ML20087K624
| ML20087K624 | |
| Person / Time | |
|---|---|
| Site: | Limerick  |
| Issue date: | 03/31/1984 |
| From: | Bitowf T, Parry G NUS CORP. |
| To: | |
| Shared Package | |
| ML20087K634 | List: |
| References | |
| NUS-4507, NUDOCS 8403260253 | |
| Download: ML20087K624 (134) | |
Text
/
NUS-4507 LIMERICK GENERATING STATION - ILTIMATE HEAT SINK EXTREME WIND HAZARD ANALYSIS Prepared for Philadelphia Electric Company by T. B. Bitowf G. W. Parry NUS CORPORATION O
i L. A. Twisdale W. A. Dunn M. B. Hardy R. A. Frank l
Applied Research Associates l
March 1984 I
Approved by:
E. R. ScTunidt, Director Systems Analysis Consulting Division NUS CORPORATION 910 Clopper Road Gaithersburg, Maryland 20878
.c nnarra%
L E
BACKGROUND
(
l Question 410.70 on the Limerick Generating Station Final Safety Analysis Report (1) asked Philadelphia Electric Company to " provide the basis for con-cluding that the design temperature for the ESW and RHRSW will not be ex-coeded, using only tornado and tornado missile protected structures, systems
-and components." In their response (PSAR Rev. 22, July 1983), Philadelphia Electric Company gave qualitative arguments for supporting their conclusion.
Subsequent to this submittal, Philadelphia Electric Company was requested by the NRC(2) to provide a probabilistic assessment to demonstrate "that the probability of exceeding 10 CFR Part 100 limits due to design basis tornado missile effects on the ultimate heat sink (UUS) shall be less than or equal per year or a mean value of 10-6 per i
to a median value of 10-7 In subsequent conversations (year, and 3,4) with the assuming loss of offsite power."
NRC, the following points of clarification were made:
1.
An analysis of the whole spectrum of tornados, not just the design basis, is required.
2.
Loss of offsita power need not be assumed if features of the plant would suggest that loss of offsite power and ultimate heat sink damage may not be concurrent.
3.
The terms " median value" and "mean value" are to be interpreted in-l the following sense: the " median value of 10-7 per year" is applic-
-able to a realistic analysis whereas the "mean value of 10-6 per 5
b year" is applicable to a conservative analysis.
At a meeting held with the NRC staff in Bethesda, Maryland on November 17, 1983, the question of damage to the ultimate heat sink as a result of the effects of high winds of nontornadic origin was raised as an extra consideration.
This report describes the methods used and the results of the analysis that was performed to estimate the frequency of exceeding 10 CFR 100 limits due to wind generated missile effects on the ultimate heat sink at the Limerick Generating Station. The overall method described results in a con-servative analysis and the target frequency of 10-6 per year is applicable.
The work was performed by NUS Corporation and their subcontractor, i
Applied Research Associates, Southeast Division of Raleigh, North Carolina.
References:
1.
Philadelphia Electric Company, Limerick Generating Station, Final Safety Analysis Report.
2.
Letter from A. Schwencer (NRC) to E. G. Bauer (PECo) dated August 8, 1983.
o o
.... _ _ ~ _.
5 3.
Telephone conversation between NRC, PECo, NUS September 16, 1983.
+
{.
4.
Presentation made by PECo to NRC at Phillips Building, Bethesda, Maryland on November 17, 1983.
i 4
j l
4 l
1 s
I
)
1 I
p 1
l 11
SUMMARY
v This report describes an analysis that was performed to estimate the frequency with which the design temperature of the ESW and RHRSW would be exceeded as a direct result of wind induced damage to unprotected parts of the heat sinks. Both straight winds and tornados are taken into account.
The conservative analysis that was performed using the computer code SORMIS-L, a modified version of the EPRI code TORMIS, results in estimates of 6.6 x 10-7 per year when only Unit 1 is operational, 7.9 x 10-7 per year when both units are operational. This yields an averaged plant lifetime value of 7.7 x 10-7 per year, which is less than the required value of 10-6 per yecr. It is therefore concluded that no changes to plant design are required to achieve acceptable protection for the Limerick Generating Station ultimate heat sink.
O iii
Table of Contents Page
Background
i lii Summary 1-1 1
Introduction 2
Definition of Plant Damage States 2-1 2.1 Introduction 2-1 2.2 The Plant Damage States 2-1 3
Windspeed Frequency Analysis 3-1 3.1 Introduction 3-1 3.2 Hurricane Winds 3-1 3.3 Extreme Straight Winds 3-3 3.4 Tornado Windspeed Frequencies 3-8 3.5 Combined Windspeed Exceedance Probabilities 3-13 3.6 Corabined Occurrence Rates for TORMIS Simulations 3-13 4
Use of TORMIS To Estimate Frequency of Damage 4-1 4.1 Introduction 4-1 4.2 Site Model 4-3 4.2.1 Missile Origin Zones 4-3 4.2.2 Structures 4-7 O
4.2.3 Targets 4-7 4.3 Missile Characterization 4-12 4.3.1 Missile Spectrum 4-12 4.3.2 Missile Population Distribution 4-12 4.3.3 Missile Injection Heights 4-17 4.4 Damage Criteria 4-19 4.4.1 Spray Network 4-24 4.4.2 Feeder Pipe 4-28 4.4.3 Cooling Tower 4-28 4.5 Summary 4-30
'5.
Results and Conclusions 5-1 5.1 Introduction 5-1 5.2 Frequencies of Events T and V 5-2 5.2.1 Event T 5-2 5.2.2 Event V 5-5 5.3 Additional Analysis of the TORMIS-L Results 5-5 5.3.1 Damage Frequency of Curb Wall 5-5 5.3.2 Missile Characteristics - Spray Networks 5-7 5.3.3 Missile Characteristics - Cooling Tower Fill Area 5-9 5.4 Sensitivity Analyses 5-9 5.4.1 Tornado Translational Speed 5-11 5.4.2 Number of Missiles 5-11 5.5 Conclusions 5-11 iv i
l
Table of Contents (continued)
Page Appendix A TORMIS Modifications To Produce TORMIS-L A-1 Appendix B TORSCR-L Postprocessor Documentation B-1 Appendix C Impact Response Analysis of Spray Arm C-1 4
t i
E f
R l
V
List of Tables Page 3-1 Annual Extreme Windspeed Data - Limerick Tower 1 3-6 3-2 Straight Windspeed Frequencies 3-7 3-3 Adjusted Occurrence Rates and Windspeed Intervals for TORRISK Windspeed Simulations 3-11 3-4 Combined Windspeed Exceedance Frequencies 3-14 3-5 Adjusted Occurrence Rates and Windspeed Intervals for TORMIS Windspeed Simulations 3-16 4-1 Limerick Station Zone and Target Envelope Coordinates 4-5 4-2 Zone Definitions 4-6 4-3 Structure and Target Description 4-9 4-4 Limerick Missile Subset Characteristics 4-13 4-5 Missile Distribution by Zone, All Missiles 4-14 4-6 Missile Distribution for Structure Origin, All Missiles 4-16 4-7 Limerick Missile Characterization 4-18 4-8 Injection Height Level Above Grade by Subset Number and Zone 4-20 4-9 Injection Height Intervals Above Structure Top by Subset and Structure 4-22 4-10 Spray Network and Feeder Pipe Sizes and Modeled Thicknesses 4-27 5-1 Base Case Frequenc} Estimates by Event and Network Damage Criteria 5-3 5-2 Base Case Varianced by Event and Network Damage Criteria 5-4 i
[h 5-3 Tower Curb Wall Damage Frequencies 5-6
\\s_sI 5-4 Effective Velocities of Missiles Entering Spray Networks 5-8 5-5 Effective Velocities of Missiles Entering Cooling Tower Fill Area 5-10 5-6 Sensitivity Analysis Frequency Estimates 5-12 O) rv vi
j'^N List of Figures Page 1-1 Spray Pond General Arrangement 1-3 3-1 Eurricane and Straight Windspeed Exceedance Probabilities 3-4 3-2 Large-Scale Tornado Regionalization, and 2-Degree Square Centered at the Limerick Site 3-9 3-3 Tornado and Combined Windspeed Exceedance Frequencies 3-12 3-4 Shifted F1 Occurrence Rate for TORMIS Simulations 3-17 4-1 Probabilistic Analysis of the Tornado Miscile Hazard 4-2 4-2 Tornado Missile Origin Zones 4-4 4-3 Plan View of Limerick Structures and Targets 4-8 4-4 Spray Pond Network Arrangement 4-25 4-5 Target Model of Networks and Failures Modes 4-26 I
l l
vii e-
-~e-gr w--
-e
=+----e e
m-+
+=------r--r----
v -
r----
u+-e-w+evewe-, - * - -rew~-~-re--T-v-~e--
r
i Chapter 1 INTRODUCTION This report describes a conservative analysis that was performed to dem-onstrate that the frequency of exceeding 10 CFR 100 limits due to wind gener-ated missile effects on the ultimate heat sink and wind induced damage to the cooling towers at the Limerick Generating Station is less t*2an or equal to 10-6 per year.
The role of the ultimate heat sink (UHS) at Limerick Generating Station (LGS) is to ensure that the temperature of the emergency service water (ESW) and residual heat removal service water (RHRSW) does not exceed the design temperature. Both the ESW and RHRSW systems are required to safely shut down the reactor in the event of a loss of offsite power or an accident. A pro-longed loss of the ESW and RHRSW functions could under these conditions lead to core melt and exceedance of 10 CFR 200 limits.
The ultimate heat sink at Limerick is a spray pond for which it has been demonstrated that under the most conservative design conditions there is a 10% margin in thermal performance (PEco, Section 9.2.6)
The spray pond is normally in the standby mode, and is designed to automatically supply water to the ESW and RHRSW systems when required.
The spray pond has four spray networks, each network having a 50% capa-O city for shutdown of two units. The layout of the spray networks is shown in k
Figure 1-1.
While all other parts of the ESW and RHRSW systems are protected
.by barriers from the effects of design basis tornado missiles the spray pond networks themselves and the feeder pipec feeding those networks are not, and are hence vulnerable to damage.
Loss of the spray pond networks as a heat sink for the ESW and RHRSW systems does not, however, lead to unavailability of those systems since the pond itself and the cooling towers can be used as heat sinks as a result of operator actions using protected equipment powered from safeguard buses.
These realignments of the systems can be initiated from the control room and all the necessary valves and pipework are protected from design basis tornado missiles. The cooling towers themselves, however, are not designed to with-stand the wind velocities experienced in severe tornadoes and are hence vulner-able to wind damage as well as missile damage.
In this study, a tornado is assumed to have the potential for damaging only those heat sink features not physically protected against tornado effects; namely the spray pond networks 1md feeder pipes, and the cooling towers.
.It is possible that offsite power would be lost as a result of a tornado strike at the plant. Because of the assumptions made in this analysis, however, the conclusions are independent of whether offsite power is available or not. No credit is taken for using the spray pond itself or any other heat dissipation
~
mechanism.
O l-1 1
ew,r---*-mw-mmu-w+-v-,wrv.------,y m
/~'\\
The first step in the analysis was to decide what is the minimum require-
. ment in terms of the number of operable spray pond spray networks and/or cool-ing towers to provide sufficient cooling for the RHRSW and ESW systems to c
-safely shut down the plant. These minimum requirements were then used to define unacceptable plant damage states, i.e., those damage states which, if uncorrected could lead to core melt through eventual unavailability of the t>
h RHRSW and ESW systems. This is described in Chapter 2 where two damage states are identified; one is appropriate while Unit 1 is operational and Unit 2 is being completed, the second is appropriate when both units are operating.
' The second stage in-the analysis is to estimate the frequency of the plant damage states. The basic tool for this part of the analysis was the
. computer code TORMIS-L, a modified version of the EPRI code TORMIS (Twisdale et al., 1981). The modifications to the code are documented in Appendix A.
This code estimates the frequencies of missile strikes on or missile damage (according to some predefined damage criterion) to specified targets. The inputs to the code include a model of the plant which describes the struc-I tures, the targets, the missile population, and the damage criteria adopted, as well as the tornado characteristics in the geographical region of interest.
The frequency of exceedance of various levels of windspeed is crucial to the determination of the frequency of the damage states and is discussed separately in Chapter 3.
The application of TORMIS-L to this problem is discussed in Chapter 4.
This chapter describes the site model and the damage criteria used for the targets. Appendix C contains backup calculations for one of the damage criteria used for the spray networks.
(]j
/'
While the code TORMIS estimates frequencies of strikes or damage to individual targets, it does not estimate the frequencies of strikes or damage to complex combinations of targets. This was performed for this analysis l
using a computer' code TORSCR,~which is described in detail in Appendix B to this report. The results of the analysis and the estimates of the frequencies i.
of the damage states are discussed in Section 5 where the conclusions of the 1
study are given.
l l
l I
l l
i ii~
1-2
..--~m..~....
-,._,,..~..,m-_
--,._,.-.,m
.,.--_w
,____, - -,_.. - -._~-. _,., _.,,-... -,.. -
II
?
- t kj E
- .5 e5 v
- 3 i.
I 35E g,i m.,
l w s i<
s n
N
'N'
/.
l
/*
le i-+ ti s
rI.'
.I l l ;l
(
i l.1 i
l l -t
.Ll-lll I lI r i ;,.i i 7 _ _, M N i
l: 1 F-l !
i 2
il T N I l -! ' I t. :
I 1 i i
!J l ll
\\
N N\\
l ri t n Q
y t
r--i,
ll
.-\\
E l
ii j l j l - i
\\
' I i i Il 1
{
i lI Ii
! j l i[ m -- 5
\\
E m
[
l11-1IIII
' \\
s e l l-I i l ll g
9 i L1 l l1 it 11 g
A%7'. E} -
[
~
>="Z~- 'j k
~ '
,;ir
,i-,
- d l
G
[ e!Iiii
=
iiii ig
,a
[
l LJ i
t l iii! si
~
i I l l l lt
' 6-2 i l{
- 'J t I !
I I
{[
4 i :.
c ti i.
i I !;
3 4
Ii l ! lil
\\
~5 d
li
...a g
3
. }
7..,7-2--
g c
- ! A ' -t 7 A t f3 ti 5
E
.,.s h I f ' ! J, t - ! - i t;
,y or.
k
!'! [ f I!!'
f.
os,1
.,&e s
f
\\
""'" "' 2'
'N_.
.. K\\k o
s 1-3
Chapter 2 f--
DEFINITION OF PLANT DAMAGE STATES
2.1 INTRODUCTION
The purpose of this chapter of the report is to define those plant dam-age states which could lead to loss of function of the heat sink for the ESW and RERSW systems. The plant damage states are defined in terms of those portions of the ESW and RHRSW systems which are not designed to withstand the effects of design basis tornados and design basis tornado missiles; namely the spray pond networks, the feeder pipes to those networks, and the cooling towers. The question of what constitutes damage to each of these targets is deferred to Chapter 4 of this report. The purpose of this section is to define those combinations of targets for which the code TORSCR will estimate the frequency. Thus a plant damage state of interest is an identification of a specific combination of spray pond networks, feeder pipes and cooling towers such that damage to each of the elements conctitutes a failure to cool ESW and RHRSW. Since there is a period when only Unit 1 will be operational and the requirements for a heat sink will be different for this period, the damage states are defined for both time periods; Unit 1 only operational, and both units operational.
2.2 THE PLANT DAMAGE STATES v
The spray pond is designed such that any one of the four networks can be used in conjunction with any train of ESW and RHRSW. Thus with one spray network adequate for shutdown of one unit, the minimum success criteria for operability of the spray pond are any two spray networks operating when both units are operational, and one spray network operating when only Unit 1 is operational.
The cooling towers can also be used as an alternative heat sink with one cooling tower being sufficient to remove heat from both units (PEco,1984).
Thus, the cooling towers are included in the minimum success criteria for successful heat removal. When only Unit 1 is operational one spray network or the Unit 1 cooling tower functional is success. When both units are operational two spray networks or one cooling tower functional is success.
Thus the damage states of interest are:
Damage state V: At least three out of four spray networks and both cool-ing towers are damaged. This is failure to provide a heat sink for the ESWS and RHRSWS when both units are operational.
Damage state T: All four spray networks and the Unit I cooling tower is damaged. This is failure to provide a heat sink for the ESWS and RHRSWS when only Unit 3 is operational.
O
\\ -)
~
2-1
These two plant damage states, T and V, define the combinations of dam-O aged targets that are used as the basi.s for the probabilistic calculations
\\
performed using TORMIS-L and 70RSCR. The criteria that are used to decide whether a target is damaged or not are discussed in detail in Section 4.4.
However, it is important to point out at this stage that a spray network is regarded as inoperable if either the network itself is damaged, or its feeder pipe is damaged. The damage criteria are applied conservatively so that there are assumed to be no partial failures.
O)
O 2-2
Chapter 3 O
WINDSPEED FREQUENCY ANALYSIS 4
3.1 INTRODUCTION
r The Limerick Generating Station is located in southeastern Pennsylvania at latitude 40.230N and longitude 75.580W. The site is located in gently rolling countryside with hill elevations of about 300 to 400 feet MSL.
In the immediate vicinity of the plant, the terrain is wooded or open country-i side with no significant topographic features. The plant structures are located on the east side of the Schuylkill River with grade elevation of about 217 feet MSL. About 5 to 6 miles west of the site, the terrain reaches an elevation of about 800 to 900 feet MSL, near French Creek State Park.
The extreme. wind climatology at Limerick is affected by thunderstorm and tornado activity, extratropical cyclones, and tropical cyclones. Hence, Limerick falls into a mixed wind climate for purposes of estimating the fre-quency of severe winds. There do not appear to be any local topographical features that would lead to significant topographic speedups or orographic-winds at the site.
The methods that are relevant to the prediction of the frequency and severity of extreme winds depend on the specific wind-producing meteorological phenomena. Regions that experience several of these wind sources are termed mixed wind climates and the analysis of extreme winds must take into account O,.
each type of storm system. In mixed wind climates, the most accurate wind-speed frequency estimates are obtair.cd from separate analyses of each storm type. For example, an extreme value statistical analysis is frequently applied to annual windspeed data (representing extensive extratropical cyclones) (Gomes et al.,1978), whereas indirect techniques (such as probabilistic simulation) have been used to predict tornado (Twisdale, 1982, Twisdale and Dunn, 1983) and hurricane (Batts et al.,1980; Twisdale et al.,1983) wind frequencies.
This section summarizes the results of analyses of extreme winds for the Limerick Generating Station. The purpose of these analyses was to determine the windspeeds at which nontornadic winds influence the severe wind frequen-cies at Limerick. It will be seen that the non-tornadic winds have no con-tribution to the frequency of the damage states defined in Chapter 2.
The scope of these windspeed analyses was limited to simple calculations based principally on published data with extrapolations to the site. In the following subsections, the extreme wind hazards from hurricane, straight winds, and tornadoes are estimated. The crossover speeds of these wind hazard curves are estimated and a combined windspeed curve is developed. This curve then provides a basis to determine occurrence rates for use in the windborne missile analysis of the spray pond networks and cooling towers.
I i
x 3-1 L
3.2 HURRICANE WINDS The Limerick site is approximately 90 miles from the Atlantic Ocean.
Hence, the intensity of tropical storms whose paths could affect the site would be significantly reduced over the peak winds that are typically exper-ienced at initial landfall. For example, measurements at Lake Okeechobee (Myers, 1954) during hurricanes of August 1949 and October 1950 and at Brookhaven National Laboratory during the hurricane of September 1938 (Myers et al., 1956) indicate significant windspeed reductions for onshore and rough terrain surface categories. For hilly terrain, such as Limerick, Schwerdt et al. (1979) suggest a frictional factor of 0.45 to reduce 10-m, 10-min over-water speeds to 10-m, 10-min overland speeds. In general, hurricanes that landfall the mid-Atlantic coast tend to fill rather rapidly and become extratropical storms during overland passage.
A simple evaluation of hurricane risks for Limerick has been made from published data. The work of Batts et al. (1980) is used in conjunction with that of Schwerdt et al. (1979). The Batts study estimates hurricane wind-speed frequencies for the Gulf and East coasts of the United States, based on data taken primarily from Ho et al. (1975) and Cry (1965). The computational procedure is the same basic computer program previously developed by Russell (1971). Schwerdt et al. update much of the information in Ho et al. and pro-vide methods for estimating Standard Project Hurricanes (SPH) and Probable Maximum Hurricanes (PMH).
The most severe hurricane threat to Limerick is estimated to correspond
(
to landfall positions in the vicinity of the Chesapeake and Delaware Bays.
Landfall in the Chesapeake Bay area, although over 175 miles from the site,
[s- -)
l could provide a storm heading in which the site is offset to the right of the l
j track centerline and, hence, on the strong side of the storm. Filling and friction effects, as a result of the 175 miles track to the site, would be i
expected to reduce significantly the peak winds experienced at Limerick. For storms that landfall farther south, such as on the North Carolina coast, the filling and friction effects would be expected to be even more significant.
A Delaware Bay hurricane landfall is also a potential threat to Limerick.
Such a landfall position is closer to the site, but it is also more likely that the site would be offset to the left of the storm centerline track (due to the typical recurvature of tropical storms in the northern latitudes).
These critical hurricane landfall positions correspond to mileposts 2300 -
2400 in Batts et al. (1980). For these milepcsts, the Batts results give the following 10-m fastest mile windspeeds at the coast for the 50, 100, and 2000 year return period hurricanes:
85, 95, and about 128 mph.
p
(__)
3-2
4 These windspeed are extrapolated to the site using the procedure sug-
= gested in NNS 23 ~ (Schwerdt et al.,1979).* First, the fastest mile wind-speeds are converted to 10-min speeds for open terrain. From Simiu et al.
(1978), one obtains 10-min speeds of 70, 79, and 102 mph. Batts used a 0.85 factor to convert 10-min speeds from overwater to overland; hence these over-land speeds convert to 10-min overwater speeds of 82, 92, and 120 mph. These i
10-min overwater speeds can be converted to 10-min site speeds using the fric-tion factors in NHS 23.
The Limerick site falls into the rough terrain cate-gory in NWS 23.
The friction coefficient for rough terrain in NWS 23 is 0.45 and is fully operative once winds have blown over 10 nmi of rough terrain.
Hence, since Limerick is about 78 nmi from the coast and is within rough ter-rain for 10 nai, the above overwater windspeeds reduce to site 10-min wiAd-speeds of 37, 41, and 54 mph, respectively.
The effects of filling once the hurricane moves inland is computed using Myers et al. (1956) by accounting for the time after landfall until the peak winds occur at the site. Application of the NWS 23 criteria results in fill-ing reduction factors of about 0.95.
Hence, one obtains 10-m 10-min wind-l speeds at Limerick of 35, 39, and 51 mph, respectively. These are adjusted.
to 2-sec gust 10-m windspeeds in rough terrain using data in Sachs (1978).
Gust windspeeds are used for ease of comparison to tornado winds, which are associated with damage-producing gusts averaged over several seconds. The final site adjusted hurricane gust windspeeds using a gust factor of 2.0 are 70, 78, and 102 mph, corresponding to exceedance frequencies of 0.02, 0.01, i
and 0.0005.
The windspeed frequency curve through these points is shown in Fig-cre 3-1(a). Without a detailed site-specific analysis, this curve provides an approximate estimate of hurricane wind frequencies for Limerick.
s.
3.3 EXTREME STRAIGHT WINDS i
Fully developed pressure systems occur frequently enough and over a suf-l ficiently large scals to be well represented by data collected at fixed ane-moneter stations. Hence, given sufficient annual extreme windspeed data at a
~
location, one can estimate from a Gumbel (extreme value) analysis the wind-speed probabilities of " straight" winds. It is generally accepted that a 20
- The inland adjustment from the Batts paper is not felt to be reasonable for the mileposts of interest. For example, from the available plots the winds are as strong or stronger 200 km inland than they are for open terrain l
at the coast. This is clearly unreasonable for the hilly terrain and wind trajectory approaches to Limerick and also illustrates sone of the difficul-
-ties in applying generic studies, such as Batts, to important sites. The use of Batts results is felt to be reasonably conservative for the coast, for example, see Tryggvason (1981) and Twisdale et al. (1983).
s 3-3
),y
,(
- ~
_E
- T_-
7 _.-
T__
l 0
i 0
n 4
sd l n n
n k
iwt 0
s c
)
,n s
i 3 p 0
e t
u s
h m
h g i
m
,iL ig l
(
c a e i
r s
i s
t s
d S 2 e
0 e e l
0 l
i p
l m
l 2
i
)
l s
j i
d I
i vn s
i e
l a0 l
0 w i
i i
t ll l
i h (1 i
h ib 5
i t
l l
lp l
1 l
et l
g l
r i
n a
i l
ia b
l do uI{\\
l t
l la p
\\*
i r
k g
o i
irhi
\\g
.\\,
i 0
p r
j PA g
S i
g
=
k*[,*
i 0 l
.W $g.(*/
s I
b ce 1
)
r l
\\
e e
(
l
\\
g.
w l
d n
lg\\
a o
.I a
i P
T l
ee k
l g) ic ).
i cx n.
i id m
i e
m re l
e0 a
m0 i
d i
R(3 iL (1 e
0 e
5 p
i s
d i
T.
_3 -. -
=-.- - -
_:- ~ -
n I
2 3
4 5
6 7
8 i
w 0
0 0
0 0
0 0
0 t
)i/
1 1
1 h
1 1
1 1
1 g
r,(s_
- T-E-
ia T_
r
=-
~_-
t f
l t
s 0
3 i
4 n
0 d
3 t
ln a
i a
k n
c e
i s s i
0 n
e t
r s
e n
0 a
u m
i 3
c a
iL ic g
n
)
r l
h ir r
c i
p r
e u s e
m u
(
H i
0 s
j i
0 d l
i e
i l
2 i
l e
1 j
i p
i l
vs j
i d
3
[
i 0 n l
5 i e
1 I
w l
e 1
r l
i u
l l
e g
1 5
l n
i a
F l
i c
l l
ir l
i 0
r 0 u L
,-il il i
H l
l 1
l l
i
)
l a
l i
(
l l
i l
l l
i i
05 i
i 1-
_=_ ^ _
~
_~, -
ET-
,3-I 2
3 4
5 6
7 8
0 0
0 0
0 0
0 0
~\\)v l
- l >_.8g.s
- o y5Sn[
1 1
1 1
1 1
1 1
(\\
$* A > m y,
to 30 year record of annual extremes provides an adequate data base for esti-O mating Sng return periods of severe winds. Recent research has suggested
\\
that shorter records may also provide reasonable estimates of extreme wind s-frequency.
Windspeed data exist for the Limerick site for the years 1972 through 1981 (cf. Castelli 1983)..These 10 years of data from Lixerick Tower 1 are in the form of annual hourly extremes at 30 feet above grade. These speeds are summarized in Table 3-1.
It is noted that when the 30-feet data were missing, windspeeds measured at the 175-or 270-feet levels were adjusted down using the power law formula with the exponent dependent on turbulence class (Castelli,1983). These windspeeds have been converted to peak 2-sec gusts for rough terrain (peak gust factor = 2.22 (Sachs,1978) and the location (9) and scale (7) parameters of the Gumbel Type I distribution estimated.
For a Type I Distribution the probability of exceeding velocity V* is given f
by
~
(
V*-9 )
P(v 3 V*) = 1 - exp
- exp 3-1 7
Table 3-2 smamarizes the estimated probabilities of exceedance for gust wind-speed from 60 to 120 mph for the Limerick tower data.
In view of the limited 10-year history of Limerick extremes and the une l
of a constant peak gust factor (which tends to minimize the variance of the extreme gusts), additional comparisons have been made to published data from
'}
surrounding NWS stations. Reading and Philadelphia, Pennsylvania, are the closest stations. The Reading data correspond to a 30-m city exposure and L
the Philadelphia data include both 30-m city and 10-m airport exposures. The Philadelphia city extremes are slightly less than these estimated for Reading.
The Reading and Philadelphia Airport extreme wind frequencies taken from Changery (1982) have been converted to 2-sec gusts and are plotted in Fig-j ure 3-1(b). The Philadelphia Airport frequencies are higher than both Reading and the Limerick site estimates, reflecting the more open exposure at the j'
Airport.
Based on the plots in Figure 3-1(b), the frequency of strong 10-m winds at Limerick is less than that at Philadelphia Airport, which is about 35 miles SE of the plant' The rolling countryside and wooded terrain tend to influence i
the boundary layer profile of the surface winds at Limerick. However, in i
view of the limited 10 year record and without an analysis of the. turbulence
(
and gust characteristics at the site, which introduce uncertainties in the conversion from hourly averages to peak gusts, it seems appropriate to slant the Limerick frequencies toward those of the Philadelphia Airport. For con-venience, the Reading 30-m curve is thus used as a convenient measure of 10-m straight winds at Limerick. This curve is thus felt to be a reasonabley con-servative estimate of the straight wind frequency at the Limerick Station.
l O
3-5 l
_. _. _ _ - - ~. - _ _ _ _ _ _ _. _. _ _ _ _., _. _.. _, _ _ _.. _ _ _ _ _. _
= -.._
t i
Table 3-1.
Annual extreme windspeed data - Limerick Tower 1 i --
Extreme Year hourly average 2-sec gust (mph)
(mph) 1972 30 67 1973 27 60 1974 28 62 l
1975 30 67 1976 32 71 1977 32 71 1978 27 60 1979 29 64 1980 25 56 1981 25 56 Sample p = 63.3 4 = 60.7 statistics a = 5.67 7 = 4.42 i-i e
a h
3-6 Y
,... _,, - _... ~,...... _. -..,. _.. _...., _,. - _. _ _ -.., _ _ _. _ _ _, _.. _.,.
_ _ _..., _ _. _, _ _.,. ~.. _
Table 3-2.
