A Mathematical Model for Determination of the Critical Hydraulic Gradient in Soil Piping

2010 ◽  
Author(s):  
Jian Zhou ◽  
Yan-Feng Bai ◽  
Zhi-Xiong Yao
Keyword(s):  
Mathematical Model ◽  
Hydraulic Gradient ◽  
Critical Hydraulic Gradient ◽  
Soil Piping

scholarly journals Research on a Critical Hydraulic Gradient of Piping in Noncohesive Soils

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Can-Hong Zhang ◽  
En-Yue Ji ◽  
Bao-Tian Wang
Keyword(s):  
Water Flow ◽  
Drag Force ◽  
Moving Objects ◽  
Cohesive Soil ◽  
Interaction Force ◽  
Hydraulic Gradient ◽  
Force Analysis ◽  
Important Condition ◽  
Critical Hydraulic Gradient ◽  
Soil Piping

The critical hydraulic gradient of cohesive soil is an important condition for judging soil piping. For force analysis of movable particles in pore channels of soil, this study proposes to consider the influence of surrounding particles on the drag force of movable particles by water flow. According to the principle of relative motion, considering the interaction force between moving objects in still water, the value of the drag force of water flow that is affected by surrounding particles is calculated, to derive the method of the critical hydraulic gradient. This calculation method is suitable for the results of previous piping tests, and the method is accurate and concise.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

Research on a Generating Method of Spiral Flutes of Hourglass Worm Gear Hob

2017 ◽  
Author(s):  
Yang Jie ◽  
Li Haitao ◽  
Rui Chengjie ◽  
Wei Wenjun ◽  
Dong Xuezhu
Keyword(s):  
Mathematical Model ◽  
Manufacturing System ◽  
Worm Gear ◽  
Virtual Manufacturing ◽  
Transmission Ratio ◽  
Method Of Determination ◽  
Generating Method ◽  
Multiple Threads ◽  
Different Shapes

All of the cutting edges on an hourglass worm gear hob have different shapes and spiral angles. If the spiral angles are small, straight flutes are usually adopted. But for the hob with multiple threads, the absolute values of the negative rake angles at one side of the cutting teeth will greatly affect the cutting performance of the hob if straight flutes are still used. Therefore, spiral flutes are usually adopted to solve the problem. However, no method of determination of the spiral flute of the hourglass worm gear hob has been put forward till now. Based on the curved surface generating theory and the hourglass worm forming principle, a generating method for the spiral flute of the planar double enveloping worm gear hob is put forward in this paper. A mathematical model is built to generate the spiral flute. The rake angles of all cutting teeth of the hob are calculated. The laws of the rake angles of the cutting teeth of four hobs with different threads from one to four threads are analyzed when straight flutes and spiral flutes are adopted respectively. The laws between the value of the negative rake angles of the hob with four threads and the milling transmission ratio are studied. The most appropriate milling transmission ratio for generating the spiral flute is obtained. The machining of the spiral flutes is simulated by a virtual manufacturing system and the results verify the correctness of the method.

scholarly journals Impacts of Consolidation Time on the Critical Hydraulic Gradient of Newly Deposited Silty Seabed in the Yellow River Delta

2021 ◽  
Vol 9 (3) ◽  
pp. 270
Author(s):  
Meiyun Tang ◽  
Yonggang Jia ◽  
Shaotong Zhang ◽  
Chenxi Wang ◽  
Hanlu Liu
Keyword(s):  
Yellow River ◽  
Yellow River Delta ◽  
Hydraulic Gradient ◽  
River Delta ◽  
Theoretical Formula ◽  
The Yellow River ◽  
The Yellow River Delta ◽  
Critical Hydraulic Gradient ◽  
Seepage Flows ◽  
The Yrd

The silty seabed in the Yellow River Delta (YRD) is exposed to deposition, liquefaction, and reconsolidation repeatedly, during which seepage flows are crucial to the seabed strength. In extreme cases, seepage flows could cause seepage failure (SF) in the seabed, endangering the offshore structures. A critical condition exists for the occurrence of SF, i.e., the critical hydraulic gradient (icr). Compared with cohesionless sands, the icr of cohesive sediments is more complex, and no universal evaluation theory is available yet. The present work first improved a self-designed annular flume to avoid SF along the sidewall, then simulated the SF process of the seabed with different consolidation times in order to explore the icr of newly deposited silty seabed in the YRD. It is found that the theoretical formula for icr of cohesionless soil grossly underestimated the icr of cohesive soil. The icr range of silty seabed in the YRD was 8–16, which was significantly affected by the cohesion and was inversely proportional to the seabed fluidization degree. SF could “pump” the sediments vertically from the interior of the seabed with a contribution to sediment resuspension of up to 93.2–96.8%. The higher the consolidation degree, the smaller the contribution will be.

Methodology of Estimation of Fire Separation Distances between Construction Facilities by Calculation

2020 ◽  
Vol 1006 ◽  
pp. 93-100
Author(s):  
Vadym Nizhnyk ◽  
Yurii Feshchuk ◽  
Volodymyr Borovykov
Keyword(s):  
Mathematical Model ◽  
Heat Flux ◽  
Linear Regression ◽  
Ignition Temperature ◽  
Oil Products ◽  
Regression Equations ◽  
Fire Load ◽  
Literary Sources ◽  
Tabular Method

Based on analysis of appropriate literary sources we established that estimation of fire separation distances was based of two criteria: heat flux and temperature. We proposed to use “ignition temperature of materials” as principal criterion when determining fire separation distances between adjacent construction facilities. Based on the results derived while performing complete factorial we created mathematical model to describe trend of changing fire separation distances depending on caloric power of fire load (Q), openings factor of the external enclosing structures (k) and duration of irradiation (t); moreover, its adequacy was confirmed. Based on linear regression equations we substantiated calculation and tabular method for the determination of fire separation distances for a facility being irradiated which contains combustible or otherwise non-combustible façade and a facility where liquid oil products turn. We developed and proposed general methodology for estimation of fire separation distances between construction facilities by calculation.

