Time-Dependent Properties of Ultrahigh-Performance Concrete: Compressive Creep and Shrinkage

Deployment 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.

In 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.

Table 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.

Total 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 ($S_{50\%}$) 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

A 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 $11.8\times {10}^{-6}$ and $13.9\times {10}^{-6}\mathrm{mm}/\mathrm{mm}/°\mathrm{C}$ ($6.6\times {10}^{-6}$ and $7.7\times {10}^{-6}\mathrm{in.}/\mathrm{in.}/°\mathrm{F}$). 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 $15\times {10}^{-6}\mathrm{mm}/\mathrm{mm}/°\mathrm{C}$ ($8.3\times {10}^{-6}\mathrm{in.}/\mathrm{in.}/°\mathrm{F}$), whereas the UHPC products tested in the current study exhibited lower CTE values. For normal-weight concrete, CTE values typically range from $9\times {10}^{-6}$ to $12.6\times {10}^{-6}\mathrm{mm}/\mathrm{mm}/°\mathrm{C}$ ($5\times {10}^{-6}$ to $7\times {10}^{-6}\mathrm{in.}/\mathrm{in.}/°\mathrm{F}$) for concrete made with siliceous aggregates and from $6.3\times {10}^{-6}$ to $9\times {10}^{-6}\mathrm{mm}/\mathrm{mm}/°\mathrm{C}$ ($3.5\times {10}^{-6}$ to $5\times {10}^{-6}\mathrm{in.}/\mathrm{in.}/°\mathrm{F}$) 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.

In 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:

Tables 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.

Some 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.

The 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.