Nonlinear Analysis Of Concrete Structures Research Articles

Identification of probabilistic distribution parameters for the mesoscopic stochastic fracture model

As a kind of multiphase composite material, the basic mechanical behaviors of concrete are randomness and nonlinearity. The mesoscopic stochastic fracture model (MSFM) which can reflect the coupling effect of randomness and nonlinearity, has been widely used for the nonlinear analysis of concrete structures. In this paper, we proposed a new stochastic modeling principle to identify the probabilistic distribution parameters of MSFM. In order to reduce the modeling works, a dimension-reduced algorithm is proposed as well. In this paper, an overview of MSFM is firstly presented to introduce the background of the research. Then the stochastic harmonic function (SHF) representation is introduced to express the random field mentioned in the MSFM, and the probability density evolution method (PDEM) is applied to obtain the theoretical probability density function (PDF) of the stress–strain relationships. Furthermore, a stochastic modeling principle is proposed, in which minimizing the Kullback–Leibler divergence (KLD) is taken as the optimization object. Based on the framework of genetic algorithm, a dimension-reduced algorithm is proposed to identify the parameters with reference to the data from tested complete curves of uniaxial compressive and uniaxial tensile stress–strain relationship of concrete. The results indicate that the proposed principle and algorithm can be used to identify the parameters of MSFM accurately and efficiently.

Artificial intelligence - finite element method - hybrids for efficient nonlinear analysis of concrete structures

Realistic structural analyses and optimisations using the non-linear finite element method are possible today yet suffer from being very time-consuming, particularly in case of reinforced concrete plates and shells. Hence such investigations are currently dismissed in the vast majority of cases in practice. The "Artificial Intelligence - Finite Element - Hybrids" project addresses the current unsatisfactory situation with an approach that combines non-linear finite element models for reinforced concrete shells with scientific machine learning algorithms to create hybrid AI-FEM models. The AI-based surrogate material model provides the material stiffness as well as the stress tensor for given concrete design parameters and the strain tensor. This paper reports on the current status of the project and findings of the calibration of the AI-based reinforced concrete material model. We successfully calibrated and evaluated k-nearest-neighbour, LGBM and ResNet algorithms and report their predictive capabilities. Finally, some light is shed on the future work of integrating the AI surrogate material models back into the finite element method in the course of the numerical analysis of reinforced concrete structures.

An eigendecomposition-based and mesh-sensitivity reduced constitutive model for nonlinear analysis of concrete structures under non-proportional cyclic loading

Emerging 3D printed concrete techniques has raised numerous possibilities in contemporary architectural creations that are often beyond the scope of prevailing structural design standards. Rigorous, three-dimensional, and nonlinear finite element analysis (NLFEA) with appropriate constitutive modelling of materials would be inevitable when analysing complex structures. However, many existing concrete models could hardly handle those structures' complicated behaviour, including crack-induced anisotropy, changeable stress transfer mechanisms, shear-slip and re-contact, mesh-size sensitivity, etc. Hence, this paper has developed a novel and experimentally validated constitutive model to tackle the above issues. The novel features include (1) highly robust total-strain formulation, (2) cyclic normal and tangential stress-strain responses, (3) a novel algorithm for uniquely fixing the 3D crack plane coordinate, (4) the equivalent strain transformation for modelling the axial-lateral strain interaction, (5) shear-slip and re-contact behaviour of cracks, and (6) mesh-size sensitivity mitigation. The proposed model was implemented into ABAQUS's user-subroutine and applied to simulate a full-scale column test with specimen height = 5 m. The tested column, subjected to a constant vertical load and a cyclic load in the horizontal direction, failed in shear. The simulation can capture the damage evolutions and hysteresis response of the tested column. Hence, the proposed modelling framework could serve as a basis for analysing and designing concrete structures with unconventional shapes under non-proportional loading.

