A gas pressure-based drift round blast design methodology 

William Hustrulid NIOSH Spokane Research Laboratory, USA 

Jeffrey Johnson NIOSH Spokane Research Laboratory, USA 

Abstract 

The National Institute for Occupational Safety and Health (NIOSH), as part of a comprehensive program to 

improve mine safety through the widespread acceptance of careful excavation principles in drifting, have 

revisited standard drift round design concepts. Although the initial emphasis was on contour row design and 

providing improved design tools for blasting with de-coupled charges, the focus has broadened into the 

development of a general gas pressure-based drift round design approach. The concept of a damage radius (Rd) 

for a given explosive-hole-rock mass combination is introduced. With the damage radius as the basic building 

block, the blast holes are positioned on the face, beginning with the buffer row, to achieve the desired 

excavation size, shape and smoothness. The design of the contour row of holes is also performed using a 

pressure-based approach. 

The paper presents in some detail the overall approach and the required gas pressure-based design equations. 

1 Introduction 

The development of all mass mining systems relies heavily on drifting. In general, it is important that these 

drifts remain stable over long periods of time both for safety and economic reasons. Hence, care must be 

exercised in the excavation process. Today, it is possible to rapidly drill the required blast holes with good 

precision using modern drill jumbos. A wide variety of explosive products are available to charge the holes and 

with the use of electronic delays the holes can be properly sequenced. The remaining ingredient is the 

availability of a practical perimeter control blast design methodology. 

Holmberg (1982) presented a very useful approach to drift blast design in his paper “Charge Calculations for 

Tunneling” which is based on the early work of Langefors and Kihlström (1963). In this approach, the face is 

divided into cut, contour, lifter, and stoping sectors. The required equations providing burden and spacing 

dimensions as a function of hole size, charge concentration, etc. are developed for application in each sector. For 

perimeter charge design, an approach based on a relationship between peak particle velocity, linear charge 

concentration, and distance has been recommended. This has become known as the Holmberg-Persson (1978, 

1979) approach. 

As part of a comprehensive program on improving mine safety through the application of careful excavation 

techniques in drift driving, the National Institute for Occupational Safety and Health (NIOSH) revisited 

traditional drift round design concepts. The initial focus was more narrowly aimed at improving contour row 

design. However, as the study proceeded, it became quite obvious that the key to successful perimeter control 

was, first and foremost, the proper design of the buffer row of holes. Rather than the four design sectors 

identified by Holmberg (1982), there are actually five: cut, buffer, contour, lifter and stoping. Except for cut 

design, which is based largely on geometrical considerations, it appeared that a gas pressure-based approach 

could be logically applied to improved blast round design both with and without perimeter control. To 

accomplish this, the concept of a damage radius (Rd) for a given explosive-hole-rock mass combination was 

introduced. With the damage radius as the basic building block, the holes are positioned on the face, beginning 
with the buffer row, to achieve the desired excavation size, shape and smoothness. Whereas the burden and 

spacing dimensions are the building blocks in a standard blast round, in this new, pressure-based approach the 

burden-spacing dimensions can be calculated, if desired, but they are an output of the design approach and not 

an input. 

A gas pressure-based approach is applied to the contour row as well. This is quite logical since, when using decoupled charges in the contour holes, the borehole wall pressure is strongly dependent on the charge diameterhole diameter ratio. The simple use of linear charge concentration is not enough to predict the damage extent. 

In perimeter control blasting, if the buffer row of holes has been properly designed, the primary function of the 

contour row is to smooth the final excavation surface and not to fragment and remove significant quantities of 

rock. With this “smoothwall” approach, much of the “burden” lying between the contour and buffer rows has 

already been fragmented and/or removed by the buffer row holes. 

The paper begins with a description of the gas pressure-based design approach and then provides a simple 

technique for estimating the damage radius associated with the buffer row of holes. It concludes with a 

discussion of smoothwall design for the contour row of holes. 

