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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Earth Sci.</journal-id>
<journal-title>Frontiers in Earth Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Earth Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-6463</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">626809</article-id>
<article-id pub-id-type="doi">10.3389/feart.2021.626809</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Earth Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>A New Relative Risk Index for Hospitals Exposed to Tsunami</article-title>
<alt-title alt-title-type="left-running-head">Baiguera et&#x20;al.</alt-title>
<alt-title alt-title-type="right-running-head">Hospital Tsunami Relative Risk Index</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Baiguera</surname>
<given-names>Marco</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1131639/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Rossetto</surname>
<given-names>Tiziana</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/256511/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Palomino</surname>
<given-names>Juan</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1116022/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Dias</surname>
<given-names>Priyan</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Lopez-Querol</surname>
<given-names>Susana</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Siriwardana</surname>
<given-names>Chandana</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1037342/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Hasalanka</surname>
<given-names>Hashan</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Ioannou</surname>
<given-names>Ioanna</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Robinson</surname>
<given-names>David</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
</contrib-group>
<aff id="aff1">
<label>
<sup>1</sup>
</label>EPICentre, Department of Civil, Environmental and Geomatic Engineering, University College London, <addr-line>London</addr-line>, <country>United&#x20;Kingdom</country>
</aff>
<aff id="aff2">
<label>
<sup>2</sup>
</label>Department of Civil Engineering, University of Moratuwa, <addr-line>Moratuwa</addr-line>, <country>Sri Lanka</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/410929/overview">Christina Robyn Magill</ext-link>, Macquarie University, Australia</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/651079/overview">Yo Fukutani</ext-link>, Kanto Gakuin University, Japan</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/954623/overview">Qi Yao</ext-link>, China Earthquake Networks Center, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Marco Baiguera, <email>m.baiguera@ucl.ac.uk</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Geohazards and Georisks, a section of the journal Frontiers in Earth Science</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>31</day>
<month>03</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="collection">
<year>2021</year>
</pub-date>
<volume>9</volume>
<elocation-id>626809</elocation-id>
<history>
<date date-type="received">
<day>06</day>
<month>11</month>
<year>2020</year>
</date>
<date date-type="accepted">
<day>04</day>
<month>02</month>
<year>2021</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2021 Baiguera, Rossetto, Palomino, Dias, Lopez-Querol, Siriwardana, Hasalanka, Ioannou and Robinson.</copyright-statement>
<copyright-year>2021</copyright-year>
<copyright-holder>Baiguera, Rossetto, Palomino, Dias, Lopez-Querol, Siriwardana, Hasalanka, Ioannou and Robinson</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these&#x20;terms.</p>
</license>
</permissions>
<abstract>
<p>The failure of hospitals in recent tsunami have caused extensive social and economic losses. A simple but quantitative approach is required to assess the resilience of healthcare systems to tsunami, which relates not only to hospital building integrity, but also to maintaining hospital functionality. This paper proposes a new tsunami relative risk index (TRRI) that quantifies the impact of tsunami on critical units, (e.g. Intensive Care Unit, Maternity Ward, etc) in individual hospitals, as well as the impact on service provision across a network of hospitals. A survey form is specifically developed for collecting of field data on hospitals for the TRRI evaluation. In its current form TRRI is designed for hospital buildings of reinforced concrete construction, as these are the building types most commonly used worldwide for housing critical units. The TRRI is demonstrated through an application to three hospitals located along the southern coast of Sri Lanka. The TRRI is evaluated for three potential tsunami inundation events and is shown to be able to identify issues with both the building and functional aspects of hospital critical units. Three &#x201c;what-if&#x201d; intervention scenarios are presented and their effect on the TRRI is assessed. Through this exercise, it is shown that the TRRI can be used by decision makers to simply explore the effectiveness of individual and combined interventions in improving the tsunami resilience of healthcare provision across the hospital system.</p>
</abstract>
<kwd-group>
<kwd>tsunami risk</kwd>
<kwd>relative risk index</kwd>
<kwd>hospitals</kwd>
<kwd>tsunami engineering</kwd>
<kwd>disaster risk reduction</kwd>
</kwd-group>
<contract-num rid="cn001">177813</contract-num>
<contract-sponsor id="cn001">Research England<named-content content-type="fundref-id">10.13039/501100013589</named-content>
</contract-sponsor>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>Hospitals and healthcare facilities are vital assets to communities and play a key role in recovery from natural disasters. During emergencies, hospital units must provide uninterrupted critical services such as emergency care to the injured, laboratories, blood banks, ambulances, pharmacies and immunization services to prevent outbreaks of diseases (<xref ref-type="bibr" rid="B37">WHO, 2010</xref>). In recognition of the critical role played by hospitals in disasters, the Hyogo Framework for Action (<xref ref-type="bibr" rid="B35">UNISDR, 2005</xref>) and subsequent Sendai Framework (<xref ref-type="bibr" rid="B34">UNDRR, 2015</xref>), have as one priority the achievement of safe and resilient hospitals through structural, non-structural and functional risk prevention. This has resulted in major global initiatives for hospital safety and several guidelines have been issued for the design, assessment and strengthening of hospital buildings for different hazards (<xref ref-type="bibr" rid="B17">FEMA, 1997</xref>; <xref ref-type="bibr" rid="B18">FEMA, 2003</xref>; <xref ref-type="bibr" rid="B20">FEMA, 2007</xref>; <xref ref-type="bibr" rid="B28">PAHO, 2008</xref>; <xref ref-type="bibr" rid="B38">WHO, 2015</xref>). However, it is only relatively recently that tsunami design codes have been issued, e.g., FEMA 55 (<xref ref-type="bibr" rid="B19">FEMA, 2005</xref>), MLIT 2570 (<xref ref-type="bibr" rid="B27">MLIT, 2011</xref>), ASCE 7&#x2013;16 Standard (<xref ref-type="bibr" rid="B3">ASCE, 2017a</xref>). These have not been implemented in the design of most healthcare facilities worldwide, and failures of hospitals in recent tsunami have caused extensive social and economic losses, (e.g. <xref ref-type="bibr" rid="B22">Kirsch et&#x20;al., 2010</xref>; <xref ref-type="bibr" rid="B15">EEFIT, 2011</xref>). One means of disaster management for reducing life loss in tsunami is evacuation to sites outside the inundation zone or to upper levels in buildings considered strong enough to withstand the tsunami inundation (e.g. <xref ref-type="bibr" rid="B26">MHNI, 2015</xref>). Clearly, the vulnerable nature and reduced mobility of hospital patients makes evacuation difficult. Moreover, evacuation is only viable for locations that have tsunami warning systems in place and which are at a significant distance from the tsunami source.</p>
<p>Despite not being designed for tsunami, most hospitals are built to higher standards than normal residential buildings and present an enhanced resistance to natural hazards that may allow them to withstand small tsunami inundation without structural damage. However, hospital resilience relates not only to hospital building integrity, but also to maintaining hospital functionality. The latter depends heavily on the integrity of both non-structural elements and the lifelines supporting the hospital operation, such electricity, water and communications. The 2011 Tohoku tsunami presented several examples of hospitals that withstood the tsunami but had compromised functionality and ability to care for patients in the aftermath due to loss of lifelines and back-up systems in the tsunami inundation (<xref ref-type="bibr" rid="B15">EEFIT, 2011</xref>, <xref ref-type="bibr" rid="B16">EEFIT, 2013</xref>; <xref ref-type="bibr" rid="B4">ASCE, 2017b</xref>).</p>
<p>Hospitals can be considered as part of a network of healthcare provision, where only some parts of the network can be relied upon for the provision of any particular healthcare service, (e.g. not all hospitals have a trauma unit). As tsunami can affect large tracts of the coastline, they can damage several hospitals and/or supporting lifelines simultaneously. This not only disrupts the provision of healthcare locally but can result in the loss of particular healthcare services across large parts of the network, (e.g. if all hospitals with trauma units are affected over an extended region). Such scenarios result in affected people having to travel large distances and wait for excessive times to obtain specific treatments.</p>
<p>The inherent organisational complexity of hospitals, and the interactions and independencies of healthcare units makes the tsunami risk assessment of hospital services a challenging task. To date, several studies have investigated the performance of individual hospital buildings for different natural hazards using advanced engineering analysis, (e.g. <xref ref-type="bibr" rid="B7">Casarotti et&#x20;al., 2009</xref>; <xref ref-type="bibr" rid="B10">Di Sarno et&#x20;al., 2011</xref>). However, the use of advanced engineering analysis for the risk assessment of several hospitals is prohibitively expensive in terms of human and computational resources, as hospitals are typically composed of several buildings, built at different times and which do not follow a standard design. Furthermore, these studies rarely consider lifelines and back-up systems explicitly. As an alternative, several hospital safety indices (<xref ref-type="bibr" rid="B28">PAHO, 2008</xref>; <xref ref-type="bibr" rid="B38">WHO, 2015</xref>) and hospital safety checklists (<xref ref-type="bibr" rid="B36">WHO, 2008</xref>; <xref ref-type="bibr" rid="B37">WHO, 2010</xref>) have been proposed that offer rapid diagnostic tools for use by policy makers and hospital managers. These indices and checklists provide a qualitative estimate of the risk to hospitals from a set of hazards, i.e.,&#x20;natural and man-made hazards. The indicators can be applied to assess either single healthcare facilities or networks of hospitals, and generally account for the potential loss of critical infrastructure lifelines. These can be used to identify potential problem areas and for the prioritization of interventions to reduce the disaster risk to hospitals. However, these methods present two major shortcomings: 1) lack of quantitative approaches to support the assessment of the relative risk associated with the hospital facilities; and 2) little consideration of the nature of single hazards, (e.g. tsunami) and their interactions and interdependencies when impacting hospital infrastructure.</p>
<p>In order to improve both the safety and resilience of healthcare systems to tsunami, a simple but quantitative approach is required for assessing tsunami risk to healthcare services distributed across networks of hospitals. Such an approach needs to focus on healthcare service continuity, and go beyond hospital building integrity to consider the integrity of the lifelines and back-up systems that support the service provision and hospital functionality. This paper presents a new tsunami relative risk index <inline-formula id="inf1">
<mml:math id="minf1">
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
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</mml:mrow>
<mml:mo>)</mml:mo>
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</inline-formula> developed to meet this need. Firstly, the components and calculation rationale for the <inline-formula id="inf2">
<mml:math id="minf2">
<mml:mrow>
<mml:mi>T</mml:mi>
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<mml:mi>R</mml:mi>
<mml:mi>I</mml:mi>
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</inline-formula> are described. A survey form, specifically developed for collecting of field data on hospitals for the <inline-formula id="inf3">
<mml:math id="minf3">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> evaluation is also presented in the Appendix. In its current form <inline-formula id="inf4">
<mml:math id="minf4">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is developed for hospital buildings of reinforced concrete construction, as these are the building types most commonly used worldwide for housing critical units, (e.g. Intensive Care Units). The <inline-formula id="inf5">
<mml:math id="minf5">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is demonstrated through an application to 3 hospitals located along the southern coast of Sri Lanka (Galle, Matara and Hambantota Districts), which were surveyed by a team of researchers from UCL and University of Moratuwa. The <inline-formula id="inf6">
<mml:math id="minf6">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is evaluated for three potential tsunami inundation events and is shown to be able to identify issues with both the buildings and functional aspects of hospital critical units. Three &#x201c;what-if&#x201d; intervention scenarios are selected and their effect on the <inline-formula id="inf7">
<mml:math id="minf7">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
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</inline-formula> is assessed. Through this exercise, it is shown that the <inline-formula id="inf8">
<mml:math id="minf8">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>R</mml:mi>
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</mml:mrow>
</mml:math>
</inline-formula> can be used by decision makers to simply explore the effectiveness of individual and combined interventions in improving the tsunami resilience of healthcare provision across the hospital system.</p>
