CIVIL ENGINEERING 365 ALL ABOUT CIVIL ENGINEERING



AbstractUltrahigh-performance concrete (UHPC) is a new class of concrete, differentiated from conventional concrete by clear distinctions in its material behaviors. Understanding and managing time-dependent properties is necessary for the appropriate use of any concrete-like material. This study investigated the time-dependent properties of a suite of commercially available UHPC-class materials, with the goal being to characterize the behaviors then propose predictive performance models. To achieve the goal of this study, compressive creep and shrinkage experiments encompassing different environmental conditions were completed. The objectives of this research were as follows: (1) quantify the compressive creep behavior of different UHPC-class materials; (2) assess the effects of strength, maturity, and loading age on UHPC creep and develop predictive equations; (3) investigate unrestrained shrinkage behaviors of UHPC-class materials; (4) evaluate the effects of different environments, including low-humidity and high-humidity and sealed conditions, on compressive creep and unrestrained shrinkage of different UHPC-class materials and develop predictive equations; and (5) determine the coefficient of thermal expansion (CTE) of UHPC-class materials at different ages.IntroductionDeployment of ultrahigh-performance concrete (UHPC) in the design of structural components has been gaining momentum in recent years (Zhang and Graybeal 2015; Verger-Leboeuf et al. 2017; Wang et al. 2021). UHPC is composed of a very dense cementitious matrix with a discontinuous pore structure that results in low permeability and high compressive strength compared to conventional concrete (Graybeal 2006; Haber et al. 2018). Furthermore, the matrix is reinforced with high volumes of fibers, which allows for postcracking tensile capacity (Haber et al. 2018). The use of UHPC for pretensioned bridge girders is appealing to bridge engineers given its superior mechanical properties and durability. UHPC provides an opportunity for pretensioned girders to span greater lengths or use shallower structural depths while delivering more durable girders compared with conventional concrete solutions. The design of pretensioned UHPC girders requires an accurate estimate of the prestress losses caused by long-term deformations, including creep and shrinkage. Creep and shrinkage deformations are particularly important in pretensioned beams and girders because they cause a gradual loss of prestress force, affecting member capacity and potentially leading to serviceability problems in the structure. The growing interest in UHPC has created an urgent need for determining time-dependent properties and performance of UHPC, particularly compressive creep and shrinkage behaviors.Concrete members mainly experience three categories of time-dependent volumetric changes over their service life: creep, shrinkage, and thermal expansion or contraction (MacGregor and Wight 2009). These volumetric changes may cause internal stresses that can lead to cracking or deformations that may in turn cause serviceability problems in concrete structures.Creep is the tendency of a material to deform under a sustained stress in the direction of the applied load. Creep of concrete is mainly affected by parameters including age at loading, duration of loading, humidity and service conditions, specimen size and geometry, and sustained stress level (ACI 2005; Burkart and Müller 2008). Fig. 1 presents a schematic representation of time-dependent deformations in a cement-based material under sustained load in compression. An instantaneous elastic deformation occurs immediately after the load is applied; this deformation depends on the elastic modulus of the material, which varies with concrete maturity and stress level. If the compressive load is sustained, the concrete deforms as the cementitious layers become thinner within the concrete. Creep deformation only represents the length change of specimens due to the applied load; therefore, to determine creep deformation, the instantaneous elastic deformation and shrinkage of the material should be deducted from total deformation over time.Researchers have investigated UHPC creep using different UHPC mix compositions, environmental conditions, and curing regimes (Graybeal 2006; Flietstra 2011; Garas et al. 2012; Xu et al. 2018; Haber et al. 2018). Although low water-to-cementitious materials ratio and high compressive strength, both common to UHPC, are generally associated with reduced creep deformations in concrete, deformations of UHPC-class materials could also be increased due to the high content of cementitious materials and the large proportion of fine aggregates. Kamen et al. (2007; 2009) reported that according to experimental data, UHPC-class materials have high instantaneous and time-dependent deformations under compression and tension when loaded at early ages. This behavior is attributed to the relatively low stiffness of the material at the early age and the material constituents (i.e., the high amount of silica fume and the high volume of paste). The authors stated that creep deformation mainly occurs in the paste of concrete; therefore, the high paste volume in UHPC materials increases creep during early age. The body of knowledge available to date is suitable for initial evaluation of creep behavior but lacks the depth necessary for development of a predictive model.Shrinkage is a reduction in volume caused by the loss of water through evaporation or chemical reactions in the concrete (ACI 2005). Shrinkage deformation is not related to externally applied mechanical loads. The shrinkage that occurs after a concrete sets is typically described as being the summation of autogenous shrinkage and drying shrinkage. Autogenous shrinkage is the internal volume reduction associated with the hydration of cementitious materials. The internal chemical reactions and hydration produce capillary stresses that remove the moisture from pore structures, resulting in shrinkage of the cementitious material (ACI 2001). Therefore, concrete