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The Significance of Dilatancy to In Situ Bed Preparation

Keith Britton

Consultant

5718 McKinley St.

Bethesda, MD 20817, USA

ABSTRACT

It is noted that longstanding problems exist in the fragmentation field.

Dilatancy is briefly described and evidence presented from in situ blasts

and computer modeling to establish it as the common factor to our old

difficulties. It is shown to be important both to the early phenomena of

the fragmentation process and to the later behavior of the moving rubble.

Implications for blast design are discussed, with examples, and it is

shown that success with uniform fragmentation is unlikely. Implications

for computer modeling are discussed.

INTRODUCTION

Despite generations of effort, blasting remains nearly as much- art as

science. Notably, aspects of seismic radiation defy satisfactory

explanation. The most successful approaches to design and analysis have

been semi-empirical and thus hazardous or inapplicable for unusual

situations. Similarly, and arguably, progress in the computer modeling of

fragmentation has faltered short of the level needed for real success in

retort blast modeling. It seems that we cannot achieve truly physics

based approaches. Is there some missing factor? It seems likely, and it

has been hypothesized that the candidate is dilatancy [1] .

Dilatancy is the tendency to volumetric increase on shearing of

brittle materials. It occurs during shear: at touching rough fracture

surfaces; where such surfaces are separated by a zone of rotating

particles; as a consequence of both slip and rotation in less well defined

distortion zones of fragment assemblies. Volume increase is not isotropic

and gives rise, where resisted, to powerful and strongly directional

compressive forces. This is commonly met with as the so-called "internal

angle offriction"

of materials. Figure 1 illustrates the phenomena.

There is no rate dependency, and fragment scale may vary from sand (the

scale at which dilatancy was originally described) to jointed rock.

Fractured rock forms the limiting case of a dense assemblage. (The

initial action of blasting is to fracture, fragmentation is the subsequent

process which separates a fractured mass into individual particles.)

433

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Figure 1 Schematic Representation of Dilatancy Effects

Two cases are important to blasting for in situ beds, the dense case

of very early fragmentation and the diffuse case where rubble with a

significant void fraction is sheared while constrained. The former occurs

where rock is forced to fail by the immediate action of explosives and

also where large masses are made to separate from the parent rock as an

indirect consequence of blasting. The latter occurs where there is

significant rubble motion. The dense case is of interest partly because

dilatancy forces may greatly modify or even inhibit the course of the

fragmentation process, and partly because, if the strain rate is high, the

forces may cause radiation of powerful seismic waves. The diffuse case is

of interest for its effect upon the ultimate bed permeability.

THE DENSE CASE EVIDENCE /

Otis Walton, of Lawrence Livermore National Laboratory (LLNL) ,

realised the significance of dilatancy for the dense case on the basis of

model behavior; if dilatancy was not permitted for polygonal particle

models, then simulations "hungup"

for lack of space for rotations and the

principle had to have physical meaning. It was discovered independently

by the author during analysis of data from Geokinetics Inc. (GEO) retorts

R27 and R28. The key evidence lay in the seismic records [1] . Soliton

waves dominated the longitudinal axis vibration for both shots, also the

transverse for R27. They were not present on the vertical axis and were

temporally separate from wave trains directly generated by the explosives,

lagging their inception by more than 100 ms. After elimination of all

other hypotheses, the following was left as an explanation:

The initial action for both rounds was to rapidly fire interlaced

arrays of charges (50-80 tonnes explosive) to evenly load the underside of

a notional rectangular slab of overburden (about 100m x 45m x 20m thick)

and so put it into vertical ballistic motion. The initial response at the

edge of the slab was elastic distortion. But when the elastic limit was

exceeded, brittle failure occurred, with consequent fragmentation and

development of shear between the rising slab and the surrounding parent

rock. Since volumetric increase was resisted, a large dilatancy force

434

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435

developed normal to the vertical shear plane, radiating a compressive

pulse. As the slab continued to rise, withdrawn wedge action provided

void and the system relaxed. The radiated wave was, therefore, soliton in

character and temporally related to the rock mechanics phenomena rather

than that of the explosives proper. It had no vertical component and was

radiated as a well defined plane wave. A seismometer positioned nearly

normal to the long side of a slab saw only a longitudinal disturbance;

one somewhat off axis saw both longitudinal and transverse components.

