On the Use of Accelerometric Data to Monitor the Seismic Performance of Non-Structural Elements in Existing Buildings: A Case Study

Abstract

Monitoring of non-structural elements is not usually implemented, despite the seismic vulnerability of these components and the significant cost associated with their replacement in case of damage. By exploiting the limited cost of commercial sensors, accelerometers were installed in an existing building to compare accelerations applied to non-structural elements in case of an earthquake with critical acceleration thresholds. The exceedance of these thresholds would indicate a possible danger for the occupants and the need for a more detailed inspection of the element, guiding prioritisation strategies in the aftermath of the earthquake. Furthermore, the real-time probabilistic assessment of potential damage to non-structural elements can serve to identify escape routes and facilitate rescue operations. Critical acceleration thresholds were defined from probabilistic considerations on the expected seismic performance of each typology of non-structural element, described by appropriately selected fragility curves. The feasibility of the proposed procedure was tested by comparing the identified acceleration thresholds with the design values of floor acceleration provided by the Italian Building Code. As a further application, critical acceleration values of the different non-structural elements were compared with a set of real floor acceleration values recorded at the top level of reinforced concrete buildings, highlighting critical non-structural element typologies.

1. Introduction

The seismic vulnerability of non-structural elements has been attracting the attention of the research community in the last few years. Recent seismic events worldwide have confirmed that non-structural elements are subjected to damage even at intensity levels for which the structure is not suffering significant problems [1,2,3,4,5]. Also, a large percentage of the post-earthquake reconstruction cost is often associated with damage to non-structural elements. For these reasons, the scientific community is focusing on the evaluation of the seismic vulnerability of non-structural elements and contents, as well as on the introduction of criteria for the design of adequate connections to the structure, with the aim of preventing damage in case of a seismic event.

Seismic monitoring techniques are more and more frequently adopted for structural elements, particularly in case of strategic structures and infrastructures (e.g., bridges [6,7]), or structures that are relevant from an architectural or artistic point of view. In addition, data from monitoring systems can be used to activate seismic protection devices or to develop early warning systems.

On the other hand, seismic monitoring of non-structural elements is not defined at the code level, nor sufficiently discussed in the literature, even though it is widely recognised that proper seismic design of a building cannot disregard the seismic assessment of the performance of the non-structural elements within the building.

A non-structural element installed inside a building is subjected to a seismic action, which depends on the dynamic characteristics of the building and can affect the element in terms of force/acceleration, or in terms of displacement/deformation. In fact, the elements are often subdivided into susceptible to deformations/relative displacements, inertial forces/accelerations, or the combination of both [8].

Recent studies [9,10] have shown that the application of monitoring can be useful, for example, to evaluate the dynamic characteristics (e.g., frequency, modal shapes, and damping) of elements installed within an existing building and their evolution as damage progresses due to the seismic action [11,12]. The dynamic response under an input force can indeed be measured by in situ dynamic tests and used to calibrate a numerical model. Although the frequency extraction procedure is simple and well known, the accuracy of the measurement of the dynamic behaviour depends on the material properties and boundary conditions of the system.

Monitoring can be relevant especially in the case of buildings and elements with complex and/or critical seismic behaviour such as, for example, critical plants or cultural heritage elements. A recent study by O’Reilly et al. [13] focused on mitigating NaTech disasters in industrial plants caused by earthquakes. They developed a comprehensive monitoring platform, employing real-time probabilistic assessment to detect potential damage to both structural and non-structural elements. The platform also considers the potential release of harmful substances. By generating navigable risk maps, the system facilitates safe navigation and evacuation of industrial plant workers during emergency situations. The study demonstrated the platform’s effectiveness through its implementation in different industrial plant layouts, showcasing its potential for enhancing worker safety and risk management.

Archila et al. [14] conducted an in situ survey campaign on different types of non-structural elements installed in hospitals, located in Vancouver (British Columbia). They obtained a database of the dynamic characteristics of the elements, mainly focusing on operational components providing essential services in strategic buildings, such as fire piping systems. The dynamic characteristics (natural frequencies, modal shapes, and damping) of piping systems, which depend on pipe diameter and constraint conditions, were obtained using the frequency domain decomposition (FDD) method. Similar studies were conducted on several non-structural elements, including steel pipe and nuclear pipe networks [15,16].

2. Methodology

This paper presents an example of seismic monitoring of non-structural elements, developed by the EUCENTRE Foundation within a research project named S.A.M.B.A. (Smart and Advanced Multitenants Building Automation), funded by the Lombardy Region (Italy). The project aimed at proposing an innovative platform for converting existing buildings into smart buildings, by means of an integrated control of mechanical systems and plants, with significant potential benefits to occupants. The platform was based on the integration of non-invasive, low-cost, and low-impact technologies, applicable to existing buildings and guaranteeing the best possible performance improvement. In particular, the focus was both on automation and efficiency of the building functions, to enhance the occupants’ comfort and, at the same time, improve their safety, paying attention in particular to the expected seismic response of non-structural elements.

