Research and Applications in Structural Engineering, Mechanics and Computation – Zingoni (Ed.)© 2013 Taylor & Francis Group, London, ISBN 978-1-138-00061-2

Causal models for the forensic investigation of structural failures

S. Arangio, C. Crosti & F. BontempiSapienza University of Rome, Italy

ABSTRACT: The structural collapses are rare events that are characterized by complex dynamics: the identifi-cation of their causes and the explanation of their developments are not straightforward processes and depend onnumerous different factors. A fundamental aspect is that, even if sometimes it is possible to identify the triggerthat have materially caused the collapse, usually there is a complex background of situations that have made theevent possible and that need to be accurately analyzed. The investigation of the interrelated aspects and con-current causes is a fundamental task to assign conveniently the civil and criminal responsibilities. Starting fromthese considerations, the aim of this paper is to present some concepts that, in the Authors’ opinion, constitute abasis for the framework of the investigation activities. In the first part of the work two concepts are discussed. Thefirst one is the concept of structural complexity, which is an attribute of the civil constructions that are charac-terized by significant interactions, strong nonlinearities, and large uncertainties. The second concept regards theextension to the Civil Engineering field of a model for the development of failures proposed by Reason (SwissCheese Model, 1990). In the second part of the paper some operational approaches are briefly introduced: thebreakdown of the problem and the analysis of the timeline; they are essential tools for the assignment of thevarious responsibility profiles. At the end of the contribution, the concept of structural dependability is recalledas an antidote to avoid failures providing high-quality structural design.

1 INTRODUCTION

The investigation of the causes of a structural fail-ure is a delicate and challenging process that baresthe intimate behavior of a structure and points out itsrelationships with the project environment.

The forensic engineer should be able to identify andexplain the causes of the structural failures, intendingwith “failure” not only the catastrophic collapses thatmay even result in loss of life, but including all thosesituations where there is an unacceptable differencebetween the expected and observed performance.

The solution is found in an iterative way, through theaccurate examination of all the available documents,including the declarations of the involved people, andby carrying out the necessary experimental and numer-ical analyses. On the whole, it is an incremental andnonlinear process that needs precise strategies for itsconvergence. In fact, even if sometimes it is possibleto identify the trigger that has materially caused thecollapse, usually there is a complex background ofsituations that have made the event possible.

A fundamental task of the investigation process isthe analysis of the conduct of the various involved parts(designers, managers, contractors, users, etc). Theircivil and criminal responsibilities have to be attributedaccording to the relevance of the consequences of thefailure for the Civil Society (Carper, 2002).

The aim of this paper is to present some conceptsthat, in the Authors’ opinion, constitute a basis forthe framework of the investigation activities. The first

one is the concept of structural complexity whilethe second one regards a model for the developmentof failures adapted from the Reason’s Swiss CheeseModel (1990).

These two concepts can be profitably applyingby making use of some operational tools, which arebriefly discussed in the second part of the paper: thebreakdown of the problem and the analysis of thetimeline; they are essential tools for the convenientassignment of the responsibility profiles.

At the end of the contribution the concept ofstructural dependability is proposed as an antidote toavoid failures providing an effective approach for ahigh-quality structural design.

2 COMPLEXITY

2.1 Definition of complexity

An interesting definition of complexity (of a system ora problem), that can be easily interpreted in an opera-tional way, comes from the graph in Figure 1 (adaptedby Perrow, 1984). The plot shows a three dimensionalreference system where the axes indicate:

1. The nonlinearities of the system/problem. In thestructural field, the nonlinearities affect the behav-ior at different levels: at a detailed micro-level, forexample, they influence the mechanical propertiesof the materials; their effect depends on the typeof materials: it is weak in case of ductile materials

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Figure 1. Aspects that increase the complexity of a problem.

while it is significant for example in case of no-tensile materials; at a macro-level the nonlinearitieshave effects on single elements or even on theentire structure; an example is given by the insta-bility phenomenon that can lead to strong nonlinearbehavior.

