# Experimental Study on Physicochemical and Mechanical Properties of Mortar Subjected to Acid Corrosion

Authors: Runke Huo; Shuguang Li; Yu Ding
Journal: Advances in Materials Science and Engineering
 (2018)

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## Abstract

The 28 days cured cement mortar samples were soaked in HCl (pH = 1 and 2) and H2O (pH = 7) solutions for 90 days. By monitoring the ion concentration of H+ and Ca2+ and measuring the changes in weight loss, longitudinal wave velocity, and uniaxial compressive strength values of the corroded mortar, the physicochemical and mechanical properties of the mortar specimens were studied. Experimental results indicate that the process of the mortar sample subjected to HCL erosion has apparent stage characteristics. In the initial stage of corrosion, the chemical reaction increased the porosity of the specimen, which leads to the decrease of longitudinal wave velocity of the samples. At the same time, the corrosion solution continuously penetrates into the mortar pore system, which leads to the increase of the mass, and it is considered that the diffusion process plays a leading role during this period. Moreover, the colloidal compounds generated by the chemical reaction can not only fill the pore space but also block the continuous reaction, which led to the increase of the longitudinal wave velocity of the specimen. With the prolonging of corrosion time and infiltration path, the pH value and the concentration of Ca2+ tend to be stable, the diffusion action is weakened, and the chemical reaction is continuous, which led to the decrease of the mass and wave velocity gradually. It is considered that the chemical reaction plays a leading role in this process. Based on the induction and analysis of the test results, a generalized porosity model regarding the increase of the porosity and the decrease of effective bearing area of the mortar sample was proposed. The relation between the uniaxial compressive strength and the corrosion time of the corroded mortar is deduced, and the unknown parameters are determined based on the regression analysis of the test data.


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## Body

## 1. Introduction

Currently, chemical attacks are widely known as one of the most significant issues concerning the construction industry. The ACI committee (2001) reported several types of chemical attacks such as acid attacks, alkali attacks, chloride ingress, carbonation, and sulfate attacks [1]. All of these chemical attacks deteriorate the overall properties of cementitious materials [2–4]. The extensive acid medium makes concrete susceptible to acid attacks. Usually, the contaminated groundwater and industrial wastewater were considered to be the main reasons for deteriorating concrete’s life. However, natural environments may also cause acid attacks on concrete structures. Acid attacks possess serious damage to the concrete structures. Many structures lose their serviceability every year due to the acidic environments [5–9]. This has led researchers to explore the deterioration properties of the acid solution of the concrete structure to find out an effective way to protect them [10]. Brown and Clifton [11] studied the mechanism of deterioration in cement-based materials and lime mortar. Sersale et al. [12] indicated that acid precipitation with a pH level ranging between 3.0 and 5.0 would affect cement and concrete. After that, a lot of literature focused on the different aspects of acid corrosion mortar matrix materials. Hu et al. [13] analyzed the change of chemical compositions and mineral compositions in hydrated cement paste which mixed with slag, fly ash, and SBR under the simulated acid rain condition. The results indicate that the acid rain attacking is an unceasing dissolution process of hydrating products such as Ca(OH)2, C-S-H gel, hydrated calcium aluminate, and hydrated calcium ferrite gel. Fan et al. [14] studied the material property of concrete under acid rain environment quantitatively. Results of concrete corrosion depth, mass loss, compressive strength, and elastic modulus were statistically analyzed and modeled. Yang et al. [15] studied the change of mortar properties in the strong acid environment. The study showed that weight loss could not accurately reflect the performance change of mortar in an acid environment, and multiple indexes are needed. Franzoni and Sassoni [16] investigated the correlation between stone microstructural characteristics and material degradation (regarding weight loss) in given environmental conditions. Song and Zhang [17] proposed a theoretical reaction rate model based on concentration boundary layer theory, and the applicability of the model was verified by the experimental data. Fan and Luan [18] indicated that the pore structure has a significant effect on the mechanical response and durability of concrete. The variation law of acoustic characteristics of sandstone in acid solution was studied by Huo et al. [19]. Experimental results showed that the acid corrosion rate of sandstone presented a certain stage characteristics. Xie et al. [20], Li et al. [21], Wei [22], and Chen et al. [23] studied the corrosion resistance of different types of cement mortar and their corrosion mechanism comprehensively. It has been found that deterioration of cementitious material specimens under acid rain attack was mainly caused by the coupling of H+ and SO42−, which led to higher porosity, and weight and strength loss of cementitious materials.Reviewing the literature, it is apparent that the acid solution has an evident influence on cementitious materials. However, most of the current research is based on the sulfuric acid-based acid solution on the corrosion of concrete materials. Actually, hydrochloric acid corrosion of mortar materials is also an integral part of the study [24, 25]. Against this background, in this paper, the physical (mass and wave velocity), chemical (ion concentration), and mechanical properties of the Ordinary Type II Portland cement which is corroded by different pH values (pH = 1 and 2) of hydrochloric acid solution, distilled water solution (pH = 7) as a reference, are systematically studied. The corrosion process of mortar attacked by hydrochloric acid was explored. The mechanism of mortar attacked by hydrochloric acid was discussed. The relationship between compressive strength and time was deduced based on the generalized porosity model. Regression analysis indicates that the strength formula based on the model addressed in this study has high prediction accuracy.


## 2. Experimental Program

### 2.1. Materials

Ordinary Type II Portland cement complying with GB175-2007 [26] was used as the primary cementing material in this study. Tables 1 and 2 summarize the main features. The natural river sand obtained from Xi’an Chang River, China, was used as fine aggregate. The river sand fine aggregate has a particle size of less than 2.5 mm. The particle size distribution of river sand fine aggregate is shown in Table 3.Table 1
The chemical compositions of cement (%).
Sample
SiO2
Al2O3
CaO
Fe2O3
MgO
SO3
K2O
Na2O
Loss of ignition
Cement
19.58
7.12
63.48
3.22
2.64
2.33
0.49
0.23
2.97Table 2
The physical properties of cement.
Sample
Specific gravity (g/cm3)
Blaine fineness (cm2/g)
Compressive strength (MPa)
3 d
28 d
Cement
3.06
3489
17.58
43.65Table 3
The particle size distribution of fine aggregate.
Sieve size (mm)
0.16
0.32
0.63
1.25
2.5
Cumulative pass amount (%)
0
5
35
75
100The acidic environment was simulated by using hydrochloric acid (pH = 1 and 2) and the distilled water (pH = 7) as a reference.


### 2.2. Fabrication of Mortar Samples

Ninety cubic mortar samples (70.7 × 70.7 × 70.7 mm3) were made at a water/cement material mass ratio (w/c) of 0.485 with a sand-to-cement ratio (s/c) of 3.0. Table 4 summarizes the range of density, longitudinal wave velocity, and porosity of samples. All samples were processed similarly according to JGJ/T 98-2011 [27] standards. The mortars were cast into molds and kept in plastic sheeting for 24 h to avoid the evaporation of water. After removing the specimens from the molds, they were cured in a curing room for 28 days at a temperature of 20 ± 2°C and relative humidity not less than 95%. Then, mortar specimens were naturally dried in a cool dark place for several days.Table 4
The physical properties of mortar.
Sample
Density (g/cm3)
Wave velocity (m/s)
Porosity (%)
Mortar
2.04∼2.12
3918∼4159
13.52∼14.16


### 2.3. Test Methods

Before soaking in the solutions, the specimens were dried in an electric oven at 105°C for 24 h, and then, the initial dry weight, longitudinal wave velocity, and compressive strength were recorded. After that, the specimens were soaked in groups in HCl (pH = 1 and 2) and H2O (pH = 7) solutions. There were three samples in each group. Reagent bottle with a volume of 10 L was used to avoid evaporation. The solution was renewed every ten days. The wet weight and longitudinal wave velocity of each sample were measured every ten days. The ion concentration of H+ and Ca2+ of the acidic media was monitored every 3, 7, and 10 days. Uniaxial compression strength following GB/T17671-1999 [28] of the specimens after being subjected to acid attack was tested at 10, 20, 30, 40, 50, 60, 70, 80, and 90 days. Before the compression strength test, all the specimens were cured in the curing room at a temperature of 20 ± 2°C and relative humidity not less than 95% for seven days. To get precise data, the tests results appeared in this paper are the average value of one group (three samples).


