Propagation Law Of Waves Research Articles

Synthetic experimental and numerical investigation on the vertical seismic effect on underground structures

Seismic damage patterns of underground structures indicate unignorable effects of vertical seismic actions. To deal with this, this study distinguished the impact of the vertical seismic effect on the seismic safety of underground structures experimentally and theoretically and provides important shaking table test results for this topic. A typical shallow buried subway station-tunnel junction structure was designed by following the Buckingham similarity law, based on which the shaking table test was performed to investigate the vertical seismic effect on underground structures. The vertical wave propagation laws of the free field, the model structure, and the soil–structure interaction (SSI) system were comparatively analyzed. Numerical simulations considering the soil’s nonlinear behaviors under vertical loads were performed using the equivalent linear analysis method and were verified by the test records. By combining both the experimental and numerical results, it was found that the surrounding soils have very weak constraints on the structural vertical movements. By distinguishing lateral soil pressures from horizontal actions, the vertical seismic action is found to be mainly an inertia force that can stimulate high-frequency vibration modes of the system and cause considerable vertical relative deformations within the underground structure. Consistent with the observed structural damage at the Daikai station, the participation of high-frequency vibration modes is a rational approach that can explain the amplification effect of vertical ground motions on structural seismic responses. In addition, the equivalent linear method is generally satisfactory for simulating the soil compressional nonlinearity.

Formulation of SH wave characteristics in nonlocal nanoplates

AbstractThe scale effect of mechanical properties is one of the most critical issues in application of the nanostructures. In order to study the scale effect on SH waves in nanoplates, a Legendre polynomial series method combined with the nonlocal theory (N‐LPSA) is developed in this paper. The presented method enables the boundary condition achieved quickly by the derived iterative solution formula of the integral, which contains nonlocal factors and Legendre polynomials. Besides, the formula of escape frequency is deduced analytically to facilitate the study of wave propagation law. Numerical comparisons show the correctness of the N‐LPSA. The results indicate that cut‐off frequencies of some higher‐order modes are higher than their escape frequencies. The anisotropy with the nonlocal effects can lead to the intersection of the modal curves, which does not appear in classical structures. Moreover, the fitting formulas of cut‐off and crossing frequencies are developed to predict the compression and the intersection of the modal curves, respectively.

Experimental Study on the Dynamic Mechanical Properties of a Jointed Rock Mass under Impact Loading

The propagation law of blast stress waves in jointed rock masses is closely related to the characteristics of the joint filling medium. The water content and thickness of the filling medium affect the propagation characteristics of the blast stress wave in the joint surface. Based on similarity theory, mortar-red clay-mortar composite specimens with different moisture contents (36%, 39%, 42%, and 45%) and medium thicknesses (3 mm, 6 mm, and 9 mm) were prepared with red clay as the filling medium. The dynamic uniaxial compression test of the specimen under different strain rates was carried out by using a variable cross-section split Hopkinson compression bar with a diameter of 50 mm. The effects of strain rate, moisture content, and medium thickness on the stress wave propagation characteristics, dynamic stress-strain curve, peak stress, crushing energy consumption density, and crushing characteristics of mortar-red clay-mortar composite specimens were analyzed. The results show that the blocking effect of joints on stress waves increases significantly with increasing filling medium thickness and water content. With increasing strain rate, the peak stress and energy of the composite specimen increase and there is an obvious strain rate effect. With the increase in the thickness and moisture content of the filling medium, the peak stress, dynamic elastic modulus, energy consumption density per unit volume, and crushing degree of the specimen gradually decrease and the nonlinear deformation is more obvious. There is a good linear relationship between the peak stress and the thickness and moisture content of the filling medium. The existence of joints greatly weakens the damage effect of stress waves on the specimens behind the joints, and with the increase in the thickness and water content of the filling medium, the degree of damage to the specimens behind the joint surface decreases under the same impact pressure and the weakening effect becomes increasingly significant.

