Application of the NIOSH-Modified Holmberg-Persson Approach to Perimeter Blast Design 

by 

Stephen Iverson, Chuck Kerkering, William Hustrulid 

NIOSH/SRL 

Abstract 

Perimeter control blasting is common in civil construction projects but not as common in mining. A 

poorly designed and executed underground mine development blast design can result in unwanted wall 

rock damage. This damage increases the risk of rock falls and injury. With the availability of good 

drilling equipment, it is a simple matter to add the few extra holes needed to change conventional 

drifting into drifting with perimeter control. 

In the 1970’s, Holmberg and Persson (H-P) introduced the Swedish approach to contour blasting and it 

has found wide acceptance due to the logical basis and ease of application. An error in the mathematics 

of the H-P approach was discovered in 2002 and use has fallen into question. 

This paper presents a modification which corrects the mathematical error. The NIOSH-modified H-P 

design curves are basically identical to the original ones in the far field but with some significant 

differences in the near field. The application of the curves remains the same. The determination of the 

required site constants and the construction of the design curves are demonstrated with respect to data 

collected at the Stillwater mine, Nye, Montana. 

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

views of the National Institute for Occupational Safety and Health. 
1. Introduction 

In underground mine development, poorly designed and executed blast designs can result in unwanted 

wall rock damage which increases the risk for injury while, at the same time, adds mining costs. 

Perimeter control blasting techniques are regularly employed in civil construction projects where the 

economic penalties for over-break and even under-break can be severe. Although perhaps not so direct 

or obvious as in civil construction, adverse consequences are also associated with poor excavation 

practices in mining. In the past, an obstacle to the use of perimeter control blasting has been the 

reluctance on the part of mine owners/operators to invest in modern drilling equipment. It is difficult to 

introduce precision blasting when the drilling is done based upon the use of jack-legs. Fortunately, most 

operators today recognize the overall economies inherent in the use of drill jumbos. With the availability 

of good drilling equipment, it is a simple matter to add the few extra holes needed to change 

conventional drifting into drifting with perimeter control. Being able to count on properly positioned and 

oriented holes is an enormous advantage to the blast designer. With the wide assortment of explosive 

products available today, the blast designer has nearly too many options. Soundly-based but easy to use 

blast design tools are needed if perimeter control blasting is to be widely adopted in practice. 

In the late 1970’s, Holmberg and Persson (H-P) introduced the Swedish approach to contour blasting 

(Holmberg and Persson (1978, 1979), Holmberg (1982)). Since that time, its use has found quite wide 

acceptance due to the logical basis and the relative ease of application. However, an error in the 

mathematics behind the H-P design curves was discovered in 2002 (Hustrulid and Lu, 2002) and the use 

of the approach has fallen into question. 

This paper begins with a review of the H-P approach and provides a modification which corrects the 

mathematical error. The construction of the NIOSH-modified H-P design curves are then demonstrated 

for the same charge geometry and charge concentrations used by H-P. It will be seen that the curves are 

nearly identical to the original H-P curves in the far field but with some significant differences in the 

near field. The application of the curves remains the same. 

The H-P approach is based upon rock damage being related to peak particle velocity. The basic equation 

upon which the design curves are based is: 

PPV = K Qα

 / Rβ (1) 

Where: 

K, α, β = constants 

PPV = peak particle velocity 

Q = charge weight 

R = distance 

Hence, a necessary part of the approach is to determine the required constants K, α, and β for the 

particular site. In the second part of the paper, a set of procedures for extracting these constants from the 

seismic signals obtained during drifting at the Stillwater mine, Nye, Montana will be demonstrated. The 

blast design curves using the NIOSH-modified H-P approach will be developed using the derived 

constants. 
 

To be able to apply the curves for perimeter control blast design, knowledge of the limiting PPV is 

required. In the case of Stillwater, the PPV limit with respect to over-break has been determined using 

the design curves together with laser scanner measurements. 

The paper concludes with some comments regarding future work. 

