1 Introduction
Green roofs, also known as living roofs or roof gardens, are becoming increasingly popular owing to their environmental and economic benefits as well as their aesthetic appeal. Environmentally, green roofs remove air pollutants [
1] and reduce energy requirements [
2–
5], thereby reducing the global carbon footprint. Studies show that buildings are among the most significant contributors to greenhouse gas emissions worldwide [
6–
8]. By adopting native plant species in buildings, the local ecosystem is improved by attracting wildlife, such as birds and bees [
9]. Economically, green roofs reduce building heating and cooling costs owing to their effective insulating properties [
10]. One of the most significant motivating factors for their use is aesthetics. They provide excellent respite and amenity to urban inhabitants; in fact, studies show that green roofs improve the well-being of occupants [
11] by reducing stress and improving their performance [
12].
Despite their increasing popularity, green roofs have not been investigated comprehensively for their potential seismic benefits. Green roofs are regarded only as added demand for buildings. The large mass that living roofs add to the top level increases gravity demand and seismic weight; however, engineers must consider beyond the loading demand to better understand responses, including floor accelerations.
Several researchers have attempted to understand the relationship between green roofs and their seismic performance. Matta and de Stefano [
13,
14] examined the use of these roofs as tuned mass dampers (TMDs). They acknowledged the variability in mass present due to natural hazard (i.e., storm surges), natural growth, and the presence of wildlife. Hence, they controlled the TMDs resonance period by applying a rolling pendulum system to effectively isolate the roof to a known period. Furthermore, they used conventional dampers to control the roof behavior. Although an interesting approach involving the application of isolation and damping to green roofs was adopted in these studies, the baseline behavior of green roofs must be established without any modification to understand their natural impact to structural behavior.
Carmody et al. [
15] performed small-scale experimental tests on single- and multi-story green roof structures and examined the process by which free water in the drainage layer contribute to the damping of the structure. Specifically, a scaled structural system was used, where water was added incrementally to the surface. They discovered that a single-story scaled structure exhibited negligible damping enhancement, whereas a three-story scaled structure exhibited an increase in damping from 0.8% to 1.4%. This suggests that the dynamics of green roof systems are more complicated than originally conceived.
A few years later, Welsh-Huggins and Liel [
16] examined green roofs from a life cycle perspective, focusing primarily on environmental impact and hazard performance. This resulted in the development of a green resilience framework. To test this framework, they numerically modeled a series of two-dimensional (2D) concrete structures with several green roof scenarios that were then subjected to earthquake excitations.
Meanwhile, Tam and Wong [
17] investigated the performance of 2D three-story steel frame structures with intensive (deep) and extensive (shallow) green roofs under seismic scenarios involving near-, mid-, and far-field excitations. Compared with a control frame with no green roof, they discovered that the green roof scenarios investigated imposed a more significant effect on the floor acceleration than on the displacement. Roofs subjected to intense seismic excitations resulted in the most significant decrease in acceleration, particularly on the floor below the roof.
Green roofs are a sustainable feature that has gained popularity in the United States owing to the development of “Leadership in Energy and Environmental Design” [
18]. Although green roofs are not a new technology, guidelines and articles addressing their design have increased significantly in the past decade [
11,
19]. The intersection of sustainability and structural resilience is crucial for the promotion of both entities. Structural resilience refers to the ability of a structure to return to operation after a natural hazard or an event. An intertwined relationship between these two fields is developing progressively, as indicated in the abovementioned studies. Increased awareness by the structural engineering community regarding the effect of the building sector on the planet’s carbon footprint has resulted in the establishment of the SE 2050 Carbon Neutral Initiative [
20]. The goal of this initiative is to motivate engineering firms to shift toward net-zero embodied carbon using less impactful building practices and structural materials. Firms are performing initial life cycle analyses on various buildings and projects within their scope to determine the best paths toward net-zero embodied carbon. In addition, the American Society of Civil Engineers (ASCE) established the ASCE 73 committee to develop “Standards on Sustainable Infrastructure.” These efforts promote improvements toward the sustainability of structural systems.