The configuration (simplified) was modeled by Otis Walton using the

LLNL DIBS computer code [1-3]. Figure 2 shows the configuration at

various times. An initial impulse is given via the lowermost block.

Velocity vectors are initially vertical or divergent. They are then

pinched together in reaction to the dilatancy force, which is radiating a

lateral compressive pulse. (The surface displacement at this point

corresponds well to the field data at peak wave amplitude.) Vectors

quickly straighten with continued displacement and system relaxation.

THE DENSE CASE - THE IMPLICATIONS

The most obvious consequence of sudden dense case dilatancy is

seismic wave radiation. Such waves differ from those directly generated

by the explosive. They originate later and in the burden rather than from

the shotpoint. They are directional rather than isotropic, so their

position and decay cause anomalies in the radiation pattern. They tend to

present a compressive wave soliton character. Frequency tends to be much

lower, but the amplitude be greater by a factor of five or more. The

last is obviously a concern for the design engineer who is constrained by

proximity to sensitive structures, surface or underground, or potential

for misfires from charge cutoffs due to ground movement. Also obvious is

the potential for research use of the waves as diagnostic or quantitative

measures of hitherto inaccessible phenomena internal to the failing mass.

For the explosives engineer, some design details deserve review. Any

shear zone will exhibit dilatancy effects. The situation is worse at the

toe of a vertical slabbing blasthole than for the column portion; the

shear is very rapidly relieved for the latter, in situ vertical stress is

not a factor and surfaces are not curvilinear. Long columns with light

burdens thus radiate less than short, and "widespacing"

designs work well

because of both increased burden per unit area sheared and wider breakout

angle. Single charge breakage tends to be curvilinear or limited extent.

Their dilatancy caused waves are, therefore, likely to be indefinite in

origin and to tend to decay by spherical divergence. Interacting charges,

especially arrays, have much more opportunity to develop larger and planar

zones of shear. (Note that delay precision may not suffice for Shockwave

interaction, but firing times still may be close enough for geometric

cooperation in burden displacement.) Radiation may thus include strong

plane waves which initially decay only by absorption and diffraction.

Further, the greater the effective precision, the greater the effect; the

larger the radiator, the more efficient the source for long wavelengths.

Related to this are rock mechanics effects as in the GEO rounds.

436

-

f T-

0.5 '.AA

Figure 3 Modeling of a Retarc

(The simulation is of the SULKY

event (1965) , illustration from

Reference 4. A retarc is a

permanent mound produced by a

charge buried too deeply to

crater. )

In general, clamping effects are more serious than seismic ones. As

compressive forces from dilatancy develop, muck motion is affected. At

LLNL, for instance, modeling [4] shows this to effect a straightening of

initially divergent motion vectors to produce the raised rim of the

nuclear retarc of Figure 3. With increasing confinement, the forces may

dominate, increasing the required specific charge for breakage by a factor

of up to five (e.g. ditch blasting [5]) or else causing the fractured rock

to totally "freeze". A nasty feedback situation occurs as the specific

charge is reduced towards the limit charge for breakage. As the breakout

angle diminishes, shear and hence dilatancy forces increase. They act

increasingly to clamp rather than expel the burden and a drasticallylarger proportion of the available energy is radiated as seismic waves.

Increasing the specific charge initially improves all aspects, but

further increase may become counter productive. Probably rotations within

an excessive shear zone consume too much void. (An extreme example is the

Coromant tunneling cut, which freezes if overcharged. [6] ) The trend is

apparent in less confined cases too, though leading to poor fragmentation

control (excess fines or microcracking) , backbreak and misfires rather

than freezing. Current thinking in the mining industry is to attempt to

improve results by minimizing energy while controlling pulse waveform.

Air decking and ISONAL[7] offer subtly different results than does simple

charge reduction; long duration, low amplitude pulses cause less local

crushing but greater effect at a distance.

