ML20079P159
| ML20079P159 | |
| Person / Time | |
|---|---|
| Site: | South Texas  |
| Issue date: | 01/06/1984 |
| From: | Simiu E NATIONAL INSTITUTE OF STANDARDS & TECHNOLOGY (FORMERL |
| To: | NRC |
| Shared Package | |
| ML20079P130 | List: |
| References | |
| NUDOCS 8401310104 | |
| Download: ML20079P159 (17) | |
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.2 '- 4 .a TECHNICAL EVALUATION OF PR BAEILISTIC RISK ASSESSMENT FOR TORNADO AND HURRICANE MISSILZ HA ARD TO THE CONTAINMENT ISOLATION VALVE COMPARTMENT EQUIPMENT SOUTH TEXAS PROJECT Emil Simiu y
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! INTRODUCTION v ! The objective of this evaluation is to assess the validity and conservatism of the approach, assumptions, and data used in the Bechtel South Texas Study E 14926-001 (August 198[ and November 1983)a to est.imate the probability of
-j tornado- and hurricane-borne missile damage to the containment isolation valve compartment (IVC) equipment. Also included in the evaluation is an assessment of the correctness of the results obtained in the study.
=o af The Bechtel South Texas Study consists of two distinct parts. The first part deals with tornado-borne missile hazards. The second part deals with hurricane-borne missile hazards. These parts are referred to in the following sections as the Tornado Study and the Hurricane Study, respectively.
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- 1. TORMADO STUDY
}l j 1.1 Assumptions Used in Tornado Study jj The following main assumption,s are used in the Tornado Study:
Mt "l 1. The distribution Ef the tornado occurrence rate, v, is consistent with ',: ! the National Weather Service record of tornado strikes for the site regions (r J! between 1953 and 1982 (Ref.1), and is modeled by a lognormal distribution.
- 2. The distribution of the path area, a, is consistent' with National Weather 1 4 Service data for tornado strikes in Texas between 1953 and 1982 (Ref.1),
and is modeled by a lognormal distribution.
- 3. The joint distribution of the tornado path area, a, and the Fujita scale, F, is consistent with the National Weather Service nationwide record of tornadoes between 1953 and 1982 (Ref.1), and is modeled by a continuous bivariate lognormal distribution.
- 4. The parameters CA/m (C = aerodynamic coefficient, A = area exposed to wind, and a = mass of missile), which characterize the behavior of the missile in flight in any given wind field and for any given initial conditions, have a single set of values corresponding to a conventional " standard missile"
. (Table D.4 of Tornado Study) . The values are based on the data on aerodynamic coefficients obtained from Ref. 2. l 5. The median surface density of potential missiles over the entire missile l- origin zone (~ 0.9 square mile) is about 1 missile /(65 ft x 65 f t) i (~6,600 missiles /sq. mile],basedonanElectricPowerResearchInstitute !2 (EPRI) survey of seven nuclear power plant sites (Ref. 3) . The surface i-
~i l' a/ The site region consists of the following countries: Matagorda, Brazoria, i, Fort Bend, Wharton, Jackson, and Calhoun.
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density has a lognormal distribution such that in 95 percent of the cases
! itislessthanabout1 missile /(40ftx40ft)[~17,000rissiles/sq.
mile] in the area that might affect the target. d
- 6. Fifty percent of the potential missiles have elevations uniformly distributed v
- between grade level and 20 ft above grade, while the remaining 50 percent are at grade level.
- 7. Ninety percent of the elevated missiles are restrained.
- 8. Sheltering by other structures and by the roof at top of the IVC is neglected.
- 9. A missile strike on any portion of the IVC top results in total failure, .:
i.e., no allowance is made for partial damage or for redundancy of components.
- 10. No allowance is made for the fact that safety related target areas are less
- than area of IVC top.
