R.F. Favreau  Ph.D.

Prof. Of Physics, Royal Military College, Kingston Ont., Blaspa inc.


P. Favreau  P.Eng. 

Mining Engineer and Senior Computer Analyst , Blaspa inc.





A)        INTRODUCTION:  Rock excavation is the first process in the cycle of operation of a mine, and efficient blasting is paramount to the profitability of the mine.


     The traditional way to design blasts has been by trial and error, based on the experience of the designer.  This is probably the only important engineering practice which continues to be done without a precise engineering technique.  The efficiency of most other mine processes has been improved by the use of high-tech, while a majority of blast design has not yet profited from the advantages of the computer.


     However, with the advent of the high-tech blast simulator BLASPA, it has become possible to design the parameters of the blast according to normal engineering practices.


     Over the last 50 years, the chemical and physical mechanisms which occur during a blast have come to be identified; they are reviewed in Appendix I.  Although these mechanisms are complex, they have nevertheless been expressed in terms of mathematical equations which have been assembled together in the computer to create the blast model BLASPA.


     This model is very comprehensive.  Each blast simulation on BLASPA monitors, during the whole blast action, the chemical reactions of the ingredients which the explosive manufacturer has put into the explosives used in the blast, and simulates all the shock waves and stress fields that fragment the rock everywhere in the bench, as well as the subsequent displacement of each fragment of rock to form the muck-pile.


     The simulation takes into account the full geometry of the blast design, i.e. the pattern, hole diameter, collar, subgrade drilling, distribution of the explosives, water in the hole, etc.  But most important, it takes into account the specific properties of the rock at your mine: Young’s modulus “Y”, Poisson’s ratio “s”, the density “d” and the Dynamic Resistance of the rock “To”.


     The simulator BLASPA has been made user-friendly in that the effects of the blasting action of the simulated shock waves, stress front and rock displacement are translated into practical outputs to which the user can easily relate: the expectation of large blocks and how to prevent them; the possibility of toe; the weakening of the rock at the back of the blast and how it promotes back-break; the displacement of the rock in various zones of the bench and how it relates to the ease of mucking; the shape of the muck pile and how it participates in the efficient action of the loaders and the control of dilution, etc.


     Although the mathematical equations that are solved during each simulation are staggering in their complexity, modern computers  allow simulations to be carried out rapidly.  The simulator may be coupled to a confidential explosive bank created specifically for each user.


     Thus the speed of carrying out the simulations, the availability of the explosive bank, together with the translation of the outputs into practical blast quality criteria mean that a blast study on BLASPA to solve a specific blasting problem can be carried out in a few hours.  In practice, about two days of training enable a user to be comfortable with the system.






     Even if BLASPA does not yet address all the kinds of blasting used in rock excavation, it presently can simulate a majority of the blasting methods in current use, especially in open-pits.  Some of the situations where a simulation blast study with BLASPA can be most useful to users of explosives are as follows:

1)   Regular review of the current blasting procedures in an open pit mine to achieve quality versus cost optimization as the type of rock varies during exploitation of the pit, as new explosives become available, if new mining practices are under consideration, if the purchase of new equipment is under consideration e.g. drill size, loader type., etc. (see section D and Figs. I and II for  examples of how to carry out a simulation blast study)




2)   When a user of explosive is about to renegotiate his long term explosive supply contract, e.g. if he wishes to compare the quality versus unit costs associated with the proposals submitted by various explosive suppliers.  In such a situation, which often involve millions of dollars in possible savings, it is well advised for mine management to have available an objective simulation study, comparing the different explosives in terms of the efficiency of their specific ingredients and physical properties under the specific rock conditions and specific mining practices of the mine, especially as such a study is easily carried out on BLASPA (see an example in Section E and Apendix. II).

3)   When a contractor bids for a large construction or other excavation job.  In such a situation, where the call for bids often includes requirements ( e.g. specified grade tolerances)  which can be simulated on BLASPA, it is well advised for the contractor to have a simulated pre-evaluation of the true excavation costs that take into account the specific properties of the rock to be excavated and the specific conditions of the call for bids.  Court records contain documented cases of claim litigation’s where contractors have lost substantially because they bid, say as an example, $8/m3 for excavated rock when in reality it was a $20/m3 job.  Simulations for a bid are only as reliable as the rock properties available, but they nevertheless can readily identify the difference between a 8$/m3 and a 20$/m3 excavation.  (See an example in section F and Appendix III).

4)   When a contractor, having bid an excavation at at unit cost lower than the actual cost, does go into a claim action.  In such a situation, it is well advised for the contractor to obtain the objective and quantitative cost evaluation available from a rigorous simulation study, especially since such information can (1) guide his decision to go or not go to court; and (2) the credibility of objective and quantitative results from a simulation blast study carry much more weight in court  or arbitration than a subjective opinion based on “experience”.

