Vibration prediction with a method based on the absorption property of blast-induced seismic waves: A case study

Serdar Ercins

doi:10.1515/geo-2022-0633

Article Open Access

Vibration prediction with a method based on the absorption property of blast-induced seismic waves: A case study

Serdar Ercins

Published/Copyright: April 19, 2024

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From the journal Open Geosciences Volume 16 Issue 1

Abstract

In cases where blast vibrations cannot be measured with seismographs, empirical formulas are commonly used to predict vibration by specifying the peak particle velocity (PPV)-scale distance (SD) relationship. A new approach that provides important information about the relationship of seismic waves generated by blasting with rocks is the seismic quality factor (Q). The Q Factor depends on variables such as measurement distance, geological conditions, frequency, and seismic velocity. In this study, the seismic data obtained from blasting were used to determine the Q factor of the field, which in turn determines the Q value of the site. Blast vibrations were calculated using field equations derived from both the conventional and Q-factor methods. The vibration values measured by seismographs were then compared with the calculated data. The Q factor method, which takes into account the frequency content of the seismic waves, the velocity of the surface waves, and the absorption and damping properties of the seismic waves, predicted the vibration velocity with values very close to reality. However, the values obtained using the PPV-SD method are incompatible with the measurement results. The Q method is highly effective in cases where vibration measurement is not feasible. Additionally, the significance of directional changes in predicting blast vibrations is emphasized.

Keywords: blasting; vibration; seismic quality factor; peak particle velocity; scaled distance

1 Introduction

Seismographs measure vibrations during blasting operations, with the highest particle velocity serving as an important damage indicator. The recorded frequency values include lateral (Tran), vertical (Vert), and longitudinal (Long), as well as the peak vector sum (PVS), which is the vector sum of these three components.

To ensure environmental continuity, it is crucial to minimize the impact of vibrations and assess the displacement and wave propagation during blasting by analyzing frequency data.

Various methods exist to detect vibrations beforehand and reduce their effects. The most commonly used approach involves the relationship between scaled distance (SD) and peak particle velocity (PPV). This relationship has been widely used in both national and local communities since the early 1960s.

There are several approaches to predicting the PPV in the literature [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28].

The seismic quality factor (Q) has been known since 1940 and provides important information about the earthquake–ground relationship [29]. Today, a different approach based on the absorption mechanism of blast-induced seismic waves is used, instead of PPV, to predict vibration at nearby settlements and close to the slopes of mine sites. This approach is based on the seismic quality factor included in geophysical theories. The reason for using the Q factor, which is frequently used in earthquake research, to predict blast vibrations is that blasting produces the same waves as earthquakes. For this reason, Q can be used to interpret the relationship between the seismic effects that occur during blasting and the rocks [30]. In 2010, Aldas [31] proposed a formula that relates the PPV prediction in mine blasting with the frequency of the generated seismic waves and the Q factor that describes the surface waves and absorption characteristics. In addition, this formula has shown successful results in metal and coal mines in the publication of Aksoy’s article [30] published in 2020.

This study utilized the “Seismic Quality Factor (Q)” method proposed by Aksoy and Aksoy [30] to predict vibrations caused by seismic waves resulting from blasting operations in a quarry in the Sivas Province of Türkiye, instead of the traditional PPV-SD method. The method allowed for the prediction of blasting-induced vibration values that vary with distance. The Q value specific to the site was determined by analyzing the geological formations through which the blasting waves passed and the absorption mechanism of the ground. Vibration values were also calculated using time and frequency parameters and incorporated into the formula. As a result, the determined PPV will vary depending on the Q value. The data obtained from the second blasting operation highlighted the significance of directional variation in vibration. The comparison between the vibration data obtained from the seismic quality factor and the data measured at the blast sites is discussed. The suitability of the method of predicting blast vibrations using the seismic quality factor for today’s conditions and requirements is evaluated in comparison to the traditional PPV-SD method.

2 Methodology used in the study

In this part, the method of determining the seismic quality factor used in blasting-induced vibration prediction and predicting vibrations using this factor is described.

2.1 Determination of seismic quality factor from blast-induced seismic waves

The seismic quality factor provides crucial information on the absorbency of the ground. Seismic wave energy is absorbed through elastic and plastic deformation of the ground. This information can be used to determine the reflection, scattering, and refraction of seismic waves, as well as the internal friction of the ground.