2 An overview of the gas pressure-based design approach 

In the way of introduction, consider the 4.5m wide by 4m high drift with arched roof shown in cross-section in 

Figure 1. The perimeter (walls and roof) is to be excavated using smoothwall blasting techniques. The following 

steps are used: 

 Step 1: Design the buffer row 

 Step 2: Add the contour holes 

 Step 3: Design the lifters 

 Step 4: Add the cut 

 Step 5: Add fill-in holes as required 

The key to the approach is the assignment of a “practical” radius of damage (Rd) to each blasthole/explosive 

combination being considered for use in the particular rock mass. By “practical” radius of damage, it is meant 

that if the rock mass lying outside of this ring were removed, the rock remaining within the ring would easily 

break apart. 

Figure 1. Example drift shape 
As can be seen in Figure 2, the practical damage zone consists of both crushing and cracking components. 

 

Figure 2. Diagrammatic representation of the crushed, cracked and damaged zones surrounding a blast 

hole 

At this point in the discussion, it will be assumed that Rd = 0.5m for the fully-coupled buffer row holes. The 

technique used for calculating Rd will be presented later in the paper. To start the design, parallel shells located 

at distances of Rd and 2Rd inside the desired contour are drawn as shown in Figure 3. 

Figure 3. First step in the buffer row design 

Next, circles of radius Rd are added. The center of the circle corresponds to a future buffer row hole location. 

Figure 4 shows the placement of the buffer row holes in the “just-overlapping” scenario. 

Figure 4. Initial placement of the buffer row roof holes 
As can be seen, there is a considerable amount of “un-touched” rock between the as-designed coverage and the 

perimeter. This is overcome by translating the holes along the design line so that they more fully overlap. Figure 

5 shows one possible arrangement. 

Figure 5. Final placement of the buffer row roof holes 

In this particular case, the distance between the buffer row holes is 1.4 Rd or 0.70m. In Figure 6, the buffer row 

has been added to the walls. 

Figure 6. Addition of the buffer row wall holes 

In step 2, the contour row holes are positioned to “smooth out” the surface created by the buffer row holes. The 

first holes placed are in the drift corners. They have the required look-out and look-up angle to provide the space 

needed for drilling the next round. The remaining holes along the roof are placed to remove the remaining rock 

cusp between adjacent damage circles. The design basis for the contour row is presented later in the paper. As 

can be seen, the amount of rock associated with each hole (the burden) is rather small (Figure 7). 

Figure 7. Addition of the contour holes 

In step 3, the lifters are added. They have extra work to do both working against gravity and against the weight 

of the overlying pile, so, even if they are the same diameter as the other holes in the round, they are often 
charged with a more energetic explosive. In this particular case, it is assumed that the associated damage radius 

is 0.7m. A lifter hole is placed in each corner and the remaining holes are positioned to cover the remaining 

distance. To improve floor evenness, the circles are overlapped (see Figure 8). 

Figure 8. Lifters added to the design 

In step 4, a four-quadrangle cut with a final side dimension of 1.4m has been selected for use. A single, large 

diameter, uncharged hole provides the initial free surface. The numbers refer to the number of the half second 

delay (No. 1 is 0.5 s delay, No. 2 is 1.0 s delay, etc.) being used. The cut has been superimposed on the design in 

Figure 9. 

Figure 9. Addition of the cut to the design 

Finally, additional “stoping” holes are added to fully cover the face. The final result is shown in Figure 10. 

Figure 10. Completion of the design with the addition of stoping holes 
Figure 11 shows one possible design for the 4.5m x 4.0m drift provided by Holmberg (1982) using the burdenspacing equations developed by Langefors and Kihlström (1963). 

Figure 11. A design provided by Holmberg (1982) 

In Figure 12, the damage radius circles have been superimposed on several of the holes. The gaps in the 

coverage are clearly seen. 

Figure 12. Superposition of influence circles on the Holmberg (1982) design 

The total number of holes in the Holmberg (1982) design (excluding the cut) is 24 whereas in the gas pressurebased design it is 40. The latter will clearly require more time to drill and to charge although with the 

application of modern technology this forms a relatively small part of the total drifting cycle. It should be 

pointed out that the designs shown in Figures 10 and 12 are not directly comparable since Holmberg (1982) did 

not include “smoothwalling” of the walls. 

