Element Analysis Of Concrete Structures Research Articles

The disturbed fracture process zone theory for the assessment of the asymptotic fracture energy of concrete

The fracture energy constitutes an important input parameter for non-linear finite element analysis of concrete structures. Characterization of such parameter based on standard RILEM three-point bending test or wedge splitting test is known to depend on the size of the specimen. For the assessment example of large hydraulic structures using non-linear finite elements, it is important to develop an experimental protocol for characterizing a size-independent fracture energy, or asymptotic fracture energy representative of the size of these structures.Characterization of the asymptotic fracture energy requires specimens with very large sizes and thus represents an important experimental challenge. This work aims to develop a new experimental protocol based on wedge splitting test on specimen with moderate size and using digital image correlation technique.The new protocol is based on the disturbed fracture process zone (DFPZ) theory developed in this work, as an interpretation theory for the boundary effect theory of Duan et al. [8]. It uses the same hypothesis of bilinear distribution of the local fracture energy as in the simplified boundary effect method (SBEM) (Abdalla and Karihaloo [1], Karihaloo et al. [21]) but requires only one set of specimens with a specific notch over depth (a/D) ratio rather than two sets of specimens with two different a/D ratios.In order to validate the developed approach and theory, an experimental programme of 14 concrete specimens is conducted. Two concrete mixtures are considered with two maximum aggregate sizes: 38 mm and 76 mm, representative of hydraulic structures.Assessment of the fracture energy using the new protocol and the protocol based on SBEM resulted in similar values for both mixtures and thus validates the new developed theory.

Modelling dowel action of discrete reinforcing bars for finite element analysis of concrete structures

In the finite element analysis of reinforced concrete structures, discrete representation of the steel reinforcing bars is considered advantageous over smeared representation because of the more realistic modelling of their bond-slip behaviour. However, there is up to now limited research on how to simulate the dowel action of discrete reinforcing bars, which is an important component of shear transfer in cracked concrete structures. Herein, a numerical model for the dowel action of discrete reinforcing bars is developed. It features derivation of the dowel stiffness based on the beam-on-elastic-foundation theory and direct assemblage of the dowel stiffness matrix into the stiffness matrices of adjoining concrete elements. The dowel action model is incorporated in a nonlinear finite element program based on secant stiffness formulation and application to deep beams tested by others demonstrates that the incorporation of dowel action can improve the accuracy of the finite element analysis.

Multi-axial strength criterion of lightweight aggregate (LWA) concrete under the Unified Twin-shear strength theory

The strength theory of concrete is significant to structure design and nonlinear finite element analysis of concrete structures because concrete utilized in engineering is usually subject to the action of multi-axial stress. Experimental results have revealed that lightweight aggregate (LWA) concrete exhibits plastic flow plateau under high compressive stress and most of the lightweight aggregates are crushed at this stage. For the purpose of safety, therefore, in the practical application the strength of LWA concrete at the plastic flow plateau stage should be regarded as the ultimate strength under multi-axial compressive stress state. With consideration of the strength criterion, the ultimate strength surface of LWA concrete under multi-axial stress intersects with the hydrostatic stress axis at two different points, which is completely different from that of the normal weight concrete as that the ultimate strength surface is open-ended. As a result, the strength criteria aimed at normal weight concrete do not fit LWA concrete. In the present paper, a multi-axial strength criterion for LWA concrete is proposed based on the Unified Twin-Shear Strength (UTSS) theory developed by Prof Yu (Yu et al. 1992), which takes into account the above strength characteristics of LWA under high compressive stress level. In this strength criterion model, the tensile and compressive meridians as well as the ultimate strength envelopes in deviatoric plane under different hydrostatic stress are established just in terms of a few characteristic stress states, i.e., the uniaxial tensile strength <TEX>$f_t$</TEX>, the uniaxial compressive strength <TEX>$f_c$</TEX>, and the equibiaxial compressive <TEX>$f_{bc}$</TEX>. The developed model was confirmed to agree well with experimental data under different stress ratios of LWA concrete.

Unified calculation method and its application in determining the uniaxial mechanical properties of concrete

This paper presents a unified calculation method and its application in determining the uniaxial mechanical properties of concrete with concrete strengths ranging from 10 to 140 MPa. By analyzing a large collection of test results of the uniaxial mechanical properties of normal-strength, high-strength and super high-strength concrete in China and performing a regression analysis, unified calculation formulas for the mechanical indexes of concrete are proposed that can be applied to various grades of concrete for determining the size coefficient, uniaxial compressive strength, uniaxial tensile strength, elastic modulus, and strain at peak uniaxial compression and tension. Optimized mathematical equations for the nonlinear stress-strain relationship of concrete, including the ascending and descending branches under uniaxial stress, are also established. The elastic modulus is almost constant throughout the elastic stage for the ascending branches of the stress-strain relationship for concrete. The proposed stress-strain relationship of concrete was applied to the nonlinear finite element analysis of both a steel-concrete composite beam and a concrete-filled steel tubular stub column. The analytical results are in good agreement with the experiment results, indicating that the proposed stress-strain relationship of concrete is applicable. The achievements presented in this paper can be used as references for the design and nonlinear finite element analysis of concrete structures.

