Attenuation Formula Research Articles

Simulation Research on the Dual-Electrode Current Excitation Method for Distance Measurements While Drilling

Based on a comprehensive analysis of the existing methods for measuring adjacent well distances, along with their advantages and disadvantages, this study employs theoretical analysis, simulation experiments, and other comprehensive research methods to investigate a distance measurement method based on current excitation. In response to the need for measuring and controlling the connection of relief wells, a method utilizing dual-electrode current excitation during drilling is proposed. This approach facilitates synchronous excitation measurements while drilling, significantly reducing both time and costs while ensuring safety and efficiency, making it particularly suitable for the connection operation of relief wells that involve safety risks. Firstly, this paper establishes a drilling with measurement model corresponding to the excitation mode, which derives the calculation formulas for the target casing current amplitude attenuation, as well as the induced magnetic field distribution within the formation. Additionally, it provides the calculation methods for determining the target well distance and azimuth direction. Lastly, the impact levels of various key factors are verified through numerical calculations and simulation analyses, which confirm the correctness and effectiveness of this distance measurement method. The findings from this research establish both a core theoretical foundation and a technological basis for the real-time measurement of adjacent well distances during relief well operations.

Analytical modelling techniques for efficient broadband noise prediction of high-speed trains

Analytical modelling techniques are presented for broadband noise prediction of high-speed trains. For interior noise problems, train body structures are modelled exactly by the dynamic stiffness method (DSM); whereas the interior acoustic cavities of the train body are modelled by the SDSM where the boundary conditions are described by modified Fourier series with a rapid convergence rate. Finally, the vibro-acoustic coupling model of the train body structures is constructed. For exterior noise problems, exterior train noise models are first formed by experimental data considering the Doppler effect; then both the DSM and theoretical attenuation formulas are used to build noise radiation models for different external environment conditions. The performance of the method is evaluated by predicting the interior sound field distribution of typical cross sections of the train body and the external radiated noise in a tunnel, or in an environment where the acoustic barrier or buildings along railways exist. Numerical results are in good agreement with the those obtained by the finite element method. Thus, the proposed methods can achieve broadband noise prediction highly accurately and efficiently, which can also serve as the benchmark for predicting the radiated noise generated by high‐speed trains.

Vibrations in piezothermoelastic micro-/nanobeam with voids utilizing modified couple stress theory

The present study examines the vibrations in micro- and nano-piezothermoelastic beams with voids. In this work, the modified couple stress theory is employed to generate closed-form formulas for deflection, volume fraction, electric potential and temperature distribution. The effects of voids, modified couple stress, beam dimensions and electric potential on energy dissipation (thermoelastic damping) are examined for beams under various boundary conditions. We have established analytical formulas for frequency shift, attenuation and thermoelastic damping. MATLAB software is used to get numerical results and exhibit them visually.

Improved Formulae for Low-Frequency Ultrasonic Attenuation in Metals

A range of ultrasonic techniques associated with the nondestructive evaluation of metals involves the propagation of low-frequency elastic waves. Metals that are isotropic and homogeneous in the macroscopic length scale contain elastic heterogeneities, such as grain boundaries within the microstructures. Ultrasonic waves propagating through such microstructures get scattered from the grain boundaries. As a result, the propagating ultrasound attenuates. The mass density and the elastic anisotropy in each constituent grain govern the degree of heterogeneity in the polycrystalline aggregates. Existing elastodynamic models consider first-order scattering effects from grain boundaries. This paper presents the improved attenuation formulae, for the first time, by including the next order of grain scattering effects. Results from investigating 759 polycrystals reveal a positive correlation between the effects of higher-order scattering from grain boundaries and the degree of heterogeneity. Thus, higher-order grain scattering effects are now known. These results motivate further investigation into higher frequencies and strongly scattering alloys in the future.

