Finite Infinite Element Research Articles

Study on the vibration characteristics and influence range of buried dam pipeline

To alleviate water resource shortages and tensions and meet the water diversion needs of different river basins, buried (cross-dam) pipelines have become an essential component of water diversion projects. They are installed in levee projects in key river basins such as the Yellow River, Jingjiang River, and Beijiang River. Due to the complex engineering structure and multiple sources of vibration excitation, if vibrations propagate along the pipeline axis towards the surrounding levee, they could have an adverse impact on the stability and safe operation of the levee. To accurately identify the vibration and transmission characteristics of the buried pipeline dikes, determine its primary vibration sources, and clarify the propagation laws of pipeline vibrations within the levee, this study, based on prototype observation data and utilizing signal fusion processing technology, investigates the inherent vibration characteristics of the buried pipeline dikes from the perspectives of excitation, transmission, and response. At the same time, by introducing the “finite element-infinite element” theory, a coupled finite element-infinite element model is established for the pipeline, levee, anchor piers, support piers, foundation, and infinite half-space. This model is then used to analyze the site response induced by flow-induced vibration in buried pipeline levee structures. The results show that the primary vibration frequencies of the buried pipeline dike structure are the unit rotation frequency of 74.4 Hz and the blade vibration frequency of 24.8 Hz. These vibration sources originate from the pump unit and propagate outward along the pipeline axis. Using the transmission range of the vibration source as the basis for determining the vibration impact range, it was established that the horizontal vibration impact of the buried pipeline extends 10 m on either side of the pipeline axis, while the vertical vibration impact extends 7.5 m below the dike crest.

Numerical Simulation of Electromagnetic Nondestructive Testing Technology for Elasto-Plastic Deformation of Ferromagnetic Materials Based on Magneto-Mechanical Coupling Effect.

A numerical tool for simulating the detection signals of electromagnetic nondestructive testing technology (ENDT) is of great significance for studying detection mechanisms and improving detection efficiency. However, the quantitative analysis methods for ENDT have not yet been sufficiently studied due to the absence of an effective constitutive model. This paper proposed a new magneto-mechanical model that can reflect the dependence of relative permeability on elasto-plastic deformation and proposed a finite element-infinite element coupling method that can replace the traditional finite element truncation boundary. The validity of the finite element-infinite element coupling method is verified by the experimental result of testing electromagnetic analysis methods using TEAM Problem 7. Then, the reliability and accuracy of the proposed model are verified by comparing the simulation results under elasto-plastic deformation with experimental results. This paper also investigates the effect of elasto-plastic deformation on the transient magnetic flux signal, a quantitative hyperbolic tangent model between Bzpp (peak-peak value of the normal component of magnetic flux signal) and elastic stress, and the exponential function relationship between Bzpp and plastic deformation is established. In addition, the difference and mechanism of a magnetic flux signal under elasto-plastic deformations are analyzed. The results reveal that the variation of the transient magnetic flux signal is mainly due to domain wall pinning, which is significantly affected by elasto-plastic deformation. The results of this paper are important for improving the accuracy of quantitative ENDT for elasto-plastic deformation.

Investigation of Metro Train-Induced Environmental Vibration Using a Coupled Sliced Finite Element-Infinite Element Model

Investigation of Metro Train-Induced Environmental Vibration Using a Coupled Sliced Finite Element-Infinite Element Model

New procedure for soil-structure interaction problems incorporating free-field effects by 2D quadratic elements

Following several decades of tragic seismic events, current national regulations emphasise the importance of considering seismic soil-structure interaction (SSSI) in the design of foundations, particularly for deep foundations in loose soils. However, incorporating the free field into the SSSI calculation model can be challenging when high order finite or infinite elements are involved.This paper presents a new procedure for considering the effect of the free field in a seismic soil-structure interaction (SSSI) model when using 8-node finite elements bounded by compatible absorbing infinite elements.The proposal, based on a new formulation of three-node column elements paired with a modification of the Cundall method, allows the calculation of the free field effects to be applied at the level of the lateral boundaries of the SSSI model, represented here by the finite-infinite element interfaces. This modification of the dissipative system, considering the kinematic effect at each time step, allows an incremental solution of the SSSI problem, taking into account the nonlinearities of the materials constituting the geotechnical profile. The test validation of the method, performed on two cases of shear wave propagation problems in soft soils, shows good results, demonstrating the usefulness of the 2D approach for SSSI problems.

