110 Distributed-Energy Blasting for NEO Destruction Leslie

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					                        Distributed-Energy Blasting for NEO Destruction
                           Leslie Gertsch1, Jason Baird2, and Paul Worsey3
                     Assistant Professor, 2Research Associate Professor, 3Professor
           University of Missouri-Rolla, Rock Mechanics & Explosives Research Center,
                    1006 Kingshighway, Rolla, MO 65409-0660, United States

Abstract                                                Contrary to some popular dramatizations,
                                                   detonation of a single large explosive within a
    Large-scale blasting techniques developed      NEO would more likely result in several sub-
for terrestrial construction and mining could,     asteroids accompanied by many overlarge
if applied to a threatening NEO, ensure that it    chunks and a myriad of fine particles. The
would be transformed into fragments too            delivered energy density must be sufficient to
small (10-30 meters) to survive passage            create new fractures throughout the body with
through Earth’s atmosphere. Additionally, this     sufficient connectivity to keep the maximum
approach could impart appropriate impulses to      fragment size below 10-30 m. An overlarge
the NEO that its impact is prevented, or, if       point charge wastes its energy in the near-field
fragmented, that fewer resulting fragments         region, and may not sufficiently fragment the
would impact Earth. This approach also would       rest of the target.
be responsive to ongoing characterization of            Distributed-energy blasting is also part of
the NEO, and to its certain departures from an     the utilization of the mineral resources that are
ideal spherical, homogeneous, continuous,          available within NEOs. Fragmentation is of
linearly elastic mass.                             primary importance to mining and processing,
                                                   as it is the first step in separating materials of
1   Introduction
                                                   interest from unwanted surrounding material
    The key to large-scale blasting in any         [1].
venue is the efficient distribution of explosive        Selection of the appropriate explosive
energy in space and time. This requires            mass per volume of unbroken rock (powder
placing the charges at appropriate depths in a     factor, or specific charge) – the first step in
three-dimensional pattern that reflects the        blast pattern design – allows one to calculate
properties of the material and the degree of       the explosive mass required to pulverize all or
fragmentation required and initiating them in      part of a NEO, given its volume. On the Earth,
the appropriate sequence; in other words,          a typical powder factor for a surface blast
careful blast design. Several separate blasts,     ranges from 0.5- to 0.76-kilogram explosive
each comprising several to several hundred         per cubic meter of rock, and produces
individual explosive charges, would be             fragments less than 3 meters in diameter. This
required to destroy a NEO above 30 meters in       powder factor is optimized for terrestrial
diameter (see Figure 1 for a representative        brittle, hard rock. Non-brittle NEOs could be
terrestrial surface blast). Accordingly, some      pulverized through this technique as well, but
mission time on-site would be necessary to         powder factor selection would require
design the blast patterns, place the charges,      additional calibration before full-scale use.
and evaluate the results before repeating for           A NEO’s fragmentability depends on its
the next blast. This approach is viable up to a    structure and the type of material it comprises.
short time prior to atmosphere entry, so the       A mechanical classification proposed by [2]
required lead-time would be determined by          divides NEOs into four broad groups:
the mechanics of preparing and launching an        0. Ice composites – very weak, containing
appropriately trained crew as well as                   ices with or without organic compounds.
performing the tasks on-site.                      1. Friable rock – similar to Group 0, but with
                                                        no volatile components. Also weak.


                                                          bench height

                                                             subdrilling               charge

                                               Figure 2. Schematic diagram of generic single-
                                               deck blasthole, showing blasthole inclination,
                                               some blasthole dimensions, and components of
                                               the charge column. After [4].

                                               Table 1. Blast designs matrix based upon NEO
                                               size (Classes 1-3) and constituents (Groups 0-3b).

                                                                Class 1    Class 2   Class 3
                                                  Group 0
                                                  Group 1
                                                  Group 2
                                                  Group 3a
                                                  Group 3b

                                               2. Hard rock – strong and brittle, the most
                                                   similar to terrestrial mining/excavation.
                                               3. Metallic:
                                                   3a. Massive metal – may be ductile.
                                                   3b. Rock-metal composites – would frac-
                                                        ture mainly at rock-metal interfaces.
                                                   Combining the classifications of NEO
                                               group and size results in the matrix shown in
                                               Table 1. Each cell will require a different
                                               basic blast pattern. Those cells that represent
                                               the more dangerous NEOs indicate the blast
                                               designs whose development should be
                                                   Powder factors for all NEOs will be much
                                               lighter than terrestrial practice (with the
                                               possible exception of Group 3a). This is due
                                               to the much lower confinement of the blast by
Figure 1. Photo sequence of a surface mine
bench blast, showing the effects of designed
                                               surrounding material, and the much lower
charge group initiation delays.                gravity loading, than experienced on Earth.