Additional assumptions, some of them tacit, are used in the Appendices to the Tornado Study. These assumptions are pointed out and commented upon subsequently in the evaluation. 1.2 Data Used in Tornado Study Data used in the Tornado Study include:
- 1. Number of tornadoes recorded in 1953-1982 in the site region defined in Section 1.1 herein. These data sre taken from Ref. 1.
- 2. Tornado path areas for tornadoes recorded in Texas in 1953-1982 (from Ref. 1).
- 3. Tornado path areas and Fujita scale classification for tornadoes recorded nationwide in 1953-1982 (from Ref. 1).
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l 4. Area and population density data for the six counties listed in item 1 of
' section 1.1, and U.S. population density data in each of the years 1950-a ,
1979.
- 5. Survey data on distributions of missiles by number and length (from 1
Ref. 3).
- 6. Aerodynamic data for various missiles listed in Table D.3 of Tornado Study (based in part on Ref. 2) .
1.3 Hathemacical Approaches Used in Tornado Study The fundamental approach to estimating the probability, P T, of damage due to tornado missile hits is the estimate the factors Po ad PH in the expression PT=Po a PH (I) where Po = probability per year that a tornado strikes the plant site, PH " Probability of hitting the target assuming that a tornado occurs at the site. In the Tornado Study an attempt is made to provide not only point estimates of PT , but confidence limits for those estimates as well. l 1.3.1 Probabilities of Tornado Occurrence at the Site. Pn. Probabilities of l ( occurrence at the site of a tornado with path area, a, are estimated as i Po(a) = 2@- (2) S l [ where v = annual frequency of a tornado occurrence in the geographical area S within which it may be assumed that tornado rates of occurrence are uniform. (In the Tornado Study, S = 10,000 sq. miles.) 4 i l-E.] <i i
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As mentioned in items 1 and 2 of Section 1.1 herein, it is assumed that the distributions of the annual occurrence rate, v, and of the tornado path area, a, are lognormal. These assumptions may be expected to provide conservative estimates as far as the 95-th percentile of the probability of damage are con-corned. It is this percentile that is used in the Tornado Study to assess the risk of damage to the IVC equipment (see Table III, p. 8 of the Tornado Study). For this reason it is tha reviewer's opinion that the results obtained in Appendix D of the Tornado Study concerning the modeling of v and a are acceptable for the, purposes of this preaabilistic risk assessment. It is noted that the estimated annual rate of tornado occurrence is adjusted upward to account for possible tornado underreporting due to low population density. This adjustment, which in the case of this project is a minor onea, is carried out in accordance with the procedure developed in Appendix B cf the Tornado Study. This procedure is based on the assumption that there is a
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statistical correlation between the number of tornadoes reported nationwide and the population density in the U.S.A. during each of the years 1950-1979. In the reviewer's opinion this procedure is reasonable. . 1.3.2 Probabilities of Hitting the Target Assuming that a Tornado Occurs at the Site. The probability'of hitting a target with area A given that a tornado l with intensity F on the Fujita scale occurs at the site is expressed in the Tornado Study as PH (F) = ap A n(F) $(z,F) (3) s af See Eq. D.36, p. D-12 of the Tornado Study. g
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where np = number of potential missiles per unit area (see item 5, Section 1.1 herein) A = area of target ri(F) = probability that a missile swept by a tornado with intensity F wi?.1 become airborne
$(z,F) = probability that a horizontal unit area with elevation z will be hit by a missile borne by a tornado with intensity F, givan that the density of missiles at the site swept by the ,
tornado is one per unit of horizontal area. 1.3.3 Probability of Injection n(F). Probabilities of injection are estimated in accordance with models and calculations presented in Appendix C of the Tornado Study. Inherent in these estimates are two assumptions, both of which are conservative. First, it is nssumed that the speed of the tornado, w, is constant throughout the tornado width. Second, it is asoumed that the random angle 8 between the drag force vector and the vertical is uniformly distributed between the values 0 = 0 and 0 = w. 'In reality, just prior to the take-off, the drag force vector and the wind velocity vector coincide, i.e., 0 = 0, so that in most cases this second assumption strongly overestimates the vertical component of the drag force at the take-off. For example, to the case 3 = w/2 there corresponds in the Tornado Study the assumption that the direction of the tornado wind speed, w, is vertical. In reality, there are strong reasons to believe that the vertical component of tornado wind speeds is always significantly less than w. The probability of injection depends upon the asaused values of the drag and lift restraint coefficients, Kg and K . LThere are few data on these values, 6 e k