The gas pressure-based approach is very logical and easy to apply, providing one has (1) a reasonable technique 

for estimating the damage radius associated with a particular hole – charge combination and (2) a “smoothwall” 

design procedure. 

The remainder of this paper will focus on one gas pressure-based approach for selecting the required values of 

Rd and some design guidelines for the “smoothwall” row of holes. Before this can be done, there must be a 

procedure for pressure calculation. This is the subject of the next section. 

3 Calculation of blasthole wall pressure 

3.1 Introduction 

An important assumption in this approach is that the damage zone radius is dependent upon the blasthole wall 

pressure. The first step is the calculation of the explosion pressure. Once this has been determined, one needs to 
obtain the pressure applied to the wall of the borehole. For fully coupled charges (the explosive entirely fills the 

hole cross-section), the wall pressure is just the explosion pressure. When using de-coupled charges, the 

explosive gases must expand to fill the cross-section with an accompanying decrease in pressure. The 

calculation of the borehole wall pressure for both cases is described in this section. 

3.2 Explosion pressure 

There are several techniques for obtaining the explosion pressure for the explosive(s) of interest. The simplest of 

these is to obtain the value directly from the explosive manufacturers. They often provide the detonation 

pressure on the specification sheets. This generally has been calculated using the relationship 

ρ D2

 Pd = e (1) 4 

Where: 

Pd = detonation pressure (MPa) 

ρ = explosive density (kg/m3 e ) 

D = detonation velocity (km/s) 

It is not known why the manufacturers provide the detonation pressure since it is not the same as the explosion 

pressure (Pe) required in blast design calculations. For practical purposes, it has been found that Pe can be 

approximated using the expression 

1 Pe = Pd (2) 2 

Or 

ρ D2

 P e

e = (3) 8 

 

The required explosive density and detonation velocity parameters are normally supplied by explosive 

manufacturers. 

For ANFO with a density ρ = 820 kg/m3 e and detonation velocity D = 3900 m/s, the explosion pressure is 

820 (3.9)2 

 Pe = = 1560 MPa 

8 

This pressure is oriented radially outward from the wall of the explosive charge. If the explosive charge was in 

intimate contact with the hole wall (fully coupled conditions), this would be the wall pressure Pw used in further 

calculations. 

As is often pointed out by explosive specialists, this approach to calculating the explosion pressure is very 

simplified and other factors need to be taken into account (confinement, diameter, ideal vs non-ideal explosives, 

etc). That is true, but then someone must supply the information in a form readily available and applicable by 

users of explosives. Until that occurs, the above approach is recommended for use. 
3.3 The pressure on the borehole wall for de-coupled charges 

Generally, the explosion pressures as calculated in the previous section are much higher than the compressive 

strength of the rock being blasted. Although this is desired when fracturing the rock in the interior part of the 

drift round, it is not true for the perimeter holes when perimeter control blasting is to be used. 

The first design requirement for the perimeter holes is to keep the borehole wall pressure less than or equal to 

the compressive strength. This is normally accomplished by using de-coupled charges. The explosion pressure 

calculated in the previous section applies at the outer boundary of the charge. To reach the borehole wall, the 

explosive gases must expand and, in the process, the pressure decreases. 

For ideal gases (gases at atmospheric pressure and room temperature), the standard expression relating pressure, 

volume and temperature is 

 Pν = nRT (4) 

Where 

P = pressure 

υ = specific volume 

n = number of moles of gas present 

T = absolute temperature 

R = the Universal Gas Constant 

Assuming isothermal expansion, one writes 

 Pwν h = Pe

ν e (5) 

Where 

Pe = explosion pressure 

υe = specific volume of the explosive 

Pw = wall pressure 

υh = specific volume of the explosive gasses filling the hole 

Assuming that 

 ρe = 0.82 g/cm3 

 

the specific volume of the explosive would be 

 υe = 1/ρ 3 e = 1/0.82 = 1.22 cm /g (6) 