Study on Microscopic Characteristics of Spatial Distribution of Fractures in Deteriorated Sandstone

In the underground environment with large buried depth and high ground stress, man-made disturbance is very easy to cause the rapid expansion of primary fractures in the rock, and then developed into the macrodynamic performance of rock. Based on the propagation law of elastic waves in discontinuous media, the application of acoustic emission detection technology can quickly determine whether there are primary fractures in the rock and predict its approximate location. In this work, CT scanning experiments of intact sandstone specimens and fractured sandstone specimens were performed. The gray value distribution of intact sandstone specimens and fractured sandstone specimens was studied. The sandstone specimens were divided into 4 zones (I~IV) from top to bottom. The height of each zone is from 0 mm to 25 mm, and the upper end face of each zone is the starting face. Acoustic emission experiments of intact sandstone and fractured sandstone are carried out based on the equilateral triangle sensor array. The dispersion of AE wave velocity and amplitude in intact sandstone specimens and fractured sandstone specimens is studied. The results show that the crack evolution law of sandstone specimens before and after preloading is closely related to the density distribution. The regular trend is from low density to high density. And the decay law of AE eigenvalue before and after preloading of sandstone specimen is consistent with the change trend of gray value. This shows that it is feasible to explore the spatial location of primary fractures and the degree of development of primary fractures in the rock through the equilateral triangle sensor array. In the actual project, it can provide some guidance and suggestions for related projects.

Experimental and numerical simulation of the propagation law of shock waves in corrugated steel-lined tunnels

Corrugated steel support structures are widely used in engineering tunnels owing to their rapid construction and high bearing performance, allowing for the complex propagation of shock waves. To clarify the propagation law of shock waves in a corrugated steel tunnel with interior lining, a 30-m-long straight tunnel was built to explore the propagation of an explosion shock wave, and three different tunnel inner walls were designed, namely, a concrete inner wall and two types of corrugated steel linings. Based on the data on the monitored shock wave, the propagation law of shock waves in the tunnel was obtained, and the influence of corrugated steel linings on the shock waves was analyzed. A finite element model of the channel was established to verify the results of experiment and determine the model and related parameters. This model was also used to perform a numerical simulation of explosion shock wave propagation in corrugated steel-lined tunnels of various sizes. Based on the experimental and numerical simulation results, a prediction model of shock wave overpressure in corrugated steel-lined tunnels was obtained. Research showed that the shock-wave energy of wavefronts near walls was diverted, the formation and propagation of waves reflected from walls was affected by corrugated steel linings, which effectively improved the attenuation efficiency of shock waves in tunnels.

The law of blast stress wave propagation and fracture development in soft and hard composite rock

The process of blasting stress wave propagation and crack propagation is directly affected by the physical properties of the rock mass and internal joints in the rock. In soft and hard rock layers, the blasting process is more complicated since the blasting stress wave needs to penetrate two kinds of rocks with different physical properties and the interface between soft rock and hard rock. In this study, the modal transformation of stress waves at the interface of layered composite rock was analyzed, and the process was reproduced by finite element analysis. Furthermore, the development law of cracks was explored. The research results demonstrated that in the single blasting-hole model, a triangular crack area caused by reflected stress waves appeared at the rock interface of rock medium I near the blast hole. In rock medium II, the tensile crack generated by the interface wave appeared on the side away from the blast hole. Besides, the development of the tensile crack was associated with the incident mode of the blast stress wave and the incident angle. In the deep hole blasting model, the incidence of the detonation wave front from hard rock to soft rock promoted the fragmentation of the hard rock.

