Failure Analysis of the Arecibo Observatory 305-Meter Telescope Collapse (2024)
Chapter: 3 Analysis
3
Analysis
CABLE SOCKET ZINC CREEP FAILURE
Thornton Tomasetti, Inc. (TT) did a more detailed analysis of six auxiliary cable sockets and concluded in its 2022 report (hereafter “TT Final Report”), “Four of the six sockets that were analyzed failed or were in the process of failing. The failures of sockets M4N-T and M4-4T occurred in the field and involved the rupture of multiple outer wires and a significant shift or complete pull-out of the core, which corresponds to core rupture.”1 An example of this failure process is generally illustrated in Figure 3-1. The specific processes in M4N-T and M4-4 will be discussed in more detail below.
Unfortunately, TT’s socket analysis focuses only on sockets that had “failed or were in the process of failing.”2 Not all spelter sockets exhibited signs of creep, and not all were examined post-failure. Four of the five auxiliary main cable sockets attached to the platform exhibited only the ⅜ inch pullout.3 TT’s Lehigh University laboratory testing demonstrated that this pullout initially occurs during the initial “seating” of a newly poured socket when it first supports its service load.4 The fifth platform axillary cable socket only had ½ inch of pullout, and no data were reported on the sixth socket. All the tower ends of the auxiliary main cables bore the same load (minus the 15.7 kips of cable weight) as their companion tower sockets. Yet five of six tower sockets had more cable pullout than their companion platform socket. While no data was available about the platform end of the sixth auxiliary cable, M4N, it would appear highly unlikely that the platform end of this cable had more pullout than the tower end’s 1.125 inches5 but went unnoticed and unreported. This pattern does not appear to have been noticed by TT, and none of the platform sockets that exhibited zero zinc creep in 23 years of service after 1997 were examined as part of the TT analysis to determine why they had no creep. It is also unlikely that each of the six platform sockets, manufactured at the same time and by the same people, had wire brooming superior to their six companion tower sockets. Thus, valuable insight into the effect of brooming was lost or why some sockets exhibited zero zinc creep.
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1 Thornton Tomasetti, Inc. (TT), 2022, Arecibo Telescope Collapse: Forensic Investigation, NN20209, prepared by J. Abruzzo, L. Cao, and P.E. Pierre Ghisbain, July 25, https://www.thorntontomasetti.com/sites/default/files/2022-08/TT-Arecibo-Forensic-Investigation-Report.pdf (hereafter “TT Final Report”), p. 44.
2 J. Abruzzo, L. Cao, and P. Ghisbain, 2022, “Arecibo Observatory: Stabilization Efforts and Forensic Investigation,” Thornton Tomasetti, Inc. (TT) presentation to the committee, February 17 (hereafter “TT presentation”), slide 28.
3 TT presentation.
4 TT Final Report, Appendix N, Figure 10, p. 7.
5 TT presentation, slide 28.
SOURCE: Thornton Tomasetti, 2022, Arecibo Telescope Collapse: Forensic Investigation, NN20209, prepared by J. Abruzzo, L. Cao, and P.E. Pierre Ghisbain, July 25, https://www.thorntontomasetti.com/sites/default/files/2022-08/TT-Arecibo-Forensic-Investigation-Report.pdf; courtesy of Thornton Tomasetti.
Based on the observed Arecibo Telescope socket slip and the results of laboratory testing, it appears that all cable pullouts greater than ½ inch may involve zinc creep.
Conclusion: Based on the observed Arecibo Telescope socket slip and the results of laboratory testing, it appears that all cable pullouts greater than ½ inch may involve zinc creep.
Material creep is a time-dependent increase in permanent deformation in polycrystalline metals and alloys under loading at effective stresses that can be well below the material’s yield strength.6,7 Creep can also occur in compression, albeit at lower rates. Creep is very different from one-time work hardening at low temperatures brought about by rapid deformation. Work hardening requires additional higher stress to achieve additional permanent deformation once hardened. Creep deformation can involve softening over time or relaxation of the deformed state at a specific temperature, which then allows additional deformation at a fixed load. Creep deformation is a function of material properties, exposure temperature and time, and the applied load. A material’s creep behavior cannot be quantified by short-term proof testing or loading to fracture quickly at high strain rates because there is insufficient time for softening. There is no substitute for long-term load exposure to quantify creep. Creep is extremely material dependent, and certain mechanisms have a very strong power law relationship to applied stress and temperature. Creep has three regimes: primary, secondary, and tertiary.
In primary creep, the strain rate decreases with time. In secondary creep, deformation continues at a steady state rate over long periods because recovery occurs dynamically such that work hardening in the zinc is balanced by recovery or softening effects. During long-term secondary creep at moderate stresses, significant permanent deformation can be achieved. The time-dependent dynamic recovery of the straining to accumulate additional permanent deformation (by dislocations and twinning) is balanced such that dislocation entanglements do not accumulate. The strain rate that can be maintained is relatively independent of total exposure time and a strong function of stress and temperature.
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6 A.J. Stavros, 1987, “Corrosion,” AMS Metals Handbook, Ninth Edition, Volume 13, ASM International, p. 432.
7 R. Abbaschian, L. Abbaschian, and R.E. Reed-Hill, eds., 2009, Physical Metallurgy Principles, Fourth Edition, Cengage Learning.
Creep follows a power law function of tensile stress but can even occur under compressive stress or pure shear stress. The creep strain rate depends on temperature, stress, shear modulus, vacancy diffusion rate, and grain size and is strongly materials dependent. Creep operates at stresses below yield and at temperatures typically above 40–50 percent of the absolute ratio of operating temperature to melting temperature (i.e., ~ T > 0.5 Tm), with temperature expressed in Kelvin. The range of TH = T(K)/Tm (K) is about 0.44 Tm at 85°F. Also, it should be noted that zinc creep can occur at a lower fraction of Tm. Furthermore, zinc creep is thermally activated, and there is no cut-off temperature since an Arrhenius-type behavior occurs. Zinc has a low activation energy for creep.8 The possibility of zinc creep leading to failure would not have been predicted at the Arecibo Telescope, given the zinc deformation, expected service life, and design stresses.
Plotting the stress/shear modulus estimate and temperature ratio for pure zinc on the reported zinc deformation map9 for 0.1 mm grains demonstrated that the Arecibo Telescope cable socket service lies in the regime of power law creep (PLC). The power law conclusion is also reported in the Wiss, Janney, Elstner Associates (WJE) report10 and has been independently recalculated with the same findings of power law creep by the committee. It should be noted that power law creep is predicted when there is high stress, moderate temperature (T/Tm ~0.4, where T/Tm is known as also TH = T(K)/Tm(K), the homologous temperature [expressed in Kelvin]), and large grain sizes, all of which were operating conditions for the Arecibo Telescope spelter sockets. The dependency of creep rate on stress has been taken to the 4th power (assumed) by TT. The creep strain is estimated to be near 10−9/sec, which also agrees with WJE’s estimate. The effective “zone” of zinc that deforms by power law creep in a spelter socket is hard to estimate, as is the local state of stress in the complex geometry of the socket. However, if a 5 cm longitudinal zone of zinc near the spelter socket tension side aperture at uniform stress underwent power law creep, that could lead to deformations up to 1 cm over 25 years.
The finite element models presented in the NASA Engineering and Safety Center report11 illustrate the detailed zinc behavior in the auxiliary cable’s spelter socket. Figure 3-2 illustrates that the compressive stress pattern is a “spheroid” shape (red color).12
The compressive contact pressures form “arch actions” (compression struts) that transfer bond/shear forces developed between individual wires and zinc to the socket interior surface. The shear forces between the zinc and the wire are balanced by tension in the wires. Figure 3-2 shows various color bands (struts) representing different stress levels, with the red color signifying the arch with the highest compression. The arch stresses are highest near the mouth of the socket. These compressive forces (which correspond to transverse forces on the wires and the socket) produce shear (friction) resistance between the wire and the zinc in those areas. The compression stress at the socket is balanced by an equal and opposite force applied by the socket walls. The vertical components of these struts help resist the cable forces. The transverse arch action compression forces also contribute to the slanted (shear) wire failures observed on some outside wires in the M4N cable. Because of the higher stresses, the front of the socket is much more important than the back in resisting cable forces. This fact was also noted by Bradon and colleagues13 in resin sockets.
Creep susceptibility depends strongly on the operating temperature relative to the material’s absolute melting temperature. Since zinc has a low melting temperature, which is required to prevent the molten socket material from heat-treating the steel wires during socket filling, it is potentially susceptible to creep at tropical temperatures. Even when the socket material starts consistent with the ASTM standard, over time, there can be diffusion of elements or zinc dislocations to allow impurity-rich areas to develop that may change the properties of the parts.
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8 T.H. Courtney, 1990, Mechanical Behavior of Materials, McGraw-Hill.
9 H.J. Frost and M.F. Ashby, 1982, Deformation-Mechanism Maps: The Plasticity and Creep of Metals and Ceramics, Pergamon Press.
10 Wiss, Janney, Elstner Associates (WJE), 2021, Auxiliary Main Cable Socket Failure Investigation, WJE No. 2020.5191, June 21.
11 G.J. Harrigan, A. Valinia, N. Trepal, P. Babuska, and V. Goyal, 2021, Arecibo Observatory Auxiliary M4N Socket Termination Failure Investigation, NASA/TM−20210017934, NESC-RP-20-01585, NASA Engineering and Safety Center, Langley Research Center, June, https://ntrs.nasa.gov/api/citations/20210017934/downloads/20210017934%20FINAL.pdf (hereafter “NESC Report”), Appendix C.
12 NESC Report, Figure C-9, p. 560.
13 J. Bradon, R.C. Chaplin, and I. Ridge, 2001, “Analysis of Resin Socket Termination for a Wire Rope,” Journal of Strain Analysis for Engineering Design 36(1):71–88, https://doi.org/10.1243/0309324011512621.
SOURCE: G.J. Harrigan, A. Valinia, N. Trepal, P. Babuska, and V. Goyal, 2021, Arecibo Observatory Auxiliary M4N Socket Termination Failure Investigation, NASA/TM−20210017934, NESC-RP-20-01585, NASA Engineering and Safety Center, Langley Research Center, June 15, https://ntrs.nasa.gov/api/citations/20210017934/downloads/20210017934%20FINAL.pdf.
If excessive zinc creep occurs, it becomes increasingly difficult for the socket to maintain the compression forces on the wires associated with the arch action on the cable. Excessive creep produces a softening in the center of the socket. The wires at the center of the cable start to shed their mechanical load and redistribute the load from the cable’s core wires to the outside wires. With further unloading of wires at the core, stresses on the outside wires increase until wire failure occurs in the most highly stressed wires. The examination of the failed M4N-T socket by NASA revealed multiple ductile (cup-and-cone) overloaded wire failures in the three outer wire rows around the perimeter of the cable near the front of the socket opening.
The structural modeling and analyses of wire brooming issues presented in the TT Final Report were based on some assumptions.14 The compression stress helps the socket resist cable forces by transferring (through compression in zinc) the inclined arch action forces to the socket’s conical surface. If pullout were to occur due to excessive creep of zinc, then the compression stress shown in Figure 3-2 (e.g., the red band) would also dissipate, and the compressive force at the surface of the core would dissipate significantly. Creep (or flow) of zinc in shear will also be accompanied by the creep of zinc in compression, thus dissipating the force in the struts. Furthermore, the angle of the compression stress was assumed to be constant (i.e., equal to the longitudinal slope of the interior surface of the socket). It was not adjusted as a function of the radius of the core. Figure 3-2 shows that the slope of the compression stress changes at different r values.
TT analyzed the sockets using the developed models to assess the effect of the extent and quality of wire brooming. They concluded that the effects of brooming imperfections were significant. However, it is important to note that the wire brooming imperfection significance is related to the extent of creep. When zinc creep becomes excessive, the compression stress weakens (due to the inelastic softening action in zinc), and the socket’s load-
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14 The computational model presented in Appendix O of the TT Final Report estimated radial and shear stresses on a zinc core with a radius of r (with r ≤ the radius at the mouth of the socket). The shear stresses at the outside surface of the zinc core were calculated based on a friction equation (i.e., a zinc-zinc friction factor multiplied by the estimated normal force). It is not clear why the shear strength of zinc material was not calculated (in presence of a normal force) in lieu of the friction calculations. An assumption may have been made that cable pullout had already occurred (due to zinc creep or flow) causing separation of the core from the rest of the socket. If it is argued that friction should be used (instead of the shear strength of zinc at the surface of the core) because of the slip, then the normal pressure must also be reduced substantially.
carrying ability dissipates. In such cases, the effects of brooming issues become magnified and significant because of the loss of the arch action. Brooming imperfections without creep would, therefore, be less significant due to the beneficial contributions of a functioning set of compression stresses.
