# Study on Notch Sensitivity of Fracture Properties of Concrete Containing Nano-SiO2 Particles and Fly Ash

Authors: Peng Zhang; Qiao-Yan Guan; Chen-Hui Liu; Qing-Fu Li
Journal: Journal of Nanomaterials
 (2013)

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## Abstract

The fracture parameters and fracture relational curves of the concrete containing nano-SiO2 and fly ash with different relative notch depth of the notched beam specimens were measured by means of three-point bending method. The results indicate that the relative notch depth of the notched specimens has great effect on ac, KICini, KICun, GF, CMODc, and the fracture relational curves of the concrete containing nano-SiO2 and fly ash. There is a tendency of increase in ac and CMODc with the increase of relative notch depth, while KICini, KICun, and GF are decreasing gradually with the increase of relative notch depth of the notched beam specimens. Besides, when the relative notch depth increases from 0.2 to 0.5, the nonlinear stage of the curve becomes shorter and shorter, and the descent stage of the curve becomes sharper and sharper. The fracture parameters of ac, KICini, KICun, GF, and CMODc and the fracture curves are sensitive to the relative notch depth, while CTODc may be not sensitive to the relative notch depth of the specimens of the concrete containing nano-SiO2 and fly ash.


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## Body

## 1. 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 [3–8].  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-SiO2 is more obvious than that of silica fume, and nano-SiO2 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-SiO2 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 [11–14]. 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 SiO2 nanoparticles on both mechanical properties and physical properties of concrete and the size effects of SiO2 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-SiO2 and waste ground ceramic simultaneously [18]. Their results indicate that the addition of nano-SiO2 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-SiO2 and fly ash; specially no significant experimental data exist on the effect of relative notch depth on fracture properties of the concrete containing SiO2 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-SiO2 particles and fly ash.


## 2. Experimental Program

### 2.1. Raw Materials

A Chinese standard (GB175-2007) [20] Portland cement Class 42.5R (which has standard compressive strength of 42.5 MPa at the age of 28 days) was used. A Chinese standard (GB/T 1596-2005) [21] Grade I fly ash was used to make the concrete. The chemical and physical properties of the cement and fly ash are presented in Table 1. In this experimental study, amorphous nano-SiO2 with a solid content of more than 99% was used. Physical properties of the nanoparticles are presented in Table 2. Coarse aggregate with a maximum size of 20 mm and fine aggregate with a 2.76 fineness modulus were used. The specific gravity and silt content of the coarse and fine aggregates were 2.74 and 0.6%, and 2.63 and 0.8%, respectively. A high range water reducing agent was used to adjust the workability of the concrete mixture. The performance indices of the high range water reducing agent are presented in Table 3. Fly ash content and nano-SiO2 content (by mass) are 15% and 5%, respectively. The mix proportion used in this study is given in Table 4.Table 1
Properties of cement and fly ash.
Composition (%)
Cement
Fly ash
Chemical compositions
SiO2
20.85
51.50
Al2O3
5.32
18.46
Fe2O3
2.69
6.71
CaO
62.97
8.58
MgO
3.66
3.93
Na2O
0.15
2.52
K2O
0.62
1.85
SO3
2.48
0.21
Physical properties
Specific gravity
3.11
2.16
Specific surface (cm2/g)
3287
2470Table 2
Physical properties of nano-SiO2.
Average particle size (nm)
SiO2 content (%)
Specific surface area (m2/g)
Apparent density (g/cm3)
PH value
30
99.5
200
±
10
0.055
5–7Table 3
Properties of high range water reducing agent.
Solid content (%)
Total alkali content (%)
Fluidity of cement paste (mm)
Density (g/cm3)
Content of Cl− (%)
PH value
30
1.2
260
1.052
0.078
4.32Table 4
Mix proportions of the concrete composites.
Cement (kg/m3)
Fly ash (kg/m3)
Nano-SiO2 (kg/m3)
Fine aggregate (kg/m3)
Coarse aggregate (kg/m3)
Water (kg/m3)
Water reducing agent (kg/m3)
395.2
74.1
24.7
647
1151
158
4.94


