Study on Notch Sensitivity of Fracture Properties of Concrete Containing Nano-SiO 2 Particles and Fly Ash

The fracture parameters and fracture relational curves of the concrete containing nano-SiO 2 and fly ash with different relative notch depth of the notched beam specimens weremeasured bymeans of three-point bendingmethod.The results indicate that the relative notch depth of the notched specimens has great effect on a c ,Kini IC ,K un IC ,GF, CMODc, and the fracture relational curves of the concrete containing nano-SiO 2 and fly ash.There is a tendency of increase in a c and CMOD c with the increase of relative notch depth, while


Introduction
Fly ash is known as a by-product of coal-burning thermal power stations, and the disposal of fly ash has become a considerable environmental problem [1,2].In order to solve the environmental problem of disposing fly ash, large quantities of fly ash are proposed to be incorporated in concrete mixes.Numerous studies have been focused on the development of concrete composites containing large amounts of fly ash [3][4][5][6][7][8].In recent years, much attention has been paid to the applications of nano-materials in civil engineering, because nanoparticles possess many special properties such as huge specific surface area and high activity due to their small size [9].The pozzolanic activity of nano-SiO 2 is more obvious than that of silica fume, and nano-SiO 2 can react with calcium hydroxide (Ca(OH) 2 ) crystals, which are arrayed in the interfacial transition zone between hardened cement paste and aggregates, and produce C-S-H gel [10].Previously, the effects of nano-SiO 2 particles on different mechanical properties of concrete composites have been studied.Li et al. investigated the improvement in compressive and flexural strengths, abrasion resistance, chloride permeability, and flexural fatigue performance of concrete containing nanoparticles [11][12][13][14].Bahadori and Hosseini studied the effects of replacing cement with colloidal amorphous silica nanoparticles on the physical and mechanical properties, durability and microstructure of concrete [15].Givi et al. investigated the effects of SiO 2 nanoparticles on both mechanical properties and physical properties of concrete and the size effects of SiO 2 nanoparticles on compressive, flexural, and tensile strength of binary blended concrete [16,17].Heidari and Tavakoli investigated the compressive strength, and water absorption of the concrete composite using nano-SiO 2 and waste ground ceramic simultaneously [18].Their results indicate that the addition of nano-SiO 2 particles greatly improves the compressive, flexural, tensile strength and toughness of concrete composites.Nanoparticles can act as heterogeneous nuclei for cement pastes, further accelerating cement hydration because of their high reactivity, as nanoreinforcement, and as nanofiller, densifying the microstructure, thereby, leading to a reduced porosity [19].
Fracture properties are extremely important for the safety and durability of concrete structures.To study crack expansion of the beam specimen of concrete, a notch should be cut in the specimen.The relative notch depth can be defined as the ratio of the notch depth to the height of the beam specimen.The conventional concrete has notch sensitivity on its fracture properties.Despite the recent efforts, few studies are available, concerning the fracture behavior of the concrete containing nano-SiO 2 and fly ash; specially no significant experimental data exist on the effect of relative notch depth on fracture properties of the concrete containing SiO 2 nanoparticles and fly ash.Therefore, we conducted this experimental study and measured the fracture toughness, fracture energy, crack mouth opening displacement, and crack tip opening displacement of the notched beam specimens to study the notch sensitivity of the beam specimens of the concrete containing nano-SiO 2 particles and fly ash.The mix proportion used in this study is given in Table 4.

Experimental Method.
A series of notched beam specimens with the size of 100 × 100 × 515 mm were prepared to determine the fracture parameters and curves.The beam specimen was sawed from the span centre of the lower surface to produce a precutting crack, the relative notch depth of which is 0.2, 0.3, 0.4, and 0.5, respectively.All the specimens were cured for 28 days before testing.Three-point bending beam method was employed to measure the fracture parameters in this study, which is an appropriate fracture testing method [22].

