Empirical Equations
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Geotechnics ◽  
2022 ◽  
Vol 2 (1) ◽  
pp. 91-113
Adam G. Taylor ◽  
Jae H. Chung

The present paper provides a qualitative discussion of the evolution of contact traction fields beneath rigid shallow foundations resting on granular materials. A phenomenological similarity is recognized in the measured contact traction fields of rigid footings and at the bases of sandpiles. This observation leads to the hypothesis that the stress distributions are brought about by the same physical phenomena, namely the development of arching effects through force chains and mobilized intergranular friction. A set of semi-empirical equations are suggested for the normal and tangential components of this contact traction based on past experimental measurements and phenomenological assumptions of frictional behaviors at the foundation system scale. These equations are then applied to the prescribed boundary conditions for the analysis of the settlement, resistance, and stress fields in supporting granular materials beneath the footing. A parametric sensitivity study is performed on the proposed modelling method, highlighting solutions to the boundary-value problems in an isotropic, homogeneous elastic half-space.

2022 ◽  
Vol 2022 ◽  
pp. 1-14
Ahmad Al-AbdulJabbar ◽  
Ahmed Abdulhamid Mahmoud ◽  
Salaheldin Elkatatny ◽  
Mahmoud Abughaban

This study presented an empirical correlation to estimate the drilling rate of penetration (ROP) while drilling into a sandstone formation. The equation developed in this study was based on the artificial neural networks (ANN) which was learned to assess the ROP from the drilling mechanical parameters. The ANN model was trained on 630 datapoints collected from five different wells; the suggested equation was then tested on 270 datapoints from the same training wells and then validated on three other wells. The results showed that, for the training data, the learned ANN model predicted the ROP with an AAPE of 7.5%. The extracted equation was tested on data gathered from the same training wells where it estimated the ROP with AAPE of 8.1%. The equation was then validated on three wells, and it determined the ROP with AAPEs of 9.0%, 10.7%, and 8.9% in Well-A, Well-B, and Well-D, respectively. Compared with the available empirical equations, the equation developed in this study was most accurate in estimating the ROP.

2022 ◽  
Vol 9 (1) ◽  
pp. 18
Aleksandr G. Novoselov ◽  
Sergei A. Sorokin ◽  
Igor V. Baranov ◽  
Nikita V. Martyushev ◽  
Olga N. Rumiantceva ◽  

This article puts forward arguments in favor of the necessity of conducting complex measurements of molecular transport coefficients that quantitatively determine the coefficients of dynamic viscosity, thermal diffusivity and molecular diffusion. The rheological studies have been carried out on the viscometers of two types: those with a rolling ball (HÖPPLER® KF 3.2.), and those with a rotary one (Rheotest RN 4.1.). The thermophysical studies have been performed using the analyzer Hot Disk TPS 2500S. The measurements have been taken in the temperature range of 283 to 363 K. The concentration of dry substances has varied from 16.2 to 77.7% dry wt. An empirical equation for calculating the density of aqueous solutions of beet molasses has been obtained. The diagrams of the dependence of the dynamic viscosity on the shear rate in the range of 1 s−1 to 500 s−1 at different temperatures have been provided. The diagrams of the dependence of the coefficients of thermal conductivity and thermal diffusivity on the temperature and the concentration of dry substances have been presented, and empirical equations for their calculation have been obtained. The findings can be used for engineering calculations of hydrodynamic and heat-exchange processes in biotechnological equipment.

2022 ◽  
Mehmet Barış Can Ulker ◽  
Emirhan Altınok ◽  
Gülşen Taşkın

Abstract Field pile load tests are fairly expensive experiments that can be applied to certain pile types required to be installed in full scale. Hence, it is neither practical nor efficient to perform a load test for every installed pile. While there exist many empirical relations for predicting pile capacities, such methods typically suffer from accuracy and generality. Therefore, current geotechnical practice still looks for methods to accommodate full-scale pile load testing to serve as both accurate and practical tools. In this study, load bearing capacities of closed and open-ended piles in cohesive and cohesionless soils are predicted using machine learning. Nine such methods are utilized in the analyses where CPT and pile data are considered as the learning features necessary to teach those methods the database gathered via a comprehensive search. Then, machine learning models are developed, and the databases are separated into five-folds according to the cross-validation-principle, which are used for both training and testing of the machine learning methods. Model predictions are validated with classical empirical equations. Results indicate that the Relevance Vector Regression and the Random Forest methods typically generate considerably better predictions than the other methods and empirical equations. Hence, machine learning methods are found as reliable tools to predict the pile load capacities of both open-ended and closed-ended piles provided that there is a large enough database and an appropriate method to use.

