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A procedure for assessing the functional reliability of hospital systems
ELSEVIER
PII: S0167-4730(96)00022-7
Structural Safety Vol. 18, No. 4, pp. 277-292, 1996 Copyright © 1996 Elsevier Science Ltd Printed in The Netherlands. All rights reserved 0167-4730/96 $15.00 + .00
A procedure for assessing the functional reliability of hospital systems Giorgio Monti a,*, Camillo Nuti b a Dipartimento di Ingegneria Strutturale e Geotecnica, Universit~t "La Sapienza "', Via A. Gramsci 53, 00197 Roma, Italy b Dipartimento di Scienze, Storia dell'Architettura e Restauro, Universith "G. D'Annunzio", Viale Pindaro 1, 65100 Pescara, Italy
Abstract
An effective reliability-based procedure is presented to assess the capability of hospitals to be functional after a seismic event of a given intensity. Every major function in a hospital depends on the joint action of various cooperating services, which in turn are made up from a certain number of sub-services. Such a complex organization is described in terms of a logical scheme and subsequently reduced to a minimal cut-set representation. For each sub-service a collapse criterion is defined, by which the strength is compared to the action load, both represented as random variables. Strengths are evaluated through assessment analyses based on design drawings. Loads are evaluated from 3-D linear dynamic analyses under seismic input. This is given by the Eurocode 8 elastic response spectrum, scaled at a given peak ground acceleration and account for the position of the sub-service within the building. By calculating the failure probability of each service by FORM (First Order Reliability Method) or SORM (Second Order Reliability Methods), the probability of functional interruption is obtained in terms of Ditlevsen bounds, conditional on a given earthquake intensity. The method helps to single out weak elements and potential sources of damage (structural, non-structural, equipment) within the hospital. This allows: (a) to investigate quantitatively the effectiveness of different upgrading criteria, (b) to select rationally intervention hypotheses, both in the retrofitting and rehabilitation of existing hospitals and in the design optimization of new ones, and (c) to evaluate different investment options for seismic vulnerability mitigation. As an example, an application to a case study hospital is presented. Copyright © 1996 Elsevier Science Ltd Keywords: Hospitals; Assessment; Retrofitting; Upgrading; System reliability; Functional collapse; Equipment
1. Introduction
Hospitals are extremely peculiar structures having the most diversified functions, ranging from those typical of hotels, offices or laboratories, to those of warehouses, where both hazardous and degradable materials are stored. Hospitals contain and preserve essential equipment for patient care and for first-aid. Basic supplies like water, electricity, oxygen and communications are needed 24 hours a day in order for the hospital to work efficiently without service interruptions that could be * Corresponding author. 277
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fatal. Moreover, equipment such as lifts and litter-lifts, essential for ensuring internal communications, should always be functioning. After having enumerated all the functions a hospital building has to accomplish, it is all too clear that when an earthquake strikes a hospital, the fact that the main structures have performed well during the seismic event is not sufficient to guarantee its overall efficiency. In fact, not only should the building be safe from the structural standpoint, but also all the above-mentioned functions should be completely guaranteed. Indeed, experiences from past earthquakes have shown that collapse of functional elements (such as X-rays, operating tables, etc.) prevented most hospitals from being fully operative during the post-quake aid operations. These considerations underline the strategic importance of hospitals in the aftermath, when extremely delicate situations arise, due to the arrival of a large number of patients and visitors while the malfunctioning probability is at its maximum. Above all, it is the problem of existing hospitals that has not been satisfactorily solved so far. In Europe seismic upgrading of existing hospitals is a critical issue, but a rational method to define an intervention strategy to obtain given reliability levels, at least in qualitative terms, has not been established yet. A feasibility study for reliability evaluation of a hospital regarded as a system was discussed in previous papers [1,2], where it was shown that every hospital activity can be represented through a logical functional scheme that can be analyzed with system reliability techniques. The results are obtained in terms of: (a) quantitative evaluation of the risk, (b) localization of critical elements, (c) evaluation of the available reliability in existing hospitals, (d) identification of intervention strategies, and (e) comparison of different upgrading hypotheses. The method considers the hospital to be a multi-functional system, in which the functions are those essential after a seismic event, such as: patient care, diagnostics, radiology, orthopedics, dialysis, pharmacy, surgery, first-aid, anti-shock care, catering, etc. Each function is made up of services, which in turn are made up of sub-services. For example, if one considers the radiology function, the X-ray machine represents, of course, one of its services; if the X-ray machine is located, say, at the third floor, then litter-lifts are considered to be a sub-service of X-rays. Again, for example, considering the surgery function, the operating theater, which is one of the services, is regarded as a series of sub-services: the room itself (partitions and structural elements) and the surgery equipment (operating table, lamps, etc.). Each sub-service is assigned a collapse criterion. deformed
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It should be clear that the fragility of a sub-service (e.g. a dialysis apparatus) depends on its strength characteristics but also on its location inside the building, because the action load varies with the floor level and also with the in-plan position within the floor. A schematic description of all the problems involved in a system functionality evaluation is presented in Fig. 1. Of course, a pure theoretical study of this subject is not conceivable. Firstly, because each hospital has its own peculiar layout that is impossible to generalize and also because many problems are related to local situations. Therefore, consideration of real cases is essential. However, the task is not as overwhelming as one would think because the number of hospital buildings in seismic areas is usually small compared to that of conventional buildings. This allows the problem to be treated on a case-by-case basis. In the following, the case study of an existing hospital is presented, where, as a first phase, the proposed methodology is applied to the surgery function.
2. Reliability of hospital systems In what follows, it should be clear that reliability and hospital terms correspond as: System Function (e.g., surgery), Component ~ Service (e.g., analysis), Sub-component ~ Sub-service (e.g., medicine cabinet, equipment, partition). The steps needed to perform the reliability analysis of a hospital can be outlined as follows (the same steps will be followed in the next section): 1. Local seismicity. Information should be gathered for the site under consideration from the analysis on catalogued events (historical data), in order to obtain the intensity associated to a given return period. Intensity values are preferably expressed in terms of Peak Ground Acceleration (PGA), due to current design specifications. 2. Functional description of the hospital. An accurate analysis of all the functions available in the hospital should be performed, starting from those related to the hospital specialization area and those essential after a seismic event. Each function should then be studied separately. 3. Logical scheme of each function. To construct the system logic means to select and to connect in a rational sequence, based on their relation to the selected function, all the services whose interruption implies failure of the function itself. All services should be localized in plan and elevation within the hospital building. Cooperation to other services and internal communications, i.e. lifts, litter-lifts and stairs, should be described in terms of horizontal and vertical paths to be followed. Essential equipment for patient survival and first-aid, and also basic supplies like water, electricity, communications should always be included as basic services of each function. 4. (Sub-) Components description. Each component (service) should be described as a series system made from sub-components (sub-services), whose failure determines its own failure. A collapse criterion should be associated to each sub-component, in terms of the sub-component strength and of the load acting on it. Strengths and loads are considered as random variables (also correlated between different sub-components), usually described by two-parameter pdf's, with mean and variance expressed in terms of an intensity measure [PGA, Modified Mercalli Intensity (MMI), etc.]. Variances can be assigned either by means of statistical analysis or by personal judgment (this also allows other types of uncertainties to be included). The determination of the mean values of strengths and loads represents the most delicate phase of the whole procedure. Conceptually, the determination of the
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strengths (Assessment Study) can be carried out independently of the determination of the loads (Response Study). In the Assessment Study strengths are estimated by means of assessment methods, separately applied to: (a) the structural elements: flexural strength of structural elements is evaluated assuming the actual material properties for concrete and steel; shear strength is evaluated as suggested in [3,4]; for both, direct examination of executive structural design and drawings is essential; (b) the whole structure: in case sufficient shear strength allows full development of elements flexural strength, structural collapse is identified with the development of a floor mechanism, whose strength can be quantified based on the index proposed in [3]; in case insufficient shear strength is detected, collapse occurs when the shear action reaches the shear strength on a single element, either beam or column; (c) the partitions: the strength of partitions at a given floor is that associated to a limit interstorey drift; (d) the equipment: the strength of the equipment can be based either on the assessment of response through shake table testing or analysis, including effects of mounting, or on the mechanical characteristics, if available as part of the rating of the equipment. If none of these data is available, an approximate estimate of the strength can be calculated, with simple geometrical considerations, in terms of the force overturning the equipment, considered as a rigid block. In the Response Study loads are evaluated through analysis of the dynamic structural response, considering the position, in plan and elevation, of the sub-services within the hospital building, as follows: (a) bending moments on elements are evaluated from dynamic analysis, while shear forces are obtained through equilibrium from the maximum nominal bending moments at the element ends; (b) as above, but in case of insufficient shear strength, the shear action is also evaluated from dynamic analysis; (c) loads on partitions are expressed in terms of the corresponding interstorey drifts, evaluated with either an infilled frame or a bare frame model; (d) loads on equipment are represented, depending on the equipment type under consideration, by either the peak absolute acceleration at the floor or the relative-to-floor displacement. Construction of floor response spectra of the above quantities can be of help for the task. The two studies are synthesized in Table 1. 5. Minimal cut-set representation of the system. The minimal cut-set representation of the system can be constructed from the system logic by means of standard methods; 6. Iterative analysis of the system with upgrades. Once the system is properly described, the reliability analysis is performed for increasing earthquake intensities. When the system functional failure probability, conditional on the earthquake event, reaches a predetermined limit value, then the local probability of failure of each sub-component is examined, so that critical components can be singled out and retrofit or intervention hypotheses can be formulated accordingly. 3. Application to a case study hospital
