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Analysis of jorum containment
Int. J. Rock Mech. Min. Sci. Vol. 8, pp. 77-96. Pergamon Press 1971. Printed in Great Britain
ANALYSIS OF J O R U M C O N T A I N M E N T * B. K. CROWLEY, H. D. GLENN, J. S. KAHN and J. M. THOMSEN Lawrence Radiation Laboratory, University of California, Livermore, California (Received 6 May 1970) Abstract--This paper describes a pioneering calculational effort that dealt with problems
relating to the stemming of an underground nuclear event before the event occurred. The Jorum Event presented two often-encountered situations: stemming of the main emplacement hole and stemming of a satellite hole. This event was unusual, however, in that portions of these holes were located below the water table. One- and two-dimensional, time-dependent, finite difference calculations that solved the conservation equations, with general equations-of-state and static and dynamic frictional forces, were used to simulate the two stemming situations. The models, assumptions and parameters used in the various calculations are discussed. Even when conservative parameters were used to represent the effects of water, the calculational results indicated that the planned stemming configurations would contain the event. GENERAL INTRODUCTION THE Jorum Event, with a yield of approximately 1 Mt, occurred beneath the Pahute Mesa at the Nevada Test Site (NTS) in September 1969. This paper contains a brief discussion of a pioneer effort to employ preshot calculations to investigate the containment problems of a satellite hole and the main emplacement hole associated with this event. The containment problems are identified, the codes and assumptions are described, calculational results are given, and finally the conclusions are presented in light of calculational limitations. This paper represents a state-of-the-art effort that deals with containment problems associated with typical stemming configurations. SATELLITE HOLE DIFFICULTIES Introduction Two possible depths of burial were considered for the Jorum Event: 990 m (3250 ft) and 1160 m (3800 ft). An instrumentation satellite hole, U20E-1, was drilled from the surface to within a horizontal distance of approximately 16 m (50 ft) from the main emplacement hole, U20E. The geometry of the drilled holes is illustrated in Fig. 1. Subsequent to some logging operations, reentry of the satellite hole became impossible beyond 2100 ft. U20E-1 was then abandoned and another satellite hole was drilled. The abandoned portion of U20E-1 from 550 m to 990 m was filled predominately with water, but it also contained some gravel and cement. This condition introduced the question of whether a 1470-ft column of fluid in close proximity to the device might represent a possible vent path to the surface. The first part of the study discussed in this report examined this question. The dynamic effects of the nuclear device on U20E-1 were examined with both one- and two-dimensional calculations for a depth of burial of 990 m, the most extreme condition. The two-dimensional TENSOR-PUFL (TP) calculation [1] examined the interaction of the Work performed under the auspices of the U.S. Atomic Energy Commission. 77 ROCK8/2---^
78
B.K. CROWLEY, H. D. GLENN, J, S, KAHN AND J. M. THOMSEN U20E
U20E - 1 Surfcce 61 m - - - ~ (200 ft)
550 m (1800 ft)
~ - ~
Water table
'iost" satelllte hole
990 rn (3250 ft) -
-
@ 1160 m - (3800 h)
Fro. 1. Vertical section showing the geometric relationships between satellite hole U20E-1 and main emplacement hole U20E. gas and rock with water in the satellite hole. After 25 msec, it was apparent that no permancnt closure o f the satellite hole had occurred. With a start being made at 25 meet, the pressure decay in the stemming was studied using one-dimensional PUTL calculation [2]. These calculations considered various material parameters and stemmiug configurations. It was concluded that the geometry and material in the abandoned portion o f U20E-1 presented no containment problem for a depth of burial of 990 m. In spite o f this favorable result, a depth of burial of 1160 m was decided upon as a precautionary measure. The second part o f this report discusses a containment study of the uncased emplacement hole at a depth of burial o f 1160 m. This study considered two stemming configurations, one of which approximates the stemming that was actually used. This part o f the study used only the one-dimensional I~LrFLcode and various frictional factors.* TENSOR--PUrL: ,4 Two-Dimensional Approach
Geometry A two-dimensional cylindrical geometry code, TENSOR--PtrFL, is used in the following analysis. TLmSORstarts with an initial 2I .6-m radius o f vaporized rock gas. This radius was * It should be called to the attention of the reader that the results of these ono-dimemi ~_av a~l amflys~ are relative. The actual displacement of the stemmtn_ois with respeet to the sm'rotmdi~g ~ , which its may be displaced aloas with the stemmt-S clueto no,~,~al~'ouml shock. Dispbcemmt ofttm surre,~,~/f,~_ medium is not considered in this one-dimensional rUVLanalysis.
ANALYSIS OF JORUM CONTAINMENT
79
obtained from a soc [3] calculation of the Jorum Event. TENSORzones of undisturbed solid rock surround the spherical region of vaporized rock gas. The PtJrL portion of this analysis initially extends from the TENSORcenter line to a radial distance of 17.0 cm. Between axial distances of 0 and 21 "6 m, the PtJFL zones contain cavity rock gas; beyond 21.6 m, the PIJFL zones contain water. A frictional drag term, rw = C~pU2/2, was used in PURL. A conservatively low value for the constant [4] 1/2 @ = 0.005 was used; U is the particle velocity of the water, and p is the density of the water zone. The equations-of-state and the approximate resulting sound speeds used in these calculations for water, concrete, sand and Jorum rock are summarized in Tables 1-4. It is instructive to note that for pressures less than 50 kb, the calculated sound speeds for Jorum rock are generally higher than those for water. However, for pressures greater than 50 kb, but less than 300 kb, the sound speed in the water is greater than in the rock. Our intent was to use the equivalent energy/volume and initial pressures as used in a I -25-Mt soc calculation.* Representing the cavity at a time when vaporization is completed. these initial conditions are: energy/volume = 1 Mb, and pressure = 1 Mb. In order to satisfy this requirement, as well as to expedite these calculations, a conservatively high value of 7 = 2.0 was used for cavity rock gas in both the TENSOR and PUFL portions of ~IENSOR-PUFL.
Graphical representation of results The objective of this two-dimensional calculation was to investigate the interaction of the shock with the rock and the water in the satellite hole. In the following discussion, this TENSOR-PUFL calculation is compared with the one-dimensional soc calculation, which considered just the cavity gas and the surrounding r o c k - - n o water. Figure 2 illustrates shock position and cavity growth as a function of time. The upper curve and symbols indicate the shock positions: (1) in the rock from soc and from the TENSOR portion of TP, and (2) in the water from the PUFL portion of TP. The lower curve and symbols indicate: (1) the cavity gas-rock interface from soc and from TENSOR, and (2) the cavity gas-water interface from FUEL. It is noted in Fig. 2 that the gas-water interface from PUrL is below the gas-rock interfaces from soc and TENSOR. This may be due to the incompleteness of our water equation-of-state below normal densities. A realistic gas-water interface is assumed to be identical with the gas-rock interface. F r o m Fig. 2, the shock positions appear essentially the same in both rock and water. This is also observed in Figs 3-5, where pressure vs axial position is given at times of 5, I0 and 25 msec. Figures 3-5 compare P u r l pressures and TENSOR pressures from zones adjacent to PURL. In Fig. 5, the soc pressures at 25 msec are also shown for comparison. The effect of the faster sound speed in the rock and its interaction with the satellite hole may be seen in Fig. 6, which is a plot of satellite hole diameter vs axial position in the satellite hole. The dimensions are plotted for different times. In all cases, the shock position in the rock precedes the shock position in the water. However, at no time does the rock shock get far enough ahead of the water shock to cause a massive closure of the satellite hole. The growing cavity does tend to pinch portions of the satellite hole. In reality, this pinching causes entrainment of some rock into the water (the mass entrainment effects were not included in the calculations). The pinched rock then becomes enveloped by the growing cavity. The constricted portions of the rock were not permitted to close completely; they * The 1- 25-Mt s o c calculation was chosen as a conservative approximation for the expected yield.
80
B. K. CROWLEY, H. D. GLENN, J. S. KAHN AND J. M. THOMSEN 200
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Fie. 2. Shock position and cavity growthas a function of time. were restricted to a minimum axial position of 10 -2 cm. At the end o f 25 msec, the shocks in water and rock are traveling at about the same velocity (see Fig. 2). The problem was terminated at 27 mscc, since the water zones near the cavity become relatively lower in density (p < 1.0) and our water equation-of-state could not realislicalty handle these low densities. Furthermore, it was apparent that r e z o m n g w a s ~ a r y . Nevertheless, the analysis did resolve the initial question :"How do the shocks in ~ r o c k and water propagate and interact 7" Pinching of the satellite hole does occur; massive closure does not appear to occur. Extrapolation of T~SOR-PC~L to later times
At 25 msee it was noted that the velociti=s in the rock and water are essent'mt!y the same (Tables 1 and 2 and Fig. 5). They remain nearly the same as long as the pressures are between 10 and 20 kb. One infers, then, that no pressure gradient egists across the rook and water. As the pressure decays to below 10 kb, the sound speed in the rock exceeds that in the water by approximately 2000 fps (Tables 1 and 2). This implies a pressure gradient, although slight, across the rock into the water. This gradient acts to prevent separation of the stemming from the rock before the shock in the water arrives at the stemming-water interface.
ANALYSIS OF J O R U M CONTAINMENT
200
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FIG, 3. Pressure as a function of axial position at 5 msec. Xcv = cavity gas-water interface (PUFL) ; X c r = cavity gas-rock interface (TENSOR).
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FIG. 4. Pressure as a function of axial position at l0 msec. Xcp = cavity gas-water interface ( P U F L ) ; cavity gas-rock interface (TENSOR).