## 2.1. Materials

Ordinary Type II Portland cement complying with GB175-2007 [26] was used as the primary cementing material in this study. Tables 1 and 2 summarize the main features. The natural river sand obtained from Xi’an Chang River, China, was used as fine aggregate. The river sand fine aggregate has a particle size of less than 2.5 mm. The particle size distribution of river sand fine aggregate is shown in Table 3.Table 1
The chemical compositions of cement (%).
Sample
SiO2
Al2O3
CaO
Fe2O3
MgO
SO3
K2O
Na2O
Loss of ignition
Cement
19.58
7.12
63.48
3.22
2.64
2.33
0.49
0.23
2.97Table 2
The physical properties of cement.
Sample
Specific gravity (g/cm3)
Blaine fineness (cm2/g)
Compressive strength (MPa)
3 d
28 d
Cement
3.06
3489
17.58
43.65Table 3
The particle size distribution of fine aggregate.
Sieve size (mm)
0.16
0.32
0.63
1.25
2.5
Cumulative pass amount (%)
0
5
35
75
100The acidic environment was simulated by using hydrochloric acid (pH = 1 and 2) and the distilled water (pH = 7) as a reference.


## 2.2. Fabrication of Mortar Samples

Ninety cubic mortar samples (70.7 × 70.7 × 70.7 mm3) were made at a water/cement material mass ratio (w/c) of 0.485 with a sand-to-cement ratio (s/c) of 3.0. Table 4 summarizes the range of density, longitudinal wave velocity, and porosity of samples. All samples were processed similarly according to JGJ/T 98-2011 [27] standards. The mortars were cast into molds and kept in plastic sheeting for 24 h to avoid the evaporation of water. After removing the specimens from the molds, they were cured in a curing room for 28 days at a temperature of 20 ± 2°C and relative humidity not less than 95%. Then, mortar specimens were naturally dried in a cool dark place for several days.Table 4
The physical properties of mortar.
Sample
Density (g/cm3)
Wave velocity (m/s)
Porosity (%)
Mortar
2.04∼2.12
3918∼4159
13.52∼14.16


## 2.3. Test Methods

Before soaking in the solutions, the specimens were dried in an electric oven at 105°C for 24 h, and then, the initial dry weight, longitudinal wave velocity, and compressive strength were recorded. After that, the specimens were soaked in groups in HCl (pH = 1 and 2) and H2O (pH = 7) solutions. There were three samples in each group. Reagent bottle with a volume of 10 L was used to avoid evaporation. The solution was renewed every ten days. The wet weight and longitudinal wave velocity of each sample were measured every ten days. The ion concentration of H+ and Ca2+ of the acidic media was monitored every 3, 7, and 10 days. Uniaxial compression strength following GB/T17671-1999 [28] of the specimens after being subjected to acid attack was tested at 10, 20, 30, 40, 50, 60, 70, 80, and 90 days. Before the compression strength test, all the specimens were cured in the curing room at a temperature of 20 ± 2°C and relative humidity not less than 95% for seven days. To get precise data, the tests results appeared in this paper are the average value of one group (three samples).


## 3. Results and Discussion

### 3.1. Analysis of Physical Properties of Mortar Subjected to Acid Corrosion

The physical properties of acid-corroded mortar are characterized by definition of mass change rate and wave velocity change rate.


#### 3.1.1. Mass Change Rate

The mass change rate of the acid-corroded mortar is defined as follows:(1)A=Mit−Mi0Mi0×100%,where A is the mass change rate of the mortar and Mi0 and Mit are the weight of the mortar before and after soaking in the acid solution, respectively.The resulting mass change rate of mortar samples in different concentrations (pH value) of solutions is shown in Figure1. It is observed in the figure that, in the first stage (0∼10 days) of soaking, the mass change rate of the specimen in three solutions increased rapidly. When the immersion corrosion reached 20 days, the mass change rate of the sample in H2O (distilled water) with pH = 7 reached the maximum value of 7.12% and then gradually stabilized. After 30 days of immersion corrosion, the mass change rate of the sample in HCl (hydrochloride) with pH = 1 and 2 reached the maximum value of 6.83% and 6.86%, respectively, and then decreased gradually. Moreover, it reduces faster in the solution of pH = 1 than that of pH = 2.Figure 1
Mass change rate (%) of the mortar specimens in solutions with different pH values.The results above demonstrate that the mass change rate of the mortar sample varies at different times in the solution with different pH values. Before the specimen reaches the maximum mass change rate, the dissolution of hydrochloric acid to mortar (chemical reaction) increases the connectivity of the porous system and the porosity of the sample, under the diffusion effect, and corrosion solution continues to penetrate into the porous spaces that were not accessible to water before acid attack, making the mass change rate of the mortar sample to increase. After the sample reaches the maximum mass change rate, it has sufficient time to react chemically with calcium hydroxide and calcium silicate hydrate in the mortar, which causes its weight to decrease gradually. Besides, the smaller the pH value (the stronger the acidity), the more the weight loss of the sample.


#### 3.1.2. Wave Velocity Change Rate

Wave velocity change rate of the acid-corroded mortar is defined as follows:(2)B=vit−vi0vi0×100%,where B is the wave velocity change rate of the mortar and vi0 and vit are the wave velocity of the mortar before and after soaking in the acid solution, respectively.Figure2 shows the wave velocity change rate (%) of the mortar specimens in solutions with different pH values. It is observed in the figure that, in the first stage (0∼10 days) of soaking in HCl solution with pH = 1, the reaction of the mortar specimen and acid solution increased the porosity of the specimen, and the chemical softening of the mortar skeleton resulted in the readjustment of the three-phase ratio of the solid, liquid, and gas phase, which reduced the longitudinal wave velocity of the mortar sample. The wave velocity change rate decreased to 10.2% after 10 days of corrosion. In the second stage (10∼20 days) of immersion, with the extension of the corrosion time and the infiltration path, the cement paste was solubilised by the acid solution and fill porous spaces that previously contained air and were not accessible to water. Moreover, colloidal compounds (silica, aluminum hydroxide, iron hydroxide, etc.) with strong adsorption capacity and compactness generated by the reaction blocked the contact between HCl solution and noncorroded mortar, the corrosion rate slowed down, and at the same time, the variation of the ratio of three-phase composition tends to improve. All this make the longitudinal wave velocity increase, and the wave velocity change rate increased to 18.6% on the 20th day. Then, the chemical reaction tends to stabilize, and the longitudinal wave velocity of the specimen decreases gradually.Figure 2
Wave velocity change rate (%) of the mortar specimens in solutions with different pH values.The changed law of wave velocity change rate of the sample in the HCl solution with pH = 2 was similar to that in the HCl solution with pH = 1. The wave velocity change rate reduced in the first stage (0∼10 days) and decreased to −10.20% on the 10th day and then, increased in the following two phases (10∼20 and 20∼30 days) with the maximum of 19.79% occurring on the 30th day, indicating that the chemical reaction rate slowed down in HCl solution with pH = 2 than that with pH = 1.Compared with the HCl solution, the wave velocity change rate of mortar soaked in the distilled water (pH = 7) was also monitored; it was found from the figure that the wave velocity changes rate of the samples reached its maximum value of 15.68% on the 20th day, and then, its change is stable basically.


#### 3.1.3. Discussion on the Mechanism of Wave Velocity Change of Acid-Corroded Mortar

Based on the Fermat Principle, Han et al. [29] established the relationship between the porosity and longitudinal wave velocity of saturated mortar and verified its applicability by experimental data. The relationship can be expressed as follows:(3)1vp=1−n0vm+n0vf,where vp is the measured longitudinal wave velocity of the saturated mortar, vm is the longitudinal wave velocity of the mortar particle skeleton, vf is the longitudinal wave velocity of the liquid in the mortar pores, and n0 is the porosity of the mortar.According to the above ideas, the present paper attempted to establish the relationship between longitudinal wave velocity and porosity of mortar subjected to acid corrosion. The following assumptions were made to simplify the analysis:(1)
The initial state of the mortar specimen is a two-phase medium composed of the solid matrix and porous, and the chemical corrosion does not make the mortar skeleton change in nature; that is,vm (5300 m/s in this paper) is unchanged before and after corrosion.(2)
It is considered that the volume of pores formed in the mortar after acid corrosion is wholly filled with acid solution, and the density of the acid solution is approximately equal to the density of water; that is,vf (1500 m/s in this paper) is unchanged.(3)
The acid-corroded mortar can be simplified as the corrosive zone and the noncorrosive zone, and the volume of the corrosive zone includes the volume of the pores increased by the chemical reaction. Also, it is affected by the decrease of pore volume due to the blocking effect of the colloidal compounds generated by the chemical reaction.(4)
It is considered that, before the corrosion time ofT, the reaction rate of mortar and hydrochloric acid is faster than that of formation of colloidal compounds, and during this period, the porosity of the mortar sample increases, which makes na>n0. After the corrosion time of T, the chemical reaction rate slows down, the formation rate of colloidal compounds accelerates, and the colloidal compounds produced by the chemical reaction will hinder the reaction between mortar and hydrochloric acid, and during this period, the porosity of the specimen decreases, which makes na<n0.According to (3) and the above assumptions, the relationship between the porosity and the longitudinal wave velocity of the acid corrosion mortar can be deduced as follows:(4)1vp1=1−navm+navf,where vp1 is the measured longitudinal wave velocity of the mortar after acid corrosion, vm is the longitudinal wave velocity of the mortar particle skeleton, vf is the longitudinal wave velocity of the acid solution, and na is the porosity of the mortar after soaking T days.Equation (3) minus (4) gets the following formula:(5)1vp−1vp1=1−n0vm+n0vf−1−navm+navf=na−n01vm−1vf.Due tovm>vf, the following equation can be obtained from formula (5) when na>n0:(6)1vp−1vp1<0,namely,vp1<vp.The results of (6) are a reasonable explanation of the phenomenon that the wave velocity change rate is negative on the 10th day (Figure 2) and the wave velocity decreases in acid solution.Due tovm>vf, the following equation can be obtained from formula (5) when na<n0:(7)1vp−1vp1>0,namely,vp1>vp.The results of (7) is a reasonable explanation of the phenomenon that the wave velocity change rate is positive on the 20th, 30th, 40th, 50th, 60th, 70th, 80th, and 90th day (Figure 2) and the wave velocity increases in acid solution.


