Application of Explosive Equivalency Approach in Blast-Induced Seismic Effect Prediction Using EXPLO5 Thermochemical Code

Abstract

Blasting is a key process that plays a significant role in various industries, including mining and construction. To measure the effectiveness and potential impact of a blast generated by different explosives, industry professionals use a widely accepted parameter known as TNT (trinitrotoluene) equivalent. This manuscript provides an overview of the approach based on the application of the explosive equivalency principle in the prediction of the seismic effects caused by the detonation of different explosives. The explosive equivalents of studied explosives are derived from the results of thermochemical calculations using the EXPLO5 code and compared to field tests. The results have demonstrated that the equivalency approach can potentially be a useful tool in the assessment of blast-induced seismic effects.

1. Introduction

Explosives have been utilized for centuries to achieve construction projects, clear land, and break rock. However, the use of explosives can have significant negative effects on the environment, i.e., blast-induced seismic effects, fly-rock, and air blasts. Among these effects, seismic effects are considered the ones with the highest importance [1]. Thus, it is crucial to control these negative effects to comply with existing regulations and laws.

The impact of blast-induced seismic effects on buildings involves three essential steps: estimation of ground motion, analysis, and the establishment of permitted PPV (peak particle velocity) limits [2]. Today, due to technological progress, only approach to achieving results differs. Many scholars have developed equations to predict ground vibration, which are summarized by Kumar et al. [3]. Some of them are adapted to specific geological conditions and areas. For example, Ozer proposed different equations for different zones and geological conditions within the “Istanbul, Kadikoy-Kartal Railway Mass Transport System” project [4]. ISEE gave the equation for the 95% confidence line for typical data from quarry blasting [5]. A similar equation for the 95% confidence line has been given by Ak et al. for measured PPV during blasting works in magnesite mines [6]. Nicholson proposed a prediction equation developed from measurements during Bengal Quarry blasting [7]. Badal, in his thesis “Blast vibration studies in surface mines”, proposed an equation for the “Jindal Power Open Cast Coal Mine” [8]. Mesec conducted his research on numerous blasting sites in deposits with different GSI (Geological Strength Index) [9]. Moreover, damage characteristics in a rock mass have been extensively studied [10]. Agrawal modified the scaled distance equation using the superimposition factor of vibration waves [11].

Most of the published articles about blast-induced seismic effects are based on a significant amount of measured values gathered during a particular project or quarry development. These data are then analyzed using statistical analysis or ANN (Artificial Neural Network) [12,13]. Considerable quantities of open-pit blast-induced seismic effects measurements can be collected to give a regression curve. Civil works usually do not have this quantity of measured data; hence, the execution of the initial test blast is fundamental for developing an equation for the safe execution of blasting works [14]. Guidelines exist for measuring instruments and installation methods during measurement [15].

To increase the precision of blast-induced seismic effect measurements, we established a research program and have performed several studies according to it. A greater number of monitoring points were used in a single measurement line [16], positioning of measurement instruments at relevant predetermined distances [17], and detecting and excluding atypical values to achieve more accurate input data and, thus, consequently, more precise results [18].

For contractors and owners, ensuring the safety of surrounding buildings during blasting works is of utmost concern [19]. In this regard, the power of an explosive is a key factor in determining its effectiveness and safety. To allow for a standard comparison of explosive power, the concept of TNT equivalent has been introduced, which enables professionals to make informed decisions in blasting operations.

The TNT equivalence, which is a common engineering tool, is one of the potential tools for improving the effectiveness of blasting and the precision of blast-induced seismic measurement results that has been widely investigated [20]. It is used to relate the effects of the yield of a certain explosive to that of TNT (or another reference explosive). It is established mainly empirically by different types of experiments, which often do not yield the same TNT equivalence values. The most used tests are the Trauzl test, plate dent, ballistic mortar, sand crush, and air blast test. Predicting blast effects on structures with TNT equivalence is certainly usable. Formby and Wharton conducted a ballistic mortar test on several commercial explosives to obtain their TNT equivalence [21]. Analysis of criteria to determine TNT equivalence has been performed using several different calculation methods for different explosive materials and charge shapes [22]. Attempts by several authors to correlate the TNT equivalent and different detonation parameters showed that there is no certain method for determining the TNT equivalent [23,24]. Most regularly, an equivalent TNT mass links the mass of a certain explosive to the equivalent mass of TNT using the ratio of their detonation heat [25]. Locking used several different equations with different detonation parameters to theoretically estimate the TNT equivalent for several standard high explosives [23]. Numerical studies of TNT equivalent were performed for various high explosives for “incident and normally reflected peak overpressure and impulse” [26]. Air blast TNT equivalence has been achieved for a variety of commercial explosives using ballistic mortar tests with 12 piezo-electric gauges, with two different calculating methods [27].

