Vibration reduction effect of retaining pile structure under the action of damping hole

Abstract

In the context of mitigating the impact of blasting-induced seismic waves on excavation processes and reducing the vibrational load on retaining pile structures, this study examines the influence of predetermined damping hole parameters on the damping effect. It also evaluates the protective efficacy of damping holes on retaining pile structures. Leveraging the foundation pit project at the Julong Avenue Station of Wuhan Metro Line 7 as a reference, on-site blasting construction was monitored to obtain vibration velocities at the top of the retaining pile structure. A numerical calculation model for blasting in the foundation pit was established using LS-DYNA software, and its reliability was verified through the integration of on-site monitoring data at the top of the retaining pile. Multiple damping hole excavation schemes were devised, and their effects on the damping effectiveness were analyzed with respect to various parameters. Safety criteria for the stability of the retaining pile structure were proposed based on the ultimate tensile stress criterion, ultimate shear stress criterion, and Mohr’s criterion. Under the optimized scheme, the dynamic response characteristics of the retaining pile structure were analyzed, and the practical application effects on-site were observed. The research findings indicate that the depth, spacing, and number of damping holes have a significant impact on the damping effect. The safety criterion for the vibrational velocity of the retaining pile structure during blasting is determined to be 26.10 cm/s. Under the optimized scheme, the vibrational velocities at various monitoring points on the retaining pile structure all fall within the safe range, with a maximum reduction rate of 30.9%.

Keywords

Vibration control retaining pile damping holes vibration damping effect safety criteria

Introduction

With the rapid development of urban underground transportation projects and high-rise and super-high-rise buildings, numerous deep excavation projects have emerged in urban areas. During the excavation of deep excavation rock layers, blasting excavation methods are commonly employed. The retaining pile structures of deep excavations are susceptible to the impact and vibration caused by blasting, leading to damage to the retaining piles and posing a significant threat to the stability of the excavation pit (Yang et al., 2023; Zheng et al., 2021; Zhu et al., 2015). In the process of blasting construction, vibration reduction measures are typically classified into two categories. The first category focuses on reducing the energy of blast-induced stress waves at their source. This involves actions such as controlling the maximum amount of explosives used in a single blast, opting for low-power explosives with reduced detonation velocities, and minimizing resistance lines (Gao et al., 2023; Navarro Torres et al., 2018; Rodríguez et al., 2021; Tian et al., 2019). However, it is noteworthy that these measures, while effective in vibration reduction, may concurrently result in decreased construction efficiency, thereby impacting the overall construction progress. The second category of vibration reduction measures is geared towards diminishing the energy of blast-induced stress waves along their propagation path. This encompasses strategies like the placement of damping holes, damping ditches, and pre-split cracks between the vibration source and the protected area. By altering the physical properties of the medium through which blast seismic waves propagate, stress waves undergo phenomena such as reflection and refraction at medium discontinuities (Chapman and Ebrary, 2004; Kennett, 1986; Sato and Fehler, 2012). These phenomena lead to a reduction in wave energy, decreased amplitude, and diminished vibrational velocity, ultimately achieving the desired vibration reduction effect (Gerald et al., 1979; Padhy and Subhadra, 2010; Ru-Shan, 1982). Among these measures, damping holes have gained widespread acceptance due to their simplicity in construction, independence from terrain constraints, and their proven effectiveness in vibration reduction(Chen et al., 2020; Li et al., 2020; Song et al., 2019; Zhang et al., 2021).

Currently, researchers have studied the damping effects of damping holes through theoretical analysis, on-site experiments, model testing, and numerical simulations.

In terms of theoretical analysis: Boarn et al. (Baron and Matthews, 1961, 1962) investigated the stress field generated in a medium when stress waves impinge upon a cylindrical cavity using integral transformation and wave function expansion methods, and derived expressions for isotropic stresses. Peralta et al. (Peralta et al., 1966) conducted research on the vibrational response issues encountered by seismic waves when propagating through infinite elastic solid spaces in the presence of fractures. Datt (Datta, 1978) employed the method of matched asymptotics to investigate the scattering of longitudinal waves, SV waves, and SH waves by cylindrical voids within a semi-infinite space. Duan et al. (Duan et al., 2022) utilized the method of gray relational analysis to study the primary and secondary relationships among various parameters of damping holes and their impact on damping effectiveness. Building upon the foundation of investigating the external elastic dynamic problems of circular cavities in a planar elastic body using the Fourier transform method, Eringen (Eringen, 1961) conducted further research to explore the propagation of elastic waves within circular cavities under the influence of impacts, explosions, and moving loads. In terms of experimental analysis: Zhu et al. (Zhu et al., 2023) conducted model experiments by applying damping holes to tunnel cross-sections to investigate the influence patterns of damping hole parameters on damping effectiveness. Uysal et al. (Uysal et al., 2008) conducted a series of field experiments to investigate the effect of whether damping holes are filled with water on the peak particle velocity.

In terms of numerical simulation: Park et al. (Park et al., 2009) employed two numerical simulation methods, Discrete Element Method (DEM) and Nonlinear Hydrocode, to analyze the damping effectiveness of damping hole parameters on ground vibrations. Bian et al. (2014) employed UDEC to investigate the influence of damping holes on ground vibrations in various directions. Lei et al. (Lei et al., 2014) utilized LS-DYNA to establish a 3D numerical blasting model with damping holes. Simulation results indicate that increasing the diameter of damping holes and reducing the spacing between them significantly enhances the damping efficiency and broadens the vibration reduction zone. Zhu et al. (Zhu et al., 2021) used the numerical calculation software ANSYS/LS-DYNA to establish the calculation model of pipeline blasting vibration with different corrosion degrees. Authors analyzed the blasting vibration characteristics and stress characteristics of corroded pipelines, and studied the failure mode of corroded gas pipelines under blasting vibration. Through small-scale blasting tests, Jiang et al. (2020a) analyzed the attenuation law of blasting vibration along the surface and the vibration velocity response characteristics of the building structure, and established a LS-DYNA numerical model to analyze and evaluate the safety of high-rise buildings under blasting vibration.

In the above-mentioned studies, the interaction between blasting seismic waves and cavities is highly intricate, and numerous uncontrollable factors during the blasting process hinder in-depth theoretical research. Testing, experiments, and numerical simulations can more effectively capture the role of damping holes during the blasting process. Previous researchers have often employed experimental methods and simplified numerical models to study the damping effects of these holes. However, such approaches lack a safety assessment specific to the protected structures, making it difficult to accurately assess the relationship between damping hole parameters and the damping effects on the protected buildings. Existing studies indicate that the safety vibration speed of retaining piles is associated with the angle of incidence of seismic waves and the material properties.