     The dispersal of the explosive within the             The aspects of NEO physical structure that
target rock mass required to achieve the              most affect blast performance are the degree
necessary powder factor is accomplished by            of pre-existing fracturing and the anisotropy
creating blastholes in the mass and filling           the fracture network causes in the NEO
them with the explosive. Specifically, the            material response to an explosion.
parameters of blast design (Figure 2) are:                 The distance between a charge and the
• Energy yield per unit volume of explosive,          nearest stiffness interface is one of the more
• Time         intervals     (delays)      between    critical variables in blast pattern design.
     detonations of individual charges or             Stiffness interfaces reflect explosive shock
     groups of charges,                               waves, converting them from compression to
• Number of charges (mass of explosive)               tension (Figure 3). Exposed rock surfaces and
     grouped to be detonated simultaneously,          major pre-existing fractures within the rock
• Charge diameter,                                    mass are the most common types. Pervasively
• Blasthole depth,                                    fractured NEOs, moderately fractured NEOs,
• Blasthole inclination,
• Sub-drilling,
• Inter-hole spacing, and
• Burden (distance between each charge and
     the nearest stiffness interface at the time of
     firing) – this varies during a blast as
     previously fired charges create new rock
     High-energy density explosives, such as
HMX or RDX, would require lower launch
mass and smaller-diameter blastholes than the
lower energy blasting agents used in terrestrial
mining. These compounds also would avoid
problems that traditional blasting agents have
in the vacuum of space (e.g., rapid oil and
water evaporation). The high-energy density
explosives are more sensitive than commercial
blasting agents, but boosters are currently
required for the initiation of traditional
blasting agents anyway. Determination of the
energy density, explosive mass, and transport
safety needs will be required. The blastholes
would be created by drilling (using an
anchoring or wrapping approach to generate
reactive forces) or by direct penetration.
     The characteristics of the target rock mass
and the purposes of the blast control the             Figure 3. Horizontal section through a blasthole,
                                                      showing three successive positions of the shock
design of the blast, beyond simply achieving          wave (A, B, and C). Radial cracking proceeds
the powder factor. The important rock mass            behind. At a free face (rock surface) the radially
characteristics are its physical structure and        expanding shock wave reflects as a tensile wave.
the locations of the stiffness interfaces, both       If the reflected tensile failures link with the
initially and after charges begin to detonate.        subsurface fractures, a crater results. From [6].

                                                                                                                       and solid NEOs will require different blast
                                                                                                                       patterns to achieve the powder factor
                                                                                                                       necessary to ensure that all fragments are
                                                                                                                       smaller than the required maximum size (this
                                                                                                                       is incorporated in Table 1). Current terrestrial
                                                                                                                       explosives require a burden of 25 to 35 times
                                                                                                                       the diameter of the explosive column for
                                                                                                                       hard,brittle (crystalline) rock [3]. In weaker
                                                                                                                       rock, the ratio can be as high as 40 [4]. As
                                                                                                                       shown in Figure 4, if the burden is too small,
                                                                                                                       explosive energy is lost as fragments are
                                                                                                                       ejected uncontrollably (flyrock) and gas
                                                                                                                       pressure escapes before moving fragments far
                                                                                                                       enough to allow subsequent detonations to
                                                                                                                       occur efficiently. On the other hand, too-high
                                                                                                                       burden results in poor fragmentation, high
                                                                                                                       ground vibrations, and excessive backbreak.
                                                                                                                            Bench height must be at least twice the
                                                                                                                       burden distance to achieve the optimum
                                                                                                                       release of explosive energy, although other
                                                                                                                       constraints often dictate bench height, such as
                                                                                                                       geological structure (e.g., rock layer thickness
                                                                                                                       or the presence of a thin weak layer).
                                                                                                                            Prediction of the size distribution of the
                                                                                                                       rock fragments from a blast is not an exact
                                                                                                                       science, unfortunately. The best predictive
                                                                                                                       tool is a robust database of previous shots in
                                                                                                                       the same circum-stances.                However,
                                                                                                                       approaches that link numerical modeling with
          Figure 4. The effect of varying values of burden,                                                            digital imaging of pre-blast rock surfaces are
          all other parameters held constant. From [6].
                                                                                                                       becoming more capable (Figure 5).
                                                                                                                            The charge diameter will be less than the
                                            Block Mass, My   1kg     10kg    100kg   1t     10t (γ= 2.65, Fs=0.6)
                                                                                                                       blasthole diameter for NEO fragmentation.
                                                                                                                       This is because the explosive will be
                            IBSD D50=2.0m, nRRD=1.5                                                                    contained within bags, or cartridges, for
               0.7                                                                                                     handling. This is often done on Earth for
fraction finer, y