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e which must therefore be assumed on the basis of judgment. The uniform distributions 0 < Kg < 5 and 1 < KL < 5 are used except as noted below. The corresponding injection probabilities are listed in Tables C-11 and C-13 and Tables D-17 and D-16 of the Tornado Study. For the restrained elevated mis-siles the lower limit of the drag restraint coefficient is Kg = 1, rather than KD = 0, and the corresponding injection probabilities are listed in Tables C-15 and D-18 of the Tornado Study. In the reviewer's opinion, the assumptions regarding the restraint coefficients used in the Tornado Study are reasonable. However, as mentioned in Section 3 of this review, these assumptions are difficult to evaluate owia3 to the lack of sufficient and clearly interpretable experimental data. 1.3.4 Height Distribution _of Airborne Missiles, $(z,F). The most elaborate
' part of the Tornado Study deals with the derivation of the function f(z,F).
The approach used to derive this function is now briefly described. First, it is postulated, as in the EPRI report NP-769 [3], that the movement of a tornado missile can be viewed as a Markov chain a . This postulate is justified, as in Ref. 3, by the assumption that the missile can be viewed as undergoing purely random tumbling, so that the aerodynamic force it will experience at any one point depends on the random position that the missile has at that point, rather than on the previous geometric attitudes of the missile. I l' a/ A Markov chain is a process in which the probability of transition from one point to another depends only on the coordinates of these points and on the state of the system at the initial point, i.e., the probability is independent of the previous history of the system. 1 7 l - i [.
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? In Ref. 2 tornado-borne miasiles were treated as six-degree-of-freedom systems, I'
I with i:umbling determined by mechanical relations, rather than occurring randomly. However, that model is not necessarily superior to the Markov chain representa-tion because it does not appear tc account for Magnus effects, random distur-bances due to turbulence inherent in the flow or induced by the missile, and random initial missile attitudes. An alternative model is one in which the missile is viewed as a esterial point subjected to drag, and the drag coeffi-cient is assumed to be uniform and equal to an average of the aerodynamic coefficients corresponding to all possible attitudes. This model is also funda-mentally unsatisfactory. In the absence of better practical choices, this reviewer is inclined to view the acceptance of the Markov chain model as a reasonable option. Once the Markov chain model for the missile motion is postulated, the second step is to define a probability density function, G(r o , oI , t o, r-r o, v-v o, t-to, F, y), such that - dP = Gdxdydz dv x dvy dvz (4) where x,y,z = coordinates in space, vx,vy ,vz = missile velocity components, and dP = probability that, given the occurrence of a tornado with intensity F and characteristics y, a missile that became airborne at movement to hits the volume dxdydz around point r during a unit time interval at moment t, with
- a velocity between 7 and v + dv (r - d + yj + zi; 7 = vxi + v yi + v Y, g where i,5,Y=unitorthogonalvectors). The function G is referred to as the ori-ginal (fundamental) Green's function of the problem. Modified Green's functions l 8 -q 3
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e* s , 1, . .. lf s can be derived by integrations and/or averaging of the original Green's functions. Modified functions correspond to (1) the probability that, given
- tha occurrence of a tornado vith intensity F and a set of characteristics y, the missile will hit the volume dxdydz around point li during a unit time inter-val at moment t with any velocity, (2) a similar probability for the case where the hit occurs over a unit area with orientation II, (3) a similar prohability averaged over all possible tornadoes having intensity F and area a.
