aSchool of Civil and Environmental Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
bGuangdong Provincial Key Laboratory of Intelligent and Resilient Structures for Civil Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
cSchool of Materials Science and Engineering, Southeast University, Nanjing 211189, China
aSchool of Civil and Environmental Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
bGuangdong Provincial Key Laboratory of Intelligent and Resilient Structures for Civil Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
cSchool of Materials Science and Engineering, Southeast University, Nanjing 211189, China
Concerns about the durability of transportation infrastructure due to freeze-thaw (F-T) cycles are particularly significant in the Chinese plateau region, where concrete aging and performance deterioration pose substantial challenges. The current national standards for the frost resistance design of concrete structures are based predominantly on the coldest monthly average temperature and do not adequately address the comprehensive effects of the spatiotemporal variance, amplitude, and frequency of F-T cycles. To address this issue, this study introduced a spatiotemporal distribution model to analyze the long-term impact of F-T action on concrete structures by employing statistical analysis and spatial interpolation techniques. Cluster analysis was applied to create a nationwide zonation of F-T action level from data on the freezing temperature, temperature difference, and the number of F-T cycles. Furthermore, this study explored the similarity between natural environmental conditions and laboratory-accelerated tests using hydraulic pressure and cumulative damage theories. A visualization platform that incorporates tools for meteorological data queries, environmental characteristic analyses, and F-T action similarity calculations was designed. This research lays theoretical groundwork and provides technical guidance for assessing service life and enhancing the quantitative durability design of concrete structures in the Chinese plateau region.
Tiejun Liu, Ming Zhang, Dujian Zou, Jiaping Liu, Jinping Ou.
Analysis and Zonation of Freeze-Thaw Action in the Chinese Plateau Region Considering Spatiotemporal Climate Characteristics.
Engineering, 2024, 42(11): 324-341 DOI:10.1016/j.eng.2024.04.016
The durability of a concrete structure is closely connected to the dynamic interplay between its inherent material resistance and the environmental stresses encountered during its service life. Engineering structures situated in diverse service environments often exhibit distinct deterioration characteristics due to various degradation mechanisms, such as carbonation, steel corrosion, salt attack, and alkali-aggregate reactions. Particularly, in cold regions, concrete structures that are in constant contact with water—exemplified by bridge piers subjected to fluctuating water levels and pavement after snowmelt—are exceptionally vulnerable to the detrimental impacts of freeze-thaw (F-T) cycles [1].
The chemical potential differences between liquid water and ice crystals in cementitious materials (CMs) drive the freezing and melting processes [2]. As the temperature decreases below freezing, ice crystals constantly form inside the capillary pores of CM. Due to the density of water being greater than that of ice crystals, to accommodate the associated volume increase with ice formation, excess water will be expelled from the capillary pores, creating water pressure in the surrounding area. Harmful stresses during the freezing process could result from hydraulic pressure, ice crystallization pressure, and the mismatch of thermal effects between the ice and solid phases [3]. Given that the tensile strength of concrete is approximately one-tenth of its compressive strength, the freezing of moisture inside capillary pores can induce internal stresses that surpass the tensile limit of the material, leading to microscopic porosity variation and macroscopic deformation [4]. Due to residual deformation, the CM microstructure, in terms of factors such as its porosity, pore shape, and pore size distribution, deteriorates, thereby leading to the degradation of the mechanical properties of the concrete [5], [6], [7], which significantly shortens the functional lifespan of the concrete infrastructure [8].
As illustrated in Fig. 1 [9], seismic action models have been progressively developed, and the evolution of structural seismic response analysis can be categorized into three phases: static analysis, response spectrum analysis, and dynamic analysis [10]. Nevertheless, related research on long-term environmental actions is still in its infancy. Currently, the description of environmental action levels in the relevant specification is qualitative [11]. Regarding F-T environmental action, which depends solely on the coldest monthly average temperature as a single parameter, the accuracy of classifying the severity of F-T actions in different regions (slightly frozen zone, cold zone, and severely cold zone), the accuracy of which needs to be further studied. Existing research suggests that the degradation process of concrete under F-T action is primarily linked to the freezing rate, duration of F-T cycles, and frequency of F-T cycles [12], [13], [14], [15]. Thus, the current qualitative categorization of F-T action levels remains at the “static analysis” stage [16], [17].
Moreover, there has been a considerable amount of experimental research dedicated to exploring the concrete damage mechanism under F-T action [18], [19], [20]. These investigations predominantly employed the “rapid freezing and thawing method” recommended by relevant specifications [21], [22], [23], a process in which concrete specimens are subjected to temperature fluctuations between (−18 ± 2) and (5 ± 2) °C, with each F-T cycle lasting two to four hours. Frost resistance was evaluated by monitoring the evolution of performance metrics such as mass loss, compressive strength, and dynamic elastic modulus throughout the F-T cycles. However, the rapid freezing and thawing method, while effective for benchmarking the frost resistance of concrete materials from intact to failure, fails to consider the spatiotemporal variability inherent in environmental conditions [24]. In other words, the spatiotemporal variability in F-T environmental action across different regions results in a variability in durability lifespan, even for identical materials [25].