2. The NIOSH-Modified Holmberg-Persson Perimeter Blast Design Approach 

Damage to structures due to surface blasting has been found to be related to the peak particle velocity 

(PPV) associated with the blast-produced seismic wave. As indicated in the Introduction, the general 

equation is 

PPV = KQα / Rβ (1) 

Where: 

PPV = peak particle velocity 

Q = charge weight/delay 

R = distance 

K, α, β = constants 

By analyzing the results of a large set of surface blasting measurements performed by the U.S. Bureau 

of Mines, Lundborg et al (1978) found that they could be well described using 

K = 700 

α = 0.7 

β = 1.5 

In this case, the charge weight Q is expressed in kilograms, the distance R is expressed in meters, and 

the resulting PPV is expressed in mm/s. Holmberg and Persson (Holmberg and Persson, 1978) applied 

equation (1) to examining the damage produced to the surrounding rock mass when using long 

cylindrical charges. They divided the long charge into a number (n) of small elemental charges of equal 

length ∆L. Assuming that the charge concentration per unit length is q, one can express the charge 

weight ∆Q for each element as 

∆Q = q ∆L (2) 

Where 

∆Q = charge weight of each elemental charge 

∆L = length of each elemental charge 

q = charge concentration per unit length 

The peak particle velocity at a given observation point due to the arrival of a particular elemental charge 

(denoted by the subscript i) may be expressed by 

∆PPVi = K (∆Q)α /Ri 

β

 = K (q∆L)α /Ri 

β (3) 
To simplify the discussion, the particular geometrical situation shown in Figure 1 will be assumed. 

Figure 1. Diagrammatic representation of the simplified charge – observer geometry used in the 

examples. 

As can be seen, the charge lies along the z axis with the r axis passing through the mid-point of the 

charge. The total PPV due to the arrival of the seismic waves from the different elemental charges is to 

be determined at an observation point (zo, ro) located along the r axis. Since the waves from the 

elemental charges travel different distances to reach the observation point, their amplitudes will be 

distance dependent. Also, in general, the arrival times and wave orientation will vary depending on the 

explosive velocity of detonation and the wave velocity through the rock mass. In their approach, 

Holmberg and Persson have assumed: 

1. The entire charge detonates instantaneously 

2. The amplitudes are simply summed without considering arrival direction 

This simplifies the situation considerably. The resulting PPV is obtained by summing the contributions 

from the different elemental charges. 

n

PPV = ∑ n ∆PPV α

i = Kq ∑(∆L) α /(R βi ) (4) 

1 1 

Holmberg and Persson replaced the summation by the following integral expression 

⎫

α

⎧

⎪ zf dz PPV = K⎨q ∫ β (5) z i ⎬ ⎪⎩ [(r − r ) 2 + (z − z ) 2

] 2α

o o ⎭

For the case shown in Figure 1, 

r = 0 
zo = 0 

Thus equation (5) becomes 

α

⎧

⎪ zf dz ⎫

PPV = K ⎨q∫ ⎬ 6) 

⎪ z

⎩ i [ β (

(r )

2 + (z) 2

] 2α

o ⎭

The integral can be numerically evaluated. The results for a 3m long charge (zi = -1.5 m and zf = 1.5 m) 

assuming that 

K = 700 

α = 0.7 

 β = 1.5 

are shown in Figure 2 for five values of q: 

q = 2.5 kg/m 

q = 1.5 kg/m 

q = 1.0 kg/m 

q = 0.5 kg/m 

q = 0.2 kg/m 
Figure 2. Peak particle velocity versus distance as a function of charge concentration. Charge length = 3 

m, observation axis along charge mid-plane. After Holmberg (1982). 

In the figure, the symbol R has been used in place of ro in keeping with H-P convention. To be able to 

use these curves for design, one must determine the PPV value associated with unacceptable damage. 

Over-break would be one type of such damage. Assume that the measured over-break for a fully charged 

wall hole (q = 1.0 kg/m) is 0.5 m. This experience point is shown in Figure 3. In this case, the 

corresponding PPV over-break limit would be of 2230 mm/sec. If it was desired to keep the over-break 

to 0.15 m or less, based upon the curves, the charge concentration in the perimeter holes should be 

reduced to 0.2 kg/m or less. This is a very easy to use perimeter blast design procedure and has found 

wide acceptance since its introduction in 1978. 
Figure 3. Addition of the experience point to the peak particle velocity versus distance curves of Figure 

2. 