mixes with low water content may be expected to have larger autogenous shrinkage due to the higher capillary stresses generated between the cement particles. Drying shrinkage is the reduction in volume caused by the loss of water when the concrete surface is exposed to drying conditions such as low relative humidity and high winds. Drying shrinkage can be defined as the time-dependent deformation at a constant temperature for a specimen that is allowed to dry and is not subjected to any externally applied mechanical loads. This drying shrinkage typically increases with higher water content in the mix design (ACI 2001). Recent studies have shown that UHPC-class materials exhibit higher autogenous shrinkage and lower drying shrinkage compared to conventional concrete due to the high content of binder and low amount of water in the mixture (Xie et al. 2018; Wu et al. 2019). Different methods are proposed in these studies to effectively reduce the autogenous shrinkage of UHPC such as reducing the binder content, incorporating shrinkage reducing admixture, and increasing fiber contents. Meng and Khayat (2018) reported that the increase of steel fiber content led to significant reduction in autogenous shrinkage of UHPC.Thermal expansion or contraction is a volumetric change of concrete that occurs due to changes in temperature. Temperature changes that result in shortening can crack concrete members that are restrained by either another part of the structure or internal reinforcement. If the volumetric and time-dependent length change of concrete members are not considered properly in the design, serviceability problems may occur. Several studies (Naik et al. 2011; Xia et al. 2017) have shown that the coefficient of thermal expansion (CTE) of concrete depends on cement paste, aggregates, moisture conditions, age, and environmental factors such as temperature fluctuations and relative humidity; coarse aggregates are a major factor influencing the CTE of conventional concrete because coarse aggregates constitute a large portion of the concrete volume. However, UHPC-class materials generally do not include coarse aggregates but do include high cementitious materials and fiber contents. A few researchers have studied the CTE of UHPC (Graybeal 2006; Hussein et al. 2016), yet there is lack of sufficient experimental data to broadly assess the CTE values for UHPC-class materials.Research ObjectivesIn this study, time-dependent properties of eight commercially available UHPC-class materials were investigated. These properties included compressive creep and shrinkage behaviors that affect prestress losses. Multiple load levels and environmental conditions were considered in the experimental program. This research was part of a larger effort to develop a prestress loss model and predictive creep and shrinkage equations for UHPC-class materials by building on the framework of the existing conventional concrete models in the AASHTO LRFD (Load and Resistance Factor Design) Bridge Design Specifications (AASHTO 2020), hereafter referred to as AASHTO LRFD. Mohebbi et al. (2019) examined the AASHTO LRFD equations for creep and shrinkage of UHPC-class materials and discussed the applicability of the parameters in the equations. The authors reported that, according to the available experimental data, the current AASHTO LRFD equations do not accurately estimate the creep coefficient and shrinkage strain of UHPCs; therefore, some parameters require recalibration. Three parameters were selected to be discussed in this paper: compressive strength, loading age and concrete maturity, and humidity effects. Other parameters (e.g., size and shape effects, time-development response) will be discussed in a separate publication focused on prestress loss modeling (Mohebbi and Graybeal 2021).The objectives of this research were to: (1) quantify the compressive creep behavior of different UHPC-class materials; (2) assess the effects of strength, maturity, and loading age on UHPC creep leading to the development of predictive equations; (3) investigate unrestrained shrinkage behaviors of UHPC-class materials; (4) evaluate different environments, including identifying the effects of low-humidity and high-humidity and sealed conditions on compressive creep and unrestrained shrinkage of different UHPC-class materials and establishing the relationships among these factors; and (5) determine the coefficient of thermal expansion of UHPC-class materials at different ages. The paper presents a summary of the testing methods used, describes experimental observations and results, and presents predictive equations that include parameters defining the time-dependent performance of UHPC-class materials. Additional figures and performance data for each UHPC-class material are presented in the Appendix.Experimental Study and Testing ProceduresCompressive CreepTo study the compressive creep behavior of UHPC-class materials, eight different commercially available UHPCs (designated U-A through U-E, U-G, U-H, and U-J; described in Appendix Table 4) were tested largely according to ASTM C1856-17 (ASTM 2017), which references ASTM C512-15 (ASTM 2015). In following this test protocol, the sole exception related to the parameters used for the applied compressive load level. ASTM C512-15 (ASTM 2015) stipulates a maximum load level of 0.4fc′, where fc′ is the measured compressive strength of concrete at the initiation of loading. In this experiment, the creep behavior of UHPC was evaluated at early and mature ages, resulting in target sustained stresses of 0.65fc′ and 0.45fc′, respectively. The target compressive strength of the early-age samples was 96.5 MPa (14 Ksi), a value commonly used as the minimum required compressive strength of UHPC for pretensioned girders at strand release. The 0.65 factor is consistent with the compressive stress limit for concrete at the time of prestress application or posttensioning in section 5.9.2.3 of AASHTO LRFD (AASHTO 2020). The target compressive strength of the mature-age UHPC specimens at the initiation of the sustained load was 137.9 MPa (20 Ksi). The 0.45 factor is consistent