ML20082N999
| ML20082N999 | |
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|---|---|
| Site: | South Texas  |
| Issue date: | 11/30/1983 |
| From: | BECHTEL GROUP, INC. |
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| 14926-001, 14926-1, NUDOCS 8312080047 | |
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Text
-
ST-HL-AE-1028 11/14/83 ERRATA I
Probabilistic Evaluation of Tornado Missile Hazard.to the Containment Isolation Valve Compartment Equipment Pg. 4, Paragraph B: Replace with the following B.
The potential missile model assumes 1.
A missile distribution based on EPRI survey without censoring as was done. for the EPRI studies.
2.
A missile density upper limit increased by a factor of 2.5 over the EPRI survey to account for local variations in missile density.
3.
One half of the potential missiles are distributed up to 20 f t above grade with the remainder at grade.
4.
The number of unrestrained potential missiles is con-servatively chosen to be 10% of all potential missiles.
Pg. D-16, Section D.10, 2nd Paragraph:
Replace the word " Twenty" in the second line with the word "Ninety".
Delete the word " elevated" in this sentence and the next.
1 i
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./L B312080047 8311J4
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PDR ADOCK 05000499 PDR ST-HL-AE-1028 11/14/83 l.
South Texas Project Probabilistic Evaluation of Hurricane-Generated Missile Ha'zard to the Containment Isolation Valve Compartment Equipment 14926-001 k..
Risk / Reliability Group Los Angeles Power Division Bechtel Power Corporation Revision 1 November 1983 t
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l l
i SOUTH TEXAS PROJECT HURRICANE MISSII.E EVALUATION REPORT
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I.
Introduction 4
This study uses Probabilistic Risk Assessment (PRA) methodology to evaluate the probability that equipment located in the containment isolation valve cubicle (IVC) might be damaged by hurricane-generated missiles. Hurricane-generated missiles include objects on or.near the plant site that could become airborne during a hurricane and be transported to the top of the IVC.
The study includes an evaluation of the likelihood of a hurricane occurrence, as well as the probability of potential missiles becoming airborne and being transported to the top of the IVC. The extent of damage is not evaluated, but is conservatively assumed to be certain and total for all missile strikes.
II.
Acceptance Criteria The NRC's acceptance criteria are contained in the " General Design Criteria (GDC) for Nuclear Plants" [1]. Specifically, GDC 2 and 4 apply to this evaluation and are summarized below:
GDC 2 requires that " Structures, systems, and components important a.
to safety shall be designed to withstand the effects of natural phenomena such as - hurricanes - without loss of capability to
(
perform their safety functions.
b.
GDC 4 requires that "... structures, systems, and components shall be appropriately protected against dynamic effects, includ-ing the effects of missiles,... from events and conditions outside the nuclear power unit."
The Standard Review Plan (SRP) [2] Section 3.5.1.4 provides further guidance in meeting GDC 2 and 4 requirements. Specifically, SRP Section 3.5.1.4 refers to the acceptance criteria of SRP 2.2.3, which states ".
. design basis events include each postulated type of accident for which the expected rate of occurrence of potential exposures in excess of the 10 CFR Part 100 guideli es is estimated to exceed the 9
j NRC staff objective of approximately 10 per year... expected rate of occurrence of potential expogures in excess of the 10 CFR 100 guidelines of approximately 10 per year is acceptable if, when combined with reasonable qualitative arguments, the realistic probability can be shown to be lower..."
r III.
Summary
^
~
The probability of failure of the equipment in the IVC to perform its safety function in the event of a hurricane is evaluated using PRA methodology., The study quantifies the probability of hurricane-generated missiles hitting the top of the IVC. The results are compared to the NRC k,,g i
1-s
acceptance criteria. The results indicate that hurricane-generated
(.
missiles are not a significant threat to the IVC equipment. The results further indicate that no physical barriers are required at the top of the IVC.
IV. Analysis Approach The probability of damage to equipment located in the IVC depends on three factors:
A.
The probability distribution function for hurricane occurrence l
at the plant site f(w).
5 B.
The conditional probability of one or more hurricane-generated missiles striking the top of any one of four IVC compartments, given the l hurricane occurrence, P I")*
H C.
