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
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.
1st: To exhibit the facts which the Report doesn’t
mention, 2nd: To confirm the Paper’s confirmed facts and the
Report’s ones on common matters. 3rd: To convince of contradictions
between the facts and the Report’s causation theory. And 4th: 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:
1st: 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.
2nd:
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.
3rd:
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 1st
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.
4th:
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.
5th: 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 3rd:
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 20th 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.
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 2nd-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.
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.
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. (1st) a latent stage of nearly 2 decades, (2nd)
an
actualized stage of about 1 yr
and (3rd)
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 𝝷p. The 𝝷p is different if the load is applied to a different cable# i point.
In a side view; 𝝷p due to load applied at each symmetric point is symmetrical. It
means that the consequences of 𝝷p. 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 𝝷p 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.
1st
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.
2nd 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.
3rd step: Wire cut-off in cables# i=7 & 9
The cut-off of element wires of cable# i=7
at the deck slab FL and sequent cables# i=9
4th 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.
5th step: Wire cut-off of cable# i=13 & sequent
step-off of E-support
This step immediately followed the 4th
step. The phenomenon is mirror-symmetric to the 4th 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 1st and W-side 2nd
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 (cv, ch) 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 cv & ch 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., mp,
cv, ch, kh,
L. 𝜔*t, W & 𝝷c (as irrelevant) and kr
& K (as negligible). cf. Fig 5 (c).
It’s a statically determinate structure. It can be solved for 𝝷p
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 kv,
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: 𝝷p produces a free vibration
in the cables. 𝝷p 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 𝝷p-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
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
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: 1st, the speed of 𝝷p development became much quicker than
in Latent Stage. 2nd, 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). 3rd, 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 1st goes down after the
one released later.’ The one released 1st (regardless
of hidden or not) hit 1st 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:
1st: Heavy
trucks (36-ton class full-loaded
weight) on the N-lane produced residual deformation to the deck slab. 2nd:
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. 3rd: It reduced the reaction at deck-slab’s S-side
shoes. 4th: Reversely, the reaction at the N-side shoe
increased. 5th, 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. 6th: 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 1st 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
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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
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Matsuno, ‘JAKARTA
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www.lba.ac.id/, 30 Apr.2013
[09] Sohei
Matsuno, ‘JAKARTA-FLOOD
PREVENTION BY TRAINING DIKE vs. GIANT SEA
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‘A
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‘LEARN BEA'S PRELIMINARY REPORT ON LUFTHANSA CRASH,’ www.iba.ac.id/documents/
[15] Sohei Matsuno, ‘STUDY
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AIRBUS CRASH & BUDGET SYSTEM -- given new data by Daallo event
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soheimatsuno.blogspot.com/2016/10/study-on-egyptair-airbus-crash.html
Oct 18, 2016
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Nov 29, 2018
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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