### 2.2. 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].


### 2.3. Determination of Fracture Parameters

In this study, the fracture properties of concrete were evaluated by the double-K fracture parameters (initial fracture toughness KICini and unstable fracture toughness KICun) [23] and fracture energy GF. The effective crack length of the three-point bending beam specimen is generally used to calculate KICini and KICun, and the effective crack length can be calculated as follows [24]:
(1)ac=2πH×arctgEB32.6PVmaxCMODc-0.1135,
where ac is effective crack length of the three-point bending beam specimen, m; PVmax is peak vertical load, kN; CMODc is critical crack mouth opening displacement, m; E is elastic modulus of the concrete composite, MPa; H is height of the beam specimen, m; B 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-SiO2 and fly ash can be calculated as follows [25]:
(2)KICini=3PiniSa02BH2f(a0H),
where KICini is initial fracture toughness, kN/m3/2; Pini is initial cracking load, kN; S is span length of the beam specimen, m; H is height of the beam specimen, m; B is width of the beam specimen, m; a0 is depth of the precutting crack of the three-point bending beam specimen, m; f(a0/H) is a function relevant to a0/H, the expression of which is as follows:
(3)f(a0H)=(1.99-a0H(1-a0H)[2.15-3.93a0H+2.7(a0H)2])×[2.15-3.93a0H+2.7(a0H)2])×((1+2a0H)(1-a0H)1.5)-1.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-SiO2 and fly ash can be calculated as follows [25]:
(4)KICun=3PVmaxSac2BH2f(acH),
where KICun is unstable fracture toughness, kN/m3/2; PVmax is peak vertical load, kN; S is span length of the beam specimen, m; H is height of the beam specimen, m; B  is width of the beam specimen, m; ac is effective crack length of the three-point bending beam specimen, m; f(ac/H) is a function relevant to ac/H, the expression of which is as follows:
(5)f(acH)=(1.99-acH(1-acH)[2.15-3.93acH+2.7(acH)2]×[2.15-3.93acH+2.7(acH)2])×((1+2acH)(1-acH)1.5)-1.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 PV-δ of the three-point bending beam specimen, the fracture energy of the concrete containing nano-SiO2 and fly ash can be calculated as follows [27]:
(6)GF=1Alig[W0+(m1+2m2)gδmax],Alig=B(H-a0),
where GF is fracture energy, N/m; Alig is area of the fracture ligament of the specimen, m2; H is height of the beam specimen, m; B is width of the beam specimen, m; a0 is depth of the notched crack, m; g is gravitational acceleration (g=9.8m/s2); m1 is weight of the specimen between the two supports, kg; m2 is additive weight of the loading facilities; δmax is the maximum mid-span deflection of the beam specimen, m; W0 is area above the axis of δ and under the relational curve of PV-δ, 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.


## 2.1. Raw Materials

A Chinese standard (GB175-2007) [20] Portland cement Class 42.5R (which has standard compressive strength of 42.5 MPa at the age of 28 days) was used. A Chinese standard (GB/T 1596-2005) [21] Grade I fly ash was used to make the concrete. The chemical and physical properties of the cement and fly ash are presented in Table 1. In this experimental study, amorphous nano-SiO2 with a solid content of more than 99% was used. Physical properties of the nanoparticles are presented in Table 2. Coarse aggregate with a maximum size of 20 mm and fine aggregate with a 2.76 fineness modulus were used. The specific gravity and silt content of the coarse and fine aggregates were 2.74 and 0.6%, and 2.63 and 0.8%, respectively. A high range water reducing agent was used to adjust the workability of the concrete mixture. The performance indices of the high range water reducing agent are presented in Table 3. Fly ash content and nano-SiO2 content (by mass) are 15% and 5%, respectively. The mix proportion used in this study is given in Table 4.Table 1
Properties of cement and fly ash.
Composition (%)
Cement
Fly ash
Chemical compositions
SiO2
20.85
51.50
Al2O3
5.32
18.46
Fe2O3
2.69
6.71
CaO
62.97
8.58
MgO
3.66
3.93
Na2O
0.15
2.52
K2O
0.62
1.85
SO3
2.48
0.21
Physical properties
Specific gravity
3.11
2.16
Specific surface (cm2/g)
3287
2470Table 2
Physical properties of nano-SiO2.
Average particle size (nm)
SiO2 content (%)
Specific surface area (m2/g)
Apparent density (g/cm3)
PH value
30
99.5
200
±
10
0.055
5–7Table 3
Properties of high range water reducing agent.
Solid content (%)
Total alkali content (%)
Fluidity of cement paste (mm)
Density (g/cm3)
Content of Cl− (%)
PH value
30
1.2
260
1.052
0.078
4.32Table 4
Mix proportions of the concrete composites.
Cement (kg/m3)
Fly ash (kg/m3)
Nano-SiO2 (kg/m3)
Fine aggregate (kg/m3)
Coarse aggregate (kg/m3)
Water (kg/m3)
Water reducing agent (kg/m3)
395.2
74.1
24.7
647
1151
158
4.94