Comparative study of thermal effect on thermoelastic double porous solid by finite element method and finite-infinite element method

In the present study, we have made a comparative study between the well-established finite element method (FEM) and finite-infinite element method (FIEM). Nine-noded infinite elements have been developed to model the half-space. Further, we assume a thermal shock which is applied on the double porosity medium. This medium is assumed to be unbounded in terms of x and y directions. For sake of simplicity, we have converted our model equations in non-dimensional form. Then after, suitable boundary conditions have been imposed in the present study. Numerical validation of the present mathematical model has been made for copper-like material. Displacement components of solid particles, volume fractions fields of double porosity solid, temperature field and stress components have been computed for the domain . Due to limitation and a better understanding of the comparative study between these two methods, we are giving 2D-graphical representation of field variables with respect to x-space for fixed value of y=1 and 3D-graphical representation for fixed value of x = 1, respectively. From the results, we find advantage of use of infinite element method over finite element method.

Seismic analysis of a half-space containing a water-filled valley under 2D oblique incident waves by finite-infinite element method

This paper presents for the first time the seismic analysis of a half-space containing a water-filled valley under 2D oblique P- and SV-waves by the finite-infinite element (FE-IFE) method. The equivalent seismic forces for the Chi-Chi Earthquake on the near-field boundary are calculated based on the exact free-field response. The effect of water-filled valleys on the seismic response of the half-space is a problem not well treated previously, which is considered through the soil-liquid interface in this paper. The present analysis procedure including the soil-liquid coupling is verified against Luco et al. for a half-space with an empty semi-circular canyon. New findings of this paper include: (1) The horizontal acceleration is amplified on the “near” side (to incident waves) of the valley, which is higher for filled valleys under P-waves, but decayed by the filled valley under SV-waves. (2) The effect of overlying water body on vertical acceleration is less significant for SV- than for P-waves. (3) For SV-waves with overly critical angles, the horizontal acceleration is larger for the “far” than “near” side, and larger difference exists for deeper filled valleys, coupled by amplified vertical acceleration. Additional observations were made for the numerical analysis inside the text.

2D and 3D soil finite/infinite element models: modelling, comparison and application in vehicle-track dynamic interaction

ABSTRACT In this work, 2D and 3D vehicle-track-soil (VTS) models are developed in a coupled manner. The VTS system is modelled as an integration of the multi-rigid-body vehicle sub-model, multi-scale finite element ballastless track sub-model and finite/infinite element (FE/IE) soil sub-model, where the IE method is introduced to deal with the boundary condition of the far-field soil. Particularly, the detailed approach for modelling the FE/IE soil sub-model is depicted in the 2D and 3D space domain, respectively. Through comparisons, it is proved that the IE method shows advantages in simulating the soil far-field region by meeting a soil boundary condition. Case studies are conducted to demonstrate the superiority and applicability of this model in improving the computational efficiency. Besides, the influence of vehicle speed on system dynamic performance is revealed, where the soil critical speed derived by the soil Rayleigh surface wave speed is explored by the vehicle-induced vibrations.

Research on seismic ground motion parameters applicable to the safety of rectangular shallow tunnel

The objective of this paper is to optimize the selection of seismic ground motion intensity indexes in the seismic fortification of urban shallow-buried rectangular tunnels. This paper takes a shallow-buried rectangular tunnel in a city as the research object, uses ABAQUS to establish a finite-infinite element coupling model, and selects 70 typical seismic ground motions for dynamic calculation. Using dynamic time history analysis method to study the seismic response of tunnel lining structure in terms of internal force, minimum safety factor and strain energy, and analyze their correlation with 15 seismic ground motion parameters. Selecting the seismic ground motion parameters with strong correlation, good effectiveness, and high credibility for safety evaluation. The research results show that: Peak acceleration (PGA) has a weak correlation with the seismic response of tunnel lining structures, and PGA as an independent seismic ground motion intensity index has greater uncertainty in the seismic fortification of tunnels; Peak displacement (PGD), Root-mean-square velocity (RMSV), Root-mean-square displacement (RMSD), and Specific energy density (SED) can be used as independent seismic ground motion intensity index, The linear regression model is used to evaluate the safety of the lining structure, and finally the evaluation result is verified by the incremental dynamic analysis method (IDA), which shows that the evaluation result is accurate. The research results can provide reference for the preliminary design of seismic fortification of rectangular shallow tunnels.