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B. K. CROWLEY, H. D. G L E N N , J. S. K A H N A N D J. M. T H O M S E N
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Fro. 5. Pressure as a function of axial position at 25 rmec. XcF ~ cavity gas-water interface (1,trFL; = caeity gas-rock interface (TENSOR); Xc = cavity gas-rock interface (soc).
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FIG. 6. Radius of water column as a function of axial position. Xcr = cavity gas-rock interface (TENSOR). TABLE
1.
JORUM
ROCK
EQUATION-OF-STATE
'TENSOR'
p
PART
USED
IN
THE
'SOC'
AND
OF 'TENSOR-PUFL'
AP
(pU)
(kb---)
~o - - 1
P 3) (g/cm
0 3 10 I0.1 23 23.1 40 75 120 200 300 400 600 800 1000 1570 2190
0 0" 0235 O. 0533 0.0675 O. 1104 0.1183 0" 1472 0" 2083 0"2794 0"3987 0" 5426 0- 6292 0" 7540 O" 8050 0"8354 0"9188 O"9827
2" 3 ( = Po) 2.353 2.421 2.454 2.553 2.571 2" 637 2" 778 2"941 3"215 3" 546 3" 745 4" 032 4" 149 4"219 4-411 4" 558
-Ap (emir.see) -0" 257 O" 306 0.0553 0" 395 0-0543 0" 51 0" 50 0"524 0-54 0" 55 O- 786 0" 835 1" 31 1.69 1-72 2" 05
Soundspeed (fps) -8430 10,040 1810 12,960 1780 16,730 16,400 17,200 17,700 18,100 25,800 27,400 43,000 55,500 56,400 67,300
ANALYSIS OF JORUM CONTAINMENT TABLE 2.
WATER
EQUATION-OF-STATE
USED
IN
83
'PUFL ~ AND
'PUFL'
PART OF 'TENSOR-PUFL'
AP
p
(pn)
(kb)
~-
0 5 10 50 200 450 2200*
0 0"1399 0.2189 0.4848 0"8640 1.2878 4.2544*
1
-- Sound speed Ap (cm//~sec) (fps)
P 3) (g/cm 1.0(= po) 1.1399 1.2189 1.4848 1.8640 2.2878 5.2544
-0-19 0-25 0"39 0"63 0"77 0-77
--
6200 8300 12,700 20,600 25,200 25,200
* Extrapolated point which maintains 25,200-fps sound speed. PUFL:
Analysis of Pressure Decay in Stemming
T o investigate later time effects, p a r t i c u l a r l y the decay o f pressure a b o v e the w a t e r table, o n e - d i m e n s i o n a l PUFL calculations were considered. These calculations all used a pressurevs-time, P(t), b o u n d a r y c o n d i t i o n on the lower water zone. This pressure history, which was o b t a i n e d f r o m the s o c calculation, is shown in Fig. 7. T h e calculations all considered a iO G
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FIG. 7. History of volume-weighted cavity pressure from soc calculation. The two curves shown above are the same; however, upper curve has been expanded 10 × on the time scale when compared with lower curve. rigid-walled, straight column, 34 cm in diameter. The effect o f gravity on the c o l u m n was considered in the calculations.
Geometry F i g u r e 8 illustrates the z o n i n g o f materials in this o n e - d i m e n s i o n a l analysis o f satellite hole stemming. T w o s t e m m i n g geometries, A a n d B, are illustrated. G e o m e t r y A consisted
84
B. K. CROWLEY, H. D. GLENN, J. S. KAHN AND J. M. THOMSEN
of a concrete plug from the surface down to 550 m (1800 ft),and water from the base of the plug down to the sphere of vaporized rock. Geometry B was composed of alternatelayers of sand and concrete in order to assessthe effectthat regions of compressibleand compaotible material can have on the pressure profilein the column. N o objectivecriterialed to specific dimensions of this stemming; it merely represents a possible sand-concrete configuration. Geometry A
1000
Geometry B
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Sliding boundary
P(t)
FIG. 8. Two stemming geometries for the satellite hole.
TABLE 3. CONCRETE EQUATION-OF-STATE USED IN 'PUFL' PROBLEMS
P
(~--1)
(kb) 0 0'2 0"5 1"0 2 5 10 20 50 100 200 500 1000 2OOO 5OOO
0
2.52o(=
0"005
2"533 2" 558 2"712 2' 805 2+943 3" 034 3" 127 3"271 3" 468 3" 742 4" 239 4" 675 5" 279 6- I49
0"015 0"076 0" 113 0" 168 0"204 0" 241 0"298 0" 376 0" 485 0" 682 0" 855 1"095 1-440
AP Ap -- Soundspecd (cm//~sec) (fps)
P (g/cm ~) ao)
--
O' 126 O"109 0"057 0" 103 0" 147 0" 235 0" 328 0'457 0" 504 0" 603 0" 777 1"49 1"29 1" 85
--
4130 3680 1870 3390 4820 7710 10,800 15~ 16,500 19,800 25,~ 48,900 42300 60,700
ANALYSIS OF JORUM CONTAINMENT
85
TABLE4. SAND EQUATION-OF-STATE USED IN ~PUFL' PROBLEMS p
AP -=
p, (g/cma)
0 0"2 0"5 1 2 5 10 20 50 100 200 500 1000 2000 5000
0 0.260 0"369 0"440 0"503 0"613 0"742 0-849 1"010 1-155 1"310 1.520 1-700 1"860 2-140
1"370(=oo) 1'726 l'876 1"973 2"059 2"210 2"387 2"533 2"754 2"952 3'165 3.452 3"699 3"918 4.302
Sound speed
(cm/~sec)
(fps)
-0.0237 0"0458 0"0717 0.1076 0"141 0.168 0.261 0.369 0"502 0"686 1-021 1.42 2"14 2-80
-778 1500 2350 3530 4630 5510 8570 12,100 16,500 22,500 33,500 46,600 70,200 91,900
I n reality, there existed a zone of concrete-grout in the vicinity of 5 5 0 - 6 7 0 m (1800-2200 ft) below the surface. This material has been described as ' p o o r grout', ' m u s h g r o u t ' a n d ' m u c k ' . Since a n equation-of-state for such materials was n o t available, this p o r t i o n o f the p r o b l e m was considered as water. The equations-of-state for these materials are given in Tables 2-4.
Parameter study PUFL is the logical code for the extension of the TENSOR-PUFLcalculation described in the preceding section. T h e geometry illustrated in Fig. 8 consists of a pipe with rigid walls, zoned as described. The P(t) from Fig. 7 was used as the b o u n d a r y c o n d i t i o n at the lower b o u n d a r y o f the pipe; i.e. the lowest water zone. A coefficient of friction for the water of C:/2 = 0.005 was used. This value was used to determine the frictional drag (wall shear stress), r~, = CrpU2/2. Six PUFL calculations were r u n - - t w o sets of three with the same s t e m m i n g geometry. W h e n zone velocity was < 10 cm/sec, the wall shear strengths for the TABLE 5. SUMMARY OF 'PUFL' PARAMETER STUDY
A. rw = 0"005 ?U2 (all cases for water) B. Frictional force/area for solids when zone velocity < I0 cm/sec = static cohesive strengths (SCS) of 1/3 psi for sand, 70 psi for concrete C. Frictional force/area for solids when zone velocity ~> 10 cm/sec Calculation 1 2 3 4 5 6
Geometry Concrete Concrete Concrete Concrete Concrete Concrete
alone alone alone and sand and sand and sand
Frictional force/area 0.1 P 0" 001 P SCS 0-1 P 0-001 P SCS
86
B.K.
CROWLEY,
H.
D.
GLENN,
J. S. KAHN
AND
J. M.
THOMSEN
solids were the static cohesive strengths of 1/3 psi for sand and 70 psi for concrete. When the zone velocity was >/ 10 cm/sec, the frictional force/area was assumed to be 0.1 P, 0"001 P, and the static cohesive strength (SCS); here P represents the current static pressure in a zone. This parameter study is summarized in Table 5.
Graphical representation of results Plots of pressure vs time for the two geometries and three different frictional terms are illustrated in Figs 9-14. Two zones were examined (Fig. 8). Zone 126 represents the first concrete zone in Geometry A. In Geometry B, it is the first sand zone above the water. Zone 188 represents the lowermost concrete zone above the lower sand region in Geometry B. In Geometry A, the concrete zone with a similar initial position is chosen. The relative positions of zones 126 and 188 as a function of time are illustrated in Figs 15-17. Zone 126 results. The initial shock arrives at the lowermost stemming, zone 126, at about 160 msec (Figs 9-11). When the friction force/area is assumed to be SCS (Fig. 9) and 0.001 l
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ANALYSIS OF JORUM CONTAINMENT 3"0 --J
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P (Fig. 10), the pressure peaks at about 200 reset. When the friction force/area is assumed to be 0.1 P (Fig. 11), the peak pressure arrives at the lowermost stemming zone at about 230 msec. The general characteristics of the pressure profiles are seen in Figs 9-11. The shapes of these curves are approximately the same, although slight variations can be seen in the peak pressure values. For the concrete, peak pressures of 3.5, 3.2 and 2.5 kb are seen in zone 126 when frictional force/area of SCS, 0.001 P and 0" 1 P, respectively, are used. The sand peak pressures are lower than the comparable pressures in concrete since, to achieve a given pressure, a larger compression is required for sand than for concrete (see Tables 3 and 4): The shapes of the 0.001 P and SCS pressure curves are more similar than in the 0" 1 P case. In general, however, there are no significant differences among these curves.