## 2.2. 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].


## 2.3. Determination of Fracture Parameters

In this study, the fracture properties of concrete were evaluated by the double-K fracture parameters (initial fracture toughness KICini and unstable fracture toughness KICun) [23] and fracture energy GF. The effective crack length of the three-point bending beam specimen is generally used to calculate KICini and KICun, and the effective crack length can be calculated as follows [24]:
(1)ac=2πH×arctgEB32.6PVmaxCMODc-0.1135,
where ac is effective crack length of the three-point bending beam specimen, m; PVmax is peak vertical load, kN; CMODc is critical crack mouth opening displacement, m; E is elastic modulus of the concrete composite, MPa; H is height of the beam specimen, m; B 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-SiO2 and fly ash can be calculated as follows [25]:
(2)KICini=3PiniSa02BH2f(a0H),
where KICini is initial fracture toughness, kN/m3/2; Pini is initial cracking load, kN; S is span length of the beam specimen, m; H is height of the beam specimen, m; B is width of the beam specimen, m; a0 is depth of the precutting crack of the three-point bending beam specimen, m; f(a0/H) is a function relevant to a0/H, the expression of which is as follows:
(3)f(a0H)=(1.99-a0H(1-a0H)[2.15-3.93a0H+2.7(a0H)2])×[2.15-3.93a0H+2.7(a0H)2])×((1+2a0H)(1-a0H)1.5)-1.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-SiO2 and fly ash can be calculated as follows [25]:
(4)KICun=3PVmaxSac2BH2f(acH),
where KICun is unstable fracture toughness, kN/m3/2; PVmax is peak vertical load, kN; S is span length of the beam specimen, m; H is height of the beam specimen, m; B  is width of the beam specimen, m; ac is effective crack length of the three-point bending beam specimen, m; f(ac/H) is a function relevant to ac/H, the expression of which is as follows:
(5)f(acH)=(1.99-acH(1-acH)[2.15-3.93acH+2.7(acH)2]×[2.15-3.93acH+2.7(acH)2])×((1+2acH)(1-acH)1.5)-1.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 PV-δ of the three-point bending beam specimen, the fracture energy of the concrete containing nano-SiO2 and fly ash can be calculated as follows [27]:
(6)GF=1Alig[W0+(m1+2m2)gδmax],Alig=B(H-a0),
where GF is fracture energy, N/m; Alig is area of the fracture ligament of the specimen, m2; H is height of the beam specimen, m; B is width of the beam specimen, m; a0 is depth of the notched crack, m; g is gravitational acceleration (g=9.8m/s2); m1 is weight of the specimen between the two supports, kg; m2 is additive weight of the loading facilities; δmax is the maximum mid-span deflection of the beam specimen, m; W0 is area above the axis of δ and under the relational curve of PV-δ, 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.


## 3. Results and Discussion

### 3.1. Effect of Relative Notch Depth on Fracture Toughness

The results of the effective crack length (ac) of the three-point bending beam specimens of the concrete containing nano-SiO2 and fly ash, with the curing period of 28 d, are shown in Figure 1. The results show that the fracture parameter of ac is greatly sensitive to the relative notch depth of notched three-point 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 ac 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 ac is determined as 32.5% for the three-point bending beam specimen with 0.5 relative notch depth.Figure 1
Effect of relative notch depth on effective crack length.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.Figures2 and 3 illustrate the variations of initial fracture toughness (KICini) and unstable fracture toughness (KICun) of the concrete containing nano-SiO2 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 KICini and KICun compared with those specimens with higher relative notch depth. Both of KICini and KICun 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, KICini may be not sensitive to the varying of the relative notch depth. According to the double-K fracture criterion, the concrete with larger KICini and KICun has higher fracture properties. The variations of KICini and KICun indicate that the fracture properties of the concrete containing nano-SiO2 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 KICini and KICun decrease with the increase of relative notch depth.Figure 2
Effect of relative notch depth on initial fracture toughness.Figure 3
Effect of relative notch depth on unstable fracture toughness.


