Previous Formulas Research Articles

Evaluation of mechanical characteristics of high strength steel fiber reinforced concrete with various concrete strengths

The performance of concrete is robust in compression but lacks tensile strength, making it brittle. Steel fibres are added to enhance concrete properties. These fibres play a crucial role in construction by improving structural performance, preventing cracks, and increasing ductility. The study investigated high-strength steel fibre-reinforced concrete (HSSFRC) with varying concrete strengths. Three high-strength concrete grades (70 MPa, 80 MPa, and 90 MPa) and different water-cement ratios (WCR) (0.25, 0.30, and 0.35) were studied. Hooked-ended 50mm steel fibres were added at content levels of 0.25%, 0.50%, 0.75%, and 1.00%. As steel fibre content increased from 0.25% to 0.75%, the compressive strength (CS) improved by 3.37%, 7.29%, and 10.54%. At the same time, the split tensile strength (STS) increased by 20.86%, 24.07%, and 26.74%. Similarly, the flexural strength (FS) increased by 19.87%, 23.12%, and 25.82% for a WCR of 0.25 in 70 MPa grade of concrete. However, adding 1.0% steel fibre led to decreased mechanical properties. The optimal steel fibre content across all concrete mixes was 0.75%. Mechanical properties weakened with higher WCR (0.25, 0.30, and 0.35). Additionally, regression analysis explored the relationships between CS, STS, and FS in the concrete mixes. The comparison between the test results and the regression analysis was carried out alongside the previous empirical formulas. Remarkably, the empirical formulas exhibited strong alignment with the experimental findings.

Refined formulation of the Taylor equation for calculating build-up factors of gamma rays in aluminium and anticipated radiation effects

Measuring the build-up of gamma rays within materials used as shields is of great importance to accurately assess radiation doses and design effective protective barriers. Taylor's formula was studied to calculate gamma-ray build-up factors, whose application is limited to a specific group of energies and a large number of parameters. The aim of this study is to improve Taylor's formula by developing mathematical formulas to calculate the parameters at each energy to include a wider range of energy and a small, fixed number of parameters. The results demonstrated that the difference between the gamma radiation dose build-up factors calculated according to the two empirical formulas (the previous traditional formula and the current improved formula) remains very small, and the values are more or less identical. In general, it is observed that the accumulation factor decreases with increasing gamma-ray energy and increases with increasing shield thickness. Researchers also explored the intricate impacts of gamma rays on aluminum shields and the subsequent reactions within the material. A number of potential interactions have been found in one of the world's leading laboratories. One of these reactions is selected in this study. It was found that increasing the gamma-ray build-up factor in aluminum is accompanied by an increase in its cross sections. This, in turn, indicates an increased probability of secondary reactions and subsequent gamma-ray emission.

Investigation of two-proton decay using modified formation probability

In this study, we investigated two-proton radioactivity using the two-potential approach with a cosh-type potential to calculate the half-lives. The depth parameter V0 = 58.405 MeV and diffuseness a = 0.537 fm in the cosh-type nuclear potential show the lowest standard deviation between the calculated and experimental half-lives. We proposed a linear formula for the formation probability using the linear relationship between log10S2p and A1/3d for the angular momentum state l = 0, 2 and 4. The model achieved the lowest standard deviation (σ = 1.09) using this linear formula compared to previous models and empirical formulas. The proposed formula significantly improved the accuracy of half-life predictions by reducing the standard deviation from 1.73 to 1.09. The predicted half-lives exhibit a hindrance factor in the range of -1.62 to 2.42, which is the lowest compared to earlier theoretical predictions. These results indicate that the proposed linear formation probability formula is suitable for reproducing experimental half-lives. The linear formula for formation probability was generalized for different angular momentum states by conducting least squares fit. We extended the half-life and formation probability predictions to 48 nuclei, and the predicted half-lives are in good agreement with the previous five theoretical models and two empirical formula predictions.

