At a constant tempe specimens were partially immersed in a saturated sodium sulfate solution with their top surfaces exposed to the atmosphere to encourage evaporation [40]. Crystallization of mirabilite due to evaporation and temperature changes. Prepared in a similar manner to test 2, but the specimens were put under tem perature [40]. Crystallization of Following ASTM C88, specimens were put through soaking and drying cycles before being fully immersed in a saturated sodium sulfate solution.
The specimens were kept in the solution for 12 to 18 hours soaked to allow for the thenardite to convert within the specimens into mirabilite. The test ran for 10 cycles of drying and soaking [40]. Crystallization of thenardite due to evaporation and temperature changes. The same steps in test 4 were followed in this test except the ASTM C88 soaking was changes and evaporation were intended to crystalize thenardite without crystalizing the mirabilite [40].
The authors concluded that crystallization associated with rapid decrease in temperature test 1 resulted in the most significant distress since it caused very rapid volume increase. The normal concrete completely deteriorated, while the air entrained concrete showed some resistance to this method.
PAGE 39 39 2. PSA test In this test, an at mosphere of controlled temperature and RH is applied to concrete specimens that are partially immersed in a sodium sulfate solution that is prepared according to ASTM C The specimens used can be of any size but must have a height th at is at least twic e the diameter.
The specimen is marked for measurements in several locations. The sulfate solution is supposed to infiltrate the specimen either by wicking action or diffusion [11]. At first, a preliminary test setup was proposed and applied on some specime ns in order to find which method would work best for a PSA test.
Paraffin oil is used to prevent the solution from evaporating during the course of the test. The oil is placed on the surface of the solution and a plexiglass tube inside an expanded polystyr ene cylinder is uti lized to isolate the specimen from the paraffin oil as shown in Figure 2 2 [11].
The deterioration is evaluated by measuring the height of the spalling above the solution level in addition to the top and bottom diameters. The study indicated that it was difficult to get accurate mass measurements for the concrete cores, because drying them removed some loose material.
As a result, the deteriorati on increased prior to the measurements, and hence mass measurements were not consistent indicators of damage. The mixt ures were selected based on their behavior in a previous test performed by the author s during which mortar prims were fully immersed in sodium sulfate in accordance with ASTM C [47].
Based on the preliminary results, the deterioration criteria when evaluating the mortar cyl inders were based on measuring the width of the spalling and recording each bottom diameters throughout the duration of the test. The mortar mixtures were put through three test environments as follows: a.
These exposures condition were selected to determine wheth er the preliminary parameters would help rank the materials based on their relative deterioration [11]. In addition, more severe deter ioration resulted from tidal zone exposure compared to the full immersion one [11]. The specimens were put through temperature cycles that took 11 hours for PAGE 41 41 each cycle in order to cause the most significant concrete deterioration.
T he specimens were immersed in three different sulfate solutions of calcium, sodium, and magnesium. The test also included outdoor testing trenches filled with sulfates, where speci mens were either buried in the soil, submersed under the sulfate solution, o r halfway submersed.
The specimens were tested for expansions and deteriorations over a period of 18 months of exposure [49]. The evaporative transport or capillary u ptake of sulfate into concrete was not explored in this laboratory test. The lack of standardized tests for the role of physical sulfate attack in concrete degradation brings up the necessity of increasing the research efforts to establish such standards a nd specifications to better understand this phenomenon [49].
In addition, different dosages of ultrafi ne nanoparticles Nano silica and Nano alumina. The specimens were monitored every 12 to 15 days and the solution was changed PAGE 42 42 every 30 days but replenished regularly between replacements. However, mixes that incorporated NS showed high surface scaling compared to the ones with NA.
Both chemical and physical sulfate attack affected the specimens and caused disintegration for mixes of that consisted of cement and NA. This leads to the possibility of such combined mechanism in the field.