The NASA investigative report on the failed M4N-T cable socket pointed to “a socket design with insufficient design criteria that did not explicitly consider socket constituent stress margins or time-dependent damage mechanisms.”15
The socket attachment design was found to have an initially low structural margin, notably in the outer socket wires, which degraded primarily due to zinc creep effects that were activated by long-term sustained loading and exacerbated by cyclic loading.16
Nothing in the NASA conclusion points to anything unique about the Arecibo Telescope. The design margin for the Arecibo Telescope’s sockets was typical of cable structures, and there was nothing unique about the Arecibo Telescope’s cables or sockets. The NASA report does not explain why the common design characteristics of the Arecibo Telescope’s sockets produced failure, which, to the committee’s knowledge, had never been previously reported in similar zinc-filled spelter sockets.
Finding: Core slippage and cable pull-out occurred by stage II creep more or less continually but slowly for over 23 years in the auxiliary cable tower sockets.
Partial pullout slippage by PLC would be expected to increase significantly when the zinc core pulls out sufficiently to diminish radial and longitudinal compression, as zinc is no longer as severely wedged in the socket. The committee believes this is a critical tipping point in the whole socket failure mechanism—that is, when core slip is advanced enough for stresses on zinc to switch from compressive wedge action such that radial compression enabled by the wedging action is relieved. As a result, the committee expects acceleration of PLC on the zinc core outside the socket aperture because it is strongly tensile stress–activated. Increased tension forces on the core are transferred to outer wires as indicated by TT and NASA, which ultimately can produce either slip or fracture. Cable tension and cable core slippage length were not directly tracible to cable pull-out probability because there are too many variables, and the sockets with the longest slip did not fail first. However, the stress dependencies are so strong in PLC that subtle differences in stress state produce large variations in creep rates observed.
Inspections performed on the Arecibo Telescope sockets in 2003 and 2011 by the structural engineering firm Ammann & Whitney (A&W) concluded, after inspecting the Arecibo Telescope auxiliary main cables in 2011, “As noted in the 2003 report, the cast zinc has separated away from the leading edge of all the sockets by up to 1/2.”17 Thus, it would appear there was no observed additional cable pullout in 8 years, so the expected pullout in the next 6 years, up to 2017, would most likely be small or non-existent.
As part of its forensic investigation, TT commissioned a socket load test, referenced earlier, conducted at Lehigh University’s Fritz Laboratory. Socket B4S-G, a backstay socket, was recovered from the collapse along with 15 feet of cable and tested under static and cyclic loads. A new zinc spelter socket was cast at the free end of the cable. This added socket was required to complete the test but does not fully represent an aged spelter socket that might contain breaks. The specimen was installed in a test frame and loaded to 100, 125, and 150 percent of the cable’s static load for 20 hours. Load cycles were applied at each of the load levels to measure the behavior of the socket under cyclic conditions. Finally, the cable was loaded to failure, which was slightly greater than the cable’s minimum breaking strength.
Cable slip was monitored at each load level. The pre-existing cable slip before loading was measured at 0.875 inches on the B4S-G socket. Cable slip continually occurred at each of the loading levels for each socket. At the initial loading of 100 percent of the static service load, the additional cable slip in the new socket was 0.03 inches.
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15 NESC Report, p. 12.
16 NESC Report, p. 12
17 TT presentation, meeting transcript minute 02:33:36.
At the 150 percent loading, the measured displacement grew close to 0.1 inches over 24 hours.18 The final displacement of the B4S-G socket was 1.375 inches (0.875-inch pre-existing slip +0.5-inch slip at failure). It should be remembered that the socket system is complex, and cable pullout alone could not reveal how many wires in the socket were already fractured during creep. “The slip rate increased substantially in B4S-G once the cable tension exceeded 75 percent of the Minimum Breaking Strength.”19 As the Lehigh University socket testing demonstrated, even a small amount of additional pullout would not be predicted to measurably impact socket strength.
Finding: The Lehigh University testing of an Arecibo Telescope socket with ⅞ inch of pullout confirmed that an Arecibo Telescope socket with only ½ inch of pullout would be expected to support the full strength of the cable with no hidden damage in the form of wire breaks.
Of course, some Arecibo Telescope socket strengths were clearly being degraded by accelerated zinc creep, a process that would have continued without Hurricane Maria. However, even though the cable loads from the wind of Maria were far below that which should have produced any additional cable pullout, this relatively small increase in cable loading appears to have significantly aggravated the creep rate of the ongoing cable pullout based on the measured cable pullouts from the A&W structural conditions from 2011 and post-Maria repair documents.
Conclusion: Based on available evidence, Hurricane Maria produced unexpected cable pullout and an unexpected acceleration in cable pullout.
Long-Term, Low-Current Electroplasticity
One of the open questions about the Arecibo Telescope’s collapse is what unique circumstances of the Arecibo Telescope caused an unprecedented and significant acceleration in the spelter socket zinc creep. Searches by all the forensic investigators produced no previous reports of such a spelter socket failure mode despite more than a century of spelter socket use. To the best of the committee’s knowledge, there are no previous reports of such spelter socket failure in more than a century of their use. The investigations did not produce a direct or plausible explanation of this unique phenomenon. The only hypothesis the committee developed that could possibly explain the measured patterns and ultimate effects of the observed socket zinc creep acceleration was the effect of electroplasticity (EP).
EP is “the reduction in flow stress of a material undergoing deformation on passing an electrical pulse through it.”20 EP was first discovered by Eugene S. Machlin, who reported in 1959 that making a 6 kV (dc) closed circuit with NaCl crystals made them weaker and more ductile.21 Later, in 1963, Troitskii and Likhtman reported the same EP effect in zinc crystals.22 In 2020, Baumgardner et al. reported the following:
A low-energy electroplastic effect in aluminum alloys at an ultra-low current density threshold between 0.035 and 0.1 A/mm2 that resulted in EP-assisted reduction in hardness of 10% and increases in creep rate up to 38% over a range in temperatures from 25°C to 100°C. Systematic experiments and ab initio calculations showed that Mg-Zn alloying elements in Al7050 were the origin of the EP effect.23
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18 TT Final Report, Appendix N, Figure 10, p. 7.
19 TT Final Report, pp. 39–40.
20 A. Lahiri, P. Shanthraj, and F. Roters, 2019, “Understanding the Mechanisms of Electroplasticity from a Crystal Plasticity Perspective,” Modelling and Simulation in Materials Science and Engineering 27(8), https://doi.org/ARTN08500610.1088/1361-651X/ab43fc.
21 E.S. Machlin, 2004, “Applied Voltage and the Plastic Properties of ‘Brittle’ Rock Salt,” Journal of Applied Physics, https://doi.org/10.1063/1.1776988.
22 O. Troitskii and V. Likhtman, 1963, “The Effect of the Anisotropy of Electron and γ Radiation on the Deformation of Zinc Single Crystals in the Brittle State,” Doklady Akademii Nauk SSSR 148:332–334.
23 C.H. Bumgardner, B.P. Croom, N. Song, Y. Zhang, and X. Li, 2020, “Low Energy Electroplasticity in Aluminum Alloys,” Materials Science and Engineering: A 798, https://doi.org/10.1016/j.msea.2020.140235.
“To date, the theories of Joule-heating, electron-wind force, and de-pinning from paramagnetic obstacles are the most commonly invoked explanations for instances of EP observed in different materials.”24 There is a more detailed and extensive listing of past EP research in Appendix C, along with references.
When an electrically conductive rod, cylinder, or cable is placed within an electromagnetic (EM) field, electrical currents are generated on the surface of the conductor at the same frequency as the EM wave. The resulting alternating electrical currents would be limited to a skin depth from the outside surface of the metal. In the Arecibo Telescope, the EM waves were high frequency (S-band radar at 2380 MHz), and thus, the skin depth would be small (on the order of microns). The Arecibo Telescope cables were not solid rods or cylinders and consisted of multiple layers of spirally wound round wires around a core element. This arrangement of wires complicates the current flow. Regardless, current always flows to a ground. The committee did not have access to the grounding circuits of the Arecibo Telescope, but, at a minimum, the towers would have had at least ground-connected lightning arrestors and extensive steel rebar from its top anchoring the saddle to the underground foundation. The lightning circuit and the rebar pattern were not described in any of the other reports, and no electrical measurements of the ground were made. It also appears from the pattern of cable pullout that the tower end of the auxiliary main cables may have had their ground connection path through the auxiliary backstay cables. In the Arecibo Telescope failure sequence, a relatively young auxiliary cable pulled out first at a load less than half its strength before two main cables that were more than twice its age pulled out of their sockets at much higher relative loads. This outcome could be explained by significant metal structural differences that affected the quality of the ground or the pattern of current flow (described below) through the zinc of their respective sockets at the tower end of the different cables.
All the Arecibo Telescope main and auxiliary cable wires terminated in (and were surrounded by) zinc within the cable end sockets. However, from an electrical perspective, the structure of the auxiliary backstay ground-end sockets and the auxiliary main tower-end sockets was substantially different at both ends from that of the original main tower-end sockets, as illustrated by Figures 3-3 and 3-4. The auxiliary backstay ground-end socket and the auxiliary main tower-end socket geometry were similar in that all the Arecibo Telescope’s EM radiation–generated current had to flow entirely through the auxiliary cable socket zinc to reach ground. The electrical connection from the auxiliary main cable end socket to the auxiliary backstay cable end socket was provided by a metal box frame that surrounded the tower top, and to which both the auxiliary main and auxiliary backstay cables were attached, as shown in Figure 3-5. Consistent with these observations, the auxiliary backstay ground-end sockets and the auxiliary main tower-end sockets had the most significant measured cable pullout, as illustrated by Figure 3-6. This pattern was not discussed or explained in the other reports.
In contrast, the current generated in the main cables flowing to the tower end socket had a path to ground that only required current to flow through the front end of the socket zinc and may have also had alternate paths to the ground. The main cables on the tower end terminated in a socket whose front rested on the back of a metal saddle secured to the tower top. To reach their socket on the back side of the saddle, the main cables passed through saddle slots, which had enough clearance to permit the cable installation. Based on the Tower 8 cable replacement drawings, which do not call out a clearance value, there was so little clearance between the cable outside diameter and the sides of the saddle slot that the cable effectively “masked” the bottom of the slot from the white paint subsequently applied to the cable/saddle assembly, which could not get past the cable to cover the slot bottom. The main cable’s paint masking of its saddle slot is shown in the drone frame capture after the failure of M4-4 shown in Figure 3-7. It also appears there could be some layers of torn lead paint that previously “bridged” the cable clearance with the saddle slot.
How much physical and electrical contact a main cable had with the saddle before its socket termination is unclear from the available evidence, and the resistance of these connections was not measured. If a main cable physically contacted any point of its saddle slot before its socket termination, this contact could provide the EM radiation–induced main cable current with an alternate parallel path to ground thus never reaching the socket zinc. Further evidence of physical contact of the main cables with their saddle slot can be seen in a photograph of the Tower 12 saddle, which is shown in Figure 3-8. Contact would appear to be the only mechanism to produce paint fracture below all four saddle slots. This same paint cracking below the main cable slots is also evident on the
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24 Lahiri et al., 2019, “Understanding the Mechanisms of Electroplasticity from a Crystal Plasticity Perspective.”
SOURCE: G.J. Harrigan, A. Valinia, N. Trepal, P. Babuska, and V. Goyal, 2021, Arecibo Observatory Auxiliary M4N Socket Termination Failure Investigation, NASA/TM−20210017934, NESC-RP-20-01585, NASA Engineering and Safety Center, Langley Research Center, June 15, https://ntrs.nasa.gov/api/citations/20210017934/downloads/20210017934%20FINAL.pdf.