For the case when 

 dh = hole diameter = 54 mm 

 de = explosive diameter = 30 mm 

the specific volume of the gasses filling the hole is given by 
⎛ d ⎜ h ⎞

2 ⎛ ⎞2

54 

ν h = ⎟ ν = ⎜ ⎟ 1.22 = 3

⎜ ⎟ e 3.95 cm / g (7)

⎝ de ⎠ ⎝ 30 ⎠

Assuming the explosive to be ANFO (Pe = 1560 MPa), the wall pressure calculated using equation (5) is 

⎛ν ⎞ ⎛1.22 ⎞ P = e 

w P e ⎜ ⎟ = 1560 ⎜ ⎟ = 482 MPa (8) ⎜ ⎟ ⎝ν h ⎠ ⎝ 3.95 ⎠

However, one cannot apply this approach for the very high pressure, high temperature explosive gas conditions 

involved here. To account for non-ideal gas behavior, the co-volume correction term introduced by Cook (1956, 

1958) and first applied by Hino (1959) for perimeter control applications will be used. It forms part of the 

Utah/NIOSH pre-splitting approach described in a recent paper by Hustrulid (2007). The relationship relating 

pressure, volume and temperature in a consistent set of units is 

 P (ν −α) = nRT (9) 

Where 

P = pressure (MPa) 

υ = specific volume (cm3/g) 

α = co-volume (cm3/g) 

n = moles/g 

R = universal gas constant = 8.314474 cm3

 – MPa / (mole – oK) 

T = temperature (o

K) 

Assuming, as before, that the expansion of the gases in the borehole occurs isothermally, one can write 

 Pw (ν h −αh ) = Pe (ν e −αe ) (10) 

Hustrulid (2007) has shown that the expression 

 α = 1.1 e -0.473/υ (11) 

may be used to relate the co-volume and the specific volume. Substituting the appropriate values into equations 

(12) and (13) 

 

 αh = 1.1e−0.473ν h (12) 

 α = 1.1e −0.473ν e

e (13) 

one finds that 

 α = 1.1 e −0.473(3.95)

h = 0.17 

 α −0.473(1.22)

e = 1.1e = 0.56 
The wall pressure with the co-volume correction becomes 

⎛ (ν e −α e ) ⎞ ⎛ 1.22 − 0.56 ⎞ Pw = Pe ⎜ ⎟ = ⎟ = ⎜ ⎟ 1560 ⎜ 272 MPa 

⎝(ν h −α h ) ⎠ ⎝ 3.95 − 0.17 ⎠

As can be seen, the co-volume correction has a major effect on the calculated wall pressure. If the compressive 

strength (σc) of the rock mass is, for example, 

 

 σc = 200 MPa 

one would expect to see crushing around the hole. If this is not permissible, one would consider changing the 

explosive, changing the hole diameter or changing the charge diameter. The calculation procedure described 

above would be repeated until the desired wall pressure is achieved. 

4 Buffer row design based on damage radius 

4.1 Introduction 

With the detonation of an explosive charge in a borehole, a shock wave is generated in the surrounding rock 

mass. Depending upon the explosive and the rock mass, somewhere in the range of 5-15% of the total explosive 

energy goes into shock energy. In spite of the relatively low amount of energy involved, the shock wave is 

thought to be responsible for most, if not all, of the new crack generation. The remaining energy is contained in 

the high pressure gases. Upon expanding, these gases produce extension in the old and new cracks and eventual 

displacement of the burden. The overall damage to the rock surrounding the borehole involves both of these 

effects. Previous investigators have generally focused on one or the other of these producers of rock damage. 

Since both contribute to the overall damage, both must be included. This section presents a pragmatic first 

approach to predicting the damage radius based on an integration of the two effects. 

4.2 The modified Ash approach 

For open pit mining applications, Ash (1963) has suggested the following relationship between the burden (B) 

and the hole diameter (dh) for fully-coupled explosives. 