Straight windspeed frequencies Philadelphiab 2-sec gust Limerick tower la Reading, PAb Airport l
windspeed (30 feet)
(30 m)
(10 m) 60 6.9 x 10-1 70 1.2 x 10-1 1.0 x 10-1 80 1.3 x 10-2 2.0 x 10-2 5.0 x 10-2 90 1.3 x 10-3 3.0 x 10-3 1.0 x 10-2 100 1.4 x 10-4 1.0 x 10-3 2.5 x 10-3 110 1.5 x 10-5 1.0 x 10-4 5.0 x 10-4 120 1.5 x 10-6 1.0 x 10-5 6.0 x 10-5 aDeveloped from basic data from Castelli (1983).
4 l
bDeveloped from Changery (1982).
i s
\\
I n
3-7
,wp.-
m-t-y-,-.9 w,-
- ,--e-w-e,www.,,--,---we,w wir
,-em..
wws w
m-m.-=.m-www
-ww.ev3===--w---=e-
3.4 TO3NADO WINDSPEED FREQUENCIES Limerick is located in tornado Region I according to WASH-1300 (Markee s
et al.,1973) and Region C according to Twisdale and Dunn (1981) and Twisdale (1982) (Figure 3-2).
In this study, the Region C data coupled with the orig-inal F-scale tornado windspeeds as proposed by Fujita (1971) were used. A site-specific tornado hazard study was not performed; however, tornado data from the National Severe Storms Forecast Center (NSSPC) 1950-1982 data base
'was obtained, and simple statistical tests performed to test the appropriate-ness of the Region C data.
1 The data from the National Severe Storms Forecast Center showed that a total of 133 tornadoes occurred within this 2-degree square of approximately 15,600 mi2 during the 1950-1982 period. The data yield a mean occurrence rate of about 2.58 x 10-4 tornadoes per mi2 per year. The unadjusted Region C occurrence rate (less this 2-degree subregion) is 2.39 x 10-4 tornadoes per mi2 per year, computed using the equation y = n/t.A and the parameter values given below:
~2-Degree (Region L)
Region C-L nn = 133 tornadoes nc-L = 5,260 (5362- (nL-31))
- tn = 33 yr (1950-1982) t -L = 29 yr (1950-1978)
C 2
AL = 15,620 mi A -L = 759,949 (775,569-A )
C L
n = 0.000258 "C-L = 0.000239 u
Hence, the site 2-degree occurrence rate is about 9 percent higher than the mean Region C occurrence rate.
I
\\
l To determine whether these mean occurrence rates are significantly dif-ferent, the following test was performed. For rare events like tornadoes, the number of tornadoes for a given region and time period can be accurately modeled by a Poisson distribution, P( A) where A = vt (see Twisdale and Dunn, 1981; Wen and Chu,1973). For A > 9, P ( A) --+ N ( A, A) (Hald,1952; Feller,- 1968).
This approximation can be used with tornado data from the 2-degree square to determine whether Limerick's tornado occurrence rates are significantly dif-ferent from the rest of Region C, i.e., Region C-L.
The hypothesis to be L = A -L or alternately H ': A -AC-L = 0.
From the above i
tested is then: HotA C
o L
L = 133 and A -L = 123, which is the number of occurrence rates, one obtains A C
l tornadoep expected in a 2-degree square from Region C-L, over 33 yearc. Fron
' the random variable, A -AC-L ~ N(133-123,133+123), construct the test statistic l-L (A -AC-L)/V256 ~ N(0,1), which equals 0.625.
From this value, and standard L
normal tables, one notes that P( l(A -AC-L)/16l >.625) = 0.53, which is L
greater than significance levels commonly used in significance tests.-
Therefore, one cannot reject Ho' and must conclude there is no significant difference between the tornado occurrence rates for Region L and Region C-L.
- Thirty-one tornados occurred in Region L in the 4-year period j
(1978-1982).
O 3-8
5 O
O O
4 d
l l
D I
I l
er p
/
i c4 i
l x timerick l
D
..:i
- .'l::::
h Station
- q4.':
Generating f:5 0
....,.g
!!!bi!!
f E
A __
~
k l
y f:,.
.i I
l l
i l
~_
i Area i
Region (upni.)
l j
A 625.628 I
i B
365.180 C
775,560 I
i D
1,205.117 Large-scale tornado regionalization, and 2-degree square centered at the Limerick site.
Figure 3-2.
i i
l 2
4 Since these means do not test to be significantly different, the O)
~ Region C occurrence rates are used in the tornado windspeed analysis. As kd developed in Twisdale and Dunn (1981) and Twisdale (1982), the updated occur-i rence rates reflect adjustments for reporting efficiency over time, direct classification errors, and unreported events due to random encounter errors.
The updated occurrence rate is 4.4 x 10-4 tornadoes per mi2 per year, as sum-l marized in Table 3-3.
The path length, width, and direction distributions for Region C are also used in the analysis (cf. Twisdale and Dunn,1981).
Since tornado path direction is potentially important in the tornado missile analysis for damage to both the spray pond and cooling towers, path direction was also analyzed. No significant differences were found between the 2-degree
]
and Region C data (Pa = 0.3) and hence the Region C data is used.
In absence of a more detailed tornado site characterization, the use of mean Region C data is judged to provide a reasonable characterization of the tornado variables for Limerick.
Tornado windspeed frequencies were estimated for Limerick using the i
TORRISK methodology developed in Twisdale and Dunn (1983). The TORRISK methodology performs tornado windspeed calculations in a Monte Carlo simula-tion procedure that treats model uncertainties and uses a stochastic model of tornado occurrence, a 3-dimensional tornado windfield model, and distributions of tornado intensities, path lengths, widths, and directions.
The results of the TORRISK analysis for Limerick using the mean Region C l
data are plotted in Figure 3-3 (a). The target area consists of an' envelope enclosing the spray pond networks and cooling towers. This target envelope is consistent with the tornado missile target data presented in Chapter 4.
O.
The windspeed exceedance probabilities correspond to windspeeds at 33 feet above grade. The three curves shown in Figure 3-3(a) correspond to three separate tornado-structure windspeed exceedance criteria (cf. Twisdale and Dunn, 1981, 1983). The union criterion corresponds to windspeed exceedance for at least one point of the target envelope. The point criterion corresponds to the probability that a single point experiences windspeeds V* and hence neglects the size of the target.- For the Limerick spray pond-cooling tower I
target area, this criterion leads to probabilities that are unconservative by an order of magnitude for severe tornado winds. This conclusion has also beer noted in Twisdale and Dunn (1983) for large target areas. The intersec-tion criterion requires that every point within the target area experience windspeeds v*.
The union.windspeed exceedance criterion is the appropriate curve to use for tornado missile analysis (Twisdale and Dunn 1983). Hence, from this analy-sis, the probabilities of tornado strike' on the spray pond-cooling tower area with any part of this area experiencing windspeeds that exceed 100,-150, 200, and 250 mph are 5 x 10-4, 2 x 10-4, 4 x 10-5, and 5 x 10-6 per year, respec-tively. Consistent with the procedure for classifying and rating tornadoes, these windspeeds correspond to damage-producing gusts averaged over a few seconds.
3-10 i-t 4
e,.-
,-..w.,
.-.-r,__,.-.--,,,.m.-,---,,e.,
vm _,
,--.,-,.,._-_,,-.,m,,,
.,,-.m,-.,,,-.,--,,m--,-,r-,,ym-,,,wc-
Table 3-3.
Adjusted occurrence rates and windspeed intervals for TORRISK windspeed simulations F-scaled Tornado Occurrence ratea windspeed intensity (per mi2 per yr)
(mph)
F0 1.3 x 10-4 40-73 F1 1.3 x 10-4 73-112 F2 1.1 x 10-4 112-157 F3 4.7 x 10-5 157-206 F4 1.4 x 10-5 206-260
~2F5 2.5 x 10-6 260-318
-All 4.4 x 10-4 40-318 aUpdated Region C occurrence rates (from Table 4 of Twisdale and Dunn,1981).
b riginally proposed F-scale windspeeds (Fujita, 0
1971).
O 1
I
~
O 3-11
3(>%
- s
- ^ _ -
__2.
_j
- d-
_:i,_
_E
~
s 1
d.
0 t
inf 0
w3 m
k 3
i 4
i d
m c
etna a
0 re 0
m ibs n
3
)
s a
h mt i
iL ou l
p i
m CG n
(
a s
s 0
d I
l 0
e l
l 2
e i
p s
I l
\\
h d
I' s
n 0 *v 5
iw d
n I
e I
1 id d
s n
s s
l t
n ie e
I bn
$, U.'
l i
c miw "g.
o g5 l
b n
a m
e l
s 0
C o
u Adr a
1 0
C q
I
\\
+,.A, 3 e
\\
I f
e
)
r l
+l*
I
(
e b
i I
a c
e a
n n
o I t a
d i
d
' h ir n
l e
c gs a
d e
li a
r r
n u
o i
H T
a c
r x
tSw 0
e 5
=5
~
_E EF-
_3 r m
d e
e 2-
- E.
p I
2 3
4 5
6 7
0 s
d 0
0 0
0 0
0 0
0 in 1
1 1
1 1
1 1
1 w
de O/"
in b
m t\\
l c
_5
~.
_E E4-
- l.
_ 2_
o 0
s t
df i
0 d
n i3 u
4 n
k w3 l
a c
n o
ot ir a
i 0
d e
d m
as
- 1el n
3 n
i 0
a mt o
g,l i
h rn iL ou in
- I.
l m
T s
a
)
i p
o TG U
,\\
c
(
g
\\*
n 0
s i
0 d
3 I
e
\\
d l
2 e
I i
p 3
\\
lj d
I s
\\
li 0*
i u
n e
I
-(g i 5 v w I
.)
r
\\
i l
1
\\
l o
ig
\\
i I
\\
l d
F g
i t
g s
a I
n i
)\\g l
rn io I
e 0
o P
i 0
T j
l
(
i NN 1
l
)
i
\\
a a
N n
i o
i i
t l
c se e
I e
i r
i t
i n
I 05 Eh- -
._i r _ _
e i
_i
. _ ~. -
- _~
j ~ -
I 2
3 4
5 6
7 8
~
0 0
0 0
0 0
o 0
t 1
1 1
1 1
1 1
l J
.> A,r
'T, l3 s o >gj8'
{\\
w's i'
iq
)
lj
' i.
i l
.. _ _. _ ~ _
3.5 COMBINED WINDSPEED EXCEEDANCE PROBABILITIES The combined probabilities of extreme windspeed exceedance events are determined as the union of independent events. Hence, the combind probabil-ity P(v 2 V*) of hurricanes (vh), straight winds (v ), and tornadoes (vt) is s
given by
(
~
P(v g V*) = P (vh ) v*) y (vs 2 V*) U (vt 2 v*)
3-2a which, for small probabilities, can be accurately approximated by P(v 2 V*) ce P(vh & V*) + P(vs 1 V*) + P (vt g V*).
3-2b Using Equation 3-2b, the combined windspeed probabilities can be computed from Figures 3-1 and 3-3 (a). Table 3-4 sununarizes the windspeed frequencies and Figure 3-3(b) illustrates the combined windspeed curve.
. From this analysis, straight winds dominate the windspeed frequencies for V* 6 90 mph. Hurricanes and straight winds are equally dominant for 90 < V* $ 105 mph. For V* > 105 mph, tornado winds dominate the severe wind risk at Limerick. The relatively low value of these crossover speeds for tornado winds reflects the conservative F-scale windspeeds used in this study, the large target area, and the union definition of tornado strike. It i
is noted that tornado windspeed dominance in the 100 to 160 mph range is expected for most sites in the eastern United States.
3.6-COMBINED OCCURRENCE RATES FOR 70RMIS SIMULATIONS The combined windspeed curve in Figure 3-3(b) provides the basis to determine occurrence rates for the TORMIS windborne missile analysis of the t
spray pond networks and cooling towers. As noted, the tornado crossover windspeed is about 105 mph. Hence, missiles produced by winds < 105 mph are more likely to be caused by hurricane or straight winds than by tornadoes.
Since the spray pond network include relatively fragile nozzles and spray arm components, missiles produced by winds < 105 mph cannot be determined a_
priori to be unimportant.
l The approach used herein to treat nontornadic winds is to adjust the tornado F-scale occurrence rates according to the combined windspeed curve in Figure 3-3(b). This approach is clearly an approximation since tornado wind-i_
fields have steep w ndspeed gradients across the path width when compared to i
j hurricanes or straight winds, which have gradual gradients over much larger areas. However, it will be seen later that the results of this study are insensitive to these approximations.
i 3
O G
t 3-13 3
l p
L ha.'
s n
i.wc._.
v m,w 4y_..c.,
..-.,._.,,-,y+
,_y
,._m.w
.,,.,,m...,.,,,,y,pe,m,9.gw,.,g,,,.e._,.,
,,.y,,,my
,,qc,,,,.wwmy..my9, e,, m,, w y m 9p-
i Table 3-4.
Combined windspeed exceedance frequencies 1
Windspeed Frequency of exceedance (yr-1)
V*
Hurricane Straight Tornado Combined (2-sec gusts) winds winds winds winds 70 2 x 10-2 1 x 10-1 7 x 10-4 1 x 10-1 6
80 1 x 10-2 2 x 10-2 6 x 10-4 3 x 10-2 90 3 x 10-3 5 x 10-3 5 x 10-4 9 x 10-3 1
100 1 x 10-3 1 x 10-3 4 x 10-4 2 x 10-3 110 1 x 10-4 8 x 10-5 3 x 10-4 5 x 10-4 120 1 x 10-5 7 x 10-6 3 x 10-4 3 x 10-4 2 x 10-4 2 x 10-4 150 4 x 10-5 4 x 1c-5 200 5 x 10-6 5 x 10-6 250 2 x 10-7 2 x 10-7 300 t
4 0
l 1
O 3-14
The normal TOMIS occurrence rates for Region C are given in Table 3-5
[
as well as the occurrence rates modified as described below.* The To MIS occur-rence rates result in essentially the same tornado strike probabilities as predicted by the TORRISK code. This is verified in Figure 3-4, which shows the ToaMIS estimated wind frequencies cenerated from 40 tornado strike simula-tions for each F-scale. From this figure, one notes that the TOMIS windspeed frequencies for F2 through F5 closely match the combined windspeed frequency curve. However, for the F1 windspeed interval (73-112 mph), hurricane and straight winds dominate the combined wind curve. To reflect the dominance of nontornadic winds over the F1 windspeed interval, the Region C TORMIS occur-rence rate has been increased by a factor of 143 to yield a 1.0 x 10-1 per l
year occurrence rate for winds > 73 aph. This factor of 143 results in an increase of the F1 TO MIS occurrence rate from 1.1 x 10-4 to 1.6 x 10-2 per mi2 per year. The combined wind occurrence rates that were used in the 10RMIS simulations for this analysis are given in Table 3-5.
It is stressed once again that the windspeeds corresponding to each F-scale are those originally proposed by Fujita (1975). These F-scale windspeeds have been argued (Twisdale i
et al.,1978) to be conservative.
- These occurrence rates are based on the same data as those in Table 3-3, but they have been adjusted to reflect path length intensity variation adjust-ment. As descibed in Twisdale and Dunn (1983), these occurrence rates are called " local-state" occurrence rates since they reflect tornado path length intensity variation in a total probability equation calculation. This develop-ment of local-state occurrence rates in TORMIS was done to increase the simula-O~
tion efficiency of the code. The occurrence rates in Table 3-3 are used in j.
W TORRISK, which performs within the code the adjt.stment for path length inten-sity variation.
t 1
l 4
h t
t O
3-15 1
Table 3-5.
Adjusted occurrence rates and windspeed intervals for 1DietIS windspeed simulations Region C Combined winds F-scale Tornado occurrence rate occurrence rato windspeed intensity (per mi2 per yr)
(per mi2 per yr)
(mph) 4 F0 2.5 x 10-4 al.0 x 10-1 40-73 F1 1.1 x 10-4 al.6 x 10-2 73 112 F2 6.1 x 10-5 6.1 x 10-5 112-157 F3 1.9 x 10-5 1,9 x 10-5 157-206 F4 3.4 x 10-6 3.4 x 10-6 206-260 2FS 3.7 x 10-7 3.7 x 10-7 260-318 All 4.4 x 10-4 1.2 x 10-1 40-318 i
aReflect nontornadic winds per Figure 3-4.
l O G
3-16
O 10-I
- i 6 i i l 'I I616 i t;i t i t i t s iptityi Limerick Shi ted 8
TORMIS Windspeed Frequencies i
i 10-2 i
e
=
l 8
i l
1 I
10-3 O
8 F2
~.
F1 < >
-- qh i
Al F1 Windsoeeds is" F3 4
~
1 i
4 b
e F4 3
q t
\\j 5 10-5 3
5 o
F5 3
=
4 g
10- 6 l:
l 10-7
_3 E
, l,l,l,li
,li ],l,l,,lililili
,,i,l,,i, i iii j iiii l
10-8 50 100 150 200 300 400 v
(
Combined Windspeeds (mph) l Figure 3-4.
Shifted FI occurrence rate for TORMIS simulations.
I 3-17
Chapter 4 13E OF TORMIS TC ESTIMATE FPEQUENCY OF DAMAGE
4.1 INTRODUCTION
The TORMIS ceae has been developed to estimate the frequency of tornado missile related events for application in nuclear power plant risk studies.
Figure 4-1, taken from Twisdale et al. (1981), indicates the various steps 1
i' associated with the analysis. The estimates are developed by a Monte Carlo simulation process, sampling from the population of possible tornados and from the missile spectrum. The tornado characteristics used in this study 2-were discussed in Chapter 3.
It is also necessary to input a site-specific missile characterization, and site-specific damage criteria. The damage cri-teria include an identification of the targets and a specification of what is regarded as damage. Section 4.2 describes in general terms the site model that identifies the missile origin zones, the structures that were included in the model (either because they were sources of missiles or had a signifi-cant shielding effect), and the locatica of the targets. The choice of targets was discussed in Chapter 2.
In Section 4.3, the missile characteri-sation adopted is described in terms of the spectrum of possible missiles, i
7 l.
their distribution among the missile origin zones, and their injection heights. The site model and characterization of the missiles were fixed on r
i the basis of a site survey performed by personnel from NUS, Applied Research Associates and the Philadelphia Electric Company on January 17, 1984. For i
the purposes of the TORMIS modeling, the site was regarded as being at a con-stant elevation which was chosen to be that of the water level in the spray i
pond. The details of how the targets were modeled and what the damage cri-teria are, are given in Section 4.4.
A special version of the TORMIS code, TORMIS-L, was prepared for this study. The modifications that were made to the EPRI version of the code are described in Appendix A.
The modifications are not fundamental modifica-tions, but were performed principally to accommodate the more complex scoring a
scheme necessary because of the multiplicity of targets defining the plant damage states. Since TORMIS cannot handle scoring the union of more than two events (where an event corresponds to missile damage to a target) and, as described in Chapter 2, it is necessary to score on the union of at least
' five events to estimate the frequency of the identified damage states, it was l
found convenient to process the results of TORMIS using a postprocessor code TORSCR. Thus, the output portion of the TORMIS code was modified to write the output onto a tape for input to TORSCR. In addition, since direct wind damage to the cooling towers is at least as important as missile damage, a
'new scoring scheme was included in the code to indicate damage when the wind velocity at the cooling towers exceeded a specified value.
l t
l 4-1 l
l.
Figure 4-1 Probabilistic Analysis of the Tornado Missile Hazard Tomado Tomado Windfield g
3,-------.
Mel h
Missile
_.-_ _ Missile Spectrum Charactenzation a
injectum Missile
. _.__ __ Trajectory Methodology Transport Analysis Plant Modeling impact Damage Criteria Analysis
- ----- and Modeling y--------------------------
Probability. __ __ ___ _ _ _
Risk
_ _ ___ _. Simulation Modeling Asses Tst Methodology l
O 4-2 l
t' ~
~-..-.-..__._,~+-~~e-.-
. = -.
4.2 SITE HODEL I
4.2.1 Missile origin Zones 1
In developing the site model, the emphasis was to realistically depict the relative positions of the structures, targets, and potential missiles.
.In the code TORMIS, the potential missiles are grouped into several missile origin zones. Consistent with the TORMIS methodology for specifying the site and missile origin zones, an inertial, Cartesian reference system was estab-lished under. the convantion that the y-axis is parallel to plant north and the x-axis points toward plant east. The plant site, extending out approxi-mately 2000 ft from the spray pond area, was divided into 19 missile origin zones, as defined in Figures 4-2 and in Tables 4-1 and 4-2.
Four modeling parameters were used as guidelines in identifying distinct i
missile zoness o Missile density o Distance from the primary target (i.e., spray pond) o General elevations o Relative fistribution of missile types The simulation technique employed in TORMIS assumes that potential missiles from a given zone are evenly distributed in the zone. Thus, in order to obtain 3
i a realistic simulation of the tornado missile hazard, it is necessary to define the site model, and thereby each missile zone to be, as near as possible,
' uniform with respect to the four identified parameters, b)
(
The site model is appropriate for the site as it existed at the time (i.e., January 1984) when the site survey was conducted. Fixing the missile locations as that which existed at this time does not account for any " clear-i i
ing" of missiles (i.e., reduction in the missile density) which, although it cannot be precisely defined, will occur as the site approaches full oper a-
-tion.
Neither does it account for any shifting of the potential missile loca-tions. However, it should be noted that a large number of potential missiles are currently concentrated about the. spray pond and any shift from the site layout.is expected to reduce the number of missiles in this area. Therefore l
the current model is conservative with respect to the risk of damage to the spray pond from missiles.
Generally speaking, the missile origin zones, as with the site, can' be l
characterized as follows. The first two layers of missile zones about the spray pond represent half of all identified zones. This concentration of zones within an area of about 500 ft of the pond is made because, based on previous work, a particularly important parameter in relation to missiles hitting a target is the relative distance of a missile from the target, with l
increasing distance relating inversely to significance. Thus, to ensure i
accuracy in the model, the zones are fashioned in " layers" of increasing size and distance from the pond, with 200 ft from the target representing the first, 500 ft representing the second,1000 ft representing the third layer, and 2000 ft representing the final layer (missiles originating at distances 4-3
O Y(f t.) b 1
2 3
2000 2
8 4
in 1000 j
7 17 18 20 21 11 39 6
\\ 30 12 33 16 33 8
'8 1 FNNNNi
[
0 lono MYY%
4000 5000 x(ft!)
(
23 l
17 / 18 ig 3
7 24 27 15 23 22 12 j
3 9
19
-1000 13 15 14 36 l
4
-2000 S
8 7
6 Legeni 1-Coordinate number 1-Zone number Figure 4-2.
Tornado missile origin zones.
O 4-4
a Table 4-1.
Limerick Station zone and target envelope coordinates Coordinate X
Y Coordinate X
Y number (ft)
(ft) number (ft)
(ft) l (a) zone coordinates 1
0 2100 21 3300 600 2
1100 2100 22 3300
-675 3
4800 2100 23 3100
-675 4
4 4800 1100 24 1650
-350 5
4800
-2100 25 1650
-675 6
3800
-2100 26 1450
-393 7
1100
-2100 27 1900
-350 8
0
~2100 28 1900
-200 9
1100 1100 29 1900 200 4
10 3800 1100 30 1900 400 1
11 3800 600 31 2900 400 12 3800
-675 32 3100 400 13 3800
-1200 33 2900 200 14 1650
-1200 34 2900
-200 l
15 1100
-1200 35 2900
-350 16 1100 100 36 3300
-1200 17 1450 600 37 2600
-350 18 1650 600 38 2800
-200 19 3100
-350 39 1100 600 1
20 3100 600 a
l t
O 4-5
i Table 4-2.
Zone definitions 4
l l
Coordinate Coordinate Zone numbers Zone numbers 1
1 7 1 11 18-30-27-24-18 2
2 4 2 12 18-20-32-30-18 3
10 5-6-10 13 20-21-22-23-20 i
4 15 6-7-15 14 31-32-19-35-31 5
16-25-14-15-16 15 24-19-23-25-24 i
i 6
39-17-26-16-39 16 30-31-33-29-30 l
7 9-10-11 9 17 28-38-37-27-28 8
21-11-12-22-21 18 38-34-35-37-38 l-9 25-22-36-14-25 19 22-12-13-36-22 10 17-18-25-26-17 1
i 4
i.
f i
I f'
i 1
' O l
4-6 l
l i
L
~ ~.
.~
i greater than 2000 ft from the target have generally been shown to have a very low probability of hitting the target (Twisdale and Dunn,1981).
l 4.2.2 Structures j
The structures modeled were those structures which have a significant bearing on missile injection (height or location) and/or on shielding the spray pond. The structures modeled explicitly do not include those struc-tures that are expected to be destroyed by a tornado (e.g., storage sheds);
these were treated instead as potential missile sources. Figure 4-3 identi-fies all structures modeled. The discussion here only addresses the non-target structures.
The first two structures modeled were the cooling towers (15 and 16) which, when exposed to high winds, may fall and become a concentrated source of potential missiles. The cooling towers also represent a distinct type of missile (i.e., concrete fragments) which, at low elevations, present little hazard, but at higher elevations (up to' 485 ft) represent a potential hazard.
The next structure modeled is the power block (17), which represents the i
reactor and turbine enclosures. This structure, while it is far from the spray pond (1700 ft) and is on a zone that has a general elevation of about
[
35 feet below the water level in the spray pond, represents a potential hazard because the buildings rise well above the reference elevation (the spray pond water level), and thus provide a favorable downward trajectory for missiles located on the roofs of the enclosures. The spray pond pump house (18) repre-O sents a structure that serves as both a nearby source of missiles and as a barrier against low-flying missiles. The last two structures modeled represent a concentrated source of missiles which is relatively close to the pond (19),
and a mound of earth (20) which is best modeled as a structure, respectively.
The position and dimensions of these structures are given in Table 4-3.
l 4.2.3 Targets b
As discussed in Chapter 1, the portions of the plant that are treated as targets are those portions of the ESWS and RHRSWS not designed to withstand design basis tornados--namely the spray pond networks (1, 2, 3, 4) and their feeder pipes (5, 6, 7, 8), together with the cooling towers (9 through 16).
The general location of these targets is indicated on Figure 4-3.
Targets 1 through 4 are the spray nozzle networks which are modeled as i
boxes which extend 4 feet in each horizontal direction and 3 feet in the ver-tical direction about the volume totally enclosing the networks to account for the potential of offset impacts (Twisdale et al.,1978).
Targets 5 through 8 are the 30" schedule 20 feeder pipes that connect to spray networks 1 through 4, respectively. The WX diuension has been increased by a factor of ten, to present a larger target area to potential missiles as a means to improve the efficiency of the simulation, and then 4 feet was added O
4-7
-. -. - -. - --...~..- - -. -. -... - -..-.-.... -. -
O LEGEND Number Targets N
1-4
- Soray Nozzle Networks Feeder Pipes 5-8 9 Tower Distribution Flumes 11 Tower Curb Walls 1000 13 Tower Fill Areas 15 Tower Shells 17
- Power Block 18
- Soray Pond Pumphouse 19
- Warehouse 20
- Hill 500 20 19 1
I 0
1 2
3 4
O 0
1500 3000 X(f t.)
.\\.
.\\.
5 6
7 8
18
-500 -
9 10
~ ' ~
11
{
15 I
I I 16 l l<
12
-1000 14 13) t
-1500 17
-2000 O
Figure 4-3.
Plan view of Limerick structures and targets.
4-8
_ _ _, ~.. _ _ _ _. _ _ _ _. _ _ _ _ _ _, _ _ _ _ _. _,.
(-
Th f%,
V V
U Table 4-3.
Structure and target description Target Surface Thickness (in)
Reference Point (ftl, Dimensions (ft)
Theta Strength No.
Type Description X
Y Z
WX KY WZ (red.)
No, Ma t'l Min Increment (pel) 1 1
Spray nozzle network 1 1992
-105 0
166 218 10 0
1 1
0.258 0.040 35,000 2
1 0.258 0.040 35,000 3
1 0.258 0.040 35,000 4
1 0.258 0.040 35,000 5
1 0.258 0.040 35,000 6
1 0.258 0.040 35,000 2
1 Spray nozzle network 2 2209
-105 0
166 218 10 0
1 1
0.258 0.040 35,000 2
1 0.258 0.040 35,000 3
1 0.258 0.040 35,000 4
1 0.258 0.040 35,000 5
1 0.258 0.040 35,000 6
1 0.258 0.040 35,000 3
1 Spray nozzla network 3 2425
-105 0
166 218 10 0
1 1
0.258 0.040 35,003 2
1 0.258 0.040 35,000 3
1 0.258 0.040 35,000 4
1 0.258 0.040 35,000 5
1 0.25e 0.040 35,000 j'
6 1
0.258
- 0. 04 0 35,000 up 4
1 Spray nozzle network 4 2642
-105 0
166 218 10 0
1 1
0.258 0.040 35,000 2
1 0.258 0.040 35,000 3
1 0.258 0.040 35,000 4
1 0.250 0.040 35,000 5
1 0.258
- 0. 040 35,000 6
1 0.258 0.040 35,000 5
1 Feeder pipe 1 2059
-200 0
33 95 6
0 1
1 0.354 0.032 30,000 2
1 0.354 0.032 30,000 3
1 0.354 0.032 30,000 4
1 0.354 0.032 30,000 5
1 0.354 0.032 30,000 6
1 0.354 0.032 30,000 6
1 Feeder pipe 2 2276
-200 0
33 95 6
0 1
1 0.354 0.032 30,000 2
1 0.354 0.032 30,000 3
1 0.354 0.032 30,000 4
1 0.354 0.032 30,000 5
1 0.354 0.032 30,000 6
1 0.354 0.032 30,000 k.
[
T b.
wJ (a)
(w) '
Table 4-3.
Structure and target descalption (continued)
Target Surface Thickness (in)
Reference Point (ft)
Dimensions (ft)
Theta Strength No.
Type Description X
Y E
WX WY W3 (rad.)
No.
Mat'l Min Increment (pel) 7 1
Feeder pipe 1 2494
-200 0
33' 95 6
0 1
1 0.354 0.032 30,000 2
1 0.354 0.032 30,000 3
1 0.354 0.012 30,000 4
1 0.354 0.032 30,000 5
1 0.354 0.032 30,000 6
1 0.354 0.032 30,000 8
1 Feeder pipe 2 2709
-200 0
33 95 6
0 1
1 0.354 0.032 30,000 2
1 0.354 0.032 30,000 3
1 0.354 0.032 30,000 4
1 0.354 0.032 30,000 5
1 0.354 0.032 30,000 6
1 0.354.