### 3.2. Analysis of Chemical Properties of Mortar Subjected to Acid Corrosion

The chemical properties of acid corrosion mortar are analyzed by monitoring the concentration of hydrogen ions (pH value) and calcium ions in the soaking solution.Figures3(a) and 3(b) show the concentration curves of H+ and Ca2+ in HCl solution (pH = 1) at each stage (10 days), respectively. As observed in the Figure 3(a), in each stage (10 days), the pH value of the solution increases with the extension of immersion time. Within 0∼10 days, the pH values of the solution were 2.7, 6.9, and 7.2 at day 3, 7, and 10, respectively. The solution was neutral after day 7. Within 10∼20 days, the change law of the pH value is basically the same as that of 0∼10 days. However, the solution showed weak acidity on day 20. With the extension of soaking time, the acidity of the solution became stronger after the end of each stage (pH = 6.2, 6.0, 5.8, 5.5, 5.1, 4.9, and 4.6 and 4.1 at day 20, 30, 40, 50, 60, 70, 80, and 90). Figure 3(b) shows that the concentration of Ca2+ increased gradually within 0∼20 days, which is 0.1295 and 0.1437 mol/L at day 10 and 20, respectively. Then, the concentration of Ca2+ is about 0.045 mol/L after the end of each stage.Figure 3
Concentration curves of (a) H+ and (b) Ca2+ in HCl solution (pH = 1) at different periods.
(a)
(b)Figures4(a) and 4(b) show the concentration curves of H+ and Ca2+ in HCl solution (pH = 2) at each stage (10 days), respectively. It can be seen from Figure 4(a) that the solution became alkaline at day 3, which demonstrates the solubility of the colloidal compounds produced by the reaction is decreased, and that it is conducive to the formation of the colloid compounds. Figure 4(b) shows that the dissolution of Ca2+ in HCl solution with pH = 2 at each stage (10 days) is basically the same as that of pH = 1.Figure 4
Concentration curves of (a) H+ and (b) Ca2+ in HCl solution (pH = 2) at different periods.
(a)
(b)The concentration curves of H+ and Ca2+ in H2O solution (pH = 7) at different periods are shown in Figures 5(a) and 5(b) compared to HCl solution. The changed law of the pH value and the concentration of Ca2+ is basically the same as that of HCl solution. The solution became alkaline at day 3 (Figure 5(a)), and the pH is between 10 and 12, which demonstrates that the mortar itself is alkaline. The maximum value of Ca2+ appeared in 20∼30 days, and then, it stabled at about 0.00001 mol/L.Figure 5
Concentration curves of (a) H+ and (b) Ca2+ in H2O solution (pH = 7) at different periods.
(a)
(b)


### 3.3. Discussion on the Mechanism of Mortar Attacked by Hydrochloric Acid

The main chemical equation for the reaction of hydrochloric acid with mortar is as follows:(8)CaOH2+2HCl⟶CaCl2+2H2OxCaO⋅ySiO2⋅nH2O+2xHCl⟶xCa2++2xCl−+ySiOH4+x+n−2yH2OAs can be seen from the above reaction formula, due to the strong acid effect of HCl solution, a large number of calcium hydroxide is neutralized and produced a mass of calcium chloride with high solubility, resulting in the decomposition of hydrated calcium silicate in the mortar samples. Hydrochloric acid, on the contrary, reacts directly with hydrated calcium silicate. In this way, the gel of the mortar pore structure is considerably damaged, causing the increase of porosity and the decrease of effective bearing area of mortar samples, resulting in the deterioration of the physical and mechanical properties of the mortar samples.Through the observation of the experiment and the analysis of the test results, it is known that the interaction between hydrochloric acid and mortar can be regarded as a physicochemical process of multiphase. The process can be divided into three stages from the outside to the inside for the mortar sample subjected to hydrochloric acid corrosion [30, 31]:(1)
The acidic medium diffuses into the pores or capillaries of the mortar. If the chemical reaction occurs faster in the wet film on the porous mortar surface, the medium is completely absorbed and does not penetrate into the inside of the mortar sample until the sample absorbs medium and is saturated, resulting in a significant increase of the porosity of the corroded area of the specimen. In this case, the process of the mortar being corroded by hydrochloric acid can be regarded as controlled by the diffusion effect.(2)
The acidic medium reacts with the various mineral compositions that make up the mortar. If the rate of penetration of acidic media into the mortar is faster than the rate at which the acidic medium is absorbed by the mortar, then the acidic medium is not all consumed in the corroded zone, but to the internal of the sample to form a broader reaction zone. In this case, the process of the mortar being corroded by hydrochloric acid can be regarded as controlled by the chemical kinetics effect.(3)
With the increase of corrosion time, the reaction products are gradually precipitated or dissolved.Therefore, under normal circumstances, it is considered that the acidic medium is completely absorbed and does not penetrate into the inside of the mortar sample in the initial stage of acid corrosion to mortar, and at this time, the reaction of mortar and hydrochloric acid is controlled by diffusion. With the prolongation of etching time, the immersion solution becomes saturated, and the acidic medium penetrates into the specimen to form a deeper reaction zone, at which time the corrosion process is controlled by chemical kinetics, and then, the reaction products are gradually precipitated or dissolved.


### 3.4. Analysis of Mechanical Properties of Mortar Subjected to Acid Corrosion

To study the deterioration degree of the mechanical properties of the mortar subjected to hydrochloric acid corrosion, the uniaxial compression test was carried out on the mortar subjected to corrosion solution with a different pH value. Based on the analysis of the increase of porosity and the decrease of effective bearing area of the mortar after hydrochloric acid corrosion, combined with uniaxial compression test results, a generalized porosity model of the compressive strength of the mortar corroded by hydrochloric acid was established, and the relationship between the uniaxial compressive strength and corrosion time was deduced.


#### 3.4.1. Compressive Strength Analysis

The uniaxial compressive strength of mortar immersed in different pH solutions for different time can be seen in Figure6 and Table 5. As observed in Figure 6 and Table 5, the smaller the pH value of the acid solution, the greater the decrease of the compressive strength of mortar. After 90 days, the compressive strength of the mortar in pH = 1 HCl solution decreased from 43.56 to 20.05 MPa, decreased by 53.97%. The compressive strength of the mortar in pH = 2 HCl solution decreased from 44.21 to 28.56 MPa, decreased by 35.40%. Besides, the strength of the dry mortar changed greatly in day 0∼30. It is reduced from 43.56 to 30.88 MPa (pH = 1 HCl) and 44.21 to 36.02 MPa (pH = 2 HCl), and the decrease range is 29.10% and 18.52%, respectively. The compressive strength change of mortar in pH = 7 H2O solution is relatively stable, and it decreased from 43.28 to 40.08 MPa, decreased by 7.39%.Figure 6
Uniaxial compressive strength of the mortar specimens in solutions with different pH values.Table 5
Uniaxial compressive strength of mortar.
HCl (pH = 1)
HCl (pH = 2)
H2O (pH = 7)
T (days)
S
M (MPa)
T (days)
S
M (MPa)
T (days)
S
M (MPa)
0
#1∼3
43.56
0
#31∼33
44.21
0
#61∼63
43.28
10
#4∼6
38.42
10
#34∼36
40.15
10
#64∼66
43.12
20
#7∼9
34.37
20
#37∼39
37.93
20
#67∼69
42.81
30
#10∼12
30.88
30
#40∼42
36.02
30
#70∼72
42.56
40
#13∼15
28.87
40
#43∼45
34.36
40
#73∼75
42.03
50
#16∼18
27.06
50
#46∼48
33.18
50
#76∼78
41.56
60
#19∼21
25.32
60
#49∼51
32.27
60
#79∼81
41.13
70
#22∼24
22.93
70
#52∼54
30.85
70
#82∼84
42.31
80
#25∼27
21.14
80
#55∼57
29.14
80
#85∼87
41.52
90
#28∼30
20.05
90
#58∼60
28.56
90
#88∼90
40.08
S represents the serial number of the mortar specimen; M represents the mean value (three samples) of compressive strength.