### 3.2. Effect of Relative Notch Depth on Fracture Energy

The variations ofGF of notched three-point bending beam specimens of the concrete containing nano-SiO2 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 GF 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 GF 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 GF can reflect how difficult the crack propagates, and the higher GF indicate that the concrete has higher fracture properties, while, on the contrary, the concrete has lower fracture properties with smaller value of GF. Therefore, the above-mentioned variations of GF indicates that the fracture properties of the concrete containing nano-SiO2 and fly ash with larger relative notch depth will be lower than the actual fracture properties of the concrete. The fracture energy GF 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 GF indicates that more energy will be consumed to make the concrete composite fracture and the concrete composite has better fracture properties. Therefore, GF is decreasing with the increase of the relative notch depth of the beam specimen.Figure 4
Effect of relative notch depth on fracture energy.Figure5 presents the typical complete curves of PV-δ of the notched three-point bending beam specimens of the concrete containing nano-SiO2 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 mid-span deflection also decreases gradually with the increase of the relative notch depth. Accordingly, the variation rule of the relational curves of PV-δ indicates that the resistance to crack propagation of the specimen is gradually decreased with the increase of relative notch depth of the specimens.Figure 5
Contrast ofPV-δ curves of different relative notch depth.


### 3.3. Effect of Relative Notch Depth on CMOD and CTOD

The different relational curves ofPV-CMOD and PV-CTOD of the three-point bending beam specimens of the concrete containing nano-SiO2 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 PV-CMOD and PV-CTOD is significant, and the variation rules of the relational curves with the varying of relative notch depth of PV-CMOD and PV-CTOD are similar to those of the relational curves of PV-δ.Figure 6
Contrast ofPV-CMOD curves of different relative notch depth.Figure 7
Contrast ofPV-CTOD curves of different relative notch depth.Figure8 presents the variations of the critical crack mouth opening displacement (CMODc) and the critical crack tip opening displacement (CTODc) of the three-point bending beam specimens of the concrete containing nano-SiO2 with different values of relative notch depth, respectively. The CMODc can be defined as the crack mouth opening displacement when the vertical load reaches the maximum value [28]. In a similar way, the CTODc 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 CMODc is significant and CMODc 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 CMODc is determined as 34.6% for the three-point bending beam specimen with 0.5 relative notch depth. However, the value of CTODc changes slightly as the relative notch depth of the specimen increases from 0.2 to 0.5. From the results of CMODc and CTODc, it can be concluded that the CMODc is sensitive to the relative notch depth, while CTODc may be not sensitive to the relative notch depth of notched three-point bending beam specimens. The variation of CMODc is similar to the effective crack length ac 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, CTODc changes slightly as the relative notch depth of the specimen increases gradually.Figure 8
Effect of relative notch depth onCMODc and CTODc.


## 3.1. Effect of Relative Notch Depth on Fracture Toughness

The results of the effective crack length (ac) of the three-point bending beam specimens of the concrete containing nano-SiO2 and fly ash, with the curing period of 28 d, are shown in Figure 1. The results show that the fracture parameter of ac is greatly sensitive to the relative notch depth of notched three-point 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 ac 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 ac is determined as 32.5% for the three-point bending beam specimen with 0.5 relative notch depth.Figure 1
Effect of relative notch depth on effective crack length.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.Figures2 and 3 illustrate the variations of initial fracture toughness (KICini) and unstable fracture toughness (KICun) of the concrete containing nano-SiO2 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 KICini and KICun compared with those specimens with higher relative notch depth. Both of KICini and KICun 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, KICini may be not sensitive to the varying of the relative notch depth. According to the double-K fracture criterion, the concrete with larger KICini and KICun has higher fracture properties. The variations of KICini and KICun indicate that the fracture properties of the concrete containing nano-SiO2 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 KICini and KICun decrease with the increase of relative notch depth.Figure 2
Effect of relative notch depth on initial fracture toughness.Figure 3
Effect of relative notch depth on unstable fracture toughness.


