**Fracture Theory Under Freeze-Thaw Cycles and Freeze-Thaw Resistance of Alkali-Slag Concrete**

Qixuan Li

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/63810

#### **Abstract**

Despite the widespread research on alkali-activated concrete, its fracture properties under freeze-thaws are rarely studied; the response surface methodology (RSM) theory has not been put forward; and unstable fracture toughness, *KIC <sup>S</sup>* , influenced by freezethaws and slag content has not been researched. The purpose of this article is to investigate the calculation method of alkali-slag concrete (ASC) fracture parameters and provide theoretical support for RSM model of ASC prepared with Na2SiO3 and NaOH composite activator. The influence law of freeze-thaw and slag content on unstable fracture toughness, *KIC <sup>S</sup>* , is put forward. Results show that after crack mouth opening displacement (CMOD) is measured, other fracture parameters including concrete effective fracture length; crack tip opening displacement (CTOD); and stress intensity factors *KIC <sup>C</sup>* , *KIC <sup>C</sup>* , and *KIC <sup>S</sup>* from closure stress σ(*w*) can be obtained according to double-*K* fracture criterion and DL/T 5332-2005 "Hydraulic concrete fracture test proce‐ dures". RSM principles and advantages, its optimization content and procedure, the data processing software Design-Expert and verification analysis procedure of RSM model are put forward. Since the ASC structure is compact, characterized for water and air penetration resistance, its antifreezing characteristic is desirable.

**Keywords:** alkali-slag concrete, fracture parameter, response surface theory, unstable fracture toughness, composite activator

## **1. Introduction**

It has been nearly 200 years since the advent of Portland cement in 1824. Then there were mortar, concrete and reinforced concrete generated from it. Concrete has become the most widely and

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

largely used construction material. Construction of highways, bridges, ports, oil platforms, airports,dams,tunnels;undergroundconstructions;andconstructionaboveandundersealevel are all inseparable from concrete. Today, with the continuous progress of human demand and technology, research on concrete materials and structures is constantly moving toward depth and breadth. High performance and new special concrete is more and more widely used in projects, the construction technology is also maturing day by day.

With social progress and the advent of low-carbon economy, environmental protection and sustainable development attract more and more attention around the world. However, cement production causes serious pollution and consumes a large amount of energy and nonrenew‐ able resources such as coal, using large amount of limestone, iron ore, clay, etc. The traditional production process emits large amount of dust, and also exhausts huge amount of CO2, SO2, NOX and other emissions. It is calculated that 1 t of cement clinker's atmospheric emissions will be 1 t of CO2, 0.86 kg of SO2, 1.75 kg of NOx and 130 kg of dust. Cement production will continue to see a significant increase from the existing level, which will cause serious burden on the environment.

Production of new green and high performance concrete should make full use of industrial waste, such as slag, fly ash, limestone, gangue, etc., with no or little use of cement clinker. Minimizing clinker production reduces the environmental impact, and making new "cement" through technical means results in green cementitious materials.

Most of the world is in cold region, where winter temperature is below-5°C and concrete damage in those areas is the most relevant to freezing and thawing. Hypothermia is very unfavorable for concrete; the low temperature and freeze-thaw cycles usually lead to concrete deterioration in airports, highways, bridges, hydraulic structures, etc. Freeze-thaw damage is a persistent historic problem, receiving widespread attention from academia and engineering field. Internationally renowned concrete expert Sun proved in 1999 that the concrete damage process is accelerated and the extent of damage increased under the simultaneous action of load and freeze-thaw cycles [1]. Therefore, freezing is an important factor affecting the durability of concrete structures. Where there are alternating positive and negative tempera‐ tures, there exists concrete freeze-thaw damage.

During freeze-thaw process, there are heaving pressure cycles inside the concrete material, producing freeze-thaw internal stress. The structural organization will appear in irreversible microscopic changes such as microcrack formation, expansion, empty initiation and crystal dislocations. Internal concrete defects will gradually expand and accumulate, causing deteri‐ oration of material macroscopic mechanical properties, and resulting in damage. Damage caused by freeze-thaw stress gradually accumulates with freeze-thaw cycles, resulting in deterioration and even damage in concrete, which can be explained with percolation theory and damage theory, namely no damage → damage (formation of microcracks) → macrocracks → damage.

Thus, concrete freeze-thaw damage mechanism mainly lies in various microcracks, defects formation and expansion under external freeze-thaw cycles, resulting in damage and failure. Concrete freeze-thaw damage process indicates its complicated constitutive behavior, and it would be difficult to achieve the desired results if only describing with classical elastic or plastic mechanics. In order to fully reflect mechanical behavior of concrete structures under external factors, concrete body must be treated as deformable solid containing microcracks, other defects and even macroscopic cracks, and studied with fracture mechanics and damage mechanics.

There are many studies about alkali-activated concrete these years including application in railway sleepers [2], characteristics after exposure to high temperature [3], mixed fine aggre‐ gates [4], static and dynamic performances [5], mechanical properties [6], durability [7], ecoefficiency [8] and heat resistance characteristics [9]. Ravikumar [10] and Neithalath [11] successively published papers about chloride ion transport and electrical impedance of alkaliactivated slag concrete. Qixuan [12] proposed the RSM model for ASC fracture property prediction. However, the RSM theory has not been clarified and systematically studied. Provis [13] summarized the progress in understanding alkali-activated materials since 2011, which is of great value. Kovtun [14] studied the chemical acceleration of blastfurnace slag activated by sodium carbonate. Ma [15] corrected one misunderstanding in the shrinkage of alkali-activated fly ash, and is beneficial for future researchers. Ke [16] implemented calcined layered double hydroxides into the controlling of sodium carbonate-activated slag cements.

As can be seen, fruitful research results have been achieved in concrete deterioration and damage, but most of them focus on properties under load conditions at room temperature, ignoring environmental impact on concrete mechanical properties. There is little research on concrete fracture properties under freeze-thaw cycles, even less analyzing concrete fracture behavior and fracture characteristics after freeze-thaw cycles. Since fracture toughness is an important basis for the analysis of concrete crack propagation stability, it is extremely urgent and necessary studying concrete fracture properties under freeze-thaw cycles.

Through calculating, calculation method of ASC fracture parameters such as critical effec‐ tive fracture length *ac*, stress intensity factor *KIC <sup>C</sup>* caused by closure stress, initiation tough‐ ness *KIC <sup>Q</sup>* and unstable fracture toughness *KIC <sup>S</sup>* are investigated. The response surface methodology theory is systematically put forward, including RSM principles and advantag‐ es, optimization content and procedure, data processing software Design-Expert and verifi‐ cation of RSM model. Influence law of freeze-thaw on *KIC <sup>S</sup>* under different slag content is studied.

