Study on the Vibration Effects of Brick–Concrete Structures Induced by Blasting in Open-Pit Mines

Abstract

Ensuring the dynamic safety of buildings near open-pit mines during blasting is a critical concern for the normal conduct of mining operations. This study investigates the effects of blasting vibrations on brick–concrete structures by using deep-hole blasting tests conducted at the mine site, employing blasting vibration monitoring and numerical simulation techniques. The peak particle velocity and energy distribution characteristics of blasting waves in structural columns and brick walls were analyzed. Furthermore, a three-dimensional numerical model was developed to analyze the response characteristics of buildings to blasting vibrations. Considering the impact of a building’s natural frequency on blasting vibrations, harmonic response was utilized to identify the natural frequencies of different components. The relationship between these frequencies and a building’s natural frequency is discussed. Dangerous frequencies and components were identified. The findings of this study can serve as a theoretical foundation for understanding the damage mechanisms of buildings under blasting waves and for controlling the impact of blasting vibration effects.

1. Introduction

Blasting is a technique that uses the energy released by explosives to destroy or deform materials, achieving specific engineering goals [1]. The peak velocity of blasting waves decreases as the distance from the blast center increases. It may also result in varying degrees of damage to non-blasted targets within a certain range. This phenomenon is known as the seismic effect of blasting. If the PPV of blasting waves exceeds the vibration safety standards for buildings or if the main frequency of these waves closely matches the natural frequency of the building, it may result in varying degrees of damage to the building [2]. Compared to natural earthquakes, blasting waves are characterized by higher frequencies and shorter durations, leading to different forms of damage in buildings. The damage is typically localized or stress-concentrated, such as cracks at door and window corners and weakly constrained areas. Frequent disturbances caused by blasting waves in open-pit mines can exacerbate these damages, leading to building injuries and destruction, affecting the normal lives of local residents [3,4,5]. Therefore, ensuring the integrity of buildings requires a clear understanding of the vibration effects of blasting waves within them.

Currently, researchers have extensively explored the impact of blasting vibrations on buildings. However, most studies focus on the dynamic response of buildings under tunnel or foundation pit blasting. For example, He et al. [6] found that the vertical peak particle velocity (PPV) decreases initially and then increases with the height of the floor, while the horizontal and radial PPV follow a different pattern. Wang et al. [7] discovered that the PPV in the vertical direction for high-rise buildings is the highest, while the PPV in the horizontal direction is relatively low. Huo et al. [8] observed that the PPV in masonry structures gradually increases from the first to the third floor, but begins to decrease at the fourth floor. Jiang et al. [9] found that the vertical PPV in reinforced-concrete structures first decreases and then increases with floor height. In contrast, Athanasopoulos et al. [10] proposed that the vertical vibration amplification effect is significant in the higher floors of reinforced-concrete structures, based on their measurements. Ren et al. [11] monitored the effects of historical PPV and found that the drum tower exhibits significant horizontal vibration, while vertical vibration shows a rapid decaying trend. To reduce the impact of tunnel blasting on buildings, Ren et al. [12] proposed a new blasting scheme. Zhang et al. [13] used blasting experiments and numerical simulation methods to analyze the dynamic response of high-rise frame buildings under the action of pit blasting. The PPV amplification effect of high-rise buildings is obvious: the amplification factor is 1.19~1.26 times.

To study the vibration response characteristics of a building’s structural components during blasting, many researchers have used numerical simulation methods to analyze the dynamic responses of buildings with various structural forms. Guan et al. [14] noted that the main vibration frequency of tunnel blasting is close to the natural frequency of building components, so different components experience more intense vibrations compared to the main structure of the building. Jiang et al. [15] used numerical simulation techniques to analyze the vibration effects of blasting on a pagoda, finding that the PPV at the top of the tower is 4.29 cm/s, significantly higher than the 0.29 cm/s at the bottom. Jayasooriya et al. [16] used LS-DYNA and SAP2000 numerical simulation software to assess the damage and residual strength of reinforced-concrete-frame structures and components under explosive loads. Wu et al. [17] used Autodyn3D to study the damage characteristics of masonry structures under the influence of blasting waves. Zou et al. [18] analyzed the blasting vibration response characteristics of residences and proposed a control standard of PPV for the damage characteristics of residences. Yuan et al. [19] studied the vibration response characteristics of high-rise buildings under the action of mine production blasting. The vertical PPV of the building was greater than the PPV in the horizontal direction. The horizontal direction PPV increased with the height of the floor, which showed an increase and then decrease, and, in the high-rise, showed an increasing trend.

