Viscous Boundaries Research Articles

Study on the seismic wave input method for earth-rock dam on overburden foundation with dynamic nonlinearity based on nonlinear artificial boundary

Accurately obtaining the seismic response of earth-rock dams on overburden foundations is crucial for seismic safety assessment and design, and a reasonable seismic input method is necessary. The seismic wave input method based on artificial boundaries is widely used in elastic foundations. However, the overburden with obvious dynamic nonlinearity is an insurmountable obstacle for the traditional method. In this research, relying on a specific earth-rock dam project, the essence of the seismic wave input method for nonlinear foundations is analyzed in detail from equivalent loads and viscous boundaries, respectively. The mechanism of inapplicability of the traditional seismic wave input method is illustrated, and an effective modified method is validated and presented. The research indicated that equivalent loads for the nonlinear dynamic response of the overburden foundation can be accurately acquired with the shear box model. The dynamic parameters of soil can be captured dynamically by the nonlinear viscous coupling boundary. The states of the lateral boundary of the overburden foundation are consistent with the free field precisely with the modified seismic wave input method by combining the shear box model and the nonlinear viscous coupling boundary. A large error will be caused by neglecting the dynamic nonlinear behavior of the overburden foundation, where the maximum deviation of peak acceleration may be over 55 % or more. A numerical model with a relatively small lateral range of overburden foundation will be obtained when the modified seismic wave input method is engaged. Moreover, the computational accuracy is enhanced remarkably, with a maximum deviation of no more than 5 %. This study provides effective theoretical support for seismic analysis and safety assessment of earth-rock dams on deep overburden foundations.

An explicit improved meshless numerical manifold method for dynamic crack propagation

Accurately simulating the dynamic propagation of cracks is critical to investigating the mechanisms of rock fracture under dynamic loading. The meshless numerical manifold method, characterized by its node-based interpolation approximation akin to the meshless method and the dual-cover of numerical manifold method, is particularly suitable for crack analysis and has been successfully applied to quasi-static crack propagation. This paper aims to extend its application to the simulation of dynamic crack propagation. Initially, the meshless numerical manifold method's nodal arrangement and numerical integration scheme are enhanced to address dynamic problems more effectively, referred to as the Improved Meshless Numerical Manifold Method (iMNMM). Subsequently, we introduce a novel mass lumping method grounded in rigorous mathematical principles, an energy-conserving extended degrees of freedom inheritance strategy and a crack propagation criterion based on dynamic stress intensity factors. Additionally, the viscous artificial boundaries and the “large mass” acceleration method are incorporated to impose the acceleration and zero-displacement boundary conditions. Further, the improved explicit meshless numerical manifold method based on the central difference method is established for dynamic crack propagation. Finally, for verification, iMNMM is tested on several numerical examples. Numerical results manifest that iMNMM can enable the simulation of dynamic crack propagation with larger, constant time steps.

Role of thermal radiation and double-diffusivity convection on peristaltic flow of induced magneto-Prandtl nanofluid with viscous dissipation and slip boundaries

Role of thermal radiation and double-diffusivity convection on peristaltic flow of induced magneto-Prandtl nanofluid with viscous dissipation and slip boundaries

Thermo-hydrodynamic Analysis of Multistep Journal Bearing using Computational Fluid Dynamics Simulation

Journal bearing is a machine element that is used to maintain the continuous rotation of the shaft on its axis. The rising demand for efficient and economical journal bearing applications has resulted in increased demand for high-speed machines. An increase in engine speed raises the distribution of pressure, temperature, and vapor volume fraction. Most of the research still only focuses on increasing pressure distribution and load-carrying capacity. However, the value of friction force, temperature distribution, and vapor volume fraction must also be considered such that the lubrication of the journal bearing is close to the real situation. Therefore, the research was conducted by varying the geometry modelling through multistep textures using viscous boundaries and thermo-hydrodynamic lubrication. Owing to the high load and speed usage on multistep journal bearings, research on the effect of eccentricity ratio and inlet and outlet temperatures on the tribological performance of multistep journal bearings was conducted. The analysis has been performed using a multistep journal bearing modelling 3D computational fluid dynamics considering the effect of cavitation on temperature. The results of this study indicate that the use of multistep textures on journal bearings can reduce friction force, temperature, and vapor volume fraction. The variation of the eccentricity ratio shows that a high eccentricity ratio leads to a high three parameters (i.e., friction force, temperature, and vapor volume fraction). Finally, for variations of inlet and outlet temperatures, such parameters are high when the inlet and outlet temperatures are high.

