LEARN FINAL REPORT OF NANFANG’AO BRIDGE

 

LEARN FINAL REPORT OF NANFANG’AO BRIDGE

 

Sohei Matsuno, Prof. (freelance), DR of Eng. (causation study)

Adviser on Technical Affairs at Jamila Restaurant,

Palembang, Indonesia, E-mail Address: soheimatsuno@gmail.com

Cover Photo Nanfang’ao Bridge after collapse (view from W)

                          Origin:  CNA file photo     Taipei, Nov 25, 2019

 

ABSTRACT

 

Nanfang’ao Bridge (the Bridge) had been constructed in 1998 at a bay mouth of fishing ports in Su’ao town, Yilan County, and collapsed at 9:30 am (L) on Oct. 1 in 2019 when an oil-tanker truck (the truck) was passing the Bridge to East. The Bridge fell into the channel. The truck fell with the Bridge and caught fire on its deck slab

This incident is a prospective theme of this Paper’s writer (him). On Nov. 25, he learnt via media, ‘a Final Nanfang’ao Bridge Collapse Report (the Report) was published 21 hours ago.’ No sooner had he known it, he started writing this Paper.

It’s said that as per the Transportation Occurrences Investigation Act, any incident such as this case is in jurisdiction of the Taiwan Transportation Safety Board (TTSB), an independent organization. Hence, it’s done the investigation of this incident.

Agencies and organizations concerned, viz., Directorate General of Highways of the Ministry of Transportation & Communications (MOTC), Maritime Port Bureau of the MOTC, Yilan County Government, Taiwan International Ports Corporation, and MMA Group are invited to participate in this investigation.

This Paper’s purpose is to present a causation hypothesis of the incident. It’s been done in the following steps.

1^st:  To exhibit the facts which the Report doesn’t mention, 2^nd: To confirm the Paper’s confirmed facts and the Report’s ones on common matters. 3^rd: To convince of contradictions between the facts and the Report’s causation theory. And 4^th: to forward the Paper’s causation hypothesis before the parties concerned.

Key words: Common factor on the earth, particular factor at the site, forced analogy in a causation theory

 

INTRODUCTION

 

Abbreviations and Definitions in this Paper

As already used in ABSTRACT, abbreviations are shown whenever the relevant word first appears, in a parenthesis ( ) immediately after the word, e.g., the writer of this paper (he), North (N), South (S), East (E) & West (W) etc. After then, the abbreviated is used throughout the Paper (except quotations).

For usually used unit-symbols, e.g., m for meter, kg for kilogram, sec for second etc are used without interpretations.

All the technical terms used in this paper carry the same definitions as used in the respective study fields concerned. It may be helpful to refer to his past papers, [01] - [21].

 

Quotations

In this Paper, sentences written by Italic letters are the quotations from Reference [22]. The ones in [ ] are his comment.

 

The Report’s Insertions

General

It’s preferable to discuss the matter by directly referring to the Report. But it’s unable. Hence, the following discussions are made based on media reports. Though he corrected some obvious mis-information in the media reports, some might be overlooked. However, the media reports’ contents are qualitatively almost the same. Hence, the inductions based on them are to be no problem at least qualitatively.

Causation Theory

The Report reveals that the corrosion due to severely salty and highly humid weather in the area exceeded too far beyond a predictable scope for the parties concerned to have taken it account for. That is, the salty rain is the Report’s cause of the Bridge collapse. Based on this recognition, the Report sets up its causation theory as follows:

(1) The Nanfang'ao bridge was located at a fishing harbor at an estuary, an area with severe salt damage and high humidity.

(2) After the bridge had been used for many years, its waterproof facilities for the stay cable system gradually deteriorated.

(3) The waterproof seam seals on the metal boxes of the divisional island and on the HDPE tube became hard and had cracked. Rain water traced the HDPE tube, leaked into the trough anchoring mechanism where it accumulated.

(4) The anchors and the steel stranded wires on the bridge end were situated in an environment with accumulated salty water, causing severe corrosion to the steel stranded wires near the surface of the accumulated water.

(5) Before the collapse, several steel stranded wires at No. 10, 11, 12, and 13 anchors on the bridge end had been corroded and broken. The effective residue cross-sectional area of the cable left was only approximately 22%–27%.

[In another page, it explains,] ‘among the 13 cables, except for cable No. 5, which had a lower total residual intensity of load due to corrosion, the rest of the cables all exceeded the standard…..’ [It needs explanations.]

Denial of Truck’s Role

The Report denies the role of the truck on the Bridge collapse, emphasizing the Bridge had been already weak by corrosion when the truck entered the Bridge. That is:

1.  When the CPC tank truck passed by No. 10 cable on the bridge, the residual strength of the corroded steel stranded wires of the No. 11 cable system could not sustain the loading and broke. Subsequently, the neighboring corroded wires of No. 10 and No. 12 cable as well as No. 9 and No. 13 cable system at the bridge end broke, resulting in a chain destruction of No. 8 anchor head, No. 6 anchor head, No. 7 cable, No. 4 and No. 5 anchor head, No. 3 anchor head, No. 2 anchor head, and No. 1 anchor head.

2.  When the destruction of the cable system of the bridge began, as the number of broken cables increased, the stress of the steel girder of the deck increased. By the time all cables were broken, the steel girder of the deck had been significantly damaged, resulting in the bridge breaking and collapsing.

Paper’s sequence of cable separations from the arch & deck-slab (both visible in video records) and Report’s sequence of real-time cable disconnections (invisible as hidden) are shown in Fig. 3 &.4.

 

Inspection and Maintenance

In a causation study, if the cause’s intensity exceeds human capacity, any artificial element becomes eligible as a cause. It’s pardonable even if the cause wasn’t taken into account at a design time. It’s the very stance of the Report. Thus, the case has been down-graded to the matter why the due inspection and maintenance couldn’t detect the development of collapse and prevent it from occurring.

The Report allocates a considerable space for the inspection-maintenance matters, and admits its unpreparedness for the case, saying as follows:

(1) After the Nanfang'ao Bridge was completed it underwent seven regular inspections, but all were superficial visual inspections that failed to take into consideration the fact that the bridge had specifically-designed features that required closer examination. In addition, no inspection was carried out in the four years prior to the incident, he said.

(2) The bridge was built in 1996 by Yilan County government and managed by the Maritime Port Bureau under the Ministry of Transportation and Communications (MOTC), before finally being transferred to MOTC-run Taiwan International Ports Corporation (TIPC), which was established in 2012.

(3) However, according to the law in Taiwan neither the bureau nor the company was the competent authority for the Nanfang'ao Bridge road as defined by the Highway Act, which stipulates that that MOTC only manages the maintenance of national highways and provincial highways, not roads in harbor areas.