Three-dimensional free bending vibrations of variable radius functionally graded circular column immersed in infinite fluid

The three-dimensional free bending vibrations of variable radius functionally graded circular column fully or partially immersed in infinite fluid are investigated for the first time using a coupled hierarchical finite-infinite element method based on curved elements. The fluid is incompressible, irrotational, and inviscid. The material properties vary continuously along the radial direction according to a simple power law function. The solid and fluid behaviors are described by the three-dimensional elasticity theory and Laplace’s equation, respectively. Coupling occurs on the interface via the boundary restraints imposed on it. Curved edges are described exactly by the blending functions. Examples of clamped-free and clamped-guided functionally graded circular columns with quadratic and cubic radius variations are used to illustrate the method. Convergence test and comparison study are conducted. New results for the frequencies of the lowest two bending modes are provided, which may serve as benchmark solutions. Furthermore, a parametric study is conducted to show the effects of various geometrical and mechanical parameters on the frequencies, modal deflections, and modal hydrodynamic pressures.

Optimization of design parameters of displacement isolation piles constructed between a high-speed railway bridge and a double-line metro tunnel: From the view point of vibration isolation effect

A double-line metro tunnel was constructed beneath an existing high-speed railway bridge in a city of east China. To avoid the unexpected displacement of the bridge resulting from the shield tunneling, the displacement isolation piles were employed between the shield tunnels and the pile foundation of the bridge. An accompanied optimization design issue of the isolation piles is analyzed in this work. The optimization target is not only that the displacement criteria of the bridge pile foundation during tunneling process must be met, but also an outstanding vibration mitigation effect in operation process should be achieved. In this work, a steady-state finite element analysis (FEA) is employed to evaluate the limit of the pile spacing according to the displacement criteria of the high-speed bridge. After that an analytical model and a three-dimensional (3D) finite-infinite element model of the bridge-foundation-tunnel system are established, respectively, for further optimization of the pile parameters from the view point of vibration isolation effect. The optimized pile spacing of the isolation piles for the real project case is finally recommended based on in-situ measurement data and the evaluation results.

Finite-infinite element analysis for flow simulation in a phreatic aquifer

Groundwater and surface water interaction is a common process of the hydrologic cycle but still challenging to be addressed in a general context. A special case of groundwater-surface water interaction is the seepage from a river/stream or canal into an adjacent phreatic aquifer, where the groundwater flow in the vicinity of the stream is crucial while the aquifer is supposed to extend to infinity, especially for the mathematical analysis. Herein, numerical solutions of 1-D Boussinesq equation and 2-D Richards equation are presented by embedding infinite elements in the finite element analysis to discretise only the key subsurface flow region close to the stream. By using the infinite elements, which extend to infinity to one direction according to appropriate shape functions, the total number of elements required to discretise the simulation area is substantially reduced. As a result, computationally efficient solutions are obtained, which is particularly important for the two-dimensional saturated-unsaturated groundwater flow described by the Richards equation, as well as sufficiently accurate, both in terms of groundwater recharge and water table in the vicinity of the stream. The finite-infinite element approach could be useful to derive accurate and fast numerical solutions under the investigation of several scenarios.

Shock absorption analysis based on the tunnel-soil-surface building interaction system

In order to apply damping technology to complex interaction system, a two-dimensional finite element-infinite element coupling model of tunnel-soil-surface building interaction system was established by ABAQUS. By analyzing the acceleration, displacement and stress response of key points of tunnel and surface buildings, the influence of the thickness and buried depth of the shock absorption layer on the damping effect of the system is studied when tunnel shock absorption layer (or foundation shock absorption layer) is set separately. And a combined shock absorption system is proposed for the complex interaction system, and the primary and secondary relationship of different factors on the damping effect is studied by orthogonal experiment. The results showed that: (1) Setting up a tunnel shock absorption layer can significantly reduce the maximum principal stress of the tunnel and the acceleration of the surface building;(2) When the buried depth of the foundation shock absorption layer was 0m, the damping effect was the best, which can significantly reduce the acceleration and relative displacement of the surface building; (3) The combined shock absorption system can achieve good damping effect under different seismic waves excitation and its damping effect was better than single shock absorption layer system.