## **2. Test materials and methods**

largely used construction material. Construction of highways, bridges, ports, oil platforms, airports,dams,tunnels;undergroundconstructions;andconstructionaboveandundersealevel are all inseparable from concrete. Today, with the continuous progress of human demand and technology, research on concrete materials and structures is constantly moving toward depth and breadth. High performance and new special concrete is more and more widely used in

With social progress and the advent of low-carbon economy, environmental protection and sustainable development attract more and more attention around the world. However, cement production causes serious pollution and consumes a large amount of energy and nonrenew‐ able resources such as coal, using large amount of limestone, iron ore, clay, etc. The traditional production process emits large amount of dust, and also exhausts huge amount of CO2, SO2, NOX and other emissions. It is calculated that 1 t of cement clinker's atmospheric emissions will be 1 t of CO2, 0.86 kg of SO2, 1.75 kg of NOx and 130 kg of dust. Cement production will continue to see a significant increase from the existing level, which will cause serious burden

Production of new green and high performance concrete should make full use of industrial waste, such as slag, fly ash, limestone, gangue, etc., with no or little use of cement clinker. Minimizing clinker production reduces the environmental impact, and making new "cement"

Most of the world is in cold region, where winter temperature is below-5°C and concrete damage in those areas is the most relevant to freezing and thawing. Hypothermia is very unfavorable for concrete; the low temperature and freeze-thaw cycles usually lead to concrete deterioration in airports, highways, bridges, hydraulic structures, etc. Freeze-thaw damage is a persistent historic problem, receiving widespread attention from academia and engineering field. Internationally renowned concrete expert Sun proved in 1999 that the concrete damage process is accelerated and the extent of damage increased under the simultaneous action of load and freeze-thaw cycles [1]. Therefore, freezing is an important factor affecting the durability of concrete structures. Where there are alternating positive and negative tempera‐

During freeze-thaw process, there are heaving pressure cycles inside the concrete material, producing freeze-thaw internal stress. The structural organization will appear in irreversible microscopic changes such as microcrack formation, expansion, empty initiation and crystal dislocations. Internal concrete defects will gradually expand and accumulate, causing deteri‐ oration of material macroscopic mechanical properties, and resulting in damage. Damage caused by freeze-thaw stress gradually accumulates with freeze-thaw cycles, resulting in deterioration and even damage in concrete, which can be explained with percolation theory and damage theory, namely no damage → damage (formation of microcracks) → macrocracks

Thus, concrete freeze-thaw damage mechanism mainly lies in various microcracks, defects formation and expansion under external freeze-thaw cycles, resulting in damage and failure. Concrete freeze-thaw damage process indicates its complicated constitutive behavior, and it

projects, the construction technology is also maturing day by day.

44 High Performance Concrete Technology and Applications

through technical means results in green cementitious materials.

tures, there exists concrete freeze-thaw damage.

on the environment.

→ damage.

#### **2.1. Raw materials and preparation**

ASC material consists of a quaternary system (slag, activator, sand, stone), and the correct choice of raw material is especially important. Through investigation and analysis, this chapter ultimately determines the test raw materials as follows:

## **(1) Activator**

Type and dosage of activator have a great impact on ASC performance. Currently, there are Na2SiO3 or K2SiO3 water glass solution and NaOH or KOH solution, and alkali metal carbo‐ nates and alkaline earth metal chlorides, among which water glass is more widely used and has better properties.

In this study, the activator is composed of Na2SiO3 sodium silicate (27.21% SiO2, 8.14% Na2O, Ms = 3.1) and NaOH complex solution, which density was 1.43 g/cm3 .

## **(2) Blast furnace slag powder**

Blast furnace slag powder is a pig iron smelting slag discharged from the blast furnace. From the aspect of chemical composition, blast furnace slag belongs to silicate material, whose chemical compositions are mainly CaO, Al2O3, SiO2, and the content is generally above 90%. In addition, there are MgO, MnO, Fe2O3, CaS, FeS and TiO2 chemical compositions.

The metallurgy blast furnace slag powder used in this study has the specific surface area of 410 m2 /kg and density of 2.86 g/cm3 . The main chemical composition of slag powder is shown in **Table 1**.


**Table 1.** Chemical compositions of slag/w%.

According to GB/T 18046-2000 "Ground granulated blast furnace slag used for cement and concrete" [17], GB/T 18736-2002 "Mineral admixtures for high strength and high performance concrete" [18] and GB/T 12957/2005 "Test method for activity of industrial waste slag used as addition to cement" [19], 7 and 28 days activity indexes of the slag are 96.2% and 105.7%, which are high.

#### **(3) Fine aggregate**

Fine aggregate should be hard, durable, clean, with smooth grain shape, good gradation and suitable fineness modulus, and the impurity should be less than a predetermined value. Besides, the natural river sand should be preferred, because it is generally hard, with good grain shape and low clay content, which is beneficial to the fresh concrete workability and hardened concrete performance. When using artificial sand, it should paid attention that the content of coarse particles and small particles are not too high. Zone II river sand should be preferred in concrete preparation.

The role of fine aggregate in the ASC is similar to forkability and strengt with filling effect on the one hand, while being the bond between coarse aggregate and cementitious materials on the other hand. This chapter uses natural river sand with fineness modulus of 2.86, densi‐ ty of 2.63 g/cm3 , bulk density of 1.50 g/cm3 and 0.5% clay content. Gradation screening test‐ ing results are shown in **Table 2**.


**Table 2.** Fine aggregates screening test results.

#### **(4) Coarse aggregate**

**(1) Activator**

410 m2

in **Table 1**.

are high.

**(3) Fine aggregate**

has better properties.

**(2) Blast furnace slag powder**

/kg and density of 2.86 g/cm3

46 High Performance Concrete Technology and Applications

**Table 1.** Chemical compositions of slag/w%.

preferred in concrete preparation.

Type and dosage of activator have a great impact on ASC performance. Currently, there are Na2SiO3 or K2SiO3 water glass solution and NaOH or KOH solution, and alkali metal carbo‐ nates and alkaline earth metal chlorides, among which water glass is more widely used and

In this study, the activator is composed of Na2SiO3 sodium silicate (27.21% SiO2, 8.14% Na2O,

Blast furnace slag powder is a pig iron smelting slag discharged from the blast furnace. From the aspect of chemical composition, blast furnace slag belongs to silicate material, whose chemical compositions are mainly CaO, Al2O3, SiO2, and the content is generally above 90%.