The activities of the EUCENTRE Foundation discussed in this paper concentrated on the seismic vulnerability of the non-structural elements installed within a real existing building, selected as a case study within the project, to show the applicability of the proposed framework. The seismic monitoring of the non-structural elements was used to develop a seismic alert system, able to identify a potentially hazardous situation for non-structural elements and eventually activate seismic protection systems, in case a critical capacity threshold is exceeded. Seismic fragility curves were selected, describing the expected seismic performance of the different non-structural elements, in terms of the probability of exceeding limit states of interest. A probabilistic approach allowed for the defining of critical acceleration thresholds, starting from the selected fragility curves.

The monitoring system consisted in triaxial accelerometric sensors installed at different positions within the building, within a device also able to measure temperature, humidity, and other parameters, with the aim of enhancing the level of comfort of people working within the building. A proper trigger algorithm was selected and implemented, making it possible to distinguish accelerations due to a seismic event from accelerations related to ambient noise or human activity. In the case of a seismic event, the floor acceleration registered by the installed sensors can be compared with the previously identified critical thresholds, making it possible to identify potential situations of danger and eventually issue an alert.

A new methodology for the seismic classification of non-structural elements was also developed within the project, starting from a conceptual framework similar to the energy classification of buildings and based on the use of fragility curves [17]. This allows for the identification of the most vulnerable non-structural element typologies, to help define mitigation strategies.

Section 3 of the paper will introduce the case study building considered for application of the proposed procedure and discuss the monitoring system installed in the building. The implemented trigger algorithm, used to identify the occurrence of a seismic event, is discussed in Section 3.2 and Section 3.3. The different typologies of non-structural elements of the building are introduced in Section 4, associating to each of them appropriately selected fragility curves and discussing the reasons behind the choice of these fragility curves among those available in the literature. If a seismic event is detected, the floor accelerations recorded by the installed sensors are compared with critical acceleration thresholds, defined as discussed in Section 5, based on probabilistic considerations. Finally, the applicability of the proposed approach will be discussed in Section 6, with reference to several examples of existing buildings.

3. Case Study Building

The case study is a reinforced concrete office building, named Co+Fabb and located near Milan, Italy. According to the building’s users, the construction was completed in 1986, a date appearing to be reasonable, considering appearance, typology, and materials. External ceramic panels cover the structure, which is also characterised by the presence of large continuous ribbon windows along the four sides, as shown in the pictures in Figure 1.

The building has an approximately square plan, and it is subdivided into four independent structural units (Figure 2a) by the presence of structural joints (Figure 2b).

The structure includes a basement and two levels (Figure 3a), plus a parking area on the roof, which can be accessed by means of an external ramp, indicated in purple in Figure 2a. The basement, connected by internal stairs, contains mainly technical rooms and laboratories and allows access to the internal courtyards (Figure 3b).

Level 1, positioned at the ground level, has a significant inter-storey height of approximately 5 m, which may be due to a different use of the building in its initial conception, such as, for example, an industrial use. The level is currently occupied by a cafeteria/restaurant and a gym.

Level 2 is dedicated to offices, and it is the level on which most non-structural elements are located and hence where most of the sensors were installed, as discussed in the following.

3.1. Acceleration Sensors Installed within the Building

To evaluate the actual acceleration at the different building levels in the case of a seismic event, a number of accelerograms were placed at different positions within the building. They were mainly positioned on the second storey, where offices are concentrated and hence where the non-structural elements of interest are located.

They were applied on structural elements, mainly on top of columns near the horizontal diaphragms (Figure 4), to monitor the peak floor acceleration occurring in the case of a seismic event, which is typically amplified with height. Whenever possible, accelerometers were positioned at the height of installation of the non-structural elements, to monitor as accurately as possible the acceleration imposed on each element. Also, attention was paid to placing them across the building’s seismic joints, to evaluate displacements imposed on the different independent building units and to monitor possible interactions between adjacent units. The final selection of the sensors’ positions was driven by a balance of feasibility considerations and technical needs, also accounting for the fact that accelerometer sensors were installed within a multi-sensor integrated node, recording also other parameters, such as temperature, humidity, and brightness. This imposed additional constraints on the sensors’ positions, as they could not, for example, be placed near heaters or windows, to avoid bias in parameter measurements.

In the case of a seismic event occurring at the building site, the recorded values of acceleration can be correlated with seismic performance parameters and capacity thresholds of the different typologies of the non-structural elements, making it possible to monitor performance and guide post-earthquake interventions.

In this specific case study, the synchronisation of the different accelerometers was not sufficiently accurate to enable a reliable estimate of inter-storey drift (through the double integration of accelerations at two consecutive levels). As will be discussed below, this parameter is, however, fundamental to evaluate the performance of elements that are sensitive to displacements/deformations, such as partitions, infills, and suspended ceilings. This aspect was not specifically investigated in this work because technological issues hampered synchronising the accelerations recorded at the different building levels, making it impossible to calculate the inter-storey drift. For these reasons, only non-structural elements that are sensitive to acceleration were considered in this example of application of the proposed procedure.

3.2. Identification of the Occurrence of Seismic Events

The introduction of the digital acquisition of seismic data raised the technical problem of continuous recording and storing large quantities of accelerometric data. A seismic network, or even a single seismic station or an accelerometric sensor, operating continuously with high recording frequencies, indeed produces a huge quantity of data, difficult to store or even to analyse. To manage these data, efficient and robust algorithms, called trigger algorithms, were developed to identify and analyse data related to seismic events and provide a real-time response. These trigger algorithms allow the seismic station to process all seismic signals in real time, but data are not saved in a permanent and continuous way. The trigger algorithm indeed identifies typical seismic signals within the seismic noise steadily present at a site. If an event is identified, recording and storing of the data start, and they are interrupted when the algorithm declares the end of the seismic event.