Tower 4 saddle in Figure 3-7. However, the committee is unaware of any contact evidence in the form of fretting marks or similar contact indications on the cable wires.
The current generated on the outside surfaces of the auxiliary cable wires (and along the embedded length of the steel wires in sockets) would necessarily flow through all the zinc in the auxiliary main and auxiliary backstay sockets. All the current induced in the outside of the main cables did not have to flow through all the zinc in the socket, just through the front socket zinc near the front face of the socket bearing on the saddle. Main cable current may also have had parallel paths to ground of some quality in front of the socket through cable contact with the metal saddle, and “bridges” of lead paint (of unknown conductivity) that formed after the paint could not get through the small cable clearance. The auxiliary backstay cable pullout on the ground-end sockets of cables B12-W, B12-E, B4N, and B4S (Figure 3-6) was measured at ⅞ inch on three of the six auxiliary backstay cables and almost 2 inches on one of them, the most measured on any socket before failure. A potential explanation for this widespread ground-end cable pullout is that the auxiliary cable EM-generated current was flowing to ground through all the zinc in the ground-end sockets, which accelerated their creep.
Further evidence that the main cable-induced current did not all flow through their tower end socket zinc is the slower rate of main cable socket strength degradation from accelerated creep compared to the auxiliary cable sockets. The auxiliary cable tower socket M4N-T failed after just 23 years of service at a load ~46 percent (600/1314) of its nominal strength.25 Despite being more than twice as old, with 57 years of service, the first main cable socket failure, of M4-4, only occurred after this socket exhibited ~62 percent (646/1044)26 of its nominal strength for almost 3 months. Both Tower 4 sockets suffered significant strength degradation from accelerated creep, but no other explanation for this disparity in socket strength degradation rate has been offered.
Current flow, albeit at much higher levels than seen at the telescope, has been shown to soften and increase the creep of zinc in a much shorter time, as cited previously. But a lower current over a much longer time could also
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25 TT Final Report, Appendix G, Figure 15, p. 12.
26 TT Final Report, Appendix G, Figure 21, p. 16.
SOURCE: Thornton Tomasetti, 2022, Arecibo Telescope Collapse: Forensic Investigation, NN20209, prepared by J. Abruzzo, L. Cao, and P.E. Pierre Ghisbain, July 25, https://www.thorntontomasetti.com/sites/default/files/2022-08/TT-Arecibo-Forensic-Investigation-Report.pdf; with photos modified from SOCOTEC Engineering, Inc. (top) and NAIC Arecibo Observatory, a facility of the National Science Foundation (middle and bottom); courtesy of Thornton Tomasetti.
SOURCE: Adapted from drone footage from NAIC Arecibo Observatory, a facility of the National Science Foundation.
SOURCE: J. Abruzzo, L. Cao, and P. Ghisbain, 2022, “Arecibo Observatory: Stabilization Efforts and Forensic Investigation,” Thornton Tomassetti, Inc., presentation to the committee, February 17, slide 28; courtesy of Thornton Tomassetti, Inc.
plausibly increase zinc creep, but far less and much more slowly. No other mechanism for increasing the ambient temperature creep rate in high-quality spelter socket zinc at these cable loads has been suggested, discovered, or reported. Long-term slightly accelerated zinc creep would eventually compromise force transfer from the wires to the conical socket through zinc.
The relatively newer auxiliary cable socket that failed first, M4N-T, was not the most heavily loaded, nor was the brooming of this socket the worst found in the Arecibo Telescope’s sockets. The reason(s) this auxiliary socket failed at less than half its strength—before 56 other main cable sockets that were more than twice its age—was not explained in any of the previously cited investigations. During a presentation of the TT Final Report, a representative of TT was not able to explain why this relatively young cable that had been determined to have a safety factor of greater than 2 suddenly failed.27
Considering that the long-term extrusion of zinc from the sockets and the subsequent pullout failure of the Arecibo Telescope cables have not been documented elsewhere, despite the long and wide use of zinc-filled cable
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27 TT presentation.
SOURCE: Adapted from National Science Foundation, 2020, “Video Footage of Collapse Arecibo Observatory,” December 1, mark 0:56 minute, https://www.nsf.gov/news/special_reports/arecibo/arecibocollapseinfo.jsp; courtesy of NAIC Arecibo Observatory, a facility of the National Science Foundation.
SOURCE: Photo IMG_2173 from January 27, 2020, inspection of Tower 12 provided to staff, with labels added by the committee; courtesy of NAIC Arecibo Observatory, a facility of the National Science Foundation.
spelter sockets, an investigation of the Arecibo Telescope’s collapse should explore possible site-specific factors that may explain the Arecibo Telescope’s socket failures. Low-current electroplasticity (LEP) offers potential explanations for the questions: Why did the Arecibo spelter sockets fail? When did this failure mode appear unique to Arecibo? and Why did a relatively new auxiliary socket fail first, before any main cable socket that was more than twice as old? LEP also offers a potential explanation of why all six auxiliary cable tower sockets had more cable pullout than their respective platform sockets on the same cable and why (at least) four of these sockets exhibited zero additional pullout in their 23 years of service after installation.
The type, size, length, and fittings of the Arecibo Telescope’s cables (whether the original cables constructed in the 1960s or the auxiliary cables installed in the 1990s) were not unusual and were catalog-selected items. The applied loads were mostly (but not all) dead loads, which were also not unusual considering that these types of cables are widely used across many applications in a wide range of industries. The 2.2 safety factor, discussed previously, ensured the applied dead loads never reached even half the cable strength, although the main cables operated at a lower, 1.98, safety factor for 30 years before the 1997 upgrade.28 Cables on the Arecibo Telescope operated in a unique EM radiation environment compared to the typical zinc spelter socket terminated cable; specifically, the Arecibo Telescope cables were suspended across the beam of the “most powerful radio transmitter on Earth.”29 The Arecibo Telescope had two high-powered radar transmitters, one at 430 MHz and another at 2,380 MHz continuous wave.30
Thus, the main and auxiliary stay cables of the Arecibo Telescope (and their sockets) were within the path of the high-power electromagnetic waves emitted by these transmitters. The tower tops (including the cable sockets at the top of the towers) were also directly exposed to radio frequency (RF) radiation. A 2005 Arecibo Telescope RF safety report31 states the following regarding maximum permissible exposure (MPE):
RF field levels at the upper elevations of the three towers can exceed the MPE limits for Occupational/Controlled exposure under some conditions. The high RF fields occur when either of the feeds is tilted to a fairly high elevation angle and the beam of energy is aimed in the direction of the tower. Under these conditions, the upper elevations of the tower are within the main beam of energy from the antenna.
The RF safety report established that the average RF field strength at the platform or the tower tops, if they are illuminated, is above the RF MPE32 limit. However, under other operating conditions, the larger illuminated area fields are not as strong. However, even under these circumstances, some current would be induced in the cables at an unknown strength. S-band radar from a source far less powerful than the Arecibo Telescope’s has been found to induce skin current at a few hundred feet that can be sensed directly by people in the beam.33
Manufacturing methods based on EP employ very high electrical current densities, on the order of 103–106 A/cm2,34 to achieve the desired deformation quickly. The electrical current densities in the cables of the Arecibo Telescope would be expected to be orders of magnitude smaller but applied over orders of magnitude longer time (e.g., decades). The M4N auxiliary cable was ~23 years old when it failed, while the main cables were 57 years old, yet failed within months of each other. However, the main cable sockets became subject to a significantly higher relative load after the M4N failure, and their strength was less degraded. This disparity in longevity and degradation might be partially explained by the fact that both the main and auxiliary cables became subject to
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28 TT Final Report, Appendix C, Table 4, p. 9.
29 A.P.V. Siemion, et al., 2011, “Developments in the Radio Search for Extraterrestrial Intelligence,” XXXth URSI General Assembly and Scientific Symposium, https://doi.org/10.1109/URSIGASS.2011.6051263.
30 J.L. Margot, A. H. Greenberg, P. Pinchuk, A. Shinde, et al., 2018, “A Search for Technosignatures from 14 Planetary Systems in the Field with the Green Bank Telescope at 1.15–1.73 GHz,” Astronomical Journal 155(5), https://doi.org/10.3847/1538-3881/aabb03.
31 RF Safety Solutions LLC, 2005, “RF Safety Report: An Analysis of RF Field Levels at the Arecibo Observatory,” report prepared for Cornell University and the Arecibo Observatory, revised August 25.
32 American National Standards Institute, ANSI Z136.1.
33 B.E. Moen, O.J. Møllerløkken, N. Bull, G. Oftedal, and K.H. Mild, 2013, “Accidental Exposure to Electromagnetic Fields from the Radar of a Naval Ship: A Descriptive Study,” International Maritime Health 64(4), https://doi.org/10.5603/IMH.2013.0001.
34 H. Conrad, 1998, “Some Effects of an Electric Field on the Plastic Deformation of Metals and Ceramics,” Materials Research Innovations 2(1):1–8, https://doi.org/10.1007/s100190050053.
the same most powerful EM current at the same time after the Arecibo Telescope’s upgrade in 1997, but the zinc in the auxiliary cable sockets had to conduct all the induced current, whereas in the main cable, the sockets may have been just one of multiple parallel paths to ground.
EP may also explain both the symmetry and asymmetry observed in the auxiliary main cable socket cable pullouts, cited earlier, which are illustrated in Figure 3-6.35
At the time illustrated by Figure 3-6, 23 years after the 1997 upgrade was completed, four of the five possibly less well–electrically grounded (as explained above) auxiliary main cable platform sockets on cables M4S, M8S, M12-W, and M12-E show only their original ~⅜ inch cable pullout. This ⅜ inch of pullout occurred after the first 18 hours of full-service loading36 of a newly made socket during the Lehigh University socket testing referenced earlier. There is no evidence that these four sockets experienced any zinc creep after they were put in service. This symmetry was not noted in the other reports.
All the tower end sockets of these auxiliary main cables, which experienced the same loading on the other end of the same cables, exhibited at least ½ inch of cable pullout (and some substantially more). Five of six tower socket cable pullouts on the auxiliary main cables exceed the platform socket pullouts on the same cable. While there was no date reported for the platform socket pullout of M4N, it is highly unlikely that a pullout greater than 1.125 inches on the tower end of this cable went unnoticed. This asymmetry was not noted either and is unlikely (odds of ~3 percent) due to random chance. It should be noted that the tower end of an auxiliary main cable has to bear the additional 15.7 kips of cable weight not borne by the platform socket. Still, this differential is substantially less than the cable-to-cable load variation or the load variation seen in the same cable as the azimuth arm rotated, as illustrated in Figure 3-9.37
The auxiliary main cable-to-cable load variation is more than 120 kips, and every auxiliary main cable sees a load variation of more than 40 kips. Yet, four of the five auxiliary man cable platform socket pullouts for which we have data were the same ⅜ inch of pullout from when they were manufactured and first loaded. It should be noted that the most lightly loaded cable in Figure 3-9 is M4N, whose tower socket failed first. Cable weight cannot explain the consistent asymmetry between the socket pullout of the platform and tower sockets of the same auxiliary cable.
Finally, differences in the interior cone shape between the platform and tower sockets do not appear to explain the asymmetric cable pullout. “Despite the exterior differences, the internal cable-to-socket connection was similar for all of the telescope’s sockets.”38
NASA concluded, “The unexpected vulnerability was further compounded by an effective design factor of safety that was significantly less than the minimum to ensure structural redundancy in the event of a cable failure.”39 However, it is important to distinguish factors of safety from redundancy. The Arecibo Telescope’s collapse illustrates the inherent non-redundancy of the three-tower arrangement of the structure with the specified cable lengths. Had a fourth tower been present (at 90-degree angles), the chances for the swinging action and collapse would have been significantly reduced, and the structure would have had some redundancy.
Conclusion: A higher factor of safety would not have offered any additional structural redundancy to the Arecibo Telescope.
A lack of structural redundancy was built into the Arecibo Telescope’s design in several places, such as the selection of three towers instead of four or the use of a single auxiliary cable instead of the original multiple parallel cables used for the main cables.
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35 TT presentation, slide 28.