scholarly journals Study on Optimal Placement and Reasonable Number of Viscoelastic Dampers by Improved Weight Coefficient Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ji-ting Qu ◽  
Hong-nan Li
Keyword(s):  
Mathematical Model ◽  
Weight Coefficient ◽  
Optimal Placement ◽  
Optimal Method ◽  
Analogy Method ◽  
Numerical Examples ◽  
Viscoelastic Dampers ◽  
Reasonable Number ◽  
Coefficient Method

A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.

scholarly journals Determination of the Vertical Load on the Carrying Structure of a Flat Wagon with the 18–100 and Y25 Bogies

2021 ◽  
Vol 11 (9) ◽  
pp. 4130
Author(s):  
Oleksij Fomin ◽  
Alyona Lovska ◽  
Václav Píštěk ◽  
Pavel Kučera
Keyword(s):  
Mathematical Model ◽  
Fatigue Strength ◽  
Service Life ◽  
Dynamic Characteristics ◽  
Dynamic Load ◽  
Field Tests ◽  
Vertical Load ◽  
Mathcad Software ◽  
The Mathematical Model

The study deals with determination of the vertical load on the carrying structure of a flat wagon on the 18–100 and Y25 bogies using mathematic modelling. The study was made for an empty wagon passing over a joint irregularity. The authors calculated the carrying structure of a flat wagon with the designed parameters and the actual features recorded during field tests. The mathematical model was solved in MathCad software. The study found that application of the Y25 bogie for a flat wagon with the designed parameters can decrease the dynamic load by 41.1% in comparison to that with the 18–100 bogie. Therefore, application of the Y25 bogie under a flat wagon with the actual parameters allows decreasing the dynamic loading by 41.4% in comparison to that with the 18–100 bogie. The study also looks at the service life of the supporting structure of a flat wagon with the Y25 bogie, which can be more than twice as long as the 18–100 bogie. The research can be of interest for specialists concerned with improvements in the dynamic characteristics and the fatigue strength of freight cars, safe rail operation, freight security, and the results of the research can be used for development of innovative wagon structures.

Non-invasive determination of the systolic peak-to-peak gradient in children with aortic stenosis: validation of a mathematical model

2000 ◽  
Vol 10 (2) ◽  
pp. 115-119 ◽  
Author(s):  
Valter C. Lima ◽  
Evan Zahn ◽  
Christine Houde ◽  
Jeffrey Smallhorn ◽  
Robert M. Freedom ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Pulse Pressure ◽  
Linear Regression Analysis ◽  
Systolic Pressure ◽  
Pressure Gradients ◽  
Non Invasive ◽  
The Mean ◽  
Congenital Aortic Valvar Stenosis ◽  
Peak Gradient

AbstractDoppler derived systolic pressure gradients have become widely applied as noninvasively obtained estimates of the severity of aortic valvar stenosis. There is little correlation, however, between the Doppler derived peak instantaneous gradient and the peak-to-peak gradient obtained at catheterisation, the latter being the most applied variable to determine severity in children. The purpose of this study was to validate a mathematical model based on data from catheterisation which estimates the peak-to-peak gradient from variables which can be obtained by noninvasive means (Doppler derived mean gradient and pulse pressure), according to the formula: peak-to-peak systolic gradient=6.02+1.49*(mean gradient)−0.44*(pulse pressure). Simultaneous cardiac catheterization and Doppler studies were performed on 10 patients with congenital aortic valvar stenosis. Correlations between the gradients measured at catheter measured, and those derived by Doppler, were performed using linear regression analysis. The mean gradients correlated well (y=0.67 × + 11.11, r=0.87, SEE=6 mm Hg, p=0.001). The gradients predicted by the formula also correlated well with the peak-to-peak gradients measured at catheter (y=0.66 × + 14.44, r=0.84, SEE=9 mm Hg, p=O.002). The data support the application of the model, allowing noninvasive prediction of the peak-to-peak gradient across the aortic valvar stenosis.

scholarly journals A Control Based Mathematical Model for the Evaluation of Intervention Lines in COVID-19 Epidemic Spread: The Italian Case Study

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 890
Author(s):  
Paolo Di Giamberardino ◽  
Rita Caldarella ◽  
Daniela Iacoviello
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Italian Case ◽  
Control Actions ◽  
Containment Measures ◽  
Asymptomatic Subjects ◽  
The Impact

This paper addresses the problem of describing the spread of COVID-19 by a mathematical model introducing all the possible control actions as prevention (informative campaign, use of masks, social distancing, vaccination) and medication. The model adopted is similar to SEIQR, with the infected patients split into groups of asymptomatic subjects and isolated ones. This distinction is particularly important in the current pandemic, due to the fundamental the role of asymptomatic subjects in the virus diffusion. The influence of the control actions is considered in analysing the model, from the calculus of the equilibrium points to the determination of the reproduction number. This choice is motivated by the fact that the available organised data have been collected since from the end of February 2020, and almost simultaneously containment measures, increasing in typology and effectiveness, have been applied. The characteristics of COVID-19, not fully understood yet, suggest an asymmetric diffusion among countries and among categories of subjects. Referring to the Italian situation, the containment measures, as applied by the population, have been identified, showing their relation with the government's decisions; this allows the study of possible scenarios, comparing the impact of different possible choices.

Sign in / Sign up

Export Citation Format

Share Document