The growth rate is small during construction but large during maintenance. Among them, the peak value of rising temperature and the temperature difference in the core and surface fluctuate upward with the increase in the number of pouring layers. The maximum peak value of rising temperature for the intermittent 3, 5, and 7 days is 13.87, 12.13, and 11.08 °C, respectively, with 25-, 32-, and 33-days occurrence time. The occurrence time is postponed as the time between pours increases. The respective temperature difference in the core and surface is 12.91, 11.30, and 10.65 °C.

Unlike the 3-day time between pours, the peak value of rising temperature of those of 5-day and 7-day times decreases by 1.74 °C (12.5%) and 2.79 °C (20.1%), respectively. Similarly, the temperature difference in the core and surface decreases by 1.61 °C (12.47%) and 2.26 °C (17.51%), respectively. For every 1 day increase in the time between pours, the peak value of rising temperature and the temperature difference in the core and surface decrease by 0.69 and 0.56 °C, respectively. We observed that increasing the time between pours significantly reduces the peak value of rising temperature and the temperature difference in the core and surface. When the time between pours is shortened, the heat released by the hydration temperature rise remains unchanged, while the overall heat dissipation decreases. After pouring, the heat generation rate becomes higher than the heat dissipation rate, and the peak value of rising temperature of the dam still increases. Therefore, the peak value of rising temperature and the temperature difference in the core and surface can be reduced by increasing the pouring time between pours.

As the time between pours increases (Figure 6c), the position of the peak value of rising temperature during construction and curing becomes higher. As the pouring progresses for the 7-day time between pours during construction, the position of the peak value of rising temperature is at 1, 2.5, 4.5, and 6.5 m, respectively. After pouring, it reaches the highest position of 8.5 m before dropping to 5.5 m. As the pouring progresses during construction for the 5-day time between pours, the position of the peak value of rising temperature is at 1, 2.5, 4.5, and 4 m, respectively. Upon completing the pouring, it reaches the highest position of 6.5 m and then drops to 5 m. For the 3-day time between pours, the position of the peak value of rising temperature is at 1, 1, 2.5, and 4 m, respectively. After pouring, it reaches the highest position of 6 m before dropping to 5 m. This drop occurs because when the time between pours is shortened, the hydration temperature rise rate remains unchanged, the heat dissipation time is reduced, and heat accumulation occurs inside the dam due to the heat of hydration. Increasing the time between pours can effectively reduce the temperature and make the distribution of the peak value of rising temperature more uniform, as previously reported elsewhere [35].

3.3. The Influence of Pouring Thickness on the Temperature Field

Figure 7a,b illustrate that as the pouring thickness increases, the peak value of rising temperature and the temperature difference in the core and surface increase. The trend of changes during pouring and curing is consistent. Here, the peak value of rising temperature and the temperature difference in the core and surface increase with the pouring layers. For pouring thicknesses of 2, 3, and 4 m, the maximum peak value of rising temperature is 11.08, 13.06, and 14.39 °C, respectively, occurring after 33, 47, and 50 days, respectively. The occurrence time is postponed as the pouring thickness increases. The maximum temperature difference between the core and surface is 10.65, 13.00, and 14.57 °C, respectively. Compared with a 2 m pouring thickness, the peak value of rising temperature increases by 3.32 °C (12.5%) and 4.49 °C (20.1%) when the pouring thickness is 3 and 4 m, respectively, with their corresponding temperature difference in the core and surface increasing by 3.06 °C (29%) and 3.8 °C (36%). For every 1 m increase in the pouring thickness, the peak value of rising temperature and the temperature difference in the core and surface increase by 2.24 and 1.90 °C, respectively.

Due to the increase in the pouring thickness, the amount of cementitious materials used increases and the heat released by the hydration temperature rise increases. After pouring, the heat generation rate becomes higher than the heat dissipation rate, so the peak rising temperature of the dam still increases. Therefore, the peak temperature rise and the core–surface temperature difference can be controlled by controlling the pouring thickness. Thus, reducing the pouring thickness can effectively reduce the temperature as previously reported [9].

