# Creep Properties of Axially Compressed Fly Ash Concrete under Sulfate Corrosion

Authors: Jian Cao; Ziyang Han; Zhifeng Du
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

Creep, sulfate erosion resistance, fly ash content of concrete, and sustained compression load are important factors that will affect the long-term performance of concrete. It is of great interest to combine these effects together to make a comprehensive investigation of fly ash concrete. However, the concrete creep under both sustained compression load and sulfate attack conditions has rarely been reported. To obtain the creep characteristics of fly ash concrete in a sulfate environment, this paper first finishes the creep experiments of fly ash concrete under sustained compression load and sulfate attack. The test factors include the load stress level, the concentration of sulfate solution, and the content of fly ash. Based on the creep mechanism of fly ash concrete under sulfate erosion, the relationship between time-dependent section area variation and creep was carried out. After comparing different creep models, the creep calculation model of fly ash concrete under sulfate erosion was built via the B4 model combined with the cross-sectional area of the damaged layer and undamaged layer of concrete. Finally, comparing the calculated values with the test results, the calculated results were in good agreement with the test data, which is of practical significance to the practical engineering application and the improvement of structural reliability.


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## Body

## 1. Introduction

The sulfate resistance of concrete has always been a widespread concern in concrete civil engineering. In the corrosive environment, there is a chemical reaction between the concrete and the eroding material [1], which produces a kind of needle-like crystal calcium vanadate with a larger volume than the original and causes expansive force in the concrete. With the increase of erosion time, the more erosion medium inside the concrete, the greater the expansive force and the microcracks are produced inside the concrete due to the expansive force [2]. With the increase of microcracks, the erosion rate and degree of erosion materials are accelerated, and the external surface of concrete shows the phenomenon of cracking or even denudation. In addition, it also involves concrete damage [3], sulfate ion diffusion in concrete [4].After fly ash is mixed into concrete, there are three major effects: morphological effect [5], activity effect [6], and microaggregate effect [7]. This will cause changes in the internal microstructure of the concrete. The substitution effect of fly ash will reduce the total cement hydration product. The secondary hydration of fly ash and cement hydration products will also have the same effect; because of the characteristics of high strength and high elastic modulus, the fly ash particles can be evenly distributed in the cement paste, preventing the mutual cohesion of cement particles, reducing the water consumption and the porosity after hardening decrease, so that the density can be improved. The addition of fly ash can have an effective impact on the performance of concrete [8] such as elastic modulus, compressive strength [9], and so on. At the same time, the content [10], type [11], and particle size [12] of fly ash will also have an effect on the properties of concrete. Nanda et al. [13] found that adding less than 30% fly ash into the concrete will improve the overall mechanical properties of concrete. The influence of mechanical properties will also lead to changes in the creep performance of concrete. Wang et al. [14] based on the B3 analysis model, studied the creep characteristics of concrete columns with or without fly ash. The results show that the creep of concrete columns with fly ash is smaller than that of concrete columns without fly ash.At present, Liu et al. [15] found the effect of fly ash content and slag on the corrosion resistance of concrete in the condition of a dry-wet cycle. The results showed that the deterioration of concrete under the dry-wet cycle is caused by the expansion of sulfate rather than chemical erosion. Torrenti et al. [16] carried out the creep test of concrete members under axial compression in ammonium nitrate solution. Then, he put forward a creep prediction model of concrete under nitrate ion erosion. Gong et al. [17] combined the sulfate resistance of concrete with the creep of concrete based on the B3 model. A creep model of sulfate-attacked concrete considering concrete damage was established. Zheng et al. [18] based on damage rheology theory, combined with the effects of moisture content and overstress; they established a creep model for water-bearing concrete. Zhang et al. [19] used a mesoscale approach to obtain a concrete creep model from a microscopic perspective based on a direct analysis of images.Actually, concrete creep is always accompanied by loads and environmental factors, which makes the deterioration law of the structure more complicated. At present, the B4 model is the latest and the authoritative calculation model for predicting concrete creep from Bazant. However, the effects of fly ash, load, and environmental factors are not considered in the model. Therefore, on the basis of the B4 model, the erosion effects of fly ash and sulfate are considered, and combined with the concrete damage theory, a creep calculation model of fly ash concrete under sulfate erosion is established. Then, the experimental scheme of creep performance of fly ash concrete under sulfate erosion is designed. Finally, the applicability of the model is verified and analyzed by comparing the calculated data with the experimental data.