"The bureau and the company did not understand maintenance and inspection methods related to bridges," the report said, adding that consequently, for many years, they only conducted general inspections.

(4) The board recommended that the MOTC list all the bridges under its jurisdiction, including those that are not categorized under the highway system and establish a maintenance mechanism.

(5) In response, Deputy Transportation Minister Wang Kwo-tsai (王國材) said the ministry is working with local governments to examine 101 bridges that need inspections or have reported damage; work is expected to be completed by 2022.

It’s in brief, ‘The unpreparedness of the parties concerned for the case is pardonable as there was no special notice for such a special Bridge.’

 

Back-up Tests and Calculations

The Report states on the matter as follows:

1.  Material test results revealed that the components of the steel stranded wires of the stay cable system of the bridge were somewhat different, possibly because they were products from different manufacturers or from different batches, but their strength and hardness [elastic modulus?] did not exhibit substantial differences.

2.  The thickness of the galvanizing layer on the surface of the steel stranded wires was uneven, which may have affected its ability to resist corrosion. Tensile test results showed that among the 13 cables, except for cable No. 5, which had a lower total residual intensity of load due to corrosion, the total residual intensity of loads of the rest of the cables all exceeded the standard of 351.36 metric tons.

3.  Tensile test results also showed that when the tensile load reach 262.42 and 319.88 metric tons, No. 10 and No. 11 upper anchor head broke, respectively. Their residual strength did not meet the test regulation of the Post-Tensioning Institute of the United States.

4.  The anchorage system recorded in the as-built drawing of the Nanfang’ao Bridge differed from the actual construction not just in the omission or miss-recording of scale labels. These differences could affect the subsequent assessment, planning, and implementation of bridge maintenance and inspection.

Summery

The Report’s insertions are in brief as follows:

(i) Over the years, rain water leaked into the anchoring mechanism and accumulated, caused corrosion to the steel stranded wires. (ii) The severity of salty rain had been too extraordinary to have dealt with it at a design time and not to detect the development of corrosion and prevent it from the collapse at the inspection-maintenance time. The inspection / maintenance system has not yet been ready to deal with such an occurrence. (iii) The salty-rain causation theory has been proven deductively by specified tests with real specimens and calculations with hi-tec application programs with a model for stress calculations.

The ministry has completed an internal review to determine related punishments, said MOTC Minister Lin Chia-lung (林佳龍).

With such a causation theory, no punish is. The Report, in effect, acquits the insiders concerned. He sympathizes with an act to minimize insiders’ trouble. However, he disagrees to accomplish the purpose by twisting the fact. It doesn’t contribute to develop the society concerned in a long run but allows the same mistake again in a short run. There’s a way to accomplish the same purpose with a rightful cause. In modern times, usually an incident emerges beyond the most sophisticated computer programs. Almost all the modern societies are governed by the programs. An incident happens beyond (not the human knowledge but) the program system. That is, the one that should be accountable for is not the human but the computer program that’s governing the human, and the system that obstructs a timely revision of the program.

 

QUESTION AND ANSWER SESSION

 

General

In this SECT., questionable points in the Report shall be clarified in a form of question and answer (Q & A) between the personified Paper and Report.

Q is really of the Paper. A is of the Paper too, putting the Paper itself fairly in the Report's position.

The session is proceeded with 2 subjects of (i) facts not taken into account in the Report and (ii) facts incompatible in the Paper and the Report.

Facts not taken into Account in the Report

Q: Please look at Cover Photo This is an image of the Bridge after the collapse. Don’t you have comments on it?

A: No, I don’t.

Q: In the Photo, the tops of both the fork supports are on the N-side of the-deck’s centerline. This is one of the characteristics of the collapse. But it’s not taken into account in the Report. Why?

A: Because the fact that you pointed in the Illus. has no relation to the cause of the Bridge collapse.

Q: Then, is its reverse ‘Your causation theory has no relation to the collapse’s characteristics,’ also true?

A: No it isn’t, because the cause of the Bridge collapse has no relation to the fact that you pointed in the Cover Pnoto.

Q: There’re many facts which you don’t address, e.g., (i) earlier step out of W-side fork support from the pier than of E-side, (ii) earlier step out of the S-side support leg than the N-side one from the E- & W-side piers, (iii) the truck having run in the N-lane toward E at 56-km/hr speed was found in the S-lane directed toward W, (iv) Deck slab’s S-side-down falling, etc. Did they all have no relation to the cause?

A: No, they didn’t. They’re all the consequences of the Bridge fall. The Bridge fall is the consequence of the corrosion caused by salty rain. In other words, the cause of all the cross-sectional phenomena that you mentioned is the Bridge collapse, and the cause of the Bridge collapse per se is the salty rain.

Q: Your insertion may be true if there’s no eccentric inciting force in the cross-section. Really, it was. Almost all the trucks on the N-lane to the E were 3-times heavier than the same trucks on the S-lans having gone back to the W after unloading. Can’t they be eligible to be the cause of the phenomena?

A: No. The truck didn’t play any role in the collapse. Rather, it was an unlucky victim who entered the Bridge which had just been in a critical condition. Further, the collapse happened with a truck which was going to E. Hence, at least, the trucks going to W shouldn’t be brought on the agenda any way.

 

Facts incompatible in the Paper and the Report

Q: There’re many discrepancies between the Paper & the Report. But in this session, Q & A shall focus on a fact check only, because the referenced facts are to be the premises in setting up the causation theory. Hence, if the facts are confirmed, the rightfulness of the theory will follow the results of the fact check. In this context, I ask ‘You say that the video records do not show the real time disconnections of cables. A Real time of each cable disconnection is unable to know.’ Elaborate it.

A: The disconnections took place either in the arch-rib or in the HDPE tube at the deck-slab FL. Hence, the videos couldn’t record the disconnection of steel stranded wires happened in the closed room. The videos recorded only the relative positions of the cables at arbitrary times after the cables came out from the places where the cables had been. The recorded time in such a manner can’t represent the real-time of disconnections. It cannot be known. The unknown sequence of disconnection has been defined by tests and calculations in the Report so that the sequence doesn’t contradict the cause. As said in the Report, ‘The bridge collapse video only shows part of the broken bridge. The actual location of failure and the sequence of the failure cannot be known.’

Q: If the sequence of cables’ disconnection has been so properly defined in the Report, the actual phenomena must be concordant with it. But it’s not. That is, you define the E-side-first cable disconnections, but the sequent deck slab fall appears in the W-side first mode. How can you justify this contradiction?

A:  It’s because the shoes at the E end was stronger than the W end ones. It’s better not to speak too much on the matter that has no relation to a main topic, as it could derail the way of essential discussions.