Several types of algorithms exist in the literature. They can be based on the amplitude, envelope, or power of the signals, either in the time or frequency domain. The simplest algorithm identifies an event when a predefined threshold is exceeded. This is rarely used for low seismicity cases, but it is often adopted in case of strong events, for which the accelerations induced by human activity and ambient noise are significantly lower than acceleration thresholds corresponding to activation of the instrument. The root-mean-square algorithm is similar, but it uses the root-mean-square values of the signal amplitude in a short time window, rather than instant amplitude values. It is less sensitive to spike-like man-made seismic noise; however, it is rarely used in practice.

Moving to more complex algorithms, they can be subdivided into three families [18]:

• Energy methods;
• Autoregressive methods;
• Neural network approaches.

Energy methods include, for example, the algorithms proposed by Allen [19] and Baer and Kradolfer [20]. In these methods, the event is declared when the ratio between the average value of the absolute amplitude of the seismic signal (or some characteristic of it) in a short time window and in a larger time window exceeds a given threshold. These algorithms are very commonly used for cases of low seismic motion.

Autoregressive methods identify the optimal arrival time after an event is identified, by studying the variation of statistical properties of the signal to identify the instant separating the seismic event from noise [21,22,23].

In the third family, a neural network is trained to recognise the arrival of a seismic event, by either working directly on the signal [24,25,26] or working on selected characteristics of the signal [27]. Examples of neural network algorithms are those by Perol et al. [28], Mousavi et al. [29], Meier et al. [30], and Zhu and Beroza [31], as discussed in Rojas et al. [32].

Despite being the most elementary ones, energy-based algorithms are the most commonly used. They are based on simple mathematical operations and require very limited computational time; hence, they are suitable for the analyses of large datasets, as well as for real-time implementation. Their main drawback is the need for a significant a priori knowledge of the signal properties to be able to calibrate their parameters (e.g., trigger thresholds, window amplitude, etc.), finding a compromise between the algorithm’s sensitivity and the frequency of false activations.

More sophisticated algorithms have been proposed in the literature (e.g., [19,33,34,35]), but they are rarely adopted in practical cases, mainly due to the difficulty of calibrating their parameters, as discussed in Joswig [34]. Other examples of complex algorithms were proposed by Reynen and Audet [36] and Tang et al. [37], with the aim of distinguishing blasts from earthquakes, in California and China, respectively.

3.3. Selected Trigger Algorithm

Among the different algorithms reported in the literature, the one indicated as “short-time-average through long-time-average”, or STA/LTA, was selected [19]. It is an energy-based algorithm, typically used for low-seismicity sites, with the aim of recording as many events as possible. It is based on the continuous calculation of the absolute average value of the signal in two windows moving in time: a short-time window, which is sensitive to seismic events, and a long-time window, which provides information on ambient noise at the site. When the ratio between the average value in the two windows exceeds a predefined threshold, the event is declared, and signal recording starts.

With respect to threshold-based algorithms, the STA/LTA has a higher capacity of detecting and recording low-amplitude earthquakes. At the same time, it is able to reduce the number of false triggers due to ambient or anthropic noise. It is particularly suitable in low seismicity sites, where the ambient noise (e.g., sea noise) is the dominant type of seismic noise, but it is also effective in the case of variations of the continuous anthropic noise, due to, for example, day/night variations of human activity. It is instead less effective in the case of irregular and large amplitude anthropic seismic noise, such as for blasts.

The selected algorithm is illustrated by means of an example in Figure 5, using a history of floor acceleration (Figure 5a), taken from the work of D’Angela et al. [38]. Figure 5b reports the corresponding absolute average value in the short-time window (black line) and in the long-time window (grey line), whereas their ratio is reported in Figure 5c (thin black line). When the ratio exceeds the predefined trigger ratio, an event is detected and data are recorded, until the ratio drops below the detrigger ratio and the event is considered to be concluded. The event window is indicated in Figure 5c with the pink box. It should be mentioned that some data have been added before (pre-trigger) and after (post-trigger) the window identified by the ratio, as highlighted in Figure 5c. Figure 5d reports the seismic signal actually recorded, after application of the trigger algorithm. It can be noted that the significant portion of the signal is entirely recorded, and only the initial zeros are removed.

The choice of the parameters of the algorithm is always a compromise among different considerations. The aim is to obtain the maximum sensitivity for a given type of signal so as to identify all events of interest, with an acceptable amount of false triggering.

