A Lecture Holmberg&Persson Math Model

8/12/2019 A Lecture Holmberg&Persson Math Model

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Mathematical Model for Near

Field Rock Damage Control(Holmberg&Persson)

1R. Holmberg Lima 2011-Nov



BackgroundProject ”Cautious Blastingtowards Open Pit Slopes”

Virgin rock, first bench

Aitik Copper Mine – a lowgrad, 0.4%Cu, mine inNorthern SwedenPegmatites and manytypes of gneiss withzones of feldspar andepidote parallel to thefoot wallBoliden Mineral, NitroNobel, SveDeFo

R. Holmberg Lima 2011-Nov 2



Aitik, Sweden


P,A&H rock mechanicslope stability analysis

indicatedγ ~57 ° β i ~ 62 ° a ~10 m

a berm widthb catch benchα bench angleβ i intermediate slope anglesγ total slope angle



AITIK

It was common that back breakreached 8 m which implied that the totalslope angle just could be 40 ° instead ofestimated 57 ° if extreme cautiousblasting was performed.Millions could be saved for each degreethe pit slope angle was increased.

A change of the blasting procedure wasneeded.

An understanding of how blastingdamage is defined and how it is causedis needed!




Alternative designs

If the last bench has a benchheight of 15 m the berm/catchbench will be 9 m if the totaloverall slope angle is 57 °.Local bench failures, back breaketc will make it impossible toachieve.

A proposal was to finalise with a30 m bench in order to achieve

broader berms.Heigh benches are not easy totrim!


Stock blast

Cautiousblasting



Tests at footwall



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Tests at footwall



Local planar failures




First approach




2nd approach

v; particle velocity mm/sQ; Charge weight kgR; Distance mk, α and β


v=k Qα /R β



Mathematical model

R i 2= R 02 + (R 0 tanΦ) 2

Q i = dx L (L= linear charge conc. kg/m)q = (v/k) 1/α = Q/R β/α

Each part Q i of the charge Q contributes to thevibration intensity defined as w= v 1/α with

w i = (k Q iα/R iβ)1/α

Integration along the charge height H gives


v=k Q α/R β



Curves of particle velocity,v versus distance, R




Aitik Copper Mine – Round

#213Bench Height 13-14 mNumber of holes 96Hole diameter 250 mm

Hole Depth 16 mSpacing 10 mBurden 8 mUnloaded hole length 3-3.5 mExplosives TNT SlurryLinear Charge concentration 75 kg/mInitiation 2 primers; one at the bottom part and one 2 m abovebottom. Nonel.




Accelerometer positions


Initiation




First measured values



Accelerometers




Back break





Damage zone?

Damage zone

Distance frombench face

Degree ofdamage



Diamond drilling


1 and 2 – Right angle todominating fractures3 was drilled dipping 50 ° to crossthe foliation



Cracks




RQDRQD=Sum of allcore pieces

larger than 10cm divided bythe bore holelength

5 m length wasused




Results At 90% probability, damage(increase of crack frequency)ceases 18.6-44.9 m along thecore length.The diamond drill holes aredrilled at an angle of 45degrees to the face.I.e. at 90% probability,damage (increase of crackfrequency) ceases 13.2-31.9m behind the last row.

At a distance of 22.6 mbehind the round theprobability is 50% fordamage.

Damage Zone ~23 m. Implies apeak particle velocity of 800mm/s.


% increase of crack frequency



Damage zoneThe typical damage in fissured rock isan irreversible separation of the two

fissure surfaces from each other,resulting in a decrease in shear strengthof the fissure. This is accompanied by aslight swelling of the rock mass

effected.




Swelling of rock mass behind

blasts




Critical vibration velocity range for

damage in different rock mass typesRock /jointclass

Criticalvibrationvelocity mm/s

Hard rock –

Strong joints>1000

Medium hardrock - no weak

joints

800-700

Soft rock – weak joints

<400

Granite may be expected to fail indynamic tension at ~30MPacorresponding to a strain of ~1% or aparticle velocity of more than 1000

mm/s.Normal fissured rock will show tensiledamage in the joints at low stress levels~700mm/sIn soft, sedimentary rock with relativelyweak joints damage may occur atvelocities lower than 400 mm/s.






Damage zone 0,6 mNot affordable for

low grade ores!


Low damage zone but expensive

Stock blastCautiousblasting



Realistic design!?Discussions led to a potentialdesign.Max damage zone = 10 m.

2 rows cautious blasting.Last row reduced to 35% of afully loaded 250 mm hole.This is the same as a fullyloaded 171 mm hole.

