Should a cable drop…
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24-10-2023 | Posted by Joaquín Martí
Concrete is today the most widely used construction material in the world because of its strength, durability, formability, and affordability. With a proper selection of its constituents, it displays good compressive strength and resistance against environmental degradation. In previous posts we have discussed its environmental impact and the problems associated with its possible chemical swelling. Today we are concerned with its cracking.
Despite the numerous advantages of concrete, it suffers from a low tensile strength; in structural members it must be reinforced with bars, cables or fibres, that can take care of the tensile demands while the concrete carries the compressive ones.
The transverse loading of beams and plates generates bending, shear, compression, and tension. In a concrete structural element, the regions in tension could fail if unreinforced. Even if reinforced, cracking may endanger the durability of the reinforcement and even lead to an immediate collapse. This of course applies both to slow or static loading, as well as to highly dynamic problems such as explosions and impacts. Hence our designs and supporting calculations must be able to deal with cracking.
To represent the behaviour of reinforced concrete we typically use the concrete damaged plasticity model, and we define the reinforcement using beam elements embedded into the host solid elements, both capabilities available in Abaqus. The post-peak behaviour of the concrete is characterised by a fracture energy.
The softening of the mechanical response that accompanies concrete cracking may complicate the convergence when solving problems by implicit integration. In such cases, the problem can be solved explicitly, with the loading applied slowly to avoid unrealistic inertial effects. In highly dynamic problems, explicit integration would have been the natural choice in any case. A discussion of explicit vs implicit integration schemes was also offered in another post.
Cracking and failure may lead to very high local strains in mesh elements that no longer carry any load. Those elements must be deleted from the mesh using an appropriate criterion. This allows studying problems such as missile penetration and blast effects.
We have modelled concrete cracking in all sorts of situations. Some are static, such as the cracking that dams may experience associated with the thermal effects of curing. Or the cracking of accropodes in coastal projects. Or the intentional cracking of a wind turbine tower to evaluate its effects on performance. Or the cracking of the connection between onshore wind turbine towers and their foundations. Or the possible concrete cracking in floating wind turbines.
We have also analysed highly dynamic problems, like the effects of underwater explosions on bridge piers. Or the effects of terrorist explosions on several major bridges and corporate buildings, problems in which concrete cracking plays a major role.
Storage tanks for liquefied natural gas (LNG) entail many cracking analyses. Some are motivated by thermal effects, as in postulated external fires or in various types of internal leaks and spillages. Others are related with impacts from accidental missiles and deflagration of explosive clouds, all of which must be contemplated in the design.
The same problems arise in nuclear power plants, which must be designed accounting for similar threats, but also require the study of the containment building response under aircraft impact or progressively increasing internal pressures in case of a severe accident.
Reliable modelling of concrete cracking is certainly not a simple problem. But it is also true that we now have the appropriate tools that allow experienced engineers to address it.