Seismic Upgrade Risk versus Benefit Shawn Callahan Mike Pollard 5/31/11.

Seismic Upgrade Risk versus Benefit

Shawn Callahan

Mike Pollard

5/31/11

Executive Summary

• Seismic upgrade is an insurance policy designed to minimize risk.

• Our goal is to determine the value of each option based on the seismic risk and benefit.

• In our WBS we calculated the cost of each option and the benefit to cost ratio (BCR).

• Conclusion:– 12.3% in 50 year event (2006 sized event)

• BCR<1 for all current options. This is due to low probability and high cost to retrofit.

– 2% in 50 year event (collapse prevention). • Option B (protects glass) BCR=16• Option D (protects against collapse) BCR>>1

Benefit cost ratio (BCR)(12.3% probability in 50 years)

based on 2006 event

• Baseline loss (2006 event): $7.7M• Estimate loss for each restraint design.• Benefit=Loss reduction ( Baseline loss- Estimated Loss)• USGS probability of 0.3g’s (2006 event) quake=12.3%.• BCR= Benefit x Probability/Cost (want > 1)

Baseline loss:Cost of 2006 earthquake

• Lost ~5 weeks of science (100k/telescope/night): $7.0M• Cost of repair (summit): $681K• Total lost: $7.7M

• see:\TSD Planning\TSD Development Projects\Seismic Upgrade\2006 Quake Recovery Doc

Estimated loss with new restraints(12.3% in 50 yrs and 6.3% in 25 yrs)

Probabilistic Loss Analysis6/1/2011 Rank

Ranking Justification

Benefit/cost ratio (25 year)

Benefit/cost ratio (50 year) Benefit Cost

Total Loss (includes downtime expense)

Lifetime (Years) 25 50Probability of PGA=0.3g(2006 earthquake) 6.3% 12.3%

Baseline:2006 Seismic Event (Zone 3 event) 56% probable $7,681,000

Option: 0Provide Spares (Only) 3

No additional protection.Assume back on sky 1 day sooner.No risk mitigation. 0.11 0.21 $200,000 $118,000 $7,481,000

Option A: Displacement:11 mmSee: WBS Option A

Not recom-mended

Highest accelerations leading to increased risk to telescope 0.20 0.39 $1,578,980 $502,020 $6,102,020

Option B: Displacement:26mm. (20% damping)See: WBS Option B 1

Best protection of telescope 0.42 0.81 $5,626,580 $854,420 $2,054,420

Option C: Displacement: 47 mm. (5% dampingl)See: WBS Option C 2

More susceptible to resonance damage 0.48 0.93 $5,546,580 $734,420 $2,134,420

Benefit (Loss reduction)Baseline loss- Estimated loss (12.3% in 50 yrs and 6.3% in 25 yrs)











Not recom-mended






USGS ProbabilityPeak Ground Acceleration (PGA) in 50 years for

Mauna Kea

• 10% probability of 0.4g PGA

• 2% probability of 1.2 g’ PGA

• Use Gutenberg-Richter recurrence relation, log(N)= a-b*M solve for a, b.

• Calculate 12.3% probability for 0.3 g PGA

Benefit to cost ratio (12.3% in 50 yrs and 6.3% in 25 yrs)











Not recom-mended






Probabilistic Seismic Hazard Analysis (a.k.a. limited liability clause)

• Probabilistic Seismic Hazard Analysis (PSHA) is a methodology that estimates the likelihood that various levels of earthquake-caused ground motion will be exceeded at a given location in a given future time period.

• Due to the infrequency of large seismic events, there is inherently a large uncertainty in USGS predictions.

• Estimates continually being improved by USGS.

Conclusion

• BCR<1for all current options. This is due to low probability and high cost to retrofit.

• Until we can achieve BCR>1 we do not recommend proceeding to PDR.

Accelerations vs. damage• The damage should be roughly

proportional to acceleration (assume constant duration).

Option A: Displacement:11 mmSee: WBS Option A 0.71g 1.45gOption B: Displacement:26mm. (20% damping)See: WBS Option B 0.51g 0.65gOption C: Displacement: 47 mm. (5% dampingl)See: WBS Option C 0.92g 1.17g

Benefit cost ratio (BCR)based on 2% in 50 year

(Restraints only prevent collapse)

• Baseline loss: Possible loss of life. Total loss of both telescopes.

• Estimate loss for each restraint design.• Benefit=Loss reduction ( Baseline loss- Estimated Loss)• USGS probability of 1.2g’s=2%• BCR= Benefit x Probability/Cost (want > 1)

“Collapse prevention” Baseline 2% probability in 50 years

• The "value of a statistical life" is $6.9 million in today's dollars, the Environmental Protection Agency reckoned in May [2011]

• In a 24 hour period assume 10 people were at risk ($70M)

• Replacement cost for two telescopes in today’s dollars ($750M?)

• Total: $820M???• (The TMT telescope cost was estimated in 2009

to be $970 million to $1.2 billion)

Collapse prevention restraint2% probability in 50 years

Loss estimate

• Options A through C already include collapse restraints.

• Option D: Design K1-style restraints for K2. Include additional uplift restraint to meet zone 4 PGA for both telescopes.

• The damage of an earthquake is proportional to the energy release:

• Option B$7.7M x 4.46=$34M. • Option D: add $85M for M1 and M2 replacement= $119M

Benefit (Loss reduction) 2% probability in 50 years

from adding collapse prevention• Benefit= Baseline loss-estimated loss

• Option B: Benefit=$820M-$34M=$786M

• Option D: Benefit =$820M-$119M=$701M

Cost

• Option B: $854k

• Option D: $120K= 16x $5k+50% (Needs refinement!)

BCR

• BCR= Benefit x Probability/Cost (want > 1)

• BCR• Option B: $701M*.02/854,420= 16• Option D: $786M*0.02 /$120K= 131

Seismic Upgrade Risk versus Benefit Shawn Callahan Mike Pollard 5/31/11.

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