0.032 30,000 9
4 Cooling tower 1 2275
-950 69 250 0
6 0
1 0
3 2
6,000 distribution flume 2
0 4.5 2
6,000 3
-1 0
0 0
10 4
Cooling tower 2 3000
-950 69 250 0
6 0
1 0
3 2
6,000 O
distribution fiume 2
0 4.5 2
6,000 3
-1 0
0 0
11 4
Tower 1 curb wall 2275
-950 0
250 0
15 0
1 0
10 2
3,000 2
0 10 2
3,000 3
-1 0
0 0
12 4
Tower 2 curb wall 3000
-950 0
250 0
15 0
1 0
10 2
3,000 2
0 10 2
3,000 3
-1 0
0 0
13 4
Tower 1 fill area 2275
-950 15.5 250 0
53 0
1 0
3 2
6,000 2
0 3
2 6,000 3
-1 0
0 0
14 4
Tower 2 fill area 3000
-950 15.5 250 0
53 0
1 0
3 2
6,000 2
0 3
2 6,000 3
-1 0
0 0
I
-l A
N O.,
J Table 4-3.
Structure and target description (continued)
Target surface Thickness (!n)
~
Reference Point (ft)
Dimensions (ft)
Theta Strength No.
Type Description X
Y E
WX WY WE (red.)
No.
Mat'l Nin Increment (ps!)
15 4
Tower 1 shell 2275
-950 75.5 185 0
20.5 0
1 0
12 2
4,000 2
0 12 2
4,000 3
-1 0
0 0
16 4
Tower 2 shell 3000
-950 75.5 195 0
20.5 0
1 0
12 2
4,000 2
0 12 2
4,000 3
-1 0
0 0
17 1
Power block 2250
-1975 0
750 325 160 0
1 0
24 2
4,000 2
1 24 2
4,000 3
1 24 2
4,000 4
1 24 2
4,000 5
1 24 2
4,000 6
1 24 0
0 18 i
Spray pont pumphouse 2325
-245 0
150 45 27 0
1 0
24 2
4,000 I
2 1
24 2
4,0>3 i
[
3 1
24 2
4,000 4
1 24 2
4,000 5
1 24 2
4,000 6
1 24 0
0 19 2
Warehouse 1650 50 0
500 200 9
0.733 1
0 24 2
4,000 2
1 24 2
4,000 3
1 24 2
- ~ 23 4
1 24 2
4,000 5
1 24 2
4,000 6
1 24 0
0 20 2
Hill 1475 225 0
550 172 39 0.733 1
0 24 2
4,000 2
0 24 2
4,000 3
0 24 2
4,000 4
0 24 2
4,000 5
0 24 2
4,000 6
-1 0
0 3
to each side. To account for this increased target size, the TORMIS hit prob-
-s abilities are subsequently reduced in the postprocessor analysis.
Targets 9 through 6 are the Unit 1 and 2 cooling towers. Each tower is modeled using four targets representing the curb wall about the cooling tower basin, the distribution flume, the fill area and shell. Each of these targets is a right circular cylinder and the tower is modeled by stacking these one on the other.
The positions and dimensions of the targets as modeled in TORMIS are given in Table 4-3, which also gives other information which is necessary input to TORMIS. For the cylindrical targets, WX is the radius and WZ the height.
4.3 MISSILE CHARACTERIZATION 4.3.1 Missile Spectrum The missile spectrue used as a basis for characterizing the various types of missiles that exist at the site consists of the 22 missile sets described in Table 4-4.
These missiles are a subset of the basic missile spectrum developed by Twisdale et al. (1978), which consists of 26 aerodynamic sets composed of various prismatic shapes and three material types. It is noted that each of the seven NRC missiles (USNRC,1975) are included as special cases in this miscile spectrum by proper specification of the depth dimension,
[)
d, the weight per unit length, w, and the minimum missile cross-sectional N,/
area, Amin (except that the 4-inch by 12-inch wood beam is modeled as 3-inch by 12-inch).
4.3.2 Missile Population Distribution The missile populations for each zone and each missile type (Table 4-4) were estimated by performing a site-specific survey and studying aerial photo-graphs of the site. The results are given in Tables 4-5 and 4-6.
A total of 118,973 potential missiles were specified in the 19 zones, and a total of 3232 missiles were assumed to originate from the top of structures or from the failure of structures. In constructing these tables, the missile popula-tion survey data for the site were subdivided into unrestrained (N') and restrained (N") missile types; in the actual analysis, the total missile population per zone was conservatively treated as unrestrained missiles.
This practice, although routine, is an added measure of conservatism in the analysis.
l l
V 4-12 I
- ~
C)g Table 4-4.
Limerick missile subset characteristics Weight Final per unit mitaile Description Depth length Amin Length / depth subset (typical) d (in.)
(lb/ft)
(in.2)
Minimum Maximum 1
Rebar 1.00 2.67 0.79 36.0 36.0 2
Gas cyliner 10.02 33.64 9.45 4.0 10.0 3
Drum, tank 19.98 23.55 311.60 2.3 6.0 4a Utility pole 13.50 32.06 143.10 31.1 31.1 5
Cable reel 42.21 140.70 126.60 0.5 0.6 6a 3" pipe 3.50 7.58 2.20 34.3 34.3 7a 6" pipe 6.63 18.90 5.60 27.2 27.2 8a 12" pipe 12.75 49.60 14.60 14.1 14.1 9
Storage bin 38.40 112.50 40.50 1.0 11.4 10 Concrete frag.
88.00 1950.00 1936.00 1.0 3.0 11 Wood beam 12.00 9.50 48.00 12.0 12.0 12 Wood plank 12.00 3.30 12.00 8.0 12.0 13 Metal siding 48.00 25.00 24.00 2.0 4.0 14 Plywood sheet 48.00 15.02 50.74 2.0 2.0 15 Wide flange 11.29 27.87 8.16 8.0 60.0 16 Channel section 5.11 11.88 3.49 9.0 80.0 17 Concrete panel 84.0 380.00 378.00 5.0 5.0 18 Small eqpt.
46.48 44.02 4.63 1.2 13.3 0
19 l
Large eqpt.
67.07 88.67 15.70 0.3 18.8 20 Steel frame, f
grating 43.31 12.37 2.22 1.0 7.5 21 Large st. frame 97.41 47.23 11.00 1.0 5.0 22 Vehicle 66.00 250.00 2574.00 2.9 2.9 aDenotes membership in NRC standard spectrum of missiles.
l i
l l
l l
l l
l
("'y l
'\\--)
l 4-13
(
~
O O
O Table 4-5.
Missile distribution by zone, all missiles Final Missile origin zone l
missile subset Description 1
2 3
4 5
6 7
8 9
10 1
Rebar 0
300 560 2,430 110 965 1,600 100 550 1,300 2
Gas cyliner 0
0 0
0 10 0
70 0
10 40 3
Drum 0
0 0
0 10 0
230 0
20 150 4
Utility pole 1,320 2,500 3,200 810 50 145 90 0
50 30 5
Cable reel 0
0 0
0 0
0 250 0
10 0
4 j
6 3" pipe 0
200 320 1,830 100 1,165 260 150 150 300 7
6" pipe 0
220 520 1,330 0
1,165 3,250 0
10 350 8
12" pipe 0
220 520 1,330 0
1,165 1,920 0
0 400 9
Storage bin 0
0 0
0 10 0
590 3
6 275 j
10 Concrete 0
0 0
0 0
0 0
0 50 0
11 Wood beam 1,375 2,500 2,250 200 1,800 75 1,796 700 310 690 12 Wood plank 1,375 2,500 2,250 200 1,122 75 155 800 1,195 70 13 Metal siding 0
250 650 2,200 300 840 1,937 74 253 833 14 Plywood sheet 0
1,500 1,300 140 1,122 30 144 400 895 420 a,
d.
15 Wide flange 0
0 0
0 0
0 2,535 0
50 1,320 16 Channel section 0
220 520-1,830 244 1,165 2,964 412 437 627 17 Concrete panel 0
0 0
0 0
0 0
0 0
0 l
18 Small eqpt.
0 0
0 0
50 0
1,140 100 20 10 l
19 Large eqpt.
0 0
0 0
10 0
25 0
15 42 20 Grating 0
0 0
0 10 0
2,490 100 500 550 21 Large frame 0
0 0
0 10 0
156 10 3
27 22 Vehicle 0
70 510 470 15 0
399 850 26 20 Totals 4,070 10,480 12,600 12,770 4,973 6,796 22,001 3,699 4,560 7,454 i
.i i
i
)
i
J O
O O
, Table 4-5.
Missile distribution by zone,all missiles (continued) 4-a.
Final Missile origin zone i
missile subset Description 11 12 13 14 15 16 17 18 19 Totals I
1 Rebar 0
0 0
0 2,200 0
300 0
750 11,165 2-Gas cylinder 0
20 0
0 600 10 20 0
0 780 3
Drum 10 0-0 0
200 10 5
0 20 655 i
4 Utility pole 10 10 40 15 12 0
0 6
0 8,288 5
Cable reel 0
0 0
10 0
7 20 0
20 317 1
6 3" pipe 20
.8 0
20 700 0
550 50 4,000 9,823 7
6* pipe 4
50 0
25 250.
100 26 0
20 7,320 8
12" pipe 20 50
_0 20 30 55 0
0 350 6,080 i
9 Storage bin 0
0 0
0-520 3
210 0
8 1,625 j
10 Concrete 0
0 0
0 150 0
0 0
0 200 11 Wood beam 100 292 20 10 2,100 200 146 200 422 15,186 12 Wood plank 70 42 0
0 1,520 30 336 0
581 12,321 l
13 Metal siding 40 12 0
0 526 60 2
0 844 8,821 l
a-14 Plywood sheet 50 47-0 0
790 25 39 0
217 7,119 j
b 15 Wide flange 620 100 0
0 800 0
150 0
250 5,825 16 Channel section 370 156 0
0 1,580 0
183 0
1,008 11,716 17 Concrete panel 0
0 0
0 0
0 0
0 0
0 18 Small eqpt.
45 8
100 25 1,050 10 20 24 25 2,627 19 Large eqpt.
9 0
0 0
40 74 2
0 6
223
[
20 Grating 602 8
0 0
190 0
10 0
340 4,800 j
21 Large frame 2
50 0
0 25 0
0 0
10 293 l
22 Vehicle 4
150 250 200 300 65 4
300 150 3,789 I
Totals 1,976 1,003 410 325 13,583 649 2,023 580 9,021 118,973 I
i I
i e
P t
Table 4-6.
Missile distribution for structure origin, all missiles i
Structure 17 18 19 15 16 Final Spray missile Power pond Cooling Cooling subset Description block pumphouse Warehouse tower 1 tower 2 Totals i
1 Rebat 2
Gas cylinder 10 10 3
Drum 7
7 4
Utility pole 5
5 5
Cable reel 1,200 1,200 4
1 6
3" pipe 50 10 60 7
6" pipe 50 10 60
{
8 12" pipe 50 50 9
Storage bin 40 40 10 Concrete frag.
344 344 688 11 Wood beam 8
100 108 12 Wood plank 40 40 f
13 Metal siding 275 275 14 Plywood sheet 15 Wide flange 16 Channel section 300 300 17 Concrete panel 160 160 320 i
13 Small eqpt.
4 40 44 19 Large eqpt.
11 11 2G Grating 1
30 31 l
21 Large frame 1
1 22 Vehicle 2
2 f
Totals 725 33 1,486 504 504 3,252 r
l l
i-O
~
4-16 i
ll,_..._
-~ - -. -
The failure of structures which are not designed to withstand the forces j
of tornadic winds was included in the assessment of the potential missiles by
\\
estimating the numbers and the characteristics of missiles that could be injected into the wind field on the collapse of a structure. Table 4-7 shows I
the conversion table used for the structures surveyed at the site to estimate the numbers and types of potential missiles.
Missiles produced from failure of the cooling towers were characterized by two different types of missile. First from each tower 344 potential mis-siles were. assumed to be generated from break up of the cooling tower shell.
These fragments had a cross section of 2 feet 10 inches by 7 feet 4 inches with lengths varying uniformly from 7 feet 6 inches to 22 feet. These frag-ments represent about one tenth of the volume of concrete of the tower shell.
Secondly, it was assumed that, from each tower 160 concrete panels with dimensions 4 inches by 84 inches by 35 feet were potential missiles originating from the canopy inside the distribution flu.ne area.
L 4.3.3 Missile Injection Heights A distinction can be made between potential missiles stored without sig-nificant physical constraints, which are thus relatively free to respond to the wind forces of a passing tornado, and those stored such that release to the wind field requires that some significant restraints be cvercome, such as i
a structural failure. The first population, designated N' and called mini-mally restrained missiles, includes those objects whose motions can be O
assumed to be dependent upon the individual aerodynamic response of each object and whose injection motion is not substantially blocked by other obstacles. For this population, the objective of the injection methodology is to provide missile release conditions to the tornado that are conservative and also account for the inherent prediction uncertainties in the complex l
injection process. The second population, denoted N" and called significant-ly restrained missiles, basically includes all those potential missiles whose responses to the tornado would depend significantly on the response of adja-
. cent objects, in addition to their own aerodynamic characteristics. Addi-
'l tional restraint forces must be overcome prior to the motion of these objects and subsequent restraints may impede. transport. The injection methodology for this class accounts for the magnitude and the sequential nature of these restraining effects.
Twisdale et'al. (1981) describe an injection model for minimally re-strained missiles that was designed to release potential missiles to the wind field at a time that would be expected to lead to maximum missile transport.
This " optimum transport" injection model leads to conservative estimates of
- hit and damage probabilities. While an option exists in TORMIS for modeling the restrained missiles, in this study the potential missile population is conservatively cimulated using the optimum transport injection model, i.e.,
all the characterized missiles are treated as members of the N' population.
O 4-17 i.-~
Table 4-7.
Limerick missile characterization Assumed number of unrestrained missiles from structure failure 1.
Metal siding structures:
i 5 channel 10 metal siding per 1000 ft2 per flcer 1
2.
Trailer:
20 beams 10 planks 10 plywood sheets 10 channel 3.
Wood structures:
)
30 plywood sheets 20 beams per 1000 ft2 per floor 20 planks 5 channels 4.
Plastic wall, metal frame structures:
10 channel 5 planks per 1000 ft2 per floor 5 plywood sheets 5.
Brick / stone house:
20 plywood sheets 20 beams 20 planks per 1000 ft2 per floor 5 small eqpt.
5 frame / grating 5 3" pipe i,
k O
4-18 i.
.. _ _ _ - _ _.., _ _ _ _ _.. _ _ _ _ _. ~.. _. _.
i t
In TORMIS, the heights at which missiles are injected are assumed uni-O formly distributed over specified intervals above the reference elevation by missile subset and missile origin zone. The reference elevation is taken to be the water elevation in the pond. The injection elevations were estimated on the basis of the distribution of the centers of mass of missiles in the injection domain. Table 4-8 lists the minimum and maximum injection heights above the reference elevation ( = 0) for each missile subset and zone.
Accounted for within the maximum initial elevation of a missile is the heAght at which temporary structures would produce missiles when destroyed by the tornado winds. In Table 4-9, the minimum and maximum injection heights above roof elevation for the structure-origin missiles are given.
1 The modeling of the site as a single elevation is, because of the topo-l graphy of the site which to the south and west generally slopes downward from i
the banks of the spray pond, a conservative approach. However, there are areas of the plant which are above the elevation of the spray pond.
In order to represent this increased elevation, an increase of an appropriate amount L
to the injection heights of missiles from those areas was made. Also, in the case of zone 4, which represents a significant population of missiles that are well below the reference elevation, this reduced elevation was compensated i
for by reducing the postulated injection heights.
I 4.4 DAMAGE CnITERIA The TORMIS methodology evaluates target damage due to tornado missile impact by scoring the following events:
1.
Missile hit, or impact, on the target.
2.
Missile hit on the target with impact velocity Vi > Vi*.
3.
Local effects missile damage to the target, i.e., perforation of l
steel targets and either scabbing or perforation of reinforced con-crete targets.
4.
Velocity exceedance for 4 impact speeds for the automobile missile.*
[
This damage assessment capability has been used in the Limerick spray I
- pond and cooling tower analysis. In addition, a windspeed exceedance cri-teria has been added to the scoring to enable assessment of cooling tower failure due to severe winds. The methods used to assess damage to each of the targets is discussed in the following subsections. It should be noted that a spray network is assumed damaged if either the network itself is dam-aged or its feeder pipe is damaged.
- The automobile is considered a " soft" missile whose icpact invokes an overall structural response failure mode, in contrast to a local penetration failure caused by rigid or "hard" missiles.
t 4-19 1
,_,.___,_~__..m._,.,.._,_,-m,
-_.,,-...,,,.,,,_.,,,,...,,_.---.,_%,,_m-m.
.,.m_.-.m_-_---_
y.
.m O
O O
Table 4-8.
Injection Height Intervals Above Reference Elevation By Subset "Mumber and tone Missile Origia tone 1 2
3 4
5 6
7 8
9 10 11 12 13 14 15 16 17 le 19 Injection Missile Height Subset Parameters Injection Reight Interval (feet) 1 Min 1
1 1
1 1
1 23 9
1 5
13 13 Max 20 30 5
4 20 10 32 16 4
12 17 20 2
Min 3
1 10 6
1 10 6
15 Max 6
5 14 10 5
14 7
17 3
Min 2
1 10 1
4 7
6 14 14 Max 4
6 14 4
6 14 7
16 16 4
Min 20 20 20 1
2 20 10 10 1
12 1
31 24 14 22 Max 40 40 40 20 20 40 20 20 2
22 10 41 34 24 32 5
Min 2
10 16 6 14 13 Max 5
12 le 9 16 16 b
d2 6
Min 5
5 1
1 5
1 23 9
1 3
1 15 5
13 15 13 C3 Max 20 25 5
4 20 10 52 11 10 4
15 18 12 17 17 20 7
Min 5
5 1
~
5 1
9 1
12 1
15 5
5 13 13 Max 20 25 20 20 10 11 6
32 2
le 9
7 32 14 8
Min 5
5 1
5 1
2 6
1 15 6
14 13 Max 20 25 20 20 6
4 10 4
18 9 24 18 9
Min 2
1 23 10 1
6 7
14 14 Max 6
!S 30 14 6
14 9 22 18 10 Min 10 15 6
Max 18 18 9
11 Min 20 20 20 1
1 10 1
23 1
1 3
1 22 1
5 5
13 13 13 Max 50 50 50 30 12 25 20 52 15 15 17 15 27 4
19 19 27 14 27 I
12 Min 20 20 20 1
1 10 1
23 1
1 3
1 5
5 13 13 Max 50 50 50 30 15 25 4
52 15 15 17 15 19 9
27 37 13 Min 15 15 1
1 10 1
23 9
1 3
1 5
5 13 13 Max 25 30 10 6
25 15 47 38 25 22 15 29 12 27 37 14 Min 15 15 1
1 10 1
23 1
1 3
1 5
5 13 13 Max 25 25 10 15 25 15 52 15 15 17 15 19 9 27 37 15 Min 1
9 1
3 1
5 13 13 Max 10 10 2
5 3
7 17 24 i
O C
O i
e h
i Table 4-8.
Injection Height Intervals Above Reference Elevation By Subset Mumber and zone (continued)
Missile Origin zone 1 2
3 4
5 6
7 8
9 10 11 12 13 14 15 16 17 10 19 I
Injection Missile Neight Subset Parameters Injection Height Interval (feet) 16 Min 15 15 1
1 10 1 23 9
1 3
1 5
13 13 Max 25 30 10 15 25 15 47 30 25 22 15 29 27 37 17 Min Man 18 Min 2
1 23 10 2
4 1
22 15 5
5 13 42 13 i
Max 10 6 52 14 4
34 15 41 34 24 12 20 44 22 3
j*
ha E'
19 Min 2
5 11 2
8 7
9 13 13 l
Max 10 10 19 10 14 14 14 22 22 20 Min 2
1 23 9
1 3
1 G
13 14 Max 6
15 52 18 3
0 15 9
22 22 21 Min 2
1 27 9
1 12 1
6 16 Max 10 100 37 18 10 22 15 14 24 22 Min 5
5 5
5 5
5 27 13 5
7 5
26 19 26 9 17 17 17 1
Max 10 10 10 10 10 10 37 le 10 12 10 31 24 31 14 22 22 22 i
4 i
i e
4 i
4 i
i
1 a
O Table 4-9.
Injection height intervals above structure V
top by subset and structure structure origin no.
17 18 19 15 16 i
l Structure height (ft) 160 27 9
96 96 i
Injection Missile height Injection height interval subset Description parameters (feet) l' 1
Rebar Min MSX 2
Gas cylinder Min 1
Max 3
3 Drum Min 4
Max 8
4 Utility pole Min 10 Max 20 1
5 Cable reel Min 1
' Max 5
L 6
.3" pipe Min 1
1 Max 5
10 7
6" pipe Min 1
1 Max 5
3 i
8 12" pipe Min 1
Max 5
l 9
Storage bin Min 3
l Max 8
'10 Concrete Min 383 383 fragment Max 483 483 11 Wood beam Min 1
1 Max 2
4 12 Wood plank Min 1
Max 10 13 Metal siding Min 1
Max 5
14 Plywood sheet Min Max i
4-22
Table 4-9.
Injection height intervals above structure
(
top by subset and structure '(continued)
Structure origin no.
17 18 19 15 16 L
Structure height (f t) 160 27 9
96 96 Injection 1
Missile height Injection height interval subset Description parameters (feet) t 15 Wide flange Min Max 16 Channel Min 1
section Max 5
17 Concrete panel Min 1
1 Max 2
2 18
. Small eqpt.
Min 1
3 Max 20 20 19 Large eqpt.
Min 5
s)
Max 15 20 Grating-Min 3
1 Max 4
10 4
21 Large frame Min 10 Max 15 22 Vehicle Min 5
Max 10 i
n 4-23 A
g,w, 99 t
3,r,-.,--,,,,vy,,y-wg,,,y&, +.
,y w vm,
,y-,,,-pr3w,,--,,wwcww,e,,,ym,,-,,,,,,,,-ww yww-y, ww w w ww,,
-w w.,-r-,-%
y-y-w w-we e m m wer,--e=w4,ei=-
} ('
4.4.1. SPRAY NETWORK '
L 7g
(-_
Each spray ~ network consists of 60 nozzle assemblies ~(with 4 spray arms c
for each nozzle assembly) and various size piping that distributes water to the nozzles. Figure 4-4 illustrates the spray pond network arrangement. The plan area of a neiwork is about 205 ft x 150 ft = 30,750 ft.2 Damage to a network is related to loss of cooling capacity of the network and can vary from merginal loss \\of spray effectiveness to total loss of spray augmentation.
For example, a few tornado' aissile impacts on nozzle assemblies would be
~
s expected to reduce the cooling capacity of the network by several percent g'
(Arizona Public Services Company, 1982). On the other hand, if 20 percent of the nozzles were damaged and one or more of the 10 inch or 16 inch distribution
' pipes were perforated by tornado missiles, then the cooling capacity of the
' damaged network would be greatly reduced. Hence, network damage is related
, 'to the' numbers, a'nd types of missiles as well as the missile impact character-
'istics. However, in view of the complicated geometry and varied fragility of
.the components that comprise a network, the following simple and conservative approach has been-used in the damage assessment:
1.
A control volume is placed around each network such that the dimen-sions enclose all the nozzle assemblies and distribution pipes. This control volume is a rectangular box, as shown in Figure 4-5.
2.
A single missile is assumed to be capable of damaging a networks i.e., the TORMIS scoring criterion in which damage can be produced by a single missile is maintained. In view of the discussion above thisgis clearly conservative.
~
3.
Each missile that hits the control volume is assumed to strike the weakest component in the network arrangement. Since it was not known a' priori which failura mode would be weakest, two different modes were investigated; perforation of the thinnest distribution pipe (see 5), and rupture of a spray arm (see 6).
4.
Tne damage potential of each missile that hits the control volume is
.related to the effective impact velocity V '. The effective velo-i city takes into account the obliquity and noncollinearity of the
' missile, as described in Twisdale et al. (1981).
5.
The perforation failure mode is evaluated by using a control volume thickness.that is equal to the minimum wall thickness of the distri-bution pipes-in the network. This thickness is 0.365 inches, which corresponds to the nominal wall thickness of the 10 inch distribu-tion pipe, as noted in Table 4-10.
Since the top surface of the control volume presents an oblique surface to predominantly horizon-tal missile ' motion, its thickness has been reduced to simulate pipe j
curvature. That is, since a 45 degree incoming missile trajectory could hit a pipe in a near normal impact, the control volume wall
' thicknesses.are~ reduced by cos 450= 0.707 to simulate an inclined target surface (see Twisdale et al. (1981 and 1978) for discussion i
o k
1.
\\~)
4-24 i
N O.
5
., - - -...,. - -.. ~...,.. -.. - - -.. -
--n--
- ~., - ~. -,
+~.w.
-~~--..~~~..~.~----a
-v
+ --.. ~.
q-
~-.
t
~
i -
}
I 5
l Ll q.
sad.
2, f
M
-L -
}-
a...e Q
N/
Nf
.N /
N/
N/
(E[< *** ""'g,. - - *** * " -
p/
s N(
/fs f
s
/ s
/ s
< s "n-4
+
1
- he -
er"? es C-C 1
t
'F s
't i
{
in j
.. - s-
/ (
/
s.
- \\,/
N,,/
N /
% g N /
\\ /
/ s x
.i
,./-
k; l
i 7
l
s.
g f s
/
N /
N /
\\ /
N
-N
/ \\
.L ',// ' Ji
/
\\
N, /
.-gy a
- ~E ~
$ ^~ '
f(
f"(
y
/ N
/ N l
l l
is.
//
ij
. [s/ -
'%(4
'l 3
g I.
. r y
s y
\\
/
% /
% /
- '/
.'4
... p ** r e ogsn ap Cf
's I
t,
s -
/j N
../ \\
/ \\
f
=
l I
f w
. i 1
4
- . A.
w-
- . H /
\\
./
.Ap/
N' /
- I /
/
- g - Q" **y_c.
M
/!
.ts I.
3 s
- f. s.
s i----
g i
- f i
__ y.
PJ
. - I r
'(
I hi I
Mtai. O'
'f gf f l
l C
j si/
N/
'l ve ta- =otas saus asseums, me aner g
g f
- i. ( < 4. s
<Nn
.oi s' fs 9
.'t.
3 N
,s 1
4 m
I r
i 1
d r
r d
r r'
sl i
8, s f f
Nf /
,, s
/
N4e
/
N'.'
T' t -- A
<gs
/s
/N
,h X
8 n
' i
/N
/ N
- \\
l l
..( 94. D wt. ene maas t
3 v3 -
si
. g~
1 u.
w t
s t-m k
q
.'M 5
1
.S-
.l*.
i 7
/,s.
<t*
3-
}c 3..
}
l
}
h
%vta m =
f t
i k,
i
. s s
"'~~*
}.
js,
i e 4.
.=
--L2k&h k.... -ry-c& "- '- W. --a - &
n.._.
5 Q, *, : C
,w..:,,c-->-
- a""~~
"'r**'*8 OG l
[
u.
(
UNtis 1 Ah0 2
{
- n., a
- r. a
-v o e w= w rer,* a s c i Y
-s.
s
.,.s FsNAL 5AFETV ANALvstS AEPORT
. a_.m..s.. 1:. *; * *
- d-6 4 3 :' :.. i ri.l.'
- r.^TH..
-P
..# 4
...or
,* s..
.a n,~ g SPRAY POND NETWORK ARRANGEMENT
.., A. A e
reaune os s t
t Figure 4-4.
Spray pond network arrangement.
i f
I I
i
.~-
y
h
.e w,
Qc
/
.i l
s\\s m
,/
m wi i 4 1
x5
/
9 g
2 EE f.
3 2
k 3
A*
4
'E a
I i
cg y
it
-f' 2
dr V
2 a
E l
a u
- t
=
2 a
jr B
gg g
lo, N-b
.b 2
g=
%./
0 i
i t
l E
u
[
l e
4 I
D
?
$. - 9 d
a 3
C E
1 3
5 8
5 '.a.
5 a
m i w g
- g d
u.
b
~
ar 7
hk 5
EE e
~
.a N~
i
-t i
i 2r 2y f
i e
%~
l
$$2 ms n
x t
8mm a
\\
\\
\\
4-26
O O
O Table 4-10.
Spray network and feeder pipe sizes and modeled thicknesses Yield Nominal wall Obliquity stress thickness, t adjustment Target Component
' Specification (ksi)
(in.)
t cos 450 Spray network Spray arm 2-in. Sch 160 35 0.344 a
Riser 4-in. Sch 80 35 0.337 Distribution pipe 6-in. Sch 60 35 0.432 0.305 1
Distribution pipe 10-in. Sch 40 35 0.365 0.258 Distribution pipe 18-in. Std 35 0.375 0.265 i
Feeder pipes Feeder pipes 30-in. Sch 80 30 0.500 0.354 l
t aThe spray arms and riser pipes are treated in the overall response failure mode.
U
?
l i
I ii.
3 i
l 4
I l
4 i
4
of obliquity and noncollinearity effects). Hence, tc reflect the obliquity of impacts on the roof of-the control volume, a thickness of 0.365 cos 450 = 0.258 inches is used. It is recognized that this correction is a very simple adjustment and.is one that is felt to be conservative. There are other factors that suggest that a concept of equivalence between pipe wall perforation and the use of a flat control volume surface should actually require an increase in the effective wall thicknesses. These factors include increased pene-tration resistance due to pipe wall curvature, increase likelihood of ricochet from an end-on impact on a small diameter curved sur-face, and the fact that every missile that enters the control volume would not hit a pipe of a particular thickness.
6.