2. The interactions and the connections between thevarious parts: if they are tight, the situations is con-sidered complex while when the connections areslack some tolerance exists.

3. The intrinsic uncertainties of the problem/system;they could have both stochastic and epistemicnature.

In this reference system the overall complexity ofthe problem/system increases as the values in the axesincrease, so passing from linear to nonlinear behav-ior, from loose to tight interactions, from low to highuncertainty.

In the Civil Engineering field, a practical (and alsocommon) case that presents the three components ofcomplexity indicated above, is the intervention onexisting adjacent masonry buildings.

According to the Eurocode 8-3, when we are deal-ing with existing masonry buildings there are somegeneral aspects that should be carefully examined:

• physical condition of masonry elements and pres-ence of any degradation or modification respect tothe original situation;

• configuration of the masonry elements and theirconnections, as well as the continuity of load pathsbetween lateral resisting elements; it is importantto keep in mind that the buildings show the levelof knowledge at the time of their construction andsome defects in the design or in the manufacturingcan exist, even if it is not evident at a first sight;

• properties of in-place materials of masonry ele-ments and connections;

• the presence of nonstructural components and thedistance between partition walls;

• information on adjacent buildings potentially inter-acting with the building under consideration.

For the definition of the structural models it shouldbe considered that:

• the geometry, the details and the dead loadare assigned but our knowledge depends on the

Figure 2. Example of an aggregate of buildings and identi-fication of a single structural unity (from Borri and De Maria,2009).

available documents and on the accuracy of theinvestigations;

• the knowledge on the mechanical properties of thematerial are related to the accuracy and reliabilityof the investigation;

• the design approach depends on the completenessand reliability of the gathered information. In orderto take into account the uncertainties, the capacityparameters can be modified by using specific con-fident factors that vary according to the level ofknowledge.

From these recommendations it is evident that, incase of interventions on existing adjacent buildings, apreventive evaluation of the interactions between thebuildings and an accurate and reliable investigation arenecessary. Moreover, even if the works will affect onlyone of the buildings, the entire design process shouldbe carried out considering the effects of the varioussteps of the work on the adjacent ones.

The Italian Building Code (NTC 2008), that couldbe considered as a draft of the Italian national annexof the Eurocodes, is even more specific on this topic.Particular attention is devoted to the assessment of thehistorical heritage and it is introduced the concept of“aggregate of buildings” in order to standardize theprocedure for dealing with adjacent buildings.

An “aggregate of buildings” is delimited by anopen space and it is composed by various adjacentnon-uniform constructions (Figure 2). The constitut-ing buildings have been built in different epochs, withdifferent materials. They had different owners andusually experienced different uses and modificationsduring time. In the analysis of a single structural unitit is necessary to take into account the possible inter-actions arising from the structural contiguity with theadjacent buildings. Neglecting these aspects can havesignificant consequences on the structures even up theoccurrence of catastrophic collapses (Figure 3).

Among the possible interactions between adjacentbuildings, it should be considered the influence ofloads (both vertical and horizontal) transmitted byfloors or walls of adjacent units and the actions ofarches or vaults that belong to contiguous buildings.The accurate representation of the unit under inves-tigation through plants and sections will allow theevaluation of the stress distribution and the effectof the interactions. In addition to the standard pro-cedure that are carried out for isolated buildings, incase of adjacent buildings it should be evaluated also

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Figure 3. An example of an aggregate of building thatexperience a catastrophic collapse: some interventions on aninternal unit were carried out without taking into account theinteractions with the adjacent units (Barletta, Italy, 2011).

Figure 4. Sensibility of the structural response to thevariation of a parameter.

the local effects due to not non-aligned floors orfacades, the influence of differences in height or stiff-ness between adjacent units, the possibility of rotationsor translations of the external walls of aggregate.

2.2 Sensibility and structural robustness

There are two other aspects that are strictly related tothe complexity of a system/problem.

The first one regards the sensibility of a responseto a specific parameter: Figure 4 shows the differ-ence in the structural response between a parameterthat strongly influences the behavior (on the left) andanother one that needs a large variation for changingsignificantly the results (on the right).