The metallurgy blast furnace slag powder used in this study has the specific surface area of

According to GB/T 18046-2000 "Ground granulated blast furnace slag used for cement and concrete" [17], GB/T 18736-2002 "Mineral admixtures for high strength and high performance concrete" [18] and GB/T 12957/2005 "Test method for activity of industrial waste slag used as addition to cement" [19], 7 and 28 days activity indexes of the slag are 96.2% and 105.7%, which

Fine aggregate should be hard, durable, clean, with smooth grain shape, good gradation and suitable fineness modulus, and the impurity should be less than a predetermined value. Besides, the natural river sand should be preferred, because it is generally hard, with good grain shape and low clay content, which is beneficial to the fresh concrete workability and hardened concrete performance. When using artificial sand, it should paid attention that the content of coarse particles and small particles are not too high. Zone II river sand should be

The role of fine aggregate in the ASC is similar to forkability and strengt with filling effect on the one hand, while being the bond between coarse aggregate and cementitious materials on the other hand. This chapter uses natural river sand with fineness modulus of 2.86, densi‐

In addition, there are MgO, MnO, Fe2O3, CaS, FeS and TiO2 chemical compositions.

**CaO SiO2 Al2O3 MgO MnO Fe2O3 TiO2 Loss** 38.95 33.91 10.71 9.41 0.31 3.28 3.43 1.27

.

. The main chemical composition of slag powder is shown

Ms = 3.1) and NaOH complex solution, which density was 1.43 g/cm3

Coarse aggregates commonly used in concrete are gravel and pebbles. The coarse aggregate should be hard, durable, clean and has a certain gradation. The main technical requirements are as follows:


This chapter uses limestone gravel (45% 5–20 mm, 55% 20–40 mm) with density of 2.76 g/cm3 and bulk density 1.69 g/cm3 .

#### **2.2. Workability and strength test**

Test workability according to GB/T 50080-2002 "Standard for test method of performance on ordinary fresh concrete" [20]. The measuring method is as follows: Add the concrete mix ac‐ cording to the provided method into the standard tapered slump cone (bottomless). After the cone is filled elaborately, lift the cartridge straight up. The mixture will appear slump because of its own weight. Measure the size of the downward slump (mm), which is slump as liquidity indicator, as shown in **Figure 1**.

**Figure 1.** Determination of concrete mixture slump.

When measuring the fresh concrete slump, visually evaluate the following properties at the same time:


"A lot" means that there is much water separating out of the bottom after pulling up the slump cone; "small" indicates that a small amount of water comes from the cone after it is pulled up; and "no" means that no water penetrates from the cone even it is pulled up.

**Figure 2.** Wt60 t Universal Bending Test Machine and 200 t Compression Testing Machine.

According to GB/T 50081-2002 "Standard for test method of mechanical properties on ordinary concrete" [21], strength tests are carried out using wt60 and 200 t Universal Testing Machine (as shown in **Figure 2**). Test the specimen flexural and compressive strength after 7 and 28 days of curing.

## **3. ASC fracture properties under freeze-thaw cycles**

## **3.1. Fracture toughness parameter calculation method**

because of its own weight. Measure the size of the downward slump (mm), which is slump

When measuring the fresh concrete slump, visually evaluate the following properties at the

**1.** Cohesiveness: observe the mutual cohesion situation of the components. Use a tamper to tap on the concrete cone side already slumped, if the cone gradually sinks after tapping, the mixture cohesiveness is favorable; on the other hand, if the cone suddenly collapses,

**2.** Water retention: According to the condition of water saturating out of the mixture, there

"A lot" means that there is much water separating out of the bottom after pulling up the slump cone; "small" indicates that a small amount of water comes from the cone after it is pulled up;

partially crack or the stones segregate, it means that its cohesiveness is bad.

and "no" means that no water penetrates from the cone even it is pulled up.

**Figure 2.** Wt60 t Universal Bending Test Machine and 200 t Compression Testing Machine.

as liquidity indicator, as shown in **Figure 1**.

48 High Performance Concrete Technology and Applications

**Figure 1.** Determination of concrete mixture slump.

are three degrees as "a lot", "small" and "no".

same time:

Crack mouth opening displacement (CMOD) was measured directly using clip-on extensom‐ eter. The extensometer was connected to computer automatic acquisition system, through which loads could be obtained [22]—crack mouth opening displacement curve under loads, which is P-CMOD curve to get CMODC. At the same time, the test can also directly measure ASC load-displacement curve that is P-V curve, and take the load when the specimen fractures at ultimate load *P*max. After *P*max and CMODC are set, concrete effective fracture length; crack tip opening displacement CTOD; and stress intensity factors *KIC <sup>C</sup>* , *KIC <sup>Q</sup>* and *KIC <sup>S</sup>* from closure stress *σ*(*w*) can be calculated according to double-*K* fracture criterion and concrete fracture toughness calculation equations formulated by DL/T 5332-2005 "Norm for fracture test of hydraulic concrete" [23].

## *3.1.1. Calculation of critical effective fracture length aC*

Due to stable crack extension phase of concrete specimens before unstable fracture, the actual crack length is greater than the initial crack length before unstable fracture. It is difficult to accurately measure critical crack subcritical extension length Δ*aC* and load when the crack starts to expand (crack initiation load, corresponding to *KIC <sup>Q</sup>*). They are usually obtained with advanced testing technologies such as photoelastic patch. Therefore, they are more frequently got through calculation.

For the standard three-point bending beam (span-height ratio *S*/*h* = 3, hereinafter the same), the load *P* and CMOD has following relationship [24]:

$$\begin{cases} \,^cMOD = \frac{6PSa}{t\hbar E} F\_1(\alpha) \\\\ F\_1(\alpha) = 0.76 - 2.28a + 3.87a^2 - 2.04a^3 \frac{0.66}{\left(1 - \alpha\right)^2} \end{cases} \tag{1}$$

where *P* is load, *N*; *S* is the test piece beam span, m; *t* and *h* are the specimen width and height, m; *a* is the effective fracture length, m; CMOD is the crack mouth opening displacement corresponding to *P*, m; *α* is the effective fracture length and specimen height ratio, *a*/*h* and *E* is the concrete calculation elastic modulus, MPa.

Wherein the elastic modulus *E* is calculated according to formula (2):

$$E = \frac{1}{tC\_i} \left[ 3.70 + 32.6 \tan^2 \left( \frac{\pi}{2} \frac{a\_0 + h\_0}{h + h\_0} \right) \right] \tag{2}$$

Where *a*<sup>0</sup> is the initial crack degree, m; *h*<sup>0</sup> is the steel sheet thickness equipped on the clip-on extensometer, m; *Ci* = *Vi* /F*<sup>i</sup>* is an initial value of the specimen, *μm*/*kN*, which is calculated with *V*, *P* values of any point of straight line segments on curve rise.