The impact of blasting vibrations on building safety has attracted considerable attention, particularly in engineering contexts such as tunnel excavation and deep-pit blasting. Most existing studies have focused on reinforced-concrete or frame structures, which typically exhibit high structural integrity and ductility. However, in the vicinity of open-pit mines, large numbers of aging brick–concrete structures are commonly found. These structures are characterized by simple construction and poor seismic performance, making them more vulnerable to localized damage under blasting-induced vibrations, such as the cracking of window walls or detachment of roof components. Despite their widespread presence in mining areas, relevant research on the dynamic responses of such masonry structures remains relatively scarce.

This paper, situated against the backdrop of open-pit mine production blasting, uses the TC-4850N vibration measurement instrument (Zhongke (Chengdu) Instruments Co., Ltd., Chengdu, China) for on-site monitoring to gather data on brick–concrete structures during blasting events. This study examines the vibration response characteristics of different components from the perspectives of PPV, main vibration frequency, and energy distribution. Using the ANSYS 2024 R2 numerical simulation software for three-dimensional modeling analysis, the hazardous frequencies and components are identified based on harmonic response. This study of the blasting vibration response characteristics of brick–concrete structures can provide a scientific foundation for establishing safety criteria for building blasting vibration. It also contributes to the optimization of blasting design parameters in open-pit mining operations. Furthermore, the findings offer a valuable reference for the vibration response of buildings in other similar blasting scenarios, demonstrating good engineering applicability and potential popularization value.

2. Project Background

2.1. Project Introduction

The experimental open-pit mine is located in China, and is one of the largest open-pit iron mines in the country. The mine covers a surface area of 3 km north–south and 1.5 km east–west, forming an essential part of the Jidong Iron Mine Area. It is classified as an Anshan-type sedimentary metamorphic iron ore deposit. The mine experiences an average of 5–6 blasting operations per day, primarily involving ore extraction and rock stripping. The blasting technique uses digital detonators for sequential hole initiation, with explosives including mixed ammonium oil and emulsion explosives. The borehole diameters range from 150 mm to 310 mm, with a diamond-shaped layout. The hole depths are between 6.5 m and 17 m, with a maximum overburden depth of 1–2 m. The spacing between holes is 4–8 m, and the spacing between rows is 3–7 m. The filling height is typically 4–8 m, with a maximum charge volume of 800 kg per section.

Due to the proximity of open-pit mines to surrounding villages and houses, it is essential to strictly control the scale of blasting and implement protective measures to prevent blasting vibrations from causing damage and ensure the normal operation of the mining area. The pump house within the open-pit mine, being a brick–concrete structure, serves as a typical building for studying the effects of blasting vibrations. The specific location of this brick–concrete structure is shown in Figure 1.

2.2. Blasting Vibration Monitoring Scheme

The blasting vibration monitoring system consists of a blasting vibration meter and a three-axis velocity sensor. To ensure high testing accuracy, the TC-4850N blasting vibration meter, developed by Zhongke (Chengdu) Instruments Co., Ltd., Chengdu, China, was used to capture blasting waves. This meter has a frequency range of 5–500 Hz, a sampling rate of 100–100,000 Sps, a resolution of 0.01 cm/s, and a maximum range of 35 cm/s, fulfilling the blasting vibration monitoring requirements. The sensor is a TCS-B3 type three-axis vibration velocity sensor produced by Chengdu Zhongke Measurement & Control Co., Ltd. This sensor can simultaneously monitor blasting waves in three directions, with a frequency response range of 1–500 Hz and a sensitivity of 26–28 V/m/s, meeting the testing requirements. The blasting vibration monitoring system is illustrated in Figure 2.

The brick–concrete structure measures 14.4 m in length, 4.7 m in width, and 4.2 m in height. Before the mine production blasting, the sensor placement areas were cleaned with a brush. The sensor was then bonded to the house’s surface using a mixture of water and gypsum powder to form a sticky paste. The TC-4850N blasting vibration meter was connected to the TCS-B3 three-axis vibration velocity sensor (Zhongke (Chengdu) Instruments Co., Ltd., Chengdu, China) via signal transmission lines, with the X-axis of the sensor pointing towards the blasting area. Parameters such as the sampling rate and sampling time were set, and the data acquisition function was activated to enter a waiting state for triggering.

The open-pit mine extends in a north–south direction, with the blasting area mainly situated between the −202 and −262 m levels on the western side of the mine. Two vibration monitoring schemes were put in place, with the surface monitoring point F, located on the south side of the house, serving as the primary monitoring point. Vibration instruments were installed at various heights on the structural column and along the horizontal direction of the brick wall. The arrangement of the surface monitoring points is depicted in Figure 3. Monitoring points C₁, C₂, and C₃ were positioned at different heights on the structural column, as depicted in Figure 4. Monitoring points W₁, W₂, and W₃ were situated along the horizontal direction of the southern brick wall. The layout of these monitoring points is illustrated in Figure 5.