The mechanical interpretation of the concept ofsensibility lead to the concept of structural robust-ness, which is schematically represent in Figure 5. Thegraph shows the variation of the quality (y-axis) in time(x-axis) of two different structural systems. The first

Figure 5. Variation in time of the performance of a robustsystem (in blue) and a not robust system (in green).

Figure 6. General model for the development of a failure –Swiss Cheese Model (Reason, 1991).

one (green curve) shows a better performance at thebeginning respect to the other one (blue curve), how-ever its performance decreases rapidly in time andit crosses the threshold that represents the minimumrequired performance earlier. On the other hand, theblue one, even if it shows a lower level of performanceat the beginning, it is able to maintain it longer andafter time it is still above the limit also in presence ofsome damage. The blue curve is representative of asystem with a robust behavior.

Those structural situations that show to be verysensible to some parameters or that are lacking ofrobustness will exhibit a complex behavior and wouldneed specific investigations (Bontempi et al., 2007).

3 SWISS CHEESE MODEL

It is interesting to observe that, even if the accidentalsituations have different nature and each one has pecu-liar characteristics, a general model able to representin a synthetic way the origin and the development of afailure can be proposed.

According to Reason (1991), it is possible to con-sider a model of development composed by varioussteps. They can be conceptual or actual steps and canregard material aspects or human behaviors: each ofthem can be seen as an ideal layer (Fig. 6).

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Figure 7. Functional/hierarchical breakdown of a prob-lem/system.

Actually, each layer has imperfections and defi-ciencies that represent fault and errors for the system(Minato, 2003; Chong & Low, 2006). In Figure 6, theseare represented by holes in the layers. The model pre-dicts that, also if a single shortage is not critical, analignment of these weaknesses (hazards), can lead toa failure. The graphical representation of the modelexplains its original name: the Swiss Cheese model(Reason, 1991).

4 BREAKDOWN

The previous sections dealt with the concept of com-plexity and with the extension of a model for repre-senting the development of a structural failure. Thisframework is still missing the operational point ofview; two operational tools that can significantly helpin the investigation are the spatial decomposition of theproblem (breakdown) and the analysis of its temporalevolution (timeline).

The hierarchical/functional breakdown of a prob-lem (or a system) can be represented graphically (asshown in Figure 7) by a pyramid, set up with vari-ous objects positioned in a hierarchical manner. Thepeak of the pyramid represents the goal (the wholeproblem), the lower levels represent a description offractional objects (the sub-problems in which the prob-lem can be divided), and the base corresponds to basicdetails. By applying a top-down approach, a prob-lem can be decomposed by increasing the level ofdetails one level at a time. On the other hand, inthose situations where the details are the starting point,a bottom-up approach is used for the integration oflow-level objectives into more complex, higher-levelobjectives. In common practice, however, actual prob-lems are unclear and lack of straightforward solutions.In this case, the strategy becomes a mixed recipe oftop-down and bottom-up procedures that may be usedalternately with reverse-engineering approaches andback analysis techniques.

The expert witness applies the breakdown approachto the various phases of the forensic investigation.

Figure 8. Example of the logical breakdown of the questionasked by the magistrate to the expert witness (the details arenot visible for privacy issues).

A first application is the decomposition of the ques-tion asked by the magistrate. Usually these questionsare complex and need to be accurately analyzed anddeconstructed.

An example is shown in Figure 8; for privacy issuesthe details are not visible, but it is possible to iden-tify clearly three main tasks with 7, 2, and 3 subtasksrespectively.

5 TIMELINE

In the previous section a first operation toll has beendiscussed, the hierarchical breakdown.

Another useful tool for the investigation of an eventis the analysis of its timeline.

