The Scottish Government

Calculation of loading in the cable

Fairhurst and FM are have calculated the bridge dead load and are in close agreement except in an area close to the towers.
Fairhurst adopted a footway loading of 0.15kN/m, and FM adopted a footway loading of 0.15kN/m ².
Fairhurst results are used in determining cable FOS.
Fairhurst are content that the calculated dead loads are accurate as their computer model profile matches survey work that they have performed.
FM's check of the dead load was independent except that WAF provided them the thicknesses of the mastic asphalt surfacing

Was the assessment subject to a Category III Check?

There was no specific requirement for a formal Category III Check but there was very close correlation between the assessments made by FM and Fairhurst, independently.
As agreed at meeting with Scottish Executive on 24 Nov 05, the assessment and checking of dead and super dead loads will be subject to Cat 3 Check certification. Note that derivation of BSALL has not been subject to an independent check.

There was a small difference between the calculated dead loads in the cable. What were the FM and Fairhurst figures and which one was used?

DL

DL, Ft, BSALL

WAF

120074

139736

FM

122590

142130

The FM model is our third one, which we considered to be the most accurate.
It was agreed at the meeting with Scot Exec on 24 Nov 05 that the WAF cable loads would be adopted. This reflected Fairhurst's greater knowledge of the bridge.
Note that Fairhurst used 0.15kN/m footway and FM 0.15kN/m ².

How has the Live Load been calculated?

A Bridge Specific Live Loading ( BSALL) has been derived for the structure by Fairhurst. It appears to have been calculated BSALL using a rectangular influence line, where successive sequences of weights of groups of vehicles were looked at with length sufficient to fill the bridge.
The BSALL is based on a 3 week period in September 2002 and 2005. Vehicle spacing was taken as 1.5m.
The BSALL used in the FOS calculations is based on 2002 data only.

We have no issue with this at such lengths, since individual odd vehicle weights will not be very important.

What limits of exceedence were set?

WAF used 5%/120 years / 1.20 = HA, which is normal.

What jam assumptions were made?

Traffic jam assumptions are based on records and on incident clearance times (in the order 30 minutes each usually).

Sensitivity is not too great.

What lane choice assumptions were made?

Lane choice - if lane was not filled they allowed nest vehicle to move over.

This is only really relevant at low traffic flows and is not unreasonable

What lane load factors were used?

Lane factors: They were quite conservative. They calculated Lane 1, and joint 1+2, and Lane 2 as well. They found Lane 2 alone to be about 0.35 times Lane 1, and had they derived Lane 2 from the Lanes 1+2 total less Lane 1, Lane 2 would have been smaller again. So their use of 0.66 is very safe-sided.

It appears that the process has been logically constructed in accordance with HA recommendations. It is almost certainly safe-sided owing to conservatism especially in Lane 2 loading.

How was the opposite carriageway loaded?

Opposite carriageway they used average weight of traffic jam ("Turkstra's rule") which FNP has used in the past. This gave them 0.33 factors at longest loaded lengths.

This is not too surprising for road with so many cars. We would expect to model simultaneous 4 lane effects, since opposite direction jams are so common. This would not make much difference.

What vehicle spacings were used?

Vehicle spacings: they used 1.5m between leading and trailing edges.

This is not too different from 5m from axle to axle which is what Eurocode suggests. Their gaps are based on approximate site observations.

Why was a cable inspection carried out?

Alastair Andrew ( FETA) attended a workshop in 1998 in the US at which the methods of inspecting and assessing main cables were discussed. This led onto the draft NHCRP Guidelines issued in 2002. These recommended that intrusive inspection of cables in major suspension bridges be carried out after thirty years of service and thereafter every ten years. The FETA board were advised of this and they took the decision to implement this draft recommendation. At this stage the bridge was 38 years old but was the oldest major suspension bridge in Europe.

Tamar Bridge in Plymouth is an older suspension bridge but this has locked coil strands, not parallel wires. Limited inspections have been undertaken at Tamar Bridge but no significant remedial work has been proposed as a result of the findings of those inspections.

How were the consultants selected?

Prequalification then price (30%)/quality tender (70%)

Team given high marks for choosing Weidlinger as sub-consultants because they are the authors of the NHCRP Guidelines.