Q: You say ‘Cable# i=11 disconnected first and cable# i=1 disconnected last.’ But, in fact, Video records obviously show ‘when # i=11 cable is still taut, # i=1 cable has already separated from the deck slab. Other plural cable in the E-side span has been seen already severed from the arch rib. Do you mean that the facts are wrong?

A: No, they aren’t. It’s your mistakes of fact.

The Paper: Thanks for your dogmatic answers. Good luck for your ochlocratic study.

The Report: Thanks for your Mensheviks questions. Good luck for your penance study.

Denial of Salty-Rain Causation Theory

This Paper had inputs from the Report and digested them. Now it’s about to enter the main SECT. where the Paper’s own causation hypothesis is exhibited. To simplify the due-discussions, he wants to clarify his stance in advance. It’s a basic denial of salty-rain causation theory, a main antithesis. He denies it on a common-sense level as follows:

1^st: Salty rain is a universal factor throughout coast areas. Hence, its effect must be universal for all steel structures in the area. If not, the cause is in the structure itself.

2^nd: Generally, collapse due to corrosion is preceded by a big deflection. The Nanfang’ao Bridge collapsed with an insignificant precursor deflection. It may be represented by {actual pavement depth (12.5 cm)} - {as built pavement depth (8.6 cm)} = 3.9 (cm). It should be more than 100 (cm), if the corrosion is the case.

3^rd: In the case of salty-water brittle fracture, the collapse with little deflection can happen.

He experienced it in 1957 when he was engaged in his 1^st work after graduation, as an engineer at Kanagawa Provincial government. It was a bridge-viaduct construction project to join an island in the Pacific Ocean coast to the Japan Honshu main-island with Jogashima Great Bridge. It’d been the biggest over-sea bridge before the Akashi Strait Bridge emerged in 1998.

One day, in a typhoon season, to have prepared for next-day’s pre-stressed concrete girders’ tendon placing, several rolls of wire were taken out from a warehouse and leaned them against warehouse’s outside wall. At night, a storm attacked the site. It lasted 40 (hrs). Wires were showered by salty rain water. 1 day later, when it was fine, wires were transported by a truck to the site and unloaded. A site engineer wondered when wires were found having popped wires at positions having been at both sides of rolls when they’d been being leaned against the wall. The cause was not salty rain but was in the wire itself. It was an oil tempered wire. The sulfur (S) component in oil had already caused brittleness of the wire; it was activated by some component in sea water. It wasn’t corrosion failure but brittle fracture. Really, it can happen anywhere if the same conditions are given. But the condition now is different from 70 yrs ago. Such a brittle wire never appears in markets today, much less if the wires were of JIS standard products as alleged. Is it JIS standard products made in Mainland China? If yes, there’s a possibility of occurrence to some extent, as Chinese made steel products are often belittle. It was 10-yrs ago in Indonesia when Chinese made auto-bicycles and 3-wheel vehicle were explosively sold as cheap prices. Now, they’ve disappeared from streets. The cause was their daily-base out-of-order whose cause was the brittleness of steel parts.

4^th: The Nanfang’ao Bridge’s element wires had double corrosion protections of HDPE tube and galvanization. The function of HDPE tube is to isolate element wires from salty water and anti vandalism. The Zinc (Zn)-galvanization of wire (Fe) is not isolating wires from salty water but stop Fe to dissolve in water (=corrosion) by using the ionization tendency of Zn > Fe. The Report says, ‘There’s uneven thickness in the galvanization layer.’ It doesn’t matter. So far as Zn remains, corrosion doesn’t occur.

5^th: Generally in any natural disaster, e.g., earthquake, cyclone, tsunami etc, their consequences occur within the duration of respective disasters. Salty rain isn’t an exception in principle. If there would be any lasting load during salty rain, it triggers collapse. Above stated 3^rd: is an example. 

Readers might have understood that the salty rain water is scarcely eligible for the cause of the Bridge collapse by nature.

Take note, before entering this Paper’s Causation Study

The Report acquitted a truck which was on the Bridge when the Bridge collapsed. Instead, it arrested salty rain that has alibi.

The Paper acquits the salty rain and arrests the truck with other heavy trucks as suspects of current offenders, together with unspecified, unqualified irregular anchors as suspects of accomplishes. The ill-designed Bridge is a principal.

Wonderful indeed, if the Report goes dignifiedly.

THE PAPER’S CAUSATION HYPOTHESIS

General

This SECT. establishes the causation hypothesis of the Bridge collapse. It’ll be proven quantitatively with the data to be given.

To fulfill the above, first, he learns the Bridge structure. Second, identifies the truck with its full-loaded & empty weight, as well as a speed when it was crossing the Bridge. Third, he realizes the Typhoon Mitag had struck the region earlier in the morning but it was fine at the time of incident, i.e., it’s no relation to the Bridge collapse. Fourth, he identifies the Bridge’s behaviors in 3 stages viz. a 2-decade-long latent, a 1-yr-long actualized and a few-sec-long collapse stages. Fifth, he analyzes the Bridge’s behavior qualitatively with a model.

Keywords in this SECT. Deck-slab’s sway displacement, steel stranded wire (element wire)’s slip-out from upper anchors, element wires’ fatigue at deck-slab FL.

 

Notices on Figs. in this SECT.

 

View point of Figs.

All explanations are done seeing the Bridge from the S-side and from W-side in its side and front view respectively. En passant, the images of the Bridge’s side view are not necessary taken from S.

 

Dimensions in Figs.

The detail data can’t be found in any search even after the issuance of the Report, except a few viz. bridge’s length, width and a Sea-water-level clearance. They’re shown in Figs. All other dimensions are by analog estimations from applicable images. There’re about ±3 (%) errors. Hence, digital calculations by scaling them don’t suit a quantitative deduction. Nonetheless, the hypothesis herewith induced is qualitatively correct.

 

Background of Nanfang’ao Bridge Design

In 1950s, the mission of a bridge was to serve economic developments by providing a structure for transportation, regardless of appearance. Following the socio-economic-cultural developments, demands for bridges have diversified. The bridge engineering itself had also developed to meet the demands. Big two of the demands were comfortable drives and beautiful looks. Both have roots in instinct, hence, irrepressible. They progressed in different modes, reflecting their respective instinct platforms of physical & mental.

