Impact of High-Performance Expansion and Shrinkage-Reducing Agents on the Mechanical Properties and Shrinkage Compensation of High-Strength Concrete

: A large number of binder ingredients such as cement and active mineral admixtures are used in the preparation of high-strength concrete, and the water:binder ratio is extremely low. This leads to a large amount of shrinkage of concrete at the early stage of curing, which poses a great threat to the safety and durability of the structure. To solve the cracking problem of high-strength concrete induced by high shrinkage, we choose to change the admixture to solve it. In this study, a high-performance expansion agent (HPEA) and shrinkage-reducing agent, which are currently studied in a small number, were selected by changing the way of admixture, and their effects on the strength and shrinkage of high-strength concrete were compared and analyzed. The results show that the addition of a HPEA is beneﬁcial to the compressive strength of concrete and sufﬁcient expansion can be obtained by using a high amount of HPEA, but there is an excessive and delayed expansion to produce cracks in the later stage. A shrinkage-reducing agent plays an adverse role in the development of concrete strength, but it performs better in inhibiting shrinkage. The combination of a HPEA and shrinkage reducing agent can largely avoid the formation of cracks, and the two have a certain synergy. The main reason is that a HPEA compensates for some of the negative effects of a shrinkage-reducing agent on concrete strength, and the shrinkage-reducing agent further strengthens the inhibition effect of a HPEA on concrete shrinkage, and to some extent avoids the risk of cracks caused by delayed expansion caused by admixture problems.


Introduction
Concrete cracking is a key factor that affects concrete pavement and its durability, and the main problem of ordinary road concrete pavement is its poor durability and easy cracking.The main reason for concrete pavement cracking is shrinkage in concrete in the process of setting and hardening, as well as damage caused by external loading and the environment during use [1].Currently, a large number of engineering examples and research data at home and abroad have shown that shrinkage is the main cause of nonstructural cracking [2][3][4].Therefore, improving the shrinkage performance of ordinary road concrete to reduce cracking has important engineering significance.
Concrete cracks are unavoidable; disasters can be minimized generally through internal maintenance, mixing with shrinkage reducers, expansion agents, and a variety of fibers to improve post-conservation [5][6][7][8][9].Among them, the expansion agent compensates for shrinkage by forming expansion elements in concrete [10][11][12][13].An agent with the right amount of expansion can improve the concrete pore structure and reduce concrete porosity [14].If the amount of admixture is too high, its resulting expansion stress could damage the internal structure of the concrete, leading to cracks, and causing a decrease in concrete strength and durability [15,16].
Applying a shrinkage-reducing agent is also an important way to prevent concrete cracking [17,18].It belongs to organic chemicals called surfactants [19,20] as they reduce the surface tension of the solution in the concrete capillaries to reduce the negative pressure in the capillary pores, thus reducing the dry shrinkage value generated during the concrete hardening process [21,22].Reducers also delay the appearance of the peak heat of hydration of the cement, which is very beneficial in alleviating shrinkage cracks related to temperature differences [23].However, retarding the heat of hydration of cement is manifested macroscopically as a delay in the setting time of concrete, which is detrimental to the development of early strength [19,24].It also introduces a portion of gas, which could reduce the compactness of the concrete structure, resulting in a decrease in concrete strength [25].Therefore, some scholars [26][27][28][29] compounded the expansion agent with a shrinkage reducer, in order to ensure that the mechanical properties of concrete are not affected, whilst achieving a better shrinkage reduction effect.Qosai et al. [26] indicated that the combination with shrinkage reducers based on CaO and MgO produced a synergistic effect of reducing the constrained shrinkage values as well as the risk of crack formation.Meanwhile, Liu et al. [27] found that a combination of an expander and shrinkage reducer performed significantly better than an individual admixture.The results showed that the addition of a shrinkage-reducing agent alone reduced the drying shrinkage by 44% and the total shrinkage by 25% at 180 d compared to unadulterated concrete, while the drying and total shrinkage at 180 d were reduced by 68% and 73%, respectively, when used in combination.
The expansion agent used in this study is high-performance concrete expansion agent (HPEA), which is mainly a double expansion agent of AFT combined with CaO.Compared with ordinary concrete expansion agents, it has better expansion performance and stability [30,31].Currently, domestic research scholars mainly studied the mechanical properties of concrete in the case of HPEA [31] or shrinkage reducer [32][33][34] alone; however, there has been less research and long-term observation on the combined use of HPEA and shrinkage reducer in concrete; therefore, this study mainly examined the shrinkage properties and mechanical strength of concrete in the case of HPEA, shrinkage reducer, and their combination.A series of tests were conducted for the shrinkage properties and mechanical strength of concrete at different ages, in order to provide a reference for actual construction.