3. Vibration Monitoring and Analysis of Building Components

3.1. Monitoring and Analysis of Blasting Vibration of the Structural Column Component

The TC-4850N vibration meter was set up according to Figure 4 to collect five sets of blasting vibration signals. Each set includes data for both the horizontal (radial and tangential) and vertical components. The monitoring data for different measurement points on the structural column are shown in

Table 1. Blasting vibration monitoring data of different measuring points of the structural column.

Time/s	Maximum Explosive Charge per Delay/kg	Blast Center Distance/m	Monitoring Points	Horizontal Radial Direction (X Direction)		Horizontal Tangential Direction (Y Direction)		Vertical Direction (Z Direction)
				PPV/ (cm/s)	Main Frequency/ Hz	PPV/ (cm/s)	Main Frequency/ Hz	PPV/ (cm/s)	Main Frequency/ Hz
1	490	581.78	F	0.058	9.22	0.063	11.02	0.062	9.46
		581.80	C1	0.059	10.22	0.082	19.69	0.071	14.71
		581.83	C2	0.075	13.09	0.124	17.01	0.082	14.88
		581.86	C3	0.096	15.82	0.153	20.66	0.084	14.71
2	500	591.31	F	0.064	8.72	0.049	20.01	0.088	14.24
		591.32	C1	0.071	9.92	0.055	19.69	0.091	19.08
		591.35	C2	0.076	10.25	0.092	20.13	0.112	19.08
		591.38	C3	0.094	14.04	0.125	20.49	0.13	19.53
3	850	328.46	F	0.234	22.35	0.175	27.39	0.268	21.74
		328.55	C1	0.229	22.52	0.324	25.25	0.337	21.74
		328.65	C2	0.326	22.52	0.492	23.81	0.414	22.32
		328.76	C3	0.427	23.36	0.595	22.52	0.419	22.52
4	325	198.52	F	0.271	18.61	0.174	11.53	0.156	26.85
		198.79	C1	0.282	18.82	0.235	14.29	0.304	19.38
		199.08	C2	0.49	19.53	0.410	19.23	0.380	19.37
		199.37	C3	0.687	20.83	0.526	21.55	0.396	19.38
5	450	219.32	F	0.456	22.09	0.711	29.85	0.924	43.96
		219.66	C1	0.517	19.38	0.719	30.86	0.933	21.19
		220.01	C2	0.762	19.69	0.946	22.73	1.135	21.01
		220.36	C3	1.066	20.16	1.150	19.08	1.134	20.83

.

Figure 6 illustrates the variation pattern of PPV at the monitoring points on the structural column. Figure 7 shows the amplification coefficients of the PPV at different measurement points, which are the ratios of the PPV at these points to those at the surface monitoring points.

As shown in Figure 6 and Figure 7, as the height of the monitoring points increases from the ground, the PPV in both the horizontal (radial and tangential) and vertical directions show a gradual increase. Compared to points C₁ and C₂, point C₃ exhibits a greater amplification coefficient for its PPV relative to the surface monitoring point. The amplification coefficients of the PPV at different points are linearly related to elevation, indicating a significant elevation amplification effect. This may be due to the weak constraint of the foundation on the superstructure, which allows for an increased vibration space in the horizontal radial and tangential directions of the structural columns. Additionally, during the propagation of blasting waves from blasting, the interaction with different parts of the building produces a superposition effect, which becomes more pronounced as the height increases, leading to an increase in peak vibration velocities.

The variation pattern of the main frequency at the structural column monitoring points is illustrated in Figure 8. The frequency ratio coefficients, which represent the ratio of the main vibration frequencies at different monitoring points to those at the surface monitoring point, are shown in Figure 9. As can be seen from Figure 8 and Figure 9, the main frequencies at different monitoring points in both the horizontal (radial and tangential) and vertical directions are primarily concentrated in the 15–25 Hz range, with relatively minor variations. Most of the frequency ratio coefficients at different monitoring points are greater than 1. This suggests that, during the propagation of blasting waves along the structural column, both amplification and attenuation effects on the main frequencies occur. The primary reason for this is that the column undergoes multimodal vibration under blasting vibrations, with different vibration modes interacting, leading to more complex changes in the main vibration frequencies.

The contour lines and fitting relationships of the PPV at the structural column and surface monitoring point are shown in Figure 10 and Figure 11, respectively. Figure 10 shows that when the PPV at the surface is constant, then, as the elevation increases, the PPV in both the horizontal (radial and tangential) and vertical directions of different monitoring points gradually increases. When the PPV at the surface exceeds 0.5 cm/s, the vibration response at different monitoring points is relatively significant. When the elevation is fixed, the higher the PPV at the surface, the greater the PPV in both the horizontal and vertical directions at different monitoring points, indicating a linear relationship between the PPV at the surface and different monitoring points. This is consistent with the statistical relationship shown in Figure 11.