with the proportional increase in strength that occurs as the compressive strength grows from 96.5 to 137.9 MPa (14 to 20 Ksi).The experimental variables included loading age, sustained stress level, relative humidity (H), and UHPC mixture. Unlike most previous studies on UHPC creep, this study investigated the effect of different environmental conditions on creep behaviors of UHPC-class materials. Environments included 80% H, 50% H, and a sealed condition. The experiments were designed to capture the data necessary to develop predictive relationships. UHPC products were supplied in preblended powder mix containing all the granular constituents. The chemical admixtures and fibers were also delivered by the UHPC manufacturers. The mix proportions and fiber properties for each UHPC-class material are given in Tables 4 and 5 in the Appendix. Further details on the mechanical behaviors of the materials can be found in El-Helou et al. (2021).Each individual creep test required four 102×203-mm (4×8-in.) cylinders and three 76×152-mm (3×6-in.) cylinders. The 76×152-mm (3×6-in.) specimens were used to test compressive strength and elastic modulus to ensure the specimens reached their target compressive strength before creep loading. The specimens were demolded 24 h after casting, and the ends of all cylinders were ground to within 0.5 degrees of parallel. The 102×203-mm (4×8-in.) cylinders were instrumented with two demountable mechanical strain gauges with a nominal gauge length of 152 mm (6 in.) at three evenly spaced locations around the circumference. All cylinders were stored in a controlled-environment room where the relative humidity was 50%±5% and the temperature was 23°C±2°C (73.4°F±3.6°F) until the specimens reached their target compressive strength. Two of the instrumented 102×203-mm (4×8-in.) cylinders were placed into the loading frames for creep testing, and the remaining two cylinders were used as companion shrinkage specimens to measure simultaneous shrinkage. The ground ends of the companion shrinkage specimens were sealed with epoxy to create the same volume-to-surface ratio as specimens installed in the creep frames.Creep testing was completed using four specially designed, hydraulically actuated load frames. The frames were located in an environmentally controlled room with 50% ± 5% humidity and temperature of 23°C±2°C (73.4°F±3.6°F). Fig. 2 shows the creep frames and the test setup. Frame I included specimens at the 80% H condition. An enclosure was built around the creep specimens in Frame I using a 406.4-mm-diameter (16-in.) clear duct. The duct was longitudinally flexible to provide easy access to the specimens, allowing frequent measurement of the specimens’ length change over time. To ensure the correct humidity condition was maintained, an automated system was installed to generate and control the humidity within the duct. The shrinkage companion samples were also placed inside the duct. The samples in Frame II and Frame IV were not covered by a duct and hence were subjected to the room’s relative humidity of 50%. Frame III contained the specimens in the sealed condition. Double layers of aluminum tape were used to seal the samples in Frame III.Each frame contained a stack of four samples, with each stack comprising two samples from each of two different UHPC-class materials. Frames I, II, and III contained the early-age samples subjected to 0.65fc′ sustained target stress, and Frame IV contained the mature samples subjected to 0.45fc′ sustained target stress. A target sustained load of 511.6 kN (115 kips) was applied to all the frames, resulting in a sustained stress of 63 MPa (9.15 Ksi) on each specimen. The loading frames operated in parallel from a single hydraulic pressure source, and the applied load was measured in Frame IV using a load cell. The oil pressures were monitored in all four frames to ensure the load was sustained during the test. Creep and companion shrinkage strain were measured using a micrometer. For each creep sample, the axial deformations recorded at the three locations around the circumference were averaged at each time step to produce average total strain. Creep strain was then calculated by subtracting instantaneous elastic deformation and companion shrinkage strain from total strain.Unrestrained ShrinkageTo study shrinkage behavior, the same UHPC-class materials used in the creep study were tested according to ASTM C157-08 (ASTM 2008) using the modifications described in ASTM C1856-17 (ASTM 2017). Specimens were unrestrained and tested in different drying conditions, specifically 50% H, 80% H, and a sealed condition. Specimens tested under different relative humidities were intended to reveal shrinkage behavior, including both internal and external drying effects. Specimens in the sealed condition were used to evaluate autogenous shrinkage because the lack of moisture exchange between the sample and the environment predisposed the observed shrinkage to be attributable to internal hydration reactions. Three replicate prismatic specimens with dimensions of 76×76×286  mm (3×3×11.25  in.) were monitored for each condition. Specimens were cast in the lab environment and were immediately covered with plastic. Specimens were removed from the molds after 24 h, except for U-A and U-G samples, which were demolded at 48 h due to the extended setting time of these materials. Afterward, specimens were stored in the previously described environmental conditions. For the specimens in the sealed condition, the six faces of the specimens were sealed using two layers of aluminum tape that were applied immediately after removal from the molds. Length-change and mass measurements started after demolding for drying specimens and after application of the tape for sealed specimens. Measurements were taken at frequent intervals over a period of approximately 300 days, in parallel with measurements taken for creep specimens, as described subsequently.Coefficient of Thermal ExpansionThermal expansion or contraction occurs due to temperature variations. The CTE is an indication of the expansion or contraction of a material as