The overall structural response failure mode is evaluated for the most fragile structural element in the network, which is the 2 inch spray arm cantilevered 5 feet from the junction box. The impact velocities required by each missile to snap-off a spray arm have been estimated and input to TORMIS. Hence, each missile that hits the control volume with an effective velocity Vi greater than (Vi')j is assumed to damage the network, where j denotes missile type. For missiles whose weight exceeds the yield capacity of the spray arm, (Vi')j = 0 and hence missile entrance is equivalent to damage.
7.
The failure mode (local perforation or spray arm rupture) that results in the higher probability of damage is used as the estimator of network failure probability.
(')
The models used to perform the perforation failure mode calculation are described in Twisdale et al. (1981 and 1978). For the spray arm failure mode, the dynamic model, example calculations, and (V ')j for each missile i
type are given in Appendix C.
I 4.4.2 FEEDER PIPE A 30 inch main feeder pipe provides water to each network. The pipe is buried over most of its length, but extends out of the ground surface at the i
edge of the spray pond. The pipe is modeled as a target from the point at I
which it is unprotected and above the ground surface to its connection point at the spray network. The pipe is assumed to be damaged if it is perforated by a tornado missile. The pipe is modeled as a rectangular box with wall thickness 0.354 inch, as noted in Table.4-10. An overall response failure mode has not been evaluated for-the feeder pipe. Damage to a feeder pipe is equivalent to damaging the network.
4.4.3 COOLING TOWER By virtue of their heights above grade, the cooling towers are vulner-able principally to direct wind pressures. Hence, tornado winds of suffi-cient magnitude are assumed to fail a tower and produce missiles that could
(
4-28 i
- _. ~,,. _.... _. - _
,___.__,_.._,.,,_,-,,m......
._r,,
.,_._,m,.,,
m.
i impact other targets such as the adjacent tower or the spray pond area. For winds less than the tower failure speed, the cooling tower basin wall, the distribution flume and fill areas are vulnerable to missile impact. Both I
direct wind damage and missile damage are considered in the TORMIS analysis.
4.4.3.1 Wind Damage The cooling towers have been designed for a basic wind of 90 mph at 30 feet above grade and up to 135 mph at 500 feet above grade (PECo, Ques-tion 410.70, Rev. 22). According to Bechtel (1983), the towers are expected to fail in tornado winds of about 150 mph. This estimate of failure windspeed is consistent with typical factors of safety in the design codes and the per-formance of the Grand Gulf cooling tower in an F2 tornado. Mcdonald (1978),
Fujita and Mcdonald (1978), Rotz (1978), and Twisdale (1978) have discussed the effects of the storm. The center of the storm, which was estimated to have peak gusts in the 140 mph range (Twisdale et al.1981) encompassed the tower, which was under construction at the 440 foot elevation above grade.
The tower was damaged locally at the constructior. height as a result of failure of the construction tower crane. The horizontal crane boom was located above the shell rim. The crane failed in the tornado wind and the vertical stem of the crane damaged the upper rim of the cooling tower shell. The pieces of
- concrete and crane boom fell just outside the cooling tower shell. The only damage to the tower was that caused by the collapse of the crane. Hence, the 150 mph estimate quoted in Bechtel (1983) is judged reasonable for hyperbolic cooling towers. The mode of failure of the Limerick towers in tornado winds is expected to be local buckling, as there is a factor of safety against over-
/
turning of about 1.5 for 360 mph winds.
For the Limerick towers, the tornado windspeed assumed to cause failure is 140 mph at the centerline of the tower at half height. This value has been set-below the 150 mph speed estimated in Bechtel (1983) to reflect uncer-tainties in the Grand Gulf tornado winds and the exact nature of turbulence and pressure distribution arising from small core tornado interaction with-cooling towers.
4.4.3.2 Missile Damage The tower basin area is vulnerable to windborne missile damage to the distribution flume, riser pipes, and curb wall. Missile perforation of the curb wall would result in rapid loss of water and perforation of the distribu-tion flume would be expected to degrade cooling tower performance by allowing a flow path by which the water could bypass much of the fill area. Hence, these targets have been modeled explicitly in TORMIS. Potential damage to the riser pipes is assessed by evaluating those missiles that enter the basin area for their damage potential, 7
i r
t N
4-29
{~
4.5
SUMMARY
This chapter and Chapter 3 have documented the input to TORMIS with respect to modeling the site in terms of the potential missiles, the targets, and the tornado characteristics expected in the region around Limerick. As explained previously, TORMIS estimates the frequency of single events or at most the union of two events. In this study, the failure criteria are in
'cerns of the union of several events. This is handled by having the results of TORMIS, which are given as the frequency with which one or more missiles strikes or damages the target, written onto a tape which is used to input the information into a postprocessor code 'IORSCR.
Use of this code and the results of the study obtained by using it are given in Chapter 5.
O i
N~-]
4-30
Chapter 5 RESULTS AND CONCLUSIONS
5.1 INTRODUCTION
The purpose of this analysis was to estimate the frequency with which 1
10 CFR Part 100 limits would be exceeded at Limerick Generating Station as a i
direct result of wind missile related damage on the ultimate heat sink. In Chapter 2 of this report compound events designated T and V were defined.
l Both of these events were unions of more fundamental events; for instance, event V was defined as the event: tornado missile damage to at least three out of four of the spray networks and damage to both cooling towers. Both of these compound events are necessary precurscrs to exceeding 10 CFR Part 100 limits under certain assumptions:
+
1.
For Event T, the assumption is that only Unit 1 is operational 2.
For Event V, the assumption is that both units are operational In order to estimate the frequency of exceeding 10 CFR Part 100 limits, it is therefore necessary to estimate the frequencies of events T and V.
The tool used to do this was the computer code TORMIS-L (a version of the EPRI code TORMIS modified for this specific problem) supplemented by a probability
)-
manipulation code TORSCR. TORMIS-L was used to sample from,the distribution of tornado characteristics and for each tornado sampled to evaluate the con-ditional probability of the fundamental events making up the compound events T and V.
So, for example, TORMIS-L evaluated the conditional proba-bility that each spray network in turn was damaged or that each cooling tower was damaged, for each tornado generated by the sampling scheme in TORMIS-L.
The distribution on tornado characteristics used in the analysis was described in Chapter 3.
The model used to characterize the site in terms of the structures and the potential missiles was discussed in Chapter 4.
In l
Chapter 4, the damage criteria used to specify when a particular target was assumed to be failed were discussed. For the spray networks two damage cri-teria were specified; the first was that if one or more missiles entered the t
network.with a velocity high enough to rupture a spray arm the network was l
considered failed, secondly if one or more missiles entered the network with sufficient velocity to perforate the thinnest of the distribution pipes the l
network was considered failed. The criterion which resulted in the highest frequency was used to give the final result of this study. A spray network was also considered failed if its feeder pipe was perforated by one or more missiles. The cooling towers were assumed to be failed if the wind velocity experienced at half height exceeded 140 mph, or if either the dictribution fiume or the curb around the cooling tower basin was penetrated by a missile.
i.
[
The code TORSCR was used to estimate the conditional probability of each j
compound event T and V given the occurrence of the tornado sampled. The overall unconditional frequency of each event was calculated by summing the products of the frequency of the sampled tornado and the conditional proba-bility of the event. This chapter describes the results of the analysis.
O 5-1
l Two hundred forty thousand missile histories were simulated from 320 tornado strikes with F1 through F5 intensities. These simulations represent gs tornado activity at the plant corresponding to over 457,000 years of 2 F1
(
\\' ;
tornado windspeed occurrences; 625,000 years of 3 F2 tornado windspeed occur-rences; 1,200,000 years of 2 F3 windspeed occurrences; 4,000,000 years of 2 F4 windspeed occurrences and 20,000,000 years of R F5 tornado windspeed occurrences.* These simulations provide the basis of the estimates for the frequencies of events T and V presented in Section 5.2.
5.2 FREQUENCIES OF EVENTS T AND V The results of the analysis for the frequencies of thcse events are dis-cussed below and are summarized in Table 5-1.
Two results are given; the first corresponds to assuming damage when one or more missiles enter with enough velocity to rupture a spray arm, and the second corresponds to assum-ing damage when one or more missiles enter with enough velocity to perforate the wall of the thinnest pipe. The results using the first damage criterion are greater than those using the second criterion in all cases and are taken as the appropriate conservative estimates.
The frequency estimates in Table 5-1 are in units yr-1 The total fre-quency for each event is given under the "All" heading and is the sum of each F-scale frequency. The two-sided 95 percent confidence bounds have been cal-culated from the sample variances, which are given in Table 5-2.
In general, the upper confidence limit is about twice the mean value. The expressions for the variance and confidence bound estimates are given in Twisdale et al.
(1981). It is noted that the confidence bounds in Table 5-1 reflect only the statistical uncertainty resulting from the Monte Carlo calculation; they do s.
not reflect model uncertainties or uncertainties in the tornado occurrence rates. However, these modeling uncertainties have been accounted for by vir-tue of the fact that the analysis presented here is a conservative calcula-tion. A more realistic calculation would be expected to produce results which are much more than a factor of two less than the mean value quoted here.
The following subsections discuss the results by event.
5.2.1 EVENT T Event T corresponds to damage to 4 out of 4 networks and the Unit 1 cooling tower. F1 tornados cannot contribute to event T since cooling tower Estimated by the relation y - (Mp}pq)/P(V3Vp4), where y is the time period in years, MylFj is the number of t5rnadoes simulated with windspeed 2Fj intensity, and P(V3VF) is the probability per year of exceeding the Fj 4
intensity lower bound windspeed.
O (O
5-2
o Table 5-1.
Base case frequency estimates by event and network damage criteria O
Network damage Tornado Frequency estimates (per year) criterion intensity Event T Event V Rupture of F1
- b e
a F2 spray arm F3 F4 6.2 x 10-7 7.2 x 10-7 F5 3.9 x 10-8 7.2 x 10-8 All 6.6 x 10-7 7.9 x 10-7 95% conf.
(0,1.4 x 10-6)c (0,2.2 x 10-6) bounds Perforation F1 of pipe walla F2 F3 F4 2.9 x 10-7 7.2 x 10-7 F5 4.7 x 10-8 1,0 x 10-8 All 2.9 x 10*7 7.3 x 10-7 95% conf.
(0,8.6 x 10-7)
(0,2.1 x 10-6) bounds aRupture of spray arm and perforation of pipe wall refer to the damage criteria for tne networks themselves; perforation of the feeder pipes consti-tures damage in both cases, bThe asterisk indicates no event successes were obtained in the TORMIS simulations.
cThe 95 percent confidence interval reflects the statistical uncertainty in the Monte Carlo method.
O 5-3
Table 5-2.
Base case variances by event and network damage criteria
(
Network damage Tornado variance estimates (per year) criterion intensity Event T Event V Rupture of F1
- b a
spray arm F2 F3 F4 1.4 x 10-13 5.1 x 10-13 FS 4.5 x 10-16 3.9 x 10-15 i
All 1.4 x 10-13 5.2 x 10-13 Perforation F1 of pipe walla F2 F3 F4 8.3 x 10-14 5.1 x 10-13 F5 1.3 x 10-17 1.0 x 10-16 All 8.3 x 10-14 5.1 x 10-13 aRupture of spray arm and perforation of pipe wall refer to the damage criteria for the networks themselves; perforation of the feeder pipes consti-l tutes damage in both cases.
bThe asterisk indicates no event successes were obtained in the TORMIS simulations.
l l
O 5-4
6 failure is postulated to occur for windspeeds >140 n'ph.
No F2 or F3 tornados O
contributed to event T in the current simulation sample size.
The tornados are not, in general, wide enough or strong enough to both damage a tower and transport missiles into all four networks.
Hence, the approximately 700 feet separation of the towers from the spray pond significantly reduces the chance of both cooling tower and spray pond damage in the same tornado. Basically, event T damage requires a relatively wide tornado whose path center line passes near the towers and spray networks such that the strong winds affect both the pond area and encompass the Unit 1 cooling tower. The estimate of the frequency of T are 2.9 x 10-7 per year for the perforation criterion and 6.6 x 10-7 per year for spray arm rupture.
2 5.2.2 EVIDIT V Event V corresponds to damage to at least 3 out of 4 networks and 2 out.
of 2 cooling towers. The results in Table 5-1 indicate that the estimated frequencies are not significantly different from those for event T.
The fact that damage to only three networks is necessary counterbalances the fact that both towers must be failed. The frequencies are 7.3 x 10-7 for the perfora-tion criterion and 7.9 x 10-7 for the rupture criterion. Again, no F1, F2, or F3 tornados contributed to these frequencies.
5.3 ADDITIONAL ANALYSIS OF THE M RMIS-L RESULTS This section discusses additional analyses of the results of TORMIS-L that serve to supplement the frequency evaluations discussed in Section 5.2.
5.3.1 DAMAGE FREQUENCY OF CURB WALL The cooling tower curb wall is an essential component to the operation of the cooling towers. The walls were modeled as target numbers 11 and 12 in the TORMIS analysis, which provides estimates of the frequency of tornado missile perforation of these walls. These targets were not included in the TORSCR analysis, but they have been analyzed directly from the TORMIS output.*
Table 5-3 summarizes the results of the review of the TORMIS-L simula-tions. The probabilities of perforating the curb wall targets were taken directly from TORMIS. They indicate that the probability of perforating the l
- These targets were added late in the project schedule, after the TORSCR t
program had been debugged and verified.
!O 5-5 l~
l,_ _ _ _. - - - - __
l Table 5-3.
Tower curb wall damage frequencies Tower 1 Tower 2 Perforate given Perforate given Tornado Perforate no damage for events Perforate no damage for events intensity curb wall T and va curb wall T and V y1
- b 7.0 x 10-6 F2 6.8 x 10-6 5.1 x 10-6 F3 1.8 x 10-6 5.0 x 10-7 F4 3.2 x 10-6 2.9 x 10-7 FS 3.7 x 10-7 i
All 1.2 x 10-5 1.3 x 10-5 aThat is, perforations that result in damage given that (1) the towers have not failed and (2) at least 3 networks have been damaged.
i bThe asterisk indicates no damages were obtained in TORMIS simulation.
I 4
O
)
i r
l
{
=
5-6
curb wall for each of the towers is about 1 x 10-5 per year. To determine if
'N) curb wall perforation would have contributed to the probabilities of events T and v in Table 5-1, the TORMIS outputs were reviewed in detail for each tor-s nado strike and each F-scale. The results indicate that all of the curb wall perforations occurred as a result of tornado damage to the towers in which less than 3 networks were damaged and/or the towers were already considered as damaged from the windspeed exceedance criteria. Hence, perforation of the curb wall does not contribute to events T and V and the results in Table 5-1 do not need to be modified. It is noted that these results were expacted in view of the 10-inch wall thickness and the fact that missile transport on the tower is closely correlated to windspeed, for which the tower is assumed to fail if V > 140 mph.
l 5.3.2 MISSILE CHARACTERISTICS - SPRAY NETWORKS The spray pond networks have been evaluated for missile damage by con-sidering distribution and feeder pipe perforation as well as rupture of the spray arm due to missile impact. Table 5-1 summarizes the damage frequencies for both failure modes. As indicated earlier, rupture of the spray arm gives the greater frequencies and hence provides the most conservative estimate of the failure frequency.
An evaluation of the types of missiles that contribute to these damage modes has been made from the TORMIS outputs. Table 5-4 summarizes the types of missiles and their mean effective impact velocities for those missiles j
that hit the network control volumes. For the F1 intensity only 5 of the 22 missile types were transported into the networks. These 5 are the lighter weight missiles and include wood beams and planks, metal siding, plywood sheets and metal grating. The F2 tornadoes transported these missiles as well as channel sections and small equipment. F3 tornadoes introduced wide flange sections and steel frames with F4 tornadoes adding 3-inch pipes. The F5 tornadoes transported these missiles as well as rebar, drums, cable reels, 6-inch pipes, storage bins, and two vehicles into the pond area. As expected, the mean effective velocity of these missiles tend to increase with F-scale, except where there is a small sample size.
Comparison of the missiles listed in Table 5-4 with the missile spectrum (Table 4-4) indicates that the following missiles were not transported into the networks in the TORMIS simulations:
Missile Subset Description 2
Gas cylinder 4
Utility pole 8
12-inch pipe 10 Concrete fragment 17 Concrete panel i
l l
l
g a
5-7
Table 5-4.
Effective velocities of missiles entering spray networks i -
Mean effective impact velocity, V'
(ft/sec) i Missile type Tornado intensity Subset number Description (Vi')jed F1 F2 F3 F4 F5 1
Rebar 208
- a 46 3
Drum 44 36b 5
Cable reel 33 78b 6
3" pipe 62 44b 18 23 7
6" pipe 32 16b 9
Storage bin 0
31b ob 83b 11 Wood beam 42 34 36 33 38 83 12 Wood plank 93 24 30 32 55 59 13 Metal siding 31 25b 75 92 75 118 14 Plywood sheet 51 64 79 80 101 76 15 Wide flange 0
25b 32b 26 16 Channel section 1 35 54b 27 38 44 18 Small eqpt.
0 50 31b 34 38 19 Large eqpt.
0 98b 20 Grating 38 54b 40 56 87 74 21 Large frame 0
109b 68b 79b l
22 Vehicle 0
ll7c l
aThe asterisk indicates no missiles of this type entered the spray networks for this F-category tornado.
bSample size is less than 5.
cVelocity shown is actual impact velocity (V1) and not effective velocity.
dEffective velocity to rupture spray arm as evaluated in Appendix C.
l l
l l
l l
I 5-8 l
l J
w - + + - -
9my
..r.+e-
-+-r,,,.--,--v_c--.-_.--ew,---,,..-w-.. _,,.,,,,-,.
ve,--e-me-em%.-.#ww,#r-,.-e~ww.w-ew--,.,,w.--w."
.-w.,,+.--.r,--e--.-
This analysis thus indicates that it is extremely unlikely that cooling tower failure (which was assumed to produce missile types 10 and 17) could generate missiles that would be transported into the spray pond or affect the other tower. Hence, these results suggest that the separation distances from the tower to the pond, and tower to tower at Limerick are adequate to take advant-age of the redundancy in the ESW and RERSW heat sinks afforded their by physical separation.
i 5.3.3 MISSILE CHARACTERISTICS - COOLING TONER FILL AREA
~
The cooling tower fill areas were not treated explicitly as safety related targets in the TORSCR analysis. Due to the nature of the fill construction, missiles that enter the fill area would not necessarily lead to significant damage or degrade the cooling capability of the tower. Hence, in view of the difficulty in establishing a damage criteria for the fill area, an evaluation of the types of missiles that hit the cooling tower fill (Targets 13 and 14) has been made.
Table 5-5 summarizes the mean effective velocities of those missiles that hit Targets 13 and 14.
For F1 tornadoes, the missiles listed include l
all those that hit the fill targets. For F2 through F5 tornadoes, the missiles listed are those that hit the fill during tcrnadoes whose windspeed did not exceed the capacity of the towers. Hence, Table 5-5 provides the indication O
of the effective velocities of those missiles that entered the fill area when the towers did not experience winds 140 mph.
Table 5-5 susmarizes the type of debris that could be transported into the fill area. A high percentage of this debris would tend to interact with the canted precast concrete louvers and fall to the ground after impact.
Less than on half of the debris would be expected to make it through the l
louvre screen. Once inside, the missile encounter a maze of supporting bent panels (in a truss type design) and splash bars.
It seems unlikely that enough debris could damage enough splash bars to seriously degrade the cool-l ing capacity of the tower.
In addition, the debris would tend to be concen-trated near grade elevation and probably around less than one third of the tower perimeter. Hence, it seems reasonable to conclude that missile damage l
to the fill area poses an insignificant incremental risk to the tower capability over the failure modes explicitly considered in this analysis.
5.4 SENSITIVITY ANALYSES In this section the results of two sensitivity studies are reported.
The first investigates the effect of a lower tornado translational velocity than is normally used in TORMIS. This was performed to investigate the con-cern raised by Reinhold in the Safety Evaluation Report on the TORMIS method-ology (USNac,1983) in which it was stated "the assumed translational velocities may be too high and will tend to produce less conservative esti-mates than are desirable." The second invest.igates the effect of decreasing O
lation is felt to be much higher than would be expected during normal the numbers of potential missiles. This is important since the present popu-operation.
5-9 I, - _. _ _ _ _. _ _ _ _ _ _
_ ~.
Table 5-5.
Effective velocities of missiles entering cooling tower fill area Mean effective impact velocity, V'
(ft/sec) i Missile type Tornado intensity Subset number Description F1 F2a p3a p4a F5a 1
Rebar
- b 55c 33c 6
3" pipe.
7c 4c 99c 23C 9
Storage bin 60c 4
11 Wood beam 24 41 55 76 12 Wood plank 30 39 45 55 65 13 Metal siding 48 55 88 105 130 14 Plywood sheet 56 73 101 89 106 16 Channel section 6
9 17 37 52 31c 36c 18 Small eqpt.
19 Large eqpt.
16C 20
' Grating 10a 33 67 53 68 aFor these F-scales, missiles listed correspond to those that hit the fill area given that the tower had not failed due to the windspeed exceedance.
bThe asterisk indicates no missiles of this type entered the fill area l
for this F-category tornado.
cSample size is less than 5.
1 l
l '
l l
l' 5-10
5.4.1 TORNADO TRANSLATIC'AAL SPEED The importance of tornado translational speed in tornado missile trans-port has been indicated in Twisdale et al. (1978) and Twisdale (1981). For the same peak tornado windspeed, lower translational speeds result in higher windspeeds on the weak side of the tornado and longer missile exposure to high winds. To test the sensitivity of the Limerick results to the TORMIS translational windspeed parameters, the F4 simulation was rerun with reduced tornado translational speeds. The mean translational speed was reduced from 45 to 30 mph and the standard deviation was reduced from 12.6 to 10.4 mph.
These parameters correspond to the F2 translational speeds used in TORMIS.
The results are summarized in Table 5-6 and indicate relatively moderate sen-sitivity. For spray arm rupture, the frequencies change from 7.2 x 10-7 to 1.2 x 10-6 for event V and from 6.2 x 10-7 to 7.5 x 10-7 for event T.
- Hence, the results are relatively insensitive to changes in the tornado transla-tional speed.
5.4.2 NUMBER OF MISSILES The potential missile population used in the base case simulation repre-sents a high level of construction activity at the plant. A total of 122,225 missiles were modeled. In later years with little or no construction activ-ity, a reduced number of potential missiles would be at the plant. To test the sensitivity of the results to a reduction in the number of missiles, the F4 simulation was rerun with the number of missiles in each zone reduced by a
[
factor of 10.
v The results of the simulation are given in Table 5-6 and show that the frequencies of events T and V are reduced substantially. This reduction is felt to be due to the fact that events T and V occur when the tornado center-line passes between the towers and the pond area. The pond targets are now on the weak side of the tornado, and fewer missiles from fewer zones enter the pond area. By studying the equations by which the conditional probabili-ties of damage are calculated, it can be seen that the sensitivity to the number of missiles would not be expected to be more than linear. Hence, the i
reduction by a factor of almost two orders of magnitude in event V is felt to be more a function of undersampling. Nevertheless, the results do show that a reduction in the number of missiles can substantially reduce the damage frequencies.
5.5 CONCLUSION
S i
I The results given in Table 5-1 are conservative estimates of the fre-quencies of the compound events T and v.
These estimates are taken as bound-ing frequencies of exceeding 10 CFR Part 100 limits under the assumptions l
_ stated in Section 5.1.
The results of the analysis are:
G.6 x 10-7 per year when Unit 1 only is in operation, j
and 7.9 x 10-7 per year when both units are in operation, J
5-11
- - + -
ww---
1.-,-
,,,-,e
,-,n.
g.,,eng
,,m
,,,-e,,
,4,,,,,,.,-,,, -----o,~4--e-.r~,y--o-,-e-
-v.,
~w
.-..my
j.
Table 5-6.
Sensitivity analysis frequency estimates i.
Frequency estimates (per year)
Network Tornado damage Case intensity criteria Event T Event V Base Case F4 Rupt. arm 6.2 x 10-7 7.2 x 10-7 j
Perf. pipe 2.9 x 10-7 7.2 x 10-7 Reduced.
F4 Rupt. arm 7.5 x 10-7 1.? x 10-6 l
tornado perf. pipe
- a 1.2 x 10-6 translational l
windspeed Reduced F4 Rupt arm 5.0 x 10-8 6.3 x 10-9 number of perf pipe missiles aThe asterisk indicates no event successes were obtained in the TORMIS simulations.
I
\\
f 5-12 j
i k
__,.m.__,,..--.
which gives an average frequency over the lifetime of the plant of 1/40(5 x 6.6 x 10-7 + 35 x 7.9 x 10-7) = 7.7 x 10'7 on the assumption that Unit 1 is
\\
in operation for 5 years until Unit 2 is completed.
It should be noted that, under the assumptions made here, the question of whether offsite power has been lost or not is irrelevant, since if both the cooling towers and the spray pond are inoperable there is no heat sink even if the pumps, valves, etc., were operational.
These results are believed to be conservative for many reasons:
1.
The potential missile population is fixed as that which exists at l
present with a construction laydown area concentrated about the spray pond. As the units are completed this area is expected to be sub-stantially cleared. As indicated by the sensitivity studies lower-ing the number of missiles can have a significant effect on lowering the calculated frequencies.
2 l
2.
The spray network damage criteria are believed to be conservative i
for many reasons:
1 Even one missile damaging a part of the network is assumed to fail the network whereas in reality the efficiency of the net-work would be expected only to be impaired slightly by single missile damage, with increasing impairment as the number of dam-r aging missiles increases (Arizona Public Service Co.,1982).
For either of the damage criteria chosen, it is assumed that any O-missile whose velocity exceeds the criterion and enters the con-l trol volume actually hits and damages the network. Since the missile might hit a stronger part of the network or even the water first, then even if it did hit the weakest part subse-quently, its effective velocity would be lower, and hence this i
application of the damage criteria is conservative.
3.
The TORMIS methodology has been judged (Simiu,1983) to be conserva-tive with respect to missile risk analysis provided, "the tornado wind velocity ranges assumed in the calculations are defensible given i
the present state of the art" and '"the assumptions concerning the locations and numbers of potential missiles present at the site are l
plausible." The first provision has been addressed by adopting the i
original F-scale speeds proposed by Fujita (1975) rather than the speeds proposed in Twisdale et al. (1978). The second has been met by performing a detailed site survey, and conservatively applying the results of that survey to all future operating periods.
4.
All the postulated missiles at Limerick were treated as minimally restrained, which injects each sampled missile near the peak aero-dynamic forces, thus maximizing transport range and impact speed, and consequently the damage frequency.
i
~.-<
'5-13
, _,.. _.., -. -, _. _. - - _, _.,. ~,.
5.
The tornado windfield parameters in TORMIS-L were adjusted to increase
[
the wind profile in the lowest 10 m.
The original profiles in TORMIS
\\~-
are believed to be representative of surface boundary conditions (Redmann et al.,1983) and empirical models (Fujita, 1978). Hence, the adjustment used in this study is felt to be an added conservatism.
6.
The original F-scale windspeeds (Fujita, 1975) were used in this ar.alysis. These windspeeds are believed to be conservative (see Twisdale (1978b) and the analysis by Ramey and Johnson (1980) of the Birmingham tornado).
7.
No credit has been taken for repair to the spray networks or partial effectiveness of damaged networks even though several hours would be available to effect repairs.
8.
The missile injection heights used in the study were chosen conservatively.
9.
Very little credit has been taken for the effective shielding afforded by the grading of the site. The site slopes away from the pond to the south and west which is the direction from which most tornadoes would come.
The degree of conservatism associated with each of these items has not, with the exception of the number of missiles, been quantified, but it is believed that removal of all these conservatisms would produce a substantial reduction in the estimated frequencies, and hence, the results quoted here
~'h should be regarded as conservative bounds.
)
l l
l l
i i
'h (G
5-14 1
.~
~ --
REFERENCES Arizona Public Services Company, Palo Verde Nuclear Generating Station Probabilistic Risk Assessment of Tornado Missile Damage to the Station Ultimate Heat Sink, 1982.
Batts, M. E., Russell, L. R., and Simiu, E., " Hurricane Wind Speeds in the United States," Journal of the Structural Division, Vol.106, No. ST10, October 1980.
1 Bechtel Power Corporation, " Report on the Effects of Postulated Failure of Cooling Towers," Philadelphia Electric Company, Limerick Generating Station, Units 1 and 2, Job 8031, December 1983.
Changery, M. J., " Historical Extreme Winds for the United States - Atlantic and Gulf of Mexico Coastlines," NUREG/CR-2639, U.S. Nuclear Regulatory Commission, Washington, D.C.,May 1982.
Castelli, F.
P., Meteorological Evaluation Services, Inc., Letter to C.
Olenik Philadelphia alectric Company, December 5, 1983.
Cry, G. W., " Tropical Cyclones of the North Atlantic Ocean-Tracks and Frequencies of Hurricanes and Tropical Storms 1871-1963," Technical Paper No. 55, U.S. Weather Bureau, U.S. Department of Commerce, Washington, D.C., 1965.
Feller, W., An Introduction to Probability Theory and Its Applications, Volume I, 3rd Edition, John Wiley and Sons, New York,1968.
\\
Fotz, J. V., " Tornado Damage Report - Grand Gulf Generating Station," Bechtel Power Corporation, San Francisco, California, April 1978.
t Fujita, T. T., " Proposed Characterization of Tornadoes and Hurricanes by Area l
and Intensity," SMRP Research Paper No. 91, University of Chicago, Chicago, Illinois, February 1971.
Fujita, T. T., " Workbook of Tornados and High Winds," SMRP Research Paper No. 165, University of Chicago, Illinois, September 1978.
Fujita, T. T., and Mcdonald, J. R., " Tornado Damage at the Grand Gulf, Mississippi Power Plant Site: Aerial and Ground Surveys," NUREG/CR-0383, U.S.
Nuclear Regulatory Commission, Washington, D.C., September 1978.
Gomes, L., and Vickery, B. J., " Extreme Wind Speeds in Mixed Wind Climates,"
Jo,urnal of Industrial Aerodynamics, 2 (1977/1978), pp. 331-334.
o Hald, A., Statistical Theory with Engineering Applications, John Wiley and
(
Sons, New York, 1952.