Extraction of stress intensity factors of biharmonic equations with free boundary conditions on crack faces (III): SIF of a thin plate subjected to the bending moment

The plate bending problems in the Kirchhoff–Love model can be reduced to biharmonic equations. In the previous papers (Kim et al., 2020; Kim et al., 2022), we derived stress intensity factors (SIF) extraction formulas of a biharmonic equation Δ2u=f in a non-convex (cracked, L-shaped) domain with various boundary conditions such as clamped, simply connected, free, and mixed. In previous papers, we could not show a general SIF formula related to Poisson’s ratio ν contained in the free boundary condition. Moreover, the previous SIF extraction formula obtained for a given Poisson’s ratio requires cumbersome line integrals. In this paper, removing the line integrals in the extraction formulas, we show improved SIF extraction formulas applicable to biharmonic equations with free boundary conditions. Thus, the new, improved SIF extraction formulas for free boundary conditions become more straightforward and can be applied to plate bending problems.

Modeling Molecular Hydrogen in Low-metallicity Galaxies

We use a suite of hydrodynamics simulations of the interstellar medium (ISM) within a galactic disk, which includes radiative transfer, a nonequilibrium model of molecular hydrogen, and a realistic model for star formation and feedback, to study the structure of the ISM and H2 abundance as a function of local ISM properties. We show that the star formation rate and structure of the ISM are sensitive to the metallicity of the gas with a progressively smoother density distribution with decreasing metallicity. In addition to the well-known trend of the H I–H 2 transition shifting to higher densities with decreasing metallicity, the maximum achieved molecular fraction in the ISM drops drastically at Z ≲ 0.2 Z ⊙ as the formation time of H2 becomes much longer than a typical lifetime of dense regions of the ISM. We present accurate fitting formulae for both volumetric and projected fH2 measured on different scales as a function of gas metallicity, UV radiation field, and gas density. We show that when the formulae are applied to the patches in the simulated galaxy, the overall molecular gas mass is reproduced to better than a factor of ≲1.5 across the entire range of metallicities and scales. We also show that the presented fit is considerably more accurate than any of the previous fH2 models and fitting formulae in the low-metallicity regime. The fit can thus be used for modeling molecular gas in low-resolution simulations and semi-analytic models of galaxy formation in the dwarf and high-redshift regimes.

Post Newtonian emission of gravitational waves from binary systems: a gauge theory perspective

Using the AGT correspondence and localization, we derive a combinatorial formula for the Post-Newtonian expansion of the wave form describing the gravitational emission from binary systems made of objects of extremely different masses. The results are written as a double instanton series describing the expansion of the gravitational wave at large distances and small velocities, and are tested against previous formulae in the literature for Schwarschild and Kerr black holes at the 5th and 3rd Post Newtonian order respectively beyond the quadrupole approximation. Tidal effects show up in the wave form at the 5th PN order, providing a quantitative measure of sizes and reflectivity properties of the gravity solution.

Cutting-edge insights: Crack growth rates in 9% Ni steel from room to cryogenic conditions influenced by crack closure and effective stress intensity factors

This study investigates the fatigue crack growth rate of 9% Ni steel at varying stress ratios under both room and cryogenic temperatures, attributing different growth rates to the phenomenon of crack closure. Traditional methods of studying crack closure, including the opening force, compliance ratio, and adjusted compliance ratio techniques, are assessed. Our results are juxtaposed with previous formulae for the opening force technique, leading to the introduction of a new formula that incorporates temperature effects by normalising the stress intensity factor with the yield strength at the respective test temperature. We highlight the adjusted compliance ratio (ACR) technique's limitations at cryogenic temperatures due to challenges in measuring notch open-crack compliance. As a solution, we present an innovative method that determines compliance using the effective elastic modulus. The mechanics behind the ACR technique are elucidated through the lens of the wedging mechanism. Our insights reveal that the ACR technique precisely calculates the effective stress intensity factor range (ΔKeff) under specific conditions. We address existing limitations by introducing a novel method, the triple compliance ratio (TCR) technique. A comparative analysis of effective stress intensity factors from all four techniques reveals the TCR technique's superior ability to correlate crack closure with crack growth. By eliminating the crack closure effect, the TCR technique offers a more accurate prediction of fatigue crack growth rate across diverse load ratios.