<p>Although the absence of numerical structural modeling to support the analysis can be seen as a limitation of this approach, the proposed relative risk index is based on objective engineering principles that are reflected in equations (and not merely expert opinions). The aim of using such an index is to be able to quickly assess a large portfolio of hospital facilities, identifying aspects of the facilities that require further detailed assessment, thus directing potential numerical modeling. For the case-study presented here, the inundation depths for the &#x201c;what-if&#x201d; intervention scenarios are based on limited onshore inundation scenarios based on the 2004 Indian Ocean Tsunami event, rather than on probabilistic data, since the latter is not available for Sri Lanka. Nevertheless, these scenarios give insight into the relative effectiveness of various mitigation measures that can be adopted by hospital administrators.</p>
</sec>
<sec sec-type="methods" id="s2">
<title>Methodology</title>
<p>The proposed Tsunami Relative Risk Index <inline-formula id="inf9">
<mml:math id="minf9">
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
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</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> aims to quantify the influence of the tsunami inundation on critical units, (e.g. Intensive Care Unit, Maternity Ward, etc) in individual hospitals, as well as the impact on service provision across a network of hospitals. The objective is to identify some of the drivers of risk to the hospital unit functionality, such that these can be prioritized for further investigation and intervention.</p>
<p>The proposed <inline-formula id="inf10">
<mml:math id="minf10">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> considers both the structural and functional attributes of hospital critical units, e.g., Intensity Care Unit, Maternity Ward, etc. The ability of a hospital critical unit to function in the aftermath of a tsunami depends on: 1) the stability of the structure where the hospital critical unit is located; 2) the integrity of non-structural elements relevant to the critical units, particularly the medical equipment that is required to ensure unit functionality; and 3) the functioning of the critical lifeline systems supporting unit functionality e.g., electric power, water supply, telecommunications, etc. Therefore, the proposed <italic>TRRI</italic>, for a hospital unit is defined as:<disp-formula id="e1">
<mml:math id="me1">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
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<mml:mo>&#x3d;</mml:mo>
<mml:mi>max</mml:mi>
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<mml:mo>,</mml:mo>
<mml:mtext>&#x2009;</mml:mtext>
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<mml:mtext>funct</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
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</mml:mrow>
</mml:msub>
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<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where <inline-formula id="inf11">
<mml:math id="minf11">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
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<mml:mtext>bldg</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> considers the ability of the structural system to resist expected tsunami actions, <inline-formula id="inf12">
<mml:math id="minf12">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
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<mml:mtext>funct</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents whether the location of the critical unit within the building puts it at high risk of loss of functionality under the expected tsunami inundation, and <inline-formula id="inf13">
<mml:math id="minf13">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
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<mml:mtext>bcs</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> describes the risk of back-up critical systems to supporting lifelines being inundated. Each <inline-formula id="inf14">
<mml:math id="minf14">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> component varies in value between 0 (no risk) and 1 (high risk). Each of these <inline-formula id="inf15">
<mml:math id="minf15">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> components are further described in the following sections.</p>
<sec id="s2-1">
<title>Building Relative Risk Index, <italic>RRI</italic>
<sub>bldg</sub>
</title>
<p>Post-tsunami reconnaissance studies provide a spectrum of tsunami-induced damage mechanisms in buildings, that result from the actions of hydrodynamic forces, buoyancy, impact from floating debris and foundation scouring (<xref ref-type="bibr" rid="B14">EEFIT, 2006</xref>). <xref ref-type="fig" rid="F1">Figure&#x20;1</xref> shows a typical load time series as a tsunami passes a building. Initially, as the front of the tsunami arrives and passes the building, there will be a sharp rise in force, which will then plateau and be maintained for several minutes, depending on the period of the wave and the proximity of the building to the shoreline. During this phase, there may be several short sharp spikes in loading from debris impacting with the building. The capacity of the building to withstand the tsunami loading will decrease during the course of inundation due to buoyancy forces reducing axial compression in vertical elements (<xref ref-type="bibr" rid="B9">Del Zoppo et&#x20;al., 2020</xref>), and due to scour undermining the foundations. The impact of scour around the building can also have a considerable impact on the structural capacity of the building, by exposing the foundations and potentially leading to local collapse of vertical structural elements when local inundation levels increase, or under the return flow of the tsunami toward the&#x20;sea.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Typical qualitative time series of loading on a building during tsunami inundation (<xref ref-type="bibr" rid="B40">Yeh et&#x20;al., 2014</xref>).</p>
</caption>
<graphic xlink:href="feart-09-626809-g001.tif"/>
</fig>
<p>The relative risk index associated with the integrity of the hospital building, indicated as <italic>RRI</italic>
<sub>bldg</sub>, looks to evaluate, in a simple way, the performance of a building subjected to the three main tsunami loading components, i.e.,&#x20;hydrodynamic loading, scouring and debris impact, as follows:<disp-formula id="e2">
<mml:math id="me2">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>bldg</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>max</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>struct</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>debris</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>where <italic>RRI</italic>
<sub>struct.</sub> represents the ability of the structural system to resist the overall tsunami hydrodynamic force (including debris damming), <italic>RRI</italic>
<sub>scour</sub> represents the ability of the building foundation system to resist scouring for the expected inundation, and <italic>RRI</italic>
<sub>debris</sub> represents the capacity and redundancy of the structure to resist debris impact from movable objects located within the hospital facility and in the surrounding areas. It is noted that each <italic>RRI</italic> component of <italic>RRI</italic>
<sub>bldg</sub> takes values between 0 (no risk) and 1 (high risk).</p>
<p>A main difference between <italic>RRI</italic>
<sub>bldg</sub> and other established tsunami building vulnerability indices for tsunami, is that <italic>RRI</italic>
<sub>bldg</sub> is based on a simplified assessment of the building failure and damage mechanisms, evaluated using physics and engineering based formulations. This is significantly different from, for example, the well-established PTVA relative vulnerability index of <xref ref-type="bibr" rid="B29">Papathoma and Dominey-Howes. (2003)</xref> and <xref ref-type="bibr" rid="B8">Dall&#x2019;Osso et&#x20;al. (2016)</xref>, which is constructed from a set of characteristics of the building that are thought to affect its tsunami resistance, combined through a weighting based on expert judgment.</p>
<sec id="s2-1-1">
<title>Index for Structural Performance Under Hydrodynamic Loading <italic>RRI</italic>
<sub>struct</sub>
</title>
<p>Tsunami hydrodynamic forces typically impact the lower floors of a building and generate large shear forces on the vertical elements of the structure, (i.e. the columns). Recent studies, (e.g. <xref ref-type="bibr" rid="B2">Alam et&#x20;al., 2017</xref>; <xref ref-type="bibr" rid="B30">Petrone et&#x20;al., 2017</xref>), have shown that in reinforced concrete (RC) structures this can lead to shear failure of columns at the ground storey, which precipitates global collapse if no strengthening measures are adopted. This failure mechanism is assumed in the development of the relative risk index for evaluating structural performance under hydrodynamic loading, <inline-formula id="inf16">
<mml:math id="minf16">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>struct</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, which is evaluated from a comparison between the overall lateral hydrodynamic force applied to the structure by the tsunami <inline-formula id="inf17">
<mml:math id="minf17">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and the shear strength of the ground floor columns <inline-formula id="inf18">
<mml:math id="minf18">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mtext>C</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> as follows:<disp-formula id="e3">
<mml:math id="me3">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>struct</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mtext>C</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>The tsunami load on a structure <inline-formula id="inf19">
<mml:math id="minf19">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is estimated using the hydrodynamic drag equation in the ASCE 7&#x2013;16 Standard (<xref ref-type="bibr" rid="B3">ASCE, 2017a</xref>), as:<disp-formula id="e4">
<mml:math id="me4">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mn>2</mml:mn>
</mml:mfrac>
<mml:msub>
<mml:mtext>&#x3c1;</mml:mtext>
<mml:mtext>s</mml:mtext>
</mml:msub>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:mtext>cx</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>where <inline-formula id="inf20">
<mml:math id="minf20">
<mml:mrow>
<mml:msub>
<mml:mtext>&#x3c1;</mml:mtext>
<mml:mtext>S</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the minimum fluid mass density, <inline-formula id="inf21">
<mml:math id="minf21">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the drag coefficient, <inline-formula id="inf22">
<mml:math id="minf22">
<mml:mi>B</mml:mi>
</mml:math>
</inline-formula> is the building width perpendicular to the flow, <inline-formula id="inf23">
<mml:math id="minf23">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the tsunami inundation depth, <inline-formula id="inf24">
<mml:math id="minf24">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the tsunami flow velocity, and <inline-formula id="inf25">
<mml:math id="minf25">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:mtext>cx</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the proportion of closure coefficient, (i.e. ratio of the closed facade to the total fa&#xe7;ade area), with a minimum value of 0.7, adopted in this study. The drag coefficient <inline-formula id="inf26">
<mml:math id="minf26">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> varies based on the <inline-formula id="inf27">
<mml:math id="minf27">
<mml:mrow>
<mml:mrow>
<mml:mi>B</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> ratio (<xref ref-type="bibr" rid="B3">ASCE, 2017a</xref>). The shear strength of the ground floor columns <inline-formula id="inf28">
<mml:math id="minf28">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mtext>C</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is estimated as the sum of the nominal design shear strength of the ground floor columns, <inline-formula id="inf29">
<mml:math id="minf29">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mrow>
<mml:mtext>CS</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, as follows:<disp-formula id="e5">
<mml:math id="me5">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mtext>C</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mtext>SC</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2217;</mml:mo>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mrow>
<mml:mtext>SC</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>where <inline-formula id="inf30">
<mml:math id="minf30">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mtext>SC</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> indicates the number of columns along the side of the building perpendicular to the tsunami flow. As this study focuses on RC structures, <inline-formula id="inf31">
<mml:math id="minf31">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mrow>
<mml:mtext>CS</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is calculated for each column according to the formulae of ACI 318 (<xref ref-type="bibr" rid="B1">ACI, 2005</xref>) as follows:<disp-formula id="e6">
<mml:math id="me6">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mrow>
<mml:mtext>CS</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>&#x3d5;</mml:mi>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mtext>n</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>&#x3d5;</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mtext>c</mml:mtext>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mtext>s</mml:mtext>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>
<disp-formula id="e7">
<mml:math id="me7">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mtext>c</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.17</mml:mn>
<mml:mo>&#xa0;</mml:mo>
<mml:msqrt>
<mml:mrow>
<mml:msub>
<mml:msup>
<mml:mi>f</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
<mml:mtext>c</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:msqrt>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>b</mml:mi>
<mml:mtext>w</mml:mtext>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>d</mml:mi>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
<disp-formula id="e8">
<mml:math id="me8">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mtext>s</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mtext>v</mml:mtext>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mtext>yt</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mi>s</mml:mi>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>where <inline-formula id="inf32">
