Empirical formulae for electric double-layer repulsion between two arbitrarily inclined clay particles

To understand the mesoscopic mechanism of clayey soil in view of macroscopic behavior, it is essential to quantitatively calculate the electric double-layer repulsion between arbitrarily inclined clay particles.However, suitable calculation methods with high efficiency and accuracy are still rare at present in literature. Based on a great number of numerical calculations of the repulsion between two inclined platy clay particles, explicit empirical formulae for estimating electric double-layer repulsion between clay particles are put forward. Comparison between the empirical solutions and corresponding numerical results shows that the proposed formulae have a reasonable accuracy, and application of the presented formula is easy and efficient.

In-Tunnel Blast Pressure Empirical Formulas for Detonations External, Internal and at the Tunnel Entrance

In order to define the loading on protective doors of an underground tunnel, the exact knowledge of the blast propagation through tunnels is needed. Thirty-three scale high-explosive tests are conducted to obtain in-tunnel blast pressure for detonations external, internal and at the tunnel entrance. The cross section of the concrete model tunnel is 0.67 m2. Explosive charges of TNT, ranging in mass from 400 g to 4 600 g, are detonated at various positions along the central axis of the model tunnel. Blast gages are flush-installed in the interior surface of the tunnel to record side-on blast pressure as it propagates down the tunnel. The engineering empirical formulas for predicting blast peak pressure are evaluated, and are found to be reasonably accurate for in-tunnel pressure prediction.

A Simple Empirical Formula for Predicting the Ultimate Strength of Ship Plates with Elastically Restrained Edges in Axial Compression

An investigation is conducted on the static ultimate limit state assessment of ship hull plates with elastically restrained edges subjected to axial compression.Both material and geometric non-linearities were considered in finite element(FE)analysis.The initial geometric imperfection of the plate was considered,while the residual stress introduced by welding was not considered.The ultimate strength of simply supported ship hull plates compared well with the existing empirical formula to validate the correctness of the applied boundary conditions,initial imperfection and mesh size.The extensive FE calculations on the ultimate strength of ship hull plates with elastically restrained edges are presented.Then a new simple empirical formula for plate ultimate strength is developed,which includes the effect of the rotational restraint stiffness,rotational restraint stiffness,and aspect ratios.By applying the new formula and FE method to ship hull plates in real ships,a good coincidence of the results between these two methods is obtained,which indicates that the new formula can accurately predict the ultimate strength of ship hull plates with elastically restrained edges.

Research and Experimental Application of Empirical Formulas to Calculate Riverbank Erosion in Tien River in the Mekong Delta

In recent years,the problem of riverbank and coastal erosion in the MD(Mekong Delta)is very complicated;landslides occur in most of the inland and coastal provinces.Most riverbank landslides occur gradually,but in contrast to sudden landslides that cause great damage,occur with increasing frequency.This shows that the trend of riverbank erosion will be more complicated and more frequent,especially in the context of extreme weather changes and changes in hydrological regime in the next time.Statistics from the authorities show that,if in 2010 the whole region had nearly 100 landslide points;by 2020 it had increased to more than 680 points;in which Dong Thap in the Tien River is one of the two localities with the most serious riverbank erosion.Currently,there are many methods used to assess and forecast the level of riverbank erosion in specific areas,such as:method of document analysis,measurement data;physical model;mathematical models and empirical formulas.In this study,the empirical formula is used to calculate the landslide level for the Tien River section in Cao Lanh,Dong Thap province.The calculation results according to the empirical formula have a certain agreement with the actual data,the correlation coefficient is 0.90 and the Nash coefficient is 0.78,the relative error of less than 15%is 80%of the cross-section.Such results have shown the possibility of applying empirical formulas to establish and calculate for other landslide areas along the banks of Hau River and MD.

Predictions of ground surface settlement for shield tunnels in sandy cobble stratum based on stochastic medium theory and empirical formulas

This paper focuses on the prediction of ground surface settlement induced by shield tunnelling in sandy cobble stratum.Based on the stochastic medium theory,an analytical solution to predict the surface settlement is developed considering the difference between soil and tunnel volume loss.Then,the effects of tunnel geometries,influence angle and volume loss on the characteristics of surface settlement are discussed.Through back analysis,a total of 103 groups of field monitoring data of surface settlement induced by shield tunnelling in sandy cobble stratum are examined to investigate the statistical characteristics of the maximum settlement,settlement trough width and volume loss.An empirical prediction is presented based on the results of back analysis.Finally,the analytical solution and empirical expression are validated by the comparisons with the results of model tests and field monitoring.Results show that the soil at ground surface has an overall dilative response for most of the shield tunnelling in sandy cobble stratum.In addition,the developed analytical solution is applicable and reasonable for surface settlement prediction.Meanwhile,the proposed empirical formula also shows good per-formance in some cases,providing an approach or a reference for engineering designers to preliminarily evaluate the surface settlement.