The TNT equivalence can also be estimated from the thermochemical equilibrium code results [28]. Thirty years ago, Copper [20] claimed that the thermochemical computer codes could not correctly predict blast waves due to an absence of “chemically reactive equations of state”. However, thanks to the progress in the field of thermochemical calculations and the development of more accurate equations of state, today’s computer codes are capable of predicting the detonation performance and TNT equivalence quite accurately [24]. Using thermochemical calculations, Jeremic and Bajic derived the TNT equivalent for a larger number of high explosives [29].

This study, as a part of the above-mentioned research program, aims to improve further the precision of blast-induced seismic effect calculation using the TNT equivalence approach, whereby TNT equivalents are calculated using the detonation parameters calculated by the thermochemical code EXPLO5. By doing so, we strive to contribute to the development of safer and more effective blasting techniques in mining projects, construction, and other relevant fields.

2. Materials and Methods

For this study, the original experimental data of Škrlec et al. [30] were taken in electronic form. To determine the blast-induced seismic effect of different explosives, the authors varied the mass of the charge weight per delay while the depth of the borehole and the size of the charge itself (cartridge) were kept constant. The test blast was carried out in the diabase rock, which is characterized by high compressive strength (

Table 1. Characteristics of diabase rock [30].

Diabase Rock
Compressive strength	200–400	MPa
Density	2.85–3.15	g/cm3
Water absorption	0.2–1	% mass
Spatial mass	2.8–3.1	g/cm3
Porosity	0.1–1	% volume

).

The explosives tested included 5 boreholes filled by EME (Emulsion explosive) charges and 5 boreholes for each EMM/EPS (Emulsion matrix/Expanded Polystyrene) mixture. The boreholes were drilled with 32 mm diameter and 240 mm depth. The charges consisted of PVC confinement 25 mm in diameter. Each explosive charge was set off separately using electric detonators of energy as reference detonator No. 4.

The ground oscillation velocities were measured for each borehole. The measurement setup is shown in Figure 1. Instantel BlastMate III and Instantel MiniMate Plus units were used to measure the ground oscillation velocity. A total of six units were used, with three units per line spaced 2 m apart.

The maximum PPV from each measurement is a function of the scaled distance (SD). The general form of dependence of PPV and SD is given by the equation [31]:

$$PPV=H{\left(SD\right)}^{-\beta }$$

(1)

where SD is the scaled distance (m/kg^1/2), H is the constant in blast design, and β is the attenuation constant. The constants H and β are defined by test blasts.

The scaled distance is given by Equation (2).

$$SD={\displaystyle \frac{R}{\sqrt{W}}}$$

(2)

where R is the distance (m) and W is the charge weight per delay (kg).

It should be noted that, in the case of using different types of explosives for blasting works within the same project, the relationship of the effect of detonation properties of diverse explosives on blast-induced seismic effect, i.e., PPV, can be achieved via the equivalent mass approach. This method involves relating the effects of the yield of a certain explosive to that of a reference explosive (usually TNT):

$$W_e=W·{\displaystyle \frac{TN{T}_e}{100}}$$

(3)

where W_e (kg) present the TNT equivalent weight, i.e., the weight of TNT that produces the same effect at the same distance as an actual explosive, W (kg) is the weight of the actual explosive, and TNT_e is the TNT equivalent for the actual explosive expressed in percentage.

Thermochemical Calculations

The detonation properties of analyzed explosives are computed using the EXPLO5 thermochemical code [32]. The code predicts detonation properties (e.g., detonation temperature, detonation velocity, pressure, the energy of detonation, heat, etc.) by applying the “chemical equilibrium steady-state Chapman–Jouguet (C-J) detonation model”. The equilibrium composition of detonation products the code calculates by mathematically describing the state of equilibrium in a multicomponent and multiphase system, applying the free energy minimization technique and mass balance principle. This method was originally developed by White et al. [33] and later adapted for computer application by Mader [34]. The method is based on the fact that in chemical equilibrium, the chemical potential of reaction products is equal to the chemical potential of reactants, i.e., the fact that in the equilibrium state, the free energy of products has the minimum value.