## 2. Materials and Methods

To deeply understand the creep performance of fly ash concrete structures under sulfate erosion, experimental studies on concrete under different test conditions were carried out, which provided a basis for the construction of a creep calculation model of fly ash concrete under sulfate erosion.


### 2.1. Material Properties

In this experiment, the selection of raw materials mainly includes the following materials: The chemical composition of 42.5 sulfate cement in the Southern cement Plant is shown in Tables1 and 2 The fine aggregate is ordinary fine sand with good gradation, the apparent density is 2.61 g/m3 and the bulk density is 1.58 kg/m3; The coarse aggregate is the crushed stone produced by Cabo Company, Liuhe District, Nanjing, has a particle size gradation of 5 mm∼20 mm, an apparent density of 2.61 g/m3 and a bulk density of 1500 kg/m3; Fly ash is the grade I fly ash produced locally in Nanchang; Admixture is the naphthalene series superplasticizer produced by Fuyang Chengnan Building Materials Co., Ltd; Sulfate is the industrial anhydrous sodium sulfate produced by Jiangxi Fidelity Salinization Co., Ltd., Class II qualified products, the products meet the standard GB/T6009-2014.Table 1
Chemical composition of cement.
Chemical compositionSiO2Al2O3Fe2O3CaOMgOSO3LOSSMass fraction (%)22.076.144.3564.481.071.140.75Table 2
Cement physical and mechanical performance parameters.
Cement parametersParameter valuesDensity (kg/m3)3000Fineness (%)22.07StabilityqualifiedCompressive strength (3 d MPa)28.9Flexural strength (3 d MPa)61.1Compressive strength (28 d MPa)6.0Flexural strength (28 d MPa)9.8Initial setting time (min)90Final setting time (min)195


### 2.2. Test Apparatus and Procedure

Preparation of fly ash concrete specimen: first, raw materials such as cement, fly ash, slag, sand, stone, etc. Are dry stirred in a mixer for two minutes according to the component ratio; evenly mix the water-reducing agent and water, and slowly add the water reducing agent during the stirring process; the stirring process lasts for about three minutes. After the slump is measured, and the slump meets the requirements, the prism of 100 mm × 100 mm × 300 mm and a cube specimen of 100 mm × 100 mm × 100 mm are cast. The benchmark concrete strength grade is set to C40; the stress level is set at 20%; Load holding time is set to 28 d; the fly ash content is set at 0%, 20%, and 40%. The concentration (mass percentage) of sulfate solution is set at 3%, 6%, and 9%. The load holding time is set to 90d. Among them, there are 3 specimens in each group, including two creep specimens and one shrinkage reference specimen. At the same time, 6 cubic specimens with a side length of 100 mm are produced in each batch of specimens, 3 as elastic modulus specimens and 3 as strength specimens. To more intuitively reflect the influence of sulfate attack on concrete performance, it is necessary to set up a control group to compare the specimens soaked in a sodium sulfate solution. In this experiment, a control group without sodium sulfate solution was arranged, which considered the creep effect of load holding time on concrete, and set it as 14 d and 28 d, the loading time as 90 d, and the fly ash content as 0%, 20%, and 40%. There are 6 groups in the experiment, with 4 specimens in each group, 2 as creep specimens and 2 as shrinkage reference specimens. The design is shown in Table3.Table 3
Test design.
GroupLoading time (d)Sulfate solution concentration (%)Fly ash content (%)190302906203909404903205906406909207903408906099090Preparation of coupling environment of load and sulfate erosion: for the way of applying load and the requirement of concrete specimen soaking in sulfate solution for a long time, combined with the actual conditions, a new practical patented water creep meter see Figure1 is used, as a loading device to carry out the test loading instrument. The principle of this practical patented water creep meter as is follows: The loading mode is to tighten the nut to make the high-strength spring produce elastic deformation according to Hooke's law. The long-term load on the concrete specimen is applied by the high-strength nut. The concrete specimen is placed in the solution container and the configured sulfate solution is added inside.Figure 1
Schematic diagram of loading of underwater creep meter.Observation and collection of data: the strain gauge is pasted on the surface of the specimen before loading, the resistance strain gauge is connected by a half-bridge, and the test data are collected by observing the resistance strain gauge. See Figure2 for the specific method.Figure 2
Half-bridge method measuring instrument and method.