The propagation distance causes a sudden weakening of the shock waves from the explosion. During the disintegration of rocks, the stress wave plays a crucial role. Natural rock masses are typically non-homogeneous. Structural planes such as joints, faults, and cracks within the rock mass prevent the propagation of stress waves and weaken their energy [32].

Calculating the seismic quality factor can help understand the effect of the ground, including scattering, weakening, and decay of seismic waves near the surface [33]. Blasts produce seismic waves similar to earthquake waves, so it is possible to determine the seismic quality factor of the environment using blasting as a source.

In the case of measurements to be made in the blast area, the seismographs are placed on the same line and the situation is studied using the principle of absorption of the seismic waves received from the seismographs with distance. Based on this principle, the seismic quality factor can be determined by measuring the ground absorption factor and the surface wave velocities. In this way, it will be possible to produce a regional seismic quality factor map. If the value of the seismic quality factor is low, the blast waves release some of their elastic energy to the ground in the form of plastic deformation. A low seismic quality factor indicates high damping in the ground, which can be caused by factors such as cracking or softness of the layer. Conversely, a high Q value indicates less damping in the layer. In soils with a high Q factor value, blast waves exhibit elastic behavior and cause minimal damage. In addition, an increase in pressure results in an increase in the Q value, indicating a reduction in energy loss.

The reflection amplitudes in seismic wave propagation environments depend not only on ground properties and incidence angles but also on frequency [34,35,36].

When determining the Q factor, calculations should be made in the frequency domain. The ground response, which expresses the expected rock behavior during blasting, is obtained from instrumental records using a seismograph. To achieve this, seismographs are placed at least two points on the same line as the blast, and measurements are taken. The natural logarithm of the ratio of the amplitude spectra of the blast-induced vibration records is then calculated. A line segment is placed on the resulting curve, and Q is calculated from the slope of this line segment [30].

As seismic waves travel from the source to the target point, they contain all geological, structural, and tectonic features of the route. Therefore, there is no need to model the geology separately. What is important here is that seismic waves should be recorded by at least two seismographs between the source and the target point. If the seismic waves are damped on the way to the target point due to different site conditions, the seismographs are shifted after each source blast. An average seismic quality factor value is determined from all the values determined for the source-target route.

The seismographs placed on the same line as the blasting point are named “Y” and “U” or the near and far stations, respectively. Borcherdt introduced the near-remote station spectral-ratio method (Figure 1), which is now commonly referred to as the standard spectral ratio (SSR) method [37]. The SSR method is widely used in the literature [38,39,40,41].

Figure 1

Near-remote station spectral-ratio method [42].

The study employed the near-far station spectral-ratio method. Figure 1 shows the near station function, represented by Y(f), given by equation (1), the far station function, represented by U(f), given by equation (2), and the near station/far station spectral ratio function, represented by ΔR(f), given by equation (3).

(1) Y ( f ) = F ( f ) ⋅ R ( f ) ,

(2) U ( f ) = F ( f ) ⋅ R ( f ) ⋅ Δ R ( f ) ,

(3) Δ R ( f ) = U ( f ) Y ( f ) ,

where f is the frequency, F(f) is the earthquake source function, Y(f) is the near station function, U(f) is the far station function, R(f) is the path function between the earthquake and the nearest station, ΔR(f) is the path difference between the near station and remote station.

When calculating the seismic quality factor (Q), it is necessary to know the seismic velocity. An alternative method to determine the Q value is to provide a predicted value for the seismic velocity. However, to address the uncertainty in velocity, Aksoy and Aksoy [30] proposed an empirical equation (equation (4)) that relates Seismic Q and velocity.

(4) Q = 0 .04736 x a 2 / 3 ,

where x is the distance from source to target, (m); a is the coefficient obtained from the slope of the curve found by spectral ratio, (unitless).

Devine [43] introduced equation (5), which is widely used to determine the maximum allowable amount of explosive for blast-induced vibration data to fall under the damage limit curves.

