Applying the spectral stochastic finite element method in multiple-random field RC structures

doi:10.1007/s11709-022-0820-6

Front. Struct. Civ. Eng.

2022, Vol. 16

Issue (4) : 434-447 https://doi.org/10.1007/s11709-022-0820-6

RESEARCH ARTICLE

Applying the spectral stochastic finite element method in multiple-random field RC structures

Abbas YAZDANI(

)

Civil Engineering Department, University of Sistan and Baluchestan, Zahedan 98167-45845, Iran

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Abstract

This paper uses the spectral stochastic finite element method (SSFEM) for analyzing reinforced concrete (RC) beam/slab problems. In doing so, it presents a new framework to study how the correlation length of a random field (RF) with uncertain parameters will affect modeling uncertainties and reliability evaluations. It considers: 1) different correlation lengths for uncertainty parameters, and 2) dead and live loads as well as the elasticity moduli of concrete and steel as a multi-dimensional RF in concrete structures. To show the SSFEM’s efficiency in the study of concrete structures and to evaluate the sensitivity of the correlation length effects in evaluating the reliability, two examples of RC beams and slabs have been investigated. According to the results, the RF correlation length is effective in modeling uncertainties and evaluating reliabilities; the longer the correlation length, the greater the dispersion range of the structure response and the higher the failure probability.

Keywords uncertainty spectral stochastic finite element method correlation length reliability assessment reinforced concrete beam/slab

Corresponding Author(s): Abbas YAZDANI

Just Accepted Date: 15 April 2022 Online First Date: 04 July 2022 Issue Date: 09 August 2022

Cite this article:

Abbas YAZDANI. Applying the spectral stochastic finite element method in multiple-random field RC structures[J]. Front. Struct. Civ. Eng., 2022, 16(4): 434-447.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-022-0820-6
https://academic.hep.com.cn/fsce/EN/Y2022/V16/I4/434

Fig.1 A schematic view of the loading and components of a concrete structure.

Fig.2 A 2D FE model and concrete beam loading.

Fig.3 Four modes of combining square elements of concrete beams with rebar bar elements.

Fig.4 A 2D FE model of a concrete slab and its loading.

Fig.5 Four modes of combining square elements of concrete slabs with rebar beam elements.

Tab.1 Statistical features of RFs for the uncertainty of concrete beam parameters

Fig.6 Geometric features of the concrete beam: (a) The 3D model with equivalent rebars; (b) meshing.

Fig.7 A 10-time greater deformation and mean displacements of the RC beam’s nodal points.

Fig.8 PDF diagram of the maximum RC beam deflection for different b_DL values and b_LL values.

Fig.9 PDF diagram of the maximum RC beam deflection for a b_DL = 4.1 m and different b_LL values.

Fig.10 CDF diagram of the maximum RC beam deflection for different b_DL values and b_LL values.

Fig.11 CDF diagram of the maximum RC beam deflection for a b_DL = 4.1 m and different b_LL values.

Fig.12 The surface of P_f variations of the RC beam for different b_DL values and b_LL values.

Fig.13 The RC beam’s P_f variations diagram for b_DL = 4.1 m and different b_LL values.

Fig.14 Failure probability coefficient of variation for RC beam.

Tab.2 Statistical features of the RF related to the concrete slab’s uncertain parameters

Fig.15 Concrete slab’s geometric features: (a) 3D model with equivalent rebars; (b) meshing.

Fig.16 Deformation and mean deflection of the RC slabs’ nodal points.

Fig.17 Deformation and mean x-direction rotation of the RC slabs’ nodal points.

Fig.18 Deformation and mean y-direction rotation of the RC slabs’ nodal points.

Fig.19 PDF diagram of the maximum RC slab deflection for different b_DL and b_LL values.

Fig.20 PDF diagram of the maximum RC slab deflection for a b_DL = 4.1 m and different b_LLs.

Fig.21 CDF diagram of the maximum RC slab deflection for different b_DL and b_LL values.

Fig.22 CDF diagram of the maximum RC slab deflection for a b_DL = 4.1 m and different b_LL values.

Fig.23 The surface of P_f variations of the RC slab for different b_DL values and b_LL values.

Fig.24 The RC slab’s P_f variations diagram for b_DL = 4.1 m and different b_LL values.

Fig.25 Failure probability coefficient of variation for RC slab.

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