The conditional probability of IVC equipment being damaged, given that the hurricane-generated missile or missiles have entered the IVC, P
- D So:
e.
f(w)P (") D(w)dw (1)
P =
H T
The hurricane occurrence rate is developed in Appendix B.
The l
cumulative probability of exceeding a given hurricane wind speed at the plant site is shown in Table I.
The conditional probability of the missile strike, given the hurricane occurrence, depends on the following subfactors:
A.
The number of potential missiles.
B.
The conditional probability of the potential missiles becoming airborne (or injected), given the occurrence of a hurricane.
C.
The conditional probability of missiles being transported from their origin to the target, given that they become airborne.
D.
The target area.
The number of potential missiles is based on data from Electric Power Research Institute (EPRI) surveys at seven nuclear power plant sites [5].
The probability of the potential missiles becoming airborne is calculated using a missile model developed at Jet Propulsion Laboratory (JPL) [6].
The. conditional probability of missiles being transported from their origin to the target is based on a statistical mechanics model [7], [8].
{.,
The area of the top of each of the four IVC compartments is 745 square feet l (total target area is 2980 square feet). The IVC height is 55 feet above grade and the grade elevation does not vary significantly 2
>w n,
within 300 feet of the IVC. The number of potential missiles and the missile density incorporated into this study are shown in Table II.
a The conditional probability of IVC equipment being damaged, given that the hurricane-generated missile or missiles have entered the IVC, is conservatively taken to be certain and total. That is, the conditional probability is taken as unity.
The result of this very ce9servativg estimate is compared with the NRC acceptance criteria of 10 and 10 per year. Because of the uncertainty of some factors, we use the median as the "best estimate" or
" recommended" value [9].
V.
Assumptions and Conservatises The following assumptions are used in this study:
A.
A hurricane missile strike on the top of any one IVC represents failure (see conservatisms A and C, below).
l B.
The distribution of potential missiles by number and length is based on an EPRI survey of seven nuclear plants (5).
C.
The conditional probability of a missile striking the target, given the hurricane occurrence, is adopted from the tornado missile isodel [7, 8,11].
D.
The frequency of hurricane wind speed is fitted with a Weibull distribution.
Conservatisms incorporated in this study are:
A.
The strike probability, in comparison to the NRC's activity release l
frequency acceptance criteria, assumes:
1.
Missile-inflicted damage is certain and total.
2.
For purposes of this study damage was not evaluated.
It is assumed that damage could lead directly to " potential exposures in excess of the 10CFR100 guidelines..." (SRP 2.2.3 acceptance criteria).
B.
The potential missile model assumes:
1.
A missile distribution based on EPRI survey without censoring as was done for the EPRI studies.
2.
A missile density upper limit increased by a factor of 2.5 over the EPRI survey to account for local variations in missile density.
l 3.
All'the missiles are distributed up to 20 feet above grade.
l
('^V I
4.
The number of unrestrained missiles was conservatively chosen to be 10% of all missiles.
3 l
. =
=
=.
C.
Geometric factors that result in further conservatisms'are:
l 4
1.
Sheltering by other structures is neglected.
2.
A missil'e strike in any IVC opening results in failure.
3.
The area of safety-related equipment inside the IVC is less than the IVC top area.
VI.
Results and Conclusions The result of the analysis is the probability of hurricane missile damage to the IVC equipment. The median (50th percentile) value is reported in Table III. The median or gest estimate" value of strike probability is approximately 1.2 x 10 per year. This is very smal l
compargdtotheNRCactivityreleaseacceptancecriteriavalueof10 to 10 per year.
The above results indicate that hurricane-generated missiles are not a significant threat to the IVC equipment. These results further indicate that no physical barriers are required at the top of the IVC to protect IVC equipment from potential hurricane-generated missiles.
VII.
REFERENCES
[1]
10 CFR Part 50, Appendix A, " Design Basis for Protection Against Natural Phenomena."
[2] Standard Review Plan, U.S. Nuclear Regulatory Commission, NUREG-75087.
[3] Nuclear Regulatory Commission, " Design Basis Tornado for Nuclear Power Plants," Regulatory Guide 1.76, April 1974.
[4]
Batts,.M.
E., "Probabilistic Description of Hurricane Wind Speeds," Journal of the Structural Division, Proceedings of i
the American Society of Civil Engineers, Vol 108, No. ST7, July 1982.