The k and β coefficients are uncontrollable parameters that have different values for each blasting site. To ensure consistency, the highest particle velocity measurements resulting from blasting must always be made in the same direction. Regression techniques are used to determine the k and β coefficients in the equation. The particle velocities obtained from vibration measurement devices in blasting operations and the applied blasting data (amount of explosive used per delay, scaled distance, etc.) are used for this purpose. The site equation was created using data obtained from previous blasting operations in the quarry where the studies were carried out. The value of k was determined as 723.417 and β was 1.292 [44]. The equation’s data were used to predict vibrations using the PPV-SD method. The resulting values were then compared to those obtained from the seismic quality factor method.

(5) PPV = k M β / 2 R β ,

where PPV is the peak particle velocity (mm/s), M is the maximum amount of explosive per delay (kg), R is the distance between blasting and measuring points (m); k, β is the site parameter.

It is clear that equation (5) only relates PPV to the explosive amount per delay, distance, and site constant parameters. It does not take into account the frequency or duration of the impact of the blast vibrations.

Aldas [31] equated the formula, widely used in mining, with the attenuation factor in the site of geophysics. She developed a new prediction equation that includes frequency and blasting relationship. This equation can determine the seismic quality factor (Q) of the rocks to which seismic waves arising from blasting operations will propagate. Equation (6) compares the formula developed based on the seismic wave frequency at the source, the propagation speed of surface waves in rocks, and the distance with the absorption formula:

(6) PPV = k M β / 2 R β = e − π QV f R R 1 / 2 ,

where Q is the seismic quality factor, V is the seismic velocity (m/s), and f is the PPV-frequency (Hz).

The frequency calculation in equation (6) introduces a new definition of PPV, referred to as “PPV-frequency” (equation (7)), in addition to the dominant frequency and zero-crossing frequency concepts found in the literature. Equation (8) is derived by adding the attenuation factor “a” to equation (7) [31].

(7) f = Q V π R ln R β − 1/2 kM β / 2 ,

(8) 1 a = Q V π f = 1 aR ln R β − 1/2 kM β / 2 ,

This new definition includes the frequency parameter, which is not commonly used in the literature formula. PPV can be calculated using the attenuation factor, ground constants, and explosive amount.

The effect time of the blast vibrations, an important parameter that is often neglected, is not found in the widely used PPV prediction formula in the literature. The traditional approach only takes into account the PPV when designing blasting parameters. However, this approach may not be able to identify the destructive effects caused by long-duration vibrations, even if the measured PPV is low [45].

3 Application of the seismic quality factor to predict vibrations from blasting

This operation was made for the prediction of vibrations caused by blasting in a limestone quarry within the borders of the Sivas Province of Türkiye, and the geology and site studies of the crushed stone quarry are given below.

3.1 Geological structure of the quarry

The quarry region features medium-thick bedded limestone that is grey or blackish. The limestone appears as a level without lateral continuity and its thickness varies. It precipitated unconformably on the ophiolite mix and gained its present position as a result of the second transfer of ophiolites in the Eocene. Its age is stated as Upper Maestrichtian-Paleocene [46].

3.2 Site studies and comparison of measured-calculated data

Two blasting operations were conducted at the site. Seismographs were placed along the same line as the blasting area and the points to be measured to record seismic data. The absorption factor of the site ground and surface wave velocities were determined using the principle of seismic wave absorption obtained from the seismographs at a distance, and Q was calculated with the obtained information. Figures 2 and 3 show the blast area and seismographs, respectively. The blast area in Figure 2 is numbered, and the seismographs in Figure 3 are positioned on the same line and also numbered as seismic recorders.

Figure 2

Location of devices in seismic quality factor measurement of the first blast.

Figure 3

Seismographs positioned on the same line of the first blast.

The data of the first blast performed are as in Table 1. Figure 4 shows the blast area of the second blast, while Figure 5 displays the numbered seismographs located on the same line (seismic recorder). The data for the second blast can be found in Table 2.

Table 1

Rock and pattern information of the first blast

Ignition type	Rock density (ton/m³)	Slice thickness (m)	Hole diameter (mm)	Hole distance (m)	Hole length (m)	Stemming (m)	Total number of holes (piece)	Amount of explosive per delay (kg)
Nonel	2.65	1.5	89	4	14	2	100	62.5

Figure 4

Seismographs positioned on the same line of the second blast.

