The Polcevera Viaduct – Ananlysis with Applied Elementh Method Public

Applied Science International, LLC 2012 T.W. Alexander Drive P. O. Box 13887 Durham, NC 27709-3887 919-645-4090 // p 919-645-4085 // f www.appliedscienceint.com

The Morandi Bridge in Genoa – Analysis with the Applied Element Method

Ahmed A. Khalil a, Cosimo Pellecchia b Emiliano De Iuliis b. Erik Maria Ricciardi b.

aApplied Science International, LLC, 2012 TW Alexander Dr., P.O. Box 13887, Durham, NC 27704, [email protected] b Applied Science International Europe, Venafrana 85 St., “La Madonnella” Mall, 86079, Venafro, IS, Italy [email protected]

Keywords: Collapse simulation; Applied Element Method; Progressive collapse. Editor: Applied Science International, LLC Distribution: Public Status : Draft V.06 Issue date: 10/10/2018 Summary The Morandi Bridge, designed by Prof. R. Morandi, was built in the 1960s. It was one of Italy’s most important bridges with pre-stressed concrete stays. The bridge collapsed on August 14, 2018, causing 43 deaths. The article describes the structural analysis performed with the Applied Element Method, implemented in the software Extreme Loading for Structures ®, with the aim to analyze the assumptions behind the collapse of the bridge. central closing girders, manage to cover 208 m in Introduction length. The Morandi Bridge in Genoa, designed by Prof. R. Morandi and built between the '63 - '66 years. The bridge connected two of the most important Italian speed-ways, the Genoa-French border and the Genoa- Po River valley. It crossed a heavily built-up area with civil and industrial buildings, beside the Polcevera River and strategic railways yards. The structure can be therefore considered as an example of a big infrastructure built inside a thick urban and industrial network. The need to cover a long spam with a small number of supports leads Prof. Morandi to design an advanced structural configuration called “Balanced Figure 1 – Picture of Polcevera Viaduct after the system”. This system consist of three up to 172 m stayed construction in 1967 cantilever box girders, which, together with 36 m The Polcevera Viaduct – Ananlysis with Applied Elementh Method Public

On August 14, 2018, one of the three balanced system theoretical results [1-17]. With AEM, the structure is collapsed, due to unknown reasons. In order to investigate modeled as an assembly of small elements, which are the reasons behind the collapse of the bridge, the AEM made by dividing the structure virtually, as shown in method has been used to create a model of the entire Figure 3. The two elements shown in Figure 3 are assumed “Balanced system”. The AEM method, despite the more to be connected by one normal and two shear springs well-known and widely used FEM method, allows the located at contact points, which are distributed around the analysis of the behavior of the bridge during all the elements edges. Each group of springs completely continuum and discrete domain, from the plastic stage to represents stresses and deformations of a certain volume. the ultimate collapse shape. The Applied Element Method Reviewing the current literature, it is noticed that methods used for structural analysis are mainly based on continuum mechanics rules, like the Finite Element Method, which cannot be applied explicitly to discrete elements. Therefore continuum mechanics-based methods cannot be extended to simulate the collapse analysis. On the other hand, analysis methods based on rules of discrete elements cannot be used to predict behavior of continuum elements.

But, as a matter of fact, structures during a collapse Figure 3 – Modelling of structure in AEM situation pass through the two stages: a continuum stage followed by a discrete stage. The analysis and simulation needs to follow both behavior stages in order to provide In AEM, each element has 3-D physical shape. One or reasonable results. A new method, that is capable of more faces can be degenerated into a point or line and predicting with a high degree of accuracy the continuum hence, 4-point, 5-point, 6 points pyramids or prisms can be and discrete behavior of structures, has been recently formed. Each element center of gravity is calculated and developed. The Applied Element Method (AEM) has been this is where the degrees of freedom (unknown proved to be the method that can track the structural displacements) are calculated. The use of 3D elements collapse behavior passing through all stages of the with springs connecting them at the faces leads to avoiding application of loads: elastic stage, crack initiation and many of the problems that exist in modeling progressive propagation in ceramic materials, reinforcement and collapse using FEM. Traditional FEM modeling of structural steel yielding, element separation, element structures uses frame elements to model columns and collision (contact), and collision with the ground and with beams, while shell elements are used to model shells and adjacent structures (Figure 2). slabs; this makes it impossible to properly model contact between different structural components. Even when using 3D FEM elements to model the structure, the time of solution is much larger than the AEM. Additionally, the FEM assumes full compatibility at the nodes which makes automatic prediction of crack location practically impossible unlike the AEM which can automatically predict crack initiation, crack widening, and element separation. Against this background, AEM method can be considered as the most reasonable method for the analysis of the collapse of the Morandi Bridge. Figure 2 – Analysis domain of AEM compare to FEM