[5] Twisdale, L. A., et al., " Tornado Missile Risk Analysis," EPRI NP-768, May 1978, EPRI NP-769, May 1978.
[6] Redmann, G. M., et al., " Wind Field and Trajectory Models for Tornado-Propelled Objects," EPRI 308, Technical Report 1, February 1976.
[7] Goodman, J. and Koch., J.
E., " Conditional Probability of the Tornado Missile Impact Given a Tornado Occurrence," Proceedings of the International ANS/ ENS Topical Meeting on Probabilistic Risk
- Assessment, Port Chester, New York, September 20-24, 1981, pp. 419-424.
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4
[8] Goodman, J. and Koch, J.
E., "The Probability of a Tornado Missile Hitting a Target," Nuclear Engineering and Design 74, (1983).
[9] Apostolakis, G., et al., " Data Specialization for Plant Specific Risk Studies," Nuclear Engineering and Design 56 (1980), pp. 321-329.
[10] Historical Extreme Winds for the United States - Atlantic and Gulf of Mexico Coastlines, prepared by M. J. Changery, NUREG/CR-2639
[11] Goodman, J. and Koch, J. E., "The Assessment of Tornado Missile Hazard to Nuclear Power Plants," Proceedings of International Conference on Numerical Methods in Nuclear Engineering, Montreal, Quebec, Canada, September 6-9, 1983.
[12] Simiu, E. and Scanlan, R. M., Wind Effects on Structures: An Introduction to Wind Engineering, John Wiley and Sons, Inc.,
New York, 1978.
[13] Batts, M.
E., et al., " Hurricane Wind Speeds in the United States,"
Journal of the Structural Division, Vol. 106, No. ST10, Proc.
Paper 15744, Oct. 1980, pp. 2001-2016.
[14] Simiu, E. and Filliben, J. J., "Weibull Distributions and Extreme Wind Speeds," Journal of the Structural Division, Vol. 106, No.
ST12, Proc. Paper 15909, Dec. 1980, pp. 2365-2374.
[15] Georgiou, P.
N., et al., " Design Wind Load in Regions Dominated
(
by Tropical Cyclones, " Proceedings of Sixth International Conference on Wind Engineering, Gold Coast, Australia, March (1983).
[16] Batts. M.
E., et al, " Sampling Errors in Estimation of Extreme Hurricane Winds," Journal of the Structural Revision vol. 106, No. ST10, pp. 2111 - 2115.
[17] Goodnan J., " Accuracy and Efficiency of the Monte Carlo Method,"
Proceedings of International Conference on Numerical Methods in l
Nuclear Engineering, CNS/ANS, Montreal, Canada. Sept. 6-9, 1982, pp. 430-441.
i 1
C' 5
TME I
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THE PROBABILITY OF EXCEEDING A GIVEN WIND SPEED, w, AT TE STP PLANT SITE PER YEAR w (m/s) w (mph)
Weibull Distribution Based Upon Table B.2
~3 50 112 5.4 x 10
~3 55 123 2.0 x 10
~4 60 134 6.1 x 10
~4 65 145 1.6 x 10
-5 70 157 2.9 x 10
-6 75 168 4.0 x 10
~7 80 179 6.0 x 10 TABLE II DISTRIBUTION OF POTENTIAL MISSILES Median (50th Percentile)
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Number of Potential Missiles on 6,000 Site and Vicinity 7
2 (2.5 x 10 ft ), y P
-4 Local Surface Density of 2.40 x 10 Potential Missiles Near the. IVC (ft 2), a P
Table III f
MEDIAN VALUE FOR THE PROBABILITY OF DAMAGE TO IVC FROM HURRICANE-GENERATED MISSILES l
l
-10 Weibull wind speed distribution at the plant 1.2 x 10 per year site, 90% restrained, 10% unrestrained potential missiles up to 20-foot above grade For uncorrelated sampling errors (see Table B.8) l
(.p.
1 i
6 1
APPENDIX A GENERAL METHOD A.1 Introduction Probabilistic evaluation of hurricane-generated missile hazard to the contain-medt isolation valve cubicle equipment is based on historical data of hurricane occurrences along the Gulf of Mexico and on a theoretical model for the conditional probability of hitting a target given the hurricane occurrence.