Unfortunately, as Hustrulid and Lu (2002) have pointed out, the step going from PPV expressed as a 

summation in equation (4) to PPV expressed by the integral in equation (5) is not correct. The exponent 

α has been moved from inside the summation sign to outside of the integral sign. Hence the curves 

shown in Figure 3 are not correct. Okay, one might say, we will simply revert back to using the 

summation expression, equation (4). 

n n α α β PPV = ∑∆PPVi = Kq ∑(∆L) /(Ri ) (4) 

1 1 

Since ∆L is the same for all of the elemental charges, this term can be removed from under the 

summation sign to yield 

n n α α β PPV = ∑∆PPVi = Kq (∆L) ∑1/(Ri ) (7) 

1 1 

It appears that one simply needs to determine the radial distance Ri from the observation point to the 

mid-point of each elemental charge, form the inverse, raise it to the power β and then to sum all of the 

contributions. However, by closely examining equation (7), it is clearly seen that the PPV depends upon 

the length of the elemental charge raised to the power α. Only for the very special case, α = 1, the 
equation is stable. For the case α > 1, the PPV decreases to zero as the elemental length decreases. For 

the case α < 1, the PPV increases to infinity as the elemental length decreases. Thus, this procedure 

cannot be followed. 

To try and retain the ease and simplicity of the Holmberg-Persson approach while correcting the 

mathematical problems, NIOSH has revisited the basic concepts involved. 

Retaining the basic H-P assumptions: 

1. The entire charge detonates instantaneously 

2. The amplitudes are simply summed without considering arrival direction 

the new solution involves determining the average travel distance R to the observation position for all 

of the elemental charges. Once R has been determined, the PPV is obtained using 

PPV = K Qα

/ R β = K (qL)α/ R β (8) 

The average travel distance, R , is, by definition (Martin, 2007), 

1 z

∫

f 

R = L [ 1 (z − z 

2

o ) + (r − r o ) 2

] 2 dz (9) 

zi 

Where: 

L = zf - zi 

The value of the indefinite integral may be written as (Weast, 1983) 

∫ (z − zo ) 2 + (r − r 2

o ) dz = 1 [(z − z − z ) 2o ) (z o + (r − r ) 2o + (r − r ) 2 o loge ((z − zo ) + (z − zo ) 2 + (r − ro )

2 ) 2 ]

For the case of a charge located along the z-axis, centered at the origin, and with the observation 

position designated as (ro, zo), one finds that 

r = 0 

and 

zo = 0 

Hence, the indefinite integral may be written as 

∫ z 2 ⎡ ⎤ + r 2 1 2 2 2 2 2 

O dz = z z + r 2 ⎢⎣ o + ro loge (z + z + ro )

⎥⎦ (10) 
For the example case of the 3m long charge, 

zi = -1.5 m 

zf = 1.5 m 

the definite integral becomes 

∫

z f 

z 2 r 2 dz ⎡ ⎤ + = z z + r 2 + r 2 log (z 2 2 ⎡ 2 2 2 2 2 2 1 1 ⎤ o 2 ⎣⎢ o f f o o e f + zf + ro ) − 2 zi z ⎦⎥ ⎣⎢ i + ro +r loge (zi + zi + ro ) zi ⎥⎦ 

Substituting the values for zi and zf, one finds 

∫

1.5

z 2 + r 2 dz ⎡ = 1.5 1.5 2 r 2 2 2 ⎤ ⎡ + 2 + r 2 2 2 2 2 1 1 ⎤ o 2 ⎢⎣ o o o log e (1.5 + 1.5 + r o ) − 2 −1.5 (−1.5) + r o +r log e (−1.5 + (−1.5) + r ) −1.5 ⎦⎥ ⎣⎢ o ⎦⎥

The value of the integral is then evaluated for chosen values of ro. For example, when 

ro = 2 m 

the value of the integral (Int) becomes 

Int = 6.5225 

The corresponding value of R is 

R = Int/L = 6.5225/3 = 2.174 m 

Assuming that 

q = 1 kg/m
 

K = 700 

α = 0.7 

β = 1.5 

the calculated value of PPV is 

PPV = K (qL)α

/ R β = 700 (1 x 3)0.7/2.1741.5 = 471 mm/s 

The process can then be repeated for different values of q and ro to obtain a set of design curves. These 

are shown in Figure 4 for the same q values as chosen by Holmberg-Persson. When ro = 0, the observer 

would be at the charge midpoint and R = L/4. In comparing the NIOSH-modified with the original 

Holmberg-Persson results, it is observed that the agreement is quite good in the far-field (for ro > 1m, ro 

> L/3). However, as one approaches the charge axis, the differences increase. The experience point, 

assuming as before that the observed over-break for a fully charged wall hole (q = 1.0 kg/m) is 0.5m, has 

been added to Figure 5. In this case, the corresponding PPV over-break limit would be about 1650 
mm/sec. The new design curves would suggest that if the charge concentration would be reduced to 

about 0.65 kg/m, no over-break should occur. There still will be “damage” to the wall rock. This will be 

discussed later in the paper. 