An empirical formula for yield estimation from singly truncated performance data of qualified semiconductor devices

The problem of yield estimation merely from performance test data of qualified semiconductor devices is studied. An empirical formula is presented to calculate the yield directly by the sample mean and standard de- viation of singly truncated normal samples based on the theoretical relation between process capability indices and the yield. Firstly, we compare four commonly used normality tests under different conditions, and simulation results show that the Shapiro-Wilk test is the most powerful test in recognizing singly truncated normal samples. Secondly, the maximum likelihood estimation method and the empirical formula are compared by Monte Carlo simulation. The results show that the simple empirical formulas can achieve almost the same accuracy as the max- imum likelihood estimation method but with a much lower amount of calculations when estimating yield from singly truncated normal samples. In addition, the empirical formula can also be used for doubly truncated normal samples when some specific conditions are met. Practical examples of yield estimation from academic and IC test data are given to verify the effectiveness of the proposed method.

An empirical formula for scattered neutron components in fast neutron radiography

Scattering neutrons are one of the key factors that may affect the images of fast neutron radiography. In this paper, a mathematical model for scattered neutrons is developed on a cylinder sample, and an empirical formula for scattered neutrons is obtained. According to the results given by Monte Carlo methods, the parameters in the empirical formula are obtained with curve fitting, which confirms the logicality of the empirical formula. The curve-fitted parameters of common materials such as 6 LiD are given.

New empirical formula for(γ, n) reaction cross section near GDR peak for elements with Z ≥ 60

A new empirical formula has been developed that describes the（7,n nuclear reaction cross sections for isotopes with Z ≥ 60.The results were supported by calculations using TALYS-1.6 and EMPIRE-3.2.2 nuclear modular codes.The energy region for incident photon energy has been selected near the giant dipole resonance（GDR peak energy.The evaluated empirical data were compared with available data in the experimental data library EXFOR.The data produced using TALYS-1.6 and EMPIRE-3.2.2 are in good agreement with experimental data.We have tested and presented the reproducibility of the present new empirical formula.We observe the reproducibility of the new empirical formula near the GDR peak energy is in good agreement with the experimental data and shows a remarkable dependency on key nuclei properties：the neutron,proton and atomic number of the nuclei.The behavior of nuclei near the GDR peak energy and the dependency of the GDR peak on the isotopic nature are predicted.An effort has been made to explain the deformation of the GDR peak in（γ,n nuclear reaction cross sections for some isotopes,which could not be reproduced with TALYS-1.6 and EMPIRE-3.2.2.The evaluated data have been presented for the isotopes ^180W,^183W,^202Pb,^203Pb,^204Pb,^205Pb,^231Pa,^232U,^237U and ^239Pu,for which there are no previous measurements.

Empirical formulas for proton decay half-lives:Role of nuclear deformation and Q-value

Two empirical formulas for the proton decay half-lives including nuclear deformation are proposed. The formula with parameter set I gives the logarithm of the proton decay half-lives as an explicit function of the orbital angular momentum with eight adjustable parameters, whereas that with set II represents the logarithm of the reduced half-lives as an implicit function of the angular momentum with seven adjustable parameters. Experimental data for the half-lives of 44 proton emitters in the ground state or isomeric state were used to obtain the parameters. The experimental and calculated Q values were used. Different sets of parameters were obtained for the ground state transition, isomeric state transition, and all transitions for both deformed and spherical nuclei. The best agreement with experimental data was observed for set I for deformed proton emitters with exr）erimental Q values.

SPAGINS:semiempirical parameterization for fragments in gamma-induced nuclear spallation

From the empirical phenomena of fragment distributions in nuclear spallation reactions,semiempirical formulas named SPAGINS were constructed to predict fragment cross-sections in high-energyγ-induced nuclear spallation reactions(PNSR).In constructing the SPAGINS formulas,theoretical models,including the TALYS toolkit,SPACS,and Rudstam formulas,were employed to study the general phenomenon of fragment distributions in PNSR with incident energies ranging from 100 to 1000 MeV.Considering the primary characteristics of PNSR,the SPAGINS formulas modify the EPAX and SPACS formulas and efficiently reproduce the measured data.The SPAGINS formulas provide a new and effective tool for predicting fragment production in PNSR.

