Finite Difference Analysis Research Articles

Full-scale field test for buried glass-fiber reinforced plastic pipe with large diameter

In this paper, we present the result of full-scale field test for buried glass fiber reinforced thermosetting polymer plastic (GFRP) pipes with large diameter (inner diameter of 2400mm). Installation of pipe takes 10days to complete 16m depth backfilling layer by layer. The vertical and horizontal ring deflections are measured for 387days. The short-term deflection measured by the field test is compared with the result predicted by the Iowa formula and the finite-difference analysis (FDA). As a result, the value calculated by the Iowa formula tends to overestimate to a considerable extent. Vertical and horizontal ring deflections calculated by the FDA agreed with test results. In addition, the long-term ring deflection is predicted by using the procedure suggested in ASTM D 5365 in the range of 40–60years of service life of the pipe based on the experimental results. From the study, it was found that the long-term vertical ring deflection up to 60years is less than the 5% ring deflection limitation.

Behaviour of segmental pipeline protective vaults subjected to fault offset

The San Francisco Public Utilities Commission is currently undertaking a seismic upgrade of Bay Division Pipelines (BDPLs) Nos. 3 and 4 located in Fremont, California. To improve the reliability of the pipelines at a crossing of the Hayward Fault, a new pipeline (BDPL No. 3X) will be constructed in a segmental reinforced concrete vault with flexible connection joints that can accommodate lateral offsets and compressive deformations during a significant fault rupture. FLAC 3D finite difference analysis was performed to enhance the understanding of the soil–structure interaction behaviour of this special design. The analysis focused on the behaviour of the segmental concrete vault when subjected to up to 2.0 m (6.5 ft) lateral fault movement. The effects of fault intersection angle, fault location, soil strength, backfill type and connection joint size on the performance of the segmental concrete vault were also evaluated. Numerical results show that the movement of the vault developed gradually without sudden or concentrated deformation in response to the increasing fault displacement. Hence, the articulated vault design can withstand significant lateral offset and compressive deformation during fault rupture through the relative slip and rotation of the flexible connection joints.

Biomechanical model-based 4DCT simulation

We present a biomechanical model-based four-dimensional computed tomography (4DCT) simulation method for examining the patient lung deformation induced by respiratory motion, given only one CT scan as an input. First, we model the lung stress–strain behaviour using a sophisticated hyperelastic model, and solve the lung deformation problem through finite element (FE) analysis. We introduce robust algorithms to segment out the diaphragm control points and spine regions to carefully define the boundary conditions and loads, and to improve the FE convergence through our mesh optimisation algorithm. Next, we treat the remaining CT volume as discretised mass points connected by springs and dampers, and simulate the motion of liver, bones and other organs using finite difference analysis. This novel heterogeneous design can leverage the advantages of both continuum mechanics and mass–spring–damper system in the way that the lung deformation is computed in very high accuracy while the deformation of the rest CT volume can be achieved under practical computation constraints. Experimental results through comparing with the manually labelled landmark points in real patient 4DCT data demonstrate that our 4DCT simulator is very accurate.

Analytical tools for calculating the maximum heat transfer of annular stepped fins with internal heat generation and radiation effects

ASFs (Annular stepped fins) require less material than ADFs (annular disc fins) while retaining the ability to produce the same cooling rate in a convection environment. A simple analysis was developed for ASFs that considered radiative heat transfer and heat generated by a nuclear reactor through linearization of the radiation terms. The linearized equations were solved by exact and approximate analytical methods. Without any linearization, a new closed-form analysis was established for the temperature profile with the help of the differential transform method. An integral differential transform method was introduced to determine the actual heat-transfer rate when heat was generated inside an ASF under nonlinear radiation surface conditions. The temperature results obtained using this analytical approach were compared with those obtained from a finite-difference analysis, and were in excellent agreement. The fin performance was defined as a function of the heat generated for a given set of design conditions. An optimization study with varying heat generation was carried out to compare the performance of ADFs and ASFs, which highlighted the superior aspects of an annular fin design.

Numerical Simulation Analysis of Isolation Pile-Steel Shotcrete Combined Support of Deep Foundation Pit Excavation

The rapid development of deep foundation pit engineering, has become an important part of the urbanization construction, which brings deep excavation support of geotechnical engineering problem research also became a major issue. This paper uses the international well-known geotechnical engineering numerical simulation software FLAC3D, through 3D finite difference numerical calculation and analysis, to better simulation calculation and analysis of deep foundation pit construction site condition, forecast after excavation of the deep foundation pit deformation displacement and dangerous position, analysis of deep foundation pit excavation process isolation pile - steel shotcrete combined support effect. Three dimensional numerical model analysis and calculation in deep foundation pit engineering design and construction scheme optimization with economy is convenient wait for a obvious advantages, can for deep foundation pit excavation of deep foundation pit support design and construction to provide effective basis.