What work was carried out in the initial desk studies?

The scoping study comprised a review of the construction history and records followed by a visual inspection of each section of the cables. These were examined for defects that might have permitted moisture ingress, such as cracked or missing paint; loose wrapping etc.

How were areas of the cable selected?

These were determined from the scoping study and previous experience from the US.

What were the reasons for the selection

The NHCRP recommendations suggest that six panels should be inspected, but eight potential locations were originally selected based on the scoping survey, previous US experience and on the basis that the chosen locations would give a good spread of results across the complete length of the cables. Two more panels were added as a reaction to the results from the first four panels as those results were varied and some panels were worse than expected. The inspections were targeted at what was thought to be the worst affected panels and those for which results could be obtained quickly bearing in mind the access problems and the desire to complete the work within one season.

In what ways (if any) did the results of the external visual inspection correlate with what was found in the later detailed internal inspections?

Generally where there were large areas of paint damage or circumferential cracks in the paint, the outer wires beneath these areas were found to be in poor condition. However, after opening up the groove in the affected area, it was found that the internal wires were not necessarily in the same condition. Generally panels had evidence of dampness on the underside of the cable which was confirmed when unwrapped.

No reliable evidence of correlation - it cannot be assumed that the panels selected for internal inspection would be the worst condition.

Were other areas of the cable inspected such as the anchorages, the cable between the side span towers?

Approximately one third of the strands in the anchorages were inspected from scaffolding.
The cables under the shrouds adjacent to the side saddles were inspected. Loose wires were found which related back to broken wires within the side saddles. The side saddles are not internally galvanised so it is possible that the failure mechanism for these wires is different. (Refer to report for West 00S-02S). It was also not possible to repair those wires that were broken within the saddle. Most of the broken wires were left in place to avoid leaving a void.

How many of the four anchorages were inspected?

Strands were inspected in each of the 4 anchorage chambers. There are 37 strands in each anchorage, each of which splay into 4 sub-strands as they approach the strand shoe. 12 out of the 37 strands were selected in each anchorage and 2 of the 4 sub-strands in each of the 12 strands were wedged open both horizontally and vertically for inspection.

Have the circumferential seals around the cable clamps been closely inspected?

Seals were visually inspected as part of the scoping study and condition survey prior to unwrapping and were generally found to be in good condition. The undersides of the cable bands are not caulked.
Above deck level, the sealant was replaced during hanger replacement in 1998-9.
In each panel inspected only the upper seal was removed and the outer wires inspected prior to rewrapping. Generally, there were crossed wires close to cable bands but the external wires in this area generally appeared to be in good condition.

Have any portions of cable inside the tower or other saddles been inspected?

No. The main tower saddles have C clamps like Severn, therefore access is impossible. FETA expressed great concern over removal of cover plates on side tower saddles as there is only a small fos against bursting. The wires under all 4 side tower cable sleeves have been inspected and the wires beneath the cable sleeves at the top of the north east tower have been inspected in both the main and side spans.

How small is the factor of safety against bursting?

Which areas were not inspected?

The length of cable between the side saddle and the face of the anchorage was not inspected because nothing un-toward was found in the scoping survey; access is very difficult and that length of cable is less exposed to the elements than other lengths.

Were the selected areas influenced by other findings?

The direction of wrapping is known for each section of cable and it was originally postulated that the direction of wrapping may have had some influence on the recently observed levels of corrosion. It is thought that wrapping downhill is preferable to wrapping uphill as the former allows any trapped moisture to escape as the cable is compacted.

This is not considered a valid postulation. All cables are subjected to wetting (at least) during the lengthy construction period, and will all start out their lives with some moisture in them. This initial moisture will have its free oxygen consumed in a short time, limiting the amount of corrosion it can cause. The damage we see today is the result of continuing intrusion of moisture by rain and passage of moist air into the cable under varying barometric pressures.

How was consistency of inspection assured?

The inspection was carried out throughout by two dedicated inspectors, Beverly Camfield and Kevin Wood. The inspections were occasionally replicated by Weidlinger inspectors, Ron Mayrbaurl and Sante Camo and the results were compared. There was little variation in the recorded condition of the wires. In addition, on their UK visits, Weidlinger inspectors would "oversee" FM inspections at random segments.