#### 3.4.2. Relationship between Uniaxial Compressive Strength and Corrosion Time of Mortar

The pore is the main reason for the impact of mortar strength. To obtain the porosity generalization model for compressive strength of mortar subjected to acid corrosion, the following assumptions are made:Take the differential unit body of mortar with unit thickness for example. The length, width, and depth of the differential element are allb, as shown in Figure 7(b). It is considered that the accumulated pore of a differential element of mortar produced by the chemical action can be obtained through the rotation of the cycloidal equation. The radius of the cycloid circle is a, as shown in Figure 7(a).(1)
Mortar sample is treated as two-phase media consisting of mortar matrix and pores.
(2)
The compressive strength of the mortar specimen is inversely proportional to the area of acid corrosion.
(3)
The increase of the pores and the decrease of the matrix bearing area of the specimen are mainly caused by chemical corrosion.Figure 7
Sketch of a generalized model of the mortar sample. (a) Cycloid model. (b) Mortar unit body.
(a)
(b)The cycloidal equation is shown as follows:(9)x=aθ−sin⁡θ,y=a1−cos⁡θ,where θ is the rotation angle of the circle in the cycloid, as shown in Figure 7(a). Cycloid volume with the x-axis as the rotation axis can be written as follows:(10)v=2∫0πaπy2dx=2∫0ππa31−cos⁡θ3dθ=5π2a3.In this case, the porosity of the differential element can be expressed as follows:(11)np=vb3=5π2a3b3.The area surrounded by the cycloid and thex-axis can be expressed by the following formula:(12)A=2∫0πaydx=2∫0πa21−cos⁡θ2dθ=3πa2.Hence, the maximum area of the rotating cycloid can be given by the following formula:(13)Amax=2A=6πa2.Because the compressive strength is proportional to the active bearing area of the sample, after soaking fort days, the compressive strength of the mortar unit can be expressed as follows:(14)σft=σf0b2−6πa2,where σft is the compressive strength after t days’ corrosion and σf0 is the initial compressive strength of the mortar unit.The following equation can be obtained from formula (11) and (14):(15)σft=σf0b2−1.40b2np2/3.Set(16)χ=σftσf0,where χ is the compressive strength ratio.Then, formula (15) can be expressed as follows:(17)χ=b21−1.40np2/3.The process of acid corrosion of the mortar specimen is the diffusion process of the hydrogen ion in the sample, and the increase of corrosion depth is the main reason for the rise in porosity. Formula (17) gives the relationship between the compressive strength ratio of the mortar element and its porosity.It is assumed that the porosity of the sample is proportional to the area of the mortar corroded by the acid solution, as shown in Figure8, the length of the cube sample is d, and the corrosion depth of the cube is dt. Then,(18)np∝d2−d−2dt2,which can also be written as follows:(19)np=γd2−d−2dt2=2γdt⋅d−d2t.Figure 8
Corrosion depth of the mortar specimen.Then, the following equation can be obtained from formula (17) and (19):(20)χ=b2−1.40b22γdt⋅d−d2t2/3.Set(21)2γdt⋅d−d2t2/3=λd2/3t+ηd4/3t.where γ, λ, and η are all undetermined coefficients.Then,χ can be expressed by formula (20) and (21):(22)χ=b2−1.40b2λd2/3t+ηd4/3t.Literature [32] and [33] obtained the damage depth formula of the one-dimensional acid corrosion through a large number of corrosion tests, which is given by(23)dt=at,where dt is the corrosion depth, t is the soaking time (day or year), and a is a influenced coefficient, which is related to the type and concentration of acid and the composition of mortar sample.The following equation can be obtained from formula (22) and (23):(24)χ=σftσf0=a1+a2t1/3+a3t2/3.where aii=1,2,3 is the experimental constant.Equation (24) expresses the relationship between uniaxial compressive strength and corrosion time of mortar under the action of the hydrochloric acid solution. aii=1,2,3 can be fitted (Figures 9(a) and 9(b)) by a regression equation with the help of the data obtained from the experiment (Table 6).Figure 9
The relationship between the compressive strength ratio and soaking time of mortar attacked by HCl solution: (a) pH = 1; (b) pH = 2.
(a)
(b)Table 6
Uniaxial compressive strength ratio of mortar.
HCl (pH = 1)
HCl (pH = 2)
T (days)
S
χ
T (days)
S
χ
10
#4∼6
0.903
0.873
0.870
10
#34∼36
0.933
0.906
0.885
20
#7∼9
0.760
0.813
0.793
20
#37∼39
0.870
0.840
0.864
30
#10∼12
0.736
0.763
0.716
30
#40∼42
0.797
0.823
0.824
40
#13∼15
0.630
0.664
0.693
40
#43∼45
0.770
0.748
0.814
50
#16∼18
0.607
0.594
0.663
50
#46∼48
0.734
0.743
0.775
60
#19∼21
0.554
0.584
0.605
60
#49∼51
0.687
0.757
0.746
70
#22∼24
0.485
0.524
0.570
70
#52∼54
0.655
0.711
0.728
80
#25∼27
0.483
0.502
0.471
80
#55∼57
0.641
0.657
0.680
90
#28∼30
0.446
0.491
0.443
90
#58∼60
0.575
0.619
0.744
S represents the serial number of the mortar specimen; χ represents the strength ratio of mortar.Then, (24) can be expressed as follows:For the hydrochloric acid solution of pH = 1,(25)χ=σftσf0=1.126−0.1t1/3−0.011t2/3.For the hydrochloric acid solution of pH = 2,(26)χ=σftσf0=1.024−0.026t1/3+0.013t2/3.The fitting curves demonstrate that the theoretical curves are generally in good agreement with the experimental results and the relationship between uniaxial compressive strength and corrosion time of mortar subjected to hydrochloric acid solution addressed in this study has high prediction accuracy.


## 3.1. Analysis of Physical Properties of Mortar Subjected to Acid Corrosion

The physical properties of acid-corroded mortar are characterized by definition of mass change rate and wave velocity change rate.


### 3.1.1. Mass Change Rate

The mass change rate of the acid-corroded mortar is defined as follows:(1)A=Mit−Mi0Mi0×100%,where A is the mass change rate of the mortar and Mi0 and Mit are the weight of the mortar before and after soaking in the acid solution, respectively.The resulting mass change rate of mortar samples in different concentrations (pH value) of solutions is shown in Figure1. It is observed in the figure that, in the first stage (0∼10 days) of soaking, the mass change rate of the specimen in three solutions increased rapidly. When the immersion corrosion reached 20 days, the mass change rate of the sample in H2O (distilled water) with pH = 7 reached the maximum value of 7.12% and then gradually stabilized. After 30 days of immersion corrosion, the mass change rate of the sample in HCl (hydrochloride) with pH = 1 and 2 reached the maximum value of 6.83% and 6.86%, respectively, and then decreased gradually. Moreover, it reduces faster in the solution of pH = 1 than that of pH = 2.Figure 1
Mass change rate (%) of the mortar specimens in solutions with different pH values.The results above demonstrate that the mass change rate of the mortar sample varies at different times in the solution with different pH values. Before the specimen reaches the maximum mass change rate, the dissolution of hydrochloric acid to mortar (chemical reaction) increases the connectivity of the porous system and the porosity of the sample, under the diffusion effect, and corrosion solution continues to penetrate into the porous spaces that were not accessible to water before acid attack, making the mass change rate of the mortar sample to increase. After the sample reaches the maximum mass change rate, it has sufficient time to react chemically with calcium hydroxide and calcium silicate hydrate in the mortar, which causes its weight to decrease gradually. Besides, the smaller the pH value (the stronger the acidity), the more the weight loss of the sample.


