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...

/pdf/theoretical-stress-strain-model-for-confined-concrete-3eemamm28s.pdf

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.

/pdf/crack-band-theory-for-fracture-of-concrete-4hm1hrkirl.pdf

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

• IN THE CREEP ANALYSIS OF concrete structures two kinds of errors are involved. One stems from the inaccurate knowledge of the creep law, and its minimization is a problem of materials re­ search. The second error is caused by the simpli­ fication of analysis, which designers introduce to avoid the complexities of an exact analysis. In the sequel, only accuracy or exactitude in the latter sense will be of concern. The simplest and the most widespread among the simplified methods of analysis is the well­ known effective modulus method, whose error with regard to the theoretically exact solution for the given creep law is known to be quite large when aging of concrete, i.e., the change of its properties with the progress of hydration, is of significance (see Table 2 discussed below). How­ ever, a surprisingly simple way of refinement of this method has been recently discovered by Trost, 1 on the basis of approximate and mostly intuitive considerations. The intent of this paper is to present a rigorous formulation of this method and to extend it to the case of a variable elastic modulus and an unbounded final value of creep.

/pdf/prediction-of-concrete-creep-effects-using-age-adjusted-1p672jklob.pdf

Prediction of Concrete Creep Effects Using Age-Adjusted Effective Modulus Method

A new physical theory and constitutive model for the effects of long-term aging and drying on concrete creep are proposed. The previously proposed solidification theory, in which the aging is explained and modeled by the volume growth (into the pores of hardened portland cement paste) of a nonaging viscoelastic constituent (cement gel), cannot explain long-term aging because the volume growth of the hydration products is too short-lived. The paper presents an improvement of the solidification theory in which the viscosity of the flow term of the compliance function is a function of a tensile microprestress carried by the bonds and bridges crossing the micropores (gel pores) in the hardened cement gel. The microprestress is generated by the disjoining pressure of the hindered adsorbed water in the micropores and by very large and highly localized volume changes caused by hydration or drying. The long-term creep, deviatoric as well as volumetric, is assumed to originate from viscous shear slips between the opposite walls of the micropores in which the bonds or bridges that cross the micropores and transmit the microprestress break and reform. The long-term aging exhibited by the flow term in the creep model is caused by relaxation of the tensile microprestress transverse to the slip plane. The Pickett effect (drying creep) is caused by changes of the microprestress balancing the changes in the disjoining pressure, which in turn are engendered by changes of the relative humidity in the capillary pores. Numerical implementation, application and comparison with test data is relegated to a companion paper that follows in this issue.

http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/365.pdf

Microprestress-Solidification Theory for Concrete Creep. I: Aging and Drying Effects

A physical-mathematical model is developed for concrete exposed to sea water. The model describes: (1)Diffusion of oxygen, chloride ions, and pore water through the concrete cover of reinforcement; (2)ferrous hydroxide near steel surface; (3)the depassivation of steel due to critical chloride ion concentration; (4)the cathodic and anodic electric potentials depending on oxygen and ferrous hydroxide concentrations according to Nernst equation; (5)the polarization of electrodes due to changes in concentration of oxygen and ferrous hydroxide; (6)the flow of electric current through the electrolyte in pores of concrete; (7)the mass sinks or sources of oxygen, ferrous hydroxide, and hydrated red rust electrodes, based on Faraday law; and (8)the rust production rate, based on reaction kinetics. To enable calculations, numerical values of all coefficients are indicated. The theory is completed by formulating the problem as an initial-boundary value problem.

/pdf/physical-model-for-steel-corrosion-in-concrete-sea-2x74l8v4q3.pdf

Physical model for steel corrosion in concrete sea structures­ theory

A new general constitutive law for creep is presented, in which the aging due to continuing hydration of cement is taken into account in a simple manner, and better justified than in existing theories. Microchemical analysis of the solidification process is used to show that the aging may be modeled as a growth of the volume fraction of load-bearing solidified matter (hydrated cement), which may be described as a nonaging viscoelastic material. It was found that a history integral should be used to express the rate, rather than the total value of the viscoelastic strain component. Other study findings are also discussed.

Zdenek P. Bazant

Papers

Prediction of Concrete Creep Effects Using Age-Adjusted Effective Modulus Method

Microprestress-Solidification Theory for Concrete Creep. I: Aging and Drying Effects

Physical model for steel corrosion in concrete sea structures theory

Solidification theory for concrete creep. I: formulation

Mechanics of Distributed Cracking

Zdenek P. Bazant

Papers

Prediction of Concrete Creep Effects Using Age-Adjusted Effective Modulus Method

Microprestress-Solidification Theory for Concrete Creep. I: Aging and Drying Effects

Physical model for steel corrosion in concrete sea structures­ theory

Solidification theory for concrete creep. I: formulation

Mechanics of Distributed Cracking

Physical model for steel corrosion in concrete sea structures theory