5)   When a user or maker of explosives requires an evaluation of the blast results to be expected under particular conditions,  BLASPA has special subroutines to address many particular blast problems, e. g.:  a subroutine to evaluate the efficiency of an explosive composed of specific ingredients blasting in a rock of specific properties, which is particularly useful to makers of explosives;  a subroutine to assist in wall control;  a subroutine to predict the intensity of vibrations near a blast of a specific explosive in a specific rock;  a subroutine to address cratering techniques in underground mining;  a subroutine to evaluate the swell of blasted rock in open-pit and underground;  a subroutine to simulate the effect of angled holes;  a subroutine to simulate the percent cast in cast blasting, as well as the possibility of coal damage;  a subroutine to simulate the effect of open cracks on the creation of blocks; a subroutine to evaluate fly rock; a subroutine to design a blast using a borehole of variable diameter size; a subroutine to optimize the overall excavation unit cost.





     Blaspa Inc. is a firm which has been in existence for 20 years, during which it developed the simulator BLASPA.  It owns the rights to the program and was formed for the purpose of making blast simulations available directly to mines, contractors and other users of explosives and to suppliers of explosives.  Access to BLASPA can be achieved as follows:

1)   A mine, contractor or supplier can have blast studies carried out by Blaspa Inc., the objectives of the studies being defined by them.

2)   If a mine, contractor or supplier is interested, Blaspa Inc. is ready to negotiate the installation of direct access at the mine via a dial-up connection.  The user at the mine inputs his blast design data directly in his PC, the simulation is carried out on a host server computer at Blaspa Inc., the results being instantaneously returned to the client PC where  the blast contours and other analysis are carried out and saved.  The mine’s rock bank and the blast study results are stored in the data base at the client PC, while his private explosive bank and the simulator are stored on the host computer at Blaspa Inc.





     As an example of the application of BLASPA of the type proposed in Section B 1) above, consider a situation in an open pit mine where it is noticed that the floor is somewhat uneven and blocks begin to be rejected at the crusher. 


     The blast designer may address these problems by trial and error, altering slightly anyone of the blast parameters such as the pattern BxS, the collar C, the subgrade drilling G, the lengths of columns L1 and L2 and the types X1 and X2 of the explosives, the hole diameter D, etc. For each alteration, he must carry out blasts in the pit till a change in the quality of the blast results is observed. After months of trials, he may find a suitable solution.


     Alternately, he may decide to carry out a simulation study. First he obtains newly  measured rock properties Y, s, d and To (a process which is easy and inexpensive), and finds that they have varied since they were last measured.  Then he simulates on BLASPA the expected effect of the previous blasting procedure in the rock having the newly measured rock properties, and finds that it gives an excavation contour for the newly measured Dynamic Resistance To of the shape shown in Fig. I(a).  This clearly identifies that toe and blocks are being produced by the old blasting procedure in the new rock.


     He then varies the blast parameters BxS, C, G, L1, L2, X1, X2, D etc. much as he would have done by trial and error in the pit, but in the computer. Each change alters the shape of the of the excavation contour, sometime making the toe or blocks worse, sometimes better. Eventually, after perhaps two hours on the computer, he finds values of the blast parameters which produce the excavation contour of the shape shown in Fig. I(b).


     The latter is expected to produce no toe or blocks since the contour fully includes the region to be excavated i. e. the region between the free faces and the hole and grade.  He may then carry out a few more simulations to seek the least costly procedure which removes toe and blocks.  He then proceeds with actual trials in the pit.


     As a second example of an application of Blaspa of the type proposed in Section B 1) above, consider a situation in an an excavation operation where  monitoring the loaders and trucks  has found that the rate of mucking goes through regular time cycles of fast mucking followed by slow mucking.


     This is a blasting problem which is much more difficult to correct by trial and error; in fact many operations may simply live with it.  If, on the other hand, the present blast procedure be examined in more details by simulations on BLASPA, it is often found that the displacement contours representing the positions of all the rock fragments at a given time during the burst out of the bench at the end of the blast have the shapes shown in Fig. II(a) (see Appendix I for an explanation of the burst out).


     The simulated results of Fig. II(a) indicate that the rock near the grade bursts out with inadequate displacement velocity, while that mid-way up the bench bursts out more than adequately.  Thus the rock near the grade is tighter and mucks less efficiently.  A simulation study on BLASPA in which the blast parameters BxS, C, G, L1, L2, X1, X2, D, etc. are varied will show how the displacement contours are altered by each change in the blast parameters.   For example, a blast procedure with different values of L2 and X2 (new explosives are simply called from the explosive bank) gives new displacement contours such as those shown in Fig. II(b). These predict that the rate of mucking the rock near the grade should be much enhanced.  In such a study, blasting and mucking costs should be involved in order to seek the minimum overall excavation  unit cost.





