simulations of an underground explosion in granite

7/27/2019 Simulations of an Underground Explosion in Granite

1/6

American Physical Society11th Topical Conference on Shock Compression of Condensed Matter

Snowbird, UTJune 27-July 2, 1999

Lawr

ence

Liverm

ore

Natio

nal

L

aboratory

UCRL-JC-134524

Simulations of an Underground Explosionin Granite

T.H. AntounO.Y. Vorobiev

I.N. Lomov

L.A. Glenn

June 14, 1999

This is a preprint of a paper intended for publication in a journal or proceedings.Since changes may be made before publication, this preprint is made available withthe understanding that it will not be cited or reproduced without the permission of theauthor.

PREPRINT

This paper was prepared for submittal to the


2/6

DISCLAIMER

This document was prepared as an account of work sponsored by an agency ofthe United States Government. Neither the United States Government nor theUniversity of California nor any of their employees, makes any warranty, expressor implied, or assumes any legal liability or responsibility for the accuracy,

completeness, or usefulness of any information, apparatus, product, or processdisclosed, or represents that its use would not infringe privately owned rights.Reference herein to any specific commercial product, process, or service by tradename, trademark, manufacturer, or otherwise, does not necessarily constitute orimply its endorsement, recommendation, or favoring by the United StatesGovernment or the University of California. The views and opinions of authorsexpressed herein do not necessarily state or reflect those of the United StatesGovernment or the University of California, and shall not be used for advertisingor product endorsement purposes.


3/6

SIMULATIONS OF AN UNDERGROUND EXPLOSION IN GRANITE

Tarabay H. Antoun, Oleg Yu Vorobiev, Ilya N. Lomov, Lewis A. Glenn

Lawrence Livermore National Laboratory, Geophysics and Global Security Division, Livermore, CA 94550

Abstract. This paper describes the results of a computational study performed to investigate thebehavior of granite under shock wave loading conditions. A thermomechanically consistentconstitutive model that includes the effects of bulking, yielding, material damage, and porouscompaction on the material response was used in the simulations. The model parameters weredetermined based on experimental data, and the model was then used in a series of one-dimensional simulations of PILE DRIVER, a deeply-buried explosion in a granite formation at the

Nevada Test Site. Particle velocity histories, peak velocity and peak displacement as a functionof slant range, and the cavity radius obtained from the code simulations compared favorably withPILE DRIVER data.

INTRODUCTION

Simulating the behavior of granite underimpact loading conditions requires the use of aconstitutive model that includes the effects ofbulking, yielding, damage, and porouscompaction on the material response. In thispaper, a constitutive model that incorporates

these features is calibrated using static data; thenit is used to perform 1D simulations of PILEDRIVER, an underground nuclear explosiondetonated in the granitic Climax Stock of Area15 at the Nevada test site [1]. The explosion wasdetonated at a depth of 462.8 m as shown inFigure 1. Data from the test included free fieldground motion measurements made usingvelocity and acceleration sensors at rangesstarting in the hydrodynamic region in thevicinity of the explosive cavity and extending outmore than 1000 m, well beyond the elasticradius.

MODEL DESCRIPTION

The rock behavior is described using anelastic-viscoplastic model, coupled with a time-dependent damage model for the deviatoricbehavior, and a Mie-Grneisen equation of state,

coupled with a porous compaction model and abulking model, for the volumetric behavior. Themodel is described in more detail in a companionpaper [2], here we only provide a summary of itsmain features.

The deviatoric model is isotropic and itdescribes the initial yield behavior with apressure-dependent yield criterion. Initialyielding is followed with a plastic strainhardening phase which persists until the loadingpath intersects the failure surface.

462.8 m

Working Point

Particle Velocity Gages(referenced in later figures)

204 m

470 m

Ground Surface

Shot Horizon

Point A

Point B

FIGURE 1. Configuration of the PILE DRIVER experimentshowing the locations of two radial particle velocity gagesdeployed during the test.


4/6

The post-failure behavior is described with adamage model similar to the Tuller-Butchermodel [3] for spall damage. With this model, thedamage parameter, , is computed using therelation

= ( )1

Adt

th

max(1 )

where max

is the most compressive principal

stress, th

is the threshold stress for damage

growth, and A is a normalizing constant thatrenders dimensionless. During the post-failureregime, the strength of granite is graduallydiminished until a minimum prescribed value isattained.