                            BBSD Armourstone blast,
               0.6          D50=0.5m, nRRD=0.7
                                                                   Transformation of IBSD to BBSD
                                                                                                                       various reasons. The coupling between the
                            BBSD Aggregates blast,                                                                     explosive column and the rock is less
               0.4          D50=0.2m, nRRD=0.9
                                                                                                                       complete, however, requiring compensatory
               0.2                                                                                                     modifications in the blast pattern design.
               0.1                                                                                                          Blasthole drilling requires less energy with
                        1                  10                  100                   1000                   10000
                                                                                                                       increasing diameter, though more and smaller
                                                       Sieve size, Dy (mm)                                             holes distribute the energy better. If the target
                                                                                                                       material is pervasively jointed or contains
          Figure 5. Blasted rock fragment size distribution                                                            veins of weaker material, smaller holes also
          related to pre-existing rock structure. From [7].                                                            cause less attenuation of the shock wave and

give better distribution of the explosive
energy, especially near the top of the hole.
    Short (tens of milliseconds) time delays
are incorporated between the detonations of
portions of column charges (in multiply
decked holes) or of groups of loaded
blastholes to allow sufficient time for the rock
to deform and fracture (Figure 6). Too-short
delays “choke” a blast, preventing proper
fragmentation and locking the fragments
                                                   Figure 6. Effect of large burdens on rock fragment
together. The minimum delay time for burden        speed and required delay time. From [6].
detachment in hard, brittle rock is 3
millisec/meter of burden. Longer delays                The spacing between blastholes within a
produce better lateral relief, improving the       row is measured perpendicular to the burden
conversion of explosive energy into material       of the row. If the blastholes are too far apart,
fragmentation and reducing excess vibration.       fragments between are too large. Too-close
    These delays could also be used to aim the     spacing, on the other hand, ejects stemming
blast impulses in the appropriate directions to    early. This causes premature splits between
control the resulting trajectories of the          blastholes that release the explosive gases too
fragments and the remaining part of the NEO.       soon, and lose their effect in moving the rock
This could be combined with precise timing of      fragments.
blast initiation within a time window when the         Blasthole inclination is adjusted when
blast would generate the largest impulses          needed to counter the effects of rock structure.
toward nonhazardous trajectories.                  The values selected depend on the directions
    Stemming is an inert material that serves      of anisotropy and the spacing and aperture
to confine the blast. It is placed within the      distributions of pre-existing joints, as do
blasthole, on top of the explosive charge, and     spacing, burden, bench height, decking, and
sometimes between portions of the charge           the time delay pattern.
column to separate it into sections that are
detonated at different times (multiple                The keys to implementation of this
decking). Insufficient stemming leads to           approach are:
uncontrolled fragment ejection and wasting of      • Accurate and precise characterization of
explosive energy, but only a little more can be       NEO material properties, structure, and
too much, leading to poor fragmentation and           mass distribution.
excessive vibrations throughout the NEO.           • Detection of and access to the NEO in
Decking is one possible method to control             sufficient time for:
fragmentation of a NEO containing pre-                - NEO characterization.
existing zones of weakness (fractures, or weak        - Explosive/Blasting agent selection.
or strong inclusions). Stemming material              - Blast pattern design.
ranges from rock chips created by drilling the        - Drilling, loading, shooting, and evalua-
blasthole to bags filled with fluid.                      ting each blast.
    Subdrilling is used when the the horizontal
surface left by the blast must be smooth and           Obstacles to implementation include:
continuous with that left by previous blasts. It   •   Development of robust technique(s) for
permits the explosive energy generated by the          multiple charge placements at variable
bottom charge to reach its full effectiveness.         depths in a micro-g body. Drilling and
                                                       penetration merit study for this.