<mml:math id="minf32">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>n</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the nominal shear strength, <inline-formula id="inf33">
<mml:math id="minf33">
<mml:mi>&#x3d5;</mml:mi>
</mml:math>
</inline-formula> is the strength reduction factor, <inline-formula id="inf34">
<mml:math id="minf34">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mtext>c</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf35">
<mml:math id="minf35">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mtext>s</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the concrete and transverse reinforcement components of shear strength, <inline-formula id="inf36">
<mml:math id="minf36">
<mml:mrow>
<mml:msub>
<mml:msup>
<mml:mi>f</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
<mml:mtext>c</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the compressive strength of concrete, <inline-formula id="inf37">
<mml:math id="minf37">
<mml:mrow>
<mml:msub>
<mml:mi>b</mml:mi>
<mml:mtext>w</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the section width, <inline-formula id="inf38">
<mml:math id="minf38">
<mml:mi>d</mml:mi>
</mml:math>
</inline-formula> is the effective depth, <inline-formula id="inf39">
<mml:math id="minf39">
<mml:mrow>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mtext>v</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the area of transverse reinforcement, <inline-formula id="inf40">
<mml:math id="minf40">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mtext>yt</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the transverse reinforcement yield strength, and <inline-formula id="inf41">
<mml:math id="minf41">
<mml:mi>s</mml:mi>
</mml:math>
</inline-formula> is the hoop spacing.</p>
</sec>
<sec id="s2-1-2">
<title>Index for Structural Stability Under Scour, <italic>RRI</italic>
<sub>scour</sub>
</title>
<p>In the aftermath of the 2004 Indian Ocean Tsunami in Sri Lanka, one of the main damage mechanisms observed for multi-story building was the undermining of foundations due to the scouring of sandy soils at the corners of buildings (<xref ref-type="bibr" rid="B11">Dias et&#x20;al., 2006</xref>). This occurred for relatively low tsunami inundation depths, (i.e. 3&#xa0;m) and resulted in the collapse of end bays of several RC buildings, such as schools. Such failure mechanisms have also been observed in several past events, with RC buildings composed of few frames and with shallow foundations being seen to be the most susceptible to this failure type (<xref ref-type="bibr" rid="B14">EEFIT, 2006</xref>; <xref ref-type="bibr" rid="B15">EEFIT, 2011</xref>; <xref ref-type="bibr" rid="B4">ASCE, 2017b</xref>).</p>
<p>Tsunami design guidelines (<xref ref-type="bibr" rid="B3">ASCE, 2017a</xref>) assume that foundations on rock or other non-erodible materials are at no risk of scour. For other types of soil, the scour depth <inline-formula id="inf42">
<mml:math id="minf42">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is related to the tsunami inundation depth <inline-formula id="inf43">
<mml:math id="minf43">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and is estimated from:<disp-formula id="e9">
<mml:math id="me9">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mn>1.2</mml:mn>
<mml:mo>&#x2217;</mml:mo>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>;</mml:mo>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mn>3.05</mml:mn>
<mml:mo>&#xa0;</mml:mo>
<mml:mtext>m,</mml:mtext>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mn>3.66</mml:mn>
<mml:mo>&#xa0;</mml:mo>
<mml:mtext>m;</mml:mtext>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2265;</mml:mo>
<mml:mn>3.05</mml:mn>
<mml:mo>&#xa0;</mml:mo>
<mml:mtext>m</mml:mtext>
<mml:mtext>.</mml:mtext>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>
<xref ref-type="disp-formula" rid="e9">Equation 9</xref> provides a simple empirical prediction based on observations of local scour depths and estimated flow depths for different sediment types in the aftermath of the 2011 Tohoku tsunami (<xref ref-type="bibr" rid="B33">Tonkin et&#x20;al., 2014</xref>). In ASCE 7&#x2013;16 the extent (length) of the scour hole around corner foundations <inline-formula id="inf44">
<mml:math id="minf44">
<mml:mrow>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (see <xref ref-type="fig" rid="F2">Figure&#x20;2</xref>) is dependent on the soil type and is calculated as follows:<disp-formula id="e10">
<mml:math id="me10">
<mml:mrow>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mtext>for</mml:mtext>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>cohesive</mml:mtext>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>soils,</mml:mtext>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mtext>for</mml:mtext>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>noncohesive</mml:mtext>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>soils</mml:mtext>
<mml:mtext>.</mml:mtext>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>
</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Example sketch illustrating the effects around building with shallow foundations on noncohesive soils and the calculations for the second footing from the left corner.</p>
</caption>
<graphic xlink:href="feart-09-626809-g002.tif"/>
</fig>
<p>This approach requires soils to be classified as cohesive or non-cohesive. No indication is however provided in the ASCE 7&#x2013;16 Standard or accompanying commentary, as to the procedure to be followed for this classification. For the <italic>RRI</italic>
<sub>scour</sub> it is proposed that a simple soil analysis, (i.e. particle size distribution analysis through sieving) be used as the basis for the classification, whereby: 1) <italic>Non-cohesive or granular soils</italic>, (e.g. gravels and sands), defined as those with less than 50% of fines content as per ASTM D2487&#x2013;17 (USCS)&#x2013;if the fines content is higher than 12% and less than 50%, then the soil is coarse grained though controlled by the fine soil nature, i.e.,&#x20;non-cohesive; 12% fines content is usually considered as a reference percentage below which soils are defined as purely granular; 2) <italic>Cohesive soils</italic>, (e.g. silts and clays), defined as those with more than 50% of fines content. If soil analysis data at the building site are not available, simple assumptions should be made to classify the soils based on local knowledge.</p>
<p>The calculation of <inline-formula id="inf45">
<mml:math id="minf45">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf46">
<mml:math id="minf46">
<mml:mrow>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is instrumental for predicting how many of the building foundations are affected by scour and the corresponding loss of bearing capacity. The tsunami resistance of the foundations depends on the type of foundation, i.e.,&#x20;deep or shallow foundations, and the number of foundation elements affected. Empirical observations from past events indicate that deep pile foundations generally provide adequate tsunami resistance, while buildings with shallow spread footings are likely to experience failure, especially at the building corners. Hence, in the development of <italic>TRRI</italic> a focus is placed on characterizing the impact of scour on shallow foundations. An approximate but quantitative procedure is proposed for calculating <italic>RRI</italic>
<sub>scour</sub> based on geotechnical engineering practice and is illustrated by the flowchart in <xref ref-type="fig" rid="F3">Figure&#x20;3</xref>.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Flowchart for estimating <italic>RRI</italic>
<sub>scour</sub>.</p>
</caption>
<graphic xlink:href="feart-09-626809-g003.tif"/>
</fig>
<p>For simple pad foundations, the overall design load-bearing capacity of the system can be estimated by multiplying the ultimate bearing capacity of individual pad foundations <inline-formula id="inf47">
<mml:math id="minf47">
<mml:mrow>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> by the number of footings <inline-formula id="inf48">
<mml:math id="minf48">
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>:<disp-formula id="e11">
<mml:math id="me11">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
<mml:mo>&#x2217;</mml:mo>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
<mml:mo>&#x2217;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>W</mml:mi>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>where <inline-formula id="inf49">
<mml:math id="minf49">
<mml:mi>W</mml:mi>
</mml:math>
</inline-formula> is the weight of the building plus loads and <inline-formula id="inf50">
<mml:math id="minf50">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the design safety factor. Typically, a large safety factor <inline-formula id="inf51">
<mml:math id="minf51">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is adopted foundation design in order to account for the uncertainty related to the soil properties and behavior. For example, a common safety factor for shallow foundations is <inline-formula id="inf52">
<mml:math id="minf52">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>. Using <xref ref-type="disp-formula" rid="e11">Eq. 11</xref>, the design load-bearing capacity of a pad foundation normalized to the building weight, <inline-formula id="inf53">
<mml:math id="minf53">
<mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mi>W</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, can be estimated as:<disp-formula id="e12">
<mml:math id="me12">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
</mml:mrow>
<mml:mi>W</mml:mi>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>when <inline-formula id="inf54">
<mml:math id="minf54">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is larger than the foundation depth <inline-formula id="inf55">
<mml:math id="minf55">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, the foundations need to be checked for loss of bearing capacity. In this paper a minimum depth <inline-formula id="inf56">
<mml:math id="minf56">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> of 1&#xa0;m is considered for shallow foundations. Depending on the extent of the local scour <inline-formula id="inf57">
<mml:math id="minf57">
<mml:mrow>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> along both sides of the building (<italic>x</italic> and <italic>y</italic> directions), a number of foundation supports <inline-formula id="inf58">
<mml:math id="minf58">
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mtext>f</mml:mtext>
<mml:mo>,</mml:mo>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> might be affected. Foundation pads are assumed to be placed at a distance <inline-formula id="inf59">
<mml:math id="minf59">
<mml:mrow>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, which corresponds to the bay length. The depth <inline-formula id="inf60">
<mml:math id="minf60">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is assumed to occur at the corner of the building. As shown in <xref ref-type="fig" rid="F2">Figure&#x20;2</xref>, half of the scour hole length <inline-formula id="inf61">
<mml:math id="minf61">
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is assumed to extend from the point of maximum scour depth (in the corner). Due to the formulations used, the larger the value of <inline-formula id="inf62">
<mml:math id="minf62">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, the larger the value of <inline-formula id="inf63">
<mml:math id="minf63">
<mml:mrow>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and greater the number of affected footings <inline-formula id="inf64">
<mml:math id="minf64">
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mtext>f</mml:mtext>
<mml:mo>,</mml:mo>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. A foundation is assumed to fail if, at the pad edges, the relevant scour hole depth equals or exceeds that of the foundation. This assumption considers the load bearing capacity of the soil beneath the foundation, (which is spreading the foundation loading outwards and downwards), to be compromised.</p>
<p>When subjected to scour, the load-bearing capacity of the foundation system is reduced and is estimated as that deriving solely from those foundations that have not been affected by scour, i.e.,:<disp-formula id="e13">
<mml:math id="me13">
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mtext>f,scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2217;</mml:mo>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2217;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>W</mml:mi>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(13)</label>
</disp-formula>In <xref ref-type="disp-formula" rid="e13">Eq. 13</xref>, <inline-formula id="inf65">
<mml:math id="minf65">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the reduced design safety factor that accounts for the effects of local scour around the foundations, and can be determined as follows:<disp-formula id="e14">
<mml:math id="me14">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mtext>f</mml:mtext>
<mml:mo>,</mml:mo>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2217;</mml:mo>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
</mml:mrow>
<mml:mi>W</mml:mi>
</mml:mfrac>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#x2192;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mtext>f</mml:mtext>
<mml:mo>,</mml:mo>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(14)</label>
</disp-formula>Having evaluated the reduced design safety factor, <italic>RRI</italic>
<sub>scour</sub> can be determined following the flowchart presented in <xref ref-type="fig" rid="F3">Figure&#x20;3</xref>, and from <xref ref-type="disp-formula" rid="e15">Eq. 15</xref>:<disp-formula id="e15">
<mml:math id="me15">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>;</mml:mo>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>scour,</mml:mtext>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>min</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>scour,</mml:mtext>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>min</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>;</mml:mo>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>scour,</mml:mtext>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>min</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>1.</mml:mn>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(15)</label>
</disp-formula>where <inline-formula id="inf66">
<mml:math id="minf66">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
<mml:mo>,</mml:mo>
<mml:mtext>min</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the minimum value of <inline-formula id="inf67">