Study on the influence of branch slope on smoke movement mechanism in bifurcated tunnel fire under natural ventilation

In order to investigate the impact mechanism of branch slope on fire smoke in underground bifurcation spaces, a series of small-scale fire experiments were conducted. This study measured relevant data under natural ventilation conditions for four different branch slopes and six fire power levels, focusing on the highest ceiling temperature in the tunnel and the attenuation pattern of ceiling temperatures along the longitudinal direction in both the main and branch tunnels. It also analyzed the temperature field, velocity field, and pressure field at the bifurcation. The results indicate that a decrease in branch slope leads to an increase in the highest temperature in the main tunnel, primarily due to the enhanced chimney effect that intensifies the entrainment of smoke and accelerates the flow of fire smoke. A modified model for the highest temperature, considering the influence of branch slope, was proposed. Branch slope has a certain impact on the longitudinal temperature attenuation of the tunnel ceiling, with a relatively weaker effect on the main tunnel. Based on empirical formulas, a formula for longitudinal temperature attenuation involving slope, including both the main and branch tunnels, was developed. Fire smoke accelerates at the bifurcation point, a phenomenon that intensifies with an increase in the slope of the branch tunnel. The research in this paper provides a reference for fire safety issues in bifurcated tunnel structures.

Vibration response prediction and vibration safety assessment method for building structures around viaducts under the action of high-speed railway trains

Concerning the cumulative damage of building structures caused by the long-term effects from high-speed railway train loads and various environmental impacts, and to ensure the service safety of building structures around viaducts, this paper establishes a vibration safety assessment method for the entire life cycle of building structures with less workload and good applicability, while ensuring the accuracy and effectiveness of the prediction of vibration response of building structures. Firstly, the vibration source function is formed based on the mechanical model of the mobile vibration source of high-speed railway trains, and the vibration wave of high-speed railway trains is numerically simulated. Then the time and frequency characteristics of the simulated high-speed railway train vibration waves are verified through on-site monitoring tests. In addition, the peak particle vibration velocity attenuation formula for the foundation site of the viaduct is derived by the dimension analysis method, and it is used to correct the attenuation characteristics of the simulated high-speed railway train vibration waves. Finally, based on the response spectrum method to realize the prediction and assessment of the overall vibration response of the building structures, and using the cumulative damage coefficient to reflect the cumulative degree of the service damage of the building structure, a vibration safety assessment method for the whole lifecycle of the building structure is proposed. The method overcomes the shortcoming that vibration velocity does not reflect the impact of service damage on the vibration safety of building structures, and avoids neglecting localized vibration damage, and is therefore useful for the rapid, overall vibration safety assessment of any long-term service building structure in a viaduct site.

Surface-Enhanced Raman Spectroscopy Substrate Time Stability Improvement Using an External Oxygen Barrier Method.

The poor time stability of surface-enhanced Raman scattering (SERS) substrates greatly limits their application potential. Although core-shell structures are commonly used to enhance stability, their complex preparation processes, high costs, and susceptibility under acidic or alkaline conditions result in serious disadvantages for practical applications. Here, we propose a new method of external oxygen barrier to improve spectral stability, in which SERS substrates are stored in an oxygen-free environment. Controlled experiments are carried out under air and vacuum. Raman spectrum intensity is measured 11 times within six months for each group. Using the attenuation formula, the Raman spectrum intensity decay results of each SERS substrate over time are obtained. The effectiveness of the external oxygen barrier method is demonstrated through curve fitting using the corresponding function. The substrate spectral attenuation rates of the vacuum group and the argon group within six months are <20%, proving the effectiveness of the external oxygen barrier method.