Analysis of Surge Shaft Excavation Process Based on 3-Dimensional Finite Difference Method

As an important part of the structure of hydroelectric power station, surge shaft is embedded in the rock mass, whose body size and loading conditions are typically complex. Thus, it is necessary to evaluate safety of the design scheme in order to ensure construction safety. With upper background, three dimensional finite difference model of the surge shaft and surrounding rock of a hydroelectric project in Zambia were established based on three dimensional nonlinear finite difference analysis method. Calculation of the surge shaft stepped excavation with supporting at all levels of the construction process was done. The deformation and stress state of the surrounding rock of surge shaft and its variation law in excavation process was analyzed. Furthermore, the stability of surrounding rocks and rationality of the designed support measures were evaluated.

Analyzing consolidation data to predict smear zone characteristics induced by vertical drain installation for soft soil improvement

In this paper, the effects of variability of smear zone characteristics induced by installation of prefabricated vertical drains on the preloading design are investigated employing analytical and numerical approaches. Conventional radial consolidation theory has been adopted to conduct analytical parametric studies considering variations of smear zone permeability and extent. FLAC 2D finite difference software has been employed to conduct the numerical simulations. The finite difference analyses have been verified using three case studies including two embankments and a large-scale laboratory consolidometer with a central geosynthetic vertical drain. A comprehensive numerical parametric study is conducted to investigate the influence of smear zone permeability and extent on the model predictions. Furthermore, the construction of the trial embankment is recommended as a reliable solution to estimate accurate smear zone properties and minimise the post construction settlement. A back-calculation procedure is employed to determine the minimum required waiting time after construction of the trial embankment to predict the smear zone characteristics precisely. Results of this study indicate that the accurate smear zone permeability and extent can be back-calculated when 30% degree of consolidation is obtained after construction of the trial embankment.

Evaluation of complex aquifers with different configurations

Three design methods are usually used in the analysis and design of ground water control systems. These methods are: the analysis using equilibrium formulas, the analysis using flow net and the analysis through numerical modeling. Numerical ground water models have proven to be essential when dealing with complex aquifer situations. One of the most known numerical models is “Modflow” which is a three dimensional finite difference model oriented for ground water modeling. The dewatering activities that take place at the Banha power station was utilized in calibrating the performance of the numerical modeling process. A parametric study was carried out with different configurations and boundary conditions. The study covers the performance of sand drains with different depths and spacing. These readings had been compared to “Modflow” results and good agreement between the field data and the analysis results had been observed.For complex ground water control problems where the assumptions of the conventional equilibrium formulas are not valid, the use of these formulas may lead to serious errors in design. In this condition, the use of 3-D finite difference analysis is essential to obtain reliable results and design for a groundwater control system.

RETRACTED ARTICLE: Explanation of liquefaction in after shock of the 2011 great east Japan earthquake using numerical analysis

During the 2011 Great East Japan Earthquake, severe liquefaction occurred in reclaimed ground in Urayasu city, Chiba prefecture. This liquefaction provided important lessons for us to re-recognize the liquefaction mechanism. A distinct feature of the liquefaction in this earthquake is that severe liquefaction happened not only in the main shock but also in an aftershock with a maximum acceleration of 25 gal. In some areas, liquefaction happened in the aftershock is even more serious than that happened in the main shock. In this paper, focus is placed on the characteristic features in the occurrence of liquefaction and consequent ground settlement. Based on the observed data, a series of dynamic–static analyses, considering not only the earthquake loading but also static loading during the consolidation after the earthquake shocks, are conducted in a sequential way just the same as the scenario in the earthquake. The calculation is conducted with 3D soil–water coupling finite element–finite difference analyses based on a cyclic elasto-plastic constitutive model. From the results of analyses, it is recognized that small sequential earthquakes, which cannot cause liquefaction of a ground in an independent earthquake vibration, cannot be neglected when the ground has already experienced liquefaction after a major vibration. In addition, the aftershock has great influence on the long-term settlement of low permeability soil layer. The observed and predicted liquefaction and settlements are compared and discussed carefully. It is confirmed that the numerical method used in this study can describe the ground behavior correctly under repeated earthquake shocks.