Rényi entropy with surface defects in six dimensions

We compute the surface defect contribution to Rényi entropy and supersymmetric Rényi entropy in six dimensions. We first compute the surface defect contribution to Rényi entropy for free fields, which verifies a previous formula about entanglement entropy with surface defect. Using conformal map to Sβ1×Hd−1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_{\\beta}^1\ imes {H}^{d-1} $$\\end{document} we develop a heat kernel approach to compute the defect contribution to Rényi entropy, which is applicable for p-dimensional defect in general d-dimensional free fields. Using the same geometry Sβ1×H5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_{\\beta}^1\ imes {H}^5 $$\\end{document} with an additional background field, one can construct the supersymmetric refinement of the ordinary Rényi entropy for six-dimensional (2, 0) theories. We find that the surface defect contribution to supersymmetric Rényi entropy has a simple scaling as polynomial of Rényi index in the large N limit. We also discuss how to connect the free field results and large N results.

Distance between consecutive elements of the multiplicative group of integers modulo n

For a prime number $p$, we consider its primorial $P:=p\#$ and $U(P):={\left(\ZZ{P}\right)}^\times$ the set of elements of the multiplicative group of integers modulo $P$ which we represent as points anticlockwise on a circle of perimeter $P$. These points considered with wrap around modulo $P$ are those not marked by the Eratosthenes sieve algorithm applied to all primes less than or equal to $p$. In this paper, we are mostly concerned with providing formulas to count the number of gaps of a given even length $D$ in $U(P)$ which we note $K(D,P)$. This work, presented with different notations is closely related to [5]. We prove the formulas in three steps. Although only the last step relates to the problem of gaps in the Eratosthenes sieve (see Section 3.2.2) the previous formulas may be of interest to study occurrences of defined gaps sequences. <ul> <li>For a positive integer $n$, we prove a general formula based on the inclusion-exclusion principle to count the number of occurrences of configurations<sup>1</sup> in any subset of $\ZZ{n}$. (see Equation (7) in Theorem 2.1).</li> <li>For a square-free integer $P$, we particularize this formula when the subset of interest is $U(P)$. (see Equation (11) in Theorem 3.2).</li> <li>For a prime $p$ and its primorial $P:=p\#$, we particularize the formula again to study gaps in $U(P)$. Given a positive integer $D$ representing a distance on the circle, we give formulas to count $K(D,P)$ the number of gaps of length $D$ between elements of $U(P)$ (see Equation (15) and Section 4.1).</li> </ul> In addition, we provide a formula (see Equation (27) in Theorem 5.1) to count the number of occurrences of gaps of an even length $N$ that contain exactly $i$ elements of $U(P)$. <sup>1</sup> <small>A defined sequence of gaps between the elements of the subset; this is referred to as a constellation in [5].</small>

Sediment transport modelling upstream of Al Kufa Barrage

Abstract This study estimated the amount of bed sediment load upstream of Kufa Barrage mainly depending on the hydrodynamic conditions, sediment concentration, and hydraulic parameters. Ten cross-sections approximately over 2 km in length in front of the barrage were selected. Velocities and suspended sediment concentrations at 0.2, 0.6, and 0.8 of the water depth at each section were recorded using an ADCP device. A depth-integrated sampling was utilized to examine the collected data from 6th January to 15th October 2022. It was noted that the effective depth-to-width computation methods and the Toffaleti sediment transport function with the Van Rijn fall velocity were the most compatible and appropriate approaches for determining the sediment transport potential in the selected reach. It was also noted that such techniques were better than the previous formulae to predict the total sediment load. The results revealed excellent agreement between the mean sediment discharge obtained using HEC-RAS 6.2, equal to 6.214 kg/s, and the mean sediment discharge obtained from the field measurements, equivalent to 7.142 kg/s.