### 2.3. Basic Creep Model

At present, it is widely recognized and used in practical engineering all over the world, including the CEB2010 series model [20], GL2000 model [21], ACI209 model [22], B3 model [23], and B4 model [24]. Among them, the physical meaning of each parameter of the B3 model is clear, and the prediction accuracy is good. More importantly, this model is a linear combination of influencing factors and time, and stable optimization parameters can be obtained in the fitting process. The B4 model is a new model based on the B3 model, which considers more parameters than the B3 model, such as fly ash, mineral powder, additives, etc. The prediction accuracy is also improved compared with the B3 model.The main research objects in this paper are fly ash content, time, sulfate concentration, and other factors. Therefore, the B4 model with more comprehensive and accurate parameters is selected as the basic creep model.The addition and content of fly ash will generate a significant impact on the properties of concrete. From the chemical composition of fly ash and cement, the addition of fly ash changes the colloid content, water-binder ratio, and strength of concrete. Therefore, on the basis of the original B4 model, the effects of fly ash, water-binder ratio, and colloid content are considered. Three correction coefficient functions are added to modify the original B4 model.:γ1,γ2, andγ3before each parameter. Because of the creep performance of fly ash concrete in sulfate environment, the dry creep and shrinkage strain are ignored when modeling. Modified calculation formula of basic creep model of fly ash concrete:(1)Jt^,t′^=γ1q1+C0t^,t^0,C0t^,t^0=γ2q2Qt^,t′^+γ3q3lnt−t′0.1+1+q4lntt′^.Where Jt^,t′^ is the concrete creep function, including elastic strain and creep strain; q1 is the instantaneous creep compliance; C0t^,t^0is the basic creep function; t^ is the calculation age of concrete creep after considering temperature correction; t′^ is the loading age after considering temperature correction; t^0 is the age after temperature correction considering the drying; γ1 is the parameter function that takes into account the effect of fly ash content on the modulus of elasticity; γ2 is the parametric function considering the influence of water-binder ratio;γ3 is the parameter function considering the effects of aggregate colloid ratio and water-binder ratio number.Researchers obtained the creep test data of different fly ash content and they are all creep curves. Creep model regression needs corresponding experimental data for regression analysis. Therefore, the data from those creep curves are used to calculate the values in the B4 model, and the SPSS software is used to regress the formula. The weighted regression of the experimental data of the researchers [25, 26] obtainsγ1,γ2, andγ3:(2)γ1=0.775+0.845E28−2.98,γ2=5.554+12.893wb−0.842,γ3=8.611+5.272a/b−3.389wb1.5.The regression coefficient residual square sumR2 is more than 0.8, which is consistent with the test data and has certain applicability. The modified B4 model can objectively reflect the creep of foundation concrete mixed with fly ash.


