Determination of the Probabilistic Properties of the Critical Fracture Energy of Concrete Integrating Scale Effect Aspects
This paper presents an extension of the validation domain of a previously validated three-dimensional probabilistic semi-explicit cracking numerical model, which was initially validated for a specific concrete mix design. This model is implemented in a finite element code. The primary objective of t...
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MDPI AG
2024-01-01
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| author | Mariane Rodrigues Rita Pierre Rossi Eduardo de Moraes Rego Fairbairn Fernando Luiz Bastos Ribeiro |
| author_facet | Mariane Rodrigues Rita Pierre Rossi Eduardo de Moraes Rego Fairbairn Fernando Luiz Bastos Ribeiro |
| author_sort | Mariane Rodrigues Rita |
| collection | DOAJ |
| description | This paper presents an extension of the validation domain of a previously validated three-dimensional probabilistic semi-explicit cracking numerical model, which was initially validated for a specific concrete mix design. This model is implemented in a finite element code. The primary objective of this study is to propose a function that enables the estimation of the critical fracture energy parameter utilized in the model and validate its effectiveness for various concrete mix designs. The model focuses on macrocrack propagation and introduces significant aspects such as employing volume elements for simulating macrocrack propagation and incorporating two key factors in governing its behavior. Firstly, macrocrack initiation is linked to the uniaxial tensile strength <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>f</mi><mi>t</mi></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>. Secondly, macrocrack propagation is influenced by a post-cracking dissipation energy in tension. This energy is taken equal to the mode I critical fracture energy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>G</mi><mrow><mi>I</mi><mi>C</mi></mrow></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> based on the linear elastic fracture mechanics theory. Importantly, both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>f</mi><mi>t</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mrow><mi>I</mi><mi>C</mi></mrow></msub></semantics></math></inline-formula> are probabilistic properties influenced by the volume of concrete under consideration. Consequently, in the numerical model, they are dependent on the volume of the finite elements employed. To achieve this objective, numerical simulations of fracture mechanical tests are conducted on a large double cantilever beam specimen. Through these simulations, we validate the proposed function, which is a crucial step towards expanding the model’s applicability to all concrete mix designs. |
| first_indexed | 2024-03-08T15:11:20Z |
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| spelling | doaj.art-f4bf54e897b44af288985b538fe54ebe2024-01-10T14:52:13ZengMDPI AGApplied Sciences2076-34172024-01-0114146210.3390/app14010462Determination of the Probabilistic Properties of the Critical Fracture Energy of Concrete Integrating Scale Effect AspectsMariane Rodrigues Rita0Pierre Rossi1Eduardo de Moraes Rego Fairbairn2Fernando Luiz Bastos Ribeiro3Civil Engineering Program, Universidade Federal do Rio de Janeiro (UFRJ), Av. Horácio Macedo, 2030, Cidade Universitária, Rio de Janeiro 21941-598, BrazilCivil Engineering Program, Universidade Federal do Rio de Janeiro (UFRJ), Av. Horácio Macedo, 2030, Cidade Universitária, Rio de Janeiro 21941-598, BrazilCivil Engineering Program, Universidade Federal do Rio de Janeiro (UFRJ), Av. Horácio Macedo, 2030, Cidade Universitária, Rio de Janeiro 21941-598, BrazilCivil Engineering Program, Universidade Federal do Rio de Janeiro (UFRJ), Av. Horácio Macedo, 2030, Cidade Universitária, Rio de Janeiro 21941-598, BrazilThis paper presents an extension of the validation domain of a previously validated three-dimensional probabilistic semi-explicit cracking numerical model, which was initially validated for a specific concrete mix design. This model is implemented in a finite element code. The primary objective of this study is to propose a function that enables the estimation of the critical fracture energy parameter utilized in the model and validate its effectiveness for various concrete mix designs. The model focuses on macrocrack propagation and introduces significant aspects such as employing volume elements for simulating macrocrack propagation and incorporating two key factors in governing its behavior. Firstly, macrocrack initiation is linked to the uniaxial tensile strength <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>f</mi><mi>t</mi></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>. Secondly, macrocrack propagation is influenced by a post-cracking dissipation energy in tension. This energy is taken equal to the mode I critical fracture energy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>G</mi><mrow><mi>I</mi><mi>C</mi></mrow></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> based on the linear elastic fracture mechanics theory. Importantly, both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>f</mi><mi>t</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mrow><mi>I</mi><mi>C</mi></mrow></msub></semantics></math></inline-formula> are probabilistic properties influenced by the volume of concrete under consideration. Consequently, in the numerical model, they are dependent on the volume of the finite elements employed. To achieve this objective, numerical simulations of fracture mechanical tests are conducted on a large double cantilever beam specimen. Through these simulations, we validate the proposed function, which is a crucial step towards expanding the model’s applicability to all concrete mix designs.https://www.mdpi.com/2076-3417/14/1/462numerical modelprobabilistic characteristicsmacrocrack propagationvolume effectfinite element method |
| spellingShingle | Mariane Rodrigues Rita Pierre Rossi Eduardo de Moraes Rego Fairbairn Fernando Luiz Bastos Ribeiro Determination of the Probabilistic Properties of the Critical Fracture Energy of Concrete Integrating Scale Effect Aspects Applied Sciences numerical model probabilistic characteristics macrocrack propagation volume effect finite element method |
| title | Determination of the Probabilistic Properties of the Critical Fracture Energy of Concrete Integrating Scale Effect Aspects |
| title_full | Determination of the Probabilistic Properties of the Critical Fracture Energy of Concrete Integrating Scale Effect Aspects |
| title_fullStr | Determination of the Probabilistic Properties of the Critical Fracture Energy of Concrete Integrating Scale Effect Aspects |
| title_full_unstemmed | Determination of the Probabilistic Properties of the Critical Fracture Energy of Concrete Integrating Scale Effect Aspects |
| title_short | Determination of the Probabilistic Properties of the Critical Fracture Energy of Concrete Integrating Scale Effect Aspects |
| title_sort | determination of the probabilistic properties of the critical fracture energy of concrete integrating scale effect aspects |
| topic | numerical model probabilistic characteristics macrocrack propagation volume effect finite element method |
| url | https://www.mdpi.com/2076-3417/14/1/462 |
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