Analysis of space debris impact source localization based on PVDF piezoelectric film

As the pace of human exploration and utilization of space continues to accelerate, space debris gradually becomes an inevitable problem affecting and threatening human space activities. When space debris strikes the spacecraft bulkhead, determining the impact source location timely and accurately is the foundation of the repair damage, and is also of great importance for the safety of astronauts' life. This paper analyzed the wave propagation law in thin plates, established a lightweight sensor array using PVDF (Polyvinylidene fluoride) circular thin-film sensors, and used a two-stage light-gas gun loading system to conduct hypervelocity collision localization experiments on impacting 2A12 aluminum plates to study the effects of sensor array radius and sensor size on localization results. The results show that the smaller the radius of the PVDF sensor array is, the more accurate the positioning result is under the premise of the same size of the PVDF circular film sensor array. On the premise of the same PVDF sensor array arrangement, the larger the PVDF circular membrane sensor is, the more accurate the positioning result is. ABAQUS finite element software is used to study the stress wave propagation of aluminum ball impacting aluminum plate at high speed, simulating space debris impacting spacecraft. The stress waveform obtained from the simulation is in good agreement with the experiment, which shows the accuracy of the numerical simulation method.

Study on Bond Defect Detection in Grouted Rock Bolt Systems under Pullout Loads

In grouted rock bolt systems, bond defects often occur, which seriously affects the safety of rock mass structures. Therefore, in this study, based on the existence of bond defects, laboratory tests were conducted to detect the location and length of bond defects and study the guided wave propagation in grouted rock bolt systems under different pullout loads. The guided wave signal was analysed in the time domain and frequency domain. In addition to the laboratory test, a numerical simulation of the effect of different bond defect locations on ultrasonic guided wave propagation in rock bolts was conducted using a damage-based model. The influence mechanism of bond defects on guided wave propagation under different pullout loads was explored. The study confirmed that there existed a stress platform in the rock bolt at the bond defect under a pullout load. The location and length of the bond defect could be detected by the stress platform and guided wave. The debonding length increased exponentially with the amplitude ratio (Q) of low frequency to high frequency, and the Q value could be used as the quantitative index of debonding length. As the pullout load increased, the impedance mismatch between the rock bolt and cement mortar (defect) increased, and the guided wave propagation in grouted rock bolt systems was irregular. The pullout load weakened the guided wave propagation law. The larger the pullout load is, the greater the weakening effect is.

Experimental and Numerical Studies on Bond Quality of Fully Grouted Rockbolt under Confining Pressure and Pull-Out Load

In mining engineering, the in situ stress changes with the stress induced by the surrounding mining activities. It positively or negatively affects the propagation of ultrasonic guided waves in rockbolts. Therefore, the effect of in situ stress in rockbolt support was determined by applying confining pressure and pull-out load in a laboratory test and using ultrasonic guided waves to test the rockbolt. Furthermore, the propagation law of ultrasonic guided waves and bond quality of the rockbolt under the interaction of the pull-out load and confining pressure were studied. Numerical simulations were performed to deduce the guided wave propagation process in grouted systems, and the influencing mechanism of the pull-out load and confining pressure on the guided wave propagation was discussed. The laboratory test and numerical simulation results show that the confining pressure weakens the guided wave propagation without pull-out load. Under the same pull-out load, the guided wave propagation gradually strengthens with increasing confining pressure. A larger confining pressure weakens the weakening effect of the pull-out load and suppresses the discreteness of the guided wave propagation. Under the same confining pressure, the guided waves did not diffract well into the cement mortar and concrete with increasing pull-out load, the confining pressure restricted the radial vibration of the guided waves, and the guided wave propagation law weakened. Thus, the pull-out load plays a weakening role in the propagation law of ultrasonic guided waves.

Application of a Simulation Method for the Shock Wave Propagation Law of Gas Explosion.