Zone 188 results. For zone 188, similar pressure-vs-time plots are illustrated in Figs 12 and 14. For both friction factors, there appears to be only a slight pressure rise, which could be attributed to numerical noise in the calculations. The sand-concrete Geometry B shows a considerably larger pressure response when a frictional foree/area of SCS rather than 0-1 P is used. When a frictional force/area of 0.001 P is used in the concrete Geometry A, there is a distinct pressure rise at about 340 msec with a peak of 770 bars at 480 msec (Figs 12-14). A 991 - - S u r f a c e + ' 660 ~ •x 65O
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] 0.5
I
I,
T
I
[ 1.0
I
T
i
I
t 1.5
~
Time - - s e ¢
l~o. 15. Physical displacement of zones 126 and 188. Friction = SCS,
ANALYSIS
OF JORUM
CONTAINMENT
89
contrast to this behaviour is shown by the sand-concrete Geometry B, where the pressure starts to rise at 700 msec and attains a peak of nearly 200 bars at about 800 msec. Here the ability to inhibit the time arrival of the shock, as well as its intensity, is exhibited by the sand-concrete stemming configuration when the frictional force/area is related to the pressure (0.001 P or 0.1 P)--see Figs 13 and 14. However, the SCS of the concrete inhibits the lower pressure response more effectively in zone 188 than does the sand-concrete configuration (refer to Fig. 12). Physical displacements for zones 126 and 188. Figures 15-17 illustrate the relative positions of zones 126 and 188. The ground surface is assumed capped by a rigid wall. The greatest relative displacement occurs in the sand--concrete geometry with the assumed SCS. Here, sand is compressed and compacted in such a manner that no motion is observed at zone 188. 991.j,
~
66o'r_ / x--
x Surface i
I
i
Zone 188 x~ ×
x
L
i
---e
J
1
~x
J
i
_:
i
J
j
i
J
x
650 r -
E
510
I
,~ 500 -c o 49O--a
Z o n e 126
-x-450 --
x-
:
• S a n d - c o n c r e t e problem X C o n c r e t e problem
"I"
20~" 10
0
I
I
1
I
] 0-5
0
I
.r
I
I
[ 1.0
--
sec
Time
I
I
I
r
I
[...
i
1.5
FIG. 16. Physical displacement of zones 126 and 188. Friction = 0"001 P. 991].
~' Surface ~ -
6 6 0 j ~ x ....
i
I
Z o n e 188
x
~
x •
x
x
E 630~ l~ 490'~~480 F -6
Zone 126
470F - - "
x*-'--&--x
-" x
x*
x----~
,
,
J~-
x~-
,
,
450[~ • Sand-concrete
/
problem
x C o n c r e t e problem I0
0
0
I
I
t
I
,
,
,
,
r
~
see
0.5
] -0 Time
,
r
I
] '5
FIG. 17. Physical displacement of zones 126 and 188. Friction = 0" 1 P.
90
B. K. CROWLEY, H. D. GLENN, J. S. KAHN AND J. M. THOMSEN
The least relative motion was observed when the frictional force/area was assumed to be 0.1 P. Some relatively slight movement is observed at zone 126; none is observed at zone 188. Comments and Recommendations
It should be noted that the most ambiguous aspect of this effort revolves around the 'correct' value for the 'frictional force/area.' There is little guidance in the literature for values of sliding friction when the materials we are concerned with are used. Values like 0" 1 P have been used, but with no experimentally based rationale behind them. The cases represented here are believed to approximate the real world better than previous stemming studies. In conclusion, the portion of the U20E-1 satellite that was filled with water and then adequately stemmed to the surface presents no serious containment problems at burial depths of 990 m (3250 ft) or deeper. EMPLACEMENT HOLE CONSIDERATIONS
Introduction
This portion of the paper examines dynamic effects in the main emplacement hole, U20E It correlates the effectiveness of two different stemming configurations (Fig. 18) in containCement
plug
Geometry 1T ~/~/¢~,~{~./~, ~ J ~~5. ~2,~, , /~ c,,,,,m,,..,, ,,,~
Sand stemmln~
I o = 1,37g/cm3
Sand stemm|ng
0ff-Cement
Geometry "[ ~/.s~eg~wem~[pL~~
Surface
0m--
plug
200 m --
i
Cement plug
] P = 1 "37g/cm 3
Sand stemm|ng
•-,,-- Zone 266 ~ , , ~ / - ~ 1000 ft
p = 1.37 g / : ~
I -~.--Zone 227
Cement
plug
400 m-
Sand
o = 1.37g/cm 3
sternmlng
Zone 175-
600m--
2OOO
Water
P =l,00g/cm 3
Water
P = 1.00 g/cm 3
800 m--
3000 1000 m-d = 160 cm
,
i
3800
)(Working polnt
d = 160cm
Working polnt ×
i
FIe. 18. Two stemming geometries for the main emplacement hole.
1150 m -
ANALYSIS OF JORUM CONTAINMENT
91
ing the Jorum Event. A dynamic study was performed (similar to the one for the satellite hole) using the one-dimensional vcrvL code [2] with various frictional factors for the different stemming materials. At similar positions, significantly greater pressures and displacements occur in the emplacement hole than in the satellite hole. This difference is attributed to the much larger diameter (160 cm) of the emplacement hole, as compared with the 34-cm diameter of the satellite hole.
Pressure Profile Above Water Column and Physical Motion of Stemming Materials in U20E Emplacement Hole Geometry Figure 18 illustrates the two stemming configurations used in the one-dimensional analysis. Each material is represented by a density, as indicated in Fig. 18, and the appropriate equation of state, as given in Tables 1-4. Both stemming geometries contain a 33-m (approximately 110-ft) section of unsolidified concrete 'mush' at the top of the emplacement hole. Although it takes approximately three weeks for a complete set to occur after pouring, the normal interval between pouring and shot time is three days. Consequently, the cohesive strength between the mush concrete and surrounding media is reduced from 70 psi (the value used in the satellite hole calculations) to approximately 10 psi. This revised cohesive strength for concrete is incorporated in the calculations. In an attempt to reduce shock propagation and motion of the sand backfill, two 16-m (approximately 50-ft) mush concrete plugs, 245 m and 370 m from the surface, were considered in one configuration (Geometry II, Fig. 18). Plugs are frequently used to prevent late-time sloughing of the sand backfill into the cavity and to add insurance against the possibility of leakage.
Boundary conditions and parameter study The geometry illustrated in Fig. 18 is a cylinder 160 cm in diameter with rigid walls; a constant 1-bar pressure is maintained at the surface. The cavity pressure as a function of time, P(t), from Fig. 7 was used to describe the driving force at the working point. A water-friction coefficient of Cs/2 = 0-005 was used in the calculation. This coefficient was used to determine the frictional drag CspU2/2. Two sets of VUFL calculations were run with the two stemming configurations shown in Fig. 18. Each configuration was run with two different friction forces. When the zone velocity was < 10 cm/sec, the wall shear strength between the stemming material and the walls of the containing cylinder was assumed to be the same as the SCS. Values of the SCS of 1/3 psi for sand and 10 psi for the mush concrete were used. When the zone velocity was /> 10 cm/sec, the frictional force/area was assumed to be 0.001 P and 0.01 P. In the absence of any experimental data, a conservative estimate of frictional force/area of 0.01 P was chosen. Even this conservative choice was found to be sufficient for containment. A more realistic estimate [3] would be in the range of 4-40 times that value. For example, Teflon on steel is 0.04 P, and hard steel on hard steel is 0 -42 P. However, to check the sensitivity of the results to this parameter, an unrealistically low estimate of 0.001 P was considered for the two geometries described in Fig. 118. Four calculations were considered: two for Geometry I, 0"01 P and 0"001 P; two for Geometry II, 0"01 P and 0.001 P. The results of these four calculations are summarized below.
92
B. K. CROWLEY, H. D. G L E N N , J. S. K A H N A N D J. M. T H O M S E N
Graphical representation of results From the lowest water zone to the first concrete plug, the two geometries have identical stemming configurations (see Fig. 18). To correlate the effectiveness of the different stemming geometries and friction factors, plots of calculated pressure vs time are given in Figs 19-21. These figures represent the pressure histories for the first two seconds of three different zones (zones 175, 227 and 266)--see Fig. 18. Zone 175 represents the first sand zone above the water level at 1800 ft below the surface. In Geometry II, zones 227 and 266 represent the bottoms of the two lower 16-m concrete plugs; in Geometry I they represent the corresponding sand zones. The vertical positions of zones 175, 227 and 266 as a function of time for a friction of 0.001 P are shown in Fig. 22. Figure 23 shows the time history of these zones for a friction of 0 "01 P. Zone 175 shock pressure results. Figure 19 indicates that the initial shock arrives at the lowest sand zone at approximately 220 msec for all four problems. The pressure peaks are a 4.0 tc~
Zone 175: Sand-water interface ( 1800 ft) • Geometry I (sand) Friction force =0.001 P
3.0
I 2,0
a Geometry I (sand) Frictlon force =0.01 P ,~ Geomeh',/11"(sand-concrete) Friction force = 0.001 P x Geometry IT (sand-concrete) Frlct|on force = 0.01 P
t
1.0
,"T'~,
0.5
~ ' ~ ,
i
1'0
,
,
~
,
~,
1"5
.
.
,
.
2.0
Time -- sac
FIG. 19. Pressure history at zone 175.
3.0
Zone 227 (1250 if)
• Geometry I (sand) Friction force =0.001 P o Geometry T (sand) Friction force =0.01 P
2.0
A Geometry 11"(sand and concrete) Frlctton force = 0.001 P x Geometry 11"(sand and concrete) Fr|ctlon force =0.01 P
I
1.0
0.5
1.0
1.5
Time - - sec
FIG. 20. Pressure history at zone 227.
