Viscoelastic Boundary Research Articles

Seismic performance analysis of shallow-buried large-scale three-box-section segment-connected pipeline structure under multiple actions

To ensure the safety operation of inter-basin water transfer project, it is important to understand the seismic performance of shallow-buried large-scale segment-connected pipeline structure under earthquake and other multiple actions. In this paper, a 3D FE model is built in details for the seismic assessment of large-scale prestressed concrete inverted-siphon shallow-buried under riverbed, and a method is proposed to realize multiple interactions of the viscoelastic boundary elements to finite elements, the compressible fluid to structure and the sealed joints made of rubber belt between adjacent segments. The inverted-siphon is longitudinally composited by 58 segments in total length of 858.64 m, and transversally consisits of three rectanguler-section boxes with net dimension of each box of 6.5 m width and 6.6 m height. The main influencing factors are set as the thickness of overburden soil, the flow condition and the engineering geological condition. The time-history analysis is carried out on the 3D FE model under Elcentro seismic wave excitation. The numerical analyses figures out the main vibration modes and vibrational frequency of this inverted-siphon, reveals the regions of peak tensile stress appeared on the concrete surface and the risk sealed joints with extremum relative displacement. This provides a scientific reference to take specific prevention measures of anti-earthquake, based on a deep understanding to the seismic cracking of concrete and the tearing broken of sealed joints for this kind of segment-connected pipeline structure.

Seismic response analysis of slope sites exposed to obliquely incident P waves

This study proposes a seismic input method for layered slope sites exposed to obliquely-incident seismic waves which transforms the waves into equivalent nodal forces that act on the truncated boundary of a finite element model. The equivalent nodal forces at the left and right boundaries are obtained by combining the free field response of a one-dimensional layered model with a viscoelastic boundary. The equivalent nodal forces at the bottom boundary are obtained by combining the incident wave field with the viscoelastic boundary. This proposed seismic input method for slope sites exposed to obliquely incident seismic waves is implemented with the aid of MATLAB software; it is applied to the seismic response analysis of slope sites in the commercial finite element ABAQUS software. The calculation results are compared with the reference solutions obtained by using the extended model to verify the correctness of the established seismic input method. The proposed seismic input method is then employed to investigate the influencing factors of the seismic response of layered slope sites exposed to oblique incidence P waves. The results show that the angle of incidence, location of the interface between soft and hard rocks, and impedance ratio have significant effects on the seismic landslide.

Investigation of the dynamic response of subgrade vibration compaction based on the finite element method

<abstract> <p>A three-dimensional finite element model of a vibratory wheel on soil is established though the use of the ABAQUS software platform to investigate the interaction between the wheel and soil and the resulting dynamic response during vibratory compaction. The extended linear Drucker Prager model is used to reflect the plastic deformation characteristics of the soil. The truncated boundary is treated by using a three-dimensional uniform viscoelastic artificial boundary method. The vibratory responses of the soil under the wheel, including the stress and contact force, are analyzed by using numerical simulations. The results show a decrease in the soil vertical stress at the edge of the vibrating wheel transverse to the wheel path, which may assist in identifying the rolling overlap width of the wheel. Along the wheel path, the vertical stress center is demonstrated to lie ahead of the vibrating wheel mass center, caused by the inclination of the wheel soil contact surface. The contact pressure and total grounding width of the soil under the wheel can be calculated by using the finite element method; only one-third of the total width could produce effective compression deformation.</p> </abstract>

New general decay results for a multi-dimensional Bresse system with viscoelastic boundary conditions

<p style='text-indent:20px;'>In this paper we consider a multi-dimensional Bresse with memory-type boundary conditions. By assuming minimal conditions on the resolvent kernel, we establish an optimal explicit and general energy decay result. This result is new and substantially improves earlier results in the literature.</p>

A stepwise artificial boundary condition for wave propagation in elasto-plastic media