The current description of damage mechanisms caused by F-T cycles on CMs is primarily based on the principles of thermodynamic equilibrium and Darcy's law. Various seminal theories have been advanced, including hydraulic pressure theory [26], [27], osmotic pressure theory [28], crystallization pressure theory [29], [30], critical degree of saturation theory [31], ice microlens theory [32], and the mechanics of porous media [4], [33]. Each of the above theoretical models has its own foundational assumptions and is applicable under specific constraints and conditions. Hydraulic pressure theory is particularly adept at explaining the degradation of ordinary hydraulic concrete and can consider factors such as air-entraining agents (AEAs) and freezing rates. Notwithstanding some criticisms [34], hydraulic pressure theory remains predominant for understanding F-T damage in concrete and has been instrumental in advancing research in this area [1], [35].
The quantitative design of the F-T durability of concrete is the key to achieving the expected service lives of engineering structures in cold regions, while crafting region-specific F-T durability designs for concrete structures necessitates a comprehensive grasp of unique environmental conditions [36], [37]. The use of the zonation map, which divides a region into zones with homogenous environmental characteristics, aids in illustrating the variation in service conditions [38]. While zonation maps for climate, ecology, geomorphology, and extreme loads have been established [39], the field of concrete durability zonation is still immature. Current zonation efforts in concrete durability can be generally classified into two categories, one focused on durability design indicators [40], [41], [42], [43] and the other on environmental action levels [44], [45], [46], [47]. Regarding F-T zonation research, Yu et al. [48] and Zhao et al. [49] established a nationwide zonation method for assessing the F-T durability of concrete, which is particularly beneficial for designing structures in regions prone to salt-induced frost damage. Furthermore, Lin and Ou [50], [51] applied the Weibull distribution for the statistical analysis of regional freezing temperatures, facilitating predictions of the F-T durability lifespan for ordinary Portland concrete. However, many zonation studies rely solely on individual F-T environmental metrics, such as the freezing temperature or the annual number of F-T cycles, to classify the impact of F-T conditions across regions. These studies typically do not offer region-specific F-T testing parameters or durability design metrics, reducing their applicability in practical engineering scenarios.
In summary, the absence of sophisticated long-term F-T environmental action models is a significant barrier to the precise quantification of F-T durability design [52]. Furthermore, there is a lack of similarity relationship between accelerated laboratory tests and actual service environments. Hence, the direct application of laboratory-derived frost resistance results in significant errors in the engineering design for the expected structural lifespans [24]. Based on the aforementioned issues, a schematic diagram illustrating the research framework is presented in Fig. 2. The second section of this study provides an overview of the methodologies employed for environmental characteristic analysis, encompassing interpolation and statistical methods, along with clustering algorithms. In the third section, we identify the regional discrepancies in F-T conditions and introduce a comprehensive long-term F-T action model for concrete to refine laboratory simulations of accelerated F-T tests. In the fourth section, F-T action level zonation considering three key indicators is established to support concrete durability design. In the fifth section, we establish a similarity relationship by calculating the equivalent number of F-T cycles for the rapid F-T method to bridge the gap between laboratory tests and real scenarios. Finally, the sixth section is dedicated to developing an analytical platform for concrete F-T actions considering regional climate characteristics to improve the applicability of research findings.
2. Materials and methods
2.1. Research scope
As China progresses with initiatives such as the Belt and Road Initiative, the transportation infrastructure in its plateau regions is being strategically developed. Nevertheless, the harsh environmental conditions of these regions—marked by extreme cold, significant temperature variations, dryness, and so forth—exacerbate the rate of F-T deterioration compared to that in the plains, presenting a significant challenge to the durability of concrete structures. This study focuses on the Chinese plateau region, which primarily refers to regions encompassing the Qinghai-Xizang Plateau, Loess Plateau, Inner Mongolia Plateau, and Yunnan-Guizhou Plateau. The main provinces in which the Chinese plateau is located are shown in Fig. 3.
2.2. Meteorological data and processing
The China Meteorological Administration (CMA) has established an extensive network of weather stations over several decades, contributing significantly to the country's developmental endeavors in sectors such as architecture, transportation, and urban planning. The present study utilized China's daily surface climate dataset (V3.0). This comprehensive dataset, spanning two decades from 2000 to 2020, incorporates daily temperature and pressure recordings from 687 weather stations, as shown in Fig. 3. The data processing involved an initial transformation of the raw data into a daily series, with the Pandas library in Python facilitating the renaming process to match the corresponding weather stations. Anomalies and missing values in the dataset were addressed through a meticulous cleaning process. Stations exhibiting continuous data gaps exceeding one month were omitted from the dataset to maintain integrity. For stations with intermittent data gaps, a methodological approach of forward and backward filling was applied to ensure a comprehensive dataset for analysis.
To enhance the temporal granularity necessary for analyzing F-T time intervals, this study further incorporated hourly meteorological data derived from the China meteorological forcing dataset [53], sourced from the National Tibetan Plateau Data Center. This dataset, presented in Network Common Data Form (NetCDF), offers an enhanced temporal resolution of three hours and a fine-scale spatial resolution of 0.1°. It spans 19 years, from 2000 to 2018. This dataset has undergone rigorous quality control to exclude nonviable values, and the Australian National University-Spline (ANU-Spline) statistical interpolation technique was applied to address spatial inconsistencies.
2.3. Meteorological data analysis
2.3.1. Spatial interpolation
The accuracy of regional environmental analysis depends on the availability of spatially continuous data, which are typically derived from point-based sampling of environmental variables. Spatial interpolation methods, therefore, play a pivotal role in environmental science by enabling the transformation of discrete point samples into continuous surfaces. These methods permit not only the estimation of environmental variables at unsampled locations but also the evaluation of associated uncertainties [54]. By interpolating the sparse weather station data across the entire nation, it is possible to gain a comprehensive understanding of the F-T environmental conditions and distinctive features of the plateau region.