Based on this, the present study relies on the blasting project at the Julong Avenue Station excavation of Wuhan Metro Line 7 to monitor on-site blasting vibrations and analyze vibration response patterns. Using LS-DYNA software, a detailed numerical computational model is established, incorporating elements that were overlooked by previous researchers, such as excavation retaining piles, reinforcement, and concrete supports. The analysis explores the impact of damping hole parameters on the damping effect. Through theoretical analysis, safety criteria for the stability of retaining pile structures are proposed based on the limit tensile stress criterion, limit shear stress criterion, and Mohr’s criterion (Jiang et al., 2018, 2020b, 2021a, 2021b, 2022, 2023). The paper analyzes the dynamic response characteristics and application effects of retaining pile structures under an optimized damping hole scheme. The research findings can provide reference and guidance for the design of blasting damping schemes.

Deep excavation blasting construction project and on-site testing

Project introduction

The Julong Avenue Station is the ninth station of the Wuhan Metro Line 7 project. Serving as a three-line interchange station connecting Line 7, Line 2, and the planned Line 18, this station has been designed as an underground three-level island platform station. The specific location of the station is illustrated in Figure 1. The station’s main structural envelope has a total length of 734 m, with an open excavation section measuring 389 m and a bored tunnel section spanning 345 m. The overall width of the envelope is 23.3 m, and it is situated at a depth of approximately 29.4 m. The total station area is 42,557 m², comprising a main building area of 29,792 m², an ancillary building area of 9047 m², and a bored tunnel section with a tunneling area of 3718 m². The station is situated on the third-level alluvial terrace of the Yangtze River, characterized by the presence of relatively thick rock layers. The bedrock consists of heavily weathered dolomite and moderately weathered dolomite. The burial depth ranges from 15.8 m to 40.1 m, with a rock mass quality rating of Level IV. The rock is relatively hard in texture, necessitating the use of blasting techniques during excavation.

Figure 1.

Julong avenue station location map.

In consideration of the specific safety requirements for this blasting operation, as well as the environmental and topographical conditions of the blasting area, and taking into account the existing equipment and construction technology, a deep-hole bench blasting method with a diameter of ϕ100 mm has been adopted. This method utilizes a double-row “flower-shaped” hole pattern and employs coupled explosives. Explosives used in this operation consist of Type 2 rock emulsion explosives. Each borehole is loaded with a continuous loading structure comprising one detonating cord detonator. Blasting is initiated on a per-hole basis, with a 50 ms delay between holes and a 110 ms delay between rows. Blasting parameters are listed in Table 1.

Table 1.

Deep-hole bench blasting parameters.

Bench height (m)	Resistance line (m)	Hole depth (m)	Charge length (m)	Blockage length (m)	Hole spacing (m)	Row distance (m)	Single-hole charge (kg)
5.0	1.0	6.0	4.0	2.0	2.6	2.0	15.0

On-site monitoring

During the excavation and blasting construction at the Julong Avenue Station pit, a total of six monitoring points were strategically positioned around the pit area in a “T” formation, as illustrated in Figure 2. Among these monitoring points, D1 to D5, a total of five instruments, are positioned along the edge of the excavation pit with a spacing of 10 m between each instrument. D3 is aligned with the blast holes, and there is a 7.6-m gap between D3 and D6. Gypsum was used to secure the sensors to the ground surface around the pit. The x-direction points to the true north, the y-direction points towards the interior of the pit, and the z-direction is oriented vertically upward. For on-site monitoring, the TC-4850 blasting monitor and its associated three-axis velocity sensors were selected as the instruments for testing the seismic effects of the blasting.

Figure 2.

Measurement points arrangement and field observation.

The Julong Avenue Station excavation pit employs a foundation system comprising drilled retaining piles and an internal support structure. The internal support system consists of reinforced concrete supports for the first and third layers, as well as steel pipe supports for the second and fourth layers. As depicted in Figure 2, the existing pit excavation and blasting plan have led to damage to the retaining piles at the construction site. Retaining piles are a critical component of the pit support structure, and their stability directly impacts the overall safety of the excavation. To mitigate the damage caused by blasting vibrations to the retaining pile structure, vibration reduction measures need to be implemented.

The vibration velocities at each monitoring point are detailed in Table 2, with D3 recording the highest blasting vibration velocity at 9.19 cm·s⁻¹. Overall, as the distance from the blast source increases, the blasting vibration velocities at the monitoring points gradually decrease. Monitoring points in the forward direction experience slightly higher blasting vibration velocities compared to those in the backward direction. The vibration velocity waveform at monitoring point D3 is depicted in Figure 3. Peak velocity values in each direction occur between 0.2 and 0.4 s, with velocities rapidly increasing shortly after the detonation of explosives, reaching their peak values and gradually diminishing afterward. Following the peak velocity, a second, smaller peak appears. This is due to the different wave velocities and reduction rates of body waves and surface waves within the blasting seismic wave. These differences result in a time delay in reaching the monitoring point, leading to the presence of two distinct velocity peaks in the velocity-time waveform.

Table 2.

Peak vibration velocity at monitoring point.

Vibration velocity	D1	D2	D3	D4	D5	D6
x-direction velocity (cm·s⁻¹)	0.81	2.01	1.87	3.21	1.01	1.39
x-direction velocity (cm·s⁻¹)	2.14	6.39	9.12	6.85	4.10	5.25
x-direction velocity (cm·s⁻¹)	1.89	6.36	6.78	4.84	3.21	5.24
Vector combined velocity (cm·s⁻¹)	2.16	6.44	9.19	6.88	4.13	5.26

Figure 3.

D3 monitoring point vibration velocity waveform.

Excavation blasting dynamic numerical calculation model

Due to limitations in on-site testing conditions, the testing plan design and operational processes were made as comprehensive and detailed as possible. However, in actual engineering projects, it is inevitable that some influencing factors may be overlooked. Additionally, on-site testing data often have limitations in quantity and are of a single nature. Referring to relevant studies, numerical simulations can help compensate for deficiencies in on-site experiments and incomplete experimental data (Sun et al., 2023; Zhang et al., 2023; Zhao et al., 2023). Based on the actual parameters of the on-site engineering and monitoring data, LS-DYNA dynamic finite element numerical software was used to conduct a numerical simulation study on the vibration reduction effects of the retaining pile structure under the influence of blasting in deep urban excavations with damping holes.

Previous researchers have often employed numerical simulations to study the effects of damping holes without establishing a numerical model based on the entire construction project. Additionally, for reinforced concrete structures, the common practice involves using equivalent representations that may not accurately replicate the actual on-site conditions. This study employs the LS-DYNA software to construct a sophisticated numerical computational model. This comprehensive model incorporates various elements such as excavation retaining piles, reinforcement, and concrete supports, providing a more accurate model of the excavation blasting construction.