Wave propagation in elasto-plastic media is often encountered in earthquake geotechnical engineering. However, dynamic boundary conditions in the numerical simulation of wave propagation problems are often developed based on linear elastic assumptions. In this study, the method of characteristics is utilized to propose a novel stepwise artificial boundary condition (S-ABC) for wave propagation in elasto-plastic media. The numerical implementation of S-ABC within a finite element procedure in time domain is developed. Typical numerical examples are chosen to verify the efficiency of this ABC, including: 1) a semi-infinite soil column model subjected to impulse load, where the influence of unloading wave front in elasto-plastic media is discussed; 2) an infinite and a finite soil column model under cyclic seismic wave input, where the proposed S-ABC is compared with the traditional viscoelastic artificial boundary condition (V-ABC). Numerical results demonstrate the significantly higher accuracy and robustness of the proposed S-ABC for nonlinear and elasto-plastic media compared to traditional V-ABC. The influence of unloading wave front on artificial boundary condition for elasto-plastic media is also revealed, which has not been reported previously.

Analysis of the Influence of Structure–Soil–Structure Interaction on the Seismic Response for Nuclear Power Plant ASTS

After the Fukushima nuclear accident in Japan, whether the structural safety of the nuclear power plant (NPP) can be guaranteed under an earthquake has been of wide concern. Automatic seismic trip systems (ASTS) have been deployed in NPPs. There are generally two units or more double units on the one NPP site, and the vibration energy of the structure can certainly affect its adjacent structures through the soil, and there is energy transfer and conversion between adjacent structures. At present, the distance between two reactors of NPPs of different reactor types is generally 100–200 m (this distance is referring to the distance between the centers of two reactors, which is slightly different for different reactor types). In the past, seismic instruments were used in the ASTS and the setting of shutdown threshold, so the impact of only one unit was considered in the structural analysis of NPPs, and the interaction of two reactors through site conditions was not considered. In addition, as the site conditions of NPPs become more and more complex, it is necessary to consider the impact of one reactor structure on another reactor structure through the soil on the same site under an earthquake. In order to analyze the influence of structure–soil–structure interaction (SSSI), a three-dimensional refined finite element model of NPPs is established in this paper. The soil–structure interaction (SSI) is considered by using viscoelastic boundary. The seismic responses of different positions of the raft foundation and NPP structure, under the conditions of considering SSI effect (one reactor) and SSSI effect (two reactors), are compared. The influence of SSSI effect on the seismic responses of the raft foundation and NPP structure is revealed. It is proposed that SSSI effect should be reasonably considered according to the site conditions for the structural analysis of NPPs for the NPP ASTS.

Seismic response of a nuclear island building with base isolation considering the soil–structure interaction effect

AbstractThis study aims to investigate the influence of soil–structure interaction (SSI) on the seismic response of a nuclear island (NI) building with base isolation. Hence, modal and dynamic time‐history analyses of the NI building with base isolation based on different soil dynamic numerical models that are applicable for homogeneous and layered sites to consider the SSI effect were conducted. After a comparison analysis of natural frequencies, floor response spectra (FRS), and acceleration response of superstructure, the following results are obtained. (i) For homogeneous sites, the degrees of freedom of the horizontal translation and torsion of the NI building with base isolation calculated using different site dynamic numerical models have equivalent natural frequencies. For layered sites, the natural frequencies increase slightly with the improvement of the shear wave velocity of the upper layered soil. (ii) For homogeneous sites, FRS calculated by the massless foundation model is generally larger than those of the dynamic model proposed by the ASCE code and the viscoelastic artificial boundary site model. Both the spectral and peak values of horizontal FRS at a low frequency band calculated by considering the SSI effect are larger than those without the SSI effect. (iii) For layered sites, both the spectral and peak values of horizontal FRS at a low frequency band have an amplification effect compared with that of a homogeneous site. (iv) For layered sites, the calculated horizontal acceleration response does not have evident law that changes with the degree of hardness and softness of the upper soil. Therefore, the SSI effect for particular homogeneous and layered sites should be considered when calculating the seismic response of the NI building with base isolation.

Linear waves at viscoelastic interfaces between viscoelastic media

Many different types of waves that propagate along interfaces are found in nature. We derive the general dispersion relation for interfacial waves along a planar viscoelastic boundary that separates two viscoelastic bulk media, from which the known dispersion relations of different interfacial waves are recovered in the respective parameter limits. Our theory allows us to model acoustic wave-guiding phenomena at biological membranes, where viscoelastic properties are particularly relevant.

