Detonation wave propagation in underground mine entries 

Alex C. Smith & Michael J. Sapko 

National Institute of Occupational Safety and Health, USA 

ABSTRACT: A series of explosive detonation experiments was conducted in NIOSH’s Bruceton and Lake 

Lynn Experimental Mines to evaluate low level (<6 psig) detonation wave propagation behavior in single and 

multiple entry configurations. Entry cross-sectional area varied from 5 to140 m2 and explosive weights of 

Pentolite ranged from 0.24 to 2.4 kg. Behavior of the detonation wave was evaluated through recording of 

the pressure as a function of time and distance from the explosive detonation in single and multiple entry interconnecting tunnels. Peak pressure from detonation of an explosive in an underground mine maintains 

magnitude for a greater distance than is the case on the surface and is shown to follow the simple scaling relationship P = 702.8(W/Vt)

0.514(0.65)n

, where P is the peak detonation pressure in kPa, W is the weight of the 

explosive charge in kg, Vt is the total volume in m3, and n is the number of splits, n = 0, 1, 2, ...n. The total 

energy, or impulse, I, generated by these detonations can be expressed as I = 1.34(W/A)0.64n, where W is the 

weight of the explosive charge in kg, A is the area of the main tunnel in m2

, and n is the number of side entries, n = 0, 1, 2, ...n. 

1 INTRODUCTION 

When considering the behavior of detonation waves 

in a confined region, one deals with the mode in 

which a detonation wave and its driver gases expand. In a free field, this spherical shock expansion 

is readily calculated and shown to follow a rather 

simple Sachs (D/W1/3) scaling law. However, inside 

a tunnel that is strong enough to withstand the explosives’ forces, the pressure measured at any given 

distance from the point of detonation does not have 

an obvious relationship with the explosive yield, 

since the spherical shock wave is interrupted by the 

interaction with the tunnel. The shock front pressure 

attenuates because of the rarefaction wave that degrades the front and because of the interaction between the moving gas and the confining walls. This 

viscous interaction is implicit in all detonation attenuation in tunnels in varying degrees depending 

upon the duration of the wave, the diameter and 

roughness of the tunnel, and the density, velocity, 

and viscosity of the gas. To completely characterize 

these shock pressure interactions would require 3-

dimensional hydrodynamic codes and the results 

would be limited in practical utility for mining engineers and mine operators. 

The mining engineer needs to be able to simply 

and accurately predict the behavior of low pressure 

detonation waves inside mine tunnels to effectively 

design underground ventilation control structures. 

In underground metal and nonmetal mines, these 

structures need to be able to withstand the air detonation pressure and impulse associated with routine 

development and production blasting. These experiments were conducted to determine the attenuation of the peak overpressure and the detonation 

wave behavior from interactions with adjacent 

crosscuts as the pressure wave travels through mine 

openings of various cross-sectional areas. The pressure waves in these experiments were produced with 

the unconfined detonation of various size explosive 

charges of Pentolite near the closed end of experimental tunnels with cross-sectional areas ranging 

from 5 to 140 m2

. 

1.1 Background 

Since World War II, there have been numerous investigations of the propagation of air detonations on 

the surface, but few reported studies have been done 

on the propagation of air detonations in an underground environment. Taylor (1968) presents an 

overview of detonation wave behavior in confined 

regions with a specific emphasis on structure design 

for the storage of fuels and explosives in tunnels, 

chambers and tunnel junctions. Curran (1966) collected data and established a pressure-distance relationship for various explosives weights in single en-
try tunnels ranging from 5 cm to 8 m in diameter. 

These results showed that the pressure could be expressed as 

P = (W/D*d2

) 0.8 (1) 

where W = charge weight; D = the distance from the 

charge; and d = the diameter of the tunnel. Peak 

overpressures ranged from about 350 to 7,000 kPa. 