Gas explosion is one of the main causes of casualties in coal mines. Studying the propagation law of shock wave of mine gas explosion can reduce the economic loss and personnel injury caused by mine gas explosion. To solve the difficulty in the research of shock wave propagation of gas explosion in the mine scale, the segmented relay simulation method of shock wave propagation of gas explosion in a coal mine was put forward, the related key problems were studied, and the results were successfully applied in Yangchangwan No. 2 Mine. The results show the following: (1) When the length of the forked roadway exceeds 50 m, the length of the forked roadway has little effect on the shock wave overpressure in the main roadway. When the length of the forked roadway is short, the closure of the forked roadway has a great influence on the change curve of the shock wave overpressure in the main roadway. Therefore, the length of the bifurcation roadway should not be less than 50 m in numerical simulation. (2) The angle of the bifurcated roadway has a great influence on the shock wave propagation of explosion in the main roadway. With the increase in the angle of the bifurcated roadway, the overpressure in the main roadway tends to increase at first and then decrease, and the peak overpressure is the highest when the angle of the bifurcated roadway is 90°. (3) The influence range of the roadway pressure-outlet boundary is about 5 m, and the dynamic parameter monitoring point should be set at about 10 m away from the pressure outlet; dynamic boundary monitoring parameters should include static pressure, dynamic pressure, and temperature. (4) When the gas explosion occurs in the heading face, the shock wave will cause great damage to the adjacent heading face. When the shock wave reaches the head-on and upper corner of the heading face, it will be reflected violently, which will cause the local overpressure to rise obviously. The peak overpressure and gas accumulation length conform to the logarithmic function.

Frequency spectrum and energy refinement characteristics of blasting vibration signals in raw water pipeline tunnel excavation

The analysis of time-frequency variation and energy refinement characteristics of blasting vibration signals has contributed to understanding the propagation law of blasting vibration wave and reducing the possible losses. Combined with the measured data of tunnel blasting excavation and based on the newly constructed wavelet function, the spectrum distribution and energy refinement characteristics of tunnel blasting vibration signals are deeply explored and studied. The results demonstrated that compared to the Fourier spectrum, the innovative method of scale energy spectrum can not only acquire the dominant frequency of the blasting vibration signals, but also the obtained spectrum curve is smoother and can clearly reflect the change trend of the signal spectrum. The newly constructed biorthogonal wavelet has the characteristics of high vanishing moment, high regularity and matching with the waveform variation of the measured blasting vibration signals, and can describe the subtle variation characteristics of blasting vibration signal frequency. The continuous wavelet transform energy spectrum can reflect the three-dimensional energy distribution of blasting vibration signal in the time-scale domain, and the occurrence time of frequency, the frequency duration interval and time range of blasting vibration signal can also be acquired. Wavelet packet algorithm can precisely calculate the energy distribution of each frequency component in the signal, the tunnel blasting vibration signals (YBJ1, YBJ2) generated near the power tower presents low frequency, while the signals (YBF3,YBF4) far away from the power tower presents relatively high frequency. Measures should be taken to control the vibration and resonance of power tower caused by tunnel blasting. This research is of great significance for recognizing the propagation law of vibration waves, reducing the impact of blasting on surrounding buildings, and ensuring the safety of tunnel construction and surrounding buildings.

Experimental study on compression mechanical characteristics of filled rock joints after multiple pre-impacts

The prefabricated artificial filled jointed rock specimens are impacted by a self-made drop hammer impact device for many times, and the specimens with different degrees of cumulative damage characteristics are obtained. Then, the static and dynamic compression mechanical properties are studied by using universal testing machine and SHPB device. Through the static compression test, the strength and deformation characteristics of jointed rock specimens after multiple impacts are obtained, and the influence of the damage degree of jointed rock specimens characterized by wave velocity on the compressive strength of filled joints is analysed. Based on the results of SHPB impact test, the dynamic strength and deformation evolution, wave propagation law and energy dissipation law of filled joints after multiple impacts are analysed. During the SHPB test, the impact failure process of rock specimens is recorded by a high-speed camera. The experimental results show that the damage degree of jointed rock samples increases nonlinearly after multiple impacts. The attenuation laws of static strength and dynamic strength of rock samples under the same damage evolution conditions are different. With the increase of impact times, the failure mode of jointed rock samples after damage is simpler and tends to compression failure.