The hospital under consideration is the Castel di Sangro Hospital, located in the Abruzzi region in Italy, which underwent in 1984 a degree 7 earthquake (MMD. The original nucleus was built in the
G. Monti, C. Nuti
Table l Studies needed for sub-componentdescription Determinationof Type of analysis Strength (AssessmentStudy) Globalbehavior
Element Structure Overall deformations
Local behavior
Loads (Response Study)
28 1
Objective Floor collapse mechanisms Pounding, openingof structuraljoints (piping) Flexural and shear strength(including buckling, bond-slip, lap-splices) Max. interstoreydrift Tilting and overturning
Beams, columns,joints
Partitions Equipment Dynamic Beams, columns,joints Floor response spectra Partitions, equipment
Actions on elements Interstoreydrift, absolute acceleration, relative-to-floordisplacement
1950s and 1960s, and subsequent expansions took place in the 1970s according to increasing demand and funding availability. The last building was completed in 1983. The whole structure consists now of seven buildings, in the following denominated as A to G (Fig. 2). The total number of beds is 134. The structure of these buildings consists of reinforced concrete (r.c.) frames, designed with the allowable stress method, according to seismic regulations that required the structures to resist horizontal forces equal to 10% of the vertical load. Design drawings and calculation reports are available, though at that time computational capability was limited and large simplifications were made in the design process. For example, actions on the elements were calculated with plane models and spatial distribution of forces among frames and r.c. walls was neglected. The type of construction is representative of r.c. buildings at that time, e.g., poor detailing for shear strength and ductility, plain reinforcing bars, distant stirrups, especially in columns, and unreinforced joints. Besides, slab-depth beams are widely used. Partitions are of the conventional type (brick masonry infills) and often contain built-in electric and medical gas lines. Equipment is not anchored. Emergency generators, as is often the case for most hospitals, provide energy to ensure functionality of all machines, with the only exception of X-rays, which are therefore backed up by portable X-ray machines. 3.1. L o c a l s e i s m i c i t y
In this century, the Abruzzi region has been shaken by two destructive earthquakes: the strongest in 1915, having a magnitude of 6.8 and its epicenter in Avezzano (some 60 km away), and the other in
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1933, with 6.8 magnitude and its epicenter in Lama dei Peligni (70 km). There have been several earthquakes of magnitude beyond 5, just to mention some: one with epicenter in Scanno (60 km) in 1904 of magnitude 5.8, one with epicenter exactly in Castel di Sangro in 1936 of magnitude 5.1; the most recent one is the 1984 quake with epicenter in Villetta Barrea (15 km) with 5.1 magnitude, which resulted in a 7.6 MMI with 0.07 g PGA. Based on the Italian Catalogue of earthquakes, the risk curve of Fig. 3 has been obtained, which defines the mean return period of earthquakes in terms of their MMI. Along the risk curve two events are put in evidence: one is that corresponding to the design intensity requested for hospitals in California (MMI = 9.5), while the other corresponds to 50% probability of occurrence in 100 years (MMI = 7.5). The latter corresponds to the above-mentioned 1984 earthquake. It should be noted that slight damage to non-structural and equipment components occurred during that event.
3.2. Functional description of the hospital The hospital has many specialties and functions. In this work attention is focused on the functionality of the surgery, therefore only services related to it are discussed, which essentially involve buildings A, C and D.
3.3. Logical scheme of the surgery function The logical scheme of the surgery function (Fig. 4) was constructed based on the following considerations. The operating theaters (OTs) are the core of the surgery function. There are three OTs in the hospital: one is located at the second floor of building A and two at the third floor of building D. The system starts from an entry point and, through a series of logical connections with cooperating services, ends in either OT. In order for the system to function, two essential services need to be operating: the external electric power supply (point 2 in Fig. 5, and box a in Fig. 4) and the switch board (point 3 in Fig. 5, and box d in Fig. 4), which distribute it. Before operations X-rays could be necessary. These are located in building D (point 11 in Fig. 5, and box c in Fig. 4). Access to OTs is ensured by two litter-lifts located either in building A or in building D. Analysis and pharmacy are two essential services in support of the OTs. There is only one analysis laboratory located at the ground floor in building C, while the pharmacy is located at the ground floor in building E.
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Proper functioning of each of the above-mentioned services depends on a certain number of sub-services, therefore each service (component) is subdivided into sub-services (sub-components). For example, service k (Fig. 4, inside frame) representing OT2 is subdivided into three sub-services: (a) the structures of building D (structural failure), (b) the partitions of the OT (functional failure due to cracking), (c) the OT equipment (collapse for tilting or overturning). Failure of either one of these three sub-services implies interruption of OT2. Note that the three OTs are in parallel, therefore it is sufficient that at least one of them works to maintain functionality of the surgery service. On the other hand, if either the switch board or the pharmacy fails, the whole system fails.
3.4. (Sub-) Components description Each sub-component is identified with the random variable pertaining to its strength and with the load random variable acting on it. An extremely simple collapse criterion, useful for practical 12
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284
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purposes, was adopted, which detects failure when the strength R becomes smaller than the corresponding load S, that is, R - S < 0. Strength characteristics were evaluated through assessment studies of the three buildings involved: D, C and A. For building C and D, of more recent construction (1969 and 1972, respectively), the strength of the structural elements, beams and columns, was evaluated based on original construction drawings, whereas building A (built in 1951) could not be analyzed with the same detail level, because the reinforcement drawings were not available.
3.4.1. Assessment study of building D Building D is by far the most important of the three, since it contains two OTs and the X-ray apparatus, and therefore particular attention was paid to it in the study. The eccentric lift group r.c. walls give rise to a mainly torsional behavior of building D. Though rather weak in reinforcement, they receive a large portion of the horizontal forces and yield at the base for a PGA of about 0.05-0.07 g. It was observed that, also reducing their stiffness at the first two levels to account for localized yielding, the global behavior of the building remains essentially unaltered. Since shear failure of the r.c. walls was excluded, it was assumed that structural failure occurs when the farthest frame from the lift group collapses. Therefore, the assessment study was limited to a single frame. In the frame, it was observed that the presence of slab-depth beams of small width, though attributing a relatively ductile behavior, weakens the floor mechanisms. However, none of these mechanisms can develop. As expected, beams resulted insufficiently transversely reinforced. The type of transverse reinforcement, obtained by bending the longitudinal bars upwards, affects the shear strength where bending terminates. More importantly, the columns also present low transverse reinforcement, with stirrups which are not properly closed. Notwithstanding the increase in shear strength contributed by the axial load, premature shear failure of a column (and therefore collapse of the frame) was predicted to occur for PGA = 0.25 g. A Coefficient of Variance (CoV) of 20% was assigned to this value. Since it is required that the OTs be aseptic, the partitions surrounding them must remain intact so that they do not produce dust. Thus, the mean limit interstorey drift was assumed as 0.002h, where h is the interstorey height. The PGA that produces such drift was evaluated with two 3-D infilled frame models of building A (OT3) and D (OT1 and OT2). With the former it was found PGA = 0.15 g, while with the latter PGA = 0.17 g for OT1 and PGA = 0.226 g for OT2. Those last values are different because they account for the different in-plan position of the two OTs in building D. Partitions at the lower floors, where the X-rays are located, may present cracking, though moderate, without compromising the X-rays functionality. Thus, the mean value of the limit interstorey drift was assumed to be 0.003h, with a corresponding PGA of 0.20 g. For all partitions a CoV of 40% was assumed to account for uncertainties of the infilled frame model. As regards the OT, the most important and delicate equipment (such as the operating table, the operating lamp and other equipment fixed on the ceiling) is usually structurally well anchored. The remaining equipment is neither critical nor particularly fragile, and if damaged can be substituted, provided sufficient storage is available. With the awareness of a necessary deeper look at the problem, in this application the mean value of the equipment strength was assumed as 0.50 g with a CoV of 40%. Analogous considerations for the X-ray equipment led to the same values. The lift engine and the related mechanical parts have been considered to resist up to accelerations
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of 0.60 g (mean value) for building D and 0.50 g for building A, both with CoV = 50%. For the lift doors, the most critical are those located on the first and the second floors, where the nucleus yields and higher deformations are expected. It was deemed that the lift doors are blocked when an interstorey drift of 0.006 h (corresponding to 20 mm), assumed as mean value, is attained. The PGAs of 0.60 g for building D and 0.50 g for building A were evaluated and a CoV = 50% was assigned. For building D the deformations were evaluated with the walls' stiffness halved.