Figure 4. The NIOSH-modified Holmberg-Persson curves for the same conditions as in Figures 2 and 3. 
Figure 5. Addition of the experience point to the peak particle velocity versus distance curves of Figure 

4. 

The conclusion is that although the design curves are somewhat different, the NIOSH modification to 

the basic Holmberg-Persson approach appears promising. The mathematical problems with the original 

approach are eliminated with a relatively simple fix. 

In practice, one develops the curves for the explosive concentrations of interest and the site constants. 

One measures the over-break/rock damage. Using this value and the curves, one can determine the 

limiting PPV. One now has a practical design tool for the site. This procedure will be demonstrated in 

the following sections. 

3. Field Data Collection Program 

3.1 Introduction 

A program of field data collection was conducted at the Stillwater mine, Nye, Montana during July 2006 

in conjunction with the blasting of three drift development rounds in the 44W development drift (see 

Figure 6). The program involved: 

- Documenting the drilling and blasting patterns used 

- Monitoring the blast vibrations 

- Surveying the placement of the blastholes and the final drift contours using a laser-based 

instrument 

- Documenting the rock mass quality 
Figure 6. Plan view of the development heading on level 44W in the Stillwater mine showing the 

locations of the geophones for the three monitored blast rounds. The sump area location is also shown. 

The purpose of the field program was to collect the information required for use in the development and 

application of the NIOSH improved perimeter blast design approach. The rock mass is norite with the 

following average properties (Johnson et al, 2003): 

- Unconfined compressive strength = 103 MPa (15,000 psi) 

- Young’s modulus = 97 GPa (14 x 106

 psi) 

- Poisson’s ratio = 0.30 

- Density = 2.8 g/cm3 

Over-break measurements from the 4400 and 4700 levels will also be presented. 

3.2 Drift Round Design 

The typical development round blast pattern and delay sequence used at the mine is shown in Figure 7. 

The nominal drift dimensions are 3.35 m wide by 3.7 m high (crown). The nominal diameter of the 

blastholes is 48 mm (1-7/8 in. bit) with the uncharged relief holes reamed to 76 mm (3 in.). All holes 

are drilled to a depth of 4.3m and charged to a length of 3.7 m. The collar is left unstemmed. There are 

42 to 43 blast holes and 4 to 6 relief holes in a round depending on the miners’ preference for spacing 

along the back and burn cut pattern. ANFO is used for the burn holes, the production holes and the rib 

perimeter holes. Dyno AP is used for the lifters and a combination of Dynosplit D and Dyno AP was 

used in the roof holes. 
Figure 7. Typical blast pattern for the development heading showing the delay sequence and the relief 

holes. 

 Table 1 lists the charge types, weights, number of sticks, relative weight strength based on ANFO, 

loaded length, and equivalent charge weights per meter of hole. Of the three explosives used, ANFO 

was the only one that was bulk loaded. There is some uncertainty regarding the charged density, the 

actual hole diameter, and the charge length. According to the mine, the average amount of ANFO used 

per hole is 1.9 kg/m (Stillwater Mining Company, 2004). During the mine visit, it was observed that 

nearly 9 - 22.7 kg bags of ANFO were used to load 30 ANFO holes, or 1.8 kg/m for the second blast 

round. Other blast rounds monitored by NIOSH personnel during the visit indicated that only 6.0 kg 

were used per hole or 1.62 kg/m. These latter values will be assumed in the analysis. 
 

Table 1. Calculated charge weights used in the three blast rounds at the Stillwater mine, July 2006. 

Number Relative Explosive 

Weight of weight charge 

per sticks Total strength length, m Equivalent 

stick, weight, compared weight per 

Explosive charge kg kg to ANFO m, kg/m
 

Production: 

 ANFO1 NA NA 6 1 3.7 1.62 

Lifter:

 DynoAP2

 0.485 11 5.34 0.88 3.7 1.27 

Trim: 

DynoAP 0.485 3 1.46 0.88 1.0 1.27 

Dynosplit D3

 0.342 3 1.03 1.13 1.8 0.64 

DynoAP 0.485 3 1.46 0.88 1.0 1.27 

1 ANFO – the as-charged specific gravity was 0.84 to 0.89 based on mine report. 

2 Dyno AP - relative weight strength is 0.88. Each 400 mm length by 32 mm diameter stick weighs 0.37 

kg

3 Dynosplit D -- relative weight strength is 1.13. Each 600 mm length by 22 mm diameter stick weighs 

0.34 kg (uncoupled charge) 

NA - not applicable 

A Trojan Stinger primer was placed at the bottom of each ANFO hole. Since the Dyno AP is cap 

sensitive, no primer was needed in the holes charged with this product. The nominal times associated 

with the Nonel LP delay detonators used in the design shown in Figure 7 are given in Table 2. 

