SFEM Analysis of Beams with Scaled Lengths including Spatially Varying and Cross-Correlated Concrete Properties.

Ewelina Korol

doi:10.3390/ma15010095

Abstract

This paper presents the results obtained for plain concrete beams under four-point bending with spatially varying material properties. Beams of increasing length but constant depth were analyzed using the stochastic finite element method. Spatial fluctuation of a uniaxial tensile strength, fracture energy and elastic modulus was defined within cross-correlated random fields. The symmetrical Gauss probability distribution function was applied for the material properties. The shape of the probability distribution function was modified by changing the coefficient of variation in order to find its right value. The correctness of the numerical solution was verified against the experimental results of Koide et al. (1998, 2000). The stochastic FEM analysis was performed with an autocorrelation length of 40 mm and material coefficients of variation of 0.12, 0.14, 0.16, 0.20 and 0.24. The comparison between numerical outcomes and experimental results demonstrated that the coefficient of variation of 0.24 gave the best agreement when referring to the experimental mean values. On the other hand, the variation of results was better captured with the coefficient of variation of 0.16. The findings indicate that the Gauss probability distribution function with cov = 0.24 correctly reproduced the statistical size effect, but its tails needed modification in order to project experimental result variation.

Highlights

Correlated Concrete Properties.The size effect in quasi-brittle materials has been commonly identified as a nominal strength reduction connected with an increasing specimen size
2000 random fields were generated for each beam size and each material
Random fieldsthe were generated for each sizesampling and eachtechnique material [11]

Summary

Introduction

The size effect in quasi-brittle materials has been commonly identified as a nominal strength reduction connected with an increasing specimen size. This statement is valid for geometrically similar structures (i.e., when a specimen is scaled in the directions of the length L and depth D simultaneously). There are two main mechanical sources of the size effect in concrete: energetic and statistical ones. The energetic size effect is connected with a strain localization phenomenon that develops before the macro-crack appears. The fracture process zone size (or strain localization zone) is a material property that is dependent mostly on the material characteristic length of a microstructure lc. The strength reduction becomes stronger with an increasing specimen size. The weakest link theory introduced by Weibull [1] postulates that a structure is as strong as its weakest component

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