3.4.2. Assessment study of building C Building C is more regular than D both in plan and elevation, but it relies on a reduced number of transversely resisting frames. However, this building contains only the analysis lab and is undoubtedly less critical than D, from the hospital system standpoint. On the whole, it results equally resistant (PGA = 0.25 g) but more deformable than building D. This is particularly felt at the partitions of the analysis lab. This has a less critical role with respect to OTs, therefore the same limit interstorey drift as the X-ray area has been assumed, which led to a PGA of 0.15 g. It should be noted that the strength of the analysis lab equipment is lower than that of the OT, because here no tilting or rocking is admitted.
3.4.3. Assessment study of building A In the absence of design drawings, since the building A was built before the others, it was deemed to assume lower strengths, higher deformability and higher values for the uncertainties.
3.4.4. Response study of buildings D, C, A The mean value of the loads was evaluated through dynamic analysis of the buildings, with 3-D elastic models. The seismic action is represented by the Eurocode 8 elastic response spectrum for medium soil, scaled to the peak ground acceleration. Only linear analyses were carded out because the linear response in terms of displacement was deemed as representative of the structural behavior until structural collapse occurs. This is a reasonable assumption due to the low ductility levels available in the structures. For the evaluation of deformations, displacement ductility was assumed as 2.5 (mean value), as a result of the low quality of detailing, with a coefficient of variation of 0.25. The load on each piece of equipment accounts for its in-plan position. For example, note that the response of building D, where two OTs are located, is mainly torsional (Fig. 6), due to the presence of lift group r.c. walls, located far from the center of mass. Therefore, the horizontal load on equipment increases with its distance from the lift group.
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Table 2 Random variables: strengths (X, lognormal) and loads (Y, normal) with adopted values for mean and coefficient of variation
(CoV) X
Mean(g),
Streng~of
X
Mean(~,
Coy(%) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.30 0.30 0.30 0.50 0.25 0.20 0.50 0.30 0.20 0.25 0.40 0.50 0.50 0.50 0.40,
20 30 50 50 20 40 40 30 50 50 40 50 50 50 20
Strength of
Y
Coy (%) Ext. power supply Gener. unit build. Gener. unit engine Gener. unit tank Building D Partitions build. D X-ray equipment Switch board build. Switch board Building A Lifts r.c. walls A Lifts doors A Lifts engine A Lifts cages A Lifts r.c. walls D
16 17 18 19 20 21 22 23 24 25 26 27 28 29
0.60 50 0.60 50 0.60 50 0.25 30 0.15 30 0.15 50 0.50 50 0.15 50 0.15 40 0.50, 40 0.17, 40 0.50, 40 0.23,40 0.50,40
Meant),
Load on
CoV (%) Lifts doors D Lifts engine D Lifts cages D Building C Partitions build. C Analysis equipment Building E Medicine cabinets Partitions area OT3 Equipment OT3 Partitions area OT1 Equipment OT1 Partitions area OT2 Equipment OT2
A Given, 0 2 1.00 A, 25 3 1.00A, 25 4 2.30 A, 25 5 1.00 A, 80 6 1.50 A, 60 7 1.20 A, 20 8 0.15 A, 80 9 2.00 A, 60 10 1.00 A, 25 11 3.00 A, 25 12 1.00 A, 25 13 2.20 A, 25
Intensity (PGA) Buildings C, D, E Part. floor X-rays X-ray equipment Building A Lifts building A Lifts building D Floor building A - - OT3 Equip. build. A - - OT3 Floor building D - - OT1 Equip. build. D - - OT1 Floor building D - - OT2 Equip. build. D - - OT2
The results of the assessment and response studies are summarized in Table 2, where the random variables of strengths and loads are listed, with their mean value and CoV.
3.5. Minimal cut-set representation of the system The minimal cut-set representation of the system can be obtained based on the logical scheme. The cut-sets list is given in Table 3, where the component numbers are the strength IDs in Table 2.
3.6. Iterative analysis of the system with upgrades The evaluation of the component failure probability is carried out by means of well-known methods such as FORM (First Order Reliability Method) and SORM (Second Order Reliability
Table 3 Cut-set logic: component number (strength ID) for each cut-set (C-S) C-S
Comp.
C-S
Comp.
C-S
Comp.
C-S
Comp.
C-S
Comp.
C-S
Comp.
C-S
Comp.
1 2 3 4 5 6 7
1-2 1-3 1-4 5-2 5-3 5-4 6-2
$ 9 10 11 12 13 14
6-3 6-4 7-2 7-3 7-4 8 9
15 16 17 18 19 20 21
10-5 10-15 10-16 10-17 10-18 11-5 ll-15
22 23 24 25 26 27 28
11-16 11-17 ll-18 12-5 12-15 12-17 12-18
29 30 31 32 33 34 35
13-5 13-15 13-16 13-18 14-5 14-15 14-16
36 37 38 39 40 41 42
14-17 19 20 21 22 23 10-26-28
43 44 45 46 47 48 49
10-27-29 24-5 24-26-28 24-27-29 25-5 25-26-28 25-27-29
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Method). The failure probability of the series-parallel system is given in terms of Ditlevsen bounds [5]. In the case at hand, having adopted simple limit state and pdf functions, results practically coincide both with FORM and SORM. For the solution, the program Strurel [6] was used. The results are presented in the following section. It should be noted that all the system failure probabilities are conditional on the earthquake event.
4. Results of the analysis Before commenting on the results, it is useful to observe that the degree 7 earthquake of 1984 reached a peak ground acceleration (PGA) of 0.07 g in Castel di Sangro. As already observed, it caused slight non-structural and equipment damages in the hospital. Some medical cabinets were overturned and some of the analysis equipment broke, but the surgery function remained operative. Two introductory analyses were carried out under PGA = 0.05 g and 0.07 g to test the model accuracy against the observed scenario. The results of these and the following analyses are depicted in Figs 7 and 8 in terms of cut-set probability of failure, conditional on a given PGA. The whole upgrading process can be appreciated in Fig. 9, where the system Pf is depicted as a function of the PGA, before and after each upgrade intervention, indicated in the square box ( " 0 " means "non-upgraded system"). The analysis for PGA = 0.05 g yielded an overall system failure probability Pe of 0.06 (Fig. 9) that practically means absence of functionality problems. In this analysis, the cut-sets that mainly contribute to the overall Pe are numbers 39 and 41, with very low values of the probability of failure
0.35
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Fig. 7. Failure probability of cut-sets for PGA = 0.07 g, 0.10 g (above) and for 0.10 g, 0.15 g after the 1st upgrade (below).
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0.04 P(F-sysbm)
= 0.1678-0.222
~, 0.03
PGA=0.15g after 3rd upgrade
oo O a.
0.02
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8
11
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40
15
13
47
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Pc-, (about 0.03). As shown in Table 3, these are single-component cut-sets, made up from component 21 and 23, respectively, which correspond to the analysis equipment and the medical cabinets. The analysis for PGA = 0.07 g showed that the probability of functional collapse of the surgery function increases up to Pf = 0.24 (Fig. 7, top left, and Fig. 9), with determinant contributions again from cut-sets number 39 and 41 (both with Pc-, = 0.11), which are therefore singled out as critical (Table 4). These two preliminary analyses confirmed the observed scenario and indirectly corroborated the accuracy of the model, which was able to identify the critical sub-services of the surgery function. Now the question is: what value of functional collapse probability should be taken as the threshold beyond which upgrade interventions are necessary? In consideration of what was observed before, it is clear that this value should be around Pf = 0.24. On that occasion the surgery function remained operative, but emergency interventions had to be realized to recuperate the overturned medical cabinets and to replace some of the broken analysis equipment. For this reason, the threshold of Pf = 0.30 is deemed to be indicative of a crisis that calls for upgrade interventions. Thus, in the following, when P~ becomes greater than 0.30, the procedures require that upgrade hypotheses of critical elements be considered.
