000004473 001__ 4473
000004473 005__ 20141118192658.0
000004473 0177_ $$2doi$$a10.3850/978-981-07-2219-7_P102

000004473 0247_ $$210.3850/978-981-07-2219-7_P102
$$adoi
000004473 04107 $$aeng
000004473 046__ $$k2012-05-23
000004473 100__ $$aHuang, Shuping
000004473 24500 $$aSparse Collocation based Stochastic Finite Element Method for Reliability Analysis of Pile Settlement

000004473 24630 $$n5.$$pProceedings of the 5th Asian-Pacific Symposium on Structural Reliability and its Applications
000004473 260__ $$bResearch Publishing, No:83 Genting Lane, #08-01, Genting Building, 349568 SINGAPORE
000004473 506__ $$arestricted
000004473 520__ $$2eng$$aUncertainty and risk are essential features of geotechnical engineering. A complex geotechnical problem would only admit numerical solutions and the material parameters show random variability in spatial distribution as well as in intensity, and may be modeled as random fields rather than random variables. A standard form of a stochastic partial differential equation (SPDE) can model the propagation of input uncertainties. Collocation based stochastic finite element method (CSFEM) uncouples the finite element analysis with stochastic analysis, which means the finite element code can be treated as a black box (Huang et al., 2007). It outperforms the Monte Carlo method for problems with relative lower random dimensions. However, when CSFEM is dealing with problems with high dimension, the number of collocation points will grow very fast, sometimes even more than Monte Carlo's. 
 Sparse grids have been applied in many fields, such as high-dimensional integration and interpolation and solution of PDEs. The sparse grid method constructs multi-dimentional interpretation functions with much fewer points. Combining CSFEM with the sparse grid method can significantly reduce the number of collocation points for high dimension problems. The settlement of an axially loaded pile with linear soil springs is used to exam the performance of CSFEM with sparse grids, where the shear modulus of soil will be modeled as a 1-D a translation lognormal field. The numerical example demonstrated that a third Hermite expansion with level 2 sparse grid is adequate to produce accurate estimates of the output CDF while requiring much fewer response evaluations as compared to direct Monte Carlo simulation. Results show that the sparse grid method outperforms the tensor product method for problems with high dimensions.

000004473 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000004473 653__ $$aRandom field, Stochastic finite elements, Polynomial chaos, Probabilistic collocation, Sparse, Pile settlement.

000004473 7112_ $$a5th Asian-Pacific Symposium on Structural Reliability and its Applications$$cSingapore (SG)$$d2012-05-23 / 2012-05-25$$gAPSSRA2012
000004473 720__ $$aHuang, Shuping$$iPhoon, Kok-Kwang
000004473 8560_ $$ffischerc@itam.cas.cz
000004473 8564_ $$s336583$$uhttps://invenio.itam.cas.cz/record/4473/files/P102.pdf$$yOriginal version of the author's contribution as presented on CD, .
000004473 962__ $$r4180
000004473 980__ $$aPAPER