scholarly journals Uncertainty of volume fraction in bimrock using the scan-line method and its application in the estimation of deformability parameters

2019 ◽  
Vol 79 (4) ◽  
pp. 1651-1668
Author(s):  
Yu-Chen Lu ◽  
Yong-Ming Tien ◽  
Charng Hsein Juang ◽  
Jeen-Shang Lin
Keyword(s):  
Analytical Solutions ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Experimental Tests ◽  
Element Model ◽  
Engineering Properties ◽  
Line Method ◽  
Analytical And Numerical Solutions ◽  
Physical Tests ◽  
Scan Line

AbstractThe volume fraction within a bimrock or bimsoil is an essential parameter that is useful for estimating the engineering properties of heterogeneous geomaterials. This paper presents analytical and numerical solutions to quantify the uncertainty of volume fraction measurements in bimrock/bimsoil using a scan-line method. The analytical solutions for the mean and variance of volume fraction estimates are based on a representative volume element model. The numerical solution is obtained through simulations of scan-line measurements. This work also employs physical tests using CT scan images from artificial bimrock/bimsoil to validate these solutions. The results demonstrate that the uncertainties of the volume fraction depend on the magnitude of the volume fraction of the blocks, the diameter of the blocks, and the length of the scan line. The proposed analytical and numerical solutions are compared with existing physical experimental tests and analytical solutions. An illustrative example to demonstrate the estimation of the uncertainty of volume fraction using the scan-line measurement is present. Finally, an example application of the volume fraction characterization in the geological engineering, in terms of Young’s modulus estimation and characterization, is provided.

scholarly journals Evaluation of hillslope storage with variable width under temporally varied rainfall recharge

2021 ◽  
Author(s):  
Ping-Cheng Hsieh ◽  
Tzu-Ting Huang
Keyword(s):  
Groundwater Flow ◽  
Analytical Solutions ◽  
Water Conservation ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Time Discretization ◽  
Third Order ◽  
Analytical And Numerical Solutions ◽  
Rainfall Recharge ◽  
Integral Transform Technique

Abstract. This study discussed water storage in aquifers of hillslopes under temporally varied rainfall recharge by employing a hillslope-storage equation to simulate groundwater flow. The hillslope width was assumed to vary exponentially to denote the following complex hillslope types: uniform, convergent, and divergent. Both analytical and numerical solutions were acquired for the storage equation with a recharge source. The analytical solution was obtained using an integral transform technique. The numerical solution was obtained using a finite difference method in which the upwind scheme was used for space derivatives and the third-order Runge–Kutta scheme was used for time discretization. The results revealed that hillslope type significantly influences the drains of hillslope storage. Drainage was the fastest for divergent hillslopes and the slowest for convergent hillslopes. The results obtained from analytical solutions require the tuning of a fitting parameter to better describe the groundwater flow. However, a gap existed between the analytical and numerical solutions under the same scenario owing to the different versions of the hillslope-storage equation. The study findings implied that numerical solutions are superior to analytical solutions for the nonlinear hillslope-storage equation, whereas the analytical solutions are better for the linearized hillslope-storage equation. The findings thus can benefit research on and have application in soil and water conservation.

Analytic and Numerical Solutions of Load and Stress of Casing and Cement in Cementing Section

2012 ◽  
Vol 268-270 ◽  
pp. 721-724
Author(s):  
Zhan Qu ◽  
Xiao Zeng Wang ◽  
Yi Hua Dou
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Element Model ◽  
In Situ Stress ◽  
Oil Field ◽  
Oil Well ◽  
Production Term

With the prolonged production term and the stimulation of the oil well in oil-field, the load which results from the in-situ stress is one of the main reasons to the casing damage. Taking the casing in Cementing section, the cement and the rock surrounding the cement into consideration, a mechanical model is established, while analytical solutions of displacement and stress distribution is obtained. The finite element method is adopted to obtain the numerical solutions of the mechanics model. The result shows that analytical solutions and finite element solutions are approximate. Finite element model of casing/cement/formation which is established in the paper can be used to analyze the load and stress distribution of worn casing with non-uniform in-situ stress.