Table 2. Nominal Detonator Delay Times (Dyno Nobel, 2007). 

Delay Number Nominal Delay Time (ms) 

0 0 

2 800 

4 1400 

5 1700 

6 2000 

7 2300 

8 2700 

9 3100 

10 3500 

12 4400 

13 4900 

14 5400 

Even though a number of different holes are shot on the same delay, the actual initiation times will 

generally be different due to cap scatter. 
 

3.3 Vibration Measurements 

Peak particle velocity (PPV) data were collected from the three sequential blast rounds using an array of 

triaxial geophones (InstantelTM part number 714A9101). The geophones were surface-mounted along the 

left rib by drilling a short hole into the rock, installing an anchor bolt, and then attaching the geophone 

onto the anchor bolt using a washer and nut. Using this attachment method, the geophones were coupled 

directly to the rock surface in a side-mounted orientation. Figure 8 shows one of the triaxial geophones 

mounted to the left rib of the development drift. Care was taken to protect the geophone cables from fly 

rock from the blast rounds and impacts from mobile equipment. 

Figure 8. Triaxial geophone mounted to the rock surface using anchor bolt. 

Three Instantel Minimate PlusTM data loggers were used to collect particle velocity data. Two triaxial 

geophones were typically attached to each data logger. Particle velocity data were collected 

continuously, triggered by the first delay and continuing a full three seconds after the last delay. 

For the first round, two geophone locations were used. For round two the number of locations was 

increased to four. The number of geophone locations in round three was three. 
 

BlastwareTM software was used to calculate vector sums of the transverse, vertical, and longitudinal 

wave forms. PPV was picked from the vector sum data for each arrival in each delay. This was possible 

because of the scatter effect that occurred from the non-electric delays. PPV data were input into a 

spreadsheet and identified by arrival time, delay, explosive type, and weight of charge. Except for delay 

0 it was not possible to attach a particular arrival time to a particular hole. For each geophone location, 

the travel distance is assumed equal to the distance from the geophone to the face of the blast plus the 

distance from the hole collar to the center of the charge as measured along the left rib. 
Figure 9. PPV versus distance curves for the lifters by round. The explosive is Dyno AP. 
Figure 10. PPV versus distance curves for the rib holes by round. The explosive is ANFO. 
Figure 11. PPV versus distance curves for the roof holes by round. The explosive is a combination of 

Dynosplit D and Dyno AP. 
Figures 9 – 11 show the PPV versus distance results obtained from the lifters, rib and back holes for the 

three rounds. The analysis of these data will be discussed in the following section. 

3.4 Over-break measurements 

Over-break measurements were based on making a three-dimensional laser scan of the excavation after 

the blast. Work is progressing on developing a method to obtain the locations of the drill holes in space 

based upon laser-scanning the blast round face. This method requires scanning the drilled face with 

tubes/pipes inserted into the holes. The tube orientations obtained from the scans together with the 

known hole lengths are then used to develop a three-dimensional picture of the actual drill pattern. This 

pattern is then compared to the post blast scan excavation limit. This method takes time and can interfere 

with production schedules. Fortunately, one drilled-face scan was made demonstrating this method. A 

cross-section showing the excavated limit and over-break measurements for an earlier blast round of the 

sump area is shown in Figure 12. This sump area is also identified in Figure 6. The drill holes were 

projected into the section and compared with the excavated limit. Over-break due to the ANFO-charged 

rib holes at this section ranged from 0.39 m to 0.54 m and averaged 0.46 m. Over-break along the back 

of that blast round was nominal with some half-casts visible. 

Figure 12. Cross-section through a room at the Stillwater mine showing the hole locations and the final 

profile as determined using the scanning laser. Level 4400, July 2006. 

Several post-blast laser scans were acquired between the sump area and the three blast rounds for which 

the PPV measurements are reported in this paper. Production schedules and access only during the 

daytime shifts prevented the use of the laser scanner for drilled-face scans. During the later period, the 

last two days, no scans were taken. Based on the scans taken, the average rib over-break was determined 

to be 0.18 m. The theoretical drift width of 3.25 m was subtracted from the average waist-high level 

scanner measurements. One half of this difference is defined as the representative rib over-break. 