temperature fluctuates and is defined as the unit change in length per degree of temperature change. To determine the CTE of UHPC-class materials, four commercially available UHPC products (U-D, U-G, U-H, and U-J) were tested according to AASHTO T 336 (AASHTO 2019) test specifications for hydraulic cement concrete. The test method determines CTE by measuring the length change of a 102×178-mm (4×7-in.) concrete cylinder in a variable-temperature water bath. The temperature was uniformly changed between 10°C and 50°C (50°F and 122°F), and the specimen’s length change was measured using an electronic transducer. The test method requires that the concrete specimen be in a saturated condition before testing. However, saturation of UHPC is problematic due to its low permeability; therefore, determining when a specific degree of saturation had been reached would have been difficult. As recommended by Graybeal (2006), the specimens were sealed before testing by applying an epoxy to the exterior surfaces of the cylinders, with the exception of the bearing points of the supports and the displacement transducer.Compressive Creep Results and AnalysisCreep Behavior of UHPCA summary of compressive creep test results is presented in Table 1. The ratio of the applied stress to the compressive strength of UHPC-class materials varied slightly from the target values due to variations in compressive strength at the initiation of loading. For specimens loaded at the early age, actual applied stress was between 0.56fc′ and 0.66fc′, and for specimens loaded at the mature age, actual applied stress was between 0.37fc′ and 0.53fc′. The initial elastic deformations reported in the table were captured immediately after applying load to the creep specimens. Measurements of all the UHPC-class materials were recorded until between 386 and 500 days after loading. In terms of measurement frequency, creep and companion shrinkage strain were measured immediately before and after loading, 2–6 h after loading, then daily for 1 week, weekly or biweekly for 13 weeks, and monthly thereafter. The last measurement of each material was then used to calculate ultimate creep strain. The ultimate creep coefficient Cu was calculated by dividing the ultimate creep strain by the instantaneous elastic strain.Table 1. Summary of results for compressive creep tests of UHPC-class materialsTable 1. Summary of results for compressive creep tests of UHPC-class materialsUHPCRelative humidity (%)Loading age (days)Compressive strength, MPa (Ksi)Elastic modulus, GPa (Ksi)Applied stress to compressive strength ratio (%)Initial elastic strain (με)Ultimate creep strain (με)Ultimate creep coefficient (Cu)50% Cu90% CuU-Aa507106 (15.4)45.7 (6,634)591,9502,6721.3761565096119 (17.2)44.4 (6,438)531,4411,0030.7046276U-Ba507109 (15.8)40.1 (5,810)581,9472,7601.4271565097142 (20.6)40.6 (5,891)441,6221,4580.9053253U-Ca503105 (15.2)38.4 (5,574)602,4363,7191.532435058172 (24.9)49.3 (7,156)371,4321,0190.7115243U-D503106 (15.4)46.1 (6,692)592,0191,8700.93156803106 (15.4)46.1 (6,692)591,9861,8060.91285Sealed3103 (15.0)44.5 (6,455)612,0052,0301.0121245010137 (19.8)46.7 (6,770)461,7021,3570.804174U-Ea50795 (13.8)29.7 (4,302)662,9987,4022.4751205084136 (19.7)36.5 (5,300)462,0762,4251.1743305U-G508113 (16.4)45.0 (6,528)561,8182,0971.154124808113 (16.4)45.0 (6,528)561,9211,9951.045202Sealed8111 (16.1)45.1 (6,541)571,8772,0801.1151745030148 (21.4)50.8 (7,365)431,5421,2040.7828335U-H502107 (15.5)43.2 (6,271)592,5672,5220.98127802107 (15.5)43.2 (6,271)592,5672,3230.91127Sealed2107 (15.5)43.2 (6,271)592,6472,3780.901275014149 (21.6)48.6 (7,054)421,7381,1920.69583U-J503103 (14.9)39.5 (5,733)612,4203,2191.33483803103 (14.9)39.5 (5,733)612,4203,1451.304111Sealed3103 (14.9)39.5 (5,733)612,4603,1451.284835022145 (21.0)44.8 (6,494)441,7051,5770.9227175According to the results, the ultimate creep coefficient for specimens loaded at the early age ranged between 0.91 and 1.53 for all of the UHPC-class materials except for U-E, for which the ultimate creep coefficient was 2.47. The ultimate creep coefficient of specimens loaded at the mature age in the same environmental condition was between 0.68 and 1.17. According to Meyers et al. (1972), typical creep coefficients for mature conventional concretes range between 1.5 and 3.0; therefore, UHPCs loaded at both early and mature ages have shown less ultimate creep compared with conventional concrete except for U-E, which had a lower compressive strength and a lower elastic modulus at the early loading age compared with the other UHPC-class materials.Results indicate that UHPC specimens loaded at the mature age showed nearly half the ultimate creep of those loaded at the early age in most of the UHPC-class materials tested in this study. As shown in Table 1, early-age specimens were continuing to develop mechanical properties (e.g., strength and stiffness) when creep loading was applied. Given that all test specimens were loaded to approximately the same level, it is clear that the proportionally higher stress on the early-age specimens caused substantially more creep.The measured deformations due to creep and companion shrinkage of all UHPC-class materials tested in this study are presented in the Appendix (Fig. 12). According to the measured data, UHPC specimens loaded at the early age reached larger long-term creep strain at a significantly faster rate than the mature-age specimens in the same environmental condition. Fig. 3 shows logarithmic plots of creep strain for all UHPC-class materials loaded at early and mature ages in 50% H. Comparison of the plots shows that ultimate creep strain among mature-age specimens was nearly half that of early-age specimens. In addition, Fig. 3 illustrates some differences in the creep behaviors of the individual UHPC-class materials.According to the measured data, most creep strain in specimens loaded at the early age occurred near the beginning of testing. Table 1 summarizes the number of days that were required for each UHPC-class material to reach 50% and 90% of ultimate creep. Fig. 4 presents the proportional relationship between intermediate creep measurements