Université de Mons
Faculté Polytechnique – Service de Mécanique Rationnelle, Dynamique et Vibrations 31, Bld Dolez - B-7000 MONS (Belgique) 065/37 42 15 –
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D. Ainalis, O. Kaufmann, J.-P. Tshibangu, O. Verlinden, G. Kouroussis, Assessing blast source pressure modelling approaches for the numerical simulation of ground vibrations, Proceedings of the 23rd International Congress on Sound and Vibration, Athens (Greece), July 10-14, 2016.
ASSESSING BLAST SOURCE PRESSURE MODELLING APPROACHES FOR THE NUMERICAL SIMULATION OF GROUND VIBRATIONS Daniel Ainalis, Olivier Kaufmann, Jean-Pierre Tshibangu, Olivier Verlinden, and Georges Kouroussis University of Mons – UMONS, Faculty of Engineering, 7000 Mons, Belgium email:
[email protected] For a long time the mining field has been subject to considerable attention and criticism in regard to blasting-induced vibrations. It is becoming increasingly common for mining sites to be situated relatively close to urban areas, and the issue of blast-induced ground vibration in these urban areas is of significant concern to not only residents, but also mine operators. There is an unavoidable compromise that exists for these sites; while it is generally accepted that the purpose of production blasting is to fragment as much rock as possible to minimise the costs, the ground vibrations generated during each blasting sequence can have detrimental effects on the structures and occupants in the surrounding urban areas. Therefore, it is of paramount importance to be able to characterise the source of blasting to predict the ground vibrations transmitted to these structures. This paper provides a review of the various approaches to model and characterise the blasting source for use in numerical simulations of ground vibration. The main focus of the review is on methods for establishing the pressure time history at the blasthole wall due to a detonated explosive charge. An overview of the blasting process and blast-induced ground vibration is also presented.
1.
Introduction
The explosive blasting of rock is undertaken for several reasons, mostly for the acquisition of usable raw material or the excavation of underground openings [1]. While site operators are primarily concerned with fragmenting as much rock as possible per production blast, the blasting process generates ground vibrations which can travel great distances. It is becoming more and more common for these sites to be located close to urban areas, where the ground vibration can have a detrimental effect on the nearby structures and inhabitants. Despite the fact that considerable progress has been made in understanding the mechanisms associated with rock fragmentation and breakage, the explosive energy is never completely consumed and is expended as ground vibrations, air blasts, etc. [2]. Of these other forms of energy expenditure, the ground vibrations are considered to be one of the most important environmental effects produced by blasting [3]. Generally speaking, the term ground vibration is associated with man-made activities and excludes natural phenomena such as earthquakes, etc. [4]. The most common sources of man-made ground vibration are shown in Table 1, along with the ranges of frequency, particle velocity, and particle acceleration. In comparison to the other sources, blasting generates very high level and frequency vibrations. Therefore, significant motivation exists to investigate blast-induced ground vibration and its associated effects on urban areas. To accurately predict these ground vibrations, the blasting source must be characterised and understood. The main focus of this paper is a review of the various approaches currently used to model the source of blasting via the pressure at the blasthole wall for numerical simulations of ground vibrations. An overview of the blasting process is also presented, along with the various factors which can influence the performance of the blast, and the subsequent ground vibrations. 1
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Table 1: Frequency and particle motion ranges for various man-made sources outlined under ISO 4866 [5]. Ground Vibration Source
Frequency Range [Hz]
Particle Velocity Range [mm/s]
Particle Acceleration Range [m/s2]
Road and rail traffic Blasting
1 – 100 1 – 300
0.2 – 50 0.2 – 100
0.02 – 1 0.02 – 50
Pile Driving
1 – 100
0.2 – 100
0.02 – 2
Outside Machinery
1 – 100
0.2 – 100
0.02 – 1
2.