Often indeed, limited amplitude events are not detected from the seismic noise and are hence lost; if instead the algorithm is set to be sensitive, there could be false identification of events, due to irregularities in the seismic noise or occasional excessive amplitude of the noise itself; this would result in the unnecessary storage of data. The success rate in identifying events of interest depends on a correct setting of the parameters. Some general indications for calibrating some of the parameters can be found in Pechmann [39], but a case-by-case definition is obviously required. In the example reported in Figure 5, the following parameters were adopted, which are considered to be a reasonable choice for low-amplitude seismic motion:

• Length (in seconds) of the short-time window: a value of 2 s was assumed.
• Length (in seconds) of the long-time window: a value of 30 s was deemed reasonable.
• Trigger ratio: it is the value of the ratio of the average values in the two considered windows that needs to be exceeded to declare a trigger condition. A value of 4 was assumed.
• Detrigger ratio: it is the value of the ratio below which the trigger is interrupted. A value of 2 was assumed.
• The length, in seconds, of the recorded signal before the event identification (pre-trigger). Being a case study in a low-seismicity site, a reasonable value was deemed to be 5 s;
• The length, in seconds, of the recorded signal after the end of the trigger condition (post-trigger). A reasonable value was deemed to be 20 s.

4. Non-Structural Element Typologies and Corresponding Fragility Curves

A survey of the case study building made it possible to identify the main typologies of non-structural elements installed within the structure on the different storeys. Offices on the second level are all covered by false ceilings, with integrated lighting elements. A suspended ceiling is also present in the cafeteria at level 1 (Figure 6a). Two typologies of partitions are used: partitions with an aluminium frame and glass/opaque panels, or drywall partitions. Offices and meeting rooms have standard equipment and furniture, including tables, bookshelves, monitors, and computers (Figure 6b,c). There are also vending machines and electrical cabinets (Figure 6d) on each level. The heating/air conditioning system is made of fan coils; there are also external air conditioning units (Figure 6e) and small and large diameter piping (Figure 6f). The building is served by elevators.

In the following, the different typologies of non-structural elements will be subdivided into the three categories identified by FEMA E-74 [40]: architectural elements (ARCH); mechanical, electrical and plumbing elements (MEP); and furniture, fixtures, equipment, and contents (FF&E). For each non-structural element typology, fragility curves were selected from the literature to describe the expected seismic performance with reference to limit states of interest. The main reasons behind the adopted selection will be discussed later on in this section.

Fragility curves provide the probability of exceedance of a predefined limit state, as a function of a parameter representing the severity of the seismic action on the non-structural element. This parameter, in the case of non-structural elements, may be a ground motion intensity measure, such as peak ground acceleration (PGA), or instead a parameter accounting for the filter effect exerted by the structure on the ground motion. Examples can be peak floor acceleration (PFA), which is typically adopted for non-structural elements whose response is sensitive to acceleration, or inter-storey drift (IDR), which is instead used for non-structural elements sensitive to displacement or deformations.

As discussed, for example, in [8,17], some of the non-structural element typologies identified within the case study building are sensitive to both acceleration and displacement/drift. This is the case, for example, of infills and partitions, whose in-plane response is typically governed by a drift parameter, whereas the out-of-plane response is governed by acceleration. Although fragility curves in terms of IDR are available for these types of non-structural elements, only fragility curves in terms of acceleration (either PGA or PFA) will be considered in this work, for reasons related to the monitoring system installed in the case study building (discussed in the Section 3).

The criteria used for the selection of fragility curves from the literature were based on the similarity of the elements’ characteristics and/or of the expected seismic performance. The curves selected for the different non-structural elements’ typologies refer to three non-structural limit states, indicated as the operational limit state (OLS), the damage limit state (DLS), and the life safety limit state (LSLS). In the literature, curves were provided for different limit state definitions, and expert judgement was used to identify a reasonable translation into the three considered levels. In general, conditions requiring a repair intervention or a check interrupting operational use, but without significant damage or risk, were associated with the OLS. Situations corresponding to economically relevant damage were associated with the DLS, whereas conditions implying an actual risk for occupants were classified as an LSLS.

It is worth mentioning that most codes, including the Italian Building Code, consider structural limit states and define the seismic action with reference to them, but they do not explicitly define limit states for non-structural elements. Whereas the definition of an operational and a damage limit state, referring to non-structural elements, appears quite trivial, for what concerns the life safety limit state, it is important to point out that it was defined with reference to occupants’ safety conditions.. This means that a life safety limit state was associated with non-structural damage conditions threatening the safety of people being within the structure. Examples could be the collapse of infills, overturning of massive elements, or even falling of heavy furniture or equipment.

Façade panels installed in the case study building consist of reinforced concrete panels, with an interposed insulating layer and a ceramic coating on the external façades. They are 20 cm thick and have variable height, depending on the inter-storey height and on the continuous ribbon windows’ dimensions. To describe their seismic behaviour, the fragility curves provided by FEMA P-58 PACT (B2011.201b typology) were selected [41,42]. For this typology, the only available fragility curve corresponds to a limit state of damage to the anchoring system, with the need to remove and completely replace the panel. Due to the danger induced by possible falling of the panel, this limit state is associated with a life safety condition. It refers in particular to the out-of-plane behaviour of the panels, which is mainly acceleration-sensitive, and for this reason it is expressed in terms of PGA. The curve was derived from experimental tests on concrete wall specimens with dimensions of 9.14 m per 3.96 m and a thickness of approximately 0.115 m. The lognormal fragility curve is shown in Figure 7a, whereas the corresponding parameters are reported in

Table 1. Median μ (units of g) and logarithmic standard deviation β (no unit) of the lognormal fragility curves in PGA for non-structural elements, with indication of the literature source from which fragility curves were selected and the category according to FEMA E-74 [37].

