1. Introduction
The increasing heights and complexity of modern buildings present increased risks of large-scale casualties and property damage in fire events, prompting growing demands for improved structural fire safety [1,2]. Specifically, buildings where service systems penetrate walls and floor slabs in complex arrangements pose a major risk as these penetrations can serve as pathways for the spread of flames and smoke. Therefore, ensuring airtight performance in these areas is essential [3,4].
Within this context, firestop systems function as critical components in maintaining the integrity of fire compartments by blocking the spread of smoke and heat during a fire [5,6]. However, the performance of firestop materials is not determined by the material alone. Factors, such as the type of penetrant, cross-sectional geometry, gap size, and installation method, collectively influence the system performance, thus necessitating ongoing experimental research [7,8,9]. Some studies have quantitatively assessed performance based on thermophysical properties, such as thermal conductivity and expansion behavior, with others analyzing area ratios to refine understanding of variable interactions [10,11].
Choi et al. [12] examined metallic and nonmetallic pipes with varying opening sizes, pipe diameters, and applied firestop materials. Their findings showed that metallic pipes exhibited performance degradation with increasing cross-sectional area owing to their high-thermal conductivity; conversely, nonmetallic pipes experienced material loss under high heat conditions, thereby making firestop fill density a more critical factor. These results highlight the need for geometry-specific evaluations and question the adequacy of uniform performance criteria.
Nevertheless, most prior studies focused on standardized circular penetrations. Research on irregular sleeve structures, such as floor-drain sleeves, which are extensively used in practice, remains limited [13,14]. Variations in upper- and lower-sleeve geometries, sleeve length, and embedment depth are common; yet, current certification systems do not provide test criteria for these cases. This either makes the verification of their performance challenging or leads to excessive testing costs.
Performance differences based on application methods (e.g., intumescent sealants, collars, and wraps) and geometries have been actively studied around the world, and comprehensive guidelines such as Sheet Metal and Air Conditioning Contractors’ National Associations [5], American Society for Testing and Materials E814 [15], Underwriters Laboratories 1479 [16], European Norms 1366-3 [17], and Promat [18] include provisions for nonstandard penetrations. In South Korea, however, such criteria remain underdeveloped, thereby limiting design flexibility. For example, in the Jecheon Sports Center, fire, smoke, and heat had spread to upper floors through unprotected penetrations, demonstrating that even wet areas can become fire pathways [19]. No firestop materials were applied, and existing regulations lacked clear testing or installation requirements. These floor-drain sleeves often exhibit irregular geometries to accommodate plumbing components like P-traps or offset connections, which require spatial configurations to maintain water seals for drainage and odor control.
Although several studies have addressed thermal performance in relation to penetrant type and material characteristics, only a few have explicitly evaluated the combined geometric effects of upper cross-sectional shape, opening area, and lower-sleeve length. Various types of floor-drain sleeves are used in practice, exhibiting considerable differences in geometry. Given the geometric variability in floor-drain sleeves and the lack of relevant research, these three parameters are expected to affect considerably firestop performance and, therefore, warrant detailed investigation through controlled experimentation.
This study aims to analyze experimentally firestop performance of floor-drain sleeves under nonstandard penetration conditions. Focus is placed on sleeve geometry, including upper cross-sectional shape, opening area, and lower-sleeve length, seeking to evaluate their thermal performance under standardized heat exposure and develop a dataset that supports predictive design without the need for testing each geometric variation. The study’s findings are intended to support the development of performance-based certification systems and geometry-informed analytical frameworks.
2. Experimental Methods
2.1. Test Matrix and Variables
This study aims to investigate experimentally how the application method of firestop material, in response to geometric configurations, affects fire resistance performance in nonstandard penetrations, especially floor-drain sleeves. Existing certification systems impose structural constraints by requiring a fixed quantity of firestop material based on the shape of the penetration or the penetrant. The goal of this study is to provide foundational data that can support the development of performance-based standards to address these limitations.