Numerical Simulation of Surface Vibration Propagation in Tunnel Blasting

In order to better study the propagation law of tunnel blasting in mountain landforms, taking the excavation blasting project of the Yangliu tunnel along the Yinsong expressway in Guizhou as the research object, the propagation law of vibration waves to tunnel blasting under the mountain tunnel was analyzed based on the ABAQUS finite element software and compared with the field monitoring data. The results show the peak vibration velocity of numerical simulation. Generally, the simulation value is slightly larger than the field monitoring value, but the average error of closing speed is less than 25% and the maximum error is less than 45%. The component velocity of surface peak vibration under blasting to load is the largest in the vertical direction. The “cavity effect” formed by the side-passing tunnel wall has the most significant amplification effect on the peak vibration velocity in the X direction of the rock and soil above it, which is about 1.62∼1.85 times and the resultant velocity is enlarged by 1.27∼1.45 times. Blasting vibration waves spread to the surface in the form of spherical waves inside the mountain, causing the vibration center of the surface to move to the area with lower elevation. The “cavity effect” caused by the side-through tunnel and the shift of the surface diffusion center to the lower part together led to the peak velocity of the lower measuring point of the Yangliu tunnel being much higher than that of the higher measuring point. The research results of this paper have certain reference significance in controlling the influence of underground blasting vibration on residential buildings in mountain areas.

The attenuation mechanism and regular of the acoustic wave on propagation path in farmland soil

Understanding the propagation process of acoustic waves in the soil is very important for designing high-performance acoustic wave detection devices. In this study, the discrete element method was used to simulate the propagation process of acoustic waves in the soil. A single factor experiment was carried out with soil compression ratio, excitation frequency, and excitation amplitude as factors. The influence of various factors on the time and frequency domain were analyzed from the perspective of the received signal and the force signal on the particle. The results showed that: with the increase of soil compression ratio, the speed of the acoustic wave, the amplitude of the received signal's first wave and the dominant frequency increased; with the increase of excitation frequency, the amplitude of the received signal's first wave decreased, and the dominant frequency and speed of acoustic wave remained unchanged; with the increase of excitation amplitude, the received signal amplitude increased, and the dominant frequency and speed of acoustic wave remained unchanged. According to the force signal of the particles on the sound wave propagation path, as the soil compression ratio increased, the dominant frequency of the acoustic wave increased, and the amplitude attenuation coefficient increased; as the excitation frequency increased, the dominant frequency and amplitude attenuation coefficient of the acoustic wave first increased and then decreased; as the excitation amplitude increased, the dominant frequency of the acoustic wave remained unchanged, and the amplitude attenuation coefficient increased. The occurrences of these phenomena were related to the natural frequency of the soil and the sound wave attenuation mechanism. During the propagation process, the dominant frequency of the sound wave would continue to attenuate and eventually reached the natural frequency, resulting in the same dominant frequency of the received signal under different excitation frequencies. Under different parameters, the decay speed of the sound wave amplitude was different, and the initial signal amplitude was different, which led to the various first wave amplitude of the received signal. The conclusion could be drawn through the simulation experiment: the DEM method could well characterize the acoustic wave propagation process in the soil and analyze the acoustic wave propagation law in the soil. Thus, it provides theoretical support and reference for the research and instrument manufacture of the acoustic wave detection of soil characteristics.

Law of Countercurrent Energy Dissipation of Fresh Air by Coal and Gas Outburst Shock Waves

Accidental coal and gas outbursts lead to major disasters in coal-producing countries and are difficult to mitigate. To elucidate the energy dissipation law for coal and gas outburst shock waves in a complex ventilation network of mines, a coal-and-gas-outburst-energy-propagation simulation and parameter determination test device were developed and used to perform physical simulation experiments under different outburst strength conditions. These experiments were combined with numerical simulations to obtain the propagation law of outburst shock waves in a roadway and analyze different outburst intensities according to the gas counterflow criterion, highlighting the hazard characteristics of shock waves in a fresh air tunnel. The results showed that when a shock wave passed through the turning roadway, its intensity and speed were greatly attenuated and that the overpressure value of a shock wave in a straight roadway was greater than that at a corner. Upon encountering a rigid wall, the superposition of the incident and reflected shock waves increased the peak overpressure of the shock wave per unit area. When a fresh air roadway is near the coal uncovering position in rock drift (“Shimen”) a corresponding counter-backflow device should be installed at the location of the connecting road near the fresh air roadway, under the condition that normal ventilation is not affected. These numerical simulation results are consistent with general experimental trends, indicating that the analyses conducted in this study are reliable and can provide a theoretical basis for the prevention of secondary disasters due to coal and gas outbursts in mines.