As the pouring thickness increases (Figure 7c), the change in the position of the peak value of rising temperature becomes less obvious. As the pouring progresses to a 2 m thickness, the position of the temperature is at 1, 2.5, 4.5, and 6.5 m, respectively. After pouring, it reaches the highest position of 8.5 m and then drops to 5.5 m. For a 3 m pouring thickness, the position of the peak value of rising temperature is at 1, 2.67, 4.67, and 6.33, respectively, as the pouring progresses. After pouring, it reaches the highest position of 8.5 m before dropping to 6 m. Similarly, for a 4 m pouring thickness, the position of the peak value of rising temperature is at 1, 2.75, 2.5, and 6.5 m, respectively. After pouring, it reaches the highest position of 8.5 m and then drops to 6 m. Since the pouring thickness increases, the hydration temperature rise rate remains unchanged, mainly affecting heat dissipation and heat conduction. The heat dissipation process in the core position of the newly poured concrete layer is slow, and the position of the peak value of rising temperature is in the core of the pouring layer. As a new layer of concrete is poured, the change pattern is the same. However, the temperature gradient increases with thickness, and the position of the peak value of rising temperature rises with pouring. Thus, the pouring thickness barely impacts the position of the peak value of rising temperature, but only delays the occurrence time.

4. Prediction of Peak Value of Rising Temperature

Figure 8, Figure 9 and Figure 10 show the variation laws of the peak value of rising temperature of rock-filled concrete with the number of pouring layers under varied rock-filling ratios, different times between pours, and varied pouring thicknesses. The peak value of rising temperature grows linearly with the number of pouring layers. The linear growth rates of the first and second layers are different from those of the last three layers, mainly because the heat dissipation of the first two layers is more substantially affected by the dam foundation. To ensure the analysis’ accuracy and eliminate the interference of the initial temperature factor of the dam foundation, the peak values of rising temperature data of the five layers and the last three layers are selected and compared using the Pearson correlation coefficient. The degree of correlation between the peak value of rising temperature and the number of pouring layers is provided in

Table 4. Pearson correlation coefficients between the five layers and the last three layers.

Calculation Number	Pearson Correlation Coefficient
	Five Layers	Last Three Layers
50-2-7	0.920	0.989
50-2-5	0.931	0.965
50-2-3	0.966	0.987
50-3-7	0.857	0.999
50-4-7	0.867	0.996
40-2-7	0.974	0.994
30-2-7	0.983	0.990

.

Table 4 suggests that in the last three layers, the peak rising temperature correlates excellently with the number of layers and a higher degree of association. It is more accurate to use the data of the last three layers to establish a mathematical model of the peak rising temperature changing with the number of layers. The peak rising temperature correlates positively with the number of layers. The variation law of the peak temperature rise with the number of layers under different calculation numbers is linearly fitted by Equation (7), and the fitting parameters for various construction parameters are listed in

Table 5. Fitting parameters under different calculation parameters.

Calculation Parameters	a	b
50-2-3	0.77	8.99
50-2-5	0.55	9.22
50-2-7	0.29	9.63
50-3-7	0.13	12.00
50-4-7	0.16	13.04
40-2-7	0.86	9.53
30-2-7	0.95	9.54

:

$$y=ax+b$$

(7)

where x is the number of pouring layers, y is the peak value of temperature rise (°C).

Taking the working condition of 50-2-7 as an example, Figure 11 compares the simulated calculation value with the predicted peak value of rising temperature of rock-filled concrete poured in ten layers.