2.0
ANALYSIS OF JORUM CONTAINMENT
.
.
.
.
t
,
,
,
,
i
,
,
,
,
1
,
93
,
,
1
Zone 266 (850 ft)
1.o
• Geometry I (sand) Friction force = 0.001 P a Geometry I (sand) Friction force = 0.01 P Geometry 11 (sand and concrete) Friction force =0.00l P
I
x Geometry ] I (sand and concrete)
~,o.5
-Overburden pressure 0
0.5
I'0 Time - - sec
1'5
2.0
FIG. 21. Pressure history at zone 266.
1180 1160 1140 <__
Air
/
Free surface
/~ 4- .....
Concrete
×_
~•j - - ~
i
~-Zone 345
1120
q
960 94O
--
_x- - o--
× ~
~x---°-
d
920 Con c re te
90C
-----x
s l ~ x Jl'~
Sand
E
~-Zone
86O 1 ~ 84O
266
~,x ~
Z
--"-
-~
.~ a2o ~
800
c
.....
760
x
-
~ .
te
Sand
\~ - Z o n e
227
700'" 680 660
-
640
-
x/X / J
_ _
0
r
--x
Geometry I (sand) Friction force = 0 ' 0 0 1 P Geometry I I (sand - c o n c r e t e )
x
_
Friction force = 0"001 P
×
600 - Water ~ - Z o n e T
x
.... •
/
-Sand
620
o~:: ~x~
._
,
,
175 r
I
0-5
r
I
r
r
r 1.0
i
7
l
l
I
I
r
T
1.5
Time -- sec
FIG. 22. Displacement histories of zones 175, 227 and 266 for a friction of 0"001 P. ROCK8/2--B
94
B. K. CROWLEY, H. D. GLENN, J. S. KAHN AND J. M. THOMSEN 1150 Air
1145 1140
:<
•
Free surface
X-
Concrefe
Lone
X
=
X'
•
345
1135
I
910 Concrete •
Sand
~-~.one 266
:c
E 780
l
Concrete
K~
Sand
,~ 770
~---Zono 227
X.,,
•
X
630
* Geomtt,/I (rod) Friction force =0-01 P
620
X Geonlefry11"($ond-concr•lep[ug6) Friction force = 0.01 P
600~" Water
'
'
~--Zone 175
'
'
0!5
t
t
t
w
Time ~
I
1.o
~
t
t
t
I
i .5
t
t
~lec
FXo.23. Displacem~t histories of zones 175, 227 and 266 for a friction of 0.01P. factor of approximately 2 . 5 higher than those obtained in the satellite hole for the lowest sand zone. This high pressure can be attributed to the reduced drag force on the water column because o f the larger diameter of the main emplacement hole. The frictional force, Ft [2], equation (12) is inversely proportional to the radius, R, of the emplacement hole: rwS m
zwS pV
~'w2~rRL ~',~ 2 m,R~L = -p R
Zone 227 shock pressure results. Pressure-vs-time plots from the four calculations for zone 227 are illustrated in Fig. 20. Shock arrival occurs about 70 msec earlier for the lower (0.001 P) frictional case. In zone 227, peak pressures for the concrete are 2.4 and 0.4 kb, when the friction force/area is 0.001 P and 0.01 P, respectively. ~ conzrete (Geometry If) peak pressures are higher than in the comparable sand zone (Geometry I). To achieve a given pressure, a smaller compression is required for the concrete than for the sand. Although greater peak pressures are seen in Geometry H for zone 227, a more important
ANALYSIS OF JORUM CONTAINMENT
95
criterion for containment is the vertical displacement associated with each stemming configuration. A discussion of the displacement results is given later. Zone 266 shock pressure results. Pressure-vs-time plots from the four calculations for zone 266 are presented in Fig. 21. This figure demonstrates the dependence of the hydrodynamic results on the frictional factors. The frictional force/area of 0-01 P was sufficient to completely attenuate the shock propagating in the stemming material, and thus prevent it from reaching the second concrete plug position. However, when the frictional force/area of 0.001 P is used, sizable pressures are obtained in zone 266 for the two geometries considered. Comparison of these results implies that appreciable positive vertical motion of zone 227 has taken place in the 0"001 P case. The previous results and discussion of pressure are essentially an introduction to the main question of stemming containment: " W h a t physical displacements are associated with the stemming material in the main emplacement hole ?"
Physical displacements of plugs and stemming material Results for 0"001 P assumptions. Figure 22 shows the displacement of the concrete plugs in Geometry II and the corresponding sand regions of Geometry I. Displacement of the surface plug, common to both problems, is also shown. With an unrealistically low friction factor of 0.001 P, the PUrL calculation showed motion beginning at the top plug at approximately 1.5 sec. This should not cause alarm, however, since these two problems were run only to determine the sensitivity of the results to the friction force. The corresponding case (i.e. frictional force/area = 0"001 P) in the satellite hole study indicated no motion occurred for the top 550 m (1800 ft) of stemming material. The difference is attributed to the larger diameter of the emplacement hole. Results for 0.01 P assumptions. Figure 23 is the same plot for the 0.01 P friction force. Since the stemming geometry in both problems is identical up to the ~rst concrete plug, the motion of zone 175 (the sand-water interface) is the same for Geometry I and Geometry II. From 0.2 to 0.5 sec, zone 175 moves 36 m, or 118 ft; no upward motion was found after 0.5 sec. The upward motion of zone 227, the first concrete plug of Geometry II, was 1 m less than the motion of the corresponding stemming material of Geometry I. Motion in both cases begins at 0-55 sec and is completed by 0.75 sec. The plug moves 4 m or 13 It; the stemming material moves 5 m or 16 ft. Finally, in both cases, no upward motion was found at zone 266, the base of the second concrete plug of Geometry I[, or the stemming material of Geometry I--indicating containment of the hydrodynamic flow for both stemming geometries. Because no corresponding case (i.e. frictional force/area = 0.01 P) was calculated for the satellite study, no comparisons of results are feasible.
Conclusions and Recommendations The primary factor in prohibiting the motion of the stemming material is the dynamic frictional force assumed between the stemming material and surrounding media. It is considerably more important than the static cohesive strengths one assumes (e.g. 10 psi vs 70 psi for concrete plugs with surrounding media). Sensitivity to the frictional factor is shown in Figs 22 and 23, which compare the results obtained by setting the frictional force/ area equal to 0.001 P and 0.01 P. When the unrealistically low estimate of frictional force/ area = 0.001 P is assumed, Fig. 22 indicates that the upward displacement of the total column of stemming material is significant. This suggests the possibility of a vent occurring. However, in Fig. 23, no physical displacement is indicated for the top 1800 ft of stemming
96
B. K. CROWLEY, H. D. GLENN, J. S. KAHN AND J. M. THOMSEN
material when the more realistic value of 0.01 P is assumed. This suggests that venting through the emplacement hole would not occur. There are no data in the literature giving values of sliding friction for the materials in the pressure and velocity range with which we are concerned. This suggests that an experimental effort could be of value. From hydrodynamic considerations, the results of the four problems considered indicate that there is little difference between the two stemming configurations. However, the emplacement of several plugs was considered advisable for prevention of late-time sloughing of stemming materials into the cavity. REFERENCES I. C R O W L ~ B. K. and BARR L. K. TENSOR-PUFL: Boundary.Condition-Linked Codes, Lawrence Radiation Laboratory, Livermore, Report UCRL-72120 (1969). 2. C R O W L ~ B. K. rUFL, an "almost ~ g i a n ' gasdynamic calculation.J. comp. Phys. 2, 61 (1967). 3. G m u o . ~ L. S. and KAHN J. S. Phenomenology of Undergrotmd Nuck~r ~ s i o n s , Proceedings of the 50th Annual Meeting of the American Geophysical Union, Washington, D.C., American Geophysical Union, Washington, D.C. (1969). 4. American Instituteof Physics Handbook, 2nd edn, McGraw-Hill, New York (1963).
