A New Philosophy for the Design of RC Structures based on Concepts of Fracture Mechanics

Abstract

The current codes for the design of RC structures are based exclusively on the characteristic compressive strength f’c of the concrete mix and ignore completely its tensile capacity. This means that as the tensile strength and the brittleness of concrete increase with an increase in f’c, the minimum reinforcement required to attain the required ductility has to be increased without utilising the higher tensile strength. This often leads to wastage of reinforcement and to severe congestion, especially near joints which in turn leads to a lack of adequate compaction and cover, i.e. to honeycombing.To avoid this we propose a completely new design philosophy based not on f’c but on the characteristic length lch of the concrete mix. The mix characteristic length was first introduced more than three decades back by Hillerborg based on the concepts of fracture mechanics. It involves three independent properties of the mix; its stiffness (E), tensile strength f’t and specific fracture energy or toughness GF [lch = (E GF)/(f’t)2]. It captures the intrinsic ductility of the mix; the larger the lch, the more ductile the mix. It is clear from the definition of lch that it decreases as f’c (and therefore f’t) increases. The new design philosophy proposes to base the design on a fixed lch of concrete mix used irrespective of its f’c. Thus, if the base lch is chosen to correspond to a mix with f’c = 40MPa, but in the actual RC structure a mix with f’c = 100MPa is used whose lch would be much smaller than the base value, then it must be increased to coincide with the base value. In turn this means that the minimum reinforcement required for RC structures of same geometry made of mixes with different f’c but the same lch will be the same and these structures will exhibit similar ductile response.As the stiffness E increases only marginally with an increase in f’c (i.e. f’t) it is clear that the toughness GF of the mix must be increased to compensate for the reduction in lch caused by the increase in f’t. This is achieved by the addition of steel fibres. The amount of fibre to be added will depend on f’t of the mix and on the type and texture of steel fibre used.This paper will summarise the research done over the past six years in Cardiff University on different RC members (long and short beams, slender columns) made from mixes with f’c = 40 and 100MPa to test the validity of this new design philosophy. The higher strength mix had to be supplemented by about 0.18% by volume 30mm long and 0.55mm diameter steel fibres for it to have the same lch as the 40MPa mix (approximately 300mm). All members of a given type e.g. slender columns were reinforced with the minimum reinforcement required for 40MPa concrete mix according to EC2. They were tested and found to exhibit exactly the same failure mode, irrespective of the mix f’c. The members made from 100MPa concrete mix with 0.18% by volume steel fibres carried more load, as expected, but failed in the same ductile manner as the corresponding members made from 40MPa mix despite the fact that they contained the same minimum reinforcement as the latter. This confirmed our suspicions that the current design code provisions for minimum reinforcement based on the mix compressive strength grossly overestimate the requirements for high strength mixes leading to wastage of steel and reinforcement congestion.