Test Materials
The binder material is ordinary Portland cement of Chinese standard P.O 42.5 (similar to ASTM Type I cement) and Class II fly ash (complies with ASTM C618 class F type) whose chemical components are shown in Table 1.The coarse aggregate is composed of 5-20 mm basalt gravel (complies with ASTM C33/C33M-18).The fine aggregate was natural sand with a fineness modulus of 2.58.The water-reducing agent was a Polycarboxylic-based superplasticizer, with a water-reducing efficiency of 25%.Detailed physical properties are shown in Table 2.The test shrinkage reduction agent was produced mainly by Wuhan Sanyuan Special Building Materials Co., Ltd.(Wuhan, China), which consisted of an amphiphilic lowmolecular-weight polyether.
The chemical composition and physical properties of HPEA are shown in Tables 1 and 3 [35].

Matching Ratio
In the test, concrete with a water:cement ratio of 0.30 is selected as the basic mix ratio.m (cement): m (fly ash): m (sand): m (gravel): m (water) = 1:0.25:1.6:2.42.The total amount of binder material was kept constant, and the HPEA was substituted with the same proportion of cement using the internal mixing method.The water-reducing agent and shrinkage reducer were mixed externally.The apparent concrete density of 2450 kg/m 3 was used as the basis for calculation, and the water-reducing agent content was 1%, the shrinkage reducer admixtures were 0.5%, 1%, and 2%, and the HPEA admixtures were 8%, 10%, and 12%.The calculated fit is shown in Table 4.

Test Method
Compressive and flexural strengths were determined according to GB/T 50081-2002 [36] (similar to European Code EN1992-1-1.The loading rate of the compressive strength test was 0.6 MPa/s, and the loading rate of the bending test was 50 N/s ± 10 N/s.), and the specifications of the flexural and compressive specimens were 100 mm × 100 mm × 515 mm and 150 mm × 150 mm × 150 mm.A total of five groups were made, with three compression and bending test pieces in each group (take the average of the measurement results).Twenty-four hours after molding, all samples were sent to the standard curing room for curing (temperature 20 ± 2 • C, relative humidity 60 ± 5%) until the age of 3, 7, 28, 60, and 90 days.The test is shown in Figure 1a.
treatment.In order to accurately compare the shrinkage rate, according to standard GB/T 50082-2009 [37], the initial setting time of concrete is assume The non-contact concrete shrinkage meter, as shown in Figure 1b, is used to a measure the concrete shrinkage rate and record the data every 1 d.
The total shrinkage of concrete measured in this study is the shrinkag due to the loss of moisture to the outside world in unsaturated air.Autogeno is the shrinkage caused by the internal drying of concrete on the premise of change with the outside.We estimated drying shrinkage by calculating the d tween total shrinkage and autogenous shrinkage, ignoring the effects of curin [26,38].The drying shrinkage measured in this study is not very accurate, hydration degree related to autogenous shrinkage is affected by curing cond study, the influence of curing conditions is ignored to estimate the drying sh   The autogenous shrinkage and total shrinkage were measured by taking the specification GB/T 50082-2009 [37], and the drying shrinkage was predicted by calculating the difference between the two.According to the design mix proportion, each group shall produce three 100 mm specifications × 100 mm × 515 mm shrinkage test pieces, and are cured at 20 ± 2 • C and 60 ± 5% relative humidity.The test sample for determining the autogenous shrinkage needs to be sealed with plastic film to prevent moisture loss.The test sample for calculating the total shrinkage value can be cured directly without sealing treatment.In order to accurately compare the shrinkage rate, according to the Chinese standard GB/T 50082-2009 [37], the initial setting time of concrete is assumed to be zero.The non-contact concrete shrinkage meter, as shown in Figure 1b, is used to automatically measure the concrete shrinkage rate and record the data every 1 d.
The total shrinkage of concrete measured in this study is the shrinkage of concrete due to the loss of moisture to the outside world in unsaturated air.Autogenous shrinkage is the shrinkage caused by the internal drying of concrete on the premise of no water exchange with the outside.We estimated drying shrinkage by calculating the difference between total shrinkage and autogenous shrinkage, ignoring the effects of curing conditions [26,38].The drying shrinkage measured in this study is not very accurate, because the hydration degree related to autogenous shrinkage is affected by curing conditions.In this study, the influence of curing conditions is ignored to estimate the drying shrinkage.