Seismic response study of shield tunnel with lateral karst cavity under SV waves

This paper investigates the seismic effects of karst cavity size and span on the shield tunnel subjected SV waves, using the case project of Dalian Metro Line 5. The viscous spring artificial boundaries are employed for the seismic input, which is validated to assure accuracy. The shield tunnel is simplified according to the method of the equivalent bending stiffness model. The deformation and stress distribution are analyzed to investigate the dynamic response of the shield tunnel under SV waves at different angles. The tunnel damage state is evaluated by the criterion proposed by authors in previous research. The results show that a larger cavity size can lead to more deformation in the tunnel. There are significant differences in the spatial distribution of deformation and stress affected by the incident angle. As the cavity size increases, the stress near the cavity decreases significantly. Only the cavity size is greater than or equal to 0.8D (D is the tunnel’s diameter), there are damage concentration areas on the bottom, and the damage area shifts towards to circumferential direction. The deformation and stress distribution are highly affected as the span increases in the Z direction, followed by the Y direction, and almost no effect in the X direction. The damage area increases as the increase of span in three directions. There are damage concentration areas of the bottom only as the span is 1.5D in the Z direction. Compared with the effect of cavity size, the results indicate that the damage concentration is not solely related to cavity span in one single direction.

Influences of Wall Configurations on Earthquake Behavior of Cantilever Retaining Walls Considering Soil-Structure Interaction Effects

Cantilever walls are frequently and necessarily built not only in earthquake prone regions but also on different foundation subsoils with various physical and mechanical characteristics. The response of these structures is a complicated soil-structure interaction (SSI) problem, in which the relative stiffness between the soil and structure is of critical importance. In addition to different soil conditions and earthquake motions, the wall configurations have an important role in the cantilever retaining wall design. Thus, the major objective of this work is to investigate the effects of various configurations on seismic response of the cantilever retaining walls considering SSI. Accordingly, the seismic response of the interaction systems is revealed using the 3D finite element models (FEM) in time domain, assuming linearly elastic behavior for the wall, and elastoplastic behavior for backfill and foundation soil. Viscous absorbent boundaries are employed to both simulate radiation scenario and avoid undesirable wave reflections generated by soil lateral boundaries. Backfill-wall interfaces are modeled using the unidirectional interface elements with nonlinear force-deflection abilities. The interaction systems are analyzed considering three different cantilever wall configurations (inverted T-type, L-type, and the wall with a base key), four different ground motion records, and four different subsoil systems. Nonlinear seismic analyses are carried out to visit how considering the variation of these parameters influences the wall behavior. The results from parametric studies show that the wall configuration, SSI effects and ground motions are remarkably influential on seismic responses of the cantilever walls such as the stresses and horizontal displacements.

Application of Three-Dimensional Explicit Discontinuous Deformation Analysis on Wave Propagation in Rock Masses Using Three Viscous Boundaries with the Remedy for Artificial Joints

Application of Three-Dimensional Explicit Discontinuous Deformation Analysis on Wave Propagation in Rock Masses Using Three Viscous Boundaries with the Remedy for Artificial Joints

Calibration of Adjustment Coefficient of the Viscous Boundary in Particle Discrete Element Method Based on Water Cycle Algorithm

The viscous boundary has a direct influence on the accuracy of structural dynamic response analysis, and the absorbing effect of the viscous boundary is controlled by the adjustment coefficient. Therefore, a calibration model of the viscous boundary’s adjustment coefficient based on the water cycle algorithm is established for the particle discrete element to improve the accuracy of dynamic response analysis. First, the traditional viscous boundary theory is utilized to realize the viscous boundary’s application method in the particle discrete element via programming. This avoids the reflection and superposition of seismic waves at the boundary and makes the structural dynamic response with the particle discrete element more real and accurate. Second, for the complex and time-consuming adjustment coefficients determination, a calibration model based on the water cycle algorithm and Latin hypercube sampling is established for the adjustment coefficients in the particle discrete element method. Finally, this calibration model is employed for the seismic response analysis of a rockfill slope, the maximum velocity of rock in this rockfill slope being about 1.30 times that of a seismic wave. Comparing the rockfill slope response with fixed and viscous boundaries, the calibration’s accuracy and the viscous boundary’s feasibility are demonstrated, further expanding the research and application of the particle discrete element method in dynamic response analysis.