A.2 Hurricane Frequency of Striking the STP Nuclear Power Plant Site According to [10), the cumulative distribution of extreme wind occurrence can be described in two ways:
-("}")
(A.1)
Fy (w) = exp
- exp h }l
(
(A.2)
F2 (W) eXP where F (w) and F are cumul'ative functions of Type I and Type II dis-tributibas,wis$n(w)tremewindspeedinsph,anda,o,andyaredistribu-ex tion parameters.
(-
Because the wind speed, w, in the formula for conditional probability of hit-ting is given in m/s, we introduce conversion coefficient p = 2.2374145, which converts m/s into sph.
We will use formulae (A.1) and (A.2) in the asqptotic area where Fy (w) and F (w) differ from unity by a small number (10 or less).
In this area, f roulae A.1 and A.2 can be simplified:
0" } "
(A.3)
Fy (w) = 1 - exp F2 (w) = 1 -
l (A.4)
Batts [4] proposed the use of a Weibull distribution, which gives the best fit for a tail:
F,(w) = 1 - exp
- f " ~ "\\ T '
l (A.5)
~*
Cy A-1 s
The density functions for hurricane occurrence for all three types of cumulative distribution given by formulae (A.3), (A.4), and (A.5) are:
a y(w)=hexp
}a (A.6) f 2 (w) = g [Sw - oli (A.7)
- f o
(
o j fw (w) = N 0" ~ "I 0" ~ "
1 (A.8) exp 0
( 0
/
( 0
)
Therefore, the probability, dP, that a hurricane with maximum wind speed in the range (w, w + dw) will Etrike the plant site is:
dP, = f (w) dw (A.9) where f(w) is one of density functions (A.6), (A.7), or (A.8).
Now we have to choose between these three distributions. The Type II distri-bution wes designed for nontrop,ical storms. According to [12), the applica-tion of Type II distribution to hurricanes leads to a ridiculous result.
Forexample,fgrtheestimated1000-yearwind(i.e.,theprobabilityof occurrence 10 per year), a value of 1250 mph is predicted by (A.7).
It is much higher than a maximum possible wind speed for hurricanes.
(
According to [12], the gradient wind, w, can be evaluated according to the formula:
w=bN (A.10) pf da where:
l h = gradient of pressure p = sir density f = Coriolis parameter
( = coefficient depending on ratio of geostrophic wind velocity and Coriolis velocity. The range for cyclonic winds is:
0.5 < ( < 1 (A.ll)
. )e k.g l
l l
A-2
Assuming the maximum pressure drop of 1 ate and minimum distance of this I
pressure drop of 1 km, we obtain the maximum value for the pressure gradient:
N = 101.3 E
(A.12) j da as Maximum hurricane wind speed, w, corresponding to this gradient of pressure at the site latitude is in the, range:
120 mph < w < 240 mph (A.13)
Analysis performed in [12, 15] indicates that Weibull distribution is more appropriate for high wind prediction than Type I distribution. Therefore, the Weibull distribution was incorporated in this study.
The STP site location is shown on Figure A-1.
It is located between mileposts 300 and 350. Cumulative distributions are shown in Table I.
A.3 Conditional Probability of Hitting a Target, Given the Hurricane Occurrence at ?lant Site I
l The conditional probability, P, of a missile hitting a target given a hurricane H
occurrence at the plant site was adopted from the tornado missile study [7, 8]:
1 H (") * "p A q (w) $ (w, z)
(A.14)
P
(
where:
n
= local density of potential missiles p
i A
= area of target
= target elevation over the ground z
q(w)
= probability of injection of potential missiles
$ (w, z) = height distribution of airborne missiles 1
The probability of injection, q(w), was calculated according to the method described in [8]. The parameters of height distribution, $ (w, z), were calculated according to the formulae given in [11].
An example of these calculations is shown in Table A.la and b.
This is based upon the Weibull distribution of hurricane wind speeds which corresponds to the best estimate speeds given in Table B.S.
The results for restrained
[
I and unrestrained missiles are given in Table A.la and Table A.lb, respectively.
