# Optimization of Mass Concrete Construction Using a Twofold Parallel Genetic Algorithm
## 1 Introduction  
When a dam or any other massive concrete structure is designed, most of the characteristics that will determine the mechanical behavior are defined, such as geometry, vertical joints, reinforcement, concrete strengths and zoning [1]. In general, as the construction site is planned and organized, a formwork system is chosen and an ice production unit is implemented in the jobsite. After that, before the beginning of the construction, the construction management team performs studies aiming to define suitable concrete mixes and carrying out tests to determine the main thermo-chemo-mechanical properties of these materials. Depending on the importance of the construction, local standards, and technologies available, these studies will be more or less thorough. In general, the thermal properties (thermal capacity, thermal conductivity, coefficient of thermal expansion) and hydration properties (adiabatic or semi-adiabatic temperature evolution) are determined for one or more mix designs in use for the structures at hand. Therefore, when massive concrete structures such as spillways, power houses, transition walls, or deep foundations, are about to be built, few variables are yet to be determined to carry out the construction of the structure. Since, in general, massive structures are built lift-by-lift in successive concrete layers these variables are [2]: (1) The thickness of the lifts; (2) The time interval between the placement of lifts; (3) The placing temperature of concrete; (4) The mix design of concrete. As a matter of fact, the concrete proportions are established in an optimized way that minimizes cement content, minimizing the effects of the heat of hydration. Therefore, it is not uncommon to have just one mix design available. In this way, depending on the type of construction, the set of variables is reduced to just the three first variables described above. The choice of these variables is governed by the risk of cracking induced by hydration heat and by the costs associated with them. It should be stressed that several other parameters intervene in the development of stresses induced by hydration. Factors that may be mentioned, for example, are the degree of restriction imposed by the foundation, the formwork system and its thermal characteristics, the evolution of the environmental temperature and wind, etc. However, these parameters are not, in real case applications, at the time of the beginning of construction, a choice for the construction management team and they should be considered as fixed given parameters. Another possibility of varying the thermal stresses at the early ages is the use of a post-cooling system using tubes which can be filled with running water or air [3]. In the present paper such systems are not considered as variables of the optimization problem. However, at the present stage of the development of the optimization procedure, they can be considered as given fixed parameters of the structure. In view of the above considerations, the optimization problem treated in this paper can be stated as: \"_Find the type of concrete, the placing temperature, the height of the lifts and the rhythm of construction that minimize the construction cost of a massive concrete structure with the constraint that thermal cracking is not allowed_\". In this way, individual construction plans must be evaluated. This is achieved by simulating the phased construction of the structure and choosing the suitable set of variables that avoid cracking originated by the heat of hydration. The simulation of the thermo-chemo-mechanical problem can be performed with the use of numerical models, generally based on the finite element method (FEM). Such models may range from simplified approaches to sophisticated thermo-chemo-mechanical models. One can refer, among others, to the works of [PERSON] et al. [4], [PERSON] and [PERSON] [5], [PERSON] and [PERSON] [6], [PERSON] et al. [7] and [PERSON] et al. [3]. A recent survey of these models can be found in [8].