Weidlinger reports that both Ron Mayrbaurl and Sante Camo trained the FM inspectors and audited their work.

When a panel was inspected by both Weidlinger and FM and there were variations in the assessed condition, were they all 'one way' or 'give and take'?

There was very close correlation between Weidlinger and FM's wire gradings. The occasional differences were between late stage 2 and early stage 3, generally 'give and take'. Only two inspectors from FM carried out the entire inspection and their comparisons in results were practically identical.
It is worth noting that the same inspector carries out the visual inspection of wires in a groove and selects a wire of a particular classification of corrosion level for tensile testing. Therefore the tensile test results for each corrosion stage will be consistent with the corrosion classification given by the inspector for each panel.

When there were variations, what was recorded, the worst condition?

Yes.

Was the recording of the stages of corrosion strictly in accordance with the NCHRP Guidelines?

Yes.

How was surface damage recorded at inspection panel sites

This was recorded photographically and also by hand. A typical record sheet has been forwarded to FNP by FM.
FNP were shown photographs showing the external condition of the cable prior to wedging and photographs taken looking into a groove. The photographs did not clearly show the condition of the wires at the bottom of the groove.

Within the NCHRP Guidelines, surface wires around the perimeter of the cable are not required to be inspected prior to wedging. Their condition is assumed based upon the condition of the surface wire at the wedge position.

Condition of corrosion protection

The original red lead paste was always found to be crumbly and dry as expected by NCHRP Guidelines.

This is consistent with inspection findings in the US and Lisbon, Portugal.

Was any damage attributed to the inspection processes?

There were 2 wires (out of the 86 total broken wires) where there is a possibility that the inspection process may have contributed to their failure:-
1. W100S-100N - One additional wire break was noticed after inspection had been carried out; this wire may already have been broken but the ends not evident until wires were disturbed during inspection.
2. E100N-98N - One additional outer wire was observed to break at the start of compaction and was subsequently repaired.
However, it is likely that these wires were already cracked and near failure.

Broken wires

Broken wires were usually found in the outer six layers. However, broken wires deeper within the cable were more difficult to find as the broken ends of the wires did not spring out like those in the outer layers. Some broken wires were found deeper in the cable but only when they were on a wedge line.

NCHRP Page 2-22 recommends additional wedge lines, particularly where several broken or Stage 4 wires are found or if cable larger than 24" diameter.

Method of recording wire condition

The method followed strictly the NCHRP guidelines. The report "tree circle" plots record the worst recorded condition of an individual wire over a 75 to 150mm length within the total length of groove opened up. Records of the condition of the wires at each ring of wedges are available and samples were sent by FM to FNP.
The condition of the wires at the bottom of the groove was assessed by eye with the aid of two powerful torches; endoscopes were not used.

Based on our review, it appears the methodology is consistent with the practice in the US.

Presumably, only the condition of the visible face of each wire was noted?

Yes.

When extra wedge lines were applied in two of the inspected sections it is noted that in both cases they allowed a less onerous condition to be recorded. Should more have been done?

The inspection was carried out in accordance with the NCHRP Guidelines which recommends 8 groove locations around the perimeter. The additional 9 ^th groove opened in two of the panels was specifically to investigate areas where a large congregation of stage 4 corrosion had been found in an adjacent groove, as well as to search for internal broken wires.
It should be noted that a 9 ^th groove was opened up at E100S-100N which allowed a slightly less onerous condition to be recorded. However, even with this refinement, this panel was found to contain the largest proportion of stage 4 corrosion out of all ten panels inspected and was subsequently used for the strength calculation.

NCHRP Guidelines recommend additional wedge lines, particularly where several broken or Stage 4 wires are found or if cable larger than 24" diameter. (Forth main cable diameter is approximately 24" diameter).

Stages of corrosion

No correlation between wire breaks and stage four corrosion.

Impact of saddle wire breaks?

Considered by FM/Weidlinger to be due to lack of zinc spray at anchorage

Recording of pits

Only observed one wire.