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Table 4 Component's strength before and after the first upgrade Cut-set
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In the analysis performed with PGA = 0.10 g, Pf is about 0.60 (Fig. 7, top right, and Fig. 9). The cut-sets that mainly contribute to this situation are of course numbers 39 and 41 (both with Pc-s = 0.28) with the addition of 38 and 14, with probability of failure of 0.17 and 0.11, respectively. As shown in Table 3, also cut-sets 38 and 14 are single-component cut-sets, each made up from component 20 (first floor partitions of building C, where the analysis lab is located) and 9 (switch board), respectively. As a first intervention hypothesis, expensive retrofit measures are excluded. Therefore, accepting a slight damage of the partitions, the intervention can be concentrated only on the non-structural elements, i.e. analysis equipment (21), medical cabinets (23) and switch board (9). Upgrade of these sub-components can easily be accomplished by improving their wall and ground anchorage and, for the first two, by also providing restraint of the contents. As a consequence of this first upgrade, the strength values were considered to increase up to the levels listed in Table 4. The upgraded system is again analyzed under the same PGA = 0.10 g. It can be observed that these simple interventions are surely beneficial for the overall functionality, resulting in a drastic reduction of the functional collapse probability Pf from 0.60 to 0.18 (Fig. 7, bottom left, and Fig. 9). As expected, a major contribution to the overall collapse probability comes from the non-upgraded partitions of building C (cut-set 38), whose failure probability remains still high (Pc-s = 0.17). This confirms that considerable improvement can be obtained by means of an accurate overview of the equipment and through simple and low-cost interventions. The system is then analyzed under PGA = 0.15 g, for which a failure probability Pf between 0.63 and 0.78 is obtained (Fig. 7, bottom right, and Fig. 9). Also in this case, functional failure is essentially imputable to the partitions of building C (cut-set 38) which now have a failure probability of 0.54. Minor contributions are brought in from the beating structure of building C (cut-set 37, component 19) with Pc-s = 0.10, and even less from cut-sets 42 and 48, both related to cracking of partitions of OT1, with Pc-s = 0.07 and 0.057, respectively. The second upgrade hypothesis aims at strengthening the analysis lab partitions of building C through the application of special sheeting to reduce their contribution to the overall failure probability. Their sustainable interstorey drift was doubled to 0.006h and an analysis was performed under PGA = 0.15 g. The partitions failure probability decreased to Pc-s = 0.040. Nonetheless, the overall Pf remained larger than the intervention threshold (about 0.30-0.43, see Fig. 9), as a result of many little contributions: Pc-~ = 0.105 from cut-set 37 (bearing structure of building C), Pc-s = 0.075 from cut-set 42 (beating structure of building A + partitions of OT1 and OT2 in building D), and P~_~= 0.058 from cut-set 48 (equipment of OT3 in building A + partitions of OT1 and OT2 in building D). It was therefore concluded that a third upgrade was needed to resist this intensity.
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Since Pf is now mainly affected by the inadequate strength of the bearing structure of building C, a radical choice would be to move the analysis lab from building C to building D. However, these drastic interventions cannot usually be done without reconsidering the overall internal organization of the hospital, also because other functions depend on the analysis lab. An alternative, though expensive, hypothesis was identified in the retrofit of building C structures. To do this, it was firstly verified that no shear failure can occur in the columns of building C. Then it was deemed to increase their ductility by a factor 1.5 with the adoption of external confinement at the base sections. The overall strength of building C was evaluated to increase from 0.25 g to 0.35 g. An additional intervention can be performed on partitions of OT1 and OT2, which mainly contribute to the failure of cut-sets 42 and 48. To this aim, the application of adhesive sheeting that delays cracking or, at least, prevents dust dispersion can be foreseen. This can increase the maximum sustainable interstorey drift from 0.002h up to 0.003h. After this third upgrade, the surgery function was analyzed under a PGA of 0.15 g. The global Pf is now decreased to 0.17-0.22 (Figs 8 and 9), well below the intervention threshold. The contributing cut-sets, all with negligible probabilities around 0.02-0.03, are: number 8 (partitions of X-ray areas in building D + generator unit), number 43 (equipment of OT1 and OT2 in building D + beating structure of building A), and number 11 (X-ray equipment + generator unit). A final analysis under PGA = 0.20 g was performed and Pf = 0.56-1.00 was obtained (Fig. 9). The critical cut-sets are in this case: number 8 (partitions of X-ray areas in building D + generator unit) with Pc-s = 0.27, number 43 (equipment of OT1 and OT2 in building D + bearing structure of building A) with Pc-s = 0.20, number 49 (equipment of the three OTs) with Pc-s = 0.19, and number 11 (X-ray equipment + generator unit) with Pc_s= 0.13. It should be noted that in this case damage is essentially non-structural, and therefore easily upgradeable, with the only exception of the bearing structure of building A. It should however be recalled that, due to the unavailability of structural drawings, the strength of building A had been attributed a low mean value (0.25 g) and a high uncertainty (50%). It is therefore deemed that an accurate in situ assessment could lead to a more reliable evaluation which could eliminate building A from the priority interventions. Provided this is true, this implies that the surgery function could be functional up to PGA = 0.20 g after a fourth very simple upgrade involving only the generator unit and the equipment of the operating theaters and of the X-ray areas.
5. Conclusions
A reliability-based procedure to evaluate the functional reliability of various functions within a hospital is presented. Each function is regarded as a logical system, whose functional collapse probability can be evaluated by: (a) constructing the logical scheme of the system, (b) assessing the strength of each system's component through examination of available information (e.g. design drawings and reports), (c) evaluating the actions through analysis of the structure's dynamic response under seismic action, and (d) performing reliability analyses of the system. The method allows the singling out of the structural, non-structural and equipment elements that represent the weak components of each function, and investigation and quantification the effectiveness of different intervention strategies. The procedure has been applied to the surgery service of an existing hospital. Large values of
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seismic functional vulnerability have been found, even for moderate earthquake intensities. Critical components, both structural and non-structural, have been singled out and the advantages related to possible upgrade hypotheses have been evaluated. It has been observed that simple interventions concerning non-structural components or equipment seem beneficial in the reduction of vulnerability and may result in significant performance improvement. Most of these basic interventions can be done directly by the hospital staff at very low cost, with substantial savings in terms of funds and time. Nonetheless, in order to achieve significant seismic protection levels, retrofit of partitions and eventually of some of the structural elements should be considered. Four upgrade interventions have been hypothesized: the first to resist a PGA of 0.10 g, the second and third to resist 0.15 g, and finally the fourth to resist 0.20 g. The first upgrade regards only anchorage of the equipment, and it is shown that significant enhancement of surgery function can be attained through an accurate overview of equipment and through simple and low-cost interventions. The second upgrade foresees only a low-cost strengthening of the partitions, but it was not effective at resisting 0.15 g. Therefore, in the third upgrade it is necessary to foresee both a structural retrofit of columns, to increase their ductility, and a series of backup interventions on the partitions of the operating theaters. A fourth upgrade involves essentially only non-structural elements. Above 0.20 g, structural upgrade is absolutely necessary. However, this would imply demolition and reconstruction of most structural parts, and this seems a rather unreasonable and uneconomical decision if compared with the mean return period of this intensity, which is about 200 years. A substantial weakness of the structural elements with respect to shear was observed, so that high danger of brittle collapse exists. This is mainly to address the scarce quality of detailing and the low quantity of transverse shear reinforcement that was adopted up to a few decades ago, particularly in columns. Structures with typical 1950s to 1970s detailing should always be attributed to low ductility levels. Upgrade interventions should aim at increasing their ductility and shear strength. Partitions are determinant for functionality, but upgrading criteria are certainly not easy to devise. Here it was deemed necessary to adopt adhesive sheeting, in order to avoid dust diffusion in the operating theaters which need to be aseptic. Piping and equipment are essential components for the overall reliability and should be studied with great attention. It is important to understand well their role within the system logic and also to evaluate their strength to horizontal actions, in terms of both absolute acceleration and relative-to-floor displacement. Upgrade can be obtained either by adequately anchoring them or through simple isolation techniques.
Acknowledgement This study was partially supported by the European Commission, DGXII, Environment Programme, Contract CT EV5 V93 0297.
References [1] Nuti, C. and Monti, G., Evaluation of vulnerability and retrofitting strategies for a hospital building. Workshop on Collaborative European Research Activities Supported by the EC for Seismic Risk Prevention and Reduction, 9-11 Nov., Bergamo, Italy, 1994.
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[2] Nuti, C. and Monti, G., Seismic reliability of hospitals systems. Proc. Seced Conf. on European Seismic Design Practice, 26-27 Oct., Chester, UK, 1995. [3] Priestley, M. J., Seible, F. and Chai, Y. H., Design guidelines for assessment retrofit and repair of bridges for seismic performance. Report SSRP-92/01, University of California, San Diego, USA, 1992. [4] Aschheim, M. and Moehle, J. P., Shear strength and deformability of RC bridge columns subjected to inelastic cyclic displacements. Report UCB/EERC-92/04, University of California, Berkeley, USA, 1992. [5] Ditlevsen, O., Narrow reliability bounds for structural systems. Journal of Structural Mechanics, ASCE, 1979, 7(4), 453-472. [6] RCP Consult, STRUREL - - a structural reliability analysis program. RCP GmbH, Miinchen, Germany, 1992.