Influence of multiple random variables on the safety of cracked tunnels under earthquake action

To explore the mechanical properties of cracked lining subjected to seismic loads based on wave theory and the extended finite element method, the dynamic viscoelastic boundary of a seismic wave and equivalent nodal force load were generated by MATLAB programming software to establish a simulation model of cracked lining structure. The internal force state change law of the lining structure was studied by varying the crack depth, crack length, secondary lining thickness, and other parameter values (including the layout between multiple cracks). Also, the safety factor of the lining crack section was obtained, and the functional relationship between the safety factor and parameter variables was established. Results show that the crack depth and secondary lining thickness were the main factors affecting the internal force of the crack section. Based on the least square method, the calculation formula and 95 % confidence interval between the minimum safety factor (Kmin) and each parameter of the crack section were obtained. Meanwhile, the Kmin prediction model was obtained via multiple nonlinear regression. When the crack depth value was 30 % of the lining thickness value, Kmin reduced 2.5 times. At 57 % crack depth of the lining thickness, the Kmin was less than the specification value, indicating that the lining structure’s safety reserve was low. Compared with the arrangement of the vertical distribution of the two cracks, the stress concentration generated when the two cracks were arranged in parallel would more likely affect the structure adversely. The findings can provide a reference for the safety study of cracked tunnels.

Seismic Response Analysis of Uplift Terrain under Oblique Incidence of SV Waves

In order to analyze the impact of seismic waves on the venue earthquake, based on the display finite element method, the viscoelastic artificial boundary is used to analyze the variation of the ground motion amplification coefficient and the Fourier spectrum of the raised terrain under different incident angles with SV wave oblique incidence on different slopes. This verification model analysis solution and numerical solution are better. The numerical simulation results show that as the degree of the slope increases, the seismic amplification coefficient increases, and its slope amplification coefficient changes significantly. The X direction coefficient is greater than Y’s magnification coefficient. The Fourier curve with a frequency of 0.2~1 Hz increases with the slope of the raised terrain; when the El Centro is incorporated at 30°, the Fourier spectrum amplitude decreases as the incident angle increases in the low-frequency band. The amplitude of the Fourier spectrum at the high-frequency band monitoring point changes with the incident angle. In the high-frequency band from 1 to 10 Hz, the rate of amplitude change is the largest. When the incident angle is at 0°, the amplification coefficient in the Y direction is basically symmetric.

Seismic responses of a liquid storage tank considering structure-soil-structure interaction

Liquid storage tanks play a very important role in the petrochemical industry, in practical applications, they are often arranged in rows with small spacing, as a result, the earthquake responses will be affected by group effect. Considering the liquid–solid-soil coupling, structure-soil-structure interaction, material nonlinearity, and viscoelastic boundary, three-dimensional numerical calculation models of liquid storage tanks with compaction pile composite foundation in loess area under the conditions of single tank and group tanks were established. The seismic responses of a single tank and group tanks were compared, the group effect on the liquid storage tank under earthquake was discussed, and the parameter analysis was conducted. The results show that the group effect had an amplification effect on the effective stress of the tank wall, the liquid sloshing wave height, and the horizontal displacement of the foundation. Under the El-Centro and the Northridge waves, the effective stresses of the tank wall were amplified by 10.07% and 35.54%, respectively. The effects of the foundation deformation parameter (elastic modulus) and strength parameters (cohesion and friction angle) on the dynamic responses of the liquid storage tanks were different, but in most cases, except for axial compressive stress, the influence coefficient of the group effect corresponding to the effective stress, the liquid sloshing wave height, and the foundation horizontal displacement were positive. The influence of the group effect on the dynamic responses of the liquid storage tank under earthquake cannot be ignored.

Study on the Testing Method of Relaxation Modulus under Spherical Indenter Loading

Viscoelastic materials are widely used in various fields. In order to better use viscoelastic materials in various working conditions, it is necessary to master the material properties of viscoelastic materials. Relaxation modulus is a characterization method of viscoelastic material properties. In this paper, by analyzing that viscoelastic materials are time-domain related parameters, the load-time curves are obtained by using the spherical indentation instrument to carry out the ramp loading indentation test at different speeds. According to the law of ramp strain history loading, the data at different velocities are summarized and a method for judging the linear viscoelastic boundary of viscoelastic materials in spherical indentation tests is obtained. Aggregate the load-time data at different speeds to obtain a set of valid data for a longer period of time. A method of measuring the relaxation modulus using the ramp-constant strain history is proposed. Compared with the ramp loading test method, it is simple and easy to operate, and it can make up for the short time period of the measured data in the ramp loading test. The experiment verifies the feasibility of the method of ramp-constant strain history.