Nonlinear finite element analysis of concrete structures using new constitutive models

Nonlinear finite element analysis was applied to various types of reinforced concrete structures using a new set of constitutive models established in the fixed-angle softened-truss model (FA-STM). A computer code FEAPRC was developed specifically for application to reinforced concrete structures by modifying the general-purpose program FEAP. FEAPRC can take care of the four important characteristics of cracked reinforced concrete: (1) the softening effect of concrete in compression, (2) the tension-stiffening effect by concrete in tension, (3) the average (or smeared) stress–strain curve of steel bars embedded in concrete, and (4) the new, rational shear modulus of concrete. The predictions made by FEAPRC are in good agreement with the experimental results of beams, panels, and framed shear walls.

Modeling dowel action of reinforcement bars for finite element analysis of concrete structures

A numerical model for the dowel action of reinforcement bars crossing cracks in concrete is developed for finite element analysis of concrete structures. The beam on elastic foundation theory is used to derive the dowel force–displacement relationship, which is expressed in a smeared form in terms of dowel stress and strain in order to be compatible with the smeared crack and smeared reinforcement models commonly used in finite element analysis. This dowel action model is incorporated in a finite element program that employs secant stiffness formulation and a displacement controlled iteration scheme for nonlinear analysis. Using the finite element program, the nonlinear behaviors of several reinforced concrete beams tested by others are analyzed well into the post-peak range. The beams are analyzed first with the dowel action neglected and then again with the dowel action incorporated. It is found that in certain cases, the dowel action can have significant effects on the shear strength and ductility of reinforced concrete beams and that the analytical results generally agree better with the experimental values when the dowel action is taken into account.

Couplings in early-age concrete: From material modeling to structural design

Couplings in early-age concrete are the cross-effects between the hydration reaction, temperature evolution and deformation which can lead to cracking. They involve complex chemo-physical mechanism that operate over a broad range of scales, from nanometer to meter. This paper explores these thermo-chemo-mechanical cross-effects from the macroscale of engineering material modeling (the typical scale of laboratory test specimens) to the level of structural design. Set within the framework of chemoplasticity, the cross-effects in the constitutive model are derived from Maxwell-symmetries, and characterize the autogeneous shrinkage, hydrate heat and strength growth due to the chemo-mechanical, thermo-chemical and chemo-plastic couplings. These couplings at a material level can be determined from standard material tests, provided that the order of coupling is known. This is shown by considering adiabatic calorimetric experiments and isothermal strength growth tests, which lead to identify an intrinsic kinetics function that characterizes the macroscopic hydration kinetics of concrete. Finally, an example of application of the model to large-scale finite element analysis of concrete structures is presented, which clearly shows the consequences of thermo-chemo-mechanical couplings for the engineering design of concrete structures at early ages.

Nonlinear finite element analysis of arch dam — I. Constitutive relationship

In nonlinear finite element analysis of concrete structures, two of the most important issues are the constitutive relationship of concrete and the nonlinear analysis process (especially cracking model). In this study, as the first part, the existing nonlinear elastic constitutive relationships of concrete are comprehensively analysed and commented upon by comparing with experimental results. Their characteristics, applicability, differences and deficiencies are reviewed. Then the concept of stress state index is proposed and introduced in the constitutive relationship to represent the effect of different stress states. A simple and reasonable constitutive relationship of concrete is suggested in the frame of nonlinear elastic theory.

Nonlinear finite element analysis of arch dam — II. Nonlinear analysis

In order to improve design criteria and reduce construction funds, it is necessary to perform nonlinear analysis of concrete arch dams. In this study, cracking models of concrete are investigated and introduced to nonlinear finite element analysis. The general steps of nonlinear finite element analysis of concrete structures are presented and a 3-D nonlinear finite element method program, NFC3D, is developed. Furthermore, a selected arch dam is comprehensively analysed by NFC3D. Many valuable results are obtained, which provide the necessary information for design engineers and show the outline of the working state under extra loading.