36 TT presentation.
37 TT Final Report, Appendix H, Figure 13, p. 10.
38 TT Final Report, p. 5.
39 NESC Report, p. 12.
SOURCE: Thornton Tomasetti, 2022, Arecibo Telescope Collapse: Forensic Investigation, NN20209, prepared by J. Abruzzo, L. Cao, and P.E. Pierre Ghisbain, July 25, https://www.thorntontomasetti.com/sites/default/files/2022-08/TT-Arecibo-Forensic-Investigation-Report.pdf; courtesy of Thornton Tomasetti.
After the Aux M4N failure and before the main cable failure, additional analyses incorrectly asserted acceptable positive margin for the remaining structure despite no understanding of why a cable had failed at half the rated breaking strength. In hindsight, the structure was vulnerable to collapse after the Aux M4N failure.40
The committee concurs with this observation. Unfortunately, the profound safety implications of this realization were not noted. Retrospective observations about the impending failure warning from the observed cable slip found in the TT 2021 report, Arecibo Telescope Collapse: Forensic Investigation Interim Report (hereafter “TT Interim Report”),41 are not found in the TT Final Report.
CABLE END SOCKETS
“The cable failures leading to the [Arecibo Telescope’s] collapse occurred at cable ends, where cables are connected to supports with zinc-filled spelter sockets.”42 “Each failure involved both the rupture of some of the cable’s wires and a deformation of the socket’s zinc.”43 “Excessive cable slip occurs in zinc-filled spelter sockets due to zinc flow and is a sign of upcoming failure through core rupture or core flow-out.”44 All the analyses done by the investigators retained by NSF have arrived at the socket pull-out and/or rupture failure of spelter sockets by zinc “flow” as the root cause of the Arecibo Telescope’s collapse. It should be noted that conventional zinc creep was a necessary but not sufficient time-dependent phenomenon to cause the Arecibo Telescope’s collapse. The zinc
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40 NESC Report, p. 12.
41 TT, 2021, Arecibo Telescope Collapse: Forensic Investigation Interim Report, NN20209, prepared by J. Abruzzo and L. Cao, November 2 (hereafter “TT Interim Report”).
42 TT Final Report, p. ii.
43 TT Final Report, p. 1.
44 TT Final Report, p. 49.
slip brought about a transfer of load to the cable’s outer steel wires, which in turn failed by a combination of cup and cone ductile fracture, wire pullout, shear stresses, and, to a small degree, hydrogen environmentally assisted cracking (HEAC). The committee concurs with the TT Final Report that cable socket failure is the key structural element in the Arecibo Telescope’s collapse.
Manufacturing the zinc spelter socket cable connections is a reasonably straightforward but manual process. The current practice requires extensive manual preparation of the cable end wires before they are individually broomed open, inserted into the socket, and encased in molten zinc, as illustrated earlier in the report (Figure 1-8). If not symmetrically broomed, some wires would be under higher tensile stress. The molten zinc is poured at 925–975°F (496–523°C). Zinc is used because its low melting point allows it to be poured over the cable wires at a temperature that will not cause the wire steel to appreciably weaken through undesired heat treatment. Conversely, overheating the zinc can affect its bonding properties and reduce the strength of the wires. All dross (foreign matter) must be removed from the surface of the pure molten zinc before pouring to prevent impurities from being poured into the socket.
Zinc is used for the sockets due to not only its low melting point but also its bonding to the galvanized surface of the wires, assisting their resistance to corrosion. Impurities of lead, cadmium, iron, and tin, which are products of the various extraction processes from sphalerite, zinc blend, or marmatite, must be controlled to prevent the formation of materials that are less resistant to corrosion. Three zinc samples were removed from the Arecibo Telescope’s spelter sockets and tested. It is reported that “All three samples met the 99.5 pure zinc requirement of the ASTM B6 standard 14 prescribed for the original socket castings.45 The NASA report concluded, “The Aux M4N socket build process and original construction was typical of zinc spelter open-end socket terminations.”46 The committee concurs.
Conclusion: The Arecibo Telescope’s socket failures were not due to deficient materials or workmanship.
WIRE BREAKS
“As reported in Phoenix, Johnson, & McGuire, 1986, wire breaks in the main cables had been ongoing since early in the life of the telescope.… The records do not show any wire breaks in the auxiliary cable system.”47 This sentence appears true right up to the first cable failure. “Every known wire break is located near a socket at a cable end.”48 The first wire break appeared in the Arecibo Telescope’s main cable M4-4 in 1962, before the telescope was even commissioned,49 and the next wire break was reported in backstay cable B8-3 less than 1 year after the telescope’s commissioning.50
What purported to be a comprehensive list of the Arecibo Telescope’s wire breaks by location was presented by WJE, shown in Table 3-1.51 TT also purported to present a comprehensive diagram of all the Arecibo Telescope’s “known wire break locations and discovery dates before the first cable failure,”52 which is shown in Figure 3-10. Both compilations reflect 40 wire breaks,53 but unfortunately, these two compilations do not agree.
For example, starting with Tower 12, the WJE table reflects two subsequent breaks in the replaced B12-3 cable, whereas the TT diagram only shows one. Similarly, the WJE table shows a wire break on the M4-1 cable that is not reflected on the TT diagram. There is a significant disparity on the M4-4 cable. Both compilations show six breaks in this cable, but the TT compilation does not appear to reflect the 1962 wire break during construction.
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45 TT Final Report, p. 22.
46 NESC Report, p. 25.
47 Wiss, Janney, Elstner Associates, 2021, Auxiliary Main Cable Socket Failure Investigation, WJE No. 2020.5191, June 21 (hereafter “WJE Report”), p. 7.
48 TT Final Report, Appendix D, p. 7.
49 WJE Report, Table 2, p. 8.
50 WJE Report, Table 2, p. 8
51 WJE Report, Table 2, p. 8
52 TT Final Report, Appendix D, Figure 13, p. 10.
53 TT Final Report, Appendix D, p. 7.
TABLE 3-1 Main and Backstay Cable Wire Breaks Recorded by Wiss, Janney, Elstner Associates
| Cable Number | Date | Location | Number |
|---|---|---|---|
| A12-3a | Dec. 12, 1966b | Lower (L) | 2 |
| Sep. 6, 1974 | L | 3 | |
| Jan. 22, 1976 | L | 1 | |
| A12-3 (1981) | Dec. 22, 1982 | L | 1 |
| Nov. 6, 2001 | L | 1 | |
| M12-2 | Sep. 23, 1968 | L | 1 |
| Sep. 22, 1969 | L | 1 | |
| M12-3 | Feb. 28, 1968 | L | 1 |
| A4-1 | Aug. 22, 1997 | L | 1 |
| M4-1 | Aug. 25, 1997 | Upper (U) | 1 |
| M4-2 | Dec. 5, 1969 | L | 1 |
| Aug. 26, 1970 | L | 1 | |
| M4-4 | 1962 Construction | L | 1 |
| Jun. 22, 1967 | L | 1 | |
| Jun. 30, 1975 | U | 1 | |
| Jan. 17, 1983 | L | 1 | |
| Jul. 28, 1983 | U | 1 | |
| Nov. 23, 1988 | U | 1 | |
| A8-1 | Mar. 20, 1970 | L | 1 |
| A8-2 | Jan. 7, 1971 | L | 1 |
| A8-3 | Feb. 11, 1964 | U | 1 |
| A8-5 | Jan. 27, 1964 | L | 1 |
| Dec. 18, 2001 | L | 1 | |
| Jul. 9, 2003 | L | 1 | |
| M8-2 | Nov. 20, 1967 | U | 1 |
| M8-4 | Mar. 20, 1973 | L | 1 |
| Jan. 28, 1983 | L | 1 | |
| Nov. 6, 2001 | Lc | 1 | |
| Jan. 13, 2014d | Lc | 9 |
a Cable replaced in 1981.
b National Astronomy and Ionosphere Center, 2007, “Primary Suspension Schematic,” DWG A-M02-005, February 23, https://naic.nrao.edu/arecibo/phil/hardware/telescope/140113_quake/Suspension%20Cable%20Breaks%20Diagram.pdf.
c Upper end of splice box.
d J.L. Stahmer, 2014, “Earthquake Damage to Main Support Cable M8-4,” Ammann & Whitney, February 18.
SOURCE: Wiss, Janney, Elstner Associates, 2021, Auxiliary Main Cable Socket Failure Investigation, WJE No. 2020.5191, June 21; courtesy of Wiss, Janney, Elstner Associates, Inc.
SOURCE: Thornton Tomasetti, 2022, Arecibo Telescope Collapse: Forensic Investigation, NN20209, prepared by J. Abruzzo, L. Cao, and P.E. Pierre Ghisbain, July 25, https://www.thorntontomasetti.com/sites/default/files/2022-08/TT-Arecibo-Forensic-Investigation-Report.pdf; courtesy of Thornton Tomasetti.
In contrast, the WJE table does not appear to reflect the second January 15, 1983, wire break at Tower 4. WJE reflects a November 23, 1988, wire break not on TT’s diagram, and TT reflects a January 3, 1989, wire break not on WJE’s table, both at the tower, so they are possibly the same wire break. Finally, in the Tower 8 backstay cable, both TT and WJE report six breaks, but some appear to be different wire breaks. TT is showing two wire breaks in cable B8-5 on July 9, 2003, and WJE is showing only one. In the Tower 8 main cables, TT reported three wire breaks in M8-4 on March 1, 2011, that do not appear on the WJE table.
The committee could not independently verify any of these wire break reports. A master compilation of these two sources of wire break data produces reports of 48 total wire breaks out of the estimated 5,256 wires in the original main and backstay cables. These breaks are expressed on a timeline in Figure 3-11. Reports reflecting only a few days reporting differences in the same location were treated as just one break.
After the 1975 upgrade, the overall rate at which wires broke was visibly reduced. This reduction was possibly related to a separate installation of a pressurized dry air system on each cable earlier in 1972.54 Despite the dry sleeve installation, “Breakage occurred at roughly a constant rate from 1972 to 1978.”55 In 1981, the cable
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54 TT Final Report, Appendix D, p. 5.
55 L. Phoenix, H.H. Johnson, and W. McGuire, 1986, “Condition of Steel Cable After Period of Service,” Journal of Structural Engineering 112(6):1264, https://doi.org/10.1061/(ASCE)0733-9445(1986)112:6(1263).
with the largest number of wire breaks, backstay cable A12-3, was removed and replaced, and the wire breaks were studied. “Analysts mentioned some possible evidence of both stress corrosion and corrosion fatigue, but the conditions of the fracture surfaces at the times of discovery were such that no definitive conclusions could be drawn.”56 It has been suggested that at least part of the cause of wire breaks could be the cable manufacturer removing the zinc galvanizing on the wires in the socket with acid before pouring the zinc. In doing this, they also removed some galvanizing for a short distance past the mouth of the socket. This gap in galvanization could lead to corrosion on the outer wires, resulting in breaks.57 However, if removing the galvanizing was a significant contributor to wire breakage, the number of wire breaks would be expected to steadily increase with more time and corrosion, contrary to what was observed.
Another potential explanation for the reduced rate of wire breaks after 1997 is that the installation of the new auxiliary cables reduced the total force/stress in the main cables, but the structural analysis using the sag surveys in the TT Final Report suggests that the actual tension was consistent with the design and virtually the same on all three sets of main cables.58 This explanation would imply the existence of some cable loading “threshold” for wire breakage, unrelated to time, that has not been reported.
The upgrade’s powerful S-band radar may have facilitated LEP zinc creep by relaxing the zinc’s shear grip on individual wires. Analysis of the combined wire break data reveals that a single cable, in a population of 27 cables, M8-4, is responsible for 15 of the 48 wire breaks. “The only new breaks on record after 2003 are located near the M8-4 cable splice.”59 If this single cable is removed from the data based on its unique circumstances, and the onset of the two different power levels of S-band radar is indicated, then Figure 3-12 illustrates a possible reason none of the auxiliary cables ever experienced a wire break. After the more powerful S-band radar came online in 1997, until the M4N-T failure, there were only four reported wire breaks in the following 23 years in the old main cables and none in the auxiliary cables, which operated their entire life in this more powerful S-band regime. It should be remembered that wire breaks only on the exterior of the cables could be seen and reported.