Effect of HPEA and Shrinkage Reducer on the Strength of Concrete
The addition of HPEA reduces the fluidity of concrete, the slump decreases to 9 cm and has a relatively obvious thickening effect, which may be attributed to the formation of ettringite and Ca(OH) 2 .Concrete data, in terms of compressive and flexural effects, are shown in Figure 2. When the curing time was 3 d, the compressive strength of the component with the addition of the expander compared to the blank group J0/H0 increased; with the increase in the amount of expander, the compressive strength of concrete decreased.This is attributed to the low strength of the early mix, and the concrete showed microexpansion under the action of the expander.The surrounding constraint also decreased after the demolding, making the concrete partially loose in the early structure.From 7 to 28 d, the compressive strength of the test group H10 became significantly higher than that of the blank group J0/H0, while the groups H8 and H12 were not much different from the blank group and had slightly lower compressive strengths than the blank group.The compressive strength tends to be stable at 60 d to 90 d, the compressive strength of concrete in group H8 was still the lowest compared to the blank group J0/H0, while the compressive strength of concrete in groups H12 became lower than the blank group, and the compressive strength of concrete in group H10 was the highest at 80.5 MPa.Although the HPEA was involved in the hydration reaction to produce a higher-strength expansion source, the water:cement ratio in the current concrete design is low, and a large amount of water is consumed by the cement in the early stage; thus, it is difficult for the expander to produce a stable expansion source and, therefore, the concrete strength is lower in the early stage.It is worth noting here that the rate of increase in group H12 s compressive strength had a small increase from 28 d to 60 d.This is attributed to the delayed expansion caused by the continued hydration of the unhydrated HPEA in the late stage of the concrete reaction; the lower strength than the blank group after 90 d is attributed to the deformation of the internal structure of the concrete due to excessive hydration products.The concrete structure formed in a delayed reaction to basic stability, while the excess HPEA continued to undergo a hydration reaction to generate expansion sources, which led to the destruction of the internal structure; this is not conducive to the long-term development of concrete strength.
In the aspect of flexural strength, the flexural strength decreased with an increase in the admixture of the HPEA.In comparison with the sample group J0/H0, the 90-day bending strength of sample H8, sample H10, and sample H12 decreased to 8.2 MPa, 8 MPa, and 7.6 MPa, respectively.This is due to the filling effect of the expansion source generated by the expander on the concrete structure.The original existence of pores to provide space for flexural strength was altered by the HPEA filling the pores, making the structure denser and, at the same time, resulting in narrower spaces for flexural strength, thus hindering flexural strength.The addition of a shrinkage-reducing agent improves the fluidity of concrete and increases the slump to 14-15 cm. Figure 3 shows the effect of different amounts of the shrinkagereducing agent on the compressive and flexural strength of concrete.The inclusion of a shrinkage reduction agent made the strength of the concrete reduce more obviously, and with an increase in the amount, the decline became more significant; the early decline in the basic was more than 10%, with the growth of age-adverse effects not improving.The compressive and flexural strengths of the concrete with a 0.5% shrinkage-reducing agent were reduced by 18.4% and 12.5%, respectively, when the maintenance reached 90 d.This mainly resulted from two reasons.On the one hand, the shrinkage reducer incorporated to reduce the concentration of alkali in the solution, regulating the relative humidity, delaying the appearance of the peak heat of hydration, and delaying the concrete setting time; these factors made the early strength of concrete develop slowly.On the other hand, with an increase in curing time, the hydration products of concrete increased, and the strength of concrete in the later stages gradually improved stability.However, due to the pre-shrinkage agent's role in increasing the porosity of concrete, a non-dense microstructure resulted, playing a detrimental role in the strength of concrete; thus, it was difficult to return strength to normal levels [39,40].