### 2.4. Sulfate Erosion Damage of Concrete under Compression

The diffusion law of sulfate ions can be fitted by Fick's second law. Because this law is subject to some limitations, it requires that the diffusive material does not react with the internal material during diffusion. However, the erosion of sulfate ions on concrete is caused by the chemical reaction with the internal material of concrete. At the same time, the complex external environment (load, duration, etc.) of a concrete structure can significantly affect the erosion rate of sulfate ions in concrete. Therefore, the effects of erosion concentration, time, and stress level on sulfate erosion rates are considered. The second law of Fick is modified, and its diffusion coefficient is as follows:(3)D=a′⋅tb′⋅expc′⋅σfcd′ne′+f′+g′⋅SVh′.Where t is the erosion time; fc is the stress level; n is the sulfate solution concentration; S/V is the component-specific surface area; a′、b′、c′、d′、e′、f′、g′、h′ are the constants related to erosion depth and erosion time, stress level, sulfate solution concentration, and component-specific surface area.Sulfate corrosion of concrete is a long-term process from surface to interior. With the development of corrosion age, the proportion of damaged sections of concrete in the cross-sectional area of the whole member increases gradually. This process can be expressed by the damage degree in the damage creep theory of concrete:α=Ad/Ac.Where Adand Acare the cross-sectional area of the damaged layer and the cross-sectional area of the undamaged layer. Combined with the sulfate diffusion model, the results can be obtained: Ad=∫0tDdt . Then, α=∫0tDdt/A−∫0tDdt Where A is the total cross-sectional area of the component.When the sulfate-eroded concrete members are loaded, the load on the concrete members is borne by both the internal uneroded damaged concrete and the damaged layer concrete. The damaged layer and the undamaged core of concrete are divided into two parts. The internal force distributed along the section is supposed toN . The damaged layer and the undamaged layer bear the stress load together, and the internal force distribution see Figure 3.Figure 3
Internal force distribution in section.The balance of the two stress loads:(4)N=Nc+Nd,N=σc1Ac+σd1Ad.WhereNis the total load; Ncis the load on undamaged concrete; Ndis the load on concrete in damaged layer;σc1is the stress acting on core undamaged concrete in initial stage; σd1 is the stress acting on the damage layer in the initial stage.


### 2.5. Creep Model of Fly Ash Concrete under Sulfate Erosion

The stress changeσd1c on the damaged layer concrete is used to measure the erosion of fly ash concrete, and then combined with the B4 model to build a new calculation model to calculate its creep.Coordination condition by deformation:(5)εc1=εd1.Then:(6)nσc1−2μcp=σd1+2αμdp.Where n is the ratio of elastic modulus of the damage layer to the elastic modulus of core concrete, n=Ed/Ec.According to radial deformation coordination conditions:(7)εc2=εd2.Then,(8)n1−μcp−μcσc1=−μdσd1−2αp.Organize the equations:(9)p=μc−μd−2μcμd−μc+1−2/αnμd1+μd⋅σc0.Where μc is the poisson ratio of undamaged layer concrete; μd is the poisson ratio of damaged layer concrete; α is the damage degree of concrete members, α=Ad/Ac;n is the ratio of elastic modulus of damaged layer to undamaged part, n=Ed/Ec;σc0 is the initial stress on the undamaged part of the concrete.Orderp=qσc0and then:(10)q=μc−μd−2μcμd−μc+1−2/αnμd1+μd.According to the creep theory of concrete under multiaxial stress [27], the effective axial creep Poisson ratio of core concreteμcp,1:(11)μcp,1=0.16−0.037q+0.007q2.The degree of axial creepc1 under uniaxial stress is obtained:(12)c1=cσc11−μcp,1q.Where c is the creep of concrete under uniaxial stress; σc1 is the axial stress of concrete under uniaxial stress.For the damaged layer and the undamaged layer, the internal force redistributes after the axial compression load, and there is no load on the outside.(13)Ncc+Ndc=0.Where Ncc=σc1cAc,σc1cis the increment of axial stress on core concrete; Nd1c=σd1cAd,σd1c denotes the increment of axial stress on damaged concrete.The increased elastic strain on the damage layer is as follows:(14)εd1c=1Edσd1c+2αμdΔp.Where εd1c is the strain increment on the damaged layer after creep; Δp is the increment of internal stress after creep.Under the action of stress, the core concrete produces creep:(15)εc1c=c1σ0+σc1cc1.According to (5), consider the effect of transverse deformation:(16)εd2c=−μdEdσd1c−2αΔp.Radial creep of undamaged concrete under maximum compression:(17)εc2c=c2p+Δp.Radial creep of concrete:(18)c2=cσ1p−μcp,2p+σc1.In (18), the lateral effective Poisson's ratio of undamaged concrete:(19)μcp,2=0.16−0.0341+1/q+0.0071+1/q2.Combined (7):(20)p+Δpc2=−μdEdσd1c−2αΔp.And then the combined (5):(21)σ0−σc1c=1Edσd1c+2αμdΔp.The stress change on the damaged layer concrete after creep is obtained:(22)σd1c=1−qc2Ed/Edc2−2μd/α+Edc11/α−2/αμdμd/α−qc2Ed/Edc2−2μd/α+Edc1⋅σ0.Finally, combined with the modified B4 model, the creep formula of fly ash concrete under sulfate erosion can be obtained:(23)εd1c=σd1c⋅Jt,t0.