Position of cracks vs. cast and vs. sector vs. longitudinal position

The wire cracks always initiate on the inside of the cast. FM estimate the residual stress to be 30 ksi (207 N/mm ²) and a stress from straightening of 37 ksi (255 N/mm ²)

Was foreign material embedded in the cable associated with locally worse wire conditions?

Yes, embedded pieces of timber and seizing straps which should not have been left inside the cable have caused locally worse wire conditions.
Internal seizing straps are impossible to remove during construction.

Inspection records indicate the presence of wood and rope in a few locations. This material has promoted corrosion of the wires in contact with it.

PH measurements

All PH measurements were neutral or slightly alkaline. Weidlinger reports that PH measurements have been taken where moisture was found on the cable surface.

They appear to be in the range PH 6 to PH 9, but there is no obvious reason for the variation.

Were all wire failure separations measured and what was the range of dimensions?

Measurement was not practical everywhere. Where gaps between the ends of broken wires were measured, measurements were in the order of 50-55mm.

Were all wire sample separations measured and what was the range of dimensions?

All gaps resulting from cutting sample wires were measured. Of the 80 sample wires removed gaps varied from 40-110mm with an average of 55mm. The larger gaps were found in the panels adjacent to the side tower saddles (longer panels).

Under the NCHRP guidelines, (C2.2.5.4 and C2.4.3.2.3) should a clamp have been removed as part of this investigation?

C2.2.5.4 refers to the second inspection, not the first. Note that U.S. bridges have suspenders at 20 to 30ft centres, Forth is 60ft. We did consider briefly removal of a clamp, but felt that the significant and expensive temporary works were not justified for the first inspection.

In view of the Stage 4 severity at several locations and that Panel 6 was adjacent to the previously inspected (and worst condition) Panel 1, removal of a cable clamp may have been warranted and should be considered for the future inspections.

Samples taken for testing

Samples of wires for testing were only taken from the outer eleven layers.

This is not common practice as it may not be representative of the larger population of wires throughout the cable cross-section.

Was consideration given to removing wire samples from deeper inside the cable by using a special tool?

It was not considered feasible to remove wires deeper due to clearance problems with the remaining wires within the wedge when cutting, re-splicing and re-tightening. Even if a special tool could be designed to pull a deeper wire out of the wedge, access for cutting and re-tightening would be very limited and damage to neighbouring wires would be more likely. FM stated that their policy was to avoid any further damage to the main cable and therefore decided not to remove samples from areas where they could not replace the wires.

Cable diameter measurements/ voids ratio at re-closure

Extensive cable diameter measurements were taken to ensure to correct level of re-compaction was achieved.

Was satisfactory re-compaction of the cable always achieved?

Generally satisfactory re-compaction was achieved. There were localised areas around crossed wires and areas where a number of repairs to broken wires had taken place where compaction was fractionally less than the rest of the panel.

Were the number and type of wires tested strictly in accordance with the guidelines?

The wire samples selected were in proportion to the quantities of each corrosion stage recommended in the NCHRP report.

Were the samples selected from representative locations within the cross-section or limited to outer wires?

The wire samples taken were limited to the depth from which they could be removed - up to 11 wires in from surface.

Water analysis

An analysis of a water sample was made but FM advised against placing too much reliance on the results.

Weidlinger states that they believe the water analysis is reliable. It is postulated by Weidleinger that the PH is rapidly neutralized by the corrosion process.

Static testing - what was the strain rate and were all samples taken to failure?

All wire tests were taken to failure. On nine out of ten tests the extensometer was removed at about 2% elongation. The extensomer was left on for only one in ten tests so that the risk of extensometer damage was reduced.

Weidlinger reports that all wire sample were tested to failure - about 700. About 10% of these had strain measured to failure. The others had strain measured to about 2% elongation, after which the extensometer was removed and the test continued to failure.
Chemical analysis at the fracture surfaces has not been performed.

Fatigue testing

No fatigue testing of wires has taken place. Fatigue testing is very useful to fairly quickly find cracks in the wires, but each specimen must be fatigue tested. This does not leave any specimens to use for determining tensile strength, as the ENTIRE LENGTH MUST BE FATIGUE TESTED SINCE WE DON'T KNOW IN ADVANCE WHERE THE CRACKS ARE. The normal tension tests are very efficient in finding cracks if the failure surface is carefully inspected; the elongation at failure and the tensile strength of each specimen are extremely good indicators as to which specimen may be cracked. The only way that we would accept fatigue testing is if we doubled the number of sample wires removed, using half for fatigue tests and the other half for tensile tests, both an expensive proposition as well as putting more ferrules into the cable that introduce voids.