Blasthole angles were assumed normal to the face and the lookout angle was not considered. 
Figures 13 and 14 are additional examples of using the drill hole projections. Figure 13 shows the case 

when Dynosplit D was used in the left wall and in the roof holes. The right wall was charged with 

ANFO. In Figure 14, the left wall was charged with ANFO and the right wall and roof holes were 

charged with Dynosplit D. Although these blast rounds are from a different level in the mine than that 

on which the PPV measurements were made, the rock type is the same. The average over-break from the 

ANFO-charged rib holes in these blast round sections was 0.20 m. 

Figure 13. Cross-section through a development round (September 2006). The left rib and the roof holes 

were charged with DynoSplit D and the right rib with ANFO. 
Figure 14. Cross-section through a development round (September 2006). The right rib and roof holes 

were charged with DynoSplit D and the left rib with ANFO. 
 

The amount of over-break from the ANFO-charged perimeter holes varied depending on location and 

method of determination. In the sump area, the over-break was quite significant at 0.46 m. For the 

development headings, the over-break was 0.18 m and 0.20 m at the two locations examined. 

4. Analysis of the Vibration Data 

4.1 Introduction 

A new theoretical approach for perimeter blast design based on using R has been presented. The basic 

equation is 

PPV = K Qα

/ R β (11) 

To apply the approach for drift design at a particular drifting site, values for K, α, and β are required. 

The steps for determining these constants using the data from Round 2 will be described in this section 

together with the application of the technique to the data collected at the Stillwater mine. 

4.2 Steps in the Process 

One can write equation (11) as 

log10 PPV = log10 K + α log10 Q - β log10 R (12) 

The first step is to plot log PPV versus log R in log10 – log10 format for constant Q. In practice, one 

makes such plots for each of the different explosive charges involved. Figures 9 – 11 shows the curves 

for the lifter holes, the rib (wall) holes and the roof (back), respectively. In this particular case: 

Q = 4.69 kg (lifters) – Dyno AP 

Q = 6 kg (rib holes) – ANFO 

Q = 3.72 kg (roof) holes – Combination of Dyno AP and Dynosplit D 

The explosives differ in energy content per unit weight and thus a normalization with respect to ANFO 

is performed. This reference explosive should be clearly indicated in the upper corner of the resulting 

design curves. 

As indicated earlier, the problem which immediately arises is the selection of the distance to be chosen. 

From the simple plan view of the roof holes shown in Figure 15, it is clear that the waves from the 

different holes must travel different distances to arrive at the monitoring points. Although some 

assumptions might be made in that regard, it will be assumed that all are placed at the center of charge 

for the hole closest to the wall. One might think that the pulse from the hole at the wall would be the 

first arrival because it has the shortest distance to travel. This however is not necessarily the case 

because the lack of precision of non-electric delays results in a distribution of actual detonation times. 

The nearest detonation could be the last to arrive. The solution is, for a given charge, the highest 

amplitude should be associated with the closest holes. Those further away would have lower amplitudes. 

This is considered to be the most important reason for the apparent “spread” in amplitudes. Taking an 

“average” value to represent the holes is not considered correct. Rather, the most regular curve of 

highest amplitude was chosen to represent each charge group. 
Figure 15. Diagrammatic representation of one set of possible paths for the seismic waves traveling from 

the roof holes to the rib-mounted geophones. 

From viewing the log PPV versus log distance plots (including those for the production holes (not 

shown)), it was found that a slope of -1 could describe the data very well. The slope is represented by 

the constant 
β = 1 

shown in equation (11). This suggests that in the medium to far field (where the measurements are being 

made), the charge in each hole can be represented by an equivalent sphere. As a result, a best fit straight 

line curve of slope -1 was placed through each of the selected curves as shown in Figure 16. 

Figure 16. PPV versus distance for the rib, lifter and roof holes. The maximum amplitude curve has been 

selected. 

For these charge lengths and distances, R ≈ R . For a given value of R, the values of PPV for the 

different Q values are read from the curves. In this case, 

R = 15 m 

was chosen. The values are 

Q (kg) PPV (mm/s) 

3.72 50 

4.69 75 

6.00 96 
In returning to the basic equation 

log10 PPV = log10 K + α log10 Q - β log10 R (12) 

it can be seen that with k constant and R constant, the log10PPV versus log10Q should plot as a straight 

line with slope α. This plot is shown in Figure 17. 

Figure 17. PPV versus Q for R = 15 m. Round 2. 