Computational model

A three-dimensional numerical model was established using LS-DYNA dynamic finite element software to simulate the dynamic response of retaining piles under the effect of excavation blasting vibrations for excavations down to a depth of 25 m with a single-hole charge of 15 kg. The numerical model utilized 8-node SOLID164 solid elements for modeling, while the internal reinforcement of the retaining piles was represented using BEAM elements. The interaction between the steel reinforcement and concrete was achieved through the CONSTRAINED functionality. Based on the actual site conditions and design specifications for the Julong Avenue Station, a 1:1 scale numerical model was created with a depth of 30 m. The overall dimensions of the model were set to 60 m × 54 m × 45 m. The model included the following layer thicknesses: The first layer, consisting of clay, had a thickness of 10 m. The second layer, which was a clay and crushed stone mixture, had a thickness of 15 m. The lower layer, composed of moderately weathered dolomite, had a thickness of 20 m. The blast hole diameter was set at 100 mm, with a spacing of 2.6 m between blast holes. The blast hole depth was 6 m, and continuous loading was used with an explosive charge height of 4 m.

It is well known that any dynamic finite-element prediction is dependent on the size and uniformity of the mesh refinement. According to Kuhlemeyer (Kuhlemeyer and Lysmer, 1973), 8–10 elements per wavelength are required to avoid any wave distortion. Therefore, the numerical model mesh density is determined to be 25 cm. For verifying the accuracy of the numerical calculation, mesh sensitivity analysis is performed with incorporation of finer mesh density of 5 cm and coarser mesh density of 50 cm, calculation results showed that the mesh density of 25 cm ensures the accuracy, and the calculation time is also with the acceptable range. According to Fondelli (Fondelli et al., 2015) and Shi (Shi et al., 2002), the use of smaller mesh elements in critical areas and coarser mesh in other regions ensures more accurate modeling for these critical areas, meeting the computational requirements.

The soil layers, surrounding rock, retaining piles, explosives, and blast mud were all partitioned using a Lagrangian mesh. A gradient mesh partitioning was employed for the site’s geological layers to conserve computational resources and enhance efficiency due to the large volume of surrounding rock. The mesh element sizes ranged from a minimum of 18.75 cm to a maximum of 134.33 cm. For the blast holes, an equally divided grid was used with rectangular cross-sections, each having a side length of 7 cm. The mesh size for retaining piles is 18.75 cm. In total, the model consisted of 3,185,170 elements and 3,488,566 nodes. The simulation was conducted using the cm-g-μs unit system.

In consideration of the specific characteristics of the actual engineering project, the top surface of the numerical model was set as a free constraint boundary condition. Additionally, non-reflective boundary conditions were applied to the surface of the surrounding rock to simulate an infinite ground. Given that a 1/2 model was constructed, symmetric constraints were applied on the symmetrical plane. The dimensions of the numerical model and boundary conditions were configured as depicted in Figure 4(a), and the steel reinforcement arrangement in the retaining piles is illustrated in Figure 4(b).

Figure 4.

Numerical calculation model. (a) Numerical model. (b) Retaining piles and steel bars.

Model parameters

(1) The selection and parameter settings for the surrounding rock and reinforced concrete material models:

Based on the design data for the Julong Avenue Station, a separate modeling approach was employed when establishing the reinforced concrete drilled cast-in-place pile model. The keyword *CONSTRAINED_LAGRANGE_IN_SOLID was utilized to define the bonding relationship between the steel reinforcement and concrete. The geological medium is discontinuous and heterogeneous, making it challenging to directly describe the surrounding rock with mathematical equations. In engineering numerical simulations, it is common to assume that the surrounding rock is continuous and isotropic. In this paper, both rock and reinforced concrete are treated as elastoplastic materials. Indoor tests were performed to select appropriate parameters for the calculation. The rock mass and reinforced concrete stain is high near the explosive detonation center, it is proper to use a plastic hardening material model, which includes the strain rate effect. Therefore, the rock and reinforced concrete material model adopted in the simulation is a kinematic hardening plastic model *MAT_PLASTIC_KINEMATIC, which is an anisotropy kinematic hardening and isotropic kinematic hardening mixed model, relevant with the strain rate and also considers the material failure effect. The specific material parameters can be found in Table 3.

(2) For the selection and parameterization of the clay material model:

Indoor tests were performed to select appropriate parameters for the calculation. The *MAT_DRUCKER_PRAGER material model was used to simulate clay, the clay and crushed stone mixture, and the blast mud in the model. Specific material parameters can be found in Table 4.

(3) Material parameters and the state equation for explosives:

For this blasting operation, Type 2 rock emulsion explosives were used, with a maximum charge weight of 15 kg per hole. Referencing relevant literature (Jiang et al., 2017a, 2017b; Lyu et al., 2023; Shi et al., 2023), the explosives were simulated using the *MAT_HIGH_EXPLOSIVE_BURN material model. The explosive’s density is 1200 kg·m⁻³, and its detonation velocity is 5400 m·s⁻¹. The JWL (Jones–Wilkins–Lee) state equation was employed to describe the relationship between pressure, internal energy, and the relative volume of the explosion products, as shown in equation (1). The relevant parameters for the explosives can be found in Table 5.

P = A (1 - \frac{ω}{R_{1} V_{0}}) e^{- R_{1} V_{0}} + B (1 - \frac{ω}{R_{2} V_{0}}) e^{- R_{2} V_{0}} + \frac{ω E_{0}}{V_{0}}

(1)

where P represents the pressure generated by the explosion; V₀ is the initial relative volume; A, B, R₁, R₂, and ω are constants determined through experimentation; E₀ stands for the specific energy of detonation per unit volume.

Table 3.

Material parameters of reinforced concrete and rock.

Material	Density (g·cm⁻³)	Young’s modulus (GPa)	Poisson’s ratio	Yield stress (GPa)	Tangent modulus (GPa)	Hardening parameter
Steel reinforcement	7.85	200.00	0.20	0.40	6.10	1.00
Concrete	2.60	31.50	0.20	0.02	0.02	1.00
Rock	2.65	45.00	0.25	0.50	0.02	0.50

Table 4.

Material parameters of clay and clay with gravel.

Material	Density (g·cm⁻³)	Elastic shear modulus (GPa)(E)	Poisson’s ratio	RKF	φ (rad)	c (GPa)(E)
Clay	1.99	4.6–3	0.26	0.50	0.26	4.2–5
Clay and crushed stone mixture	2.2	4.0–3	0.25	0.50	0.65	3.0-5
Stemming	1.88	3.0–3	0.28	0.50	0.24	3.0-5

Note: RKF is the shape parameter of the failure surface.

Table 5.

Explosives material and equation of state parameters.

Density (g·cm⁻³)	Detonation velocity (m·s⁻¹)	Explosive pressure (GPa)	A (GPa)	B (GPa)	R ₁	R ₂	ω	E₀ (GPa)	V ₀
1.2	5400	27	214.4	18.2	4.2	0.9	0.15	4.19	1.0

Model reliability verification

A comparative analysis was performed between the simulation results and on-site blasting monitoring data to validate the reliability of the numerical simulation method and its results. Based on the on-site construction and monitoring conditions, the D3 monitoring point was initially selected for a vector-summed velocity waveform comparison, as shown in Figure 5. The vector-summed velocity waveform obtained through on-site monitoring closely resembles the one from numerical simulation, and their attenuation patterns are generally similar. Although the numerical simulation yielded a slightly higher peak velocity compared to the on-site monitoring results, the peak velocity error in the vector combined velocity was only 7.07%. This indicates that the numerical simulation results are highly reliable.

