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

A simple method is presented by which the linear creep function of concrete can be approximated, with any desired accuracy, by Dirichlet series with variable coefficients. Smooth fits of the best known data on creep at constant temperature and water content are demonstrated. It is shown that the approximation is equivalent to the Kelvin chain model with age-dependent properties. Other approximations leading to the Kelvin chain are also presented. It is found, however, that no Kelvin chain approximation can avoid negativeness of some spring moduli for some periods of time, which precludes physical interpretation of hidden strains. But representations with Maxwell chain are free from this deficiency. The Dirichlet series approximation allows formulation of an efficient algorithm of step-by-step time integration of creep problems, for which arbitrary increase of the time step is possible and storage of the stress history can be dispensed with.

Dirichlet series creep function for aging concrete

The nonlocal generalization of Weibull theory previously developed for structures that are either notched or fail only after the formation of a large crack is extended to predict the probability of failure of unnotched structures that reach the maximum load before a large crack forms, as is typical of the test of modulus of rupture (flexural strength). The probability of material failure at a material point is assumed to be a power function (characterized by the Weibull modulus and scaling parameter) of the average stress in the neighborhood of that point, the size of which is the material characteristic length. This indirectly imposes a spatial correlation. The model describes the deterministic size effect, which is caused by stress redistribution due to strain softening in the boundary layer of cracking with the associated energy release. As a basic check of soundness, it is proposed that for quasibrittle structures much larger than the fracture process zone or the characteristic length of material, the probabilistic model of failure must asymptotically reduce to Weibull theory with the weakest link model. The present theory satisfies this condition, but the classical stochastic finite-element models do not, which renders the use of these models for calculating loads of very small failure probabilities dubious. Numerical applications and comparisons to test results are left for Part II.

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Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. i: theory

Fracture experiments were conducted at temperatures from 20 to 200 C (68 to 392 F) to determine the dependence of the Mode I fracture energy of concrete on temperature as well as the specific water content. The fracture energy values were determined by testing geometrically similar specimens of sizes in the ratio 1:2:4:8 and then applying Bazant's size effect law. Three-point bend specimens and eccentric compression specimmns are found to yield approximately the same fracture energies, regardless of temperature. To describe the temperature dependence of fracture energy, a recently derived simple formula based on the activation energy theory (rate process theory) is used and verified by test results. The temperature effect is determined both for concrete predried in an oven and for wet (saturated) concrete. By interpolation, an approximate formula for the effect of moisture content on fracture energy is also obtained. This effect is found to be small at room temperature but large at temperatures close to 100 C (212 F).

Zdenek P. Bazant

Papers

Dirichlet series creep function for aging concrete

Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. i: theory

Effect of Temperature and Humidity on Fracture Energy of Concrete

Crack band model for fracture of geomaterials.

A correlation study of formulations of incremental deformation and stability of continuous bodies