The fact that “Every known wire break is located near a socket at a cable end” could be the result of observational bias in that wire breaks in the suspended cable lengths would be more difficult to see from the towers or platform. As noted earlier, wire cable wire breaks were an explicit inspection item on the Arecibo Telescope’s Preventive Maintenance Report.60 However, even in the removed cable discussed previously, no mid-cable wire breaks were reported,61 so this explanation is unlikely. The initial S-band radar was added to the Arecibo Telescope after 1974, with the completion of the first upgrade. The LEP-assisted zinc creep may have reduced the zinc’s ability to tolerate the shear stress necessary to break a wire, or perhaps interfered with a corrosion mechanism. However, the potential impact of the LEP is confounded by the addition of cable moisture controls. The lower-frequency radars the Arecibo Telescope had when commissioned in 1963 do not appear to have impacted wire breakage. After 1975, the rate at which wires broke reduced visibly. The wire breakage appears to be reduced still further by the addition of more power S-band radar with the 1997 upgrade. The mechanism by which the radar could have reduced wire breakage is unknown, but possibly the more powerful S-band radar facilitated LEP zinc creep through some “relaxing” of the zinc’s shear grip on individual wires to the point that wire breakage in the original main cable wires disappeared for 20 years. No wire ever visibly broke outside any auxiliary cable socket in the 23 years they operated, although it should be remembered that the auxiliary cables continuously operated at a higher factor of safety—that is, a lower relative load—than the main cables. Although wire breaks were found to be unrelated to the cable load or the likelihood of cable or socket failure, this virtual disappearance of wire breaks does not appear to have been noticed or explained.
Post the 1997 upgrade, the Arecibo Telescope maintenance records reflect documentation of “wire breaks,” with all occurring in the main cables “near a socket at a cable end”62 until 2003. No further main cable broken
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56 Phoenix et al., 1986, “Condition of Steel Cable After Period of Service,” pp. 1264–1265.
57 Phoenix et al., 1986, “Condition of Steel Cable After Period of Service.”
58 TT Final Report, Appendix G, Figure 15, p. 12.
59 TT Final Report, Appendix D, p. 7.
60 A. VanderLey, 2022, “Arecibo Observatory: Failure Event Sequence,” National Science Foundation presentation to the committee January 25, slide 50.
61 Op. cit., Phoenix et al., 1986, “Condition of Steel Cable After Period of Service,” p. 1264.
62 TT Final Report, Appendix D, p. 7.
NOTE: Dry air sleeves were installed on the cables in 1972 and on the auxiliary cables in 1995.
wires were reported right up to the first cable failure. No wire breaks were reported in any Arecibo Telescope auxiliary cable,63 although clamps were observed at the platform end of the M12 cables, the tower end of the M8N cable, and both ends of the M8S cable.64 The M4N cable that failed first had no reported clamps or wire breaks. Ray Lugo, University of Central Florida, told the committee that he asked the WSP, WJE, and TT team, “So what is the standard? You know, can you have five wire breaks? Can you have 10? Whatever? And so, I was actually told that there is no standard.”65 The number of wire breaks was found to be unrelated to the load in the cable.
The M4N failure caused four new wire breaks at the tower end of in [sic] M4-4 Drone photos taken shortly after the failure show the deformation of the zinc casting of the M4-2 and M4-4 tower-end sockets. It is not clear whether these deformations occurred before or during the M4N failure. The zinc castings deformed in a pattern consistent with the cables slipping out of the sockets.66
However, the Tower 4 cable that suffered the most reduction in strength through wire failure, M4-1, with 11 known wire breaks,67 never failed before the Arecibo Telescope collapse.
The aftermath of the second cable failure. “Shortly after the M4-4 failure, three new wire breaks were observed in M4-1, and a new wire break was observed in M4-2 near Tower 4 (Figure 16). Four wire breaks were also observed in M4-2 near the platform.”68
Finding: Socket M4N-T had no broken wires and was the first to fail.69 The main cable with the most wire breaks, M4-1 with 11 wire breaks, did not fail before the collapse. No correlation was found between the number of broken wires and the likelihood of socket failure.
Other processes that can cause failure at applied stresses below cable yield strength include corrosion, stress corrosion cracking, hydrogen-assisted cracking, creep, and fatigue. Each of these mechanisms was analyzed collectively in the WJE, NASA, and TT reports. Each mechanism was dismissed as the primary cause of failure at Arecibo based on the evidence at hand and analysis provided by TT, SOCOTEC Engineering, Inc., WJE, or NASA, except for zinc creep and “flow.” A more detailed discussion of the Arecibo Telescope’s potential failure mechanisms is found in Appendix B.
EARTHQUAKE
Puerto Rico experiences routine seismic activity because of its location along the boundary between the Caribbean and North American plates. “Since the telescope’s completion in 1963, more than 200 earthquakes of moment greater than 4.5 occurred within 200 km (125 miles) of AO [Arecibo Observatory].”70 On January 7, 2020, Puerto Rico experienced a magnitude 6.4 earthquake located on the southern coast of the island about 29 miles from the AO. This earthquake and the resulting aftershocks occurred after the auxiliary cable pullout was first noted and measured (May 2018 and February 2019) and 8 months before the first cable failure.
As part of its forensic analysis, TT performed a structural response analysis of the Arecibo Telescope for both the original design and upgraded structure. Recorded ground accelerations at the site (accounting for time delays based on the shear wave velocity of the ground near the surface at the site) were used as the boundary conditions for the analysis. As a comparison, TT also plotted the Design Earthquake Response Spectrum per ASCE 7-16
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63 TT, 2021, Arecibo Telescope Collapse: Forensic Investigation Interim Report, NN20209, prepared by J. Abruzzo and L. Cao, November 2 (hereafter “TT Interim Report”), Figure 7, p. 8.
64 TT Final Report, Appendix D, Figure 15, p. 11.
65 R. Lugo and F. Cordova, 2022, “Perspectives on Grant Award and Operations of Arecibo Observatory Cooperative Agreement by the University of Central Florida,” University of Central Florida presentation to the committee, February 17, meeting minute 49:36.
66 TT Interim Report, p. 11.
67 TT Final Report, Appendix E, p. 14.
68 TT Final Report, Appendix E, p. 9.
69 TT presentation.
70 TT Final Report, p. 12.
standard. The modeled earthquakes were “significantly less severe than the current design earthquake for the AO site.”71 In their finite element models, the maximum normalized stress range was 8 percent in the original structure and 5 percent in the upgraded structure. The lowest calculated safety factor for the earthquake loading condition before the first failure was 1.9.
WIND SPEED CONSIDERATION IN THE ARECIBO TELESCOPE’S DESIGN
The various engineering consultants, TT, WJE, A&W, and NASA, referred to different wind speeds in their reports. From Appendix J of the TT Final Report:72
The structural drawings for the original structure indicate a design wind speed of 140 mph. (p. 1)
Before the first upgrade of the telescope, a feasibility study by Ammann & Whitney (A&W) determined that the speed of 140 mph corresponds to the 300-year wind event at the telescope’s site and that the 100-year wind speed is only 114 mph. A&W’s structural drawings for the first upgrade indicate a design wind speed of 110 mph, suggesting that the 100-year wind event was selected as design event. (pp. 1–2)
A&W confirmed the two speeds of 110 mph and 123 mph for the global and local design of the upgrade respectively and, to our knowledge, the final design was based on those wind speeds. (p. 2)
First, the design wind speed was lowered from 140 mph to 110 mph between the original design and the second upgrade. (p. 2)
The use of “lowered” is misleading and seems to imply that the second upgrade’s design used a lower design wind speed when these two different wind speeds are for different return periods, 300-year versus 100-year. These two wind speeds are essentially equivalent and should have resulted in the same member design when the appropriate factors and coefficients are applied.
GOVERNING CABLE DESIGN STANDARDS
The existing standard that governed the design and installation of structural cables in the Arecibo Telescope’s upgrade was “Structural Applications of Steel Cables for Buildings.”73,74 However, the “Recommendations for Stay Cable Design, Testing, and Installation”75 could have also been consulted. These two standards have fundamental and substantial differences in scope, design approach, qualification testing, inspection requirements, terminology, etc. The types of cables covered by the ASCE 19 standard are structural wire ropes and strands (except 7-wire prestressing strands). Strands are defined as “a plurality of wires helically twisted about an axis,” and ropes are defined as “a plurality of strands twisted about an axis or about a core that may be a strand or another wire rope.” The Post-Tensioning Institute (PTI) DC-45 standard addresses the design, testing, and installation of stay cables for cable-stayed bridges. The cables covered under this standard include those that consist of parallel wires, 7-wire strands, or bars. Stay cables used in modern cable-stayed bridges in the United States (since the 1990s) consist of multiple parallel greased-and-sheathed 7-wire strands terminated at anchorage plates using specially designed wedges. The parallel strands are then encased in high-density polyethylene pipes. The design of such stay cables is covered under the PTI DC-45 provisions.
Poured spelter socket cable end fittings (zinc or resin) and wire ropes/strands are not used in the main stay cables of modern cable-stayed highway bridges, but they are often used in pedestrian cable-supported bridges.
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71 TT Final Report, Appendix K.
72 TT Final Report, Appendix J, pp. 1–2.
73 ASCE (American Society of Civil Engineers), 2016, “Structural Applications of Steel Cables for Buildings,” ASCE/SEI 19-16.
74 This standard was produced by Committee 19 of the ASCE. The modern version of this standard was first published in 1996 (ASCE 19-96) and later updated in 2010 (ASCE 19-2010) and 2016 (ASCE 19-2016). The ASCE 19 standards traces back to an earlier standard published by the American Iron and Steel Institute (AISI) in 1966 (Tentative Criteria for Structural Applications of Steel Cables for Buildings).
75 PTI, 2018, “PTI DC45.1-18: Recommendations for Stay Cable Design, Testing, and Installation,” DC-45 Stay Cable Bridge Committee.
The design of the non-parallel wire ropes and strands is covered under the ASCE 19 standard. The cables are terminated at end fittings that may be poured sockets, swaged sockets, or mechanical loops with sleeve and thimble. These cables have been widely used over many decades in numerous industries (including naval, mining, construction machinery, and oil/gas). In bridges, the wire ropes/strands are still used in movable bridges and for hanger cables of major highway suspension bridges (but not the main cables of suspension bridges or stay cables in cable-stayed bridges). In the Arecibo Telescope, the type of cables used in the original 1960s design, as well as the cables added in the 1990s, were spiral wire strands with zinc-filled sockets, which would most suitably fall under the ASCE 19 standard.
While the PTI DC-45 standard has stringent and specific quality control and qualification test requirements (Section 4.0) that must be performed by independent testing laboratories, quality control, and cable testing under the ASCE 19 standard (when specified or left to the discretion of the engineer) can typically be performed and reported by the fabricator/manufacturer of the cable (e.g., Section 5.2). In PTI DC-45, the load requirements during the qualification tests are pre-defined and are not project-specific. All stay cables of a particular size, regardless of the calculated load demand in a particular location in the structure, must be subjected to the same loading (stress) condition meant to achieve a uniform level of high quality across the board.
Another major difference is the handling of the design requirements for the anchorage (in PTI DC-45 terminology) or end fittings (in the ASCE 19 terminology). In PTI DC-45, any failure in the anchorage components during qualification tests is cause for the rejection of the cable, implying that the strength in the anchorage during the final qualification test must be higher than the strength of the free length of the cable during the same test. In ASCE 19, end fittings are required to “develop an ultimate strength greater than the specified minimum breaking strength.”76 Therefore, under ASCE 19, the end fitting could have a lower actual strength than the cable itself as long as they have a higher strength than the “specified” (not actual) cable minimum breaking strength. In structural engineering, there is a strong tradition of not allowing the connection to control the design of the structure. The failure of the steel cable (in its free length away from the ends) would be associated with far more ductility than a sudden and brittle failure at the end connections. Therefore, the probability of failure at the connection (end fitting or anchorage) should be minimized to an acceptable level.
The cable design processes in ASCE 19 are currently based on the allowable stress design, while the design processes in PTI DC-45 are based on the load and resistance factor design (LRFD). A safety factor of 2.2 is specified in the ASCE 19 standard. In PTI DC-45, the load factors for various types of loads are varied based on the load combinations and requirements specified in the American Association of State Highway and Transportation Officials (AASHTO) LRFD Bridge Design Specifications.