Substitute *P*max and *CMODC* into formula (1) and get the nonlinear equation of *aC*. Through iteration, *aC* can be calculated, but the procedure is cumbersome. Literature [24] provides a simplified formula as follows:

$$CMOD = \frac{P}{Et} \left[ 3.70 + 32.60 \text{tg}^2 \left( \frac{\pi}{2} \alpha \right) \right] \tag{3}$$

Where the symbols have the same meaning as in Eqs. (1) and (2).

Calculations show that when 0.2≤*α*≤0.75, the maximum relative error between formula (3) and formula (1) is 2%. Therefore, *aC* can be calculated according to formula (3):

$$a\_c = \frac{\pi}{2} h a \text{rectg} \sqrt{\frac{Et}{32.6P} \text{C} MOD\_c - 0.1135} - h\_0 \tag{4}$$

#### *3.1.2. Calculation of stress intensity factor KIC C caused by closure stress*

Because of the cracks stable expansion phase before concrete unstable fracture, according to the fictitious crack model, when the crack opening displacement *w* is smaller than *w*<sup>0</sup> (*w*0 is the opening displacement when cracks cannot transfer stress), it can still pass the stress σ(*w*), which is called closure stress. Therefore, in addition to external loads, there also exists the closure stress preventing crack propagation in three-point bending beam. Stress intensity factor caused by closure stress σ(*w*) at the crack tip is denoted as *KIC <sup>C</sup>* . Shilang X et al. derived standard threepoint bending beam specimen *KIC <sup>C</sup>* calculation formula based on fictitious crack model [25]:

$$K\_{\mathcal{K}}^{\mathcal{C}} = \int\_{a\_0}^{a} \frac{2}{\sqrt{\pi a}} \sigma(u) F(u, v) d\mathbf{x} \ (a \le a\_c) \tag{5}$$

$$F(u, \nu) = \frac{3.52(1 - u)}{(1 - u)^{\frac{\lambda'}{2}}} - \frac{4.35 - 5.28u}{(1 - \nu)^{\frac{\lambda'}{2}}} + \left[\frac{1.30 - 0.30u^{\frac{\lambda'}{2}}}{(1 - u^{\frac{\nu}{2}})^{\frac{\lambda'}{2}}} + 0.83 - 1.76u\right][1 - (1 - u)\nu]$$

Fracture Theory Under Freeze-Thaw Cycles and Freeze-Thaw Resistance of Alkali-Slag Concrete http://dx.doi.org/10.5772/63810 51

$$\frac{\sigma(\mu)}{f\_l} = \beta + (1 - \beta) \frac{\mu - \frac{\nu\_0}{\nu}}{1 - \frac{\nu\_0}{\nu}}$$

2 0 0

2

p

é ù æ ö + = + ê ú ç <sup>+</sup> <sup>ë</sup> <sup>÷</sup> *<sup>i</sup>* <sup>è</sup> øû

Where *a*<sup>0</sup> is the initial crack degree, m; *h*<sup>0</sup> is the steel sheet thickness equipped on the clip-on

Substitute *P*max and *CMODC* into formula (1) and get the nonlinear equation of *aC*. Through iteration, *aC* can be calculated, but the procedure is cumbersome. Literature [24] provides a

<sup>2</sup> 3.70 32.60

Calculations show that when 0.2≤*α*≤0.75, the maximum relative error between formula (3) and

Because of the cracks stable expansion phase before concrete unstable fracture, according to the fictitious crack model, when the crack opening displacement *w* is smaller than *w*<sup>0</sup> (*w*0 is the opening displacement when cracks cannot transfer stress), it can still pass the stress σ(*w*), which is called closure stress. Therefore, in addition to external loads, there also exists the closure stress preventing crack propagation in three-point bending beam. Stress intensity factor caused

<sup>2</sup> () (,) ( )

3.52(1 ) 4.35 5.28 1.30 0.30 (,) 0.83 1.76 [1 (1 ) ]

é ù -- - =- + ê ú + - -- - - - ë û *uuu Fuv u uv*

*IC c*

*<sup>K</sup> u F u v dx a a <sup>a</sup>* s

33 1 2 2 2 2

ë

formula (1) is 2%. Therefore, *aC* can be calculated according to formula (3):

2 32.6 *C C*

*Et a harctg CMOD <sup>h</sup> P*

*<sup>P</sup> CMOD tg Et*

é ù = + ê ú

<sup>1</sup> 3.70 32.6tan

extensometer, m; *Ci*

simplified formula as follows:

= *Vi*

50 High Performance Concrete Technology and Applications

*V*, *P* values of any point of straight line segments on curve rise.

Where the symbols have the same meaning as in Eqs. (1) and (2).

p

by closure stress σ(*w*) at the crack tip is denoted as *KIC*

0

p

(1 ) (1 ) (1 )

*u v u*

*a*

*a C*

*3.1.2. Calculation of stress intensity factor KIC*

point bending beam specimen *KIC*

*a h <sup>E</sup> tC h h*

0

/F*<sup>i</sup>* is an initial value of the specimen, *μm*/*kN*, which is calculated with

2

p

æ ö ç ÷ è øû

a

<sup>0</sup> 0.1135

*C caused by closure stress*

= - - (4)

*<sup>C</sup>* calculation formula based on fictitious crack model [25]:

<sup>=</sup> £ ò (5)

3 2

(3)

*<sup>C</sup>* . Shilang X et al. derived standard three-

(2)

$$\beta = \frac{\sigma\_s(CTOD\_c)}{f\_l} \\ CTOD\_c = CMOD\_c \left\{ (1 - \beta)^2 + (1.081 - 1.149\alpha)(\beta - \beta^2) \right\}^{1/2}$$

$$\sigma\_S(CTOD\_C) = f\_i \left[ 1 + \left( C\_1 \frac{CTOD\_C}{w\_0} \right)^3 \right] \exp\left( -C\_2 \frac{CTOD\_C}{w\_0} \right) - \frac{CTOD\_C}{w\_0} \left( 1 + C\_1^3 \right) \exp\left( -C\_2 \right),$$

In the formula, *u* = *x*/*a*; *v* = *a*/*h*; *a* is the effective fracture length, m; *x* is the distance from integral point to initial crack tip, m; *ft* is concrete tensile strength, MPa, generally take *ft* = 0.95 *fSP* [26]; β = *a*0/*ac*; *CTODC* is the crack tip critical level opening displacement, m; *C*1 and *C*2 are concrete material constant; and w0 is the crack opening displacement when transfer stress is zero, mm, and is relevant with concrete characteristics such as strength.

