Keywords

1 Review and Analysis of Related Work

RCC dams consist of concrete placed at a lower water-to-cement ratio as compared to conventional concrete with the aid of compaction equipment and methodologies normally employed for earthfill placement. RCC has gained worldwide acceptance as an alternative to conventional concrete in dam construction due to the construction advantages and proven performance [6]. When RCC was first introduced in dam construction in the early 1990’s, for a time it was thought that there was no problem in the temperature control of RCC because the amount of cement in RCC was much less than that in the conventional concrete. But sometime later, it was discovered that RCC still has the problem of temperature control when it is used in dam construction [9].

Mass concrete placement requires precautions to minimize cracking. During the hydration process, cement liberates a substantial amount of heat with a resulting rise of the concrete temperature. It often reaches about 40–70 ℃ [5], after the maximum temperature is reached inside the RCC dam, the latter cools down slowly to a constant temperature. This temperature variation can induce two kinds of problems. First, the heat generated creates temperature gradients between the surface and the RCC core. The resulting non-uniform temperature distribution generates undesired stresses. Second, the reduction of the global concrete temperature to the final equilibrium temperature induces volumetric changes that lead to additional stresses if the mass concrete is externally restrained [2]. These temperature gradients induce cracks in the structures, which harm their integrity, permeability, and durability.

To find the optimum construction method to avoid thermal cracks before the structure construction, numerical simulations with Finite Element Method (i.e. FEM) can be carried out and it can be checked for cracking. In a simulation, some parameters can be assumed, such as the kind of cement, mixed design of concrete, casting schedule, RCC placement temperature, and curing method, etc. [5]. Many finite element software packages can be used to predict the heat generated by the concrete. Such as ANSYS, COSMOS/M, ABAQUS and ADINA.

Several techniques are reported in the literature for designers to evaluate the thermal performance of concrete, the structural configuration, and construction requirements. These techniques range from complex three-dimensional finite element analysis methods to simple manual computation. Another research determined the thermal and structural stresses and temperature control requirements for the 60 m high Tannur RCC dam in Jordan [7]. Temperature distribution in the Al-Mujib roller compacted concrete (RCC) Gravity Dam was also investigated in another study [8]. Moreover, another study investigated the development of the Modulus of Elasticity of young RCC dams [3].

2 Location and Description of the Dam

The Metolong Dam project located in Lesotho, a landlocked country in Southern Africa, consists of an approximately 73 m high RCC gravity dam with a crest length of approximately 210 m. The dam would store an estimated 53 million m3, and a reservoir with an upstream reach of approximately 16 km. The full supply level will be at 1671 masl.

3 Dam Wall Profile

The upstream face of the dam is vertical from El 1671 to foundation level. The stepped downstream slope is at 0.8:1 (see Fig. 1).

Fig. 1.
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Maximum cross-section of the Metolong Dam spillway.

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4 Material Properties and Environmental Conditions

The model properties used were assessed from available data and typical RCC properties. The density, modulus, Poisson ratio, specific heat and thermal conductivity are given in Tables 1 and 2. A convection coefficient for air was used, which is consistent with moderate wind speed.

Table 1. Properties Adopted for Thermal Analysis for Metolong Dam.
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The thermal expansion coefficient is another property used in the analysis on thermal stress in concrete. A typical coefficient of thermal expansion of 8.6 × 10–6/deg C, was adopted for the concrete.

Table 2. Specific Parameters used in the Analysis.
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5 Methodology

The dam is to be modeled as a two-dimensional transient heat transfer model using a birth and death element (see Fig. 2) to simulate the real construction process of the dam. The computer program ANSYS was to be used to simulate the construction process. PLANE77 thermal element type available in ANSYS element library was used. Each element has one degree of freedom temperature at each of its 8 nodes to simulate irregular shape and is applicable to a two-dimensional steady-state or transient thermal plain strain analysis. Plane strain is the condition for which the strains perpendicular to the plane of the analysis are maintained at zero. Temperatures calculated in the thermal model were used as loads for the structural model. The thermal time steps were aligned to those of the structural model. Thermal structural analysis was carried out by replacing the PLANE77 thermal element by an equivalent structural element called PLANE183 see Fig. 3. Gravity loads due to self - weight of the rock foundation and the RCC and thermal loads from thermal analysis were included in the structural analysis. Figure 4 shows only the finite element mesh for the cross sections of the dam (non-overspill section) with a 3 m layer thickness. Non-linearity of modulus of elasticity in structural analysis regarding its temporal variability is to be included in this analysis. The model developed by Conrad et al. (2003) will be used to study the effect of variation of elastic modulus with time for the RCC dam [3]. At an early age, the RCC temperature would vary significantly due to the heat of hydration, and the corresponding large strains would generate significant stresses depending on the elastic modulus. In the numerical analysis the change in the modulus of elasticity with time for RCC is incorporated according to the following equation:

$$ E\left( t \right) = E_{max} \, x\, {\text{exp}}\left( {a\, x\, t^{b} } \right) $$
(1)

where a and b are model parameters, equal to –5 and –0.63, respectively. t is the time [3]. For thermal and structural analysis, the full Newton-Raphson method with adaptive descent is used to solve the non-linear equations. Automatic time stepping is used to increase the number of sub- steps when convergence is not occurring within a given number of equilibrium iterations. When convergence occurs rapidly the number of sub-steps decreases to speed run-time. The non-linear solution control functions are implicit in ANSYS, and default parameters were used as well.