Due to the complexity of the mine environment, topographical and geological factors, vibrometer errors, and other reasons, the measured blast vibration signal will be contaminated. In order to obtain the real blasting waves, they need to be measured using blasting vibration signal noise reduction. Before analyzing the energy distribution characteristics of blasting waves, the measured blasting waves were processed using the method described in reference [20] to filter out most high-frequency noise and retain the useful components of the measured signal. The vibration signals from the C₁, C₂, and C₃ measurement points, under identical blasting conditions, were selected for analysis after noise reduction. The sampling frequency of the blasting vibration monitoring instrument is 5000 Hz. According to Shannon’s sampling theorem, the Nyquist frequency is 2500 Hz. The signal was decomposed into nine levels using the db8 wavelet basis, resulting in ten frequency bands. The energy distribution of these bands is shown in

Table 2. Energy distribution of different frequency bands at the monitoring points of the structural column.

Number of Frequency Bands	Frequency Band/Hz	Energy/(cm/s)2			Proportion/%
		Signal C1	Signal C2	Signal C3	Signal C1	Signal C2	Signal C3
1	0~4.8828	0.252	0.263	0.224	5.291	4.084	2.621
2	4.8828~9.7656	1.374	1.431	1.459	28.847	22.224	17.074
3	9.7656~19.5313	1.021	1.151	1.813	21.436	17.875	21.217
4	19.5313~39.0625	1.097	2.250	3.674	23.032	34.943	42.996
5	39.0625~78.125	0.665	0.666	0.689	13.962	10.343	8.063
6	78.125~156.25	0.286	0.585	0.594	6.005	9.085	6.951
7	156.25~312.5	0.067	0.093	0.092	1.407	1.444	1.077
8	312.5~625	0.000	0.000	0.000	0	0	0
9	625~1250	0.001	0.000	0.000	0.021	0	0
10	1250~2500	0.000	0.000	0.000	0	0	0
amount to		4.763	6.439	8.545	100	100	100

. An analysis of variance (ANOVA) was conducted to evaluate the differences in energy proportions across different measurement points. The results indicate that the variation among the groups was not statistically significant (F = 1.56 × 10⁻⁹, p = 1.00), suggesting a consistent energy distribution trend across all monitoring locations.

As shown in Table 2, The energy of different signals is primarily concentrated below 312.5 Hz, with the energy in the 312.5~2500 Hz band nearly zero, indicating that most high-frequency noise has been filtered out. As the height of the measurement points increases, the total energy of the blasting vibration signal gradually increases, demonstrating an elevation amplification effect. The total energy at point C₂ is approximately 1.35 times higher than at point C₁, and it is about 1.79 times higher at point C₃. The 19.5313~39.0625 Hz band shows a significant energy amplification, followed by the 9.7656~19.5313 Hz band. The energy of different signals is mainly concentrated in the 4.8828~39.0625 Hz band, with the C₁ signal primarily concentrated in the 4.8828~9.7656 Hz band and the C₂ and C₃ signals mainly concentrated in the 19.5313~39.0625 Hz band.

The instantaneous energy spectrum clearly illustrates the relationship between time and instantaneous energy. The instantaneous energy spectrum of the monitoring points is shown in Figure 12. As illustrated in Figure 12, the horizontal radial instantaneous energy at different monitoring points is mainly distributed within the 0.5~1.5 s time interval. Multiple peaks appear at different time points due to the small inter-hole delay time of 24 ms, which causes multiple adjacent peaks to form the main peak segment. The timing of the instantaneous energy peaks varies among different monitoring points, but they are all close to the PPV moments of the actual blasting vibration signals measured at each point. Taking the instantaneous energy peak at C₁ as a reference, the instantaneous energy peaks at C₂ and C₃ show varying degrees of amplification, consistent with the variation pattern of the PPV. This is because the greater the PPV of the point, the greater the dynamic stress generated in the structure, and thus the more energy it carries and releases.

3.2. Monitoring and Analysis of Blasting Vibration of the Masonry Wall Component

In Figure 5, three measurement points are equipped with blasting vibration monitoring instruments to collect the vibration signals during production blasting. The data on the vibration monitoring at different measurement points of the brick wall are shown in

Table 3. Blasting vibration monitoring data of different monitoring points of the brick wall.