Study on the Combined Effect of Inclined Natural Fracture and Water Jet Slot on the Blast-Induced Crack Propagation Law

For the purpose of uncovering the influence law on the explosion stress wave transmission and blast-induced crack propagation by inclined natural fracture and water jet slot, the influential mechanism for the transmission law of explosion stress wave due to inclined natural fracture was analyzed based on stress wave theory in this article. Next, the evolution law of explosion stress wave and blast-induced crack propagation affected by inclined natural fracture and water jet slot were simulated by ANSYS/LS-DYNA, and an experiment was conducted to understand the crack propagation law under explosion shock wave loading. The results indicate that the existence of inclined natural fracture will affect the “guiding effect” of water jet slot on blast-induced crack propagation by changing the propagation path and mechanical properties of the explosion stress wave. When the distance between inclined natural fracture and blast hole is too small, the water jet slot cannot play a guiding role in propagation process of blast-induced main crack. With the increase of the distance, the propagation direction of blast-induced crack is affected by both inclined natural fracture and water jet slot. When the distance increases further and exceeds a certain value, inclined natural fracture cannot affect the guiding effect of water jet slot in propagation process of blast-induced main crack.

Investigating dynamic fracture in marble-mortar interface under impact loading

• Compared with the M-S-750 series specimens, the transgranular phenomenon is more common in the M-R-750 series specimens. • The crack propagation velocity in the BSCT specimen is lower than the speed of Rayleigh wave in the M40 mortar. • With the increase of loading rate, the crack propagation speed between CPG adjacent wires does not necessarily increase. • The discrepancy of wave impedance between marble and mortar results in the existence of shear stress in the interface zone of the BSCT specimen. • Compared with the BSCT specimens with smooth interfaces, the fracture properties ( K 1 and G ) of the BSCT specimens with rough interfaces are improved significantly. The mechanical property of the mortar-rock interface is a key factor in dominating the effectiveness of many reinforcement measures in rock mass engineering. Investigating the mortar-rock interface is of important practical consequences. In this paper, a bi-material single cleavage triangle (BSCT) configuration, composed of marble and mortar, was employed in a split Hopkinson pressure bar (SHPB) experiment with interface roughness and loading rates considered. The experimental–numerical method was used to obtain the crack initiation energy release rate G and the complex stress intensity factor ( K = K 1 + i K 2 ) of the onset interface crack. Besides, AUTODYN software was applied for analyzing the propagation law of stress waves in the BSCT specimen, and the failure mechanism of the mortar-rock interface was revealed. The results show that the interface crack growth rate in the BSCT specimen is lower than the P-wave, S-wave, and Rayleigh wave in the M40 mortar. The discrepancy of wave impedance between marble and mortar results in the existence of shear stress in the interface zone of the BSCT specimen. As the loading rate increases to 920 GPa/s, the fracture properties ( K 1 and G ) of all BSCT specimens are significantly improved. The improvements in the fracture properties are more significant for the BSCT specimens with rough interfaces compared to the BSCT specimens with smooth interfaces.

Propagation laws of discontinuous gas supply in the excavation roadway.

