3.3 Tension softening behavior
Tension softening is a basic material property which represents the relationship between the cohesive stress and the corresponding crack opening across the fracture process zone(FPZ)of concrete.The softening curve is essential for predicting the fracture behavior of concrete,and can be obtained by direct tensile test for practical applications,there are two simplified models for describing the strain-softening relationship of concrete:bilinear[3]and exponential[14].The bilinear strain-softening diagram is also adopted in the CEB-FIP Model Code.
Figure 8 Parametric effects on fracture energy of AASFC and ultimate load of the beams
On the basis of TPB tests,the tension softening curve can be determined indirectly by a backward analysis[15,16].The software CONSOFT[17]originally developed by Prof.Volker Slowik and his colleagues at the University of Applied Sciences in Leipzig Germany was utilized to determine the softening curves of the PC and AAS concrete and mortar.For the inverse analyses,the cohesive crack model[15]as well as an evolutionary optimization algorithm[18]is adopted.The applied optimization method is based on a biologically motivated approach.By stepwise updating the assumed softening curve and re-analyzing in several iterations,the numerical results can be fitted to the experimental ones.When a satisfactory fit of the numerical to the experimental results is met,the assumed softening curve is considered to be the one characterizing the behavior of the material[19].The boundary effect[20]is also taken into account.When the crack tip approaches the specimen boundary,the size of the fracture process zone is reduced and the full amount of the fracture energy can no longer be activated.As a result,the local fracture energy decreases near the end of the crack path.
Figure 9 shows the normalized bilinear tension-softening curves of PC and AAS geopolymer concrete and mortar with compressive strength of 30,50 and 70 MPa.Figure 9(a)shows that the normalized bilinear softening curves of PC concrete and AAS geopolymer concrete are generally the same given the same compressive strength although the decrease of the initial descending part of AAS geopolymer concrete is slightly slower than that of PC concrete in the case of C30.Figure 9(b)clearly shows that PCM usually has gentler first descending slopes than AASM at all the three compressive strength levels.For both AAS geopolymer and PC concrete and mortar,the first descending slope becomes sharper with the strength increase.
Figure 9 Bilinear tension softening curves of PC and AAS geopolymer concrete and mortar
Figure 10 shows the normalized bilinear tension-softening curves of PC concrete,AAS geopolymer concrete and AASFC gepolymer concrete with different alkali concentration,modulus,slag/FA ratio and water/binder ratio.It is seen for the first descending part all tested parameters had a marginal effect.For the second descending part,the alkaliconcentration had the least ef fect on the normalized softening curve(Figure 10(a));the modulus between 1.0 and 1.5 just led to a marginal change of the shape of the softening curve but a further increase of the modulus to 2.0 may increase the free-stress crack width(Figure 10(b));the ef fect of slag/fly ash on the softening curves is not deterministic.The slag seems to have an optimal ratio,which may need further research.It is seen that using the slag/FA ratio of 50/50 and using 100%slag almost led to the identical normalized tensionsoftening curves(Figure 10(c));the effect of water/binder ratio is similar to that observed for PC concrete.The higher compressive strength,the more brittle tension softening curves(Figure 10(d)).
Figure 10 Parametric effects on the bilinear tension softening curves of AASFC