The Mie-Grneisen equation of state, whichdescribes the behavior of non-porous granite1, is

supplemented with an analytic porouscompaction model that describes the relationshipbetween pressure and porosity. Also included inthe volumetric behavior description is a dilatancymodel which relates bulking to plasticdeformation in such a way as to ensurethermomechanical consistency with the secondlaw of thermodynamics.

The model is implemented in VGR, a two-dimensional Eulerian code with adaptive meshrefinement capabilities.

SIMULATION RESULTS

Our investigation included both static anddynamic simulations. Statically, the behavior ofgranite in triaxial compression was simulated atdifferent levels of confining pressure. Thenumerical simulations closely resembled a seriesof experiments performed by Schock et al. [4] toexamine the yield, bulking and failurecharacteristics of Climax Stock granodiorite, thesame rock formation where PILE DRIVER wasdetonated. These static simulations were used todetermine the material parameters for the yieldand bulking models. As indicated in [2], the

simulation results are in good agreement with thestatic data.With the model calibrated based on the static

data, we performed a series of 1D, spherically

1We performed some simulations using a tabular equation ofstate for granite, but this did not seem to have a significanteffect on the results.

symmetric, PILE DRIVER simulations. Theexplosive source was approximated by depositingenergy uniformly in a cavity containing an idealgas with a density equal to that of granite, and aratio of specific heats of 1.17. In the simulations,the post-failure damage model parameters werevaried in an effort to obtain a reasonable fit tothe PILE DRIVER data (the post-failure modelwas not exercised in the static simulationsbecause the static measurements did not includepost-failure data). However, an adequate fit tothe data could not be achieved using thestatically-calibrated model. To improve theagreement between the simulation results and thePILE DRIVER data, it was necessary to lowerthe strength of granite in the dynamic simulationsas shown in Figure 2.

20

15

10

5

0

VON

MISESSTRESS(kbar)

2520151050

PRESSURE (kbar)

Static Data

Onset of Yield

Failure

PILE DRIVER Stress Path

Range = 50 m

80 m

100 m

PILE DRIVER

Onset of Yield

Failure

FIGURE 2. Yield and failure surfaces used in the static anddynamic simulations. Stress paths from the PILE DRIVERsimulation at three different ranges are also shown.

The yield and failure stresses measuredstatically using relatively small, defect-freesamples had to be reduced by about 50% tosatisfactorily reproduce the dynamic data. Thisfinding is in line with experimental data thatshow the strength of granite and other geologicmaterials to be size-dependent, decreasing withincreasing specimen dimensions. Fig. 2also shows several stress path trajectoriesexperienced by the material at different ranges

away from the charge cavity. Each trajectoryconsists of a monotonic loading path duringwhich several inelastic processes take placeincluding yielding, compaction and bulking. Asthe stress path reaches the failure surface,damage begins to develop causing the materialto unload. The unloading path is a complex


5/6

function of damage kinetics which depend onthe stress magnitude and the duration of loadapplication. It is shown in Fig. 2 that at higherstress (50-m-range), damage develops quicklyand the loading path falls rapidly off the failuresurface. At lower stress, damage develops at aslower rate, thus allowing the material to stay on,or near the failure surface longer, which givesrise to the loops observed in the stresstrajectories at ranges of 80 m or greater.Figures 3 and 4 compare simulation results withmeasurements of radial particle velocity historiesand corresponding displacement histories atranges of 204 m and 470 m from the center of thecharge. These two positions correspond to pointsA and B in Fig. 1. The velocity waveforms arecharacterized by a positive phase representingthe outward motion of the rock, followed by arebound phase during which the materialcontracts and displaces radially inward towardthe explosive source.

Analysis of the simulation results made itpossible to associate processes in the constitutivemodel with measured waveform features. Forinstance, the peak particle velocity attenuationas a function of scaled slant range, shown inFigure 5, is strongly influenced by porouscompaction (in addition to its characteristicdependence on the divergent flow field). Thisattenuation is further complicated by the yielding

and damage processes that determine theresidual strength of the material behind the shockfront. A stronger material allows

40

30

20

10

0

-10

VELOCITY(m/s)

0.750.500.250.00

TIME (s)

2.0

1.5

1.0

0.5

0.0

-0.5

DISPLACEMENT(m)

Velocity

Displacement

Experimental DataSimulation Results

FIGURE 3. Comparison of simulated and measured radialvelocity and displacement histories at a slant range of 204 m(Point A in Figure 1).

more of the release waves emanating from theexplosive source to catch up with the main shock

front and cause it to attenuate at a faster rate,thereby diminishing the peak velocity amplitude.