and ultimate creep for each UHPC-class material in 50% H. Results demonstrate that 50% of ultimate creep in the specimens loaded at the early age occurred within 7 days after loading, and 90% of ultimate creep was attained between 27 and 156 days after loading [Fig. 4(a)]. Results for the early-age specimens are particularly relevant to the creep behavior of pretensioned UHPC girders because the prestressing force is expected to be transferred into the girder at a target compressive strength of 96.5 MPa (14 Ksi). According to the creep behavior of the specimens, it can be concluded that larger prestress losses, creep, and deformations, including camber, are likely to occur in UHPC pretensioned girders if the strands are released when the compressive strength and the elastic modulus of UHPC are lower. In addition, secondary curing of the pretensioned girders after releasing the strands may not effectively reduce creep behavior in the girders because a large proportion of creep may occur within a short timeframe after strand release.For specimens loaded at the mature age [Fig. 4(b)], 50% of ultimate creep was attained between days 4 and 53 depending on the UHPC material, and 90% of ultimate creep was attained between days 83 and 335. This difference in creep behavior between early-age and mature-age UHPC indicates that if a UHPC develops a larger proportion of its mechanical properties before loads are applied, then ultimate creep is significantly less, and the timeframe to reach ultimate creep strain is longer than that of the specimens loaded at the early age.Effect of Strength of UHPCTo quantify the strength effect for a UHPC in a 50% H environment, the ultimate creep coefficient of each UHPC-class material (Cu) was normalized by the ultimate creep coefficient of the early-age specimens (Cue) in the same class material. A strength-correction factor was then calculated for each mature-age specimen. The strength-correction factor modifies the ultimate creep strain of mature-age specimens with higher compressive strength based on the ultimate creep strain of the specimens loaded at an early age. To develop a predictive model for the strength-correction factor, normalized creep values were plotted versus compressive strength measured at the initiation of loading. Results are presented in Fig. 5.Strength-correction factors varied between 0.5 and 0.85 for all the UHPC-class materials tested in this study. Section 5.4.2.3 in the AASHTO LRFD (AASHTO 2020) recommends a strength-correction factor for conventional concrete. The strength-correction factor value is 1.0 for conventional concrete with a compressive strength of 27.6 MPa (4 Ksi) at release and a final compressive strength of 34.5 MPa (5 Ksi) at service, which is 1.25 times the initial compressive strength at prestress transfer (Tadros et al. 2003). The AASHTO LRFD correction factor is used to modify the ultimate creep (and shrinkage) of conventional concrete with a different compressive strength at release. The AASHTO LRFD equation in its present form is not likely to apply to UHPC-class materials because UHPC exhibits considerably higher compressive strengths at release and service compared with conventional concrete. However, a similar approach was implemented to develop a new strength-correction factor kf for UHPC-class materials [Eq. (1)]. The equation proposes a value of 1.0 for creep of UHPC-class materials with a compressive strength of 96.5 MPa (14 Ksi) in a 50% H environment at release and a compressive strength of 124 MPa (18 Ksi) at service; then, the equation modifies the ultimate creep of UHPCs for higher compressive strength at release. The proposed strength correction factor is also plotted in Fig. 5. Results demonstrate reasonable agreement between the measured UHPC data and the proposed equation (1) where fci′ = UHPC compressive strength at the time of load application or prestress transfer.Effects of Loading Age and Maturity of UHPCThe creep behavior of concrete depends on the maturity and age of the concrete when load is initially applied. To assess the loading age and maturity effects on UHPC, Fig. 6 plots normalized creep values, as previously discussed, versus UHPC age at the time of loading. Early-age values, which in this normalized plot equal 1.0, are plotted along with the normalized mature-age values that varied between 0.5 and 0.85. The proposed loading age correction factor in Eq. (2) and the AASHTO LRFD (AASHTO 2020) provision in section 5.4.2.3 are also plotted in Fig. 6. In these relationships, ti is the age of concrete (in days) at first load application (i.e., prestress transfer). The creep coefficient of UHPC may not begin to decrease until after the material is more mature than a comparable conventional concrete; therefore, the AASHTO LRFD relationship has been revised to set the factor as 1.0 before 7 days and to use an updated recalibrated relationship after 7 days. The proposed relationship also has a floor of 0.5, which occurs at approximately 100 days (2) Loading age correction factor={1for  ti<7(ti−6)−0.15≥0.5for  ti≥7}Effects of Relative Humidity and Environmental ConditionsRecall that in this study three environments were evaluated: 80% H, 50% H, and a sealed condition. Creep behaviors of U-D, U-G, U-H, and U-J specimens were evaluated in these conditions. The performance of each material is presented in the Appendix (Fig. 13). Test results demonstrate a slight difference in creep behaviors among UHPC-class materials in different environmental conditions. The ultimate creep strain for all four UHPC-class materials in 80% H was less than that of the UHPC-class materials in 50% H. To develop a predictive linear relationship between UHPC creep and relative humidity, six different creep coefficient data points for each UHPC-class material, measured on different days, were selected and are presented in Fig. 7. The selected data points included the early measurements, recorded within the first 28 days, and the later measurements, recorded between 55 and 445 days. Results show that the high-humidity environment reduced the creep coefficient and that the slope was