A physically comfortable drive is a common desire for bridge users & bridge engineers, though it hadn’t been taken into account for a long time. In fact, until 1940s, bridges still used to be constructed having chosen a point where it needed least efforts to work out. Road alignments were forced to join it with acute curves. Drivers were obliged to reduce speed and managed to pass acute curves. Travelers also suffered from discontinuous centrifugal force due to big curvature, and negative acceleration force by braking. It was since 1950s, road alignment of elegant curvature changes with transient curves precedes bridge designs. A bridge is forced to follow the design criteria at the given site. The users are nowadays enjoying comfortable drives with a constant high speed. A point in issue is that comfortableness is a feeling for a physical input to which everybody has a common sense. The bridge engineers agree to and fully meet the users’ demand.

On the other hand, the beautiful looks are a subject to structural & aesthetic designers from different study platforms of technique and art. The beauty is a mental response to a physical input. Everybody has more or less a different sense on an object. That is, there’re different feelings among them. Worse still, the structural & aesthetic designers municipally lack a sense of their counterparts’ platforms. Sophistication in the technique and abstraction in the arts since the 20^th century have been abetting this trend. The abstraction is explained by artist as: “Each object has each essential character that can’t be seen by general people. The artists show it by abstraction so that the people of standard sense can see it.” As most of people (structural designers as well) don’t like to be ranked lower than the standard level in a human class, they unanimously say, “I can see it.” Thus, the bridge design is apt to go with Andersen’s Emperor's New Clothes effect, i.e., in favor of aesthetic designers. A fashion show is a chance for dress designers to show off their abstraction works derived from an aesthetic point of view. The clothes of abstract design are impractical, hence, revisions are to be exerted in order to garner people’s acceptance. This function doesn’t work in the bridge design.

The Bridge’s 24-hour traffic was only 100 (cars) on average, while tourism ceremonies, provably last 1-week with decoration plates fixed on the staying cables. The primary purpose of the Bridge was a tourism promotion. Traffic was a secondary one.

Against this background, the design had been done likely under the leadership of aesthetic designers that gave aesthetic uniqueness. It was OK. But it brought about structural uniqueness as well. It might have been not OK. This is the point in the issue.

Structural Uniqueness of the Bridge

General

The Bridge collapsed due to its structural uniqueness. Despite its fatal nature, aesthetic designers didn’t abstract it, as it falls outside the scope of their ability. Structural designers also didn’t point it out, as it’s beyond the scope of their sophistication, i.e., the scope of applicable advanced computer programs.

 

How Unique is the Bridge?

The Bridge’s feature before collapse is shown in Fig. 1 & Photo 1.

SL: Support Leg, SH: Support Horisontal beam, ms: Movable Shoes. fs: Fixed Shoes, CB: Cable, DS: Deck Slab

Fig. 1 General view of the Bridge  

               Photo 1 Bridge probably months before collapse (N-side view)

Its framework (main structure) isn’t a tide arch as popularly called, but a fixed arch to a pair of fork supports (supports) which are vis-à-vis placed on a substructure (piers). The supports are tied by cables at their bottoms so as to prevent them from moving apart. It’s still in unbalance without the arch, hence, during construction, it must be temporarily supported. SH (horizontal beam of the lower part of the support) is used for this need. After the fixation of the arch, the main structure becomes an internally 2^nd-degree of statically indeterminate structure, both in a side-view and a cross-section. It’s externally a statically determinate structure. Though the main structure isn’t familiar, it’s still in a scope of existing computer programs.

Fig. 2 Components of Main Structure (fixed arch to supports)

A cable-stayed deck slab (auxiliary structure) is attached to the arch to transmit live loads to the main structure. Thus, a superstructure was formed on the substructure. 

Fig. 3 Components of Auxiliary Structure (cable stayed deck slab)

In cross-section, it comprises an arch rib, a stay cable and a cable-stayed deck slab. The cable and the deck slab sway independently when the live load is applied to the deck slab asymmetrically, i.e., on either N- or S-lane. It needs 2 independent coordinates to define the status of double pendulums, i.e., the statuses of cable (simple pendulum) and the deck slab (physical pendulum). Hence, it’s a 2-degree of freedom system. This kind of ‘relative angular displacement between a deck slab’s and a cable’s axes doesn’t exist in ordinary cable-stayed structures. Check all types of cable stayed bridges such as arch, suspension & inclined-cable-stayed bridges in the world. If there would be such one, it’ll fall sooner or later.

 

Bridge’s behavior to collapse

 

General

The Bridge’s behavior developed time-wise in 3 stages, viz. (1^st) a latent stage of nearly 2 decades, (2^nd) an actualized stage of about 1 yr and (3^rd) a collapse stage of 3.95 sec. They’re briefly explained in this Sub-sect.

 

Latent Stage

Explanations are to be done with Fig. 5 (c) which is across-sectional model for a static analysis of the Bridge.

1’: 𝝷 after expansion discrepancy, 

2’: slacking after ditto. 3’: fatigue after ditto

Fig. 4 𝝷 (1, 1’), slacking (2, 2’) & fatigue (3, 3’) vs. cable# i

When it’s subjected to a load on the N-lain, the model’s deck slab inclines at 𝝷_p. The 𝝷_p is different if the load is applied to a different cable# i point. In a side view; 𝝷_p due to load applied at each symmetric point is symmetrical. It means that the consequences of 𝝷_p. such as wedge slacking at upper anchors and wire fatigue at deck-slab FL are also symmetrical. They are shown in Fig 4. It’s true so far as the structure is symmetrical. Really in the latent stage, structure is keeping its symmetry.

In the cross-section, the effect of 𝝷_p is asymmetrical. Hence it caused an asymmetric residual deformation of N-side low. But its magnitude was too small to have been detected in this stage. cf. Fig. 4.

 

Actualized Stage

In this stage, wire slip-out at the upper anchors had become long, so the sagging of deck slab had also become big. It made the residual deformation in the latent stage to have been actualized with 3 troubles, viz. discrepancy at the expansion-joints, unevenness of deck-slab FL, & broken handrails at both sides of the Bridge between cable# i=5 & 8. Having lost the constraint at the W-side bridge end, the symptoms were rapidly accelerated especially in the W-side of the Bridge. It’s shown by horizontal portions (1’, 2’ & 3’) in Fig. 4. They were direct indication of increased wire slip-out which was the cause of the would-be Bridge collapse to happen in less than 1 (yr). Nobody came up with it. Then, superficial repair works were done.

 

Collapse Stage

Before entering this topic, the beginning & end of the collapse stage must be defined.

The collapse was initiated by the slip out of several element wires in the cable# i=8. There were still 2 remnant element wires in the anchor. But they were already in a losing posture (falling position from which it is impossible to recover). Hence, when the majority of element wires slipped out in the upper anchor of cable# i=8 is ‘Time 0’ of the collapse stage. 3.95 (sec) later, the N-side leg of E-side support stepped off the pier. At this moment, the Bridge was in a losing posture. Hence, ‘Time 3.95’ is the end of the collapse stage.