EXPLO5 has the potential to use a number of equations of the state of gaseous detonation products. For this analysis, the modified Becker–Kistiakowsky–Wilson (MBKW) equation of state is used, given that earlier research demonstrated that it best explains the behavior of low-density explosives [35].

Different approaches have been used to estimate the strength of an explosive relative to TNT based on the results of thermochemical calculations. Basically, all the approaches are based on the interpretation of the relative strength in terms of certain detonation properties [23,24]. Most frequently, the heat of detonation (Q) is used to estimate the TNT equivalent [23]:

$$TN{T}_e\left(Q\right)={\displaystyle \frac{Q}{Q_{TNT}}}\times 100$$

(4)

In [24], the authors analyzed the accuracy of several approaches for the evaluation of relative strength in terms of the Trauzl test and found that the best concurrence between experimental results and calculation is obtained using the product between the heat of detonation (Q) and the square root of the volume of detonation products (V₀):

$$TN{T}_e\left(Q{V}_0\right)={\displaystyle \frac{Q{V}_0^{0.5}}{{\left(Q{V}_0^{0.5}\right)}_{TNT}}}\times 100$$

(5)

In this study, we also used the detonation energy, E₀ (i.e., maximum available energy for doing mechanical work), the detonation pressure (p_CJ), and velocity of detonation (D) to estimate the TNT equivalent:

$$TN{T}_e\left(E_0\right)={\displaystyle \frac{E_0}{E_{0\left(TNT\right)}}}\times 100$$

(6)

$$TN{T}_e\left(p_{CJ}\right)={\displaystyle \frac{p_{CJ}}{p_{CJ\left(TNT\right)}}}\times 100$$

(7)

$$TN{T}_e\left(D\right)={\displaystyle \frac{D}{D_{\left(TNT\right)}}}\times 100$$

(8)

The detonation energy in Equation (6) is derived from the expansion isentrope of detonation products as described in [36].

3. Results and Discussion

The parameters of detonation for explosives used in this study are calculated using the EXPLO5 thermochemical code, applying the Chapman–Jouguet detonation model. The calculated detonation parameters, along with the experimentally determined detonation velocities, are given in

Table 2. Detonation parameters of used explosives.

Explosive	Volume Ratio (%)	Density (g/cm3)	Dexpt. * (m/s)	Calculated Detonation Parameters
				D (m/s)	pCJ (GPa)	Q (kJ/kg)	E0 (kJ/cm3)	T (K)
Emulsion explosive (EME)	100	1.175	5534	5559	8.03	2779.78	3.68	2217
EMM/EPS (50/50)	50/50	0.627	3051	3413	2.16	2645.42	1.91	2261
EMM/EPS (40/60)	40/60	0.437	2491	2785	1.06	2469.27	1.26	2138
EMM/EPS (30/70)	30/70	0.302	2089	2399	0.59	2284.85	0.81	2012
EMM/EPS (20/80)	20/80	0.218	1710	2137	0.36	1974.69	0.52	1804

* D_expt experimental detonation velocity measured in steel tubes 21.5 mm inner diameter, 150 mm long, 2.7 mm wall thickness, D, p_CJ, Q, E₀, and T are calculated detonation velocity, pressure, heat, energy, and temperature, respectively.

.

It can be seen from Table 2 that experimental and calculated detonation velocities for EME differ by less than 1%, while in the case of EMM/EPS mixtures, the difference increases as the amount of EPS increases, reaching ~25% for the mixture containing 80% of EPS. As shown in our previous studies [35,37,38], EXPLO5 can predict the detonation velocity of a large series of different explosives with an error of less than 5%, so a large discrepancy observed between experimental and calculated detonation velocities for mixtures containing a larger amount of EPS points to the conclusion that these explosives behave non-ideally. Among other things, the non-ideal behavior manifests in a decrease in detonation velocity with an explosive charge diameter decrease, and ideal detonation codes always predict larger detonation velocities than the experimental ones.