The blasting process
To undertake a production blast, a series of blastholes are drilled into the rock mass and then explosive charges are placed in each blasthole (possibly with stemming and confining material). The explosives are then detonated in a specific sequence to break the rock mass. Once the blast has completed, the fragmented material is recovered and transported for delivery or further processing. The detonation of an explosive charge involves a rapid and stable chemical reaction which travels through the explosive charge at its Velocity of Detonation (VoD) and produces very high temperature and density gases [6]. For the detonation of most high explosives, the VoD can range from 1,500 – 9,000 m/s and the pressure can range from 1 – 14 GPa [7, 8]. The detonation process involves two markedly different phenomena. Firstly, the rapid detonation of the explosives produces a supersonic shock wave which travels through the explosive charge and is the cause of rock fragmentation. Secondly, the high pressure gas which follows the shock wave penetrates into the surrounding rock mass through existing or recently created fractures. The shock waves have a short duration (a few milliseconds) and cause the blasthole to rapidly expand and contract, which imparts pressure waves into the surrounding medium [9]. The waves propagate away from the blasthole and their travel path can be complex due to not only site geology, but also that interference of the waves from each blasthole can occur [10, 11]. Of these factors, it has been argued that the geology has the principal influence on the waveform’s final amplitude and shape [10]. An explosive detonation can be either ideal or non-ideal. An ideal detonation releases all the energy within the reaction zone and contributes to the pressure generated at the shock front [12]. In a non-ideal detonation, some of the energy is instead released (relatively) far behind the shock and does not contribute to the total generated pressure. Generally, in an ideal detonation the peak pressure is reached in a short time and decays rapidly, while a non-ideal detonation takes a longer time to not only reach its peak pressure (lower than ideal detonation peak pressure), but also to decay [7]. 2.1 Blast-induced ground vibration The blasting process generates waves which are three-dimensional and have complex travel paths. The travel path and attenuation of these waves are influenced by many factors including the geometry, geology, distance, fractures, and voids, amongst others. The blasting process is known to generate three different types of waves. The P-wave and S-wave are both body waves, and the third wave is a surface wave known as the Rayleigh wave (R-wave) for homogeneous media. The properties of each of the three different types of waves are given in Table 2. From a ground vibration perspective, there are two distinct zones of interest. The first zone is the near-field region, which is the area immediately surrounding the blasthole. In this zone the surrounding rock mass is subjected to significant strains, experiences inelastic behaviour such as shearing, crushing, and fragmenting, and the vibration attenuates nonlinearly [13]. The second zone is the farfield region, where the waves are known to have a constant propagation velocity and a peak amplitude lower than the rock’s elastic limit [6]. Essentially, the far-field region begins once the ground vibration no longer causes permanent deformation of the ground. The far-field region theoretically has no limit and is of significant importance because this is the region where blast-induced ground vibrations can cause damage to structures and infrastructure (both above and below ground). 2
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Table 2: The three wave types which occur in blasting and their properties [14]. Wave
Type
Particle Motion
Relative Speed
Energy from Input [%]
P-Wave
Body
Longitudinal
Fastest
7
S-Wave
Body
Perpendicular
Between other two
26
R-Wave
Surface
Elliptic and retrograde
Slowest
67
Kutter and Fairhust [6] stated that, in terms of ground vibration, the near-field region can be considered to act as a stress filter and determines what percentage of the explosive-generated waves is emitted to the inner boundary of the far-field region. The location of the transition between the nearand far-field regions has never been clearly defined and depends on the design of the production blast and the surrounding geology of the site. To illustrate the difference in identifying the transition region, one study by Siskind et al. [15] found the near-field region to be within 152.4 m (500 ft) of the blasthole, while in a later study by Siskind et al. [16] the near-field region was within 91.4 m (300 ft) of the blasthole. 2.2 Blasting factors on ground vibration Production blasts are acknowledged to be a complex phenomenon and their performance and subsequent ground vibrations can be influenced by a variety of factors. Rosenthal and Morlock [17] presented a summary of the most common variables in blasting and their influence on the generation of ground vibration, shown in Table 3. Of the various factors, the explosive charge weight, delay interval between shots (firing time between blastholes), the level of confinement of the blasthole (how well the blasthole is covered), and the type and level of overburden have the most significant influence on the ground vibrations generated in comparison to the other factors listed. Table 3: List of various factors and their influence on ground vibration, from [17]. Ground Motion Influence Factor
Significant
Moderate
Insignificant
Within site operator’s control Charge weight per delay
✓
Delay interval
✓ ✓
Burden and spacing Amount of stemming
✓
Type of stemming
✓
Charge length and diameter
✓
Charge depth
✓ ✓
Angle of blasthole Direction of initiation
✓
Charge weight per delay
✓
Charge depth
✓
Charge confinement
✓
Out of site operator’s control ✓
General surface terrain Overburden type and depth Wind and weather
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✓ ✓
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3.
