A stress‐strain model is developed for concrete subjected to uniaxial compressive loading and confined by transverse reinforcement. The concrete section may contain any general type of confining steel: either spiral or circular hoops; or rectangular hoops with or without supplementary cross ties. These cross ties can have either equal or unequal confining stresses along each of the transverse axes. A single equation is used for the stress‐strain equation. The model allows for cyclic loading and includes the effect of strain rate. The influence of various types of confinement is taken into account by defining an effective lateral confining stress, which is dependent on the configuration of the transverse and longitudinal reinforcement. An energy balance approach is used to predict the longitudinal compressive strain in the concrete corresponding to first fracture of the transverse reinforcement by equating the strain energy capacity of the transverse reinforcement to the strain energy stored in the concret...

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Theoretical stress strain model for confined concrete

http://mech.spbstu.ru/images/b/bd/Potyondy_Cundall_2004_A_bonded-particle_model_for_rock.pdf

A bonded-particle model for rock

A fracture theory for a heterogenous aggregate material which exhibits a gradual strain-softening due to microcracking and contains aggregate pieces that are not necessarily small compared to structural dimensions is developed. Only Mode I is considered. The fracture is modeled as a blunt smeard crack band, which is justified by the random nature of the microstructure. Simple triaxial stress-strain relations which model the strain-softening and describe the effect of gradual microcracking in the crack band are derived. It is shown that it is easier to use compliance rather than stiffness matrices and that it suffices to adjust a single diagonal term of the complicance matrix. The limiting case of this matrix for complete (continuous) cracking is shown to be identical to the inverse of the well-known stiffness matrix for a perfectly cracked material. The material fracture properties are characterized by only three parameters—fracture energy, uniaxial strength limit and width of the crack band (fracture process zone), while the strain-softening modulus is a function of these parameters. A method of determining the fracture energy from measured complete stres-strain relations is also given. Triaxial stress effects on fracture can be taken into account. The theory is verified by comparisons with numerous experimental data from the literature. Satisfactory fits of maximum load data as well as resistance curves are achieved and values of the three material parameters involved, namely the fracture energy, the strength, and the width of crack band front, are determined from test data. The optimum value of the latter width is found to be about 3 aggregate sizes, which is also justified as the minimum acceptable for a homogeneous continuum modeling. The method of implementing the theory in a finite element code is also indicated, and rules for achieving objectivity of results with regard to the analyst's choice of element size are given. Finally, a simple formula is derived to predict from the tensile strength and aggregate size the fracture energy, as well as the strain-softening modulus. A statistical analysis of the errors reveals a drastic improvement compared to the linear fracture theory as well as the strength theory. The applicability of fracture mechanics to concrete is thus solidly established.

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Crack band theory for fracture of concrete

A plastic-damage model for concrete

National Institute of Standards and Technology における超伝導研究及び生活

This paper presents a model for the characterization of concrete creep and shrinkage in design of concrete structures (Model B3), which is simpler, agrees better with the experimental data and is better theoretically justified than the previous models. The prediction model B3 is calibrated by a computerized databank comprising practically all the relevant test data obtained in various laboratories throughout the world. The effect of concrete composition and design strength on the model parameters is the main source of error of the model. A method to reduce this error by updating one or two model parameters on the basis of short time creep tests is given. The updating of model parameters is particularly important for high strength concretes and other special concretes containing various admixtures, super plasicizers, water-reducing agents and pozzolanic materials. This new model allows a more realistic assessment of the creep and shrinkage effects in concrete structures, which significantly affect the durability and long time serviceability of civil engineering infrastructure.

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Creep and shrinkage prediction model for analysis and design of concrete structures: model b3

A brittle aggregate composite such as portland cement concrete or mortar is modeled in two dimensions as a system of perfectly rigid particles of various sizes separated by interface layers that are characterized by a given force-displacement relation for the normal and tangential components. The force-displacement relation exhibits for the normal component a tensile strength limit followed by a sudden drop of force to zero. The system of rigid particles is generated randomly. The particles are not allowed to overlap and are generally not in contact; however, when the distance between the particles is less than a certain limit, a deformable interface layer is introduced. Numerical simulation of a fracture specimen with a notch shows that the fracture front consists of an irregular band of interparticle cracks the width of which is about three maximum particle sizes. The interparticle cracks remain continuous and do not coalesce into a continuous line fracture until the deformation is very large. The load-displacement relation exhibits gradual softening after the peak force, with a rapid force decrease followed by a long tail of slowly decreasing force. These features qualitatively agree with observations of concrete.

Interface element modeling of fracture in aggregate composites

Temperature effect on concrete creep modeled by microprestress-solidification theory

The propagation of an element-wide blunt smeared crack band in a finite element mesh is analyzed. The results strongly depend on element size; e.g., a four times reduction in element size causes a 3.5 times reduction in the load to cause further crack propagation in a reinforced concrete planel. An energy criterion for crack band extension in concrete with a dense regular reinforcing grid is formulated and it is shown to be objective, i.e., the results for greatly different element sizes cioncide. This is achieved, however, only if bound slip near the crack band is also taken into account. An approximate formula for the lenght of bond slip of the bars crossing the crack band is derived, and for implementation in finite element programs an expression for an equivalent lenght of free bond slip (slip without bond stresses) is determined. The energy criterion is also generalized for nonlinear material behavior numerical results are given.

Fracture Mechanics of Reinforced Concrete

The general microplane model formulated in Part I of this study is calibrated and verified by comparison with numerous nonlinear triaxial test data from the literature and good agreement is achieved. The model involves many fewer material parameters than the previous phenomenologic macroscopic models. Numerical implementation is also considered.

Zdenek P. Bazant

Papers

Creep and shrinkage prediction model for analysis and design of concrete structures: model b3

Interface element modeling of fracture in aggregate composites

Temperature effect on concrete creep modeled by microprestress-solidification theory

Fracture Mechanics of Reinforced Concrete

Microplane Model for Brittle‐Plastic Material: II. Verification