ANALYSIS OF J O R U M C O N T A I N M E N T * B. K. CROWLEY, H. D. GLENN, J. S. KAHN and J. M. THOMSEN Lawrence Radiation Laboratory, University of California, Livermore, California (Received 6 May 1970) Abstract--This paper describes a pioneering calculational effort that dealt with problems
relating to the stemming of an underground nuclear event before the event occurred. The Jorum Event presented two often-encountered situations: stemming of the main emplacement hole and stemming of a satellite hole. This event was unusual, however, in that portions of these holes were located below the water table. One- and two-dimensional, time-dependent, finite difference calculations that solved the conservation equations, with general equations-of-state and static and dynamic frictional forces, were used to simulate the two stemming situations. The models, assumptions and parameters used in the various calculations are discussed. Even when conservative parameters were used to represent the effects of water, the calculational results indicated that the planned stemming configurations would contain the event. GENERAL INTRODUCTION THE Jorum Event, with a yield of approximately 1 Mt, occurred beneath the Pahute Mesa at the Nevada Test Site (NTS) in September 1969. This paper contains a brief discussion of a pioneer effort to employ preshot calculations to investigate the containment problems of a satellite hole and the main emplacement hole associated with this event. The containment problems are identified, the codes and assumptions are described, calculational results are given, and finally the conclusions are presented in light of calculational limitations. This paper represents a state-of-the-art effort that deals with containment problems associated with typical stemming configurations. SATELLITE HOLE DIFFICULTIES Introduction Two possible depths of burial were considered for the Jorum Event: 990 m (3250 ft) and 1160 m (3800 ft). An instrumentation satellite hole, U20E-1, was drilled from the surface to within a horizontal distance of approximately 16 m (50 ft) from the main emplacement hole, U20E. The geometry of the drilled holes is illustrated in Fig. 1. Subsequent to some logging operations, reentry of the satellite hole became impossible beyond 2100 ft. U20E-1 was then abandoned and another satellite hole was drilled. The abandoned portion of U20E-1 from 550 m to 990 m was filled predominately with water, but it also contained some gravel and cement. This condition introduced the question of whether a 1470-ft column of fluid in close proximity to the device might represent a possible vent path to the surface. The first part of the study discussed in this report examined this question. The dynamic effects of the nuclear device on U20E-1 were examined with both one- and two-dimensional calculations for a depth of burial of 990 m, the most extreme condition. The two-dimensional TENSOR-PUFL (TP) calculation [1] examined the interaction of the Work performed under the auspices of the U.S. Atomic Energy Commission. 77 ROCK8/2---^
78
B.K. CROWLEY, H. D. GLENN, J, S, KAHN AND J. M. THOMSEN U20E
U20E - 1 Surfcce 61 m - - - ~ (200 ft)
550 m (1800 ft)
~ - ~
Water table
'iost" satelllte hole
990 rn (3250 ft) -
-
@ 1160 m - (3800 h)
Fro. 1. Vertical section showing the geometric relationships between satellite hole U20E-1 and main emplacement hole U20E. gas and rock with water in the satellite hole. After 25 msec, it was apparent that no permancnt closure o f the satellite hole had occurred. With a start being made at 25 meet, the pressure decay in the stemming was studied using one-dimensional PUTL calculation [2]. These calculations considered various material parameters and stemmiug configurations. It was concluded that the geometry and material in the abandoned portion o f U20E-1 presented no containment problem for a depth of burial of 990 m. In spite o f this favorable result, a depth of burial of 1160 m was decided upon as a precautionary measure. The second part o f this report discusses a containment study of the uncased emplacement hole at a depth of burial o f 1160 m. This study considered two stemming configurations, one of which approximates the stemming that was actually used. This part o f the study used only the one-dimensional I~LrFLcode and various frictional factors.* TENSOR--PUrL: ,4 Two-Dimensional Approach
Geometry A two-dimensional cylindrical geometry code, TENSOR--PtrFL, is used in the following analysis. TLmSORstarts with an initial 2I .6-m radius o f vaporized rock gas. This radius was * It should be called to the attention of the reader that the results of these ono-dimemi ~_av a~l amflys~ are relative. The actual displacement of the stemmtn_ois with respeet to the sm'rotmdi~g ~ , which its may be displaced aloas with the stemmt-S clueto no,~,~al~'ouml shock. Dispbcemmt ofttm surre,~,~/f,~_ medium is not considered in this one-dimensional rUVLanalysis.
ANALYSIS OF JORUM CONTAINMENT
79
obtained from a soc [3] calculation of the Jorum Event. TENSORzones of undisturbed solid rock surround the spherical region of vaporized rock gas. The PtJrL portion of this analysis initially extends from the TENSORcenter line to a radial distance of 17.0 cm. Between axial distances of 0 and 21 "6 m, the PtJFL zones contain cavity rock gas; beyond 21.6 m, the PIJFL zones contain water. A frictional drag term, rw = C~pU2/2, was used in PURL. A conservatively low value for the constant [4] 1/2 @ = 0.005 was used; U is the particle velocity of the water, and p is the density of the water zone. The equations-of-state and the approximate resulting sound speeds used in these calculations for water, concrete, sand and Jorum rock are summarized in Tables 1-4. It is instructive to note that for pressures less than 50 kb, the calculated sound speeds for Jorum rock are generally higher than those for water. However, for pressures greater than 50 kb, but less than 300 kb, the sound speed in the water is greater than in the rock. Our intent was to use the equivalent energy/volume and initial pressures as used in a I -25-Mt soc calculation.* Representing the cavity at a time when vaporization is completed. these initial conditions are: energy/volume = 1 Mb, and pressure = 1 Mb. In order to satisfy this requirement, as well as to expedite these calculations, a conservatively high value of 7 = 2.0 was used for cavity rock gas in both the TENSOR and PUFL portions of ~IENSOR-PUFL.
Graphical representation of results The objective of this two-dimensional calculation was to investigate the interaction of the shock with the rock and the water in the satellite hole. In the following discussion, this TENSOR-PUFL calculation is compared with the one-dimensional soc calculation, which considered just the cavity gas and the surrounding r o c k - - n o water. Figure 2 illustrates shock position and cavity growth as a function of time. The upper curve and symbols indicate the shock positions: (1) in the rock from soc and from the TENSOR portion of TP, and (2) in the water from the PUFL portion of TP. The lower curve and symbols indicate: (1) the cavity gas-rock interface from soc and from TENSOR, and (2) the cavity gas-water interface from FUEL. It is noted in Fig. 2 that the gas-water interface from PUrL is below the gas-rock interfaces from soc and TENSOR. This may be due to the incompleteness of our water equation-of-state below normal densities. A realistic gas-water interface is assumed to be identical with the gas-rock interface. F r o m Fig. 2, the shock positions appear essentially the same in both rock and water. This is also observed in Figs 3-5, where pressure vs axial position is given at times of 5, I0 and 25 msec. Figures 3-5 compare P u r l pressures and TENSOR pressures from zones adjacent to PURL. In Fig. 5, the soc pressures at 25 msec are also shown for comparison. The effect of the faster sound speed in the rock and its interaction with the satellite hole may be seen in Fig. 6, which is a plot of satellite hole diameter vs axial position in the satellite hole. The dimensions are plotted for different times. In all cases, the shock position in the rock precedes the shock position in the water. However, at no time does the rock shock get far enough ahead of the water shock to cause a massive closure of the satellite hole. The growing cavity does tend to pinch portions of the satellite hole. In reality, this pinching causes entrainment of some rock into the water (the mass entrainment effects were not included in the calculations). The pinched rock then becomes enveloped by the growing cavity. The constricted portions of the rock were not permitted to close completely; they * The 1- 25-Mt s o c calculation was chosen as a conservative approximation for the expected yield.
80
B. K. CROWLEY, H. D. GLENN, J. S. KAHN AND J. M. THOMSEN 200
/
160
Shockpos|t|onin
~o~k(*)
140!
and water
(~)~,t t /
~
i
.Z/ E
soc
120i-X
I
. . . .
i
PUFL
= 100 < 8O
/y
f~ENSO~g .... k)
6O .irl~.'~".
4O
t
posltbn
/
PUFL(g~-wo~,)-/
2O 0
)interia •
LSOC (g~-rock)
~ l ~
This decrease may be unmallitia due to water :~onel near cavity not ullng a gas equatlon-of-state
I
I 10
l
,I 20
I
I
~
30 Time - -
I 40
l
I 50
I,
,I 60
..l
70
mse~
Fie. 2. Shock position and cavity growthas a function of time. were restricted to a minimum axial position of 10 -2 cm. At the end o f 25 msec, the shocks in water and rock are traveling at about the same velocity (see Fig. 2). The problem was terminated at 27 mscc, since the water zones near the cavity become relatively lower in density (p < 1.0) and our water equation-of-state could not realislicalty handle these low densities. Furthermore, it was apparent that r e z o m n g w a s ~ a r y . Nevertheless, the analysis did resolve the initial question :"How do the shocks in ~ r o c k and water propagate and interact 7" Pinching of the satellite hole does occur; massive closure does not appear to occur. Extrapolation of T~SOR-PC~L to later times
At 25 msee it was noted that the velociti=s in the rock and water are essent'mt!y the same (Tables 1 and 2 and Fig. 5). They remain nearly the same as long as the pressures are between 10 and 20 kb. One infers, then, that no pressure gradient egists across the rook and water. As the pressure decays to below 10 kb, the sound speed in the rock exceeds that in the water by approximately 2000 fps (Tables 1 and 2). This implies a pressure gradient, although slight, across the rock into the water. This gradient acts to prevent separation of the stemming from the rock before the shock in the water arrives at the stemming-water interface.
ANALYSIS OF J O R U M CONTAINMENT
200
h'"
81
] XCp= 35,6 I X
=35.9
~we~
1oo
@,,~',~e =4 • • • IA
I ca,.
lo • PUFL TENSOR
t: r •
%0
,
f
l
10
'3
I
20
r
e
I
30
r
40
L,
I
.I,
50
60
r 70
Axial position - - rn
FIG, 3. Pressure as a function of axial position at 5 msec. Xcv = cavity gas-water interface (PUFL) ; X c r = cavity gas-rock interface (TENSOR).
100 Xcp = 37. ~
•
~al~
..s=F
• I
XCT = ,43. B
%%~a go•
10
• PUFL TENSOR
• z~
1.o
~.
I lO
~
I 20
~
T 30
i
f f I r [ 40 50 60 Axial position - - In
i
r 70
~
~,~ 80
I . F 90 100
FIG. 4. Pressure as a function of axial position at l0 msec. Xcp = cavity gas-water interface ( P U F L ) ; cavity gas-rock interface (TENSOR).
.~i~ci,- =
B. K. CROWLEY, H. D. G L E N N , J. S. K A H N A N D J. M. T H O M S E N
82 10g
I
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l
'T
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~
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t
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t
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l
/ - 5 2 X c SOC t"
x SOC
~
":2
~X ~' x ~
20
30
X
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I'''~
1
~
'q
' .....
xxx
~
• PUFL .~ TENSOR
. , ,... .
.