Study on the propagation and attenuation characteristics of tunnel blasting vibration waves at different blast center distances

Accurately determining the parameters of the dynamic constitutive model is significant to analyzing the dynamic response characteristics of the surrounding rock at the proximal and distal ends of a railroad tunnel blasting. Hence, this paper analyzes the propagation and attenuation of blasting vibration waves in the rock by utilizing the vibration velocity monitoring data of the Xinbin Tunnel at the Liaoning section of the Shenbai High-speed Railway. The data are provided by the drilling and blasting method. Additionally, the IA-BP inverse analysis method was established to invert the parameters of the JH-2 constitutive model of the rock by numerically analyzing the simulated blasting vibration waves using the inversion parameters. The results highlight that the inversion value obtained by the IA-BP algorithm is slightly different from the calculated test value but still highly accurate, demonstrating the rationality of the inverse analysis method. Meanwhile, the numerical simulation results supplement the proximal vibration velocity, which is difficult to monitor in the project. This is because the vibration velocity of the tunnel surrounding the rock has a noticeable directional effect. Specifically, the vibration velocity law varies as the blast center distance increases, where the peak vibration velocity direction at the far end of the blast changes from the Y direction (vertical direction) to the Z direction (blast direction). The linear attenuation formula of the vibration velocity in the three principles of the tunnel arch, arch shoulder, and arch foot is obtained by fitting, which is an adequate prediction of the safety of the subsequent construction.

Usage of radial basis function neural network for dual-energy radiative detection system for measuring the oil pipelines scale layer

Scaling oil pipelines over time leads to issues including diminished flow rates, wasted energy, and decreased efficiency. In order to take preventative measures in a timely manner and avoid the aforementioned issues, it is crucial to get a precise gauge of the scale within the pipe. Non-invasive gamma attenuation systems are one of the most accurate detection methods. In this investigation, he Monte Carlo N Particle (MCNP) technique was used to model a scale thickness measuring system including a test pipe, two sodium iodide detectors, and a dual-energy gamma source. The three-phase flow was created by simulating water, gas and oil in a homogenous flow regime in the test pipe. Additionally, a scale of varying thicknesses was installed inside the conduit. The photon intensity on the opposite side of the pipe was measured by detectors when gamma rays shone through it. Photopeaks of 241 Am and 133 Ba of the transmission detector and the total count of the scattering detector were derived from the signal received by the detectors. Since there are different variables such as scale layer and volume fractions in the present study, it is not possible to use regular known attenuation formulas for calculating the thickness. So, in this paper, RBF was implemented to solve this issue. By training and optimizing a RBF network, we were able to predict the thickness of a scale with an RMSE of 0.057. Having such a small margin for error confirms the validity of the suggested technology and its practical use in the petroleum and petrochemical industries.

Practical calculation methods for ground noise correction factors in airport noise prediction model

This paper describes the results of a study to improve the calculation method for predicting aircraft noise around Japanese airports using our prediction model. The model limited the calculation frequency for the insertion loss caused by noise barriers and buildings to a single 250 Hz, which does not reflect the actual frequency spectrum of aircraft. Therefore, to simulate more realistic conditions, we calculated a synthetic attenuation chart from the frequency spectra of several representative aircraft models and included the chart in our model. We then compared the calculated values with the measured values to verify the validity and discussed the influence of this change on the airport noise contours. In addition, for noise propagation of engines and auxiliary power units on the ground, an improved calculation formula for ground surface attenuation, taking into account the ground condition, has already been reported. In this paper, we report on the implementation of this calculation formula in our model and discussion of the calculation results.

Attenuation characteristics of shock waves in drilling and blasting based on viscoelastic wave theory

This study investigates the propagation and attenuation characteristics of shock waves produced by drilling and blasting. The focus is on a novel method for calculating the attenuation of the shock wave pressure. Based on the propagation of shock waves in a rod with a variable section and a Maxwell model for rock, theoretical solutions for the attenuation of the blast-induced shock wave pressure were derived and the main factors influencing the attenuation speed were analyzed. The attenuation law of shock waves for siltstone, limestone, and granite, with common borehole diameters of 76–150 mm and initial shock pressures of 1–6 GPa, was analyzed through numerical simulations. The results show that the shock wave falls off as the square root of the relative distance. The attenuation speed of the shock wave is mainly related to the borehole size, rock properties, and shock wave intensity. The attenuation speed increases with increasing initial shock pressure on the borehole wall, but decreases with increasing borehole radius. Compared with soft rock, the shock wave pressure attenuates faster in hard rock. Combining theoretical analysis and numerical simulations, an exponential attenuation coefficient was introduced to the attenuation formula. Statistical analysis shows that the exponential attenuation coefficient is linearly proportional to the initial shock pressure. Furthermore, a new method for calculating the attenuation of shock wave pressure was proposed, reflecting the comprehensive influence of rock characteristics and shock wave intensity. The new method is an improvement over existing methods, which only consider the effect of rock properties on shock wave attenuation. The reliability of the new method was verified against the results of field tests. The findings provide a theoretical basis for the optimization of blasting parameters and assessments of blast-resistance for structures.