Determination of Fracture Parameters.
In this study, the fracture properties of concrete were evaluated by the double- fracture parameters (initial fracture toughness  ini IC and unstable fracture toughness  un IC ) [23] and fracture energy   .The effective crack length of the three-point bending beam specimen is generally used to calculate  ini IC and  un IC , and the effective crack length can be calculated as follows [24]: where   is effective crack length of the three-point bending beam specimen, m;   max is peak vertical load, kN; CMOD  is critical crack mouth opening displacement, m;  is elastic modulus of the concrete composite, MPa;  is height of the beam specimen, m;  is width of the beam specimen, m.With the measured initial cracking load and the depth of the precutting crack of the three-point bending beam specimen, the initial fracture toughness of the concrete containing nano-SiO 2 and fly ash can be calculated as follows [25]: where  ini IC is initial fracture toughness, kN/m 3/2 ;  ini is initial cracking load, kN;  is span length of the beam specimen, m;  is height of the beam specimen, m;  is width of the beam specimen, m;  0 is depth of the precutting crack of the threepoint bending beam specimen, m; ( 0 /) is a function relevant to  0 /, the expression of which is as follows: With the measured peak vertical load and the effective crack length of the three-point bending beam specimen, the unstable fracture toughness of the concrete containing nano-SiO 2 and fly ash can be calculated as follows [25]: where  un IC is unstable fracture toughness, kN/m 3/2 ;   max is peak vertical load, kN;  is span length of the beam specimen, m;  is height of the beam specimen, m;  is width of The fracture energy is resulting from integration of the load-displacement curve per unit of the fractured surface of the specimen [26].With the measured ultimate mid-span deflection and the relational curve of   - of the three-point bending beam specimen, the fracture energy of the concrete containing nano-SiO 2 and fly ash can be calculated as follows [27]: where   is fracture energy, N/m;  lig is area of the fracture ligament of the specimen, m 2 ;  is height of the beam specimen, m;  is width of the beam specimen, m;  0 is depth of the notched crack, m;  is gravitational acceleration ( = 9.8 m/s 2 );  1 is weight of the specimen between the two supports, kg;  2 is additive weight of the loading facilities;  max is the maximum mid-span deflection of the beam specimen, m;  0 is area above the axis of  and under the relational curve of   -, N⋅m.There are 6 specimens for each relative notch depth, and the average value of the 6 values of calculation is adopted as the final result.bending beam specimens of the concrete containing nano-SiO 2 and fly ash, with the curing period of 28 d, are shown in Figure 1.The results show that the fracture parameter of   is greatly sensitive to the relative notch depth of notched threepoint bending beam specimens, and the effective crack length of the specimen with smaller relative notch depth is more sensitive to the relative notch depth.However, in general, there is a tendency of increase in   with the increase of relative notch depth of the specimens.Compared with the three-point bending beam specimen with 0.2 relative notch depth, the increase of   is determined as 32.5% for the threepoint bending beam specimen with 0.5 relative notch depth.

Results and Discussion
To some extent, the effective crack length represents the actual length of the crack in the calculating of the fracture parameters.The actual length of the crack is longer than the depth of the precutting crack of the specimen because there is a stage of steady expanding before unstable fracture occurs, and the propagation length of the crack is the difference of the actual length of the crack and the depth of the precutting crack of the specimen.The larger the depth of the precutting   crack, the larger the effective crack length.Therefore, the relative notch depth of the beam specimen increases with relative notch depth.

Journal of Nanomaterials
Figures 2 and 3 illustrate the variations of initial fracture toughness ( ini IC ) and unstable fracture toughness ( un IC ) of the concrete containing nano-SiO 2 and fly ash at 28 days curing period with the increase of the relative notch depth of notched three-point bending beam specimen, respectively.As can be seen from the figures, the three-point bending specimens with larger relative notch depth have lower  ini IC and  un IC compared with those specimens with higher relative notch depth.Both of  ini IC and  un IC are decreasing gradually with the increase of relative notch depth with the relative notch depth less than 0.5.When the relative notch depth is more than 0.3,  ini IC may be not sensitive to the varying of the relative notch depth.According to the double-K fracture criterion,  the concrete with larger  ini IC and  un IC has higher fracture properties.The variations of  ini IC and  un IC indicate that the fracture properties of the concrete containing nano-SiO 2 and fly ash with smaller relative notch depth will be higher than the actual fracture properties of the concrete.The value of the fracture toughness of the concrete composite has great relation with the peak vertical load of the beam specimen.In general, the fracture toughness of the concrete composite is increasing with the increase of the peak vertical load.From the testing process, it can be seen that the specimen with smaller depth of the precutting crack can afford the larger peak vertical load.As a result, the  ini IC and  un IC decrease with the increase of relative notch depth.