International publications in the area of structural The Balanced system of the Morandi engineering verify that the AEM can cover with a Bridge reasonable accuracy the fields of application. The method In the following, a brief description of the structural accuracy is compared with more than 50 experimental and system is given, along with the description of the structural The Polcevera Viaduct – Ananlysis with Applied Elementh Method Public elements and details implemented in the corresponding AEM model. The structural system consists of a three-span continuous girder resting on four supports, with two end cantilevers bearing the 36mt span pre-stressed concrete deck. The two external supports of the three-span girder are provided by two pre-stressed stay-cables passing over a suspension tower, called “antenna”, located on the axis of the system. The top of the antenna is 90mt above the ground and about 45mt over the roadway deck.

Figure 6 – The trestle in the AEM model

The reinforcement details of the connection cross girders are given as assumptions, while some data on the reinforcement of the main H shape columns was available (Figure 7).

Figure 4 – Picture of the model of a balanced system

Figure 5 shows the model of the balanced system in ELS software.

Figure 5 – Image of the AEM model of the balanced system

Figure 7 – RC trestle reinforcements detail – Comparison Each balanced system consists of: between as-built drawings and AEM model 1) A reinforced concrete trestle composed by four H shaped columns connected by cross girders 2) A tower, called “Antenna”, made up of four (Figure 6). inclined columns with variable hollow section. The tower is completely independent from the trestle system. The Polcevera Viaduct – Ananlysis with Applied Elementh Method Public

Figure 10 – Hollow sections of the four RC columns of the tower, implemented in the AEM model

3) A continuous box girder of pre-stressed concrete Figure 8 – The “Antenna” in the AEM model with six longitudinal ribs.

The reinforcements of the four columns and the longitudinal connection beams are implemented in the AEM model (Figure 8). Transversal beam reinforcements are only supposed because no data were available.

Figure 11 – The pre-stressed concrete box girder in the AEM model

Pre-stressed cables of 21Ø7 were located across the transversal beams and at the connection with the trestle (Figure 12).

Figure 9 – Antenna reinforcements detail – Comparison between as-built drawings and AEM model

Antenna’s columns were designed with a hollow section; hole’s diameter varied between 1 and 1, 25mt (Figure 10). The Polcevera Viaduct – Ananlysis with Applied Elementh Method Public

Figure 12 – Box girder detail – Pre-stressed cables at the Figure 14 – Pre-stressed cables in the bottom deck of the box connection with the cross girders - Comparison between as- girder in the AEM model builtdrawings and AEM model Reinforcements of girders between the main ribs are given Pre-stressed cables are fully implemented in the AEM as assumptions (Figure 15). model (Figure 13).

Figure 15 – The reinforcement of the cross girders between the main ribs in the AEM model

4) The box girder works as a continuous girder on four supports. The trestle above described provides the first two supports on the center of the system. The other two supports are provided by the stay-cables passing over the top of the tower.

Figure 13 – Box girder detail – Pre-stressed cables at the connection with the trestle - Comparison between as-built drawings and AEM model

The six pre-stressed ribs are connected by a number of cross beams and by the bottom and top deck. The bottom deck is pre-stressed with 30 cables 21Ø7 (Figure 14).

Figure 16 – The stay-cables in the AEM model

The Morandi Bridge was considered at the time of the construction an example of advanced engineering for bridge, thanks to the originality of the solution designed by Morandi and based on the use of pre-stressed concrete The Polcevera Viaduct – Ananlysis with Applied Elementh Method Public stays. The first step in the building phase was the tensioning of the main tendors (16 x 16T + 4 x 12T Strands) that were supposed to support the dead load of the box girder. Successively, concrete shells were cast in situ, in segmental way, from the deck up to the antenna. The obtained concrete beams were then post-tensioned using additional tendors (28 x 4 T Strands).

Figure 18 – Stay-cables – Primary (red) and secondary (green) tendors in the AEM model

In this way, the designer reached the aim to minimize the variations of tensions (fatigue loading) in the Strands, because all the stay-beams in pre-stressed concrete were working under the effects of the traffic. In the AEM model both primary and secondary tendors are assumed bonded with the concrete. The supported steel plate on the top of the tower is not implemented in the AEM model (Figure 19).

Figure 17 – Stay-cables connection - Comparison between as- built drawings and AEM model

After the tensioning, the secondary cables were extended to the anchoring points and the gap was concreted. The extensions of the tendors were tensioned as well and finally all the tendons were grouted. In this way, the post- tensioned stay beam bears the live load of the bridge.

Figure 19 – Stay-cables: connection with the tower - Comparison between as-built drawings and AEM model

The Polcevera Viaduct – Ananlysis with Applied Elementh Method Public

5) The box girder is connected to the four supports The Gerber girders are simply supported by each balanced (trestle and cables) through two pre-stressed cross system. The reinforcements, as well as the pre-stressed girders. cables are implemented, in the AEM model (Figure 23).

