Concrete is a material that can develop cracks under certain loading conditions. Kot Engenharia concrete fracture mechanics to understand the propagation of these cracks and assess the integrity of existing structures. So, read on and learn how this technique contributes to accurate structural diagnostics and safer interventions.

1. Mechanical behavior of concrete

Since reinforced concrete is a composite material, it has physical properties that differ from the materials that make it up on their own.

Single-strand steel reinforcement bars are responsible for providing ductility to the parts, with high tensile strength, while concrete provides compressive strength. Thus, when loads are applied to a concrete part, cracks commonly appear in the tensioned region.

Concrete has a behavior known as partially brittle, which is characterized by a small region of linearity followed by softening, resulting in non-linear behavior. In addition, the interaction of defects inherent in concrete, such as voids and microcracks, results in a typical tensile response. The behavior of concrete is characterized by a linear elastic region followed by a softening region before maximum stress. After developing maximum stress, concrete exhibits an increase in deformation with a reduction in stress, which characterizes thesoftening region. Materials with such behavior are classified asquasi-brittle.

                                                    Figure 1 - Typical stress-strain curve for concrete,^Eis secant^modulus and _Eit tangent^modulus .

2. Some manifestations of cracks in parts

Cracks can originate during the construction of the piece itself, resulting from autogenous stresses due to the concrete solidification process—if the solidification process of the piece is not controlled, cracks may occur. The amount of water required for the concrete during the solidification process is essential to prevent rapid hardening, which results in excessive cracking.

                                                                           Figura 2 – Exemplo de fissura desenvolvida devido a retração no processo 
                                                                         de endurecimento do concreto – Fonte: PCA – Portland Cement Association.

Excessive cracks expose the reinforcement to moisture and can cause various pathological manifestations in reinforced concrete. Among these, the most common is corrosion of the reinforcement, whose expansive reactions cause displacement of the concrete.

Another manifestation, in turn, corresponds to the alkali-aggregate reaction, which is enhanced or even triggered by the presence of excessive moisture inside the concrete.

                                                                           Figura 3 – Exemplo de manifestação patológica – reação álcali-agregado
                                                                                                  – Fonte: PCA – Portland Cement Association.

3. Mechanics of concrete fracture

The study of crack propagation in reinforced concrete members can be carried out using fracture mechanics; however, it is important to note that certain particularities must be considered. The use of linear models (MFEL – linear elastic fracture mechanics) is not very appropriate for reinforced concrete members due to the behavior of the material.

Crack propagation mechanisms in reinforced concrete parts are non-linear, mainly due to the existence of a cementitious matrix, fine aggregate and coarse aggregate, where each of these phases has different fracture toughness properties.

                      Figure 4 – Example of crack propagation in concrete, (a) high toughness of the aggregate in relation to the cementitious matrix,                                                                                                        (b) aggregate toughness slightly higher than the matrix, Chen, Y. P., 2006.

For numerical analyses, appropriate propagation models should be applied to reproduce the elasto-plastic behavior of the fracture process zone (FPZ), which forms in the vicinity of the crack. In addition, another aspect that adds nonlinearity to crack propagation behavior is the toughness mechanisms that form during the propagation process, calledcrack arresting mechanisms.

                    Figure 5 - Regions developed near a crack, (L) linear region, (F) in the process of fracture, (N) non-linear, Bazant and Oh (1983).

4. Study model

In a typical fracture mechanics analysis model, a crack is initially added, which is propagated at each step of the analysis. In this calculation procedure, the stresses in the part are modified due to the presence of the crack, which alters the direction of crack propagation at each step of the analysis.

                            Figure 6 – Simulation of crack propagation (embedded crack) in a concrete part – through an initial crack, the model reproduces the propagation trajectory based on the stress field.

During a propagation simulation, it is possible for the crack to stabilize, resulting in a crack that propagates and remains stable after a certain length.

One of the most commonly used models to represent nonlinearity at the crack tip is the cohesive crack model. This model consists of adding stresses at the crack tip to represent the fracture process region (FPR – fracture process region). This region is characterized by the accumulation of microcracks and interlocking of the aggregate, and is considerably larger when compared to the plastic zone in a ductile material such as steel, for example. This condition makes it impossible to use linear elastic fracture mechanics (LEFM) in concrete elements.