A modified Mazars damage model with energy regularization

This paper presents a modified Mazars damage model, based on a strain formulation, for the physically nonlinear analysis of concrete structures. The main objective is to propose a modified damage model, in which both tension and compression damage evolution laws are regularized using a classical fracture energy methodology. The original loading functions are maintained, including their thermodynamic consistencies. The most relevant modification of the model is introduced in the damage evolutions laws, which are updated in order to produce similar stress–strain relations to those presented in fib Model Code 2010. The softening branch under both compressive and tensile strains is regularized with fracture energy. The damage model is then benchmarked with classical experimental and numerical tests considering monotonic loadings. The new constitutive relation was implemented in the commercial software ABAQUS via user subroutine UMAT. Research needs towards a definition of a generalized damage model with energy regularization are discussed and presented.

Experimental Study on Axial Tensile Stress-Strain Relationship of High Crack Resistance Concrete

For demand of high crack resistance of concrete, the calcium-magnesium expansion agents and basalt fiber are chosen. The study of the full stress-strain curve of concrete under uniaxial tensile can comprehensively reflect its mechanical properties. The uniaxial stretch tests are used to study the concrete axial tensile constitutive model, and then the corresponding curve and formula are obtained in this paper. The influence of different dosages and water-binder ratio on the characteristic points of the curve is studied, and a suitable mathematical expression for the axial tensile stress-strain curve is proposed. Studies have shown that by adopting the method of dual admixture of expansive agent and basalt fiber, the toughness, tensile strength, ductility, and even other properties of concrete can be significantly improved. This shows that the dual admixture of the two materials has a strong toughening effect on concrete. With the amount of fiber content, the amount of expansion agent and the water-binder ratio is respectively 1%, 7% and 0.42, the performance of concrete shows the best state. The proposed calculation formula is in good agreement with the experimental results, which can provide a theoretical basis for the design and nonlinear analysis of concrete structures.

Copula-Based Quantification of Probabilistic Dependence Configurations of Material Parameters in Damage Constitutive Modeling of Concrete

The constitutive model of concrete is the key basis for nonlinear analysis of concrete structures under disastrous dynamic actions, e.g., earthquakes. The material parameters of the constitutive model of concrete are essentially probabilistically dependent. However, in practice, it is mostly assumed that these parameters are either independent or perfectly dependent. In the present paper, the quantification of probabilistic dependence configurations between random material parameters and their effects on stochastic structural responses are investigated. Based on the ample amount of data from tested complete curves of compressive stress-strain relationships of concrete with different strength grades, the parameters in the damage constitutive model of concrete are samplewise identified. Further, the probabilistic dependence configurations are studied based on copula theory, which is also considered as a data-mining tool. The complete constitutive curves of concrete are generated according to the obtained dependence configurations and marginal distributions. Then, combined with the probability density evolution method, the stochastic response analysis of concrete structures is carried out. The analysis results show that the dependence among the strength, peak strain, and the parameter of the descendent segment cannot be ignored. Due to the constraint of dependence configurations, the distribution characteristics of the generated point set are substantially consistent with the tested results, and the generated complete stress-strain curves agree well with the tested curves at both the level of sample and the level of second-order moments. In addition, no abnormal complete stress-strain curves, e.g., those with low strength and sharp descendent segment, which are unlikely to occur in the test, are generated. The dependence configuration of the parameters of concrete has considerable effects on the response and reliability of concrete structures, and may even lead to the change of overall structural failure mode. Consequently, ignoring the probabilistic dependence of material parameters may yield misleading results for decision making. Problems to be further studied are also discussed.

Simulation of Crack Propagation in Some Self-Compacting Concrete Structures and Determination of Their Strength and Ductility Performances