Optimized distance measures on hesitant fuzzy numbers: An application

As the rapidly progressing applications of uncertainty theories, the need for modifications to some of their existing mathematical tools or creating new tools to deal correctly with them in various environments is also exposed. Hesitant fuzzy numbers (HFNs), as a particular case of fuzzy numbers, are not an exception to this rule. Considering the necessity of determining the distance between given HFNs in many of their practical applications, this article shows that the existing methods either do not provide correct results or are not able to meet the needs of users. This paper aims to present new methods for distance measures of hesitant fuzzy numbers. To do them, three prevalent distance measures, i.e., the generalized distance measure, the Hamming distance measure, and the Euclidean distance measure, will be optimized into three distinct trinal categories. With the approach of reducing error propagation via reducing some unnecessary mathematical computations, new distance measures on HFNs will be introduced, first. The middle is the modification of the first category, which is more suitable when the given HFNs are equal-distance by the previous formula. Also, as the third category, the weighted form of these distance measures has been proposed, to be used where the real and membership parts of HFNs are not of equal importance. As an application of these, a TOPSIS-based technique for solving multi-attribute group decision-making problems with HFNs has been proposed. A numerical example will be implemented to describe the presented method. Finally, along with the validation of the proposed method, its numerical comparison with some other existing methods will be discussed in detail.

Non-Axisymmetric Bouncing Dynamics on a Moving Superhydrophobic Surface

The phenomenon of droplet impact on moving surfaces is widely observed in fields such as transportation, rotating machinery, and inkjet printing. Droplets exhibit non-axisymmetric behavior due to the motion of solid surfaces which significantly determines core parameters such as contact time, maximum spreading radius, and bounding velocity, thereby affecting the efficiency of related applications. In this study, we focus on the kinetics and morphology of the non-axisymmetric bouncing behaviors for droplets impacting on a moving superhydrophobic surface (SHPS) within the normal (Wen) and tangential (Wet) Weber numbers. Considering the influences of the moving surface on the contact area and contact time, the previous scaling formula for the horizontal velocity of droplets has been improved. Based on the velocity superposition hypothesis, we establish a theoretical model for the ratio of the maximum spreading radius at both ends depending on Wen and Wet. This research provides both experimental and theoretical evidence for understanding and controlling the non-axisymmetric behavior of droplets impacting on moving surfaces.

A molecular dynamics study on supercritical evaporation of ammonia droplets in multi-component environments

The evaporation characteristics of ammonia fuel droplets in single and multi-component supercritical environments were studied using molecular dynamics simulations. A new approach for determining the supercritical transition of droplet evaporation modes was proposed from the perspective of atomic pair entropy fingerprints. Some improvements of the previous pair entropy fingerprint formulas were conducted to better analyze the variations in the disorder of fuel molecules during evaporation. The transition moment of droplet evaporation under supercritical conditions was based on the degree of fuel molecular disorder within the vapor–liquid mixing layer. Then, the effects of ambient conditions on the mode transition of droplet evaporation were studied. The findings indicated that the supercritical transition would not be obvious if ambient pressure was high enough. The existence of polar molecules in the environment can accelerate the mode transition. In addition, the diffusion tendency of the ambient gas components into the droplets was investigated. It was found that polar molecules diffused more strongly into the ammonia droplet than non-polar molecules.

The productivity segmented calculation model of perforated horizontal wells considering whether to penetrate the contaminated zone

Perforation technology is often used to improve the productivity of horizontal wells in oilfield exploitation. During the perforation process, the formation seepage mode and productivity will change accordingly whether the contaminated zone is shot through. If we continue to use the previous productivity formula, it will cause a large calculation error and bring economic loss to the development of oil and gas fields. Firstly, based on the principle of equivalent seepage resistance, the reservoir-hole inflow profile in these two cases is analyzed in detail, and the reservoir-hole seepage model is constructed in different regions. The perforated horizontal well section is divided into N micro-unit sections, and the pressure drop model in the wellbore is constructed using the fluid mechanics theory. A new perforated horizontal well productivity prediction model is then created by coupling the reservoir-hole seepage model with the pressure drop model in the wellbore as a whole to accurately reflect the production performance of the perforated horizontal well. Through comparison and verification, it is concluded that the calculation results of the model are more precise, which can greatly reduce the productivity error. This method is reasonable and practical. When the oilfield’s actual well data is substituted into this model, it is discussed and analyzed that the reservoir’s physical characteristics, contamination level, and perforation completion parameters all have an impact on the productivity of horizontal wells, with the original formation’s permeability and reservoir contamination thickness having the most pronounced effects. These findings may effectively direct the design of technological processes and performance impact prediction.

Study on thermal conductivity of improved soil under different freezing temperatures.