Empirical Neutron Cross Section Formulae for (n, p) and (n, d) Reactions of He-3 Target

In this work, new cross section formulae for (n, p) and (n, d) reactions of He-3 have been investigated as a function of incident neutron energy. The new Empirical formulae were produced by using the least squares method to the experimental cross sections data, which were taken from Experimental Nuclear Reaction Data EXFOR Database Version of 2021. Several functions were examined to choose the best one that fits the data. Statistical hypothesis testing was used to insure how well the suggested equations fit the set of data. Two statistical indicators were used for each case for goodness-of-fit. Very high compatibility was found between the empirical values and the experimental data for both reactions.

Updating empirical results of wind loads on cooling towers for turbulence intensity effects

Variations of wind effects on large cooling towers observed at different turbulence intensities for our previous full-scale measurements might be caused by the inherent uncertainties in our physical experiments.Accordingly,the one-way analysis of variance(ANOVA)technique is employed for analyzing the data measured on the prototype Pengcheng cooling tower.Because ANOVA indicates that the variations of full-scale wind effects are basically the effects of turbulence intensity,the empirical results of wind loads on cooling towers obtained by generalizing physical experimental data without considering the turbulence intensity effects are updated using model test results obtained in multiple flow fields.The empirical fluctuating wind pressure distribution is updated based on the fact that the fluctuating wind pressure coefficient linearly increases with the increase in the turbulence intensity,and the empirical formulae of the spectra and the coherences is updated based on conservative assumptions.Comparisons of the empirical results and full-scale measurement data suggest that the original empirical results are either too conservative or unsafe for use.However,economic efficiency and conservativeness will be balanced if the updated empirical results are employed for the wind engineering design.

Theoretical study of electron-impact broadening for highly charged Ar XV ion lines

Spectral line widths produced by collisions between charged particles and emitters are of special interest for precise plasma spectroscopy.The highly charged Ar XV ion is demonstrated to have strong intrashell electron interactions,which manifest as an atomic system with many resonance structures,due to the quasi-degeneracy of orbital energies.In this paper we use the relativistic R-matrix method to investigate the electron-impact broadening of highly charged Ar XV ion spectral lines under the impact approximation.It is found that the results considering resonance structures are significantly different from those of the distorted wave approach.Furthermore,we propose a new empirical formula with a correction term to take into account the effect of resonances for electron-impact widths over a relatively wide range of plasma conditions.The corresponding fitting parameters of the new empirical formula for all 47 calculated transitions are also given with an estimated accuracy within 1%,which should be convenient for practical applications.The dataset that supported the findings of this study is available in Science Data Bank,with the link https://doi.org/10.57760/sciencedb.j00113.00101.

Calculation of Motor-pumped Well’s Drawdown in Land Consolidation

[Objective] The aim was to explore the measurement methods of drawdown of motor-pumped well in land consolidation. [Method] Based on pumping information, the relation curve of drawdown and pumped volume was drawn and the empirical formula was concluded, with examples. [Result] The type of drawdown （h） and flow volume （Q） includes linear type, parabolic type, exponential curve and logarithmic curve. Graphical method and calculus of differences are available for determining the type of curve. [Conclusion] The empirical formula based on pumping test reflects relation between drawdown and pumping volume, which is simple and effective.

The Driftless Electromigration Theory(Diffusion-Generation-Recombination-Trapping Theory)

Electromigration is the transport of atoms in metal conductors at high electronic current-densities which creates voids in the conductors and increases the conductors＇ electrical resistance. It was delineated in 1961 by Huntington; then modeled by the empirical electrical resistance formula derived by Black in 1969 to fit the dependences of the experimental electrical resistance and failure data on the electrical current density and temperature. Tan in 2007 reviewed 40-years＇ ap- plications of the empirical Black formula to conductor lines interconnecting transistors and other devices in silicon integrated circuits. Since the first Landauer theory in 1957,theorists have attempted for 50 years to justify the drift force or electron momentum transfer assumed by Black as some electron-wind force to impart on the metal atoms and ions to move them. Landauer concluded in 1989 that the electron wind force is untenable even considering the most fundamental and complete many-body quantum transport theory. A driftless or electron-windless atomic void model for metal conductor lines is reviewed in this article. It was developed in the mid-1980 and described in 1996 by Sah in a homework solution. This model accounts for all the current and temperature dependences of experimental resistance data fitted to the empiri- cal Black formula. Exact analytical solutions were obtained for the metal conductor line resistance or current, R （t）/R （0） = J（t）/J（0） = [1-2（t/τα）^1/α]^-1/2 ,in the bond-breaking limit with α = 1 to 2 and diffusion limit with α = 2 to 4,from low to high current densities, where τα is the characteristic time constant of the mechanism, containing bond breaking and diffusion rates and activation energies of the metal.