•   Safety issues regarding transport of             2    Overall Concept
    explosives/blasting agents. They could be
    manufactured on-site for those Group 0                  The destruction of a threatening NEO
    NEOs that contain the appropriate raw               using this approach would consist of two
    materials, reducing or eliminating the              separate missions: Characterization (evalua-
    mass of explosives that must be launched            tion) and destruction (mitigation). Figure 7
    from Earth.                                         illustrates the overall sequence of operations.
                                                            The uncrewed evaluation mission should
                                                        arrive as much earlier than the mitigation
                     MITIGATION          CHARACTER-
                                             IZATION    mission as possible, following a shortest-time
                     arrive at NEO                      path. Its purpose would be to map, measure,
                         vicinity             ongoing   and monitor the NEO, focusing on its interior
                                             evaluation structure from surface to depth. This activity
                     classify NEO              of NEO   would continue throughout the mitigation
                                                        mission and beyond, monitoring fragment
                      test blast(s)                     paths until it is clear that all were no longer
                                                        threatening Earth. The minimum information
                                                        needed includes material density, stiffness,
    Class 1             Class 2                Class 3  tensile strength, the pre-existing fracture
    1 blast            2-5 blasts             >5 blasts network, and the spatial variations of all these
                                                        on a resolution of 3-5 meters (vertical and
                                                        horizontal). However, the evaluation mission
   design single                 design blast           is not the focus of this paper and is not
   blast pattern                  sequence,             discussed further.
                               sizes, locations             The lead time required for complete
       emplace                                          mitigation of a NEO threat using this
    explosives                                          technique will vary depending on the size of
                                                        the NEO, its time to impact, and the above-
       detonate                                         mentioned unknowns with regard to
                                                        development of the technique; larger bodies
       evaluate                                         and those in Groups 0, 1, and 3 will require
        results                                         more time on-site. However, it is possible that
                                                        the blasting could be design to alter the NEO
    secondary                                           trajectory enough to miss the Earth, without
  fragmentation                                         need to reduce the entire NEO to small pieces.
      if needed                                         This would reduce the effective time required.
                                                            As with any proposed NEO mitigation
                                                        technique, it would be prudent to perform a
    continuing                                          limited test mission, perhaps on the Earth’s
   monitoring of
                                                        moon, rather than waiting for the do-or-die
                                                        scenario presented by an imminent NEO
Figure 7. Schematic diagram of distributed-energy       impact. At least one, and probably several,
blasting mission. Each blast consists of multiple       practice runs should be performed as well on
charges in space and time. Red outlines indicate        the NEO to calibrate the powder factor
the mitigation mission. Blue outlines indicate the      selection and to determine the drillability of
evaluation mission. Shading signifies technologies
requiring modification for use on NEOs.                 the constituent materials.

3   Key Features                                  geometric positions (particularly depth) in the
                                                  target material mass. The Research and
    The key features of this approach are:        Development Degree of Difficulty for
•   Comprehensive, precise characterization       adapting terrestrial techniques is estimated to
    of the NEO in space, on surface, and at       be R&D3-II (moderate difficulty, probability
    depth; characterization that continues        of success greater than 90%), due to the
    during explosives emplacement and             availability of two alternative methods that
    initiation. This will be the source of        can be developed independently: drilling and
    comparative data during the evaluation        direct penetration.      Presently, important
    following each blast.                         components of these methodologies that
•   Blast pattern design to fragment the NEO,     would be used with a NEO (see recent work
    with maximum resulting particle size less     by NORCAT and Honeybee Robotics) are
    than 10-30 m. This includes selection of      TRL-4 to 5.
    charge size (physical size and energy),
    emplacement geometry, and time delays.        4   Limitations
•   Effective method(s) to emplace explosives
                                                      This concept is based on terrestrial
    at controlled depths within the NEO.
                                                  experience in rock of many types, from very
•   Blast initiation control, allowing for
                                                  tough rocks to cohesive soils. Under Earth-
    selection of the appropriate blast window
                                                  surface conditions, effective blasting of pure
    with respect to rotational position of the
                                                  metal (e.g., iron or copper) is difficult due to
                                                  the metals’ ductility. However, where
•   Evaluation of the results of the blast.       shadowed from solar radiation, the low
                                                  temperatures of interplanetary space may
    The technologies and capabilities required    increase the brittleness of high-grade metals to
for this concept are in place and in operation    acceptable levels for this fragmentation
on Earth. As an idea of the scale of present      technique. This would require careful timing
Earth operations, 2.52 million metric tons of     of blast initiation, which is already possible
explosives and blasting agents were sold in the   with the electronic detonators commonly used
U.S. in 2004 for rock breaking in mining and      in terrestrial blasting operations. However,
construction [5].                                 the expected cohesiveness of metal NEOs also
    Each element of this system exists in         makes them amenable to orbit deflection, by
either commercial form (the drill and blast       explosives or other means.
portion) or as a NASA asset (launch vehicles).        Application of distributed-energy blasting
The technology readiness level (TRL) is,          without full understanding of the body of
therefore, high. The material fragmentation       knowledge gained by terrestrial experience
aspect is TRL-6; full systems tested repeatedly   would reduce its effectiveness for NEO
in relevant environments other than space.        destruction.     As is the case for many
For all components other than explosives          technologies dealing with natural materials as
emplacement, space qualification is expected      they are found (rather than as they can be
to be straightforward. The launch and             manufactured or simulated), re-invention from
transport-related systems, by time of deploy-     basic principles is much more difficult than it
ment, would presumably be TRL-8 or 9.             can appear. Many of the effects of blast
    The only process that requires maturation     design parameter variation presented in the
is the explosives emplacement system –            Introduction are not readily apparent to the
specifically, the method by which explosive       non-practitioner; they result from observations
charges are placed precisely at the appropriate   and research spanning several hundred years.