Figure 5

Location of devices in seismic quality factor measurement of the second blast.

Table 2

Rock and pattern information of the second blast

Ignition type	Rock density (ton/m³)	Slice thickness (m)	Hole diameter (mm)	Hole distance (m)	Hole length (m)	Stemming (m)	Total number of holes (piece)	Amount of explosive per delay (kg)
Nonel	2.65	1.5	89	4	14	2.5	95	60

4 Results

The study conducted several blasting operations in a quarry located in Sivas Province. Seismographs were used to measure vibration data and were placed at different distances and positions from the blast point. The seismic amplitudes recorded by seismographs 1, 2, and 3 in Figure 3 are shown in Figure 6.

Figure 6

Time-dependent variation of seismic amplitudes recorded by seismographs.

Figure 7 displays the Q values that were calculated from the slope of the spectral ratios of the seismic waves received from the far and near station at points 1–2, 1–3, and 2–3.

Figure 7

Spectral ratio plot between 1–2, 1–3, 2–3 points and Q values calculated in three components.

Table 3 shows the measurement data of the seismographs placed on the same line in two different directions during the blasting operation.

Table 3

Blast data recorded by seismographs

Device No	Distance to blast area (m)	Measured value of the device (mm/s)
Device No	Distance to blast area (m)	Tran	Hz	Vert	Hz	Long	Hz	PVS
1	100	13.97	85	14.60	30	26.16	10	28.18
2	200	3.175	11	2.159	12	3.683	8.8	4.131
3	300	2.790	5.2	1.474	7.4	2.569	6.9	3.782
4	130	14.60	11	10.92	13	11.18	9.1	15.13
5	210	7.493	8.5	4.191	14	8.636	8.3	10.83

Particle velocities predicted to be created by seismic waves generated in the first blasting operation at different distances are calculated using equation (6) and presented in Table 4. The seismic quality factor in equation (6) was determined as 4.961 based on the calculation in Figure 7. The value of V in equation (6) was determined as 1,000 m/s using seismic data obtained from two seismographs on the same line with the Seisblast [47] and Seisblast-Plus software. The seismic waves’ dominant frequency is 20 Hz on average for distances of 100 and 200 m, and 15 Hz for 300 m distances (Figure 8).

PVS = e − π 4 .961⁎1000 20⁎100 100 1 / 2 = 28 .19 mm/s ,

PVS = e − π 4 .961⁎1000 20⁎100 200 1 / 2 = 5 .62 0 mm/s ,

PVS = e − π 4 .961⁎1000 15⁎100 300 1 / 2 = 3 .345 mm/s .

Table 4

The values of vibrations caused by blasting, calculated with the Q Factor and measured with seismographs

Operation 1 – Direction 1
Parameters	Seismographs
Parameters	1	2	3
Q	4.961	4.961	4.961
V	1,000	1,000	1,000
F	20	20	15
R	100	200	300
Calculated PVS, mm/s	28.19	5.620	3.345
Measured PVS, mm/s	28.18	4.131	3.782

Figure 8

Values calculated based on distance in the Seis Blast application, 1–2–3, (Seis Blast-Plus).

The time-dependent variations of the seismic amplitudes recorded by the seismographs numbered 4 and 5 in Figure 3 are shown in Figure 9.

Figure 9

Time-dependent variation of seismic amplitudes recorded by seismographs.

Figure 10 shows the Q values calculated from the slope of the spectral ratios of the seismic waves (between 4 and 5 points) received from the far and near station.

Figure 10

Spectral ratio graph between 4 and 5 points and Q values calculated in three components.

Table 5 shows the PPV generated by the seismic waves from the first blasting operation at various distances, along with data obtained from the fourth and fifth seismographs installed in the opposite direction. The average seismic quality factor was calculated as 2.89, as shown in Figure 10. The value of V in equation (6) was determined as 1,200 m/s using seismic data from two seismographs on the same line, with the assistance of Seisblast software. The seismic data show an average dominant frequency of 15 Hz at a distance of 130 m and 10 Hz at a distance of 210 m (Figure 11).