Eleven sleeve types—five square (designated SA to SE) and six round (designated as RA to RF)—were selected based on actual construction products. The test variables focused on lower-sleeve length and upper-opening area, while other conditions were kept constant. These sleeves differed in geometric attributes, such as upper- and lower-sleeve lengths and upper-opening area, as summarized in Table 1. The upper-sleeve length was not treated as an independent variable as it was inherently determined by subtracting the lower-sleeve length from the fixed slab thickness (150 mm). Focus was thus placed on lower-sleeve length as this was a more relevant heat parameter. The upper- and lower-sleeve lengths in Table 1 were not obtained from manufacturer specifications but were defined based on the external geometry of each sleeve. As shown in Figure 1, the boundary between the upper and lower sections was determined at the point of a marked change in outer cross-sectional shape. This approach enabled consistent dimensional classification across sleeve types. The experimental design primarily focused on two key geometric variables: lower-sleeve length and upper-opening area. Other factors were kept relatively constant within the test setup to minimize external influence. Because the test specimens were based on actual commercial products, geometric shapes and dimensional parameters (e.g., lower-sleeve length and opening area) were inherently coupled. As a result, the influence of each variable cannot be completely isolated, and the possibility of confounding factors should be taken into account when interpreting the results. Representative specimens used in the experiment are shown in Figure 2, while Figure 1 illustrates cross-sectional schematics and thermocouple placement locations.
The firestop material used in the experiment was a commercially available firestop material from a domestic supplier (Company S). It exhibits expansion up to approximately 30 times its original volume at high temperatures and has a density of approximately 1.2 g/cm3. For the test, the material was cut into pieces with dimensions of 10 (thickness), 40 (width), and 225 mm (length). It was installed at the bottom of the sleeve opening and fixed directly to the underside of the slab using 0.5 mm thick galvanized-steel sheets.
2.2. Experimental Method
Tests were conducted according to Korean Standards (KS) F International Standardization Organization (ISO) standard 10295-1:2021 [20], with heating based on the ISO 834 time–temperature curve [21]. All tests were performed independently in a horizontal furnace with internal dimensions of 3 m (width) × 4 m (length). Eleven sleeve types were selected from extensively used commercial products commonly applied in construction practice. All specimens were tested simultaneously in a single fire exposure setup under identical conditions. Each sleeve type was tested twice, and the average temperature values from the two trials were used for the analysis. In all cases, the two measurements showed consistent patterns of thermal behavior, confirming the reproducibility of the observed trends.
Each test specimen was installed in an autoclaved, lightweight, aerated, concrete slab (thickness = 150 mm) and comprised a floor-drain sleeve, a penetrant polyvinyl chloride pipe, firestop material, and fixing steel plates. The penetrant was a nonmetallic pipe fixed to protrude 1000 mm below the sleeve (diameter = 60 mm). As illustrated in Figure 1, five K-type thermocouples were attached to each specimen: one at the top center of the sleeve opening (trench center), two at the sleeve side (trench side), and two within the water seal. The thermocouples used had a maximum temperature range of 1200 °C and a precision of ±1.5 °C. Temperature data were automatically recorded at 1 min intervals using a data logger (MV2000, Yokogawa Electric Co., Tokyo, Japan), which was configured to simultaneously measure up to 40 channels. For clarity of presentation, the plotted temperature–time curves were rendered with smooth lines.
Figure 3 presents both the ISO 834 standard’s time–temperature curve and actual furnace temperatures measured during testing [21]. As the purpose of this study was not to determine compliance with regulatory pass/fail criteria, absolute thresholds, such as the 180 °C limit for insulation failure, were not applied. Instead, the analysis focused on the trend of temperature increase over time and comparative thermal transfer characteristics depending on sleeve geometry.
3. Results
3.1. Analysis of Fire Resistance Characteristics Based on Sleeve Geometry
Figure 4 and Figure 5 depict the time–temperature curves plotted for square and round floor-drain sleeves, respectively. Despite the use of identical firestop materials, the temperature rise patterns varied depending on the sleeve geometry, suggesting that the structural shape, rather than the material itself, can influence considerably the fire resistance performance.
