Crack analysis of reinforced concrete by finite element method and crack queuing algorithm

Abstract

Crack width is one important consideration in both serviceability and durability design of reinforced concrete structures and should be evaluated to ensure compliance with design codes. Existing empirical formulas from design codes, which do not agree with each other, have limited ability to evaluate crack spacing and crack number results in complicated circumstances. Hence, a newly proposed finite element method, which is designed for crack analysis of reinforced concrete under general conditions, is herein developed.

A crack queuing algorithm, which is previously used to simulate the crack propagation in cement paste, is proposed to improve the conventional smeared crack model. Incorporated with crack queuing, the proposed finite element method can produce a clearly defined discrete crack pattern without adopting discrete crack elements, re-meshing and re-numbering. Apart from the crack pattern, tensile stress redistribution can be successfully simulated by allowing only one concrete element to crack and conducting re-analysis for other uncracked concrete elements afterwards.

Verifications of proposed finite element method are conducted afterwards. Tests under various circumstances, such as bending, direct tension, shrinkage effect, early-age thermal effect, are compared with analytical results provided by finite element analysis. Clearly defined 2-dimensional crack patterns, which are provided by finite element analysis, show good agreement with measured crack patterns. Besides, as the discrete crack pattern can be simulated, crack width can be directly calculated from nodal displacements. The proposed finite element analysis, after comparing with test results and numerical results from design codes, is proved to have the ability of predicting crack width, crack number, crack spacing results with reasonable accuracy.

In order to further elaborate the superiority and uniqueness of crack queuing algorithm, finite element analysis with and without crack queuing are compared to reveal the improvement in delivering discrete crack pattern without enlarging the computational expenses from refining loading increment step sizes.

Regarding constitutive modelling, residual strain is adopted to reflect the stress path dependent stress-strain relation. The damage modulus method employed, without updating stiffness matrix during iterations, has the ability of modelling post-peak behavior of concrete. Biaxial stress states of concrete is adaptively converted into two independent uniaxial stress-strain states by using equivalent uniaxial strains and biaxial strength envelope. In addition, the failure criteria comprise of a tensile strength criterion without strain softening and a fracture toughness criterion to control the influence of mesh size on cracking. In addition, steel reinforcing bar is modelled by discrete bar element and steel bar-concrete interface is modelled by interface element.

The new finite element method can be a useful tool for further analyzing the loading conditions, which are not covered in current design codes, and developing scientific equations and rules for the design of crack control steel reinforcement.