The sequence of the collapse has been observed at every 1/60-sec increment, e.g., the W-side support fell down 4/60 (sec) after the cable# i=1 had disconnected. The E-side support followed it after 10/60 (sec). Many phenomena occurred in less than 1/60-sec, e.g., the two legs of each support on each pier didn’t step off the pier at the same time. There was a time lag of less than 1/60 (sec), i.e., the S-side leg stepped off first and the N-side leg next. Without the recognition of this fact, the undeniable S-side-inclined falling down of the deck slab can’t be explained.

The behavior of the Bridge in this stage is represented by the sequence of the disconnection of cables. It developed in 5 steps as follows: cf. Fig. 1 & Table 1.

1^st Step: Slip-out of majority of element wires from the upper anchor at cable# i=8

The truck was running on the bridge’s N-lane to E at an average 56-km/hr speed. The collapse started with slipping-out of element wires from the upper anchor of cable# i=8 when the truck’s rear wheels were just at the very cable point. A cable is a bundle of 7 or 13 (?) parallel element wires housed in a spiral HDPE tube. The slip-out didn’t take place once for all but 2 element wires were still working until having been cut off by increased tensile stress at deck-slab FL where fatigue cracks should’ve been developing. It needed 75/60 (sec) to have finalized the cut-off work of 2 remnant element wires. Really, the slip-out of element wires can’t be seen in monitoring videos when truck’s rear wheels are at the cable# i=8 point, but seen after the truck has run 56000*75/60/3200=22 (m), i.e., when its rear wheels are at the cable# i=10 point.

2^nd Step: Slip-out of element wires from upper anchors of cables# i=2←6

This is a series of element wires’ slip-out from the upper anchors of cables# i=2←6. The slip-out didn’t happen all for once. In cable# i=5 & 3, one of the element wires kept working for a moment. Due to this effect, the disconnections of the cables# i=5 & 3 were retarded. But element wires’ sequence of real time slip-out from upper anchors and the sequence of separation from the arch rib can’t occur in different sequences. Both happened in the sequence of cables# i=2←6.

3^rd step: Wire cut-off in cables# i=7 & 9 12 at deck-slab FL

The cut-off of element wires of cable# i=7 at the deck slab FL and sequent cables# i=9 12 cut-offs of the same mode as the cable# i=7 are the 3^rd step of the collapse stage.

4^th step: Wire cut-off of cable# i=1, and a sequent step-off of W-support

This step was initiated by the disconnection of cable# i=1. The disconnection was the wire cut-off at the deck-slab FL. (The Report describes, ‘the cable# i=1 was disconnected at its upper anchor.’ This is one of the Report’s obvious mistakes of fact.) At this moment, the support rotated anticlockwise, so slightly in motion and so shortly time-wise but apparently visible in video records. The support stepped off the pier in an order of the S-leg first and the N-one next, having resulted in a S-ward inclined fall of the deck slab.

5^th step: Wire cut-off of cable# i=13 & sequent step-off of E-support

This step immediately followed the 4^th step. The phenomenon is mirror-symmetric to the 4^th step’s case space-dimensionally but asymmetric time-dimensionally, i.e., there was a short but identifiable time lag between the 2 steps.

The above mentioned sequence of cable separation from arch rib and deck-slab FL shown in video records should be parallel to the real-time sequence of disconnection happened in hidden places. The Report practically reveals, ‘the real sequence is opposite to the sequence seen in video records, i.e., it happened in an E-side 1^st and W-side 2^nd sequence.’

See? The truck, its front wheels fell into the E-side expansion gap, was hanging there while the deck slab was still kept by the pier. At this very scene, the W-side deck slab had already hit the sea water.

 

Analysis of the Bridges’ Behavior

 

General

The producer of the stages stated above was an angular displacement 𝝷 in Fig. 5. It did 2 jobs, (i) vibrations of cables and (ii) repeated bending in cables at deck-slab FL. The 2 jobs caused 2 consequences, (i) wedge-slacking at upper anchors & (ii) element wires’ fatigue at the deck-slab FL.

They finally resulted in the slip-out & cut-off of element wires at the respective places. This SECT. analyzes bridge’s aspect stage-by-stage with a model set-up for this purpose. cf. Fig. 5.

 

Preliminary knowledge

Before entering discussions, there’re 2 subjects that should be explained first. They’re the fatigue of wire and the loosening of wedge. Both are caused by alternating force, but in different manners.

The fatigue is governed by the magnitude of alternating stress and its number of cycles (nc). That is, the frequency of alternating stress plays no role in fatigue. The greater the magnitude of alternating stress is, the less the nc of causing fatigue fracture is. There’s a fatigue limit. If alternating stress is less than the fatigue limit of the material, fatigue never happens even if nc is infinitive. In dynamic analysis, the alternating force is often represented by an expression, ‘F = F₀*sin (𝜔*t)’. The relation between angular velocity (𝜔) and nc is: nc = 𝜔*t/(2π). It means that nc is a number how many 2πs (i.e., waves) are in an arbitrary duration of t. It’s a dimensionless number. This nc and F₀ define the fatigue.

In the case of the cables under consideration, the alternating force works under a tension regime; hence, the fatigue limit is less than the case of under a neutral regime. Including this matter, it’s recommended to learn the fatigue with any applicable text books. There’re a lot of them.

The wedge- / nut-loosing, on the other hand, occur with the high frequency & a lesser magnitude in the vibratory force. The wedge- / nut-loosing are quite common phenomena that appear not only in civil engineering structures but in all kinds of machines & a variety of homely used utensils. As it is rather practical than academic nature, there’re many patents publications to prevent wedges / nuts from loosing but fewer study papers on it than on fatigue. There’s no method that is universally applicable to all kinds of wedge- / nut-loosening. In case of structures, it’s executed as per oral instructions at sites rather than written documents or drawings. For instance, in the case of friction joint, the nuts of high-tension bolts are fixed by welding after tightening. But their feature is case-by-case different.

The biggest market of the wedge- / nut-anchor in structure is post-tension pre-stressed concrete (PC). In this system, the anchor itself is fixed in concrete. The wedges or nuts are covered by mortal capping after the wires have been tightened. Further, the space between a tendon and a sheath is filled by mortar grouting later. Since then, the wires are fixed to concrete and the movement of the tendon relative to the anchor is only due to the elastic deformation of the girder (minor). That is, there’s no need to wary about the anchors’ long-time function. But in the case where wires won’t be bonded with concrete by grouting later, the anchors must function for a long time. There’re many products to meet this need. The superficial imitation anchors won’t meet the purpose.