A study on the crack propagation, strength and ductility performances of some self-compacting concrete (SCC) structures with and without steel fibers can be made through experiments. But testing is laborious. For large structure like dam, testing is impossible. Sometimes, there could be insufficient laboratory facilities. Under such circumstances, the non-linear analysis of concrete structures became a novel design tool. It employs the power of computer simulation using finite element method (FEM) based software to support the structural engineers. The ATENA software uses smeared crack approach and is based on the Bazant’s crack band theory. The experimental total fracture energies of both SCC and steel fiber reinforced SCC (Steel fibers of length 25mm@ 0.6% by volume of mix) beams of strength M50 determined by RILEM’s work of fracture method, corresponding material properties and tension softening behavior are used as input data in the software. The simulated load-deflection/CMOD curve could be used to access the strength and ductility performances of the structures. The strength is identified by peak load and ductility by extension of tail end of this curve beyond yield load. Hence, this paper presents an appropriate methodology to determine the performances by simulation. Ductility is the desired property required for structures during earthquake. This can be improved by increasing the main steel reinforcement, incorporate fiber reinforced plastic (FRP) and steel tubes to impart it. But this could be uneconomical. In such cases, it is to be investigated that ductility can be improved by incorporating steel fibers of appropriate aspect ratio and volume in the mix. The ductility ratio (μ) determined from the load-deflection/CMOD curves is further used to evaluate the response reduction factor(R) by an empirical formula as established in earlier investigation. The R used in base shear formula of IS 1893(Part-I)-2002 code considers the ductility property of the structures that are subjected to lateral base shear during earthquake. Thus this study is carried out to identify the usefulness of simulation technique which is a new and robust tool to assess these performances of the structures using ATENA software that avoid the tedious testing procedures. This study investigates the influence of steel fibers in SFRSCC structures to improve their strength and ductility performances compared to SCC structures.

Nonlinear analysis of concrete structures using GFEM enrichment strategy with a microplane constitutive model

Abstract One of the most widespread methods to the nonlinear analysis of structures is the Finite Element Method (FEM). However, there are phenomena whose behavior is not satisfactorily simulated by the standard FEM and this fact has quickened the development of new strategies such as the Generalized Finite Element Method (GFEM), understood as a variation of the FEM. In parallel, nonlinear analysis of concrete structures requires the use of constitutive models that represents the nucleation and propagation of cracks. In this paper it is used an anisotropic constitutive model, based on the microplane theory, which is able to represent the behavior of concrete structures, together with the GFEM approach. These resources are incorporated on the INSANE system (INteractive Structural ANalysis Environment), used in the numerical simulations presented here to demonstrate the feasibility of using the GFEM enrichment strategy, in the nonlinear analysis of concrete structures, with validation made from comparisons with experimental results available in the literature.

Investigation of Fracture Properties by Inverse Analysis on Selected SCC Concrete Beams with Different Amount of Fibres

Self-compacting concrete (SCC) and Steel fibre reinforced concrete (SFRC) have higher tensile strength capacity, limited crack width and higher post peak capacity, as well as easier construction handling. Thus SFRC allows for advanced and innovative design of concrete structures. However, the current wider structural applicability of the discussed composite material is limited by lack of knowledge and recommendations for advanced design and analysis considering non-linear calculation as well corrosion related durability. Therefore, it is necessary to have knowledge of several physical and mechanical properties or to be able to identify the properties of interest. The article presents the results of the identification of fracture properties of selected self-compacting concrete that are suitable for nonlinear finite element analyses. Moreover, the ability of selected concrete to the ingress of chlorides is of particular interest as well. Interest in material properties consisted of concrete tensile strength, modulus of elasticity, softening factors and specific fracture energy. The procedure for identifying material properties by inverse analysis was applied. New knowledge of material properties can be used to analyse similar tasks, especially in the case of nonlinear analysis of concrete structures.

Non-linear analysis of concrete structures: a practical design approach to Eurocode

Reinforced concrete is an inherently non-linear material with non-linear compressive behaviour, concrete cracking and reinforcement yielding altering the stiffness and causing redistribution of forces within statically indeterminate structures. A practical design approach is described that has been developed to ensure robust computation of serviceability limit state and ultimate limit state demand in line with Eurocode BS EN 1992, including explicit modelling of material and geometric non-linearities and construction imperfections. The approach uses the MAT_CONCRETE_EC2 material model within the LS-DYNA finite-element analysis package and has been extensively used during the detailed engineering design of the concrete gravity substructure for the White Rose Extension Project off the coast of Newfoundland, Canada. The material model and validation of its behaviour in accordance with the Eurocode standard are described, along with other typical engineering applications where the approach may be of benefit. Specific benefits and implementation challenges encountered during the design process are also highlighted with a non-linear buckling assessment case study.