Buildings 2023, 13, x FOR PEER REVIEW 7 of 17 The addition of a shrinkage-reducing agent improves the fluidity of concrete and increases the slump to 14-15 cm. Figure 3 shows the effect of different amounts of the shrinkage-reducing agent on the compressive and flexural strength of concrete.The inclusion of a shrinkage reduction agent made the strength of the concrete reduce more obviously, and with an increase in the amount, the decline became more significant; the early decline in the basic was more than 10%, with the growth of age-adverse effects not improving.The compressive and flexural strengths of the concrete with a 0.5% shrinkage-reducing agent were reduced by 18.4% and 12.5%, respectively, when the maintenance reached 90 d.This mainly resulted from two reasons.On the one hand, the shrinkage reducer incorporated to reduce the concentration of alkali in the solution, regulating the relative humidity, delaying the appearance of the peak heat of hydration, and delaying the concrete setting time; these factors made the early strength of concrete develop slowly.On the other hand, with an increase in curing time, the hydration products of concrete increased, and the strength of concrete in the later stages gradually improved stability.However, due to the pre-shrinkage agent's role in increasing the porosity of concrete, a non-dense microstructure resulted, playing a detrimental role in the strength of concrete; thus, it was difficult to return strength to normal levels [39,40].To further explore the synergistic effects of a HPEA and shrinkage reducer, the strength of the HPEA with a 10% dose was selected for compounding with a shrinkage reducer in this study.The effect of the results is shown in Figure 4, where the age of the concrete in the cases of compounding compressive and flexural strength is greater than the single shrinkage reduction agent and less than the strength of the single HPEA.This is attributed to the early stage of the hydration reaction, where the expander played a part in the expansion with loosening and shrinkage, suppressing the hydration effect of superposition in the later stage because of the adverse effects of the shrinkage-reducing agent, thus reducing part of the concrete's strength.In the case of the same amount of HPEA, the strength of concrete decreased with an increase in shrinkage reducer, which indicates that it was difficult to compensate for the higher strength depreciation of the shrinkage reducer in terms of the strengthening effect of the expander.
In summary, in the case of the HPEA compounded with a shrinkage-reducing agent, The fluidity of concrete is basically unchanged.Ca(OH)2 and calcium alumina produced by the former contributed to the development of concrete strength to some extent.However, due to the current design of high-strength concrete with its low water:cement ratio, the HPEA usually lacks the free water required for its hydration, resulting in a discontinuous hydration reaction, and delayed expansion at a later stage; these undermine the structural stability strength.Moreover, with the addition of a shrinkage reduction agent, reducing the water surface tension inside the concrete at the same time reduces the additional pressure of capillaries in the process of water loss.The reduction in tension to a certain extent makes the water distribution more uniform, which the HPEA plays a certain role in promoting.The shrinkage reducer also reduces the evaporation rate of the void solution, and retains part of the water; thus, the HPEA can better contribute to a positive To further explore the synergistic effects of a HPEA and shrinkage reducer, the strength of the HPEA with a 10% dose was selected for compounding with a shrinkage reducer in this study.The effect of the results is shown in Figure 4, where the age of the concrete in the cases of compounding compressive and flexural strength is greater than the single shrinkage reduction agent and less than the strength of the single HPEA.This is attributed to the early stage of the hydration reaction, where the expander played a part in the expansion with loosening and shrinkage, suppressing the hydration effect of superposition in the later stage because of the adverse effects of the shrinkage-reducing agent, thus reducing part of the concrete's strength.In the case of the same amount of HPEA, the strength of concrete decreased with an increase in shrinkage reducer, which indicates that it was difficult to compensate for the higher strength depreciation of the shrinkage reducer in terms of the strengthening effect of the expander.
In summary, in the case of the HPEA compounded with a shrinkage-reducing agent, The fluidity of concrete is basically unchanged.Ca(OH) 2 and calcium alumina produced by the former contributed to the development of concrete strength to some extent.However, due to the current design of high-strength concrete with its low water:cement ratio, the HPEA usually lacks the free water required for its hydration, resulting in a discontinuous hydration reaction, and delayed expansion at a later stage; these undermine the structural stability strength.Moreover, with the addition of a shrinkage reduction agent, reducing the water surface tension inside the concrete at the same time reduces the additional pressure of capillaries in the process of water loss.The reduction in tension to a certain extent makes the water distribution more uniform, which the HPEA plays a certain role in promoting.The shrinkage reducer also reduces the evaporation rate of the void solution, and retains part of the water; thus, the HPEA can better contribute to a positive effect on concrete strength to offset the negative impact of the shrinkage reducer, and the two result in a good synergistic effect [41,42].