Time/s	Maximum Explosive Charge per Delay/kg	Blast Center Distance/m	Monitoring Points	Horizontal Radial Direction (X Direction)		Horizontal Tangential Direction (Y Direction)		Vertical Direction (Z Direction)
				PPV/ (cm/s)	Main Frequency/ Hz	PPV/ (cm/s)	Main Frequency/ Hz	PPV/ (cm/s)	Main Frequency/ Hz
1	700	303.41	F	0.083	16.34	0.082	16.89	0.112	22.32
		303.75	W1	0.137	16.69	0.156	19.08	0.116	16.03
		308.72	W2	0.105	19.23	0.334	22.94	0.065	27.17
		313.69	W3	0.107	20.83	0.151	19.23	0.125	22.94
2	800	539.83	F	0.11	22.12	0.178	24.27	0.114	25.77
		540.03	W1	0.124	22.94	0.214	24.04	0.124	20
		545.02	W2	0.099	21.55	0.319	24.27	0.098	19.53
		550.01	W3	0.075	17.70	0.204	22.12	0.075	24.27
3	200	565.31	F	0.04	23.36	0.056	22.32	0.036	21.01
		565.41	W1	0.049	21.74	0.052	18.380	0.039	21.37
		570.35	W2	0.040	25.00	0.088	22.94	0.028	18.94
		575.3	W3	0.019	29.76	0.022	18.80	0.022	21.93
4	200	735.51	F	0.014	9.9	0.01	12.74	0.009	13.7
		735.59	W1	0.025	22.12	0.021	21.19	0.023	23.36
		740.17	W2	0.024	17.12	0.045	19.41	0.015	23.58
		744.76	W3	0.025	14.29	0.022	20.66	0.020	20.16
5	600	303.41	F	0.069	32.47	0.083	14.71	0.081	17.01
		303.76	W1	0.095	16.67	0.133	19.23	0.109	20.16
		308.72	W2	0.093	21.01	0.297	25.25	0.062	17.12
		313.69	W3	0.091	24.04	0.153	16.78	0.085	18.52

.

The variation patterns of the PPV at different monitoring points of the brick wall are illustrated in Figure 13. The ratio of the PPV at different monitoring points (specifically, the ratio of the PPV at W₂ and W₃ points to that at W₁ point) is depicted in Figure 14.

As shown in Figure 13 and Figure 14, the PPV in the horizontal tangential direction first increases and then decreases. Specifically, the PPV at the middle of the wall component is higher than at the ends, with a ratio greater than 1. This is because the W₁ and W₃ points are near the edges of the wall and the columns, while the W₂ point is closer to the middle of the wall. Consequently, the W₂ point has more freedom in the horizontal tangential direction compared to the W₁ and W₃ points. The vertical PPV at different monitoring points generally first decreases and then increases, meaning that the PPV at the middle of the wall is lower than at the ends, with a ratio less than 1. There is no clear pattern in the variation in the PPV in the horizontal radial direction. However, the PPV in the horizontal radial direction at the W₃ measurement point is lower than that at the W₁ point, indicating a decaying trend in the horizontal radial PPV.

The distribution of the main frequencies of blasting waves from different monitoring points on a brick wall is shown in Figure 15. The frequency ratio coefficients for different monitoring points on the brick wall are illustrated in Figure 16. The frequency ratio coefficient is the ratio of the main frequency of the W₂ and W₃ points to that of the W₁ point.

As shown in Figure 15 and Figure 16, the main frequencies in different directions are primarily concentrated in the 15–30 Hz range. The main frequencies in the horizontal radial and vertical directions are relatively dispersed, while those in the horizontal tangential direction are more concentrated. This suggests that there is no clear propagation pattern for the main vibration frequencies of blasting waves from different directions on a brick wall. The frequency ratio coefficients at different monitoring points vary around 1, indicating that both amplification and attenuation effects of blasting waves coexist. This may be due to the combined effects of the propagation and reflection characteristics of blasting waves, the natural frequency of the brick wall, and the damping effect.

The contour lines of the PPV at the brick wall and surface monitoring points are shown in Figure 17. Figure 17 shows that when the PPV at the surface is constant, as the horizontal distance increases, the horizontal tangential PPV at different monitoring points first increases and then decreases. The radial PPV generally show a decaying trend, while the vertical PPV generally show a decreasing trend followed by an increasing trend. When the PPV at the surface exceeds 0.08 cm/s, the vibration responses at different monitoring points are relatively significant.

The fitting relationships of the PPV at the brick wall and surface monitoring points are shown in Figure 18. Figure 18 also indicates that there is a linear relationship between the PPV at the surface and at different monitoring points, suggesting that the PPV in both the horizontal and vertical directions at different monitoring points of the wall components increase with the increase in the PPV at the surface, consistent with the trends observed in Figure 17.