Sensitivity-based reliability analysis of earth slopes using finite element method

For slope stability analysis, an alternative to the classical limit equilibrium method (LEM) of slices is the shear strength reduction method (SRM), which can be integrated into finite element analysis or finite difference analysis. Recently, probabilistic analysis of earth slopes has been very attractive because it is capable to take the soil uncertainty into account. However, the SRM is less commonly extended to probabilistic framework compared to a variety of probabilistic LEM analysis of earth slopes. To overcome some limitations that hinder the development of probabilistic SRM stability analysis, a new procedure based on recursive algorithm FORM with sensitivity analysis in the space of original variables is proposed. It can be used to deal with correlated non-normal variables subjected to implicit limit state surface. Using the proposed approach, a probabilistic finite element analysis of the stability of an existing earth dam is carried out in this paper.

Simple Method for Predicting Temperatures in Reinforced Concrete Beams Exposed to a Standard Fire

In performance-based fire safety design, the fire performance of a structure needs to be accurately evaluated, which requires the accurate prediction of temperatures in the structure. While a finite-element or a finite-difference analysis may be carried out for this purpose, structural engineers generally prefer a simpler method. This paper therefore presents a simple, design-oriented method for predicting temperatures in RC beams under a standard fire exposure. Results from finite element heat transfer analysis are first examined to identify the key parameters that determine temperature distributions in RC beams. On the basis of this knowledge, a simple method in the form of handy formulae and diagrams is derived from regression analysis of finite element temperature data, with due consideration of the effects of beam geometry and fire exposure duration. The accuracy of the proposed method is demonstrated by comparing its predictions with temperature data from both finite element analysis and laboratory tests. The proposed method is believed to be attractive to practicing engineers for use in the fire resistance evaluation of RC beams exposed to a standard fire because of its simplicity and accuracy.

On the mathematical theory of the microstructure evolution during the final stage of liquid phase sintering

A new mathematical theory of the microstructure evolution during the final isothermal stage of liquid phase sintering has been developed. The basis of this theory has been formed by materials science and continuum mechanics. The microstructure evolution has been described by the system of non-linear differential equations, which contain more than ten parameters. Finite difference analysis has been performed for a heavy alloy cylindrical specimen. The results of the calculations have been compared with experimental data.

Evaluation of coefficient of consolidation for dilatory dissipation in piezocone test in overconsolidated cohesive soils

The interpretation method for dilatory dissipation, showing an initial temporary increase in pore pressure, in piezocone tests in overconsolidated clayey soils was investigated in this study. Finite difference analyses on the dissipation after cone penetration were performed with various ground conditions. The spatial distribution of initial excess pore pressure induced by cone penetration was determined from experimental estimations through in-situ tests and laboratory physical model tests and theoretical predictions by the cavity expansion theory and critical state soil mechanics. A method to evaluate the coefficient of consolidation from dilatory dissipation results was developed through the assessment of numerical simulation results. Comparing the application results with the laboratory-determined values, it was verified that the proposed approach provided a reliable and consistent evaluation of the coefficient of consolidation.

Evaluation of directional drilling implication of double layered pipe umbrella system for the coal mine roof support with composite material and beam element methods using FLAC 3D

This study demonstrates possible scenarios of double-layered umbrella pipe system installed over a longwall take down room in a western coal mine, where holes are drilled and cased from an adjacent entry in advance of undermining. Finite difference analysis in FLAC 3D with strain hardening gob model is used because this method is a complex and rigorous way for solving boundary value problems, such stress and strain in a continuum and at an excavation boundary due to undermining. Support system was simulated with two different methods: composite material method and beam element method. We realized that the composite material method is very conservative compared to beam element method. Thus, in the rest of the simulation, we used the beam element method to investigate the effect of different angles of umbrella pipes on the roof support. To validate the modeling results, we compare the numeral modeling results with empirical formula widely used in subsidence calculation. Also, this computer simulation compared displacement of roof between in the presence and absence of this pipe umbrella support system. In this paper, we demonstrated that a relative stiffness increase ∼185% for a reinforced zone can decrease the displacement ∼ 12.5 cm (∼ 5 in.) in the longwall recovery room roof based on results from the equivalent stiffness method. This reduction is a substantial amount, which could be really beneficial to mine operators during mining processes.

Finite difference analysis of the transient temperature profile within GHARR-1 fuel element

Mathematical model of the transient heat distribution within Ghana Research Reactor-1 (GHARR-1) fuel element and related shutdown heat generation rates have been developed. The shutdown heats considered were residual fission and fission product decay heat. A finite difference scheme for the discretization by implicit method was used. Solution algorithms were developed and MATLAB program implemented to determine the temperature distributions within the fuel element after shutdown due to reactivity insertion accident. The simulations showed a steady state temperature of about 341.3K which deviated from that reported in the GHARR-1 safety analysis report by 2% error margin. The average temperature obtained under transient condition was found to be approximately 444K which was lower than the melting point of 913K for the aluminium cladding.Thus, the GHARR-1 fuel element was stable and there would be no release of radioactivity in the coolant during accident conditions.