The effect of the seismic performance of green roofs on structural behavior has been investigated in previous studies. Nonetheless, the features of green roofs and the corresponding effects structural behavior can be further investigated. This study addresses several inadequacies in knowledge, including 1) the linearity of green roof soil substrates, 2) the sensitivity of response to green roof layouts, and 3) modeling nuances. Specifically, these aspects were investigated by analyzing the sensitivity of structural performance to green roof layouts based on three-dimensional nonlinear time-history data conducted in SAP2000 [
21]. Although examples of full roof systems are available, most are restricted to spaces allocated for vegetation to accommodate other rooftop features, including heating, ventilation and air conditioning (HVAC) machinery. The findings of this study will allow one to approach green roof structural analysis more effectively and understand the potential effects of green roofs such that design optimizations can be performed to ensure structural resilience. The following sections provide an outline of the structural system used and the manner in which sensitivity studies were conducted.
2 Method
To achieve the study objectives, an archetype-braced frame from Federal Emergency Management Agency (FEMA) P-1051, which serves as an emergency operation center, was used [
22]. The structure (see Fig.1) features a symmetric configuration with a floor plan measuring approximately 100 ft × 150 ft (30.5 m × 45.7 m) for three main stories. The roof features a unique penthouse design measuring 50 ft × 100 ft (15.2 m × 30.5 m), which allows two roof levels to be analyzed. The first floor is 14 ft (4.3 m) tall, whereas the remaining stories are 12 ft (3.7 m) tall. The structural system members and layout are shown in Fig.2–Fig.6. The gravity loading system comprises composite steel–concrete slabs supported by steel beams and girders. The main lateral force-resisting system comprises concentrically braced frames.
Two structural scenarios were considered: a control frame and a green roof. The control frame was imposed with dead and live loads measuring 93 psf (4453 N/m
2) and 80 psf (3830 N/m
2), respectively, on each main floor. Meanwhile, the roof was imposed dead and live loads measuring 15 psf (718 N/m
2) and 20 psf (958 N/m
2), respectively. A shallow extensive green roof comprising low-lying foliage such as herbs or perennials was implemented. The soil substrate was approximately 6 inches (15.2 cm), which resulted in a dry weight of 28 psf (1341 N/m
2) and saturated weight of 41 psf (1963 N/m
2), based on loadings by Green Roof Technology [
23]. A saturated weight was used to modify the control structure to ensure that the roof members can support additional loads. This practice is consistent with the current industry efforts for ensuring maximum load use. Both structures were modeled using the SAP2000 software.
The main structure was imposed with 2% damping. Subsequently, the soil material for the green roof was investigated (as described in Subsection 3.1). Compared with structural materials, soil can behave both linearly and nonlinearly. Abundant information is available regarding soil behavior in the context of geotechnical and foundation engineering. However, the soil behavior on a green roof is unique. Soil with linear behavior will exhibits a constant level of stiffness when subjected to dynamic loading and hence a constant damping value. However, soil with nonlinear behavior will experience a decrease in stiffness at higher strain values, thus resulting in hysteretic behavior. Soil that yields a significant hysteretic loop dissipates more energy and hence exhibits increased damping [
24].
Four scenarios were considered for the green roof system, as shown in Fig.7. These layouts were considered to examine the variations in response due to symmetric and asymmetric green roof designs. An additional complexity level was introduced by examining the placement on two different roof levels. The four layouts exhibited variable amounts of weight owing to the size of the green roofs. The fundamental period of the structure without a green roof was 0.2 s. For layout 1, the fundamental period increased by 25% to 0.25 s, whereas those of the other layouts remained similar to the period of the control frame, since less weight was introduced to the structure in those layouts.
3 Results
Two main studies were conducted. In the first study, the soil material of the green roof was examined to quantify its appropriate damping value. Using the information obtained, the structural performance of various green roof layouts were examined in the second study.
3.1 Damping
To analyze the linearity of the green roof growing medium, DeepSoil [
25] was used. DeepSoil is typically used to analyze the profile of a soil subjected to dynamic loading. However, it can also provide insights into the characteristics of soil. The purpose of the analysis performed in this study is to 1) determine whether the green roof soil yields a linear or nonlinear response to dynamic loads, and 2) to determine the soil’s average damping ratio under dry and saturated conditions.
A typical green roof growing medium does not belong strictly to only one of the standard soil classifications, such as silt, clay, sand, or gravel. Based on information the soil compositions of various green roof growing media obtained from the FLL Guidelines, the typical green roof growing medium is classified as organic soil [
19]. This classification is beneficial as it allows one to predict the soil performance when it is subjected to dynamic loading.