Blasting source pressure models
The rapid advancement of computational power has enabled researchers to develop sophisticated numerical models which are able to provide more realistic representations of physical phenomena. For the numerical simulation of blast-induced ground vibrations, it is essential that the model includes the geologic geometry (e.g. layers, discontinuities, etc.), realistic material behaviour appropriate to the strain rate and scale of the issue, and reasonable boundary conditions [3, 18]. Various researchers have developed rock and ground vibration models based on various numerical methods, such as the discrete element method, the finite element method, the finite difference method, etc. While outside the scope of this paper, a review of the various numerical methods available to model seismic wave propagation in one-, two-, and three-dimensional media is presented by Semblat [19]. This section is focused on the approaches used in numerical simulations for modelling the blasting source through the pressure applied to the blasthole wall. It is incredibly difficult to experimentally measure the pressure generated at the blasthole wall. No measurements have been made available in the published literature as current transducers are unable to withstand the significant pressures and temperatures experienced during detonation [20]. Due to this inability to measure the blasthole wall pressure during detonation, researchers must make use of empirical formulas or detonation theories to estimate the pressure time history. A typical example of the blasthole wall pressure time histories for ideal and non-ideal detonation (explosives properties used from [21]) is given in Fig. 1.
Figure 1: Typical example of pressure time histories for ideal (left) and non-ideal (right) detonation.
3.1 Equation of state As the explosive detonation process involves thermo-chemo-physical transformations, one approach which can be used to estimate the blasthole wall pressure is through the use of an Equation of State (EoS). Many EoS have been developed to determine the detonation pressure 𝑃, however the John-Wilkinson-Lee (JWL) EoS is most commonly used, shown in Equation (1) [22, 23]. The JWL EoS requires knowledge of the explosive material properties, volume, and energy of the detonation process [23]. The JWL EoS is commonly used due to its experimental basis, and simple form [24]. Despite these advantages, it has been noted that the explosive constants are difficult to determine for non-ideal detonations [25]. Several researchers have used the JWL EoS to establish the blasthole wall pressure, for example see [25-28]. 𝜔 𝜔 𝜔𝑒 𝑃 = 𝐴 (1 − ) 𝑒 −𝑅1 𝑉 + 𝐵 (1 − ) 𝑒 −𝑅2𝑉 + (1) 𝑅1 𝑉 𝑅2 𝑉 𝑉 where 𝐴, 𝐵, 𝑅1 , 𝑅2 , and 𝜔 are explosive constants, 𝑉 is the specific volume, and 𝑒 is the specific energy.
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3.2 Simple pressure functions The next category of models is the use of simple mathematical functions to describe the pressure time history at the blasthole wall. Some simple shapes which have been used over the years include Gaussian [29], triangular [30, 31], and Ricker wavelet [3] functions. Gaussian functions were originally used in order to avoid numerical errors due to the very high amplitude and short duration excitation in blasting [24]. As an alternative approach to using a simple function, Saharan and Mitri [24] proposed a new method to establish an “optimised pressure profile” based on peak blasthole pressure and tabular load amplitude data. As part of this new method, the authors first estimated the blasthole wall peak pressure 𝑃𝑏 using Equation (2) [32]. Next, load amplitude data is used to describe the decay from the peak pressure (value of 1) by 90, 99 and 99.9 % over times based on ideal and non-ideal detonation theory. 𝑉𝑂𝐷 2 𝑃𝑏 = 𝜌 ( ) (𝑟𝑐 )2𝛾 [𝑃𝑎] 8
(2)
where 𝜌 is the explosive density, 𝑉𝑂𝐷 is the velocity of detonation, 𝑟𝑐 is the coupling ratio (explosive diameter divided by the blasthole diameter), and 𝛾 is the adiabatic exponent. A typical example of some simple pressure functions for typical explosive properties are shown in Fig. 2. From the figure it is clear that the Gaussian and triangular functions do not realistically represent the blasthole wall pressure in comparison to the typical examples shown in Fig. 1. The ‘optimised pressure profile’ (not shown in full due to the long decay time) appears to provide an improved representation of the blasthole wall pressure time history but is limited to the special case used by the authors (explosive properties and blasthole geometry). These functions are generally overly simplified to the point that they do not provide even a remote representation of the blasthole wall pressure time history.