Based on the influence of moisture content, dry density and temperature (≦ 0°C) on the thermal conductivity of lime-modified red clay, the thermal conductivity was measured by transient hot wire method. A total of 125 data were obtained and the evolution law of thermal conductivity with influencing factors was analyzed. The fitting formula of thermal conductivity of lime-modified red clay and a variety of intelligent prediction models were established and compared with previous empirical formulas. The results show that the thermal conductivity of lime-modified red clay increases linearly with water content and dry density. The change of thermal conductivity with temperature is divided into three stages. In the first stage, the thermal conductivity increases slowly with the decrease of temperature in the temperature range of-2°Cto 0°C. In the second stage, in the temperature range of-5°Cto (-2)°C, the thermal conductivity increases rapidly with the decrease of temperature. In the third stage, in the range of-10°Cto (-5)°C, the thermal conductivity changes little with the decrease of temperature, and the fitting curve tends to be stable. The fitting formula model and various intelligent prediction models can realize the accurate prediction of the thermal conductivity of lime-improved soil. Using RMSE (Root Mean Square Error) and MAPE (Mean Absolute Percentage Error) to evaluate the model, it is found that the GBDT decision tree model has the best prediction effect, the RMSE value of the predicted value is 0.084, and the MAPE value is 4.1%. The previous empirical models have poor prediction effect on the thermal conductivity of improved red clay. The intelligent prediction models such as GBDT decision tree with strong universality and high prediction accuracy are recommended to predict the thermal conductivity of soil.

Should we consider the sex when estimating bone age from hand bone biometrics?

Recently, it was proposed to estimate age from the biometric information of hand bones. We observed that these estimations became less precise as children get older, especially from the age of 13-15years. This study aimed to evaluate the influence of considering sex for age estimation based on hand bones biometrics. The study sample consisted of metacarpals and proximal phalanges measurements collected on 1003 medical images performed at Nancy and Marseille Hospitals of individuals aged under 21years. This sample was divided into two subgroups delineated by the age of 13, as it is a relevant legal threshold for most European countries. First, the influence of sex on the hand bones biometrics and on the estimated age was evaluated. Then, based on these results, new sex-specific age estimation formulas were constructed from linear models and their precision was assessed using residual analysis, in comparison with previous global formulas. An influence of sex was only highlighted from the age of 13 and for the total study sample. Thus, new sex-specific age estimation formulas were built for the [1-21] global sample and the [13-21] subsample. Even though the differences with the previous formulas were minor, age was more accurately estimated when sex was considered. Considering sex in age estimation is relevant when relying on hand bone biometrics. A new tool was proposed to select the most appropriate age estimation formula, based on the discriminant analysis result and the a priori knowledge of the sex.

Estimating the energy flux of transverse waves associated with Kelvin-Helmholtz instability in solar coronal loops

Context. The energy flux of kink waves in coronal loops has been estimated in previous studies. Recent numerical simulations have revealed that kink oscillations can induce a Kelvin-Helmholtz Instability (KHI) in magnetic flux tubes. This non-linear process breaks the assumptions that have typically been included in previous eigenmode analyses. Therefore, the current analytical expressions of energy flux need to be re-examined. Aims. In the present work, we aim to compare our numerical energy flux with previous analytical formulae and establish modifications to the estimation of the energy flux of kink waves in coronal loops. Methods. Working within the framework of ideal magnetohydrodynamics (MHD), we conducted three-dimensional (3D) simulations of kink oscillations in coronal cylinders. Forward models were also employed to translate our numerical results into observables using the FoMo code. Results. We find that the previous estimation of the energy flux of kink waves is reasonable up to the point before the KHI is fully developed. However, as small vortices develop, the energy flux derived from the analytical formula becomes smaller than the total Poynting flux calculated from our numerical results. Furthermore, when degrading the original numerical resolution to match a realistic instrumental resolution, for instance, the Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter (SO), the energy flux becomes much smaller than the numerical value. Conclusions. The energy flux calculated from the analytical formula should be modified by multiplying it by a factor of about 2. When it comes to the energy flux estimation based on SO/EUI observations, this factor should be between about 3 and 4.