### 3.1.2. Wave Velocity Change Rate

Wave velocity change rate of the acid-corroded mortar is defined as follows:(2)B=vit−vi0vi0×100%,where B is the wave velocity change rate of the mortar and vi0 and vit are the wave velocity of the mortar before and after soaking in the acid solution, respectively.Figure2 shows the wave velocity change rate (%) of the mortar specimens in solutions with different pH values. It is observed in the figure that, in the first stage (0∼10 days) of soaking in HCl solution with pH = 1, the reaction of the mortar specimen and acid solution increased the porosity of the specimen, and the chemical softening of the mortar skeleton resulted in the readjustment of the three-phase ratio of the solid, liquid, and gas phase, which reduced the longitudinal wave velocity of the mortar sample. The wave velocity change rate decreased to 10.2% after 10 days of corrosion. In the second stage (10∼20 days) of immersion, with the extension of the corrosion time and the infiltration path, the cement paste was solubilised by the acid solution and fill porous spaces that previously contained air and were not accessible to water. Moreover, colloidal compounds (silica, aluminum hydroxide, iron hydroxide, etc.) with strong adsorption capacity and compactness generated by the reaction blocked the contact between HCl solution and noncorroded mortar, the corrosion rate slowed down, and at the same time, the variation of the ratio of three-phase composition tends to improve. All this make the longitudinal wave velocity increase, and the wave velocity change rate increased to 18.6% on the 20th day. Then, the chemical reaction tends to stabilize, and the longitudinal wave velocity of the specimen decreases gradually.Figure 2
Wave velocity change rate (%) of the mortar specimens in solutions with different pH values.The changed law of wave velocity change rate of the sample in the HCl solution with pH = 2 was similar to that in the HCl solution with pH = 1. The wave velocity change rate reduced in the first stage (0∼10 days) and decreased to −10.20% on the 10th day and then, increased in the following two phases (10∼20 and 20∼30 days) with the maximum of 19.79% occurring on the 30th day, indicating that the chemical reaction rate slowed down in HCl solution with pH = 2 than that with pH = 1.Compared with the HCl solution, the wave velocity change rate of mortar soaked in the distilled water (pH = 7) was also monitored; it was found from the figure that the wave velocity changes rate of the samples reached its maximum value of 15.68% on the 20th day, and then, its change is stable basically.


### 3.1.3. Discussion on the Mechanism of Wave Velocity Change of Acid-Corroded Mortar

Based on the Fermat Principle, Han et al. [29] established the relationship between the porosity and longitudinal wave velocity of saturated mortar and verified its applicability by experimental data. The relationship can be expressed as follows:(3)1vp=1−n0vm+n0vf,where vp is the measured longitudinal wave velocity of the saturated mortar, vm is the longitudinal wave velocity of the mortar particle skeleton, vf is the longitudinal wave velocity of the liquid in the mortar pores, and n0 is the porosity of the mortar.According to the above ideas, the present paper attempted to establish the relationship between longitudinal wave velocity and porosity of mortar subjected to acid corrosion. The following assumptions were made to simplify the analysis:(1)
The initial state of the mortar specimen is a two-phase medium composed of the solid matrix and porous, and the chemical corrosion does not make the mortar skeleton change in nature; that is,vm (5300 m/s in this paper) is unchanged before and after corrosion.(2)
It is considered that the volume of pores formed in the mortar after acid corrosion is wholly filled with acid solution, and the density of the acid solution is approximately equal to the density of water; that is,vf (1500 m/s in this paper) is unchanged.(3)
The acid-corroded mortar can be simplified as the corrosive zone and the noncorrosive zone, and the volume of the corrosive zone includes the volume of the pores increased by the chemical reaction. Also, it is affected by the decrease of pore volume due to the blocking effect of the colloidal compounds generated by the chemical reaction.(4)
It is considered that, before the corrosion time ofT, the reaction rate of mortar and hydrochloric acid is faster than that of formation of colloidal compounds, and during this period, the porosity of the mortar sample increases, which makes na>n0. After the corrosion time of T, the chemical reaction rate slows down, the formation rate of colloidal compounds accelerates, and the colloidal compounds produced by the chemical reaction will hinder the reaction between mortar and hydrochloric acid, and during this period, the porosity of the specimen decreases, which makes na<n0.According to (3) and the above assumptions, the relationship between the porosity and the longitudinal wave velocity of the acid corrosion mortar can be deduced as follows:(4)1vp1=1−navm+navf,where vp1 is the measured longitudinal wave velocity of the mortar after acid corrosion, vm is the longitudinal wave velocity of the mortar particle skeleton, vf is the longitudinal wave velocity of the acid solution, and na is the porosity of the mortar after soaking T days.Equation (3) minus (4) gets the following formula:(5)1vp−1vp1=1−n0vm+n0vf−1−navm+navf=na−n01vm−1vf.Due tovm>vf, the following equation can be obtained from formula (5) when na>n0:(6)1vp−1vp1<0,namely,vp1<vp.The results of (6) are a reasonable explanation of the phenomenon that the wave velocity change rate is negative on the 10th day (Figure 2) and the wave velocity decreases in acid solution.Due tovm>vf, the following equation can be obtained from formula (5) when na<n0:(7)1vp−1vp1>0,namely,vp1>vp.The results of (7) is a reasonable explanation of the phenomenon that the wave velocity change rate is positive on the 20th, 30th, 40th, 50th, 60th, 70th, 80th, and 90th day (Figure 2) and the wave velocity increases in acid solution.


## 3.1.1. Mass Change Rate

The mass change rate of the acid-corroded mortar is defined as follows:(1)A=Mit−Mi0Mi0×100%,where A is the mass change rate of the mortar and Mi0 and Mit are the weight of the mortar before and after soaking in the acid solution, respectively.The resulting mass change rate of mortar samples in different concentrations (pH value) of solutions is shown in Figure1. It is observed in the figure that, in the first stage (0∼10 days) of soaking, the mass change rate of the specimen in three solutions increased rapidly. When the immersion corrosion reached 20 days, the mass change rate of the sample in H2O (distilled water) with pH = 7 reached the maximum value of 7.12% and then gradually stabilized. After 30 days of immersion corrosion, the mass change rate of the sample in HCl (hydrochloride) with pH = 1 and 2 reached the maximum value of 6.83% and 6.86%, respectively, and then decreased gradually. Moreover, it reduces faster in the solution of pH = 1 than that of pH = 2.Figure 1
Mass change rate (%) of the mortar specimens in solutions with different pH values.The results above demonstrate that the mass change rate of the mortar sample varies at different times in the solution with different pH values. Before the specimen reaches the maximum mass change rate, the dissolution of hydrochloric acid to mortar (chemical reaction) increases the connectivity of the porous system and the porosity of the sample, under the diffusion effect, and corrosion solution continues to penetrate into the porous spaces that were not accessible to water before acid attack, making the mass change rate of the mortar sample to increase. After the sample reaches the maximum mass change rate, it has sufficient time to react chemically with calcium hydroxide and calcium silicate hydrate in the mortar, which causes its weight to decrease gradually. Besides, the smaller the pH value (the stronger the acidity), the more the weight loss of the sample.


## 3.1.2. Wave Velocity Change Rate

Wave velocity change rate of the acid-corroded mortar is defined as follows:(2)B=vit−vi0vi0×100%,where B is the wave velocity change rate of the mortar and vi0 and vit are the wave velocity of the mortar before and after soaking in the acid solution, respectively.Figure2 shows the wave velocity change rate (%) of the mortar specimens in solutions with different pH values. It is observed in the figure that, in the first stage (0∼10 days) of soaking in HCl solution with pH = 1, the reaction of the mortar specimen and acid solution increased the porosity of the specimen, and the chemical softening of the mortar skeleton resulted in the readjustment of the three-phase ratio of the solid, liquid, and gas phase, which reduced the longitudinal wave velocity of the mortar sample. The wave velocity change rate decreased to 10.2% after 10 days of corrosion. In the second stage (10∼20 days) of immersion, with the extension of the corrosion time and the infiltration path, the cement paste was solubilised by the acid solution and fill porous spaces that previously contained air and were not accessible to water. Moreover, colloidal compounds (silica, aluminum hydroxide, iron hydroxide, etc.) with strong adsorption capacity and compactness generated by the reaction blocked the contact between HCl solution and noncorroded mortar, the corrosion rate slowed down, and at the same time, the variation of the ratio of three-phase composition tends to improve. All this make the longitudinal wave velocity increase, and the wave velocity change rate increased to 18.6% on the 20th day. Then, the chemical reaction tends to stabilize, and the longitudinal wave velocity of the specimen decreases gradually.Figure 2
Wave velocity change rate (%) of the mortar specimens in solutions with different pH values.The changed law of wave velocity change rate of the sample in the HCl solution with pH = 2 was similar to that in the HCl solution with pH = 1. The wave velocity change rate reduced in the first stage (0∼10 days) and decreased to −10.20% on the 10th day and then, increased in the following two phases (10∼20 and 20∼30 days) with the maximum of 19.79% occurring on the 30th day, indicating that the chemical reaction rate slowed down in HCl solution with pH = 2 than that with pH = 1.Compared with the HCl solution, the wave velocity change rate of mortar soaked in the distilled water (pH = 7) was also monitored; it was found from the figure that the wave velocity changes rate of the samples reached its maximum value of 15.68% on the 20th day, and then, its change is stable basically.