<mml:math id="minf67">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> along both sides of the building. For <inline-formula id="inf68">
<mml:math id="minf68">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, the foundations are unlikely to be able to carry the gravity loads, i.e.,&#x20;<italic>RRI</italic>
<sub>scour</sub> &#x3d; 1. This means that when the number of affected foundation supports, <inline-formula id="inf69">
<mml:math id="minf69">
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mtext>f</mml:mtext>
<mml:mo>,</mml:mo>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, along any side of the building is equal or greater than 50% of the total number of foundation supports <inline-formula id="inf70">
<mml:math id="minf70">
<mml:mrow>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mtext>f</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> along that side of the building, the foundation system is considered at risk of failure, i.e.,&#x20;<italic>RRI</italic>
<sub>scour</sub> &#x3d;&#x20;1.</p>
</sec>
<sec id="s2-1-3">
<title>Index for the Capacity and Redundancy of the Structure to Resist Debris Impact, <italic>RRI</italic>
<sub>debris</sub>
</title>
<p>Generally, tsunamis transport a large volume of debris, including trees, cars, containers, utility poles and wood-frame houses. The perimeter structural components that are oriented perpendicular to the direction of the flow are at the greatest risk of impact. For instance, the loss of a perimeter column may compromise the ability of a structure to support gravity loads. The ASCE 7&#x2013;16 Standard (<xref ref-type="bibr" rid="B3">ASCE, 2017a</xref>) provides a framework for the calculation of the impact forces determined by debris. This includes the effects of the impact by floating wood poles, logs and vehicles, which should be taken into account when tsunami depths are larger than 0.9&#xa0;m. <italic>RRI</italic>
<sub>debris</sub> is presented in this paper for the common case where debris consists mainly of logs (or similar). However, by changing the debris impact loads, <italic>RRI</italic>
<sub>debris</sub> can be modified to account for potential impacts from shipping containers, ships, barges and other large objects. Such sized debris should be considered if the hospital is in close proximity to a port or container&#x20;yard.</p>
<p>In the <italic>RRI</italic>
<sub>debris</sub> evaluation, the maximum instantaneous debris impact force (<italic>F</italic>
<sub>ni</sub>) is first calculated using the impulse-momentum based formulation in the ASCE 7&#x2013;16 Standard:<disp-formula id="e16">
<mml:math id="me16">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>ni</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:msqrt>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:msqrt>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(16)</label>
</disp-formula>where <inline-formula id="inf71">
<mml:math id="minf71">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the orientation coefficient (given as 0.65 by ASCE 7&#x2013;16), <inline-formula id="inf72">
<mml:math id="minf72">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the maximum tsunami flow velocity at the building site. <inline-formula id="inf73">
<mml:math id="minf73">
<mml:mi>k</mml:mi>
</mml:math>
</inline-formula> is the effective stiffness of the impacting debris and <inline-formula id="inf74">
<mml:math id="minf74">
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the mass of the debris. A minimum weight of 454&#xa0;kg and minimum log stiffness of 61,300&#xa0;kN/m are nominal values assumed in the ASCE 7&#x2013;16 Standard.</p>
<p>The debris impact of a log is a dynamic event. However, an equivalent static approach can be used by multiplying the debris force in <xref ref-type="disp-formula" rid="e17">Eq. 17</xref> by a dynamic response factor <inline-formula id="inf75">
<mml:math id="minf75">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mtext>max</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. The latter can be estimated based on the ratio of the impact duration to natural period of the impacted structural element. The impulse duration <inline-formula id="inf76">
<mml:math id="minf76">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is given in ASCE 7&#x2013;16 as follows:<disp-formula id="e17">
<mml:math id="me17">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>ni</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(17)</label>
</disp-formula>Considering an exterior column of a RC building, the natural period of the column (<italic>T</italic>
<sub>col</sub>) can be estimated assuming fixed end boundary conditions:<disp-formula id="e18">
<mml:math id="me18">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mtext>col</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mi>&#x3c0;</mml:mi>
<mml:mrow>
<mml:mo>[</mml:mo>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mi>L</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:mn>22.373</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
<mml:msqrt>
<mml:mrow>
<mml:mfrac>
<mml:mi>&#x3c1;</mml:mi>
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:msqrt>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(18)</label>
</disp-formula>where <inline-formula id="inf77">
<mml:math id="minf77">
<mml:mi>L</mml:mi>
</mml:math>
</inline-formula> is the unbraced column length, <inline-formula id="inf78">
<mml:math id="minf78">
<mml:mi>&#x3c1;</mml:mi>
</mml:math>
</inline-formula> is the column mass per unit length, <inline-formula id="inf79">
<mml:math id="minf79">
<mml:mi>E</mml:mi>
</mml:math>
</inline-formula> is the modulus of elasticity of concrete and <inline-formula id="inf80">
<mml:math id="minf80">
<mml:mi>I</mml:mi>
</mml:math>
</inline-formula> is the second moment of area of the column section (<xref ref-type="bibr" rid="B32">Robertson, 2020</xref>). ASCE 7&#x2013;16&#x20;<italic>Table&#x20;6.11-1</italic> gives the values of the dynamic response factor <inline-formula id="inf81">
<mml:math id="minf81">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mtext>max</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> based on the ratio <inline-formula id="inf82">
<mml:math id="minf82">
<mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mtext>d</mml:mtext>
</mml:msub>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mtext>col</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>. The equivalent static load for debris impact <inline-formula id="inf83">
<mml:math id="minf83">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mtext>i</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is calculated as:<disp-formula id="e19">
<mml:math id="me19">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mtext>i</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>max</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>ni</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(19)</label>
</disp-formula>The force given by <xref ref-type="disp-formula" rid="e19">Eq. 19</xref> should not exceed the force from the alternative simplified impact load <inline-formula id="inf84">
<mml:math id="minf84">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>i</mml:mtext>
<mml:mo>,</mml:mo>
<mml:mtext>max</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, given in ASCE 7&#x2013;16 Standard as:<disp-formula id="e20">
<mml:math id="me20">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>i,</mml:mtext>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>max</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1,470</mml:mn>
<mml:mo>&#x2217;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(20)</label>
</disp-formula>where <inline-formula id="inf85">
<mml:math id="minf85">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the orientation coefficient, taken as 0.65 (<xref ref-type="bibr" rid="B3">ASCE, 2017a</xref>). Furthermore, the value obtained in <xref ref-type="disp-formula" rid="e20">Eq. 20</xref> can be reduced by 50%, (i.e. 478&#xa0;kN), if the site is not exposed to impact by containers, ships and barges. Therefore the debris impact force <inline-formula id="inf86">
<mml:math id="minf86">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>debris</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is estimated as:<disp-formula id="e21">
<mml:math id="me21">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>debris</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>min</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mtext>i</mml:mtext>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>i,</mml:mtext>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>max</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(21)</label>
</disp-formula>If <inline-formula id="inf87">
<mml:math id="minf87">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mtext>debris</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> exceeds the shear strength of the considered column, <inline-formula id="inf88">
<mml:math id="minf88">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mrow>
<mml:mtext>SC</mml:mtext>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (calculated using <xref ref-type="disp-formula" rid="e6">Eq. 6</xref>), then the structural system is at risk of local collapse and potential loss of stability, i.e.,&#x20;<inline-formula id="inf89">
<mml:math id="minf89">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>debris</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>The redundancy present in the structure can be beneficial to the stability of the building. In the context of RC structures, <italic>RRI</italic>
<sub>debris</sub> is calculated by taking the ratio between the number of impacted columns over the total number of columns present in the seaward side of the building. As the number of impacted columns cannot be predicted, it is assumed that two vertical columns (probably the corner columns) located within the seaward face of the building might fail due to debris impact. This assumption is based on observations that debris impact can be particularly common and severe for exposed corner columns of frames (<xref ref-type="bibr" rid="B14">EEFIT, 2006</xref>). Therefore, <italic>RRI</italic>
<sub>debris</sub> is calculated as follows:<disp-formula id="e22">
<mml:math id="me22">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>debris</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mn>2</mml:mn>
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mtext>SC</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(22)</label>
</disp-formula>
</p>
</sec>
</sec>
<sec id="s2-2">
<title>Index Representing Risk to Critical Unit Functionality, <italic>RRI</italic>
<sub>funct</sub>
</title>
<p>
<italic>RRI</italic>
<sub>funct</sub> looks to represent the risk to continued function of a critical unit after a tsunami. The index is based on the location of the critical unit within the hospital complex with respect to the tsunami inundation. It is assumed that if the critical unit is inundated, the resulting damage to non-structural elements and medical equipment may prevent the unit from being fully operational in the aftermath of the event. <italic>RRI</italic>
<sub>funct</sub> is therefore binary, taking a value of zero if the critical unit lies outside the inundation zone or is located in a storey of the building above the local inundation depth, or 1 otherwise.</p>
</sec>
<sec id="s2-3">
<title>Index Representing Tsunami Risk to Lifeline Back-Up Systems, <italic>RRI</italic>
<sub>bcs</sub>
</title>
<p>The loss of essential lifelines such as power, water, wastewater, natural gas, can severely limit the functionality of hospitals and their critical units. For instance, one of the case-study hospitals presented later in the report, i.e.,&#x20;the Mahamodara Teaching Hospital, suffered the failure of backup generator, water supply and sewer systems when it was inundated during the 2004 Indian Ocean Tsunami (<xref ref-type="bibr" rid="B21">Harlan, 2016</xref>).</p>
<p>From <xref ref-type="bibr" rid="B28">PAHO (2008)</xref> and <xref ref-type="bibr" rid="B38">WHO (2015)</xref> it is possible to identify eight main lifeline systems that are required to ensure the functionality of hospital critical units: Power (P), Air conditioning (HVAC), Telecommunications (TLC), Water Supply (WS), Fire Protection (FP), Waste Water (WW), Medical Gas (MG) and Fuel and Gas reserves (FG). Where national or regional lifelines are compromised, as can be the case in a large tsunami, the presence of back-up systems can provide immediate continuity in the aftermath of a disaster, for a few hours or even days. Hence, the proposed index <italic>RRI</italic>
<sub>bcs</sub> considers whether the back-up systems to lifelines needed for the functioning of critical units are 1) located within the hospital premises and 2) whether they are likely to be damaged under the expected inundation, as follows:<disp-formula id="e23">
<mml:math id="me23">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>bcs</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mtext>P</mml:mtext>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>H</mml:mi>
<mml:mi>V</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>C</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>HVAC</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>T</mml:mi>
<mml:mi>L</mml:mi>
<mml:mi>C</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>TLC</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>W</mml:mi>
<mml:mi>S</mml:mi>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>WS</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>F</mml:mi>
<mml:mi>P</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>FP</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>W</mml:mi>
<mml:mi>W</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>WW</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>M</mml:mi>
<mml:mi>G</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>MG</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>F</mml:mi>
<mml:mi>G</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>FG</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mtext>P</mml:mtext>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>HVAC</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>TLC</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>WS</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>FP</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>WW</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>MG</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mi>F</mml:mi>
<mml:mi>G</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(23)</label>
</disp-formula>where <inline-formula id="inf90">
<mml:math id="minf90">
<mml:mi>P</mml:mi>
</mml:math>