Ho, F.
P., Schwerdt, R. W., and Goodyear, H.
V., "Some Climatological Char-acteristics of Hurricanes and Tropical Storms, Gulf and East Coasts of the United States," NOAA Technical Report NWS 15, U.S. Department of Commerce, Washington, D.C., May 1975.
n v
R-1 l
_ - - _ - _ - - - =.. _.. - -, -.......... -.. -.,. -.. _ _ ~ -. _. - _.
Markee, E. H., Beckerley, J. G., and Sanders, K. E., " Technical Basis for Interim Regicnal Tornado Criteria," WASH-1300, 1974.
Mcdonald, J.
R., ' Assessment of Tornado Damage to the Grand Gulf Nuclear Generating Station," Institute of Disaster Research, Texas Tech University, Lubbock, Texas, June 1978.
j Myers, V. A., " Characteristics of United States Hurricanes Pertinent to Levee Design for Lake Okeechobee, Florida," Hydrometeorological Report, No. 32, U.S. Weather Bureau, U.S. Department of Commerce, Washington, D.C.,1954, pp. 106.
Myers, V. A., and Jordan, E. S., " Winds and Pressure Over the Sea in the Hurri-cane of September 1938," Monthly Weather Review, Vol. 84, No. 7,1956,
~
pp. 261-270.
PECo, Final Safety Analysis Report, Limerick Generating Station, Philadelphia Electric Company l
PECo, Letter from L. P. Pyrih to E. R. Schmidt (NUS) - March 5,1984.
Ramey, G. E. and Johnson, R.
C., "Windspeed Analysis of the 1977 Birmingham Tornados," Journal of the Structures Division, ASCE, Vol. 100, No. 579, i
September 1980.
2 Redmann, G. H. et al., "Windfield and Trajectory Models for Tornado-Propelled Objects," EPRI NP-2898, Electric Power Research Institute, Palo Alto, California, March 1983.
(
Russell, L.
R.,
" Probability Distributions of Hurricane Effects," Journal of the Waterways, Harbors, and Coastal Engineering Division, Proceedings ASCE, Vol.
97, No. WWl, Proc. Paper 7886, February 1971, pp. 139-154.
i Sachs, P., Wind Forces in Engineering, Pergamon Press, New York,1978.
Schwerdt, R. W., Ho F. P., and Watkins, R. P., " Meteorological Criteria for Standard Project Hurricane and Probable Maximum Hurricane Windfields, Gulf and East Coasts of the United States," NOAA Technical Report NWS 23, U.S.. Department of Commerce, Washington, D.C., September 1979.
Simiu, E., and Scanlan, R. H., Wind Effects on Structures An Introduction to Wind Engineering, John Wiley and sons, New York, 1978.
Tryggvason, B. V., " Defining the Wind Climato in Regions Affected by Hurri-canes," Pourth U.S. National Conference en wind Engineering, University of Washington, Seattle, Washington, July 1981.
Twisdale, L. A., " Ground Survey of the Grard Gulf Generating Station Tornado l
L of April 17, 1978," Special Report Prepared for Electric Power Research l
Institute, Palo Alto, California, May 1978.
l Twisdale,-L. A., " Tornado Data Characterization and Windspeed RJsk," Journal of the Structural Division, ASCE, Vol. 104, No. 5710, October 1978b, pp. 1611-1620.
R-2
7-g Twisdale, L.
A.,
" Risk-Based Design Against Tornado Missiles," Preprint 3596,
(
Civil Engineering and Nuclear Power, ASCE, Boston, Massachusetts, April
)
1979.
Twisdale, L. A.,
Dunn, W.
L.,
and Davis, T.
L.,
" Tornado Missile Transport Analysis," Nuclear Engineering and Design, 51, 1979.
Twisdale, L.
A.,
" Regional Tornado Data Base and Error Analysis," Preprint, AMS 12th Conference on Severe Local Storms, San Antonio, Texas, January 1982.
Twisdale, L.
A., " Wind-Loading Underestimate in Transmission Line Design,"
Transmission and Distribution, December 1982.
Twisdale, L. A.,
and Dunn, W.
L., " Tornado Missile Simulation and Design Methodology," EPRI NP-2005, Electric Power Research Institute, Palo Alto, California, August 1981.
Twisdale, L. A., and Dunn, W. L., "Probabilistic Analysis of Tornado Wind Risks," Journal of Structural Engineering, Vol. 109, No. 2, February 1983.
Twisdale, L.
A., Dunn, W.
L., and Alexander, B. V., " Extreme Wind Risk Analy-sis of the Indian Point Nuclear Generating Station," Final Report 44T-2171, Research Triangle Institute, Research Triangle Park, North Carolina, March 1983.
'[~'N Twisdale, L. A., et al., " Tornado Missile Risk Analysis," NP-768 and NP-769,
\\s,/
Electric Power Research Institute, Palo Alto, California, May 1978.
USNRC (U.S. Nuclear Regulatory Commission), Standard Raview Plan, Missiles Cenerated by Natural Phenomenon," Section 3.5.1.4, Washington, D.C.,
Noverber 1975.
Wen, Y.
K.,
and Chu, S.
L., " Tornado Risks and Design Wind Speed," Journal of the Structural Division, Proceedings ASCE, Vol. 99, No. ST12, December 1973.
i l
1 m
(
l
~~ >
R-3 l
> ],
(
APPENDIX A V
TORMIS MODIFICATIONS TO PRODUCE TORMIS-L A.1 Code Dimensioning The TORMIS code used dynamic dimensioning in many of the subroutines and required that the MAIN program be dimensioned consistently with the data for a given run.
In the TORMIS-L version, the entire code uses fixed dimensioning; the dimension sizes in the TORMIS-L code allow the maximum values of the variables shown in Table A-1.
A.2 Windspeed Exceedance at Cooling Towers The TORMIS-L code allows the user to specify 0 5 NFAIL 5 2 targers for which a horizontal windspeed exceedance criterion is checked.
If NEAIL 4.s input as zero, then no windspeed exceedance checking is performed.
If NEAIL > 0, the user inputs a record for each target to be checked giving the target number, ITF(I), the windspeed to be exceeded. WINDF(I), and the height at which the horizontal windspeed is to be evaluated, ZTF(I), where I can take on the values 1 and 2.
To find the maximum horizontal windspeed at the center of the target and the height of interect, a cartesian S-T system is constructed as in Fig. A-1, where the S axis identifies the offset distance from the tornado track (T
]
'j axis) to the target center.
Using simple arguments of vector addition (see Fig. A-2), the maximum horizontal windspeed at offset S and elevation z during passage of the tornado, V(S), can be expressed as
- 2 T + k[U (r,z)sinB - U (r,z)cosBl V(S) = v(S T.,z) =
U S
r
+ (U (r,z)cosB + U (r,z)sinB]2 (A-1)
O r
where v(S,T,z) is the net horizontal windspeed at offset S and height z when the tornado center is at track position T; T is the track position at which m
v(5,T,z) is maximized; UT is tornado translational velocity; k=1
,T 20 (A-2a) m i
(A-2b)
= -l
,Tm<0 U (r,z) and Ug(r,z) are the radial and tangential windspeed components, r
respectively, of the vortex at radial distance r from vortex center and height z;
m ]Il 2
(A-3) r = [S2+T 1
(-)
A-1 t-
TABLE A-1.
MAXIMUM VALUES OF THE VARIABLES USED IN DIMENSIONING TORMIS-L U
Maximum i -
Variable Value Description i
NUMTAR 22 The number of target structures NTAR 132 The number of target walls (surfaces) l NTARM 12 The number of targets supporting potential missiles NSSET 26 The number of final missile subsets NSSETT 25 NSSET-1 4
NZ 20 The number of origin zones NZM 32 NZ + NTARM NZC 60 The number of zone coordinates NZCP 300 24 NZC + P, where P = the maximum number of intersection points of any straight line with the
[
zone lines.
NPPE 10 The number of points identifying the plant target polygon.
NTARSR 1
The number of targets for which safety-related regions are to be specified.
\\-
MAXSAR 1
The maximum number of safety-related regions on any target surface.
4 e
l 1
A-2 i
-._-,y_
Y d (Plant North)
O Target Tornado Track S
R i
S Tm
=
X d
S Figure A-1.
Geometry for Determining Maximum Horizontal Windspeed, V(S )
7 O
0 3
'4 u,
V(S )i N
U T,
e
}B N
N J
m S
S i
Figure A-2.
Maximum Horizontal Windspeed as Vector Sum of Vortex Windfield Componer.ts O
A-3 l
and p
(,)
B = tan-I(S/T ) c (-w/2,x/2)
,Tm*O (A-4a) m
= w/2
,S20 m
(A-4b)
I
=0
= -z/2
,5<0 Equation A-1 holds for a translating cyclonic vortex with counterclockwise air flow; the convention is that U is negative for a radial inflow (as in Fig.
r A-2), positive for a radial outflow, and UO is positive for counterclockwise flow.
The value of I can be approximated from m
Tm = (R2-5) lSl 5 R/T (A-Sa) 2
= 7lSl/2 lSl > R/T (A-Sb) where R = R(z) = Ro + a(z - 33)
,05z56 (A-6a)
=Ro + o(6 - 33)
,z>6 (A-6b) is the radius to maximum tangential windspeed of the stationary vortex, with
-~g o = R(z = 33 ft), o is a slope parameter that is sampled for a given tornado R
(
/
uniformly from the interval (0,0.3); 6 = 400 ft, the approximate boundary layer thickness; y is the magnitude of the ratio of radial to tangential windspeeds at r = R ; and o
T = [1 + y2]I/2 (A-7)
The approximation of Eq. A-Sa is quite good and indicates that for of'fset distances near the vortex centerline the maximum horizontal windspeed is i
achieved near the core radius.
For lSl > R/T it can be shown that l
05T 5 ylSl and so Eq. A-Sb is reasonable, especially since for offsets m
l outside the core, v(5,T,Z) varies slowly with T.
However, to account for any error introduced, the calculated maximum horizontal windspeed of Eq. A-1 is increased according to j
V(S ) = 1.02 v(Sr,T,z) lSl 5 R/T (A-8a)
I
= 1.04 v(Sr.T.,z) lSl > R/T (A-8b)
Validation tests of this model will be discussed later in this appendix.
Letting z = ZTF(I) and obtaining U and UO from the tornado windfield r
l model, we can obtain estimates of the maximum windspeed that would be experienced at the target center and elevation of interest.
If this windspeed l
l v
A-4
s.
is less than the specified windspeed, the tower is assumed not to fail and the
[}
variable ITWIND(I) is assigned the value 0; if greater, tower failure is
\\ _/
assumed and ITWIND(I) is assigned the value unity, i.e.,
ITWIND(I) = 0 if V(S ) < WINDF(I)
(A-9a)
I 1 if V(S ) 2 WINDF(I)
(A-9b)
=
I A.3 Output Data Set for Postprocessor Analysis In order to perform the more involved scoring of multiple redundant targets required for the Limerick analysis, an output option to write the necessary parameters to logical unit 4 was added.
This output data set can be accessed after the TORMIS run is completed and analyzed using the post-processor described in Appendix B.
The variables written to this output data set and the formats used are given in Table A-2; the variables are defined in Table A-3.
In order to implement this output option, the user specifies the logical input variable ROUT = True, as described later in Table A-4.
The information written to this output data set consists of three records of general information, including the number of tornadoes simulated, the tornado F'-scale intensity levels, the number of safety-related targets, the tornado occurrence rates and the numbers of nonautomobile and automobile potential missiles assumed at the plant.
For each simulated tornado there is one record, identified by the value MI = 1 in column 2, that gives pertinent tornado characteristics and includes the integers ITWIND(1) and ITWIND(2) y whose values indicate whether or not the specified targets (cooling towers)
)
failed due to windspood exceedance durir.g thic tornado strike.
(J For each misr*1e that hits a safety-related target, a record is printed out giving information about the missile including its input position and velocity.
These records are identified by the value MI = 2 in column 2.
For every I-J-K target-event-zone combination for which there is a non-zero probability of target I being damaged to level J by missiles originating in zone K, a record is printed out using the identifier MI = 3 in column 2. A record is also printed out with MI = 4 in column 2 for every target-event combination that has a nonzero damage probability integrated over all zones.
Finally, at the end of the simulation run a record with IEND in coluons 2-5 is printed out to indicate the ond of the data set.
A.4 Additional Changes Several minor changes have been made to TORMIS to facilitate the I/O processing in the TORMIS-L version. These changes are highlighted in Tables A-4 and A-5.
(m)
A-5 V
TABLE A-2.
TORMIS-L OUTPUT DATA SET s
Record Variables Format 1
NUMTOR, NSAME, KTINT, INTEN NUMSAF, NZ 6Il0 2
OCCUR (I),
I=1,2,...,7 7E10.3 3
NNMIS, NNAUTO 2Il0 4
MI(=1), TWT, PSTR, UMAX, ITWIND(1),
I2, 3E12.4, ITWIND(2) 213 5
MI(=2), MSSET, LENGTM, IZ, IWALL, X1, Yl, I2, I4, F10.3, Zl, VX, VY, VZ, VE, NWT 2I4, 8E12.4 Record 5 is repeated for every missile history that results in an impact on a safety-related target during the current tornado history.
6 MI( = 3), I, J, K. PMNZ, ITNM I2, 3I4, E13.5, 18 Record 6 is repeated for every zone, K, that contributes a non-zero probability, PMNZ, of damaging target I to damage level J given the current tornado strike.
[~'h 7
MI( =4), I, J PMN, PMNS I2, 2I4, 4X
\\~s/
2E13.5 Record 7 is repeated for every non-zero probability, PMN, of damaging target I to level J by the potential missiles in all zones, given the current tornado strike.
Records 4-7 are repeated NUMTOR times, i.e.,
for each simulsted tornado. At the end of the entire simulation record 8 is output.
8 IEND IX, A4 E
Note: The DCB characteristics for this outputdata set are:
RECFM=VB, LRECL-130, BLKSIZE=2600.
I v
A-6
TABLE A-3.
DEFINITION OF OUTPUT VARIABLES
\\
Variable Description Units NUMTOR The number of tornadoes to be generated within each specified intensity classification.
NSAME The number of missile histories per tornado.
KTINT Lower value of T'-scale intensity tornadoes to be sampled; if KTINT=INTEN, only tornadoes from a single F'-scale are sampled.
INTEN Upper value of F'-scale intensity tornadoes to be sampled.
NUMSAF The number of the last safety-related target.
NZ The total number of missile origin zones.
OCCUR (I)
The tornado occurrence rate for F'-scale (yr-I tornadoes of intensity I in the plant mi-2) vicinity.
NNMIS The total number of potential missiles, less the automobiles, in the plant zones.
NNAUTO The total number of automobile potential missiles in the plant zones.
/si
(_,)
MI An integer that is used to indicate the type of record, according to the following convention:
MI-1, tornado characteristic record
[ TWT,PSTR....ITWIND(2)]
MI-2, missile record [MSSET LENGTH,...,HWT]
MI-3, zone probability record [I,J K,PMNZ,ITNM]
MI-4, ternado probability record [I,J.PMN PMNS)
TWT The variance reduction history wei ht for the F
current simulated tornado.
PSTR The tornado origin area for the current (mi2) simulated tornado.
UMAX The maximum horizontal windspeed of the (ft/sec) translating tornado at 33 ft elevation.
ITWIND(J)
An integer whose value indicates whether or not the Jth target specified for windepeed exceed-ance testing (i.e., cooling tower J. J=1 or 2) experiences horizontal windspeeds in excess of the specified windspeed, WINDF(J), at the specified height, ZTF(J), during passage of the current simulated tornado.
\\
I v
{
\\
4 TABLE A-3.
DEFINITION OF OUTPUT VARIABLES (Continued)
(v~\\
Variable Description Units MSSET The final missile subset number.
LENGTH The missile length.
(ft)
IZ The zone of origin of the missile, with IZ S NZ+NTARM, where NZ is the number of missile zones and NTARM is the number of structures that support missiles.
IWALL The wall number that is hit by the missile (NWALL in the normal TORMIS line printer output).
(X1,YI,Zl)
The coordinates of the impact point.
(ft)
(VX,VY,VZ)
The missile impact velocity components.
(ft/sec)
VE The effective impact velocity.
(ft/sec)
HWT The variance reduction missile history weight.
I The target number ISNUMSAF J
The damage level, where:
J-1, impact by penetrator missile with V 2 VDAM N
J-2, impact by penetrator missile
)
J-3, damage by penetrator missile to WTL s_,
thickness J=4, damage by penetrator missile to WTL+WTH thickness J-5, damage by penetrator missile to WTL+2*WTH thickness J-6, damage by penetrator missile to WIL+3*WTH J=7, impact by vehicle missile J=8, impact by vehicle missile with V 2 VAUTO(I)
J=9, impact by vehicle missile with V 2 VAUTO(2)
J-10, impact by vehicle missile with V 2 VAUTo( 3)
J=ll, impact by vehicle missile with V 2 VAUTO( 4)
K The missile zone of origir..
PMNZ The single-missile probability of damaging (yr-l) l target I to level J due to missiles in zone K given the simulated tornado strike.
l ITNM The number of potential missiles within the intersection of zone K and the tornado damage path.
l l
l'('~)
l
\\
\\~-
A-8 l
4 1
1 TABLE A-3.. DEFINITION OF OUTPUT VARIABLES (Continued) i Variable Description Units 1
PMN The single-missile probability estimate of (yr-l) damaging target I to level J due to all missiles at the plant, given the simulated j
tornado strike.
f.
PMNS The multiple-missile probability estimate of (yr-l) e damaging target I to level J due to all missiles at the plant given the simulated tornado strike.
i I
i i
1 e
I l
I r
j l
1 i
l I
r l
i i
l n
I-i i
I r
O A-9
TABLE A-4.
TORMIS-L PROGRAM INPUT s
\\m-Record No.
Vari. Lie E,nc Format Control Data 1
HEADER (I). I = 1,2,...
18 18A4 2
RINT, RECONI, RECONR, LCALC,' ROUT'uRDCF, 7( 9X, LI)
RVEFF 3
NUMTOR NSAME, KTINT, INTEN, FMAX SIl0 4
IX, IXL, IXM, IXK 4I20 If RINT = F Skip record 5 5
IMAX, JMAX, DOUT, RELERR, ABSERR 2Il0,3E10.3 If RECONI = F, skip record 6 6
NSSET, KNRC, NUMBO, KRIC, KI, KRITE 6Il0 If RECONR = F, skip record 7 7
AIRDEN, G, TIS, ALPHA,LZETA 5F10.0
~
Variance Reduction Data 8
IMWIND, INTPOS, IMIDIR, IMSPOS, IMINOR, (y,%)
IMMIS, IMHIGH 7(9X,L1)
I 9
IMRES, SDAM, IRR 3(9X,L1)
If IMWIND = F, skip record 10 10 RWHL F10,0 If ItiTPOS = F, skip record 11 11 YTSID 110.0 If INTDIR = F, skip record 12 12 TDIRIF(I)
I =
1,2,...,8 8F10.0 If ININO2 = F, skip record 13 13 BETA F10.0 i
If IMMIS = F, skip record 14 14 CDFMI(I). I = 1,2,...,NSSET-1 8F10.0 If IMMIGH = F, skip record 15 15 ZIMR F10.0 If IMRES = F, skip record 16 I
A-10 I
1 TABLE A-4.
TORMIS-L PROGRAM INPUT (Continued)
Record i
No.
Variable Name Format 16 IMPSIN, FIMR Il0, F10.0 If SDAM = F, skip record 17 17 NUMDAM, FRACD Il0, F10.0 If IRR = F, skip record 18 18 PKILL F10.0 Tornado Strike Data i
19 RETOR, AREGN 9X, L1, F10.0 20 OCCUR (I)
I = 1,2,...,7 7E10.3 21 WINDC(I). I = 1,2,...,6 6Y10.0 If RETOR = F, read record 22, then skip to record 29 If RETOR = T, skip record 22 22 REGION Il0 1
23 TRANSL( I), I - 1,2,...,6 6F10.0 24 TRANSW(I), I =
1,2,...,6 6F10.0 d
25 TORDIR(I), I = 1,2,...,8 8F10.0 26 PWC(I,J), J = 1,2,3,4; I = 1 4F10.0 Repeat record 26 for I = 2,3,4 27 PL(I,J), J = 1,2,...
5; I = 1 5F10.0 Repeat racord 27 fer I = 2,3,4,5 l
28 PW(I,J,K), K = 1,2,...,5; J = 1; I = 1 5F10.0 Repeat record 28 for J = 2,3,...,6; I = 2,...,5 Plant Data 29 REDAM, ISCORW 2(9X L1) 30 NZ, NZC, NZCP, NPPE 4Il0 l
31 XZC(I), I = 1,...,NZC 8F10.0 32 YZC(I), Z = 1,...,NZC 8F10.0 33 LCONZ(I,J), J = 1,2,...,5; I = 1 SIl0 Repeat record 33 for I = 2,3,...,NZ 34 XPE(I), I = 1,...,NPPE 8F10.0 m
A-11
-u-L
.1!._
TABLE A-4.
TORMIS-L PROGRAM INPUT (Continued)
\\,._
/
Record No.
Variable Name Format 35 YPE(I), I =
1,...
NPPE 8F10.0 36 XCO, YCO, RTO, ZS, NORTH, XCIT, YCIT 7F10.0 37 NUMTAR, NTAR, NTARM, NUMSAF, MTARA, MTARB, NTARSF, MAXSAF 8Il0 38 TYPTAR(I), XTR, YTR, ZC(I), k'X, WY, WZ, THETA (I), I=1 Il0,7F10.0 Repeat record 38 for I = 2.3....NUMTAR 39 MTL( K)., STRENG(K), WTL(K), WTH(K),
NSAF(K), K = 1 Il0,3F10.0,Il0 If NSAF(K) = 0, skip record 40 40 XLS(M,L), YLS(M,L), WXSAF, WYSAF, L = 1 4F10.0 Repeat record 40 for L = 2,3,...,NSAF(K)
Repeat records 39 and 40 for K =
2,3,...
NTAR 41 NFAIL Il0
.If NFAIL 1 0, skip; record;42 42 ITF(I),1WINDF(I),~ ZTF(I),LI=1 Il0,2F10.0 Repeat recordi42_if NFAIL-2 If REDAM = F, skip record 43 43 IDAMC, KB), K5RL, RS, CUW, ER, WUW Il0,6F10.0 44 NMZ(I), I - 1,2,....NZ 8F10.0 If IMSPOS = F, skip record 45 45 IMNMZ(I), I = 1,2,...,NZ 8F10.0 If NTARM s 0, skip records 46-48 46 NTART(I), I = 1,2,....NTARM 8IiG 47 NMS(I), I =
1,2,...
h' FARM 8F10.0 i
l If IMSPOS = F, skip record 48 l
48 IMNMS(I), I = 1,2,....NTARM 8F10.0 i
Missile Data 49 REMIS 9X,L1 50 VAUTo(I), I = 1,2,3,4 4F10.0
(
l
%J A-12
TABLE A-4.
TORMIS-L PROGKAM INPUT (Continued) p k,,)
Record No.
Variable Name Format If REMIS = F, skip records 51-54 51 NSET, LKEY 2Il0 52 MTRANS(I,J), J = 1,2; I =
1,2,...
NSSET 16I5 53 D(I), W(I), AMIN (I), VDAM(I), I = 1 4F10.0 54 LODMIN(I), LODM(I) LODS(I) LODMAX(I),
I=1 4F10.0 Repeat records 53 and 54 for I = 2,3....,NSSET If IMPSIN < 1, skip record 55 55 MFMIN, MFMAX, VEMIN, VFMAX 4F10.0 If RCDF = T, skip record 56 56 ICDFMZ(K), ! K - =.1,'2,... NSSET,..IE= I!
8I10 Repeat record 56 for I = 2,3,...,NZ If RCDF = F, skip record 57 57 CDFMZ(I,K), K = 1,2,....NSSET-1; J = 1 8F10.0
(T Repeat record 57 for I = 2,3....,NZ I
58 ZSMIN(I,K),1, ZSMAX(I,K)_,11:K i= 71,2,3,'4; ;I = :1 8F10.0 59 ZSMIN(I,K), ~-ZSMAX(I,K)',T K f= r 5,6,...,NSSET; I =.1 8F10.0 Repeat lines 58 and 59 for I =
2,3,...,NZ If NTARM $
0, skip records 60-63 If RCDF = T, skip record 60 60 ICDFMS(K);;,K =21,2,...~,NSSET;;1;= 1 8Il0 Repeat record 60 for I 2,2,....NIAT.M l
If RCDF = F, skip record 61 61 CDFMS(I,K), K = 1,2,...,NSSET-1; I = 1 8F10.0 l
Repeat record 61 for I = 2,3,...,NIARM 62 ZSSMIN(I,K)',- ZSSMAX(I,K),iK;= f1',2,3,4;
~
Ii= f.1::r 8F10.0 63 ZSSMIN(I,K),1ZSSMAX(I;K),i-K.[= ;5,6?... ;NSSET; IL=il 8F10.0 Repeat records 62 and 63 for I = 2.3....,NTARM im t
)
Q A-13
TABLE A-5.
DEFINITION OF INPUT VARIABLES FOR TORMIS-L CODE
[\\
U Name Identification Units control Data HEADER (I),
Literal field for title and run information.
I-1,17 HEADER (18)
The characters LEND are put in column 69-72 for output to the data set for post processor analysis (used only if ROUT = T).
RINT Logical variable; integrator variables are read in if T, default values used if F.
RECONI Logical variable; integer control variables are read in if T, default value used if F.
RECONR Logical variable; real control variables are read in if T, default values used if F.
LCALC Logical variable; if T, the output P(A) tornado origin areas are multiplied by the occurrence rates; if F, the P(A) are as described for TORMIS.
ROUT Logical variable; special tornado and history fx
(
results written to logical unit 4 if T, not
\\
written if F.
l RCDF Logical variable; if T, CDFMZ and CDFMS are read in; if F, ICDFMZ and ICDFMS are read in and CDFMZ and CDFMS are calculated by the code.
RVEFF Logical varable; if T, the V ' > VDAM event is i
scored on effective missile impact velocity, V '; if F, the Vi) VDAM event is ccored on i
total missile velocity at lapset, V.
i NUMTOR The number of tornadoes to be generated within each-specified F'-scale intensity classification.
NSAME The number of missile histories per tornado.
KTINT Lower value of F'-scale intensity tornadoes to be sampled; if KTINT=INTEN, only tornadoes from a single F'-scale are sampled.
INTEN Upper value of F'-scale intensity tornadoes to be sampled.
f N/
A-14
i
~
IABLE A-5.
DEFINITION OF INPUT VARIABLES FOR TORMIS-L CODE (Continued)
(Q
~
Name Identification Units FMAX The maximum F'-scale tornado intensity level for the site.
IX,IXL, Random number generator input integers (must be IXM,IXK odd integers).
IMAX The maximum number of time steps allowed before automatic termination of a trajectory computa-tion.
Default value is 400.
JMAX The number of time steps between missile orientation updates.
Default value is 10.
DOUT The integration time step.
Default value is (sec) 0.01.
RELERR The relative error convergence criterion for the integration routine.
Default value is i
0.001.
ABSERR The absolute error convergence criterion for the integration routine. Default value is 0.001.
'N NSSET The number of missile subsets.
Default value b
is 7.
KNRC A key to indicate whether or not the missile spectrum is to be limited to the seven NRC missiles, where:
1, NRC missile spectrum al, generalized missile spectrum ar described in Ref. 1.
Default value is 1.
. NUMB 0 The number of times a mias11e is allowed to hit the ground before the history is terminated (21).
Default value is 1.
KRIC Integer key specifying whether or not the missile ricochets, where:
0, no missile ricochet n, missile ricochets n times before history termination.
Default value is' O.
N/
A-15
TABLE A-5.
DEFINITION OF INPUT VARIABLES FOR TORMIS-L CODE (Continued)
O Name Identification Units
- KI Integer key to specify damage options; where:
0, V)VDAM only event evaluated l
1, damage model also utilized.
Default value is 1.
KRITE Output print option:
1, Final summary printed 2, Final summary and tornado summaries printed 3 Final summary, tornado summaries, and individual missile summaries printed 4, Final summary and history results that end in impacts on safety-related target printed The negctive values of the integers 1, 2, and 3 also result in similar printout to output device 1.
Default value is 3.
AIRDEN The air density used for the aerodynamic force (slugs /
calculation.
ft )
2 G
The value of the acceleration due to gravity.
(ft/sec )
TTS The value of the standard normal variate with i
cumulative probability level 1=a/2 for estab-i
[sl lishing the two-sided 1-a confidence interval
\\--
l on P(AlI )j.
Default value is 1.96.
3 I
ALPHA The tornado windfield parameter a.
ZETA The tornado windfield parameter C.
Variance Reduction Data I.VWIND Logical variable; if I, importance scmpling on windspeed is employed.
.lMIPOS Logical variable; if T, importance aampling on tornado offset position fres a trunested normal function is eeployed.
IMTDIR Logical variable; if I, importance sampling on i
tornado direction according to TDIRIF is used.
IMSPOS Logical variable; if T, stratified sampling on missile initial position according to INNMZ and IMNMS.
O A-16
~.
TABLE A-5.
DEFINITION OF INPUT VARIABLES FOR TORMIS-L CODE (Continued) pq.,T Name Identification Units IMINOR Logical variable; if T, importance sampling on missile initial azimuthal angle is employed.
IMMIS Logical variable for importance sampling on missile type selection; if F, no importance sampling and missile subset (IA) selected from cumulative distribution function (CDFMZ (IZ,IA)), where IZ= zone number; if T, missile subset (IA) selected from importance cumulative distribution function (CDFMI (IA)).
IMHIGH Logical variable; if T, importance sampling on missile initial (injection) height selected from trapezoidal density function between minimum and maximum storage heights; if F, missile injection height sampled uniformly.