For the analysis, a single column measuring 6 inches (15.2 cm) thick on a bedrock was considered; notably, shallow/extensive green roofs are typically characterized by a thickness of 6 inches (15.2 cm). In DeepSoil, several user-defined parameters must be defined, which are described below.
1) Shear wave velocity. The shear wave velocity,
Vs, can be obtained easily for standard soils such as clay and sand; however, the variability of organic soils renders the classification of
Vs difficult. Said and Bin [
26] investigated the wave velocity of peat and organic soils. Green roof growing media cannot be classified strictly as peat soil as they contain some peat mixed to aid plant growth. The Vs for peat soils ranges from 85.4 to 314.6 ft/s (26 to 96 m/s), whereas that for soft clays ranges from 200.9 to 283.4 ft/s (61 to 86 m/s) [
26]. Because growing media can exhibit the characteristics of both peat and clay, the shear wave velocity was averaged over both conditions at approximately 200 ft/s (61 m/s).
2) Shear strength. The shear strength of soil depends on various aspects of soil; however, investigations show that the organic matter in organic soils significantly affects the shear strength of the latter. Ekwue [
27] investigated the mechanism by which the shear strength of organic soils are modified by the constituent organic matter. The results showed that organic matter afforded higher aggregate stability and hence organic soils with a higher overall shear strength. Two cases were compared: soil with peat, and soil with grass. As time progressed, the soil with peat indicated a decrease in shear strength from 323 to 249 psf (15.5 to 11.9 kN/m
2), whereas the soil with grass indicated an increase in shear strength from 400 to 510 psf (19.2 to 24.4 kN/m
2). The roots in the grass contributed to firm soil, whereas the peat caused the soil to crumble. Similar to the case of shear wave velocity, the average values obtained between the abovementioned two scenarios can be considered owing to the presence of both peat and roots. As time progresses, the shear strength of the growing medium increases owing to the collective presence of roots, although peat can still disrupt the aggregate stability. An average value was specified for the shear strength, i.e., 370 psf (17.7 kN/m
2).
3) Thickness and unit weight. Green roofs may exhibit the same thickness and unit soil weights depending on whether the green roof is extensive or intensive. Online resources abound regarding green roof systems such as Green Roof Technology [
23]. The G2 system was used because it is the deepest and heaviest extensive green roof. Extensive green roof soil substrates can vary in depth depending on the foliage type used for the system. The soil substrate depth determines the amount of additional loading to be applied to the structure. An extensive green roof was used to limit the demand for the structure while reaping the environmental benefits of a green roof with minimal foliage maintenance. In this study, the deepest soil substrate associated with an extensive green roof was considered to accommodate the maximum load added to the roof. Considering the versatility and adaptability of green roof systems, if a client wishes to modify the foliage over time, the most appropriate method is to implement the deepest soil substrate possible on their green roof system. This method considers the unexpected overgrowth of foliage and is thus beneficial to extensive green roofs, which are not maintained as regularly as intensive roof systems.
4) Reference curve. A reference curve is required for the curves of G/Gmax vs. strain (%) and damping ratio (%) vs. strain (%) where G/Gmax is the ratio of current and initial shear moduli. The G/Gmax curve represents the soil at an initial strain value and shows that the stiffness decreases as the strain increases. The damping ratio curve shows that damping increases with strain. These curves are critical as they enable the program to reveal the soil behavior at specified strain values. In DeepSoil, preloaded reference curves for sand or clay can be used and a user-defined curve can be input. Because green roof soil has not been widely tested, an adequate preloaded reference curve is not available. Therefore, a user-defined curve is preferable.
Data for the user-defined curve were obtained from Kallioglou et al. [
28]. Herein, the testing procedure and the results of laboratory studies conducted on organic soils using resonant column tests are summarized. Different types of natural and laboratory-formed (model) organic soil specimens were tested. However, results obtained from organic cohesive soils and peats are prioritized in this study as they are the most similar to the soil composition of the growing medium. The curve that depicts the most similar unit weight to the G2 soil of green roofs was selected. Hence, two specimen curves were used in the DeepSoil study: a high organic black clay (C7) and black clayey peat (P1). The data for the reference curve are listed in Tab.1 and Tab.2.
5) Curve fitting. Both modulus reduction and damping curve fitting (MRDF) with the University of Illinois at Urbana–Champaign reduction factor or MRDF with Darendeli reduction factor curve fitting procedures yielded similar results; therefore, either one can be used provided that the reduction factor formulation is based on the same option.