Figure 5.

Comparison of vibration speed waveforms.

A comparative analysis was conducted between the peak velocity values obtained from on-site monitoring (D1 to D5) and the numerical simulation results, as shown in Table 6. The peak velocity values in various directions from the numerical simulation closely match those obtained from on-site monitoring, with relative errors for all directions being less than 10%. This further underscores the reliability of the model and the selected material parameters. It’s worth noting that the peak velocities in the y-direction at all monitoring points are higher than those in the other two directions. Therefore, the y-direction is considered the primary vibration direction during blasting and serves as a key parameter for subsequent analysis.

Table 6.

Comparison of on-site monitoring and numerical simulation of peak vibration velocity.

Monitoring point	Measured vibration velocity (cm·s⁻¹)			Simulated vibration velocity (cm·s⁻¹)			Relative error
Monitoring point	x	y	z	x	y	z	x	y	z
D1	0.81	2.14	1.89	0.88	2.34	2.06	8.64%	9.34%	8.99%
D5	2.01	6.39	6.36	2.20	6.92	6.93	9.45%	8.29%	8.96%
D3	1.87	9.12	6.78	2.01	9.86	7.25	7.49%	8.11%	6.93%
D4	3.21	6.85	4.84	3.48	7.52	5.23	8.41%	9.78%	8.06%
D5	1.01	4.10	3.21	1.10	4.47	3.51	8.91%	9.02%	9.35%

Analyzing the impact of damping hole parameters on damping effect through numerical simulations

According to the site conditions of Julong Avenue Station, to study the impact of damping hole parameters on vibration reduction effects, a controlled variable approach was employed to investigate the diameter, depth, spacing, and number of damping holes. Using the original model without damping holes as the control group, five monitoring points on the stepped blasting surface (as shown in Figure 6) were selected. The peak vibration velocity in the y-direction at each monitoring point was used as the reference baseline for comparison.

Figure 6.

Damping holes and measurement points placement.

On top of the original model, a row of damping holes with different diameters was established. The peak vibration velocities in the y-direction at the five monitoring points were recorded. This data was used to determine the impact of damping hole diameter on the vibration reduction effect. The optimal diameter (the one resulting in the highest vibration reduction rate) was identified for the subsequent study on damping hole depth. The effects of damping hole depth, spacing, and number were also investigated using the same approach. The simulation of damping hole excavation schemes is summarized in Table 7.

Table 7.

Vibration damping hole excavation plan.

Scheme	Hole diameter a (cm)	Hole depth h (m)	Hole spacing d (m)	Number of rows
0	-	-	-	-
1	60	6	0.2	1
2	80	6	0.2	1
3	100	6	0.2	1
4	100	5.5	0.2	1
5	100	6	0.2	1
6	100	6.5	0.2	1
5	100	7	0.2	1
7	100	7	0.3	1
8	100	7	0.4	1
9	100	7	0.2	2

The impact of damping hole diameter on vibration reduction effects

To study the impact of different damping hole diameters on vibration reduction effects, simulations were conducted for models with a single row of damping holes with a hole spacing d = 0.2 m, hole depth h = 6 m, and three different hole diameters a = 60 mm, 80 mm, and 100 mm. The peak y-direction vibration velocities v_y (cm·s⁻¹) at five monitoring points on the stepped blasting surface in the simulation results were selected. The vibration reduction rates for each monitoring point were calculated and compared, as shown in Table 8. The changing trends of vibration reduction rates at different monitoring points for various hole diameters are illustrated in Figure 7, providing the vibration characteristics of the damping holes with different diameters.

Table 8.

Peak vibration velocity and damping rate of each measurement point with different hole diameter.

Measuring point	a = 60 mm		a = 80 mm		a = 100 mm
Measuring point	v _y	Damping rate(%)	v _y	Damping rate(%)	v _y	Damping rate(%)
1	26.16	7.21	25.99	7.81	25.94	8.02
2	26.53	7.64	26.43	8.01	26.37	8.20
3	26.93	9.01	26.84	9.31	26.69	9.82
4	31.12	7.01	31.03	7.31	30.96	7.52
5	32.81	7.80	32.74	8.01	32.73	8.03

Figure 7.

Vibration damping rate of each measurement point with different hole diameters.

Vibration reduction rate calculation equation is shown in equation (2)

i = \frac{v_{0} - v_{1}}{v_{0}} \times 100 %

(2)

where i represents the vibration reduction rate (%); v₀ is the vibration velocity without damping holes (cm·s⁻¹); v₁ is the vibration velocity with damping holes (cm·s⁻¹).

Combining Table 8 with Figure 7, it can be concluded that, as the damping hole diameter increases, there is an overall trend of decreasing vibration velocity within the isolation area. However, the impact on the vibration reduction rate is not particularly significant, suggesting that the diameter of the damping hole has a relatively minor effect on the vibration reduction.

The impact of damping hole depth on vibration reduction effects

To study the impact of different damping hole depths on vibration reduction effects, simulations were conducted for a single row of damping holes with the optimal diameter a = 100 mm and a fixed hole spacing d = 0.2 m. Five different models with hole depths h = 5 m, 5.5 m, 6 m, 6.5 m, and 7 m were simulated. The peak y-direction vibration velocities v_y (cm·s⁻¹) at five monitoring points on the stepped blasting surface in the simulation results were selected. The vibration reduction rates for each monitoring point were calculated and compared, as shown in Table 9. The changing trends of vibration reduction rates at different monitoring points for various hole depths are illustrated in Figure 8, providing the vibration characteristics of the damping holes with different depths.

Table 9.

Peak vibration velocity and damping rate of each measurement point in different hole depth.

Measuring point	h = 5.0 m		h = 5.5 m		h = 6.0 m		h = 6.5 m		h = 7.0 m
Measuring point	v _y	Damping rate(%)	v _y	Damping rate(%)	v _y	Damping rate(%)	v _y	Damping rate(%)	v _y	Damping rate(%)
1	26.16	7.21	25.99	7.81	25.94	8.02	25.08	11.05	24.48	13.16
2	26.97	6.12	26.74	6.92	26.37	8.20	25.47	11.34	24.86	13.46
3	27.59	9.03	26.78	9.51	26.69	9.82	25.84	12.68	25.23	14.75
4	31.19	6.83	31.03	7.29	30.96	7.52	29.91	10.64	29.24	12.63
5	32.97	7.35	32.84	7.72	32.73	8.03	31.67	11.01	30.84	13.34

Figure 8.

Vibration reduction rate of each measurement point in different hole depths.

