Finite Difference Analysis Research Articles

Monitoring and numerical investigation of a rigid inclusions–reinforced industrial building

This paper describes a case history of a pile-supported industrial structure with an area improvement ratio of 2.2%. Field-monitored data from the contact pressures acting on the pile, the mattress, and underneath the concrete slab; pore-water pressures; settlements; and vertical strains in the inclusions are reported and discussed. The case history is back-analyzed by performing a three-dimensional (3D) finite difference analysis. The measured and computed results are compared and discussed. Based on the field observations of the contact stresses and pore-water pressures and the numerical simulations of the industrial structure construction, it is clear that there was a load transfer from the soil to the piles due to soil arching. The measured contact pressure acting on the pile was approximately six times higher than that acting on the soil located between the piles. Numerical predictions of the stress reduction, differential settlement, and pile strain are consistent with the measured values during construction of the industrial structure. This concurrence of the numerical and experimental data permits evaluation of these behaviors at the end of the industrial building construction.

Predictive assessment of heat exchange performance of geothermal piles

Heat exchange performance of geothermal piles with single U-shaped circulation tube is quantified as a function of design, operational and site-specific variables. A finite difference model is developed to simulate heat transport by circulation fluid and heat conduction in pile and surrounding soil. Finite difference analyses (FDAs) are performed to quantify the effects of several input parameters on heat transfer performance of a geothermal pile. Based on FDA results, closed-form equations are proposed that can be used in calculation of power output from a single geothermal pile with U-shaped circulation tube embedded in it. Parameter sensitivity study and advanced first order second moment (AFOSM) reliability analysis are performed to determine the hierarchy of different input variables in order of their relative impacts on heat transfer performance. Thermal conductivity of soil, initial temperature difference between circulation fluid and ground, and radius of the circulation tube are identified as the three most important parameters that control heat transfer through geothermal piles.

Prediction of seismic displacement of dry mountain slopes composed of a soft thin uniform layer

In this paper, the earthquake-induced permanent seismic displacement of dry mountain slopes is calculated from a series of two-dimensional dynamic nonlinear finite difference analyses. The mountain slopes considered are composed of a thin, soft, uniform soil layer underlain by an inclined bedrock parallel to the slope. The material properties of the soil, thickness of the soil layer, and slope inclination angles are varied. Equivalent acceleration time histories are calculated at potential sliding surfaces to derive amplification factors, and a Newmark sliding block analysis is used to calculate the seismic displacements. The calculated seismic displacements of the mountain slopes are compared with those predicted by empirical displacement models. The results show that mountain slopes composed of soft soil layers with a shear wave velocity less than or equal to 200m/s cannot be modeled as a rigid block because the displacement under strong ground motions will be greatly overestimated. The displacement prediction is significantly enhanced if the slope is modeled as a flexible sliding mass and the amplification characteristics are accounted for. A new flexible sliding block model, which uses multiple ground motion parameters, is shown to provide a reliable estimate of the sliding displacement. The success rate of the model to predict the landslide hazard category ranges from 52 to 88.3%.

Stress Distribution on Blasting Gallery Barrier Pillar due to Goaf Formation During Extraction

Semi-mechanised blasting gallery mining is a sustainable option to achieve higher production and productivity from underground thick coal seams. Judicious design of underground blasting gallery panel requires understanding of stress distribution on barrier pillars during different stages of extraction. This paper presents a study of stress distribution in and around barrier pillar for the different stages of extraction in the blasting gallery panel. Finite difference analysis taken up for final excavation (depillaring) in the panel with different stages of extraction. Analysis revealed that the stress transferred on barrier pillar increased as progress of excavation increased. Maximum stress was observed at a distance of 10 and 12 m from the pillar edge for virgin and goaved out panel sideby respectively, which gradually decreased towards centre of the pillar.

Numerical Investigation of the Undrained Compression and Pull-Out Capacity of Suction Foundations in Clay

Abstract This paper presents the results of three-dimensional finite difference analysis of suction foundations in uniform and non-uniform clays under undrained conditions. The Tresca criterion was used to simulate the stress-strain response. The bearing capacity of the foundations was investigated, with the degree of nonhomogeneity (kD/sum) of soil varying from 0 to 5, and the embedment depth being up to four times the foundation diameter. The end bearing capacity factor in compression and the reverse bearing capacity factor in tension were both calculated and were compared with each other under different foundation displacements. Numerical results showed that the ultimate bearing capacity factor can have the same value in cases of both compression and tension. The recommended ultimate bearing capacity factor is determined on the basis of the embedment ratio and displacement magnitude, and the displacement is not more than 30% of the foundation diameter. Finally, two equations are proposed to evaluate both the bearing capacity factor and the effective depth factor.