Recently, Dobrilović et al. [24] have demonstrated that ideal detonation codes can be used to predict the TNT equivalent and relative strength of explosives from the heat of detonation and the volume of detonation products for both ideal and nonideal explosives. In light of this finding, and aware of the limitation of ideal detonation codes when it comes to accurate prediction of D and p of commercial explosives, in this research, we used the ideal detonation code, but we calculated the TNT equivalent using different detonation parameters.

Although, in most studies, TNT is used as a reference explosive when comparing the effect of the yield of a certain explosive, in this study we have chosen EME as a reference explosive. The main reason for choosing EME is that both EME and EMM/EPS mixtures belong to the same class of explosives—commercial explosives. This is important because, according to Marshall [39], the equivalency principle can provide suitable results for an equal class of explosives, i.e., explosives that perform in the same manner. Compared to TNT, which behaves ideally, explosives used in this study exhibit non-ideal behavior and have significantly lower values of detonation parameters.

With regards to the above, Equations (4)–(8) change in such a way that the detonation parameters for EME are used instead of those for TNT, and the TNT equivalent (TNTe) is replaced by EME equivalent (EMEe). The EME equivalents for EMM/EPS mixtures are calculated based on the detonation parameters given in Table 2 and using modified Equations (4)–(8). The results are given in

Table 3. Calculated EME equivalents for tested explosives.

Explosive	Density (g/cm3)	EME Equivalent (%)
		Equation (4)	Equation (5)	Equation (6)	Equation (7)	Equation (8)
Emulsion explosive (EME)	1.175	100.00	100.00	100.00	100.00	100.00
EMM/EPS (50/50)	0.627	95.17	98.46	96.98	26.87	61.39
EMM/EPS (40/60)	0.437	88.83	92.95	91.94	13.19	50.10
EMM/EPS (30/70)	0.302	82.20	87.24	85.89	7.33	43.16
EMM/EPS (20/80)	0.218	71.04	76.61	75.83	4.44	38.45

.

It is evident from Table 3 that Equations (4)–(6) give fairly similar EMEe values (difference up to 7.3%), while Equation (8) gives significantly lower values of EMEe. On the other hand, the EMEe values calculated by Equation (7) greatly deviate from the values obtained by other equations. Which of the equations given in Table 3 gives better results, i.e., which detonation parameter enables the most accurate estimation of the peak particle velocity by applying the equivalence principle, will be discussed below.

In the experiment [30] carried out using EME explosives, the authors measured PPV as a function of charge weight and distance from the blast (Figure 1). For analysis, only measurements from Line 1 were used since the PPV values for Lines 1 and 2 are similar, with small discrepancies due to microgeological conditions and different directions. The maximum PPV from each blast and monitoring position (MO) for EME are given in

Table 4. Measured maximum PPV vs. charge weight and distance from blast point for EME [30].

Explosive	W (g)	R (m)	SD (m/kg0.5)	PPV (mm/s)
EME	73.24	2	7.390	33.3
		4	14.780	26.3
		6	22.171	21.8
	72.36	2	7.435	27.3
		4	14.870	21.7
		6	22.305	8.25
	73.11	2	7.397	39.6
		4	14.794	28.6
		6	22.190	6.98
	73.18	2	7.393	44.8
		4	14.786	13.3
		6	22.180	6.22

.

The dependence of experimentally measured PPV on the explosive mass and distance from the blast is expressed through the scaled distance (Equation (1)). Taking the logarithm of both sides in Equation (1) yields the following equation:

$$\log \left(PPV\right)=\log \left(H\right)+\beta ·\log \left(SD\right)$$

(9)

When plotted in log–log coordinates, Equation (9) gives a linear PPV-SD relationship of the form:

$$y=a+bx$$

(10)

where y = log(PPV), a = log(H), x = log(SD), and b = β.

One can easily determine the constants a and b in Equation (10) and the constants H and β in Equation (9) through the linear regression analysis. The slope of line (b) is computed from the expression [40]:

$$b=\left\{\sum \left(x_i·y_i-n·x·y\right)\right\}/\left\{\sum \left(x_i-n·x^2\right)\right\}$$

(11)

and intercept a is computed from the expression:

$$a=y-b·x$$

(12)

The coefficient of correlation r is obtained by evaluating the expression [40]:

$$r=\left\{\sum \left(x_i·y_i-n·x·y\right)\right\}/{\left[\left\{\sum \left(x_i-n·x^2\right)\right\}\left\{\sum \left(y_i^2-n·y^2\right)\right\}\right]}^{1/2}$$

(13)

and the sample standard deviation is evaluated from:

$$s={\left[\left\{\sum \left(y_i^2-n·y^2\right)-\sum {\left(x_i·y_i-n·x·y\right)}^2/\sum \left(x_i-n·x^2\right)\right\}/n\right]}^{1/2}$$

(14)

where n is the number of points, x_i and y_i are the ith variable in the set i = 1 to n, and x and y are the means of each of the variables in the given set [40].