At least, an anchor must exhibit greater strength than the tendon itself. It’s so specified in general standard specifications. The used anchors didn’t satisfy this general rule. It’s an obvious breach of general specifications. The act must be held accountable for the breach, regardless of the principal cause, the structural uniqueness.

 

Modeling of the Bridge for Analysis

For a dynamic analysis, a model must be set up. Next, equations of motion shall be composed. The system parameters in the equations of motion are defined by the structural data. Only the damping coefficients (c_v, c_h) must have been measured by full-scale in-situ tests. If not tested, choose a greater value, even the value of corresponding to over-damping may be used, as the values of c_v & c_h must have been really great. cf. Fig. 5 (b).

In static analyses, a model needs much less parameters than a model for dynamic analyses. To learn the qualitative behavior of the cable-stayed deck slab, a model for a static analysis is enough. The most important thing is, ‘Not to overlook an essential element in the real structure.’ Analyses by sophisticated application soft with a wrong model make nonsense.

(a)    Ordinates       (b) For dynamic analysis     (c) For static analysis

Fig. 5  Models for analyses

The model for static analyses is given by subtracting following parameters from the dynamic model, i.e., m_p, c_v, c_h, k_h, L. 𝜔*t, W & 𝝷_c (as irrelevant) and k_r & K (as negligible). cf. Fig 5 (c). It’s a statically determinate structure. It can be solved for 𝝷_p easily if the deck-slab cross-section is given and no sectional deformation is assumed. Then, the final targets, alternating stress in element wires at deck-slab FL and free vibration of cables, can be obtained. Calculations are to be done only at a cross-section of the center-cable# i=7 where the conditions are severest.

Note 1: A model at any other cable# i is the same as the one at cable# i=7. Only change k_v, vs. the position of cable# i. The model is internally symmetrical. It’s also externally symmetrical ‘as far as sliding shoes’ sole and bearing plates are contacting at both the N & S sides.

Note 2: 𝝷_p produces a free vibration in the cables. 𝝷_p works once at every truck pass. A free vibration doesn’t occur in the deck slab as its damping is great. But the free vibration in a cable lasts long time in the cables, as they work as taut strings whose damping is much less than the deck slab’s. This free vibration in cables were the cause of upper anchors’ wedge slacking.

 

Stage-by-Stage Analyses

The Bridge collapse is characterized by 2 kinds of cable disconnections, viz., wire slip-out from the upper anchors and wire cut-off (fatigue rupture) at the deck-slab FL. The analyses of aspects of the collapse in this SECT. are, after all, the analyses of these 2-kinds of cable disconnection.

At cable# i=1 & 13, the deck slab was constrained its movements by a pair of sway bracings and legs’ horizontal beams  at their lower parts, hence, the 𝝷_p-effect didn’t appear at these points. Further, in the upper anchor at cable# i=7, wedge slacking didn’t take place. Its cause is, ‘for this anchor, a qualified product was used probably by the maker as a promotion.’

 

Analysis of latent Stage

Bridge’s cable-stayed deck slab was still being under the original symmetrical structural regime. Hence, the effects of 𝝷 on wire slip-out at upper anchors and wire cut-off at deck–slab FL were also symmetrical about the centerline.

The former was promoted by cables’ free vibrations as taut strings excited by . It grew from cable# i = 6 & 8 gradually to cable# i=2. cf. Fig. 4. The cause of an exceptional behavior of cable# i=7 has been already explained.

In this connection, there’s a fact that should call readers’ attention. It’s the effect of decoration plates fixed to cables at the time of tourism promotion ceremony. cf. Photo 2.

Photo 2 Bridge decorated by plates fixed on cables

A matter is forced vibration by flatter of decoration plates and sequent free vibrations of cables. Rough trial calculations reveal that the effect of the flatter during a 1-week-long ceremony is equivalent to 10-yr-long heavy trucks’ excitation effect. The effect of decoration plates’ flatter might have been greatest at cable# i=8 as the most plates were fixed it.

It seems that the ceremony of decoration plate fixing never happened twice, not because of anxiety of bridge safety but provably difficulty to fix decoration plates to cables against the flatter.

The latter merely followed nc of . In this case, cables’ free vibrations did little on wire cut-off because of their lesser amplitude.

Despite the same products, the same wire slip-out didn’t happen in the lower anchors, as the vibration energy of cables was absorbed by the deck slab, hence, didn’t reach the lower anchors.

Wire slip-out and cut-off were both difficult to detect because of slow progress (former) and small magnitude (latter). The former was not realized up to the Actualized Stage, and the latter is even up to the investigation days.

 

Analysis of Actualized Stage

In this Stage, the latent weakness of the Bridge was actualized by 3 symptoms, viz., (i) discrepancy at expansion joints, (ii) unevenness on the deck-slab FL and (iii) the broken handrails at both bridge sides of around the span-center. The symptoms were treated superficially without diagnosing the cause. The treatments were done in the order of inconvenience, probably, (i) -> (ii) -> (iii). The Paper supposes the jobs were done in the 1-yr long Actualized Stage. The bases how to suppose the 1-yr long Actualized Stage are: 1^st, the speed of 𝝷_p development became much quicker than in Latent Stage. 2^nd, the construction periods of the 3 jobs were estimated as follows: The method of treatment (i) is unknown. The re-tightening of cables at the lower anchors was not done. If it would be done, it should take 1-yr long. For unknown cause, such a big operation won’t be. Nonetheless, it must have taken the long time as the repair of an expansion joint is generally difficult. It provably needed 4 (months). Job (ii) is easy. It doesn’t take more than 1 (month). As to (iii), cf. Photo 2. There can be seen the newly fixed handrail in between cable# i=5 & 8. They hadn’t yet been painted, hence, it looks black. Further, readers are requested to see video records which show the falling Bridge. You can realize a 12-colum of newly painted handrails in both sides of the Bridge in the scope of cable# i=5~8. The 2*33=66-m long handrails of the type of the Bridge may take 4-months long. Together with time for production, delivery, rain etc of 2-months, the construction period was estimated at about 11 (months). 3^rd, The paint status reveals the Bridge fell within 1 (month) after painted.

In this Stage, the Bridge’s cable-stayed deck slab had lost its symmetry in the side view, as the vertical movement at the movable shoe side was unrestrained. But, at the fixed-shoe side, deck-slab’s uplifting was still restrained. Under this condition, the slip-out of element wires was accelerated more remarkably in the Bridge’s relative W-side, i.e., in the cable# i=2 ~ 6 & 8.

Despite the cause of these troubles was just the same as the cause of the Bridge collapse to have happened months later, there was no action, since nobody came up with their analogy. See Fig. 5.

