Re-examination of the shock wave’s peak pressure attenuation in soils
Introduction
The problem of an underground explosion in soil is of great complexity and the prediction of its shock wave front parameters is of much interest [1], [2], [3], [4], [5]. The shock wave propagation is accompanied by rather large soil deformations with irreversible bulk compaction [6], [7] and it is strongly attenuated as a result. Some aspects of the shock wave’s attenuation in soils are still obscure and require further research. Therefore, the prediction of the shock wave parameters is commonly relied upon empirical expressions. These expressions are commonly based on fitting of test data to empirical expressions.
The common expression that describes the magnitude of the peak pressure at the shock front as function of the distance is the following power law [8], [9], [10]:where:
A - a constant;
f - a coupling factor depending on the scaled depth of burial (d/W1/3) of the explosive;
ρ - the undisturbed soil’s density;
C - the seismic velocity of sound;
- the acoustic impedance of the soil medium;
R - the distance measured from the charge centre;
W - the explosive weight;
k - a constant attenuation factor.
Sometimes a similar expression to Eq. (1) is used without explicit expression of the acoustic impedance [4], [32], [38]:
The same general expression of this power laws appears in different references [11], [12], in different unit systems, and refers to different shapes of the explosive material but mostly to spherical charges. All the references generally describe the type of soil, and provide the recommended values for the attenuation factor that characterizes this type of soil. Calculation of the resulting pressure is then straightforward.
A common graphical description of the power law is a straight line on a logarithmic scale, where the slope equals to the attenuation factor.
A well-known reference that is commonly used for evaluation of the peak pressure is TM5-855-1 [8], or the programmed version CONWEP [13]. Sometimes caution is required in performing the calculations, when a mixed unit system is used [8], [12] (e.g. p(R) [psi]; [psi/fps]; R [ft]; W [lb]). Other references use metric unit systems as well [14], [15], [16], [17], [18], [19], [20]. Table 1 summarizes the parameters for several types of soils described in [8], [12]. At a first glance Eq. (1) and the accompanied Table 1 seems to enable the peak pressure prediction at distance R in a given type of soil. A closer examination of the table raises some questions with regard to the clarity, precision and uniqueness of the definitions of the types of soils under consideration, in light of the absence of important information such as the specific composition of the soil, the degree of saturation and the size of particles and their distribution.
Nevertheless, if a certain definition of a soil type is sufficiently close to a given soil under consideration, the pressure variation with distance may be calculated.
Extending the review to other references shows that different references provide rather similar attenuation factors for sandy soils, however some of them provide somewhat different attenuation factors with regard to a spherical charge explosion in saturated sandy clays, as shown in Table 2. We realize that reference [21] mentions an attenuation factor k = 1.5 for a spherical explosion in saturated sandy clays whereas another reference [8] recommends an attenuation factor of k = 2.5 for the same soil definition. These two suggested attenuation factors for the same type of soil differ considerably.
Two major questions then arise on that regard:
- -
Which is the more appropriate attenuation factor for that type of soil? Is it k = 2.5 or whether is it k = 1.5?
- -
Why different references recommend similar attenuation factors for sands while there appear different attenuation factors for saturated sandy clays?
Definitely, these questions evoke some thoughts.
This confusing data for the same type of soil appears once again for another type of soil. The literature survey identifies a similar observation for spherical explosions in loamy soils (Table 3). Most references [4], [8], [22] recommend an attenuation factor of k = 2.7–2.8 for a spherical explosion in this type of soil, whereas another reference [19] recommends k = 1.6.
This observation is similar to the one above regarding the saturated sandy clay hence it raises up similar questions as above.
All the above specified attenuation factors refer to the explosion of a spherical TNT charge in soil. Only limited data is available for cylindrical charges. Barlas [14] suggests an attenuation factor of k = 2.4 for “sandy loam” and Luchko [15] suggests k = 2.17 for “loamy soils” when the cylindrical charge is vertical.
As expected, the attenuation factors in the case of a cylindrical charge (k = 2.17–2.4) are somewhat smaller than the values for a spherical charge (k = 2.7–2.81) in the same type of loamy soil.
Section snippets
Comparison of test data with equation (1)
Leong et al. [12] describe a recent series of tests that had been carried out on two types of soils, denoted as “partially saturated soil” and “wet soil”, and the peak pressure measurements at a limited number of three scaled distances from the explosion source are given. Plotting the test measurements on a logarithmic scale shows that they nicely fit a straight line (Fig. 1).
The slope of the linear fit yields the experimental value of the attenuation factor. The experimental attenuation factor
Experimental aspects for predictions deviations
In the series of tests described above, a single explosion is reported for every scaled distance and charge weight within a rather limited range of scaled distances. A limited number of different scaled distances were examined (Table 4). The measured pressures fall nicely along a straight line in a logarithmic scale. Under these conditions there are no further experimental aspects to be considered beyond those mentioned above.