Based on the experimental data given in Table 4, the fitting constants a and b (Equation (10)) for EME are derived using the Instantel Blastware application. The application works by importing data directly from records and by manually entering the values of the actual charge weight per delay (W) and the distance of the monitoring points from the explosion (R) for each MO into the application. The values of PPV are recorded by the instruments at the monitoring points, based on which the application calculates the fitting constants (best-fit line) and additionally calculates and presents a 95% confidence line with equation (upper limit). The output results for monitoring points in Line 1 for EME are shown in Figure 2.

Since the Instantel Blastware application does not give the fitting constants a and b for the best-fit line, the same is calculated by CurveExpert—curve fitting and data analysis code. The constants H and β in Equation (9), calculated from constants a (a = log(H)) and b (b = β), and final equations for the best-fit line and 95% confidence lines are:

Best-fit line:

$$PP{V}_{EME}=395.64·S{D}^{-1.161} (\sigma = 7.306 mm/s, r = 0.8357)$$

(15)

95% confidence line, upper limit:

$$PP{V}_{EME}=852.7·S{D}^{-1.161}$$

(16)

95% confidence line, lower limit:

$$PP{V}_{EME}=183.7·S{D}^{-1.161}$$

(17)

Once the fitting constants for the reference explosive EME are determined, the equivalence principle can be applied to predict the blast effect, i.e., PPV value at a specified distance and charge weight, for any explosive, provided its EME_e is known. For illustration, let us assume we want to predict the PPV, which will be generated by the detonation of 15.5 g of an explosive X at a distance of 6 m. The EME_e of explosive X equals 38.5%. The equivalent weight of EME (W_e), which gives the same effect as 15.5 g of explosive X, can be obtained by Equation (3) ($W_e=W·EM{E}_e/100=5.97 \mathrm{g}).$ The scaled distance for EME equals $SD\left(W_e,R\right)=R/\sqrt{W_e}=6/\sqrt{5.97/1000}=77.7 \mathrm{m}/{\mathrm{kg}}^{0.5}$. By substituting the value of SD (W_e, R) in Equation (15), we obtain PPV = 2.53 mm/s. Therefore, 15.5 g of explosive X will produce PPV = 2.53 mm/s at a distance of 6 m, the same as 5.97 g of EME at the same distance. Similarly, we can predict a mass of mixture X that will give the same value of PPV, at 6 m distance, as 72 g of reference explosive EME. In this case W_e = 72 g, SD(W_e,R) = 22.3 m/kg^0.5, and the calculated PPV for that SD (Equation (15)) will be 10.7 mm/s. The mass of mixture X, which will produce PPV = 10.7 mm/s at R = 6 m, equals $W=W_e/(EM{E}_e/100)=187 \mathrm{g}$.

To validate the above-described equivalency approach to predict blast-induced seismic effects, we used the experimentally measured PPV vs. charge weight and distance data from Škrlec et al. [30] for four mixtures based on an emulsion matrix (EMM) and expanded polystyrene (EPS). It is well known that the performance (or power) of explosives determined by different tests does not follow the same ranking order. For example, for blasting work, the detonation heat and the amount of detonation products are the most significant parameters. However, if an explosive performs strong disintegration work, then the most important parameters are the velocity of detonation and pressure [34]. Maienschein [28] claims that the detonation energy calculated by thermochemical codes allows assessment of the TNT equivalency with respect to peak pressure, while the heat of detonation allows estimation of TNT equivalency with respect to quasi-static pressure at a long time. However, we could not find any previous research on which detonation parameter is best to use to derive TNT or any other explosive equivalence concerning PPV values.