Fatigue testing is not specified in the NCHRP Guidelines because it is recognized that fatigue is not normally an issue in the cable service loads. However, it is our experience that fatigue testing is useful in identifying incipient cracking in wires that perform well in static tests. This may be advisable in determining a more reliable estimate of the percent of cracked wires in the stage 3 and 4 population. Faber Maunsell/Weidlinger's comments (opposite) are noted. It was agreed that this would be reviewed again in the brief for the Lehigh University Tests programmed for early 2006.

Beyond which layer were repairs impossible because of difficult access?

Repairs were not possible beyond 11 wires in from surface.

Corrosion protection re-establishment - lead paste/wrapping/painting

Red lead to the original specification has been applied together with an improved paint system on top of the wrapping wire.

Selection of testing establishments

FM were very pleased with the firm selected to carry out the wire testing. Bodycote did a very professional job.

Has consideration been given to re-inspection of the panel which is in the worst condition ?

No, this is not a requirement of the NCHRP guidelines.

Stress/strain plots

FM to supply FNP with some typical Stress/Strain plots including plots for wires with pre-existing cracks.
Four plots were handed over on 24.11.5, refs 111.10; 151.10; 171.09 and 171.10.
Ron Mayrbaurl states that 80 specimens have full plots to failure and that the wire is uniform and ductile.

What was the original wire specification?

The wire was manufactured at Dorman Long works in Lackenby. There was only one source for the steel but early results showed two types of Stress/Strain curve. Some wire samples had 0.7% carbon and others 0.8%.
FM provided details of the wire specification to FNP.

Original spec called for .75 to .80% Carbon. Four samples have been tested for chemical analysis and ranged from 0.74% to 0.80%, indicating good quality, uniform wire (based on these very limited number of samples). Weidlinger reports that there is apparently good correlation between tested wire strengths and carbon content (the stronger wires having the higher carbon) as expected.

Has any loss in strength of the cable as it passes around saddles and shoes been taken into account?

No. The major effect on cable strength is cracks in the wires. At strand shoes, the bend is considerably sharpened, which reduces the tensile stress on the inside of the curvature of the wires. We have not found cracks in these wires on three bridges on which wires were removed from around the strand shoes, only general corrosion resulting in loss of area leading to failure of wires. The increased curvature should not have an effect on the strength of a "good" wire.
The curvature around saddles also reduces the tensile stress on the inside of the wire cast. Several wires were found broken about 8" inside the cable bent saddle at one location. These wires failed by cracking in the tangent area where the wire separates from the saddle.
The transverse pressure on the wires at the bottom of the saddles will reduce the yield strength in longitudinal tension slightly, and probably also the tensile strength, but this was not considered.

Broken wire vs sector

No analysis of the positions of wire breaks has been performed.

Weidlinger states that with few exceptions broken wires tend to be located within the outer 6 wire rings. Our review of the preliminary report confirms this.

Cracks vs Stage of corrosion

Ron Mayrbaurl reports that Weidlinger used a slightly modified Stage classification. Stage four wires are defined as having 25% or more of the surface corroded rather than 30%, as specified in the NCHRP Guidelines. This results in a larger percentage of Stage 4 wires and no cracks found in wire classified as Stage 3. Weidlinger is currently reassessing the strength calculations, considering the outer six wire rings as a separate population. This further reduces the projected number of cracked wires, as they are a larger percentage of a much smaller population than the entire Stage 4 population.

Establishment of crack initiation mechanism

It is understood that FM have instigated research into the causes of crack initiation. No conclusions have been presented.

The exact mechanism of crack initiation is still not fully understood. However, in general it is commonly accepted that it begins with embrittlement due to hydrogen absorption. The hydrogen is generated by the galvanic reaction of the zinc-iron-electrolyte battery. The embrittled wire surface is made susceptible to cracking at pre-existing flaws or corrosion pits.