different for each of the UHPC-class materials. In addition, results associated with the sealed condition of the selected data points are presented at the end of the horizontal axes in Fig. 7. These results represent the basic creep of the UHPC-class materials, which is defined as creep without moisture exchange between concrete and the environment (ACI 2005). The difference in overall maximum creep coefficient between the sealed condition specimens and the 80% H specimens was 0.11. These results demonstrate that a sealed condition is not necessarily equivalent to a high-humidity condition because a UHPC with a low water-to-cementitious-materials ratio in a sealed condition might exhaust the mix water and cease hydrating earlier than the same UHPC would in a high-humidity environment.To determine the effect of humidity on creep behavior of UHPC-class materials, the measured creep strain (C) of UHPCs was normalized by the creep strain of specimens in 50% H (C50%) recorded at the same age. Results are presented in Fig. 8. Because the goal was to determine the long-term effect of humidity on UHPC creep in the context of long-term prestress loss estimation, data points measured after day 56 were used to calculate the relationships, and earlier measurements were excluded. A line of best fit based on the linear regression analysis was then plotted. The equation for UHPC-class materials is shown in Fig. 8. The light gray dashed lines are the line of best fit of each UHPC material, and the black dashed line is the line of best fit of all the measured data. Section 5.4.2.3 in the AASHTO LRFD (AASHTO 2020) provision recommends a humidity correction factor to modify the creep coefficient of conventional concrete in different environments. This factor is inversely proportional to relative humidity, and at 70% H is 1.0. For the purpose of comparison with the measured UHPC data, the AASHTO LRFD equation was normalized by its value at 50% H (Fig. 8). The results demonstrate that, as expected, the slope of the line of best fit for UHPC-class materials was less than the AASHTO LRFD equation for conventional concrete. This finding is not unexpected given that UHPC-class materials have more a compact microstructure and their pores have greater discontinuity compared with conventional concrete. A humidity predictive model for creep of UHPC khc is proposed in Eq. (3), delivering a value of 1.0 for 50% H and applying a correction factor for other humidity conditions; where H in Eq. (3) is relative humidity in percent (3) Shrinkage Results and AnalysisTable 2 summarizes key experimental results for shrinkage behavior of UHPC-class materials. Recall that the shrinkage results presented in this study do not include the early shrinkage occurring between setting and demolding the specimens. The goal of this study is to evaluate the shrinkage of UHPC-class materials within the context of its effect on prestress losses. According to the results, the total shrinkage strain (in microstrain) of UHPCs in the 50% H drying condition varied between 300 (U-D) and 812 με (U-C) except for U-E material, which was 1,283 με. The autogenous shrinkage strain of UHPCs varied between 202 (U-D) and 872 με (U–E), as determined by the results from the sealed samples. The shrinkage strain of UHPCs was commonly within the range associated with well-designed conventional concrete mixes. Because the mix design volume fractions, water contents, types of cementitious materials, and inert materials within each UHPC-class material were different, the shrinkage value for some products was higher than others. Results indicated that materials with higher water content tended to exhibit more shrinkage and creep; for example, material U-E employed the highest water content and exhibited substantially more shrinkage and creep than the other UHPC-class materials.Table 2. Summary of results for shrinkage of UHPC-class materialsTable 2. Summary of results for shrinkage of UHPC-class materialsUHPCRelative humidity (%)Total shrinkage strain, S (με)Total mass reduction (%)50% S90% SU-Aa506990.722891Sealed6020.052160U-Ba507411.4640180Sealed4770.0928180U-Ca508120.557180Sealed7880.1014180U-D503000.451456801780.141456Sealed2020.052256U-Ea501,2830.88790Sealed8720.08728U-G505180.50857803250.02714Sealed3910.061421U-H503650.7228211802280.2456211Sealed2700.0556211U-J506110.592790805520.152790Sealed5840.042790Total shrinkage of UHPCs in the 80% H environment was between 178 (U-D) and 552 με (U-J), which was observed to be less than that of the UHPCs in either the sealed condition or the 50% H condition. This level of shrinkage indicates that the higher-humidity environment reduced total shrinkage of the UHPCs tested in this study. In other words, there was minimal to no drying shrinkage for UHPC in an 80% H environment. This finding is consistent with French standard recommendations for UHPC-class materials wherein UHPC drying shrinkage is neglected for environmental relative humidities greater than 80% [French standard NF P18-710 (French Standard 2016)]. In addition, the total mass reduction of the UHPC-class materials is given in Table 2. Results show that the total mass reduction of UHPCs was minimal—less than 1.46% even in the 50% H drying condition. However, UHPC specimens in the sealed and higher-humidity conditions exhibited less mass reduction compared with those in the 50% H drying condition.Results of total, drying, and autogenous shrinkage strain for all UHPC-class materials measured in this study are plotted and presented in the Appendix (Figs. 14 and 15). Results show that the shrinkage rate of UHPCs was higher during the early-age timeframe, with 50% of total shrinkage being attained between 7 and 56 days for all the UHPC-class materials. The ages at which each UHPC-class material reached 50% and 90% of total shrinkage strain in the different environmental conditions are summarized in Table 2. In addition, autogenous shrinkage strain of UHPCs was nearly as large as total shrinkage strain. Fig. 9 presents autogenous shrinkage versus total shrinkage for UHPC-class materials in 50% H. Lines of identity and best fit are