Structural Behaviour of Historical Stone Arches and Vaults: Experimental Tests and Numerical Analyses

2014 ◽  
Vol 628 ◽  
pp. 43-48 ◽  
Author(s):  
Marco Bovo ◽  
Claudio Mazzotti ◽  
Marco Savoia
Keyword(s):  
Mechanical Response ◽  
Numerical Solutions ◽  
Experimental Tests ◽  
Element Model ◽  
Seismic Effect ◽  
Structural Behaviour ◽  
In Situ Tests ◽  
Different Types ◽  
Non Linear ◽  
Stone Arches

Recent seismic events showed the dramatic need, especially in case of historical and existing buildings, of important strengthening activities to be carried out. In order to properly design them, a careful assessment of real structural behaviour and load-carrying capacity of these buildings is strongly required. This is particularly important when dealing with constructions made of heterogeneous materials like masonry or stonework, where often conventional analysis techniques do not behave satisfactorily. This paper presents the results of an extensive experimental and numerical investigation on historical stone arches and vaults. A series of in-situ tests were carried out on different types of stone arches belonging to a large building of the XIX century, with the purpose of investigating their mechanical response and obtaining the structural behaviour of stonework under different types of in-plane loads. The experimental results were compared with the numerical solutions obtained by a detailed finite element model of a portion of the structure. Numerical linear and non-linear FE analyses were conducted in order to reproduce the experimental tests and analyse the interaction between series of arches that are linked by cross vault or tunnel vault. Finally, non-linear analyses with vertical and horizontal loads were carried out with the scope of simulating the seismic effect and to verify the ductility of this type of vaulted structures.

scholarly journals Analytical solutions for dense, inclined, granular flow over a rigid, bumpy base

2021 ◽  
Vol 249 ◽  
pp. 03039
Author(s):  
James Jenkins ◽  
Diego Berzi
Keyword(s):  
Analytical Solutions ◽  
Granular Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Gravitational Flow ◽  
Approximate Analytical Solutions ◽  
The Mean

We first phrase a boundary-value problem for a dense, steady, fully-developed, gravitational flow of identical inelastic spheres over in inclined bumpy base in the absence of sidewalls. We then obtain approximate analytical solutions for the profiles of the solid volume fraction, the strength of the velocity fluctuations, and the mean velocity of the flow. We compare these with those obtained in numerical solutions of the exact equations.

Analytical and Numerical Solutions of the Riccati Equation Using the Method of Variation of Parameters. Application to Population Dynamics

2020 ◽  
Vol 15 (10) ◽  
Author(s):  
Orestes Tumbarell Aranda ◽  
Fernando A. Oliveira
Keyword(s):  
Population Dynamics ◽  
Pattern Formation ◽  
Riccati Equation ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Original Equation ◽  
Analytical And Numerical Solutions ◽  
Variation Of Parameters ◽  
Approximate Analytical Solutions ◽  
Independent Variable

Abstract This work presents new approximate analytical solutions for the Riccati equation (RE) resulting from the application of the method of variation of parameters. The original equation is solved using another RE explicitly dependent on the independent variable. The solutions obtained are easy to implement and highly applicable, which is confirmed by solving several examples corresponding to REs whose solution is known, as well as optimizing the method to determine the density of the members that make up a population. In this way, new perspectives are open in the study of the phenomenon of pattern formation.