On the other hand, the incorporation of fly ash in NA mixes helped improve their resistance to che m ical sulfate attack [3]. Mortar was chosen over concrete since it has higher permeability which was expected to shorten the time of testing [5]. All the mixes in this study were made with type V cement to lower the chance of any c hemical attack interference. The specim ens were put through thermal cycling in a thermally controlled water bath.
Every 24 hours was considered a complete cycle that started by warming up the bath until it re ached 30 tion was replaced every five days, and the specimens were inspected every ten days. Mass loss, ultrasonic pulse velocity UPV , and resonant frequency measurement method s were evaluated in this study to find the most appropriate assessment technique of the Slag performed significantly better compared to fly ash mortar mixes which still improved the resistance of mortar mixes against P SA [5].
The tests showed that the extent and ra te of deterioration was best described by mass loss compared to the other methods used. Using UPV and fundamental resonant frequency to calculate the durability factors did not give favorable results. The authors recommend the use of concrete specimens in this test method as the next step of research [5].
PAGE 44 44 Figure 2 1. Phase diagram of Sodium sulfate [37] with permission from Elsevier Figure 2 2. Ferra ris et. This can cause concrete to fail in 5 years or less in severe cases of sulfate attack [4,50]. Both internal and external sources can supply sulfate ions to the concrete. External sulfate ions penetrate into the concrete through the concrete pore network from water or soil in contact with the concrete.
Internal sulfate attack can happen when the c oncrete is exposed to excessive temperatures, usually at early ages [4]. The chemical reactions between external or internal sulfate ions and the different consti [22]. Sulfate ions diffuse into the concrete in the case of external sulfa te attack and form gypsum by reacting with portlandite or calcium silicate hydrate C S H , and in a later stage the formed gypsum can react with C 3 A to form ettringite [24] as shown in Equation s 3 1 and 3 2 [25].
Monosulfoaluminate will react with the gypsum formed from the sulfate penetration PAGE 46 46 and water to produce ettringite, as shown in Equation 3 3, or from other phases shown in Equation s 3 4 to 3 6 [11,25]. For external sulfate ions, the rate o f deterioration is controlled by the ion penetration rate.
Since the sulfate ions must penetrate into the concrete before damage can be meas ured, a long test d uration is often required. Several theories have been proposed to explain the expansion mechanism upon and the crystallization pressure the ory [23]. The crystallization pressure theory is the more recent one and has been experimentally verified [28,29].
It is considered to be a more plausible mechanism of ettringite expansion. This theory explains the mechanical work exerted by confined crystals which cause ettringite to expand as shown in Equation 3 7 [34]. In addition, the results of the chemical sulfate attack tests were use d to validate that the dam age inflicted on the mixtures tested in physical sulfate attack exposures was not due to their susceptibility to chemical sulfate attack.
Table 3 1 shows the mixture designs of the tested mortar mixes with single, binar y, and ternary blends at different dosages of SCMs. The fine aggregate on the other hand, was a natura l siliceous sand with apparent specific gravity and absorption of 2.
Table 3 2 shows the concrete mixtures properties used in this study. PAGE 49 49 3. T he criteria were applied on both the mortar and concrete mixes of this study. The severity of exposure to sulfate SO 4 2 is divided to four ca tegories by the ACI guide to durable concrete starting from harmless S0 to very severe S3 and based on these categories, expansion limits were established for the ASTM C test. Mortar or concrete mixtures can be assigned to a specific exposure categ ory depending on their expansion results after the end of the sulfate exposure.
A mix is considered acceptable for use in S1 exposure environment if its expansion is less than 0. The mix that shows an expansion of less than 0. Although the test only required six bars, an extra bar was made in case one was broken during the demolding process. After the initial curing , the compressive strength of two cubes was measured following ASTM C [58] and if they yielded a mean c ompressive strength of 20 MPa psi or more, the initial comparator readings of the mortar bars were taken in accordance with ASTM C [57].