6) Water table. Although a natural water table does not exist in a man-made soil medium, a water table element was applied to represent the saturation level in the soil column. To simulate the behavior under both dry and fully saturated conditions, two iterations were conducted for each reference curve (C7s and P1). In one iteration, the water table at the top of the soil layer was selected for the saturated condition, whereas the other iteration did not involve a water table. For the condition without a water table, the dry unit weight was used for G2 green roof soil.
7) Bedrock. The DeepSoil program is typically used to analyze the profile of soil under a building or site. However, a green roof is located on the top of a building or terrace. In this study, a rigid bedrock was used to model a fixed building.
A nonlinear analysis method was used because the goal of this study was to observe if the green roof soil presented nonlinear characteristics and thus hysteretic behavior. A time-domain solution type and non-Masing hysteretic re/unloading formulation were used. A non-Masing hysteretic re/unloading formulation was used instead of a Masing re/unloading formulation, because non-Masing is generally more realistic. Additionally, non-Masing captures the damping behavior of soils subjected to laboratory testing more accurately than Masing [
29]. The reference soil samples used were tested in a laboratory; therefore, non-Masing as more applicable.
Five input motions, i.e., Imperial Valley, Chi Chi, Kobe, Northridge, and Parkfield, were selected to perform testing under various dynamic loading conditions. These motions were selected because they are consistent with the seismic design parameters of the investigated structure, including SMS = 1.4, SM1 = 0.9, and at least 3 miles (4.8 km) from the fault.
A frequency-independent damping matrix was used to consider the current stiffness. As the aim of this study was to determine the appropriate damping ratio for the soil substrate, frequency-independent damping was utilized as it allows the eigenvalues and eigenvectors of the damping matrix to be solved and requires no specifications of modes or frequencies, unlike Rayleigh Damping [
25]. DeepSoil implements a viscous damping formulation to model a slight strain damping in the material. Hence, the use of a frequency-independent damping formulation is recommended to accommodate artificial damping presented in other approaches [
30,
31].
For all soil analyses, the results were predominantly linear with slight hysteresis, as shown in Fig.8. Tab.3 summarizes the maximum strain and the corresponding damping for each iteration and ground motion. Based on these results, the average shear strain was 0.005%, which resulted in a damping level of 2.5%. The ground motions used for this analysis were motions captured at the ground level. Based on these motions, the soil was predominantly linear with slight hysteresis, as shown in Fig.3. Although floor-level accelerations can be subjected to motion amplification, the amplification level necessary to generate significant nonlinearities, and thus to increase the damping ratio, is not be feasible. Consequently, the green roof damping level was set to 2.5%.
3.2 Nonlinear time-history analyses
The structural system described in Section 2 was further defined to include the green roof system. The green roof must be modeled with different damping ratios; however, SAP2000 does not offer a direct method that can assign different damping values to specific elements, unlike other analysis software (e.g., OpenSees). Hence, a new material known as “green roof” was defined in this study; it was assigned the corresponding weight and damping ratio (2.5%) associated with an extensive roof. Subsequently, it was applied to a shell area that encompassed the respective roof areas for each scenario. Rayleigh damping was applied to the main structure and was anchored at the first and second modes of the structure based on a 2% damping ratio.
The structures were subjected to a nonlinear time-history analysis based on three ground motions: El Centro (Imperial Valley), Northridge, and Kobe from the Pacific Earthquake Engineering Research Center Strong Motion Database [
32]. Three-component excitations were applied to the structures with relative floor displacements, and the absolute floor accelerations were recorded. Floor-level responses were prioritized, as nonstructural content generally contributes to the highest financial loss and is an indicator of post-hazard performance. Notably, many types of nonstructural content, including equipment and machinery, are displacement and/or acceleration sensitive.
The observed responses to a control system without a green roof were compared. As shown in Tab.4–Tab.7, the results of two nodes are presented with the decrease percentage. These nodes are shown on the main and penthouse roof levels, as shown in Fig.1. The result shows that the addition of green roofs for all four layouts decreased both the maximum accelerations and displacements at the abovementioned two levels. In a few instances, particularly for the Northridge excitation, the responses increased as compared with the case of the control system.