Attractive for the mine asdecoupled charges in 250 mmholes not needed.Further investigations to confirm171 mm holes damage zone.


Stock blast10 m damagezone

Reduced charge conc in the last2 rows

Cautiousblasting



Kidd Creek




Kidd Creek




Brenda MineOverall slope angle 45 ° exclrampsBackbreak Prod row; 10 m

Pretrim; Reduced subdrillingand chargeTrim; 70 kg ANFO + 2waxed cardboard tubes with70 kg ANFO each

Deck charging; Testedpreviously but gave not thesame results as decoupledcharges. And moreexpensive.




Continuation to verify the

Curves


Cautious blastingwith 171 mm hole

diameter was testedat the Aitik mine.Hole inclination 70° Observations

DisplacementPeak particlevelocities



Accelerometer positions

Smoothblasting Φ=171mmLinear chargeconcentration32 kg/mTNT slurry




Results - PPV


Hole # Distance (m) a (g) v (mm/s)B 8,5 1031,0 1442,0C 13,9 303 562

D 26,9 29 283



Results - Displacement. Most

severe at surface.


Extenso-meter

Distance toblast hole (m)

Displace-ment (mm)

E1 8,5 37,8E2 14,1 14,4E3 27,3 2,6



Leveäniemi Iron Ore MineTest site Sector 1Aand 4B

Foliation dips 55° Strikes parallell tothe pit limit

Typical failures:Plane shear failuresalong the foliation




Sector 1A




Data Biotite schist

Tensile strength 17.8 MPaUniaxial compressive strength 102.7 MpaDensity 2.74 g/cm 3

Shear strength 42.2 kPa

Elastic Modulus of 39.9 GPaPoisson´s ratio 0.18




Typical production round #81

TNT-slurry 1.5 g/ccCord ,100 ms between rows

V1-V3 denotes PPV sensors






Back break




Measurements V1-V3 PPV sensorsE1-E3 Extensometers

S1-S10 Holes forseismic measurementsP3 & P4 Core drilling –pre and post blast


Last row ofround #81



Extensometers8, 12 and 16 m fromblast

D=22 mm iron barsgrouted at thebottom of the holes




Displacements


Relativedisplacement Vertical

displacement

Distance fromlast row (m)




Horisontal displacement

Round #88 At surface the followinghorisontal displacements

were measured:


Horizsontaldisplacements(cm)

7.0 16.5-23.911.5 10.3-15.319.5 1.5-6.7




Estimated separation of

weakness planes


Distance from

last row (m)

Depth

(m)

Measuredverticaldisplacement

(mm)

Separationat 8 cracksper m

(mm) *8 0-6 151 3.26-16 74 0.9

12 0-6 131 2.76-16 49 0.6

16 0-6 57 1.26-16 18 0.2

*Crack frequency measured on the core after blasting



Core drillingCore drilling 20 m,inclined 45° fromsurface towards thebottom of the round.




RQDCore drilling 45° fromsurface towards thebottom of the round.RQD is decreased alongwhole core lengthSurface – heavilyfractured from earlierblasting


Pre-blastPost-blast

Distance from surface



Point Load Index Test

Strength higher after blast!Possible explanation -The boiotit schist has a number of

potential weakness planes. Each ofthem with an unique strength.Blasting introduces dynamic loadsand several low strength weaknessplanes will be fractured. The coreexamined after the blast willtherefore contain more fractures.Core pieces selected for the PointLoad Index Test will obviously notcontain the low strength weaknessplanes and consequently a higheraverage of the strength will beachieved.




Laboratory experimentsIntact rock 12 MPaInvestigate shear strength of joints after theyopened up.Equipment; Two steel plates parallell to eachother, separated 1 cm.Plates; Three throughgoing holes where threerock core samples with diameter 30 mm can bemounted.’ Structures in cores mounted parallell to theplates.Movements increase the aperture along the

fractured weakness planes. After a predetermined temporary aperture , thesurfaces are repositioned into contact and theapparatus is ready for shearing.The equipment could also provide a remainingaperture of the joints before shearing started-


• Weakness planes given a temporary apertureof 0.3 mm still had intact rock bridges

covering 7% of the area of the weaknessplane.• The remaining aperture of more than 0.4mm shows that the peak angle of friction isclose to the calculated basic angle of friction.



Seismic measurements

At 5 m depth and 21 m from last row the rock masscontinuity was disturbed.Seismic signals showed lower frequencies and velocities.