Enhancing predictive power by unamalgamating multi-item scales.

The generally small but touted as "statistically significant" correlation coefficients in the social sciences jeopardize theory testing and prediction. To investigate these small coefficients' underlying causes, traditional equations such as Spearman's (1904) classic attenuation formula, Cronbach's (1951) alpha, and Guilford and Fruchter's (1973) equation for the effect of additional items on a scale's predictive power are considered. These equations' implications differ regarding large interitem correlations enhancing or diminishing predictive power. Contrary to conventional practice, such correlations decrease predictive power when treating items as multi-item scale components but can increase predictive power when treating items separately. The implications are wide-ranging. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Study on energy excitation effect and structure optimization of vibratory vibrator considering captured road

This paper focuses on the influence of road weight captured by vibration on vibratory vibrator energy excitation and the optimization of vibratory vibrator baseplate when there is road instead of direct contact between baseplate and the ground. For this purpose, based on the vibration attenuation formula of the foundation surface, the variation law of the captured road weight is obtained. The excitation dynamics model considering the captured road weight is constructed and verified. The energy excitation effect of vibration system is analyzed. By using topology optimization method, the baseplate is optimized, and the comparative study of vibratory vibrator excitation effect before and after optimization is carried out. In the process of energy transmission of the vibrator, the reaction mass will consume most of the energy, the actual output vibratory wave energy is only 5.5% of the total energy. The octagonal I-steel baseplate can reduce its weight by 442 kg while ensuring its rigidity, and the energy excitation effect is relatively improved by 18.2%. The research will provide a reference for improving the energy excitation effect of vibratory vibrator considering the weight of the captured road.

Analytical investigation into the powder distribution and laser beam-powder flow interaction in laser direct energy deposition with a continuous coaxial nozzle

The powder distribution and interaction between the laser beam and powder flow affect the deposition quality during the process of laser direct energy deposition with a continuous coaxial nozzle. In this paper, some key analytical formulae related to the laser beam-powder flow interaction are comprehensively deduced and validated. The powder distribution formulae for different regions are first established considering the divergence angles of powder jet. The energy attenuation formulae of laser beam passing through the powder flow are derived considering the change of powder distribution from annular to circular Gaussian modes. The temperature formulae of powder particles passing through the laser beam are derived based on a proposed temperature formula with the solid-liquid phase transition, and the powder temperature is also further analyzed. These formulae are validated by published deposition examples and used to analyze the laser beam-powder flow interaction.

A new visual approach with the concentration calibration method for the hydrogen leakage and distribution research

Hydrogen security is an intrinsic requirement for the increasing development of hydrogen energy. The evolutional regularity of hydrogen leakage including hydrogen concentration and its distribution plays a key role in hydrogen leakage prevention, hence essential for safety research. It is difficult to measure hydrogen concentration distribution covering the whole area as a measurement plane due to the discreteness or invasiveness of the conventional sensing method. To solve the problem, this paper proposed a new method for quantitative analysis of hydrogen leakage distribution with a visual imaging experiment. Firstly, a series of imaging experiments under different leakage concentrations were performed based on the schlieren technique. A new calibration method is developed to deal with the mapping relationship between the jet leakage concentration and the gray value of the schlieren image. Therefore, the different gray values of the schlieren image are labeled as different hydrogen concentrations. Then, by extracting the quantitative concentration information in the axial and radial direction of the schlieren image, the concentration attenuation formulas in these two directions can be obtained. The proposed visual approach together with the gray calibration method are verified by comparative experiments, and the attenuation formula accurately represents the jet concentration distribution with an average error of less than 10%.