Considering the above-mentioned, the first step in the validation of the approach was to find which detonation parameter, i.e., which equation for the calculation of EME_e (Equations (4)–(8)), correlates best with the measured PPV. The analysis showed that EME_e derived from Q, E₀, and QV₀^0.5 (Equations (4)–(6)), give similar results and all of them overpredict PPV, EME_e derived from p_CJ (Equation (7)) greatly underpredicts PPV, while EME_e derived from detonation velocity (Equation (8)) best reproduce experimental PPV-SD data for all studied explosives. For illustration, the results of the analysis for EMM/EPS-40/60 mixture are given in Figure 3. Considering that, further validation is achieved using EME equivalents calculated by Equation (8).

As a part of the validation, we compared the experimental PPV-SD(W) data given in

Table 5. Measured maximum PPV vs. charge weight and distance from blast point for EMM/EPS mixtures [30].

Explosive	EMEe/100 (Equation (8))	Experimental Data			Calculated Equivalent Weight and Scaled Distance
		W (g)	R (m)	PPV (mm/s)	SD(W, R) (m/kg0.5)	We (g)	SD(We, R) (m/kg0.5)
EMM/EPS-50/50	0.614	42.40	2	21	9.713	26.03	12.395
	0.614	42.40	4	7.75	19.426	26.03	24.791
	0.614	42.40	6	8.38	29.139	26.03	37.186
	0.614	42.54	2	15	9.697	26.12	12.375
	0.614	42.54	4	16.4	19.394	26.12	24.750
	0.614	42.54	6	6.22	29.091	26.12	37.125
EMM/EPS-40/60	0.501	33.79	2	17.9	10.880	16.93	15.372
	0.501	33.79	4	7.75	21.760	16.93	30.743
	0.501	33.79	6	3.94	32.641	16.93	46.115
	0.501	33.79	2	16.8	10.880	16.93	15.372
	0.501	33.79	4	5.21	21.760	16.93	30.743
	0.501	33.79	6	4.83	32.641	16.93	46.115
	0.501	33.81	2	12.3	10.877	16.94	15.367
	0.501	33.81	4	6.98	21.754	16.94	30.734
	0.501	33.81	6	3.81	32.631	16.94	46.101
	0.501	33.51	2	15.7	10.926	16.79	15.436
	0.501	33.51	4	2.41	21.851	16.79	30.871
	0.501	33.51	6	4.32	32.777	16.79	46.307
EMM/EPS-30/70	0.432	23.64	2	14.7	13.008	10.21	19.791
	0.432	23.64	4	6.73	26.016	10.21	39.582
	0.432	23.64	6	3.3	39.024	10.21	59.373
	0.432	23.65	2	4.57	13.005	10.22	19.787
	0.432	23.65	4	7.24	26.010	10.22	39.573
	0.432	23.65	6	4.57	39.015	10.22	59.360
	0.432	23.72	2	18.4	12.986	10.25	19.757
	0.432	23.72	4	3.94	25.972	10.25	39.515
	0.432	23.72	6	2.67	38.958	10.25	59.272
	0.432	23.20	2	9.65	13.131	10.02	19.978
	0.432	23.20	4	3.05	26.261	10.02	39.955
	0.432	23.20	6	3.81	39.392	10.02	59.933
EMM/EPS-20/80	0.385	15.23	2	4.7	16.206	5.86	26.119
	0.385	15.23	4	2.92	32.412	5.86	52.237
	0.385	15.23	6	4.32	48.618	5.86	78.356
	0.385	15.64	2	6.48	15.992	6.02	25.774
	0.385	15.64	4	3.94	31.985	6.02	51.548
	0.385	15.64	6	2.54	47.977	6.02	77.322
	0.385	15.84	2	5.59	15.891	6.10	25.611
	0.385	15.84	4	3.3	31.782	6.10	51.221
	0.385	15.84	6	1.9	47.673	6.10	76.832
	0.385	15.67	2	10.9	15.977	6.03	25.749
	0.385	15.67	4	3.56	31.954	6.03	51.499
	0.385	15.67	6	1.9	47.931	6.03	77.248

Note: SD (W, R)—scaled distance for specified actual weight (W) and distance R, SD (W_e, R)—scaled distance for equivalent weight (W_e) and distance R.

against the data calculated by Equation (15) using EME equivalent weight (PPV-SD(W_e)). The best-fit curve for EME explosives is also given for the comparison (Figure 4).