The blasting vibration signals at the horizontal radial points of W₁, W₂, and W₃ under the same blasting conditions were analyzed using the method described in reference [14] to reduce noise in the measured blasting waves and to analyze the propagation patterns of energy along the brick wall. The energy distribution across different frequency bands is shown in

Table 4. Energy distribution of different frequency bands at the monitoring points of the brick wall.

Number of Frequency Bands	Frequency Band/Hz	Energy/(cm/s)2			Proportion/%
		Signal W1	Signal W2	Signal W3	Signal W1	Signal W2	Signal W3
1	0~4.8828	0.209	0.211	0.191	3.256	4.06	5.715
2	4.8828~9.7656	1.252	1.061	0.946	19.508	20.416	28.306
3	9.7656~19.5313	1.029	0.915	0.601	16.033	17.606	17.983
4	19.5313~39.0625	2.631	2.235	0.864	40.994	43.006	25.853
5	39.0625~78.125	0.623	0.529	0.512	9.707	10.179	15.32
6	78.125~156.25	0.578	0.174	0.168	9.006	3.348	5.027
7	156.25~312.5	0.094	0.072	0.060	1.465	1.385	1.795
8	312.5~625	0.000	0.000	0.000	0	0	0
9	625~1250	0.002	0.000	0.000	0.031	0	0
10	1250~2500	0.000	0.000	0.000	0	0	0
amount to		6.418	5.197	3.342	100	100	100

. The ANOVA results indicate that the variation among the groups was not statistically significant (F = 6.48 × 10⁻⁹, p = 1.000), suggesting a consistent energy distribution trend across all monitoring locations (W₁, W₂, W₃). As shown in Table 4, as the horizontal distance increases, the total energy of the blasting vibration signals gradually decreases. The energy at point W₂ is 1.35 times lower than that at point W₁, and the energy at point W₃ is 0.52 times lower than that at point W₁. This is because the blasting waves’ front expands with increasing distance, leading to a gradual decrease in energy per unit area. During the propagation of the blasting waves, high-frequency components decay faster than low-frequency components.

The energy proportion of the horizontal radial signal is shown in Figure 19. The maximum energy proportion of W₁ and W₂ signals is mainly concentrated in the band of 19.5313–39.0625 Hz, whereas the W₃ signals are mainly concentrated in the band of 4.8828–9.7656 Hz. As the blasting wave propagation distance gradually increases, the energy gradually concentrates towards the lower-frequency bands, which are close to the intrinsic frequency of the structure. This is more likely to cause structural resonance, which is more harmful. The energy of the blasting waves at different monitoring points on the wall components is primarily below 312.5 Hz, with the peak energy of the W₁ and W₂ signals distributed in the 19.5313~39.0625 Hz band and the peak energy of the W₃ signal distributed in the 4.8828~9.7656 Hz band.

The instantaneous energy spectrum of the brick wall monitoring points is shown in Figure 20. As illustrated, the instantaneous energy peak at different monitoring points varies significantly. Point W₁ has the highest instantaneous energy peak of 0.147 J, while Point W₃ has the lowest, 0.076 J. The instantaneous energy peaks at different points typically appear after 0.5 s due to the residual instantaneous energy following the initial wave. This residual energy is further amplified by the superposition effect of blasting waves from other boreholes. The vibration velocities at different points do not coincide with the timing of the instantaneous energy peaks, indicating that the instantaneous energy is influenced by the PPV, its duration, and the main frequency.

4. Dynamic Response of a Building Under Blasting Vibration

4.1. Numerical Model Establishment

Based on the actual dimensions of the brick–concrete structure, a three-dimensional numerical model (14.4 m × 4.7 m × 4.2 m) was established to study the dynamic response of the house under blasting vibration. The numerical simulation software used was ANSYS 2024 R2. The finite element type was SOLID 186 three-dimensional high-order solid cells. The three-dimensional numerical model is shown in Figure 21.

The numerical model consists of components such as ring beams, walls, columns, and roofs. The walls are solid masonry walls, with beams and columns having a cross-sectional size of 240 mm × 240 mm. The inner and outer walls are 240 mm thick, and the floor slab is 100 mm thick. The material of the numerical model is C30 concrete, a linear elastic isotropic material with an elastic modulus of 30 GPa, a Poisson’s ratio of 0.15, and a density of 2700 kg/m³. The masonry has a density of 1900 kg/m³, an elastic modulus of 27 GPa, and a Poisson’s ratio of 0.15. A hexahedral mesh was created for the numerical model. In order to balance the computational accuracy and resources, the mesh size was set to 10 cm. Each part of the house was simulated as a whole connection using Bonded Contact. The bottom of the numerical model was fixedly supported. Dynamic loads were applied in the horizontal radial direction, horizontal tangential direction, and vertical direction. The mesh division and loading-added way of the numerical model is shown in Figure 22.