The slope is determined to be 

α = 1.4 

knowing 

α = 1.4 

and 
 

β = 1 

one can solve for K. In this particular case it is 

K = 171 

The final design equation becomes 

PPV = 171 (qL)1.4 / R 

Since the charge length is 

L = 3.7 m 

the charge concentrations for the different charge groups become 

Charge Group q (kg/m) 

Rib holes 1.62 

Lifters 1.27 

Back holes 1.00 

The design curves for each of these charge concentrations are shown in Figure 18. 
 

Figure 18. The NIOSH-modified Holmberg-Persson curves using the site constants determined for the 

Stillwater mine. L = 3.7 m. 

4.3 Limiting PPV Values 

For the ANFO loaded wall holes in Figure 12, the amount of over-break is of the order of 

OB = 0.5 m 

where OB is the over-break. 

For the Dyno AP/Dynosplit D loaded roof holes the over-break was minimal. Applying this information 

to the design chart shown in Figure 19, it is seen that the 

PPV limit = 1850 mm/s 

Since the maximum calculated PPV for the roof holes is only 1170mm/s, no over-break was expected 

and such was the case. 

Figure 19. Addition of the experience point to the peak particle velocity versus distance curves of Figure 

18. 
 

4.4 Definition of Undesired Blast Damage 

In this paper, the amount of over-break (excavation outside of the line of perimeter holes) has been 

selected as the measure of undesired blast damage since it could be easily quantified using the laser 

scanner. This is the simplest measure and the one easiest for miners to understand since it can be directly 

translated into economic terms due to (1) the additional scaling time required, (2) the extra muck to be 

moved, and (3) the need for extra reinforcement due to wider spans and higher walls. For civil 

engineers, it may translate into the need to replace the removed rock with concrete. Over-break can be 

easily quantified using normal surveying techniques. The PPV limits assigned on this basis using the 

NIOSH-modified Holmberg-Persson design curves apply to over-break and hence one should use the 

notation PPVlim (over-break). From the Stillwater mine results, this limit appears to be 

PPVlim (over-break) = 1850 mm/s 

Holmberg and Persson have designated the limiting PPV based on new crack formation in the 

surrounding rock mass. Using their design curves they found that 

PPVlim (new crack formation) = 700 – 1000 mm/s 

for Swedish igneous rocks. By simply applying the 1000 mm/s limit to the design curves developed for 

the Stillwater mine based on the current work (see Figure 20), one would predict the following cracking 

limits: 

Holes Explosive Extent of Cracking (m) 

Rib ANFO 1.8 

Lifters Dyno AP 1.1 

Roof Dynosplit D/ Dyno AP 0.5 

These seem quite high and future NIOSH field work will incorporate techniques to try and quantify the 

cracking limit as well as the over-break limit. At this point in time, primary reliance will be based on 

application of the Micro-Velocity Probe. The results will be the subject of a future paper. 
Figure 20. Addition of the Swedish granite fracture damage limit to the peak particle velocity versus 

distance curves of Figure 18. 

5. Summary and Conclusions 

The Holmberg-Persson perimeter blast design approach has found widespread use since its introduction 

in 1978. It is logical and easy to apply. Unfortunately, a recently discovered mistake in their equation 

development has raised questions regarding the whole procedure. As part of a comprehensive perimeter 

blast design research and development program, NIOSH has reviewed the basics of the HolmbergPersson design approach and has introduced the modification described in this paper which retains the 

simplicity of the procedure while correcting the mathematical problems. The NIOSH-modified 

Holmberg-Persson design curves, although slightly different in appearance from those originally 

presented by Holmberg-Persson, are easy to develop and use. 

The basis for the design approach is the peak particle velocity expressed as 

PPV = KQα / Rβ

where 

PPV = peak particle velocity 

Q = charge weight 

R = distance 

α, β = constants 
 

To be able to use the design approach, one must select values for the constants. One way has simply 

been to assume the values suggested by Holmberg-Persson: 

PPV = peak particle velocity (mm/s) 

Q = charge weight (kg) 

R = distance (m) 

K = 700 

α = 0.7 

β = 1.5 

Another way is to make site measurements of PPV recorded at different distances from a drift blast 

round. From the captured signals, the PPV values corresponding to the different explosive charge 

weights are identified. NIOSH has used this latter procedure at the Stillwater mine. The details of the 

approach needed to extract the constants have been provided. One of the interesting findings is that β, 

the power of the distance, can be well represented by 

β = 1 

This is quite logical since for the far field measurements (R>> charge length) typically made in the mine 

environment, the charge may be represented by a sphere. The task then becomes one of finding K and α. 