5   Primary Features                              over-large fragments there are produced, the
                                                  more time will be required to bring them
    The primary features (total mass, volume,     below the maximum size.            Secondary
energy requirement, class of launch vehicle,      fragmentation is expected to use the same
rendezvous, landing, NEO attachment) of a         blasting techniques as primary fragmentation,
mission utilizing the proposed approach will      but with more emphasis on Class 1 shots and
depend mainly on the characteristics of the       splitting designs.
target NEO, particularly its class, size, and
nearness. The most sensitive mass variables       7   Assurance of Reliability
are those that scale directly with NEO size,
including explosive mass, consumables for              As with any space mission, NEO
explosive emplacement, and consumables for        destruction using distributed energy blasting
human and robotic crew consumption.               would involve a complex, irregularly repeated
Equipment mass will be less sensitive, since      sequence of operations, and would rely on the
most machinery has a non-zero, though finite,     effective performance of numerous systems
working life.                                     and systems of systems. NASA and the
                                                  aerospace industry have developed procedures
6   Required Duration                             through experience for assuring the reliability
                                                  of the launch and transportation aspects of
    Once the target NEO has been reached by       such missions. Only the fragmentation aspects
the mitigation mission, the time needed to        are dealt with in this paper. Two particular
destroy the NEO depends on its size. NEOs of      activities would tend to reduce the risk of
simple structure and smaller than some            adverse outcomes:         Calibration shots to
minimum size (Class 1) would require only a       determine the powder factor(s) required, and
single blast of up to several hundred charges.    inclusion of secondary fragmentation capa-
Class 2 NEOs would require up to five blasts,     bilities in the mission profile.
and Class 3 NEOs would require a significant           At least one test shot would be performed
number of blasts. The particulars of the basic    on the NEO to calibrate the powder factor(s)
blast pattern for each NEO would be governed      needed for the materials comprising it. This
by the Group to which it belongs (see Intro-      would be done for every material type that
duction for the NEO fragmentability classifi-     constitutes either a major part of the NEO or a
cation).                                          major part of any single blast. The
    Each blast would require a minimum of         distributions of sizes and trajectories of the
two weeks on-site to accomplish, including        fragments produced would provide a measure
evaluation but not secondary blasting, once       of the effectiveness of the blast. Repeated
the general blast pattern design has been         calibration shots may be required if the results
determined for the combination of physical        indicate unexpected mechanisms in action.
properties unique to that NEO. Every blast,            In the event of a fragment exceeding the
however, will have its own peculiarities due to   maximum permitted size because of unknown
spatial variations in the properties of the NEO   geological features (voids, jointing, fractures,
constituents. This time estimate assumes that     etc.) in the blasted rock, precise secondary
explosive emplacement will not require a          blasting would be performed to split it into the
significantly longer time portion than in         appropriate size and number of fragments.
current practice.                                 This capability would consist of application of
    The amount of time necessary for              the same drilling and blasting techniques
secondary blasting will depend on the success     employed with the original NEO, but
of the original blast. Obviously, the more        customized to the smaller (but still over-large)