 B = KB dh (14) 

Where 

KB = constant 

Ash (1963) found that when using ANFO (with a density of 0.82 g/cm3

) to blast average rock (density of 2.65 

g/cm3

), the use of 

 KB = 25 

provided very satisfactory results. By way of an example, if the hole diameter (dh) is 0.10m, then the appropriate 

burden would be 

 B = 25 (0.10) = 2.5m 

When using explosives of greater specific energy (energy/volume) than ANFO to blast the average rock, one 

would use 
 KB = 30 

Or even 

 KB = 35 

For surface blast design, Hustrulid (1999) recommended that designers think in terms of cylindrical fragmented 

plugs of rock surrounding each hole. For the “just-touching” scenario, the radius of influence (R) of the plug is 

equal to B/2. Equation (14) can be written as 

 2R = KB dh 

But since 

 dh = 2 rh 

Then 

 R = KB rh (15) 

For the present application, it will be assumed that the damage radius is equal to the radius of influence. 

 Rd = R (16) 

And hence 

 Rd = KB rh (17) 

Or 

 R d /r h = K B (18)

It is important to have an expression for Rd that can be applied to different explosive – rock combinations. Based 

upon energy considerations, Hustrulid (1999) has shown that 

ρ s 2.65 Rd / r = 25 e ANFO 

h (19)

ρ ANFO ρ rock 

Where 

ρe = explosive density (g/cm3

) 

ρ g 3

rock = rock density ( /cm ) 

sANFO = weight strength with respect to ANFO 

ρANFO = ANFO density (g/cm3

) 

If ANFO of density 0.82 g/cm3

 (sANFO = 1) is used in 38mm diameter holes in granite of density 2.65 g/cm3, one
 

finds that the damage radius is 

 Rd = 25 (0.019) = 0.48m 

If an emulsion with the following properties 
 ρe = 1.15 g/cm3

 sANFO = 0.88 

is used instead, then 

ρ e s ANFO 2.65 1.15(0.88) 2.65 Rd / rh = 25 = 25 = 27.8 ρ ANFO ρ rock 0.82 2.65

The corresponding damage radius would be 

 Rd = 27.8 (0.019) = 0.53 m 

If the comparison basis is the explosion pressure rather than the explosive energy, one can write 

P 2.65 R / r = 25 e Exp

d h (20) Pe ANFO ρ rock 

Where 

Pe Exp = explosion pressure for the explosive 

Pe ANFO = explosion pressure for ANFO 

The specification sheets provided by an explosive manufacturer indicate that 

 Pe ANFO = 1550 MPa 

 Pemulsion = Pe EXP = 3150 MPa 

One finds that 

P 2.65 3150 2.65 R 25 e Exp

d / rh = = 25 = 35.6

P e ANFO ρ rock 1550 2.65

For the 38 mm diameter hole filled with emulsion, the damage radius would be 

 Rd = 35.6 (0.019) = 0.68 m 

This pressure-based approach appears to provide results more in keeping with those of Ash (1963) and thus is to 

be recommended for use in underground blast design. As indicated, this is a simple and easy to understand 

technique to estimate the damage radius. It involves the use of readily available explosive and material 

properties. 

 

4.7 Preliminary recommendations for buffer row design 

Although several other approaches are available for estimating the damage radius Rd associated with fully 

coupled charges, it is recommended that the modified Ash approach based on explosion pressure (equation (20)) 

be applied. 

5 Design of the contour row 

5.1 Introduction 

 
 

As was indicated earlier, the primary task of the contour holes is simply to smooth the surface produced by the 

buffer row of holes. The actual “burden” is small. It is not, as is often stated, the distance to the buffer row since 

the fragmentation of the inter-lying rock is largely the responsibility of the buffer holes. The spacing-burden 

ratio for the contour row of holes is high. In this section, a rule for the spacing of the contour line of holes will 

be given. 