## 3.1.3. Discussion on the Mechanism of Wave Velocity Change of Acid-Corroded Mortar

Based on the Fermat Principle, Han et al. [29] established the relationship between the porosity and longitudinal wave velocity of saturated mortar and verified its applicability by experimental data. The relationship can be expressed as follows:(3)1vp=1−n0vm+n0vf,where vp is the measured longitudinal wave velocity of the saturated mortar, vm is the longitudinal wave velocity of the mortar particle skeleton, vf is the longitudinal wave velocity of the liquid in the mortar pores, and n0 is the porosity of the mortar.According to the above ideas, the present paper attempted to establish the relationship between longitudinal wave velocity and porosity of mortar subjected to acid corrosion. The following assumptions were made to simplify the analysis:(1)
The initial state of the mortar specimen is a two-phase medium composed of the solid matrix and porous, and the chemical corrosion does not make the mortar skeleton change in nature; that is,vm (5300 m/s in this paper) is unchanged before and after corrosion.(2)
It is considered that the volume of pores formed in the mortar after acid corrosion is wholly filled with acid solution, and the density of the acid solution is approximately equal to the density of water; that is,vf (1500 m/s in this paper) is unchanged.(3)
The acid-corroded mortar can be simplified as the corrosive zone and the noncorrosive zone, and the volume of the corrosive zone includes the volume of the pores increased by the chemical reaction. Also, it is affected by the decrease of pore volume due to the blocking effect of the colloidal compounds generated by the chemical reaction.(4)
It is considered that, before the corrosion time ofT, the reaction rate of mortar and hydrochloric acid is faster than that of formation of colloidal compounds, and during this period, the porosity of the mortar sample increases, which makes na>n0. After the corrosion time of T, the chemical reaction rate slows down, the formation rate of colloidal compounds accelerates, and the colloidal compounds produced by the chemical reaction will hinder the reaction between mortar and hydrochloric acid, and during this period, the porosity of the specimen decreases, which makes na<n0.According to (3) and the above assumptions, the relationship between the porosity and the longitudinal wave velocity of the acid corrosion mortar can be deduced as follows:(4)1vp1=1−navm+navf,where vp1 is the measured longitudinal wave velocity of the mortar after acid corrosion, vm is the longitudinal wave velocity of the mortar particle skeleton, vf is the longitudinal wave velocity of the acid solution, and na is the porosity of the mortar after soaking T days.Equation (3) minus (4) gets the following formula:(5)1vp−1vp1=1−n0vm+n0vf−1−navm+navf=na−n01vm−1vf.Due tovm>vf, the following equation can be obtained from formula (5) when na>n0:(6)1vp−1vp1<0,namely,vp1<vp.The results of (6) are a reasonable explanation of the phenomenon that the wave velocity change rate is negative on the 10th day (Figure 2) and the wave velocity decreases in acid solution.Due tovm>vf, the following equation can be obtained from formula (5) when na<n0:(7)1vp−1vp1>0,namely,vp1>vp.The results of (7) is a reasonable explanation of the phenomenon that the wave velocity change rate is positive on the 20th, 30th, 40th, 50th, 60th, 70th, 80th, and 90th day (Figure 2) and the wave velocity increases in acid solution.


## 3.2. Analysis of Chemical Properties of Mortar Subjected to Acid Corrosion

The chemical properties of acid corrosion mortar are analyzed by monitoring the concentration of hydrogen ions (pH value) and calcium ions in the soaking solution.Figures3(a) and 3(b) show the concentration curves of H+ and Ca2+ in HCl solution (pH = 1) at each stage (10 days), respectively. As observed in the Figure 3(a), in each stage (10 days), the pH value of the solution increases with the extension of immersion time. Within 0∼10 days, the pH values of the solution were 2.7, 6.9, and 7.2 at day 3, 7, and 10, respectively. The solution was neutral after day 7. Within 10∼20 days, the change law of the pH value is basically the same as that of 0∼10 days. However, the solution showed weak acidity on day 20. With the extension of soaking time, the acidity of the solution became stronger after the end of each stage (pH = 6.2, 6.0, 5.8, 5.5, 5.1, 4.9, and 4.6 and 4.1 at day 20, 30, 40, 50, 60, 70, 80, and 90). Figure 3(b) shows that the concentration of Ca2+ increased gradually within 0∼20 days, which is 0.1295 and 0.1437 mol/L at day 10 and 20, respectively. Then, the concentration of Ca2+ is about 0.045 mol/L after the end of each stage.Figure 3
Concentration curves of (a) H+ and (b) Ca2+ in HCl solution (pH = 1) at different periods.
(a)
(b)Figures4(a) and 4(b) show the concentration curves of H+ and Ca2+ in HCl solution (pH = 2) at each stage (10 days), respectively. It can be seen from Figure 4(a) that the solution became alkaline at day 3, which demonstrates the solubility of the colloidal compounds produced by the reaction is decreased, and that it is conducive to the formation of the colloid compounds. Figure 4(b) shows that the dissolution of Ca2+ in HCl solution with pH = 2 at each stage (10 days) is basically the same as that of pH = 1.Figure 4
Concentration curves of (a) H+ and (b) Ca2+ in HCl solution (pH = 2) at different periods.
(a)
(b)The concentration curves of H+ and Ca2+ in H2O solution (pH = 7) at different periods are shown in Figures 5(a) and 5(b) compared to HCl solution. The changed law of the pH value and the concentration of Ca2+ is basically the same as that of HCl solution. The solution became alkaline at day 3 (Figure 5(a)), and the pH is between 10 and 12, which demonstrates that the mortar itself is alkaline. The maximum value of Ca2+ appeared in 20∼30 days, and then, it stabled at about 0.00001 mol/L.Figure 5
Concentration curves of (a) H+ and (b) Ca2+ in H2O solution (pH = 7) at different periods.
(a)
(b)


## 3.3. Discussion on the Mechanism of Mortar Attacked by Hydrochloric Acid

The main chemical equation for the reaction of hydrochloric acid with mortar is as follows:(8)CaOH2+2HCl⟶CaCl2+2H2OxCaO⋅ySiO2⋅nH2O+2xHCl⟶xCa2++2xCl−+ySiOH4+x+n−2yH2OAs can be seen from the above reaction formula, due to the strong acid effect of HCl solution, a large number of calcium hydroxide is neutralized and produced a mass of calcium chloride with high solubility, resulting in the decomposition of hydrated calcium silicate in the mortar samples. Hydrochloric acid, on the contrary, reacts directly with hydrated calcium silicate. In this way, the gel of the mortar pore structure is considerably damaged, causing the increase of porosity and the decrease of effective bearing area of mortar samples, resulting in the deterioration of the physical and mechanical properties of the mortar samples.Through the observation of the experiment and the analysis of the test results, it is known that the interaction between hydrochloric acid and mortar can be regarded as a physicochemical process of multiphase. The process can be divided into three stages from the outside to the inside for the mortar sample subjected to hydrochloric acid corrosion [30, 31]:(1)
The acidic medium diffuses into the pores or capillaries of the mortar. If the chemical reaction occurs faster in the wet film on the porous mortar surface, the medium is completely absorbed and does not penetrate into the inside of the mortar sample until the sample absorbs medium and is saturated, resulting in a significant increase of the porosity of the corroded area of the specimen. In this case, the process of the mortar being corroded by hydrochloric acid can be regarded as controlled by the diffusion effect.(2)
The acidic medium reacts with the various mineral compositions that make up the mortar. If the rate of penetration of acidic media into the mortar is faster than the rate at which the acidic medium is absorbed by the mortar, then the acidic medium is not all consumed in the corroded zone, but to the internal of the sample to form a broader reaction zone. In this case, the process of the mortar being corroded by hydrochloric acid can be regarded as controlled by the chemical kinetics effect.(3)
With the increase of corrosion time, the reaction products are gradually precipitated or dissolved.Therefore, under normal circumstances, it is considered that the acidic medium is completely absorbed and does not penetrate into the inside of the mortar sample in the initial stage of acid corrosion to mortar, and at this time, the reaction of mortar and hydrochloric acid is controlled by diffusion. With the prolongation of etching time, the immersion solution becomes saturated, and the acidic medium penetrates into the specimen to form a deeper reaction zone, at which time the corrosion process is controlled by chemical kinetics, and then, the reaction products are gradually precipitated or dissolved.


## 3.4. Analysis of Mechanical Properties of Mortar Subjected to Acid Corrosion

To study the deterioration degree of the mechanical properties of the mortar subjected to hydrochloric acid corrosion, the uniaxial compression test was carried out on the mortar subjected to corrosion solution with a different pH value. Based on the analysis of the increase of porosity and the decrease of effective bearing area of the mortar after hydrochloric acid corrosion, combined with uniaxial compression test results, a generalized porosity model of the compressive strength of the mortar corroded by hydrochloric acid was established, and the relationship between the uniaxial compressive strength and corrosion time was deduced.