Forensic analysis of Malin landslide in India

A devastating landslide occurred on 30th July 2014, resulting in the burial of a village of about 40 houses called Malin, in western India and also led to about 160 deaths. The landslide was triggered by heavy rainfall in the area and mass movement of debris. The paper investigates slope failure in the Malin area using back analysis and numerical methods. Site investigation was conducted to obtain representative information of the area. Finite difference analyses using FLAC 2D is performed for the failed slope to determine the possible cause of failure. Analysis results show that slope failure occurred due to the loss of suction strength at the interface between rock and local soil.

Shear strength of granular soils from the simulation of dynamic penetration tests

Abstract This paper presents a model for the numerical simulation of dynamic penetration tests in cohesionless soils. In the model, dynamic penetration equations are solved by finite difference analysis in the time domain to produce the discretization of the penetration system. The approach allows essential effects of the soil influence to be accounted for, including the dynamic soil resistance by viscous damping during penetration. The model performance has proved by comparisons between the static and dynamic resistance to reproduce the variation with time of measured force, velocity, displacement and energy associated with the interaction mechanism around split-spoon samplers when penetrating in the ground. A realistic representation of the dynamic penetration mechanism allows the internal friction angle of the soil to be estimated. The proposed methodology accounts for scale effects and produces values of φ′ within the same order of magnitude as those estimated from piezocone test data.

Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method

Pulsed electric fields of sufficient magnitude and duration trigger functional responses and modifications in biological cells. Transient nanometer-sized pores are believed to form within nanoseconds in cell membranes exposed to high-intensity (MV/m) nanosecond pulsed electric fields (nsPEFs), and while it is clear that polar water molecules play a key role in electroporation, no signature for pore initiation has yet been identified. To address this, we combine molecular dynamics simulations and quasi-static 3-D finite-difference analysis to investigate the electrostatic interactions that drive pore formation in homogenous lipid bilayers exposed to intense nsPEFs. The developed methodology uniquely enables the extraction of 3-D spatiotemporal profiles of electric potentials, electric fields, and electric field gradients in biological membranes with atomistic detail and sub-nanosecond resolution. As a result, this study captures and elucidates several dynamic phenomena observed experimentally and provides a fundamental framework for further development.

Influence of Anisotropy on Pavement Responses Using Adaptive Sparse Polynomial Chaos Expansion

Modeling the spatial variability that exists in pavement systems can be conveniently represented by means of random fields; in this study, a probabilistic analysis that considers the spatial variability, including the anisotropic nature of the pavement layer properties, is presented. The integration of the spatially varying log-normal random fields into a linear-elastic finite difference analysis has been achieved through the expansion optimal linear estimation method. For the estimation of the critical pavement responses, metamodels based on polynomial chaos expansion (PCE) are developed to replace the computationally expensive finite-difference model. The sparse polynomial chaos expansion based on an adaptive regression-based algorithm, and enhanced by the combined use of the global sensitivity analysis (GSA) is used, with significant savings in computational effort. The effect of anisotropy in each layer on the pavement responses was studied separately, and an effort is made to identify the pavement layer wherein the introduction of anisotropic characteristics results in the most significant impact on the critical strains. It is observed that the anisotropy in the base layer has a significant but diverse effect on both critical strains. While the compressive strain tends to be considerably higher than that observed for the isotropic section, the tensile strains show a decrease in the mean value with the introduction of base-layer anisotropy. Furthermore, asphalt-layer anisotropy also tends to decrease the critical tensile strain while having little effect on the critical compressive strain. (C) 2015 American Society of Civil Engineers.