The solution was made at least 24 hours before submerging the bars to allow for it to cu re. The pH level was checked to be between 6 and 8 as per the standard test requirements. After the initial reading , the subsequent readings were taken at weeks 1, 2, 3, 4, 8, 13, and The solution was replaced with a new one at the time of each measurement age. T he average length change readings of the mortar mi xtures tested were calculated using Equation 3 9.
PAGE 51 51 3. For every mix, three steel prism molds were assembled with gauge studs at tached to each i nner mold end in accordance with ASTM C [57] as shown in Figure 3 3. Figure 3 4 shows a freshly finished prism before being covered and left for 24 hours for initial curing.
All the mixtures were mixed following ASTM C [59] and after moist curing for 28 days, initial length readings of the prisms were taken. In addition, the prisms were weighed after each length measurement to monitor their weight change during the course of the test since the specimens could show weight deterioration sooner than length expansion due to their large size.
After the initial reading , the prisms were put in a sealable container that contains 3. After every scheduled reading, the prisms were submerged in fresh sulfate solution and sealed in a container as shown in Figure 3 6. These result s were expected, and they fall in line with ACI guide to durable concrete.
PAGE 52 52 Out of t he 8 binary mortar mixes tested in this study only one mix failed at the six months point and between 39 weeks to 12 months three more mixes failed. Type IL with the same metakaolin replacement percentage showed strong resistance to sulfate attack at only 0. T he resutls of the tested binary mixes are shown in Figure 3 9.
The ternary mortar mixes showed high resistance to sulfate attack as seen in Figure 3 10 , and only two mixes failed after six months of exposure out of 17 ternary mixes in this study. Moreover, 12 months which was not expected since it contained slag cement that is known for its resistance to sulfate attack.
PAGE 53 53 The rest of the ternary mixes passed the ASTM C test which means that regardless of the cement type used, the SCM combinations included in each of those mixes increased th eir resistance to the ingress of the sulfates during the 18 months of exposure. Silica fume and slag gave the best results when included in ternary blends and proved to be most effecti ve in overcoming fly ash and metakaolin shortcomings.
In addition, the weight change of every mix was also low and the highest was around 70g as seen in Figure s 3 15 through 3 17 since all the specimens are still absorbing the solution due to their large dimensions. The specimens were made with lager dimensions which in turn added to the tim e needed for the sulfate to ingress through the specimens and hence the results are not expected to be collected during the time specified by ASTM C The test will continue on the concrete specimens a longer period of time until the effects of the chem ical sulfate attack have manifested the exposure.
Such resistance of the fly ash, slag, and silica fume is mostly attributed to the lower permeability due to small pore struc t ures gained from the use of slag, silica fume and fly ash [62]. Metakaolin i s known to have high alumina contents [64] However, combining metakaolin with a limestone blended cement Type IL gave a longer resistance against sulfa t e attack that only failed after 15 months of exposure reaching 0.
Silica fume and slag gave the best results when included in ternary blends and proved to be most effective in overcoming Fly ash and metakaolin shortcomings. All the tested concre t e prisms showed no failure readings after 18 months of exposure.
The concrete prisms will need to be kept under exposure for a longer period of time so that a PAGE 55 55 more realistic conclusion is reached about the performance of the materials used in the tested m i xtures. Silica fume and slag nullified the negative effects of both fly ash and metakaolin and it is recommended to add slag to metakaolin and silica fume to fly ash to increase their resistance to sulfate attack.
Concrete specimens are expected to show similar trends to the mortar on es but wi ll need more than 18 months to show clear results due to their large dimensions. PAGE 56 56 Table 3 1. Mixture designs of the mortar mixes. Design properties of the concrete mixes. Figur e 3 1. Mortar bars and cubes covered with plastic plates in the curing chamber Photo courtesy of author PAGE 59 59 Figure 3 2.
A concrete prism after finishing Photo courtesy of author Figure 3 5. Prisms in the sulfate solution bef ore being sealed Photo courtesy of author Figure 3 7. Ordinary cement mortar expansion results 0 0. Binary mortar mixes expansi on results 0.