It can be observed from Figure 4 that a satisfactory agreement between the experimental and predicted PPV-SD data exists for all explosives. It should be noted that the experimental PPV-SD data for EME (Figure 2) exhibit a significant scattering of the results, especially in the area of lower SD, i.e., closer to the blast point. In this region, PPV exponentially increases with the decrease of SD, so a small variation in measured distance or explosive weight may cause a significant change in PPV, which results in larger experimental errors. For example, for SD ≈ 10 m/kg^0.5, the PPV ranges between 48.5 mm/s and 27.3 mm/s (the difference is 21.2 mm/s, almost double). For EMM/EPS mixtures, for SD = 10–15 m/kg^1/2, the minimum and the maximum PPV differ between 5 and 13.5 mm/s. With that in mind, it can be concluded that the predicted PPV values for EME/PPS mixtures are within experimental error (Figure 4).

To further validate the equivalency approach for blast-induced seismic effect prediction, we analyzed how accurately the weight of explosives that will generate a specified PPV value at a specified distance from the blast point can be predicted. For this, we took the PPV limit value from the HR DIN 4150:2011 standard [41] (

Table 6. Guideline values for vibration velocity to be used when evaluating the effects of short-term vibration on structures as per HR DIN 4150:2011 [41].

Line	Type of Structure	Vibration at the Foundation at a Frequency of			Vibration at Horizontal Plane of Highest Floor at All Frequencies
		1 Hz to 10 Hz	10 Hz to 50 Hz	50 Hz to 100 Hz *)
1	Buildings used for commercial purposes, industrial buildings, and buildings of similar design	20 mm/s	20–40 mm/s	40–50 mm/s	40 mm/s
2	Dwellings and buildings of similar design and/or occupancy	5 mm/s	5–15 mm/s	15–20 mm/s	15 mm/s
3	Structures that, because of their particular sensitivity to vibration, cannot be classified under lines 1 and 2 and are of great intrinsic value (e.g., listed buildings under preservation order)	3 mm/s	3–8 mm/s	8–10 mm/s	8 mm/s

(*) At frequencies above 100 Hz, the values given in this column may be used as minimum values.

) as the maximum permitted value for “dwellings and buildings of similar design and/or occupancy” (Line 2), which equals 20 mm/s.

The value of SD at which a specified PPV of 20 mm/s is reached for individual explosives is determined from experimental PPV-SD data as illustrated in Figure 5. The best-fit equations for EMM/EPS explosives are obtained by the regression analysis of experimental PPV-SD data given in Figure 4. The results of the regression analysis are summarized in

Table 7. Best-fit line equations and scaled distance corresponding to PPV = 20 mm/s for studied explosives.

Explosive	Best-Fit Line Equation	SD (PPV = 20 mm/s) (m/kg1/2)
EME	$PP{V}_{EME}=395.64·S{D}_W^{ -1.161}$ σ = 7.306 mm/s, r = 0.8357	13.07
EMM/EPS (50/50)	$PP{V}_{EMM/EPS \left(50/50\right)}=112.72·S{D}^{-0.801}$ σ = 3.929 mm/s, r = 0.8014	8.65
EMM/EPS (40/60)	$PP{V}_{EMM/EPS \left(40/60\right)}=276.25·S{D}^{-1.234}$ σ = 7.306 mm/s, r = 0.9439	8.40
EMM/EPS (30/70)	$PP{V}_{EMM/EPS \left(30/70\right)}=135.14·S{D}^{-1.003}$ σ = 3.504 mm/s, r = 0.7448	6.76
EMM/EPS (20/80)	$PP{V}_{EMM/EPS \left(20/20\right)}=74.68·S{D}^{-0.881}$ σ = 1.65 mm/s, r = 0.7751	4.46

.

From the best-fit line equations for individual explosives (Table 7), and with a PPV limit value of 20 mm/s taken from the standard, the SD is calculated according to the equation:

$$SD={\left({\displaystyle \frac{PPV}{H}}\right)}^{{\displaystyle \frac{1}{-\beta }}}$$

(18)

The results of the calculation are summarized in Table 7.

As expected, the SD shifts to lower values (i.e., closer to the explosion point) with a decrease in detonation performance. From the known values of SD corresponding to PPV = 20 mm/s, one can calculate the maximum permitted weight of individual explosives at a specified distance from the blast point using Equation (2). The results of the calculation are given in

Table 8. Experimental and predicted maximum permitted weights at different distances that generate PPV = 20 mm/s.