</inline-formula>, <inline-formula id="inf91">
<mml:math id="minf91">
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>V</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>C</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, etc. are the critical back-up systems and <inline-formula id="inf92">
<mml:math id="minf92">
<mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mtext>p</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf93">
<mml:math id="minf93">
<mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mtext>HVAC</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, etc. are the corresponding weights. As for the case of the critical unit functionality, the back-up systems are assumed non-functional if inundated by the tsunami. Hence, P, HVAC, etc., take a value of zero if the relevant back up system is located outside the inundation zone or is in a storey of the building above the local inundation depth, or 1 otherwise. An appropriate evaluation of the back-up system risk requires an understanding of these systems within the local context, and visual surveys play a key role in this. For example, in many hospital complexes the main HVAC systems may be complex mechanical systems with significant plant located within a hospital building, or housed in their own building. Alternatively, the HVAC system can be a distributed system across the hospital, as is seen in hospitals in Sri Lanka, where ventilation and air-conditioning equipment are distributed along the exterior walls of the hospital buildings and localized in each&#x20;unit.</p>
<p>Evaluation of the back-up system weights also accounts for the local context. The weights are determined by from a ranking of the back-up systems in order of importance for the continued functioning of the critical unit being assessed. This ranking is determined from a structured expert elicitation technique termed <italic>paired comparison</italic>. The paired comparison method is well established, and although simple, it is reproducible, accountable and neutral. In this method, participants are invited to complete a ranking exercise individually without being influenced by an in-depth prior discussion of how critical each back-up system is. Participants are invited to compare every two back-up systems (one in a row and another in the column in the table) and using their judgment to identify which is the more important for the continued functioning of critical hospital units. If they believe the system in the row is more important than the one in the column, they enter &#x201c;R&#x201d; in the relevant box. If they believe the contrary is true then &#x201c;C&#x201d; is entered into the box. Else if they believe both the back-up systems are of equal importance, &#x201c; &#x3d; &#x201d; is entered into the relevant box (<xref ref-type="table" rid="T1">Table&#x20;1</xref>).</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Fac-simile of the paired comparison questionnaire.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Which system is more critical in case of a tsunami?</th>
<th align="center">System 1</th>
<th align="center">System 2</th>
<th align="center">System 3</th>
<th align="center">&#x2026;</th>
<th align="center">System n</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">System 1</td>
<td align="left"/>
<td align="center">R</td>
<td align="center">C</td>
<td align="center">&#x3d;</td>
<td align="left"/>
</tr>
<tr>
<td align="left">System 2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="left">System 3</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="left">&#x2026;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="left">System n</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
</tr>
</tbody>
</table>
</table-wrap>
<p>The participants&#x2019; opinions are treated with equal weights. Only the participants who are found to provide very inconsistent responses, such that they appear statistically random are excluded, (i.e. consistent answers are those for which if A &#x3e; B and B &#x3e; C then A &#x3e; C is true). The paired comparison responses are then analyzed using the probabilistic inversion technique, as described in <xref ref-type="bibr" rid="B24">Kraan and Bedford (2005)</xref> and implemented in the free-software &#x201c;UNIBALANCE&#x201d; (<xref ref-type="bibr" rid="B25">Macutkiewicz and Cooke, 2006</xref>). This produces a mean score for each back-up system as well as the standard deviation around this mean score, which represents the level of disagreement within the expert group. These mean scores are adopted as the weights for the different back-up systems in the <italic>RRI</italic>
<sub>
<italic>bcs</italic>
</sub> calculation.</p>
<p>The level of agreement among the participants is examined in three different ways. Firstly, the degree of agreement is estimated by measuring how closely the pattern of the participants pairwise preferences match. Secondly, the degree of concordance is examined by measuring how similar the rank orders are among the group of participants. Thirdly, a chi-square test is used to check whether the group ranking preferences are made at random. Here, <italic>p</italic>-values below 0.05 indicate that the group ranking preferences have a structure and are not random. By contrast, <italic>p</italic>-values above 0.05 suggest a lack of consensus within the group regarding the ranking preferences.</p>
</sec>
</sec>
<sec id="s3">
<title>TRRI Rapid Visual Survey (RVS) Form</title>
<p>The <italic>TRRI Rapid Visual Survey (TRRI-RVS)</italic> form is developed to assist surveyors in assessing existing health facilities in terms of the integrity of hospital buildings, lifelines and back-up systems that support the service provision and hospital functionality. The <italic>TRRI-RVS</italic> form is presented in the Appendix (see <xref ref-type="sec" rid="s12">Supplementary Material</xref>). The Rapid Visual Survey consists of two sections:<list list-type="simple">
<list-item>
<p>1) <italic>Hospital Profile</italic> (&#x201c;<italic>Form H</italic>&#x201d;)<italic>.</italic> Through this form, surveyors collect general information about 1) the hospital location; 2) hospital type and hospital capacity, e.g., catchment population; 3) tsunami evacuation plans and disaster response plans; 4) hospital building locations within the healthcare facility; 5) location of critical hospital units within buildings, e.g., ICU, Labor Rooms, Maternity Wards, Pediatric Wards, Operating Theaters; and 6) presence and location of back-up supply systems.</p>
</list-item>
<list-item>
<p>2) <italic>Building Structural and Non-Structural Assessment</italic> (&#x201c;<italic>Form B</italic>&#x201d;). Through this form, surveyors gather information about: 1) the hospital building, e.g., number of storeys, year of construction, inter-storey height, and location of critical units; 2) the building surroundings, e.g., presence of containers, perimeter walls and vegetation; 3) building layout and elevation; 4) structural and non-structural systems; 5) The dimensions and structural details of the main structural elements, e.g., RC columns. The technical information is gathered using equipment such as rebar detector, laser distance meter, tape measure, and 3D cameras.</p>
</list-item>
</list>
</p>
<p>The <italic>TRRI-RVS</italic> form is specifically developed for collecting the attributes of hospital surroundings, buildings, critical units, lifeline and back-up systems required to evaluate <italic>TRRI</italic>. This form is used in the survey of Sri Lankan hospitals used to test the <italic>TRRI</italic> in this&#x20;paper.</p>
</sec>
<sec id="s4">
<title>Case-Study Application: Hospitals in Sri Lanka Southern Province</title>
<p>Sri Lanka provides universal healthcare to its people through an established and robust healthcare system. Thanks to this, no major disease outbreaks occurred after the 2004 tsunami (<xref ref-type="bibr" rid="B6">Carballo et&#x20;al., 2005</xref>), which hit two-thirds of the coastline affecting one million people. However, over 17% of all healthcare institutions were severely damaged, causing an estimated &#xa3;40&#xa0;M worth of losses (<xref ref-type="bibr" rid="B23">Komesaroff and Sundram, 2006</xref>). Over the last 15&#xa0;years some of the affected health infrastructure of Sri Lanka has been re-built further inland, but some significant hospitals still lie within 2&#x2013;3&#xa0;km from the coast and are at potential threat from tsunami inundation. The Sri Lankan Ministry of Health (MoH) in collaboration with World Health Organization (WHO) has been working to strengthen the health sector for emergencies, through the development of a comprehensive national disaster management plan (<xref ref-type="bibr" rid="B38">WHO, 2015</xref>). However, this plan comprises capacity building in emergency management and health financing, and does not yet look at the structural, non-structural and functional performance of hospitals in natural hazards. Furthermore, as Sri Lanka is threatened by distal tsunami generated either at the Sunda trench or Makran Subduction zone, the main disaster management approach considered to date is the evacuation of hospitals (<xref ref-type="bibr" rid="B13">DPRD, 2015</xref>).</p>
<p>In this case study application, three hospitals in Galle, Matara and Hambantota Districts in Sri Lanka are selected for testing whether the <italic>TRRI</italic> can be used to 1) identify weaknesses in the systems supporting the functionality of critical units in individual hospitals, and 2) as a tool for use in prioritizing interventions for improved functional resilience across a series of hospitals.</p>
<p>The three hospitals selected are the District General Hospital (DGH) in Matara and the base Hospitals (BH) in Balapitiya and Tangalle. These are chosen as they are key hospitals for the Southern Province, geographically distributed across the Province (<xref ref-type="fig" rid="F4">Figure&#x20;4</xref>) and all located within 400&#xa0;m from the coast (base Hospitals) or a litte further (approx. 600&#xa0;m) but near a waterway that discharges into the sea (DGH Matara). The case study application focuses on the five critical units that were indicated as the most important in the case of a disaster by the Disaster Preparedness and Response Division (DPRD) of the Sri Lankan Ministry of Health, Nutrition and Indigenous Medicine. These are: 1) Intensive Care Units (ICU); 2) Operating Theaters (OT); 3) Labor Rooms (LR); 4) Maternity Wards (MW); and 5) Pediatric Wards (PW). In the three hospitals, 19 buildings were found to house these critical units, and were surveyed by a joint team from UCL and University of Moratuwa in April 2019 using the form described in <italic>TRRI Rapid Visual Survey (RVS)&#x20;Form</italic>.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Case-study hospitals in Southern Province, Sri Lanka.</p>
</caption>
<graphic xlink:href="feart-09-626809-g004.tif"/>
</fig>
<p>Thirteen of the buildings are reinforced concrete moment resisting frame structures of 2&#x2013;4 storeys. These house 85% of all the critical units in these three hospitals. The remaining six buildings are one-storey load-bearing unreinforced masonry (URM) structures (<xref ref-type="fig" rid="F5">Figure&#x20;5</xref>). These structures are highly vulnerable to tsunami and would not be expected to be in an operational state following tsunami inundation. Hence, this assessment concentrates on the assessment of the 22 critical units housed in the RC buildings. The survey of these buildings highlighted that most of the critical units are located at the ground floor and are therefore at high risk from damage if the tsunami inundation reaches the building. The soil type at each hospital is determined as non-cohesive from observational and borehole data analysis. Hence all buildings are susceptible to scour in this case study application. None of the buildings assessed were located near ports and harbors, and are therefore not exposed to impact from containers, ships or barges. Consequently, the assumption of logs as debris is appropriate for this case&#x20;study.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Statistics of the hospital buildings and critical&#x20;units.</p>
</caption>
<graphic xlink:href="feart-09-626809-g005.tif"/>
</fig>
<p>The surveys showed the HVAC to be a local system of air conditioning units attached to the walls of critical units. Hence, they will continue to function if the critical unit is not inundated. The location of TLC systems is assumed to be in the hospital administrative offices. This is because Hospital Directors and administrative staff typically have access to the emergency systems for communicating with the national and district-level healthcare networks. Where back-up systems were not recorded during the field survey it is assumed they are missing. As this is detrimental to functional resilience, these back-up systems are still included in the calculation of <italic>RRI</italic>
<sub>bcs</sub> and contribute to increasing its value. For example, no fire alarms, extinguishers or other fire protection systems were observed in any of the assessed buildings, hence a value of <italic>FP</italic> &#x3d; 1 is applied for all buildings within the <italic>RRI</italic>
<sub>bcs</sub> calculation.</p>
<sec id="s4-1">
<title>Hazard Scenarios</title>
<p>A probabilistic tsunami hazard analysis for the Indian Ocean by (<xref ref-type="bibr" rid="B5">Burbidge et&#x20;al., 2009</xref>) shows that tsunami wave heights along the Sri Lankan coast could reach between 2.9&#x2013;3.7&#xa0;m for a return period of 2000&#xa0;years, with the south-east coast being associated with the highest hazard. However, this study does not provide the associated probabilistic tsunami onshore inundation depths (that would typically exceed the above) which would be what is required for the TRRI assessment.</p>
<p>A tsunami hazard map for Sri Lanka with associated inundation information was published by the Disaster Management Center (<xref ref-type="bibr" rid="B12">DMC, 2012</xref>), part of the Ministry of Public Administration and Disaster Management. This map is however not based on a probabilistic tsunami hazard assessment, but on deterministic inundations predicted by a numerical simulation of the 2004 Indian Ocean Tsunami by (<xref ref-type="bibr" rid="B39">Wijetunge, 2009</xref>). The DMC map identifies three distinct tsunami hazard zones along the Sri Lankan coast: 1) low hazard, where the inundation depth, <inline-formula id="inf94">
<mml:math id="minf94">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mn>0.5</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>m</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>, 2) moderate hazard, where <inline-formula id="inf95">