In the square-sleeve configuration, temperatures at the trench center were typically higher than at other locations. Notably, the SC sleeve type exhibited an abrupt increase in the temperature near the end of the test, reaching 254.9 °C at 120 min. As the underside of the slab was sealed with the same material across all the specimens, this result was likely not due to a sealing failure but was rather caused by heat accumulation or transfer concentrated by cross-sectional asymmetry or local geometric irregularities. Additionally, in some cases, the sleeve itself was possibly ignited at high temperatures, leading to flame generation and a rapid temperature spike. Sleeve type SB exhibited an early rise in temperature, which then plateaued after approximately 110 min, whereas sleeve type SC demonstrated an abrupt increase between 100 and 120 min, suggesting an accumulated heat inflow followed by a localized thermal response. This outcome is attributed to the extremely short lower-sleeve length and narrow upper-opening area in the SC sleeve type, which shortened the radiant heat path and induced localized thermal accumulation. In contrast, specimens with deeper sleeve embedment exhibited suppressed peak temperatures due to more effective dispersion of radiant energy. These trends align with the findings of Heo et al. (2021), who demonstrated that cross-sectional geometry and heat inflow paths influence considerably radiant heat behavior in precast concrete slabs [22].
Among the square sleeves, the SE sleeve type maintained temperatures below 60 °C at all measurement points, and its curve remained smooth throughout the entire heating period and across all measurement positions. Specifically, no abrupt increase was observed at the trench center, and the temperature trend remained stable overall. This indicates that the structural shape and firestop material may have been wellaligned, forming a uniform heat barrier. These results suggest that even within the same shape category, stable thermal insulation can be achieved when structural alignment is ensured.
For round sleeves, temperature increases were typically more moderate than in square sleeves, and the temperature differences between the trench center and water seal locations were smaller. All the six round sleeve types exhibited similar curve gradients and peak temperature ranges, implying that geometric symmetry may contribute to structural integrity and stable thermal diffusion. While a few cases showed rapid temperature increases during the initial phase of testing, the curves tended to flatten afterward, possibly owing to differences in radiative heat transfer caused by the initial geometry. Overall, the round sleeves exhibited smaller variations among the products, indicating that geometric stability may contribute to more consistent fire-resistance performance.
3.2. Time–Temperature Distribution by Measurement Location
Figure 6, Figure 7 and Figure 8 compare the time–temperature curves plotted at three locations—water seal, trench side, and trench center—and analyze the temperature rise characteristics at 30 min intervals based on sleeve geometry.
The water seal was the location closest to the heated surface and thus received the thermal input first. Up to 60 min, all configurations maintained temperatures below 30 °C. However, after this point, a pronounced temperature increase was observed in square sleeves. The SC sleeve type reached 160.9 °C, while the sleeve types SB and SD exceeded 80 and 60 °C, respectively, indicating a cumulative temperature increase in several cases. In contrast, round sleeves consistently remained below 40 °C across the entire test duration, thus exhibiting a more stable thermal distribution. Overall, the square sleeves exhibited higher temperatures than did the round ones, suggesting that heat concentration patterns varied with geometry. Square sleeves are structurally prone to localized heat accumulation along corners or junctions, which may compromise their thermal uniformity. Conversely, round sleeves, allow a more even heat diffusion along curved surfaces, limiting localized accumulation. Even under identical material conditions, differences in geometry and alignment influenced considerably the heat transfer behavior, possibly resulting in varying fire-resistance performances.
At the trench side, temperature distributions were typically slightly higher than at the water seal, with most specimens maintaining levels between 20 and 40 °C. Some round sleeves, such as types RC and RE, exhibited relatively higher temperatures, possibly owing to their larger trench surface area and extended horizontal heat-transfer paths. While extreme geometric differences were not prominent at this location, certain square sleeves (e.g., type SC) did show anomalous spikes in temperature.
The trench center corresponds to the upper central axis of the sleeve, where radiant heat can enter directly along the vertical direction. Most conditions remained within the 30–90 °C range; the only case which exceeded 100 °C was the SC sleeve type. In that instance, the temperature increased abruptly to 254.9 °C at 120 min, marking the highest recorded value among all test conditions. All other square and round sleeves remained below 100 °C, with square ones again showing slightly higher overall temperatures than the round ones. While most conditions maintained consistent thermal blocking performance at the center axis, the SC sleeve type likely experienced heat concentration owing to geometric or structural misalignment.