As mentioned above, the transport model used was developed specifically for winds characteristic of tornados. This implies a high degree of randomness in wind direction at a particular location during a single storm. The model thus assumes that the direction of missile transport is isotropic. The applicability to the straight line hurricane winds s
depends upon a consideration of the different wind directions that can occur at a particular site for a large number of storms rather than for a single storm as for tornados. The data [10] indicate a fair degree of randomness in wind direction at the site over the period l
A-3
=
.L_.,_.,.-__.__,
.oa of data collection. Since our analysis is based on a large sample of
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hurricanes with long recurrence intervals the transport model developed assuming a random wind direction can be used here with a high degree of confidence.
A.4 Damage Probability to IVC Per Year The annual damage probability, P, t the IVC can be calculated by formula:
T o
f(w) PH (w) dw (A.15)
P =
T "o
since P = 1 f r all strikes, D
H (w) is given by formula (A.14) and f(w) by formula (A.8).
where P
(
(J
[
A-4
' ~
w
$(z,w) p (w) m/s sph q(w)
(z=55 ft)
H 88.0000 197
.00000
.23934+00
.00000 o
89.0000 199
.20000-02
.24581+00
.35160-93
- 90.0000 201
.16000-01
.25227+00
.28868-02 91.0000 204
.27000-01
.25871+00
.49959-02 92.0000 206
.35000-01
.26514+00
.66370-02 93.0000 208
.55000-01
.27155+00
.10682-01 94.0000 210
.77000-01
.27793+00
.15306-01 95.0000 213
.10100+00
.28429+00
.20536-01 96.0000 215
.12200+00
.29063+00
.25359-D1 97.0000 217
.12200+00
.29693+00
.25909-01 98.0000 219
.11700+00
.30321+00
.25372-01 103.0000 230
.17300+00
.33407+00
.41334-01 108.0000 242
.23500+00
.36395+00
.61170-01 113.0000 253
.26100+00
.39273+00
.73309-01 118.0000 264
.34000+00
.42033+00
.10221+00 123.0000 275
.35500+00
.44671+00
.11342+00 126.0000 286
.38500+00
.47186+00
.12993+00 133.0000 298
.39000+00
.49577+00
.13829+00 138.0000 309
.43800+00
.51849+00
.16242+00 143.0000 320
.46800+00
.54003+00
.18076+00 148.0000 331
.46200+00
.56044+00
.18518+00
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Table A.la: Height distribution, $(z,w), Injection Probability q(w) and conditional probability of hitting, P (w), as functions of wind speed, w; H
based upon Weibull parameters corresponding to Table B.2; restrained missiles.
s i
l t
l t
A-5
(~
w
$(z,w) p (w) m/s aph q(w)
(z=55 ft)
H 81.0000 181
.00000
.19396+00
.00000 82.0000 183
.11000-01
.20042+00
.15768-02
- 83.0000 186
.30000-01
.20690+00
.44393-02 84.0000 188
.36000-01
.21339+00
.54941-02 85.0000 190
.48000-01
.21988+00
.75482-02 86.0000 192
.68000-01
.22637+00
.11009-01 87.0000 195
.10900+00
.23285+00
.18153-01 88.0000 197
.11900+00
.23934+00
.20370-01 89.0000 199
.14400+00
.24581+00
.25315-01 90.0000 201
.13600+00 25227+00
.24537-01 91.0000 204
.14300+00
.25871+00
.26460-01 96.0000 215
.19600+00
.29063+00'
.40740-01 101.0000 226
.25900+00
.32183+00 59615-01 106.0000 237
.28500+00
.35212+00
.71774-01 111.0000 248
.36900+00
.38135+00
.10064+00 116.0000 260
.38100+00
.40943+00
.11157+00 121.0000 271
.41900+00
.43630+00
.13075+00 126.0000 282
.42000+00
.46194+00
.13876+00 131.0000 293
.46600+00
.48635+00
.16209+00 136.0000 304
.49900+00
.50955+00
.18185+00 141.0000 315
.48800+00
.53155+00
.18552+00 146.0000 327
.53800+00
.55241+00
.21255+00
(
151.0000 338
.57200+00
.57216+00
.23407+00 Table A.lb: Height distribution, $(z,w), Injection Probability, q(w), and conditional probability of hitting, P (w), as functions of wind speed, w; H
based upon Weibull parameters corresponding to Table B.2; for unrestrained missiles.
i I
i e
l A-6
APPENDIX B
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SENSITIVITY OF RESULTS TO ERRORS IN TE HURRICANE WIND SPEED DATA B.1 Backaround Although historical data does exist for extreme wind speeds along the Gulf of Mexico coastline [10] it has been shown that predictions of extreme wind speeds in hurricane-prone regions cannot in general be based solely upon a statistical analysis of th.ese data [12]. Indirect methods are therefore commonly employed. Historical data are used to make statistical inferences concerning the various climatological characteristics of hurricanes in the region of interest and probabilistic models for each of these characteristics are developed.