From Figure 8, it is evident that different damping hole depths have a significant impact on the vibration reduction effect. As shown in Table 9, when the damping hole depth is less than the blast hole depth (6 m), the vibration reduction rate for monitoring point 3 remains relatively stable at around 9.5% as the damping hole depth increases. However, when the damping hole depth exceeds the blast hole depth, the vibration reduction rate increases notably with increasing damping hole depth. For example, when the damping hole depth increases from 6.0 m to 7.0 m, the vibration reduction rate increases by nearly 5%.

The impact of damping hole spacing on vibration reduction effects

To study the impact of different damping hole spacings on vibration reduction effects, simulations were conducted for a single row of damping holes with the optimal diameter a = 100 mm and optimal hole depth h = 7 m. Three different models with hole spacings d = 0.2 m, 0.3 m, and 0.4 m were simulated. The peak y-direction vibration velocities v_y (cm·s⁻¹) at five monitoring points on the stepped blasting surface in the simulation results were selected. The vibration reduction rates for each monitoring point were calculated and compared, as shown in Table 10. The changing trends of vibration reduction rates at different monitoring points for various hole spacings are illustrated in Figure 9, providing the vibration characteristics of the damping holes with different spacings.

Table 10.

Peak vibration velocity and damping rate of each measurement point at different hole spacing.

Measuring point	d = 0.2 m		d = 0.4 m		d = 0.6 m
Measuring point	v _y	Damping rate(%)	v _y	Damping rate(%)	v _y	Damping rate(%)
1	24.48	13.16	25.31	10.23	25.99	7.83
2	24.86	13.46	25.72	10.46	26.43	7.99
3	25.23	14.75	26.18	11.54	26.86	9.24
4	29.24	12.63	30.08	10.13	30.71	8.26
5	30.84	13.34	31.68	10.99	32.40	8.96

Figure 9.

Vibration reduction rate of each measurement point with different hole spacing.

From Figure 9, it can be observed that changing the spacing of the damping holes has a significant impact on the vibration reduction effect. According to Table 10, when the damping hole spacing increases from 0.2 m to 0.4 m, the vibration reduction rate for monitoring point 3 decreases by nearly 3%. Further increasing the damping hole spacing to 0.6 m results in a decrease of nearly 2% in the vibration reduction rate. The observation reveals that as the spacing increases, the damping effectiveness of the damping holes diminishes, and the vibration reduction rate experiences a roughly consistent decline with the expanding spacing.

The impact of the number of damping hole rows on vibration reduction effects

To study the impact of different numbers of damping hole rows on the vibration reduction effect of the retaining pile, simulations were conducted using a model with the optimal hole diameter a = 100 mm, optimal hole depth h = 7 m, and optimal hole spacing d = 0.2 m arranged in a double-row “flower-shaped” pattern of damping holes. In practical engineering, the construction of three rows of damping holes involves a large quantity of work and low efficiency, so the condition of three rows of damping holes was not considered. The peak y-direction vibration velocities v_y (cm·s⁻¹) at five monitoring points on the stepped blasting surface in the simulation results were selected. The vibration reduction rates for each monitoring point were calculated and compared, as shown in Table 11, providing the vibration characteristics of different numbers of damping hole rows.

Table 11.

Peak vibration velocity and damping rate at each measurement point for different rows.

Measuring point	Single row		Double row
Measuring point	v _y	Damping rate(%)	v _y	Damping rate(%)
1	24.48	13.16	22.51	20.16
2	24.86	13.46	22.59	21.34
3	25.23	14.75	22.32	24.58
4	29.24	12.63	25.83	22.80
5	30.84	13.34	25.91	27.19

Table 11 shows that increasing the number of damping hole rows from a single row to double rows results in an approximately 10% increase in the vibration reduction rate at each monitoring point. This indicates that increasing the number of damping hole rows can enhance the vibration reduction effect.

Safety criteria for retaining pile vibration velocity and vibration reduction effect

Safety criterion

Reference to relevant literature (Achenbach et al., 1992; Wang, 1985), based on stress wave theory and using the principles of ultimate tensile stress, ultimate shear stress, and the Mohr criterion, the criteria for blast-induced vibration velocity, ensuring the safety of the retaining pile structure, are determined. According to the study by Jiang and Zhou (2012): Equations (3) ∼ (6) constitute the blasting vibration velocity criteria model determined by the limit strength criteria. Concrete, as well as harder rocks like sandstone and limestone, primarily experience shear or tensile failure. According to the Mohr criterion, equation (7) represents the strength enveloping curve in this context. Equation (8) represents the normal stress acting on the shear sliding surface when the stress wave propagates to the free surface. Equation (9) describes the dynamic stress within the rock mass caused by the explosive impact load at the stress wave front, derived from free surface continuity conditions and Newton’s third law. Equation (11) represents the relationship between the reflection angle (β) of reflected transverse waves and the incident angle (α) of longitudinal waves. The resistance of concrete to tensile strength under blasting vibration is enhanced, as expressed in equation (12), which signifies the relationship between static tensile strength of concrete and dynamic tensile strength. The model for the blast-induced vibration velocity criteria for retaining piles, as determined by the ultimate strength criteria, is as follows

v_{p} (σ) = \frac{[σ_{t}] [\tan β \tan^{2} (2 β) + \tan α]}{[\tan β \tan^{2} (2 β) - \tan α] \cdot \cos α} \cdot \sqrt{\frac{(1 + μ) (1 - 2 μ)}{E_{d} (1 - μ) \cdot ρ}}

(3)

v_{p} (τ) = \frac{[τ] [\tan β \tan^{2} (2 β) + \tan α]}{[2 \tan β \tan^{2} (2 β)] \cdot \cot (2 β) \cdot \cos α} \cdot \sqrt{\frac{(1 + μ) (1 - 2 μ)}{E_{d} (1 - μ) \cdot ρ}}

(4)

v_{s} (σ) = \frac{[σ_{t}] [\tan β \tan^{2} (2 β) + \tan α]}{(- 2 \tan α) \cdot \tan (2 β) \cdot \cos α} \cdot \sqrt{\frac{2 (1 + μ)}{E_{d} \cdot ρ}}

(5)

v_{s} (τ) = \frac{[τ]}{\cos α} \cdot \sqrt{\frac{2 (1 + μ)}{E_{d} \cdot ρ}}

(6)

{\begin{cases} {[τ]}^{2} = {(σ + σ_{t 0})}^{2} \tan^{2} ϕ_{0} + (σ + σ_{t 0}) σ_{t 0} \\ \tan ϕ = \frac{1}{2} {(\frac{σ_{c}}{σ_{t 0}} - 3)}^{1 / 2} \end{cases}

(7)

{\begin{cases} σ_{p} = σ_{pr} \sin α = R_{0} σ_{Pi} \sin α \\ σ_{s} = σ_{sr} \sin α = [(R_{0} - 1) \tan 2 β] τ_{Si} \sin α \end{cases}

(8)

{\begin{cases} σ_{Pi} = c_{P} ρ v_{P} \\ τ_{Si} = c_{S} ρ v_{S} \end{cases}

(9)