.1
~
:
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~ o~-
,x
x
IQ
tea O"
10
40
50
60
70
80
90
100
110
120
130
140
150
Axial position -- m
Fro. 5. Pressure as a function of axial position at 25 rmec. XcF ~ cavity gas-water interface (1,trFL; = caeity gas-rock interface (TENSOR); Xc = cavity gas-rock interface (soc).
e
~o-
L. 1
Xcr
.
rl ii
-i
100 Axlal I~Itlon
- -
m
FIG. 6. Radius of water column as a function of axial position. Xcr = cavity gas-rock interface (TENSOR). TABLE
1.
JORUM
ROCK
EQUATION-OF-STATE
'TENSOR'
p
PART
USED
IN
THE
'SOC'
AND
OF 'TENSOR-PUFL'
AP
(pU)
(kb---)
~o - - 1
P 3) (g/cm
0 3 10 I0.1 23 23.1 40 75 120 200 300 400 600 800 1000 1570 2190
0 0" 0235 O. 0533 0.0675 O. 1104 0.1183 0" 1472 0" 2083 0"2794 0"3987 0" 5426 0- 6292 0" 7540 O" 8050 0"8354 0"9188 O"9827
2" 3 ( = Po) 2.353 2.421 2.454 2.553 2.571 2" 637 2" 778 2"941 3"215 3" 546 3" 745 4" 032 4" 149 4"219 4-411 4" 558
-Ap (emir.see) -0" 257 O" 306 0.0553 0" 395 0-0543 0" 51 0" 50 0"524 0-54 0" 55 O- 786 0" 835 1" 31 1.69 1-72 2" 05
Soundspeed (fps) -8430 10,040 1810 12,960 1780 16,730 16,400 17,200 17,700 18,100 25,800 27,400 43,000 55,500 56,400 67,300
ANALYSIS OF JORUM CONTAINMENT TABLE 2.
WATER
EQUATION-OF-STATE
USED
IN
83
'PUFL ~ AND
'PUFL'
PART OF 'TENSOR-PUFL'
AP
p
(pn)
(kb)
~-
0 5 10 50 200 450 2200*
0 0"1399 0.2189 0.4848 0"8640 1.2878 4.2544*
1
-- Sound speed Ap (cm//~sec) (fps)
P 3) (g/cm 1.0(= po) 1.1399 1.2189 1.4848 1.8640 2.2878 5.2544
-0-19 0-25 0"39 0"63 0"77 0-77
--
6200 8300 12,700 20,600 25,200 25,200
* Extrapolated point which maintains 25,200-fps sound speed. PUFL:
Analysis of Pressure Decay in Stemming
T o investigate later time effects, p a r t i c u l a r l y the decay o f pressure a b o v e the w a t e r table, o n e - d i m e n s i o n a l PUFL calculations were considered. These calculations all used a pressurevs-time, P(t), b o u n d a r y c o n d i t i o n on the lower water zone. This pressure history, which was o b t a i n e d f r o m the s o c calculation, is shown in Fig. 7. T h e calculations all considered a iO G
10 5
2 [ IO 4
!
to o 13_
fO 3
~o2
r I0
1 20 Upper
0
Io0
200 Lower
J
r
P
30
40
50
60
F 70
500
600
700
curve--msec 300
400
curve
lime-
m sec
FIG. 7. History of volume-weighted cavity pressure from soc calculation. The two curves shown above are the same; however, upper curve has been expanded 10 × on the time scale when compared with lower curve. rigid-walled, straight column, 34 cm in diameter. The effect o f gravity on the c o l u m n was considered in the calculations.
Geometry F i g u r e 8 illustrates the z o n i n g o f materials in this o n e - d i m e n s i o n a l analysis o f satellite hole stemming. T w o s t e m m i n g geometries, A a n d B, are illustrated. G e o m e t r y A consisted
84
B. K. CROWLEY, H. D. GLENN, J. S. KAHN AND J. M. THOMSEN
of a concrete plug from the surface down to 550 m (1800 ft),and water from the base of the plug down to the sphere of vaporized rock. Geometry B was composed of alternatelayers of sand and concrete in order to assessthe effectthat regions of compressibleand compaotible material can have on the pressure profilein the column. N o objectivecriterialed to specific dimensions of this stemming; it merely represents a possible sand-concrete configuration. Geometry A
1000
Geometry B
Cormrete//H/H/Rigid H/H.wall /,~ ...~ Sand-concre.////////t~/,
-
I
1+,.I
E I
~L
500 -
500
g
++t1++i ~J d=34cm
d=34¢m [
0 -
10oo P (t)
Sliding boundary
P(t)
FIG. 8. Two stemming geometries for the satellite hole.
TABLE 3. CONCRETE EQUATION-OF-STATE USED IN 'PUFL' PROBLEMS
P
(~--1)
(kb) 0 0'2 0"5 1"0 2 5 10 20 50 100 200 500 1000 2OOO 5OOO
0
2.52o(=
0"005
2"533 2" 558 2"712 2' 805 2+943 3" 034 3" 127 3"271 3" 468 3" 742 4" 239 4" 675 5" 279 6- I49
0"015 0"076 0" 113 0" 168 0"204 0" 241 0"298 0" 376 0" 485 0" 682 0" 855 1"095 1-440
AP Ap -- Soundspecd (cm//~sec) (fps)
P (g/cm ~) ao)
--
O' 126 O"109 0"057 0" 103 0" 147 0" 235 0" 328 0'457 0" 504 0" 603 0" 777 1"49 1"29 1" 85
--
4130 3680 1870 3390 4820 7710 10,800 15~ 16,500 19,800 25,~ 48,900 42300 60,700
ANALYSIS OF JORUM CONTAINMENT
85
TABLE4. SAND EQUATION-OF-STATE USED IN ~PUFL' PROBLEMS p
AP -=
p, (g/cma)
0 0"2 0"5 1 2 5 10 20 50 100 200 500 1000 2000 5000
0 0.260 0"369 0"440 0"503 0"613 0"742 0-849 1"010 1-155 1"310 1.520 1-700 1"860 2-140
1"370(=oo) 1'726 l'876 1"973 2"059 2"210 2"387 2"533 2"754 2"952 3'165 3.452 3"699 3"918 4.302
Sound speed
(cm/~sec)
(fps)
-0.0237 0"0458 0"0717 0.1076 0"141 0.168 0.261 0.369 0"502 0"686 1-021 1.42 2"14 2-80
-778 1500 2350 3530 4630 5510 8570 12,100 16,500 22,500 33,500 46,600 70,200 91,900
I n reality, there existed a zone of concrete-grout in the vicinity of 5 5 0 - 6 7 0 m (1800-2200 ft) below the surface. This material has been described as ' p o o r grout', ' m u s h g r o u t ' a n d ' m u c k ' . Since a n equation-of-state for such materials was n o t available, this p o r t i o n o f the p r o b l e m was considered as water. The equations-of-state for these materials are given in Tables 2-4.
Parameter study PUFL is the logical code for the extension of the TENSOR-PUFLcalculation described in the preceding section. T h e geometry illustrated in Fig. 8 consists of a pipe with rigid walls, zoned as described. The P(t) from Fig. 7 was used as the b o u n d a r y c o n d i t i o n at the lower b o u n d a r y o f the pipe; i.e. the lowest water zone. A coefficient of friction for the water of C:/2 = 0.005 was used. This value was used to determine the frictional drag (wall shear stress), r~, = CrpU2/2. Six PUFL calculations were r u n - - t w o sets of three with the same s t e m m i n g geometry. W h e n zone velocity was < 10 cm/sec, the wall shear strengths for the TABLE 5. SUMMARY OF 'PUFL' PARAMETER STUDY
A. rw = 0"005 ?U2 (all cases for water) B. Frictional force/area for solids when zone velocity < I0 cm/sec = static cohesive strengths (SCS) of 1/3 psi for sand, 70 psi for concrete C. Frictional force/area for solids when zone velocity ~> 10 cm/sec Calculation 1 2 3 4 5 6
Geometry Concrete Concrete Concrete Concrete Concrete Concrete
alone alone alone and sand and sand and sand
Frictional force/area 0.1 P 0" 001 P SCS 0-1 P 0-001 P SCS
86
B.K.
CROWLEY,
H.
D.
GLENN,
J. S. KAHN
AND
J. M.
THOMSEN
solids were the static cohesive strengths of 1/3 psi for sand and 70 psi for concrete. When the zone velocity was >/ 10 cm/sec, the frictional force/area was assumed to be 0.1 P, 0"001 P, and the static cohesive strength (SCS); here P represents the current static pressure in a zone. This parameter study is summarized in Table 5.
Graphical representation of results Plots of pressure vs time for the two geometries and three different frictional terms are illustrated in Figs 9-14. Two zones were examined (Fig. 8). Zone 126 represents the first concrete zone in Geometry A. In Geometry B, it is the first sand zone above the water. Zone 188 represents the lowermost concrete zone above the lower sand region in Geometry B. In Geometry A, the concrete zone with a similar initial position is chosen. The relative positions of zones 126 and 188 as a function of time are illustrated in Figs 15-17. Zone 126 results. The initial shock arrives at the lowermost stemming, zone 126, at about 160 msec (Figs 9-11). When the friction force/area is assumed to be SCS (Fig. 9) and 0.001 l
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,
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FiG. 9. Pressure profiles for zone 126. Friction = SCS. '
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FiG. 10. Pressure profiles f o r zone 126. F r i c t i o n = 0.001 P.
2,4
ANALYSIS OF JORUM CONTAINMENT 3"0 --J
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11. Pressure profiles for z o n e 126. Friction := 0-1 P.
FIG.