<mml:math id="minf95">
<mml:mrow>
<mml:mn>0.5</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>m</mml:mtext>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>m</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>, and 3) high hazard, where <inline-formula id="inf96">
<mml:math id="minf96">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mtext>m</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>. <xref ref-type="fig" rid="F6">Figure&#x20;6</xref> illustrates the tsunami hazard map for the city of Matara, where DGH Matara is located.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Tsunami hazard map for the city of Matara (<xref ref-type="bibr" rid="B12">DMC, 2012</xref>).</p>
</caption>
<graphic xlink:href="feart-09-626809-g006.tif"/>
</fig>
<p>In the absence of probabilistic tsunami onshore inundation information and a detailed topographical map, this study employs a simplified approach for the development of three tsunami inundation scenarios to check the performance of TRRI for different hazard intensities. The first realization, indicated as Hazard Level 1, is derived directly from the DMC map and represents the 2004 Indian Ocean Tsunami. It should be noted that the DMC map only defines distinct inundation depths and geographical boundaries for the moderate tsunami hazard zone. Hence, this zone is adopted as a reference for estimating the inundation depth at the hospital building locations. This is done by first drawing a transect indicating the shortest distance between the coast and the building being assessed. A linear relationship is assumed to describe the change in inundation depth along the transect between the seaward and inland boundaries of the moderate hazard zone, as shown in <xref ref-type="fig" rid="F7">Figure&#x20;7</xref>. The inundation depth at the building location <inline-formula id="inf97">
<mml:math id="minf97">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is then calculated from:<disp-formula id="e24">
<mml:math id="me24">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mi>min</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mi>d</mml:mi>
<mml:mi>D</mml:mi>
</mml:mfrac>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mi>max</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mi>min</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(24)</label>
</disp-formula>where <inline-formula id="inf98">
<mml:math id="minf98">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>max</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf99">
<mml:math id="minf99">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mtext>min</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the Hazard Level-based tsunami inundation depths at the edges of the moderate hazard band, <italic>D</italic> is the width of the moderate hazard zone along the transect, and <italic>d</italic> is the distance along the transect of the building to the edge of the moderate hazard&#x20;zone.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Method for calculating the Hazard Levels.</p>
</caption>
<graphic xlink:href="feart-09-626809-g007.tif"/>
</fig>
<p>The second and third tsunami inundation scenarios, indicated as Hazard Levels 2 and 3, are derived by increasing the inundation depths defining the DMC moderate hazard zone by 1.5&#xa0;m and 3&#xa0;m, respectively. By so doing, more severe inundations are produced at the hospital sites in terms of depth and inland extent, helping to demonstrate the methodology. A limitation of such an approach is that the hazard levels do not reflect a specific probability of occurrence. <xref ref-type="table" rid="T2">Table&#x20;2</xref> lists the resulting tsunami inundation depths for each buildings.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Hazard data for the surveyed hospital buildings.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Hospital</th>
<th rowspan="2" align="center">Building Id</th>
<th rowspan="2" align="center">Total no. of storeys</th>
<th rowspan="2" align="center">Critical unit</th>
<th colspan="3" align="center">
<inline-formula id="inf100">
<mml:math id="minf100">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">h</mml:mi>
<mml:mrow>
<mml:mtext>TSU</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (m)</th>
</tr>
<tr>
<th align="center">Hazard level 1</th>
<th align="center">Hazard level 2</th>
<th align="center">Hazard level 3</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="5" align="left">Balapitiya</td>
<td align="center">B7</td>
<td align="center">4</td>
<td align="center">ICU (x2)</td>
<td align="center">0.00</td>
<td align="center">0.00</td>
<td align="center">1.37</td>
</tr>
<tr>
<td align="center">B6</td>
<td align="center">3</td>
<td align="center">LR</td>
<td align="center">0.00</td>
<td align="center">0.00</td>
<td align="center">1.13</td>
</tr>
<tr>
<td align="center">B9</td>
<td align="center">1</td>
<td align="center">OT</td>
<td align="center">0.00</td>
<td align="center">0.00</td>
<td align="center">1.05</td>
</tr>
<tr>
<td align="center">B10</td>
<td align="center">3</td>
<td align="center">ICU, OT</td>
<td align="center">0.00</td>
<td align="center">0.00</td>
<td align="center">1.08</td>
</tr>
<tr>
<td align="center">B11</td>
<td align="center">2</td>
<td align="center">ICU, MW</td>
<td align="center">0.00</td>
<td align="center">0.00</td>
<td align="center">1.18</td>
</tr>
<tr>
<td rowspan="5" align="left">Matara</td>
<td align="center">M1</td>
<td align="center">3</td>
<td align="center">ICU (x2)</td>
<td align="center">0.57</td>
<td align="center">2.08</td>
<td align="center">3.58</td>
</tr>
<tr>
<td align="center">M12</td>
<td align="center">3</td>
<td align="center">OT</td>
<td align="center">0.43</td>
<td align="center">1.93</td>
<td align="center">3.43</td>
</tr>
<tr>
<td align="center">M15</td>
<td align="center">3</td>
<td align="center">ICU</td>
<td align="center">0.43</td>
<td align="center">1.93</td>
<td align="center">3.43</td>
</tr>
<tr>
<td align="center">M27</td>
<td align="center">2</td>
<td align="center">ICU, LR, MW, OT</td>
<td align="center">0.52</td>
<td align="center">2.01</td>
<td align="center">3.51</td>
</tr>
<tr>
<td align="center">M33</td>
<td align="center">1</td>
<td align="center">MW</td>
<td align="center">0.00</td>
<td align="center">0.87</td>
<td align="center">2.37</td>
</tr>
<tr>
<td rowspan="3" align="left">Tangalle</td>
<td align="center">T1</td>
<td align="center">3</td>
<td align="center">PW (x2)</td>
<td align="center">0.00</td>
<td align="center">0.00</td>
<td align="center">0.35</td>
</tr>
<tr>
<td align="center">T4</td>
<td align="center">2</td>
<td align="center">ICU</td>
<td align="center">0.00</td>
<td align="center">0.00</td>
<td align="center">0.67</td>
</tr>
<tr>
<td align="center">T9</td>
<td align="center">2</td>
<td align="center">MW (x2)</td>
<td align="center">0.00</td>
<td align="center">0.29</td>
<td align="center">1.79</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s4-2">
<title>Weighting of Back-Up Systems for <italic>RRI</italic>
<sub>bcs</sub>
</title>
<p>A small pool of five hospital administrators (doctors) from Sri Lanka participated in the paired comparison of back-up systems for the evaluation of <italic>RRI</italic>
<sub>bcs</sub>. <xref ref-type="table" rid="T3">Table&#x20;3</xref> presents the resulting mean scores, standard deviation, overall ranking and weights for the back-up systems. The <italic>p</italic>-values of individual participants is found to be less than 0.05, indicating that no participant randomly ranked the back-up systems. The high values of coefficients of concordance (0.73) and agreement (0.47) suggest an overall agreement among the participants regarding the position of each back-up system in the ranking order. The <italic>p</italic>-value below 0.05 obtained for the chi-square test also indicates that the group ranking preferences have a structure and are not random. In particular, the water supply and electric power systems have the two highest best estimate ranking scores, while fire protection and air conditioning the lowest.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Summary of results for the performed rankings.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Back-up systems</th>
<th align="center">Weight mean</th>
<th align="center">Weight st. Dev</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Electric power (EP)</td>
<td align="center">0.81</td>
<td align="center">0.11</td>
</tr>
<tr>
<td align="left">Water supply (WS)</td>
<td align="center">0.80</td>
<td align="center">0.15</td>
</tr>
<tr>
<td align="left">Telecommunications (TLC)</td>
<td align="center">0.62</td>
<td align="center">0.22</td>
</tr>
<tr>
<td align="left">Medical gas (MG)</td>
<td align="center">0.52</td>
<td align="center">0.21</td>
</tr>
<tr>
<td align="left">Fuel and gas services (FG)</td>
<td align="center">0.37</td>
<td align="center">0.26</td>
</tr>
<tr>
<td align="left">Wastewater (WW)</td>
<td align="center">0.36</td>
<td align="center">0.20</td>
</tr>
<tr>
<td align="left">Fire protection (FP)</td>
<td align="center">0.25</td>
<td align="center">0.21</td>
</tr>
<tr>
<td align="left">Air conditioning (HVAC)</td>
<td align="center">0.20</td>
<td align="center">0.14</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s5">
<title>Results of the Assessment of Critical Units for Sri Lankan Hospitals</title>
<p>
<xref ref-type="table" rid="T4">Table&#x20;4</xref> presents the values of <italic>TRRI</italic> calculated for the five critical units of the three case-study hospitals, for the three hazard scenarios presented in <italic>Hazard Scenarios</italic>. Under Hazard Level 1, none of the buildings containing critical units in BH Balapitiya and BH Tangalle are subjected to tsunami inundation. Despite this, the <inline-formula id="inf101">
<mml:math id="minf101">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>bcs</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values for these hospitals are non-zero due to their both not having any fire protection system, and BH Tangalle missing power and water back-up systems. For DGH Matara, the values of <inline-formula id="inf102">
<mml:math id="minf102">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>bldg</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> indicate that only building M15 would be likely to collapse due to scour (<inline-formula id="inf103">
<mml:math id="minf103">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>scour</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, see <xref ref-type="table" rid="T5">Table&#x20;5</xref>), with the other buildings not suffering major damage, (i.e. <inline-formula id="inf104">
<mml:math id="minf104">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>bldg</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>0.5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>). Despite the good building performance, five of the critical units would be directly inundated <inline-formula id="inf105">
<mml:math id="minf105">
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>funct</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, and four more critical units would likely be non-functional due to compromised back-up systems <inline-formula id="inf106">
<mml:math id="minf106">
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mtext>bcs</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>. The latter is due to the main back-up systems in this hospital being inundated. The consequence is that under this hazard scenario (and also for Hazard Levels 2 and 3), DGH Matara is predicted to lose functionality in all its critical units. Across the network of these three hospitals, this would mean a reduction of 40&#x2013;45% in the number of ICU and MW units, and of 50% in the number of LR and OT units. Loss of critical unit functionality at DGH Matara would put particular stress on BH Tangalle, which is the closest hospital to it, and which has only two ICU units overall (only one in an RC building) and no Operating Theater.</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Summary of <italic>TRRI</italic> calculated for the critical units under three hazard levels.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Unit</th>
<th rowspan="2" align="center">Bldg id</th>
<th rowspan="2" align="center">Floor</th>
<th colspan="4" align="center">Hazard level 1</th>
<th colspan="4" align="center">Hazard level 2</th>
<th colspan="4" align="center">Hazard level 3</th>
</tr>
<tr>
<th align="center">Bldg</th>
<th align="center">Funct</th>
<th align="center">Bcs</th>
<th align="center">
<italic>TRRI</italic>
</th>
<th align="center">Bldg</th>
<th align="center">Funct</th>
<th align="center">Bcs</th>
<th align="center">
<italic>TRRI</italic>
</th>
<th align="center">Bldg</th>
<th align="center">Funct</th>
<th align="center">Bcs</th>
<th align="center">
<italic>TRRI</italic>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">ICU</td>
<td align="center">B11</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.3</td>
<td align="center">0.3</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">M15</td>
<td align="center">GF</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">T4</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.5</td>
<td align="center">0.5</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.8</td>
<td align="center">0.8</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">B10</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.4</td>
<td align="center">0.4</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">M27</td>
<td align="center">GF</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">B7</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.4</td>
<td align="center">0.4</td>
<td align="center">1.0</td>
<td align="center">0.0</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">M1</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.5</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">M1</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.5</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">B7</td>
<td align="center">2&#xa0;F</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.4</td>
<td align="center">0.4</td>
<td align="center">1.0</td>
<td align="center">0.0</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">LR</td>
<td align="center">B6</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.4</td>
<td align="center">0.4</td>
<td align="center">0.3</td>
<td align="center">1.0</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">LR</td>
<td align="center">M27</td>
<td align="center">GF</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">M33</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">T9</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.5</td>