     As an example of the application of BLASPA to assist a mine during its negotiations with suppliers for a long term explosives supply contract, a simulation study on BLASPA can be carried out which evaluates the quality of the blasts results to be expected with the explosives proposed by the different suppliers, taking into account the ingredients in these explosives , the mine’s specific rock properties and mine practices, as well as the costs involved.


     The first part of such a study consists of simulated results which establish the quality of blast results which the mine requires for efficient operation; these are evaluated from the mine’s opinion regarding the quality of the results achieved with known past and present procedures and, for convenience, each quality factor is rated as 100 in part (a) of Appendix II.


     Part (b) of Appendix II then presents the patterns and unit blasting costs which simulations have shown to be required with each explosive proposed by a supplier, if the required quality of blast results is to be achieved.


     Part (c) of Appendix. II presents the expected quality and unit blasting costs, if each supplier’s explosive is used in the mine’s rock in the pattern proposed by the bidding suppliers.  Appendix II assumes two suppliers, A and B, whose proposed explosives are labeled A1, A2, B1.


     The unit excavation cost usually comprises the proposed explosive and accessories costs and the drilling costs; any other cost may be added, if the mine so wishes.  Also, any additional way of comparing the bids which the mine wishes may be simulated and added to the table, e. g.  the use of split loads, or special emphasis on ease of  mucking the grade, etc. The study report also normally presents curves like those in Figs. I and II, which helps to explain the evaluation of the quality of the blast results.





     As an example of the application of BLASPA to assist a contractor to prepare a bid for an excavation project, Appendix III shows the results of simulations based firstly on normal rock properties and then on the rock properties measured from a rock sample obtained at the site.  The costs are based on the unit operation costs supplied confidentially by the contractor.


     Column (a) presents the simulated unit excavation cost  for normal values of rock properties for this kind of operation, as deduced from Blaspa Inc.’s extensive rock property data bank, using the pattern proposed by the contractor in his initial bid. Column (b) presents the pattern simulated on BLASPA for the same situation, indicating that in a normal rock the contractor’s procedure is very conservative and would allow substantial expansion of the pattern.


     Column (c ) simulates the contractor’s proposed pattern, but in a rock having the properties measured on a sample from the site; the quality of the blast results is bad and the unit excavation cost is very high. Column (d) simulates the appropriate blasting method for the measured rock properties; the quality of the results is now satisfactory, but the unit cost is about 50% above the bid cost.


      The conclusion from this study is that the contractor stands to loose a substantial amount of money if he is awarded the contract on the basis of his original bid, especially since difficult blasting often increases the costs of the rest of the work.  A contractor is well advised to have access to the results of a study like that of Appendix III before he actually submits his bid.





     The article reviews the principles which form the basis for the blast simulator BLASPA, and presents some examples to illustrate its application to practical situations in mines and excavation contracts.


     The simulator BLASPA is now directly available to mines, contractors and suppliers of explosives via the firm Blaspa Inc. which has been created for this purpose.  Access may be either through blast studies carried out by Blaspa Inc. on instructions from the customer, or a direct access contract may be negotiated with a large scale user.


     In the past, a majority of blasts were designed by trial and error.  Many industries have significantly improved their efficiency by calling on the computer.  It would be normal if, in the future, most blast designs would be carried out with the assistance of simulations on BLASPA.





(1) COOK, 1958.

      The science of high explosives, Reinold Publishing

(2) ATCHISON, DUVAL, 1957.

     Rock breakage by explosives, U. S. Bureau of Mines Report No. 5356.

(3) FAVREAU , 1969.

Generation of strain waves in rock by an explosion in a spherical cavity, Journal of Geophysical Research, vol. 74, p. 4267.

(4) FAVREAU, 1985.

Quantitative evaluation of cast blasting by airborne surveys and simulations, Pennsylvania Blasting Conference, Pennsylvania State University

(5) FAVREAU, 1994.

     Optimization of overall excavation costs in a coal strip mine, INFOR vol. 32, no. 2, May 1994.






     The simulator BLASPA applies the fundamental principles of Physics and Chemistry to express mathematically the mechanisms involved when explosives are used to break and move brittle rock.  The main mechanisms are outlined in Fig. III.  In Fig. III(a), the detonation of the explosives has converted the latter into very high pressure gases (Cook 1958), the transition occurring as the detonation head sweeps the explosive column at a rate called the  Detonation Velocity.