## 2.1. Material Properties

In this experiment, the selection of raw materials mainly includes the following materials: The chemical composition of 42.5 sulfate cement in the Southern cement Plant is shown in Tables1 and 2 The fine aggregate is ordinary fine sand with good gradation, the apparent density is 2.61 g/m3 and the bulk density is 1.58 kg/m3; The coarse aggregate is the crushed stone produced by Cabo Company, Liuhe District, Nanjing, has a particle size gradation of 5 mm∼20 mm, an apparent density of 2.61 g/m3 and a bulk density of 1500 kg/m3; Fly ash is the grade I fly ash produced locally in Nanchang; Admixture is the naphthalene series superplasticizer produced by Fuyang Chengnan Building Materials Co., Ltd; Sulfate is the industrial anhydrous sodium sulfate produced by Jiangxi Fidelity Salinization Co., Ltd., Class II qualified products, the products meet the standard GB/T6009-2014.Table 1
Chemical composition of cement.
Chemical compositionSiO2Al2O3Fe2O3CaOMgOSO3LOSSMass fraction (%)22.076.144.3564.481.071.140.75Table 2
Cement physical and mechanical performance parameters.
Cement parametersParameter valuesDensity (kg/m3)3000Fineness (%)22.07StabilityqualifiedCompressive strength (3 d MPa)28.9Flexural strength (3 d MPa)61.1Compressive strength (28 d MPa)6.0Flexural strength (28 d MPa)9.8Initial setting time (min)90Final setting time (min)195


## 2.2. Test Apparatus and Procedure

Preparation of fly ash concrete specimen: first, raw materials such as cement, fly ash, slag, sand, stone, etc. Are dry stirred in a mixer for two minutes according to the component ratio; evenly mix the water-reducing agent and water, and slowly add the water reducing agent during the stirring process; the stirring process lasts for about three minutes. After the slump is measured, and the slump meets the requirements, the prism of 100 mm × 100 mm × 300 mm and a cube specimen of 100 mm × 100 mm × 100 mm are cast. The benchmark concrete strength grade is set to C40; the stress level is set at 20%; Load holding time is set to 28 d; the fly ash content is set at 0%, 20%, and 40%. The concentration (mass percentage) of sulfate solution is set at 3%, 6%, and 9%. The load holding time is set to 90d. Among them, there are 3 specimens in each group, including two creep specimens and one shrinkage reference specimen. At the same time, 6 cubic specimens with a side length of 100 mm are produced in each batch of specimens, 3 as elastic modulus specimens and 3 as strength specimens. To more intuitively reflect the influence of sulfate attack on concrete performance, it is necessary to set up a control group to compare the specimens soaked in a sodium sulfate solution. In this experiment, a control group without sodium sulfate solution was arranged, which considered the creep effect of load holding time on concrete, and set it as 14 d and 28 d, the loading time as 90 d, and the fly ash content as 0%, 20%, and 40%. There are 6 groups in the experiment, with 4 specimens in each group, 2 as creep specimens and 2 as shrinkage reference specimens. The design is shown in Table3.Table 3
Test design.
GroupLoading time (d)Sulfate solution concentration (%)Fly ash content (%)190302906203909404903205906406909207903408906099090Preparation of coupling environment of load and sulfate erosion: for the way of applying load and the requirement of concrete specimen soaking in sulfate solution for a long time, combined with the actual conditions, a new practical patented water creep meter see Figure1 is used, as a loading device to carry out the test loading instrument. The principle of this practical patented water creep meter as is follows: The loading mode is to tighten the nut to make the high-strength spring produce elastic deformation according to Hooke's law. The long-term load on the concrete specimen is applied by the high-strength nut. The concrete specimen is placed in the solution container and the configured sulfate solution is added inside.Figure 1
Schematic diagram of loading of underwater creep meter.Observation and collection of data: the strain gauge is pasted on the surface of the specimen before loading, the resistance strain gauge is connected by a half-bridge, and the test data are collected by observing the resistance strain gauge. See Figure2 for the specific method.Figure 2
Half-bridge method measuring instrument and method.