The maximum difference between the predicted and the calculated values is 0.62 °C, and the error range is 5.26%. As the number of pouring layers increases, the temperature difference and error range increase. According to the above rules, projections were carried out regarding the extant research [32]. The disparity between the predicted value of 21.36 °C and the actual value of 18.60 °C amounts to 2.75 °C, which represents a deviation rate of 14.7%. Meanwhile, according to the requirement in the Standard [36], the peak value of rising temperature should not be higher than 50 °C. The maximum number of pourable layers and pouring height under various working conditions are predicted according to the mathematical models in Table 5, and the results provided in

Table 6. Maximum number of layers allowed for pouring and critical temperatures under different working conditions.

Calculation Parameters	Number of Layers	Height (m)	Critical Temperature (°C)
50-2-3	53	106	49.80
50-2-5	74	148	49.92
50-2-7	139	278	49.94
50-3-7	292	876	49.96
50-4-7	231	924	50.00
40-2-7	47	94	49.95
30-2-7	42	84	49.44

.

We observed that as the rock-filled ratio increases, the maximum number of layers allowed for pouring increases, and the minimum pourable dam height is 84 m. As the time between pours increases, the maximum number of pourable layers increases, and the minimum pourable dam height is 106 m. Furthermore, as the pouring thickness increases, the maximum number of pourable layers increases, and the minimum pourable dam height is 278 m. Here, increasing the rock-filled ratio, time between pours, and pouring thickness can retard the growth trend of the peak value of rising temperature rise, while increasing the pouring thickness can effectively control the temperature and prevent cracking. Considering various factors comprehensively (such as construction techniques), the rock-filled ratio can be increased and the time between pours can be shortened to accelerate the construction progress in the construction and pouring of medium–low dams. In the construction and pouring of high dams, these three parameters can be changed to accelerate the construction.

5. Conclusions

This paper adopts the research method of finite element simulation to study the influence of three construction parameters, namely rock-filled ratio, time between pours, and pouring thickness, on the variation characteristics of the internal temperature field of rock-filled concrete. The following conclusions are obtained:

(1) With the progress of concrete pouring and the increase in time, during the construction period, the peak value of rising temperature, the temperature difference in the core and surface, and the position of the peak value of rising temperature show an increasing trend; during the intermittent process between layers of pouring, the peak value of rising temperature, the temperature difference in the core and surface, and the position of the peak value of rising temperature all show a fluctuating trend of first rising and then falling; during the curing period, the peak value of rising temperature, the temperature difference in the core and surface, and the position of the peak value of rising temperature first increase and then decrease.

(2) When the time between pours and pouring thickness remain unchanged, as the rock-filled ratio increases, the peak value of rising temperature and the temperature difference in the core and surface show a decreasing trend, and the position of the peak value of rising temperature remains unchanged during the construction period and rises during the curing period. When the rock filling rate is 30%, the peak value of rising temperature and the temperature difference in the core and surface reach their maximum values of 14.44 °C and 15.56 °C, respectively. When the rock-filled ratio and pouring thickness remain unchanged, as the time between pours is extended, the peak value of rising temperature and the temperature difference in the core and surface show a decreasing trend, and the position of the peak value of rising temperature rises. When the time between pours is 3 days, the peak value of rising temperature and the temperature difference in the core and surface reach their maximum values, which are 12.91 °C and 13.87 °C, respectively. When the rock-filled ratio and time between pours remain unchanged, as the pouring thickness increases, the peak value of rising temperature and the temperature difference in the core and surface increase. Here, the position of the peak value of rising temperature does not change significantly. When the pouring thickness is 4m, the peak value of rising temperature and the temperature difference in the core and surface reach their maximum values of 14.15 °C and 14.39 °C, respectively.

(3) The relationship between the peak value of rising temperature of rock-filled concrete and the number of layers is linear, and the error of the model prediction value is 5.26%. The research found that without temperature control measures for rock-filled concrete, building high dams over 100 m is feasible. By increasing the rock-filled ratio, shortening the time between pours, and increasing the pouring thickness, higher dams can be built.