Orientation becomes important for formations with a pronounced

fracture bedding/jointing lattice. Where slip on planar fractures can

contribute to loosening, dilatancy effects are modified. Both the

orientation and spacing of the lattice need to be considered when

evaluating a lithology for in situ processing, and the lattice dimensions

may render test blasting at reduced scale misleading or pointless. Early

GEO retorts were not orientated to the jointing and failed to properly

break overburden despite presplits. Accurate alignment cured the problem

and presplits were not necessary. Similarly, early workers at Anvil

Points were able to document the extra cost of advancing a face downdiprather than cross-

or updip. In the first case, block rotations were

437

avoided, in the second, the ramp effect of the beddings increased the

vertical clamping force at the toe for the bad case. Often, quite minor

geometric rearrangements can have significant effect, notably in approach

to precision alignments, and such can often be enhanced or inhibited by

adjustingcharge cooperation by repositioning or timing change.

Void requirement is an important economic and technical factor for in

situ processing. It determines the fraction which must be mined out for

Modified In Situ (MIS) approaches and the degree of surface uplift needed

for those of the GEO type. Previously, it was assumed that the overall

void percentage would simply be mechanically imposed by the mining or

lifting scheme. It may now be seen, however, that the intrinsic dilatancy

characteristics of the particular oil shale are a factor. In principle,

Green River oil shale may be significantly distorted, with slippage on the

bedding/jointing lattice, without much dilation, but similar distortion

for New Albany Shale would require much more void space. The latter can

now be seen as intrinsically poorly suited to in situ processing by the

methods developed for the former, or for that matter, by any approach

which disorders the bed. All is not yet lost, however.

For oil shales with retorting characteristics suited to in situ

processing with a very low void percentage (low thermal swell, not

intumescent, low pour point oil) , the possibility remains of the invention

of some novel blast design which retains order in the bed while separating

the fragments sufficiently to introduce permeability. Possibilities do

come to mind, modified cratering designs, controlled subsidence etc. But,

though we are now better placed to evaluate them than we were, all appear

exotic relative to established technology, and all seem likely to suffer a

high bed pressure drop (which might be minimized with a high degree of

passage linearity) . A further interesting alternative exists, however,

that of simply making a bad retort bed. Previously, it had been

considered that only liquid fuel production was useful but, if recovery is

not so optimized and instead the burn is run as a gasification, then a

much higher degree of heterogeneity may be tolerable.

THE DIFFUSE CASE

Again, there was parallel independent but convergent progress from

field data and computer modeling. The author studied some dozens of cores

taken through the rubble of in situ retorts. Material remained ordered

(though fractured) with but little dilation, or was randomized with high

percentage void. Breakage was clearly bimodal, implying that a mechanism

ensured that the lower void limit for randomized material was greater than

the maximum for ordered material, all available void being redistributed

to the two fractions. Where the disordered zone was thin, comminution was

marked. The explanation was forthcoming from computer modeling work at

LLNL investigating the phenomenology of flow in granular materials.

Several models have been used at LLNL to study granular flow[8] .

(This differs from the quasi-static case more commonly studied in soil and

rock mechanics. The distinction is analogous to that between study of the

viscosity of a fluid versus the shear strength of a solid.) The relevant

insights were derived from models where the particles were simplified to

438

uniform disks or spheres. Assemblages were sheared and the particle

motions studied, available void, friction and other factors being varied.

Salient findings for disks were as follows: at moderate void percentages,

particles settled into two populations, regular arrays with little

relative motion and separating, turbulent, high void zones of rotating

particles; 20% seemed to be a critical void percentage; forces were

non-linear, increasing sharply as the void approached 20%. Limited work

was performed with the 3-dimensional case of spheres, but it was possible

to provoke a similar"crystallization"

bounding a turbulent region.

Dilatancy effects are limited with these simplifications to effects

from the dynamic turbulent rotations (projected particle dimensions do not

change with rotation) . Presumably, use of polygonal particles would have

affected results, but primarily regarding the low void zones. (The

simplified shapes coulu"crystallize"

to a tight and regular packing; the

polygonal equivalent is preservation of an original order.) Further, and

as seen in the cores, comminution may become pronounced in the rotational

shear zone. This may act simply to conserve available void where the zone

is thin. It becomes important in thicker zones for shales like the New

Albany (which breaks in a very brittle, glassy manner with conchoidal

facets and feather edges) ,if the fines produced greatly affect

permeability. In short, the message from our new understanding of

particle flow dilatancy is depressing; any attempt to produce uniform

fragmentation and permeability at moderate void is doomed by physical law.