IMRES Logical variable, used only when IMPSIN23; if T, importance sampling on missile horizontal restraining force (horizontal restraint selected from trapezoidal density function).
SDAM Logical variable; if T, splitting is employed s
[G
]
at last reorientation before hitting a target.
IRR Logical variable; if T, Russian roulette is employed and missile histories are terminated with probability "PKILL."
RWHL Ratio of importance pdf on tornado windspeed at high end of interval to that at low end.
YTSTD Importance sampling parameter on tornado off-set.
The standard deviation of the truncated normal pdf equals YISTD*Z2, or YISTD*R!nX, whichever is larger.
Z2 is the projection af the plant safety envelope.
TDIRIF(J)
Tornado direction importance distribution func-tion by octant from East (J=1) to SE (J=8).
BETA A number greater than zero and less than or equal to one, which specifies the extent to which missile initial orientations which tend to be favorable to vertical missile injection will occur, where B=1 implies uniformally m-l A-17 i
-. ~.
_=
TABLE A-5.
DEFINITION OF INPUT VARIABLES FOR TORMIS-L CODE (Continued) pQ a
Name Identification Units random initial orientation (no importance sampling) and the extent of importance sampling increases as 8 decreases.
Default value is 1.
CDFMI(I).
The modified cumulative distribution function I-1,2,...,
describing the number of missiles to be sampled NSSET-1 assuming importance sampling on missile type (subset), where CDFMI(I)-CDFMI(I-1) = the probability with which missiles are to be sampled from subset I.
ZIMR Ratio of high to low probabi.lity density values of trapezoidal importance sampling function on missile initial height.
IMPSIN An integer which selects the injection sampling scheme to be used, where:
0, maximum transport injection mode
>0, first exceedance mode injections.
For first exceedance mode, IMPSIN is an importance sampling key, where:
1 no importance sampling 2, importance sampling to force selected i
restraint force to be less than maximum injection force, FHMAX, if FHMAX)HFMIN, the minimum horizontal restraint 3, importance sampling to select horizontal restraint force from trapezoidal pdf defined between NFMIN and HEMAX 4, combination of both importance sampling options described in 2 and 3 above.
Default value is 0.
FIMR Ratio of h4.gh to low probability density values of trapezoidal importance sampling density function on missile horizontal restraining l
force.
NUMDAM The number of subhistories for splitting on missiles which hit structures with velocities t
above a cutoff velocity.
FRACD The fraction of the damage velocity for a given missile subset, VDAM(MSSET), which establishes the cutoff velocity for splitting on missiles that hit targets.
(
V)
A-18 j.
i
IABLE A-5.
DEFINITION OF INPUT VARIABLES FOR TORMIS-L CODE (Continued) g-O Name Identification Units PKILL The probability of history termination for Russian roulette conditions.
Tornado Data RETOR Logical variable; if T, region-dependent tornado parameter cumulative distribution functions are read in;~if F, default CDF's used.
2 AREGN The area of the tornado region used to (mi )
determine the occurrence rates.
OCCUR (J)
The tornado occurrence rate for F'-scale (yr tornadoes of intensity J per year per square mi-2) mile in the plant vicinity.
WINDC(J)
Upperbound windspeed correlation to the Jth (ft/sec)
F'-scale intensity tornado.
REGION An integer that specifies which of the four tornado regions the r efault tornado data should l
be taken from, where:
REGION =1 specifies f-s
(
)
Region A. REGION =2 specifies Region B, REGION =3 l
specifies Region C, and REGION =4 specifies Region D.
This parameter is not used if RETOR=T.
TRANSL(J)
Upperbound of FPP tornado path length scale for (mi) the Jth PL rating.
TRAK!W(J)
Upperbound of FPP tornado path width scale for (ft) the Jth Py rating.
TORDIR(J)
Tornado direction distributicn function by octant from East (J=1) counterclockwise to SE (J=8).
PWC(I,J)
The path width correlation to local F-scale, i
normalized by row.
l l
PL(I,J)
Distribution function path length correlation for I intensity tornadoes by J path width classifications.
PW(I,J,K)
Distribution function path width correlation for I intensity tornadoes and J path length classification by K path width classifications.
m l
A-19
~-
l
TABLE A-5.
DEFINITION OF INPUT VARIABLES FOR TORMIS-L CODE (Continued) k-m Name Identification Units Plant Data REDAM Logical variable; if T, the damage variables IDAMC, KB1, KBRL, RS, CUW, ER, and WUW are read in; if F, default values are used.
ISCORW Logical variable; if T, target scoring is by wall; if F, target scoring is by structure.
NZ The total number of missile origin zones.
NZC The total number of points defining all the zones.
1 NZCP A number (>NZC) used for dimension sizes resulting from the tornado path intersection with the predefined zones. To determine NZCP, evaluate the maximum number of intersection points (P) of a line drawn through the missile origin zones. Then hZCP2NZC+4P.
NPPE The number of points that define the polygon composing the plant safety envelope.
)
XZC(J)
The x-component in the plant frame of the Jth (ft) zone point.
YZC(J)
The y-coordinate in the plant frame of the Jth (ft) zone point.
LCONZ(I,J)
A connectivity array in which elements of row I specify in a sequential order the points defining the Ith zone.
XPE(J),
X and Y coordinates of the Jth point defining (ft)
YPE(J) the plant safety envelope (in sequence).
XCO,YC0 Plant cartesian coordinates of the center of (ft) j the major target circle.
RTO Radius of the major target circle.
(ft)
ZS The height (above reference) at which the base (ft) l' of the tornado tracks through the plant area.
NORTH
-The angle, measured CCW, from plant north to (rad) true north, e
hs_J A-20 l
l I
t
~
TABLE A-5.
DEFINITION OF INPUT VARIABLES FOR TORMIS-L CODE (Continued)
(3 O
Name Identification Units XCIT,YCIT Plant cartesian coordinates of the reference point in the target cluster for importance sampling on tornado offset.
NUNTAR The total number of target structures.
NTAR The total number of target surfaces.
NTARM The number of target structures supporting potential missiles on their top surfaces.
NUMSAF The number of the last safety-related target.
MTARA,HIARB The target numbers (structure numbers, if ISCORW=F, wall numbers of ISCORW=T) for which union and intersection damage probabilities are desired.
If either or both are zero, no union and intersection calculations are made.
NTARSF The number of target walls for which subareas are to be specified.
MAXSAF The maximum number of subareas which any one l
wall contains.
l ps TYPIAR(I)
An integer which specifies the type of the Ith l
g l
target structure, as follows:
1, Rectangular parallelepiped parallel to x-y axes 2, Rectangular parallelepiped rotated through THETA (I) from the x-axis 3, Vertical cylin6er with hemispherical top 4, Vertical cylinder with flat top 5, Upper hemisphere.
XTR,YTR The x-and y-coordinater of the lower left-(ft)
[
hand corner of target wall 2, if TYPTAR=1 or 2 L
or the coordinate: of the center of the target, if f7PTAR=3, 4, or 5.
l ZC(I)
The elevation of the base of the Ith target (ft) cylinder.
1 WX The length of walls 2 and 4 of the target (ft) structure, if TYPTAR=1 or 2 or the radius of the structure, if TYPTAR=3, 4, or 5.
)
i
- x__,
A-21
[
TABLE A-5.
DEFINITION OF INPUT VARIABLES FOR TORMIS-L CODE (Continued)
O Name Identification Units WY The length of walls 1 and 3 of the target (ft) structure, if TYPTAR=1 or 2; undefined if TYPTAR=3, 4, or 5.
KZ The height of wall 1 of the target structure.
(ft)
THETA (I)
The CCW angle through which target I of type (rad) 1 (THETA =0) or 2 (0(THEIA<w/2) has been rotated from the x-axis.
4 MTL(K)
An integer which specifies the wall material of the surface numbered K=NWALL(I,J), where:
(0, imaginary surface 0, concrete 1
steel.
STRENG(K)
The concrete strength of wall K or the steel (psi) yield strength of wall K.
WIL(K)
The lower value of wall thickness used for (in.)
damage assessment.
WTH(K)
The increment of wall thickness used for (in.)
7- ~
damage assessment.
l NSAF(K)
The number of subareas on wall K.
XLS(M,L)
The x-coordinate of the lower left-hand corner (ft) of the Lth subarea on the Mth wall which contains subareas.
YLS(H,L)
The y-coordinate of the lower left-hand corner (ft) of the Lth subarea on the Mth wall which contains subareas.
WXASF The width of the subarea.
(ft)
WYSAF The height of the subarea.
(ft)
IDAMC-
-A damage criterion integer for concrece i
barriers, where:
0, acabbing analysis performed l
1, perforation analysis performed.
Default value is 0.
KB1 Concrete penetration coefficient in NDRC model.
Default value is 163.0.
KBRL Steel barrier penetration coefficient in BRL i
model.
Default value is 1.0.
l (T
Q A-22 i
i I
~
..n n -
,,,,-w-,,--.,-n.,
TABLE A-5.
DEFINITION OF INPUT VARIABLES FOR TORMIS-L CODE (Continued)
O Name Identification Units RS Concrete acabbing thickness reduction factor.
Default value is 1.0.
CUW Concrete unit weight.
Default value is 150.0.
(lb/ft3)
ER Coefficient of restitution (ER$1.0).
Default value is 1.0.
WUW Wood unit weight.
Default value is 40.0.
(lb/ft3)
NMZ(I)
The total number of missiles in zone I.
IMNMZ(I) the number of missiles specified in zone I for sampling on missile initial position (used only if IMSPOS=T).
NTART(I)
The number of the Ith target structure which contains potential missiles on top, where I=1,2,...,NTARM.
NMS(I)
The number of potential missiles on target structure NTART(I).
IMNMS(I)
The number of missiles specified on structure I g-g for sampling on missile initial position (used i
only if NTARM)0 and IMSPOS=T).
y Missile Data REMIS Logical variable; if F, missile data for NRC spectrum are used; if T missile data are read in.
VAUTO(I)
The Ith automobile velocity for target (ft/sec) scoring, I-1,2,3,4.
NSET The number of missile sets.
LKEY A key which indicates how siasile length-to-
[
diameter ratio (LOD) is selected, where:
<0, LOD =LODM, where LODM is input separately
=0, LOD selected from uniform density function between LODMIN and LODMAX f
>0, LOD selected from truncated normal density function between LODMIN and LODMAX with mean LODN and standard deviation LODS.
l l
i-G A-23 l
t i
I
TABLE A-5.
DEFINITION OF INPUT VARIABLES FOR TORMIS-L CODE (Continued) s Name Identification Units MTRANS(I,2)
A missile transformation array. The elements of the first column (I,1) define the set number for subset I; the second column, (I,2), defines the consecutive storage set position, not exceeding NSET.
D(I)
The characteristic diameter of missile subset I.
(in.)
W(I)
The weight per unit length of missiles in (1b/ft) subset I.
AMIN (I)
The minimum impact area of missiles in subset (in.2)
I.
VDAM(I)
The input velocity for subset I for the (ft/sec) comparative impact velocity definition of damage success.
LODMIN(I)
The minimum length to diameter ratio (LOD) of missiles in subset I.
LODM(I)
The mean value of the truncatea normal density function on LOD for subset I.
)
LODS(I)
The standard deviation of the truncated normal density function on LOD for subset I.
LODMAX(I)
The maximum value of LOD for subset I.
HFMIN Lower value, as multiple of missile weight, of the interval over which horizontal restraining force is chosen for N
nissile population (used only if IMPSIh>3).
HFMAX Upper value, as eultiple of missile weight, of the interval over which horizontal restraining force is chosen for F
missile population (esed only if Ih'PSIN)3).
VFMIN Lower value, as multiple of missile weight, of the interval over which vertical restraining force is chosen for N
missile population (used only if IMPSIN)3).
VFMAX Upper value, as multiple of missile weight, of the interval over which vertical restraining force is chosen for N
missile population (used only if IMPSIN)3).
A-24
TABLE A-5.
DEFINITION OF INPUT VARIABLES FOR TORMIS-L CODE (Continued)
~s (N
s Name Identification Units ICDFMZ(K)
The number of missiles in subset K sampled K=1,2,...,
from zone I (used only if RCDF = False).
The NSSET cumulative distribution function CDFMZ is constructed from ICDFMZ in the code.
CDFMZ( I.K)
The cumulative distribution function on I=1,2,....NZ; missile subset for missiles in zone I where K-1,2,....
CD^ MZ(I,K)-(CDFMZ(I K-1) = the relative r
NSSET-1 fraction of all missiles in zone I which are in missile subset K (read in only if RCDF = True).
ZSMIN(I K),
The minimum and maximum assumed storage (ft)
ZSMAX(I,K) heights, respectively, within zone I of missiles in subset K.
ICDEMS( K),
The number of missiles in subset K to be K=1,2,...,
sampled from structure number I (used only if NSSET RCDT = False).
CDFMS(I,K)
The cumulative distribution function on missile I-1,2,...,
subset, K, for missiles originating on KTARM; structure I (read in only if RCDF = True).
i K=1,2,....NSSET-1
%.J ZSSMIN(I K),
The minimum and maximum assumed storage (ft) i ZSSMAX(I,K) heights, respectively, of missiles within subset K above the top of structure I.
l 7-~,)
tv A-25 l.
A.4.1 Occurrence Rate Calculation
)
An option has been added that automates the occurrence rate s-calculation in the TORMIS-L code.
The logical input variable LCALC is used to select the option.
If LCALC = True, the output P(A) tornado origin area values are multiplied by the occurrence rates; if False, the output P(A) values are as described for TORMIS in Ref. 18.
If LCALC = True, it is also necessary to input the variable AREGN, the area of the tornado region used to determine the occurrence rates.
A.4.2 Tornado Windfield Profile Parameters In order to allow sensitivity studies of the tornado windfield, the parameters ALPHA and ZETA (a and () of the windfield model have been made into optional input variables.
They are assigned the default values a = 10, G = 25 by the TORMIS-L code; if values other than these are desired, it is necessary to specify RECONR = True in record 2 and input the desired values for a and C in record 7.
A.4.3 Missiles Originating From Wind-Failed Structures Another change was made in creating the TORMIS-L code for injecting missiles above structures that are subject to the windspeed exceed-ance test described previously in Section V of this appendix.
In the missile selection subroutine, all structure origin missiles are subject to the following test: if the missile is above a structure for which the windspeed
'g exceedance test was performed and the structure did not fail during this s,)
tornado history (ITWIND = 0), then the chosen missile is disregarded and a new missile is chosen.
This avoids injecting concrete missiles from the cooling tower shell for those tornadoes that do not cause cooling tower failure due to windspeed exceedance.
A.4.4 Cumulative Distribution on Missile Type In order to simplify the inputting of missile distribution data, an option was introduced using the logical variable RCDF.
If RCDF = False.
the number of missiles in each subset is input in integer form for each zone or structure and the cumulative distribution functions, CDFMZ and CDFMS, are l
calculated in the code; if RCDF = True, CDFMZ and CDFMS are input as described in Ref. 24.
This change allows the missile distribution data, e.g., from Tables IV-Sc and IV-6c, to be input directly withoat the user having to compute the cumulative. distribution functions.
i A.4.5 Effective Velocity Exceedance l
The TORMIS code scored a damage event based on a missile impacting a target with velocity, V, greater than a specified velocity, VDAM, for each i
missile subset. An option has been introduced that allows the user to score l
1 i g A-26
/
this damage event on the basis of effective missile velocity, V ', being i
greater than VDAM. The logical input variable RVEFF is used to specify the option according to: RVEFF = True, Vg' ) VDAM; RVEFF = False, Vi) VDAM.
A.4.6 Injection Heights The injection heights above grade elevation, ZSMIN and ZSMAX and above structures, ZSSMIN and ZSSMAX, are input in feet in the TORMIS-L version instead of inches as in TORMIS. Also, in the TORMIS-L version the injection heights are input for each final missile subset, for consistency with the specification of other missile data, rather than by missile aerodynamic set as in the original TORMIS.
A.5 TORMIS-L Code Validation The modifications to TORMIS described in this appendix have been vali-dated by independent means.
In the first place, the changes were validated by comparing the results of~a sample problem run with the TORMIS-L code to the same sample' problem run with a previously validated version of TORMIS. The results were identical.
The values of a and C are printed out so that the user can verify that either the default values or the intended values were used. The change regarding noninjection of missiles above structures that did not fail was also verified. The code was run.before the change was implemented for a sample O '
problem in which arbitrary missiles from two tall structures were injected and hit structures even though only one tall structure failed due to windspeed exceedance. The code was then modified and the sample problem rerun. This time, only missiles from the tall structure that did fail resulted in target impacts.
The inputting of missile distributions by missile numbers instead of cumulative distribution functions was easily checkad by comparing the output CDFMZ and CDFMS values calculated by the TOP. MIS-L code to the known values calculated by hand _fer previous samplo pechless. The V ' )JVDAM change vas i
validated by reviewing individual missile impact output lines from the code before and after the change was made and verifying that the Vi) VDAM and V' ) VDAM averts.wers properly scored.
i l
The windspeed exceedence calculat. ion was validated in the following The track position for maximum windspeed, T., was calculated E
manner.
according to Eqs. A-5 and V(S ) was determined from Eq. A-1.
Values of I
intermediate variables R, T, r, and S were printed out and checked by hand To demonstrate that V(S ) was indeed the maximum horizontal calculations.
I windspeed during storm passage, an iterative calculation was performed to scalculate the not horizontal windspeed at the target offset and elevation for ten tornado track positions T on each side of T (at 20-ft intervals). These calculations verified that for all four tornadoes tested, the V(S ) calculated I
from Eq. A-1 was greater.than the maximum v(S,T,z).
I O
A-27 b
I 2
w y,
4 2
-e---,-w...-
9
--ip
.y,.m.,
,- ~
.,,,=y,-wp.-%.-mren., w 3, -, m w e-wy--,--emm----,w,
,wg,e,yy-,-e-e e-y,-,----+,e,e,-,<-n-a weweg
.=. = - - -
APPENDIX B d
TORSCR-L POSTPROCESSOR DOCUMENTATION B.1 Introduction TORSCR (for TORais Scoring) is a FORTRAN'77 program written to analyze the output data set produced by TORMIS-L, as described in Appendix A.
The format of the input data set is given in Table A-2.
TORSCR computes proba-bilities for the compound events of interest, which dafine damage to the spray pond network and cooling tower facilities.
B.2 TORSCR's Operation 10 or 1024 possible For the ten spray network and cooling tower targets, 2 outcomes define the sample space.
By subsetting to the largest compound (and all-inclusive) event, this number reduces to 756 elementary outcomes for which probabilities need to be computed. Since equations for calculating damage probabilities from target hits (as opposed to misses) were the only equations feasible, much processing was required to produce the needed probabilities of elementary outcomes, which are combinations of both hits and misses.
The following subsections illustrate the approach.
B.2.1 Two Examples f~A
( ),
Consider the following sample space composed of intersections of three events A, B, and C, each representing a hit on one of three targets (see Fig. B-1).
The intersections are the elementary outcomes composing the sample space, S.
For the three events A, B, and C, there are 23 elementary outcomes in the sample space.
We can represent all possible elementary outcomes as rows of a matrix of l's and O's which indicate hits and misses, respectively, on the targets A, B, and C.
'Next consider a sample space of four events, each representing a hit on 4
one of leur targets, and 2 elementary outcomes, each representing a specific combination of hits and misses on those four targets (see Fig. B-2).1 One row of the associated matrix represents one elementary outcome in the sample spaca.
Suppose we want to corpute the probability of outcoce 7 using only the probabilities for A, B, C, and D (hits) and not the probabilities of their complements (misses). We are limited to using intersections or compound events that contain no complements of A, B, C, and D; that is 3 For ease of illustration, outcomes 6 and 11 are not shown in the accom-panying Venn diagram, Fig. B-2(a).
/N.
4
\\.J' B-1
(
)
A Outcome A
B C
1.
0 0
0 AR 1.
2.
1 0
0 AE
- 8. 4-3.
0 1
0 ABC 4.
O ABf 5.
3.
7-5.
0 0
1 ABC C
B 6.
1 0
1 AFC 7.
0 1
1 ABC 8.
I 1
1 ABC N
)
(a) Venn Diagram (b) Outcome Table Figure B-1.
Three Event Example S
Outcome A
B C
0 or l
1.
0 0
0 0
AE6 2.
1 0
0 0
ABCD 3.
0 1
0 0
KBM l
4.
I 1
0 0
ABG A
B 27 4.
3.
)
5.
0 0
1 0
ABCD 6.
1 0
1 0
AECU g
i-
- e. f/
7.
0 1
1 0
ABCD 0.
l I
8.
I 1
1 0
ABCD l
C 1.
0 0
E 11.
0 1
0 1
ABE0 12.
I 1
0 1
ABCD 13.
0 0
1 1
ABCD 14.
1 0
1 1
AECO 15.
0 1
1 1
ABCD 16.
I 1
1 1
ABCD l
(a) Venn Diagram (b) Outcome Table Figure B-2.
Four Event Example
~B-2
_ - _ _. _. _ - _ _ _ _ _ _.... -. _. ~,. _. - _. _.. _ _ _. _.. _ - - - - - _ _ -
P(7) = P(A3CD) = P(BC) - P(ABC) - P(BCD) + P(ABCD)
= P(BC) - [( PABC) - P( ABCD) ] - (P(BCD) - P( ABCD) ] - P( ABCD)
= P(BC) - P(8) - P(15) - P(16)
(B-1)
B.2.2 Order of Calculations Equation B-1 demonstrates how the probabilities of the elementary outcomes are calculated in the postprocessor. A 756 x 11 matrix is generated to store those outcomes of interest, with the first column containing a count of targets missed for that outcome and the remaining columns indicating a hit or miss on targets 1 through 10.
The rows are then ordered ascendingly by the values in the first column.
This technique places outcomes containing the fewest misses first in order of calculation.
After declarations and initializations, TORSCR reads the TORMIS-L generated data stream.
TORSCR then generates the matrix of elementary outcomes. Table B-1 illustrates the initial segment of this outcome matrix.
The postprocessor runs through the matrix of O's and l's from top to bottom calculating an upper probability limit for each elementary outcome, P*ow( j ).
For the example in Fig. B-2, this corresponds to computing P(BC) as a preliminary step to computing P(ABCD).
These event probabilities are then adjusted down to exact probability estimates as per Eq. B-1, by subtracting the probabilities of appropriate elementary outcomes, which are computed from:
j-1 Prow (j) = Prow (j) - 1 I(1,j) P ow(i)
, j =
1,..
756 (B-2) r i=1 vhere Prow (j) is the upper limit of Prow (j) based only on the probabilities associated with targets hit in outcome (j), ignoring probabilities associated with the targets missed.
I(i.j) is an indicator function that is 1 only when outcome (1) has hits on the same targets as in outcome (j) and fewer misses; I(i j) = 0 otherwise.
Finally, the probabilities of elementary outcomes (which are disjoint events) are summed, weighted, averaged and weighted again to produce proba-bility estimates for the ccmpound events of interest, together with their variance estimatos.
A listing of TORSCR is given in Table B-2.
The output listing for the combined F-scale analysis for the missile entrance criteria is given in Table B-3.
\\
B-3
TABLE B-1.
BEGINNING SECTIONS OF OUTCOME MATRIX 3
d 1
1 8
1 1
1 1
1 3
1 1
1 1
1 8
1 1
4 1
1 1
1 1
1 1
1 1
1 3
1 1
0 1
0 1
1 1
1 4
1 1
e 1
1 1
1 1
1 1
1 3
g g
g g
g g
g g
g 1
1 1
1 1
1 1
1 1
4 1
3 g
g 1
1 g
1 1
1 1
g 1
1 1
1 1
1 8
1 1
1 1
3 e
1 1
1 e
1 1
1 1
8 1
1 1
1 1
1 1
1 1
1 3
0 1
1 1
1 1
1 8
1 1
1 1
1 1
1 1
8 1
1 1
3 1
e 1
1 0
1 1
8 1
1 1
1 1
1 1
0 1
1 1
1 1
3 3
e g
1 g
g g
g g
1 1
1 1
1 1
1 1
1 1
1 8
3 1
1 0
9 1
1 1
1 1
0 1
1 1
1 8
1 1
1 1
1 1
3 3
1 e
1 1
1 1
1 0
1 1
1 1
1 1
1 1
1 8
1 1
3 1
1 1
1 8
8 1
1 1
4 1
0 1
1 1
1 1
1 1
1 1
3 1
e e
1 1
1 1
1 0
1 2
1 1
1 1
1 1
1 1
8 8
3 8
1 1
1 8
1 1
0 1
1 2
1 1
1 1
1 1
8 1
9 1
3 1
1 e
1 e
8 1
1 1
1 2
1 1
0 1
1 8
1 1
1 1
3 1
1 1
1 1
1 1
0 9
4 2
1 1
1 1
1 1
8 8
1 1
3 1
e 1
1 8
9 1
1 1
1 2
8 1
1 1
1 1
1 8
1 1
3 8
1 9
1 0
1 1
1 1
1 2
e 1
1 0
1 1
1 1
1 1
3 1
0 0
1 S
1 1
1 1
1 2
1 8
1 1
1 1
1 8
1 1
3 1
8 1
8 1
1 1
1 1
8 2
1 1
1 0
1 0
1 1
1 1
3 9
1 0
1 1
1 0
1 1
1 2
1 0
0 1
1 1
1 1
1 1
3 1
0 0
1 1
1 8
1 1
1 2
1 0
1 8
1 1
1 1
1 1
3 0
1 1
e 1
1 1
1 1
0 2
1 1
0 1
1 1
1 8
1 1
3 8
1 1
1 1
1 0
1 1
0 2
1 1
1 1
1 0
8 1
1 1
3 1
8 1
1 1
1 8
1 1
8 2
8 1
1 1
1 1
1 1
1 0
3 0
1 1
1 0
4 1
1 1
1 2
1 1
1 1
1 1
1 8
9 1
3 1
1 1
1 0
1 0
1 1
2 1
0 1
1 1
1 1
1 1
0 3
8 1
1 8
1 1
8 1
1 1
2 1
1 1
1 1
8 1
1 9
1 3
1 0
1 0
1 1
8 1
1 1
2 1
1 1
1 1
1 1
8 1
8 3
1 8
8 9
1 1
1 1
1 1
2 1
1 1
0 1
1 1
0 1
1 3
1 1
8 1
1 1
0 1
1 8
2 1
1 0
1 1
1 1
1 1
9 3
0 1
1 9
1 1
1 1
8 1
l 2
1 1
1 1
0 1
1 1
S 1
3 1
1 9
8 1
1 9
1 1
1 2
1 1
1 1
0 1
9 1
1 1
3 1
0 1
0 1
1 1
1 0
1 l
s }
2 1
1 0
0 1
1 1
1 1
1 3'
1 1
1 1
1 1
8 8
9 1
/
2 1
1 1
0 1
1 1
1 1
0 3
1 1
1 0
1 1
8 1
1 8
2 1
1 1
9 1
1 1
1 e
1 3
0 1
1 0
0 1
1 1
1 1
2 1
1 1
8 9
1 1
1 1
1 3
1 1
9 1
1 8
1 8
1 1
2 1
1 1
0 1
1 C
1 1
1 3
1 8
1 8
8 1
1 1
1 1
2 1
1 1
1 S
S 1
1 1
1 3
1 1
1 1
8 1
8 1
1 8
2 1
1 1
1 1
1 0
1 1
S 3
1 1
0 8
1 1
1 1
8 1
2 1
1 0
1 1
1 8
1 1
1 3
1 1
1 9
1 8
1 8
1 1
2 1
1 8
1 0
1 1
1 1
1 3
8 1
9 9
1 1
1 1
1 1
2 1
1 1
1 e
1 1
e 1
1 3
1 1
1 1
1 9
8 1
1 8
2 1
1 0
1 1
1 1
1 8
1 3
e 1
1 1
0 1
9 1
1 1
2 1
0 1
1 1
1 1
0 1
3 1
e e
1 1
1 1
1 1
8 2
1 9
1 1
1 0
1 1
1 1
3 e
1 1
1 8
1 1
1 8
1 2
1 1
1 1
8 1
1 1
1 0
3 1
1 1
1 1
8 1
8 8
1 2
1 0
1 1
1 1
0 1
1 1
3 1
1 9
8 1
1 1
8 1
1 2
8 1
1 1
1 1
1 1
0 1
3 1
9 1
1 0
1 8
1 1
1 2
9 1
1 1
1 1
0 1
1 1
3 1
1 1
1 8
1 1
8 8
1 2
8 1
0 1
1 1
1 1
1 1
3 1
8 1
1 0
1 1
1 8
1 2
8 1
1 1
1 9
1 3
1 1
3 1
1 e
1 0
1 3
1 1
1 2
1 1
1 1
1 8
1 0
1 1
3 1
3 1
8 1
1 1
8 1
1 2
0 1
1 1
0 1
1 1
1 1
3 1
1 0
1 0
1 1
1 0
1 l
2 1
S 1
1 0
1 1
1 1
1 3
9 1
1 8
1 1
1 9
1 1
2 1
1 1
1 1
0 1
1 1
9 3
e 1
0 1
1 1
1 1
1 8
2 0
8 1
1 1
1 1
1 1
1 3
S S
1 1
1 1
1 1
1 8
3 S
1 1
1 1
8 1
1 1
9 3
e 1
1 1
1 1
1 8
1 8
3 1
9 1
1 1
0 1
1 1
8 3
1 8
1 1
1 1
1 8
1 8
3 1
1 0
1 1
8 1
1 1
9 3
1 1
1 8
8 1
1 1
8 1
3 1
1 1
4 9
1 1
1 1
9 3
1 1
9 1
1 1
1 0
1 8
3 1
1 1
0 1
8 1
1 1
8 3
1 1
1 8
1 1
1 9
1 8
3 8
1 1
1 1
0 1
0 1
1 3
1 1
1 1
1 1
0 1
8 8
3 1
1 1
8 e
1 1
0 1
1 3
1 1
8 8
8 1
1 1
1 1
3 1
e 1
1 1
e 1
e 1
1 3
1 1
1 8
1 1
1 8
8 1
O B-4
TABLE B-2.