Ternary mortar mixes expansion results Figure 3 OPC concrete mixes expansion results Fi gure 3 Binary Concrete mixes expansion results Ternary Concrete mixes expansion results Figure 3 Weight change in OPC concrete prisms Weight change in binary concrete prisms Figure 3 Cement paste can be deg raded both chemically and physically by sulfate attack [4]. Depending on the mechanism involved, sulfate attack can lower the conc This can cause concrete to fail in 5 years or less in severe cases of sulfate attack [4].
Concrete deterioration that occurs from crystallization and phase transitions of some salts is called physical salt attack PSA , and is also called salt hydration, salt scaling, or salt weathering [5].
While phase transitions are chemical reactions, the salts do not react with the cement hydration products. In PSA, the interaction between the salts and concrete occurs in the form of p ressures in the pores a physical mechanism. Damage as a result of the chem ical reactions between sulfate ions with the cement hydration products is typically referred to as chemical sulfate attack or just sulfate attack [5]. Cementitious systems have been designed to resist sulfate attack since the s [6] , and the introduction of sulfate resistant cements in the mid s significantly decreased the number of occurrences of chemical sulfate attack [7].
In addition, standardized accelerated tests for sulfate attack have been developed over the years such as ASTM C and ASTM C, although these tests are not safe from criticism [8] PAGE 68 68 and only measure the resistanc e to chemical sulfate attack using expansion [47,69]. Currently Development of a standardized test would help in efforts to provide guidanc e on materials and mixture proportions to preven t PSA [5]. For instance, practicing engineers routinely assigned any di stress to chemical sulfate attack if sulfate ions were found in soil or groundwater.
The Portland Cement Association PCA performed long term studies of concrete exposed to sulfate environments, and pictorially reported sulfate damage on concrete but did not discuss the ca uses of such distress until recently in a report that found PSA to be the cause of far more damage than chemical sulfate attack in those specimens [5,36]. Scaling and flaking of the concr typical signs of PSA because salts tend to crystallize in pores around the evaporation surfaces [70].
PSA depends on t he buildup of salt crystals inside concrete pores which creates pressure inside the pores that eventually leads to progressive scaling and flaking of the concrete surface [3]. PSA is thought to occur as a result of repeated ph ase changes that cause crystallization pressures in concrete pores, causing damage. Damage from sodium sulfate in particular was observed to occur during the wetting cycles as the sulfate solution becomes supersaturated with mirabilite after the dissolution of thenardite [23].
This transition occurs at ambient temperatures and humidities, potentially causing daily cycles with PAGE 69 69 the diurnal temperature and humidity changes. Figure 4 2 shows the stages of PSA damage on a specimen that was exp osed to such cycles in lab environment and eventually showed surface scaling. Continuous evaporation of sulfate solutions at the concrete surface leads to the formation of efflorescence which is usually harmless.
In contrast, surface scaling can be caused by subflorescence that accumulate in the layers beneath the surface at the same time.
Salt crystals during formation pressurize the pore walls in the subflorescence zone until the tensile streng th of the walls is surpassed, marking the start of deteriorati on that can be accelerated with the increase of the moisture and soluble and soluble salt contents [39,70,71]. Equation 4 1 describes how the crystallization pressure P can b e calculated as follows [3,72,73] : Where R is the ideal gas constant, T is the absolute temperature, V S is the molar volume of solid salt, C is the actual concentration, and C S is the saturation concentration.
Crystallizatio n pressure is applied from precipitation inside the pores of mirabilite [23]. The damage mechanism of PSA and whether it is independent from chemical sulfate attack is still controversial. Some studies conc luded that sulfate from sodium sulfate salts would react chemically with the Ca OH 2 from the hydration products to form calcium sulfate, a salt with low solubility and low propensity for PSA.