Although both the water seal and trench center were directly exposed to heat, the heat-transfer patterns varied considerably over time depending on the sleeve geometry. The water seal responded more quickly to heat input, and the performance differences were influenced by the integrity of the lower sealing. The trench center, despite receiving vertical radiant heat, showed stable blocking in all cases except in configurations, such as type SC, where incomplete thermal boundaries allowed excessive heat ingress. These results highlight that geometric features, continuity of insulation layers, and structural alignment can directly influence the fire resistance performance. These findings are consistent with thermal modeling principles presented by Wickström (2016), who emphasized that geometrical boundary conditions and radiative heat transfer paths critically govern the temperature distribution in fire-exposed structures [23].
3.3. Analysis of Temperature Distribution Characteristics Based on Sleeve Geometry
To analyze quantitatively the effects of the upper-opening area and lower-sleeve length on temperature rise over time, temperature data measured at the water seal, trench side, and trench center were compared (see Figure 9, Figure 10 and Figure 11). Because each location would differ in flame exposure path, radiant heat transfer, and thermal buffering structure, correlations with geometric parameters were interpreted separately.
At the water seal—the location closest to the heat source—longer lower-sleeve lengths and larger upper-opening areas were associated with lower temperature increases. The lower-sleeve length extended the path of radiant heat through the slab, thereby forming a thermal buffer zone. The upper-opening area helped disperse the radiant energy across a wider surface, thereby mitigating localized heat concentration. At the 120 min mark, the coefficient of determination (R2) between the lower-sleeve length and temperature was relatively high at 0.83, reflecting a structural modulation effect on the cumulative radiant heat. The correlation with the upper-opening area was weaker (R2 = 0.33), suggesting a limited contribution from physical dispersion. Notably, the SC sleeve type, with the shortest lower-sleeve length (30 mm) and the smallest upper-opening area (22,500 mm2), recorded the highest temperature at the water seal of 160.9 °C, indicating ineffective radiant heat shielding under these conditions.
At the trench side, the temperature distributions remained low and stable across all test conditions and showed very weak correlation with geometric variables (R2 ≈ 0.15–0.18). As this measurement point was located away from the centerline, it was possibly affected more by external cooling and test setup conditions than by sleeve geometry. Therefore, it appears to have limited direct dependence on geometric parameters and may be more useful as a supplementary evaluation location.
The trench center—where vertical radiant heat input is most concentrated—exhibited the highest quantitative correlation with the geometric parameters. At the 120 min mark, the correlation with lower-sleeve length reached R2 ≥ 0.93, and the correlation with upper-opening area was R2 = 0.42 at 90 min. Shorter lower-sleeve lengths and smaller upper-opening areas were associated with higher temperatures. The SC sleeve type, under the same conditions (30 mm lower-sleeve length and 22,500 mm2 upper-opening area), exhibited the highest trench center temperature of 254.9 °C at 120 min—the highest recorded among all the test configurations. These results suggest an interaction effect where extremely short lower-sleeve lengths, combined with small upper-opening areas, lead to intensified radiant heat concentration and localized overheating.
Additionally, many of the square sleeve types included in the study had both short lower-sleeve lengths and small upper-opening areas. These characteristics, combined with geometric asymmetry, possibly contributed to complex heat accumulation patterns. Thus, the temperature rise tendencies of the square sleeves may reflect not only the effects of shape but also the overlapping influence of multiple geometric parameters. The aim of future experimental designs should be on the isolation of the effects of geometry from those of component-level variables.
Compared with previous studies on cylindrical sleeve systems incorporating nonmetallic pipes [12], the present results exhibited considerably different thermal behavior despite the use of the same pipe diameter (60 mm). In the earlier tests, the peak temperature at the penetration center typically remained within the range of 120–150 °C. However, in the current study, the test configuration employed a noncylindrical sleeve divided into upper and lower parts, with the upper opening area and lower sleeve length considered as independent geometric variables. Under the most critical condition, for the SC sleeve type, with the shortest lower-sleeve length (30 mm) and smallest upper-opening area (22,500 mm2), the recorded peak temperature reached 254.9 °C. This suggests that even with the same or smaller lower opening diameter, the shortened sleeve depth and reduced upper area attributes can increase the radiant heat concentration. Therefore, while previous studies emphasized that the opening area was the dominant variable, the present findings demonstrate that sleeve depth and asymmetric geometry affect considerably thermal shielding. These results empirically highlight the limitation of conventional evaluation frameworks that rely solely on penetration area, especially in noncylindrical, multipart sleeve systems.