Spatial interpolation encompasses several methodological frameworks classified broadly into three categories: non-geostatistical, geostatistical, and hybrid approaches. The choice of method can significantly influence the estimated outcomes due to the inherent assumptions of each technique. For the zonation of meteorological variables, inverse distance weighting (IDW) and ordinary kriging (OK) methods are commonly applied. IDW, a non-geostatistical method, estimates values based on nearby data points, assigning greater weights to nearer observations and thus diminishing the influence of those farther away. This method is particularly effective in situations where the studied variable's impact decreases with distance. OK is a geostatistical method and presupposes the spatial variability of data as a stationary random process. It utilizes variogram models to quantify spatial dependency and, apart from offering estimates, provides an error quantification, thus setting a robust framework for spatial prediction and uncertainty quantification.
In the context of this research, zonation maps were constructed utilizing the OK interpolation method due to its comprehensive analytical capabilities. Spatial analysis was conducted by adopting the World Geodetic System 1984 (WGS 1984) reference frame for geographic referencing, with the Albers projection applied for coordinate system transformation.
2.3.2. Statistical method
A probability density function (PDF) characterizes the probability of a continuous random variable occurring in a specific interval around certain values [55]. The typical PDFs employed for modeling the distribution of meteorological variables include the normal, exponential, Weibull, gamma, and generalized extreme value distributions. These functions quantitatively describe the distribution characteristics of environmental parameters, which are crucial for predicting the service life of concrete structures by integrating time-dependent reliability and durability into design considerations.
In contrast to continuous variables, discrete data tendencies and representativeness are often determined using metrics such as the mean and various quantiles. The mean accurately conveys the data's average value, while the median, which does not rely on the distribution's shape, provides a robust measure of the central location that remains unaffected by outliers. This attribute renders this approach particularly trustworthy for datasets that exhibit anomalies or are not symmetrically distributed. Quantiles partition the range of a random variable probability distribution into equal segments, encompassing the median (or second quartile), quartiles, and percentiles. These segments avoid the necessity of defining the relation between the mean and variance of the variable with continuous functions. Descriptive statistics, including the mean, standard deviation, and quantiles, are commonly applied to describe the basic characteristics of datasets. In contrast, PDFs facilitate more extensive statistical evaluations such as probability assessments, hypothesis testing, and model fitting.
2.3.3. Kolmogorov-Smirnov (K-S) test
The K-S test is a nonparametric method for statistically determining whether a sample aligns with a proposed theoretical distribution. It assumes a null hypothesis that the sample adheres to the given theoretical distribution. This test evaluates this hypothesis by examining the maximum difference between the empirical cumulative distribution function (ECDF) of the sample and the cumulative distribution function (CDF) of the theoretical model, along with the computed P value. Conventionally, a P value below the significance threshold (commonly 0.05) leads to rejection of the null hypothesis, indicating that the sample does not follow the suggested distribution.
2.3.4. K-means clustering
Clustering is a frequently employed unsupervised learning technique that categorizes samples into various groups based on key indicators, leading to a high level of similarity within the same group and a low level of similarity between different groups. The K-means clustering algorithm operates through an iterative process aiming to diminish a predefined loss function by establishing and adjusting cluster centroids. The fundamental mechanism of the K-means algorithm consists of initially setting the centroids and then aligning the clusters to minimize the loss function, followed by keeping the clusters constant and recalibrating the centroids. This alternation continues, steadily reducing the loss function until convergence, at which point the positions of the centroids and the cluster assignments of samples are both fixed. Nonetheless, known for its swift convergence, scalability, and simplicity in interpretation, K-means is susceptible to the initial choice of centroids and the presence of outliers, with the determination of the optimal cluster count (K) often being based on empirical assessment.
3. Long-term F-T action model
The broad latitudinal span and varied terrain elevations of China give rise to marked thermal gradients from north to south, nonuniform precipitation distributions, and diverse aridity levels. The orographic effect of western China's mountains acts as a barrier to maritime moisture, resulting in the prevalence of deserts and arid terrains. Climate conditions in the plateau areas are notably more complicated and variable than those in the plains and are influenced by factors such as intense solar irradiance and elevated atmospheric transparency. These elements contribute to significant temperature shifts within a day and a high frequency of F-T cycles. The F-T cycles in the laboratory test have a periodic pattern with fixed temperatures and cooling and warming times. From a fatigue perspective, the F-T action on concrete in laboratory tests can be viewed as a generalized “cyclic temperature load” with equal amplitude [56], [57]. In the actual service environment, fluctuations in on-site temperature are caused by changes in solar radiation received by the ground and atmosphere due to the rotation of the Earth, which also has an approximately cyclic pattern [48], [58], [59]. Therefore, this study assumes that the F-T temperature history experienced by concrete structures in actual service environments is the same each year, and the F-T action on concrete in the field is considered a generalized “cyclic temperature load” with variable amplitude.