Non-Structural Element	Source	Category	LSLS
			µ	Β
Façade panels	FEMA P-58 PACT [38]	ARCH	0.5	0.5
Glazed elements and aluminium-glass partitions	Mattei and Bedon [40]	ARCH	0.25	0.45

.

To describe the acceleration-sensitive seismic behaviour of glazed elements and windows in general, as well as the expected performance of glass partitions, the fragility curves in terms of PGA proposed by Mattei and Bedon [43] were selected. They are based on numerical modelling of a single panel spanning between inter-storey floors, considering a single ultimate limit state, corresponding to glass fallout, which was associated with an LSLS.

The performance of vertical drywall partitions was described by the fragility curves derived by Retamales et al. [44], based on experimental tests carried out at the laboratory of the University of Buffalo (USA).

They considered three limit states:

• DS1, associated with the OLS, corresponding to only superficial damage to the walls (cracks along corner beads, cracks along joint paper tape, screws pulled out from connections of gypsum boards to steel framing).
• DS2, associated with the DLS, corresponding to local damage to gypsum wallboards and/or steel frame components (crushing of wall corners, out-of-plane bending, and cracking of gypsum wallboards at wall intersections, damage to screws connecting wallboards to boundary studs, bending of boundary studs, buckling of diagonal braces (partial height partition walls), damage to gypsum wallboards around ceiling connectors or damage induced by ceiling impact).
• DS3, associated with the LSLS, corresponding to severe damage to walls (tears in steel tracks around connectors of track to concrete slab, track fasteners passing through track webs, track flanges bent at wall intersections, hinges forming in studs, partition wall collapse).

Most of the ceilings installed in the building are suspended, with an external grid, although other typologies can be found (Figure 6a,c). Their seismic behaviour was described by means of the fragility curves derived by Soroushian et al. [45] from the results of the shaking table experimental campaign carried out at the UNR-NEES of the University of Nevada.

They considered several specific limit states, which were then grouped into the following:

• DS1, associated with an OLS, described as “ceiling tiles dislodge and fall”;
• DS2, associated with a DLS, described as “ceiling grid and tile damage”;
• DS3, associated with an LSLS, described as “major ceiling damage and some grid collapse”.

Fragility curves for electrical panels and server racks, considering their internal components and connections, were provided and discussed in FEMA P-58 PACT Background Document BD-3.9.16 (D5012.032 typology). The document illustrates several typologies of racks and installation. To be conservative, the most vulnerable condition was considered, corresponding to “unanchored panels”. Curves are provided for a single limit state, described as corresponding to an inoperative condition, which was associated with the OLS.

Fragility curves for internal and external air conditioning units were taken from FEMA P-58 PACT (D3031.011 typology). The curves refer to “unanchored and not vibration isolated large chillers” (D3031.011d). This typology was deemed to be a conservative hypothesis, since the air conditioning units installed in the building are surely smaller and typically supported by metal clamps anchored to the walls (Figure 6e). A single limit state was considered, indicating a condition of “damaged, inoperative”, which was associated with the OLS.

The seismic fragility of small and large diameter piping was described according to Soroushian et al., [46,47], which concentrates in particular on fire sprinkler piping systems, whose functionality is fundamental in the case of a seismic event. It is assumed that these fragility curves can be associated with all typologies of piping systems installed in the considered case study building, with the only distinction based on the diameter (small if less than 5 cm, large otherwise). The work includes an exhaustive treatment of several types of piping, with variations on the types of braces, weights, joints, and location of restrainers. Among them, the most vulnerable typology was selected, i.e., grooved solutions for small diameter piping and unbraced solutions for larger diameter piping. Fragility curves for the former type were derived from numerical simulations [46,47], whereas for the latter from experimental tests carried out at the E-Defense laboratory in Japan [48]. Results are available for three limit states, which were associated with the OLS, the DLS, and the LSLS.

Among the different typologies of traction elevators considered in the FEMA P-58 BD-3.9.14 PACT, varying as a function of the installation period, the most vulnerable typology was selected, i.e., the oldest elevators (typology D1014.012). Fragility curves were derived after observation of empirical damage that occurred during the 1994 Northridge earthquake [49], considering a single global limit state, identified based on a number of specific limit states for the fundamental components of the elevator system. It was decided to associate this global limit state with a damage limit state (DLS).

Bookshelves, cabinets, and vending machines are indicated as free-standing vertical elements, due to their standing position, typically without any connection to the wall, with the exception of very slender elements. Their mass is usually strongly dependent on the content. Fragility curves in PFA proposed by Di Sarno et al. [50], originally derived for hospital cabinets, were adopted. They refer to two limit states, i.e., rocking, assumed to correspond to a DLS (due to potential damage to contents) and overturning, assumed to be an LSLS.

Workstations in the building’s offices consist of simple tables, sometimes with storage modules with doors and drawers. They are generally indicated as desktops and workstations, and their performance is described by the fragility curve provided by FEMA P-58 PACT (E2022.001 typology). This curve refers to unanchored workstations, installed on a carpeted floor and corresponds to a damage limit state in which some elements need to be replaced (hence associated with a DLS).

For hanging monitors anchored to the walls, fragility curves were taken from FEMA P-58 PACT (E2022.021 typology). They refer to a single damage limit state, consisting in falling of the monitor, with a consequent loss of functionality. This was associated with an LSLS, since falling of a monitor from height can induce a life safety threat to human life.