<td align="center">0.5</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">0.8</td>
<td align="center">1.0</td>
<td align="center">0.6</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">M27</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.2</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.7</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">T9</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.5</td>
<td align="center">0.5</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.8</td>
<td align="center">0.8</td>
<td align="center">0.6</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">B11</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.3</td>
<td align="center">0.3</td>
<td align="center">1.0</td>
<td align="center">0.0</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">B9</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.3</td>
<td align="center">0.3</td>
<td align="center">0.3</td>
<td align="center">1.0</td>
<td align="center">0.4</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">M27</td>
<td align="center">GF</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">B10</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.4</td>
<td align="center">0.4</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">M12</td>
<td align="center">2&#xa0;F</td>
<td align="center">0.2</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.6</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">PW</td>
<td align="center">T1</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.5</td>
<td align="center">0.5</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.8</td>
<td align="center">0.8</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">PW</td>
<td align="center">T1</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.5</td>
<td align="center">0.5</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.8</td>
<td align="center">0.8</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Summary of <italic>RRI</italic>
<sub>bldg</sub> calculated for the critical units under three hazard levels.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Unit</th>
<th rowspan="2" align="center">Bldg id</th>
<th rowspan="2" align="center">Floor</th>
<th colspan="4" align="center">Hazard level 1</th>
<th colspan="4" align="center">Hazard level 2</th>
<th colspan="4" align="center">Hazard level 3</th>
</tr>
<tr>
<th align="center">Struct</th>
<th align="center">Debris</th>
<th align="center">Scour</th>
<th align="center">Bldg</th>
<th align="center">Struct</th>
<th align="center">Debris</th>
<th align="center">Scour</th>
<th align="center">Bldg</th>
<th align="center">Struct</th>
<th align="center">Debris</th>
<th align="center">Scour</th>
<th align="center">Bldg</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">ICU</td>
<td align="center">B11</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.3</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">M15</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.4</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">T4</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.1</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.1</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">B10</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.3</td>
<td align="center">0.3</td>
<td align="center">0.5</td>
<td align="center">0.5</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">M27</td>
<td align="center">GF</td>
<td align="center">0.1</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.7</td>
<td align="center">0.2</td>
<td align="center">0.4</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">B7</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.3</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">M1</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.1</td>
<td align="center">0.2</td>
<td align="center">0.5</td>
<td align="center">0.5</td>
<td align="center">0.8</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">M1</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.1</td>
<td align="center">0.2</td>
<td align="center">0.5</td>
<td align="center">0.5</td>
<td align="center">0.8</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">B7</td>
<td align="center">2&#xa0;F</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.3</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">LR</td>
<td align="center">B6</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.3</td>
<td align="center">0.3</td>
<td align="center">0.3</td>
</tr>
<tr>
<td align="left">LR</td>
<td align="center">M27</td>
<td align="center">GF</td>
<td align="center">0.1</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.7</td>
<td align="center">0.2</td>
<td align="center">0.4</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">M33</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.6</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">T9</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.6</td>
<td align="center">0.3</td>
<td align="center">0.3</td>
<td align="center">0.6</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">M27</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.1</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.7</td>
<td align="center">0.2</td>
<td align="center">0.4</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">T9</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.6</td>
<td align="center">0.3</td>
<td align="center">0.3</td>
<td align="center">0.6</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">B11</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.3</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">B9</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.1</td>
<td align="center">0.3</td>
<td align="center">0.3</td>
<td align="center">0.3</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">M27</td>
<td align="center">GF</td>
<td align="center">0.1</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.7</td>
<td align="center">0.2</td>
<td align="center">0.4</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">B10</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.3</td>
<td align="center">0.3</td>
<td align="center">0.5</td>
<td align="center">0.5</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">M12</td>
<td align="center">2&#xa0;F</td>
<td align="center">0.1</td>
<td align="center">0.0</td>
<td align="center">0.2</td>
<td align="center">0.2</td>
<td align="center">0.6</td>
<td align="center">0.1</td>
<td align="center">0.4</td>
<td align="center">0.6</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">PW</td>
<td align="center">T1</td>
<td align="center">GF</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
</tr>
<tr>
<td align="left">PW</td>
<td align="center">T1</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
<td align="center">0.0</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Under Hazard Level 2, BH Balapitiya remains outside the inundation zone, but building T9 of BH Tangalle is subjected to a small inundation of 0.29&#xa0;m depth. This inundation is insufficient to cause structural damage in this building but does compromise the functionality of one of the Maternity Wards, as this is located at the ground floor of T9. Moreover, all other critical units in BH Tangalle are seen to be at significant risk of functionality loss from damaged back-up systems. Hazard Level 2 imposes a larger inundation depth at DGH Matara, which results in three predicted building collapses <inline-formula id="inf107">
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</inline-formula> for all units. If this can be prevented, BH Tangalle would be able to operate 50% of its the Maternity and Pediatric Wards (since buildings T1 and T9 have <inline-formula id="inf112">
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</inline-formula>, respectively, and their first floors have <inline-formula id="inf113">
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<p>The results of the analysis of <italic>TRRI</italic> for the three hospitals and Hazard Levels shows a high vulnerability of back-up systems and critical units under low levels of tsunami inundation. This is caused by most being located on the ground floor of inundated buildings (see <xref ref-type="table" rid="T4">Table&#x20;4</xref>). These two components of <italic>TRRI</italic> are seen to dominate whether or not critical units will be operational after a &#x201c;small to moderate&#x201d; tsunami event (Hazard Levels 1 and 2). Note that <italic>TRRI</italic> &#x3d; 1.0 for nearly half of the units (45% of the total) at Hazard Level 2, although <inline-formula id="inf114">
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</inline-formula> only for 18% of them. Hence, re-positioning critical units and back-up systems to higher floors within the surveyed buildings would improve the functional resilience of the hospitals. Building failure plays an increasing role in the critical unit operationality for &#x201c;moderate to high&#x201d; tsunami events (Hazard Levels 2 and 3). At Hazard Level 3, all 22 units have <italic>TRRI</italic> &#x3d; 1.0, of which 13 units (59%) also have <inline-formula id="inf115">
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</inline-formula>. In particular scour of foundations can precipitate building failure. Protection against scour would require the installation of piles or deeper foundations. This is more appropriate as a design improvement for future hospital buildings, since this can be disruptive and expensive as a retrofit intervention.</p>
</sec>
<sec id="s6">
<title>What-If Scenarios</title>
<p>Given the findings in <italic>Results of the Assessment of Critical Units for Sri Lankan Hospitals</italic>, this section presents a comparison of the effectiveness of three possible interventions in reducing the immediate loss of operationality of critical units after a tsunami. The intervention effectiveness is examined by running &#x201c;what-if&#x201d; scenarios, wherein the intervention is applied to all buildings and <italic>TRRI</italic> is recalculated. The effectiveness of the intervention on each critical unit type is represented as the ratio between the number of functional units for the intervention and baseline scenarios (Note: the baseline is the no-intervention scenario). The &#x201c;what-if&#x201d; scenarios considered are:<list list-type="simple">
<list-item>
<label>&#x2022;</label>
<p>What-if 1 (WI1) consists in the relocation of back-up systems to places that are not affected by the tsunami inundation, e.g., by either relocating or elevating the system to be outside the inundation zone. Within this scenario, any missing back-up system, other than Fire Protection and HVAC (as these are co-located with the critical unit) are installed.</p>
</list-item>
<list-item>
<label>&#x2022;</label>
<p>What-if 2 (WI2) consists in the relocation of critical units one storey up from their current position in the building that houses them. Where the unit is already located in the uppermost floor of the building, it is assumed to remain in its current position.</p>
</list-item>
<list-item>
<label>&#x2022;</label>
<p>What-if 3 (WI3) combines the effects of adopting WI1 and WI2, i.e.,&#x20;both relocation of back-up systems and critical units. In this case Fire Protection and HVAC are also installed if missing, and are assumed to be co-located with the newly positioned critical&#x20;units.</p>
</list-item>
</list>
</p>
<p>
<xref ref-type="table" rid="T6">Table&#x20;6</xref> presents the <italic>TRRI</italic> resulting from implementation of the three &#x201c;what-if&#x201d; scenarios and the baseline (no intervention) scenario for the three Hazard Levels. <xref ref-type="table" rid="T7">Table&#x20;7</xref> summarizes the effectiveness of each &#x201c;what-if&#x201d; scenario in increasing the number of operational critical units after a tsunami, as compared to the baseline scenario. In <xref ref-type="table" rid="T7">Table&#x20;7</xref>, the effectiveness of the &#x201c;what-if&#x201d; scenario, indicated as <inline-formula id="inf116">
<mml:math id="minf116">
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</mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>, is calculated for each critical unit type, as follows:<disp-formula id="e25">
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<label>(25)</label>
</disp-formula>where <inline-formula id="inf117">
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<mml:mi>n</mml:mi>
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</inline-formula> is the total number of units (for each type), <inline-formula id="inf118">
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</inline-formula> is the number of operational units in the &#x201c;what-if&#x201d; scenario, and <inline-formula id="inf119">
<mml:math id="minf119">
<mml:mrow>
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</inline-formula> is the number of operational units for the baseline scenario.</p>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>Summary of <italic>TRRI</italic> for the critical units under three hazard levels: baseline scenario and three different What-If (WI) scenarios.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Unit</th>
<th rowspan="2" align="center">Bldg id</th>
<th rowspan="2" align="center">Floor</th>
<th colspan="4" align="center">
<italic>TRRI</italic>&#x2014;hazard level 1</th>
<th colspan="4" align="center">
<italic>TRRI</italic>&#x2014;hazard level 2</th>
<th colspan="4" align="center">
<italic>TRRI</italic>&#x2014;hazard level 3</th>
</tr>
<tr>
<th align="center">Base-line</th>
<th align="center">WI1</th>
<th align="center">WI2</th>
<th align="center">WI3</th>
<th align="center">Base-line</th>
<th align="center">WI1</th>
<th align="center">WI2</th>
<th align="center">WI3</th>
<th align="center">Base-line</th>
<th align="center">WI1</th>
<th align="center">WI2</th>
<th align="center">WI3</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">ICU</td>
<td align="center">B11</td>
<td align="center">GF</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.3</td>
<td align="center">0.1</td>
<td align="center">0.3</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">M15</td>
<td align="center">GF</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">T4</td>
<td align="center">GF</td>
<td align="center">0.5</td>
<td align="center">0.1</td>
<td align="center">0.5</td>
<td align="center">0.1</td>
<td align="center">0.8</td>
<td align="center">0.1</td>
<td align="center">0.8</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">B10</td>
<td align="center">GF</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.4</td>
<td align="center">0.1</td>
<td align="center">0.4</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.5</td>