Effect of Shrinkage-Reducing Agent and HPEA on the Autogenous Shrinkage of Concrete
Figure 5 shows the results of different doses of HPEA on the Autogenous shrinkage of concrete.The addition of the expander made the concrete expand before shrinking; the initial expansion increased with the dosing of the HPEA, and the autogenous shrinkage of concrete developed rapidly before 3 d and increased gradually after 3 d.It was found that the autogenous shrinkage of the concrete before 3 d significantly improved, with a 66% reduction in the autogenous shrinkage of sample H8 compared to J0/H0.After completing autogenous shrinkage, both experimental groups H10 and H12 underwent actual expansion, with expansion values of 25 µε and 288 µε, respectively.The expansion was caused by the hydration of the HPEA to produce calcium alumina as well as Ca(OH) 2 ; on the other hand, expansion is also attributed to a large amount of heat of hydration generated in the early stage of cement hydration.In this period, the expansion effect was stronger than the autogenous shrinkage caused by the drying that was occurring inside the concrete.As time passed, the water in the concrete gradually decreased, and the concrete gradually dried out, causing the shrinkage rate to increase significantly, especially in the first 3 d.After 3 d, due to the increase in concrete strength, there was a part of the concrete internal binding force that was partially offset by the expansion force generated by the HPEA, resulting in a decrease in the expansion and gradually becoming flat.It is noteworthy that sample H12 swelled again after 60 d.This delayed expansion reflects the fact that the HPEA failed to fully exert its compensatory effect on concrete autogenous shrinkage in the early stage, and the low water-to-binder ratio design made the concrete lack free water for its reaction.The HPEA reacted with capillary water and binder water in the concrete, only after 60 d of reaction, to undergo delayed expansion [27].
The autogenous shrinkage of concrete that occurred with a shrinkage reducer was similar to that with an HPEA, where there was also a process of expansion before shrinkage.With an increase in the amount of shrinkage reduction agent, the autogenous shrinkage value gradually reduced, as can be seen from Figure 6, compared with the blank group J0/H0.The experimental groups J0.5, J1, and J2 had autogenous shrinkage values that decreased by 21.4%, 49%, and 67.2%, respectively.On the one hand, since shrinkagereducing agents have a prolonging effect on the setting time of concrete and the hydration reaction of cement is slowed down, this reduces part of the additional stresses in concrete due to water loss, which in turn reduces the shrinkage stresses due to capillary water loss [43].On the other hand, the shrinkage-reducing agent also produced partial expansion in the early stages, which compensated for some of the shrinkage.