Weibull [1968], from the Royal Swedish Fortification Administration, conducted many experiments 

in partially closed chambers to measure the peak 

pressure from the detonation of TNT charges. The 

main purpose of these tests was to provide the basis 

for developing a nuclear detonation simulator to 

compare peak pressures and durations of detonation 

waves. To produce detonations of long duration, 

four partially closed chambers were used, in which 

TNT charges of different weights were detonated. 

The results showed that the pressure correlated with 

the charge weight to volume ratio, 

P = K*(W/V) (2) 

where W = the weight of the charge and V = the 

volume of the chamber. The fit of the experimental 

data to this relationship is fairly good. This straight 

line was empirical and was not founded theoretically. 

Most explosives, upon detonation, release from 

1,000 to 1,200 kcal/kg of explosive. Therefore, the 

charge weight to volume ratio can be considered as 

an energy density of kcal per unit volume. For the 

same mass of charge, the energy release should 

show a continual increase in overpressure with decreasing chamber volume. The basic approach in 

this study was to consider the explosive energy to 

heat up the explosive gas to equilibrium values of 

pressure and temperature. The explosive gases are 

treated as ideal and are obtained from the ideal gas 

law: 

P = E (γ-1)/V (3) 

where P = pressure; E = the internal energy of the 

gas; γ = the ratio of specific heats; and V = the initial 

volume of the containing chamber. E is taken to be 

the chemical energy of the explosive and is equal to 

WQ, where W is the mass of explosive. Q is about 

1100 – 1200 cal/g for most explosives. Equation 2 

can then be written in terms of pressure as: 

P= (W/V) Q (γ-1) (4) 

Equation (4) suggests that the equilibrium pressure from the detonation of a particular explosive 

should scale with the ratio of W/V where V is considered the expansion volume through which the explosive energy is deposited. 

The current study was conducted to explore the 

utility of extending this simplified charge 

mass/volume scaling relationship for peak overpressures up to 40 kPa, and determine the decay in peak 

pressure with distance and the impulse behavior for 

both single and with parallel entries with interconnecting cross-cuts. Given a peak pressure at one 

location, this method could be used by a mine operator to predict the peak overpressure and impulse that 

one might expect at a given location outby the 

source of the detonation. Such relationships are 

also useful for predicting the safe stand-off distance 

for secondary rubble blasting underground to reduce 

the exposure of underground workers to damaging 

air-detonations. Such data can also be used by accident investigators to re-construct explosion events 

and locate the origin of the explosion based on detonation pressure damage along the various paths of 

propagation. The current emphasis of this study, 

however, is to provide ventilation engineers with a 

simple, reliable method to predict low-level detonation overpressures and impulses as a function of distance and charge weight from routine underground 

production blasting. Such methodology can aid in 

the design of air-blast resistant and economical ventilation control structures used for coursing fresh air 

to various working sections of the mine. 

2 EXPERIMENTAL 

Experiments were conducted in the NIOSH Lake 

Lynn Experimental Mine (LLEM), the NIOSH 

Bruceton Experimental Mine (BEM), and on the surface at NIOSH’s Lake Lynn Laboratory facility 

(Triebsch 1990). The Lake Lynn Laboratory (LLL) 

is a unique mining research laboratory designed to 

provide a modern, full-scale mining environment for 

the testing and evaluation of mine health and safety 

technology. Although the facility was developed 

with mining research in mind, it also serves as an 

ideal facility for the study of a wide range of explosion or fire phenomena in underground or confined 

spaces. The LLL consists of both surface and underground test sites and is sufficiently isolated from 

residents to allow mine/tunnel fire research and 

large-scale explosion testing of gases, dusts, and 

chemicals. The underground mine entries were developed adjacent to an abandoned commercial limestone quarry and underground limestone mine. The 

entries of the abandoned limestone mine, labeled as 

the old workings in figure 1, are approximately 5 m 

wide by 9 m high. The LLEM contains 5 drifts, 

shown in figure 1 as A, B, C, D, and E. These entries were developed to approximate the size of a 

typical Pittsburgh seam coal mine, about 6 m wide 

by 2 m high, and range from 200 to 500 m in length. 