<td align="center">0.5</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">M27</td>
<td align="center">GF</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">B7</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.4</td>
<td align="center">0.1</td>
<td align="center">0.4</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">M1</td>
<td align="center">1&#xa0;F</td>
<td align="center">1.0</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">M1</td>
<td align="center">1&#xa0;F</td>
<td align="center">1.0</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
<td align="center">0.5</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">ICU</td>
<td align="center">B7</td>
<td align="center">2&#xa0;F</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.4</td>
<td align="center">0.1</td>
<td align="center">0.4</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">LR</td>
<td align="center">B6</td>
<td align="center">GF</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.4</td>
<td align="center">0.1</td>
<td align="center">0.4</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.5</td>
<td align="center">0.3</td>
</tr>
<tr>
<td align="left">LR</td>
<td align="center">M27</td>
<td align="center">GF</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">M33</td>
<td align="center">GF</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">T9</td>
<td align="center">GF</td>
<td align="center">0.5</td>
<td align="center">0.1</td>
<td align="center">0.5</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.8</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.6</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">M27</td>
<td align="center">1&#xa0;F</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">T9</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.5</td>
<td align="center">0.1</td>
<td align="center">0.5</td>
<td align="center">0.1</td>
<td align="center">0.8</td>
<td align="center">0.1</td>
<td align="center">0.8</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">0.6</td>
<td align="center">1.0</td>
<td align="center">0.6</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">B11</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.3</td>
<td align="center">0.1</td>
<td align="center">0.3</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">B9</td>
<td align="center">GF</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.3</td>
<td align="center">0.1</td>
<td align="center">0.3</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">M27</td>
<td align="center">GF</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.7</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">B10</td>
<td align="center">GF</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.2</td>
<td align="center">0.1</td>
<td align="center">0.4</td>
<td align="center">0.1</td>
<td align="center">0.4</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.5</td>
<td align="center">0.5</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">M12</td>
<td align="center">2&#xa0;F</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">0.6</td>
<td align="center">1.0</td>
<td align="center">0.6</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
</tr>
<tr>
<td align="left">PW</td>
<td align="center">T1</td>
<td align="center">GF</td>
<td align="center">0.5</td>
<td align="center">0.1</td>
<td align="center">0.5</td>
<td align="center">0.1</td>
<td align="center">0.8</td>
<td align="center">0.1</td>
<td align="center">0.8</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
</tr>
<tr>
<td align="left">PW</td>
<td align="center">T1</td>
<td align="center">1&#xa0;F</td>
<td align="center">0.5</td>
<td align="center">0.1</td>
<td align="center">0.5</td>
<td align="center">0.1</td>
<td align="center">0.8</td>
<td align="center">0.1</td>
<td align="center">0.8</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
<td align="center">1.0</td>
<td align="center">0.1</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T7" position="float">
<label>TABLE 7</label>
<caption>
<p>Summary of the effectiveness of each What-If (WI) scenario.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Unit</th>
<th colspan="3" align="center">
<italic>E</italic>
<sub>WI</sub>&#x2014;hazard level 1</th>
<th colspan="3" align="center">
<italic>E</italic>
<sub>WI</sub>&#x2014;hazard level 2</th>
<th colspan="3" align="center">
<italic>E</italic>
<sub>WI</sub>&#x2014;hazard level 3</th>
</tr>
<tr>
<th align="center">WI1</th>
<th align="center">WI2</th>
<th align="center">WI3</th>
<th align="center">WI1</th>
<th align="center">WI2</th>
<th align="center">WI3</th>
<th align="center">WI1</th>
<th align="center">WI2</th>
<th align="center">WI3</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">ICU</td>
<td align="center">0.22</td>
<td align="center">0</td>
<td align="center">0.44</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0.11</td>
<td align="center">0</td>
<td align="center">0.11</td>
<td align="center">0.22</td>
</tr>
<tr>
<td align="left">LR</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0.50</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0.50</td>
<td align="center">0</td>
<td align="center">0.50</td>
<td align="center">0.50</td>
</tr>
<tr>
<td align="left">MW</td>
<td align="center">0.20</td>
<td align="center">0</td>
<td align="center">0.20</td>
<td align="center">0.20</td>
<td align="center">0.20</td>
<td align="center">0.40</td>
<td align="center">0.20</td>
<td align="center">0</td>
<td align="center">0.40</td>
</tr>
<tr>
<td align="left">OT</td>
<td align="center">0.25</td>
<td align="center">0</td>
<td align="center">0.50</td>
<td align="center">0.25</td>
<td align="center">0</td>
<td align="center">0.50</td>
<td align="center">0</td>
<td align="center">0.25</td>
<td align="center">0.25</td>
</tr>
<tr>
<td align="left">PW</td>
<td align="center">0<xref ref-type="table-fn" rid="Tfn1">
<sup>a</sup>
</xref>
</td>
<td align="center">0<xref ref-type="table-fn" rid="Tfn1">
<sup>a</sup>
</xref>
</td>
<td align="center">0<xref ref-type="table-fn" rid="Tfn1">
<sup>a</sup>
</xref>
</td>
<td align="center">0<xref ref-type="table-fn" rid="Tfn1">
<sup>a</sup>
</xref>
</td>
<td align="center">0<xref ref-type="table-fn" rid="Tfn1">
<sup>a</sup>
</xref>
</td>
<td align="center">0<xref ref-type="table-fn" rid="Tfn1">
<sup>a</sup>
</xref>
</td>
<td align="center">0.50</td>
<td align="center">0.50</td>
<td align="center">1.0</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="Tfn1">
<label>
<sup>a</sup>
</label>
<p>indicates that all critical units were predicted as functional in the baseline scenario for the Hazard Level considered.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>From <xref ref-type="table" rid="T6">Tables 6</xref> and <xref ref-type="table" rid="T7">7</xref> it is observed that moving the back-up systems to a safe location (WI1) significantly improves the number of operational MW, OT and PW available after tsunami for all Hazard Levels, but is not effective in improving the number of operational ICU and LR units with respect to the baseline for tsunami above Hazard Level 1. This is because many critical units remain vulnerable to direct tsunami inundation.</p>
<p>Implementation of WI2 provides no/little improvement over the baseline scenario for Hazard Levels 1 and 2, as the failure of back-up systems in DGH Matara and BH Tangalle compromise their critical unit operationality and BH Balapitiya is not inundated at these Hazard Levels. However, for Hazard Level 3, despite inundation of BH Balapitiya, some of the back-up systems are not compromised and by elevating the critical units their risk of direct inundation is reduced and their operationality maintained.</p>
<p>An increased effectiveness is observed for What-If scenario 3, as compared to either WI1 or WI2 individually. The combined intervention on back-up systems and critical units is more beneficial than the sum of their individual effects. This is because in WI3 any missing back-up systems are added to the hospital buildings, and the HVAC and Fire Protection systems are moved to upper levels with the critical units, thus joining the other back-up systems in being in a safe location. This results in <italic>RRI</italic>
<sub>bcs</sub> values close to zero, which when combined with the reduced risk of critical unit inundation, results in 95%, 82%, and 64% of all critical units being operational under Hazard Levels, 1, 2, and 3, respectively. It is highlighted that even in WI3, ICU and OT remain at significant risk from tsunami of Hazard Level 3, with only one quarter of the units predicted to remain operational. To further increase their tsunami resilience, interventions would be needed on the buildings that house these critical units, in order to improve their structural and foundation systems. The <italic>TRRI</italic> analysis prioritizes buildings M1, M15, and M27 in DGH Matara for such interventions, as these are predicted to suffer heavy damage and/or collapse under the tsunami hazard scenarios, even though the risk to back-up systems and critical units can be reduced through&#x20;WI3.</p>
<p>The suggested interventions are not based on financial considerations or other constraints, and are applied to all three hospitals. However, it is clear that the <italic>TRRI</italic> and proposed efficiency measure <inline-formula id="inf120">
<mml:math id="minf120">
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mtext>WI</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> can be adopted for other What-If scenarios that could apply more targeted or different interventions on single hospitals or buildings to optimize the cost-to-benefit. The advantage of the <italic>TRRI</italic> is that such interventions can be explored across single or multiple hospitals in a manner that is not computationally expensive and does not require high levels of technical expertise.</p>
</sec>
<sec sec-type="conclusion" id="s7">
<title>Conclusion</title>
<p>This paper presents a new tsunami relative risk index <inline-formula id="inf121">
<mml:math id="minf121">
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>R</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> for the assessment of risk to critical units in hospitals exposed to tsunami inundation. The <italic>TRRI</italic> is a quantitative index that considers tsunami risk to 1) the hospital buildings housing critical units, with tsunami hydrodynamic loading, debris impact and scour considered, 2) the critical units themselves and 3) the critical back-up systems that support the functioning of critical units. Each component of tsunami risk is evaluated on a scale of 0 (no risk) to 1 (high risk), and the overall risk to the critical unit is taken as the highest value from the three components. A methodology is provided for the simple evaluation of the tsunami risk indices for each component that draws upon engineering principles and practice, physical interpretation of tsunami risk and expert elicitation. The <italic>TRRI</italic> approach is tested for a case study of three hospitals in Sri Lanka, wherein the <italic>TRRI</italic> is used to assess the number of critical units (that are housed in reinforced concrete buildings) remaining operational after tsunami inundations of three intensities. It is demonstrated that the <italic>TRRI</italic> approach allows the identification of the drivers of loss of operationality of critical units under the different hazard scenarios. The <italic>TRRI</italic> analysis for the three hospitals show a high functional vulnerability of back-up systems and critical units under low levels of tsunami inundation. These findings can inform decisions to be made as to interventions for improving the operational resilience of critical units within a single hospital complex, as well as across a network of hospitals to ensure health service provision. The latter is demonstrated by conducting a series of &#x201c;what-if&#x201d; scenarios for different interventions on the case study hospital network and re-calculating the <italic>TRRI</italic> values for each critical unit. Comparison of the number of critical units predicted to be functional after a tsunami under the baseline scenario, (i.e. no intervention) and the different &#x201c;what-if&#x201d; scenarios, allows the identification of individual and combined interventions in improving the tsunami resilience of healthcare provision across the hospital system. For the three hospitals in Sri Lanka, relocating back-up systems and units to safe locations would be an effective intervention; however, under large tsunami events the hospital buildings and their foundations are predicted to suffer heavy damage and/or collapse.</p>
</sec>
</body>
<back>
<sec id="s8">
<title>Data Availability Statement</title>
<p>The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.</p>
</sec>
<sec id="s9">
<title>Author Contributions</title>
<p>TR, MB, and PD developed the aim, goals and scope of this study. MB, JP, DR, CS, and HH carried out the fieldwork activity in Sri Lanka. TR, MB, JP, PD, SLQ, and II developed the methodology. MB and JP developed the R script to perform the analysis. MB, TR, JP, and PD contributed to writing the text and producing the figures presented.</p>
</sec>
<sec id="s10">
<title>Funding</title>
<p>This work is part of the project titled &#x201c;Hospital Engineering Assessment for Resilience to Tsunami and Storm surge&#x2014;Sri Lanka&#x201d; (HEARTS-SL), funded by Research England (Award 177,813) via Global Challenges Research Fund. The project grant was awarded to Prof Tiziana Rossetto.</p>
</sec>
<sec sec-type="COI-statement" id="s11">
<title>Conflict of Interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<ack>
<p>The authors acknowledge the support of Disaster Preparedness and Response Division (Ministry of Health, Nutrition and Indigenous Medicine, Sri Lanka) in providing valuable advice and assistance; and also the cooperation of the directors of the hospitals surveyed. Other members that are acknowledged for their support and help are Dr. Carmine Galasso and Prof Ian Eames from UCL, and Eng. Devmini Kularatne, Eng. Ishani Shehara, Mr. S. Harisuthan and Mr. Bahirathan Koneswaran from University of Moratuwa.</p>
</ack>
<sec id="s12">
<title>Supplementary Material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/feart.2021.626809/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/feart.2021.626809/full&#x23;supplementary-material</ext-link>.</p>
<supplementary-material xlink:href="datasheet1.pdf" id="SM1" mimetype="application/pdf" xmlns:xlink="http://www.w3.org/1999/xlink"/>
<supplementary-material xlink:href="datasheet2.pdf" id="SM2" mimetype="application/pdf" xmlns:xlink="http://www.w3.org/1999/xlink"/>
</sec>
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