Effect of Shrinkage-Reducing Agent and HPEA on the Autogenous Shrinkage of Concrete
Figure 5 shows the results of different doses of HPEA on the Autogenous shrinkage of concrete.The addition of the expander made the concrete expand before shrinking; the initial expansion increased with the dosing of the HPEA, and the autogenous shrinkage of concrete developed rapidly before 3 d and increased gradually after 3 d.It was found that the autogenous shrinkage of the concrete before 3 d significantly improved, with a 66% reduction in the autogenous shrinkage of sample H8 compared to J0/H0.After completing autogenous shrinkage, both experimental groups H10 and H12 underwent actual expansion, with expansion values of 25 με and 288 με, respectively.The expansion was caused by the hydration of the HPEA to produce calcium alumina as well as Ca(OH)2; on the other hand, expansion is also attributed to a large amount of heat of hydration generated in the early stage of cement hydration.In this period, the expansion effect was stronger than the autogenous shrinkage caused by the drying that was occurring inside the concrete.As time passed, the water in the concrete gradually decreased, and the concrete gradually dried out, causing the shrinkage rate to increase significantly, especially in the first 3 d.After 3 d, due to the increase in concrete strength, there was a part of the concrete internal binding force that was partially offset by the expansion force generated by the HPEA, resulting in a decrease in the expansion and gradually becoming flat.It is noteworthy that sample H12 swelled again after 60 d.This delayed expansion reflects the fact that the HPEA failed to fully exert its compensatory effect on concrete autogenous shrinkage in the early stage, and the low water-to-binder ratio design made the concrete lack free water for its reaction.The HPEA reacted with capillary water and binder water in the concrete, only after 60 d of reaction, to undergo delayed expansion [27].The autogenous shrinkage of concrete that occurred with a shrinkage reducer was similar to that with an HPEA, where there was also a process of expansion before shrinkage.With an increase in the amount of shrinkage reduction agent, the autogenous shrink- reducing agents have a prolonging effect on the setting time of concrete and the hydration reaction of cement is slowed down, this reduces part of the additional stresses in concrete due to water loss, which in turn reduces the shrinkage stresses due to capillary water loss [43].On the other hand, the shrinkage-reducing agent also produced partial expansion in the early stages, which compensated for some of the shrinkage.For the shrinkage reducer and HPEA compound, the autogenous shrinkage curve is shown in Figure 7.It can be seen that early concrete shrinkage decreased with an increase in shrinkage reducer, which is consistent with the law when the two are blended separately.With an increase in the amount of shrinkage reducer, the peak shrinkage gradually decreased, and the shrinkage rate began to decline.Compared with the concrete mixed with expander and shrinkage reducer alone, the compounding of the shrinkage reducer and the expander was better in shrinkage compensation; the test group J2/H10 compensated the autogenous shrinkage in the early stage and obtained an actual expansion of 80 με.This may be attributed to the fact that the combination of the two agents allowed the concrete to obtain a higher initial expansion through the use of the expander in the early stage, while the rate of cement hydration slowed down by the inclusion of the shrinkage reducer, resulting in a reduction in autogenous shrinkage of the concrete in later stages.At the same time, the free water treated by the shrinkage reducer also had a certain promotion effect on the hydration of the expander; under the current low water:cement ratio design, this water reacted with the HPEA to generate a more stable source of expansion in the early stage which reduced the residual HPEA, and to some extent, reduced the problem of cracking due to delayed expansion in later stages.For the shrinkage reducer and HPEA compound, the autogenous shrinkage curve is shown in Figure 7.It can be seen that early concrete shrinkage decreased with an increase in shrinkage reducer, which is consistent with the law when the two are blended separately.With an increase in the amount of shrinkage reducer, the peak shrinkage gradually decreased, and the shrinkage rate began to decline.Compared with the concrete mixed with expander and shrinkage reducer alone, the compounding of the shrinkage reducer and the expander was better in shrinkage compensation; the test group J2/H10 compensated the autogenous shrinkage in the early stage and obtained an actual expansion of 80 µε.This may be attributed to the fact that the combination of the two agents allowed the concrete to obtain a higher initial expansion through the use of the expander in the early stage, while the rate of cement hydration slowed down by the inclusion of the shrinkage reducer, resulting in a reduction in autogenous shrinkage of the concrete in later stages.At the same time, the free water treated by the shrinkage reducer also had a certain promotion effect on the hydration of the expander; under the current low water:cement ratio design, this water reacted with the HPEA to generate a more stable source of expansion in the early stage which reduced the residual HPEA, and to some extent, reduced the problem of cracking due to delayed expansion in later stages.