The sudden increase in the pressure applied to the rock near the wall of the borehole causes the latter to expand, thereby generating strong shock waves in the rock mass (Favreau 1969); these travel away from their explosive source toward the free faces of the solid rock bench.  During this phase, the shock waves act on the rock in compression; they cause little fragmentation because rock is very resistant to compressive failure (Duvall 1987).  Fig. III(b) shows how the compressive shock waves, after reflection at the boundaries of the bench, travel back through the rock mass; on the return passage, however they act on the rock in tension because reflection at the rock/air boundary has converted them from compressive to tensile.  The passage of the tensile waves initiates primary cracks in the rock mass, because rock is not resistant to tensile failure.  As the compressive and tensile waves travel across the rock, their intensity attenuates; nevertheless, if the distance from the borehole to the free faces of the bench is not excessive, the reflected tension wave will still have adequate intensity to initiate primary cracks all the way back to the line of the boreholes.  The weakening of the rock induced by the primary cracks near the borehole will allow the high pressure gases, which had been under containment by the solid rock around the borehole , to resume their blasting action as shown in Fig. III(c).  As can be seen in Fig. III(c), this new blasting action takes place as follows:  the gases create a quasi-static stress field whose intensity diminishes from the vicinity of the borehole to that of the air/rock boundary, the most rapid drop in stress occurring near the dashed line representing the front that separates fully broken rock from that which has only been weakened by the primary cracks.  The large stress gradient just to the right of this front further fragments the weakened rock, converting it to fully broken rock, so that the front progresses from left to right converting primary cracks into full fragmentation.  When the front reaches the free faces of the rock mass, Fig. III(d), the whole rock bench is fully broken and it bursts out, throwing the various fragments ahead into the muck-pile of broken rock.








Explo-  Pattern  Grade      Blocks   Back     Average      Grade        Fragmen-      Cost

sive       (ft.xft.)  Rupture                 Break   Movement  Movement  tation          ($/m3)

(a) Quality of Blast Results Required by the Mine:

A1          19x21       100          100       100          100               100            100            2.85

(b) Procedure which Simulations Show to Give the Quality of Blast Results Required by the Mine:

A1*         19x21       100         100        100          100              100            100            2.85

A2        15.5x17.5    103           96          89          108                98            108            3.64

B1        16.5x18.5    111         106        100          101                93            108            3.34

(c) Procedure the Supplier Recommends:

A1           20x22        96            98        100           91                 92             93             2.57

A2           17x19        96            93          89           91                 87             95             3.05

B1           19x21      100          100        100           76                 76             87             2.38


(1)  A low value of Grade Rupture predicts the expectation of toe.  A low value of Blocks predicts the expectation of blocks.  A low value of Back-break predicts less back-break.  A low value of Movement, and especially a low value of Grade Movement, predict slow mucking.

(2)  The study on BLASPA indicates that the procedures recommended by the suppliersare inadequate.  The best deal for the mine is probably the present procedure.

(3)   In the study the bench height H=40’, L1=30’, G=5’, C=15’, D=12”; these may be modified for each procedure as required.

*Supplier A is currently supplying explosive A1 in 19x21, with satisfactory results but $/m3 deemed high by the mine.




                                           (a)               (b)                 (c)               (d)

Pattern (ft.xft.)                 7x8              9x10              7x8              5x6       

Blocks                                 0                  0                 10%              0

Toe                                      0                  0                 12%              0

Drill $                                 99                 99                 99                99

Drillers $                            30                 30                 30                30

Drill accessories $             20                 20                 20                20

Explosives  $                      11                 11                 11                11

                loading $           13                 13                 13                13

              accessories $       21                 21                 21                21

Loading $                         63.84           102.60           63.84            34.20

Extra loading $                   0                   0                31.92               0

Trucking $                       75.60           121.50           75.60            40.50

Bulldozer $                      16.80             27.00           16.80              9.00

Extra bulldozer $               0                    0                8.40                 0

Reblast toe & blocks         0                     0                188                 0

                                       _______         _______     _______      ________

                                        350.24           445.10          578.56         277.70

$/m3                                 7.35               5.81             12.14           10.88


The above simulations assume all dry holes;  simulations should normally also be

 carried out for the expected wet holes.

(a) Blast procedure proposed by the contractor in his initial bid, simulated with BLASPA in a rock assumed to be of normal properties.

(b) Satisfactory blast procedure simulated with BLASPA in the same rock of normal properties.

(c) Blast procedure proposed by the contractor in his initial bid, as simulated with BLASPA in the actual rock.

(d) Blast procedure simulated with BLASPA in the actual rock.




BLASPA home page