Table 5

The values of vibrations caused by blasting, calculated with the Q Factor and measured with seismographs

Operation 1 – Direction 2
Parameters	Seismographs
Parameters	4	5
Q	2.89	2.89
V	1,200	1,200
F	15	10
R	130	210
Calculated PVS, mm/s	15.00	10.30
Measured PVS, mm/s	15.13	10.83

Figure 11

Values calculated based on distance in Seisblast-Plus application, 4–5.

In Figure 4, the time-dependent variations of the seismic amplitudes recorded by the seismographs numbered G1, G2, I1, and I2 are shown in Figure 12. Figure 13 shows the Q values calculated from the slope of the spectral ratios of the seismic waves (between points G1–G2 and I1–I2) received from the far and near stations.

Figure 12

Time-dependent variation of seismic amplitudes recorded by seismographs.

Figure 13

Spectral ratio graph between G1–G2, I1–I2 points, and Q values calculated in three components.

In the second blasting operation, the measurement data of the seismographs placed on the same line in two different directions are given in Table 6.

Table 6

Blast data recorded by seismographs

Device No	Distance to blast area (m)	Measured value of the device (mm/s)
Device No	Distance to blast area (m)	Tran	Hz	Vert	Hz	Long	Hz	PVS
G1	110	48.39	34	39.75	39	41.19	12	55.62
G2	220	6.604	13	3.429	15	7.747	16	8.866
I1	110	11.43	11	3.937	20	13.08	9.0	15.59
I2	220	5.833	6.2	3.500	13	7.716	9.8	8.208
D1	468	1.651	7.3	0.889	20	1.270	6.4	1.769

Table 7 shows the particle velocities that will be created by the seismic waves at different distances between the points G1–G2 and I1–I2 where the seismographs are installed during the second blasting operation. Additionally, Figures 14 and 15 show the values calculated using the Seisblast-Plus application.

Table 7

The values of vibrations caused by blasting, calculated with the Q Factor and measured with seismographs

Operation 2 – Direction 1			Operation 2 – Direction 2
Parameters	Seismographs		Parameters	Seismographs
Parameters	G1	G2	Parameters	I1	I2
Q	3.55	3.55	Q	3.6	3.6
V	3,500	2,000	V	1,000	1,000
F	21	21	F	20	11
R	110	220	R	110	220
Calculated PVS, mm/s	53.18	8.730	Calculated PVS, mm/s	13.99	8.167
Measured PVS, mm/s	55.62	8.866	Measured PVS, mm/s	15.59	8.208

Figure 14

Values calculated depending on distance in Seisblast application, G1–G2.

Figure 15

Values calculated depending on distance in Seisblast application, I1–I2.

The vibration values for the first and second blasting operations were predicted using the PPV-SD method, as calculated by equation (5). Seismographs were placed at the measurement distances specified in Tables 3 and 6 for 62.5 and 60 kg explosives per delay, respectively, and vibration data were recorded. The measured vibration values for the blasting operations, as recorded by the seismographs, and the predicted vibration value calculated using the PPV-SD method and Q factor are presented in Table 8.

Table 8

The values of vibrations caused by blasting, calculated with the PPV-SD method and measured with seismographs

Device No	Distance to blast area (m)	Measured PVS (mm/s)	Calculated PPV-SD (mm/s)	Calculated Q Factor (mm/s)
1	100	28.180	27.260	28.190
2	200	4.131	11.133	5.620
3	300	3.782	6.593	3.345
4	130	15.130	19.423	15.000
5	210	10.830	10.452	10.300
G1	110	55.620	23.474	53.180
G2	220	8.866	9.587	8.730
I1	110	15.590	23.474	13.990
I2	220	8.208	9.587	8.160
D1	468	1.760	3.615	1.720

5 Discussion

The Q-factor approach is effective in minimizing vibrations by analyzing frequency, wave speed, and absorption parameters in detail using modern technology. The PPV-SD method, which has achieved successful results in minimizing vibrations with the knowledge and technology of the 1960s and based on only a few variables, is insufficient to minimize vibration today, especially in close settlements and slopes in the mine. This is because this formula does not include “frequency,” which is the most critical parameter in minimizing vibration. It also does not include the parameters of absorption and wave velocity. The formula is based on an empirical formula derived from 30 or more field blasting data. It loses validity when the site formation changes.