In addition, a physical model of the hurricane wind structure is developed. Using this information a large number of hurricanes are simulated by Monte Carlo techniques. From these simulated hurricanes, the largest wicd speeds are used to estimate the cumulative distribution function of hurricane wind speeds at the site of interest.
This technique is susceptible to several errors which can generally be classified into four categories [12): (1) sampling errors due to the lisiited amount of historical data used to develop the statistical model of the hurricane, and the limited number of hurricanes generated by Monte Carlo simulation; (2) probabilistic modeling errors due to the imperfect choice of distribution functions to which the climatological data are fitted;
(
(3) observational errors in the measurement of actual wind speeds; and (4) physical modeling errors due to the imperfect representation of the i
dependence of wind speeds on various parameters.
l The purpose of this appendix is to evaluate the impact that these errors may have on the results of this study. The procedure will be to examine the fastest-mile wind speed predictions for various recurrence intervals
. given by different authors using somewhat different models. From this, a best-estimate will be predicted for each recurrence interval along with a distribution of wind speeds around each recurrence interval which accounts for the possible errors. A Monte Carlo technique will be used to select a wind speed value for each recurrence in*,erval. These wind speeds will be used to fit'a Weibull distribution for hurricane wind speeds which can then be used to predict the damage.
bability as indicated in the main body of the report (See figure B.la). Reg ; ting this Monte Carlo simulation numerous times will provide an indication of the sensitivity of the final l
results to the choice of best fit for the Weibull distribution of hurricane wind speeds.
Since various selection effects could result in the errors associated with fastest-mile wind speed predictions at the different recurrence intervals not being entirely independent, this sensitivity study was performed twice.
The first study was'done assuming the errors in the selection of fastest-mile l
The l
wind speeds at each recurrence interval were completely uncorrelated.
,~
second study assumed these errors to be 100% correlated.
(See figure B.lb)
B-1 s
, ~, _ _., _,
.n.
B.2 Data
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The first task is to determine best-estimate fastest-mile wind speeds for several different recurrence intervals.
Intervals of 25, 50, 100 and 2000 years were chosen. Although mentioned earlier that a wind speed distribution based solely upon historical data is not acceptable, the results from that data are presented here for comparison with that generated by the hurricane sifulation studies.
Historical data are presented in [10). Data for the South Texas Project Site is determined by linear interpolation of the data presented for Corpus Christi and Galveston. The applicability of linear interpolation is discussed in [13). The data for Corpus Christi are for winds at a height of 10m; those for Galveston are for winds at 30m. Because the potential missiles are distributed up to 20 ft(~6m) the 10m data are considered more appropriate. The data for Galveston were converted to 10m winds according to equation 3.1.1 of reference [12]:
U(Z ), In[(Z -Z )I l (B.1) y y d o
U(Z )
In[(Z -2 )I l 2
2 d o
where U(Z ) = wind speed at height Z g
g Z
= 0.7 for STP Z
= 0.0 for STP d
then U(10) = 0.708 U(30)
Table B.1 shows the results for the four recurrence intervals.
Two independent simulation studies were considered, each using slightly different physical models [13], [15]. Table B.2 shows the appropriate data for the plant site for the simulation study [13).
Data in [15] are presented in terms of mean hourly extremes in m/s.
Conversion to uph is straightforward.
Conversion of the data to fastest-mile wind speeds is accomplished by multiplying the mean hourly extremes by an appropriate coefficient as discussed in [12). The results are presented in Table B.3.
B.3 Discussion of Errors The four types of errors mentioned previously imply some uncertainty in the specification of the fastest-mile wind speeds at various recurrence intervals.