An explosion with a discontinuous gas supply (DGS-explosion) is more complicated than a common secondary explosion. We present the results of a study on the propagation laws of the DGS-explosion induced by a gas explosion in excavation roadways. A rectangular tube was established using ANSYS, similar to an excavation roadway in an underground coal mine. The gas, flame, and shock wave propagation laws were determined by analyzing the explosive gas as it exited the excavation roadway. The results show that the initial explosion caused the flame generated in the DGS-explosion to be significantly stretched. Moreover, the shock wave was reflected by the end of the tube, which resulted in the reverse migration of the local gas after the DGS-explosion. Meanwhile, with the increase in local gas concentrations, the pressure peak and the entire explosion system can increase after the DGS-explosion. The flame region, temperature peak, and flame irregularity in the tube positively correlate with the concentration. These results can provide theoretical support and an experimental basis for preventing and responding to accidents caused by gas explosion accidents.

Optimization of Pre-Splitting Blasting Hole Network Parameters and Engineering Applications in Open Pit Mine

In order to optimize the parameters of a pre-splitting blasting hole network, taking an open-pit mine in Inner Mongolia as the engineering background, the numerical models of different pore sizes and hole spacing were established by LS-DYNA software. The stress wave propagation law, peak stress change and rock fracture state under various working conditions were analyzed. The optimization formula of a hole network relationship was proposed and verified on site. The results show that the shock wave generated by the explosion propagates rapidly upward from the explosion source and forms a plastic flow zone around the two boreholes. The energy consumption is the largest at this stage. With the propagation of the stress wave, energy dissipates, and its waveform gradually attenuates to a compression wave and seismic wave. In each working condition, a 110 mm aperture first cracked in the stress wave superposition area compared with other working conditions, while a 120 mm aperture delayed evolution to the seismic wave compared with different borehole aperture, and the energy attenuation rate is the slowest. Meanwhile, the fastest energy attenuation rate is with the 130 mm borehole aperture. With the attenuation of the propagation energy of the stress wave, among the four measuring points set at the center of the connection between the two boreholes, the Y-direction stress of the observation points B, C and D is stable between 2.3 and 3.5 MPa, and the Y-direction stress of the observation point A is strenuous between −1.3 and 1.2 MPa. The B, C and D observation points of 90–130 mm aperture conditions showed rock cracking at 7–9 times, 7–9 times, 7–10 times, 7–11 times, and 7–11 times hole spacing, respectively. The cracks of the two boreholes were interconnected. The optimal hole network relationship is obtained by fitting: y = 1.12 + 0.076x, where y is the optimal hole diameter and hole spacing multiple, and x is the hole diameter, which is verified by engineering. After blasting, the slope is smooth and smooth, and the half-hole rate is guaranteed to be above 90%.

Flame behavior, shock wave, and instantaneous thermal field generated by unconfined vapor-liquid propylene oxide/air cloud detonation

Energy output and heating effects are essential for vapor-liquid fuel/air cloud detonation in the fuel-air explosive (FAE) applications or explosion accidents. The purpose of this study is to examine the dynamic large-size flame behavior, shock wave propagation law, and instantaneous thermal field generated by unconfined vapor-liquid propylene oxide (PO)/air cloud detonation. Based on computational fluid dynamics (CFD) and combustion theory, a numerical simulation is used to study the detonation process of a PO/air cloud produced by a double-event fuel-air explosive (DEFAE) of 2.16 kg. The large-scale flame behavior is characterized. The flame initially spreads radially and laterally in a wing shape. Subsequently, the developed flame increases with a larger aspect ratio. Moreover, the propagation laws of shock waves at different heights are discussed. The peak pressure of 1.3 m height level with a stepwise decline is obviously different from that of the ground with an amplitude of reversed 'N' shape. In the vast majority of the first 6.9 m, the destructive effect of the shock wave near the ground is greater than that of the shock wave at 1.3 m height. Furthermore, the dynamic instantaneous isothermal field is demonstrated. The scaling relationship of various isotherms in the instantaneous thermal field with the flame and initial cloud is summarized. The comprehensive numerical model used in this study can be applied to determine the overpressure and temperature distribution in the entire fuel/air cloud detonation field, providing guidance for assessing the extent of damage caused by DEFAE detonation.