2022 ◽  
Vol 10 (1) ◽  
pp. 50
Miyoung Yun ◽  
Jinah Kim ◽  
Kideok Do

Estimating wave-breaking indexes such as wave height and water depth is essential to understanding the location and scale of the breaking wave. Therefore, numerous wave-flume laboratory experiments have been conducted to develop empirical wave-breaking formulas. However, the nonlinearity between the parameters has not been fully incorporated into the empirical equations. Thus, this study proposes a multilayer neural network utilizing the nonlinear activation function and backpropagation to extract nonlinear relationships. Existing laboratory experiment data for the monochromatic regular wave are used to train the proposed network. Specifically, the bottom slope, deep-water wave height and wave period are plugged in as the input values that simultaneously estimate the breaking-wave height and wave-breaking location. Typical empirical equations employ deep-water wave height and length as input variables to predict the breaking-wave height and water depth. A newly proposed model directly utilizes breaking-wave height and water depth without nondimensionalization. Thus, the applicability can be significantly improved. The estimated wave-breaking index is statistically verified using the bias, root-mean-square errors, and Pearson correlation coefficient. The performance of the proposed model is better than existing breaking-wave-index formulas as well as having robust applicability to laboratory experiment conditions, such as wave condition, bottom slope, and experimental scale.

2021 ◽  
Vol 8 ◽  
Feng Lin ◽  
Cai Lin ◽  
Hui Lin ◽  
Xiuwu Sun ◽  
Li Lin

To evaluate bioturbation coefficients (DB) and mixing depths (L), 210Pb and 226Ra activity was measured in two sediments cores (from water depths of 5,398 m and 4,428 m), which were collected from seamount areas in the Northwest Pacific. Using a steady-state diffusion mode, we estimated DB values of 16.8 and 24.1 cm2/a, higher than those in abyssal sediments and those predicted by traditional empirical equations. Corresponding L values varied between 19.3 and 23.1 cm. These high values indicate that seamounts are the area of active bioturbation. A one-dimensional model for the transport of total organic carbon (TOC) from the surface layer of sediments to the deep layer was developed using the distribution pattern of the specific activity of excess 210Pb (210Pbex) and its relationship with TOC. The model showed that the TOC flux transmitted downward by bioturbation was 0.09 mmol/(cm2⋅a) and 0.12 mmol/(cm2⋅a).

2022 ◽  
A. Veselovsky

Abstract. The article presents the calculations of diffusion indices of saturation of high-strength cast iron VCh 60 from powder filling. Carbide-forming elements were used as diffusers: vanadium, chromium and manganese. As a result of the research, empirical equations have been established for predicting the thickness of strengthening diffusion coatings depending on the temperature and saturation time.

UKaRsT ◽  
2021 ◽  
Vol 5 (2) ◽  
pp. 204
Kevin Martandi Setianto ◽  
Cecilia Lauw Giok Swan ◽  
Paulus Pramono Rahardjo

The problem in the construction method of the bored pile is the contamination of mud or the other contaminant that can cause the modulus of elasticity of concrete to decrease. This research determines the modulus of concrete on a bored pile foundation instrumented with fiber-optic (FO) with a manual calculation based on strain data during loading test, validated with the results of research in the laboratory and numerical analysis. Fiber optic was used to measure the strain along with the pile during the loading test. The bored pile foundation is divided into 12 segments with the same strain characteristics, and then the modulus value is calculated. The result is the modulus value of each segment is different, and the value of the modulus changes along with the increase in strain; the modulus will decrease as the strain increases. This differs from the theory that the modulus has a fixed value approximated by empirical equations. Made a cylindrical concrete sample on both sides, which installed a FO to record the strain during the loading test. The result is true that the modulus is not constant but decreases as the strain increases. It is shown in the result of analysis to fiber-optic measurement data. Created a model in Plaxis2D for validation, and the results are not much different from the manual calculation.

A Ghassemzadeh ◽  
A Dashtimanesh ◽  
M Habibiasl ◽  
P Sahoo

In this paper, an attempt has been made to predict the performance of a planing catamaran using a mathematical model. Catamarans subjected to a common hydrodynamic lift, have an extra lift between the two asymmetric half bodies. In order to develop a mathematical model for performance prediction of planing catamarans, existing formulas for hydrodynamic lift calculation must be modified. Existing empirical and semi-empirical equations in the literature have been implemented and compared against available experimental data. Evaluation of lift in comparison with experimental data has been documented. Parameters influencing the interaction between demi-hulls and separation effects have been analyzed. The mathematical model for planing catamarans has been developed based on Savitsky’s method and results have been compared against experimental data. Finally, the effects of variation in hull geometry such as deadrise angle and distance between two half bodies on equilibrium trim angle, resistance and wetted surface have been examined.

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