3.1. Determination of the F-T cycles and principal F-T months
The pore size, distribution, shape, and porosity are decisive factors in determining the freezing point of the pore fluids and the subsequent frozen volume [58]. The extent of internal freezing in concrete is further controlled by the saturation degree, solution concentration, and inherent material properties. Currently, the scientific community has not reached a consensus on a standardized temperature for the phase transition between ice and water in concrete [60]. Referencing the Kelvin equation's correlation between the freezing point and the radius of the capillary meniscus [61], [62], it is deduced that for concrete capillary pores measuring approximately 100 nm in diameter, internal moisture crystallizes at approximately −3 °C. Furthermore, experimental work by Chen et al. [63] suggested that the internal freezing point in concrete fluctuates between −4.8 and −2.5 °C, depending on the saturation level, while the thawing point consistently remains at 0 °C. Their findings also confirmed that the temperatures measured in field samples are consistent with the ambient air temperatures.
For the purposes of this study, a singular F-T cycle is characterized by the occurrence of the day's maximum temperature increasing above 0 °C, coupled with the minimum temperature decreasing below −3 °C.
Using this criterion, the average annual number of F-T cycles over 21 years was computed for each weather station, and the mean values of the average annual number of F-T cycles were then obtained for each province, as shown in Fig. 4. Qinghai and Xizang exhibit a greater average annual number of F-T cycles than northeastern regions, such as Heilongjiang and Jilin, as well as northern regions, such as Hebei and Shandong. Notably, the average annual number of F-T cycles varies considerably among cities within the same province, indicating potential inaccuracies that may arise from the use of provincial administrative borders to demarcate zones of different F-T action zones. OK interpolation was adopted to create Fig. 5, which is a contour that maps out the national distribution of average annual number of F-T cycles, revealing a stark disparity between plateau areas and plains. The Qinghai-Xizang Plateau, in particular, experiences the greatest average annual number of F-T cycles, reaching a maximum of 188 cycles.
As previously mentioned, the use of the coldest month's average temperature as a metric to assess the severity of the F-T action in diverse regions is a common practice in existing studies and guidelines [11]. However, in some regions, temperatures throughout the coldest month may consistently remain below the freezing point of capillary water, in which case the influence of frost is less pronounced than that in the case of recurrent F-T cycles. Consequently, this study computed the frequency of monthly F-T cycles across different regions, as depicted in Fig. 6. For instance, F-T cycles predominantly occur in March, April, and November for Nagqu City, Xizang, while for Garze Tibetan Autonomous Prefecture, Sichuan, they occur mainly in January, February, and December. These findings highlight the variability in F-T months and their frequency across various regions.
To determine the principal F-T months, the average annual number of F-T cycles was divided by 30, yielding a quotient (X) and a remainder (Y). If the remainder (Y) exceeds 15, the principal F-T months are rounded to X + 1. If Y is less than 15, the principal F-T months are X. The following in-depth analysis of F-T actions focuses on temperature records from these principal F-T months. Fig. 7(a) shows the month with the most severe F-T actions at each weather station. By employing the monthly average daily minimum temperature as a criterion, we also calculated the cumulative monthly average of daily minimum temperatures for 687 stations over 21 years. Then, we identified the month corresponding to the minimum value as the coldest month. The coldest month for each weather station is plotted in Fig. 7(b). January is the coldest month in the majority of Chinese cities. In addition, a comparison of Figs. 7(a) and (b) indicates that in the plains of north-central China, the month with the most severe F-T action generally coincides with the coldest month (January). Conversely, in northeast China and the plateau regions, such a direct correlation is not observed. This discrepancy arises because, during the coldest month in plateau areas, temperatures often stay below the freezing point for longer durations, subjecting concrete structures to extended periods of freezing.
3.2. F-T temperature curve
F-T cycles essentially refer to the alternating changes of negative and positive temperature over time, which results in phase changes and the movement of internal moisture within concrete, ultimately exerting forces on the concrete matrix. For a visual illustration of F-T temperature fluctuations across different regions, the daily maximum and minimum temperatures during the principal F-T month were retrieved and connected, as shown in Fig. 8 (taking Nagqu in Xizang as an example). In this study, these graphical depictions are referred to as the actual F-T temperature curves, representing the natural F-T cycles that concrete structures encounter in situ. An assessment of these actual F-T temperature curves revealed a consistent pattern within the same geographical region across consecutive years, indicating relative stability in the annual changes in temperature. Comparing the temperature range −18-5 °C of the laboratory test, a significant discrepancy was revealed between the in situ conditions of concrete and those simulated in controlled laboratory experiments.
Drawing upon meteorological datasets covering two decades, we generated 21 actual F-T temperature curves for each weather station. To distill the essence of these curves and streamline the analytical procedure for F-T temperature assessment, the notion of a characteristic F-T temperature curve was introduced. The characteristic curves strive to capture the typical distribution characteristics of the F-T temperatures over 21 years. Using the statistical methodologies mentioned in Section 2.2, three characteristic curves were established: the mean, median, and mode F-T temperature curves, as demonstrated in Fig. 9. A comparison between these derived curves and the actual F-T temperature curves revealed a high degree of consistency, indicating that these extracted curves captured the overarching trend, central tendencies, and prevalent patterns inherent in the actual F-T temperature curves well.
3.3. Simplified F-T temperature curve
The characteristic F-T temperature curves shown in Fig. 9 lack discernible patterns, which complicates the task of approximating them with specific functions. Furthermore, the temperature data represented in these curves are based on daily measurements, presenting considerable challenges for simulating these conditions in a laboratory setting. To address these complexities, this section introduces a methodology to simplify the characteristic F-T temperature curves, thereby facilitating the design of more representative accelerated F-T tests for concrete.