## 2.3. Basic Creep Model

At present, it is widely recognized and used in practical engineering all over the world, including the CEB2010 series model [20], GL2000 model [21], ACI209 model [22], B3 model [23], and B4 model [24]. Among them, the physical meaning of each parameter of the B3 model is clear, and the prediction accuracy is good. More importantly, this model is a linear combination of influencing factors and time, and stable optimization parameters can be obtained in the fitting process. The B4 model is a new model based on the B3 model, which considers more parameters than the B3 model, such as fly ash, mineral powder, additives, etc. The prediction accuracy is also improved compared with the B3 model.The main research objects in this paper are fly ash content, time, sulfate concentration, and other factors. Therefore, the B4 model with more comprehensive and accurate parameters is selected as the basic creep model.The addition and content of fly ash will generate a significant impact on the properties of concrete. From the chemical composition of fly ash and cement, the addition of fly ash changes the colloid content, water-binder ratio, and strength of concrete. Therefore, on the basis of the original B4 model, the effects of fly ash, water-binder ratio, and colloid content are considered. Three correction coefficient functions are added to modify the original B4 model.:γ1,γ2, andγ3before each parameter. Because of the creep performance of fly ash concrete in sulfate environment, the dry creep and shrinkage strain are ignored when modeling. Modified calculation formula of basic creep model of fly ash concrete:(1)Jt^,t′^=γ1q1+C0t^,t^0,C0t^,t^0=γ2q2Qt^,t′^+γ3q3lnt−t′0.1+1+q4lntt′^.Where Jt^,t′^ is the concrete creep function, including elastic strain and creep strain; q1 is the instantaneous creep compliance; C0t^,t^0is the basic creep function; t^ is the calculation age of concrete creep after considering temperature correction; t′^ is the loading age after considering temperature correction; t^0 is the age after temperature correction considering the drying; γ1 is the parameter function that takes into account the effect of fly ash content on the modulus of elasticity; γ2 is the parametric function considering the influence of water-binder ratio;γ3 is the parameter function considering the effects of aggregate colloid ratio and water-binder ratio number.Researchers obtained the creep test data of different fly ash content and they are all creep curves. Creep model regression needs corresponding experimental data for regression analysis. Therefore, the data from those creep curves are used to calculate the values in the B4 model, and the SPSS software is used to regress the formula. The weighted regression of the experimental data of the researchers [25, 26] obtainsγ1,γ2, andγ3:(2)γ1=0.775+0.845E28−2.98,γ2=5.554+12.893wb−0.842,γ3=8.611+5.272a/b−3.389wb1.5.The regression coefficient residual square sumR2 is more than 0.8, which is consistent with the test data and has certain applicability. The modified B4 model can objectively reflect the creep of foundation concrete mixed with fly ash.