 

Analysis of Collapse Stage

(1) Sequence of cable disconnection

'The sequence of cable disconnection' is a password to solve the Bridge collapse. But the Report’s causation theory isn’t compatible with the video recorded sequence of collapse. Hence, the Report must start with a denial of the facts recorded by videos. The Report does it by advocating, ‘The failure of the steel stranded wires and the anchor head occurred inside the structure. The actual location of failure and the sequence of the failure cannot be known.’

Really, a cable consists of plural element wire. The element wires do not disconnect once, but little-by-little. Last, there’d be 0~1~2 remnant element wire(s) that’s (are) in a losing posture. The section at this time is a disconnected section. But it’s not a disconnected time as the cable is still connected. When the remnant element wire(s) is (are) disconnected, it’s the time of disconnection.

If the cable disconnection is thus defined time- & location-wise, the sequence of cables’ separation from the arch rib or from the HDPE protection at the deck-slab FL timely & analog-wise correspond to the real time disconnection, though there’re very little time lags (maybe <1/60-sec) between them. Ask Galileo Galilee, or learn yourself from drop tests at: the Torre di Pisa, ‘if a falling body released 1^st goes down after the one released later.’ The one released 1^st (regardless of hidden or not) hit 1^st the ground.

In fact, the cable disconnection started with wire slip-out in W-side upper anchors. It was followed by the E-side wire cut-off at deck-slab FL. If the opposite is true, sun will rise from West.

Now, see Table 1. As wire slip-out & cut-off developments during Latent & Actualized Stages depended on 𝝷’’s development (Item A), the sequence of cable disconnections at Collapse Stage (row B) should also conform to row A too. Their sequence was observed in video records as shown in the Row B. The Report’s imagined sequence (Item C) is also shown in the Row C of Table-1.

Table 1 𝝷 's progress & Sequence of cable disconnection

Item	Sequence of disconnection (# i)
A	7	8	6	5	4	3	2	9	10	11	12	1	13
B	8	6	5	4	3	2	7	9	10	11	12	1	13
C	11	10	12	13	9	8	7	6	4	5	3	2	1

Numbers of bold in B & C rows show the ones that have discrepancies with the progress of 𝝷 shown in the A row. The cause of an irregular aspect of cable# i=7 has been already explained. The total discrepancies in C row reveal a logical flaw in the Report’s causation theory.

Note: Numbers with underline show wire cut-offs at the deck-slab FL. Other ones show wire slip-outs at the upper anchors.

(2) Sequence of supports’ stepping off

It’s observed in video records as follows:

W-side support fell 4/60 (sec) after the cable# i=1 had disconnected. The E-side support followed it after 10/60 (sec). The two legs of each support on each pier didn’t step off the pier at the same time. The S-side leg stepped off first and N-side leg followed it with a time lag of less than 1/60 (sec).

There’re 2 asymmetrical aspects whose mechanism must be explained, viz.: (i) In a side view, why did the W-side support step off prior to the E-side support? (ii) In a cross-section, why did each support’s S-side leg step off prior to its N-side leg?

The structure is internally symmetrical; hence, it’s no cause to produce an asymmetrical consequence. The cause is external and is asymmetrical per se. A sole answer is, “an external load of 3-times heavier trucks on the N-lane than on the S-lane.”

The practitioner of (i) is, ‘prior E-side cable disconnections to W-side.’ Its mechanism has been already explained earlier.

As to the mechanism of (ii), the effect of “heavier weight of trucks on the N-lane than on the S-lane” is a little more complicated than of (i). It’s explained as follows:

1^st: Heavy trucks (36-ton class full-loaded weight) on the N-lane produced residual deformation to the deck slab. 2^nd: The same trucks on the S-lane after unload is about 12-ton weight. They were too light to eliminate the caused residual deformation. The effect had been accumulated. 3^rd: It reduced the reaction at deck-slab’s S-side shoes. 4^th: Reversely, the reaction at the N-side shoe increased. 5^th, When W-side support was pulled inward by the sagging tie cables, there was a lesser frictional resistance at the S-side leg’s supporting point. 6^th: It resulted in the earlier step off of the S-side leg than the N-side one. The phenomenon happened miller-symmetrically in the E-side support a moment later than the W-side.

The deck-slab played no role in the mechanism. It’s intact after collapse as seen in the Cover Photo. The dead weight of the deck slab was handed over to the 2-tie cables (arranged between both the supports through the deck-slab body and anchored at the supports’ bottoms) after the stay cables abandoned the deck slab. The tie cables sagged and pulled the supports inward. As a result, of course, the S-side support leg stepped off first and N-side one later,

(3) Behavior of Deck-Slab Fall

An S-side-inclined fall of the deck slab can be recognized in video records by the feature of splashing water when the deck slab hit the sea water.

The problem of N-ward biased positions of the fork-support tops relative to the deck-slab center line after the collapse can be explained as follows:

(i)     Fill a sink in your kitchen with water. (ii) Hold a kitchen board with its shorter sides on the sink being inclined a little lower toward you. (iii) Release your holding so that the board drops. (iv) Observe phenomena when the board hit the sink’s water surface.

You’ll see (a) the lower side of the kitchen board hit the kitchen water surface 1^st and produce a low water splashes of low height, (b) the higher side hit water next with higher water splash and (c) the board moves toward you.

Phenomena corresponding to (a) & (b) can be seen in video records of Bridge collapse too. But (c) is invisible in videos. However, it must have occurred in the Bridge collapse as well. This is the cause why both the for-support tops are seen relative N to the deck-slab’s center line. cf. Cover Photo

 

CONCLUSIONS AND RECOMMENDATIONS

 

This paper summarizes its conclusions as follows:

(1)     The Bridge would’ve been designed with standard live loads (e.g., TL-20).

(2)    The 36-ton full-load weight truck triggered the Bridge collapse. It’s recorded in monitoring videos.

(3)    The truck had passed the same class bridges and reached the site without trouble. Hence, the truck isn’t a principal cause. The Bridge must have been weak already. Up to this point, there’s no difference between the Paper & the Report.

(4)    The difference is in the nature of the weakness. The Paper says, ‘The weakness is inborn (original), and was actualized by heavy trucks.’ The Report says, “The weakness is acquired (pandemic), and was developed by salty rain.”

(5)      The salty rain isn’t easy to be the cause by nature, much less if it contradicts with the facts. The Report cannot help denying the facts. Really, the Report does it when it says, ‘The video records do not show the sequence of collapse.’

(6)      The method of anchorage of a stay cable is usually either nuts or wedges both of which are friction based. They’re apt to loosen by high frequency vibration. Regular products have a device to prevent it. The anchors used in the Bridge are the imitations of one of regular products, except the one used at the cable# i=7 (center cable). It might have been copied by local smiths, having been shown the model & its drawings. These imitations couldn’t bear the vibration caused by the uniqueness of the Bridge.