3.4. Correlation Analysis of Geometric Variables and Temperature Responses by Measurement Location
In this study, Spearman’s rank correlation coefficient (Spearman’s ρ) was employed to analyze the relationship between geometric variables and time-dependent temperature, considering the limited sample size. The analysis was performed based on three measurement positions—water seal, trench side, and trench center—and the results were interpreted separately according to the distinct heat transfer conditions at each location. Descriptive statistics for all variables are summarized in Table 2, and the correlation coefficients by location and time point are provided in Table 3.
At the trench side, no significant correlations were found between body length, lower sleeve length, or upper volume and the temperature at any time point. Only the upper opening area exhibited a significant positive correlation at the 30 min mark (r = 0.806, p < 0.01), suggesting that larger openings may help distribute initial radiative heat. However, the effect diminished over time, indicating that external factors likely outweighed the influences of geometric conditions at subsequent stages.
At the trench center—where direct radiative heat exposure is concentrated—the geometric variables demonstrated the strongest correlation with thermal behavior. The upper opening area exhibited considerable negative correlations throughout the full time range from 30 to 120 min (r = −0.630 to −0.788), and the upper volume exhibited a significant negative correlation at 60 min (r = −0.627, p < 0.05). These results indicate that narrower openings and smaller volumes intensify thermal accumulation and lead to faster temperature rises. Although the lower sleeve length did not exhibit significant correlation in this rank-based analysis, it had previously exhibited a high coefficient of determination (R2 > 0.9 at 120 min) in the regression model. This suggests that while monotonic relationships may not be strong at individual time points, the cumulative influence of the lower sleeve on heat buffering becomes more apparent in long-duration fire exposure. The difference likely reflects the methodological contrast between regression-based explanatory power and rank-based correlation testing.
At the water seal position, significant negative correlations were found between the upper opening area and temperature at 60 min (r = −0.756), 90 min (r = −0.834), and 120 min (r = −0.697). Other variables did not yield definitive correlation outcomes. As this location was situated below the slab and exposed to indirect radiative heat, it was considered that the upper geometry played a partial role in localized thermal control. Similar to the trench center case, the explanatory power of the lower sleeve length observed in the regression analysis was not fully reflected here, which can be attributed to the limitations of point-in-time rank analysis for capturing structural accumulation effects.
4. Discussion
This study demonstrated that the fire-resistance performance of floor-drain sleeves was significantly influenced by structural geometry, particularly the lower-sleeve length and upper-opening area. These variables affected heat accumulation and diffusion patterns, as confirmed by regression (R2) and rank-based correlation (Spearman’s ρ) analyses.
Among the geometric variables, the lower-sleeve length consistently exhibited strong negative correlations with peak temperature, especially at the trench center, where direct radiant inflow occurred. When this length was short, radiant heat was concentrated, resulting in abruptly increased temperatures—a finding reinforced by R2 values > 0.9. Likewise, a smaller upper-opening area was associated with higher thermal concentration, exhibiting repeated negative correlations in both statistical models.
These findings suggest that material performance and specific geometric configurations must be considered when evaluating firestop systems, especially those with nonstandard designs. While round sleeves exhibited more consistent and stable performance owing to geometric symmetry, square sleeves showed vulnerability due to shape-induced asymmetry and dimensional limitations.
Importantly, these empirical results highlight the limitations of current regulatory frameworks, which often evaluate fire resistance primarily based on material type and penetration area, without adequately accounting for sleeve geometry, depth, or asymmetry. Existing standards, developed primarily for conventional pipe penetrations, may underestimate the risk presented by atypical configurations, such as floor-drain sleeves.
Therefore, the findings support the need for performance-based assessment systems that incorporate geometric parameters as essential variables in certification protocols. Specifically, the lower-sleeve length and upper-opening area should be introduced as standard input parameters in design evaluation, especially when dealing with multicomponent or noncylindrical assemblies.
These implications align with recent movements in building code reform and performance-based fire engineering, emphasizing scenario-specific assessment criteria rather than uniform prescriptive thresholds. Incorporating these geometry-sensitive metrics into test standards and certification guidelines could enhance fire-safety evaluations of real-world construction components that diverge from conventional assumptions.
