Formulation of the theory of critical distance for fatigue characteristic in concrete incorporating various water-cement ratios

Abstract

The employment of the Theory of Critical Distances (TCD) in the research of fatigue damage in concretes is a fairly recent development. TCD is primarily used to characterise fatigue and fracture behaviours of concrete. Previous research have discussed on the accuracy of TCD application in concrete under high-cycle fatigue conditions. The research tested the TCD formulation on two batches of concrete mix differs in terms of their water-cement ratio. In comparison, the accuracy of TCD is proven judging exceptionally small errors that occurred between the theoretical and tested outcomes for both batches. However, although TCD is proven to be accurate, the percentage errors display severe inconsistency when being compared side-by-side between two batches of concrete. Thus, TCD seems to be susceptible to the change of water-cement ratio. It is beneficial to comprehend that fatigue and fracture assessment method like TCD relies chiefly on the tensile characteristics. Unfortunately, the effects of water-cement ratio has been overlooked since the resulted difference in tensile strength is commonly small and often considered insignificant for concrete. Moreover, there are no documented standard procedures on fatigue test in plain concretes, and thus the studies of fatigue and fracture in concrete become stumbled and slow. Accordingly, the theoretical establishment of linking the static behaviours, which are surely less cumbersome to characterise, to those of fatigue is necessary. Therefore, this research aims to study in detail the numerical characterisation of cracks in concrete governed by water-cement ratio through a proposed linkage relationship between the static and fatigue condition. Three important outputs were obtained to achieve the aim of this research. First objective is to conduct the fatigue testing in analysing the fatigue properties in concrete. Secondly, a unified linkage is formulated using Buckingham’s Pi technique for achieving the third objective. Thirdly, a closed-form TCD formulation covering the variation of the water-cement ratio is then proposed. Since fatigue testing method of concrete has no officially developed, both ACI 215-75R and RILEM TC 89-FMT were utilised complimentarily. For static testing of the concrete’s tensile properties, the methodology presented by Xiao Zhi Hu was adopted. A three-point bending test configuration is utilised onto plain concrete beam following the static and fatigue respective methodologies since both testing configuration are similar. ABAQUS computational engineering software is used to formulate TCD covering the variation of the water-cement ratio. By proving mathematically the linkage between static and fatigue parameters of concrete, it may cause TCD formulation remained unstable towards different water-cement ratio in concrete mix more intelligible. From the analysis of fatigue property in concrete, the increasing fatigue limit of 2.883 MPa, 3.022 MPa, and 3.903 MPa with the increment of water-cement ratio 0.3, 0.4, and 0.5 respectively is significant and non-linear. Hence, fatigue limit of concrete is not simply obtained by converting it from static strength by a single magnitude. Using Buckingham’s Pi, the connection between static and fatigue properties is revealed in terms of ?1 and ?2. The ?1 and ?2 represent a group of static and fatigue properties of concrete respectively. The link established shows that ?2 is equal to approximately half of ?1. Yet, individual linkage between parameters remained for future research. Consequently, the research has solved the issue by incorporating water-cement ratio in TCD by introducing equations in the form of polynomial which is KIc = 0.7826ft – 309.935Wc4 + 495.999Wc3 – 289.485Wc2 + 72.31Wc – 8.5516 and Power Law KIc = 0.77 ft - 2.3Wc0.102. Both of the equations are identical but in different forms. The equations formed are related to TCD and incurring water-cement ratio elements. Hence, provide better understanding of how TCD can be utilised for fatigue analysis on concrete structure.