The best we can hope for is some scheme of controlled heterogeneity.

COMPUTER MODELING

Dilatancy has indirect significance as a factor in the computer

modeling of fragmentation. It has been shown that the phenomena observed

at the GEO site can be implied from theresults'

of simulations using a

comparable geometry. It has also been noted that phenomena observed

during the modeling of shearing flow corresponds strikingly to that

implied from the rock rubble of actual retort shots. But this is true

only for models where dilatancy effects are permitted or are minimal due

to the degree and type of simplification. In other cases, model behavior

may be unrealistic. Figure 4, output of the BLOCKS code of Sandia

National Laboratory [9] , would be rejected out of hand by anyone familiar

with crater blasting. (The upper surface of the burden is concave, for

instance, where it should be convex.) On the other hand, their grossly

simplified codes BUMP and CAROM produced quite plausible output. Such

are useful, but they do not take the place of more capable models like the

DIBS code, which produced Figure 3. Complex modeling has been mostly the

province of supercomputers and the national Laboratories. Model and code

development and 3D versions will probably remain. so, but 32 bit personal

computers are now capable of running codes of the caliber needed by blast

design engineers. Without such support, the subtleties, complexities and

opportunities presented by dilatancy will be hard to handle.

439

Figure 4 Cratering Simulation

- Without Dilatancy Capability

(Output from BLOCKS code. Code

was written after DIBS code but

is not now in use.)

CONCLUSIONS

It is concluded that: consideration of dilatancy effects is needed for any

future in situ blast design; dilatancy will be a limiting factor for some

approaches; uniform fragmentation at medium void is a mirage; inclusion of

dilatancy is a requirement for any physics based fragmentation model, but

that such is both practicable and sufficient to finally advance the

modeling art to a level of real usefulness to the blasting engineer.

REFERENCES

1 Britton K. and Walton O.R. (1987) "Brittle Fracture Phenomena - An

Hypothesis"

Proc. @nd Int. Symp. on Rock Fragmentation by Blasting

Keystone, CO (Soc. Exp. Mech., Bethel, CT) pp 16-29

2 Walton O.R. (1980) "Particle Dynamics Model cf GeologicalMaterials"

Lawrence Livermore National Laboratory, Rept. UCRL-52915

3 Walton O.R. (1982) "Explicit Particle Dynmics Model For Granular

Materials"

Proc. 4th Int. Con. on Numerical Methods in Geomechanics Vol 3,

Z. Eisenstein, ed. A.A. Balkema, Rotterdam, 1982 pp 1261-1268

4 Butkovich T.R., Walton O.R. and Heuze F.E. (1988) "Insights in

Cratering Phenomenology Provided by Discrete ElementModeling"

UCRL-97338

Preprint of paper for presentation at 29th U.S. Symp. on Rock Mechanics,

Minneapolis, MN, June 13-15

5 "Blasters' Handbook"

1977 E.I. Du Pont de Nemours, Wilmington, DE

pp 427-428

6 Langefors U. and Kihlstrom B. (1963) "The Modern Technique of Rock

Blasting"John Wiley & Sons, New York

7 Nielsen Kai and Heltzen Anders M. (1987) "Recent Norwegian Experience

with Polystyrene DilutedANFO"

Proc. @nd Int. Symp. on Rock Fragmentation

by Blasting Keystone, CO (Soc. Exp. Mech., Bethel, CT) pp 231-238

8 Walton O.R. and Braun R.L. 1987 "Viscosity, Granular-Temperature, and

Stress Calculations for Shearing Assemblies of Inelastic, FrictionslDisks"

J. Rheology, 30 (5) pp 949-980

"Stress Calculations for Assemblies of Inelastic Spheres in UniformShear"

Acta Mechanica 63 pp 73-86

9 Taylor L.M. (1983) "Blocks: A Block Motion Code for Geomechanics

Studies"Sandia National Laboratories, Albuquerque, NM SAND 82-2373