plotted. The slope of the line of best fit was 0.8, indicating that the average autogenous shrinkage strain of the UHPC specimens during the timeframe from demolding through the final mature-age measurement was approximately 80% of total shrinkage strain.To investigate the effects of different environmental conditions, unrestrained shrinkage behaviors of U-D, U-G, U-H, and U-J were evaluated. The individual shrinkage behavior of each material is presented in Fig. 16 in the Appendix. Results demonstrate that total shrinkage of the UHPCs in the 50% H drying condition was higher than that in the sealed and 80% H conditions. In fact, higher humidity reduced total shrinkage by 41%, 37%, 37%, and 10% for U-D, U-G, U–H, and U-J, respectively, compared with those of the UHPCs measured in 50% H. In addition, total shrinkage of UHPCs in 80% H was similar to that in the sealed condition. These observations were consistent for all four UHPC-class materials; however, U-J exhibited minimal differences in total shrinkage measured among different environmental conditions.To consistently present the relationship between total shrinkage of UHPCs and relative humidity, six different data points for each UHPC-class material, as measured on different days, were selected and are shown in Fig. 10. The selected data points included early-age measurements, recorded within the first 28 days, as well as the long-term measurements, recorded between days 56 and 295. In addition, results associated with the sealed condition for the selected data points were presented at the end of the horizontal axes in Fig. 10. Results indicate that total shrinkage increased as humidity decreased and that the effect of the change in humidity builds with time. In the sealed condition, results show that total shrinkage strain of UHPCs was similar to and often slightly greater than shrinkage strain measured in the high-humidity environment.To develop a relationship for a predictive model, measured shrinkage strain (S) was normalized by the shrinkage strain of specimens measured in 50% H (S50%) recorded at the same age. Results are presented in Fig. 11. The purpose of this study was to develop a numerical model to account for the long-term effect of humidity on the shrinkage behavior in UHPC-class materials and to estimate long-term prestress losses; therefore, data points measured after day 56 were used to calculate the relationships, and the early-age measurements were excluded. A line of best fit was then plotted, as shown in Fig. 11. The light gray dashed lines are the line of best fit of each UHPC material, and the black dashed line is the line of best fit of all the measured data. Comparison of data shows that the U-J material was less susceptible to the high-humidity condition compared with other UHPC-class materials.Section 5.4.2.3.3 in AASHTO LRFD (AASHTO 2020) recommends a humidity correction factor to modify the total shrinkage strain of conventional concrete to account for environments with different relative humidity [Eq. (4)]. For the purpose of comparison with the measured UHPC data, the AASHTO LRFD equation was normalized by its value at 50% H [Eq. (5)] and is presented in Fig. 11. Results demonstrate that the slope of the line of best fit for the UHPC-class materials was close to that of the AASHTO LRFD normalized line. Therefore, it is concluded that the current humidity correction factor in AASHTO LRFD (AASHTO 2020) can be appropriately used for UHPC-class materials (4) (5) Normalized AASHTO:khs(AASHTO)khs(AASHTO@H=50%)Coefficient of Thermal Expansion ResultsA summary of CTE results for U-D, U-G, U-H, and U-J at different ages is given in Table 3. According to these results, the coefficient of thermal expansion of the UHPC materials was between 11.8×10−6 and 13.9×10−6  mm/mm/°C (6.6×10−6 and 7.7×10−6  in./in./°F). In addition, small differences were observed between CTE values measured at different ages for UHPC-class materials. The weight of the specimens was also measured before and after the CTE test to examine the effectiveness of the sealing epoxy. It was observed that UHPC gain weight was less than 0.04% of the specimen weight, indicating the effect of the water saturation of concrete on CTE results was eliminated. Graybeal (2006) reported that the average CTE of a UHPC was approximately 15×10−6  mm/mm/°C (8.3×10−6  in./in./°F), whereas the UHPC products tested in the current study exhibited lower CTE values. For normal-weight concrete, CTE values typically range from 9×10−6 to 12.6×10−6  mm/mm/°C (5×10−6 to 7×10−6  in./in./°F) for concrete made with siliceous aggregates and from 6.3×10−6 to 9×10−6  mm/mm/°C (3.5×10−6 to 5×10−6  in./in./°F) for concrete made with limestone or calcareous aggregates (MacGregor and Wight 2009). These findings indicate that the UHPC-class materials exhibited CTE values close to the normally expected values for conventional concrete made with siliceous aggregates.Table 3. Summary of results for coefficient of thermal expansion of UHPC-class materialsTable 3. Summary of results for coefficient of thermal expansion of UHPC-class materialsUHPCAge (days)CTE (×10−6  mm/mm/°C)Average CTE (×10−6  mm/mm/°C)Standard deviation (×10−6  mm/mm/°C)Weight gain (%)U-D241, 25212.7, 12.612.70.1<0.01U-G736, 736, 74013.9, 13.7, 13.913.80.1<0.02U-H2, 6, 811.9, 11.8, 12.011.90.1<0.0128, 29, 3012.1, 12.2, 12.012.10.1<0.03U-J14, 20, 2112.6, 12.6, 12.112.40.3<0.03121, 121, 12212.9, 12.8, 12.812.80.1<0.04ConclusionsIn this study, the time-dependent properties of UHPC-class materials that affect prestress losses were investigated, including compressive creep, unrestrained shrinkage, and thermal expansion and contraction. The creep and shrinkage tests were conducted in different environments, including low-humidity (50% H), high-humidity (80% H), and sealed conditions. This research was part of a larger effort to develop prestress loss models and structural design guidance for pretensioned UHPC girders. Results of this study combined with the current AASHTO LRFD (AASHTO 2020) specifications, and the results of an ongoing, large-scale testing program will be used to develop new