Additionally, the buildup of high concentrations of sulfate salts at the concrete surface from wicking and evaporation could cause classical chemical su lfate attack [38]. On the other hand, sulfate crystals accumulation on specim ens in field studies indicate that sulfate salts crystallization is also responsible for concrete deterioration [21] which is most likely not solely due to chemical sulfate attack.
The approach of proposed PSA tests found in the literature have been built on mimicking the condit ions where PSA has been found to occur in the field [11,36]. These conditions involve subjecting test specimens to partial immersion, full immersion and drying cycles, or full imm ersion.
The immersion and drying cycles method induces phase transition between mirabilite and thenardite by changes in internal RH. Full immersion on the other hand, is more rapid and severe when specimens are thermally cycled in highly concentrated solutions [5]. This study aims to compare potential methods for accelerating damage cau sed by PSA for use in a standardized test method. This was accomplished by testing c oncrete mixtures with different water cement ratios in partial and full immersion in sodium sulfate solutions at different concentrations under different temperature and re lative humidity cycling regimens for comparison.
PAGE 71 71 4. Table 4 1 shows the mix proportions of the tested mixes, while Table 4 2 shows the compositions of the cem ent types as measured by X Ray Fluorescence XRF [77].
Moreover, X Ray Diffraction and Rietveld Refinement were used to analyz e the cement composition, as shown in Table 4 3 [77]. Miami Oolite limestone was used as the coarse aggregate in this study an d according to tests performed according to ASTM C [55] it had an apparent speci fic gravity of 2.
Moreover, the fine aggregate was a natural siliceous sand that when tested per ASTM C [56] had an apparent specific gravity of 2. The examined test methods were divi ded into three environments as follows: a. Environment 1: 8 hours drying and 16 hours wetting i. Environment 2: 16 hours drying and 8 hour s wetting i. Environment 3: 16 hours cooling and 8 hours heating i.
PAGE 72 72 4. At day 30 , the initial weights of the specimens were taken before the commencement of the PSA test. The cycling regimen lasted for days, during which the specimen weights were taken every 15 days. The specimens were then left for six hours before taking their weights.
The debris was also collected from the solution in which t he cylinders were immersed using vacuum filtration Figure 4 7. The s olution s were filtered on day s 15 and 30 of each cycling month to collect any PAGE 73 73 scaled off concrete particles. Figure 4 8 shows a typical specimen setup.
This test was run for cycles where ever y 24 hours makes one cycle. The solutions were changed every 5 days, and the specimen s were weig hted every 10 days. On the days the specimens were measured, they were inspected and weighed at the end of the hot stage before being put in new solutions.
The old solutions w ere vacume filtered and the filter pap ers used were oven dried to determine the mass loss of the specimens. Type IL cement at 0. The 0. Also, the damage was noticed around the aggregates close to the surfaces of the specimens whic h could be attributed to the weak interfacial trans ition zone ITZ and local changes in water migration paths around aggregates from which concrete deterioration was found to start in some sulfate tests performed on fully immersed specimens [38].
The visual damage was also very mi nimal as shown in Figures 4 1 8 through 4 Overall, the period of cooling or wetting was not long enough for the environment to induce damage to the specimens.
The damage, however, was only found on the bottom third of the cylinders. Figure 4 2 5 shows the mass loss of the specimens during the course of the test. Figures 4 26 through 4 28 show the visual damage after the temperature cycles were completed. However, at the end of the hot cycle during measurements taking, a mass of solid sodi um sulfate was still present, as shown in Figure 4 A complete set of each test exposure was run for a few cycles while recording the temperatures from the thermocouples.
Figures 4 30 though 4 3 2 show one full cycle 24 hours of temperature measurements for environments E1, E2, and E3, respectively. This indicates that damage does not occur or is minimal at high temperatures and low relative humidity. The third environment had the highest mass loss of all environments tested, and the crystallization of the solution around the specimens was mostly noticed during the cold period of each cycle during which the specimens were mostly covered with a highly crystallized solution while during the hot hours t he crystallization decreased to the bottom third of the specimens.