The width of the positive phase of the velocitywaveform is strongly dependent on bulking. Theincreased volume associated with bulking causesthe pressure in the material to be higher than itwould be if bulking was suppressed. The workdone by this higher pressure causes an increasein the outward displacement of the rock. Thiseffect is manifested as a widening of the positivephase of the simulated velocity waveforms. It isalso manifested as an increase in the peakdisplacement observed at various ranges awayfrom the explosive source. The peakdisplacement attenuation is depicted in Figure 6.As shown, the simulation results are inagreement with the data from PILE DRIVER, andthey follow the same trend as several otherspherical wave experiments in granite.

The rebound phase in the velocity records islargely due to yielding and damage. As the mainwave propagates outward from the source, thematerial behind the shock front first yields, thenfails due to the accumulation of damage. Thedamaged region encompasses a portion of theflow field nearest the charge cavity, while theyielded region extends further out into the flowfield. Our simulations show that the materialbehavior during the rebound phase is stronglyinfluenced by the impedance mismatch at the

interface between the yielded and damagedregions: the larger the mismatch, the moreprominent the rebound.

8

6

4

2

0

-2

VELOCITY(m/s)

0.750.500.250.00

TIME (s)

0.5

0.4

0.3

0.2

0.1

0.0

-0.1

DISPLACEMENT(m)

Experimental DataSimulation Results

Velocity

Displacement

FIGURE 4. Comparison of simulated and measured radialvelocity and displacement histories at a slant range of 470 m(Point B in Figure 1).


6/6

0.1

1

10

100

1000

VELOCITY(m/s)

4 6 810 2 4 6 8100 2 4 6 81000 2 4

SCALED RANGE (m/kt1/3

)

Simulation

Data

PILEDRIVERHARDHATSHOALHOGGARACE (SRI)

FIGURE 5. Comparison of simulated peak velocity attenuationwith measurements from several spherical wave experiments ingranite.

The motion of the cavity boundary wasmonitored throughout the simulation. The periodof cavity oscillation was found to depend on thesize of the damaged region. The simulatedcavity size was also influenced by damage, andit agreed well with the measured values ofbetween 40.1 and 44.5 m.

SUMMARY

This paper reported progress in our ongoingeffort to characterize the behavior of graniteunder impact loading conditions. Test data, in theform of velocity histories, peak velocity and peakdisplacement as a function of slant range, andcavity radius compare favorably with the resultsof simulations performed assuming that thegranite in the PILE DRIVER testbed (i.e., largescale) is weaker than is indicated by laboratory

measurements on relatively small (2 cm) anddefect-free samples. This finding is in line withexperimental data that show the strength ofgranite and other geologic materials to be size-dependent, decreasing with increasing specimendimensions. Present and future efforts arefocused on further constraining the model

0.001

0.01

0.1

1

10

SCALED

DISPLACEMENT

(m/kt1/3)

4 6 810

2 4 6 8100

2 4 6 81000

2 4

SCALED RANGE (m/kt1/3

)

Simulation

DataPILE DRIVERHARDHATSHOALHOGGAR

FIGURE 6. Comparison of simulated peak displacementattenuation with measurements from several spherical waveexperiments in granite.

using static data, investigating the effects ofsurface reflections using 2D simulations, andusing the model to investigate scaling effectsassociated with underground explosions ingranite.

ACKNOWLEDGMENTS

Work performed under the auspices of the U. S.Department of Energy by the LawrenceLivermore National Laboratory under ContractW-7405-ENG-48.

REFERENCES

1. Perret, W. R., 'Free Field Ground Motion in Granite,'Report No. POR-4001, Sandia Laboratory,Albuquerque, New Mexico (1968).

2. Vorobiev, O. Y., Antoun, T., Lomov, I., and Glenn,L., 'A Strength and Damage Model for Rock UnderDynamic Loading,' to be published in the presentproceedings.

3. Tuller, F. R., and Butcher, B. M., Int. J. fract. Mech.,4(4), 431-437 (1968).

4. Schock, R. N., Heard, H. C., and Stephens, D. R.,J.Geophys. Res., 78(36), 5922-5941 (1973).

simulations of an underground explosion in granite

Documents