Effect of HPEA and Shrinkage Reducer on Drying and Total Shrinkage of Concrete
The incorporation of HPEAs as shrinkage reduction measures for concrete has been commonly studied and used [43].HPEAs can effectively reduce the drying shrinkage of concrete within a certain range.Figure 8 shows the drying and total shrinkage of concrete mixed with different doses of HPEA over 90 d.The drying shrinkage of concrete was cal-

Effect of HPEA and Shrinkage Reducer on Drying and Total Shrinkage of Concrete
The incorporation of HPEAs as shrinkage reduction measures for concrete has been commonly studied and used [43].HPEAs can effectively reduce the drying shrinkage of concrete within a certain range.Figure 8 shows the drying and total shrinkage of concrete mixed with different doses of HPEA over 90 d.The drying shrinkage of concrete was calculated by subtracting the autogenous shrinkage from the total shrinkage [27].The drying shrinkage of the J0/H0 group developed rapidly in the early stage, stabilized at around 28 d, and reached 94 µε at 90 d, while the total shrinkage reached up to 650µε.With the increase in the dosage of the expansion agent, the drying and total shrinkage of concrete began to decrease.Compared with the test group H0/J0, the drying shrinkage of the test group H8 decreased by 62% in 90 days.This is attributed to the fact that the hydration of the HPEA produced products such as calcium alumina and Ca(OH) 2 , which filled the pores inside the concrete and made the concrete denser, thus improving the ability of the concrete to resist shrinkage and deformation; at the same time, during the hydration process, an increase in hydration products made the concrete undergo a certain amount of micro-expansion, which also offset part of the drying shrinkage.The test groups H10 and H12 produced partial expansions at 90 d of 14 µε and 40 µε, respectively.Observing the curves, it can be found that the difference between the drying shrinkage of the H10 and H12 groups was not significant, and the reason for this, as mentioned before, is mainly due to insufficient water in the concrete for the reaction of the expander.Some studies show that the water required for the complete reaction of the expansion agent exceeds 50% of the total water consumption [44].While the hydration reaction occurs, the ionic concentration of the solution inside the concrete slurry increases, which partially adversely affects the expansion originating from the expander [45].The effect of the shrinkage reducer admixture on the drying and total shrinkage of concrete was similar to that of the HPEA, as shown in Figure 9.The 90 d drying shrinkage of the test group with 0.5%, 1%, and 1.5% of shrinkage reducer was reduced by 26%, 28%, and 20%, respectively.Compared to the blank group, the addition of shrinkage reducer effectively reduced the drying and total shrinkage of concrete; however, the inhibition effect on concrete shrinkage does not increase with the increase in dosage, Test group J1.5 added a higher amount of the shrinkage-reducing agent but showed the highest dry shrinkage after 90 days.This may be attributed to the fact that, on the one hand, the shrinkage reducer reduced the capillary pressure by reducing the surface tension of the void liquid, which reduced the shrinkage stress caused by its drying; this achieved the effect of reducing the drying shrinkage.On the other hand, because the shrinkage-reducing agent retards the hydration rate of cement in a dry environment, which leads to incomplete hydration of cement, the hydration products of cement were not sufficient to fill the pore structure, leaving many harmful pores that adversely affected the shrinkage resistance of concrete [46].It is worth mentioning that the addition of a shrinkage-reducing agent also introduced a portion of gas, which further increased the number of harmful pores.When the admixture was too large, these pores promoted more than inhibited the drying shrinkage and caused a greater degree of shrinkage.The effect of the shrinkage reducer admixture on the drying and total shrinkage of concrete was similar to that of the HPEA, as shown in Figure 9.The 90 d drying shrinkage of the test group with 0.5%, 1%, and 1.5% of shrinkage reducer was reduced by 26%, 28%, and 20%, respectively.Compared to the blank group, the addition of shrinkage reducer effectively reduced the drying and total shrinkage of concrete; however, the inhibition effect on concrete shrinkage does not increase with the increase in dosage, Test group J1.5 added a higher amount of the shrinkage-reducing agent but showed the highest dry shrinkage after 90 days.This may be attributed to the fact that, on the one hand, the shrinkage reducer reduced the capillary pressure by reducing the surface tension of the void liquid, which reduced the shrinkage stress caused by its drying; this achieved the effect of reducing the drying shrinkage.On the other hand, because the shrinkage-reducing agent retards the hydration rate of cement in a dry environment, which leads to incomplete hydration of cement, the hydration products of cement were not sufficient to fill the pore structure, leaving many harmful pores that adversely affected the shrinkage resistance of concrete [46].It is worth mentioning that the addition of a shrinkage-reducing agent also introduced a portion of gas, which further increased the number of harmful pores.When the admixture was too large, these pores promoted more than inhibited the drying shrinkage and caused a greater degree of shrinkage.
effect on concrete shrinkage does not increase with the increase in dosage, Test group J1.5 added a higher amount of the shrinkage-reducing agent but showed the highest dry shrinkage after 90 days.This may be attributed to the fact that, on the one hand, the shrinkage reducer reduced the capillary pressure by reducing the surface tension of the void liquid, which reduced the shrinkage stress caused by its drying; this achieved the effect of reducing the drying shrinkage.On the other hand, because the shrinkage-reducing agent retards the hydration rate of cement in a dry environment, which leads to incomplete hydration of cement, the hydration products of cement were not sufficient to fill the pore structure, leaving many harmful pores that adversely affected the shrinkage resistance of concrete [46].It is worth mentioning that the addition of a shrinkage-reducing agent also introduced a portion of gas, which further increased the number of harmful pores.When the admixture was too large, these pores promoted more than inhibited the drying shrinkage and caused a greater degree of shrinkage.The synergistic effect of the shrinkage reducer and HPEA on drying and total shrinkage is shown in Figure 10, where the drying and total shrinkage of concrete had a significant reduction.In comparison with sample J0/H0, the 90-day drying shrinkage of samples J0.5/H10, J1/H10, and J2/H10 was reduced by 20%, 37%, and 40%, respectively, and the total shrinkage was reduced by 70%, 83%, and 87%, respectively, with the same HPEA admixture (10%).This may be attributed to the fact that the incorporation of a shrinkagereducing agent reduces the evaporation of water, which allows more water to react with the HPEA to generate stable expansion elements to fill the harmful pores caused by the shrinkage-reducing agent.A shrinkage reduction agent exists to delay the role of the hydration reaction, which also avoids the HPEA because of excessive water over-expansion caused by the internal microstructure of concrete damage.In terms of total shrinkage, the limited initial expansion in the early stage resulted in the total deformation of concrete at 90 d still being in a shrinkage state.The synergistic effect of the shrinkage reducer and HPEA on drying and total shrinkage is shown in Figure 10, where the drying and total shrinkage of concrete had a significant reduction.In comparison with sample J0/H0, the 90-day drying shrinkage of samples J0.5/H10, J1/H10, and J2/H10 was reduced by 20%, 37%, and 40%, respectively, and the total shrinkage was reduced by 70%, 83%, and 87%, respectively, with the same HPEA admixture (10%).This may be attributed to the fact that the incorporation of a shrinkagereducing agent reduces the evaporation of water, which allows more water to react with the HPEA to generate stable expansion elements to fill the harmful pores caused by the shrinkage-reducing agent.A shrinkage reduction agent exists to delay the role of the hydration reaction, which also avoids the HPEA because of excessive water over-expansion caused by the internal microstructure of concrete damage.In terms of total shrinkage, the limited initial expansion in the early stage resulted in the total deformation of concrete at 90 d still being in a shrinkage state.According to the above test results, in general, the HPEA is the most suitable agent for inhibiting the drying shrinkage of high-strength concrete.Moreover, the test group of compound shrinkage reducer and the expander proved to be excellent in the inhibition of According to the above test results, in general, the HPEA is the most suitable agent for inhibiting the drying shrinkage of high-strength concrete.Moreover, the test group of compound shrinkage reducer and the expander proved to be excellent in the inhibition of total shrinkage.