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r , r 0'4 0-6
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x.X-x, . . . . . . . . . . . . . . . . . . T
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r
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Fla. 12. Pressure profiles for z o n e 188. Friction = SCS.
1.0
"~'---]"--~
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Initially at ~ame to Sand-concrete problem Z position ) × C . . . . . fe problem
0'8
l.O
1"2
Time
1-4 --
1.6
1"8
2.0
2"2
sec
Fta. 13. Pressure profiles for z o n e •88. Friction = 0.001 P.
2"4
88
B. K. CROWLEY, H, D. G L E N N , J. S. K A H N A N D J. M. T H O M S E N 0.2
. ~ , ~ k ,°verburden ~r
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Time - -
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sac
Fzo. 14. Pressure profiles for zone 188. Friction = O. 1 P.
P (Fig. 10), the pressure peaks at about 200 reset. When the friction force/area is assumed to be 0.1 P (Fig. 11), the peak pressure arrives at the lowermost stemming zone at about 230 msec. The general characteristics of the pressure profiles are seen in Figs 9-11. The shapes of these curves are approximately the same, although slight variations can be seen in the peak pressure values. For the concrete, peak pressures of 3.5, 3.2 and 2.5 kb are seen in zone 126 when frictional force/area of SCS, 0.001 P and 0" 1 P, respectively, are used. The sand peak pressures are lower than the comparable pressures in concrete since, to achieve a given pressure, a larger compression is required for sand than for concrete (see Tables 3 and 4): The shapes of the 0.001 P and SCS pressure curves are more similar than in the 0" 1 P case. In general, however, there are no significant differences among these curves.
Zone 188 results. For zone 188, similar pressure-vs-time plots are illustrated in Figs 12 and 14. For both friction factors, there appears to be only a slight pressure rise, which could be attributed to numerical noise in the calculations. The sand-concrete Geometry B shows a considerably larger pressure response when a frictional foree/area of SCS rather than 0-1 P is used. When a frictional force/area of 0.001 P is used in the concrete Geometry A, there is a distinct pressure rise at about 340 msec with a peak of 770 bars at 480 msec (Figs 12-14). A 991 - - S u r f a c e + ' 660 ~ •x 65O
t
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+ ~
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1 50o490 - -
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.
.
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Sand-concrete problem
× ~ncmte
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10
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~
Time - - s e ¢
l~o. 15. Physical displacement of zones 126 and 188. Friction = SCS,
ANALYSIS
OF JORUM
CONTAINMENT
89
contrast to this behaviour is shown by the sand-concrete Geometry B, where the pressure starts to rise at 700 msec and attains a peak of nearly 200 bars at about 800 msec. Here the ability to inhibit the time arrival of the shock, as well as its intensity, is exhibited by the sand-concrete stemming configuration when the frictional force/area is related to the pressure (0.001 P or 0.1 P)--see Figs 13 and 14. However, the SCS of the concrete inhibits the lower pressure response more effectively in zone 188 than does the sand-concrete configuration (refer to Fig. 12). Physical displacements for zones 126 and 188. Figures 15-17 illustrate the relative positions of zones 126 and 188. The ground surface is assumed capped by a rigid wall. The greatest relative displacement occurs in the sand--concrete geometry with the assumed SCS. Here, sand is compressed and compacted in such a manner that no motion is observed at zone 188. 991.j,
~
66o'r_ / x--
x Surface i
I
i
Zone 188 x~ ×
x
L
i
---e
J
1
~x
J
i
_:
i
J
j
i
J
x
650 r -
E
510
I
,~ 500 -c o 49O--a
Z o n e 126
-x-450 --
x-
:
• S a n d - c o n c r e t e problem X C o n c r e t e problem
"I"
20~" 10
0
I
I
1
I
] 0-5
0
I
.r
I
I
[ 1.0
--
sec
Time
I
I
I
r
I
[...
i
1.5
FIG. 16. Physical displacement of zones 126 and 188. Friction = 0"001 P. 991].
~' Surface ~ -
6 6 0 j ~ x ....
i
I
Z o n e 188
x
~
x •
x
x
E 630~ l~ 490'~~480 F -6
Zone 126
470F - - "
x*-'--&--x
-" x
x*
x----~
,
,
J~-
x~-
,
,
450[~ • Sand-concrete
/
problem
x C o n c r e t e problem I0
0
0
I
I
t
I
,
,
,
,
r
~
see
0.5
] -0 Time
,
r
I
] '5
FIG. 17. Physical displacement of zones 126 and 188. Friction = 0" 1 P.
90
B. K. CROWLEY, H. D. GLENN, J. S. KAHN AND J. M. THOMSEN
The least relative motion was observed when the frictional force/area was assumed to be 0.1 P. Some relatively slight movement is observed at zone 126; none is observed at zone 188. Comments and Recommendations
It should be noted that the most ambiguous aspect of this effort revolves around the 'correct' value for the 'frictional force/area.' There is little guidance in the literature for values of sliding friction when the materials we are concerned with are used. Values like 0" 1 P have been used, but with no experimentally based rationale behind them. The cases represented here are believed to approximate the real world better than previous stemming studies. In conclusion, the portion of the U20E-1 satellite that was filled with water and then adequately stemmed to the surface presents no serious containment problems at burial depths of 990 m (3250 ft) or deeper. EMPLACEMENT HOLE CONSIDERATIONS
Introduction
This portion of the paper examines dynamic effects in the main emplacement hole, U20E It correlates the effectiveness of two different stemming configurations (Fig. 18) in containCement
plug
Geometry 1T ~/~/¢~,~{~./~, ~ J ~~5. ~2,~, , /~ c,,,,,m,,..,, ,,,~
Sand stemmln~
I o = 1,37g/cm3
Sand stemm|ng
0ff-Cement
Geometry "[ ~/.s~eg~wem~[pL~~
Surface
0m--
plug
200 m --
i
Cement plug
] P = 1 "37g/cm 3
Sand stemm|ng
•-,,-- Zone 266 ~ , , ~ / - ~ 1000 ft
p = 1.37 g / : ~
I -~.--Zone 227
Cement
plug
400 m-
Sand
o = 1.37g/cm 3
sternmlng
Zone 175-
600m--
2OOO
Water
P =l,00g/cm 3
Water
P = 1.00 g/cm 3
800 m--
3000 1000 m-d = 160 cm
,
i
3800
)(Working polnt
d = 160cm
Working polnt ×
i
FIe. 18. Two stemming geometries for the main emplacement hole.
1150 m -
ANALYSIS OF JORUM CONTAINMENT
91
ing the Jorum Event. A dynamic study was performed (similar to the one for the satellite hole) using the one-dimensional vcrvL code [2] with various frictional factors for the different stemming materials. At similar positions, significantly greater pressures and displacements occur in the emplacement hole than in the satellite hole. This difference is attributed to the much larger diameter (160 cm) of the emplacement hole, as compared with the 34-cm diameter of the satellite hole.
Pressure Profile Above Water Column and Physical Motion of Stemming Materials in U20E Emplacement Hole Geometry Figure 18 illustrates the two stemming configurations used in the one-dimensional analysis. Each material is represented by a density, as indicated in Fig. 18, and the appropriate equation of state, as given in Tables 1-4. Both stemming geometries contain a 33-m (approximately 110-ft) section of unsolidified concrete 'mush' at the top of the emplacement hole. Although it takes approximately three weeks for a complete set to occur after pouring, the normal interval between pouring and shot time is three days. Consequently, the cohesive strength between the mush concrete and surrounding media is reduced from 70 psi (the value used in the satellite hole calculations) to approximately 10 psi. This revised cohesive strength for concrete is incorporated in the calculations. In an attempt to reduce shock propagation and motion of the sand backfill, two 16-m (approximately 50-ft) mush concrete plugs, 245 m and 370 m from the surface, were considered in one configuration (Geometry II, Fig. 18). Plugs are frequently used to prevent late-time sloughing of the sand backfill into the cavity and to add insurance against the possibility of leakage.
Boundary conditions and parameter study The geometry illustrated in Fig. 18 is a cylinder 160 cm in diameter with rigid walls; a constant 1-bar pressure is maintained at the surface. The cavity pressure as a function of time, P(t), from Fig. 7 was used to describe the driving force at the working point. A water-friction coefficient of Cs/2 = 0-005 was used in the calculation. This coefficient was used to determine the frictional drag CspU2/2. Two sets of VUFL calculations were run with the two stemming configurations shown in Fig. 18. Each configuration was run with two different friction forces. When the zone velocity was < 10 cm/sec, the wall shear strength between the stemming material and the walls of the containing cylinder was assumed to be the same as the SCS. Values of the SCS of 1/3 psi for sand and 10 psi for the mush concrete were used. When the zone velocity was /> 10 cm/sec, the frictional force/area was assumed to be 0.001 P and 0.01 P. In the absence of any experimental data, a conservative estimate of frictional force/area of 0.01 P was chosen. Even this conservative choice was found to be sufficient for containment. A more realistic estimate [3] would be in the range of 4-40 times that value. For example, Teflon on steel is 0.04 P, and hard steel on hard steel is 0 -42 P. However, to check the sensitivity of the results to this parameter, an unrealistically low estimate of 0.001 P was considered for the two geometries described in Fig. 118. Four calculations were considered: two for Geometry I, 0"01 P and 0"001 P; two for Geometry II, 0"01 P and 0.001 P. The results of these four calculations are summarized below.