Analysis of the damage threshold of the GaAs pseudomorphic high electron mobility transistor induced by the electromagnetic pulse

An electromagnetic pulse（EMP）-induced damage model based on the internal damage mechanism of the Ga As pseudomorphic high electron mobility transistor（PHEMT） is established in this paper. With this model, the relationships among the damage power, damage energy, pulse width and signal amplitude are investigated. Simulation results show that the pulse width index from the damage power formula obtained here is higher than that from the empirical formula due to the hotspot transferring in the damage process of the device. It is observed that the damage energy is not a constant, which decreases with the signal amplitude increasing, and then changes little when the signal amplitude reaches up to a certain level.

Experimental study on the wave loads of twin-plate breakwaterunder oblique waves

In this study, systematic physical model tests were performed to investigate the wave forces on the twin-plate breakwater under irregular waves. Based on the experimental results, the effects of the relative plate width B/L,wave height Hs/D and incident angle θ0 on the wave forces were analyzed and discussed. The results showed that:(1) The envelopes of the total wave pressure were generally symmetrical along the direction of plate width under the incident angles(θ0) being 0°, 15°, 30°, 45° and 60°. In particular, the envelopes of wave pressure atθ0=30° were larger than all other cases.(2) The synchronous pressure distribution of the breakwater under oblique wave action was more complicated comparing to the normal incident waves.(3) Based on data analysis, an empirical formula was obtained to estimate the total vertical force of the twin-plate breakwater.This empirical formula can be a good reference for the design basis of engineering applications under specified wave conditions.

Shear creep characteristics and constitutive model of limestone

The characters of limestone in weak interlayer of a high rocky slope in Xuzhou, China, are studied by shear static test and shear creep test. The results show that limestone specimens have attenuation creep properties and constant rate creep properties, almost have no accelerated creep properties. The exponential type empirical formula is selected to fit creep grading curves by polynomial regression analysis method, and the square sums of the fitting results residual are in the order of 10^(-7). Then grade creep curves at every shear loads are set up. Combining creep rate-time curve, the creep properties of limestone are analyzed. As the physical meaning of component model is clearer, the Poytin–Thomson model is set up. Through the least square method, the optimal parameters of Poytin–Thomson model are obtained,and the sums of squared residuals belong to 10^(-3)order of magnitude, which can meet the accuracy requirements of engineering calculation. So the Poytin–Thomson model can reflect the shear creep characteristics of limestone very well.

Analysis of phreatic evaporation law and influence factors of typical lithology in Hebei Plain

Based on three typical mediums(sandy loam, loam and sandy clay loam) in Hebei Plain, this paper designs phreatic evaporation experiments under different lithology and phreatic depth. Based on the analysis of experimental data, the phreatic evaporation law and influencing factors of three mediums were studied. The results showed that:(1) The shallower the phreatic depth, the larger the phreatic evaporation.(2) Sandy clay loam has the biggest response to the increase of the phreatic depth, sandy loam is the second and loam is the smallest.(3) The limit depth of phreatic evaporation of sandy clay loam is about 3 m and that of loam and sandy loam is about 2 m and 3 m, seperately.(4) By fitting the daily evaporation of phreatic water and phreatic depth, the results showed that sandy loam and sandy clay loam are exponential functions and loam is power functions.

Numerical Study on Breaking Criteria for Solitary Waves

Studies of the breaking criteria for solitary waves on a slope are presented in this paper. The boundary element method is used to model the processes of shoaling and breaking of solitary waves on various slopes. Empirical formulae that can be used to characterize the breaking of solitary waves are presented. These include the breaking index, the wave height, the water depth, and the maximum particle velocity at the point of breaking. Comparisons with the results of other researches are given.