fragment. Over-large fragments generated in        rock fragmentation, that interact with com-
the initial stages of mitigation could be of the   plex, pre-existing, imperfectly constrained
same class as the original NEO, or a smaller       natural phenomena.
class.                                                 The number of personnel required would
                                                   depend on the methods developed to emplace
8   Potential Unintended Consequences              explosives and on the size and group of the
                                                   NEO. Some techniques are more adaptable to
    As for any type of NEO mitigation
                                                   automation than others; the most likely
mission, potential unintended consequences
                                                   approach is a hybrid in which some operations
                                                   are automated (such as drill string addition
• Decreased time before the main body of
                                                   and subtraction, common on Earth) while
    the NEO impacts Earth. This could happen
                                                   others are monitored by humans (such as fault
    if a blast were initiated outside the safe
                                                   detection) and yet others are performed by
    initiation time window (defined by the
                                                   humans (such as blast pattern design).
    NEO’s rotational state and location with
    respect to Earth). The impulse imparted to     10 Summary
    the remaining intact mass of the NEO
    would then be oriented toward Earth-               Large-scale surface blasting techniques
    impact instead of away from it. This           developed for terrestrial construction and
    would have to be accompanied or                mining could, if applied to a threatening NEO,
    followed by reduction or elimination of        be a feasible approach to ensure that it would
    mission capability to conduct secondary        be transformed into fragments too small (10-
    fragmentation, for the worst case to occur.    30 meters) to survive passage through Earth’s
• Creation of too many over-large fragments        atmosphere. A limited test mission on the
    for secondary fragmentation to be              Earth’s moon would improve assurance of
    completed before one or more of them           mission success.
    impacts Earth. This occurrence could also          Additionally, this approach could impart
    enlarge or multiply the impact zone. This      appropriate impulses to the NEO such that its
    could occur in any of the three NEO            impact is prevented, or, if fragmented, that
    classes or groups.                             fewer resulting fragments would impact Earth.
• Crippling or destruction of mission assets           The most appropriate total approach to
    prior to completion of mitigation. The         NEO impact hazard mitigation is to develop a
    difficulty of recovery from this occurrence    number of complementary techniques whose
    would depend on the mitigation stage           applicability overlaps, which together can deal
    during which it occurred, and the type and     with any of the potential Earth-impactors
    extent of the damage.                          currently existing in the Solar System.
                                                       See [8] for additional illustrations and
9   Cost Driving Technical Characteristics         discussion.
    Problems that arise during the mitigation      11 References
mission would be solved mainly by humans
on-site in communication with Earth, assisted      [1] Gertsch, L.S. and R.E. Gertsch, 2000.
by semi-automated systems not significantly            “Mine planning for asteroid orebodies,”
advanced beyond current terrestrial practice.          presented at 2nd Space Resources
    The major advantage of humans on-site is           Utilization Roundtable, Colorado School
their superior capability in solving unantici-         of Mines, 8-10 Nov 2000, abstract 7030
pated problems, especially in activities such as       (

 [2] Gertsch, Richard, John L. Remo, and
     Leslie Sour Gertsch, 1997. “Near-Earth
     resources,” in Near-Earth Objects, Vol.
     822 of Annals of the New York Academy
     of Sciences, p 468-510.
[3] Explosives and Rock Blasting, Atlas
     Powder Co., Dallas, TX, 1987.
[4] Handbook of Surface Drilling and
     Blasting, Tamrock Inc., Tampere,
     Finland, 1978.
[5] “Explosives,” published online by the U.S.
     Geological Survey,
     accessed 15 May 06.
[6] Bauer, Alan and William A. Crosby,
     1982. “Mine Operation: Blasting,” Chap.
     6.2 in Surface Mining, Bruce A.
     Kennedy, editor, published online by the
     Society for Mining Metallurgy and
     Exploration Inc., Littleton, CO,
     accessed 24 Jun 06.
[7] Lu, P. and J.-P. Latham, 1998. “A model
     for the transition of block sizes during
     blasting,” FRAGBLAST - The
     International Journal for Fragmentation
     and Blasting, Vol. 2, p 341-368.
[8] Gertsch, Leslie, Jason Baird, and Paul
     Worsey, 2006. “Distributed-Energy
     Blasting for NEO Destruction,”
     presentation to NASA NEO Detection,
     Characterization, and Mitigation
     Workshop, Vail, Colorado, 26-29 June
     2006 (to be posted on http://