Since the integral nonlinearity and integral singularity when *u* = 1, the above *KIC <sup>C</sup>* calculation process becomes very complicated. Literature [27] simplified it as follows: make *F* (*u*, *v*)= *A*⋅*u* + *B* + 1 / 1−*u* <sup>2</sup> , then the simplified *KIC <sup>C</sup>* calculation method is given as follows:

$$K\_{K}^{C} = 2\sqrt{\frac{a}{\pi}} \times \left[\frac{A \cdot D}{3} u^{3} + \frac{A \cdot F + C \cdot D}{2} u^{2} + C \cdot F \cdot u - D\sqrt{1 - u^{2}} + F \cdot \arcsin(u)\right]\_{\frac{v\_{0}}{v}}^{v} \tag{6}$$

Where *v*<sup>0</sup> <sup>=</sup>*a*<sup>0</sup> / *<sup>h</sup>* ; *<sup>A</sup>*<sup>=</sup> 2.23*<sup>v</sup>* <sup>2</sup> <sup>+</sup> 1.16*<sup>v</sup>* <sup>+</sup> 0.17 (1 − *v*) 1.5 ;*<sup>C</sup>* <sup>=</sup> 1.65*<sup>v</sup>* <sup>2</sup> <sup>+</sup> 1.67*<sup>v</sup>* <sup>+</sup> 0.24 (1 − *v*) 1.5 ;*<sup>D</sup>* <sup>=</sup> *<sup>f</sup> <sup>t</sup>* <sup>−</sup> *<sup>σ</sup><sup>s</sup> <sup>v</sup>* <sup>−</sup> *<sup>v</sup>*<sup>0</sup> *<sup>v</sup>*; *<sup>F</sup>* <sup>=</sup> *<sup>v</sup>σ<sup>s</sup>* <sup>−</sup> *<sup>v</sup>*<sup>0</sup> *<sup>f</sup> <sup>t</sup> <sup>v</sup>* <sup>−</sup> *<sup>v</sup>*<sup>0</sup> and the other symbols are the same as defined above.

Paper [28] points out that when CTOD = CTODC, *C*1, *C*2 and *w*0 values have little effect on *KIC <sup>C</sup>* , and *C*<sup>1</sup> = 3, *C*<sup>2</sup> = 7 and *w*<sup>0</sup> = 0.16 mm are generally preferable for concrete. Qijin Zhang also calculated *C*<sup>1</sup> = 3, *C*<sup>2</sup> = 7 and *w*<sup>0</sup> = 0.16 mm; *C*<sup>1</sup> = 2, *C*<sup>2</sup> = 6 and *w*<sup>0</sup> = 0.14 mm; and *C*<sup>1</sup> = 4, *C*<sup>2</sup> = 8 and *w*0 = 0.18 mm through experiments, to verify the impact degree of changing these three parameters on *KIC <sup>C</sup>* . Results show that, using different *C*1, *C*<sup>2</sup> and *w*0, the calculated *KIC <sup>C</sup>* was close to each other [29]. Therefore, this paper directly takes *C*1 = 3, *C*2 = 7 and *w*0 = 0.16 mm.

#### *3.1.3. Calculation of initiation toughness KIC Q and unstable fracture toughness KIC S*

The formula in [25] derived computational formula of *KIC <sup>S</sup>* with the boundary collocation method: for the standard three-point bending beam specimen, *KIC <sup>S</sup>* can be calculated as follows: 1

*F*

$$\begin{aligned} K\_{\stackrel{\text{AC}}{\text{C}}}^S &= \frac{1.5 P\_{\text{max}} S}{t h^2} \sqrt{a\_c} F\_1(a) \\\\ \sigma(a) &= \frac{1.99 - \alpha (1 - \alpha)(2.15 - 3.93\alpha + 2.7\alpha^2)}{(1 + 2\alpha)(1 - \alpha)} \end{aligned} \tag{7}$$

$$P\_{\text{max}} = F\_{\text{max}} + \frac{mg}{2} \times 10^{-2}$$

Where *P*max is the ultimate load, kN; *F*max is the maximum load, KN; *m* is the mass between specimen seats, kg; *g* is the acceleration of gravity, 9.81 m/s2 ; *S* is the beam span, m; and *α* is the critical effective fracture length and specimen height ratio, *ac*/*h*.

Thus, the following is obtained:

$$K\_{\rm \mathcal{K}}^{\mathcal{Q}} = K\_{\rm \mathcal{K}}^{\mathcal{S}} - K\_{\rm \mathcal{K}}^{\mathcal{C}} \tag{8}$$

Thus, according to Eq. (7), concrete *KIC <sup>S</sup>* can be calculated; *KIC <sup>C</sup>* is calculated according to formula (6); and then *KIC <sup>Q</sup>* is obtained according to Eq. (8).

In addition, DL/T 5332-2005 "Norm for fracture test of hydraulic concrete" also gives *KIC Q* calculation formula similar to formula (7). Only when calculating *KIC <sup>Q</sup>*, a is taken as *a*0, *F* is for the crack initiation load *FQ*, *α* is the initial crack length and specimen height ratio *a*0/*h*, namely

$$K\_{\rm IC}^{\mathcal{Q}} = \frac{1.5 \left( F\_{\mathcal{Q}} + \frac{m \mathbf{g}}{2} \times 10^{-2} \right) \mathbf{S}}{t \hbar^2} \sqrt{a\_0} F\_{\mathbf{i}}(a) \tag{9}$$

$$F\_{\mathbb{I}}(\alpha) = \frac{\mathbb{I}.99 - \alpha(\mathbb{I} - \alpha)(2.15 - 3.93\alpha + 2.7\alpha^2)}{\left(\mathbb{I} + 2\alpha\right)(\mathbb{I} - \alpha)^{3/2}}$$

In the formula, initiation load *F*Q transforms into corresponding load of elected segment turning point. A large number of experiments show that most of the turning point is in the range of (0.6∼0.9)*F*max.