### 3.4.1. Compressive Strength Analysis

The uniaxial compressive strength of mortar immersed in different pH solutions for different time can be seen in Figure6 and Table 5. As observed in Figure 6 and Table 5, the smaller the pH value of the acid solution, the greater the decrease of the compressive strength of mortar. After 90 days, the compressive strength of the mortar in pH = 1 HCl solution decreased from 43.56 to 20.05 MPa, decreased by 53.97%. The compressive strength of the mortar in pH = 2 HCl solution decreased from 44.21 to 28.56 MPa, decreased by 35.40%. Besides, the strength of the dry mortar changed greatly in day 0∼30. It is reduced from 43.56 to 30.88 MPa (pH = 1 HCl) and 44.21 to 36.02 MPa (pH = 2 HCl), and the decrease range is 29.10% and 18.52%, respectively. The compressive strength change of mortar in pH = 7 H2O solution is relatively stable, and it decreased from 43.28 to 40.08 MPa, decreased by 7.39%.Figure 6
Uniaxial compressive strength of the mortar specimens in solutions with different pH values.Table 5
Uniaxial compressive strength of mortar.
HCl (pH = 1)
HCl (pH = 2)
H2O (pH = 7)
T (days)
S
M (MPa)
T (days)
S
M (MPa)
T (days)
S
M (MPa)
0
#1∼3
43.56
0
#31∼33
44.21
0
#61∼63
43.28
10
#4∼6
38.42
10
#34∼36
40.15
10
#64∼66
43.12
20
#7∼9
34.37
20
#37∼39
37.93
20
#67∼69
42.81
30
#10∼12
30.88
30
#40∼42
36.02
30
#70∼72
42.56
40
#13∼15
28.87
40
#43∼45
34.36
40
#73∼75
42.03
50
#16∼18
27.06
50
#46∼48
33.18
50
#76∼78
41.56
60
#19∼21
25.32
60
#49∼51
32.27
60
#79∼81
41.13
70
#22∼24
22.93
70
#52∼54
30.85
70
#82∼84
42.31
80
#25∼27
21.14
80
#55∼57
29.14
80
#85∼87
41.52
90
#28∼30
20.05
90
#58∼60
28.56
90
#88∼90
40.08
S represents the serial number of the mortar specimen; M represents the mean value (three samples) of compressive strength.


### 3.4.2. Relationship between Uniaxial Compressive Strength and Corrosion Time of Mortar

The pore is the main reason for the impact of mortar strength. To obtain the porosity generalization model for compressive strength of mortar subjected to acid corrosion, the following assumptions are made:Take the differential unit body of mortar with unit thickness for example. The length, width, and depth of the differential element are allb, as shown in Figure 7(b). It is considered that the accumulated pore of a differential element of mortar produced by the chemical action can be obtained through the rotation of the cycloidal equation. The radius of the cycloid circle is a, as shown in Figure 7(a).(1)
Mortar sample is treated as two-phase media consisting of mortar matrix and pores.
(2)
The compressive strength of the mortar specimen is inversely proportional to the area of acid corrosion.
(3)
The increase of the pores and the decrease of the matrix bearing area of the specimen are mainly caused by chemical corrosion.Figure 7
Sketch of a generalized model of the mortar sample. (a) Cycloid model. (b) Mortar unit body.
(a)
(b)The cycloidal equation is shown as follows:(9)x=aθ−sin⁡θ,y=a1−cos⁡θ,where θ is the rotation angle of the circle in the cycloid, as shown in Figure 7(a). Cycloid volume with the x-axis as the rotation axis can be written as follows:(10)v=2∫0πaπy2dx=2∫0ππa31−cos⁡θ3dθ=5π2a3.In this case, the porosity of the differential element can be expressed as follows:(11)np=vb3=5π2a3b3.The area surrounded by the cycloid and thex-axis can be expressed by the following formula:(12)A=2∫0πaydx=2∫0πa21−cos⁡θ2dθ=3πa2.Hence, the maximum area of the rotating cycloid can be given by the following formula:(13)Amax=2A=6πa2.Because the compressive strength is proportional to the active bearing area of the sample, after soaking fort days, the compressive strength of the mortar unit can be expressed as follows:(14)σft=σf0b2−6πa2,where σft is the compressive strength after t days’ corrosion and σf0 is the initial compressive strength of the mortar unit.The following equation can be obtained from formula (11) and (14):(15)σft=σf0b2−1.40b2np2/3.Set(16)χ=σftσf0,where χ is the compressive strength ratio.Then, formula (15) can be expressed as follows:(17)χ=b21−1.40np2/3.The process of acid corrosion of the mortar specimen is the diffusion process of the hydrogen ion in the sample, and the increase of corrosion depth is the main reason for the rise in porosity. Formula (17) gives the relationship between the compressive strength ratio of the mortar element and its porosity.It is assumed that the porosity of the sample is proportional to the area of the mortar corroded by the acid solution, as shown in Figure8, the length of the cube sample is d, and the corrosion depth of the cube is dt. Then,(18)np∝d2−d−2dt2,which can also be written as follows:(19)np=γd2−d−2dt2=2γdt⋅d−d2t.Figure 8
Corrosion depth of the mortar specimen.Then, the following equation can be obtained from formula (17) and (19):(20)χ=b2−1.40b22γdt⋅d−d2t2/3.Set(21)2γdt⋅d−d2t2/3=λd2/3t+ηd4/3t.where γ, λ, and η are all undetermined coefficients.Then,χ can be expressed by formula (20) and (21):(22)χ=b2−1.40b2λd2/3t+ηd4/3t.Literature [32] and [33] obtained the damage depth formula of the one-dimensional acid corrosion through a large number of corrosion tests, which is given by(23)dt=at,where dt is the corrosion depth, t is the soaking time (day or year), and a is a influenced coefficient, which is related to the type and concentration of acid and the composition of mortar sample.The following equation can be obtained from formula (22) and (23):(24)χ=σftσf0=a1+a2t1/3+a3t2/3.where aii=1,2,3 is the experimental constant.Equation (24) expresses the relationship between uniaxial compressive strength and corrosion time of mortar under the action of the hydrochloric acid solution. aii=1,2,3 can be fitted (Figures 9(a) and 9(b)) by a regression equation with the help of the data obtained from the experiment (Table 6).Figure 9
The relationship between the compressive strength ratio and soaking time of mortar attacked by HCl solution: (a) pH = 1; (b) pH = 2.
(a)
(b)Table 6
Uniaxial compressive strength ratio of mortar.
HCl (pH = 1)
HCl (pH = 2)
T (days)
S
χ
T (days)
S
χ
10
#4∼6
0.903
0.873
0.870
10
#34∼36
0.933
0.906
0.885
20
#7∼9
0.760
0.813
0.793
20
#37∼39
0.870
0.840
0.864
30
#10∼12
0.736
0.763
0.716
30
#40∼42
0.797
0.823
0.824
40
#13∼15
0.630
0.664
0.693
40
#43∼45
0.770
0.748
0.814
50
#16∼18
0.607
0.594
0.663
50
#46∼48
0.734
0.743
0.775
60
#19∼21
0.554
0.584
0.605
60
#49∼51
0.687
0.757
0.746
70
#22∼24
0.485
0.524
0.570
70
#52∼54
0.655
0.711
0.728
80
#25∼27
0.483
0.502
0.471
80
#55∼57
0.641
0.657
0.680
90
#28∼30
0.446
0.491
0.443
90
#58∼60
0.575
0.619
0.744
S represents the serial number of the mortar specimen; χ represents the strength ratio of mortar.Then, (24) can be expressed as follows:For the hydrochloric acid solution of pH = 1,(25)χ=σftσf0=1.126−0.1t1/3−0.011t2/3.For the hydrochloric acid solution of pH = 2,(26)χ=σftσf0=1.024−0.026t1/3+0.013t2/3.The fitting curves demonstrate that the theoretical curves are generally in good agreement with the experimental results and the relationship between uniaxial compressive strength and corrosion time of mortar subjected to hydrochloric acid solution addressed in this study has high prediction accuracy.