Furthermore, the analytical approach demonstrated here—combining regression and correlation to interpret structural influence—offers a methodological foundation for future standard development, as well as for simulation-based evaluation tools that reflect complex geometries. These contributions may assist regulatory bodies in rationalizing firestop performance criteria and developing more robust, flexible guidelines applicable to diverse field conditions.
5. Conclusions
This study quantitatively analyzed the influence of structural variables pertaining to floor-drain sleeves, such as sleeve cross-sectional shape, upper-opening area, and lower-sleeve length, on fire resistance performance. By applying the same firestop material across all test cases, this experimental study evaluated temperature distributions resulting from various geometric configurations and assessed the thermal response at key locations within the sleeve as well as correlations between variables. The significance of this study lies in its structural, performance-based approach to interpreting the fire behavior of complex, nonstandard penetration systems.
First, the sleeve cross-sectional shape was found to affect heat diffusion pathways and structural conformity. Square sleeves, owing to their asymmetric geometry and tendency to concentrate radiant heat, exhibited unstable high-temperature responses at the trench center. In contrast, round sleeves showed uniform thermal dispersion and a more stable temperature distribution.
Second, the water seal and trench center emerged as key locations sensitive to geometric variables. Particularly, the trench center showed clear temperature variation depending on the lower-sleeve length and upper-opening area, owing to direct exposure to vertical radiant heat. In the case of the SC sleeve type with a lower-sleeve length of 30 mm and an upper-opening area of 22,500 mm2, the temperature peaked at 254.9 °C, demonstrating that inadequate structural design can significantly degrade fire performance.
Third, quantitative analysis revealed that longer lower-sleeve lengths consistently led to lower temperatures, with a maximum coefficient of determination (R2) of 0.93, indicating it is the most influential variable for controlling radiant heat transfer. While larger upper-opening areas also correlated with reduced temperatures, the effect was weaker (R2 up to 0.42) and often dependent on the combined interaction with lower-sleeve length.
In addition, rank-based correlation analysis confirmed the statistical significance of the upper-opening area, showing repeated negative correlations with temperature at both the trench center and water-seal positions. Although the lower-sleeve length did not consistently yield significant rank correlation, its high explanatory power in regression models suggests that it plays a cumulative role in heat buffering over prolonged exposure conditions. These findings reinforce the complementary value of correlation and regression approaches in evaluating the thermal behavior of firestop systems.
Notably, the greatest temperature increases occurred when both the lower-sleeve length and upper-opening area were small—a condition more commonly observed in square sleeves. However, to distinguish the effect of geometric shape from that of dimensional parameters, additional controlled experiments are needed.
In summary, this study provides empirical evidence that sleeve geometry design can significantly affect fire resistance performance, extending beyond material application alone. As the experiments were conducted using commercially available products, the results have practical implications for regulatory systems.
However, it should be noted that not all geometric factors could be fully controlled as the specimens were based on actual construction products. Therefore, this study focused on a set of key variables that yielded visually observable and structurally significant influences. Each condition was tested in duplicate, and while the results were consistent enough to reveal clear trends, statistical generalization remains limited. In future studies, we plan to conduct precision-controlled experiments that isolate single variables; based on the findings, the scope will be expanded to include additional parameters excluded in this study. Furthermore, although smoke-leakage performance (L) was not evaluated in this study, it is extensively regarded as a critical criterion in fire safety. Including L-value measurements would help establish a more comprehensive basis for firestop performance evaluation and will be considered as an essential component in future research. Future research should involve precision-controlled experiments that isolate single geometric variables, alongside simulation-based analyses of radiant heat transfer, to develop an integrated experimental–analytical framework for performance evaluation. These efforts will support the advancement of firestop system certification, improve performance assessment criteria, and rationalize nonstandard structural designs.