LISTING 0F TORSCR PROGRAM g~sg
.40 0 C.______________________________________________________________
q /
@@@20 C 6 THIS VERSION CAN r*0CCES DATA Foi ONt 04 ML.T!vLE F-SCA.ES.
@@@*4 C s AND PRODUCE ESTI=.ATES FOR UD TO 9 COMPOUND EVENTS.
94@5@ C +--------------------------------------------------------------
@@ded LOGICAL LWR I TE. M*R ! ?E. M.RI'E 64@70 DOUB.C PRECISION P-Om t ?56). PMNV t 1@),0=NSv t 17). ScO A (9 6. 5 09aO (9). A.
e@@6@
4DMNorMNS.PPMN,PPMN5.DN. TWT.GSTR.SJM(9).TER*.P(3).PVARn98. PLOW.B.C,
$@998 8D.E.F.Fr. BASIC.PSUF(9),VARSUM(9) PTOT(9),v44 TOT (9) S DERR.PHIGH D@t@@
DIMENSION ITWINDt2). OCCUR (7),
p@11@
ANDIANO(11).FATRIXt756,11) 9412d CHARACTER EN(9)
$@l34 C
$@t40 C INITIALIZATIONS
@@154 C
@@l64 READ (6.1@t3) (EN(1),I=1.3),JLVENT
@@t78 MWRITE=. FALSE.
@@180 LWRITE=. FALSE.
@@194 MWRITE=. FALSE.
6@200 F=1.es-1@
@@214 FF=1.0-F
@@220 DO 200 !=1,9
@@ 2 30 PTOT(!)=@.
80240 264 VA R TOT ( ! ) r'@.
64254 C 642E@ C GENERATE ORDERED PIANO RuLL MAT 4!X S4278 C
@@284 N=0 64294 DO 1 !=1.2 66304 DO 1 J-1,2
@@310 DO 1 K=1,2 98320 DO 1 L=1,2 94330 DO 1 M = 1. 2
(N 9e344 DO 1 I I - 1, 2
(
)
89354 DO 1 JJ=1.2
@@364 DO 1 M K - 1, 2 94374 DO 1 LL=1,2 D@384 DO 1 MM=1.2 44394 NDIANO(1)=@
64444 NDIANO(11)=I-1
@@410 NDIANO( 4)=J-1 0@42@
NPIANO(9)=n-1
@@430 NDIANO(8)=L-1 64444 NPIANO(7)=M-1 SO45@
NAIANOt6)=II-1 90460 NDIANO(51=JJ-1 96474 NOIANO(4)=KK-1
@@460 NDIANO(3)=LL-1 94490 NOIANO(2)=9M-1 9@5@@
NSUM1=NPIANO(2)+NDIANO(6) 94519 NSuM2=NPIANO(3)+NDIANO(7) 9052e NSUM3=NPIANO(4)+NDIANO(8) e@530 NbuM4=NDI ANO (5) +NDI ANO (9)
D@54e IF (NSUF1.EO.2) N5JM1=1 SdSte IF (NSUM2.EO.2) NSu=2=1 ee*Ee IF (NSUM3.EO.2) NSUM3=1 4457e IF (NSUM4.EO.2) NSJo*=1 de58@
NSUME = NS*.'M 1 + N3uP2 + NuuM 3 + NSUM 4
@@* 99 IF (NSUM6.GE.3)
GOTO 2 946@e GOTO 1 94610 2 nan +1
@@624 DO 3 aN=2.11 9463e IF (NDIANO(IN).EO.1) OOTO 3 84046 NDIANO(1)=NPIANO(1)+1 B-5
TABLE B-2.
LISTING OF TORSCR PROGRAM (Continued)
\\
eM54 3 CONTINwE d@m6J DU 5 I"=1,11 46074 5 mA*R:xtN.!*)=NDIANOe:Ma dd68@
1 CCNTINUE 4369t C ALL MUNDs R (1.11. 7LL. *4T 9; K. N' *! AN0)
@@7dd C
$@710 C INPUT CLNTRO. Dd'A ed720 C 6d730 til READ (5,2@01) NUMTON. NS A*L. MT INT. ! NTEN. NL*SAF, NZ
- 87*@
WR I ?E ( 3. E-@ 11 ) NumTO;,hSAmE,KTINT,1N'EN.NUFSAF,NZ 99754 RcAD(5.2003) (OCCUR (I), !=1,73 ed760 WRITE (3,2103) (OCCUR (!),
! = 1, 7 )
8@774 READ (5.2001) NNm!S.NNAUTO
@@780 WRITE (3.2012) NN'IS.NNAUTO
@d794 DN=DFLCAT(NNMIS) ed840 A=1./DN 60810 DO 14 IS=1,9 94820 SCOR(IS)=@.
9@830 14 SCORSO(IS)=@.
@@860 C 90850 C TORNADO LOOP 608La C 44878 DO 11 LL=1.NU* TOR 84886 00 15 !=1,10
@@890 PMNV(!)=0.
ed9e4 15 P*NSV(I)=0.
80918 DO 33 IS=1.9 edS26 33 SUM (S) =d.
00934 RcAD(5.2087) Tkt. PLT R. UFOX. ! ? WIND ( 1 ). I TW!.ND (2 )
6494@
IF (MWRITE) WRITE (3.2.87) LL, TWT. PSTR. UMAX. ITm!ND (1). I' WIND (d i 9@958 C
$d300 C INPUT TA93ETo: VENT DATA
[ s) 94974 C q,/
44980 13 READ (5.2402) P 99994 IF (MI.EO.0) GOTO 10 d1982 BACKSPACE (5) 41018 GO 70 (12.20,30,40), PI
$1@29 20 READ (5.2068) MSET LENG'H.!!,IWALL.X1,Y1,Z1,VX,VY.VZ.vE.hW' 91034 IF (LWRITE) WRI'E(3.2168) P!,MSSET,LENGTM,IZ,IWALL,11,Y1,Z1, sie*@
SVX,VY,VZ,vE,HwT 01054 GO TO 13 l
91968 38 READ (5,2091) 1.J,k,PMNZ,ITNM 91478 IF (LWRITE) WRITE (3.2191) MI,I,J.K.PMNZ,ITNM i
0148@
GO TO 13 I
81994 49 READ (5,2092) I,J.PmN. PMNS l
Gitte IF (LWRITE) WRITE (3.2192) MI,I.J.PMN. PMNS 81110 C 0112e C EVENT =JEVENT FOR TARGETS 1-4 4 EVENT =3 FC9 TANGsTS 5-14 l
81134 C l
81149 IF (((J.NE.JEVENT).OH.(I.GT.43).AND.
l 81150 8 ( ( J. NE. 3). OR. ( 5. GT. ). OR. (1. GT.10) ) ) GOTO 13 811E0 C 01178 C CHECK AND ADJUST pmNSV(!=1.10) 81160 C 0119e IF (I.LT.5.ON.
I.GE.9) GUTO 31 41244 C l
81218 C ADJUST FEEDtR PIPE P105 ABILITIES FCH AGTUAL DIMENS:CNS l
01216 C 01238 PMN = PMN e 9.1 01264 C e12:@ C CCFPUTE PMNS =1.-(1.-PMN)eeND 01269 C 4127e IF (:mN.LT.FF) GOTO 44 0128e DmN=0.1
$1294 pmns = 1. 0 (g) 81344 GOTO 32
\\._./
B-6 l
l l
l r
w y
,y w y
_y
TABLE B-2.
LISTING OF TORSCR PROGRAM (Continued)
/S e 3:e 44 Ir (c=N.sv.F) GaTO 45 V
e 3:e omN=e..
e13:a c =Ns=e. e 013=4 GUTO 32 81350 45 B = 1. -999 e1360 C=D60G10(b) 8137A D=DNoC 01364 C=10.eeD 0133@
G*N5 = 1. -E 91424 31 IF (DPNS.LE.1.0) GOTO 32 e1414 W11TE(3.1242) 1.J.s*NS 81424 PMNS =
- 1. 4 41434 32 PMN3V(I)=sMNS ela=d C 01458 C COM$uTE EQUIVALENT S:NG.E M:SSILE D40BABI.ITY 91460 C 41474 IF (PMNS.Ot.
F-) GuTO 41 41464 IF (DMNS.LE. F 3 GOTO 42 01494 GOTO 43 81544 41 P*NV(I)=@.1 41518 GOTO 13 01514 42 PMNVIID=4.9 01534 GOTO 13 e15 4 C G1554 C COMPUTE AMNVt!)=1.-(1.-PMNS)**(1./DN) 01564 C 01574 43 B-1.-DmNS 8156@
C=DLOGle(B) 0159@
D=A*C 616@@
E=10.**D 01618 PMNV(!) = 1. -E 01618 GO TO 13
$1624 10 CuNTINUE f-~g (d
j 916*e C s
$1650 C COMBINE CLOLING TC-Ev w'ND & MISSILE DA*Aus 41600 C 01673 DO 210 !=9.10 216EJ M=I-8 81654 IF (ITw!ND(4).EO.0) GLTO 210 41760 DMNSVII)=1.@
01714 PMNVt!) = 1. 0 01724 214 CONTINUE 01718 Ir (MwRITE) ww!TE(3.1@00) (GMNSVt:),I=1.14) 01744 IF (MWRITE) WRITE (3,1@@@) (PMNV(I),I=1,10) 017*8 DO 12 !=1,8 61760 12 NDIANO(I)=4 01770 C 01764 C OUICK SCREEN ON PPNV(!)
81754 C 018@@
D0 16 !=1,8
@l814 IF (PMNSVi!).LE. F) GOTO 16 01826 No!ANO(I)=1 01838 16 CONTINUE 01863 NSUM1 =NP I ANO ( 1 ) +NDI ANO (5 )
41454 NSUM2=NDIANO(2)+NPIANO(6) 41864 NScM3=NDIANO(3)+N~sIANO(7) 018?9 NSUM4=NDIANOt4)+NDIANO(8) 21084 IF (NSUM1.ED.28 NhuM1=1 81834 IF (NSUM2.ED.2) NSLM2=1 019d6 IF (NSUM3.EQ.2) NdUM3=1 9191@
!F (NSUM4.EO.2) NSU*4=1 e1929 NSUM5=NSUM1+NSUM2+NSUM3=NSaP4 81934 IF (KWRITE) WRI'E(3.1@t6) NSUF5 41342 IF (NSUMS.LE.2) GsTO 25 81954 C PPNSVt9) =DFuGAT(IWINDt1))
'g e1960 C DMNSV ( 10 ) = DrLC AT ( ITw!ND (2 ) )
k B-7
l TABLE B-2.
LISTING OF TORSCR PROGRAM (Continued)
(3 als7. C p -visi
= m Sv.s.
s
)
.:9s0 C D-~vt1@i --mNSvtie>
~~-
e19+0 C 824+d C CQmPuTE BAS:C RCW P dO B A51. ! T !iS. 3*0wtJ)
@2@.0 C
@it2@
Do 12e J-1.756 92034 GR3wtJ).@.
$24*0 DO 118 K=1.1@
44954 IF t imAT R1 x t J, K,1 ). EO. '11. AND. tP=NSV t K). LE. F)) GUTO 12@
$2@6@
IF t imATR1x tJ. K+13. EO. 0). AND. tDmNSV t h). GE. FF) ) GOTO 124 Sd@78 11@ CONTINUE S2988 IF (KWRITE) WNITEt3.1@@7) J.tmATR:xtJ.KK) KK-1.11) 82994 C 021@@ C ROW CONTRIBUTES 9211e C S2128 DO 112 K=1.9 82130 IF (*ATRIxtJ.K+13.EO.0) GOTO 112 4214@
F e >*%5=kPN5V t K) 421*e PEmN =DMNVtK) 02164 GCTC 114 e2174 112 CONTINJE
@2180 113 WRITEt3.1@@1) J. 4 8219@
STOG S220e 114 IF (K.GL.9) GOTO 113 82214 KD=K+1 62229 DO 118 L=KP.10 82234 IF tmATR xtJ,L+1).EQ.9) GOTO 118 62248 C 42254 C COMPUTE PKOwtJ)=-1.+DGmNS+DMNSVIL)+t1.-DuMN-DmNVtL))**DN 02264 C
@2278 Ie (PPMNS.GT.FF) GOTO 56 42284 IF (DmNSVtL).GT.FF) GOTO 57
$2294 PRCw(Ja=-1.+POMNS+PmNSVtL) 42304 B 1.-DDmN-DMNV(w)
)
82318 IF (P.LE.F) GCTO 54
,\\s,/
42328 IF (B.LT.FF) GQTO 55
- 2330 PROWtJ)=PROWtJ)+1.
s2348 GOTO 54 42354 55 C=D.CGIStB) 42364 D=DNoC d2374 E=19.**D
$2364 P40W t J ) =DROW t J) +E
$2394 GuTO 54 42*44 56 DROktJ)=&MNSV(L) 82418 GOTO 54 42424 57 DRCWlJ)=DPMNS 42438 54 IF (P10wtJ).O.FF) P<0wtJ)=1.0 42444 IF (PROW 4J).LE.F)
PRCW4J)=0.9 92454 DPMNS=PROWlJ) 42460 IF (DGmNS.GE. FF) GO'O 51 02478 IF (DumNS.LE. F ) GOTO 52 42464 GOTO 53 42490 51 DD*N=0.1 d2544 GOTO 117
@2510 52 POmN=0.8 02524 GOTO 117 42534 C 02544 C COMPUTE DwmN=1.-41.-DwmNSpeett./DN) 02550 C 42568 53 B=1.-DDPNS 82574 C=DLOGletB) 42584 D=A*C 42594 E=19.**D 826@@
DwmN = 1. - E 92619 117 IF (MwRITE) W41 Tit 3.10e8) J.K.940wtJ).Dw'N.D=rNS 82624 114 CONTINUE A
(J B-8
TABLE B-2.
LISTING OF TORSCR PROGRAM (Continued) 42L30 C 446*4 C MAKE Ruw ADJUS*=LN?t s
tiL5a C
- 1EEa EASIC=ARDW(J) 42E72 IF (J.EO.1) GOTO 21 02 Lab Jk=J-1 41634 DO 21 !=1.JD 427dd IF (MATRIX (I.1).GL. MATRIX (J,1)) GOTO 119 82714 DO 22 JJ=2.11 42723 NDIFF= MATRIX (!.JJ)-MATRIX (J.JJ) 9273@
IF (NDIFF.LT.9) GOTO 21 62748 22 CONTINUE 62754 DROW ( J) =D ROW (J) -D ROW ( I )
827E2 21 CONTINUE 92774 119 IF
(* WRITE) WRITE (3.10@5) J. BASIC. DR06 (J), (MAT A: x (J. x ), K=1,11 )
e2784 C 02798 C COMSINE ROW PPDBABILITIES -- SCORE O.
T, u V.
R& X C0900RND EVENTS 92800 C Os => 3/4 N 82810 C Ta 4/4 N&
1/1 T 8282@ C Us 4/4 N & => 1/2 7 82834 C Vs => 3/4 N &
2/2 T 82848 C Re 4/4 N 82850 C Xs (4/4 N &
1/2 T) Om V
$286@ C 82078 NSUM1= MATRIX (J.2)+ MATRIX (J.6) 92884 NSU*.2= MATRIX (J.3)+ MATRIX (J.7) e2894 N5uM3= MATRIX (J.4)+ MATRIX (J.8) 92900 NSUM4= MATRIX (J.5)+ MATRIX (J.9) 42918 NSUM6= MAT RI X (J.10) + M AT RI X (J,11 )
82924 IF (NSUM1.EO.2) NSUM1=1 82934
!F (NSUM2.EO.23 N5uM2=1 02944 IF (NSuM3.EO.2) NSUM3=1 8295@
IF (NSUM4.EG.2) NSJM4=1 82904 NSJM5=NSUM1+NSUM2+NSUM3+NSUM4
\\-
82974 IF (NSUMS.NE.43 GOTO 123 d298@ C l
8299@ C EVENT R 03W4 C 03410 SJM(5)= SUM (5)+DRCW(J) 93424 IF (MATRIX (J,10).EO.0) GOTO 123 03434 C 43040 C EVENT T 03d54 C 036E0 SUM (3)= SUM (3)+DMOW(J) 93470 C
(
83648 C EVENT O 23899 C l
i 03104 123 SLM(4)= SUM (4)+0wC=(J) l 83119 IF ((NSUMS.NE.4).CR.(NSUME.LT.11) GOTO 121 I
e312e C 03130 C EVENT U S314e C S3154 SUM (11= SUM (1)+DROW(J) 83164 121 IF(((NSUMS.LT.31.OR.(NSU-6.NE.2)).AND.
i l
8317@
((NSUMS.NE.4).ON.(NSUME.NE.1))) GOTO 123 i
estee C l
8319e C EVENT X 432fd C 0321e SUM (6) = SUM (6) +DROW ( J )
03229 IF (tr. SUMS.LT.3).OR.(NSUM6.NE.2)) GOTO 12e 83234 C 03240 C EVENT V
$3254 C 03260 SUM (2) = SUM (2) + D RDW (J )
93278 las CONT:NUE d32ee DO 24 I S= 1, 9
~_-
l l
.B J l
i TABLE B-2.
LISTING OF TORSCR PROGRAM (Continued)
(/
S
@3:9@
t4m= sum (Is>* ev.PsTR e3344 seO*i!Si=Scou!
)+ s e x,
e231d 24 SC01LO(IS)=5C04sO(IE)+TE9"e*2
@33L@
25 :: (m=R TE) WitT.(3.1@o31 tSJMtI).I=1,9s.(suCw(I).:=1.9,
d332@
&(5COREQt:1.I=1.9) 43344 11 CCNTINUE 03354 DN=DFLOAT(NUMTOR) 83364 DO 169 ! = 1. 9 93374 IF (SCOR(!).LT.F) GOTO 169 03384 D(I)=SCOR(II/DN I
03390 PVAR(I)=(SCD45G( )-(((SCOR(I))**23/DN>l/(DNe(DN-1.3) e3444 169. CONTINUE 83414 WRITE (3.te@4) MT INT. JiVENT. (EN ( I), I = 1,9 6, 934c4 S(Pt!), Int.9),(PVAR(1).1=g.9) 03434 KT=dTINT+1 e3440 DO 171 1=1.9 83450 PSUM(!)= OCCUR (KT)*G(Il 83464 VARSUM(I)=PVAR(I)eOCCuR(KT)**2 83474 PTOT(1)=PTOT(II+PSuM(1) 83484 171 VARTOT ( 1 ) =VARTOT (! ) +VARSUM ( I) 93494 WRITE (3.1910) (PSUM(1),1=1,9),(VARSUM(I).I=1,93 03544 WRITE (3.10@9) MI 03518 IF (MI.EO.8) GLTD 111 83520 WRITE (3.1811) 83534 DO 175 I=1.9 83568 STDERR=1.96* SORT (VARTOT(I))
83559 P OW
=9 TOT (I)-S'D:3R 83564 PHIGn =PTOT(I)+STDEAR 83570 IF (DLOW.LT.O.0) PLOW = 0. 4 9358@
175 WRITE (3.1912) I.DLCW.PTOT(I).PHIGH.VARTO'(I)
$3*90 1998 FOR*AT(19613.6) l 93600 1@@l FORMAT ('
- WARNINGe
- eFOR J. K m'. 2:4)
@3613 1 @@2 FCRMAT ('
- NOTE ***:.J. PMNS =',2!4.E18.14:
[h d26Ld 1@43 FOR*AT ('
SUMS. SCORES. 8 SCORES SQUARED',/.9E14.6./.
t 43634 49E14.6./,9E14.0)
'N-036*G 1404 FORMAT (*
SUMMARY
STATISTICS FOR F =', IZ, i
$3659 8'
& JEVENT ='.12. /,4 X, ' EVENT 1 =', A1. EX. ' EVENT 2=', A 1,6 X.
(
$3664 4 ' EVENT 3='. A1, 6 X, ' EVE NT4 ='. A1. 6 X. ' EVENT 5=',41. 6 X, ' EVENT 6='. A 1. 6 X, 42678 4' EVENT 7=', A1,6X, ' EVENT 8=', A1,6 X, ' EVENT 9=',41 l
83684
& /. ' MEAN T.O.A.
& VAR (ME AN)'. /.
l 83690 49E14.6 /,9E14.6)
S3764 10@5 FORMAT ('
J. 0LD P ( ROW), NEW P ( ROW ), ROW e ',14,2E14. 6,1114) 83718 1946 FORMAT ('
NSUM5 =' 13) l 93720 1997 FORMAT ('
J. ROW (J) =',12I4) 43738 1948 FORMAT ('
J.K. PROW (J) PPMN.PPMNSa'.214.3E14.6) 93749 1@@9 FCRMAT(' MI m',12) 83754 1919 FORMAT ('
P(EVENT) 8 VAR (P)'. /,9E14. 6. /. 9E14. 6) 93764 1911 FORMAT (/.'
- STATISTICS FOR COMPOLND EviNTS. WITH 95% C.I.***'
/.
83776 8'
EVENT'. 5 X. ' PLOW'. 5X. 5X. ' PTOT'. 5X. 5X, ' PHIGH', 4 X,4 X. ' VARTOT' )
@3784 1812 FOMMAT(14.2X.4t14.6) 83794 1813 FOR=4T(9A1.11) 83800 2@01 FCRMAT(8:18) 83819 2411 FOwrAT (/' NUMTOM.NbAmt,KTINT,1NTEN,NUMSGF.NZe'.6110) 83824 2012 FORMAT ('
NN IMS. NN AUTD='. 2110 )
83834 2002 FOMMAT(12) 838 8 1403 FORMAT (7E18.3) 83854 2183 FORMAT (*
OCCUHtt-7)=',7hte.3) i 83864 2487 FORMAT (2X.3E12.4.2I3) l 03870 2187 FORMAT (/' LL, TWT, PbT R. UM A X. I TWIND ( 1-2) =',13. 3E 12. 4. 2 2 3 )
4388e 2088 FORMAT (2X I4.F14.3.2!4.8E12.4) 83890 2188 FOR*AT(* M I. MSSET. L ENGTH. ! Z. Ih4LL, X 1, Y 1. Z 1, VX. VY, VZ. VE. MW'='.
43948 1 /.12,I4.F14.3.214.8E12.4)
- 3919 2489 FCRMAT(' I TF, W INDF, Z TF'.14,2F 10. 3 3 e3928 2@90 FCRMAT(//18A4) 03938 2491 FORMAT (2X 3!4.E13.5.18) 839 4 2191 FORMAT ('
M I,1. J. K. PMNZ. !TNM=' 12. 314. E 13. 5.18) i (N
{c/
B '10
TABLE B-2.
LISTING OF TORSCR PROGRAM (Continued) 02954 2P92 FOqmAT(25.2!*.4x,2 13.5) t
\\~,/
83364 2192 FCAmAft' M I,1. J. PmN. PMNS =', 12.214.2E13.51
@3978 STOP 92962 END e3999 SU5 40Li1NE MU 4Dt R i.. L. m. mo? R X. LA 43L )
p.ggg g,__...............
=.___........ ____...................... _.
e441e C 1 THIS SLB40gTINE US S mFAx 'O AS.ENDING Y OND=9 AN INTEG.R mw?R;I
94933 C +------------------------------------------------------------------
94644 DPENSION MATRIX (m,L),LARSE(L) 9 954 DO 6 !=1.M 0486@
CA.L MFAX(A,L.M.M-!+1,*ATR:x.J.;A<G-)
9*e74 DO 6 JJ=1.L 9*@84 MATR E(J.JJ)=t4T9:x(M-!=1,JJ) e649d 6
MATRIxtM-1+1,JJ)= AR6EtJJ) 94184 RETURN 04110 END 94128 SUBROUTINE M*Ax(4.L M.N. MATRIX,J.LARGil 84134 C +--------
-
8*140 C 1 THIS SUBROUTINE F!%CS TH2 RLW WITH THE LA13L5T Or Ni=M INTE3eRS 94154 C 1 FROM TmE MTH COLUMN OF PATR1x.
e4164 C +==--
-=
=--==
- =--
=---
S4178 DIPENSION MATR13(M L),LAR3 EEL) 84184 DO 2 !=1 L S4194 2 LARGE(I)=MATRIXtt,1) 8420e J=1 0*210 IF ( N. EO,1 ) GOTO 7 e*228 DO 6 1 =2. N 0423d IF (PATRI X (!. 6). Li. LAM 3 (K) ) Go?O 6 S*244 D3 4 11=1.L i
942*@
4 LARGE(II)= MATRIX (I.II) 04264 J=1 e=278 6 CONTINUE
/s 9*i84 7 RETURN
\\ ))
94298 END END OF DATA i
[
l 4~-
B-11 i
(R)
(0
)
gy n/
v TABLE B-3.
TORSCR OUTPUT LISTING
- 15. 3.06 JOB 9592 IEF677! WARNING *ESSAGEtS) FL9 J.B TCRSCON2 ISSUED 15.13.@6 JOB 9592 DLDLICA*ED @@@@t 15.13.@6 JOB 9532 e TORSCCR2 STAR ED - INIT 5 - CLADS 3 - Svs 0165 15.14.36 JCB 9592 TIME =
351 Cru=
328 !/O=
22 EST EXEC CCST=9 14.75 15.14.36 JOB 9592 EXCPS: DIS 4=
964 UR=
765 ' AC E =
@ Mt4 ARA.INC.NM.LIMER 15.14.36 JOB 9592 OUTPUT LINEG=
681 CARDS =
@ PLOTS =
0 EST COST =S 44 15.14.36 JOB 9592 * 'ORSCOR2 ENDED
JES2 JCB STATISTICS ------
29 FEB 84 JOB EXECUTION DATE 8 CARDS READ 7@7 SYSOUT PRINT RECORDS
@ SYSOUT PUNCH RC09DS 1.48 MINUTES ELAPSED TIME
--- TORSCOR2 JOB 09592------4AN 15:14 2/29/84 (TODAY p-----PRINTe TSO
--RC--STEP-----PROC-----PRCCSTEP--COM=ENTS C
FTVCLG STEPA L
FTVCLG STEDA 4 G FTVCLG STEPA
DDNAME---STEP-
--CL ASS - R :CONDS-HELD--D ST---- rO 4'S--L'CS--cCB-CCPI ES--
1 LOG A
15 NO ARA.
2 JCL A
38 NO A9A.
3 MESSAGES
- A 19 NO A4A.
t2 4 SYSORINT C A
479 NO A NA.
h 5 SYSTEhM C A
13 NO ANA.
ha 6 SYSPRINT L A
65 NO A *A.
7 SYSTERM L A
1 NO ARA.
8 FT@3F@@t G A
77 NO A 1A.
9 FT06F@@t G A
1 NO A 1 A.
a.)
f BROWSE - FTe3F@et STEPA G
NUM TO R. NSAME, HT I NT, I NTEN, NLMS AF, N Z =
79 750 1
1 14 19 OCCUR (1-7t= 9.1$fE+@e 9.160E-81 8.610E-04 G.190E-@4 8.340E-@5 9.37@E-@6 9.00@C+@9 NNIMS.NNAUTO=
11844@
3785 2
SUMMARY
STATISTICS FOR F = 1 8 JEVENT = 2 EVENT 1=U EVENT 2=V EVENT 3=T EVENT 4=Q EVENT 5=R EVENT 6=x EVENT 7=.
EVENT 8=.
EVENT 9=.
MEAN T. O. A.
4 VAREMEAN)
@.@ M @.*@D+@@
9.e@@@@@D+e@
- 0. OMM0D + 0e 9.9478590-@t
@.179791D-et 0.e@@M@D+@@
@.8M@@@D+0@
8.@@@ M@D+e@
@.@@@@eeD+00 4.@@ M@@D+@c G.@@@@@@D+0@
0.304@@@D+@@
9.4@5184D-@2 4.302258D-@3 d.@@@@@@D+@@
8,@@@@e@D+09 e.@@@@@@D+@@
e.@@@eceD+0e PEEVENT) & VAR (P)
@.@@M@@D+ee G.Ge@@eeD+@@
8.Oe@@@@D+@e G.151657D-82 9.287665D-@3 8.Be@@e@D+@e 9.@e@eeeD+@e G.940@@@C+@e 4.@@e900D+00 O.@@@@ND+@e 9.Ge@@@@D+@@
0.900@@@D+@@
e.183727D-@5 9.7737790-@7 e.@@@@@@D+@@
9.@e@ee@D+ee
- 9. @f MN D + @@
4.2004880+0e MI
=@
l l
It. t.
88 I.t.
I.
I,I I.I 23 O O, O 79 9
+
+
+
+
+
9 0
t P
e G4 H9 e
9.
r) p1 3
4O OO GS e
@4 84 9 F
99 99 F
9 94
>- 69 90 7
7 99 S9 Z
9 69 7
99 W
69 hl 69 99 W
9 W
G9
& *d 49 99 99 99 99 99 99 49 W
99 ed
@9 99 W 69 99 W
%9
@ G.
9%
99 99 99 GS 59 9%
G9
\\
99 49 69 69 99 99 99
%9 s
49 99 G. *s
% 's 59 S *s NS NS
+
+ +
. + + + +
. + +
+ +
. + +
++
e CO 00 s
On on s
CO 00 s
CO CO 40
's m O9 m
9 *A N *e G
%9
%9 C
%9
- e *e e-Gb 69 s
- 49
% "s t
G9 GG e-
- 9
- a. %
7
%9 99 7
59 89 7
69 49 7
@9 59 W
99 bl 49
%9 be
@9 NG W
%9 99
$9 69
- s s 5%
> 59 GG 59 69 W
99
@9 W
69 49 W
99 69 be G. 9
- 6. %.
99 99 99 99 99 99 69 69 99 99 99 99 69 99 99 99 69 69 s 's 69 69 69 99 NS P
. + +
++
p
. ++
+ +
m
. + +
+ +
e
. + +
+ +
=
0 00 CD a
e QQ 00 O
00 00 3
00 00 b
99 M9 P
G *s b
99 99 b
69 99 GS 69 F
G 6#
49
%9 G9 6-
&G N9 2
GO 99 7
96 99 2 69 99 2
SG GS uf 99 59 W
%9 99 W 99
@9 W
99 99 j
> 9e se 59 se
> e9 es 99 89 W
69 99 W
99 G. G.
W G. G.