The entries, in conjunction with the novel use of two 

explosion-proof bulkhead doors that can be positioned to open or close an entry, can be made to 
simulate room-and-pillar and longwall mine configurations. 

The BEM, shown in figure 2, is an underground 

research facility located at Bruceton Pa. The BEM 

has been used since 1910 to conduct gas and dust 

explosion research focused on improving mine 

safety. The BEM consists of smaller entries that are 

about 2.7 m wide by 1.8 m high and about 400 m 

long. Experiments in the BEM single entry and the 

LLEM larger entries allowed the development of 

geometric size scaling relationships for modeling the 

pressure decay with tunnel distance and tunnel 

cross-sectional area, and with added cross-cuts. For 

the surface experiments, a Pentolite explosive charge 

ranging from .24 to .45 kg was detonated 1.8 m from 

the Lake Lynn quarry floor. For all the underground 

experiments, a Pentolite explosive charge, ranging 

from .24 to 2.4 kg, was detonated in the center of the 

entry, one entry width from the closed end of the 

tunnel. The pentolite explosive charges up to 0.45 

kg were single cast explosive boosters. For experiments using explosive charges up to 1 kg, combinations of .24 and .45 kg cast boosters were ganged together using tape. In the experiments using 2.2 kg 

of pentolite, two different geometrical configurations of 0.45 kg cast boosters were used. In one configuration, 6 or the 0.45 boosters were ganged together. In the other configuration, 6 of the 0.45 kg 

boosters were taped together vertically, forming a 

linear explosive charge. 

Multiple Entry Tests

Unconfined 

Explosive

Single

Entry 

Tests

Cross sectional Area 13 m3

Cross Sectional Area

140 m2

Unconfined Open cross-cuts

Explosive

Lake Lynn Laboratory

Figure 1. The Lake Lynn Experimental Mine (LLEM). 

To conduct experiments in the E-drift, the movable bulkhead was closed and the explosive was 

detonated in the center of the entry about 3 m from 

the closed end. The experiments in the BEM single 

entry and the E drift were conducted because they 

permitted the observation of the pressure wave 

propagation through single tunnels of 5- and 13-m2

cross-sections without side branches. Experiments 

were also conducted in the multiple entry sections of 

the Lake Lynn the new and old workings, to observe 

the effect of pressure venting on the peak pressure as 

the pressure pulse propagated through the cross-cuts 

into the parallel entries. For example, if the explosive charge was detonated in the closed end of the A 

drift entry, the pressure wave in A-drift would 

propagate from the closed end and some of the energy would be vented into B-drift as the wave passed 

through each intersection. Experiments in B-drift 

permitted venting into both A and C drifts reducing 

the peak over pressure with each passing cross-cut. 

3 INSTRUMENTATION 

Near field pressure pulses were recorded using 

Endevco1

 (Model 8530C-15) piezo-resistive absolute pressure transducers with a range of 0-100 kPa 

or 0- 350 kPa and a resonance frequency of 

180,000 Hz. The signal from each transducer was 

amplified by an Endevco (Model 136) DC amplifier 

with a 40 kHz filter. Additionally, B&K (Model 

4036) microphones were used when maximum pressures were expected to less than 3 psig. The transducers and microphones were housed in a blunt cylinder, which was wrapped with 15-cm thick foam 

and mounted on tripods, shown in figure 3, at the 

geometric center of the entry cross-section at distances from the explosive ranging from 8 to 425 m. 

The sensor mounting followed recommendations 

from Walton (1981) for a blunt cylinder mount when 

making measurements in complicated detonation 

fields, where small errors in wave shape are preferable to large errors caused by misalignment. Since 

the sensing diaphragm is parallel to the direction of 

the detonation wave propagation, the resulting measurement can be considered as the static pressure. 

Data from the pressure transducers and microphones 

were recorded with a WINDAQ 720 A/D converter 

located up to 125 m from the transducers. Data was 

recorded at sampling rates ranging from 2000 to 

66,666 samples per second per channel. 