Based on Tab.4, the acceleration and displacement values did not decrease significantly in general. Layout 1 resulted in a decrease in the acceleration and displacement by 21% and 32%, respectively, at the maximum; and by 16% and 22%, respectively, on average. However, as shown in Tab.8, when the worst layout design was adopted, the acceleration and displacement increased in some cases, as indicated by a negative percent decrease. On average, layout 2 increased the acceleration and displacement by 1% and 2%, respectively. Similarly, layouts 3 and 4 exhibited variability in performance, exhibiting both increases and decreases. However, on average, layout 3 decreased the joint acceleration by 17% and decreased the joint displacement by 19%. Meanwhile, layout 4 decreased the joint acceleration by 7% and decreased the joint displacement by 10%.
A comparison of the maximum percentage difference in the drift of the various green roof layouts and that of the control system without a green roof is presented in Tab.8–Tab.10. The result shows that the magnitude of the percentage difference varied, although two observations were noteworthy. First, in the lower two levels, the drifts for each of the layouts increased, with layout 4 presenting the highest increase. Second, the upper two floors were significantly affected by the green roof across all layouts. The drifts decreased significantly owing to the additional loading from the green roofs.
The main conclusion inferred is that implementing green roofs can reduce the structural responses at the two roof levels. This may be a crucial feature of green roofs because the nonstructural content at the roof levels, such as HVAC, can be damaged owing to extreme structural behaviors. Thus, implementing a green roof can effectively improve structural resilience.
A point system was developed to evaluate the performance of various layouts. Floor displacements and accelerations were recorded at one point on each floor of the building, which resulted in a total of four joints. Horizontal and vertical responses were recorded for each joint, which resulting in four responses: the maximum horizontal floor displacement, maximum vertical floor displacement, maximum horizontal floor acceleration, and maximum vertical floor acceleration. The maximum horizontal results were calculated using SRSS procedures [
33]. For each ground motion, 16 responses were considered across the four joints; therefore, a total of 48 responses were considered across the three ground motions.
Tab.11–Tab.13 present the points awarded for each joint and ground motion. The cumulative scores are presented in Tab.14. Based on these calculations, layout 1 performed the best as it achieved the lowest cumulative floor accelerations and floor displacements. Interestingly, layout 2 performed the worst, which suggests sensitivity to the aspect ratio due to the reduced roof plan and additional weight concentration at the penthouse level. These two results suggests that a relationship exists between the amount of additional weight and potential damping from the green roof that contributes to the seismic response. The size of layout 1 is twice that of the green roof for layout 2.
Layout 4 ranked the second worst in terms of performance. In layout 4, although the weight was concentrated on the lower roof level, it was distributed asymmetrically. Layouts 3 and 4 were comparable in terms of weight added; however, their performances were not comparable. This suggests that a relationship exists that can potentially be optimized by understanding the sensitivities between the added weight and positioning within a structure.
4 Conclusions
In this study, the layout and damping of green roofs were investigated to examine their effects on structural performance. Four green roof layouts with variable added weights and symmetry were considered and several key findings were obtained.
First, the behavior green roof soil for an extensive system can be regarded as linear. Although green roof soil does not exhibit hysteretic behavior, based on the strain observed for an organic material, a damping ratio exceeding the standard 2% (which is typically applied to steel structural systems) was indicated. This study focused on an extensive green roof; thus, the appropriate damping ratio for deeper soil substrates should be investigated in future studies.
Second, green roofs can reduce floor displacements and accelerations compared with structures without green roofs. This is an important finding as it presents the added benefit of green roofs. The implementation of green roofs may not only address environmental concerns and provide occupant amenity, but also increases structural and nonstructural resilience. The extent of improvement afforded by green roofs varied for each scenario.
The point system allowed us to generate cumulative scores to evaluate the performances of the various layouts. The best performance was achieved by the heaviest doubly symmetric system, i.e., layout 1. Layout 2, which was the lightest and had the smallest footprint, achieved the least performance improvement. Layouts 3 and 4 were extremely similar in terms of added weight to the roof; however, their distributions differed between symmetric and asymmetric designs. These results suggest that, although all the layouts investigated improved the structural performance, their performances can be further maximized.
The results presented herein may promote further investigations into the implementation of green roof systems and their effect on structural/nonstructural performances. The parameter sensitivity of green roofs as well as structural responses under resonant and nonresonant motions should be considered to in future studies such that the behavior distribution can be fully captured to support the design optimization of green roofs. The development potential of this field is vast and new methods should be identified to integrate sustainable features into the practical components of seismic technology.
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