A hybrid boundary method for seismic wave propagation problems in slopes

The seismic behavior of a slope site has a critical impact on its stability and the seismic response of structures located on or near the slope. In this paper, a hybrid boundary method(HBM) is proposed for the site response analysis of slopes. Viscous and viscous-spring boundaries are applied in the HBM and equivalent loads are calculated separately on the bottom and the lateral boundary. A horizontally extended model is used to verify the HBM. The results show that the maximum error of the HBM is only 2.010%. On the ground surface of the slope site, amplification occurs at the crest side and de-amplification occurs at the toe side under various cases. The ratio of the maximum and minimum PGA on the ground surface could exceed 2. Therefore, great attention should be paid to the spatial variability of ground motion on slope sites. The HBM is also compared with four conventional approaches. The maximum errors of all the conventional approaches exceed 70%. These examples demonstrate that the HBM has much higher accuracy in practice than conventional approaches.

Effect of seismic wave propagation in massed medium on rate-dependent anisotropic damage growth in concrete gravity dams

Seismic modeling of massive structures requires special caution, as wave propagation effects significantly affect the responses. This becomes more crucial when the path-dependent behavior of the material is considered. The coexistence of these conditions renders numerical earthquake analysis of concrete dams challenging. Herein, a finite element model for a comprehensive nonlinear seismic simulation of concrete gravity dams, including realistic soil-structure interactions, is introduced. A semi-infinite medium is formulated based on the domain reduction method in conjunction with standard viscous boundaries. Accurate representation of radiation damping in a half-space medium and wave propagation effects in a massed foundation are verified using an analytical solution of vertically propagating shear waves in a viscoelastic half-space domain. A rigorous nonlinear finite element model requires a precise description of the material response. Hence, a microplane-based anisotropic damage-plastic model of concrete is formulated to reproduce irreversible deformations and tensorial degeneration of concrete in a coupled and rate-dependent manner. Finally, the Koyna concrete gravity dam is analyzed based on different assumptions of foundation, concrete response, and reservoir conditions. Comparison between responses obtained based on conventional assumptions with the results of the presented comprehensive model indicates the significance of considering radiation damping and employing a rigorous constitutive material model, which is pursued for the presented model.

Numerical modeling of seismic ground response considering the coupled effect of slope and soil layering

Seismic waves change as they pass through the soil layers. This change can be due to soil layering or existence of surface topography, which is estimated by ground response analysis. In this study, the coupled effect of soil layering and topographic irregularity is considered to evaluate the interaction of these two factors. In the first part, using two-dimensional finite element method (FEM) and viscous boundaries, the Gilroy region is simulated and one of the devastating earthquakes in this area, Loma Prieta (1989), applied to the model as an incident wave. The results are compared with those of recorded data to evaluate the performance of the model. In the second part, different slopes are assumed to exist in the Gilroy region and the seismic site response considering the coupled effect of soil layering and topographic irregularity is estimated using a nonlinear approach. In this part, characteristics of the soil layers are considered as same as the Gilroy region. Obtained results show that the amplification generally increases with increasing the slope angle. Comparing the results of free field condition with those of slope region reveals that the coupled effect of soil layering and topographic irregularity cannot be ignored and should be evaluated using accurate and practical approach.