PII: S0167-4730(96)00022-7
Structural Safety Vol. 18, No. 4, pp. 277-292, 1996 Copyright © 1996 Elsevier Science Ltd Printed in The Netherlands. All rights reserved 0167-4730/96 $15.00 + .00
A procedure for assessing the functional reliability of hospital systems Giorgio Monti a,*, Camillo Nuti b a Dipartimento di Ingegneria Strutturale e Geotecnica, Universit~t "La Sapienza "', Via A. Gramsci 53, 00197 Roma, Italy b Dipartimento di Scienze, Storia dell'Architettura e Restauro, Universith "G. D'Annunzio", Viale Pindaro 1, 65100 Pescara, Italy
Abstract
An effective reliability-based procedure is presented to assess the capability of hospitals to be functional after a seismic event of a given intensity. Every major function in a hospital depends on the joint action of various cooperating services, which in turn are made up from a certain number of sub-services. Such a complex organization is described in terms of a logical scheme and subsequently reduced to a minimal cut-set representation. For each sub-service a collapse criterion is defined, by which the strength is compared to the action load, both represented as random variables. Strengths are evaluated through assessment analyses based on design drawings. Loads are evaluated from 3-D linear dynamic analyses under seismic input. This is given by the Eurocode 8 elastic response spectrum, scaled at a given peak ground acceleration and account for the position of the sub-service within the building. By calculating the failure probability of each service by FORM (First Order Reliability Method) or SORM (Second Order Reliability Methods), the probability of functional interruption is obtained in terms of Ditlevsen bounds, conditional on a given earthquake intensity. The method helps to single out weak elements and potential sources of damage (structural, non-structural, equipment) within the hospital. This allows: (a) to investigate quantitatively the effectiveness of different upgrading criteria, (b) to select rationally intervention hypotheses, both in the retrofitting and rehabilitation of existing hospitals and in the design optimization of new ones, and (c) to evaluate different investment options for seismic vulnerability mitigation. As an example, an application to a case study hospital is presented. Copyright © 1996 Elsevier Science Ltd Keywords: Hospitals; Assessment; Retrofitting; Upgrading; System reliability; Functional collapse; Equipment
1. Introduction
Hospitals are extremely peculiar structures having the most diversified functions, ranging from those typical of hotels, offices or laboratories, to those of warehouses, where both hazardous and degradable materials are stored. Hospitals contain and preserve essential equipment for patient care and for first-aid. Basic supplies like water, electricity, oxygen and communications are needed 24 hours a day in order for the hospital to work efficiently without service interruptions that could be * Corresponding author. 277
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fatal. Moreover, equipment such as lifts and litter-lifts, essential for ensuring internal communications, should always be functioning. After having enumerated all the functions a hospital building has to accomplish, it is all too clear that when an earthquake strikes a hospital, the fact that the main structures have performed well during the seismic event is not sufficient to guarantee its overall efficiency. In fact, not only should the building be safe from the structural standpoint, but also all the above-mentioned functions should be completely guaranteed. Indeed, experiences from past earthquakes have shown that collapse of functional elements (such as X-rays, operating tables, etc.) prevented most hospitals from being fully operative during the post-quake aid operations. These considerations underline the strategic importance of hospitals in the aftermath, when extremely delicate situations arise, due to the arrival of a large number of patients and visitors while the malfunctioning probability is at its maximum. Above all, it is the problem of existing hospitals that has not been satisfactorily solved so far. In Europe seismic upgrading of existing hospitals is a critical issue, but a rational method to define an intervention strategy to obtain given reliability levels, at least in qualitative terms, has not been established yet. A feasibility study for reliability evaluation of a hospital regarded as a system was discussed in previous papers [1,2], where it was shown that every hospital activity can be represented through a logical functional scheme that can be analyzed with system reliability techniques. The results are obtained in terms of: (a) quantitative evaluation of the risk, (b) localization of critical elements, (c) evaluation of the available reliability in existing hospitals, (d) identification of intervention strategies, and (e) comparison of different upgrading hypotheses. The method considers the hospital to be a multi-functional system, in which the functions are those essential after a seismic event, such as: patient care, diagnostics, radiology, orthopedics, dialysis, pharmacy, surgery, first-aid, anti-shock care, catering, etc. Each function is made up of services, which in turn are made up of sub-services. For example, if one considers the radiology function, the X-ray machine represents, of course, one of its services; if the X-ray machine is located, say, at the third floor, then litter-lifts are considered to be a sub-service of X-rays. Again, for example, considering the surgery function, the operating theater, which is one of the services, is regarded as a series of sub-services: the room itself (partitions and structural elements) and the surgery equipment (operating table, lamps, etc.). Each sub-service is assigned a collapse criterion. deformed
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It should be clear that the fragility of a sub-service (e.g. a dialysis apparatus) depends on its strength characteristics but also on its location inside the building, because the action load varies with the floor level and also with the in-plan position within the floor. A schematic description of all the problems involved in a system functionality evaluation is presented in Fig. 1. Of course, a pure theoretical study of this subject is not conceivable. Firstly, because each hospital has its own peculiar layout that is impossible to generalize and also because many problems are related to local situations. Therefore, consideration of real cases is essential. However, the task is not as overwhelming as one would think because the number of hospital buildings in seismic areas is usually small compared to that of conventional buildings. This allows the problem to be treated on a case-by-case basis. In the following, the case study of an existing hospital is presented, where, as a first phase, the proposed methodology is applied to the surgery function.
2. Reliability of hospital systems In what follows, it should be clear that reliability and hospital terms correspond as: System Function (e.g., surgery), Component ~ Service (e.g., analysis), Sub-component ~ Sub-service (e.g., medicine cabinet, equipment, partition). The steps needed to perform the reliability analysis of a hospital can be outlined as follows (the same steps will be followed in the next section): 1. Local seismicity. Information should be gathered for the site under consideration from the analysis on catalogued events (historical data), in order to obtain the intensity associated to a given return period. Intensity values are preferably expressed in terms of Peak Ground Acceleration (PGA), due to current design specifications. 2. Functional description of the hospital. An accurate analysis of all the functions available in the hospital should be performed, starting from those related to the hospital specialization area and those essential after a seismic event. Each function should then be studied separately. 3. Logical scheme of each function. To construct the system logic means to select and to connect in a rational sequence, based on their relation to the selected function, all the services whose interruption implies failure of the function itself. All services should be localized in plan and elevation within the hospital building. Cooperation to other services and internal communications, i.e. lifts, litter-lifts and stairs, should be described in terms of horizontal and vertical paths to be followed. Essential equipment for patient survival and first-aid, and also basic supplies like water, electricity, communications should always be included as basic services of each function. 4. (Sub-) Components description. Each component (service) should be described as a series system made from sub-components (sub-services), whose failure determines its own failure. A collapse criterion should be associated to each sub-component, in terms of the sub-component strength and of the load acting on it. Strengths and loads are considered as random variables (also correlated between different sub-components), usually described by two-parameter pdf's, with mean and variance expressed in terms of an intensity measure [PGA, Modified Mercalli Intensity (MMI), etc.]. Variances can be assigned either by means of statistical analysis or by personal judgment (this also allows other types of uncertainties to be included). The determination of the mean values of strengths and loads represents the most delicate phase of the whole procedure. Conceptually, the determination of the
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strengths (Assessment Study) can be carried out independently of the determination of the loads (Response Study). In the Assessment Study strengths are estimated by means of assessment methods, separately applied to: (a) the structural elements: flexural strength of structural elements is evaluated assuming the actual material properties for concrete and steel; shear strength is evaluated as suggested in [3,4]; for both, direct examination of executive structural design and drawings is essential; (b) the whole structure: in case sufficient shear strength allows full development of elements flexural strength, structural collapse is identified with the development of a floor mechanism, whose strength can be quantified based on the index proposed in [3]; in case insufficient shear strength is detected, collapse occurs when the shear action reaches the shear strength on a single element, either beam or column; (c) the partitions: the strength of partitions at a given floor is that associated to a limit interstorey drift; (d) the equipment: the strength of the equipment can be based either on the assessment of response through shake table testing or analysis, including effects of mounting, or on the mechanical characteristics, if available as part of the rating of the equipment. If none of these data is available, an approximate estimate of the strength can be calculated, with simple geometrical considerations, in terms of the force overturning the equipment, considered as a rigid block. In the Response Study loads are evaluated through analysis of the dynamic structural response, considering the position, in plan and elevation, of the sub-services within the hospital building, as follows: (a) bending moments on elements are evaluated from dynamic analysis, while shear forces are obtained through equilibrium from the maximum nominal bending moments at the element ends; (b) as above, but in case of insufficient shear strength, the shear action is also evaluated from dynamic analysis; (c) loads on partitions are expressed in terms of the corresponding interstorey drifts, evaluated with either an infilled frame or a bare frame model; (d) loads on equipment are represented, depending on the equipment type under consideration, by either the peak absolute acceleration at the floor or the relative-to-floor displacement. Construction of floor response spectra of the above quantities can be of help for the task. The two studies are synthesized in Table 1. 5. Minimal cut-set representation of the system. The minimal cut-set representation of the system can be constructed from the system logic by means of standard methods; 6. Iterative analysis of the system with upgrades. Once the system is properly described, the reliability analysis is performed for increasing earthquake intensities. When the system functional failure probability, conditional on the earthquake event, reaches a predetermined limit value, then the local probability of failure of each sub-component is examined, so that critical components can be singled out and retrofit or intervention hypotheses can be formulated accordingly. 3. Application to a case study hospital
The hospital under consideration is the Castel di Sangro Hospital, located in the Abruzzi region in Italy, which underwent in 1984 a degree 7 earthquake (MMD. The original nucleus was built in the
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Table l Studies needed for sub-componentdescription Determinationof Type of analysis Strength (AssessmentStudy) Globalbehavior
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Local behavior
Loads (Response Study)
28 1
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Beams, columns,joints
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Actions on elements Interstoreydrift, absolute acceleration, relative-to-floordisplacement
1950s and 1960s, and subsequent expansions took place in the 1970s according to increasing demand and funding availability. The last building was completed in 1983. The whole structure consists now of seven buildings, in the following denominated as A to G (Fig. 2). The total number of beds is 134. The structure of these buildings consists of reinforced concrete (r.c.) frames, designed with the allowable stress method, according to seismic regulations that required the structures to resist horizontal forces equal to 10% of the vertical load. Design drawings and calculation reports are available, though at that time computational capability was limited and large simplifications were made in the design process. For example, actions on the elements were calculated with plane models and spatial distribution of forces among frames and r.c. walls was neglected. The type of construction is representative of r.c. buildings at that time, e.g., poor detailing for shear strength and ductility, plain reinforcing bars, distant stirrups, especially in columns, and unreinforced joints. Besides, slab-depth beams are widely used. Partitions are of the conventional type (brick masonry infills) and often contain built-in electric and medical gas lines. Equipment is not anchored. Emergency generators, as is often the case for most hospitals, provide energy to ensure functionality of all machines, with the only exception of X-rays, which are therefore backed up by portable X-ray machines. 3.1. L o c a l s e i s m i c i t y
In this century, the Abruzzi region has been shaken by two destructive earthquakes: the strongest in 1915, having a magnitude of 6.8 and its epicenter in Avezzano (some 60 km away), and the other in
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3.2. Functional description of the hospital The hospital has many specialties and functions. In this work attention is focused on the functionality of the surgery, therefore only services related to it are discussed, which essentially involve buildings A, C and D.