This approach segregates F-T temperatures for each principal F-T month into three periods: the early, middle, and late parts of the month. Subsequently, the frequency distribution of the daily extreme temperatures over 21 years is computed for each period. The distfit library in Python was employed to fit the probability density distribution of daily extreme temperatures. An example is provided with Nagqu's most severe months of F-T action, as depicted in Fig. 10. The normal distribution was used to fit both the PDF and the CDF of the daily maximum and minimum temperatures. The normality of the data was assessed with the K-S test. As shown in Fig. 11, the temperatures predominantly conformed to a normal distribution, as indicated by P values ≥ 0.05.
Notably, the selection of representative values is related to specific engineering scenarios. To simplify this program, only the statistical values such as the mean, median, mode, and quantiles are used as the representative values for each period in the subsequent analysis, as illustrated in Table 1. The introduction of the first quartile for the daily minimum temperatures and the third quartile for the daily maximum temperatures serves to enhance the severity in the design of concrete F-T accelerated tests.
This study analyzed the process of deriving simplified F-T temperatures in Nagqu by utilizing the mean value of daily extreme temperatures for each period, as detailed in Table 1. The principal F-T months in Nagqu, identified as March, April, November, October, and December, collectively contribute to 15 distinct groups of F-T temperatures, as presented in Fig. 12. The trend of the F-T extreme temperatures in Nagqu exhibits an initial increase followed by a decrease over the months. Upon comparing the characteristic F-T temperature curve with the simplified F-T temperature curve, it was found that the simplified curve is in agreement with the trends and amplitudes of the characteristic curve. This consistency underscores the efficacy of the simplified F-T temperatures in capturing the essence of the characteristic curves.
The characteristic F-T temperature curves and the simplified F-T temperature curves collectively provide a two-layered representation of F-T action at the daily and decadal levels, respectively. The former can be applied to develop an accelerated F-T test in the laboratory, and the latter is more suitable for numerical modeling of concrete deterioration due to F-T action in a manner that more accurately reflects the natural service environment. Additionally, simplified F-T temperature curves are used in the fifth section of this paper to evaluate the similarity between F-T cycles experienced under actual service conditions and those induced by rapid F-T cycles in the laboratory setting.
3.4. Time interval of F-T cycles
The severity of F-T damage is influenced not only by the range of F-T temperatures but also by the time interval of a single F-T cycle. A shorter time interval implies a more rapid rate of temperature change within the same temperature extremes, which can inflict greater deterioration on concrete structures. Thus, this section focuses on the time interval of an F-T cycle in the plateau regions of China.
By the end of 2021, China had 10 930 surface weather observation stations; however, there was a significant disparity in the station distribution between the densely distributed central and southeastern coasts and the sparsely distributed western highlands. Moreover, China's surface climate data daily value dataset (V3.0) used above lacks hourly data, so the cooling and warming durations within each F-T cycle cannot be studied with this dataset. Consequently, we predominantly utilized hourly raster temperature data spanning from 2000 to 2018 derived from the National Tibetan Plateau Data Center. Initially, 153 sample locations were selected across the plateau to ensure comprehensive coverage, as illustrated in Fig. 13. Subsequently, meteorological data for each sample point were retrieved based on their geographic coordinates. Python was used for data processing and analysis, and ArcMap software was used for spatial localization, data interpolation, and the creation of contour and isopleth maps.
Similar to the process described in Section 3.1, the initial step of this data analysis involves identifying the principal F-T month at each sample point. Then, the moments of the daily maximum and minimum temperatures were recorded during the principal F-T months. For instance, point 37, depicted in Figs. 14(a) and (b), typically experiences daily maximum temperatures at approximately 9:00, while the daily minimum temperatures are generally recorded at 0:00. The time intervals between these daily extreme temperatures at the 153 sample points were statistically recorded, as illustrated in Fig. 14(c). Analysis reveals that the time intervals between thawing and freezing temperatures predominantly span 6, 9, and 12 hours among these sample points, with 9-hour sample points occurring most frequently. Notably, the durations required for the cooling and warming processes of F-T cycles differ. In this study, the minimum cooling or warming duration was utilized to evaluate the similarity of F-T actions in Section 5 and to inform the development of accelerated F-T testing procedures in laboratory settings.
4. Zonation of F-T action levels
4.1. Clustering of F-T indicators
The degradation of concrete under F-T action is multifaceted and determined by internal concrete properties and varied regional climates. It is impractical to examine every factor impacting the F-T durability of concrete. In this study, discernible and definitive factors were adopted to quantify F-T action levels: the temperature difference, freezing temperature, and average annual number of F-T cycles. For each weather station, the average annual number of F-T cycles, and the mean values of the daily minimum temperature and the temperature difference during principal F-T months were documented. Weather stations with fewer than 15 F-T cycles annually were ignored in the analysis of the F-T action level. The K-means clustering algorithm was then used to classify the 403 remaining stations.
To determine the optimal number of clusters, as illustrated in Fig. 15, we initially employed the elbow method to assess the inertia for cluster numbers ranging from two to ten. The number of clusters at which the inertia value began to stabilize was considered a candidate. This was followed by calculating silhouette scores for these potential cluster numbers. The analysis revealed that the most suitable number of clusters was five, as indicated by a silhouette score of 0.552. A score exceeding 0.5 suggests that the number of clusters is reasonably well-fitted. However, the choice of the number of clusters is somewhat subjective, reflecting the specific differences between the data and the research objectives.
