Three-dimensional Propagation Of Mode-Ⅰ Crack In Concrete Based On Boundary Effect

The problem of crack is closely related to safety,stability and durability of concrete structures.At present,the crack has become one of the main inducements of disease in concrete dams.Therefore,it is of great significance to study the fracture characteristics of concrete for the safe operation of dams.It should be noted that the arch dam is irregular three-dimensional(3-D)shell structure with variable thickness and the stress condition is very complicated,which results the assumption of plane problem about the fracture analysis cannot be applied on it.In addition,it is found that the crack profile and propagation trajectory are geometrically irregular,and the traditional two-dimensional(2-D)model and analysis method cannot reflect the nonlinear distribution of the crack front.Therefore,it is of great theoretical significance and engineering application value to establish the propagation criterion of 3-D crack propagation path and predict the propagation process of 3-D crack under various possible conditions.From the perspective of concrete specimens,this paper took Mode-Ⅰ crack as the research object and used the method of combining experiment and numerical simulation to conduct 3-D crack propagation analysis.The main work was shown as follows:(1)Three-point bending test of concrete specimens with different thicknessIn this paper,the thickness of specimen was taken as a variable.The length of the specimen is 500mm,the span is 400mm,the height is 100mm,the ratio of pre-set crack length to specimen height is 0.3.The thickness is chosen as 40mm,80mm,100mm,120mm and160mm,respectively.The crack initiation load,peak load,critical crack length,the complete load-loading point displacement curve(P-δ)and load-crack opening displacement curve(P-CMOD)can be obtained directly from the three-point bending test.It is found that there was almost no obvious thickness size effect on the double-K fracture toughness and the critical crack length when the thickness of the specimen changed.The fracture energy of the specimen was calculated according to the P-δcurve.It is found that the fracture energy increased with the increase of the thickness of the specimen when the thickness was greater than 100mm within the quantitative calculation and research range of this experiment.(2)Multi-stage crack propagation dyeing testThe dyeing test was carried out on concrete specimens with thickness of 40mm,80mm,100mm,120mm and 160mm,and the crack propagation trajectories under different load levels were obtained.Considering the alkaline nature of concrete,phenolphthalein alcohol solution was selected as dyeing agent.Six load levels in the process of crack propagation were selected for dyeing.According to the dyeing results,for specimens with the same thickness,the difference of crack propagation length between the surface and center of the specimen first increased and then decreased.For specimens with different thickness,the crack front propagation trajectory was irregular when the thickness of the specimen was greater than80mm.However,when the thickness of the specimen was equal to 40mm,and the crack front propagation trajectory was approximately a straight line.(3)Numerical simulation of 3-D crack propagation based on thickness boundary effectIn the numerical simulation part,the fictitious crack model and the mode-I crack initiation criterion based on the fracture initiation toughness were used to simulate the whole process of fracture propagation.In order to reflect the influence of the thickness boundary,a bilinear softening curve considering the g_f distribution in the thickness direction and a trilinear model of crack initiation toughness considering the thickness boundary effect were proposed based on the boundary effect of concrete fracture energy.The finite element models of semi-structure of specimens with different thickness were established by APDL command flow,and the mesh near the crack tip was encrypted.Combined with the influence of thickness boundary,the whole process of 3-D crack propagation was simulated.Finally,by comparing the P-CMOD curves and crack propagation trajectories of experiment and numerical simulation,the feasibility of the theoretical models proposed in this paper were verified.(4)Influence analysis of softening curve in numerical calculationIn this paper,3-D crack propagation numerical verification was performed based on two softening curves.The two numerical calculation methods were denoted as numerical 1 and numerical 2 respectively.Compared with the falling segment of P-CMOD curve,numerical 1was closer to the test result.Compared to the crack front propagation path diagram,the crack propagation path of numerical 2 closed to the straight line and it cannot reflect the tendency that the crack front was not uniformity.Besides,for specimens with the same thickness,the difference between the crack propagation length between the surface and center increased first and then decreased in numerical 1,but there was no such obvious tendency in numerical 2,which was quite different from the staining test results.In summary,it was proved that the softening curve in numerical 1 selected in this paper was in good agreement with the test results and was closer to the real situation of crack propagation.