The various consultants involved in this matter have referred to a standard published by AASHTO (AASHTO M 277) to assert that there is an acceptable “one-sixth of the diameter of the cable” limit for the pullout of the wires from the zinc sockets under service load conditions.77 This pullout limit is a technically incorrect application of this standard.
The AASHTO M 277 defines the scope of the standard as follows:
This specification covers steel wire rope for use in movable bridges. Both operating and counterweight ropes are included in nominal 6 × 19 rope construction. Suitable sockets are also included.
The AASHTO M 277 addresses a specific type of wire rope (6 × 19 construction) for a specific application (movable bridges). Section 7.5 of M 277 describes ultimate strength testing requirements and provides minimum strength values for 6 × 19 ropes up to 2½ inches diameter. The wire rope in the M4N-T socket was a vastly different 1 × 127 construction, which was 3.25 inches in diameter. Structural engineers contracted to evaluate the cable slippage and failures did not address this disparity between this standard’s scope and the Arecibo Telescope’s cables.
AASHTO M 277 Section 8.1 states:
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76 ASCE, “Structural Applications of Steel Cables for Buildings,” Standard ASCE 19-16, Section 3.3.2, “End Fittings,” p. 6.
77 American Association of State Highway and Transportation Officials (AASHTO), 2019, “Standard Specification for Wire Rope and Sockets for Movable Bridges,” M 277-06.
When stressed to 80 percent of its ultimate strength under the test specified in Section 7.5, to slip not more than one-sixth the nominal diameter of the rope. If a greater movement shall occur, the method of attachment shall be changed until a satisfactory one is found. [emphasis added].78
This important last sentence was not quoted in the various Arecibo Telescope forensic reports cited earlier.
Finding: The applicability of AASHTO M 277 to the very different Arecibo Telescope cables was never established by any consultant.
Finding: The specified cable loading at 80 percent ultimate strength for accepting a one-sixth diameter pullout was never attained in any socket of the Arecibo Telescope.
Conclusion: The one-sixth diameter pullout should not be an allowable limit of the Arecibo Telescope’s cable pullout, especially considering the observed non-conforming condition of the sockets.
Before the failure of the first cable, eight Arecibo Telescope sockets, shown in Figure 3-13, exhibited pullouts of more than one-sixth cable diameter. Yet none of these cables were slated for replacement. Thus, it is not clear how the contracted structural engineers viewed the applicability of the AASHTO M 277 standard to the unique Arecibo Telescope configuration.
Finding: With a one-sixth diameter pullout measured at loads less than 50 percent of the cable’s maximum strength (the loading of all the Arecibo Telescope sockets), the AASHTO M 277 criteria for permissible slip was not met.
According to Section C1.2 of the ASCE 19-16 standard, a proof load test may be performed on a cable assembly (typically 50 percent of the rated minimum breaking strength of the cable but not more than the pre-stretching force applied in the fabrication shop). The following statement is from Section C1.2 of the ASCE 19-16 (this statement was not present in the earlier editions of the standard):
Fittings attached with zinc spelter sockets will normally exhibit a small displacement of the zinc cone when seating into the socket during the proof test. This is observed where the cable exits the socket by comparing the positioning of the zinc at the socket base before and after the proof test. This displacement is a normal result of socket loading, and unless excessive, is not an indication of poor workmanship or design.79
ARECIBO TELESCOPE CABLE LOAD
The TT Final Report states that “excessive cable slips and eventual cable failures would not have occurred if the cable system had been designed with a safety factor of at least 3.0 under gravity loads” and recommended “using a safety factor of at least 4.0 under transient loads.”80
The committee agrees with the NASA assessment81 that the primary factor contributing to the failure of the M4N socket and the subsequent collapse of the structure was excessive zinc creep in the sockets. Long-term creep disrupted the force transfer mechanism in the sockets and redistributed forces from the strand’s center wires to the outside wires as zinc pullout progressed. The fact that zinc creep was the primary factor is well established through microstructural assessments performed by NASA and the observed recrystallization of zinc.
However, the committee disagrees that a relatively high “gravity-load” fraction of the total load alone can explain the observed zinc creep and unprecedented failure of the Arecibo Telescope’s sockets. TT presents no
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78 AASHTO, 2019, M 277-06, Section 8.1.
79 ASCE, 2016, “Structural Applications of Steel Cables for Buildings (19-16),” Section C1.2, p. 36.
80 TT Final Report, p. 50.
81 NESC Report.
SOURCE: Thornton Tomasetti, 2022, Arecibo Telescope Collapse: Forensic Investigation, NN20209, prepared by J. Abruzzo, L. Cao, and P.E. Pierre Ghisbain, July 25, https://www.thorntontomasetti.com/sites/default/files/2022-08/TT-Arecibo-Forensic-Investigation-Report.pdf; courtesy of Thornton Tomasetti.
evidence or data on the ratio of “gravity-load” to live load in any population spelter socket applications. Bridge literature generally indicates that a more significant live load requires a higher safety factor to address fatigue. The zinc-filled, spelter socket–terminated cable has a decades-long track record, is in widespread use across many industries, and remains a standard offering in many, if not all, cable manufacturer catalogs even today.82,83,84 The committee has searched the literature and has found no other documented instances of this type of failure, although warnings to inspect spelter sockets for “any signs that the wires may be pulling out of the zinc” can be found in spelter socket manufacturer catalogs.85 To the best of the committee’s knowledge, there is no other documented failure of a zinc-filled cable-spelter socket via cable pullout in the past 100 years.
The head of the TT investigative team also noted the unprecedented nature of this type of failure.86 Considering that this type of socket is ubiquitous in all types of industries, applications, and loadings, it is highly unlikely that
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82 Sullivan Wire Rope & Rigging, Inc., 2014, “Catalog,” https://www.sullivanwirerope.com/catalog.
83 Crosby, “The Crosby Group Catalog,” https://www.thecrosbygroup.com/crosby-catalog, accessed June 1, 2023.
84 Union, “Spelter Sockets,” https://www.unionrope.com/products/slings/spelter-sockets, accessed June 1, 2023.
85 Hanes Supply, Inc., “Technical Master Catalog,” https://www.hanessupply.com/catalogs, accessed June 1, 2023.
86 TT presentation.
the observed mode of failure is due to the influence of a higher dead load fraction of total load alone, and no such influence is found in the literature or cited by TT. Other site-specific factors must also be at play. The previous discussion of the uniquely powerful electromagnetic radiation of the Arecibo Telescope and the possible production of LEP deserves investigation since it remains the only site-specific factor the committee could uncover that might explain the substantial zinc creep acceleration and pullout of the Arecibo Telescope cables.
The NASA report also takes issue with the design safety margins for all the Arecibo Telescope’s sockets, even those that have no evidence of any creep. In civil/structural engineering design, localized higher stress areas are not allowed to control the design of the entire component if the material is sufficiently ductile and can allow redistribution of stresses elsewhere in case of yielding. This approach has resulted in the successful long-term performance of these types of sockets. It is the uniquely excessive creep that made the difference in the Arecibo Telescope cables.
The engineering consultants evaluating the condition of the Arecibo Telescope structure (before and after the first cable failure) had consistently and extensively relied on their safety factor calculations based on an estimated ratio of nominal cable strength to cable load. While the cable tension can be estimated through detailed cable sag, the consultants’ use of the original and unimpaired nominal cable strength (as capacity) was fundamentally unsound, especially considering the observed zinc pullout of the M4N-T socket at a load of less than half the cable’s nominal strength and the subsequent failure of the first cable. Even after the M4N-T failure illustrated this discrepancy, the consultants continued calculating safety factors and assessed remaining strength based on the cables’ original nominal strength. In a report written after the failure of M4N-T, one consultant wrote that “the current capacity/demand ratios for the primary structural elements and the suspension system as a whole are significantly greater than one rather than just barely greater than one” and “when there are no significant loads other than gravity acting on the system, failure of additional cables in the near future is unlikely.”87
TT’s recommendation to raise the safety factor in all spelter socket cable structural design from 2.2 to 3.0 or 4.0 means recommending a significant overdesign of the entire cable suspension system, driven by TT’s design uncertainties of the capacity of the end connection sockets. The committee considers this recommendation to be unjustified by the evidence and based on TT’s misunderstanding of what caused the unprecedented Arecibo Telescope socket failures. There is a long-standing tradition in civil/structural engineering of avoiding making the connections the controlling design elements, as connection failures are typically brittle and sudden. A change in the factor of safety from 2.2 to 3.0 or 4.0 in a design means that the number of wires or strands in a cable, that may be hundreds of feet long, must be increased by 36 percent and 82 percent, respectively, just to meet TT’s uncertainty over the long-term performance of the cable end connection that has only manifested itself in a single unique installation in the past 120 years. Also, more steel for a given tension leads to higher cable sag, which increases local demand on anchorages for variable loading. If the issue of excessive creep were proven to apply to other cables (or had been observed in other cables) under high dead loads (i.e., not specific to the Arecibo Telescope’s site conditions), then a reasonable approach would be to avoid using zinc sockets for such cables and maintain the existing factors of safety and the efficient quantity of steel used. Zinc sockets are not the only options for such major structural cables. None of the inclined stay cables used in major cable-stayed highway bridges built in the United States in at least the past 25–30 years includes any zinc-filled sockets similar to the Arecibo Telescope’s cables.
Conclusion: The TT recommendation for raising the safety factor in ALL spelter socket cable structural design from 2.2 to 3.0 or 4.0 would result in significant increase in strand number and cable size. Connections should not be the controlling design elements.
Finding: The TT recommendation to increase the safety factor for socket cable design is not justified by the evidence. It is unclear how high the safety factor must become to sufficiently suppress power law creep in circumstances such as EM-induced LEP and high local stresses at specific locations in the Arecibo Telescope spelter sockets.
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87 UCF, 2020, “NSF Proposal Number: 2102922. Management and Operations of the Arecibo Observatory,” proposal to NSF, October 19, page 86/495.
RISK CONSIDERATIONS
Probability of Failure
The current standard of practice for conventional structures produces an expected probability of failure on the order of 10−5 per year for components like cable M4-N (e.g., ASCE 7-2288). Based on this annual failure probability, the theoretical probability that this cable would fail in 25 years of service is small, much less than 1 percent. When the total number of cables and the service life is considered (27 original cables installed in 1963 and 12 auxiliary cables installed in 1997), the probability of at least one cable failing by 2020 is calculated to be about 2 percent.89 Therefore, the failure of M4-N in 2020 is unexpected but possible based on this perspective from the standard of practice for conventional structures. However, it is questionable whether the standard of practice captured in ASCE 7-22 for structures primarily associated with steel and concrete frames applies to this telescope structure with a system of cables supporting a platform.
A structure somewhat analogous to the Arecibo Telescope is a floating offshore platform for producing oil and gas. The floating platform has a system of nominally 10 mooring lines90 generally made of steel wire rope and subjected to relatively large, sustained tension loads that hold the floating platform on station. The value of this analogy is that there is experience available for hundreds of floating platforms with decades in service. An industry survey of mooring line failures over 13 years found that the frequency of failure for a single line was 2.5 × 10−3 per year.91 If this failure probability is applied to the lines in the telescope, the probability of at least one line failing between 1963 and 2020 is 99 percent, and the expected number of line failures is 4.5 lines. This expectation of four to five failures of lines is consistent with the observed performance of the Arecibo Telescope’s support system: one backstay cable was replaced in 1981 due to six broken wires; a cable connection was bypassed in 1997 due to damage during installation; a cable was bypassed in 2014 due to wire breaks in response to damage from a magnitude 6.4 earthquake; and cable M4N failed in 2020.
Furthermore, the frequency of multiple line failures in an event for offshore mooring systems was about 10 percent of the frequency for single line failures. Applying this analogous conditional frequency to the Arecibo Telescope support system gives a 40 percent conditional probability that at least two lines would fail together between 1963 and 2020.92 Therefore, the failure of cables M4-N and M4-4 within several months of one another at AO in 2020 would not be unexpected, given the experience with offshore mooring systems.