A consideration'of those errors will help in the choice of a best estimate for each wind speed and a measure of the error inherent in each number. For each recurrence interval the wind speed is assumed to be distributed normally about g
the best estimate value. Observational errors are accounted for by resorting B-2 1-----
,->----+-.y g-
,e--
---w--
y---w e
-,--ww-y rm-
to the Monte Carlo hurricane simulation studies and are responsible for the t'
differences between Table B.1 and Tables B.2 and B.3.
The two simulation studies, [13] and [15), represent the use of different physical and proba-bilistic models. Therefore, allowance can be made for the effects of modeling errors by choosing the most conservative of the results. For these reasons the results in Table B.2 have been selected as the best-estimate values for the given recurrence intervals.
Shlingerrorscanbeevaluatedtoprovideanestimateofthespreadofthe i
distribution of errors around the best-estimate value. The sampling error due to the limited amount of historical data is discussed in [16] and is estimated to be about 6-10% [13]. Data reported in [13] reduces this type of error by using a smoothing technique where the fastest-mile wind speed j
at each milepost is calculated by finding the average of the reported speed at that milepost and those for the two nearest neighbor mileposts. This increases the data set by a factor of three and, hence, reduces the error by a factor of 43. The relative error due to this type of sampling error is, therefore, 0.035 to 0.058. A value of 0.045, which shall be denoted as 6, was chosen for this study.
7 The second type of sampling error, that due to the limited number of hurricanes in the simulations, is determined by the inherent accuracy of the Monte Carlo method. This type,of error is discussed in [17]. For an N-year recurrence interval wind speed, w, the standard deviation of the distribution of speeds about the best estimate is given by:
1-(
1 (B.2) d Aw =
g
.g where n
= number of simulations f(w) = density function for the Weibull distribution Table B.4 shows the results of the calculation for n = 1000 (the number of l
simulations used in [13]).
for N=50, n=1000, and a Type I For the purpose of comparison, the value of 6= 0.018.7 Thus, the relative error used distribution, is given by [16] as 62 here is generally at least twice this value.
The two types of sampling errors can be combined by the following equation:
6=
6 2,3 2 (B.3) y l
B-3
The final.results are shown in Table B.5 o
B.4 Best-Fit Weibull Distribution Now that the errors are quantified, Monte Carlo techniques can be employed to select a set of wind speeds, one for each recurrence interval, for each simu-lation used in the study. Each set of four wind speeds must be fit to a Weibull distribution for use ultimately in calculating the damage probability.
1 The fitting procedure is basically a least-squares method. Denote the four wind speeds to be fitted by w. where i = 1, 2, 3, 4 correspond to recurrence intervals of25,50,100and2000yearsrespectively. A value for the Weibull tail-length parameter, y, is chosen and the location parameter, a(y), and the scale parameter, o(y) (see equation A.8), are calculated from:
w2 ~ "1 (In N ) Y - (In N ) Y 2
y Y
a(y) = v - o (in N )
(B.5) 2 2
An error function is then evaluated:
4 2
fw.(y) - w*.)
(.
1 E=
1 I
(B.6) 1(
"i
)
.1=
where w. (y) is the fitted wind speed value according to the current choice of y An iteration is performed on y in order to minimize the value of E.
B.5 Results of Sensitivity Studv.
f The procedure described in section B.4 is repeated for each simulation. This results in a different Weibull distribution and, hence, a different damage probability for each si:aulation. One hundred simulations were carried out for the case where the errors were considered to be completely uncorrelated and twenty were done for the case where the errors were 100% correlated.
The absolute range of fitted wind speeds obtained for various recurrence intervals are given in tables B.6 and B.7.
Considering the number of simulations done for each case, the ranges can be assumed to be essentially the same.
O G
B-4
Damage probabilities can be calculated for each simulation using the methods outlined in Appendix A.
A summary of the results from all of the simulations is given in Table B.8.
The apparent differences in the results between the cases for correlated and uncorrelated errors are slight enough to be con-sidered as an artifact of the Monte Carlo simulation technique rather than any real difference.
k 4
6 B-5 l
I Recurrence Corpus Christi Galveston Galveston Interpolation for Interval (10m)
(30m)
(10m) plant site (10m) 25 yr-105' 88 62.3 83.65 50 yr 116 94 66.6 91.30 100 yr 124 98 69.4 96.70 1000 yr 145 111 78.6 111.8 Table B.1: Fastest mile wind speed data based upon historical records [10).