Figure 20 – Pre-stressd cross girders in the AEM model

The reinforcements of these cross girders are unknown and therefore supposed.

Figure 23 – Gerber girders - Comparison between as-built drawings and AEM model

Since only one of the three balanced system collapsed, just one system is analyzed. The Gerber girders are supported on one side by the balanced system and on the opposite side by Z direction constrains, imposed to the AEM

elements. In order to allow the sliding along the horizontal Figure 21 – AEM model – Detail of the connection between the axes, between the box girder and the two Gerber girders, a box and the cross girder bearing material is implemented as interface material 6) The Gerber girders: a precast deck composed by between the elements (Figure 24). six pre-stressed concrete girders with transversal connections is located between each balanced system.

Figure 24 – AEM model – Bearing material spring implemented as interface material between the main box girder Figure 22 – Gerber girder in the AEM model and the two Gerber girders

The Polcevera Viaduct – Ananlysis with Applied Elementh Method Public

Material properties Concerning the applied Live Load, the analysis is performed with the aim to reproduce the actual load at the According with design data and specimens tests the time of the collapse. Newspapers reports the presence of following values are assumed for concrete properties. about 35 cars and 3 tracks. Cars are implemented by modelling each 2 points of the axles with a axle’s load Maximum Young’s Element compressive modulus equal to 2 ton; Trucks consists of 5 load axles at equal stress [kg/cm²] [kg/cm²] distance, resulting a total load of 44 ton (the max allowed Not pre -stressed 380 350.000 load of a full load trucks by Italian’s regulation). Both cars Pre -stressed 520 400.000 and trucks loads are included, along the two directions, Table 1 – Concrete properties with an average speed equal to 100km/h.

Steel reinforcement properties are reported in Table 2.

Young’s Yield stress Element modulus [kg/cm²] [kg/cm²] Not pre -stressed 2700 2.100.000 Pre -stressed 4400 2.100.000 Table 2 – Steel reinforcement properties

Steel properties for cables and tendors are assumed as follow.

Yield stress Element Diameter [cm] [kg/cm²] Cables 0.7 17.000 Figure 25 – AEM model – Plot of the compressive stress due to Strands 1.27 17.000 the vehicles loads, along the bridge’s deck, in a certain time of Table 3 – Cables and strands properties the analysis

All the pre-stressed cables and strands are assumed to work with pre-stressed forces equal to 0.8, the values of Analysis results their yield forces. A more accurate analysis can be As explained above, the analysis is performed assuming performed with a parametric control displacement pre-stressed forces equal to 0.8 the values of yield forces analysis that follow all the construction stages of the of the cables and strands. In the absence of live load, this balanced system, providing reasonable assumptions on the leads to disproportionate displacements of the deck, stress state of the cables. although within a range of 15cm (Figure 26). The model could be refined with a construction stages analysis, Loads comparing the applied pre-stressed force and the The following dead loads have been considered in the corresponding displacement. However, within the aims of analysis: this work, the obtained configuration will be assumed for the further dynamic analysis. Specific Total Element weight Depth [m] weight [kg/m³] [kg/m] Concrete 2500 0.3 13500 Binder 2400 0.06 2592 Asphalt 1300 0.05 1170 Table 4 – Dead load

In addition, a linear load equal to 580kg/m has been implemented for taking in account the weight of the RC guardrail. The Polcevera Viaduct – Ananlysis with Applied Elementh Method Public

Figure 26 – Vertical displacements in the balanced system Time: 4.0 sec. without live loads

The failure of the pre-stressed stay cables, due to corrosion, is believed to be the reason of the collapse of the bridge. In order to analyze this assumption, a progressive area reduction of the strands is implemented in the analysis. Based on this assumption, the analysis shows that the first failure of stays cables occurred in the connection at the top of the Antenna.

Time: 5.0 sec.

Time: 2.0 sec.

Time: 10.0 sec.

Time: 3.0 sec.

