1D infinite element for dynamic problems in saturated porous media

Khalili, Nasser; Valliappan, S.; Yazdi, Javad Tabatabaee; Yazdchi, Mohammadreza

doi:10.1002/(sici)1099-0887(199709)13:9<727::aid-cnm102>3.0.co;2-i

Cited by 21 publications

(10 citation statements)

References 16 publications

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“…Published literature reveals several numerical models taking advances of both finite and boundary element approaches, which are called a hybrid method presented by Tzong and Penzien (1983), Yadzchi et al (1999) and Wolf and Song (1996). In some cases finite model is combined with infinite elements at truncated boundaries on SSI models, handled by Medina and Penzien (1982), Khalili et al (1997), Kim and Yun (2000) and Seo et al (2007). Some studies based on a coupling procedure of finite element (FE) and scaled boundary finite element (SBFE) for three-dimensional dynamic analysis of unbounded SSI can be found in Song and Wolf (1998) as an effective tool for solving the wave propagation problems in the time domain.…”

Section: E ç Elebi Et Al: Non-linear Finite Element Analysis For Prmentioning

confidence: 99%

Non-linear finite element analysis for prediction of seismic response of buildings considering soil-structure interaction

Çelebi

Göktepe

Karahan

2012

Nat. Hazards Earth Syst. Sci.

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Abstract. The objective of this paper focuses primarily on the numerical approach based on two-dimensional (2-D) finite element method for analysis of the seismic response of infinite soil-structure interaction (SSI) system. This study is performed by a series of different scenarios that involved comprehensive parametric analyses including the effects of realistic material properties of the underlying soil on the structural response quantities. Viscous artificial boundaries, simulating the process of wave transmission along the truncated interface of the semi-infinite space, are adopted in the non-linear finite element formulation in the time domain along with Newmark's integration. The slenderness ratio of the superstructure and the local soil conditions as well as the characteristics of input excitations are important parameters for the numerical simulation in this research. The mechanical behavior of the underlying soil medium considered in this prediction model is simulated by an undrained elastoplastic Mohr-Coulomb model under plane-strain conditions. To emphasize the important findings of this type of problems to civil engineers, systematic calculations with different controlling parameters are accomplished to evaluate directly the structural response of the vibrating soil-structure system. When the underlying soil becomes stiffer, the frequency content of the seismic motion has a major role in altering the seismic response. The sudden increase of the dynamic response is more pronounced for resonance case, when the frequency content of the seismic ground motion is close to that of the SSI system. The SSI effects under different seismic inputs are different for all considered soil conditions and structural types.

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Section: E ç Elebi Et Al: Non-linear Finite Element Analysis For Prmentioning

confidence: 99%

Non-linear finite element analysis for prediction of seismic response of buildings considering soil-structure interaction

Çelebi

Göktepe

Karahan

2012

Nat. Hazards Earth Syst. Sci.

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“…In other words the two compressional waves c 1 and c 2 are related to each other, which is modeled by the mentioned weighting factors. These factors can be determined by the one‐dimensional analytical solution of a poroelastic rod 26, 27 and, hence, are only an approximation for the application in three‐dimensional problems. The most meaningful property of these weighting factors is that their sum is equal to one, i.e. Following the work of Khalili et al 26, the wave weighting factors are defined in one dimension as where the superscript K of the wave weighting factors denotes the affinity to the Khalili infinite element.…”

Section: Infinite Element For Poroelastodynamicsmentioning

confidence: 99%

“…These factors can be determined by the one‐dimensional analytical solution of a poroelastic rod 26, 27 and, hence, are only an approximation for the application in three‐dimensional problems. The most meaningful property of these weighting factors is that their sum is equal to one, i.e. Following the work of Khalili et al 26, the wave weighting factors are defined in one dimension as where the superscript K of the wave weighting factors denotes the affinity to the Khalili infinite element. The coefficients v

_{italici}^{1}

and v

_{italici}^{2}

, with i = 3, 4, are obtained from the analytical one‐dimensional solution and are defined in (4).…”

Section: Infinite Element For Poroelastodynamicsmentioning

confidence: 99%

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Infinite elements in a poroelastodynamic FEM

Nenning

Schanz

2010

Num Anal Meth Geomechanics

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An infinite element is presented to treat wave propagation problems in unbounded saturated porous media. The porous media is modeled by Biot's theory. Conventional finite elements are used to model the near field, whereas infinite elements are used to represent the behavior of the far field. They are constructed in such a way that the Sommerfeld radiation condition is fulfilled, i.e. the waves decay with distance and are not reflected at infinity. To provide the wave information the infinite elements are formulated in Laplace domain. The time domain solution is obtained by using the convolution quadrature method as the inverse Laplace transformation. The temporal behavior of the near field is calculated using standard time integration schemes, e.g. the Newmark method. Finally, the near and far field are combined using a substructure technique for any time step. The accuracy as well as the necessity of the proposed infinite elements, when unbounded domains are considered, is demonstrated by different examples. Copyright © 2010 John Wiley & Sons, Ltd.

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“…However, the first explicit mapping was developed by Beer and 13 Meek (1981), who used a shape function to map a finite domain onto an infinite domain, thereby 14 splitting the mapping into two parts for finite and infinite directions. elements can also be grouped into static and dynamic types (Khalili et al 1997). 10…”

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confidence: 99%

Advantages of Infinite Elements over Prespecified Boundary Conditions in Unbounded Problems

Erkal

Laefer

Tezcan

2015

J. Comput. Civ. Eng.

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24This paper promotes the further development and adoption of infinite elements for unbounded 25 problems. This is done by demonstrating the ease of application and computational efficiency of 26 infinite elements. Specifically, this paper introduces a comprehensive set of coordinate and field 27 variable mapping functions of one-dimensional and two-dimensional infinite elements, not 28 previously available. Performance is then benchmarked against various parametric models for 29 deflection and stress in two cases: (1) a circular, uniformly-distributed load and (2) a point load 30 on a semi-infinite, axi-symmetrical medium. The results of each case are compared with its 31 closed-form solution. As an example, when the vertical deflections in example 2 are compared to 32 the closed form solution, the 45% error level generated with fixed boundaries and 14% generated 33 with spring-supported boundaries is reduced to only 1% with infinite elements, even with a 34 coarse mesh. Perceptions about the complexity in using infinite elements and the prior absence 35 of comprehensive comparisons of equivalent meshes may account for the slow rate of adoption 36 of this powerful approach. 37

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1D infinite element for dynamic problems in saturated porous media

Cited by 21 publications

References 16 publications

Non-linear finite element analysis for prediction of seismic response of buildings considering soil-structure interaction

Non-linear finite element analysis for prediction of seismic response of buildings considering soil-structure interaction

Infinite elements in a poroelastodynamic FEM

Advantages of Infinite Elements over Prespecified Boundary Conditions in Unbounded Problems

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