By applying the Fokker-Planck equation to the func-tion G and intsgrating and aversging the results as done,to obtain the probabi-lities (2) and (3) above, the Tornado Study derives closed form relations for the function $(z,F), i.e., for the probability that the horizontal unit area with elevation z will be hit by missiles borne by tornadoes with intensity F , that sweep an area for which the surface density of potential missiles is 1 alssile/fc 2. The reviewer has verified the derivations leading to the expressions for $(z,F) and has concluded, to the best of his ability, that they are correct. He believes that the statistical mechanics approach on which these. expressions are based can provide useful insights into the question of tornado-borne missile damage, and acceptable order of magnitude estimates of probabilities of tornado-borne missile hits. h 1 1 1 t ,1
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- 2. HURRICANE STUDY The probability, PT, of damage due to hurricane-borne missile hits is written es i es
} PT = f f(w) PH (w) dw (5)
{ 0 where f(w) = probability density function of hurricane wind speeds, w, at the site, and Pg(w) = probability of one or more hurricane-borne missiles striking the top of any one of four IVC compartments, given the occurrence of a hurricane with speed w. The probability PH(w) is modeled in a manner identical to that uses in the Tornado Study. (Note that in the Tornado Study the dependence of the probability PH upon Fujita scale F is converted into a dependence upon wind speed w, since to each intensity on the Fujita scale there corresponds a range of speed w.) Calculated values of PH (w) for restrained and unrestrained missiles are listed t for various wind speeds w in Tables A1.a and A1.b of the Murricane Study'. The probability density function," f(w), is assumed to be consistent with the values of Tables I and B.2 of the Hurricane Study. l 2.1 Probability PH To the extent that the model of the probability PH is acceptable for tornado winds, it can also be considered acceptable for hurricanes, with the following qualification. The height distribution of airborne missiles, $(z,w) (discussed in Section 1.3.4 of this report) is dependent upon (1) th wind field within the storms being considered, and (2) the probability distribution of the direc-tions of translation of the storms. In the case of hurricanes, both these fac-tors differ from their tornado counterparts. In particular, hurricanes tend to
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is based assumes uniform directional distribution of those velocitier. Note, however, that $(z,w), as tabulated in Tables A1.a and A1.b of the Hurricane 4 Study, is of the order' of 0.20 or higher, and that, by definition, $(z,w) < 1. Therefore, accounting for differences between the respective wind fields and directions of translation could increase $(z,w) by a factor of the order of i at most five. (Note that $(z,w) could also decrease.) Since the estimated median value of the probability of damage to the IVC from hurricane-generated missiles is 1.2 x 10-10 per year (Table III of Hurricane Study), a function 4(z,w) estimated on the basis of assumptions different from those used in the Tornado Study would not alter in this case the conclusion that the risk of damage to the IVC is acceptable. However, this statement is correct only to , the extent that the assumption used in the Hurricane Study with respect to the probability density function of hurricane wind speeds is acceptable. This assumption is examined below. 2.2 Probability Distribution of Hurricane Wind Speeds The probability density function of the hurricane wind speeds used in the Hurricane Study is consistent with the values listed in Table I therein. Reference 5 lists parameters of the Weibull distributions that best fit hurricane wind speeds generated by Monte Carlo simulation in accordance with the procedure described in Ref. 4. Table 2.2.1 shows the values of these parameters for mileposts 300 and 350 (see Fig. A-1 of Hurricane Study) . 11 i
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. Milepost 300 350 y a i u a i J
-1,328.5 1,344.0 30 -435.9 453.9 11 Note: u and a correspond to speeds averaged over 1 minute and are expressed in knots.
Wind speeds corresponding to various probabilities of exceedence based on the parameters of Table 2.2.1 are shown in Table 2.2.2, which also includes the values estimated in the Hurricane Study. Table 2.2.2 Wind Speeds Corresponding to Vari 8us Probabilities of Exceedencea Table I,
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- Probability of Exceedence Hurricane Study Based on Ref. 5 Per Year (at Site) IIileoost 300 Milepost 350 5.4 x 10-3 112 105 105 6.1 x 10-4 134 124 124 2.9 x 10-5 157 144 145 6.0 x 10-7 179 161 154 a Wind speeds in aph averaged over 1 minute.