prestress loss models for pretensioned UHPC girders (Mohebbi and Graybeal 2021).The following conclusions were reached based on the test results and observations made during this study: 1.UHPCs loaded at both early and mature ages exhibited less ultimate creep compared with the normally expected value for conventional concrete. The ultimate creep coefficient for specimens loaded at a mature age was between 0.68 and 1.17.2.The ultimate creep for UHPC specimens loaded at a mature age was approximately half the ultimate creep for specimens loaded at an early age. Results demonstrated that 50% of ultimate creep in the specimens loaded at an early age in the 50% H environment had been attained between 1 and 7 days after loading, and 90% of ultimate creep had been attained between 27 and 156 days. This finding indicates that delaying the application of sustained compressive forces onto UHPC until it approaches its final mechanical properties can significantly reduce the effects of creep on the member.3.The strength effect on creep behavior of UHPC-class materials was evaluated, and a new strength correction factor was developed [Eq. (1)]. In addition, the applicability of the loading age correction factor in the AASHTO LRFD (AASHTO 2020) specifications was examined relative to the creep of UHPC-class materials. A revised factor, shown in Eq. (2), was proposed to better align with the UHPC data.4.The effect of humidity on creep and unrestrained shrinkage among UHPC-class materials was investigated. A new correction factor, shown in Eq. (3), was developed to account for the effect of humidity on creep. In addition, it was observed that the shrinkage humidity correction factor in the AASHTO LRFD (AASHTO 2020) was acceptable for UHPC-class materials.5.The shrinkage of the eight UHPC materials tested at 50% H ranged from approximately 300 to 1,300 με at 300 days after demolding. This finding indicates that UHPC mix designs can offer widely varying shrinkage performance and that UHPC shrinkage may exceed shrinkage levels commonly observed in conventional concrete.6.The drying shrinkage of UHPC in the 50% H laboratory environment was small, indicating that UHPC formulations may be less susceptible than conventional concrete to drying effects commonly encountered in construction environments. In addition, autogenous shrinkage of UHPCs was observed to be much greater than drying shrinkage, with measured autogenous shrinkage strain approximately 80% of measured total shrinkage strain.7.CTE results revealed that the UHPC products exhibited CTE values between 11.8×10−6 and 13.9×10−6  mm/mm/°C (6.6×10−6 and 7.7×10−6  in./in./°F). CTE values for most of the UHPC-class materials tested in this study were within the range of the normally expected value for conventional concrete made with siliceous aggregates.Appendix. UHPC Material Performance DataTables 4 and 5 present the mixture composition of UHPC-class materials used in this study. Further details on the mechanical behaviors of the materials can be found in El-Helou et al. (2021). Figs. 12 and 13 present the individual creep behavior of UHPC-class materials in different environmental conditions. As shown in Fig. 13, an unloading occurred in Frame I, containing U-H and U-J materials in 80% H, at 100 days. The unloading was due to a power outage in the research laboratory. The issue was resolved within a day, and the samples were reloaded. Fig. 14 presents the unrestrained shrinkage behavior of UHPC-class materials in 50% H environment. The drying shrinkage was calculated by subtracting the measured autogenous shrinkage from the measured total shrinkage at 50% H for each material. It was observed that the external drying effect was minimal, and the autogenous shrinkage was greater, and in some products significantly greater, than the drying shrinkage. For better demonstration of the shrinkage behavior of different UHPC-class materials, the logarithmic plots of the shrinkage strain of all UHPCs in the drying condition of 50% H are shown in Fig. 15. Fig. 16 presents the unrestrained shrinkage behavior of U-D, U-G, U-H, and U-J in 50% H, 80% H, and a sealed condition.Table 4. Mixture composition of UHPC-class materialsTable 4. Mixture composition of UHPC-class materialsMaterials and fiber supplierU-AU-BU-CU-DU-EU-GU-HU-J Premix2,078a2,0862,1362,1951,9202,1002,2142,182 Water165210159130225135166166 Admixtures13.728.7—b53.04448—b, c73.4 Fiber volume content (2%)16452/106d, e16115615680/80d, e165157Fiber supplierF-AF-BF-CF-DF-DF-EF-DF-D Product line11/2e1111/2e11Table 5. Steel fiber propertiesTable 5. Steel fiber propertiesFiber propertiesF-AF-CF-DProduct line1121112MaterialSteelSteelSteelSteelSteelSteelSteelShapeHookedStraightStraightStraightStraightStraightHookedTensile strength (MPa)1,1002,1002,1002,4002,6002,8502,850Length (mm)30132013131325Cross-sectional shapeRoundRoundRoundRoundRoundRoundRoundDimension (mm)0.550.30.30.30.20.20.3Data Availability StatementSome or all data, models, or code generated or used during the study are proprietary or confidential in nature and may only be provided with restrictions. Anonymized data of vendor and product names are confidential.AcknowledgmentsThe research discussed herein was funded by the US Federal Highway Administration and would have not been possible without the dedicated effort and support of the federal and contract staff associated with the FHWA Structural Concrete Research Program. Likewise, the authors would like to thank the support of the US National Research Council through its Postdoctoral Research Associateship Program. All images and tables in this manuscript and the associated appendices were developed by and are sourced to the Federal Highway Administration.References AASHTO. 2019. Standard method of test for coefficient of thermal expansion of hydraulic cement concrete. AASHTO T 336-15. Washington, DC: AASHTO. AASHTO. 2020. LRFD bridge design specification. 9th ed. Washington, DC: AASHTO. ACI (American Concrete Institute). 2001. Control of cracking in concrete structures. ACI 224R-01. Farmington Hills, MI: ACI. 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