If however an extended series of tests was discussed, with repeated
Theoretical aspects for predictions deviations
There are two conflicting observations that come up as result of the implementation of the power law relationship with the constant exponent to predict a given series of tests, as discussed in the above. On the one hand, utilization of the power law relationship with the experimental parameters of these specific series of tests yielded large differences from the measured pressures. In other words all parameters were calibrated to the specific series of tests that the power law relationship
Background
The problem of shock wave propagation in soils and its attenuation with distance strongly depends on highly non-linear constitutive properties (that is on the soil irreversible compaction which is associated with energy dissipation) [16], [24], [25]. Commonly rather simple models are used to represent the soil medium behavior, such as elastic [26], [27] or elastic plastic with elastic bulk deformation [28], [29]. However, enhanced representation of the soil behavior should account for the bulk
Discussion and conclusions
The paper investigates the pressure attenuation in soils due to the explosion of a buried charge. The common power law expression for the shock pressure attenuation is examined. It was found that very large discrepancy is expected between the predicted and measured data. It was further observed that even if the specific soil parameters are used, the discrepancy is still considerable. This discrepancy may result from the variation of properties and test conditions between repeated tests in the
References (73)
- et al.
Modeling of wave propagation induced by underground explosion
Computers and Geotechnics
(1998) - et al.
Re-examination of peak stress and scaled distance due to ground shock
International Journal of Impact Engineering
(2007) - et al.
A comparative study of buried structure in soil subjected to blast load using 2D and 3D numerical simulations
Soil Dynamics and Earthquake Engineering
(2005) - et al.
Internal blast loading in a buried lined tunnel
International Journal of Impact Engineering
(2008) - et al.
Underground explosion of cylindrical charge near a buried wall
International Journal of Impact Engineering
(2008) - et al.
Numerical analysis on dynamic deformation mechanism of soil under blast loading
Soil Dynamics and Earthquake Engineering
(2003) - et al.
High-order Eulerian Godunov method for elastic-plastic flow in solids
Journal of Computational Physics
(2001) - et al.
Parameterization of the porous-material model for sand with different levels of water saturation
Soil Dynamics and Earthquake Engineering
(2008) Strength of rock-like materials
International Journal of Rock Mechanics and Mining Science
(1968)- et al.
Mechanics of deep underground explosions. Philosophical Transactions of the Royal Society of London
Series A, Mathematical and Physical Sciences
(1964)
Review of nuclear weapons effects
Annual Review of Nuclear Science
Dynamics of intense underground explosions
Journal of the Institute of Mathematics and Its Applications
Cavitation in solid medium
Journal of Engineering Mechanics
The dynamics of explosion and its use
Free-field grund shock pressures from buried detonations in saturated and unsaturated soils
Fundamental of protective design for conventional weapons
The effect of degree of saturation of sand on detonation phenomena associated with shallow-buried and ground-laid mines
Shock and Vibration
Explosive loading of engineering structures
CONWEP, ver. 2.1.0.1
Behaviour of cylindrical blast waves in soils according to stress and strain measurements
Combustion, Explosion, and Shock Waves
Parameters of cylindrical blast waves in water-impregnated sandy loam
Journal of Applied Mechanics and Technical Physics
Determination of dynamic compressibility of soils
Soil Mechanics and Foundation Engineering
Propagation of cylindrical blast waves in a multicomponent, viscoplastic medium having variable viscosity
International Applied Mechanics
Experimental investigations of the compressibility of argillaceous soils subjected to underground explosions
Journal of Applied Mechanics and Technical Physics
Experimental investigation of the compressibility of loams during an explosion
International Applied Mechanics
A spherical explosion wave in soils
Combustion, Explosion, and Shock Waves
Blast and ballistic loading of structures
Experimental data on stress-wave parameters in the earth due to underground and surface explosions
Journal of Applied Mechanics and Technical Physics
Spherical blast waves in soils inferred from stress and strain measurements
Journal of Applied Mechanics and Technical Physics
Numerical investigation of effects of water saturation on blast wave propagation in soil mass
Journal of Engineering Mechanics
Dynamics of Structures
Computational methods for transient analysis
The finite element method
Numerical methods in coupled systems
A coupled simulation of an explosion inside a lined cavity surrounded by a plastic compressible medium
International Journal for Numerical Methods in Engineering
Cited by (40)
Ground deformation and blast wave propagation in dry sand subjected to buried explosion: A centrifuge modelling study
2024, International Journal of Impact EngineeringExperimental and numerical study on explosion cratering and coupled ground shock in clay
2024, International Journal of Impact EngineeringInvestigating the dynamic response of a double-box utility tunnel buried in calcareous sand against ground surface explosion
2024, Tunnelling and Underground Space TechnologyDamage and deformation behavior of reinforced concrete pipes with varying joints under surface explosion
2024, Engineering Failure AnalysisExperimental and numerical study on ground shock propagation in calcareous sand
2023, International Journal of Impact EngineeringExperimental study on anti-shallow-buried-explosion capacity of a corrugated steel-plain concrete composite structure
2023, International Journal of Impact EngineeringCitation Excerpt :The results showed that with the increase of explosive burial depth H, the ground impact parameters will also increase, and the range of increase thereof is large at first, then small. When there is no significant increase, the corresponding depth is the critical depth of ground impact [32]. To ensure the transmission of explosive energy underground, the coupling factor 0.56 m/kg1/3 in TM5-855-1 was adopted to describe the critical depth of ground impact [33].