Determination of Material Parameters for Nonlinear Analysis of Reinforced Concrete

The aim of the paper is a nonlinear analysis of concrete structures. For these type of tasks is an important suitable choice of model input parameters and concrete. Especially if the analysis is preceding the results of an experiment, which can determine the exact properties of concrete. The following properties of concrete are needed for nonlinear analysis: tensile strength and compressive strength of concrete. There are more procedures how to determine some unknown input parameters. The paper presents some approaches to calculating and selecting parameters, which are based primarily on the recommendations of the Model Code and professional articles. Specifically, the numerical analysis performed in our developed program which allows observing a nonlinear behaviour of concrete at loading case.

Deteriorating beam finite element for nonlinear analysis of concrete structures under corrosion

A three-dimensional reinforced concrete (RC) deteriorating beam finite element for nonlinear analysis of concrete structures under corrosion is presented in this study. The finite element formulation accounts for both material and geometrical nonlinearity. Damage modelling considers uniform and pitting corrosion and includes the reduction of cross-sectional area of corroded bars, the reduction of ductility of reinforcing steel and the deterioration of concrete strength due to splitting cracks, delamination and spalling of the concrete cover. The beam finite element is validated with reference to the results of experimental tests carried out on RC beams with corroded reinforcement. The application potentialities of the proposed formulation are shown through the finite element analysis of a statically indeterminate RC beam and a three-dimensional RC arch bridge under different damage scenarios and corrosion penetration levels. The results indicate that the design for durability of concrete structures exposed to corrosion needs to rely on structural analysis methods capable to account for the global effects of local damage phenomena on the overall system performance.

Static and dynamic physically non-linear analysis of concrete structures using a hybrid mixed finite element model

A new hybrid-mixed stress finite element model for the static and dynamic non-linear analysis of concrete structures is presented and discussed in this paper. The main feature of this model is the simultaneous and independent approximation of the stress, the strain and the displacement fields in the domain of each element. The displacements along the static boundary, which is considered to include inter-element boundaries, are also directly approximated. To define the approximation bases in the space domain, complete sets of orthonormal Legendre polynomials are used. The adoption of these functions enables the use of analytical closed form solutions for the computation of all linear structural operators and leads to the development of very effective p-refinement procedures. To represent the material quasi-brittle behaviour, a physically non-linear model is considered by using damage mechanics. A simple isotropic damage model is adopted and to control strain localisation problems a non-local integral formulation is considered. To solve the dynamic non-linear governing system, a time integration procedure based on the use of the @a-HHT method is used. For each time step, the solution of the non-linear governing system is achieved using an iterative algorithm based on a secant method. The model being discussed is applied to the solution of two-dimensional structures. To validate the model, to illustrate its potential and to assess its accuracy and numerical efficiency, several numerical examples are discussed and comparisons are made with solutions provided by experimental tests and with other numerical results obtained using conventional finite elements (CFE).

A GPU-Based Parallel Procedure for Nonlinear Analysis of Complex Structures Using a Coupled FEM/DEM Approach

This study reports the GPU parallelization of complex three-dimensional software for nonlinear analysis of concrete structures. It focuses on coupled thermomechanical analysis of complex structures. A coupled FEM/DEM approach (CDEM) is given from a fundamental theoretical viewpoint. As the modeling of a large structure by means of FEM/DEM may lead to prohibitive computation times, a parallelization strategy is required. With the substantial development of computer science, a GPU-based parallel procedure is implemented. A comparative study between the GPU and CPU computation results is presented, and the runtimes and speedups are analyzed. The results show that dramatic performance improvements are gained from GPU parallelization.

