Tensile behavior by Weibull analysis in binary, ternary and quaternary concretes designed with micro and nano-silica additions

This work presents experimental and computational findings related to tensile strength of binary, ternary and quaternary Portland cement concretes and nanosilica, fly ash and/or silica fume as mineral admixtures. The data was processed using both Gaussian and Weibull statistical approaches. This latter is a useful technique leading with failures in brittle materials which do not follow a Gaussian behavior. Therefore, this work study the tensile behavior up to quaternary concretes. It is very important to study deeply this field of the mechanical behavior because the fracture strength of brittle materials such as concrete usually exhibits significant statistical scatter (Smallman & Ngan 2007). In this sense, in 1939 the Swedish engineer Weibull (Meyers & Chawla 2009) introduced its empirically distribution function (Eq. 1) based on brittle materials. (1) f X ( x | φ , β , λ ) = λ β ( x − φ β ) λ − 1 exp { − ( x − φ β ) λ } https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315207681/cd556cd4-4dcf-4efe-8e29-56fc67b8bfbd/content/eq152.tif"/>

where x ≥ φ; φ ∈ ℝ; β and λ ∈ ℝ⁺. Equation (1) represents the failure probability of the samples with φ, β, and λ represent the location, scale, and shape Weibull parameter, respectively. The location parameter represents the minimum strength to failure, the scale parameter represents the characteristic strength, and the shape parameter, also called the Weibull modulus, represents the scatter in strength measures.

Despite the importance of reliability analyses of brittle materials, many studies assess the Weibull modulus, λ, only for plain concrete specimens (Toasa Caiza & Ummenhofer 2011) while there is scarce data particularly for concretes containing additions of nano-particles in binary, ternary and/or quaternary concrete mixes. In the present work, the data was modeled using a two-parameter Weibull approach. Figure 1 illustrate the Weibull modulus of the concrete systems at 28 age of testing. The results obtained here suggest that some specific proportions of mineral additions (micro and/or nano-SiO₂) improve the material’s microstructure and could increase the tensile strength of concretes and simultaneously permit to reduce the scatter on tensile failures as measured by the Weibull modulus. Figure 1 BLUE intervals (90%) for Weibull modulus at 28 days. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315207681/cd556cd4-4dcf-4efe-8e29-56fc67b8bfbd/content/fig168_1.tif"/>