## 3.2. Effect of Relative Notch Depth on Fracture Energy

The variations ofGF of notched three-point bending beam specimens of the concrete containing nano-SiO2 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 GF 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 GF 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 GF can reflect how difficult the crack propagates, and the higher GF indicate that the concrete has higher fracture properties, while, on the contrary, the concrete has lower fracture properties with smaller value of GF. Therefore, the above-mentioned variations of GF indicates that the fracture properties of the concrete containing nano-SiO2 and fly ash with larger relative notch depth will be lower than the actual fracture properties of the concrete. The fracture energy GF 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 GF indicates that more energy will be consumed to make the concrete composite fracture and the concrete composite has better fracture properties. Therefore, GF is decreasing with the increase of the relative notch depth of the beam specimen.Figure 4
Effect of relative notch depth on fracture energy.Figure5 presents the typical complete curves of PV-δ of the notched three-point bending beam specimens of the concrete containing nano-SiO2 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 mid-span deflection also decreases gradually with the increase of the relative notch depth. Accordingly, the variation rule of the relational curves of PV-δ indicates that the resistance to crack propagation of the specimen is gradually decreased with the increase of relative notch depth of the specimens.Figure 5
Contrast ofPV-δ curves of different relative notch depth.


## 3.3. Effect of Relative Notch Depth on CMOD and CTOD

The different relational curves ofPV-CMOD and PV-CTOD of the three-point bending beam specimens of the concrete containing nano-SiO2 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 PV-CMOD and PV-CTOD is significant, and the variation rules of the relational curves with the varying of relative notch depth of PV-CMOD and PV-CTOD are similar to those of the relational curves of PV-δ.Figure 6
Contrast ofPV-CMOD curves of different relative notch depth.Figure 7
Contrast ofPV-CTOD curves of different relative notch depth.Figure8 presents the variations of the critical crack mouth opening displacement (CMODc) and the critical crack tip opening displacement (CTODc) of the three-point bending beam specimens of the concrete containing nano-SiO2 with different values of relative notch depth, respectively. The CMODc can be defined as the crack mouth opening displacement when the vertical load reaches the maximum value [28]. In a similar way, the CTODc 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 CMODc is significant and CMODc 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 CMODc is determined as 34.6% for the three-point bending beam specimen with 0.5 relative notch depth. However, the value of CTODc changes slightly as the relative notch depth of the specimen increases from 0.2 to 0.5. From the results of CMODc and CTODc, it can be concluded that the CMODc is sensitive to the relative notch depth, while CTODc may be not sensitive to the relative notch depth of notched three-point bending beam specimens. The variation of CMODc is similar to the effective crack length ac 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, CTODc changes slightly as the relative notch depth of the specimen increases gradually.Figure 8
Effect of relative notch depth onCMODc and CTODc.


## 4. Conclusions

In this study, the fracture parameters and fracture relational curves of the concrete containing nano-SiO2 and fly ash with different relative notch depth were measured by the method of notched three-point bending beam specimens. From this study, it can be concluded that the relative notch depth of notched three-point bending beam specimens has great effect on the fracture parameters of ac, KICini, KICun, GF, and CMODc and the relational curves of PV-δ, PV-CMOD, and PV-CTOD of the concrete containing nano-SiO2 and fly ash. There is a tendency of increase in ac and CMODc with the increase of relative notch depth, while KICini, KICun, and GF are decreasing gradually with the increase of relative notch depth of notched three-point bending beam specimens. When the relative notch depth increases from 0.2 to 0.5, the nonlinear stage of the curve becomes shorter and shorter, and the descent stage of the curve becomes sharper and sharper. The fracture parameters of ac, KICini, KICun, GF, and CMODc and the fracture curves are sensitive to the relative notch depth, while CTODc may be not sensitive to the relative notch depth of notched three-point bending beam specimens.



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*Source: 381682-2013-12-28.xml*