Numerical Modeling of Marine Self-Potential from a Seafloor Hydrothermal Ore Deposit

The redox field generated by electrically conductive minerals is one of the main constituents of self-potentials. It can be explained by electrochemical reactions in which conductors participate. The location and outline of seafloor hydrothermal ore deposits can be detected using marine self-potential anomalies that can be approximated through a marine geobattery model. The numerical modeling of marine self-potentials could be the foundation of corresponding data inversion and interpretation and improving the application effect of the self-potential method in detecting seafloor hydrothermal ore deposits. In this study, the inert electrode model and the on-land geobattery model are introduced to build the marine geobattery model, and the finite-infinite element coupling method is derived to deal with the truncated boundary problem effectively. Also, two tests are conducted to study the effect of model parameters on ground self-potential anomalies. A seafloor sulfide deposit model is built to study the self-potential characteristics. The numerical modeling results suggest that the precision and efficiency of the coupled method are superior to that of the traditional finite element method. Self-potential anomalies are greatly affected by medium resistivity, complex terrain, and amplitudes of embedded redox fields. Gradient changes in embedded redox fields do not cause significant self-potential anomalies but lead to mutations of current sources. The self-potential anomaly from the sulfide deposit model shows that the self-potential method can be effectively used to explore seafloor hydrothermal deposits that accompany negative self-potential anomalies above the ore bodies. The coupled method is quite suitable for multi-source models such as self-potential models.

Study on Acoustic Radiation Calculation and Far Field Criterion of Oil pan

Diesel engine with low vibration and noise characteristics will be a major trend for the future development. As the shell part on the engine, the vibration and noise control of the oil pan is an urgent problem to be solved. It is of practical significance to predict the oil pan vibration and radiation noise during the design phase. An oil pan of diesel engine was taken as the research object, the finite element model of the oil pan was established and the finite element method (FEM) was used to calculate the oil pan vibration response. Three different numerical calculation methods (Finite element-boundary element hybrid method, finite element-infinite element hybrid method, finite element-automatic matching layer technology) were used to calculate radiated sound power level of the oil pan respectively. The calculation accuracy and efficiency of three different calculation methods were compared and analyzed. The results show that the finite element-boundary element method is more suitable for the calculation of the acoustic radiation of the oil pan. Finally, a method based on the directivity of acoustic radiation to determine the far-field acoustic radiation is proposed and verified.

3D Forward Modeling of Seepage Self-potential Using Finite-infinite Element Coupling Method

The streaming potential in porous media is one of the main constituents of the self-potential. It has attracted special attention in environmental and engineering geophysics. Forward modeling of streaming potentials could be the foundation of corresponding data inversion and interpretation, and improving the application effect of the self-potential method. The traditional finite element method has a large subdivision area and computational quantity, and the artificial boundary condition is not suitable for complex models. The Helmholtz-Smoluchowski equation is introduced for evaluating the streaming potential. Then three new shape functions of the multidirectional mapping infinite elements are proposed and the finite-infinite element coupling method is deduced for reducing the subdivision scale and improving both the calculation efficiency and accuracy. The correctness and validity of the new coupled method are verified by a resistive model in homogeneous half-space. Besides, a seepage model with complex terrain and a landfill model with dynamic leakages are modeled using the improved coupled method. The results show that the accuracy of the improved coupled method is superior to the unimproved coupled method, and is better than the finite element method. Also, the coupled method has better adaptability to complex models and is suitable for the accurate simulation of dynamic multi-source seepage models.

Numerical modeling of biogeobattery system from microbial degradation of underground organic contaminant

Redox fields observed near contaminated sites are related to electrochemical and electrobiological reactions. The term biogeobattery is used to describe the redox processes in underground organic contaminated sites which are biogeochemical systems, where bacteria, conductive minerals, oxygen, and organic contaminants create numerous anode–cathode pairs by transferring electrons from reducing areas under the water table or other anaerobic conditions to oxidizing areas above the water table. A numerical biogeobattery model established based on the geobattery and inert electrode model is the theoretical basis for numerical modeling. A coupled method of tetrahedral finite elements and hexahedral infinite elements is proposed for the algorithm basis of numerical modeling. Then a small-scale biogeochemical system and a field-scale landfill system are modeled using the numerical biogeobattery model and the finite–infinite element coupling method. The results suggest that the accuracy of the coupled method is superior to the finite element method. The amplitude change in the embedded redox field has a great effect on self-potential anomalies, while the gradient change in the embedded redox field has no significant impact on self-potential anomalies. The resolution of the surface self-potential decreases with the depth of biogeochemical systems. The biogeobattery model based on the inert electrode model is an effective numerical model in biogeochemical systems.