Small surface scaling began to occur, with more damage likely with additional cycles. Another PSA study by Haynes et al. That study found much higher percentages of mass loss t han found in this study. Hence, s maller specimens increase the surface area volume ratio which in turn increases the evaporation, wicking, salt accumulation, and damage. The authors concluded that it could be used in accelerated testing methods for PSA, but also recommend ed testing concrete specimens as the next step.
The very high concentration resulted in damage on only the lower third of the cylinders in this study. The results show that the generation of the erosion products in cement concrete is related to temperature, relative humidity, and sulfate ion concentration, which affect each other. However, the corresponding formation [ ] concentration and temperature of anhydrite are more than 4. Therefore, there is a significant difference in the theoretical temperature from that reported by existing documents.
The mechanism of sulfate attack on cement and concrete was investigated based on principles of chemical thermodynamics. The XRD spectra show that the phase composition, intensity, and width of diffraction peaks of erosion products in cement are changed before and after sulfate attack. The sulfate solution concentration and erosion age have significant effects on the mechanical properties of the specimens. Although the compressive strength of the paste and mortar attacked by sulfate for 4 months decreases with the increase of sulfate solution concentration, the corresponding compressive strength of the concrete first increases and then decreases.
This is due to the double effects, i. The data used to support the findings of this study are available from the corresponding author upon request.
This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors. Read the winning articles. Journal overview. Special Issues. Academic Editor: Mohammad A. Received 18 Sep Revised 16 Dec Accepted 28 Jan Published 09 Mar Abstract Based on principles of chemical thermodynamics, the relationship between temperature and the Gibbs free energy of erosion products generated during the sulfate attack on cement concrete was deduced.
Introduction Sulfate attack on cement concrete can degrade the durability and reduce the service life of concrete building structures [ 1 , 2 ]. Theoretical Analysis The sulfate attack on cement concrete is a complex physical and chemical process [ 4 , 5 ]. Qualitative Analysis of the Erosion Products of Sulfate Attack on Cement Concrete The relationship between thermodynamic equilibrium constant and the Gibbs free energy of the reaction can be used to characterize the spontaneity of the generation of erosion products [ 27 ], written as equation 1.
Critical Ion Concentration of Erosion Products of the Sulfate Attack on Cement Concrete Some researchers [ 27 ] proposed the expression of the thermodynamic equilibrium constant, written as where stands for the thermodynamic equilibrium constant at standard conditions. Correspondingly, the decomposition reactions of the cement hydration products can be expressed as follows [ 19 , 33 , 34 ]: The reference values recommended by researchers [ 35 , 36 ] are listed in Table 1. Table 1. Table 2.
Table 3. Table 4. Table 5. Figure 1. Gibbs free energy of various erosion products under different conditions versus temperature. Figure 2. Curves of critical sulfate ion concentration and thermodynamic equilibrium constant with temperature. Figure 3. Variation curves of critical ions for different erosion products in system versus temperature. Figure 4. Curves of thermodynamic equilibrium constant and critical concentration of sulfate ion versus temperature.
Table 6. Figure 5. Figure 6. Figure 7. XRD spectra of phase composition of specimens attacked by sulfate solution. Figure 8. Mechanical properties of different specimens attacked by sulfate solution.
References A. Yao and J. Etris, Y. Fiorni, and K. Dhole, M. Thomas, K. Folliard, and T. Santhanam, M.
Cohen, and J. View at: Google Scholar O. View at: Google Scholar L. Pel, H. Huinink, K. Kopinga, R. Jiang, D. Niu, L. Yuan, and Q. Valencia, G. William, A.
Eugenia, and G. Axel, R. Torben, and C. View at: Google Scholar C. Michael, K. Steven, and B. Hekal, E. Kishar, and H. Liu, S. Different sulfates can effect the concrete differently. Magnesium sulfate is the most severe because of the presence of magnesium ions. These ions can cause additional corrosive reactions through the formation of Mg OH 2 and ettringite. It is also an important index that shows the degree of concrete degradation by sulfates and quantitatively characterizes the rates and processes of concrete damage, cracking, and spalling.