(7)      Then, the usage of the irregular product is the principal cause? No, because no lower anchor of the same imitation was broken. Since the vibratory impact didn’t reach the lower anchors as it was absorbed by a concrete slab under which the lower anchors were set.

(8)      Shortly, Report’s causation theory is laymen's forced analogy.

(9)      The Paper induces its causation hypothesis as follows:

(i) A principal cause is the unique design that produced an unusual 𝝷 motion on the Bridge. (ii) The used anchors of imitation lost their function sooner than the specified one. (iii) The disconnection of E-side cables at deck-slab FL was the consequence of the W-side cable disconnection. At the deck slab FL, the element wires had already developed fatigue cracks, and it was the cause why the disconnections happened there.

(10)  The use of imitation anchors instead of regular ones (shown in the as-built drawing) prompted the date of occurrence.

 

This Paper summarizes its recommendations as follows:

(1)   An accident investigation shouldn’t include stake holders in a working group so as to hold the independency of the investigation.

(2)   An investigation should be done under an open condition so that it could absorb expertise more widely.

(3)   He, as a human, sympathizes with a motif to help insider parties. But disagrees to doing it by twisting truth. There’s a way to achieve the same purpose with truth. Instead of saying, ‘The cause is beyond the human knowledge,’ say, ‘The cause is beyond the currently applicable computer programs.’ Most of accidents nowadays belong to this scope. Not humans but the system is responsible for the incident.

(4)   There’s a one-for-all method to save the Bridge, Keeping the uniqueness of the structure almost as it is. Replace a cable# i=7 with cables shown in Fig. 5 (a) red lines. In this way, wire slip-out at the upper anchor and wire cut-off at deck-slab FL won’t happen. It lengthens Bridge’s life about 40 more yrs.

(5)   It’s a general tendency for heavy-haulage operators to let a heavy track run fast on a bridge. Their reasoning is, ‘It shortens a loading time. The truck can pass before the bridge may fall.’ He doesn’t discuss it. But it’s really a wrong concept. Keep load & speed limitations < 2*design load & < 20 (km/hr) respectively.

 

REFERRENCES

 

[01] Sohei Matsuno, Zul Hendri, ‘A STUDY ON THE CAUSE OF KUKAR Bridge COLLAPSE,’ www.iba.ac.id, Jan. 6, 2012

[02] Sohei Matsuno, Zul Hendri, ‘’A STUDY ON THE CAUSE OF KUKAR BRIDGE COLLAPSE (sequel),’ www.iba.ac.id/

[03] Sohei Matsuno, ‘UIBA'S AND HAPPY PONTIST'S KUKAR Bridge COLLAPSE THEORY,’ www.iba.ac.iddocuments/83

[04] Sohei Matsuno, ‘2011 JAPAN QUAKE OVERPOWERS PLATE TECTONICS’, repo.ia.ac.id/index

[05] Sohei Matsuno, ‘SUMATRA-JAVA LINKAGE PROJECT OF FEASIBILITY’,

www.akademika.iba.ac.id/, Aug. 1 2012

[06] Sohei Matsuno, ‘CAUSE & PREVENTION OF COASTAL FLOOFING, JAKAETA FLOODING AS A CASE,’ 

www.iba.ac.id/

[07] Sohei Matsuno, ‘JAKARTA FLOOD PREVENTION PROJECT WITH A TRUE CAUSE,’ www.iba.ac.id/ 8 Mar 2013

[08] Sohei Matsuno, ‘JAKARTA FLOOD PREVENTION WITH A TRUE CAUSE (sequel),’ www.lba.ac.id/, 30 Apr.2013

[09] Sohei Matsuno, ‘JAKARTA-FLOOD PREVENTION BY TRAINING DIKE vs. GIANT SEA WALL,’ www.iba.ac.id/,

[10] Sohei Matsuno, ‘SEA LEVEL RISE AND COASTAL FLOODING (JAKARTA), www.iba.ac.id/

[11] Sohei Matsuno et al, ‘A CAUSAL STUDY ON THE AIRASIA AIRBUS CRASH EVENT,’ www.iba.ac.id/  2015

[12] Sohei Matsuno, Asmadi, ‘A STUDY ON LUFTHANSA GERMANWINGS AIRBUS  CRASH EVENT,’ www.iba.ac.id/documents/, 2015

[13] S. Matsuno, ‘STUDY ON LUFTHANSA GERMANWINGS AIRBUS CRASH,’

        www.iba.ac.id/

[14] Dr. Sohei Matsuno, MS. Pujiono, ‘LEARN BEA'S PRELIMINARY REPORT ON LUFTHANSA CRASH,’ www.iba.ac.id/documents/

[15] Sohei Matsuno, ‘STUDY ON RUSSIAN METROJET AIRBUS CRASH,’ soheimatsuno.blogspot.com/, Jan 8, 2016

[16] Sohei Matsuno, ‘REVIEW OF AIRBUS CRASH & BUDGET SYSTEM -- given new data by Daallo event & AirAsia –‘soheimatsuno.blogspot.com/, May 30 2016

[17] Sohei Matsuno, ‘STUDY ON EGYPTAIR AIRBUS CRASH,’

soheimatsuno.blogspot.com/2016/10/study-on-egyptair-airbus-crash.html Oct 18, 2016

[18] Sohei Matsuno, Kimora Matsuno, ‘LEARN AIRBUS CRASH FROM METROJET-/EGYPTAIR-EVENT,’ soheimatsuno.blogspot.com/, Nov 29, 2018

[19] Sohei Matsuno, Kimora Matsuno, ‘STUDY ON AIRBUS CRASH BY ANALOGY TO DISHWASHER SLUMP,’

          soheimatsuno.blogspot.com/2018/06/study-on-airbus-crash-by-analogy-to.html Jun 6, 2018

[20] Sohei Matsuno, ‘LEARN KRAKATAU (2018) BY ANALOGY TO KRAKATAU (1883)’ soheimatsuno.blogspot.com › 2019/06 ›, Jun 3, 2019

[21] Sohei Matsuno, ‘COUNTERMEASURES AGAINST CORONAVIRUS-2019’ http://soheimatsuno.blogspot.com/2020/07/, Jul. 7 2020

[22] Final Report Released on Nanfangao Sea-Crossing Bridge ...

www.ttsb.gov.tw › english › post 2020/11/25 — News title: Final Report Released on Nanfangao Sea-Crossing Bridge Collapse Date: November 25, 2020 Content: At 9:30 am on October 1, 2019