An Arc-Consistent Viscous-Spring Artificial Boundary for Numerical Analysis of Seismic Response of Underground Structures

A new arc-consistent viscous-spring artificial boundary (ACVAB) was proposed by changing a traditional flat artificial boundary based on the theory of viscous-spring artificial boundaries. Through examples, the concept underpinning the establishment and specific setting of the boundary in the finite element software were described. Through comparison with other commonly used artificial boundaries in an example for near-field wave analysis using the two-dimensional (2D) half-space model, the reliability of the ACVAB was verified. Furthermore, the ACVAB was used in the numerical analysis of the effects of an earthquake on underground structures. The results were compared with the shaking table test results on underground structures. On this basis, the applicability of the ACVAB to a numerical model of seismic response of underground structures was evaluated. The results show that the boundary is superior to common viscous-spring boundaries in terms of accuracy and stability, and therefore, it can be used to evaluate radiation damping effects of seismic response of underground structures and is easier to use.

A parabolic local problem with exponential decay of the resonance error for numerical homogenization

This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro–macro-coupling, where the macromodel describes the coarse scale behavior, and the micromodel is solved only locally to upscale the effective quantities, which are missing in the macromodel. The fact that the microproblems are solved over small domains within the entire macroscopic domain, implies imposing artificial boundary conditions on the boundary of the microscopic domains. A naive treatment of these artificial boundary conditions leads to a first-order error in [Formula: see text], where [Formula: see text] represents the characteristic length of the small scale oscillations and [Formula: see text] is the size of microdomain. This error dominates all other errors originating from the discretization of the macro and the microproblems, and its reduction is a main issue in today’s engineering multiscale computations. The objective of this work is to analyze a parabolic approach, first announced in A. Abdulle, D. Arjmand, E. Paganoni, C. R. Acad. Sci. Paris, Ser. I, 2019, for computing the homogenized coefficients with arbitrarily high convergence rates in [Formula: see text]. The analysis covers the setting of periodic microstructure, and numerical simulations are provided to verify the theoretical findings for more general settings, e.g. non-periodic microstructures.

An Arc-consistent Viscous-spring Artificial Boundary for Numerical Analysis of the Seismic Response of Underground Structures

A new arc consistent viscous-spring artificial boundary (ACVAB) was proposed by changing a traditional flat artificial boundary based on the theory of viscous-spring artificial boundaries. Through examples, the concept underpinning the establishment, and specific setting of, the boundary in the finite element software were described. Through comparison with other commonly used artificial boundaries in an example for near-field wave analysis using the two-dimensional (2-d) half-space model, the reliability of the ACVAB was verified. Furthermore, the ACVAB was used in the numerical analysis of the effects of an earthquake of underground structures. The results were compared with shaking-table test results on underground structures. On this basis, the applicability of the ACVAB to a numerical model of the seismic response of underground structures was evaluated. The results show that the boundary is superior to common viscous-spring boundaries in terms of accuracy and stability, and therefore it can be used to evaluate radiation damping effects of seismic response of underground structures and is easier to use.

Influences on the Seismic Response of a Gravity Dam with Different Foundation and Reservoir Modeling Assumptions

The seismic design and dynamic analysis of high concrete gravity dams is a challenge due to the dams’ high levels of designed seismic intensity, dam height, and water pressure. In this study, the rigid, massless, and viscoelastic artificial boundary foundation models were established to consider the effect of dam–foundation dynamic interaction on the dynamic responses of the dam. Three reservoir water simulation methods, namely, the Westergaard added mass method, and incompressible and compressible potential fluid methods, were used to account for the effect of hydrodynamic pressure on the dynamic characteristics and seismic responses of the dam. The ranges of the truncation boundary of the foundation and reservoir in numerical analysis were further investigated. The research results showed that the viscoelastic artificial boundary foundation was more efficient than the massless foundation in the simulation of the radiation damping effect of the far-field foundation. It was found that a foundation size of 3 times the dam height was the most reasonable range of the truncation boundary of the foundation. The dynamic interaction of the reservoir foundation had a significant influence on the dam stress.

Evaluation of Ground Motion Amplification Effects in Slope Topography Induced by the Arbitrary Directions of Seismic Waves

The incident directions of seismic waves can change the ground motions of slope topography. To elaborate on the influences of the directions of seismic waves, a dynamic analysis of the slope topography was performed. Seismic waves were input using an equivalent nodal force method combined with a viscous-spring artificial boundary. The amplification of ground motions in double-faced slope topographies was discussed by varying the angles of incidence. Meanwhile, the components of seismic waves (P waves and SV waves), slope materials and slope geometries were all investigated with various incident earthquake waves. The results indicated that the pattern of the amplification of SV waves was stronger than that of P waves in the slope topography, especially in the greater incident angels of the incident waves. Soft materials intensely aggravate the acceleration amplification, and more scattered waves are produced under oblique incident earthquake waves. The variations in the acceleration amplification ratios on the slope crest were much more complicated at oblique incident waves, and the ground motions were underestimated by considering only the vertical incident waves. Therefore, in the evaluation of ground motion amplification of the slope topography, it is extremely important to consider the direction of incident waves.

Exact Artificial Boundary Conditions for Quasi-Linear Problems in Semi-Infinite Strips

In this paper, the exact artificial boundary conditions for quasi-linear problems in semi-infinite strips are investigated. Based on the Kirchhoff transformation, the exact and approximate boundary conditions on a segment artificial boundary are derived. The error estimate for the finite element approximation with the artificial boundary condition is obtained. Some numerical examples show the efficiency of this method.