Effect of Air Inlet Spacing on Air Distribution and Ventilation Performance of Stratum Ventilation Using Multiple Parallel Jets

An appropriate layout of air terminals can improve the thermal comfort and air quality for room occupants. Stratum ventilation (SV) can efficiently provide thermal comfort and quality of inhaled air. However, investigations into the impact of the supply air inlet spacing on performance under SV are lacking. This study conducted experimental measurements and numerical simulations to analyze the effect of the supply inlet spacing on the air distribution and ventilation performance of the SV. Six theoretical axial velocity attenuation formulas were verified using experimental results. The effective draft temperature for SV (EDTS), air diffusion performance index (ADPI), the local mean age of air (LMAA), and energy utilization coefficient (EUC) were used as the evaluation indexes. The results indicated that the modified Abramovich formula was the most suitable for predicting the attenuation of the axial velocity of multiple parallel jets under SV. At an air supply spacing of 650 mm, the position near the central air supply inlet experienced a cold thermal environment with high air velocity and low air temperature; the positions on both sides of the room were warmer owing to insufficient airflow. The air distribution at these positions improved with increasing air inlet spacing, but some areas could not be covered by the supply airflow. The optimal value of ADPI corresponded to an air inlet spacing of 800 mm, whereas optimal LMAA and EUC corresponded to a spacing of 950 mm. Analysis of a multi-objective optimization method indicated that an air inlet spacing of 800 mm provided optimal overall performance.

Dynamic Response and Failure Mechanism of Deep-Buried Tunnel with Small Net Distance under Blasting Load

Under blasting load, a series of safety problems, such as lining cracking and surrounding rock instability, are prone to occur in deep-buried tunnels with a small net distance. It is significant to understand the dynamic response and failure mechanism of tunnels under blasting. The blasting attenuation formula is optimized through theoretical analysis and field experiments. The measuring point vibration is monitored in real time and the tunnel blasting model is established by ANSYS/LS-DYNA software. The model was set as having no reflective boundary and an uncoupled charge structure was used. The attenuation law of blasting seismic waves is studied from the adjacent tunnel lining and the direction of the tunnel cross-section and length. The inner and outer sides of the tunnel lining are investigated, respectively. The displacement and acceleration of lining measuring point are also analyzed. The dynamic response of the tunnel lining under blasting excavation is analyzed from multiple angles. The results show that the arch foot on the inner side of the lining (the side in contact with the tunnel headroom) is the first to generate vibration. On the outside of the lining (the side in contact with the rock),the peak vibration velocity is reached after blasting load unloading. There is little difference in the vibration velocity at different positions of the transverse section, but great difference in the vibration velocity of the longitudinal section. The influence of the horizontal displacement was greater than that of the vertical displacement. The vibration acceleration of the measuring point at the arch foot of the section is the largest and the detonation is also the largest.

Calculation of hole spacing and surrounding rock damage analysis under the action of in situ stress and joints

In situ stress and joints have a significant impact on the propagation and attenuation pattern of blast stress waves, and they are two important factors that must be considered for tunnel blasting hole network deployment. This paper proposes a blast stress wave attenuation equation and a peripheral hole distance calculation method under the combined action of in situ stress and joints. First, the static and dynamic parameters of the jointed slate are obtained by drilling core samples in the field and conducting indoor tests. Next, considering the geometric and physical attenuation of the blast stress wave, the attenuation formula of the blast stress wave under the combined action of in situ stress and joints is derived. Based on the theory of the combined action of stress waves and explosive gas, a formula for calculating the peripheral hole distance that integrates the effects of in situ stress, joints, and tensile strength of the rock body is proposed. Finally, LS-PREPOST software is used to analyze the damage to the surrounding rock, verified by an on-site blasting test. The results show that the blast stress wave attenuation formula proposed in this paper can accurately predict the stress wave peak value under the combined action of in situ stress and joints. Combining the geological conditions and blasting parameters of the Bayueshan Tunnel study section, the optimal peripheral hole spacing is calculated to be 45 cm. The average over-excavation value of the grade IV surrounding rock is controlled within 22 cm and the over-consumption of concrete per linear meter is controlled within 100% using the peripheral hole layout method and the hole network layout parameters proposed in this paper. The research results provide a reference for the control of over-excavation and under-excavation in large-section tunnel blasting.