Unconfined Explosive

Pressure Transducers

Cross Sectional Area, 5 m2

Main Entry, 400 m long

Scale, m

0 100

Figure 2. Bruceton Experimental Mine (BEM) 

 1

 Reference to a specific product does not imply endorsement 

by NIOSH. 
Transducer

Transducer housing

Foam padding

Figure 3 Microphone housed in blunt cylinder and

mounted on tripod. 

3 RESULTS 

3.1 Surface Detonations

Initial experiments were conducted on the surface 

at the LLL in order to ensure the validity of the instrumentation and analysis methodology. On the 

surface, the detonation wave propagates in a hemispherical fashion away from the charge. The volume of influence is 

Vt = 2/3 π D3 (5) 

where D = the hemispherical radial distance from 

the point charge. Data from the surface shots correlated well with the charge to volume density, shown 

in figure 4, where 

W/Vt ~ W/(2/3 π D3) ~ K (W 1/3/D) (6) 

This expression is the reciprocal of the conventional Hopkinson “cube root” scaling relationship 

for surface detonations of D/W 1/3.

3.2 Single Entry 

Figure 5 illustrates a typical pressure history recorded by the pressure transducer for single entry 

experiments in the BEM and LLEM E drift. For this 

particular experiment, the pressure transducer was 

located 49 m from the 0.45 kg explosive charge 

detonated 3 m from the closed bulkhead door in the 

E drift of the LLEM. The time scale should be considered as relative time since time zero does not start 

with the detonation of the explosive. One can see 

the arrival of the leading edge of the shock wave 

closely followed by the reflected pressure pulse from 

the closed end. The reflected pressure wave traveled 

about 6.2 m further than the incident pressure wave 

and lags about 18 ms behind the incident pressure 

pulse. 

The maximum peak pressure, usually the reflected pressure pulse, is plotted for the single entry 

experiments in figure 6 against the ratio of explosive 

charge mass to volume (W/Vt), where W is the explosive charge mass in kg and Vt is the product of 

the cross-sectional area of the mine entry in m2 and 

the distance in meters from the closed end of the 

tunnel to the pressure transducer. The range of 

weights of explosive used for the single entry study 

ranged from 0.24 to 0.9 kg, while the single tunnel 

cross-sectional area ranged from 5 to 13 m2. This 

simple correlation for a single entry fits the data 

quite well for experimental overpressures from 5 to 

50 kPa. The best fit to the data was given by the use 

of the power formula as follows: 

P = 702.8 (W/Vt) 0.514 (7) 

 

where P = the maximum pressure rise in kPa at the 

transducer, Vt is the product of the cross-sectional 

area of entry, A, in m2, D is the distance from the 

closed end of the tunnel in m, and W is the explosive 

charge weight in kg. The fit has a correlation coefficient, R2

, of 0.968. 

The results of the experiments show that for single entries or tunnels, the peak pressure for explosives detonated in free space decays with distance to 

the - 0.514 power for maximum pressures up to50 

kPa, at distances from 25 to 425 m. 

4 TUNNELS WITH SIDE BRANCHES 

To study the detonation wave pressure decay in entries with single and multiple side branches, experiments were conducted in the A and B drifts and the 

old workings of the LLEM. A schematic of the experiments is shown in figure 7. Explosive charges 

ranging from .24 to .45 kg in A drift and .24 kg in B 

drift were detonated 3 m from the closed end and the 

pressure measured at various locations away from 

the detonation. In the old workings, explosive 

charges ranging from .48 to 2.4 kg were detonated 

3 m from a closed entry and the pressure measured 

downstream from the detonation. Figure 8 shows 

the plot of the peak pressure before the intersection, 

or incident pressure, versus and the peak pressure after the intersections, or transmitted pressure. The 

incident pressure directly across the intersection was 

found to be relatively constant over the pressure 

range of study and is about 65% of the peak pressure 

upstream of the intersection for both single and double splits, as shown by the slope of the best fit line. 