Dynamic Response of a Single Pile Embedded in Sand Including the Effect of Resonance

In this paper, responses of a single pile embedded in sand soil (loose and dense) under dynamic loading (sinusoidal dynamic vibrations of 0.1 g to 0.5 g) have been investigated by two-dimensional analysis using the finite element method (FEM). Viscous (dashpot) boundaries have been used for taking the boundary effects of far-field into account. The applicability and accuracy of site responses of two-dimensional analysis due to the FEM modelling have been well verified with one-dimensional site responses. The results indicate that the relative density of sand (loose, dense) becomes prominent for the displacements of the pile, specifically under the frequency effects of resonance. While the pile in loose sand causes the displacements of 0.1 m to 0.5 m, the pile in dense sand leads to the displacements of 0.05 m to 0.25 m, proportionally with the dynamic loads from 0.1 g to 0.5 g. Moreover, the displacements reach their peak value at the frequency ratio of the resonance case. Viscous boundaries are found sufficient for modelling excessive displacements due to dynamic loading. However, the displacements reveal that high vibrations (> 0.1 g for loose sand, > 0.2 g for dense sand) influencing the pile deformations are critical for the issues of settlements. This is more significant for the resonance case in order for ensuring sufficient design. Consequently, the findings from the study are promising good contributions for pile design under the dynamic effect.

Hybrid grid generation for viscous flow simulations in complex geometries

In this paper, we present a hybrid grid generation approach for viscous flow simulations by marching a surface triangulation on viscous walls along certain directions. Focuses are on the computing strategies used to determine the marching directions and distances since these strategies determine the quality of the resulting elements and the reliability of the meshing procedure to a large extent. With respect to marching directions, three strategies featured with different levels of efficiencies and robustness performance are combined to compute the initial normals at front nodes to balance the trade-off between efficiency and robustness. A novel weighted strategy is used in the normal smoothing scheme, which evidently reduces the possibility of early stop of front generation at complex corners. With respect to marching distances, the distance settings at concave and/or convex corners are locally adjusted to smooth the front shape at first; a further adjustment is then conducted for front nodes in the neighbourhood of gaps between opposite viscous boundaries. These efforts, plus other special treatments such as multi-normal generation and fast detection of local/global intersection, as a whole enable the setup of a hybrid mesher that could generate qualitied viscous grids for geometries with industry-level complexities.

Silent Boundary Scheme and Analysis of Existing Methods of providing Silent Boundary

For dynamic analysis, it is required to provide viscous boundaries in PLAXIS to reduce the boundary effects and to prevent the reflection of waves from boundaries. So, a study has been carried out to compare the various methods of providing silent boundaries and to see the effectiveness of viscous boundaries used in PLAXIS. In this work, three methods of providing silent boundaries, which are viscous boundaries, local damping, and extended boundary, are analyzed using a 2D finite element program in FORTRAN by considering the simple problem of a two-dimensional vertical bar. Parameters, such as, normal stress at the bottom, vertical displacement at the top, potential energy, kinetic energy, strain energy, and total energy of bar are determined with and without using the above three methods of providing silent boundaries. Results are compared using graphs. It was observed that standard viscous boundaries are not much effective for static analysis but most effective for dynamic analysis.

Modeling the effects of slip on dipole–wall collision problems using a lattice Boltzmann equation method

We study the physics of flow due to the interaction between a viscous dipole and boundaries that permit slip. This includes partial and free slip, and interactions near corners. The problem is investigated by using a two relaxation time lattice Boltzmann equation with moment-based boundary conditions. Navier-slip conditions, which involve gradients of the velocity, are formulated and applied locally. The implementation of free-slip conditions with the moment-based approach is discussed. Collision angles of 0°, 30°, and 45° are investigated. Stable simulations are shown for Reynolds numbers between 625 and 10 000 and various slip lengths. Vorticity generation on the wall is shown to be affected by slip length, angle of incidence, and Reynolds number. An increase in wall slippage causes a reduction in the number of higher-order dipoles created. This leads to a decrease in the magnitude of the enstrophy peaks and reduces the dissipation of energy. The dissipation of the energy and its relation to the enstrophy are also investigated theoretically, confirming quantitatively how the presence of slip modifies this relation.