## 2.4. Sulfate Erosion Damage of Concrete under Compression

The diffusion law of sulfate ions can be fitted by Fick's second law. Because this law is subject to some limitations, it requires that the diffusive material does not react with the internal material during diffusion. However, the erosion of sulfate ions on concrete is caused by the chemical reaction with the internal material of concrete. At the same time, the complex external environment (load, duration, etc.) of a concrete structure can significantly affect the erosion rate of sulfate ions in concrete. Therefore, the effects of erosion concentration, time, and stress level on sulfate erosion rates are considered. The second law of Fick is modified, and its diffusion coefficient is as follows:(3)D=a′⋅tb′⋅expc′⋅σfcd′ne′+f′+g′⋅SVh′.Where t is the erosion time; fc is the stress level; n is the sulfate solution concentration; S/V is the component-specific surface area; a′、b′、c′、d′、e′、f′、g′、h′ are the constants related to erosion depth and erosion time, stress level, sulfate solution concentration, and component-specific surface area.Sulfate corrosion of concrete is a long-term process from surface to interior. With the development of corrosion age, the proportion of damaged sections of concrete in the cross-sectional area of the whole member increases gradually. This process can be expressed by the damage degree in the damage creep theory of concrete:α=Ad/Ac.Where Adand Acare the cross-sectional area of the damaged layer and the cross-sectional area of the undamaged layer. Combined with the sulfate diffusion model, the results can be obtained: Ad=∫0tDdt . Then, α=∫0tDdt/A−∫0tDdt Where A is the total cross-sectional area of the component.When the sulfate-eroded concrete members are loaded, the load on the concrete members is borne by both the internal uneroded damaged concrete and the damaged layer concrete. The damaged layer and the undamaged core of concrete are divided into two parts. The internal force distributed along the section is supposed toN . The damaged layer and the undamaged layer bear the stress load together, and the internal force distribution see Figure 3.Figure 3
Internal force distribution in section.The balance of the two stress loads:(4)N=Nc+Nd,N=σc1Ac+σd1Ad.WhereNis the total load; Ncis the load on undamaged concrete; Ndis the load on concrete in damaged layer;σc1is the stress acting on core undamaged concrete in initial stage; σd1 is the stress acting on the damage layer in the initial stage.


## 2.5. Creep Model of Fly Ash Concrete under Sulfate Erosion

The stress changeσd1c on the damaged layer concrete is used to measure the erosion of fly ash concrete, and then combined with the B4 model to build a new calculation model to calculate its creep.Coordination condition by deformation:(5)εc1=εd1.Then:(6)nσc1−2μcp=σd1+2αμdp.Where n is the ratio of elastic modulus of the damage layer to the elastic modulus of core concrete, n=Ed/Ec.According to radial deformation coordination conditions:(7)εc2=εd2.Then,(8)n1−μcp−μcσc1=−μdσd1−2αp.Organize the equations:(9)p=μc−μd−2μcμd−μc+1−2/αnμd1+μd⋅σc0.Where μc is the poisson ratio of undamaged layer concrete; μd is the poisson ratio of damaged layer concrete; α is the damage degree of concrete members, α=Ad/Ac;n is the ratio of elastic modulus of damaged layer to undamaged part, n=Ed/Ec;σc0 is the initial stress on the undamaged part of the concrete.Orderp=qσc0and then:(10)q=μc−μd−2μcμd−μc+1−2/αnμd1+μd.According to the creep theory of concrete under multiaxial stress [27], the effective axial creep Poisson ratio of core concreteμcp,1:(11)μcp,1=0.16−0.037q+0.007q2.The degree of axial creepc1 under uniaxial stress is obtained:(12)c1=cσc11−μcp,1q.Where c is the creep of concrete under uniaxial stress; σc1 is the axial stress of concrete under uniaxial stress.For the damaged layer and the undamaged layer, the internal force redistributes after the axial compression load, and there is no load on the outside.(13)Ncc+Ndc=0.Where Ncc=σc1cAc,σc1cis the increment of axial stress on core concrete; Nd1c=σd1cAd,σd1c denotes the increment of axial stress on damaged concrete.The increased elastic strain on the damage layer is as follows:(14)εd1c=1Edσd1c+2αμdΔp.Where εd1c is the strain increment on the damaged layer after creep; Δp is the increment of internal stress after creep.Under the action of stress, the core concrete produces creep:(15)εc1c=c1σ0+σc1cc1.According to (5), consider the effect of transverse deformation:(16)εd2c=−μdEdσd1c−2αΔp.Radial creep of undamaged concrete under maximum compression:(17)εc2c=c2p+Δp.Radial creep of concrete:(18)c2=cσ1p−μcp,2p+σc1.In (18), the lateral effective Poisson's ratio of undamaged concrete:(19)μcp,2=0.16−0.0341+1/q+0.0071+1/q2.Combined (7):(20)p+Δpc2=−μdEdσd1c−2αΔp.And then the combined (5):(21)σ0−σc1c=1Edσd1c+2αμdΔp.The stress change on the damaged layer concrete after creep is obtained:(22)σd1c=1−qc2Ed/Edc2−2μd/α+Edc11/α−2/αμdμd/α−qc2Ed/Edc2−2μd/α+Edc1⋅σ0.Finally, combined with the modified B4 model, the creep formula of fly ash concrete under sulfate erosion can be obtained:(23)εd1c=σd1c⋅Jt,t0.