It is seen from Table 2.2.2 that the hurricane wind speed probabilities assumed in the Hurricane Study are comparable to those based on the Weibull parameters of Ref. 5. To the extent, then, that the estimates of hurricane wind speeds based on Ref. 4 (or, equivalently on Ref. 5) are acceptable, it follows from 12 e 4 1
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As in the case of tornadoes, estimates of extreme hurricane wind speeds corresponding to very small exceedence probabilities are uncertain. However, the reviewer feels that estimates based on Ref. 4 are comparable in terms of reliability to those obtained in the current state-of-the-art for tornado winds. O i i
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- 3. ASSESSMENT OF BECHTEL SOUTE TEXAS STUDYa -
SUMMARY
In this reviewer's opinion, the approach used in the Bechtel South Texas Study is physically and asthematically acceptable for engineering purposes. The assumptions used ther 2in appear to be conservative, although reservations are expressed concerning:
- 1. The feasibility of estimating tornado and hurricane wind probabilities corresponding to mean recurrence intervala of the order of tens of thou-sands of years or more from data recorded over 30 years or so. It is the reviewer's opinion that no literal meaning should be attached to such estimates as carried out by current methods, including the methods used in the Bectcel South Texas Study. However, thesa estimates have some validity in a relative sense, i.e., they are capable of providing compara-tive engineering assessments of hazards associated with strong winds. As such, the reviewer feels that the estimates obtained in the Bechtel South Texas Study are reasonable and acceptable given the present state-ol-the-art.
- 2. The surface density of the potential missiles is assumed to have a median of 1 missile /65 ft x 65 ft (or about 6,600 missiles /sq. mile). Although this assumption is consistent with data published in Ref. 3, it is possible that the actual surf ace density of potential missiles will be higher. In order to minimize this probability, the Regulatory Staff should, in the reviewer's opinion, be satisfied that structures located within, say, 200 m of the IVC are capable of withstanding the Design Basis Tornado without loss of integrity.
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3 3. The possibility that missiles lighter than those assumed in the Bechtel I ~J South Texas Study (e.g., two by fours) might be availabla, become airborne, rj
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.j 4. The possibility that the assumptions used in the Bechtel South Texas Study concerning the missile injection do not correspond sufficiently closely to i;
I the unknown physical reality. As indicated in Section 1.3.3, although they appear reasonable, these assumptions are difficult to evaluate owing to the lack of sufficient ant' clearly interpretable data. The reviewer believes that the numerical ra4ults based on these assumption 4 are credible (e.g., it appears credible that the median probability of injection of standard unrestrainet missiles in storms with maximum winds of less than 183 mph is zero - see Tab'.a A1.b of Hurricane Study). However, this is to some degree a subjective view. With the above' reservations, it is the reviewer's opinion that the conclusions of the Bechtel South Texas Study concerning the tornado and hurricane missile hazard to the IVC equipment are acceptable. 't.
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; REFERENCES U.S. Tornado Breakdown by Countrie_s 1953-1982, U.S. Department of Commerce, 1.
.h National Severe Storms Forecast Center, Federal Butiding, 601 E'. 12th Street, j Kansas City, Missouri 64106.
- 2. Redmann, G. M., et al., Wind Field and Trajectory Models for Tornado-4 Propelled Objects. EPRI 308, Technical Report 1, February 1976.
- 3. Twisdale, L. A. , et al. , Tornado Missile Risk Analysis, EPRI NP-768 and EPRI NP-769, May 1978.
- 4. Batts, M.E. et al., " Hurricane Wind Speeds in the United States," Journal of the Struct. Division, ASCE, October 1980, pp. 2001-2016.
- 5. Batts, M.E., "Probabilistic Description of Hurricane Wind Speeds," Journal of the Struct. Division, ASCE, July 1982, pp. 1643-1647.
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