The establishment of a time-varying model of sulfate diffusion depth is the basis for both the design of concrete structures against sulfate attack and the improvement of structure durability.
As described in the second section of this paper, some relevant studies are still conducted, but the results are relatively inconclusive. Regarding this aspect, the mechanism analysis and experimental study were combined, and the progress of concrete degradation depth by sulfates was systematically studied in this paper, which has comprehensively considered a mass of parameter of complex environments for the first time.
Some models have already been established for the prediction of sulfate diffusion depth. These models can be generally divided into empirical and mechanism models that help to better understand the process of sulfate attacks. Although there are some limitations, these models were used as the research foundation of this study. Therefore, firstly it is necessary to briefly introduce and analyze these models.
Atkinson et al. Based on the regression analysis of a series of data, Atkinson et al. The porosity of concrete mainly affects the transport rate of sulfates and generally can be quantified by introducing the diffusion coefficient, an important factor in predicting sulfate diffusion depth in later models. The model considered the effect of the diffusion coefficient or in fact the porosity of concrete; however, the diffusion coefficient was considered as a constant, 3.
The accuracy of the model has not been experimentally verified and cannot be universally applied. Skalny et al. As for the pure mechanism models, Li et al. In this model, parameter is a relatively abstract concept that reveals the capacity of concrete to consume sulfate media, and the correctness of the model is difficult to verify and has never been experimentally verified directly.
Considering the problem of diffusion reaction, Lee et al. Therefore, these two models are essentially the same, only in different manifestations.
As shown by the analysis of the above models, the existing prediction models for the depth of concrete degradation by sulfates are not perfect, and one of their major defects is that they did not consider the effect of the diffusion characteristics of the sulfates in concrete or the time-varying feature of their diffusion characteristics on the development of diffusion depth, not to mention that some of them have not been experimentally verified to prove their correctness.
Although sulfate ions can enter into concrete by many methods such as permeation, capillary adsorption, and diffusion [ 1 ] in reality, diffusion is the main method of transportation.
Based on this background and the following rational assumptions, in this study, the time-varying characteristics of sulfate diffusion depth dominated by diffusion are firstly derived: 1 In a pure immersed aggressive environment, the sulfate ions enter into concrete mainly by diffusion. Generally, it is difficult to directly express the distribution gradient by an accurate explicit equation.
However, according to the study by Tixier and Mobasher [ 19 ], the effect of simplifying the curved distribution of the concentration of sulfate ions into a linear distribution on the accuracy of analysis can be neglected. Therefore, in this study, the concentration of sulfates was assumed to have a linear distribution with the change of depth, as shown in Figure 1 where is the diffusion depth; thus: where is the concentration of the sulfates on concrete surface, and is the initial concentration of the sulfates in the concrete.
Suppose that the diffusion amount of a unit volume of sulfate ions at time is chemically absorbed by all the calcium aluminates of concrete within the range when sulfate ions enter into concrete; the law of conservation of mass can be expressed as follows: where is the molar concentration of calcium aluminates.
Combining 7 and 9 , the following relationship can be obtained:. Integrating both sides of 10 within the sulfate diffusion depth yields. Expanding and rearranging the integrals of 11 , the sulfate diffusion depth can be expressed as follows:. As can be seen in 12 , sulfate diffusion depth is a complex variable and depends on the following parameters: the effective diffusion coefficient , the concentration of the sulfates on the concrete surface , the concentration of the sulfates initially existing in the concrete , the weighted mean stoichiometric number of the chemical reaction , the concentration of calcium aluminates , and the degradation time.
Moreover, it should be noted that the effective diffusion coefficient heavily depends on the porosity or the pore structure of concrete and changes as the variation of the porosity of concrete due to the sulfate attack; the sulfate diffusion depth model has in fact indirectly considered the effect of the porosity of concrete by introducing the effective diffusion coefficient into the model.