The experience from offshore mooring system cables is also insightful into the patterns of line failures:93 (1) the majority of failures occurred at or near terminations (connections); (2) failures were nearly always caused by a reduction in capacity rather than an overload; and (3) failures were more frequent both early in the service life (e.g., damage caused by handling and installation) and later in the service life (e.g., corrosion, fatigue, stress corrosion cracking [SCC], or HEAC). A notable conclusion from this experience was that using a larger factor of safety in design would generally not have prevented failures but may have delayed them.94 The committee could find no evidence that any mooring line experience was considered in the Arecibo Telescope’s original design or
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88 ASCE, 2022, “Minimum Design Loads and Associated Criteria for Buildings and Other Structures,” ASCE 7-22, Table 1.3.2, for a structure in Risk Category I.
89 This calculation assumes that the chance of failure is independent between cables, which is reasonable since the governing uncertainty is the capacity of the cable and factors that may affect it from fabrication, handling, installation, and degradation processes over time in service, and that the chance of failure is a constant with time, which is debatable since there can be degradation with time. However, the target probability of failure given in ASCE 7-22 is a nominal value for a 50-year service life that implicitly accounts for the possibility of degradation with time.
90 The word line is used here to include the cable and connections.
91 E. Fontaine, A. Kilner, C. Carra, D. Washington, et al., 2014, “Industry Survey of Past Failures, Pre-Emptive Replacements and Reported Degradations for Mooring Systems of Floating Production Units,” OTC 25273, Houston, TX.
92 The probability of failure per line is assumed to be 2.5 × 10−3 per year; the probability of failure per year for at least one line in the system is 1 − (1 − 2.5 × 10−3)N where N is the number of lines in the system during that year; and the probability of failure per year for multiple lines in the system is assumed to be 10 percent of the probability of failure for at least one line in the system.
93 P. Smedley and D. Petruska, 2014, “Comparison of Design Requirements and Failure Rates for Mooring Systems,” Proceedings of the Offshore Structural Reliability Conference, American Petroleum Industry, Houston, TX.
94 NESC Report.
its subsequent upgrade. The committee also found no evidence that this experience was consulted after any cable failures or the subsequent analysis of the Arecibo Telescope’s collapse by any of the involved experts.
Consequences of Failure
The consequences of even one cable failure for the Arecibo Telescope system were significant. The failure of line M4N-T in August 2020 caused damage to the dish and the Gregorian dome on the access platform as the line swung away from the tower, making the telescope inoperable. When one end of a 700-foot cable drops, with one end still supported at a 500-foot elevation, the unsupported 200 feet of cable that smashes into the ground weighs approximately 2 tons. This initial line failure could have injured or killed workers, and even visitors if it had happened later in the day rather than in the middle of the night. The National Science Foundation (NSF) established a safety zone in the vicinity of the dish after this unexpected cable failure.95 A week after this first cable failure, “NSF requests safety plan prior to approving work at site” and “communicates to UCF [University of Central Florida] and AO” that “safety of personnel is the highest priority.”96 The failure of a second tower cable in November 2020 was followed by the complete Arecibo Telescope collapse 3 weeks later. The complete collapse destroyed the dish, the access platform, and the Gregorian dome; destroyed the support towers; and damaged the Visitors Center and the Learning Center. This complete collapse could have injured or killed workers if it happened a few weeks earlier.
There are, again, useful comparisons concerning consequences between the telescope support system and mooring systems for offshore platforms. As with the telescope, offshore mooring systems are generally designed so that the loss of at least two lines is necessary to lead to a failure of the mooring system, which means a failure to keep the offshore platform on station. However, in contrast to the telescope, failure of an offshore mooring system is generally not catastrophic because there are safety systems to minimize hydrocarbon releases if the platform moves off station, and the platform itself does not typically sink (although it may cause collateral damage if it impacts other vessels off station), a broken line is not likely to hit personnel, and offshore platforms are evacuated in advance of hurricanes.
Risk Management
The risks associated with failure in a structural support system can be managed by reducing the probability of a failure or reducing the consequences of failure. For the Arecibo Telescope, several measures were taken to reduce the probability of failure. The original cable support system had a redundant cable design for the three towers, with four main cables along each load path. Corrosion protection was applied and maintained throughout the service life. The cables were regularly inspected for broken wires, and cables were periodically replaced or bypassed when showing signs of distress. The system was inspected after major events, including hurricanes and earthquakes.
However, there were several notable measures not taken that could have further reduced the probability of the Arecibo Telescope’s support system failure. First, the auxiliary cable system to support weight added to the platform in 1997 was designed with only one cable along each load path; the platform shifted and rotated suddenly when cable M4N-T failed, distributing loads in an uncontrolled (not-designed-for) manner to the remaining cables. Second, action was not taken quickly when a cable needed repair. Only the damaged M8-4 cable was scheduled for repair after Hurricane Maria, but it still had not been repaired/replaced by the time cable M4N failed 3 years later.97 When M4N failed, there was no plan in place to quickly replace it to restore the system before M4-4 failed 3 months later. Third, the service life of the system was not clearly defined after the 1997 upgrade. The longer a structure is in service, particularly in a corrosive environment with loading from hurricanes and earthquakes, the more likely it is that damage will occur. Fourth, a detailed risk analysis was not conducted.
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95 NSF, “Report on the Arecibo Observatory, Arecibo Puerto Rico Required by the Explanatory Statement Accompanying H.R. 133, Consolidated Appropriations Act, 2021,” https://www.nsf.gov/news/reports/AreciboReportFINAL-Protected_508.pdf, accessed June 1, 2023, p. 1.
96 A. VanderLey, 2022, “Arecibo Observatory: Failure Event Sequence,” National Science Foundation presentation to the committee January 25 (hereafter “NSF presentation”), slide 28.
97 NSF presentation, slide 15.
Often, a failure modes and effect analysis (FMEA) is sufficient. In this case, the value of the functional system to the science program, coupled with its novelty and a lack of an inclusive code or standard to fully address the system, indicates that a failure modes effects and criticality analysis (FMECA) was warranted. FMEA is a bottom-up, inductive analytical method that may be performed at either the functional or piece-part level. FMECA extends FMEA by including a criticality analysis, which charts the probability of failure modes against the severity of their consequences and looks at the systems as a whole. In February 2020, “structural engineers [WSP Global, Inc.] were on site and performed inspection of the towers, cables, and platform primary structural elements. No additional damage was noted to have been found during those inspections.”98 Not taking measures such as the following—(1) performing thorough structural assessments by licensed engineers to continue operations after Hurricane Maria in 2017, the earthquake in January 2020, or a specified duration in service (say 50 years); (2) developing and implementing a plan to replace cables after a specified period in service; or (3) developing and implementing a plan to increase the rigor and frequency of inspections with time in service—all may have increased the probability of failure.
Conclusion: The consequences of a structural failure of the Arecibo Telescope were not seriously considered in decision-making during design and operation or in extending the telescope’s life. In particular, there was no formal consideration that the health and safety of the workers and the public were at risk in the event of a structural failure. The design to convert it into a telescope with public visitors and the re-design to add the Gregorian dome were not conducted using more stringent standards for critical structures like bridges, even though workers and the public in the Visitor’s Center and the Learning Center could have been harmed in the event of a single cable failure or a catastrophic collapse. The potential life and safety consequences associated with a single cable failure or a catastrophic system collapse on workers and the public were not considered when damage was detected to cable M8-4 after Hurricane Maria or in the decision-making to continue operations in 2017.99
Finding: The performance of the Arecibo Telescope’s cable support system, with multiple lines requiring repair and replacement over its 60-year service life, was not unusual or unprecedented.
Conclusion: The risk of a structural collapse could have been reduced if more rigorous inspections and assessments had been conducted to evaluate the integrity of the cables and connections. These inspections should have been comprehensive and done with an understanding of all potential failure mechanisms, including those time-dependent degradation processes that can operate below 50 percent of the cable-breaking strength.
STRUCTURAL ROBUSTNESS
Structural robustness is defined as the inherent health and strength of the structural system to withstand external demands without degradation or loss of functionality. Some of the measures to enhance robustness include the following:
- Increasing the accuracy and reliability of the design loads;
- Establishing a clear, simple, logical design;
- Providing redundancy in the design;
- Employing experienced and qualified design team, contractors, and inspectors;
- Providing quality assurance over the design, construction, maintenance, and inspection over the life of the facility; and
- Increasing the factor of safety in critical elements.
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98 NSF presentation, slide 21.
99 NSF, 2017, “Environmental Impact Statement for Arecibo Observatory, Arecibo, Puerto Rico,” July 27, https://www.nsf.gov/mps/ast/env_impact_reviews/arecibo/eis/FEIS.pdf.
Increasing the factor of safety in the design of the members—or oversizing them—has advantages and disadvantages. Where structural members are over-sized, the over-sized connections themselves may create problems in fabrication and quality assurance. Huge weldments and huge bolted connections are more difficult to build, and maintaining quality may be more difficult. Therefore, the decision to increase the factor of safety should be made carefully, taking into account all the issues that may be affected. For the reasons cited elsewhere in this report, the committee does not agree with TT’s recommendation to increase the factor of safety for the Arecibo Telescope. Oversizing in response to technical unknowns is not prudent and may not help if material failure can occur at less than 50 percent of breaking load or yield strength through unappreciated mechanisms such as LEP, hydrogen embrittlement (HE), SCC, or creep. Oversizing can only help by lowering the applied stress below the threshold for the material degradation process.
Redundancy
In structural engineering, a redundant structure is one where the structural system has alternate load paths so that the removal/failure of a member does not initiate a total collapse of the system. Critical members of the structural system should be designed such that one of these members could be removed without the failure of the whole structure. It may be impractical or impossible to design for the simultaneous removal of several or all of the critical members. Considering various scenarios of individual member failures, the structural engineer should propose reasonable approaches, discuss them with the owner and/or stakeholders, and jointly decide on a system.
Based on the committee’s experience, a typical approach is to consider the joint probability of several critical members failing simultaneously and then apply a smaller safety factor for these simultaneous failure load cases. Employing such a method ensures that the increase in material quantities is nominal.
More redundancy is required for more critical structures, structures with longer design lives, structures exposed to the environment, structures subject to fatigue, and structures where individual members, due to corrosion or other degradation, must be replaced over time. The designer should consider possible risks and provide sufficient internal redundancy where justified. A structural system with three supporting legs is inherently non-redundant, as removing one of the legs will cause a total collapse.
With a three-legged system, there is no practical way to replace a set of cables (to one tower) that may have been entirely severed for any reason. Applying the redundancy concept, a four-legged system can be designed to provide a higher confidence of tower reliability if cables are severed. Theoretically, in that failure scenario for a four-legged design, the designer could consider the tower loss and calculate additional forces in the remaining cables and check the remaining tower resistance to the increased lateral loads, and design accordingly. Furthermore, the four-legged system allows the installation of a temporary overhead cable system in case of emergencies. Regardless of tower configuration, design for cable replacement is a normal feature of cable-supported structures, and it will require special strength margins or member redundancy.
The first socket failure occurred at the end of an isolated cable (M4N), whose tension could not be redistributed to adjacent cables. Instead, this first failure resulted in a rotation of the platform and tension changes throughout the cable system. Designing cable systems with multiple adjacent cables on each span provides redundancy. In the event of a cable failure, the remaining adjacent cables can sustain the increased load for some time assuming they have not lost capacity or seen it reduced by degradation, allowing and easing the replacement of the failed cable or cables.100
The original design of the three towers had significant reserve capacity, corroborated by the fact that the 1997 upgrade to the telescope added 40 percent to the weight of the suspended structure. Still, it did not require the three towers to be structurally reinforced. The towers seemed to have factors of safety that were higher than required.
The original 1963 design of the telescope did have redundant cable design in each tower (but not the whole system). However, the 1997 upgrade lacked redundancy in its design, as single auxiliary cables were used on either side of each tower to accommodate the additional platform load. Loss of an auxiliary cable would, at a minimum,
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100 TT Final Report, p. 50.
substantially rotate and shift the platform, rendering it useless. These single auxiliary cables are M4N and M4S, connecting the platform to Tower 4, and at B4N and B4S, connecting Tower 4 to Anchorage 4.101 The same design was used at Tower 8 and Tower 12. With this change to the original 1963 design, the whole cable system was no longer redundant, and the reliability of the original cable design was compromised.