Solution for Soil–Structure Interaction with Direct Infinite Element in Time Domain

This paper presents a procedure for simulating soil–structure interaction in time domain using two direct infinite elements coupled with an absorbing layer. The infinite elements are built from the exponential decay formulation, while the absorbing layer is expressed in the form of a concentrated damping matrix. In this method, the absorbing layer, applied between the mesh and infinite elements, ensures the dissipation function, whereas the infinite elements provide the necessary static part of the boundary. Using an implicit integration scheme, the procedure was tested in axisymmetric and plane strain conditions under heavy sides and rectangular impulse loadings for classical soil–structure interaction cases. The results show good performances of the method compared to conventional boundaries, viscous boundaries, and extrapolation algorithm. Easy to implement in a finite element code, the method may be applied for different kinds of direct infinite elements providing a good compromise for far-field simulation in soil–structure interaction problems.

Dynamic response of rock slopes to oblique incident SV waves

Most dynamic response analyses of rock slopes only consider the vertical incidence of seismic waves. However, obliquely incident waves dominate in near-field seismic areas. This paper presents a new seismic input method that considers near-field oblique incidence based on mechanisms of artificial viscous boundaries and the influence of incident angle on the dynamic response of rock slopes. Three numerical model slopes with different slope angles of 30°, 45° and 60° are excited with the El Centro earthquake record assuming varying incident angles from 0° to 90°. The results show that the incident angle significantly affects the dynamic response of the slopes. The most damaging incident directions are approximately perpendicular to the slope surface, rather than in the vertical direction. The dynamic response of the slopes will be underestimated if only the vertical incidence is considered. The incident angle affects the reflection wave field in the slope and the areas affected by the reflection waves decrease with increasing slope angle. However, the predominant period of the response spectrum of the rock slopes is not sensitive to the incident angle and location. This study unveils the dynamic mechanism of earthquake-induced rock slides, which is of significance for earthquake hazard prevention.

Three new boundary conditions for the seismic response analysis of geomechanics problems using the numerical manifold method

The numerical manifold method (NMM) provides a unified approach to address continuum-discontinuum problems in geotechnical engineering. Owing to the dynamic nature of its governing equations, the NMM should be suitable for modelling dynamic problems such as those associated to earthquakes. However, due to the current limitations in far-field boundary conditions implemented in the original NMM formulation, NMM has not been used to carry out seismic response analysis. In the present study, three new boundary conditions have been developed to extend the capability of the NMM to conduct seismic response analysis: (1) the classical viscous boundary condition, which allows for the absorption of the seismic wave energy at the boundaries, based on the viscous boundaries, and the seismic motion input method is also proposed; (2) the free field boundary condition, which captures the free field motion and absorption of the reflected waves at the sides of the model. The algorithms to generate free field mesh and its coupling calculations with the main mesh are also presented; (3) the static-dynamic unified boundary, which models the transition from fixed boundary condition in static state to free field boundary condition in seismic state, thus ensuring the accuracy and consistency of the numerical simulation. Finally, five numerical examples are shown to validate the proposed methods. The numerical results indicate that the improved NMM can be successfully adopted for seismic response analysis.

Singularly Perturbed System of Parabolic Equations in the Critical Case

We examine a system of singularly perturbed parabolic equations in the case where the small parameter is involved as a coefficient of both time and spatial derivatives and the spectrum of the limit operator has a multiple zero point. In such problems, corner boundary layers appear, which can be described by products of exponential and parabolic boundary-layer functions. Under the assumption that the limit operator is a simple-structure operator, we construct a regularized asymptotics of a solution, which, in addition to corner boundary-layer functions, contains exponential and parabolic boudary-layer functions. The construction of the asymptotics is based on the regularization method for singularly perturbed problems developed by S. A. Lomov and adapted to singularly perturbed parabolic equations with two viscous boundaries by A. S. Omuraliev.

Boundary Effects in Simulation of Soil-Structure Interaction Problems

This paper presents the influence of boundary conditions in numerical simulation of soilstructure interaction problems. It discusses aspects related to a seismic load influencing a soil medium and a frame structure resting on the soil. The soil conditions are represented by 30 m soft, medium, and dense soil deposits with four layers resting on bedrock. The side boundaries of the finite element model are simulated as fixed, viscous boundaries and newly developed infinite elements. The results from the performed analysis show that, in addition to the structural properties and soil characteristics, the choice of side boundaries also plays an important role in seismic response of RC frame structures.