A comparative analysis of seismic response of shallow buried underground structure under incident P, SV and Rayleigh waves

In this study, A time-domain seismic response analysis method and a calculation model of the underground structure that can realize the input of seismic P, SV and Rayleigh waves are established, based on the viscoelastic artificial boundary elements and the boundary substructure method for seismic wave input. After verifying the calculation accuracy, a comparative study on seismic response of a shallow-buried, double-deck, double-span subway station structure under incident P, SV and Rayleigh waves is conducted. The research results show that there are certain differences in the cross-sectional internal force distribution characteristics of underground structures under different types of seismic waves. The research results show that there are certain differences in the internal force distribution characteristics of underground structures under different types of seismic waves. At the bottom of the side wall, the top and bottom of the center pillar of the underground structure, the section bending moments of the underground structure under the incidences of SV wave and Rayleigh wave are relatively close, and are significantly larger than the calculation result under the incidence of P wave. At the center of the side wall and the top floor of the structure, the peak value of the cross-sectional internal force under the incident Rayleigh wave is larger than the calculation result under SV wave. In addition, the floor of the underground structure under Rayleigh waves vibrates in both the horizontal and vertical directions, and the magnification effect in the vertical direction is more significant. Considering that the current seismic research of underground structures mainly considers the effect of body waves such as the shear waves, sufficient attention should be paid to the incidence of Rayleigh waves in the future seismic design of shallow underground structures.

Stability conditions of explicit integration algorithms when using 3D viscoelastic artificial boundaries

Stability conditions of explicit integration algorithms when using 3D viscoelastic artificial boundaries

Numerical investigation of viscoelastic boundary layer in forced convection flow on surface under prescribed heat flux

AbstractThe paper intends to analyze numerically the effect of forced convection with viscoelastic boundary on porous media subjected to constant heat flux on the surface. The modified Navier–Stokes equations in nondimensional forms are formulated and modeled with Darcy–Forchheimer–Brinkman to solve the equations using bvp4c with MATLAB package. The numerical results are found for local Nusselt number, shear stress, temperature distribution, and finally the velocity of the boundary layer over a horizontal plate. The analysis includes the influence of several parameters, such as Forchheimer, porous media, Nusselt number, and viscoelastic on distributions of velocity and temperature. Also, the effects comprise the friction and heat transfer coefficients. The numerical results under constant heat flux indicate an increase in shear stress and boundary layer velocity as the Darcy parameter increases and at the same time, the values of temperature and Nusselt number are decreased. A significant increase was observed for the values of Nusselt number, temperature, and shear stress under large values of the Forchheimer parameter. The numerical results show a good agreement with available previous works.

Study on Early Warning of Karst Collapse Based on the BP Neural Network

In order to comprehensively grasp the dynamics of karst collapse, promote the comprehensive prevention and control level of karst collapse, and prevent secondary disasters caused by lava collapse, this study presents a method of karst collapse early warning based on the BP neural network. This method does not need to set the sliding surface in the finite element calculation model. The stress of the sliding surface is fitted according to the spatial stress relationship of the deep karst layer through the improved BP neural network PID control algorithm and BP neural network algorithm, which avoids the modeling and mesh generation of the complex sliding block and has good accuracy and ease of use. According to the basic theory of the BP neural network, the calculation formulas of multilayer feedforward and error back propagation processes are derived, and the two-dimensional and three-dimensional finite element models of gravity dams without and with sliding blocks are established, respectively. Finally, according to the common formulas of viscoelastic artificial boundary and equivalent load, the two-dimensional and three-dimensional input programs of the karst fluid state are compiled, and a neural network early warning model is obtained. The experimental results show that the process karst state simulated by the algorithm is very close to the actual situation, and the minimum value of antisliding coefficient and its occurrence time can be accurately predicted, with an error range of less than 3%. Conclusion. BP neural network prediction can effectively predict karst collapse, with higher prediction accuracy, and can effectively simulate the actual collapse risk.