Penilaian Organolpetik Dan Analisis Keamanan Sediaan Lipstik Berbahan Dasar Lemak Tengkawang

Tengkawang fruit can be processed into a form of high economic value fat. This is due to its properties which are similar to cocoa butter so it is widely used as Cocoa Butter Substitutes (CBS) on various cocoa fat products, one of which is lipstick. Manufacturing and analysis of the performance of tengkawang fat-based lipstick has been done. However, to ensure a cosmetic product is safe to use, it is necessary to use safety and irritation tests. This study aims to analyze the safety level of the tengkawang fat-based lipstick through an organoleptic test, microbial contamination, and simple irritation test. There are four lipstick formulations used in this activity, the two best formulations (m3 and m5) from the previous year's research, two modification formulas of the previous formula (m3i and m5i) and commercial lipstick as a comparison (control). Organoleptic tests will be carried out on four types of lipstick formulas which include texture, gloss, odor, color and spreadability of the lipstick. This test uses a scoring system. panelists for the organoleptic test were 34 people with an age range of 17-45 years. Another analysis is the microbial contamination and simple irritation tests following the procedures of the Indonesian National Standard (SNI) 16-4769-1998 concerning lipstick. The microbial contamination test was carried out in two stages, the first for fresh lipstick (finished production) and the second for lipstick that had been stored for four months. A simple irritation test analysis was carried out by applying lipstick to the mice's skin. The results showed that from an organoleptic point of view, the lipstick with the formula m5 was the most preferred by the panelists. In terms of safety for use, the microbial contamination test showed no presence of microbes in the lipstick preparation. A simple irritation test showed no signs of irritation after 24, 36, 48, and 136 hours of observation, which indicated that the lipstick made from tengkawang fat was safe to use.

Prediction and optimization of productivity and lifespan in multi-well enhanced geothermal system

Engineering case studies have revealed that multi-well enhanced geothermal system is efficient for large-scale geothermal energy utilization. However, current research on the productivity and lifespan of multi-well enhanced geothermal system is limited to rough estimation by thermal storage volume, without a fast and accurate prediction method. To solve this problem, the multi-well enhanced geothermal system is divided into several double-well enhanced geothermal systems. The numerical simulation and previous empirical formulas for double-well enhanced geothermal system are used to propose a new multi-well enhanced geothermal system empirical formula in this study. The proposed formula is applicated using the Rehai geothermal field in Yunnan, China by three-well model and six-well model respectively. The results show that the heat production and lifespan of the enhanced geothermal system with six wells arrangement are higher compared to the three wells arrangement. Moreover, the productivity and lifespan of enhanced geothermal system with injection pressure difference and injection temperature of 1.0 MPa and 293.16 K for thermal medium are significantly better than those of 2.5 MPa and 353.16 K, respectively. Therefore, during enhanced geothermal system construction, both productivity and investment should be considered, and the number of injection wells should be maximized. Low-temperature thermal medium and low injection-production pressure differences should be selected for maximum heat production during the operation. This research presents a fast and accurate prediction method for predicting and evaluating the heat transfer performance of large-scale multi-well EGS which is helpful for EGS commercial use.

Investigation of the Sheltering Effects on the Mobilization of Microplastics in Open-Channel Flow.

Microplastics (MPs) can be sheltered by bed grains, resulting in a higher threshold of mobilization compared with those moving on a smooth bed. Only one formula considering the sheltering effects has been proposed for the critical shear stress (τc) of MP mobilization by including the densities and sizes of MPs and bed grains, but it is inaccurate for MPs of certain materials such as PS and shows limitations in understanding the sheltering effects. Additionally, no method exists for the critical depth-averaged velocity (Uc). In this study, experiments were conducted measuring both τc and Uc of MPs (made of PA, PVC, and PET) deposited on rough beds of different roughnesses, with a focus on the sheltering effects. A power law relationship between τc and the density and size of MPs was found, and a new formula for estimating τc was proposed for MPs, which reduced the errors by approximately 40% compared with that of the previous formula (27.8%). To explicitly quantify the sheltering effects in MP mobilizations, hiddenness (ΔZ), exposure (ΔH), and longitudinal exposure (ΔX) were introduced, all of which were observed to follow a normal distribution. A semiempirical method for Uc was then proposed incorporating the new measures, which reduced the errors by around 70% compared to the methods developed for estimating the Uc values of sediments.