#### **3.2. RSM model analysis**

Most structures in cold regions of northern China are under the impact of low temperature and freeze-thaw action, resulting in freeze-thaw damage. Freezing and thawing have a significant impact on the safety and durability of concrete structures in cold regions. There are lots of researches about effect of freeze-thaw cycles on Portland cement, but study on ASC performance degradation under freezing and thawing is still insufficient. In this study, the development law of ASC fracture properties under freezing and thawing is studied. According to ASC fracture parameters before and after freeze-thaw cycles: double-*K* fracture toughness *KIC <sup>Q</sup>* and *KIC <sup>S</sup>* , CMOD and effective fracture length test, sol ratio, slag content and age are selected as parameters, and *KIC <sup>Q</sup>*, *KIC <sup>S</sup>* , CMODC and ac are response values. Using RSM and BBD methods, influence law and degree of parameters and their interaction on ASC fracture parameters before and after freeze-thaw cycles are investigated. With Design-Expert 7.0 statistical analysis software, the regression equation prediction model is obtained, and response surface is analyzed, whose effects on ASC fracture properties are obtained.

With many specimens, the test duration time is long. In order to ensure the relationship between material strength and fracture toughness, concrete strength measurement is carried out with fracture tests.

## *3.2.1. RSM principles and advantages*

max 2 1 1.5 ( ) *<sup>S</sup> IC c P S <sup>K</sup> a F th* <sup>=</sup>

aa

2 *max mg P F* - = +´

Where *P*max is the ultimate load, kN; *F*max is the maximum load, KN; *m* is the mass between

*<sup>S</sup>* can be calculated; *KIC*

In addition, DL/T 5332-2005 "Norm for fracture test of hydraulic concrete" also gives *KIC*

the crack initiation load *FQ*, *α* is the initial crack length and specimen height ratio *a*0/*h*, namely

2

1.99 (1 )(2.15 3.93 2.7 ) ( ) (1 2 )(1 )


In the formula, initiation load *F*Q transforms into corresponding load of elected segment turning point. A large number of experiments show that most of the turning point is in the

Most structures in cold regions of northern China are under the impact of low temperature and freeze-thaw action, resulting in freeze-thaw damage. Freezing and thawing have a

a

2 0 1

<sup>2</sup> ( )

a

 a

 a 2

 a

1.99 (1 )(2.15 3.93 2.7 ) ( ) (1 2 )(1 )


a

max 10

1

a

specimen seats, kg; *g* is the acceleration of gravity, 9.81 m/s2

Thus, the following is obtained:

Thus, according to Eq. (7), concrete *KIC*

(6); and then *KIC*

range of (0.6∼0.9)*F*max.

**3.2. RSM model analysis**

the critical effective fracture length and specimen height ratio, *ac*/*h*.

*<sup>Q</sup>* is obtained according to Eq. (8).

*Q IC*

*F*

a

calculation formula similar to formula (7). Only when calculating *KIC*

1.5 10

æ ö ç ÷ + ´ è ø <sup>=</sup> *Q*

1 3/2

aa

*mg F S K a F th*

*F*

52 High Performance Concrete Technology and Applications

a

3/2

2

 a  a

(7)

; *S* is the beam span, m; and *α* is

*<sup>C</sup>* is calculated according to formula

(9)

*<sup>Q</sup>*, a is taken as *a*0, *F* is for

*Q*

2

 a

*QSC KKK IC IC IC* = - (8)

In examining the impact of multivariate on concrete performance, other factors are usually fixed, while changing a single factor. Although certain effect could be received, the test amount is large and it is unable to investigate the interaction among various factors. RSM was proposed by Box and Wilson [30] in 1951, which is a combination of mathematical and statistical methods, which obtains certain data with reasonable experimental design and tests. The functional relationship between factor and response value is fitted using multiple quadratic regression equation, and the optimal process parameters are found through regression analysis, so RSM is a statistical method for solving multivariate problems.

This method is mainly used to analyze the response of interest affected by a number of variables through modeling and analysis, which can combine random and deterministic simulation problems together more easily. In this way, influence of each variable on indicators (response) in the experiment will be reflected, and the impact of interactions between variables can also be reflected, whose inner relationship is revealed with a perspective view. The ultimate aim is to optimize the response, becoming suitable for solving issues related to nonlinear data processing.

As a new experimental optimization and data processing method, RSM includes experimental design, modeling, model suitability testing, finding the best combination of conditions, and many other testing and statistical techniques that can be very suitable for experimental design and response surface analysis on experimental results.

Through process regression and response surface, contour line drawing, the response corre‐ sponding to each factor level can be easily obtained. Based on the response value of each factor level, the predicted optimal response value and corresponding experimental condi‐ tion can be found, thus obtaining experimental optimal conditions ultimately.

Compared with traditional mathematical statistical methods (linear regression analysis and orthogonal design), RSM has a clear advantage in comparison. Although regression equation between the factors and response value can be obtained with experimental data through linear regression analysis, a large amount of data is required, costing much time and effort. It discusses the impact of only one factor and cannot consider the combined effect of several factors; orthogonal design focuses on scientific and reasonable arrangement for the test; and several factors may be considered at the same time and the best combination of factor levels can be found. But only isolated experimental points can be analyzed for orthogonal design, then preferred combination can only be selected from preset several experimental levels. As a result, a clear function expression, namely the regression equation between the factor and response value, cannot be given on the entire region.

The optimal condition obtained is not in the true sense, which can only be the ideal condition, so the optimal factor combination and response value cannot be given on the entire region. The RSM can consider a number of factors that affect the product at different levels; using experimental data, optimal combination problem affected by many factors can be solved through mathematical model, which is more effective than single factor analysis. Since rational experimental design is adopted, taking into account test random error, a comprehensive study on experiments with little time and small number of experiments can be conducted.

During optimization of experimental conditions, each level of experiment can be analyzed continuously. If processing response surface analysis on the experimental data is obtained, the forecasting model will generally be a curved surface, that the forecasting model is obtained continuously and then the best combination of each factor and optimal response on the entire area can be obtained.

Meanwhile, RSM fits unknown complex function on a small area with a linear or quadratic polynomial model, which has relatively simple calculation, and the obtained regression equation has higher precision.