Effect of Relative Notch
Depth on Fracture Energy.The variations of   of notched three-point bending beam specimens of the concrete containing nano-SiO 2 and fly ash with 0.2, 0.3, 0.4, and 0.5 relative notch depth at 28 days curing period are illustrated in Figure 4. From the figure, it can be seen that a considerable decrease for   of the concrete was observed by increasing the value of relative notch depth of the notched specimen when the relative notch depth is less than 0.5.Compared with the relative notch depth of 0.2, the decrease of   was determined as 5.2%, 9.3%, and 12.8% for the three-point bending beam specimen with 0.3, 0.4, and 0.5 relative notch depth, respectively.The value of   can reflect how difficult the crack propagates, and the higher   indicate that the concrete has higher fracture properties, while, on the contrary, the concrete has lower fracture properties with smaller value of   .Therefore, the above-mentioned variations of   indicates that the fracture properties of the concrete containing nano-SiO 2 and fly ash with larger relative notch depth will be lower than the actual fracture properties of the concrete.The fracture energy   of concrete composite represents the energy necessary to create a unit area of fracture surface.Then the specimen with smaller relative notch depth needs more energy to create a certain area of fracture surface than the specimen with larger relative notch depth.The higher   indicates that more energy will be consumed to make the concrete composite fracture and the concrete composite has better fracture properties.Therefore,   is decreasing with the increase of the relative notch depth of the beam specimen.Figure 5 presents the typical complete curves of   - of the notched three-point bending beam specimens of the concrete containing nano-SiO 2 and fly ash with different values of relative notch depth.From the curves, it can be seen that the nonlinear stage of the curve becomes shorter and shorter, and the descent stage of the curve becomes sharper and sharper when the relative notch depth increases from 0.2 to 0.5.Besides, the area surrounded by the curve and the coordinate axis decreases gradually and the maximal midspan deflection also decreases gradually with the increase of the relative notch depth.Accordingly, the variation rule of the relational curves of   - indicates that the resistance to crack propagation of the specimen is gradually decreased with the increase of relative notch depth of the specimens.

Effect of Relative Notch Depth on CMOD and CTOD.
The different relational curves of   -CMOD and   -CTOD of the three-point bending beam specimens of the concrete containing nano-SiO 2 and fly ash at 28 days curing period with different values of relative notch depth are given in Figures 6 and 7, respectively.From the curves, it can be seen that the effect of the relative notch depth on the curves of   -CMOD and   -CTOD is significant, and the variation rules of the relational curves with the varying of relative notch depth of   -CMOD and   -CTOD are similar to those of the relational curves of   -.
Figure 8 presents the variations of the critical crack mouth opening displacement (CMOD  ) and the critical crack tip opening displacement (CTOD  ) of the three-point bending beam specimens of the concrete containing nano-SiO 2 with different values of relative notch depth, respectively.The CMOD  can be defined as the crack mouth opening displacement when the vertical load reaches the maximum value [28].In a similar way, the CTOD  can be defined as the crack tip opening displacement when the vertical load reaches the maximum value.It can be generally seen that the effect of the relative notch depth of the specimen on  CMOD  is significant and CMOD  increases gradually as the relative notch depth of the specimen increases from 0.2 to 0.5.Compared with the three-point bending beam specimen with 0.2 relative notch depth, the increase of CMOD  is determined as 34.6% for the three-point bending beam specimen with 0.5 relative notch depth.However, the value of CTOD  changes slightly as the relative notch depth of the specimen increases from 0.2 to 0.5.From the results of CMOD  and CTOD  , it can be concluded that the CMOD  is sensitive to the relative notch depth, while CTOD  may be not sensitive to the relative notch depth of notched threepoint bending beam specimens.The variation of CMOD  is similar to the effective crack length   as the relative notch depth increases from 0.2 to 0.5.With the relative notch depth increases, the actual crack mouth opening displacement corresponding to the peak vertical load increases gradually.However, the actual crack tip opening displacement varies a little when the vertical load reaches the peak value.For this reason, CTOD  changes slightly as the relative notch depth of the specimen increases gradually.

Figure 2 : 2 ;
Figure 2: Effect of relative notch depth on initial fracture toughness.

Figure 3 :
Figure 3: Effect of relative notch depth on unstable fracture toughness.

Figure 4 :
Figure 4: Effect of relative notch depth on fracture energy.

Figure 5 :
Figure 5: Contrast of   - curves of different relative notch depth.

Table 1 :
Properties of cement and fly ash.

Table 3 :
Properties of high range water reducing agent.

Table 4 :
Mix proportions of the concrete composites.
the beam specimen, m;   is effective crack length of the threepoint bending beam specimen, m; (  /) is a function relevant to   /, the expression of which is as follows: Figure 6: Contrast of   -CMOD curves of different relative notch depth.