The 1997 upgrade should have maintained the cable redundancy of the original design, but it did not. Considering the magnitude of the renovation, it should have brought the entire structural system to conform to the current codes, technologies, and design methodologies of 1997. The lesson for NSF is that facility upgrades should not be allowed to compromise the reliability and redundancy of the existing facility. Fundamentally, it is better design practice for a structure to have alternate load paths (i.e., to have redundancy) than to have over-sized structural members (i.e., members with higher than required factors of safety). Given that the loss of the single M4N cable did not immediately fail the system, it is likely that an operative operations and maintenance program that included cable replacement at given performance thresholds or design life could have precluded failure.
Conclusion: The Arecibo Telescope structure was not tolerant of cable failure due to the lack of redundancy in the 1997 upgrade, where a single auxiliary cable was used on each load path instead of multiple auxiliary cables.
MONITORING
A highly stressed critical structural member should have triggered a higher-than-normal observation program, including some form of definitive, repeatable measurement of socket performance with measurable performance limits prescribed by the designer to facilitate the interpretation of the measurement. Greater urgency for inspection and maintenance, when cable slippage is observed, is warranted. Especially if it is recognized that there are material failure modes that can occur at a fraction of the wire yield strength, such as LEP, SCC, HE, corrosion fatigue, and PLC, which are time-dependent and reduce load capacity over time.
Monitoring Program Used for the Cable Sockets
Throughout the life of the Arecibo Telescope, the condition of the cable system and the maintenance operations were routinely inspected, and cable conditions were recorded locally by AO staff. Occasional structural inspections were also reported by the Engineer of Record, A&W, between 1972 and 2011. The available information is generally less comprehensive and detailed after the second upgrade in 1997, and the scope of the inspections performed by A&W was reduced.102
The monitoring program for the sockets used over the life of the tower consisted of periodic visual inspections. There was no systematic methodology for observing and recording the performance of the sockets. A comprehensive review of the inspection history for the structure by TT103 showed no systematic inspection of the sockets nor any formal monitoring program in which systematic measurements or records were made of the socket performance.
Photos of cable pullout were taken at various times. Examples include Figures 14, 15, 16, 18, 23, 24, 30, 34, and 43 in the TT Final Report. Some of these photos include a ruler showing the amount of pullout at the time of the photo. These illustrate that meaningful measurements of pullout could have been made and tracked systematically. TT reported no evidence of any systematic monitoring or tracking of socket conditions. No records of measurements of slip over time for specific sockets have been found.
The cable slips were measured at the tower and ground ends of the auxiliary cables after the first cable failure and at the platform ends after the collapse, as shown in Figure 3-14. One-third of the cable slips exceeded the AASHTO limit (only after the connection is loaded to 80 percent of its nominal strength) of one-sixth of the cable
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101 TT Final Report, Figure 22.
102 TT Final Report, p. 8.
103 TT Final Report, Appendix D, p. 12.
SOURCE: Thornton Tomasetti, 2022, Arecibo Telescope Collapse: Forensic Investigation, NN20209, prepared by J. Abruzzo, L. Cao, and P.E. Pierre Ghisbain, July 25, https://www.thorntontomasetti.com/sites/default/files/2022-08/TT-Arecibo-Forensic-Investigation-Report.pdf; courtesy of Thornton Tomasetti.
diameter.104 The maximum cable slip was observed at the ground end of B12W. It had increased from 1.5 inches in May 2018 to more than 1.75 inches in September 2020, which prompted the plans for interim repair with a friction clamp after the first cable failure.105
Before breaking free on August 8, 2020, the end of cable M4N at the top of Tower 4 had slipped by more than 1 inch from its socket. This 1-inch slip is approximately one-third of the cable’s diameter and significantly more than typically observed in structural cables terminated with zinc-filled spelter sockets. Notably, while this slip was observed and recorded, it did not trigger any extra attention or action.
TT characterized these measurements into three categories: those less than D/6, those between D/6 and D/3, and those greater than D/3. TT does discuss the reasoning for using these limit values, apart from the misapplied D/6 discussed previously. Still, they indicate what should have been done to establish performance criteria for a
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104 AASHTO, 2019, “Standard Specification for Wire Rope and Sockets for Movable Bridges,” M 277-06.
105 TT Final Report, Figure 24.
socket health monitoring program. In simple monitoring terms, one often establishes a (ideally nonjudgmental) traffic light system: green for OK, yellow for Caution, and red for Take Action. Using this for illustration, Figure 25 in the TT Final Report would show 2 of 23 sockets in a red state and 6 of 23 in a yellow state. Taken together, 8 of 23 sockets, or 1/3 of the sockets, had displacements after the collapse that could have been considered excessive and warranting detailed examination. (One socket could not be characterized and is not included in this count.)
Role of Performance Monitoring for Critical Structures
In the context of this document, a critical structure is one that poses a high threat to life should it collapse. The Arecibo Telescope met this definition of a critical structure. Performance standards are higher for a critical structure due to their higher risks.
While not regulatorily mandated, good practices in civil engineering usually promote adopting a systematic performance monitoring program to (1) verify that the facility is performing to the design specifications and (2) detect any indications of deteriorating performance that would necessitate actions to mitigate a potential collapse. The need for these practices is especially true for critical structures. Systematic performance monitoring entails conducting and documenting measurements and observations in a predetermined manner at fixed time intervals that enable competent experts to assess the variations in performance over time and to identify any unacceptable levels of risks that require corrective measures. The level and sophistication of a performance monitoring program for a constructed facility usually increase with increasing risks and should increase in frequency as the structure ages.
What Monitoring Was Possible and Practical?
It is not unusual for a cable to slightly displace out of a spelter socket when it is first loaded as the zinc casting seats within the socket’s cone, and ⅜ inch was measured in the Arecibo Telescope’s socket testing at Lehigh University. It is expected that some displacement out of a spelter socket will occur when the load is applied during construction. Then any further displacement will diminish to a small amount or zero unless a new load is added, such as by wind or earthquake. Monitoring of the extraction pullout of each socket could have been performed and used as a quantitative metric of socket performance. Figure 23 from the TT Final Report illustrates how visible the socket pullout was at the end of each socket.
At least one definitive criterion for the allowable slip of cable at spelter sockets existed based on judgment and experience.106 This standard applies to moveable bridge cables. The similarity of the two cable systems was enough that other consultants looked to this standard for establishing a maximum pullout limit for the Arecibo Telescope’s cables. This standard limits allowable slip to one-sixth of the cable diameter when proof-loaded to 80 percent of the cable’s minimum breaking strength, a load level that was never seen by the Arecibo Telescope’s cables. Arecibo cable diameter was 3 to 3⅝ inches, so a possible pullout threshold limit was approximately ½ inch. For the telescope’s main and backstay cables, this limit corresponds to a maximum slip between 0.5 and 0.6 inches.107
A slippage of ½ inch could have been easily recorded by manual means periodically using a camera, aided with a ruler or micrometer for scale, as is shown in some of the figures in the TT Final Report.108 The ease of recording such slips is demonstrated by Figures 23 and 24 from the TT Final Report, shown below in Figure 3-15. TT Figure 23 shows a 1.125-inch pullout of M4N-T on February 19, 2019 (538 days before it failed). Figure 24 shows an increased pullout of B12W-G of more than ¼ inch between May 15, 2018, and September 18, 2020. Automated monitoring using displacement transducers and data loggers could have been added at any point to obtain more precise data to reveal trends with time and events, possibly gaining insight into the slip mechanism and its correlation with site events. Such measurements with appropriate interpretation could also have provided
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106 AASHTO, 2019, “Standard Specification for Wire Rope and Sockets for Movable Bridges,” M 277-06.
107 From TT Final Report, the cables reported max load was approximately 62 percent of their minimum breaking strength so these displacement limits should be reduced to approximately 0.4 to 0.5 inches. A ½ inch amount would have been a reasonable practical limit to set to trigger further attention to the socket.
108 TT Final Report.
SOURCE: Thornton Tomasetti, 2022, Arecibo Telescope Collapse: Forensic Investigation, NN20209, prepared by J. Abruzzo, L. Cao, and P.E. Pierre Ghisbain, July 25, https://www.thorntontomasetti.com/sites/default/files/2022-08/TT-Arecibo-Forensic-Investigation-Report.pdf; modified from photos from NAIC Arecibo Observatory, a facility of the National Science Foundation; courtesy of Thornton Tomasetti.
indicators that contingency measures should be engaged to avoid the collapse or at least steps to be taken to reduce the risks to people and property.
TT concluded,
It is now clear from our study that excessive cable slip occurs in zinc-filled spelter sockets due to zinc flow and is a sign of upcoming failure through core rupture or core flow-out. Excessive cable slip was observed on the first socket that failed at least a 1½ years before the collapse but was not identified as an immediate structural concern. Monitoring the cable slip and slip rate is a reasonable method to determine if a socket is failing, and the limit of one-sixth of the cable diameter appears to be a reasonable threshold for slip monitoring based on what was observed on the telescope’s sockets. Cable slip can cause the rupture of individual outer wires before complete socket failure. A socket exhibiting outer wire ruptures should, therefore, be closely inspected and monitored for cable slip in its connections. However, monitoring wire ruptures is not sufficient, or even directly correlated, to determine if a socket is failing.109
Further from TT,
A safe cable system can still be designed with a lower safety factor, such as the 2.2 safety factor prescribed in ASCE 19. However, in that case, the sockets should be inspected regularly to measure cable slip. A socket should be replaced or bypassed when excessive cable slip indicates that zinc flow continues to occur over time. Limiting the allowable cable slip to one-sixth of the cable diameter is reasonable until further studies are performed.110
The following captures key points relative to the monitoring of the cable sockets:
- Cable sockets may be the structure’s weak point.
- Cable socket pullout was expected to remain negligible after initial loading.
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109 TT Final Report, p. 49.
110 TT Final Report, p. 50.
- There were multiple indications of excessive cable slip in the sockets.
- The observatory would have benefitted from a systematic monitoring program to monitor cable pullout of the sockets and a contingency plan to deal with unacceptable pullout (a pullout of more than D/6). Pullout of 1.5 inches, increasing to 1.75 inches, was observed in September 2020 on B12W, with more than 1 inch observed on M4N. These exceed D/6 by far and should have immediately triggered a systematic monitoring program post-Maria. Monitoring is meant to include systematic quantified measurements of performance that can be duplicated by an independent person. While visual inspections are an important aspect of monitoring, they are not sufficient to provide definitive quantitative data over time.
- There was never a systematic monitoring program in place for the facility.
Finding: Meaningful measurements, documented with photos, of socket slip could have been obtained with simple equipment such as a ruler or micrometer.
Conclusion: Such measurements at sufficient intervals would have indicated excessive socket slip and that the cable performance was not uniform across the structure.
Conclusion: Differentials in cable slip and/or measurements warranted serious investigation by experts knowledgeable in socket performance. Any recommendations from such experts would have to be implemented.
These recommendations related to critical structure performance monitoring are based on lessons learned from the Arecibo Telescope collapse and the experience of the committee members.
Recommendation: The facility owner/operator should ensure that an operations and maintenance manual for the structure is commissioned and is available during the operation of the structure. The manual should:
- Identify performance standards of the facility to help detect unexpected, potentially dangerous performance and deteriorating performance with time;
- Provide a monitoring and inspection plan that considers potential critical failure modes (and necessary inspection expertise to address them) and include physical variables to monitor, locations to monitor, and the recommended frequency of monitoring. The plan should recognize that some time-dependent failure modes can operate at low loads in contradiction with the safety factor. It should also provide limit values for warning levels and action levels for each performance variable to be monitored. (Warning level is the point where performance becomes concerning, and further evaluation of the safety of the structure should be made. The limit level endurance limit is the point where the performance is becoming threatening to life, and people should be removed from harm’s way.); and
- Indicate the expected service life of the facility and its key components.
Recommendation: The facility owner/operator should:
- Implement the monitoring plan and keep it operational for the life of the structure. For structures with long life expectancies, this may require updating to account for mechanisms and degradation that are a function of age; and
- Engage a qualified professional to evaluate the monitoring data at least annually, assess the safety of the structure, and provide recommendations for changes to the structure and changes to the monitoring plan as needed.