Element size effects in nonlinear analysis of reinforced concrete members

This paper presents the results of an investigation into the effect of finite element size in nonlinear finite element analysis of concrete structures. The influence of element size on different behavioural aspects of reinforced concrete structures including the load-displacement and load-strain characteristics, crack pattern and ultimate load are discussed along with a comparison with the experimental data where available. To eliminate the dependence of the computed results on the finite element size, a simple procedure for calculating the ultimate tensile strain of concrete was developed and implemented into the nonlinear finite element formulation. The proposed model gives good agreement with the experimental results. In particular, the new model can be used effectively with relatively coarse finite element meshes with reasonable accuracy.

Embedded representation of fracture in concrete with mixed finite elements

AbstractAs an alternative to the smeared and discrete crack representations, an embedded representation of fracture for finite element analysis of concrete structures is presented. The three‐field Hu–Washizu variational statement is extended to bodies with internal discontinuities. The extended variational statement is then utilized for formulating elements with a discontinuous displacement field. The new elements are capable of modelling different deformation modes of an internal discontinuity at the element level. The satisfactory performance of the embedded crack representation is verified by several case studies on concrete fracture.

Nonlinear finite element analysis of concrete structures

This paper deals with three-dimensional nonlinear finite element analysis of concrete structures. A new three-parameter failure criterion, formulated in terms of three stress invariants, is suggested for plain concrete. The criterion can accurately describe available experimental data throughout the stress range from tensile stresses to high compressive stresses. The constitutive matrix of a cracked concrete element is deduced by coupling the normal and tangential effects of crack bands. The modeling of reinforcement and its interaction with concrete are also discussed. Numerical examples of plain and reinforced concrete are presented. The computational results compare satisfactorily with experimental data.

Nonlinear analysis of concrete structures

Solution capabilities for two- and three-dimensional nonlinear finite element analysis of concrete structures are presented. The concrete material is modeled including the triaxial nonlinear stress-strain behavior, tensile cracking, tension-stiffening, compression crushing and strain-softening. The results of various sample analyses are given to demonstrate the constitutive model and the solution strategies. These analyses include the response predictions of a test beam and of small scale models of two reactor vessels.

Comment on Orthotropic Models for Concrete and Geomaterials

Incrementally linear constitutive equations that are characterized by an orthotropic tangential stiffness or compliance matrix have recently become widely used in finite element analysis of concrete structures and soils. It does not seem to be, however, widely appreciated that such constitutive equations are limited to loading histories in which the prinicipal stress directions do not rotate, and that a violation of this condition can sometimes have serious consequences. It is demonstrated that in such a case the orthotropic models do not satisfy the form‐invariance condition for initially isotropic solids, i.e., the condition that the response predicted by the model must be the same for any choice of coordinate axes in the initial stress‐free state. An example shows that the results obtained for various such choices can be rather different. The problem cannot be avoided by rotating the axes of orthotropy during the loading process so as to keep them parallel to the principal stress axes, first, because t...

Strain-Rate Effect in Rapid Triaxial Loading of Concrete

Presented is a generalization of time-independent nonlinear triaxial constitutive relations for concrete to model short-time viscoelastic effects. The effect of strain-rate magnitude upon the initial elastic modulus, the peak stress, and the sharpness of the stress peak is taken into account. To obtain a model that also exhibits short-time rapid creep and stress relaxation, the incrementally linear constitutive law fully characterized by tangential moduli is replaced by a nonlinear first-order differential equation in stress, strain, stress rate and strain rate. This requires introduction of the (apparent) instantaneous modulus, the relaxation time and retardation time. The irreversibility at unloading, caused by the short-time viscoelastic mffects, is also analyzed. The model allows more realistic dynamic finite element analysis of concrete structures.

On three-dimensional nonlinear analysis of concrete structures

Solution capabilities for three-dimensional geometric and material nonlinear finite element analysis of concrete structures are presented. The concrete material is modeled including triaxial nonlinear stress-strain behavior, tensile cracking, compression crushing and strain-softening. The objective in this work was the development of a practical nonlinear concrete analysis capability. The material model can also be employed to represent some rock materials. The results of various sample analyses are given, in which the stability and accuracy of the finite element representations have been studied.

Nonlinear finite element analysis of concrete structures

Abstract The article discusses the major sources of nonlinearities in reinforced concrete structures. An outline is given of a large number of proposed mathematical models for the material behaviour of concrete and reinforcement and for the interactive behaviour between the two materials. Further, it is discussed how the finite element method may be applied effectively in the analysis of different types of reinforced concrete structures. In particular, it is explained that special precaution must be exercised in order to develop efficient and reliable solution algorithms for the nonlinear equations. Several computational examples are presented involving nonlinear collapse or cyclic behaviour of structures like beams, shear walls and slabs.