Fig. 16(a) presents a three-dimensional scatter plot of the 403 stations subjected to F-T action. The plot revealed a high density of stations within each cluster, demonstrating the effectiveness of the clustering approach. A clear, progressive distinction in the average annual number of F-T cycles, minimum temperatures, and temperature differences across different levels of F-T action was observed, implying significant regional variations in F-T environmental conditions throughout China.
4.2. Zonation map of F-T action level
When considering the additional 284 stations where F-T actions are ignored, China can be segmented into six distinct levels of F-T action severity. Table 2 presents the critical conditions for each F-T action level, including the station number and center coordinates. Notably, from Figs. 16(b) and (c), it is clear that the difference in average annual number of F-T cycles is the most obvious among the different F-T action levels. Therefore, taking the average annual number of F-T cycles as the zonation indicator, the detailed thresholds of this zonation indicator were established, as shown in Table 2.
Fig. 17(a) shows the national distribution of each cluster. OK interpolation was utilized to establish the national zonation of F-T action level, as presented in Fig. 17(b). The clustering categories of weather stations were in line with their respective F-T action levels.
The six distinct zones corresponding to the F-T action levels in Fig. 17(b) were defined separately as the nonfrozen zone, slight F-T zone, light F-T zone, moderate F-T zone, severe F-T zone, and extreme F-T zone. The basic F-T environmental conditions and geographic locations of each zone are described in detail below, providing an essential reference for preliminary evaluations of F-T action potentials under specific project scenarios.
(1) Nonfrozen zone. This zone is characterized by fewer than 15 F-T cycles per year and is located mainly in the south of the Qinling-Huaihe Line.
(2) Slight F-T zone. Exhibiting 15 to 39 F-T cycles annually, with an average of 26 cycles, this zone has an average freezing temperature of −3.2 °C and an average temperature difference of 8.7 °C. It encompasses the northern Jiangsu Plain, the central Shandong Mountains, the mountainous regions of the Weihe Plain, the Tacheng Basin, the Ertix River Valley, the Altai Mountains, the Three Rivers Plain, and its southern mountainous regions.
(3) Light F-T zone. This zone experiences 40 to 59 F-T cycles yearly, averaging 49 cycles, with an average freezing temperature of −6.6 °C and temperature difference of 10.6 °C. It includes the southern Loess Plateau, parts of the North China Plain, the Hulunbuir Plain, the central region of the Greater Khingan Mountains, the Changbai Mountains in the Lesser Khingan Mountains, the Songliao Plain, and the Junggar Basin, among other areas.
(4) Moderate F-T zone. With 60 to 79 F-T cycles annually, averaging 71 cycles, and an average freezing temperature of −8.0 °C and temperature differences of 12.3 °C, this zone covers the Tarim and eastern Xinjiang basins, the northern and southern Greater Khingan Mountains, the Yanshan Mountains, the eastern Loess Plateau in the Taihang Mountains, the Inner Mongolian Plateau, and the Hetao Plain, among other areas.
(5) Severe F-T zone. This zone, which experiences 80 to 119 F-T cycles annually with an average of 97 cycles and an average freezing temperature of −8.8 °C and temperature difference of 14.4 °C, includes the western Loess Plateau, the Qaidam Basin and the northern flank of the Kunlun Mountains, parts of the Tarim Basin, the alpine basin of the Qilian-Qingdong Plateau, the Hexi Corridor, and the western Inner Mongolian Plateau, among other areas.
(6) Extreme F-T zone. The annual number of F-T cycles exceeds 120, with an average of 147 cycles, an average freezing temperature of −10.4 °C and an average temperature difference of 16.4 °C. Most of the Qinghai-Xizang Plateau falls under this zone, demanding the highest F-T resistance in construction materials due to intense and frequent F-T action.
5. Similarity between actual service environment and accelerated tests
5.1. Hydraulic pressure theory
The primary mechanism leading to concrete deterioration under F-T cycles is attributed to the internal pore stress of the concrete exceeding its ultimate resistance, resulting in expansion deformation and cracking. Fig. 18 illustrates the process wherein water within capillary pores starts to freeze as temperatures drop, leading to the enlargement of ice crystals. This process forces some water out, and under hydraulic pressure, this water is propelled through the capillary channels toward the nearest air voids. Darcy's law can be used to calculate the pressure generated by a certain amount of water moving a certain distance within a given time. If the distance for water movement is too long or if the freezing rate is too rapid, the resultant hydraulic pressure may surpass the tensile strength of the concrete, causing tensile failure. Hydraulic pressure (Pmax, Pa) is mathematically expressed in Eq. (1).
where η represents the dynamic viscosity coefficient of capillary water (Pa·s), which is a function dependent on temperature [64], [65]; s denotes the saturation of capillary water (%), which is assumed to be 1, because this study focuses on hydraulic concrete structures that are regularly subjected to water exposure; u represents the amount of ice formation per 1 °C decrease in temperature within capillary pores in 1 m3 of concrete (°C−1); R signifies the freezing rate (°C·s−1), which can be calculated based on the F-T temperatures and time intervals; K represents the permeability coefficient of concrete (m2), which can be calculated by the capillary porosity [65]; L and rb indicate the spacing factor (m) and the air void radius (m) within concrete, respectively. Powers conducted detailed calculations on the distribution and spacing of air bubbles within the concrete [26] and provided a relationship between the paste-to-air ratio (volume fraction of the cement paste in the concrete (Fp)/air content of concrete (A)) and the spacing factor (L), as illustrated in Eq. (2). Notably, powers assumed a homogenous dispersion of air voids with consistent diameters when deriving the equation of the spacing factor.
where Fp represents the volume fraction of the cement paste in the concrete (%); rb is the air void radius (m), which takes 100 μm, because this study assumes a uniform size of air voids, based on the experimental data from Li et al. [66]; A indicates the air content of concrete (%), which is impacted by the chemical process of the AEA reducing the liquid surface tension, as well as the process of entrainment and entrapment of a great number of voids during concrete mixing.