Figure 2: Comparison of simple pressure functions used to approximate blasthole wall pressure.
3.3 Pressure-decay functions There have been several pressure-decay functions which have been used to model the pressure time history applied to the blasthole wall over the years. One of the first pressure-decay models used in explosive-rock interaction was a simple power law by Sharpe [33] and is shown in Equation (3). 𝑃 = 𝑃𝑃 𝑒 −𝛼𝑡
(3)
where 𝑃𝑃 is the peak pressure at the blasthole wall, 𝛼 is a constant, and 𝑡 is the time.
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Sharpe’s pressure-decay model was later modified and expanded by Duvall [34]. This pressuredecay function, shown in Equation (4), has also been used by other researchers to numerically simulate the generated blast vibrations [35, 36]. 𝑃 = 𝑃𝑃 (𝑒 −𝛼𝑡 − 𝑒 −𝛽𝑡 )
(4)
where 𝛼 and 𝛽 are constants. When examining the dynamic fracturing of rock, Cho and Kaneko [36] developed and used a modified version of Duvall’s pressure-decay model to simplify the changes in rise and decay times, shown in Equation (5). 𝑃 = 𝑃𝑃 𝜁(𝑒 −𝛼𝑡 − 𝑒 −𝛽𝑡 ) 𝜁=
𝑡𝑟 = (
(5)
1 −𝛽𝑡
(𝑒0−𝛼𝑡 − 𝑒0
)
1 𝛽 ) log ( ⁄𝛼 ) (𝛽 − 𝛼)
where 𝛼 and 𝛽 are constants, and 𝑡𝑟 is the rise time (time of peak pressure). Jong et al. [37] adapted Starfield and Pugliese’s [38] pressure-decay function to predict the blasthole wall pressure time history, given in Equation (6). This function involves the use of a damping factor 𝛿 based on the rise time and is calculated using Equation (7). 𝑃 = 4𝑃𝑃 (𝑒 −𝛿𝑡/√2 − 𝑒 −√2𝛿𝑡 )
(6)
√2 ln(1/2) (7) 𝑡𝑟 A comparison of the various pressure-decay functions is presented in Fig. 3. From the figure, the simple power law model proposed by Sharpe does not describe the initial increase in pressure to the peak amplitude, however the pressure-decay functions by Duvall [34] and Cho and Koneko [36], and Jong et al. [37] both provide a more realistic representation of the blasthole wall pressure time history. 𝛿=−
Figure 3: Typical pressure-decay functions used to simulate the blasthole wall pressure time history.
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3.4 In-situ measurement As previously mentioned, it is not practical to measure the pressure applied to the blasthole wall during the detonation process. However, Resende et al. [3] suggested that if acceleration vibration measurements are made close to the blasthole then these recorded time histories can be directly used as an input for numerical models. While measurement techniques in the far-field are well established, few researchers have focused on the measurement of near-field vibration, however in recent times more measurements are being made closer to the blasthole [39]. In the near-field, the selection of an appropriate sensor to measure the rock mass response is not straightforward due to the high pressures and temperatures generated.
4.
Discussion and conclusions
Accurately characterising the blasting source for use in numerical simulations has long been investigated by researchers. Despite the fact that improvements have been made in modelling the source of blasting, this is a complex process that still requires further research and investigation. One of the most popular approaches for simulating the source of blasting is through the use of the pressure time history at the blasthole wall. Researchers have at their disposal numerous methods for modelling the blasthole wall pressure time history. Simple mathematical shapes have been used, including Gaussian, and triangular functions, however these do not provide a realistic representation of the applied pressure during detonation. Pressure-decay functions are quite common and depending on the model used, these functions are able to provide a more realistic representation of the blasting pressure time history. Finally, another alternative approach is to undertake actual in-situ measurements of the ground vibration at a location close to the blasthole. These measurements can be directly used as an input into a numerical model to simulate the propagation of ground vibrations due to blasting, however they are difficult to make due to the high pressures in this region. The development of any numerical ground vibration simulation requires that the source of blasting is correctly implemented and the user must exercise care in the selection of the most appropriate pressure time history model to use. The selected model must be able to take into account various factors which can affect the blasting source: ideal or non-ideal detonation, explosive properties, production blast geometry, and firing times, amongst others. Further work to be undertaken will involve the evaluation of these various pressure functions for use in ground vibration numerical models.
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