Flow and Heat Transfer of Gold-Blood Nanofluid in a Porous Channel with Moving/Stationary Walls

2016 ◽  
Vol 33 (3) ◽  
pp. 395-404 ◽  
Author(s):  
S. Srinivas ◽  
A. Vijayalakshmi ◽  
A. Subramanyam Reddy
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Analytical Solutions ◽  
Transfer Rate ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Porous Channel ◽  
Nanoparticle Volume Fraction ◽  
Similarity Transformations ◽  
Flow And Heat Transfer

AbstractThe present study investigates the flow and heat transfer characteristics of blood carrying gold nanoparticles in a porous channel with moving/stationary walls in the presence of thermal radiation. Blood is considered as Newtonian fluid which is the base fluid and gold (Au) as nanoparticles. The governing equations are transformed into system of ordinary differential equations by using similarity transformations. The analytical solutions are obtained for the flow variables by employing homotopy analysis method (HAM). The analytical solutions are compared with the numerical solutions which are obtained by shooting technique along with Runge-Kutta scheme. It was noticed that there is a good agreement between analytical and numerical results. The influence of various parameters on velocity, temperature and heat transfer rate of gold-blood nanofluid has been discussed in detail. The temperature of the nanofluid increases with increasing the nanoparticle volume fraction. The heat transfer rate at the top wall increases with increasing nanoparticle volume fraction while it decreases for a given increase in radiation parameter.

scholarly journals A numerical frame work of magnetically driven Powell-Eyring nanofluid using single phase model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Wasim Jamshed ◽  
Mohamed R. Eid ◽  
Kottakkaran Sooppy Nisar ◽  
Nor Ain Azeany Mohd Nasir ◽  
Abhilash Edacherian ◽  
...  
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Dissipative Flow ◽  
Uniform Medium ◽  
Heat Transport Properties ◽  
Flow Heat ◽  
Frame Work ◽  
Slippery Surface ◽  
Nanoparticle Shapes

AbstractThe current investigation aims to examine heat transfer as well as entropy generation analysis of Powell-Eyring nanofluid moving over a linearly expandable non-uniform medium. The nanofluid is investigated in terms of heat transport properties subjected to a convectively heated slippery surface. The effect of a magnetic field, porous medium, radiative flux, nanoparticle shapes, viscous dissipative flow, heat source, and Joule heating are also included in this analysis. The modeled equations regarding flow phenomenon are presented in the form of partial-differential equations (PDEs). Keller-box technique is utilized to detect the numerical solutions of modeled equations transformed into ordinary-differential equations (ODEs) via suitable similarity conversions. Two different nanofluids, Copper-methanol (Cu-MeOH) as well as Graphene oxide-methanol (GO-MeOH) have been taken for our study. Substantial results in terms of sundry variables against heat, frictional force, Nusselt number, and entropy production are elaborate graphically. This work’s noteworthy conclusion is that the thermal conductivity in Powell-Eyring phenomena steadily increases in contrast to classical liquid. The system’s entropy escalates in the case of volume fraction of nanoparticles, material parameters, and thermal radiation. The shape factor is more significant and it has a very clear effect on entropy rate in the case of GO-MeOH nanofluid than Cu-MeOH nanofluid.

scholarly journals Interlocking birch plywood structures

2021 ◽  
pp. 095605992110222
Author(s):  
Chrysl A Aranha ◽  
Markus Hudert ◽  
Gerhard Fink
Keyword(s):  
High Surface ◽  
Surface Hardness ◽  
Experimental Tests ◽  
Digital Fabrication ◽  
Element Model ◽  
Component Level ◽  
Geometrical Properties ◽  
Stiffness Properties ◽  
The Face ◽  
Strength And Stiffness

Interlocking Particle Structures (IPS) are geometrically stable assemblies, usually fabricated from plate type elements that are interconnected by slotted joints. IPS are demountable and their components have the potential to be used and reused in different structures and configurations. This paper explores the applicability of birch plywood panels, which are characterized by a high surface hardness, for this type of structural system. Experimental tests were conducted to determine the mechanical properties of birch plywood plates. Moreover, IPS connections with different geometrical properties were investigated for two different load exposures: bending and rotation. The characteristics under bending exposure are influenced by the orientation of the face-veneers. For the rotational load exposure, very small strength and stiffness properties have been identified. A linear elastic finite element model is presented that shows a wide agreement with the test results. The study serves as an initial probe into the performance of IPS structures at the component level. Various aspects that are relevant for the design of IPS, such as the assembly, the accuracy and challenges regarding digital fabrication, the durability, and the structural performance are discussed.

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