5.2 Spacing based on the force equilibrium approach 

Sanden (1974) applied the force-equilibrium approach in developing a hole spacing (S) relationship for presplitting. The same approach will be applied to this contour blasting application. Consider the radial stress acting 

on the boundary of hole of radius ‘rh’ as shown in Figure 13. 

Figure 13. Diagrammatic representation of two holes in the contour row 

Only the right hand side of the left hole will be considered. The incremental force (dFi) in the radial direction 

produced by the pressure Pw acting over a small incremental area rh dθi on the circumference of a hole of unit 

length is given by 

 dF i = −Pw rh dθ i (21)

The component of the force acting in y - direction, normal to the line connecting the hole center lines is given by 

 dF yi = −Pw rh sinθ i dθ i (22) 

The total force in the y-direction is obtained by adding up (integrating) these contributions. This may be 

expressed as 

F π 2

 y = −∫ rh Pw sinθ dθ (23)

0 

The result is 

 Fy = rh Pw (24) 

Since there are two contributing holes, the total driving force is 

 FD = 2 rh Pw (25) 

The resisting force, FR, is 
 F R = σ t (S − 2 r h )) (26)

Where: 

S = hole spacing 

σt = tensile strength of the rock mass 

 

Equating the driving and resisting forces one finds that 

⎛ P + σ ⎞ S = 2r t 

h ⎜ w ⎟ (27) ⎜ ⎟ ⎝ σ t ⎠

If the wall pressure is designed to be equal to the compressive strength (σc), equation (27) then becomes 

⎛σ + σ ⎞ ⎛σ ⎞ ⎛σ ⎞ S = dh ⎜ c t ⎟ = d ⎜ c + ⎜ 1⎟ ≅ ⎜ ⎟ h ⎟ d (28) σ

h ⎜ c ⎟ ⎜ ⎟ ⎝ t ⎠ ⎝ σ t ⎠ ⎝ σ t ⎠

By knowing or estimating the compressive strength/tensile strength ratio one can obtain a maximum value for 

the perimeter row hole spacing. As was indicated earlier, the spacing of the perimeter holes is coordinated with 

the buffer row spacing. In actual practice, one would compare the latter value with that given by equation (28). 

If it is greater, than design adjustments would need to be made. 

 

5.4 Preliminary contour row design recommendations 

The following steps are followed in the contour row design: 

 1. The compressive strength of the rock is determined. It provides an upper limit for the borehole wall 

pressure. 

 2. For the chosen perimeter hole diameter, borehole wall pressures are calculated using the co-volume 

approach described in this paper for the candidate explosive products. The best product with respect to the 

pressure limit is selected. Alternatively, for a particular explosive product, one can select the required borehole 

diameter. 

 3. The maximum borehole spacing is calculated using equation (28). This value is compared to the spacing 

determined by the buffer row design. If the latter value is greater than that determined from equation (28), 

design adjustments are made. 

 

6. Concluding remarks 

This paper has presented a gas pressure-based approach to drift round design. It is logical and easy to apply. The 

key to the practical application of this design approach is the ability to estimate the radius of damage 

surrounding fully-coupled buffer row blast holes. The recommended approach is based on the early work of 

Ash (1963). Once the buffer row holes have been designed, the contour holes are placed to smooth the 

excavation surface. The contour row charge concentration is selected based upon keeping the borehole wall 

pressure at or below the compressive strength of the rock. Contour row hole spacing is based upon the 

guidelines provided by Sanden (1974) as well as practical considerations (removing the rock cusps left in the 

buffer row design). This damage radius approach may be applied both to the lifter row design and to the stoping 

hole design. The cut design is largely based on geometrical considerations and has not been addressed in this 

paper. 

 
Disclaimer 

The findings and conclusions in this paper are those of the authors and do not necessarily represent the views of 

the National Institute for Occupational Safety and Health. 

Acknowledgements 

The work has been conducted at the Spokane Research Laboratory of the National Institute of Occupational 

Safety and Health (NIOSH). The authors gratefully acknowledge the assistance of Steve Iverson, Jami Dwyer, 

Carl Sunderman, Paul Pierce and Ken Strunk. 

 

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