Conceptualization, H.-B.C. and J.-O.P.; methodology, H.-B.C. and S.-Y.H.; software, H.-D.L. and S.-Y.H.; validation, A.-Y.J. and J.-O.P.; formal analysis, H.-B.C. and H.-D.L.; investigation, A.-Y.J. and J.-O.P.; resources, A.-Y.J. and J.-O.P.; data curation, H.-B.C. and H.-D.L.; writing—original draft preparation, H.-B.C.; writing—review and editing, A.-Y.J. and J.-O.P.; visualization, H.-D.L. and S.-Y.H.; supervision, A.-Y.J.; project administration, A.-Y.J.; funding acquisition, A.-Y.J. and J.-O.P. All authors have read and agreed to the published version of the manuscript.
Not applicable. This study did not involve humans or animals.
Not applicable.
The raw data supporting the conclusions of this article will be made available by the authors on request.
The authors declare no conflicts of interest.
Footnotes
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Figure 1 Schematic illustration of floor-drain sleeves and thermocouple locations: (a) square floor-drain trap and (b) round floor-drain trap.
Figure 2 Example specimens of floor-drain sleeves used in the experiment: (a) square floor-drain trap and (b) round floor-drain trap.
Figure 3 Standard and measured furnace temperatures during floor-drain sleeve tests.
Figure 4 Temperature–time curves for square floor-drain sleeves. Types (a) SA, (b) SB, (c) SC, (d) SD, and (e) SE.
Figure 5 Temperature–time curves for round floor-drain sleeves. Types (a) RA, (b) RB, (c) RC, (d) RD, (e) RE, and (f) RF.
Figure 6 Temperature variations at the water seal for square and round sleeves: (a) square and (b) round floor-drain sleeves.
Figure 7 Temperature variations at the trench side for square and round sleeves: (a) square and (b) round floor-drain sleeves.
Figure 8 Temperature at the trench center for square and round sleeves: (a) square floor-drain sleeves; (b) round floor-drain sleeves.
Figure 9 Effects of sleeve geometry on water-seal temperature. (a) Upper-opening area and (b) lower-sleeve length (n = 11).
Figure 10 Effects of sleeve geometry on trench side temperature. (a) Upper-opening area and (b) lower-sleeve length (n = 11).
Figure 11 Effects of sleeve geometry on trench center temperature. (a) Upper-opening area and (b) lower-sleeve length (n = 11).
Geometric properties of floor-drain sleeves used in the experiment (sleeve types are labeled for shape (S: square, R: round) and geometry (A–F)).
| Square | Round | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Type-SA | Type-SB | Type-SC | Type-SD | Type-SE | Type-RA | Type-RB | Type-RC | Type-RD | Type-RE | Type-RF | |
| Upper-sleeve length (mm) | 95 | 90 | 120 | 110 | 90 | 95 | 95 | 105 | 90 | 90 | 95 |
| Lower-sleeve | 55 | 60 | 30 | 40 | 60 | 55 | 55 | 45 | 60 | 60 | 55 |
| Upper-opening | 24,336 | 24,025 | 22,500 | 20,164 | 24,336 | 30,465 | 24,593 | 26,288 | 27,745 | 24,871 | 28,938 |
Descriptive statistics of geometric variables of floor-drain sleeves.