An example in shown in Figure 9 where it is shownthe timeline of an event that started as a demolition andreconstruction of a building but ended with a catas-trophic collapse. The chain starts with the conceptionof the intervention and the relative administrative prac-tices needed to have the feasibility of the work verifiedby the public administration; then, there is the designphase that lasts up to the realization. For each phase theattention is focused on different aspects and differentpeople are involved:

1) during the administrative practices, the techniciansof the public administration should verify the fea-sibility of the intervention from the point of viewof the existing city plan;

2) during the design phase (considering both architec-tural and structural design) the attention is focusedof the conception of the work; the entire project willbe analyzed and the respect of the codes will beverified by architects and engineers. In this phase,specific aspects, as for example the influence ofadjacent building, should be investigated in detail;

3) during the realization phase, the attention is focusedboth on the people that materially make the worksand on the managers of the site; specific documentsand plans need to be drafted (as the safety plan and

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Figure 9. Example of timeline for the analysis of a work of demolition and reconstruction that turned into a collapse.

Figure 10. Example of the identification of the causal jointof the timeline in Figure 9 and definition of the varioustriggers.

the demolition plan); all the involved people (con-tractors, managers, designers, etc) have to carryout activities of control. Also some representativesof the institutions should carry out supervisoryactivities.

Even if the phases are represented separate andsequential, between them numerous overlapping andmutual influences exist (Suraji et al., 2001).

An accurate analysis of the entire process will showthat one of these steps plays a central role: this one canbe considered the causal joint of the entire process; allthe events that led to the collapse rotate around thispoint.

Once the causal joint is identified, the other steps,that led to the failure, can be consequently ordered andthe entire event is understood (Figure 10).

It is important to point out that, according to Rea-son’s model, even if the collapse has been materially

Figure 11. Example of the responsibility profile associatedto the timeline of Figure 9.

activated by a specific trigger (number 4 in the Figure),it was prepared and made possible by other acts, thatsometimes are also distant in time, and that usuallycannot be detected by a superficial interpretation ofthe event (Augenti & Parisi, 2009; Brady, 2012; Love,2008; Petrosky, 1992).

6 RESPONSABILITY PROFILE

Starting from the timeline in Figure 9 and accordingwith the identified causal joint, it is possible to define aprofile that measures the responsibility of the involvedpeople, as schematically shown in Figure 11.

It is possible to note that also this representation iscoherent with Reason’s model that states that it is notthe last actor that necessarily should be considered themost, or even the only, responsible of the disaster, butthe whole process should be evaluated.

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7 CONCLUSIONS

In this work, some general concepts that, in theAuthors’ experience, constitute a basis for the frame-work of the forensic investigation activities have beendiscussed. It has been shown that it is necessary tostart analyzing the peculiar complexities that charac-terize each problem. In this sense it is often useful toevaluate the sensibility to specific parameters and theexistence (or not) of structural robustness. Then, Rea-son’s model for the development of failures has beenextended to the case of Civil Engineering structures,showing that a failure is usually caused by multipleconcurrent causes. Even if a collapse is materially acti-vated by a specific trigger, its initial causes should lookfor in other acts, which sometimes are also distant intime. This aspect should be considered also when thevarious responsibilities are assigned.

Tragic events as the structural collapses make thetechnicians reflect on the approach that are com-monly used for the structural design and facilitatethe introduction of new concepts, as that of structuraldependability that has been recently proposed. It isa global concept that describes the aspects assumedas relevant to describe the quality of a system andtheir influencing factors (Bentley, 1993). It has beenoriginally developed in the Computer Science fieldbut it can be reinterpreted in the Civil engineering(Arangio et al., 2010). The dependability reflects theuser’s degree of trust in the system, i.e., the user’s con-fidence that the system will operate as expected andwill not ‘fail’ in normal use: the system shall give theexpected performance during the whole lifetime.

The use of this concept would include the structuralPerformance-Based Design in a holistic framework.

ACKNOWLEDGMENTS

The team www.francobontempi.org from SapienzaUniversity of Rome is gratefully acknowledged. Thiswork was partially supported by StroNGER s.r.l. fromthe fund “FILAS – POR FESR LAZIO 2007/2013 –Support for the research spin off”.

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