R_{0} = \frac{t an β \tan^{2} (2 β) - \tan α}{t an β \tan^{2} (2 β) + \tan α}

(10)

\frac{\sin α}{\sin β} = \frac{c_{P}}{c_{S}} = [\frac{2 (1 - μ)}{1 - 2 μ}]

(11)

[σ_{t}] = \bar{K_{D}} σ_{t 0}

(12)

where v_p(σ) and v_p(τ) represent the safe vibration velocities determined by the ultimate tensile stress criterion and the ultimate shear stress criterion under P-wave action, respectively (cm·s⁻¹). v_s(σ) and v_s(τ) represent the safe vibration velocities determined by the ultimate tensile stress criterion and the ultimate shear stress criterion under S-wave action, respectively (cm·s⁻¹). α represents the incident angle and the reflected angle of the longitudinal wave (°). β represents the reflected angle of the transverse wave (°). [σ_t] stands for the ultimate tensile strength of the retaining pile material (MPa). [τ] represents the ultimate shear strength of the retaining pile material (MPa). E_d. stands for the dynamic elastic modulus, μ represents the Poisson’s ratio, and ρ denotes the density (GPa). ϕ₀ is the inclination angle of the envelope line asymptote (°), σ_c stands for compressive strength (MPa), and σ represents the normal stress (MPa). σ_p represents the normal stress generated on the shear sliding surface under the action of P-waves (MPa), and σ_s represents the normal stress generated on the shear sliding surface under the action of S-waves (MPa). σ_pi represents the normal stress generated by the incident longitudinal waves (MPa), and τ_si represents the shear stress generated by the incident transverse waves. (MPa) v_p denotes the particle velocity induced by longitudinal waves (cm·s⁻¹), and v_s represents the particle velocity induced by transverse waves (cm·s⁻¹). c_p is the longitudinal wave propagation velocity (cm·s⁻¹), c_s is the transverse wave propagation velocity (cm·s⁻¹), and R₀ is the reflection coefficient of stress waves.

According to the design specifications for the on-site excavation, the retaining piles are constructed using C35 concrete cast-in-place piles. The layout of the construction site is illustrated in Figure 10. When the explosive stress wave propagates from the blasting center area towards the vicinity of the retaining pile structure, the angle of stress wave incidence (α) falls within the range of 0° to 28°, α∈(0°,28°). The values for the Poisson’s ratio of materials referenced in equation (11) and Table 13 are utilized to determine the angle of reflection (β), which ranges from 0° to 10.1°, β∈(0°,10.1°).

Figure 10.

Schematic diagram of project.

Based on the concrete strength values specified in the concrete structural design code for C35 concrete (MHURDPRC, 2010), the dynamic tensile strength is determined using equation (12). Considering the characteristics of concrete materials, the dynamic modulus of elasticity is generally assumed to be 1.2 times the static modulus of elasticity. This leads to the calculation of the dynamic modulus of elasticity for C35 concrete. The parameters used for C35 concrete material are provided in Table 12.

Table 12.

Material parameters of C35 concrete.

Compressive strength σ_c (MPa)	Static tensile strengthσ_t0 (MPa)	Dynamic tensile strength σ_t (MPa)	Density ρ (g·cm⁻³)	Static elastic modulus E_d0 (GPa)	Dynamic elastic modulus E_d (GPa)	Poisson’s ratio μ
23.4	2.2	2.728∼3.256	2.6	31.5	37.8	0.2

The values of v_p(σ), v_p(τ), v_s(σ), and v_s(τ) at various angles of incidence for C35 concrete are calculated using the material parameters determined from Table 12 and equations (3)∼(8). The results are presented in Table 13.

Table 13.

Safety vibration velocity.

v_p(σ) (cm·s⁻¹)	v_p(τ) (cm·s⁻¹)	v_s(σ) (cm·s⁻¹)	v_s(τ) (cm·s⁻¹)
26.10∼31.16	145.93	68.33∼81.55	50.00

Under the action of Р-waves at different incident angles, the variation of the explosion safety velocity determined by the limit stress criterion is shown in Figure 11. As the incident angle decreases, the value of the explosion safety velocity decreases.

Figure 11.

Safety vibration velocity.

Based on the similar geological conditions and retaining pile conditions of Julong Avenue Station, it can be concluded from the comprehensive calculation results that the safety velocity standard of concrete retaining pile structure using C35 specification is 26.10 cm·s⁻¹. When the stress waves generated by the explosion impinge on the protected object, the smaller the incident angle, the more susceptible the protected object is to damage.

Vibration reduction effect

Based on the impact of the parameters of the damping holes as discussed above, the optimized design scheme for the damping holes is presented in Table 14, in line with the engineering requirements.

Table 14.

Optimization of vibration damping hole parameters.

Hole diameter a (mm)	Hole depth h (m)	Hole spacing d (m)	Number of rows
100	6.5	0.2	2

After implementing the optimized damping hole design scheme at the construction site, the damage to the retaining pile structure caused by the impact of blasting seismic waves has been effectively reduced. The application results are presented in Figure 12(a). For analysis, we selected a retaining pile post located closest to the blast hole and established 20 monitoring points at 1-m intervals from the bottom of the retaining pile, as depicted in Figure 12(b). By comparing the peak vibration velocities between the schemes with and without damping holes, we can assess the vibration reduction effect on the retaining pile.

Figure 12.

Field application effect and retaining pile measurement points. (a) Application effect. (b) Monitoring point layout.

We selected the peak y-direction vibration velocities v_y (cm·s⁻¹) at the 20 monitoring points on the retaining pile from the simulation results. The comparison of the two schemes is shown in Figure 13(a). By calculating the vibration reduction rate at each monitoring point, we can observe the variation in vibration reduction at different points along the retaining pile under the condition of damping holes, as depicted in Figure 13(b). This illustrates the reduction effect of vibration velocity from the bottom to the top of the retaining pile when damping holes are installed.

Figure 13.

Peak vibration velocity and damping rate change. (a) Peak vibration velocity. (b) Damping rate.

From Figure 13(a), it can be observed that the maximum velocity on the retaining pile after installing damping holes is 25.57 cm·s-1, which is consistently below the blast-induced vibration velocity safety criterion. From Figure 13(b), compared to the scheme without damping holes, the vibration velocities at various monitoring points on the retaining pile significantly decrease, with a reduction rate mainly ranging from 15% to 30%. Even at locations farther from the bottom of the retaining pile, there is still an approximately 25% reduction rate, indicating that the installation of damping holes can effectively mitigate the impact of seismic waves from blasting on the retaining pile.