| Group | N | Minimum | Maximum | Mean | Standard Deviation | |
|---|---|---|---|---|---|---|
| Trench | 30 min | 11 | 0.10 | 2.40 | 0.97 | 0.67 |
| 60 min | 11 | 1.05 | 12.60 | 5.15 | 3.31 | |
| 90 mn | 11 | 4.00 | 28.50 | 12.09 | 6.83 | |
| 120 min | 11 | 10.90 | 37.65 | 20.22 | 8.07 | |
| upper-sleeve length | 11 | 90.00 | 120.00 | 97.73 | 9.84 | |
| lower-sleeve length | 11 | 30.00 | 60.00 | 52.27 | 9.84 | |
| upper-opening area | 11 | 20,164.00 | 30,465.07 | 25,296.68 | 2919.87 | |
| upper volume | 11 | 2,162,250.00 | 2,894,181.00 | 2,459,816.73 | 269,729.57 | |
| Trench center | 30 min | 11 | 0.40 | 8.70 | 3.89 | 2.62 |
| 60 min | 11 | 4.90 | 56.60 | 15.56 | 15.11 | |
| 90 mn | 11 | 9.10 | 61.40 | 24.38 | 18.55 | |
| 120 min | 11 | 13.00 | 254.90 | 50.02 | 70.22 | |
| upper-sleeve length | 11 | 90.00 | 120.00 | 97.73 | 9.84 | |
| lower-sleeve length | 11 | 30.00 | 60.00 | 52.27 | 9.84 | |
| upper-opening area | 11 | 20,164.00 | 30,465.07 | 25,296.68 | 2919.87 | |
| upper volume | 11 | 2,162,250.00 | 2,894,181.00 | 2,459,816.73 | 269,729.57 | |
| Water seal | 30 min | 11 | 2.25 | 15.65 | 5.95 | 3.86 |
| 60 min | 11 | 8.45 | 71.75 | 22.27 | 18.23 | |
| 90 mn | 11 | 13.65 | 79.50 | 32.90 | 21.17 | |
| 120 min | 11 | 22.85 | 160.90 | 51.52 | 42.10 | |
| upper-sleeve length | 11 | 90.00 | 120.00 | 97.73 | 9.84 | |
| lower-sleeve length | 11 | 30.00 | 60.00 | 52.27 | 9.84 | |
| upper-opening area | 11 | 20,164.00 | 30,465.07 | 25,296.68 | 2919.87 | |
| upper volume | 11 | 2,162,250.00 | 2,894,181.00 | 2,459,816.73 | 269,729.57 | |
Correlation analysis of geometric variables and temperature.
| Group | 30 min | 60 min | 90 min | 120 min | Upper- | Lower- | Upper- | Upper Volume | |
|---|---|---|---|---|---|---|---|---|---|
| Trench side | 30 min | 1.000 | |||||||
| 60 min | 0.773 ** | 1.000 | |||||||
| 90 mn | 0.536 | 0.882 *** | 1.000 | ||||||
| 120 min | 0.364 | 0.700 * | 0.909 *** | 1.000 | |||||
| upper-sleeve | −0.162 | 0.095 | 0.081 | 0.029 | 1.000 | ||||
| lower-sleeve | 0.162 | −0.095 | −0.081 | −0.029 | −1.000 ** | 1.000 | |||
| upper-opening | 0.806 ** | 0.492 | 0.296 | 0.169 | −0.272 | 0.272 | 1.000 | ||
| upper volume | 0.582 | 0.582 | 0.473 | 0.364 | 0.462 | −0.462 | 0.688 * | 1.000 | |
| Trench center | 30 min | 1.000 | |||||||
| 60 min | 0.856 ** | 1.000 | |||||||
| 90 mn | 0.711 * | 0.882 *** | 1.000 | ||||||
| 120 min | 0.601 | 0.736 ** | 0.936 *** | 1.000 | |||||
| upper-sleeve | −0.127 | −0.086 | 0.205 | 0.491 | 1.000 | ||||
| lower-sleeve | 0.127 | 0.086 | −0.205 | −0.491 | −1.000 *** | 1.000 | |||
| upper-opening | −0.630 * | −0.702 * | −0.752 ** | −0.788 ** | −0.272 | 0.272 | 1.000 | ||
| upper volume | −0.588 | −0.627 * | e | −0.327 | 0.462 | −0.462 | 0.688 * | 1.000 | |
| Water seal | 30 min | 1.000 | |||||||
| 60 min | 0.809 ** | 1.000 | |||||||
| 90 mn | 0.855 ** | 0.973 *** | 1.000 | ||||||
| 120 min | 0.873 *** | 0.873 *** | 0.909 ** | 1.000 | |||||
| upper-sleeve | 0.334 | 0.124 | 0.234 | 0.477 | 1.000 | ||||
| lower-sleeve | −0.334 | −0.124 | −0.234 | −0.477 | −1.000 *** | 1.000 | |||
| upper-opening | −0.574 | −0.756 ** | −0.834 ** | −0.697 * | −0.272 | 0.272 | 1.000 | ||
| upper volume | −0.264 | −0.555 | −0.555 | −0.245 | 0.462 | −0.462 | 0.688 * | 1.000 | |
Notes: Correlation coefficients are Spearman’s ρ. Significance levels: p < 0.05 (*), p < 0.01 (**), p < 0.001 (***), two-tailed.
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; Hyung-Do, Lee; Seung-Yong, Hyun