The Polcevera Viaduct – Ananlysis with Applied Elementh Method Public

Time: 15.0 sec. Conclusion The study, which is far from the validation of the reasons behind the collapse of the bridge, aims, on other hands, to show the capabilities provided by the AEM method in the field of the collapse analysis. The lack of as-built drawings and tests results of the specimens collected after the collapse does not allow the performing of a more accurate and reliable analysis. However, the capabilities of the AEM method, both in terms of implemented details and analysis accuracy, are documented in this study. The availability of the whole data collected, pre and post the collapse, would lead to an advanced analysis, which may Time: 15.0 sec. be used as a validated evidence of the reason of the Figure 27 – Analysis result collapse. Moreover, a further validation of the analysis can be provided by the overlap of the collapse shape, resulted Such detected failure shows a correspondence with the from the analysis, and the actual point cloud of the debris video of the collapse. In fact, in both scenarios, the antenna heap. Previous comparisons, in others case of studies, is still standing while the main deck is already collapsed. showed deviance between the analysis performed and the (Figure 28). actual collapse shape within 1mt of margin [18]. Annexes The video of the simulation performed is shown at the following link: https://youtu.be/Sult2iy18Wc Abbreviations ASI Applied Science International, LLC

AEM Applied Element Method FEM Finite Element Method ELS Extreme Loading for Structures RC Reinforced Concrete References [1] Meguro K. Applied Element Method: A new efficient tool for design of structure considering its failure behaviour. Urban Scurity 2001:18. Figure 28 – Actual video of the collapse – the still standing [2] Meguro K, Tagel-Din H. Applied Element antenna can be noticed while the deck is already collapsed ; the Method for structural analysis: Theory and application for same behavior results from the analysis. linear materials. Structural Eng./ Earthquake Eng., JSCE In conclusion, based on available data so far and at the 2000;17(1):15. light of the analysis performed, the hypothesis that the [3] Meguro K, Tagel-Din H. Applied Element collapse was caused by the failure of the stay cables, can Simulation of RC Structures under Cyclic Loading. J. be considered reasonable. Struct. Eng. 2001;127(11):1295–305. The Polcevera Viaduct – Ananlysis with Applied Elementh Method Public

[4] Tagel-Din H, Meguro K. Applied Element [15] Helmy H, Salem H, Mourad S. Progressive Method for Simulation of Nonlinear Materials: Theory collapse assessment of framed reinforced concrete and Application for RC Structures. Structural Eng./ structures according to UFC guidelines for alternative path Earthquake Eng., JSCE 2000;17(2):137–48. method. Engineering Structures 2012;42:127–41. [5] Tagel-Din H, Meguro K. Applied Element [16] Khalil AA. Enhanced Modeling of Steel Method for Dynamic Large Deformation Analysis of Structures for Progressive Collapse Analysis Using the Structures. Structural Eng./ Earthquake Eng., JSCE Applied Element Method. Journal of Performance of 2000;17(2):215–24. construced facilities 2012;2012(November/Dezember):24. [6] Dinu F, Marginean I, Dubina D. Experimental testing and numerical modelling of steel moment-frame [17] Grunwald C, Riedel W, Iuliis E de, Khalil AA, connections under column loss. Engineering Structures Kostack K, Pellecchia C et al. Report on Model 2017;151:861–78. Enhancement and Validation Cases: Deliverable 3.2 for the EU Project INACHUS (Grant FR7-SEC-2013-1 N. [7] Zerin AI, Hosoda A, Salem H, Amanat KM. 607522); 2016. Seismic Performance Evaluation of Masonry Infilled Reinforced Concrete Buildings Utilizing Verified [18] Christoph Grunwald, Ahmed A. Khalil, Benjamin Masonry Properties in Applied Element Method. ACT Schaufelberger, Erik Maria Ricciardi, Cosimo Pellecchia, 2017;15(6):227–43. Emiliano De Iuliis , Werner Riedel - Reliability of collapse simulation – Comparing Finite and Applied Element [8] Cismasiu C, Ramos AP, Moldovan ID, Ferreira Method at different levels / Engineering Structures 176 DF, Filho JB. Applied element method simulation of (2018) 265-278. experimental failure modes in RC shear walls. Computers and Concrete 2017;19(4):365–74. [9] Elshaer A, Mostafa H, Salem H. Progressive collapse assessment of multistory reinforced concrete structures subjected to seismic actions. KSCE J Civ Eng 2017;21(1):184–94. [10] Garofano A, Lestuzzi P. Seismic Assessment of a Historical Masonry Building in Switzerland: The “Ancien Hôpital De Sion”. International Journal of Architectural Heritage 2016;10(8):975–92. [11] Salem H, Mohssen S, Nishikiori Y, Hosoda A. Numerical Collapse Analysis of Tsuyagawa Bridge Damaged by Tohoku Tsunami. J. Perform. Constr. Facil. 2016;30(6):4016065. [12] Kim H-S, Wee H-H. Separation strain for progressive collapse analysis of reinforced concrete building using applied element method. Advances in Structural Engineering 2016;19(3):437–48. [13] Salem HM, Helmy HM. Numerical investigation of collapse of the Minnesota I-35W bridge. Engineering Structures 2014;59:635–45. [14] Park H, Suk C-G. Evaluation of Progressive Collapse-Resisting Capability of RC Structures due to Load Redistribution. Journal of Korean Society of Hazard Mitigation 2013;13(6):67–74.