These results are somewhat consistent with studies at higher incident pressures ranging from 50 to 

1700 kPa (Taylor 1968). Taylor’s data shows that 

the transmitted shock pressure downstream of an intersection is about 75% of the incident shock pressure upstream of the intersection for both single and 
double branches. The resulting side branch shock 

pressure is about 35% of the incident shock pressure 

upstream of the intersection for both single and double branches in our study. This sharp pressure drop 

in the side tunnel would indicate to the mine ventilation engineer that the strength of the ventilation control structure would be about one-third that necessary to resist the detonation pressure in the main 

tunnel. It is also shown that unless these side tunnels are long, there will be reflected pressure that 

exceeds the side on pressure in the main tunnel. 

However, the weakness of ventilation control structures that are drag sensitive (flex with loading) can 

be improved by positioning them in the short side 

tunnels, because the dynamic pressure impulse is reduced. In addition, there are other key advantages 

for placing ventilation control structures in side 

branches to blasting to protect structures from the fly 

rock produced during production blasting. 

Since it has been shown that the pressure loss 

across an intersection is constant, the downstream 

line-of-site- pressure should be a function of the 

weight of the explosive charge and the distance from 

the charge, as expressed in equation (7), and the 

number of intersections between the charge and the 

measuring location. Correcting the pressure drop in 

the main tunnel for the influence of side branches by 

the use of the factor from figure 7 as (.65)n 

P = 702.8 (W/Vt) 0.514 (.65) n, (8) 

where, P = the maximum pressure rise in kPa at the 

transducer, Vt is the product of the cross-sectional 

area of entry, A, in m2, D is the distance from the 

closed end of the tunnel in m, W is the explosive 

charge weight in kg, and n is the number of intersections between the explosive and the measuring location. 

The experimental peak pressure from the single 

entry detonations and those conducted in the entries 

with side branches is plotted in figure 9 against the 

predicted peak pressure using equation 8. The 

measured pressure agrees quite well with the predicted pressure, with the fit having a correlation coefficient, R2

, of 0.9703. 

4.1 Impulse 

Another important parameter in designing underground ventilation control structures is the total energy, or impulse, generated by these detonations. 

While the peak pressure decays with distance from 

the charge, the total energy of the detonation is generally conserved over the length of the tunnel. This 

can be seen in figure 10, where the pressure, in kPa, 

and the impulse, in kPa-s, are shown 23, 46, and 91 

m from the explosive charge as a function of time. 

The peak pressure decreases from 72 to 38 to 26 kPa 

at 23, 46, and 91 m, respectively, while the impulse 

remains constant at about 0.1.5 kPa-s at each location. 

The impulse, I, measured in a tunnel should be 

proportional to the mass of the explosive and the 

cross-sectional entry of the tunnel in which the explosive is detonated: 

I = k (W/A) (9) 

where W = the weight of the explosive in kg, and 

A = the cross-sectional area of the tunnel in m2. 

Figure 11 shows the impulse as a function of W/A 

for all detonations in single entry configurations in 

the LLEM and BEM mine experiments. The results 

show a good correlation, with a k equal to 1.34 and a 

R2

 of 0.9508. 

Since most ventilation controls in underground 

mines will be in crosscuts incident to the pressure 

wave, it is important to know the impulse perpendicular to the primary detonation wave. The energy 

split in a single tunnel with 1 side branch is illustrated in figure 7. To determine the pressure at position D in the tunnel, one has to consider the loss of 

energy through the three preceding side branches. 

As the pressure pulse passes position n 1 the energy 

splits. Some portion the energy vents through the 

side tunnel while the remainder continues down the 

tunnel towards n 2. Again, the energy splits as it 

passes through n 2 and n 3. The energy split at each 

intersection in B drift is shown in figure 7c. As the 

pressure pulse passes position n1, and each succeeding intersection, the energy splits three ways, two 

perpendicular to the main tunnel and the remainder 

continuing down the main tunnel. The energy split 

in the LLEM large-opening area is shown in figure 

7d. In this set-up, the side tunnels were staggered 

so the energy splits by one-half at each intersection 

with a side tunnel. 