92
B. K. CROWLEY, H. D. G L E N N , J. S. K A H N A N D J. M. T H O M S E N
Graphical representation of results From the lowest water zone to the first concrete plug, the two geometries have identical stemming configurations (see Fig. 18). To correlate the effectiveness of the different stemming geometries and friction factors, plots of calculated pressure vs time are given in Figs 19-21. These figures represent the pressure histories for the first two seconds of three different zones (zones 175, 227 and 266)--see Fig. 18. Zone 175 represents the first sand zone above the water level at 1800 ft below the surface. In Geometry II, zones 227 and 266 represent the bottoms of the two lower 16-m concrete plugs; in Geometry I they represent the corresponding sand zones. The vertical positions of zones 175, 227 and 266 as a function of time for a friction of 0.001 P are shown in Fig. 22. Figure 23 shows the time history of these zones for a friction of 0 "01 P. Zone 175 shock pressure results. Figure 19 indicates that the initial shock arrives at the lowest sand zone at approximately 220 msec for all four problems. The pressure peaks are a 4.0 tc~
Zone 175: Sand-water interface ( 1800 ft) • Geometry I (sand) Friction force =0.001 P
3.0
I 2,0
a Geometry I (sand) Frictlon force =0.01 P ,~ Geomeh',/11"(sand-concrete) Friction force = 0.001 P x Geometry IT (sand-concrete) Frlct|on force = 0.01 P
t
1.0
,"T'~,
0.5
~ ' ~ ,
i
1'0
,
,
~
,
~,
1"5
.
.
,
.
2.0
Time -- sac
FIG. 19. Pressure history at zone 175.
3.0
Zone 227 (1250 if)
• Geometry I (sand) Friction force =0.001 P o Geometry T (sand) Friction force =0.01 P
2.0
A Geometry 11"(sand and concrete) Frlctton force = 0.001 P x Geometry 11"(sand and concrete) Fr|ctlon force =0.01 P
I
1.0
0.5
1.0
1.5
Time - - sec
FIG. 20. Pressure history at zone 227.
2.0
ANALYSIS OF JORUM CONTAINMENT
.
.
.
.
t
,
,
,
,
i
,
,
,
,
1
,
93
,
,
1
Zone 266 (850 ft)
1.o
• Geometry I (sand) Friction force = 0.001 P a Geometry I (sand) Friction force = 0.01 P Geometry 11 (sand and concrete) Friction force =0.00l P
I
x Geometry ] I (sand and concrete)
~,o.5
-Overburden pressure 0
0.5
I'0 Time - - sec
1'5
2.0
FIG. 21. Pressure history at zone 266.
1180 1160 1140 <__
Air
/
Free surface
/~ 4- .....
Concrete
×_
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i
~-Zone 345
1120
q
960 94O
--
_x- - o--
× ~
~x---°-
d
920 Con c re te
90C
-----x
s l ~ x Jl'~
Sand
E
~-Zone
86O 1 ~ 84O
266
~,x ~
Z
--"-
-~
.~ a2o ~
800
c
.....
760
x
-
~ .
te
Sand
\~ - Z o n e
227
700'" 680 660
-
640
-
x/X / J
_ _
0
r
--x
Geometry I (sand) Friction force = 0 ' 0 0 1 P Geometry I I (sand - c o n c r e t e )
x
_
Friction force = 0"001 P
×
600 - Water ~ - Z o n e T
x
.... •
/
-Sand
620
o~:: ~x~
._
,
,
175 r
I
0-5
r
I
r
r
r 1.0
i
7
l
l
I
I
r
T
1.5
Time -- sec
FIG. 22. Displacement histories of zones 175, 227 and 266 for a friction of 0"001 P. ROCK8/2--B
94
B. K. CROWLEY, H. D. GLENN, J. S. KAHN AND J. M. THOMSEN 1150 Air
1145 1140
:<
•
Free surface
X-
Concrefe
Lone
X
=
X'
•
345
1135
I
910 Concrete •
Sand
~-~.one 266
:c
E 780
l
Concrete
K~
Sand
,~ 770
~---Zono 227
X.,,
•
X
630
* Geomtt,/I (rod) Friction force =0-01 P
620
X Geonlefry11"($ond-concr•lep[ug6) Friction force = 0.01 P
600~" Water
'
'
~--Zone 175
'
'
0!5
t
t
t
w
Time ~
I
1.o
~
t
t
t
I
i .5
t
t
~lec
FXo.23. Displacem~t histories of zones 175, 227 and 266 for a friction of 0.01P. factor of approximately 2 . 5 higher than those obtained in the satellite hole for the lowest sand zone. This high pressure can be attributed to the reduced drag force on the water column because o f the larger diameter of the main emplacement hole. The frictional force, Ft [2], equation (12) is inversely proportional to the radius, R, of the emplacement hole: rwS m
zwS pV
~'w2~rRL ~',~ 2 m,R~L = -p R
Zone 227 shock pressure results. Pressure-vs-time plots from the four calculations for zone 227 are illustrated in Fig. 20. Shock arrival occurs about 70 msec earlier for the lower (0.001 P) frictional case. In zone 227, peak pressures for the concrete are 2.4 and 0.4 kb, when the friction force/area is 0.001 P and 0.01 P, respectively. ~ conzrete (Geometry If) peak pressures are higher than in the comparable sand zone (Geometry I). To achieve a given pressure, a smaller compression is required for the concrete than for the sand. Although greater peak pressures are seen in Geometry H for zone 227, a more important
ANALYSIS OF JORUM CONTAINMENT
95
criterion for containment is the vertical displacement associated with each stemming configuration. A discussion of the displacement results is given later. Zone 266 shock pressure results. Pressure-vs-time plots from the four calculations for zone 266 are presented in Fig. 21. This figure demonstrates the dependence of the hydrodynamic results on the frictional factors. The frictional force/area of 0-01 P was sufficient to completely attenuate the shock propagating in the stemming material, and thus prevent it from reaching the second concrete plug position. However, when the frictional force/area of 0.001 P is used, sizable pressures are obtained in zone 266 for the two geometries considered. Comparison of these results implies that appreciable positive vertical motion of zone 227 has taken place in the 0"001 P case. The previous results and discussion of pressure are essentially an introduction to the main question of stemming containment: " W h a t physical displacements are associated with the stemming material in the main emplacement hole ?"
Physical displacements of plugs and stemming material Results for 0"001 P assumptions. Figure 22 shows the displacement of the concrete plugs in Geometry II and the corresponding sand regions of Geometry I. Displacement of the surface plug, common to both problems, is also shown. With an unrealistically low friction factor of 0.001 P, the PUrL calculation showed motion beginning at the top plug at approximately 1.5 sec. This should not cause alarm, however, since these two problems were run only to determine the sensitivity of the results to the friction force. The corresponding case (i.e. frictional force/area = 0"001 P) in the satellite hole study indicated no motion occurred for the top 550 m (1800 ft) of stemming material. The difference is attributed to the larger diameter of the emplacement hole. Results for 0.01 P assumptions. Figure 23 is the same plot for the 0.01 P friction force. Since the stemming geometry in both problems is identical up to the ~rst concrete plug, the motion of zone 175 (the sand-water interface) is the same for Geometry I and Geometry II. From 0.2 to 0.5 sec, zone 175 moves 36 m, or 118 ft; no upward motion was found after 0.5 sec. The upward motion of zone 227, the first concrete plug of Geometry II, was 1 m less than the motion of the corresponding stemming material of Geometry I. Motion in both cases begins at 0-55 sec and is completed by 0.75 sec. The plug moves 4 m or 13 It; the stemming material moves 5 m or 16 ft. Finally, in both cases, no upward motion was found at zone 266, the base of the second concrete plug of Geometry I[, or the stemming material of Geometry I--indicating containment of the hydrodynamic flow for both stemming geometries. Because no corresponding case (i.e. frictional force/area = 0.01 P) was calculated for the satellite study, no comparisons of results are feasible.
Conclusions and Recommendations The primary factor in prohibiting the motion of the stemming material is the dynamic frictional force assumed between the stemming material and surrounding media. It is considerably more important than the static cohesive strengths one assumes (e.g. 10 psi vs 70 psi for concrete plugs with surrounding media). Sensitivity to the frictional factor is shown in Figs 22 and 23, which compare the results obtained by setting the frictional force/ area equal to 0.001 P and 0.01 P. When the unrealistically low estimate of frictional force/ area = 0.001 P is assumed, Fig. 22 indicates that the upward displacement of the total column of stemming material is significant. This suggests the possibility of a vent occurring. However, in Fig. 23, no physical displacement is indicated for the top 1800 ft of stemming
96
B. K. CROWLEY, H. D. GLENN, J. S. KAHN AND J. M. THOMSEN
material when the more realistic value of 0.01 P is assumed. This suggests that venting through the emplacement hole would not occur. There are no data in the literature giving values of sliding friction for the materials in the pressure and velocity range with which we are concerned. This suggests that an experimental effort could be of value. From hydrodynamic considerations, the results of the four problems considered indicate that there is little difference between the two stemming configurations. However, the emplacement of several plugs was considered advisable for prevention of late-time sloughing of stemming materials into the cavity. REFERENCES I. C R O W L ~ B. K. and BARR L. K. TENSOR-PUFL: Boundary.Condition-Linked Codes, Lawrence Radiation Laboratory, Livermore, Report UCRL-72120 (1969). 2. C R O W L ~ B. K. rUFL, an "almost ~ g i a n ' gasdynamic calculation.J. comp. Phys. 2, 61 (1967). 3. G m u o . ~ L. S. and KAHN J. S. Phenomenology of Undergrotmd Nuck~r ~ s i o n s , Proceedings of the 50th Annual Meeting of the American Geophysical Union, Washington, D.C., American Geophysical Union, Washington, D.C. (1969). 4. American Instituteof Physics Handbook, 2nd edn, McGraw-Hill, New York (1963).