To improve the frost resistance of concrete, a crucial strategy is to refine its internal pore structure. The incorporation of AEA is a widely recognized approach to achieve this. By generating air voids ranging in size from tens to hundreds of micrometers, these agents create zones within the concrete that can accommodate stress induced by hydraulic or osmotic pressures during F-T cycles. The fundamental principle for the successful implementation of these air voids lies in the adequate contact of air and water during the concrete mixing process. However, regional atmospheric conditions can significantly influence the efficacy of air entrainment. Li et al. [66] revealed that the lower atmospheric pressures of plateau regions can drastically diminish the air content, pore structure, and stability of air-entrained concrete compared to those produced in areas at standard atmospheric pressure. To account for this variation, a loss coefficient of air content, which depends on the water-to-cement ratio (w/c) and atmospheric pressure, was derived from the empirical findings of Li et al. [66], as exhibited in Fig. 19. By employing Eqs. (3), (4), the air content A in concrete under varying atmospheric pressures can be obtained.
$D=0.00632P-0.39714{}^{w}/{}_{c}+0.52087$
$A=D{{A}_{0}}$
where D represents the air void loss factor; A and A0 indicate the air content in the concrete with and without air void loss (%), respectively; P is the atmospheric pressure (kPa).
5.2. Equivalent number of F-T cycles for the rapid F-T method
The discrepancies between natural F-T cycles and laboratory simulations present a notable challenge in accurately predicting the service life of concrete structures. It is essential to create a similarity relationship to bridge this gap. The rapid freezing and thawing method adopted in laboratory tests provides a controlled and uniform cycle of temperature and time intervals, similar to constant-amplitude fatigue loading. Conversely, actual F-T cycles in the field are subject to variability, both temporally and spatially, much like variable-amplitude periodic fatigue loading. According to the linear cumulative damage proposed by Miner [67], the damage sustained by concrete under multiple real-world fatigue loadings can be quantified and translated into an equivalent number of constant-amplitude loadings in a laboratory setting that would impart identical damage levels. This equivalency is mathematically represented with Eq. (5).
where Neq represents the equivalent number of F-T cycles of the rapid freezing and thawing method in the laboratory; Ni is the repetition number of each group of F-T temperatures in the simplified F-T temperature curve, which is 10; NF and NF,i denote the fatigue life or frost resistance of the concrete in the laboratory and in the actual service environment, respectively.
The resistance or service life of materials subjected to fatigue loading can be determined through the stress-life cycle curve. This methodology was applied by Tepfers [68] to estimate the fatigue life of concrete under tensile stress and subsequently confirmed by Oh [69] via flexural fatigue tests of concrete. Additionally, research by Liu and Tang [70] and Yu et al. [48] confirmed that the stress magnitude and the fatigue life for concrete subjected to F-T cycles are consistent with the S-N curve, as presented in Eqs. (5), (6).
where Pmax and Pmax,i denote the maximum hydraulic pressure inside the concrete under the rapid freezing and thawing method and the actual F-T environment, respectively; C represents a constant; ζ is an empirical coefficient, and 0.946 is taken for ordinary Portland concrete [70].
According to the hydraulic pressure model outlined in Eq. (1), the freezing rate, denoted as R, and an air void parameter, denoted as ϕ(L), are pivotal in determining the maximum hydraulic pressure within the concrete matrix. Therefore, the ratio of the maximum hydraulic pressure (κi) was computed as shown in Eq. (8).
${{\kappa }_{i}}=\frac{{{P}_{\max,i}}}{{{P}_{\max }}}=\frac{{{R}_{i}}\phi {{\left( L \right)}_{i}}}{R\phi \left( L \right)}=\lambda \frac{{{R}_{i}}}{R}$
where ϕ(L)i and Ri are the air void parameter and freezing rate for each period in the actual service environment, respectively; λ denotes the ratio of the air void parameter between the actual F-T environment and the rapid freezing and thawing method.
Integrating Eqs. (6), (7), we derived the correlation between the frost resistance cycles observed in the rapid freezing and thawing method and those in natural F-T conditions, as expressed in Eq. (9). Further synthesizing Eqs. (6), (7), yields the corresponding F-T cycles representative of the accelerated method, as described in Eq. (10).
It is critical to recognize that the diminished atmospheric pressure typically found in plateau regions may lead to the depletion of entrained air voids in concrete when it is freshly mixed. The degree to which these air voids are lost is affected by the w/c as well as the atmospheric pressure. Consequently, in the computation of the equivalent number of F-T cycles, the characteristics of the materials, environmental influences, and air void parameters must be considered. Referring to the concrete mix proportions used by Du et al. [71], the detailed parameters for calculating the similarity of F-T cycles are presented in Table 3. Through this analytical process mentioned above, we computed the equivalent number of F-T cycles for the rapid freezing and thawing method corresponding to 687 cities nationwide.