The sulfate diffusion depth model of 12 is derived in a pure immersed aggressive environment; however, the practical environment of sulfate degradation is more complex. Consequently, 12 is further derived in this section to properly consider the time-varying characteristics of the diffusion coefficient, concentration, and temperature of sulfate solution.
The diffusion coefficient reflects the diffusion rate of the sulfate ions in concrete material and closely related to the number and structure of the internal pores of concrete.
In the above diffusion equation, is assumed to be a constant, which is inconsistent with that of a practical situation, as the actual diffusion coefficient will differ significantly from the initial diffusion coefficient after the permeation and chemical reaction of sulfates [ 30 ].
Tumidajski et al. Although the initial diffusion coefficient is of important material parameter that quantifies the ability of concrete to resist the sulfate attack, it is actually hardly possible to obtain the initial diffusion coefficient directly by test as no diffusion occurs. Thus, the time-dependent effective diffusion coefficient given by 14 is recalculated using another referenced diffusion coefficient corresponding to any point of time , instead of. Thus, with 14 , it is easy to get.
Dividing 14 to 15 , the following equation is derived:. Therefore, the effective diffusion coefficient can be expressed by. Substituting 17 into 12 , a time-varying model of diffusion depth is developed:.
Existing studies indicate that, among the aggressive environment parameters, the concentration of solution, temperature [ 10 — 13 ], and mode of degradation e.
To evaluate the effect of the accelerated degradation modes on diffusion depth, Atkinson and Hearne [ 33 ] studied the correlation of concrete performance deterioration between the two following modes: soaked in sulfate solution on a long-term basis and dry-wet cycle.
It was found that the performance of concrete in the two degradation systems could be equated by an equivalent coefficient of 8. In other words, the rate of the performance deterioration of concrete caused by dry-wet cycle was eight times that of the concrete caused by pure soaking.
Dry-wet cycle accelerated the effect of ionic crystallization on the microstructure of capillary pores, further changing the diffusion characteristics of sulfate ions and thus affecting diffusion depth. Therefore, based on the experiment conducted by Atkinson and Hearne, in this paper, the acceleration effect of dry-wet cycle on the rate of sulfate diffusion is simply equivalent to the amplification adjustment of the diffusion coefficient as follows: defined as the coefficient of influence of dry-wet cycle on the diffusion coefficient of concrete.
Substituting it into 18 , it yields. Notably, 19 considers the effects of the time-varying characteristics of the diffusion coefficient and parameters of complex environments. Therefore, this model can be universally applied to a certain extent.
For a specific aggressive environment, the model parameters, , , , and so forth, are unique. Consequently, for any two given points of time and , the two corresponding depths of sulfate diffusion, and , can be calculated as follows:.
Dividing 20b by 20a , it yields where. The attenuation coefficient of diffusivity or in a specific environment can be solved from 21 and given by.
Thus, based on the two given diffusion depths by sulfate, and , at any two points of time and substituting 22b into 21 , the diffusion depth corresponding to any point of time can be calculated by. Therefore, Model 19 has a great engineering significance that, for a concrete structure actually subjected to sulfate attack, if the diffusion depths e.
It is self-evident from 24 — 26 that only one measured diffusion depth value at any point of time is needed to evaluate the progress of diffusion depth and hence 24 — 26 are probably more advantageous than However, as aforementioned, a mass of parameter of sulfate aggressive environment has significantly affected the sulfate diffusion process, and thus a relatively major error cannot be avoided if the degradation information at one point of time is relied solely on to infer the overall development.
Therefore, in this study, the degradation information at any two points of time is preferably used by the model 19 to predict diffusion depth, with greater advantages in terms of the rationality and accuracy of prediction that will be further demonstrated in the following model verification and comparison.
The rationality of 24 — 26 is still in doubt.
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