CALCULATIONS BlastCalc and VibeSD Created by Brent Buffham © 2021 Currently only available in Metric Units Blasting Calculator Vibration Calculator Go Back Calculations used in the Applications. These are written in a Microsoft Excel Format for you to easily consume into your Excel sheets. Replace the words with the appropriate cell Reference. Vibration Scaled Distance - Formula from the AS2187.2 Appendix J. Variables = VIBRATION (millimeters/second), KCONSTANT(1-10000), DISTANCE (meters), WEIGHT (kilograms), AVALUE (> -1.0; Generally -1.6), BVALUE (0.5 [square root] Calculations = • VIBRATION = KCONSTANT * ( DISTANCE / ( POWER( WEIGHT, BVALUE ) ) )^AVALUE • KCONSTANT = VIBRATION / ( DISTANCE / POWER( WEIGHT, BVALUE) )^AVALUE • DISTANCE = POWER( ( VIBRATION / KCONSTANT ) , 1 / AVALUE )* POWER( WEIGHT, BVALUE ) • WEIGHT = POWER( DISTANCE / POWER( ( VIBRATION / KCONSTANT) , 1 / AVALUE ),(1/BVALUE )) • AVALUE = LOG( VIBRATION / KCONSTANT) / LOG( DISTANCE / POWER( WEIGHT, BVALUE )) • BVALUE = LOG( DISTANCE * (POWER( ( KCONSTANT / VIBRATION ) , ( 1 / AVALUE )))) / LOG( WEIGHT ) Blasting Calculations - Various Sources. • HOLE INFLUENCE AREA = BURDEN * SPACING • HOLE INFLUENCE VOLUME = HOLE INFLUENCE AREA * BENCH HEIGHT • HOLE INFLUENCE TONNES = HOLE INFLUENCE AREA * ROCK DENSITY • PATTERN AREA = HOLE INFLUENCE AREA * NUMBER OF HOLES • UNCHARGED VOLUME = PATTERN AREA * (STEMMING LENGTH + INERT LENGTH) • UNCHARGED TONNES = UNCHARGED VOLUME * ROCK DENSITY • SIN ANGLE = SIN((90-HOLE ANGLE) * (PI() /180)) • VERTICAL LENGTH = BENCH HEIGHT + SUBDRILL LENGTH • HOLE LENGTH = VERTICAL LENGTH / SIN ANGLE • HOLE RADIUS = (DIAMETER / 2) * 1000 • VOLUME PER METER = (PI() * POWER(HOLE RADIUS, 2)) / 1000 • VOLUME PER HOLE = VOLUME PER METER * HOLE LENGTH • VOLUME PER STEMMING LENGTH = VOLUME PER METER * STEMMING LENGTH • STEMMING MASS = VOLUME PER STEMMING LENGTH * STEMMING DENSITY • VOLUME PER INERT LENGTH = VOLUME PER METER * INERT LENGTH • CHARGE VOLUME = VOLUME PER HOLE - VOLUME PER INERT - volPerStemmingLength • CHARGE MASS = CHARGE VOLUME * PRODUCT DENSITY • TOTAL DRILL METERS = HOLE LENGTH * NUMBER OF HOLES • VOLUME PER INERT ZONE = VOLUME PER INERT LENGTH * NUMBER OF HOLES • CHARGE MASS PER METER = VOLUME PER METER * PRODUCT DENSITY • TOTAL CHARGE METERS = (HOLE LENGTH - INERT LENGTH - STEMMING LENGTH) * NUMBER OF HOLES • TOTAL EXPLOSIVE MASS = CHARGE MASS * NUMBER OF HOLES • TOTAL BLAST ROCK VOLUME = HOLE INFLUENCE VOLUME * NUMBER OF HOLES • TOTAL BLAST ROCK TONNES = HOLE INFLUENCE TONNES * NUMBER OF HOLES • POWDER FACTOR VOLUME = TOTAL EXPLOSIVE MASS / TOTAL BLAST ROCK VOLUME • POWDER FACTOR TONNES = TOTAL EXPLOSIVE MASS /TOTAL BLAST ROCK TONNES • VERTICAL ENERGY = (HOLE LENGTH - INERT LENGTH - STEMMING LENGTH) / HOLE LENGTH * 100 • BURDEN STIFFNESS = BENCH HEIGHT / BURDEN • SPACING SPEED = SPACING DELAY TIME / SPACING • BURDEN SPEED = BURDEN DELAY TIME / BURDEN • STAGGERED HYPOTENUSE = POWER(POWER(BURDEN,2) + POWER((SPACING/2),2), 0.5 ) • SQUARE HYPOTENUSE = POWER(POWER(BURDEN,2) + POWER(SPACING,2), 0.5 ) • TIMING RELIEF STAGGERED = (SPACING DELAY TIME + BURDEN DELAY TIME) / STAGGERED HYPOTENUSE • TIMING RELIEF SQUARE = (SPACING DELAY TIME + BURDEN DELAY TIME) / SQUARE HYPOTENUSE • SDoBCONSTANT1 = 0.0005 • SDoBCONSTANT2 = 0.00923 • SDoBCONSTANT3 = 1/3 • DIAMETER IN MM = DIAMETER * 1000 • DIAMETER IN METERS = DIAMETER • LIMIT M VALUE GREATER THAN 100MM = 10 • LIMIT M VALUE LESS THAN OR EQUAL TO 100MM = 8 • M VALUE UNLIMITED = (HOLE LENGTH - STEMMING LENGTH) / DIAMETER IN MM • M VALUE = MIN(IF(DIAMETER IN MM < 100, 8, 10), (HOLE LENGTH - STEMMING LENGTH) / DIAMETER IN MM) • SCALED DEPTH OF BURIAL = (STEMMING LENGTH + (SDoBCONSTANT1 * M VALUE * DIAMETER IN MM) / (SDoBCONSTANT2 * DIAMETER IN MM * POWER((M VALUE * PRODUCT DENSITY),SDoBCONSTANT3)) • DIAMETERS PER STEMMING LENGTH = STEMMING LENGTH / DIAMETER IN METERS; • DIAMETERS PER SUDRILL LENGTH = SUBDRILL LENGTH// DIAMETER IN METERS • DIAMETERS PER SPACING LENGTH = SPACING / DIAMETER IN METERS • DIAMETERS PER BURDEN LENGTH = BURDEN / DIAMETER IN METERS • DIAMETERS PER BENCH HEIGHT = BENCH HEIGHT// DIAMETER IN METERS • ANFO AMOUNT = TOTAL EXPLOSIVE MASS * ANFO PERCENTAGE • EMULSION OR MATRIX AMOUNT = TOTAL EXPLOSIVE MASS * EMULSION OR MATRIX PERCENTAGE • FUEL OIL AMOUNT = ANFO AMOUNT * FUEL OIL PERCENTAGE • AMMONIUM NITRATE AMOUNT = ANFO AMOUNT - FUEL OIL AMOUNT Overpressure Scaled Distance - Formula from the AS2187.2 Appendix J. Variables = DECIBELS (millimeters/second), KCONSTANT(1-100), DISTANCE (meters), WEIGHT (kilograms), AVALUE (> -1.0; Generally -1.45), BVALUE (0.3333 [cube root] Calculations = • DECIBELS = =20 * LOG10((((KCONSTANT * POWER((DISTANCE / (POWER(WEIGHT, (AVALUE)))),BVALUE))) * 1000 / (2 * POWER(10, -5)))) • KCONSTANT = =((((1000000000 * 0.00002) * POWER(10, DECIBELS / 20) / 1000000000) / 1000) / POWER(DISTANCE / POWER(WEIGHT, BVALUE), AVALUE)) • DISTANCE = POWER((((1000000000 * 0.00002) * POWER(10, (DECIBELS / 20)) /1000000000 / KCONSTANT) / 1000), 1 / AVALUE) * POWER(WEIGHT, (BVALUE)) • WEIGHT = POWER((DISTANCE / POWER(((((1000000000 * 0.00002) * POWER(10, (( DECIBELS) / 20)) / 1000000000) / 1000) / KCONSTANT), 1 / AVALUE)), (1 / BVALUE)) • AVALUE = LOG10((((1000000000 * 0.00002) * POWER(10, ((DECIBELS) / 20)) / 1000000000) / 1000) / KCONSTANT) / (LOG10(DISTANCE / POWER(WEIGHT, (BVALUE)))) • BVALUE = LOG10(DISTANCE * (POWER((KCONSTANT / (((1000000000 * 0.00002) * POWER(10, ( (DECIBELS) / 20)) / 1000000000) / 1000)), (1 / AVALUE)))) /LOG10(WEIGHT) Ideal Decomposition of Nitromethane Chemistry Ideal and only relavant for a sense check. •3NH4NO3 + 2CH3NO2 -> 4N2 + 2CO2 + 9H2O Thank you. 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