3.3. Logical scheme of the surgery function The logical scheme of the surgery function (Fig. 4) was constructed based on the following considerations. The operating theaters (OTs) are the core of the surgery function. There are three OTs in the hospital: one is located at the second floor of building A and two at the third floor of building D. The system starts from an entry point and, through a series of logical connections with cooperating services, ends in either OT. In order for the system to function, two essential services need to be operating: the external electric power supply (point 2 in Fig. 5, and box a in Fig. 4) and the switch board (point 3 in Fig. 5, and box d in Fig. 4), which distribute it. Before operations X-rays could be necessary. These are located in building D (point 11 in Fig. 5, and box c in Fig. 4). Access to OTs is ensured by two litter-lifts located either in building A or in building D. Analysis and pharmacy are two essential services in support of the OTs. There is only one analysis laboratory located at the ground floor in building C, while the pharmacy is located at the ground floor in building E.
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Proper functioning of each of the above-mentioned services depends on a certain number of sub-services, therefore each service (component) is subdivided into sub-services (sub-components). For example, service k (Fig. 4, inside frame) representing OT2 is subdivided into three sub-services: (a) the structures of building D (structural failure), (b) the partitions of the OT (functional failure due to cracking), (c) the OT equipment (collapse for tilting or overturning). Failure of either one of these three sub-services implies interruption of OT2. Note that the three OTs are in parallel, therefore it is sufficient that at least one of them works to maintain functionality of the surgery service. On the other hand, if either the switch board or the pharmacy fails, the whole system fails.
3.4. (Sub-) Components description Each sub-component is identified with the random variable pertaining to its strength and with the load random variable acting on it. An extremely simple collapse criterion, useful for practical 12
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purposes, was adopted, which detects failure when the strength R becomes smaller than the corresponding load S, that is, R - S < 0. Strength characteristics were evaluated through assessment studies of the three buildings involved: D, C and A. For building C and D, of more recent construction (1969 and 1972, respectively), the strength of the structural elements, beams and columns, was evaluated based on original construction drawings, whereas building A (built in 1951) could not be analyzed with the same detail level, because the reinforcement drawings were not available.
3.4.1. Assessment study of building D Building D is by far the most important of the three, since it contains two OTs and the X-ray apparatus, and therefore particular attention was paid to it in the study. The eccentric lift group r.c. walls give rise to a mainly torsional behavior of building D. Though rather weak in reinforcement, they receive a large portion of the horizontal forces and yield at the base for a PGA of about 0.05-0.07 g. It was observed that, also reducing their stiffness at the first two levels to account for localized yielding, the global behavior of the building remains essentially unaltered. Since shear failure of the r.c. walls was excluded, it was assumed that structural failure occurs when the farthest frame from the lift group collapses. Therefore, the assessment study was limited to a single frame. In the frame, it was observed that the presence of slab-depth beams of small width, though attributing a relatively ductile behavior, weakens the floor mechanisms. However, none of these mechanisms can develop. As expected, beams resulted insufficiently transversely reinforced. The type of transverse reinforcement, obtained by bending the longitudinal bars upwards, affects the shear strength where bending terminates. More importantly, the columns also present low transverse reinforcement, with stirrups which are not properly closed. Notwithstanding the increase in shear strength contributed by the axial load, premature shear failure of a column (and therefore collapse of the frame) was predicted to occur for PGA = 0.25 g. A Coefficient of Variance (CoV) of 20% was assigned to this value. Since it is required that the OTs be aseptic, the partitions surrounding them must remain intact so that they do not produce dust. Thus, the mean limit interstorey drift was assumed as 0.002h, where h is the interstorey height. The PGA that produces such drift was evaluated with two 3-D infilled frame models of building A (OT3) and D (OT1 and OT2). With the former it was found PGA = 0.15 g, while with the latter PGA = 0.17 g for OT1 and PGA = 0.226 g for OT2. Those last values are different because they account for the different in-plan position of the two OTs in building D. Partitions at the lower floors, where the X-rays are located, may present cracking, though moderate, without compromising the X-rays functionality. Thus, the mean value of the limit interstorey drift was assumed to be 0.003h, with a corresponding PGA of 0.20 g. For all partitions a CoV of 40% was assumed to account for uncertainties of the infilled frame model. As regards the OT, the most important and delicate equipment (such as the operating table, the operating lamp and other equipment fixed on the ceiling) is usually structurally well anchored. The remaining equipment is neither critical nor particularly fragile, and if damaged can be substituted, provided sufficient storage is available. With the awareness of a necessary deeper look at the problem, in this application the mean value of the equipment strength was assumed as 0.50 g with a CoV of 40%. Analogous considerations for the X-ray equipment led to the same values. The lift engine and the related mechanical parts have been considered to resist up to accelerations
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of 0.60 g (mean value) for building D and 0.50 g for building A, both with CoV = 50%. For the lift doors, the most critical are those located on the first and the second floors, where the nucleus yields and higher deformations are expected. It was deemed that the lift doors are blocked when an interstorey drift of 0.006 h (corresponding to 20 mm), assumed as mean value, is attained. The PGAs of 0.60 g for building D and 0.50 g for building A were evaluated and a CoV = 50% was assigned. For building D the deformations were evaluated with the walls' stiffness halved.
3.4.2. Assessment study of building C Building C is more regular than D both in plan and elevation, but it relies on a reduced number of transversely resisting frames. However, this building contains only the analysis lab and is undoubtedly less critical than D, from the hospital system standpoint. On the whole, it results equally resistant (PGA = 0.25 g) but more deformable than building D. This is particularly felt at the partitions of the analysis lab. This has a less critical role with respect to OTs, therefore the same limit interstorey drift as the X-ray area has been assumed, which led to a PGA of 0.15 g. It should be noted that the strength of the analysis lab equipment is lower than that of the OT, because here no tilting or rocking is admitted.
3.4.3. Assessment study of building A In the absence of design drawings, since the building A was built before the others, it was deemed to assume lower strengths, higher deformability and higher values for the uncertainties.
3.4.4. Response study of buildings D, C, A The mean value of the loads was evaluated through dynamic analysis of the buildings, with 3-D elastic models. The seismic action is represented by the Eurocode 8 elastic response spectrum for medium soil, scaled to the peak ground acceleration. Only linear analyses were carded out because the linear response in terms of displacement was deemed as representative of the structural behavior until structural collapse occurs. This is a reasonable assumption due to the low ductility levels available in the structures. For the evaluation of deformations, displacement ductility was assumed as 2.5 (mean value), as a result of the low quality of detailing, with a coefficient of variation of 0.25. The load on each piece of equipment accounts for its in-plan position. For example, note that the response of building D, where two OTs are located, is mainly torsional (Fig. 6), due to the presence of lift group r.c. walls, located far from the center of mass. Therefore, the horizontal load on equipment increases with its distance from the lift group.