Fig. 2.
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Birth and death element.

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Fig. 3.
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PLANE77/PLANE183 element types.

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Fig. 4.
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Finite element mesh of section (spillway section).

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6 Effect of RCC Placement Temperature

The RCC placement temperature varied from 18 ℃ to 32 ℃, and the temperature was calculated accordingly, it is observed that the peak temperature increases with the increasing of the RCC placement temperature. Figures 5, 6, 7, 8, 9, 10 and 11 show the variation of peak temperature development with time at different locations and elevations of the dam and its effect on the RCC Block length.

Fig. 5.
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Effect of placement temperature on the peak temperature in the dam.

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Fig. 6.
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Effect of placement temperature on the block length.

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Fig. 7.
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Temperature time history at dam base for different placement temperature.

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Fig. 8.
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Temperature time history at 21 m from dam base for different placement temperature (location b2).

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Fig. 9.
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Temperature time history at 39 m from dam base for different placement temperature (location c2).

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Fig. 10.
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Temperature distribution along dam width (path 0) at dam base at 350 days (end of hydration) for different placement temperature.

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Fig. 11.
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Temperature distribution along dam height (path 3) at dam center at 350 days (end of hydration) for different placement temperatures.

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7 Effect of RCC Young Modulus on the Thermal Stresses and Block Length

In general, the modulus of elasticity in compression is defined as the ratio of normal stress to its corresponding strain for compressive stress below the proportional elastic limit of the material (Andriolo, 1998). In this study the effect of varying the elastic Young modulus was studied, three different values were used to study the sensitivity of E with the thermal stress induced due to varying the RCC placement Temperature. Figure 12 shows the variation of RCC placement temperature with Young Modulus. Figure 13 shows their effect on the development of thermal stresses with time.

Fig. 12.
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Effect of RCC Young Modulus on the block length.

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Fig. 13.
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Valley stress (x-direction) in the Dam base center (b0).

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8 Effect of Strain Capacity

Tensile strain capacity TSC (εtc) is the change in length per unit length that can be sustained in concrete prior to cracking. TSC is dependent on time and rate of loading and many other factors among them are type of aggregate, aggregate shape characteristics, and strength of the RCC mix. Conrad, M. (2006), introduced an empirical formula to estimate the TSC which is based on the below formula [4]. Usually, for RCC this value of TSC ranges from 20–140 × 10–6 mm/mm.

$$ TSC = \frac{{f_{t} }}{{E_{eff} }} $$
(2)

with:

TSC = Tensile strain capacity;

ft = Direct tensile strength (MPa);

Eeff = Effective Young’s Modulus (MPa).

In this study, three values were used with different RCC placement Temperature see, Fig. 14 shows the effect of TSC with block length and using different RCC placement Temperature.

Fig. 14.
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Effect of Strain Capacity on the block length.

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9 Effect of Layer Thickness

Usually, RCC dams are constructed in layers, each layer has thickness of 3 m constructed in 10 days. In this study the dam is modeled in three different thickness i.e., 2.5 m, 3 m and 3.5 m each constructed in 10 days. Figures 15 and 16 show the effect of layer thickness on the peak temperature and on the block length, Figs. 17 and 18 show temperature time history at different locations and elevations of the dam.

Fig. 15.
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Effect of layer thickness on the peak temperature in the dam.

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Fig. 16.
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Effect of layer thickness on the block length.

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Fig. 17.
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Temperature time history at dam base different layer thickness

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Fig. 18.
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Temperature distribution along dam width (path 3) at dam center at end of hydration for different layer thickness

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10 Conclusions

A parametric study is carried out in this research to study the effect of several parameters affecting the temperature and thermal stress distributions in RCC dams. The RCC placement temperature, the Modulus of Elasticity, tensile strain capacity, placement schedule of RCC layers, number of layers, and thickness of each layer were all considered in the analysis. The sensitivity of each one of the parameters listed above is investigated and the results is presented in form of tables and graphs. The results presented in this study clearly demonstrate the effect of each of the studied parameters and provide a better understanding of the effect of each parameter affecting the temperature distribution and thermal stresses in the RCC dams.