In both schemes, overall vibration velocities gradually attenuate with increasing distance from the blast source. In the range of 1 to 10 m from the bottom of the retaining pile, the peak vibration velocity exhibits a decay characteristic with increasing distance from the blast center, consistent with the relationship between the intensity of blasting seismic waves and the distance from the blast center. In the range of 10 to 20 m from the bottom of the retaining pile, the vibration velocity generally shows a decreasing trend, with sudden increases in vibration velocity occurring at specific locations. This is attributed to the occurrence of elevation amplification effects, where the attenuation trend of blasting vibration velocity is less pronounced compared to the amplification trend. The attenuation effect does not dominate in this case; instead, the elevation amplification effect is predominant. Subsequently, attenuation and elevation amplification effects alternate, leading to multiple locations where vibration velocities suddenly increase.

As is well known, when a building is subjected to seismic forces and has a small protrusion at the top, the small protrusion, due to its relatively small mass and stiffness, experiences significant vibration velocity at each reversal moment. This phenomenon, known as the whip effect, is crucial in seismic engineering. Similarly, for retaining piles, which are complex structural elements, protrusions caused by the casting process lead to the same amplification effect.

Conclusion

Based on the actual engineering conditions of Julong Avenue Station, this paper focuses on the deep excavation retaining pile structure, studying the impact of various factors of damping holes on the vibration reduction effect through on-site monitoring and numerical simulation. Utilizing theoretical analysis, a safety criterion for the stability of the retaining structure is proposed. Under the optimal damping hole scheme, the on-site application and effectiveness are evaluated. The main conclusions of this paper are as follows:

(a) The diameter of the damping hole has a minimal impact on the vibration reduction rate. When the damping hole depth is equal to or less than the blast hole depth, increasing the damping hole depth does not significantly alter the vibration reduction rate. However, beyond 0.5 m beyond the blast hole depth, the vibration reduction rate increases significantly. Damping hole spacing and number of rows have a substantial impact on the vibration reduction rate.

(b) Based on stress wave theory and following the criteria of ultimate tensile stress, ultimate shear stress, and the Mohr criterion, the safe blasting vibration velocity criterion for the retaining pile structure using C35 concrete is determined to be 26.10 cm·s⁻¹.

(c) In this project, the optimal configuration is identified as double rows of damping holes with a diameter of 100 mm, a depth of 6.5 m, and a spacing of 0.2 m. Under this scheme, the maximum vibration velocity on the retaining structure is 25.57 cm·s⁻¹, which is below the safe blasting vibration velocity criterion. The maximum reduction rate is 30.9%, and the minimum is 12.9%, demonstrating that appropriately setting damping hole parameters can effectively reduce the impact of blasting seismic waves on the retaining structure.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: National Natural Science Foundation of China (Grant Nos.41972286, No.42072309, No.42102329) and State Key Laboratory of Precision Blasting and Hubei Key Laboratory of Blasting Engineering, Jianghan University (No.PBSKL2023A1).

ORCID iDs

Nan Jiang

Chuanbo Zhou

References

Achenbach

Hong

(1992) Wave propagation in elastic solid[M]. Shanghai, China: Tongji University Press, 20–22. (in Chinese).

Baron

Matthews

(1961) Diffraction of a pressure wave by a cylindrical cavity in an elastic medium. Journal of Applied Mechanics 28: 347.

Baron

Matthews

(1962) Displacements and velocities produced by the diffraction of a pressure wave by a cylindrical cavity in an elastic medium. Journal of Applied Mechanics 29: 347.

Bian

Liu

(2014) Numerical simulation for the damping effect of empty holes on blasting vibration. Advanced Materials Research 936: 1490–1495.

Chapman

Ebrary

(2004) Fundamentals of Seismic Wave Propagation. Cambridge, UK: Cambridge University.

Chen

Wang

, et al. (2020) Optimization of close-range blasting design with vibration-damping and speed-reduction for open-pit mine in an arid region. IOP Conference Series: Earth and Environmental Science 555: 012082.

Code for Design of Concrete Structures GB 50010-2010 (2018) Beijing, China: China Architecture & Building Press. (in Chinese).

Datta

(1978) Scattering of elastic waves - ScienceDirect. Mechanics Today: 149–208.

Duan

Zhang

, et al. (2022) Analysis and application of vibration damping hole in tunnel working face based on grey correlation analysis. Shock and Vibration 2022: 8442130.

10.

Eringen

A, C

(1961) Propagations of elastic waves generated by dynamical loads on a circular cavity. Journal of Applied Mechanics 28: 218.

11.

Fondelli

Andreini

Facchini

(2015) Numerical simulation of dam-break problem using an adaptive meshing approach. Energy Procedia 82: 309–315.

12.

Gao

Cheng

Ren

, et al. (2023) Experimental study on frequency modulation damping effect of digital detonator in road clearance blasting. Shock and Vibration 2023: 4645101.

13.

Gerald

Einar

Kenneth

(1979) Seismic wave attenuation in rocks. Reviews of Geophysics 17(6): 1155–1164.

14.

Jiang

Gao

Zhou

, et al. (2018) Effect of excavation blasting vibration on adjacent buried gas pipeline in a metro tunnel. Tunnelling and Underground Space Technology 81: 590–601.

15.

Jiang

Jia

Yao

, et al. (2021a) Experimental investigation on the influence of tunnel crossing blast vibration on upper gas pipeline. Engineering Failure Analysis 127: 105490.

16.

Jiang

Lyu

, et al. (2023) Vibration effect and ocean environmental impact of blasting excavation in a subsea tunnel. Tunnelling and Underground Space Technology 131: 104855.

17.

Jiang

Zhang

Zhou

, et al. (2020a) Influence of blasting vibration of mlemc shaft foundation pit on adjacent high-rise frame structure: a case study. Energies 13: 5140.

18.

Jiang

Zhou

Zhang

(2017) Propagation and prediction of blasting vibration on slope in an open pit during underground mining. Tunnelling and Underground Space Technology 70: 409–421.

19.

Jiang

Zhou

(2012) Blasting vibration safety criterion for a tunnel liner structure. Tunneling and Underground Space Technology 32: 52–57.

20.

Jiang

Zhu

, et al. (2020b) Safety assessment of buried pressurized gas pipelines subject to blasting vibrations induced by metro foundation pit excavation. Tunnelling and Underground Space Technology 102: 103448.

21.

Jiang

Zhu

Zhou

, et al. (2021b) Blasting vibration effect on the buried pipeline: a brief overview. Engineering Failure Analysis 129: 105709.

22.

Jiang

Zhu

Zhou

, et al. (2022) Safety criterion of gas pipeline buried in corrosive saturated soft soil subjected to blasting vibration in a coastal metro line. Thin-Walled Structures 180: 109860.

23.

Kennett

BLN

(1986) Seismic wave propagation in stratified media. Geophysical Journal of the Royal Astronomical Society 68(6): 79.

24.

Kuhlemeyer

Lysmer

(1973) Finite element method accuracy for wave propagation problems. Journal of the Soil Mechanics and Foundations Division 99(5): 421–427.

25.

Lei

Kang

Zhao

, et al. (2014) Numerical simulation and experimental study on vibration-decreasing function of the barrier holes. Applied Mechanics and Materials 602-605: 53–59.