By utilizing the equivalent number of F-T cycles for each weather station and applying the OK interpolation technique, we constructed a zonation map, as shown in Fig. 20. Predominantly, the regions most adversely affected by severe F-T cycles are located in Xizang, western Sichuan, southern Xinjiang, and parts of Qinghai and Gansu. If the frost resistance cycle of concrete is 300 in accelerated laboratory tests, the service life under actual environmental conditions is less than ten years. Moreover, the greater the w/c is, the greater the equivalent number of F-T cycles is, which is particularly noticeable in regions where the number of F-T cycles exceeds 35. This is attributed to the fact that an increased w/c enhances the workability of the concrete but may also lead to an inconsistent distribution of air voids throughout the material. The atmospheric pressure has a profound influence on this distribution, increasing the likelihood of air void rupture within the concrete structure. Such occurrences significantly affect the air void parameters referenced in Eq. (10), thereby increasing the equivalent number of F-T cycles.
6. Platform for F-T action analysis of concrete
The preceding analysis clearly describes the vast disparities in F-T environments impacting concrete across various Chinese regions. The complexity of these environments defies the use of a singular deterministic function or methodology capable of covering all the unique F-T environmental characteristics effectively. Despite our efforts to demarcate national zones of F-T action levels through cluster analysis, this approach does not accurately capture the complex variability and uniqueness of real-world engineering environments specific to each city. Consequently, we developed an interactive interface, designed to assimilate the comprehensive body of work presented in this study. This platform is engineered as a multifaceted tool, facilitating the retrieval of meteorological data, the analysis of environmental characteristics, and the similarity analysis of F-T action. Its primary objective is to offer a robust technical foundation for the prediction of concrete service life and the formulation of durability designs tailored to actual engineering scenarios.
The analysis platform dedicated to concrete F-T actions was constructed utilizing the PyQt5 library within Python. It has four core functions, as illustrated in Fig. 21.
(1) Meteorological data query. This component permits users to access and retrieve meteorological data specific to the 687 weather stations and 153 sample points included in this research. It has been designed for user-friendly interactions, facilitating the reanalysis of meteorological data related to various regions.
(2) Environmental analysis. By entering the geographical locations of existing or prospective construction projects, users can extract the frequency distributions, principal months, and PDFs of critical environmental parameters, such as temperature, humidity, and atmospheric pressure. The information collected from this analysis can provide a fundamental basis for the design of laboratory-accelerated F-T tests.
(3) F-T action analysis. This module delivers essential data such as the average annual number of F-T cycles, principal F-T months, and the actual F-T temperature curves across different regions. Additionally, it offers simplified F-T temperature curves and time intervals, which are vital for the conceptualization of accelerated F-T test protocols in laboratory settings.
(4) Similarity of F-T action. Building on the foundation established by function 3, this module calculates the similarity coefficient and the equivalent number of F-T cycles between the rapid freezing and thawing method used in laboratory settings and real-world service environments. This provides a predictive function for assessing the frost resistance of various concrete materials.
7. Conclusions
This study provided a comprehensive evaluation of F-T cycles across various service conditions in the Chinese plateau region, introduced a long-term environmental model of F-T processes that accounts for regional climate characteristics, formulated a national zonation for F-T action levels, established a similarity relationship between accelerated laboratory tests and real service environments, and created an accessible platform for improving the applicability of research findings. The key findings were as follows:
(1) In most cities in China, January is typically the coldest month; however, the severity of F-T cycles does not coincide with this period in the Chinese plateau region. Hence, using January's average temperature as the primary criterion for classifying F-T action levels is inaccurate.
(2) The actual F-T temperature curve reflects the F-T cycles that concrete endures in its service environment, and the variations across different years are not significant. Characteristic curves that represent the mean, median, and mode temperatures can be used to efficiently reflect the trend, centroid, and typical distribution patterns of the actual F-T temperature curve.
(3) There is a marked discrepancy between the F-T temperatures that concrete endures in actual service environments and those used in controlled laboratory tests. A simplified F-T temperature curve and time intervals are proposed for refining laboratory simulations of accelerated F-T tests.
(4) The severity of F-T cycles can be effectively indicated by factors such as temperature differences, freezing temperature, and the number of F-T cycles. The F-T action in China can be divided into six distinct zones: the nonfrozen zone, the slight F-T zone, the light F-T zone, the moderate F-T zone, the severe F-T zone, and the extreme F-T zone. The regions most impacted by F-T action, including Xizang, western Sichuan, southern Xinjiang, and parts of Qinghai and Gansu, were identified.
(5) The developed F-T action analysis platform can be used to perform meteorological data queries, F-T action analyses, and similarity assessments, offering technical support for concrete service life prediction and quantitative design in real-world engineering scenarios.
Nonetheless, this study is an initial step toward a full understanding of long-term environmental impacts of F-T cycles on concrete. Future research directions include:
(1) Clarifying the definition of a single F-T cycle as experienced by concrete in actual service conditions, supported by additional experimental evidence.
(2) Validating the findings through on-site experiments and continuous monitoring to confirm the reliability of the proposed models and methods.
(3) Investigating more complicated service environments, such as the influence of ionic presence in saline solutions and varying degrees of concrete saturation.
Acknowledgments
This work was supported by the National Key Research and Development Program of China (2021YFF0500801), the Joint Funds of the National Natural Science Foundation of China (U23A20658), and the National Natural of China (52025081). The dataset was provided by the National Tibetan Plateau/Third Pole Environment Data Center.
Compliance with ethics guidelines
Tiejun Liu, Ming Zhang, Dujian Zou, Jiaping Liu, and Jinping Ou declare that they have no conflict of interest or financial conflicts to disclose.
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