The practical steps needed to accomplish this are provided in the paper. The PPV versus distance design 

curves with the linear charge concentration, q, as a parameter based upon the Stillwater site constants 

have been included. 

The final step in the process is the determination of the limiting PPV values. A scanning laser has been 

used to survey the blast rounds prior to firing to locate the blast holes in space and again after firing to 

determine the final contour. From these scans, the amount of over-break can be determined. In one test, 

the average over-break for the ANFO-charged wall holes was about 0.5m. Using the design curves one 

finds that 

PPVlim (over-break) = 1850 mm/s 

Applying this limit to the roof holes charged with a combination of Dynosplit D and Dyno AP, one 

would not expect any over-break. The measured over-break was of the order of 0.1m which could have 

been due to the ANFO-charged buffer row. 

Identification of the new fracture formation limit and the calculation of 

PPVlim (new crack formation) 

is part of the continuing NIOSH research and development program. The new perimeter blast design 

procedures described in this paper are being incorporated in a special drift blast design software 

package. 

NIOSH is currently expanding the study by making measurements at a number of other mines. 
 

6. Acknowledgements 

The authors acknowledge the Stillwater Mining Company and specifically the help of Radford Langston 

and John Marjerison for providing two active development drifts to facilitate research in monitoring the 

blast vibrations and measuring over-break. NIOSH personnel and contractors involved in the research 

and data collection included Edward McHugh, Tom Brady, Rimas Pakalnis, Timothy Orr, Cristian 

Caceras, Jami Dwyer, Phillip Joggerst, and Joel Warneke. 

7. References 

Dyno Nobel. 2007. www.dynonobel.com. 

Weast, R. C. (editor-in-chief), 1983, Handbook of Chemistry and Physics, 64th edition, 1983-1984, CRC 

Press, Inc. 

Holmberg, R., and P-A. Persson. 1978. The Swedish approach to contour blasting. Proceedings of the 4th 

Conference on Explosives and Blasting Technique. SEE. Pp 113-127. 

Holmberg, R., and P-A. Persson. 1979. Design of tunnel perimeter blasthole patterns to prevent rock 

damage. Proceedings, Tunneling ’79. Editor, M J. Jones. Institution of Mining and Metallurgy, London, 

UK. 

Holmberg, R., and W. Hustrulid. 1981. Swedish cautious blast excavation at the CSM/ONWI test site in 

Colorado. Pp 232-252. Proceedings, 7th Conference on Explosives and Blasting Technique. SEE. 

Holmberg, R. 1982. Charge calculations for tunneling. Section 7.5: Blasting, Chapter 1. Underground 

Mining Methods Handbook (W.A. Hustrulid, editor). SME. 1982. pp 1580-1589. 

Hustrulid, W., and R. Holmberg. 1991. Drilling and Blasting. Chapter 5 in Underground Structures – 

Design and Construction (R.S. Sinha, editor). Elsevier. Pp 141-223. 

Hustrulid, W., and W. Lu. 2002. Some General Design Concepts Regarding the Control of BlastInduced Damage During Rock Slope Excavation. Proceedings, FragBlast7. Beijing, China. 

Hustrulid, W, 2004, “Evaluate the Effects of Blasthole Loading Accuracy and Over-break in Various 

Geologic Environments”, Final Report – NIOSH Contract S0265130, October 31. 

Johnson, J., T. Brady, M. MacLaughlin, R. Langston, and H. Kirsten, 2003, “In Situ Stress 

Measurements at the Stillwater Mine, Nye, Montana”, in Soil and Rock America 2003, 12th PanAmerican Conference on Soil Mechanics and Geotechnical Engineering and the 39th U.S. Rock 

Mechanics Symposium, Volume 1, Cambridge, MA, Massachusetts Institute of Technology, 2003, pp. 

337-344. 

Knutti, T. 2007. Personal communication. Dyno Nobel. August. 
Lundborg, N., Holmberg, R., and P-A. Persson. 1978. The dependence of ground vibrations on distance 

and charge size. Report R11:78. Byggforskning. In Swedish. 

Martin, P.A. 2007. Personal communication. Department of Mathematical and Computer Sciences. 

Colorado School of Mines. August. 

Persson, P.A., R. Holmberg and J. Lee, 1994, “Rock Blasting and Explosives Engineering”, CRC Press, 

540 pp. 

Stillwater Mining Company, 2004, “Report on Drill and Blast Audit at the Stillwater Mining Company, 

Nye Mine”, Confidential report, 22 pp.