For monitors, printers and, in general, electronic equipment resting on a smooth surface, fragility curves provided by FEMA P-58 PACT (E2022.023 typology) were used. They refer to a single limit state, consisting in falling of the equipment, with a consequent loss of functionality. This condition was associated with a DLS, since falling of these elements is not generally constituting a life safety risk for occupants.

Figure 7 shows a plot of the selected fragility curves. In particular, Figure 7a reports fragility curves in terms of PGA, whereas the other three plots show fragility curves in terms of PFA for all considered non-structural typologies, subdivided into the three categories of FEMA E-74 [37], i.e., ARCH (Figure 7b), MEP (Figure 7c), and FF&E (Figure 7d). In the plots, continuous lines refer to fragility curves corresponding to the life safety limit state, dashed lines to the damage limit state, and dotted lines to the operational limit state.

All selected fragility curves are defined by a lognormal distribution, depending on two parameters, i.e., median and logarithmic standard deviation, which are summarised in Table 1 (for curves expressed in PGA) and

Table 2. Median μ (units of g) and logarithmic standard deviation β (no unit) of the lognormal fragility curves in PFA for non-structural elements, with indication of the literature source from which fragility curves were selected and the category according to FEMA E-74 [37].

Non-Structural Element	Source	Category	OLS		DLS		LSLS
			µ	β	µ	β	µ	Β
Vertical drywall partitions	Retamales et al. [41]	ARCH			0.7	0.25	0.8	0.25
Ceilings	Soroushian et al. [42]	ARCH	0.79	0.41	2.12	0.41	2.82	0.41
Electrical panels and server racks	FEMA P-58 PACT [38]	MEP	1.60	0.40
Internal and external air conditioning units	FEMA P-58 PACT [38]	MEP	0.20	0.4
Small diameter piping	Soroushian et al. [42]	MEP	0.21	0.47	0.38	0.47	0.82	0.47
Large diameter piping	Soroushian et al. [42]	MEP	0.14	0.49	0.32	0.49	0.71	0.49
Elevators	FEMA P-58 PACT [38]	MEP			0.32	0.60
Freestanding vertical elements (bookshelves, cabinets, vending machines)	Di Sarno et al. [45]	FF&E			0.34	0.23	1.07	0.40
Desktops and workstations	FEMA P-58 PACT [38]	FF&E			1.00	0.40
Hanging monitors	FEMA P-58 PACT [38]	FF&E					2.50	0.50
Monitors, printers, and electronic equipment	FEMA P-58 PACT [38]	FF&E			0.40	0.50

(for curves in PFA).

5. Identification of Critical Acceleration Thresholds for NSEs

To define critical acceleration thresholds quantifying the expected seismic performance of non-structural elements, it is necessary to establish an acceptable value for the probability of exceedance of a given limit state, which should be a compromise between safety and cost. As discussed, for example, in [51], whereas the probability of structural failure (i.e., building collapse or failure of structural components like beams or columns) is at the basis of structural design enforced by building codes, the design of non-structural parts of buildings does not have a probabilistic basis. Moreover, the additional cost required to enhance structural safety has the benefit of reducing costs associated with loss of life and property, with a benefit typically larger than the added cost. The same type of calculation is not straightforward for non-structural elements.

In the case of structures, indications of the acceptable failure probability can be found in the literature. A typical value of the acceptable structural collapse probability is 10⁻³, for a 475-year return period of the seismic action (e.g., [52]). Elsewhere, probabilistic acceptance criteria provided in American codes [53,54] for seismic performance assessment at the collapse limit state are related to the 10th percentile of a fragility curve [54].

For non-structural elements, the only attempt to define acceptable failure probabilities that we found in the literature (see also [51]) is the work by Porter et al. [52]. They proposed values of failure probability for life-safety critical equipment systems, distinguishing the case in which they are positioned within ordinary buildings (10⁻³ acceptable failure probability) and emergency-response facilities (10⁻⁴ acceptable failure probability) and values of one order of magnitude higher for operational equipment. The applicability of these values was tested referring to high-rise buildings located in the highly seismic San Francisco Bay Area. For this reason, the proposed values are not directly applicable for the case study building considered in this paper, which requires a case-specific calibration.

In this work, critical acceleration thresholds were defined by means of probabilistic considerations, starting from the selected fragility curves. Fragility curves indeed provide the probability of exceeding a given limit state as a function of a ground motion intensity measure. If they are read in the opposite sense, they can provide the value of the ground motion intensity measure corresponding to a predefined probability of exceedance, identified as critical for the non-structural element in relation to a given limit state condition.

It was decided to adopt a critical probability of exceedance of the different damage states of 16%, which turns out in identifying as critical the intensity measure corresponding to the 16^th percentile of the fragility curve. These probability thresholds were assumed using engineering judgement and based on the considerations previously discussed; they can be easily modified to reflect the collapse probabilities considered appropriate by government jurisdictions or by other authorities using this methodology to establish seismic design requirements and seismic assessment criteria for non-structural elements.