What progress has been made to determine the mechanism for crack initiation?

Work is just starting at Lehigh.

What percentage of Stage 3 wires have been assumed to have cracks?

None.
Tests on 17 Stage 3 wires did not find any cracks. On another bridge, where 3 or 4 cracks were found in wires that were graded Stage 3, two panels were reopened after a few years and samples of Stage 3 and 4 from greater depths removed for testing. No cracks were found in Stage 3, and two of the previously tested samples were looked at again; it was determined that they were on the borderline between Stage 3 and Stage 4, and that Stage 3 should be considered without cracks.

Calculation of remnant strength based on results of testing

The calculation of the rate of deterioration of the cable strength is based on NCHRP Guidelines which are derived from data from US bridges.

The calculated cable strength is based on the extrapolated number of wires in each Stage of corrosion as inspected and the tested strength of the wires in those stages, not on any US data. The rate of deterioration has been projected using a calculation method proposed in the NCHRP Guidelines. It is based on several assumptions and some very limited (and ongoing) laboratory testing conducted in the US to determine corrosion rates in accelerated corrosion testing chambers.

What information has been used to model the deterioration through the various stages of corrosion?

The question is assumed to mean "what information has been used to model the deterioration over time?"
The starting point is the condition of the cable at the time of inspection. Additional information used is from a study underway in Boston, in which wires under tension are subjected to "environments", either liquid or damp, that would cause first the zinc to dissolve (react to the acidity in the environment) and then the steel underneath to corrode. Each series of tests is scheduled to run for 2 years. In the first series, four of the specimens yielded useful data that indicate that the time taken from one stage to the next is linear up to Stage 4. Thus far, stage 4 has not been exceeded, and no cracks have been initiated. The next series, that is now underway, has been designed to use the most promising environments to attempt to advance corrosion into crack initiation, as well as to verify the data from the first series.
In the absence of actual data, it has been assumed that the time from reaching Stage 4 to initiation of a crack, and then for crack growth and failure, and then further to failure of all wires in the group being evaluated is at the same rate.
Other data used is the location of broken wires in the cable (mostly on the bottom, with one on the side of the cable; the location of cracked wires found in the samples removed (mostly on the bottom and one on the side); and the depth of broken wires and cracked wires inside the cable (again, mostly in the outer six rings, except for three in the interior, one of which is clearly caused by a piece of wood found in the cable.
Using the condition at inspection as the starting point, the progression of Stages (or "categories", since the calculation must advance beyond Stage 4) at any location in the cable is a linear calculation.

What is the original strength of the cable based on the brittle wire model, and how does this compare with the nominal assumed original strength of the cable.

Original nominal design strength is 349274kN.
Original brittle wire strength is 345198kN.

C2.2.5.2 of the guidelines gives an estimated error in the minimum strength calculation based on the adequacy of sampling. What estimated error has been calculated?

This has not yet been estimated. It is a time consuming procedure. It will probably be on the order of 5 to 7%.

The response does not appear to fit with the estimated error anticipated in the Guidelines.

Has the effect of the wrapping wire on the development of tension in broken wires been taken into account?

This would increase the estimated cable strength, but only if the wrapping is removed over several contiguous panels during an inspection prior to measuring wire end separations, in which case the calculated effective development length will be too long, resulting in too low an estimated strength. Since the wrapping was not removed from panels adjacent to the evaluated panels in this inspection (with the exception of one panel adjacent to E100S-100N, and then only after wire end separations were measured), the effect of wire wrapping is automatically included in the calculation of the effective length. The development of tension is only applied to wire breaks in adjacent panels, not to wire breaks in the evaluated panel.
Some measurements that have been made indicate that, for surface wires, the wrapping could redevelop the wire tension in as little as ten feet, but no information is available for deeper wires (The wire tension is not the same as the wire strength!). We consider that ignoring the wrapping wire is conservative. On the Forth Bridge, the effective development length has been estimated as 5 panels (a broken wire will redevelop its strength in two panels ( i.e., after passing through three cable bands).

When were the cable clamp bolt tensions last checked and what proportion of the bolts needed re-tightening?

The cable band bolts were replaced in 1998-99. No retensioning has been carried out since.