26.

Wang

Liang

, et al. (2020) Energy and vibration absorption characteristics of damping holes under explosion dynamic loading. ACS Omega 5: 17486–17499.

27.

Lyu

Zhou

Jiang

(2023) Experimental and numerical study on tunnel blasting induced damage characteristics of grouted surrounding rock in fault zones. Rock Mechanics and Rock Engineering 56: 603–617.

28.

Navarro Torres

Silveira

LGC

Lopes

PFT

, et al. (2018) Assessing and controlling of bench blasting-induced vibrations to minimize impacts to a neighboring community. Journal of Cleaner Production 187: 514–524.

29.

Padhy

Subhadra

(2010) Attenuation of high-frequency seismic waves in northeast India. Geophysical Journal International 181: 453.

30.

Park

Jeon

(2009) A numerical study on the screening of blast-induced waves for reducing ground vibration. Rock Mechanics and Rock Engineering 42: 449–473.

31.

Peralta

Carrier

Mow

(1966) An approximate procedure for the solution of a class of transient-wave diffraction problems. Journal of Applied Mechanics 33: 168.

32.

Rodríguez

García de Marina

Bascompta

, et al. (2021) Determination of the ground vibration attenuation law from a single blast: a particular case of trench blasting. Journal of Rock Mechanics and Geotechnical Engineering 13: 1182–1192.

33.

Ru-Shan

(1982) Attenuation of short period seismic waves due to scattering. Geophysical Research Letters 9: 9.

34.

Shi

Zhao

, et al. (2002) Development and application of the adaptive mesh technique in the three-dimensional numerical simulation of the welding process. Journal of Materials Processing Technology 121: 167–172.

35.

Sato

Fehler

(2012) Seismic wave propagation and scattering in the heterogeneous Earth. Seismic Wave Propagation and Scattering in the Heterogeneous Earth. Berlin: Springer.

36.

Shi

Jiang

Zhou

, et al. (2023) Safety assessment of ancient buddhist pagoda induced by underpass metro tunnel blasting vibration. Engineering Failure Analysis 145: 107051.

37.

Song

Mao

Tian

, et al. (2019) Optimization analysis of controlled blasting for passing through houses at close range in super-large section tunnels. Shock and Vibration 2019: 1941436.

38.

Sun

Jiang

Zhou

, et al. (2023) Safety assessment for buried drainage box culvert under influence of underground connected aisle blasting: a case study. Frontiers of Structural and Civil Engineering 17: 191–204.

39.

Tian

Song

Wang

(2019) Study on the propagation law of tunnel blasting vibration in stratum and blasting vibration reduction technology. Soil Dynamics and Earthquake Engineering 126: 105813.

40.

Uysal

Erarslan

Cebi

, et al. (2008) Effect of barrier holes on blast induced vibration. International Journal of Rock Mechanics and Mining Sciences 45: 712–719.

41.

Wang

(1985) Stress Wave basis. Beijing, China: National DefenceIndustry Press, 54–56. (in Chinese).

42.

Yang

Zeng

Liu

, et al. (2023) Real-time monitoring for effects of vibration and temperature of construction site on steel assembly bracing of foundation pit. Buildings 13: 450.

43.

Zhang

Zhou

(2022) Study on dynamic response and safety control of reinforced concrete rigid frame structure under foundation pit blasting. International Journal of Protective Structures 14: 204141962211361.

44.

Zhang

Wang

, et al. (2021) Assessing and controlling of boulder deep-hole blasting-induced vibrations to minimize impacts to a neighboring metro shaft. Archives of Civil and Mechanical Engineering 21: 66.

45.

Zhang

Jiang

Zhou

, et al. (2023) Mechanical behaviors and failure mechanism of HDPE corrugated pipeline subjected to blasting seismic wave. Alexandria Engineering Journal 67: 597–607.

46.

Zhao

Jiang

Zhou

, et al. (2023) Safety assessment for a ballast railway induced by underground subway tunnel blasting: a case study. International Journal of Protective Structures 15: 204141962211506.

47.

Zheng

Ren

, et al. (2021) The influence of partial pile cutting on the pile-anchor supporting system of deep foundation pit in loess area. Arabian Journal of Geosciences 14: 1229.

48.

Zhu

Jiang

Zhou

, et al. (2021) Dynamic failure behavior of buried cast iron gas pipeline with local external corrosion subjected to blasting vibration. Journal of Natural Gas Science and Engineering 88: 103803.

49.

Zhu

Qin

Lin

(2015) Analytical study on dynamic response of deep foundation pit support structure under the action of subway train vibration load: a case study of deep foundation pit of the new museum near metro line 2 in chengdu, China. Shock and Vibration 2015: 535196.

50.

Zhu

Zhao

, et al. (2023) Experimental study of vibration reduction effect of barrier holes under blasting. Rock Mechanics and Rock Engineering 56: 1185–1198.

Scheme	Hole diameter a (cm)	Hole depth h (m)	Hole spacing d (m)	Number of rows
0	-	-	-	-
1	60	6	0.2	1
2	80	6	0.2	1
3	100	6	0.2	1
4	100	5.5	0.2	1
5	100	6	0.2	1
6	100	6.5	0.2	1
5	100	7	0.2	1
7	100	7	0.3	1
8	100	7	0.4	1
9	100	7	0.2	2

Scheme	Hole diameter a (cm)	Hole depth h (m)	Hole spacing d (m)	Number of rows
0	-	-	-	-
1	60	6	0.2	1
2	80	6	0.2	1
3	100	6	0.2	1
4	100	5.5	0.2	1
5	100	6	0.2	1
6	100	6.5	0.2	1
5	100	7	0.2	1
7	100	7	0.3	1
8	100	7	0.4	1
9	100	7	0.2	2

Vibration reduction effect of retaining pile structure under the action of damping hole—A case study

Abstract

Keywords

Introduction

Deep excavation blasting construction project and on-site testing

Project introduction

On-site monitoring

Excavation blasting dynamic numerical calculation model

Computational model

Model parameters

Model reliability verification

Analyzing the impact of damping hole parameters on damping effect through numerical simulations

The impact of damping hole diameter on vibration reduction effects

The impact of damping hole depth on vibration reduction effects

The impact of damping hole spacing on vibration reduction effects

The impact of the number of damping hole rows on vibration reduction effects

Safety criteria for retaining pile vibration velocity and vibration reduction effect

Safety criterion

Vibration reduction effect

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iDs

References

Scheme	Hole diameter a (cm)	Hole depth h (m)	Hole spacing d (m)	Number of rows
0	-	-	-	-
1	60	6	0.2	1
2	80	6	0.2	1
3	100	6	0.2	1
4	100	5.5	0.2	1
5	100	6	0.2	1
6	100	6.5	0.2	1
5	100	7	0.2	1
7	100	7	0.3	1
8	100	7	0.4	1
9	100	7	0.2	2