G. G 69 69 W
.99 99 69 99 99 69 99 69 V
4e 4
4 4
w w
w N
99 99 99 99 99 Om 9-
@M O
99 99 99 99 69 S*
69 9
- O O
w
+ +
++
9 w
++
+ +
9 w
+ +
e t 9
w
+ e e e e
9 e
00 OO e
CO DO
- e e
OO CO e
CO DO 4
+
99 89 99 99
+
bH NM
+
G.e d a) g W
SS 99 W
%9 99 W
P-
@N 90 W
oN 6N g
9 7
99 99 9
/
99 9
2 6*
40 G
2 b eiJ MC G
W 99
%9 9
bl 99 99 9
W 98 4 @
6 W
NG AN y
N S.
M S.
N 99 9%
49
@ a NM n6 m%
eM
> se es W
99 89 w
69 G. G
@ m.
N. u W
Wa N. a W
9 9
e 9
O 99 99
%9 99 99 99 99 9e Z
w 9
9 9
9 H
I 99 44 4
Ga 69 e
we em e
-9
@ M.
M W
GW 99 W
49 W
GD G.*
W G9 9
9 2
+ +
e e 6
7
+ s e e 9
E
++
1 I 9
r + +
e s b
e OO Oc b
a 00 00 b
e 00 00 6
s GO 00 y
NM o
SM 4m MM bl se
@9 4 M.
n
@N eG nM e
09 c
o 4 P1 4?
>- 4M 4 4 e-QQ No e
4o el 4 D
9 7
H.* 9 C. O G
/
40 M@
9 7
- N CN 9
7 P- @
M N.
bl
=.
i.1 bl
- T1
- ) 'al W
- N
@ 10 bt il P) e-A U
04 NN O
- =
PO
@9 O
O SJ b1 @
e) *
- 9 W N P3 b" d" 9
W
>=
9 W
@M 4*
9 W
w AJ.
N. ^J bM D
t i
t t
I C
W 99 GS W
99 99.
W 99 99 W
69 99
}
9 9
9 9
1
(
/
g 4
e 4
4 49
-G O M.
- e de SM
-9 49 9 M.
G M.
g/
y i
93 9
- el 99 G
- 41 49 69 69 p
9 61 N
(
69 O
++
e I b9 0
+ +
e 1 69 0
++
e 1 69 0
+ +
s e 2
e 00 CD e
00 00 e
OO DO s
- 0. 0 0C O
4 4
M9 e?
4 4
49 n9 4
4 N *s W
9 H
9
> ma sa G
F MN 44 9
Ob GP G
H NN Ge e
Z
7 99 89 9@ >7 99 69 5 @ >Z Gd DN 8@ >7 o@ G# WW 99 99 N. WW $1 @ N4 N
- b3 W MN 61 9 N. WW 96 96 N. 31
- a >
59 99 7GOM) Md
- M 790M>
790M> 95 49 79 @" O NM e G W W W 09 G9 M td 69 99 e e W @d N. a N. a k*be Ause A m% e k* re C9M 69 69 C@ M 99 G9 GSM G9 GG GSM GG $9 mi N ma M @ e 4 m8 O TW N. W FW EW J9 8 69 69 39 8 @9 99 3% B Ga @N 39 9 ed @ M.
- 2. M M
69 F. M 99 Ga Z. @* k> + 6 e s Z@ 99 89 GS 69 .a k> + + ++ k> + t e e k> + + + + M. 8 OO DO 7 8 OO OO 7 8 OO DO 7 e 9 OO DO F W99ENa SS et W9 %E4=99 99 ut 9 9 F N a 6 S eN W99ENaM4 41 M i F 40FZ99 9 6 4 00- Z%9 99 e 40FZNM Me 40FZ9@ MN 294kTGs4 RS 44 7 CSS 99 ZC447G9* 44 Z94k7CNM 4@ i M 98 WWGS s we 9 biW99 G9 wSe WWMP e P1
- a s e W W aj e
-3 o >-W m>FNd . *.e m > 3. v @ 99 em.*E99 G9 .* am> Ebb NH na U b3 -
- 6. a
>-79W
- U W - 6 9. a 9. u.
>- W
- U W ~ N. 4.
P. 01 >W o ') b8 - 9 9 69 E a M 29. o R ZG w E /9 .a we F C69 ASS w9 F G99069 = 9.. > 499Q99
- k. 9 M
GSSO 99 P-a m > m. m > w F m > w e o w g E 2 1 2. ~ v
- 1. e.
~ W .esk e99Cge .9 po ee9499 .Ge> e49Co* ae esec@M OG 69>99 W UC W OG 69)@ w W OG .$9>G- . S Q > 9 *s E9Fb3 ++ e e E O > >- 3 t SFh3 ++ ++ E s okS + e e e + + + + JOSCQQeOO Ga J m e. C. O O e n O C a 3 m.8. C. O O e O O 3 m S G. O O e O O Ca a N fT NS 99 mb
- 1
%G 4 *J mNG e 9,. 5 9 t/t b c e e@ os
- > + O. % & > b 9 Z. *s
- e. *>e. o. 9 9 a
/.e. / > o O. 6 a t - @ J
- 7. s Z > >- O. h1 G P M 7 1 99a 99
%9 s si &b 7&7 7E F 727 9@e%@ 7 6 9 t
- s N F "*
e . G W h' 6 9 7 Tp 9 9 E* . (1 be F 9 9 7 8 9 9 7 * . G tijF M @ 7 0 4 9 Fw GW> tl @ 7 w eJ = OEmE> 59W99 Or up > ssW99 Ormt> M.. W - M Ormt> @ @ t.t sM K U.5. E W Z G 6 > 9 9 8 p us 2 9 9. W b 3 >3 b >%98 > *J P L W Z W - > fJ a e eJE E W F @ e. bl > eJ o e 3 G EU G E U ** 3 G LUw3 ..W ... Q .W 292@ WSS-GGa 3 t1
- 1 W95-69=
DUZW We9-9Ga QU7m W99*99= s u7 L Q E ZO / E Q L 20/ E G E cO2 L Q F B-13 I i %d m t43 C M CO U w CZ w &M w 4 W DA .. N a nNa999 H-
- 99-699 3
e 8 s e e i + + + C Q Q Q Q Q Q rs o n >- W D 4 4e*99G / D g OmebN.esss y b090OdG999 m eAOAM4N999 CMcM9..N &99 CM
- H
- 9. s. 9 O
e W e 999999996 o J n n n aJ M n 9 e 9 ess99ssse m g U e e e e e e *++ Q00000 g I*PdJON 000 1E 999 41 0 4
- S b M W 9 6 6 W
@
- N S G S.* ** @* @G 9 9 J
ITGW M Za@O@@@@%9% 4 4 ^J. 4 M. @. e 9 9 9 H 3 999999996 I (85 n el O 6J M H 9 9 9 F 999999699 7 e e e e e e +++ De Q00000000 W H 9 C C.4 N M 9 9 6 bbb e nJ M G s 9 0040M49996+ QHSGC**S966+ / 4 *85ee-1 W 4 0 & 6 9 + [ . N...M. N. 9 9 9. > 3 Na 9 9 9...g UU 29499d9895 4G99999%ee r e +e ++ e + + + g C 0000000000 b 69499N996 3M9*9s499e4 mob 9699e9990 UJN9M99W959
- Q N 9 % "J 9 0 S b S E
- 9. *. 9 9
- G. G. 9 0 FW
.h 999999999k
- 4. -
.m2 + eWa8JMemdbOP+= e> +e aw +e y B-14 .-.,_._2._ I z.- l: B.3 Validation 1 ( Validation of TORSCR was performed by running the code many times, a few l tornado'es at.a time, always printing out several intermediate steps in the l ' calculations, and checking the-results against upper limits fer the TORSCR estimates that were hand calculated. 1 4 b I i-4 4 i i-i i i I l r i, B-15 /"'% APPENDIX C U IMPACT RESPONSE ANALYSIS OF SPRAY ARM C.1 General In this appendix, the procedures used to assess damage of the nozzle spray arm to missile impact are developed and the results of the analysis are presented. The analysis treats impact response of the cantilevered arm and estimates the threshold impact velocity for each missile type that would fail the arm and hence rupture the pipe. In general, the procedures that are used in the assessment follow the guidelines and procedures for missile impact analysis recommended in ASCE Manual 58. Structural Analysis and Design of Nuclear Plant Facilities [C-1] for hard missile impacts with modifications to account for soft missile deformations and motion of the target during the initial ~ contact phase of the impact. C.2 Procedure for Hard Missile Impact The procedures for hard missile impact assume that both energy and momentum are conserved during impact with the energy absorption capacity being limited by an allowable ductility criteria. Thus, mvg = mv + M vt (C-1) e /~% (v) l and 1 1 1 mv12 = av 2 + - M vt (C-2) e 2 2 2 where m = missile mass; M = target effective mass; vi = missile velocity e before impact; v = missile velocity after impact; and vt = target velocity m after impact. Defining the coefficient of restitution vt - Vm (C-3) e= vi and substituting into Eq. C-1 yields f alme vt "l Vi(1 + e) (C-4) (1 + m/M, and c'l) C-1 ( m/M, - e N j [ e} (C-5) vm"' Vi N-( 1 + m/Mef Note that for m/M, > e, the missile velocity is directed toward the target and represents residual kinetic energy that the target must absorb in addition to that imparted during the initial impact. To survive the impact, the strain energy capacity of the target (SE ) must be greater than the t kinetic energy imparted to the target (KE ). The kinetic energy imparted to t the target is given by 1 t for m/M, 5 e (C-6) KE "-MVet 2 and 1 1 (C-7) +-MV for m/M, ) KEt= mvm e et 2 2 In the current problem, the missile masses of interest are relatively large compared to the effective mass, M, of the target during the initial e contact phase. Assuming a fully elastic impact (e = 1) by a hard missile, the total energy imparted to the target is constant, independent of the effective mass of the target, and equal to the initial kinetic energy of the missile. r'^ For significantly plastic impacts (e < 1), Eq. C-6 may govern and the energy [ (,,g/ transmitted to the target may be sensitive to the effective mass of the l target. It is noted that for hard missile impacts, e = 1 is often assumed, which results in a conservative estimate of the kinetic energy transferred to the target. C.2.1 Effective Mass of Target When impact occurs, the initial target response is highly local-ized. During this initial phase of response, plastic hinges form at some distance from the point of impact. This distance is a function of the energy of the impact and the resistance of the target. If the capacity of the structure is sufficient to sustain this initial phase of response, the hinges propagate toward the beam support where the structure enters the static collapse mode. Reference C-1 suggests that the minimum effective target mass during this initial response phase be taken as the area bounded by d /2 around t the periphery of the impact. Thus, for impact at the free end of a cantilever beam d ts (M ) min " Ft (d, + --) (C-8a) 2 V C-2 where pt = mass per unit length of the target, dm = diameter of the missile and dt = depth of the target in the direction of travel. The upper bound of h effective mass is the fraction of the total target mass determined based upon the deformed shape of the target. Assuming that the static collapse mode consists of a hinge located at the fixed support of the beam, one obtains Ft A (C-8b) (M ) = e,,x where ) = target span length. A more accurate estimate of the target effective mass can be obtained if the location of the plastic hinge is known. Expressions that can be used to estimate the location of the plastic hinge were developed by Conroy [C-2}, who investigated the response of infinitely long fixed-fixed beams subjected to a finite distributed blast loading at midspan. These expressions are d ' 12 M d,t -1/2 m o x ( t) = - - (C-9) o 2 _ ft P(t)dt, O -1/2 d, 12 M d,t o I x1( t) = - + (C-10) 2 _ ft P(t)dt'_ 0 where M = fully plastic moment of the beam; / P(t)dt is the impulse delivered o to the target through time t; and x and x1 are hinge locations on either side o l of the center point of the impact. Use of these equations results in the following expression for the effective mass for a cantilever beam subjected to a free end impact Pt M = - [x1(t) + x (t) + d,} (C-11) e o 2 i ( C.2.2 Target Strain Energy The spray arm nozzle is modeled as a cantilever beam with a span length of 60 inches. As shown in Fig. C-1, the missile orientation and velocity vector are assumed to be normal to the cantilever beam. The assumed static collapse mode consists of a hinge at the fixed support, with an approximately linear deformed shape. Thus, the energy absorption capacity of the target is given by R, Xe set = + R (X ~X ) (C-12) m m e i 2 I O b C-3 ~. _. _ - -, / "m / ut, E, I V s o i f /
- s:
t=60 / (a) Schematic / I ) [ 3 - - ~ ~ ~ _, ' ~ ~, 'p Ft f,6 = N 8 3EI ~s s s y s (b) Elastic Deformed Shape O / hinge R Mg / X = uX m e s if (c) Static Collapse Mode Figure C-1. Analytical Model of Spray Arm i een' C-4 where set = target strain energy; R = static collapse load; X, = effective /.S yield displacement (elastic under a static load R ); and X = maximum m \\ allowable displacement. Using the definition of allowable ductility X, p = -- (C-13) j X, one obtains set =R X,(p - 1/2) (C-14) m The ductility p for a steel member in flexurel is taken as 20 from Ref. C-1 so that set = 19.5 R X (C-15) m e C.3 Soft Missile Impact Analysis of soft missile impact on the nozzle is accomplished by modifying the previous procedure for hard missile impact to account for the strain energy absorbed in deforming the missile. The energy absorbed in deforming the missile is determined by calculating the crushed length of the missile during the initial contact period and determining the strain energy required to deform the missile by this amount. A procedure for the analysis of soft missile impact on rigid targets is presented in ASCE Manual 58. However, since the target is assumed to be rigid, the deformations of the sof t (f-^s) missile are such that all of the initial kinetic energy of the missile is absorbed in deforming the missile. A modified procedure was therefore + developed to account for the deformation of the spray arm during the initial impact phase. The soft missile impact analysis procedures and the modifica-tions to account for nonrigid targets are presented in the following subsections. C.3.1 Soft Missile Impact on a Nontigid Structure The load imposed on a rigid structure by a deformable missile can be treated as having two parts: the force exerted in crushing the missile and the rate of change of momentum of the missile. Thus, the load is given 'oy [C-1] f dx 3 2 l (C-16) F(t) = P (x) +,(x){ c ( dt ) i where P = missile crushing strength at the impact interfaca; y,= mass per c unit length of uncrushed missile; dx/dt = v, = velocity of uncrushed portion of the missile; and F = force applied to the rigid structure. For a deform-able missile of constant cross-section, mass, and strength, Eq. C-16 becomes p) C-5 q v l c + Mm m(t)2 (C-17) . F( t) = P V ,_s { l / The deceleration of the uncrushed mass, m, is caused by the crushing force P so that c -P -P c c (C-18) a (t) = = m m(t) pm(L-Xm(t)) where L =-length of the missile and x (t) = crushed length of missile. m Knowing the current velocity and crushed length of the impacting missile, and assuming the acceleration to be constant over some period at, the common kinematic relationships between acceleration, velocity, and displacement as a function of time can be used to determine the conditions at time t = t + At v ( t + at) = v,(t) + a ( t) at (C-19a) m m 1 x (t + At) = x (t) + v (t) at + a (t) At2 (C-19b) m m m m 2 Equation C-17 is then used to calculate the current impact force. It is also possible to use Axm (or av ) as the independent variable by rearranging m Eqs. C-19. In the current analysis, Av is used as the independent variable m so that Eq. C-19 becomes {, - av m at = (C-20) am Equations C-17 through C-20 are solved iteratively until the missile velocity v, 5 0 at some time td. Since these equations are based on the assumption of a rigid target, they provide a conservative estimate of the pressure time history during impact. However, as mentioned earlier, this procedure overestimates the strain energy absorbed by the missile. This is -illustrated in the example in Ref. C-1 by the fact that the strain energy absorbed by the utility pole missile is equal to the initial kinetic energy of the missile. This is due to the assumption of a rigid target. Since, in the case of the spray arm nozzle, the mass of the target is small compared to the mass of the missile, the target is accelerated very quickly and the motion of i the target during the initial impact phase becomes important. To account for the motion of the target during the initial impact phase Eq. C-17 has been modified as follows c + Mm r(t)2 (C-21) F(t) = P V where v (t) is the relative velocity between the target and missile, i.e., r (C-22) vr"Vm t -V f) \\ C-6 l 1 The velocity of the target effective mass at a point in time is calculated [~'h using the force determined from Eq. C-21 and the following equations assuming ~ (_,) constant acceleration over the time step at F(t) at(t) = (C-23) M (t) e vt(t+At) = vt(t) + xt(t)At (C-24) 1 2 (C-25) xt(t+At) = xt(t) + vt(t)At + at(t)At 2 Axr = Ax,- Axt " AX - (Xt(t) - xt(t+At)) (C-26) m These equations are then solved iteratively in time until the relative velocity becomes zero. This procedure can then be used to estimate the force time history imparted to the target and the deformation of the missile during this initial impact phase. However, since the resistance capacity of the target will decelerate the target mass, the missile will reimpact the target so that use of this force time history to calculate the response of the target will lead to an unconservative estimate of the target damage. A more appro-priate approach is to subtract the strain energy absorbed in deforming the missile during this initial contact phase from the initial kinetic energy of the impacting missile and use the residual kinetic energy in the conservation f-~ of momentum and energy calculations for hard missiles presented earlier. This leads to a conservative estimate of target damage since any strain energy ( f ^# absorbed in deforming the missile during subsequent impacts is neglected. C.3.2 Summary - Iterative Solution for Soft Missile Impact on Nonrigid Target In summary, the following procedure is used to predict the damage threshold velocity for soft missile impact on a nonrigid target. I 1) Choose Av, increment i 2) Calculate current missile acceleration -Pc am" p(1-x) 3) Calculate At = Av,/am I i ( ) C-7 %+ d I i L 4) Calculate crushed length of misaile 1 Ax, = v,At.+ a,(At)2 2 5) Calculate force imparted to target c + Um r(t-1)2 F=P V 6). Calculate effective mass of target f x1 X dm o M = pt I.-+-+- e ( 2 2 2 7) Calculate current target acceleration at = F/M, 8) Calculate target velocity and displacement i 1 xt " Xt+Vt At + at At2 2 vt " Vt + at at vr"Vm -Vt 9) Calculate relative velocity and relative displacement vectors i-vr"Vm t V ~ Ax
- AX OX t
m m
- 10) Update missile velocity and crushed length t = t + At I
v, = v, + Av, xn"Xm + AXm
- 11) Repeat steps 2-8 until vr*O i
C-8 i l
- 12) Calculate KE imparted to structure b
KEt " KEm - SEm 13) Compare KEt with set The above procedure must be solved iteratively to yield the velocity causing damage. This was accomplished by writing a small FORTRAN program to perform the above calculations. C.3.3 Example Calculation The following calculations summarize the procedure for a wood plank impact on the spray arm. 1) Missile Properties (wood properties assume southern pine industrial 86 KD grade 1" board) Nominal Dimensions: 1 in x 12 in Static Compressive Strength: 1950 psi (from Ref. C-3) Weight: 3.3 lb/ft DIF: 1.27 [Ref. C-2] >fs Crushing strength: F = DIF c = 1.27(1950) = 2477 psi e a Mass per Unit Length: w 3.3 = 0.0007124 lb/sec /in2 2 Fm _ = = 12g 12(386) 2) Target Properties Pipe OD = 2.375 in t = 1.1875 in o i Pipe ID = 1.773 in ri = 0.8867 in ave = 1.037 in r i Yield Stress = 35,000 psi DIF = 1.4 [Ref. C-4) o.,) i C-9 - _ _... _. _ _ _ _ _, _ _ -,. _ _ _ _ ~. _, _ _,.. _ _ _., _..... Plastic Centroid: 4(r 3-r1 ) 3 o = 0.6648 in Yp
- 3% _q )
2 2 El=atic Moment of Inertia: I= = 1.0767 in4 64 Plastic Moment at Support: Will investigate moment capacity at three cross-sections as shown in Fig. C-2. A-A: Spray arm pipe B-B: Weld / pipe composite C-C: Socket / pipe composite Section A-A: No = 2(DIF)a (u rt)yp y .O/ = 2(1.4)(3400)(z)(1.037)(0.301)(0.6648) = 63,890 in-lb Section B-B: Solving iteratively for al, a2 yields a1 = 51.8 a2 = 56.5 2 sin a fr 3 - ri3) o yi = l j y1 =.908, y2 = 1.086 3a ( r, - ri2j o Ai = ai(r 2 - ri ) A1 =.564, A2 =.475 2 o O C-10 O Spray Arm (Schedule 160 2 in Pipe) Ah W/JGJG N 5 Socket Connection E, (304 55) 92L 8T r r g =2(DIF)e,(trt)) I NA M Section A-A T = (,-a2)I'3 "'2 I l I I '3 C = ey(r2 ~'l )**2 '3 ~I2 I j
- *'l u\\b
)i Y 3*'2 2 MA C05 02' C05 'l x y. = (A ig + 2Ah2)DIF e, M g a l Sections B-2 & C-C i Figure C-2. Spray Arm End Support Schematic O C-11 t O Mo = (DIF)a (Al y1 + 2 A2 Y2) y (1.4)(80,000)[(0.564)(0.908) + 2(0.475)(1.086)] = 177,800 in-lb l = ) Section C-C: -Identical to B-B except ey = 30,000 Mo = 64,830 in-lb Pipe cross-section controls and Mo = 63,890 in-lb e Static Collapse Load: M 63,890 o Rm = -- = = 1,065 lb A 60 Checking shear in weld 2-ri ) = 1.51 in2 2 Aw = w(ro Rm w = -- - 705 psi o g-~ Aw [ g Effective Yield Displacement: Rm3 (1065)(60)3 3 X = = e 3EI 3(29,000,000)(1.0767) = 2.455 Strain Energy Capacity: set = 19.5 R X, = 19.5(1065)(2.455) = 50,970 in-lb Mass per Unit Length: i y 490(2x)(1.037)(.301) j' Pt = - (2xrt) = g 386(1728) = 0.001441 lb-sec /in2 2 J e ....c ,.,,-,---..w-- -_,..,-y ,,.-..,,-.-._,.,,,-.,w_, ,3 w,.,9-.py,.-+-e-,,,,-w,,wm.-ry,-,,~.7 ,y.--,%e.,-,. - --, 3-., ...vw-c- Substituting the missile and target properties into the FORTRAN algorithm () developed to solve for the soft missile impact on a nonrigid target and \\~,1 solving iteratively for the minimum velocity causing collapse yields v1 = 92.8 fps A typical printout a single iteration for the wood plank is presented in Table C-1. C.4 Results of Impact Analysis The results of the impact analysis on the spray arm nozzle are summarir.ed in Table C-2. Calculations were done for all missiles for which the weight of the missile did not exceed the static collapse resistance, R /DIF. Calcula-m tions were performed for both nominal wall and corroded wall thicknesses. Two types of missile impact orientations were also analyzed: missile secondary axis parallel to the target longitudinal axis and missile secondary axis transverse to the target longitudinal axis. Calculations for several missile types indicated that transverse impacts generally resulted in lower velocities for damage and hence this orientation was used in the remaining calculations. Also shown in the table are the missile properties used in the analysis. Sensitivity to the impact location on the spray arm was also investigated and no significant variations resulted. C.5 -References C-1. Structural Analysis and Design of Nuclear Plant Facilities, American Society of Civil Engineers, New York, New York, 1980. y j C-2. Conroy, M. F., "The Plastic Deformation of Built-in Beams Due to Distributed Dynamic Loading," Journal of Applied Mechanics, September 1964, pp. 507-514. C-3. Timber Construction Manual, American Institute of Timber Construction, New York, New York, 1966. C-4. Meyer, R. W., and Kellogg, R. M., " Structural Use of Wood in Adverse Environments," Society of Wood Science and Technology, VanNostrand Reinhold Company, New York. l l (A) U C-13 a 5 4 a 6, N.* N *w N + e + ut e.s g., 6
- ,*.e w
r, e a. e te e. cq Sr b 6e
- S*.*.
e., r .a 4 4 4 tai ' ' b
- e N *,'
e 6
- o
- N e
>
- e.s
- e p
Fs
- Ps vs *w
- o 4 s 4 b'
.I (sf 9
- e s
- 4.1
- d 4 4i tJJ E
6
- 1 s, e.~;
6.-. J w U e-= CM aW g% avMJ _g
- J k *J 4 4 4 tdJ M
= t e see L; 8,e, $ t'.s JZ F re. w ==g C % in. L ) MJ
- o t e
W G. e.-o E b P. P - @ $ N 's 4 + 4 OW L h.3 e re-e e1 a w
- e rts g g@
W *st f5' Qg G 4 4 al' WQ M >= D3 {, p( 8 e4
- d W 4 QJ
" ' ' ' *l ~ l 3D n
- 4 MV F
s ' st t.: e L&J - J 5 e r, e i.i. EC (! bt P.s (* i t1 w O es as sti 5 % r. r,. J nis ** sr es.. e-qp (A
- * $ 1 e'el 37 4 ** P1
. e. e-W ** .. e W W *. *w *v G 6 's
- J rs G 6e gy t.8 tr 4. t +
+ e+ + + + 'E"""C > ha
- s! t.' 8 ' bl bl.tl les bl of 6 4
E
- e 6
eit ..P. t 49 (, %. ist 6, 9 44 4 >C t (J P. ru 4 (9
- t. AJ *s.>
r.fJ P-GNav 7 s en ec r1 e.4. o e**. O u.s e en + 4 e r1 G 31 ees t... .e c fu bt b' n)a b a C U =* e e e e e.. .I e i s* P1 e o. -e t . e Fe O' ~ / U 4 ) .e % m.try O F I Er >. *. =
- D14 vi el..
g e + e. e
- v N N % @
gg N P R 8 4 5 g 9 9 8 t*' 8 h! +++ + 4 O 'es 4 . I e.e hJ Id LI W G to ? k % e l & *'u r
- .o
=J
- W 6
Y ET est es g' 61 tr*
- t s @ te h e Ya e', N *e CD b
ee / 8 .e
- > 9.o *.o a
.s e.s ti O
- )
in 4 4 4 4 g i e, s e t,i e) ( p hl C 8 6 n' Ist s.: t.s y tot i ei O / f3 1 & e qu p) 1 3 1G 7 C (r of. cre cr. >
- O l ti O
(A I t D 5 c' tv @ t hi D W U liv (') U 9 G w est w e e 3 //> 0 bl 7 et 1 ... 1P E 9 0 0 .si? fJ bi ta' e'l _t er est tr i l I i U e T 01 > e er 6 .1 oo e O tal = U1 M
- b' 19
..i ta = >t7 bi 6. ** (D t t1 @ P1 P1 > e. Isl hp O' O &N% Id te'. .O O tel W e
- bl 6
(D **
- 1 Q
he t J / 7/ el It' ll 8 . Y ese bl + e. be 9 8 5 W > t **.a?
- ;t J a v'
- D-bl h*
> v Un eO 6-h16 % ** 2%6 e e Y 1 ** U
- e.u @.+
7 U) ta' e (n > - (f. @ Q bl C1 t'l (D (A O e th G ee G e *) t. I tes G e
- s ID /
r ui of C C. s. : 8 U1 G C U1 e .J tr G h3 U1 o
- O m o
- l * * * * >
tt
- e
- r) 8 e * ** C3 *e' un I tal
- . G &
. Ist i En *
- r** iS G 13 Q G > (3 in O >.J 5' t-
't > e. C 7 e in Q ft e e eri di 87 t** Q G
- e 9
a *
- tt et s
- >e>@
C-14 O O o TABLE C-2. RESULTS
SUMMARY
FOR SPRAY ARM NOZZLE DAMAGE ANALYSIS Dimensions Mass / Unit I* Pact Velocity' Length Final Minimum Total Crushs Ib-sec2 Causing Damage (f s)
P Missile Diameter 3 Width Length 2 Weight Strength Subset Description (in.)
(in.)
(in.)
(psi) in2 1
Rebar 1.000 36.0 8
84,000
.000576 207.7 70.1 226 50,400
.008342 35.1 I
2 Gas Cylinder 3.469 82.9 163 50,400
.005084 44.0
)
3 Drum 19.918 4
Utility Pole 13.500 420.0 1,122 7.750
.006921 5
Cable Reel 12.700 23.2 272 2,858
.030380 33.3 6
3-in Pipe 3.500 120.0 76 49,000
.001636 61.9 7
6-in Pipe 6.630 180.0 284 49,000
.004080 31.7 8
12-in Pipe 12.750 180.0 743 49,000
.010710
?
9 Storage Bin 1.055 38.40 238.0 2,232 50,400
.024290 G
10 concrete Frag 22.000 88.00 176.0 28,600 7,800
.421000 11 Wood Beam 4.000 12.00 144.0 158 2,858
.002850 42.3 f
12 Wood Plank 1.000 12.00 120.0 33 2,477
.000712 92.8 13 Metal Siding 0.500 48.00 144.0 300 50,400
.005397 30.5 l
14 Plywood Sheet 1.000 48.00 96.0 106 2,4775
.002850 51.3 15 Wide Flange 0.723 11.29 34.0 892 50,400
.006016 6
16 Channel section' O.683 5.11 227.4 225 50,400
.002565 35.2
]
17 Concrete Panel 4.500 84.00 420.0 13,300 7,800
.082040 j
18 Small Eqpt.
2.153 2.15 330.0 1,236 50,400
.009503 19 Large Eqpt.
3.962 3.96 640.5 4,733 50,400
.019140 20 Grating 0.051 43.31 184.1 190 50,400
.002670 38.3 j
21 Large Frame 0.113 97.41 292.2 1,150 50,400
.010200 l
22 Vehicle 50.73 50.73 191.4 3,988 50,400
.053970 1
]
1 Based on minimum area.
2 Average of maximum and minimum values.
Dynamic increase factor (DIF) taken as 1.4 for steel, 1.27 for wood, and 1.3 for concrete.
3 Impact velocity not calculated where missile weight exceeds yield force.
5 Assumed same as plank.
Equivalent rectangular dimensions based on area.
6