All wind speeds are in miles per hour.
Recurrence Fastest-Mile Wind Speed Interval in uph at 10m 25 83.1 50 94.5 100 104.7 2000 135.9 Table B.2: Fastest-mile wind speed data for plant site based upon Monte Carlo hurricane simulation study [13).
Recurrence Mean Hourly Mean Hourly Correction to Fastest-Mile Interval Extreme (m/s)
Extreme (mph)
Fastest-Hile Wind Speed (mph) 25 28 62.7 1.28 80.2 50 31 69.4 1.29 89.5 100 35 78.3 1.30 101.8 2000 47 105.2 1.32 138.8 Table B.3: Fastest-mile wind speed data for plant site based upon Monte Carlo hurricane simulation study [15).
B-6 l
.~.
Recurrence Aw Relative Error Interval (yr)
(mph) 62
- 0"I" 25 2.774 0.0334 50 3.354 0.0355
_ 100 4.254 0.0406 2000 12.252 9.0902 Table B.4: Sampling errors due to a limited number of hurricane simulation.
Best-Estimate Fastest-Mile l
Recurrence Relative Sampling Wind Speed, (mph)
Standard Deviation Interval (yr) error, 6 (From Table B.2)
(mph) 25 0.0560 83.1 4.65 50 0.0573 94.5 5.41 100 0.0606 104.7 6.34 2000 0.1008 135.9 13.70 Table B.5: Best-estimate and standard derivation for fastest-mile wind speeds of various recurrence intervals.
l l
i Recurrence Range of Fitted Fastest-Mile Interval (yrs; Wind Speeds (mph) l 25 75.1 - 91.3 50 87.0 - 103.8 100 91.2 - 116.9 2,000 109.2 - 160.5 i
10,000 119.0 - 177.3 l
100,000 132.0 - 211.0 l
1,000,000 142.3 - 247.0 l
Table B.6: Range of fitted fastest-mile wind speeds for various recurrence
(.r intervals for completely uncorrelated errors.
B-7 s
~
Recurrence Range of Fitted Fastest-Mile Interval (yrs)
Wind Speeds (mph) 25 75.4 - 91.1 50 85.6 - 103.8 100 94.0 - 115.5 2,000 120.2 - 157.7 10,000 130.3 - 177.0 100,000 142.2 - 201.7 1,000,000 151.5 - 224.1 Table B.7: Range of fitted fastest-mile wind speeds for various recurrence intervals for 100% correlated errors.
5th Percentile Median 95th Percentile
-14
-10
-7 Completely uncorrelated 4.43 x 10 1.20 x 10 3.26 x 10 errors
-15
-11 100% correlated errors 6.57 x 10 7.49 x 10 8.53 x 10" Table B.8: Damage probability estimates assuming 10% unrestrained and 90%
restrained poteittial missiles.
h i.
B-8
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l W(2003) 8 lW W(100) l 3
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i i
i W (25)
W(50)
W;(100)
W;(2000) i i
WIND SPEED Figure B.la: Representation of Monte Carlo simulation procedure for uncor-related errors. w(25), w(50), w(100) and w(2000) represent best estimate wind speeds for recurrence intervals of 25, 50, 100 and 2000 years respec-tively. The gstimated probability distribution functions are shown in each t
case. The i Monte Carlo trial selects at random the four wind speeds w (25), w. (50), w (100) and w.(2000). These four values are used to fit
~
g g
a Weibull* distribution. Notel The distributions shown are not intended to be accurate representatives of the actual wind speed distribution, but are for illustration' purposes only. ThisfittedWeigglidistributionisthen used to calc *ulate a damage probability for the i trial.
(
B-9
-.--,=.
t i
n E
3 o
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i l W(25) l W(50)
! W(l00)
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I I
W;(25)
W(50)
W;(100)
W;(2000)
WIND SPEED Figure B.lb: Representation of Monte Carlo simulation for 100% correlation of errors., Note th'at each sample wind speed, w (x), has the same relative g
error (for example, 10) although the absolute magnitude of the error may differ due to the different distributions at each recurrence interval.
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