The Q factor method analyzes seismic data recorded by two seismographs on the same line. These data take into account the absorption and damping characteristics of seismic waves, the frequency content of possible surface waves, and their velocities. By measuring two seismic data near the blast area, vibration velocities can be accurately estimated at close range. Unlike the PPV-SD formula, the Q factor method requires only one pilot hole blast and two seismographs to be repeated in the changed formation.

Aksoy and Aksoy [30] stated that the PPV-SD method does not consider frequency, requires at least 30 blasting data to be valid, loses validity when the formation changes, and needs 30 blasting data to be renewed. The formula is only sensitive to explosive limitation, and vibration rates cannot be accurately predicted near the explosion area. The vibration values were measured at distances of 100 and 200 m, resulting in 12.07 and 2.338 mm/s, respectively. The Q factor method was used to calculate the vibrations, resulting in 12.327 and 2.159 mm/s, respectively. The results were found to be quite close.

The Q factor method requires seismic data from multiple seismographs on the same line with only one blasting or pilot hole operation. This method predicts vibration velocities with values close to reality by considering the frequency content, absorption and damping properties of seismic waves, and the velocity of surface waves. It has been shown to be effective even at close distances.

Fuławka et al. [48] employed quantitative methods based on in situ seismic measurements to evaluate blasting efficiency. They claimed that the results would facilitate the determination of blasting parameters. The method is applicable in underground mines, quarries, and open pits where monitoring the seismic effect of blasting is necessary.

The impact of blast-induced vibrations on structures and living organisms is not solely determined by the maximum particle velocity. Frequency is also a crucial parameter, with low-frequency vibrations being particularly damaging to structures. Therefore, it is essential to accurately predict vibrations prior to blasting to minimize any physical or psychological effects on the environment.

6 Conclusions

There is limited literature on the results of predicting blast-induced vibration using alternative methods, particularly in quarry areas, compared to traditional methods.

Table 8 shows a comparison between the vibration measurement data obtained from seismographs placed on the same line as the blasting area during the first and second blasting operations and the predicted vibration values obtained from the PPV-SD and Q factor methods. The Q factor method yielded more effective results.

At the measurement site, the Q value in all components was approximately average. Specifically, it was 4.961 in the first direction in the first blasting, 2.890 in the second direction, 3.550 in the first direction, and 3.600 in the second direction in the second blasting. These values can be used to predict the particle velocities created by seismic waves in cases where measurements cannot be made at the operation site.

The PPV-SD method is inadequate for predicting vibration values at points in different directions where the amount of explosive used per delay and the scaled distance range are equal. When examining the vibration values in the G1-I1 and G2-I2 directions at equal distances during the second blasting operation from Table 8, values of 55.620 and 15.590 mm/s were measured at points 110 m away from the blasting point in the G1-I1 direction, and values of 8.860 and 8.200 mm/s were measured at points 220 m away from the blasting point in the G2-I2 direction. In the Q method, the values at G1-I1 points were 53.180 and 13.990 mm/s, and at G2-I2 points were 8.730 and 8.160 mm/s. The vibration values were calculated using two methods. The measured and calculated values were found to be very close to each other. In the PPV-SD method, a single value of 23.474 mm/s was calculated at G1-I1 points, and a single value of 9.587 mm/s was calculated at G2-I2 points. The PPV-SD method calculates a single value because the explosive per delay and measurement distance values are identical, and seismic wave frequency and surface wave propagation speed in rocks are not considered.

During the second blasting operation at the site, the PVS value was measured in two directions, G1-G2 and I1-I2, at equal distances. The PVS value in the G1–G2 direction was 55.620 mm/s, while in the I1–I2 direction, it was 15.590 mm/s. This indicates that seismic waves propagating in different directions from the detonation point can result in significantly different vibration rates at the same distances. Furthermore, the directional examination of seismic wave absorption is necessary due to factors such as the structural-tectonic composition of the Earth.

The study concludes that the Q factor method is highly effective in predicting vibrations resulting from quarry blasting.

Conflict of interest: Author states no conflict of interest.

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Received: 2024-02-10

Revised: 2024-03-31

Accepted: 2024-04-01

Published Online: 2024-04-19

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/geo-2022-0633

Keywords for this article

blasting; vibration; seismic quality factor; peak particle velocity; scaled distance

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