Numerical Investigations on Seismic Response of Structures under the Effect of Infinite Boundary of Soil-Structure Interaction

The damage caused by large earthquakes is not only due to structures but also due to the soil failure, where the dynamic response varies considerably from the fixed base state because of the interaction between the ground and the structure. The main objective of this paper is to study the effect of the infinitely extended soil on the dynamic response of the structure. A three-dimensional dynamic analysis of reinforced concrete buildingconsidering the effect of soil-structure interaction is performed. Building with a different number of stories rest on soil with various characteristics have been taken into consideration. For simulation of wave propagation due to far-field effects, coupled finite-infinite elements is presented for modeling the soil. The infinite boundary provides a powerful tool for dealing with wave propagation problems. The analysis is performed through a finite element method which is implemented in ABAQUS program. An earthquake load is applied in the horizontal direction with various boundary conditions such as; free, and infinite boundary. The effect of boundary on the dynamic response of structure are investigated. The significant difference in dynamic response is observed when infinite boundaries are used, especially in the case of soft soil, where the existence of infinite elements leads to absorption of energy and thus greatly reduce the lateral displacement of the structure.

Dynamic response of soft soils in high-speed rail foundation: in situ measurements and time domain finite element method model

The dynamic response of soil to vibrations induced by moving trains has been widely studied using in situ measurements. However, few in situ tests have been conducted to measure the resulting vibration of foundation soils, especially for the foundation of high-speed rail (HSR) in a soft area. In this study, a number of field experiments were conducted on Shanghai–Hangzhou HSR in a suburb of Shanghai, China. The testing instruments were installed in foundation soils just beneath the HSR track to measure the vibration induced by trains moving at different speeds. Test results show the frequencies of foundation soil vibration are characterized by the train speed and geometrical features of the trains and slab track. In the frequency domain, the dominant frequency bands for vertical acceleration, velocity, and displacement of foundation soil decrease successively. In the time domain, the magnitudes of vibration levels at different locations in a soil foundation decrease gradually with increasing distance from the track. Furthermore, higher train speed can result in higher vibration level. Based on the field conditions, a three-dimensional dynamic finite–infinite element model is developed in the time domain. It shows the model is capable of capturing the primary characteristics of train-induced vibration in the field.

Analysis of the Vibration Mitigation Characteristics of the Ballasted Ladder Track with Elastic Elements

Despite the fact railways are seen as an environmentally friendly and sustainable form of transport, however, the train-induced vibration has been seen as a negative environmental consequence. The ballasted ladder track is one type of ballasted track with longitudinal sleepers. The elastic elements can not only protect the track structure but also control the vibration. To investigate the vibration mitigation effects of ballasted ladder track with elastic elements, a finite element - infinite element (FE-IFE) model was built considering the elastic elements of under-sleeper pads (USPs) and under-ballast mats (UBMs). This model was validated by a laboratory test. Then, the moving train load was obtained based on the multi-body dynamics (MBD)-finite elements method (FEM) analysis. The vibration mitigation effects of the ballasted ladder track with different types of elastic elements were calculated compared with the ballasted tracks without elastic elements. The results indicate that: (1) the ballasted ladder track has the advantage of vibration reduction at low frequencies, with a maximum vibration attenuation of 25.2 dB and an averaged vibration attenuation of 19.0 dB between 5 and 20 Hz through the ballast. (2) The ballasted ladder track with USPs or UBMs can provide better vibration attenuation between 30 and 100 Hz, but it induces a vibration amplification between 5 and 30 Hz. (3) The ballasted ladder track with elastic elements in different cases can provide different vibration mitigation effects. The ballasted ladder track with both USPs and UBMs can provide the best mitigation effect with an average vibration mitigation of approximately 15 dB and a maximum vibration mitigation of 30 dB between 30 and 100 Hz.

Dynamic Impedance of the Wide-Shallow Bucket Foundation for Offshore Wind Turbine Using Coupled Finite–Infinite Element Method

The dynamic impedances of foundation play an important role in the dynamic behavior and structural stability of offshore wind turbines (OWT). Though the behaviors of bucket foundation, which are considered as a relatively innovative foundation type under static loading, have been extensively investigated, the corresponding dynamic performances were neglected in previous research. This study focuses on the dynamic impedances of wide-shallow bucket foundations (WSBF) under the horizontal and rocking loads. Firstly, the numerical model was established to obtain the dynamic impedances of WSBF using the coupled finite-infinite element technique (FE-IFE). The crucial parameters affecting the dynamic responses of WSBF are investigated. It is shown that the skirt length mainly affects the rocking dynamic impedance and the diameter significantly affects the horizontal and coupling impedances, especially when the diameter is larger than 34 m. The overall dynamic responses of WSBF are profoundly affected by the relative soil thickness and the multi-layer soil stiffness. Additionally, dynamic impedances of WSBF are insensitive to the homogeneous soil stiffness. Lastly, the safety threshold curve was calculated according to the OWT, which can provide essential reference for the design of the OWT supported by large scale WSBF.