## *3.2.2. Optimization content and procedure*

RSM optimization is usually divided into three parts:


Specific steps of RSM optimization are as follows:

Compared with traditional mathematical statistical methods (linear regression analysis and orthogonal design), RSM has a clear advantage in comparison. Although regression equation between the factors and response value can be obtained with experimental data through linear regression analysis, a large amount of data is required, costing much time and effort. It discusses the impact of only one factor and cannot consider the combined effect of several factors; orthogonal design focuses on scientific and reasonable arrangement for the test; and several factors may be considered at the same time and the best combination of factor levels can be found. But only isolated experimental points can be analyzed for orthogonal design, then preferred combination can only be selected from preset several experimental levels. As a result, a clear function expression, namely the regression equation between the factor and

The optimal condition obtained is not in the true sense, which can only be the ideal condition, so the optimal factor combination and response value cannot be given on the entire region. The RSM can consider a number of factors that affect the product at different levels; using experimental data, optimal combination problem affected by many factors can be solved through mathematical model, which is more effective than single factor analysis. Since rational experimental design is adopted, taking into account test random error, a comprehensive study

During optimization of experimental conditions, each level of experiment can be analyzed continuously. If processing response surface analysis on the experimental data is obtained, the forecasting model will generally be a curved surface, that the forecasting model is obtained continuously and then the best combination of each factor and optimal response on the entire

Meanwhile, RSM fits unknown complex function on a small area with a linear or quadratic polynomial model, which has relatively simple calculation, and the obtained regression

**1.** Experimental design: there are many experimental design methods for response surface analysis, the most commonly used are Central Composite Design (CCD), Box-Behnken Design (BBD) and Plackett-Burman Design (PBD); experimental design factors may be

**2.** Analysis: complete corresponding statistical analysis such as nonlinear data fitting variance analysis, to obtain the corresponding surface equation, and evaluate the fitting

**3.** Optimization: in this module, optimization requirements can be set up, such as the highest value, lowest value or others; the software automatically calculates the optimal experi‐ ment value, and provides one or more experimental conditions under optimal results.

on experiments with little time and small number of experiments can be conducted.

response value, cannot be given on the entire region.

54 High Performance Concrete Technology and Applications

area can be obtained.

equation has higher precision.

encoded or not coded.

result and effectiveness.

*3.2.2. Optimization content and procedure*

RSM optimization is usually divided into three parts:


According to the fitting equation obtained, a response surface plot can be used to obtain the optimum value; equation solving method can also be used to obtain the optimum value. In addition, using some of the data processing software, the optimal results can be easily obtained. Statistical analysis softwares often used are SAS, SPSS and Design-Expert.

The optimization result obtained from response surface analysis is a prediction, which needs to be verified through experiments. If the corresponding prediction and experimental results are consistent according to predicted experimental conditions, then the response surface optimization analysis is successful; otherwise, it is needed to change the response surface equation, or reselect reasonable experimental factors and levels.

#### *3.2.3. Data processing software Design-Expert*

As the world's top-level experimental design software, Design-Expert is the easiest to use and most complete with best affinity. In RSM optimization test papers already published, Design-Expert is the most widely used software. Design-Expert software is a handy business software for response surface optimization, and it is very convenient to use in experimental design and data processing. Although not as powerful as SAS, Design-Expert can be easily used in CCD or BBD response surface analysis, the quadratic polynomial surface analysis can be accessed very well and the data processing requirements can be satisfied. Some of the operations are more convenient than SAS, and the three-dimensional effect is more intuitive. The optimiza‐ tion results analyzed with RSM can be automatically obtained by the software, without solving surface equation with mathematical tools like MATLAB.

During process of using the software, in order to access the experimental condition predictive value with relative accurate optimal results, the decimal digits of factor level can be set as two or more. Of course, the number of effective digits under actual experimental conditions should also be taken into account in setting the effective number of bits.

With the improvement of computer performance, RSM has become an optimization technique with high-precision, wide application and practical value. It is mainly used in three aspects [31, 32]: (1) describing the impact of a single test variable on response values; (2) determining the relationship between variables; and (3) describing the combined effects of all variables on response value.

Thus, RSM can be used in agriculture, biotechnology, food, chemistry, manufacturing and other fields, which has already been widely used in the optimization design, reliability analysis and calculation, kinetics, engineering process control and other aspects. RSM has become an effective way to reduce development costs, optimize processing conditions, improve product quality and solve practical problems in production process. But it has been rarely applied in civil engineering, even less in concrete. Therefore, this section briefly describes the RSM application principles, advantages and steps, hoping to help more researchers use RSM technology, for convenient and effective solution in the design and data processing problems, especially hoping to make RSM more widely used in concrete engineering.



**Table 3.** Levels of factors of RSM.

Fracture Theory Under Freeze-Thaw Cycles and Freeze-Thaw Resistance of Alkali-Slag Concrete http://dx.doi.org/10.5772/63810 57


**Table 4.** BBD test design and the results.

During process of using the software, in order to access the experimental condition predictive value with relative accurate optimal results, the decimal digits of factor level can be set as two or more. Of course, the number of effective digits under actual experimental conditions should

With the improvement of computer performance, RSM has become an optimization technique with high-precision, wide application and practical value. It is mainly used in three aspects [31, 32]: (1) describing the impact of a single test variable on response values; (2) determining the relationship between variables; and (3) describing the combined effects of all variables on

Thus, RSM can be used in agriculture, biotechnology, food, chemistry, manufacturing and other fields, which has already been widely used in the optimization design, reliability analysis and calculation, kinetics, engineering process control and other aspects. RSM has become an effective way to reduce development costs, optimize processing conditions, improve product quality and solve practical problems in production process. But it has been rarely applied in civil engineering, even less in concrete. Therefore, this section briefly describes the RSM application principles, advantages and steps, hoping to help more researchers use RSM technology, for convenient and effective solution in the design and data processing problems,

**−1 0 1**

*<sup>S</sup>* **/MPa·m1/2** *CMODC***/mm** *aC***/mm**

especially hoping to make RSM more widely used in concrete engineering.

A/S A 0.54 0.56 0.58

Age/days C 28 60 92

*<sup>Q</sup>***/MPa·m1/2** *KIC*

 −1 −1 0 7.723353 11.93899 0.1257 68.3752 1 −1 0 4.322432 7.597456 0.1213 65.7866 1 0 −1 4.288812 7.586042 0.1212 65.7278 0 0 0 4.235751 7.546166 0.1207 65.4336 1 0 1 4.253227 8.028535 0.1152 62.1978 0 0 0 4.431611 8.196176 0.1162 62.7861 0 0 0 8.249791 12.45929 0.1293 69.9074 0 1 −1 4.199010 7.977579 0.1149 62.0213 −1 0 1 8.224674 12.43252 0.1291 69.8436

) B 0.40 0.42 0.44

**Factor Code Levels of code**

**)** *<sup>C</sup>***/***<sup>d</sup> KIC*

also be taken into account in setting the effective number of bits.

56 High Performance Concrete Technology and Applications

response value.