Table 1. Impulses before and after intersections in single entries with side branches

Drift Before After 1st After 2nd After 3rd

Intersection Intersection Intersection intersection 

A .153 .096 (60%) .059 (62%) .044 (74%) 

B .028 .020 (71%) .0012 (62%) 

Large .069 .041 (57%) .025 (63%) 

Opening

Table 1 shows the averages of all the transmitted 

impulses across an intersection in the A and B drifts 

and the LLEM large-opening area. The percent 

transmitted ranged from 57% to 74% with an average of 64%. This agrees with the results for the 

pressure loss across these intersections, which averaged about 35%, or 65% transmission. Thus, the 

impulse in a side branch can be stated as: 

Iincident = 0.36*Itotal (10) 
The impulse in the main tunnel can then be expressed from equation 9 as: 

I = 1.34 (W/A) (.64)n

 (11) 

where W = the weight of the explosive charge in kg; 

A = the area of the main tunnel in m2; and n = the 

number of side intersections, n = 0, 1, 2, ...n. 

5 ACKNOWLEDGMENTS 

The work of Gerald Morrow and Michael DiMartino, Electronics Technicians and William Slivensky 

and Cindy Hollerich, Physical Science Technicians, 

who instrumented and conducted the unconfined 

detonation experiments at the Bruceton and Lake 

Lynn Experimental Mines, is gratefully acknowledged. Without their help, this study could not have 

been completed. 

6 SUMMARY 

Peak overpressure from unconfined explosive detonations in tunnels decays much more slowly with 

distance underground and is influenced by the number of intersections. The total energy, or impulse, 

from these detonations remains generally constant 

with distance and is also in influenced by the number of intersections. Peak pressure decay from underground experiments conducted in the BEM and 

the LLEM was shown to correlate well with P = 

702.8(W/Vt) 0.514 (.65) n. The impulse in a single entry tunnel with side branches correlated well with = 

1.34(W/A)(.64)n, where n = number of intersections, 

n = 0, 1, 2, ...n, for unconfined charge weights, W, 

ranging from 0.24 to 2.4 kg and cross-sectional areas 

ranging from 5 to 140 m2

. 

These relationships are useful to predict the behavior of low pressure waves inside mine tunnels 

from the unconfined explosive detonation as a function of tunnel distance, cross-sectional area, number 

of intersections, and weight of explosives to effectively design underground ventilation control structures. This relationship is also useful for predicting 

the safe stand-off distance for secondary rubble 

blasting underground to reduce the exposure of underground workers to damaging air-blasts. Such 

data can also be used by accident investigators to reconstruct explosion events and locate the origin of 

the explosion based on blast pressure damage along 

the various paths of propagation. 

7 REFERENCES 

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data report 1, TR SL_84_22, U.S. Army Corps of Engineers, 

Waterways Experiment Station, Vicksburg, MS. 

Curran, D.R. 1996. Underground storage of ammunition - experiments concerning accidental detonation in an underground chamber, Norwegian Defense Research Establishment. 

Taylor, W.J. 1968. Blast wave behavior in confined regions. 

Prevention of and protection against explosion of Munitions, 

fuels and other hazardous mixtures. Annals of the New York 

Academy of Sciences, Volume 152, Art. 1, October 28, 1968 

pages 357-361. 

Triebsch, G.F. & Sapko, M.J. 1990. A state-of-the-art mining 

research laboratory. Proc. Int. Symp. On Unique Underground Structures, June 12-15, 1990, Denver, CO, USA 

Walton, W.S. 1981. Improvement of air blast measurement. 

U.S. Army test and evaluation command, Report No. APGMT-5481. Aberdeen Proving Ground, Maryland, March 

1981. 

Weibull, H.R.W. 1968. Pressures recorded in partially closed 

chambers at explosion of TNT charges, Royal Swedish Fortification Administration, Stockholm, Sweden; Prevention of 

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other hazardous mixtures. Annals of the New York Academy of Sciences, Volume 152, Art. 1, October 28, 1968 pp. 

357-361.