Test d=102 mm




Round #99




PPV for Round #81 and #99




Avoid cord VOD cord =7000m/s

VOD TNT Slurry =4500 m/sI.e. Detonation isoccuring at sametime in 3-4 holesdepending on thewave velocity in therock.




Leveäniemi -Summary


Meaasurements Damage zone

Extensometers - vertical displacement ~20 mEDM - Horisontal displacement ~22.5 mCrack frequency . Pre- and Post-blast cores >20 mSeismic >21 mPPV (v=750 mm/s) ~23 mShear strength tests on cores with simulated blast damages ~20 m



Proposed design


Total slope angle 42 ° Foliation 55° Berm 6.2 m

Final wall; Sector 1A and 4B



Inclined holes




Vertical holes




Final wall.




Final wall




Sublevel caving




Tunnelling




Tunnelling






(SveBeFo) Continued tests 1990-2000


Vånga Smooth Blasting Tests1. Started in 1991 and continue in direct co-operation withDyno Nobel & Swedish National Road Authority.2. Tests made in 2-4,5 m granite benches, blasting singleholes and groups of holes.3. Main test factors have been

- the blast hole diameter, d= 24-64 mm

- the decoupling ratio or charge size- the explosive type- burden and spacing- initiation delay between adjacent holes.





4. Post-blast work includes- post-split excavation of intact blocks- cutting of blocks with diamond saw

- crack visualization with dye penetrant - crack lengthmeasurements.5. During the years more than 200 holes & 250 saw cuts havebeen blasted and inspected












After the blast, large blocks aredrilled and taken out with quarrymen ´s blasting techniques to avoiddisturbing the crack pattern

The blocks are split to size withwedges and cut horizontally in alarge diamond circular cut-off saw.








Explosive Density VOD Energy Fumes harge dia.Lin. Conc. Hole dia. CouplingKg/liter m/s m/s l/kg mm kg/m mm ratio

Gurit 1,00 2000 3,50 930 17,0 0,23 51 0,33Gurit 1,00 2000 3,50 930 22,0 0,40 64 0,34

Kimulux 42 1,15 4800 3,20 903 22,0 0,44 64 0,34Emulet 20 0,22 1850 2,35 1125 bulk 0,45 51 1,00Detonex 80 1,05 6500 5,95 780 10,6 0,08 51 -

Secti o n n o Date Exp l o si ve Ch arg e Ho l e In i ti atio n B*S Sec tio n sh o w sd i a. m m d i a. m m m effect o f:

5:2 jun-92 Gurit 17 51 pyrotechnic 0,8 - 0,5 ordinary initiation, reference6:3:1-6:3:3 maj-93 Gurit 17 51 EPD, instantan. 0,8 - 0,5 instantaneous intiation

H2:4-H3:4 aug-94 Gurit 17 51 EPD, At = 1 ms 0,5 1 0,5 zipper blastingJ2-J3 aug-94 Gurit 22 24 EPD, instantan. 1,0 - 0,8 less decoupling

E7:1 -E8:1 jun-94 Gurit 22 64 EPD, instantan. 0,8 - 0,8 larger S/BM6:2 apr-95 Kimulux 42 22 64 EPD, instantan. 1,0 - 0,8 highVOD, 4800 m/s

G14:1-G15:1 jun-94 Kimulux 42 22 64 EPD, instantan. 1,0 - 0,8 highVOD, 4800 m/s39:3 sep-94 Gurit 17 51 EPD, scattered 0,8 - 0,5 side hole







(SveBeFo) Continued tests 1990-2000With other factors kept constant: The resulting crack lengths decrease with a decreasing coupling ratio.Fully charged holes show a more complex crack pattern withinteracting cracks.

A higher VOD generates many short cracks around the bore hole.Crack lengths may increase with increasing burden and arc-shapedsubsurface cracks may appear when spacing is increased.




(SveBeFo) Continued tests 1990-2000The time delay of initiation is important;

zero delay gives the shortest crackscrack lengths increase with the delay

a delay as low as 1 ms give crack lengths more like singlehole blastseven a linear sequence of 1 ms delays is inferior toinstantaneous initiationtraditional smooth blasting thus gives unnecessarily longcracks.





SveBeFo has tested the influence ofthe burden and the spacingthe hole or charge sizethe decoupling ratiothe VODthe initiation delay time between holes

2003 Swebrec (Swedish Blasting Research Centre)

was formed and the researchers lead by Prof. FinnOuchterlony has continued to measure and refinethe Rock Damage Models.




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A Lecture Holmberg&Persson Math Model