Safety formats for non-linear analysis of concrete structures

For realistic modelling of reinforced concrete structures, non-linear models are often inevitable, which raises the question of an appropriate safety format for non-linear analysis. This paper gives an overview of available safety formats and discusses their advantages and disadvantages. An analysis of available round robin tests and modelling competitions shows that current safety formats do not properly account for the modelling uncertainty of non-linear analysis. Based on this observation a new safety format was proposed which allows one to explicitly account for the modelling uncertainty. To avoid any interaction of the modelled response with the safety format, the mean in situ material parameters should be used in the non-linear analysis and a resistance safety factor is used to assure the intended reliability level. The application of the new safety format to beam sections loaded in bending showed that it offers a reliability level that is in good agreement with the target reliability.

Damage analysis of concrete structures using polynomial wavelets

This paper presents and discusses a hybrid-mixed stress finite element model based on the use of polynomial wavelets for the physically non-linear analysis of concrete structures. The effective stress and the displacement fields in the domain of each element and the displacements on the static boundary are independently approximated. As none of the fundamental equations is locally enforced a priori, the hybrid-mixed stress formulation enables the use of a wide range of functions. In the numerical model reported here, all approximations are defined using complete sets of polynomial wavelets. These bases present some important features. In one hand, the functions are orthogonal, which is an important issue when implementing hybrid-mixed stress elements as it ensures high levels of sparsity. On the other hand, the polynomial wavelet basis is defined through linear combinations of Legendre polynomials. This fact enables the use of closed-form solutions for the computation of the integrations involved in the definition of all linear structural operators. A simple isotropic damage model is adopted and a non-local integral formulation where the strain energy release rate is taken as the non-local variable is considered. The numerical model is both incremental and iterative and is solved with a modified Newton–Raphson method that uses the secant matrix. Classical benchmark tests are chosen to illustrate the use of the model under discussion and to assess its numerical performance.

Safety format in non-linear analysis of concrete structures

It is only comparatively recently that the more advanced forms of non-linear analysis have been much used in practice. This leads to issues of how the safety factors should be applied as the partial safety factor format used in current design standards was largely developed for use with linear analysis. Various approaches have been developed and problems with some (notably that advocated by EN 1992-2) are identified. The simple approach of analysis of the structure with design properties throughout is advocated for most cases. However, it is noted that, because this underestimates stiffness, it could be unsafe where imposed deformations are critical. The topic is of major importance because there is no agreed solution to how safety factors should be applied to non-linear analysis, because non-linear analysis is being increasingly used in practice and because the author is aware of several cases where the material partial safety factors have been omitted, giving unsafe results.

Effect of Selected Parameters of Non-Linear Analysis of Concrete Structures

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Cellular Finite Beam Element for Nonlinear Analysis of Concrete Structures under Fire

A novel approach to nonlinear finite-element analysis of concrete structures exposed to fire is presented. The proposed formulation refers to frame systems, but it can be extended to other types of structures. The main novelty of this formulation is the use of a special class of evolutionary algorithms, known as cellular automata, to describe the heat transfer process induced by fire and to create an effective link between the simulation of the thermal process and the structural analysis. The heat transfer process is reproduced by considering heat conduction, heat convection, and thermal radiation. The temperature effects on the structural performance are taken into account by means of temperature-dependent thermal and mechanical properties of concrete and steel. In this way, the general criteria for nonlinear finite-element analysis of concrete structures are applied to formulate a cellular reinforced concrete beam element with temperature-dependent characteristics. The effectiveness and applicability in engineering practice of the proposed formulation is demonstrated through applications. The results prove the accuracy of the proposed procedure and show that, for statically indeterminate structures, fire safety needs to be evaluated at the global level by taking into account the actual role played by the structural scheme.

The influence of different safety formats proposed by Eurocode 2 on the deformability and design of slender structural elements

This paper provides new information about the differences between the two methodologies proposed by Eurocode 2 (EC2) for the nonlinear analysis of concrete structures. Proceeding from the evaluation of the second-order effects on a structural element, the results of a parametric study on isolated columns are compared, using a nonlinear analysis program especially developed for this kind of structure. Subsequently, the outcomes from the application of each safety format are contrasted in analysing the lateral deformability of the structure. In addition, an ultimate limit states design of the required cross-section mechanical reinforcement for each safety format leads to some comments about the influence of these procedures on structural design and assessment.