4.2. Harmonic Response Analysis of Building Components and Identification of Natural Frequency

4.2.1. Harmonic Response Analysis of House Components

Modal analysis is a fundamental method in dynamic analysis, capable of determining the natural frequencies and corresponding modes [21,22]. By applying zero-displacement constraints to the bottom of the ground beam in the numerical model, modal analysis is performed to obtain the natural frequency and mode of the building. The first ten natural frequencies of the building are listed in

Table 5. The first ten natural frequencies of the house.

Order	1	2	3	4	5	6	7	8	9	10
Frequency/Hz	6.99	8.7	9.41	11.3	12.7	12.96	13.2	13.25	14.61	15.32

.

The first ten mode shapes of the house are shown in Figure 23. According to

Table 6. PPV and corresponding frequency of components.

Component	X Direction		Y Direction		Z Direction
	Frequency/Hz	PPV/(cm/s)	Frequency/Hz	PPV/(cm/s)	Frequency/Hz	PPV/(cm/s)
Window wall	6.991	0.055	6.991	22.073	6.991	0.417
	13.138	0.137	11.124	14.164	11.483	0.179
	14.384	0.111	—	—	13.227	0.142
Gate wall	6.991	0.752	6.991	0.384	6.991	0.243
	11.358	5.032	8.918	0.245	12.896	0.251
	13.138	7.448	12.592	0.463	—	—
Longitudinal wall	6.991	0.019	6.991	21.139	6.991	0.359
	14.384	0.101	11.483	10.780	11.402	0.152
	—	—	—	—	13.138	0.132
Pillar	6.991	0.341	8.777	0.250	8.639	0.112
	13.138	0.468	12.592	0.321	11.402	0.059
	—	—	—	—	13.227	0.084
Beam	13.317	0.303	6.991	0.598	6.991	0.642
	14.383	0.274	8.820	0.606	11.402	0.267
	—	—	12.642	0.585	—	—
Roof	13.317	0.238	6.991	0.594	6.991	53.680
	14.384	0.225	8.855	0.581	11.402	10.606
	—	—	12.642	0.668	—	—

, the natural frequencies of the house increase from 6.99 Hz at the first order to 15.32 Hz at the tenth order. To prevent resonance between the blasting vibration and the building structure, the blasting vibration frequency should not be close to the natural frequencies of the house. As shown in Table 6 and Figure 23, the gate wall mainly exhibits horizontal radial deformation, while the window wall and longitudinal walls mainly exhibit horizontal tangential deformation. The roof primarily shows vertical deformation. This is because the gate wall and transverse walls have greater horizontal radial freedom, the window wall and longitudinal walls have greater horizontal tangential freedom, and the roof has a larger vertical freedom.

The main frequency of the blasting waves from open-pit deep-hole blasting ranges from 10 to 60 Hz. As shown in Table 6, the first ten natural frequencies of the house are between 6 and 16 Hz, which overlaps with the main frequency of the blasting waves from open-pit deep-hole blasting. Therefore, it is necessary to study the vibration response of the house under different loads using harmonic response analysis. This paper uses the modal superposition method to conduct harmonic response analysis on the house using the ANSYS numerical simulation platform. The harmonic response analysis covers a sweep frequency range of 0–100 Hz, with a load step of 5 Hz, to extract the velocity-frequency response curves of the building components in different directions [23]. The horizontal tangential response curves of different components are shown in Figure 24. The PPV and corresponding frequencies of different components are shown in Table 6.

As indicated in Table 6, the horizontal radial PPV of gate walls and columns are relatively high, while the horizontal tangential PPV of window walls and longitudinal walls are higher. The vertical PPV of the roof are also significant, which aligns with the deformation analysis of the house’s modal behavior. However, the peak values of certain components at specific frequencies have significantly increased. According to Figure 23 and Table 6, when the mode direction is aligned with the excitation direction, the components tend to exhibit more pronounced responses. For instance, the PPV of the window wall in the horizontal tangential direction is approximately 21 times higher than that of the horizontal radial PPV, and the PPV of the gate wall in the horizontal radial direction is approximately 29 times higher than that of the horizontal tangential PPV. Therefore, window walls, gate walls, longitudinal walls, and the roof can be considered as hazardous components of the house. The maximum PPV of the window wall, longitudinal wall, and roof components all correspond to a frequency of 6.991 Hz, indicating that the fundamental frequency significantly influences the dynamic response of the components. As shown in Table 6, under harmonic excitation at frequencies of 6.991 Hz, 11.124 Hz, 11.483 Hz, and 13.138 Hz, the PPV in specific directions of the window wall, door wall, longitudinal wall, and roof increased significantly. This indicates that when the dominant frequency of the blasting seismic wave approaches the house’s natural frequency, the vibration of the structural components is markedly amplified. Based on the house’s vibration mode and its first ten natural frequencies, the frequencies of 6.991 Hz, 11.302 Hz, and 13.202 Hz can be identified as critical or hazardous. Accordingly, the window walls, door walls, longitudinal walls, and roof should be regarded as vulnerable components.