Seismic Response and Damage Analysis of Large Inverted Siphon Structure

Large-scale inverted siphon is a key hydraulic structure for building a national water network and realizing the spatial balance of water resources, and its safety under the action of earthquakes has become the focus of trans-basin water transfer projects. In this paper, Xiazhuang inverted siphon of water diversion in Central Yunnan is taken as the research object. Viscoelastic artificial boundary was used to simulate seismic waves spread in the soil, which include the natural site seismic waves and the waves fitted manually according to the site conditions. A three-dimensional finite element model of soil-structure-fluid interaction was established by software of ABAQUS, in which the fluid-structure interaction was simulated by user-defined element (UEL) built on additional Mass Method. Seismic response and damage analysis of large inverted siphon structure are carried out by the model. The results show that the dynamic displacement of the inverted siphon pipe is mainly horizontal sloshing, and the dynamic response of the pipe increases due to the water in the pipe; even the dynamic stress value in some areas is close to the design value of the concrete tensile strength. The damage analysis of inverted siphon pipe shows that the plastic deformation and the damage area develop rapidly with the increase of the peak ground acceleration (PGA), and the tensile damage area is generally larger than the compression damage area. The damage factor of the pipe under the working condition of the water is obviously larger relative to the working condition of no water. Therefore, it is suggested that the damage effect of earthquake should be considered in the design of large inverted siphon in high-intensity area.

Force relaxation of contact between a flat-ended cylindrical indenter and a poroviscoelastic layer

Interpreting the contact force relaxation between an indenter and a poroviscoelastic material at a fixed displacement to obtain the materials properties is a challenging task, because both fluid drainage and solid viscoelasticity contribute to the relaxation. In this research, the indentation of a poroviscoelastic layer caused by a flat-ended cylindrical indenter is formulated analytically by the displacement functions in the Laplace-transformed domain. The contact force of the indenter at a fixed displacement was expressed by a closed-form in the transformed domain and numerically inverse-transformed to the time domain. The force relaxation is analyzed for combinations of three drainage conditions prescribed on the layer top and two boundary conditions prescribed on the layer bottom. The closed-form solution can approach that of the flat-indentation on a poroviscoelastic half-space, when the layer is very thick compared to the indenter radius. In addition, finite element simulations of the flat-indentation on poroviscoelastic layers were carried out as a comparison for the semi-analytical results. The relaxation ratios at the limits of the drained-nonviscoelastic state, the nondrained-viscoelastic state and the drained-viscoelastic state are shown for different ratios of the layer thickness to the indenter radius, and verified with the corresponding elastic solutions. The effects of the viscoelastic characteristic time on the force relaxations are also presented for different viscoelastic properties and boundary conditions.

Bending and vibration studies of FG porous sandwich beam with viscoelastic boundary conditions: FE approach

Bending and vibration characteristics of FG porous sandwich beam with viscoelastic boundary conditions are investigated. Complex shear modulus and associated loss factor are considered for the viscoelastic interlayer. The beam is constrained by viscoelastic supports (VES) at either end. Complex stiffness model is adopted for VES. The transverse deflection, natural frequency, loss factors, and mode shapes are obtained by varying VES stiffness. Furthermore, the study is extended to sandwich beams with various (H, O, V, and X) porosity patterns. The results convey that VES contribution in vibration damping is more predominant when the supports are less stiff (more viscous).

An Explicit Finite Element Method for Saturated Soil Dynamic Problems and Its Application to Seismic Liquefaction Analysis

An explicit finite element method is proposed to solve the u-p-formed dynamic equation of saturated porous media. In this method, a special discretization is implemented to discretize the global computational domain into local node systems of the individual nodes, and the dynamic equation of each local node system corresponding to each node is discretized by the completely explicit integration method in the time domain. By cycling through all the nodes, the dynamic responses of the global computational domain are obtained. In addition, a viscoelastic artificial boundary is added in the method. In numerical examples, the proposed FEM is verified by the good agreements between the results obtained from the proposed method and the analytical and numerical solutions of existing methods, respectively. After being embedded in OpenSees software, the proposed method is implemented into analysis of the seismic responses of liquefiable site.