지진 시 산사면의 영구변위 추정식 개발

Empirical seismic displacement equations based on the Newmark sliding block method are widely used to develop seismic landslide hazard map. Most proposed equations have been developed for embankments and landfills, and do not consider the dynamic response of sliding block. Therefore, they cannot be applied to Korean mountain slopes composed of thin, uniform soil-layer underlain by an inclined bedrock parallel to the slope. In this paper, a series of two-dimensional dynamic nonlinear finite difference analyses were performed to estimate the permanent seismic slope displacement. The seismic displacement of mountain slopes was calculated using the Newmark method and the equivalent acceleration time history. The calculated seismic displacements of the mountain slopes were compared to a widely used empirical displacement model. We show that the displacement prediction is significantly enhanced if the slope is modeled as a flexible sliding mass and the amplification characteristics are accounted for. Regression equation, which uses PGA, PGV, Arias intensity of the ground motion and the fundamental period of soil layer, is shown to provide a reliable estimate of the sliding displacement. Furthermore, the empirical equation is shown to reliably predict the hazard category.

Thermal Considerations with Respect to Sliding Contact at High Speed

This paper attempts to trace the movement of a sled along a track at speeds up to Mach 4.5. The sled is supported with slippers that are loosely connected to the rail in such a way that sliding is allowed relative to the stationary rail, but the aerodynamic forces acting on the vehicle create bouncing effects within its movement. The model developed makes use of a finite-difference analysis of sliding and bouncing with a one-dimensional differential equation that includes possible melting. The results from this approach are incorporated into a two-dimensional finite-element model that treats the solution incrementally in time within a quasi-steady-state fashion. The results display temperature as a function of conduction and convection including the boundary-layer and Couette conditions along the lower surface. The aerodynamics and boundary layer along the leading edge and top surface are also included. The finite difference is integrated into a finite-element analysis to evaluate sliding, bouncing, and aerodynamic effects on a slipper as it traverses a rail at high velocity. The importance of the research is to determine the temperature profile that can be incorporated into a mechanical evaluation as related to material wear.

Simulation of snow melting pavement performance using measured thermal properties of graphite-modified asphalt mixture

Chemical melting agents are traditional methods for snow-removing applications. Due to their adverse environmental impact, thermo-snow melting pavements with conductive fillers are becoming frequently used. In this study, the thermo-physical properties of graphite-modified asphalt mixtures (GMAM) and the sensitivity of snow melting pavements were investigated. The microstructure of GMAM was analysed at extremely high magnification to observe the distribution of conductive fillers in the mixture. Two different mixing processes were adopted to mould asphalt mixtures: dry mixing and wet mixing. The conductivity was compared to evaluate the effects of asphalt mixture preparing methods and the quantity of graphite on the thermal properties of GMAM. A one-dimensional finite difference analysis was performed to determine the efficiency of GMAM for snow melting processes. Microstructure analysis was conducted on scanning election microscope (SEM) images of the fractured surface of specimens. Thermal testing and analysis results indicated that graphite improves the conductivity of asphalt mixtures and shortens the time required for snow melting. The numerical analysis results showed that environmental factors have significant effects on pavement surface temperature, and adjusting the heat source temperature can substitute the changes in environmental conditions. According to the micro-analysis, graphite particles form clusters throughout the asphalt mixture.

Thermoelastic analysis for a slab made of a thermal diode-like material

This research investigates the thermoelastic transient behavior of a thermally loaded slab made of a thermal diode-like material which has two directional thermal conductivity values (low and high). Finite difference analysis is used to obtain the elastic response of the slab based on the temperature solutions. It is found that the rate of heat transfer through the thickness of the slab decreases with reducing the ratio between the low and high thermal conductivity values (R). In addition, reducing R makes the slab less responsive to the thermal load when heated from the direction associated with the low thermal conductivity value.

Fault detection and diagnosis with parametric uncertainty using generalized polynomial chaos

This paper presents a new methodology to identify and diagnose intermittent stochastic faults occurring in a process. A generalized polynomial chaos (gPC) expansion representing the stochastic inputs is employed in combination with the nonlinear mechanistic model of the process to calculate the resulting statistical distribution of measured variables that are used for fault detection and classification. A Galerkin projection based stochastic finite difference analysis is utilized to transform the stochastic mechanistic equation into a coupled deterministic system of equations which is solved numerically to obtain the gPC expansion coefficients. To detect and recognize faults, the probability density functions (PDFs) and joint confidence regions (JCRs) of the measured variables to be used for fault detection are obtained by substituting samples from a random space into the gPC expansions. The method is applied to a two dimensional heat transfer problem with faults consisting of stochastic changes combined with step change variations in the thermal diffusivity and in a boundary condition. The proposed methodology is compared with a Monte Carlo (MC) simulations based approach to illustrate its advantages in terms of computational efficiency as well as accuracy.

