Study On Crack Propagation In Concrete And Lightly Reinforced Concrete Beams Based On Fracture Mechanics

Concrete is a composite material consisting of hardened cement matrix,aggregate and interface between them.The bearing capacity of concrete depends on the mechanical properties of each phase and their interaction.It is of great significance to deeply study the fracture characteristics of mortar-rock interface,the fracture mechanism of concrete and the fracture process of reinforced concrete(RC)to evaluate the safety of concrete structure.Therefore,the intention of this paper is to study the crack propagation process of concrete material based on fracture mechanics theory.The detailed content are as follows:(1)Based on the cohesive stress model and the stress intensity factor(SIF)-based crack propagation criterion,a new analytical method for calculating the completed crack propagation process in quasi-brittle materials like rock and concrete was proposed.Given the elastic modulus,the tensile strength,the fracture energy and the initial fracture toughness,the crack propagation process of the three-point bending(TPB)beam can be simulated by using the proposed method which considers the crack mouth opening displacement(CMOD)as the control parameter,and the fracture parameters such as load-crack mouth opening displacement(P-CMOD)curve,crack extension resistance(KR)curve and fracture process zone(FPZ)length can be analytically obtained.20 TPB beams of rock with different dimensions were tested to obtain the P-CMOD curves.To verify the validity of the proposed analytical method,the P-CMOD curves of rock and the P-CMOD curves of concrete obtained from the literature were calculated respectively,and it showed a reasonable agreement with the experimental data.Based on the analytical method of calculating the fracture process of quasi-brittle material,the effects of the distribution of crack opening displacement(COD)along beam height and the closure effect of COD induced by the cohesive force on the calculated results were discussed,and the size effects of KR curve and FPZ length were analyzed.(2)Based on the cohesive stress model,a numerical method for evaluating the crack propagation process of layered mortar-rock composite beams under mode I fracture was proposed.This method assumes that crack begins to propagate when the SIF produced by the external load and the cohesive stress acting on the FPZ of mortar and rock reaches the initial fracture toughness of the material where the crack tip is located.The complete fracture process of a crack perpendicular to the interface,including the initial crack starts to propagate,to passing through the interface and to approaching the boundary of the specimen,was predicted by using the proposed method and finite element software.Meanwhile,the simulation considers COD as the control parameter.9 mortar-rock layered beams with different initial crack lengths which equal to the heights of interface layer were tested under TPB to obtain the initial cracking load,then the SIF(KICini,i)of each specimen was calculated by the initial cracking load.The calculation results showed that KIC,ini,i could be used as a material property of the rock interface,and therefore the proposed crack propagation criterion for perpendicular cracks terminating at the interface was verified.Moreover,24 mortar-rock layered TPB beams with different dimensions and initial crack lengths which are smaller than the heights of interface layer were tested to obtain the P-CMOD curves.The calculated P-CMOD curves were compared with the experimental data to examine the validity of the proposed method,and the results were in reasonable agreement.Moreover,the effects of the initial fracture toughness,the tension-softening constitutive law.and the geometrical parameters on the crack propagation process of layered mortar-rock composite beams were analyzed;(3)A three-dimensional numerical method was proposed to simulate the crack propagation process of TPB beam of concrete.By using this method,not only the P-CMOD curve,KR curve and FPZ length can be obtained,but also the crack propagation process along width can be simulated,and the distribution of crack tip along width within different crack propagation length can be obtained.To verify the feasibility of the proposed numerical method,the simulated P-CMOD curves were compared with the experimental P-CMOD curves measured by fracture test of 21 TPB concrete beams with different dimensions and radios of initial crack length to beam height(a0/D),and the results were in good agreement.Based on the three-dimensional numerical method proposed in this paper,the effect of specimen width on the crack propagation process of TPB beam was studied,and the variation of the maximum difference of crack length along width during the crack propagation process was analyzed.Moreover,the effect of specimen dimension on the maximum difference of crack length along width was discussed;(4)Based on the SIF-based crack propagation criterion,an analytical method for calculating the completed crack propagation process of lightly RC beams was proposed.The constraint effect of steel bar on concrete crack was replaced by a pair of concentrated forces acting on crack faces based on the trilinear bond-slip model of steel-concrete interface,and the fracture parameter of RC in the crack propagation process was determined by the initial fracture toughness of concrete.To verify the validity of the proposed analytical method,the P-CMOD curves of RC TPB beam were calculated by this method,and it showed a reasonable agreement with the experimental data obtained from the literature.The KR resistance curves and FPZ lengths of lightly RC beams were also obtained.The effects of the specimen dimension,a0/D,the reinforcement ratio,the concrete cover and the interfacial bond-slip relationship on the crack propagation process of lightly RC beam were investigated through parametric analyses;(5)A three-dimensional numerical method was proposed to simulate the crack propagation process of lightly RC beams.In this method,nonlinear spring elements with different stress-displacement relations were set up on the FPZ of concrete and on steel-concrete interface to characterize the softening behavior of concrete and the bond-slip behaviour between steel bars and concrete,respectively.It is assumed that crack begins to propagate when the maximum SIF at the crack tip along width reaches the initial fracture toughness of concrete.To verify the validity of the proposed method,the completed crack propagation processes of lightly RC TPB notched beams were simulated by this method,and the calculated P-CMOD curves showed a reasonable agreement with the experimental data obtained from the literature.Then,the variation of interfacial bond stress between steel bar and concrete during crack propagation process was analyzed,and the effects of specimen dimension and the interfacial bond-slip relationship on the crack propagation process of lightly RC beam were discussed.