4.2.2. Identification of Natural Frequency of House Components

As can be seen from Table 6 and Figure 24, multiple peaks appear in the response curves of different components. The frequency corresponding to the PPV should be identified to determine whether it is the natural frequency of the component, and the reasons for the peaks appearing in the component should be analyzed.

According to the literature [23], when the phase angle corresponding to the PPV of a component changes dramatically to around 180°, it can be determined that this is the component’s natural frequency. This can be identified by analyzing the response curves of other components. The natural frequencies of different components are listed in

Table 7. Natural frequency of components and corresponding phase angle.

Component	X Direction		Y Direction		Z Direction
	Frequency/Hz	Phase Angle/°	Frequency/Hz	Phase Angle/°	Frequency/Hz	Phase Angle/°
Window wall	14.384	169.890	6.991	175.820	—	—
Gate wall	—	—	8.918	176.680	—	—
Longitudinal wall	6.991	179.690	11.483	178.630	—	—
Pillar	6.991	178.950	8.855	177.860	8.777	179.250
Beam	14.384	178.720	8.820	176.420	—	—
Roof	14.384	175.730	8.855	177.440	—	—

. Figure 25 shows the ‘vibration velocity-frequency’ response curve and phase angle change for the horizontal tangential direction of the window wall component. As shown in Figure 25, at a frequency of 6.991 Hz, the vibration velocity of the window wall component reaches its peak, with the phase angle rapidly changing from −176.91° to 179.87° (approaching 180°), a change of 356.78° (approaching 360°). Therefore, 6.991 Hz can be considered the natural frequency of the window wall component. At a frequency of 11.124 Hz, the phase angle changes gradually, but the vibration velocity of the window wall component peaks. This may be due to the natural frequency of the longitudinal wall component being 11.483 Hz, which is close to 11.124 Hz. Due to the mutual coupling of spatial vibration systems among the components, the vibration of the longitudinal wall component can drive significant vibrations in the window wall through connections between structures, resulting in two peaks on the response curve.

As shown in Table 6 and Table 7, the PPV corresponding to the natural frequency of the component is not the maximum vibration velocity in the response curve. For example, the horizontal tangential response curve and phase angle variation in the longitudinal wall component are illustrated in Figure 26. The frequency 11.483 Hz corresponds to a significant change in the phase angle, indicating that it is the natural frequency. The PPV at this frequency is 10.780 cm/s, while the maximum vibration velocity 21.139 cm/s in the response curve corresponds to a frequency of 6.991 Hz.

The natural frequencies of different components are compared to the first ten natural frequencies of the house, as shown in Figure 27. It can be seen that the natural frequencies of different components closely match or correspond to the first ten natural frequencies of the house. This indicates that the overall natural frequency of the house is not controlled by a single component, but is a comprehensive performance of the coupling effect of multiple components. The natural frequencies of these components are obviously different, indicating that the participation degree and dominant modes of each component in the overall dynamic response of the house are different. Compared to other components, the window wall and longitudinal wall have significantly lower natural frequencies, which are close to the overall low-order natural frequency of the house. The natural frequencies of the column, beam, and the roof correspond to the middle-order and high-order natural frequencies of the house. Therefore, the overall natural frequency of the house can be regarded as composed of the natural frequencies of different components. The natural frequencies of different components not only determine their own vibration characteristics, but also affect the dynamic behavior of the whole structure through a coupling relationship.

5. Conclusions

This paper integrates theoretical analysis, blasting vibration monitoring, and numerical simulation to investigate the impact of blasting vibrations on brick–concrete structures, leading to the following primary conclusions. The natural frequencies of different components were identified, and the hazardous frequencies and hazardous components of the houses were determined. The findings offer both theoretical guidance and an engineering reference for establishing safety assessment standards for brick–concrete structures subject to blasting vibration.

(1) When blasting waves propagate along the structural column and brick wall, the PPV and the energy characteristics show obvious differences in the horizontal and vertical directions. The PPV at the surface monitoring points and those at the house exhibit a linear relationship.

(2) The fundamental frequency of the building (6.991 Hz) significantly influences the PPV of different components. Amounts of 6.991 Hz, 11.302 Hz, and 13.202 Hz can be regarded as the critical frequencies for the house. The window walls, gate walls, longitudinal walls, and roof can be considered to be critical components.