Entrance Region Flow in Concentric Annuli with Rotating Inner Wall for Herschel–Bulkley Fluids

A finite difference analysis of the entrance region flow of Herschel–Bulkley fluids in concentric annuli with rotating inner wall has been carried out. The analysis is made for simultaneously developing hydrodynamic boundary layer in concentric annuli with the inner cylinder assumed to be rotating with a constant angular velocity and the outer cylinder being stationary. A finite difference analysis is used to obtain the velocity distributions and pressure variations along the radial direction. With the Prandtl boundary layer assumptions, the continuity and momentum equations are solved iteratively using a finite difference method. Computational results are obtained for various non-Newtonian flow parameters and geometrical considerations. A significant asymmetry is found in the entrance region which is gradually reduced as the flow develops. For smaller values of aspect ratio and higher values of Herschel–Bulkley number the flow is found to stabilize more gradually. Comparison of the present results with the results available in literature for various particular cases has been done and found to be in agreement.

The Cell Method: An Overview on the Main Features

Abstract The Cell Method (CM) is a computational tool that maintains critical multi-dimensional attributes of physical phenomena in analysis. This information is neglected in the differential formulations of the classical approaches of finite element, boundary element, finite volume, and finite difference analysis, often leading to numerical instabilities and spurious results. This paper highlights the central theoretical concepts of the CM that preserve a more accurate and precise representation of the geometric and topological features of variables for practical problem solving. Important applications occur in fields such as electromagnetics, electrodynamics, solid mechanics and fluids. CM addresses non-locality in continuum mechanics, an especially important circumstance in modelling heterogeneous materials.

The Algebraic Formulation: Why and How to Use it

Abstract Finite Element, Boundary Element, Finite Volume, and Finite Difference Analysis are all commonly used in nearly all engineering disciplines to simplify complex problems of geometry and change, but they all tend to oversimplify. This paper shows a more recent computational approach developed initially for problems in solid mechanics and electro-magnetic field analysis. It is an algebraic approach, and it offers a more accurate representation of geometric and topological features.

유한차분해석과 한계평형해석의 비교를 통한 평면파괴 사면 쏘일네일링 보강효과 연구

유한차분해석과 한계평형해석의 비교를 통한 평면파괴 사면 쏘일네일링 보강효과 연구

Multivariate adaptive regression splines model for reliability assessment of serviceability limit state of twin caverns

Construction of a new cavern close to an existing cavern will result in a modification of the state of stresses in a zone around the existing cavern as interaction between the twin caverns takes place. Extensive plane strain finite difference analyses were carried out to examine the deformations induced by excavation of underground twin caverns. From the numerical results, a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines (MARS) has been used to relate the maximum key point displacement and the percent strain to various parameters including the rock quality, the cavern geometry and the in situ stress. Probabilistic assessments on the serviceability limit state of twin caverns can be performed using the First-order reliability spreadsheet method (FORM) based on the built MARS model. Parametric studies indicate that the probability of failure Pf increases as the coefficient of variation of Q increases, and Pf decreases with the widening of the pillar.

Study on the Seepage and Stability of Carbon Dioxide Geological Storage in Scrap Metal Mine: A Finite Difference Analysis

The carbon dioxide geological storage is one of the most effective ways to slow down the earth's climate warming. The ideal location for storage is in the deep scrap mines. Because of the characteristics of the deep underground condition, the long-term mechanical stability must have close relationship with the geostress fields and permeability, whose development can determine and reflect the mechanical behaviors of carbon dioxide geological storage. The permeability of host rock is affected by existing joints and discontinuity surfaces. Furthermore, as the liquid carbon dioxide is injected into the geological storage, the injection pressure and buoyancy force will change the state of geostress obviously. In this paper, based on mechanical properties of the host rock (granite), coupled brittle shear constitutive model was adopted and the analysis module was implemented in software FLAC3D. Then, with the in situ survey of joints in the host rock and the monitoring of in situ geostress, the permeability characteristics and geostress inverse analysis were input in FLAC3D. At last, fluid-solid coupled model was used to analyze the seepage characteristics of each phase after the injection and long-term storage of liquid carbon dioxide. Therefore, the systematic analysis of the storage stability of carbon dioxide geological could be carried out.