Due to the characteristics of the monitoring system installed in the building, the intensity measure used for the identification of the critical threshold is peak floor acceleration (PFA). Indeed, accelerometers are installed on the different building levels, and hence they directly measure floor acceleration, which is also the parameter used for the definition of most of the selected fragility curves. However, for some non-structural elements (e.g., façade panels, glazed elements, and aluminium glass partitions), fragility curves are expressed as a function of PGA, rather than PFA. In this case, the critical acceleration value in terms of PFA was obtained by multiplying the critical value in PGA for a building amplification coefficient used in current codes [53,54,55,56,57,58]. This coefficient was defined according to the simplified formulation for defining floor response spectra, included in the explicative document of the Italian Building Code [57]:

$$\frac{\mathrm{PFA}}{\mathrm{PGA}}=\left(1+\frac{z}{H}\right)$$

(1)

where z is the height of the non-structural element’s centre of mass from the foundation level, and H is the building height from the ground level.

For the sake of simplicity, it was assumed that all typologies of non-structural elements are installed on floor 2 of the building, where offices are located (see Figure 3), which means at z = 8.9 m. The values of the critical thresholds obtained with this approach for the considered non-structural elements are reported in

Table 3. Evaluation of critical threshold values in terms of PFA for some non-structural elements for which available fragility curves are in terms of PGA.

Non-Structural Element	Critical PGA [g]	z [m]	H [m]	Critical PFA [g]
Façade panels	0.304	12.5	12.8	0.601
Glazed elements	0.160	11.3	12.8	0.301
Aluminium glass partitions	0.160	10.3	12.8	0.289

. The height of the non-structural element’s centre of mass from the foundation level (z) was evaluated by considering the distance from the floor of the element and its height measured by an in-situ survey.

Table 4. Critical acceleration values for all non-structural elements installed on floor 2 of the case study building and indication of the corresponding limit state.

Non-Structural Element Typology	ID Elements	OLS	DLS	LSLS
Façade panels	ARCH 1			0.601
Vertical drywall partitions	ARCH 2		0.546	0.624
Glazed elements	ARCH 3			0.301
Ceilings	ARCH 4	0.525	1.41	1.875
Aluminium glass partitions	ARCH 5			0.289
Electrical panels and server racks	MEP 1	1.075
Internal and external air conditioning units	MEP 2	0.135
Small diameter piping	MEP 3	0.132	0.238	0.514
Large diameter piping	MEP 4	0.086	0.197	0.436
Elevators	MEP 5		0.180
Freestanding vertical elements (bookshelves, cabinets, vending machines)	FF&E 1		0.270	0.720
Desktops and workstations	FF&E 2		0.671
Hanging monitors	FF&E 3			1.519
Monitors, printers, and electronic equipment	FF&E 4		0.244

summarises the values of critical peak floor acceleration obtained for all non-structural element typologies installed in the case study building (on floor 2), specifying the limit state corresponding to the acceleration thresholds.

6. Application of the Seismic Alert Procedure to Existing Buildings and Discussion of the Results

The lack of seismic events after installation of the sensors in the case study building, due to the low seismicity of the area, prevented the application and testing of the proposed procedure using real records at the site. To show the feasibility of this approach, the decision was made to compare the critical acceleration values of the different non-structural elements with the design values of floor acceleration provided by the Italian Building Code [56,57] for the different limit states.

As already mentioned, the code indicates return periods of seismic action and hence of the design peak ground acceleration, only for structural limit states, without defining a correspondence between structural and non-structural limit states. In this example, the seismic action corresponding to a structural limit state was used for non-structural elements, assuming this can be considered conservative.

For this comparison, PFA was calculated according to the simplified formulation for the seismic demand on non-structural elements, reported in the commentary to the code [50]:

$$S_a\left(T_a\right)=\left\{\begin{array}{l}\alpha S \left(1+\frac{z}{H}\right)\left[\frac{a_p}{1+\left(a_p-1\right){\left(1-\frac{T_a}{a{T}_1}\right)}^2}\right]\ge \alpha S per T_a<a{T}_1\\ \alpha S \left(1+\frac{z}{H}\right)a_p per a{T}_1\le T_a<b{T}_1\\ \alpha S \left(1+\frac{z}{H}\right)\left[\frac{a_p}{1+\left(a_p-1\right){\left(1-\frac{T_a}{b{T}_1}\right)}^2}\right]\ge \alpha S per T_a\ge b{T}_1\end{array}\right.$$

(2)

and assuming that the non-structural element period is equal to zero (this hypothesis is valid when the non-structural element is rigidly connected to the structure):

$$\mathrm{PFA}=\alpha ·S \left(1+\frac{z}{H}\right)$$

(3)

where

• α is the ratio between the peak ground acceleration on soil type A (a_g) for the considered limit state and the gravity acceleration, g;
• S is the coefficient accounting for soil type and topographic conditions.

Table 5. PFA values calculated according to the code for the different building levels and limit states.

Limit State	PGA = α∙S [g]	Floor	PFA [g]
OLS	0.023	1	0.0289
		2	0.0390
		3	0.0460
DLS	0.030	1	0.0377
		2	0.0509
		3	0.0600
	0.063	1	0.0792
LSLS		2	0.107
		3	0.126

summarises the values of PFA calculated for the different building levels. It can be observed that, for all considered limit states and for all building levels, the PFA code values are always higher than the critical acceleration values reported in Table 4.