Slag content/(g/cm3

**Table 3.** Levels of factors of RSM.

**Test number Design of tests Test results** *A B***/(g/cm3**

#### *3.2.4. Verification of RSM model*

Setting *KIC <sup>S</sup>* as response, using Design-Expert software, BBD test data are used for quadratic regression according to **Tables 3** and **4**. Based on initial fitting equation, insignificant items are manually removed for optimization. Lack of fit of the model is ultimately determined as 0.84, the SNR value Adeq Precision is also high (142.350), showing that this model can be used to predict; Pred*R*<sup>2</sup> (0.9983) and Adj*R*<sup>2</sup> value (0.9993) difference is very small, indicating a high degree of the response surface equation optimization, which fits well. The regression model is as shown in Eq. (10):

$$\begin{aligned} K\_{\mathcal{K}}^{\mathcal{S}} &= 8.02 + 0.18A + 0.085B + 2.34C + 0.035AB \\ &+ 0.082AC + 0.093BC + 0.067B^2 + 1.82C^2 \end{aligned} \tag{10}$$

Variance analysis is done to the model and significance test is done to the regression coeffi‐ cients, as shown in **Tables 5** and **6**.


**Table 5.** Variance analysis of the model.


**Table 6.** Significance test of the regression coefficients.

#### **4. Influences of freeze-thaw on** *KIC <sup>S</sup>* **under different slag content**

Influence of freeze-thaw on *KIC <sup>S</sup>* under different slag content is shown in **Figure 3**.

Various factors may result in the material deterioration and failure of concrete as described above, and the seriousness caused depends to a great extent on the porosity and permeability of internal texture of concrete itself [33, 34]. Generally, if the compactness of a concrete structure is poor or its internal porosity is considerable, more possibly various liquids and gases penetrate into its interior with more quantity and larger depth, than the carbonation layer, and chemical corrosion of concrete and the rust of reinforcement is accelerated, even the liquid can pass easily through the structure.

**Figure 3.** Influence of freeze-thaw on *KIC <sup>S</sup>* under different slag content.

The main factors having influence on texture and porosity of concrete are water-cement ratio (or water-binder ratio); kind and fineness of cement; kind of aggregate; producing quality and curing condition. Producing quality and curing condition can be paid attention during construction, but the first three factors are mainly influenced by material characteristic itself.

ASC has a compact structure, which is able to well resist penetration of water and air. Since the strength enhancement of ASC tends to grow at a relatively slow speed, when it is exposed to freeze-thaw cycles, ASC could continue to form hardened structure, which is beyond the destroying speed. Therefore, ASC could be a desirable material to resist carbonation as well as freeze-thaw attack in concrete structures.

## **5. Conclusions**

**Regression coefficient Standard deviation Lower confidence**

**Table 6.** Significance test of the regression coefficients.

58 High Performance Concrete Technology and Applications

**4. Influences of freeze-thaw on** *KIC*

Influence of freeze-thaw on *KIC*

pass easily through the structure.

**Figure 3.** Influence of freeze-thaw on *KIC*

**limit of 95%** 

*<sup>S</sup>* **under different slag content**

*<sup>S</sup>* under different slag content is shown in **Figure 3**.

Various factors may result in the material deterioration and failure of concrete as described above, and the seriousness caused depends to a great extent on the porosity and permeability of internal texture of concrete itself [33, 34]. Generally, if the compactness of a concrete structure is poor or its internal porosity is considerable, more possibly various liquids and gases penetrate into its interior with more quantity and larger depth, than the carbonation layer, and chemical corrosion of concrete and the rust of reinforcement is accelerated, even the liquid can

*<sup>S</sup>* under different slag content.

*A* 0.18 0.017 0.14 0.22 <0.0001 *B* 0.085 0.017 0.045 0.12 0.0011 *C* 2.34 0.017 2.30 2.38 <0.0001 *AB* 0.035 0.024 −0.021 0.092 0.1837 *AC* 0.082 0.024 0.026 0.14 0.0096 *BC* 0.093 0.024 0.037 0.15 0.0052 *B*<sup>2</sup> 0.067 0.024 0.012 0.12 0.0223 *C*<sup>2</sup> 1.82 0.024 1.76 1.87 <0.0001

**Upper confidence limit of 95%** 

*P* **value**


## **Acknowledgements**

The author wishes to express his gratitude and sincere appreciation to the National Natural Science Fund [Grant Number: 51578540] for financing this research work and several ongoing research projects related to the properties of ASC.

## **Author details**

Qixuan Li

Address all correspondence to: liqixuan19921210@163.com

Air Force Engineering University, Xi'an, China

## **References**


[8] Kim SW, Jang SJ, Kang DH, Ahn KL, Yun HD. Mechanical properties and eco-efficiency of steel fiber reinforced alkali-activated slag concrete. Mater 2015; 8(11): 7309–7321. doi: 10.3390/ma8115383.

**Acknowledgements**

**Author details**

Qixuan Li

**References**

research projects related to the properties of ASC.

60 High Performance Concrete Technology and Applications

Address all correspondence to: liqixuan19921210@163.com

1519–1523. doi:10.1016/S0008-8846(99)00097-6.

2016; 28(2). doi:10.1061/(ASCE)MT.1943-5533.0001406.

Air Force Engineering University, Xi'an, China

10.1016/j.jclepro.2015.06.026.

j.conbuildmat.2015.08.009.

J 2015; 112(6): 791–800.

12909. doi:10.1016/j.ceramint.2015.06.131.

The author wishes to express his gratitude and sincere appreciation to the National Natural Science Fund [Grant Number: 51578540] for financing this research work and several ongoing

[1] Sun W, Zhang YM, Yan HD, Mu R. Damage and damage resistance of high strength concrete under the action of load and freeze-thaw cycles. Cem Concr Res 1999; 29(9):

[2] Shojaei M, Behfarnia K, Mohebi R. Application of alkali-activated slag concrete in railway sleepers. Mater Des 2015; 69: 89–95. doi:10.1016/j.matdes.2014.12.051.

[3] Ren WB, Xu JY, Bai EL. Strength and ultrasonic characteristics of alkali-activated fly ash-slag geopolymer concrete after exposure to elevated temperatures. J Mater Civ Eng

[4] Mithun BM, Narasimhan MC. Performance of alkali activated slag concrete mixes incorporating copper slag as fine aggregate. J Clean Prod 2016; 112: 837–844. doi:

[5] Gao Y, Xu JY, Bai EL, Luo X, Zhu JS, Nie LX. Static and dynamic mechanical properties of high early strength alkali activated slag concrete. Ceram Int 2015; 41(10): 12901–

[6] Okoye FN, Durgaprasad J, Singh NB. Mechanical properties of alkali activated flyash/ Kaolin based geopolymer concrete. Constr Build Mater 2015; 98: 685–691. doi:10.1016/

[7] Torres-Carrasco M, Tognonvi MT, Tagnit-Hamou A, Puertas F. Durability of alkaliactivated slag concretes prepared using waste glass as alternative activator. ACI Mater