Free vibration analysis of a string with vibration suppressor

When an elevator rope for a high-rise building is forcibly excited by the displacements of the building induced by wind forces and/or by long-period ground motion. In previous paper, when elevator cage is stationary, a new practical method for reducing the rope vibration by using vibration suppressors is proposed for relaxing the restricted elevator operation. The advantage of using the vibration suppressors for reducing the rope lateral vibration is demonstrated through numerical calculation. Further, when center of the rope is pulled, theoretical solution to the free vibration of the rope with vibration suppressors has been presented. However, when 1/N position of the rope is pulled, theoretical solution to the free vibration of the rope with vibration suppressors has not yet been obtained. In this paper, a theoretical solution to the free vibration of the rope with vibration suppressors is presented, when 1/N position of the rope is pulled. Finite difference analysis of the rope vibration with vibration suppressors are also performed. The effect of the number of vibration suppressors on the natural frequency and rope deflection are clarified. The calculated results of the finite difference analyses are in fairly good agreement with the calculated results of the theoretical solution.

Research of the characteristics of photonic crystals based on air holes sub-wavelength imaging

Negative refractivity has been extensively studied, especially in the perfect imaging photonic crystal slab, for its fantastic characteristics. The photonic crystals sub-wavelength imaging is investigated by finite-difference time-domain (FDTD) simulation and numerical analysis. Impact of wavelength and temperature drift on the sub-wavelength imaging of photonic crystal with negative refraction has been studied in this paper.

J1810101 釣合いおもりの上下振動を利用したエレベータ・ロープの横振動抑制([J181]昇降機システムの安全とダイナミクス)

An elevator rope for high-rise building is forcibly excited by the displacement of the building caused by earthquakes and wind forces. In high-rise building, the elevator rope may resonate with the natural frequency of the building; hence, effective solution to reduce the rope displacement is demanded. In this paper, it is confirmed to suppress of the transverse vibration of elevator rope using vertical vibration of counterweight. Rope lateral vibration is controlled by fluctuating rope tension using up-and-down motion of this counterweight. Finite difference analyses of rope vibration with counterweight are performed to verify of this method. Experiments involving forced vibration of a rope whose length is constant are performed. The optimal natural frequency of vertical vibration is about 2 times of the natural frequency of the rope.

Earth pressure distribution behind rigid non-yielding walls under the effect of repeated loading on backfill

One of the most important factors in optimized design of non-yielding retaining walls like basement walls and bridge abutments is to determine the exact variation of earth pressure acting on such walls. In this paper, the distribution of at rest earth pressure behind a laboratory model of a fixed and rigid retaining wall with a cohesionless dry backfill is measured under the effect of static and repeated loads. The same conditions of the experimental model are then simulated numerically with a two-dimensional finite-difference analysis computer code. For the purpose of model verification, the results of numerical model are compared to the results of the experimental model, which is similar in geometrical and geomechanical properties. Cyclic surcharges with different amplitudes and frequencies are applied in different distances from the wall, and the earth pressure distribution, the resultant force, and its point of application are investigated. The effect of soil and loading parameters on the at rest earth pressure is also evaluated, and a parametric study has been carried out. The results of model show a significant increase in the earth pressure due to cyclic loading compared to static loading, especially in the initial cycles of loading. It indicates that the effect of cycling nature of loading should be essentially taken into account in the design of retaining walls.

Behavior of one-way reinforced concrete slabs subjected to fire

A finite difference analysis was performed to investigate the behavior of one-way reinforced concrete slabs exposed to fire. The objective of the study was to investigate the fire resistance and the fire risk after extinguishing the fire. Firstly, the fire resistance was obtained using the ISO834 standard fire without cooling phase. Secondly, the ISO834 parametric fire with cooling phase was applied to study the effect of cooling time. Accordingly, the critical time for cooling was identified and the corresponding failure time was calculated. Moreover, the maximum risk time which is the time between the fire extinguishing and the collapse of slab was obtained. Sixteen one-way reinforced concrete slabs were considered to study the effect of important parameters namely: the concrete cover thickness; the plaster; and the live load ratio. Equations for heat transfer through the slab thickness were used in the fire resistance calculations. Studying the cooling time revealed that the slabs are still prone to collapse although they were cooled before their fire resistance. Moreover, increasing the concrete cover thickness and the presence of plaster led to an increase in the maximum risk time. However, the variation in the live load ratio has almost no effect on such time.