## 3.4.1. Compressive Strength Analysis

The uniaxial compressive strength of mortar immersed in different pH solutions for different time can be seen in Figure6 and Table 5. As observed in Figure 6 and Table 5, the smaller the pH value of the acid solution, the greater the decrease of the compressive strength of mortar. After 90 days, the compressive strength of the mortar in pH = 1 HCl solution decreased from 43.56 to 20.05 MPa, decreased by 53.97%. The compressive strength of the mortar in pH = 2 HCl solution decreased from 44.21 to 28.56 MPa, decreased by 35.40%. Besides, the strength of the dry mortar changed greatly in day 0∼30. It is reduced from 43.56 to 30.88 MPa (pH = 1 HCl) and 44.21 to 36.02 MPa (pH = 2 HCl), and the decrease range is 29.10% and 18.52%, respectively. The compressive strength change of mortar in pH = 7 H2O solution is relatively stable, and it decreased from 43.28 to 40.08 MPa, decreased by 7.39%.Figure 6
Uniaxial compressive strength of the mortar specimens in solutions with different pH values.Table 5
Uniaxial compressive strength of mortar.
HCl (pH = 1)
HCl (pH = 2)
H2O (pH = 7)
T (days)
S
M (MPa)
T (days)
S
M (MPa)
T (days)
S
M (MPa)
0
#1∼3
43.56
0
#31∼33
44.21
0
#61∼63
43.28
10
#4∼6
38.42
10
#34∼36
40.15
10
#64∼66
43.12
20
#7∼9
34.37
20
#37∼39
37.93
20
#67∼69
42.81
30
#10∼12
30.88
30
#40∼42
36.02
30
#70∼72
42.56
40
#13∼15
28.87
40
#43∼45
34.36
40
#73∼75
42.03
50
#16∼18
27.06
50
#46∼48
33.18
50
#76∼78
41.56
60
#19∼21
25.32
60
#49∼51
32.27
60
#79∼81
41.13
70
#22∼24
22.93
70
#52∼54
30.85
70
#82∼84
42.31
80
#25∼27
21.14
80
#55∼57
29.14
80
#85∼87
41.52
90
#28∼30
20.05
90
#58∼60
28.56
90
#88∼90
40.08
S represents the serial number of the mortar specimen; M represents the mean value (three samples) of compressive strength.


## 3.4.2. Relationship between Uniaxial Compressive Strength and Corrosion Time of Mortar

The pore is the main reason for the impact of mortar strength. To obtain the porosity generalization model for compressive strength of mortar subjected to acid corrosion, the following assumptions are made:Take the differential unit body of mortar with unit thickness for example. The length, width, and depth of the differential element are allb, as shown in Figure 7(b). It is considered that the accumulated pore of a differential element of mortar produced by the chemical action can be obtained through the rotation of the cycloidal equation. The radius of the cycloid circle is a, as shown in Figure 7(a).(1)
Mortar sample is treated as two-phase media consisting of mortar matrix and pores.
(2)
The compressive strength of the mortar specimen is inversely proportional to the area of acid corrosion.
(3)
The increase of the pores and the decrease of the matrix bearing area of the specimen are mainly caused by chemical corrosion.Figure 7
Sketch of a generalized model of the mortar sample. (a) Cycloid model. (b) Mortar unit body.
(a)
(b)The cycloidal equation is shown as follows:(9)x=aθ−sin⁡θ,y=a1−cos⁡θ,where θ is the rotation angle of the circle in the cycloid, as shown in Figure 7(a). Cycloid volume with the x-axis as the rotation axis can be written as follows:(10)v=2∫0πaπy2dx=2∫0ππa31−cos⁡θ3dθ=5π2a3.In this case, the porosity of the differential element can be expressed as follows:(11)np=vb3=5π2a3b3.The area surrounded by the cycloid and thex-axis can be expressed by the following formula:(12)A=2∫0πaydx=2∫0πa21−cos⁡θ2dθ=3πa2.Hence, the maximum area of the rotating cycloid can be given by the following formula:(13)Amax=2A=6πa2.Because the compressive strength is proportional to the active bearing area of the sample, after soaking fort days, the compressive strength of the mortar unit can be expressed as follows:(14)σft=σf0b2−6πa2,where σft is the compressive strength after t days’ corrosion and σf0 is the initial compressive strength of the mortar unit.The following equation can be obtained from formula (11) and (14):(15)σft=σf0b2−1.40b2np2/3.Set(16)χ=σftσf0,where χ is the compressive strength ratio.Then, formula (15) can be expressed as follows:(17)χ=b21−1.40np2/3.The process of acid corrosion of the mortar specimen is the diffusion process of the hydrogen ion in the sample, and the increase of corrosion depth is the main reason for the rise in porosity. Formula (17) gives the relationship between the compressive strength ratio of the mortar element and its porosity.It is assumed that the porosity of the sample is proportional to the area of the mortar corroded by the acid solution, as shown in Figure8, the length of the cube sample is d, and the corrosion depth of the cube is dt. Then,(18)np∝d2−d−2dt2,which can also be written as follows:(19)np=γd2−d−2dt2=2γdt⋅d−d2t.Figure 8
Corrosion depth of the mortar specimen.Then, the following equation can be obtained from formula (17) and (19):(20)χ=b2−1.40b22γdt⋅d−d2t2/3.Set(21)2γdt⋅d−d2t2/3=λd2/3t+ηd4/3t.where γ, λ, and η are all undetermined coefficients.Then,χ can be expressed by formula (20) and (21):(22)χ=b2−1.40b2λd2/3t+ηd4/3t.Literature [32] and [33] obtained the damage depth formula of the one-dimensional acid corrosion through a large number of corrosion tests, which is given by(23)dt=at,where dt is the corrosion depth, t is the soaking time (day or year), and a is a influenced coefficient, which is related to the type and concentration of acid and the composition of mortar sample.The following equation can be obtained from formula (22) and (23):(24)χ=σftσf0=a1+a2t1/3+a3t2/3.where aii=1,2,3 is the experimental constant.Equation (24) expresses the relationship between uniaxial compressive strength and corrosion time of mortar under the action of the hydrochloric acid solution. aii=1,2,3 can be fitted (Figures 9(a) and 9(b)) by a regression equation with the help of the data obtained from the experiment (Table 6).Figure 9
The relationship between the compressive strength ratio and soaking time of mortar attacked by HCl solution: (a) pH = 1; (b) pH = 2.
(a)
(b)Table 6
Uniaxial compressive strength ratio of mortar.
HCl (pH = 1)
HCl (pH = 2)
T (days)
S
χ
T (days)
S
χ
10
#4∼6
0.903
0.873
0.870
10
#34∼36
0.933
0.906
0.885
20
#7∼9
0.760
0.813
0.793
20
#37∼39
0.870
0.840
0.864
30
#10∼12
0.736
0.763
0.716
30
#40∼42
0.797
0.823
0.824
40
#13∼15
0.630
0.664
0.693
40
#43∼45
0.770
0.748
0.814
50
#16∼18
0.607
0.594
0.663
50
#46∼48
0.734
0.743
0.775
60
#19∼21
0.554
0.584
0.605
60
#49∼51
0.687
0.757
0.746
70
#22∼24
0.485
0.524
0.570
70
#52∼54
0.655
0.711
0.728
80
#25∼27
0.483
0.502
0.471
80
#55∼57
0.641
0.657
0.680
90
#28∼30
0.446
0.491
0.443
90
#58∼60
0.575
0.619
0.744
S represents the serial number of the mortar specimen; χ represents the strength ratio of mortar.Then, (24) can be expressed as follows:For the hydrochloric acid solution of pH = 1,(25)χ=σftσf0=1.126−0.1t1/3−0.011t2/3.For the hydrochloric acid solution of pH = 2,(26)χ=σftσf0=1.024−0.026t1/3+0.013t2/3.The fitting curves demonstrate that the theoretical curves are generally in good agreement with the experimental results and the relationship between uniaxial compressive strength and corrosion time of mortar subjected to hydrochloric acid solution addressed in this study has high prediction accuracy.


## 4. Conclusions

Based on the results of this study, the following conclusions can be drawn:(1)
The different stages of immersion corrosion were quantitatively described with the defined mass change rate and wave velocity change rate as well as the concentration changes of H+ and Ca2+ in the immersion solution, which adequately reflected the process of the mortar sample being corroded by hydrochloric acid comprehensively. Moreover, the relationship between the porosity and the wave velocity of the mortar corroded by hydrochloric acid was tried to establish, by which the mechanism of wave velocity variation appeared in the experiment can be well explained.(2)
The mechanism of mortar attacked by hydrochloric acid was discussed. The analysis showed that the process of the mortar sample subjected to hydrochloric acid erosion had apparent stage characteristics. In the initial stage of immersion corrosion, the chemical reaction increased the pH value and the concentration of Ca2+, and the porosity of the specimen also increases, which lead to the decrease of longitudinal wave velocity. Meanwhile, the corrosion solution continuously penetrates into the mortar pore system under the diffusion effect, which leads to the increase of weight of the specimen, and it is considered that the diffusion process plays a leading role during this period. The colloidal compounds generated by the reaction can not only fill the pore space but also block the continuous reaction to some extent, which leads to the increase of the longitudinal wave velocity of the specimen. With the prolonging of corrosion time and infiltration path, the pH value and the concentration of Ca2+ in soaking solution tend to be stable, the diffusion action is weakened, and the chemical reaction is continuous, which led to decrease of the weight and the wave velocity of the specimen gradually. It is considered that the chemical reaction plays a leading role in this process.(3)
Based on the induction and analysis of the test results, a generalized porosity model considering the increase of the porosity and decrease of the effective bearing area of the mortar sample in the corrosion process was proposed. The relation between the uniaxial compressive strength and the corrosion time of the corroded mortar is deduced, and the unknown parameters are determined based on the regression analysis of the test data.



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*Source: 3283907-2018-06-20.xml*