R (m)	EME		EMM/EPS (50/50)		EMM/EPS (40/60)		EMM/EPS (30/70)		EMM/EPS (20/80)
	WEP (g)	Wfit (g)	WEP (g)	Wfit (g)	WEP (g)	Wfit (g)	WEP (g)	Wfit (g)	WEP (g)	Wfit (g)
1	5.85	5.85	9.54	13.36	11.68	14.17	13.56	21.88	15.22	50.27
2	23.42	23.42	38.14	53.46	46.74	56.69	54.25	87.53	60.90	201.09
3	52.69	52.69	85.82	120.28	105.16	127.55	122.07	196.95	137.02	452.45
4	93.66	93.66	152.57	213.84	186.95	226.76	217.01	350.13	243.60	804.36
5	146.35	146.35	238.39	334.12	292.11	354.31	339.08	547.07	380.62	1256.81
6	210.74	210.74	343.28	481.14	420.64	510.20	488.28	787.79	548.09	1809.81
7	286.84	286.84	467.25	654.88	572.54	694.44	664.60	1072.27	746.02	2463.35

Note: W_fit, W_EP—maximum permitted weights determined from experimental data using best-fit curve and estimated applying the equivalency principle, respectively.

.

However, if experimental PPV-SD data are not available, one can apply the equivalency principle to estimate the maximum permitted weights at specified distances. This can be achieved in the following way: first, using the best-fit equation for reference explosive, the SD value at which the specified PPV value is reached is calculated using Equation (18). Then, from the known SD value (in this case for PPV = 20 mm/s, SD = 13.07 m/kg^1/2 for EME as reference explosive), the maximum permitted weight at a specified distance is calculated by Equation (2). Then, the maximum permitted weights of any other explosive can be calculated by Equation (3), applying the equivalency principle and knowing their EMEe.

As visible from Table 8 and Figure 6, the weights predicted using the equivalency principle (WEP) are lower than those determined from the best-fit equation of experimental PPV-SD data. The difference between predicted and experimental PPV values goes from 17.6% for EMM/EPS-40/60 to 69.7% for EMM/EPS-20/80. In our opinion, there are two key reasons for such large differences. The first is generally a large scattering of measured PPV values, which could primarily be attributed to the small amount of explosive used in the experiment (15–42 g for EMM/EPS mixtures).

The second reason lies in the fact that the PPV range in the experiments was significantly below the PPV limit value of 20 mm/s. For example, the maximum mean PPV value for EMM/EPS-20/80 mixture at SD ≈ 16 m/kg^1/2 equals only 6.9 mm/s, for EMM/EPS-30/70 mixture at SD ≈ 13 m/kg^1/2 equals 11.8 mm/s, etc. That means that SD which corresponds to PPV = 20 mm/s (Equation (18)), calculated by the best-fit equation, is significantly outside the range of experiments. The extrapolation outside the range of experimental data used for fitting, results in less accurate SD values derived based on experimental data. This is especially visible for EMM/EPS-20/80 mixture, for which the experimental PPV range is the narrowest (up to 6.9 mm/s), and which shows the largest difference between predicted and experimental PPV values (Figure 6).

4. Conclusions

The possibility of the application of the equivalence approach in the prediction of blast-induced seismic effects is studied in this work. After a thorough analysis of the results, the following conclusions were drawn:

(a)

The results have shown that the equivalency approach is a potential tool in the assessment of the blast-induced seismic effect. It is especially useful in the situation when the type of explosive is changed within a single project;

(b)

It was demonstrated that the best results are obtained when the equivalent weight of the studied explosive is calculated as a ratio of detonation velocities of studied and reference explosives;

(c)

Analysis of experimental results has shown that the measurement uncertainty is quite high. This may be attributed to the fact that the weight of the explosives used in the tests was too small (15–75 g). To validate the approach, it is necessary to improve the accuracy of experimental measurements, which can be achieved by using larger samples, including the amounts required for mass blasting at open pits;

(d)

The advantage of the approach is that EMEe is determined using detonation velocity, the parameter that is relatively easy to measure experimentally;

(e)

Experimental PPV-SD data in this study are analyzed using Blastware 10.74 (Instantel application) and Curve Expert 1.4, however, any other software capable of performing regression analysis may be used.

Following the Conclusions, point (c) specifically, the plan for further study is to extend the research with larger quantities of explosives, including the amounts required for mass blasting at open pits, and more measurement positions to improve accuracy for application of explosive equivalency in blast-induced seismic effect calculations.