# FE-Study on the Effect of Gradient Concrete on Early Constraint and Crack Risk
## 1 Introduction  
In recent decades, durability of concrete and reinforced concrete has been an important research issue. Also, modeling of young hardening concrete using finite-element analysis has received a lot of attention. A relatively new field of research is the concept of gradient concrete, which is also the main aspect in this article. These three fields of research (durability, gradient concrete, and finite element analysis of young hardening concrete) are combined in this study to simulate the effect on crack risk in durable concrete structures made of gradient concrete. Durability in reinforced concrete structures is important, because many structures with a very long lifetime, for example tunnels, bridges, watergates or protective structures, are mainly made of reinforced concrete. Important infrastructure projects are built under assessment principles and constructional design patterns for a working life of up to 200 years [1]. During the lifetime of a reinforced concrete structure both the concrete and the reinforcement are exposed to environmental influences. The main influences are corrosion induced by carbonation of the concrete, corrosion induced by chloride, freeze-thaw attack, chemical attacks or abrasive wear as already stated in present codes such as [2]. In recent years, performance-based design concepts for durability of reinforced concrete structures against carbonation of the concrete have been developed (e.g., [3; 4; 5; 6]). To achieve long lifetimes of concrete structures the engineer needs to select the right materials and carefully elaborate the construction. The concrete surface, respectively the concrete zone nearthe surface, is exposed to the environment. Often the core of a concrete part has no requirements related to the resistance against environmental influences. Only the zone near the surface requires a high durable concrete, which leads to high cement content and low w/c ratios. In mass concrete structures thermal stresses during hydration are a known problem [7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. These thermal stresses can lead to cracks in the concrete. Durable but cracked concrete does not protect the reinforcement properly, therefore cracks have to be reduced or crack width has to be controlled. As a result, one main requirement for the core of a mass concrete part is low hydration energy. Obviously, the core and the surface zone have different requirements to concrete composition. The idea is to use concrete with high durability in the outside zone of the concrete part and concrete with low hydration energy in the central zone. In large-scale dams or watergates, concrete sections with zones of different properties were used for a long time [17]. As mentioned before, gradient concrete is a relatively young research topic. Ongoing research shows that it is possible to create concrete with different density and strength, so-called \"gradient-concrete\" [18; 19; 20]. Gradient concrete is also a main content in this publication. If gradient concrete appears to be a good solution in construction engineering, affordable methods to produce gradient concrete in precast or even in in situ concrete are going to be developed. Currently 3D concrete printers are under development [18; 21; 22; 23; 24; 25; 26; 27]. Not only can density be varied along the cross-section, but also other concrete properties, for example gradual durability, are possible as well. To analyze the complex behavior of gradient concrete during hardening, numerical models are required. It is possible to model the complex interactions in hardening concrete using numerical material models and finite element analysis. There are already models which are capable of very detailed simulation of the behavior of the concrete [28; 29; 30; 31; 32]. These so-called \"hygro-thermo-chemo-mechanical-models\" consider moisture transport, chemical processes, temperature evolution and mechanical aspects including creep and shrinkage.