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Non-local damage model for concrete under variable amplitude loading
... Some distinctive and important observations were obtained from laboratory testing. For example, under fatigue loading, the cyclic strain, the indicator of irreversible fatigue life, cyclic creep, and fatigue range that is higher than monotonic state strain, and the accumulated ultimate and plastic strains after each cycle before rupture, are dependent on the applied fatigue loading cycles of the concrete materials [1,7,[10][11][12][13][14]. Nucleation, interaction, and multi-microdefects growth are the main causes for the weakening of Young's modulus of elasticity in the fatigue process [15][16][17], and the mechanical behavior of concrete materials under fatigue loading is governed by microdefects like kinetics of the microstructure of the concrete materials. ...
A R T I C L E I N F O Keywords: Post-fatigue characteristics High-strength concrete Coupled 3D fatigue-static loading Physico-mechanical properties Fatigue damage model Empirical prediction model A B S T R A C T Concrete structures suffer some damage yet not failed under fatigue load, and then continue to bear 3D redistributed stress. For this, the 3D fatigue loading considering various fatigue factors (e.g. confining stress, axial static stress (ASS) and force amplitude (FA), frequency, and cycle number) is first carried out, and then the 3D static loading is performed. The post-fatigue characteristics of high-strength concrete (e.g. P-wave velocity, S-wave velocity, porosity, gas permeability, triaxial compression strength, and elastic modulus) are gained. The results indicate that 3D fatigue loading weakens mechanical properties, delays wave propagation, and increases seepage paths. An obvious stress threshold is exhibited with increasing axial static stress and force amplitude, that is 80% triaxial compressive strength, where the physico-mechanical characteristics are rapidly weakened due to the energy dissipation caused by crack growth rises increasingly. Compared with 1D fatigue loading, the frequency turning point of weakening effect from decreasing to increasing is advanced under 3D fatigue loading due to the application of 3D stress exacerbates the heat accumulation and creep damage generation. Interestingly , the fatigue damage is likely to be more sensitive to axial load compared to confining stress during 3D fatigue loading. In other words, the promotion effect of axial fatigue load on damage is larger than the restriction of confining stress. Furthermore, the fatigue damage models considering various fatigue factors are proposed. Then, the empirical prediction models of this damage variable to mechanical parameters (strength and elastic modulus) and permeability are established to predict the capacity loss caused by fatigue loading in the design of concrete construction. The testing results in this context could facilitate our understanding of post-fatigue characteristics of high-strength concrete subjected to 3D fatigue loading and guide the safe design of concrete construction.
A closed-form expression for the dual of dissipation potential is derived within the framework of irreversible thermodynamics using the principles of dimensional analysis and self-similarity. Through this potential, a damage evolution law is proposed for concrete under fatigue loading using the concepts of damage mechanics in conjunction with fracture mechanics. The proposed law is used to compute damage in a volume element when a member is subjected to fatigue loading. The evolution of damage from microcracking to macrocracking of the entire member is captured through a series of volume elements failing one after the other. The number of loading cycles to failure of the member is obtained as the summation of number of cycles to failure for each individual volume element. A parametric study is conducted to determine the effect of the size of the volume element on the model’s prediction of fatigue life. A global damage index is also defined, and the residual moment carrying capacity of damaged beams is evaluated. Through a deterministic sensitivity analysis, it is found that the load range and maximum aggregate size are the most influencing parameters on the fatigue life of a plain concrete beam.
Currently, the maintenance and repair of civil engineering infrastructures (especially bridges and highways) have become increasingly important, as these structures age and deteriorate. Interface between two different mixes or strengths of concrete also appear in large concrete structures involving mass concreting such as dams, nuclear containment vessels, cooling towers etc., since joints between successive lifts are inevitable. These joints and interfaces are potential sites for crack formation, leading to weakening of mechanical strength and subsequent failure. In case of a bi-material interface, the stress singularities are oscillatory in nature and the fracture behavior of a concrete-concrete bi-material interface is much more complicated. A comprehensive experimental work has been undertaken for characterization of the behavior of different concrete-concrete interfaces under static and fatigue loading. The effect of specimen size on the concrete-concrete interfaces is studied and the non-linear fracture parameters such as fracture energy, mode I fracture toughness, critical crack tip opening displacement, critical crack length, length of process zone, brittleness number, size of process zone, crack growth resistance curve and tension softening diagram. These parameters are required for modeling the concrete-concrete interfaces in non-linear finite element analysis. Presently, the advanced non-destructive techniques namely acoustic emission, digital image correlation and micro-indentation have great capabilities to characterize the fracture behavior. The damage in plain concrete and concrete interface specimens is characterized both qualitatively and quantitatively using acoustic emission technique by measuring the width of fracture process zone and width of damage zones. The DIC technique is used to obtain the fracture parameters such as mode I and mode II fracture toughness and critical energy release rate. The micro-mechanical properties are obtained by performing depth-sensing micro-indentation tests on the concrete-concrete interfaces. Civil engineering structures such as long-span bridges, offshore structures, airport pavements and gravity dams are frequently subjected to variable-amplitude cyclic loadings in actual conditions. Hence, in order to understand the fracture behaviour under fatigue loading, the fatigue crack growth in plain concrete and concrete-concrete interface is also studied using the acoustic emission technique. An attempt is made to apply the Paris’ law, which is applicable to mechanical behaviour of metals, for acoustic emission count data. All these studies show that, as the difference in the compressive strength of concrete on either side of the interface increases, the load carrying capacity decreases and the fracture parameters indicate the increase in the brittleness of the specimens. It is concluded that the repair concrete should be selected in such a way that its elastic properties are as those of the parent concrete.