Conclusions
In this study, the effects of a HPEA and shrinkage-reducing agent on the mechanics and shrinkage of high-strength concrete at 20 ± 2 • C were studied to solve the crack damage caused by concrete shrinkage.According to the test results, the following conclusions are drawn.
(1) A HPEA can promote the development of early compressive strength of high-strength concrete, but it has a negative impact on the development of flexural strength.
The autogenous shrinkage and dry shrinkage of high-strength concrete decrease with the increase in HPEA content.An appropriate amount of HPEA can solve the shrinkage problem of concrete, but it needs to be well controlled.The insufficient amount of HPEA can not fully compensate for the shrinkage of concrete, while the excessive amount of HPEA can delay the expansion and lead to cracking, which makes it difficult to solve the concrete crack problem by using HPEA alone.(2) A shrinkage-reducing agent will reduce the hydration rate of high-strength concrete, prolonging the curing time, and is not conducive to the development of early strength of concrete, but it has obvious advantages in reducing the drying shrinkage of concrete, with the drying shrinkage reduction of more than 20%.However, the effect of the shrinkage-reducing agent is limited, and there is still a shrinkage phenomenon when adding high dose of the shrinkage-reducing agent.Therefore, adding an expansion agent alone can not solve the crack problem of concrete.
(3) The combined use of a HPEA and expansion agent shows a synergistic effect on high-strength concrete.With the increase in the content of the shrinkage-reducing agent, the strength of high-strength concrete at all ages decreases, but is still higher than that of the components added with the shrinkage-reducing agent alone.When the content of the shrinkage reducing agent is 2% and the content of the HPEA is 10%, the synergistic effect of the two admixtures is better, and the shrinkage effect of high-strength concrete is the strongest.There is still shrinkage due to an insufficient HPEA dosage, and the concrete does not get enough expansion at the early stage.In order to solve the problem of concrete shrinkage cracks, we will take the HPEA as the basis to seek other additives to carry out the research of synergy.

Figure 1 .
Figure 1.High-strength concrete test.(a) Strength test of high-strength concrete.(b shrinkage measurement and structural schematic diagram.

Figure 1 .
Figure 1.High-strength concrete test.(a) Strength test of high-strength concrete.(b) Non-contact shrinkage measurement and structural schematic diagram.

Figure 2 .
Figure 2. Influence of HPEA on the compressive strength and flexural strength of concrete.Figure 2. Influence of HPEA on the compressive strength and flexural strength of concrete.

Figure 2 .
Figure 2. Influence of HPEA on the compressive strength and flexural strength of concrete.Figure 2. Influence of HPEA on the compressive strength and flexural strength of concrete.

Figure 3 .
Figure 3.Effect of shrinkage-reducing agent on the compressive strength and flexural strength of concrete.

Figure 3 .
Figure 3.Effect of shrinkage-reducing agent on the compressive strength and flexural strength of concrete.
13,  x FOR PEER REVIEW 9 of 17 effect on concrete strength to offset the negative impact of the shrinkage reducer, and the two result in a good synergistic effect[41,42].(a) Compressive strength (b) Flexural strength

Figure 4 .
Figure 4. Effect of HPEA and shrinkage-reducing agent on the compressive strength and flexural strength of concrete.

Figure 4 .
Figure 4. Effect of HPEA and shrinkage-reducing agent on the compressive strength and flexural strength of concrete.

Figure 5 .
Figure 5.Effect of HPEA on the autogenous shrinkage of concrete.

Figure 5 .
Figure 5.Effect of HPEA on the autogenous shrinkage of concrete.

Figure 6 .
Figure 6.Effect of shrinkage-reducing agent on the autogenous shrinkage of concrete.

Figure 6 .
Figure 6.Effect of shrinkage-reducing agent on the autogenous shrinkage of concrete.

Figure 7 .
Figure 7. Effect of HPEA and shrinkage-reducing agent on the self-shrinkage of concrete.

Figure 7 .
Figure 7. Effect of HPEA and shrinkage-reducing agent on the self-shrinkage of concrete.

Figure 8 .
Figure 8. Effects of HPEA on concrete drying and total shrinkage.

Figure 8 .
Figure 8. Effects of HPEA on concrete drying and total shrinkage.

Figure 9 .
Figure 9.Effect of shrinkage-reducing agent on concrete drying and total shrinkage.Figure 9. Effect of shrinkage-reducing agent on concrete drying and total shrinkage.

Figure 9 .
Figure 9.Effect of shrinkage-reducing agent on concrete drying and total shrinkage.Figure 9. Effect of shrinkage-reducing agent on concrete drying and total shrinkage.

Figure 10 .
Figure 10.Combined effect of HPEA and shrinkage-reducing agent on concrete drying and total shrinkage.

Figure 10 .
Figure 10.Combined effect of HPEA and shrinkage-reducing agent on concrete drying and total shrinkage.

Table 2 .
Physical-mechanical properties of used material.

Table 3 .
Physical and chemical properties of HPEA.