## 3. Results and Discussion

The calculated data of the modified creep calculation model of fly ash concrete under sulfate erosion are compared with the experimental values, and the results see in Figures4∼6.Figure 4
Comparison of calculation and experimental results, experimental conditions: 0% fly ash specimen in 3% sulfate solution.Figure 5
Comparison of calculation and experimental results, experimental conditions: 20% fly ash specimen in 6% sulfate solution.Figure 6
Comparison of calculation and experimental results, experimental conditions: 40% fly ash specimen in 9% sulfate solution.It can be seen from Figure4 that the creep value calculated by the creep prediction model is in good agreement with the measured value of a 0% fly ash specimen in a 3% sulfate solution and can accurately reflect the development trend of concrete creep. When the holding age is 0–10 days, the calculated value of the model is good for the prediction of creep, and the maximum deviation is 4.73% at 10 days. After that, the predicted value of creep is smaller than the measured value. The maximum deviation was 14.21% in 90 days.It can be seen from Figure5 that the creep values calculated by the creep prediction model are in good agreement with the measured values of 20% fly ash specimens in a 6% sulfate solution and can accurately reflect the development trend of concrete creep. When the holding age is 0–10 days, the calculated value of the model is good for the prediction of creep, and the maximum deviation is 2.24% at 10 days. And the deviation increases gradually, the maximum deviation is 30–70 days and 18.56%. After 70 days, the deviation is slightly reduced; the 90-day deviation is 14.75%, which means the predicted value of creep is larger than the measured value.It can be seen from Figure6 that the creep values calculated by the creep prediction model are in good agreement with the measured values of 40% fly ash specimens in 9% sulfate solution and can accurately reflect the development trend of concrete creep. When the holding age is 0–10 days, the calculated value of the model is good for the prediction of creep, and the deviation value is 3.86% at 10 days. After that, the deviation increases gradually, and the maximum deviation in 10–70 days is 21.54% in 30 days. The deviation decreased slightly after 70 days, the deviation value at 90 days was 10.54, and the predicted value of creep was larger than the measured value.The results show that the modified creep model under sulfate erosion can be used to predict the creep of concrete under sulfate erosion, but due to the limitation of test conditions and time, the model is suitable for cases where the concentration of sulfate solution is less than 10%, the content of fly ash is less than 30%, the stress level is between 20% and 40%, and the initial and middle stage of creep.


## 4. Conclusion

At present, the ordinary concrete creep model cannot be directly used to predict the creep of fly ash concrete under the coupling action of load and sulfuric acid. The B4 model is a new model based on B3 model. Compared with the B3 model, more factors such as fly ash, mineral powder, additives, etc., are considered in the B4 model. The prediction accuracy is also improved compared with the B3 model. Its most important feature is that other creep models can be obtained by modification combining the relation between time-dependent section area variation and creep, modified Fick's second law, and the B4 model. The creep model of fly ash concrete under axial compression and sulfate erosion is proposed. Compared with the experimental results, the calculated values of the modified model are in good agreement with the experimental results. The prediction model can not only be used in the creep prediction of concrete in water conservancy buildings in coastal areas or inland areas with a high content of erosive substances (salt lakes, etc.), but also in the durability performance analysis of fly ash concrete. It could be helpful in future projects.Due to the limitation of test conditions and time, the creep test in this paper is only 90 days, which shows that the calculation accuracy of this model is good in predicting the early and middle stages of creep of fly ash concrete under sulfate erosion. As for the long-term creep performance of fly ash concrete under sulfate erosion, the creep performance of fly ash concrete under sulfate erosion needs to be further considered.



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*Source: 6307740-2022-09-12.xml*