J
I
J J
\
Fig. 6. Model of building D (left) and first modal shape (in plan) (righ0.
286
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Table 2 Random variables: strengths (X, lognormal) and loads (Y, normal) with adopted values for mean and coefficient of variation
(CoV) X
Mean(g),
Streng~of
X
Mean(~,
Coy(%) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.30 0.30 0.30 0.50 0.25 0.20 0.50 0.30 0.20 0.25 0.40 0.50 0.50 0.50 0.40,
20 30 50 50 20 40 40 30 50 50 40 50 50 50 20
Strength of
Y
Coy (%) Ext. power supply Gener. unit build. Gener. unit engine Gener. unit tank Building D Partitions build. D X-ray equipment Switch board build. Switch board Building A Lifts r.c. walls A Lifts doors A Lifts engine A Lifts cages A Lifts r.c. walls D
16 17 18 19 20 21 22 23 24 25 26 27 28 29
0.60 50 0.60 50 0.60 50 0.25 30 0.15 30 0.15 50 0.50 50 0.15 50 0.15 40 0.50, 40 0.17, 40 0.50, 40 0.23,40 0.50,40
Meant),
Load on
CoV (%) Lifts doors D Lifts engine D Lifts cages D Building C Partitions build. C Analysis equipment Building E Medicine cabinets Partitions area OT3 Equipment OT3 Partitions area OT1 Equipment OT1 Partitions area OT2 Equipment OT2
A Given, 0 2 1.00 A, 25 3 1.00A, 25 4 2.30 A, 25 5 1.00 A, 80 6 1.50 A, 60 7 1.20 A, 20 8 0.15 A, 80 9 2.00 A, 60 10 1.00 A, 25 11 3.00 A, 25 12 1.00 A, 25 13 2.20 A, 25
Intensity (PGA) Buildings C, D, E Part. floor X-rays X-ray equipment Building A Lifts building A Lifts building D Floor building A - - OT3 Equip. build. A - - OT3 Floor building D - - OT1 Equip. build. D - - OT1 Floor building D - - OT2 Equip. build. D - - OT2
The results of the assessment and response studies are summarized in Table 2, where the random variables of strengths and loads are listed, with their mean value and CoV.
3.5. Minimal cut-set representation of the system The minimal cut-set representation of the system can be obtained based on the logical scheme. The cut-sets list is given in Table 3, where the component numbers are the strength IDs in Table 2.
3.6. Iterative analysis of the system with upgrades The evaluation of the component failure probability is carried out by means of well-known methods such as FORM (First Order Reliability Method) and SORM (Second Order Reliability
Table 3 Cut-set logic: component number (strength ID) for each cut-set (C-S) C-S
Comp.
C-S
Comp.
C-S
Comp.
C-S
Comp.
C-S
Comp.
C-S
Comp.
C-S
Comp.
1 2 3 4 5 6 7
1-2 1-3 1-4 5-2 5-3 5-4 6-2
$ 9 10 11 12 13 14
6-3 6-4 7-2 7-3 7-4 8 9
15 16 17 18 19 20 21
10-5 10-15 10-16 10-17 10-18 11-5 ll-15
22 23 24 25 26 27 28
11-16 11-17 ll-18 12-5 12-15 12-17 12-18
29 30 31 32 33 34 35
13-5 13-15 13-16 13-18 14-5 14-15 14-16
36 37 38 39 40 41 42
14-17 19 20 21 22 23 10-26-28
43 44 45 46 47 48 49
10-27-29 24-5 24-26-28 24-27-29 25-5 25-26-28 25-27-29
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Method). The failure probability of the series-parallel system is given in terms of Ditlevsen bounds [5]. In the case at hand, having adopted simple limit state and pdf functions, results practically coincide both with FORM and SORM. For the solution, the program Strurel [6] was used. The results are presented in the following section. It should be noted that all the system failure probabilities are conditional on the earthquake event.
4. Results of the analysis Before commenting on the results, it is useful to observe that the degree 7 earthquake of 1984 reached a peak ground acceleration (PGA) of 0.07 g in Castel di Sangro. As already observed, it caused slight non-structural and equipment damages in the hospital. Some medical cabinets were overturned and some of the analysis equipment broke, but the surgery function remained operative. Two introductory analyses were carried out under PGA = 0.05 g and 0.07 g to test the model accuracy against the observed scenario. The results of these and the following analyses are depicted in Figs 7 and 8 in terms of cut-set probability of failure, conditional on a given PGA. The whole upgrading process can be appreciated in Fig. 9, where the system Pf is depicted as a function of the PGA, before and after each upgrade intervention, indicated in the square box ( " 0 " means "non-upgraded system"). The analysis for PGA = 0.05 g yielded an overall system failure probability Pe of 0.06 (Fig. 9) that practically means absence of functionality problems. In this analysis, the cut-sets that mainly contribute to the overall Pe are numbers 39 and 41, with very low values of the probability of failure
0.35
0.14
[ P(F-ay,=.) = 0..01-0...I
P(F-system) = 0.2359-0.2436 I 0.3
0.12
I mA= o.oTg 1-
0.1
0.25
o u) 0.08
0.2
0 0.06 u~
,0,0.15
~" 0.04
• " o.1
0.02
0.05 39
41
38
I FGA= 0.10g
0
14
30
41
30
C u t - S e t no.
37
14
C u t - S e t no.
0.7
0.2
P(F-system)
x
I P(F-system) : 0.6284-0.7768
0.1789-0.188 0.6
0.15
PGA : 0.10g
Q ~ 0
after 1st upgrade
0.1
~" 0.5
~
O.
er I st upgrade
~ 0.4 0.3
• "o.2
0.05
0.1
~ 38
/----~ / - - 7 37
42 Cut-Set no.
40
0
38
37
42
48 8 Cut-Set no.
43
11
Fig. 7. Failure probability of cut-sets for PGA = 0.07 g, 0.10 g (above) and for 0.10 g, 0.15 g after the 1st upgrade (below).
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G. Monti, C. Nuti
0.04 P(F-sysbm)
= 0.1678-0.222
~, 0.03
PGA=0.15g after 3rd upgrade
oo O a.
0.02
0.01 43
8
11
49
40
15
13
47
Cut-Set no. Fig. 8. Failure probability of cut-sets after the 3rd upgrade.
Pc-, (about 0.03). As shown in Table 3, these are single-component cut-sets, made up from component 21 and 23, respectively, which correspond to the analysis equipment and the medical cabinets. The analysis for PGA = 0.07 g showed that the probability of functional collapse of the surgery function increases up to Pf = 0.24 (Fig. 7, top left, and Fig. 9), with determinant contributions again from cut-sets number 39 and 41 (both with Pc-, = 0.11), which are therefore singled out as critical (Table 4). These two preliminary analyses confirmed the observed scenario and indirectly corroborated the accuracy of the model, which was able to identify the critical sub-services of the surgery function. Now the question is: what value of functional collapse probability should be taken as the threshold beyond which upgrade interventions are necessary? In consideration of what was observed before, it is clear that this value should be around Pf = 0.24. On that occasion the surgery function remained operative, but emergency interventions had to be realized to recuperate the overturned medical cabinets and to replace some of the broken analysis equipment. For this reason, the threshold of Pf = 0.30 is deemed to be indicative of a crisis that calls for upgrade interventions. Thus, in the following, when P~ becomes greater than 0.30, the procedures require that upgrade hypotheses of critical elements be considered.
1
-i--[]
IowerUpperboundb°Und []
UPGRADE[
/I
0.8
,
I / ~ ~0.6 _]L intervention threshold ,~/
~o.4
•
I
a.
#
0.2 0.05
)9"
,,"~ ,//
JIT1
/
,'/,
#-Y 0.1
0.15 PGA
./ 0.2
(g)
Fig. 9. System failure probability as function of PGA and upgrades.