The cohesive zone then corresponds to a micro-fractured region where there are ligaments responsible for transferring stress, while the material located outside the fractured region maintains its strength unchanged.

                                                                                       Figure 7 - Cohesive crack model proposed by Hillerborg.

The technique of concrete fracture mechanics can be applied to study the pattern of crack propagation in reinforced concrete members. Therefore, this numerical analysis model approach numerical analysis particularly important for determining the pattern of cracks and their causes, allowing the same crack pattern observed in the field to be reproduced.

This technique can also be applied in cases where it is necessary to determine the remaining life of reinforced concrete parts with significant cracks. The example below shows a transverse beam of a viaduct with cracks, where fracture mechanics is a tool for determining the severity of the crack, the reduction in the strength of the part, and the cause of the damage.

                                                      Figura 8 – Exemplo de fissura importante em uma viga transversal de viaduto rodoviário
                                                                        que pode ser investigada pela técnica da mecânica da fratura não linear.

Crack analysis is with Kot Engenharia

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FAQ

1. O que significa dizer que o concreto é um material parcialmente frágil (quasi-brittle) e o que é o softening?

Diferente de materiais puramente frágeis (que se rompem abruptamente após atingirem sua tensão máxima) ou dúcteis (que se deformam plasticamente mantendo a carga), o concreto possui um comportamento misto. A sua curva de tensão-deformação apresenta uma pequena fase linear, seguida pelo amolecimento (softening). Esse fenômeno ocorre após o material atingir sua tensão de pico: o concreto continua a se deformar, mas sua capacidade de carregar tensões diminui gradativamente devido à abertura interna de microfissuras.

2. Por que a Mecânica da Fratura Elástica Linear (MFEL) não é adequada para avaliar elementos de concreto armado?

A MFEL assume que o material é homogêneo e que a zona de plastificação na ponta da trinca é desprezível, o que funciona bem para aços de alta resistência. O concreto, porém, é um material heterogêneo composto por matriz cimentícia, agregados finos e graúdos. A propagação de uma fissura nele envolve múltiplos mecanismos não lineares de ganho de tenacidade, conhecidos como crack arresting mechanisms, como o desvio da trinca ao redor dos agregados e o intertravamento mecânico de blocos, exigindo modelos numéricos não lineares.

3. O que é a Zona de Processo de Fratura (ZPF) e como o modelo de trinca coesiva de Hillerborg a simula?

A ZPF é a região microfraturada que se desenvolve imediatamente à frente da ponta visível de uma trinca no concreto, caracterizada pelo acúmulo de microfissuras e atrito entre os agregados. Para simulá-la numericamente, o engenheiro utiliza o Modelo de Trinca Coesiva de Hillerborg. Esse método insere tensões residuais fictícias de fechamento nas faces internas da ponta da trinca, representando matematicamente a capacidade que esses ligamentos microscópicos ainda têm de transferir esforços antes da separação completa do material.

4. Quais são as principais patologias estruturais aceleradas pela presença de fissuras sem controle?

A abertura de fissuras funciona como uma porta de entrada para agentes agressivos externos. As principais consequências patológicas são:

• Corrosão das armaduras: A umidade e o oxigênio alcançam o aço estrutural, gerando reações expansivas que causam o desplacamento (expulsão) do concreto de cobrimento.

• Reação Álcali-Agregado (RAA): A infiltração excessiva de água dispara ou potencializa reações químicas internas deletérias entre os álcalis do cimento e a sílica reativa dos agregados, provocando um gel expansivo que destrói a matriz do concreto de dentro para fora.

 

5. Como a análise por mecânica da fratura apoia o diagnóstico de viadutos, pontes e grandes estruturas de concreto?

Em estruturas de grande porte, como as vigas transversais de viadutos, o surgimento de fissuras severas gera dúvidas sobre a segurança da operação. A mecânica da fratura não linear permite construir modelos numéricos que inserem uma trinca inicial e simulam sua evolução passo a passo sob o campo de tensões real do ativo. Isso possibilita reproduzir em ambiente digital o mesmo padrão de dano observado em campo, identificando a causa raiz da falha, medindo a perda real de capacidade de carga e definindo se a estrutura precisa de reforço urgente ou se possui vida útil remanescente segura.