On the evolution of pebble-accreting planets in evolving protoplanetary discs

ABSTRACTWe examine the migration of luminous low-mass cores in laminar protoplanetary discs where accretion occurs mainly because of disc winds and where the planet luminosity is generated by pebble accretion. Using 2D hydrodynamical simulations, we determine the eccentricities induced by thermal forces as a function of gas and pebble accretion rates, and also evaluate the importance of the torque exerted by the solid component relative to the gas torque. For a gas accretion rate $\dot{M}= 2\times 10^{-8}\, \mathrm{ M}_\odot$ yr−1 and pebble flux $\dot{M}_{\mathrm{ peb}}=170\, \mathrm{ M}_\oplus$ Myr−1, we find that embryo eccentricities attain values comparable to the disc aspect ratio. The planet radial excursion in the disc, however, causes the torque exerted by inflowing pebbles to cancel on average and migration to transition from outward to inward. This is found to arise because the magnitude of thermal torques decreases exponentially with increasing eccentricity, and we provide a fitting formula for the thermal torque attenuation as a function of eccentricity. As the disc evolves, the accretion luminosity becomes at some point too small to make the core eccentricity grow such that the solid component can exert a non-zero torque on the planet. This torque is positive and for gas accretion rates $\dot{M} \lesssim 5\times 10^{-9}$M⊙ yr−1 and pebble fluxes $\dot{M}_{\rm {peb}} \lesssim 120\, \mathrm{ M}_\oplus $ Myr−1, it is found to overcome the gas torque exerted on cores with mass $m_\mathrm{ p}\lesssim \, 1\,\mathrm{ {M}}_\oplus$, resulting in outward migration.

Study on the migration law of gas explosion disaster products in complex air network of mine

ABSTRACT Underground mine gas explosion will produce a shock wave and harmful gas at high temperatures. Firstly, this paper studies the attenuation formula and attenuation coefficient of the shock wave. Comparison and analysis of three shock wave attenuation formulas based on experimental burst data from two large tunnels. It is found that the shock wave attenuation formula of the dimensional method agrees well with the experimental data. Based on the gas explosion accident at the Tunlan Mine. The calculated shockwave pressure on the blast shield is 78,915 N, which is greater than the mass of the explosion-proof cover itself at 35,280 N, the same as the fact that the explosion-proof is jacked up observed in the accident report. The accuracy of the shock wave attenuation formula and attenuation coefficient is verified. Secondly, based on the dispersion theory, the migration law of harmful gas after an explosion is analyzed, and the superposition and separation law of harmful gas in branch roadway is studied. Taking CO as the index gas, the concentration change of CO near the explosion source of Tunlan Mine is analyzed by using Ventsim software. Simulation results show that the maximum peak values of monitoring points 5 and 6 of branch roadways are 9000 ppm, which is the same as the maximum peak concentration of monitoring point 1. And the maximum peak values of monitoring points 3 and 4 are 13300 ppm, which is the same as the maximum peak concentration of monitoring point 2. The simulation results confirm the gas migration law of branch roadway. Studying the attenuation law of explosion shock waves and the propagation law of harmful gas can reduce the unnecessary loss caused by blind rescue and provide theoretical support for formulating a mine emergency rescue plan. It also provides a basis for developing underground anti-shock wave buffer facilities.