289
G. Monti, C. Nuti
Table 4 Component's strength before and after the first upgrade Cut-set
39 41 14
Sub-component
Analysis equipment (21) Medical cabinets (23) Switch board (9)
Before 1st upgrade
After 1st upgrade
Mean value (g)
CoY (%)
Mean value (g)
CoY (%)
0.15 0.15 0.20
50 50 50
0.60 0.60 0.60
30 30 30
In the analysis performed with PGA = 0.10 g, Pf is about 0.60 (Fig. 7, top right, and Fig. 9). The cut-sets that mainly contribute to this situation are of course numbers 39 and 41 (both with Pc-s = 0.28) with the addition of 38 and 14, with probability of failure of 0.17 and 0.11, respectively. As shown in Table 3, also cut-sets 38 and 14 are single-component cut-sets, each made up from component 20 (first floor partitions of building C, where the analysis lab is located) and 9 (switch board), respectively. As a first intervention hypothesis, expensive retrofit measures are excluded. Therefore, accepting a slight damage of the partitions, the intervention can be concentrated only on the non-structural elements, i.e. analysis equipment (21), medical cabinets (23) and switch board (9). Upgrade of these sub-components can easily be accomplished by improving their wall and ground anchorage and, for the first two, by also providing restraint of the contents. As a consequence of this first upgrade, the strength values were considered to increase up to the levels listed in Table 4. The upgraded system is again analyzed under the same PGA = 0.10 g. It can be observed that these simple interventions are surely beneficial for the overall functionality, resulting in a drastic reduction of the functional collapse probability Pf from 0.60 to 0.18 (Fig. 7, bottom left, and Fig. 9). As expected, a major contribution to the overall collapse probability comes from the non-upgraded partitions of building C (cut-set 38), whose failure probability remains still high (Pc-s = 0.17). This confirms that considerable improvement can be obtained by means of an accurate overview of the equipment and through simple and low-cost interventions. The system is then analyzed under PGA = 0.15 g, for which a failure probability Pf between 0.63 and 0.78 is obtained (Fig. 7, bottom right, and Fig. 9). Also in this case, functional failure is essentially imputable to the partitions of building C (cut-set 38) which now have a failure probability of 0.54. Minor contributions are brought in from the beating structure of building C (cut-set 37, component 19) with Pc-s = 0.10, and even less from cut-sets 42 and 48, both related to cracking of partitions of OT1, with Pc-s = 0.07 and 0.057, respectively. The second upgrade hypothesis aims at strengthening the analysis lab partitions of building C through the application of special sheeting to reduce their contribution to the overall failure probability. Their sustainable interstorey drift was doubled to 0.006h and an analysis was performed under PGA = 0.15 g. The partitions failure probability decreased to Pc-s = 0.040. Nonetheless, the overall Pf remained larger than the intervention threshold (about 0.30-0.43, see Fig. 9), as a result of many little contributions: Pc-~ = 0.105 from cut-set 37 (bearing structure of building C), Pc-s = 0.075 from cut-set 42 (beating structure of building A + partitions of OT1 and OT2 in building D), and P~_~= 0.058 from cut-set 48 (equipment of OT3 in building A + partitions of OT1 and OT2 in building D). It was therefore concluded that a third upgrade was needed to resist this intensity.
290
G. Monti, C. Nuti
Since Pf is now mainly affected by the inadequate strength of the bearing structure of building C, a radical choice would be to move the analysis lab from building C to building D. However, these drastic interventions cannot usually be done without reconsidering the overall internal organization of the hospital, also because other functions depend on the analysis lab. An alternative, though expensive, hypothesis was identified in the retrofit of building C structures. To do this, it was firstly verified that no shear failure can occur in the columns of building C. Then it was deemed to increase their ductility by a factor 1.5 with the adoption of external confinement at the base sections. The overall strength of building C was evaluated to increase from 0.25 g to 0.35 g. An additional intervention can be performed on partitions of OT1 and OT2, which mainly contribute to the failure of cut-sets 42 and 48. To this aim, the application of adhesive sheeting that delays cracking or, at least, prevents dust dispersion can be foreseen. This can increase the maximum sustainable interstorey drift from 0.002h up to 0.003h. After this third upgrade, the surgery function was analyzed under a PGA of 0.15 g. The global Pf is now decreased to 0.17-0.22 (Figs 8 and 9), well below the intervention threshold. The contributing cut-sets, all with negligible probabilities around 0.02-0.03, are: number 8 (partitions of X-ray areas in building D + generator unit), number 43 (equipment of OT1 and OT2 in building D + beating structure of building A), and number 11 (X-ray equipment + generator unit). A final analysis under PGA = 0.20 g was performed and Pf = 0.56-1.00 was obtained (Fig. 9). The critical cut-sets are in this case: number 8 (partitions of X-ray areas in building D + generator unit) with Pc-s = 0.27, number 43 (equipment of OT1 and OT2 in building D + bearing structure of building A) with Pc-s = 0.20, number 49 (equipment of the three OTs) with Pc-s = 0.19, and number 11 (X-ray equipment + generator unit) with Pc_s= 0.13. It should be noted that in this case damage is essentially non-structural, and therefore easily upgradeable, with the only exception of the bearing structure of building A. It should however be recalled that, due to the unavailability of structural drawings, the strength of building A had been attributed a low mean value (0.25 g) and a high uncertainty (50%). It is therefore deemed that an accurate in situ assessment could lead to a more reliable evaluation which could eliminate building A from the priority interventions. Provided this is true, this implies that the surgery function could be functional up to PGA = 0.20 g after a fourth very simple upgrade involving only the generator unit and the equipment of the operating theaters and of the X-ray areas.
5. Conclusions
A reliability-based procedure to evaluate the functional reliability of various functions within a hospital is presented. Each function is regarded as a logical system, whose functional collapse probability can be evaluated by: (a) constructing the logical scheme of the system, (b) assessing the strength of each system's component through examination of available information (e.g. design drawings and reports), (c) evaluating the actions through analysis of the structure's dynamic response under seismic action, and (d) performing reliability analyses of the system. The method allows the singling out of the structural, non-structural and equipment elements that represent the weak components of each function, and investigation and quantification the effectiveness of different intervention strategies. The procedure has been applied to the surgery service of an existing hospital. Large values of
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291
seismic functional vulnerability have been found, even for moderate earthquake intensities. Critical components, both structural and non-structural, have been singled out and the advantages related to possible upgrade hypotheses have been evaluated. It has been observed that simple interventions concerning non-structural components or equipment seem beneficial in the reduction of vulnerability and may result in significant performance improvement. Most of these basic interventions can be done directly by the hospital staff at very low cost, with substantial savings in terms of funds and time. Nonetheless, in order to achieve significant seismic protection levels, retrofit of partitions and eventually of some of the structural elements should be considered. Four upgrade interventions have been hypothesized: the first to resist a PGA of 0.10 g, the second and third to resist 0.15 g, and finally the fourth to resist 0.20 g. The first upgrade regards only anchorage of the equipment, and it is shown that significant enhancement of surgery function can be attained through an accurate overview of equipment and through simple and low-cost interventions. The second upgrade foresees only a low-cost strengthening of the partitions, but it was not effective at resisting 0.15 g. Therefore, in the third upgrade it is necessary to foresee both a structural retrofit of columns, to increase their ductility, and a series of backup interventions on the partitions of the operating theaters. A fourth upgrade involves essentially only non-structural elements. Above 0.20 g, structural upgrade is absolutely necessary. However, this would imply demolition and reconstruction of most structural parts, and this seems a rather unreasonable and uneconomical decision if compared with the mean return period of this intensity, which is about 200 years. A substantial weakness of the structural elements with respect to shear was observed, so that high danger of brittle collapse exists. This is mainly to address the scarce quality of detailing and the low quantity of transverse shear reinforcement that was adopted up to a few decades ago, particularly in columns. Structures with typical 1950s to 1970s detailing should always be attributed to low ductility levels. Upgrade interventions should aim at increasing their ductility and shear strength. Partitions are determinant for functionality, but upgrading criteria are certainly not easy to devise. Here it was deemed necessary to adopt adhesive sheeting, in order to avoid dust diffusion in the operating theaters which need to be aseptic. Piping and equipment are essential components for the overall reliability and should be studied with great attention. It is important to understand well their role within the system logic and also to evaluate their strength to horizontal actions, in terms of both absolute acceleration and relative-to-floor displacement. Upgrade can be obtained either by adequately anchoring them or through simple isolation techniques.
Acknowledgement This study was partially supported by the European Commission, DGXII, Environment Programme, Contract CT EV5 V93 0297.
References [1] Nuti, C. and Monti, G., Evaluation of vulnerability and retrofitting strategies for a hospital building. Workshop on Collaborative European Research Activities Supported by the EC for Seismic Risk Prevention and Reduction, 9-11 Nov., Bergamo, Italy, 1994.
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[2] Nuti, C. and Monti, G., Seismic reliability of hospitals systems. Proc. Seced Conf. on European Seismic Design Practice, 26-27 Oct., Chester, UK, 1995. [3] Priestley, M. J., Seible, F. and Chai, Y. H., Design guidelines for assessment retrofit and repair of bridges for seismic performance. Report SSRP-92/01, University of California, San Diego, USA, 1992. [4] Aschheim, M. and Moehle, J. P., Shear strength and deformability of RC bridge columns subjected to inelastic cyclic displacements. Report UCB/EERC-92/04, University of California, Berkeley, USA, 1992. [5] Ditlevsen, O., Narrow reliability bounds for structural systems. Journal of Structural Mechanics, ASCE, 1979, 7(4), 453-472. [6] RCP Consult, STRUREL - - a structural reliability analysis program. RCP GmbH, Miinchen, Germany, 1992.