This means that, under the considered assumptions, none of the non-structural elements installed in the case study building would exceed its critical acceleration threshold, and therefore there would be no need for any alarm or seismic protection activation.

Figure 8 shows a comparison of the critical values for the different typologies and limit states considered (Table 4) and the values of PFA provided by the simplified Italian Building Code formulation for the considered site. It can be observed that critical acceleration values for the different limit states (indicated with different colours) are systematically higher than the corresponding code value (horizontal lines). This means that, if we assume non-structural elements have the capacity corresponding to the defined threshold, they will satisfy a seismic assessment using code demand (simply comparing capacity and demand in terms of PFA).

As a further application of the proposed approach, the decision was made to compare the critical acceleration values of the different non-structural elements with a set of real floor acceleration values recorded at reinforced concrete buildings, referred to in the following as floor motion set (FM set). In particular, the FM set considered in this study is derived from the 24 floor motions selected by D’Angela et al. [38]. The FM set is selected within the database provided by CESMD [59] and is related to ground motions having a PGA not smaller than 0.05 g. It corresponds to accelerations recorded at the top floor of the buildings, so they represent the most amplified responses of each building floor motions. More details on the main characteristics of the building set and the floor motions are reported in D’Angela et al. [38].

Figure 9 shows the comparison of critical acceleration values for the different non-structural elements and the median and 16^th and 84^th percentiles PFA values of the FM set. The comparison shows that, for some non-structural elements installed within the case study building, the critical values associated with the three considered limit states may be exceeded. Considering the median PFA value of the FM set, critical acceleration values for the LSLS are exceeded for ARCH 3 and ARCH 5 elements; critical acceleration values for the DLS are exceeded for MEP 3, MEP 4, MEP 5, FF&E 1, and FF&E 4 elements; and critical acceleration values for the OLS are exceeded for MEP 2, MEP 3, and MEP 4 elements. Also, more conservatively, it is interesting to note that with respect to the 84^th percentile of the PFA values of the FM set, all critical acceleration values are exceeded, with the exception of the values for the LSLS of ARCH 4, FF&E 1, and FF&E 3, the value for the DLS of ARCH 4, and the value for the OLS of MEP 1.

Hence, from this comparison, considering the median value of the FM set, it can be assumed that, during a seismic event, the elements that can trigger an alert are the following: glazed elements and aluminium glass partitions for the LSLS, small and large diameter piping, elevators, freestanding vertical elements, and electronic equipment for the DLS, and internal and external air conditioning units, small diameter piping, and large diameter piping for the OLS.

7. Conclusions

The objective of this paper is to propose a methodology for seismic monitoring of non-structural elements, applying it to a real case study building in which several sensors were installed. The methodology was also applied to an ideal case, using a set of real floor acceleration values recorded at reinforced concrete buildings, since the case study building has not undergone any seismic events since the monitoring system was installed.

In the proposed methodology, accelerations recorded by the installed accelerometers are firstly filtered through a trigger algorithm that can identify the occurrence of a seismic event. In this case, the recorded peak acceleration on a building storey is compared with critical acceleration thresholds, previously associated with the different typologies of non-structural elements included in the building. If the critical acceleration threshold of a given non-structural element is exceeded, several mitigation actions could be implemented, starting from issuing a visual/sound alert, up to more decisive actions to safeguard the occupants’ safety.

In the proposed applications, critical thresholds are defined as corresponding to a 16% probability of limit state exceedance from fragility curves selected from the literature. The definition of the acceptable probability of exceedance is an important point of the methodology, obviously affecting the results, and it is based on a compromise between safety and cost, which should be established at the governmental level, also considering how often earthquakes are expected to occur in a given area [51]. In high seismicity areas, where moderate earthquakes are frequent, any increase in building costs will be offset by reduced costs of damage. In low to medium seismicity areas, seismic design requirements are instead typically related to life safety considerations, since the expected savings in terms of damage during rare earthquakes are not sufficient to justify an increase in building costs. The choice of using a 16% probability of exceedance has been calibrated on the case study building. For different applications, different values of probability could be selected, possibly varying depending on the limit states, to account for a higher acceptable probability for lower damage states. As an alternative, critical acceleration thresholds corresponding to limit states of interest could be evaluated analytically, for example using equilibrium equations to calculate the acceleration corresponding to the overturning of a freestanding non-structural element (e.g., cabinets, bookshelves, etc.), or the acceleration corresponding to yielding or failure of the connection of a given non-structural element to the building walls.

The proposed approach is innovative, in the sense that seismic monitoring of non-structural elements is currently not usually considered in existing buildings. This approach is very simple to implement and not expensive, as it is based on the use of commercial sensors that can be easily installed in any existing structure. The results provided by this monitoring system can be very useful for establishing prioritisation schemes, with the aim of improving both occupants’ safety and comfort.

Possible improvements in the proposed methodology could consist in its application to different case study buildings, allowing to better calibrate the critical acceleration thresholds for different seismicity contexts and non-structural element typologies. The procedure could be easily extended to drift-sensitive non-structural elements, provided that deformation/displacement time histories on the different levels are available. To improve the description of the seismic performance of the different typologies of non-structural elements, specific fragility curves could be derived, possibly based on experimental shake table tests on similar prototypes (e.g., [60]).