Reliability analysis
Contribution of broken wires

The contribution of broken wires to the strength of the cable away from the breaks has been taken into account in the calculations.

This is standard practice.

Have the repaired and replaced wires been taken into account?

Yes

What are the latest figures for loss of strength?

Current cable strength (based on nominal fraction of cracked wires and only outer 6 rows containing cracked wires, brittle wire model) is 322095kN.
Original strength (brittle wire model) is 345198kN.

Would say 12 months of acoustic monitoring provide any data useful for the deterioration model?

Acoustic monitoring will provide data on wire breakage rate and location only. It will not provide data on rate of corrosion - e.g. rate of stage 3 to stage 4.

How has Weidlinger calculated the rate of strength degradation in future years?

Weidlinger has used the hypothesized method presented in the NCHRP Guidelines, which are not supported by historical or other data except for some limited laboratory testing conducted in the past at Columbia University and currently underway at Altrans in Massachusetts. These tests have attempted to mimic the conditions inside a bridge cable and produce accelerated corrosion conditions that could be correlated with the observed conditions on bridges. We will review the methodology and results in detail as soon as we receive the calculations from Weidlinger.
In the first deterioration model presented, no loss in strength has been assumed for the first ten years. Thereafter, a linear deterioration from Stage 1 to Stage 4 has been assumed.

This is related to the calculation of remnant strength discussed above.

In the deterioration model it is assumed that the cable begins to deteriorate from Day 1, but at what age is it considered that strength loss begins?

From the table in 6.6 below, it can be seen that strength loss starts to occur just before 1991.

What is considered to be a 'wide' range for carbon content? i.e. at what point does the 'Brittle Wire Method' become the inappropriate method to use for the estimation of cable strength?

On the Williamsburg Bridge, the carbon content varied from 0.60% to 1.00%. This is a wide range. On the Forth the carbon content varies from 0.74% to 0.80%. This is a normal range for bridge wire, that results in an approximately 2% lower cable strength when using the brittle-wire model. (see below, under brittle-wire vs. limited ductility models. No investigations have been made into the exact range that would be considered too wide.

Using the brittle wire model may give a conservative estimate of the loss in strength. What would be the difference if the limited ductility model was used?

This will be the first bridge inspection in which a reasonably accurate calculation using the limited ductility model will even be possible, since most tensile tests have the extensometer removed from the specimen at a maximum of 2.5% elongation, nowhere near failure. An estimate made using this model on another bridge with the ultimate strain for each sample wire calculated by projecting upward from the elongation measured after failure using Young's modulus resulted in a cable strength that was 3% greater that that found using the brittle-wire model.
Weidlinger has developed a revision to the brittle-wire model that uses the full length stress-strain diagrams that were developed for one specimen from each of the 80 sample wires removed from the Forth Road cables. This should bring the results from the brittle-wire and limited ductility models closer, as the wires in both models will break in the same order. Preliminary results indicate that this revision will result in about a 2% increase in the current cable strength at panel E 100S-100N and about 3% for the new cable condition. The final numbers will be provided after checking.
The application of the limited ductility model is still to be done; the data from the above mentioned analysis is to be used for this.

What are the latest estimates of Factors of Safety and over what future period are they projected?

Year

nom cbl strength
kN

Strength loss
%

FOS

1964

345198

0.0%

2.47

1983.4

345,198

0.0%

2.47

1991

343,321

0.5%

2.46

1997

336,777

2.4%

2.41

2004

322,095

6.7%

2.31

2009

305,838

11.4%

2.19

2014

282,327

18.2%

2.02

2019

247,446

28.3%

1.77

What is the latest deterioration model plot?

See Deterioration Model Plot, opposite

Are the FoS conclusions based on the maximum load being applied to the worst section of cable?

Yes, on the basis that only a small sample of the cable has been inspected.

Is adopted practice consistent with UK practice on reliability?

The use of a single factor for all structures is not supported by the reliability based methods of analysis in use in the UK. However, the use of a global factor as an indicative value is not without merit, but must recognise the relative uncertainty in the load prediction and strength assessment of each individual structure.

What is being proposed as an intervention strategy?

FETA is seeking consultancy services for dehumidifying the cables.