Showing papers by "Zdenek P. Bazant published in 1997"

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

Abstract: 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.

Scaling of Structural Failure

Abstract: This article attempts to review the progress achieved in the understanding of scaling and size ef­ fect in the failure of structures. Particular emphasis is placed on quasi brittle materials for which the size etTect is important and complicated. After reflections on the long history of size effect studies, attention is focused on three main types of size effects, namely the statistical size effect due to randomness of strength, the energy release size effect, and the possible size effect due to fractality of fracture or microcracks. Definitive conclusions on the applicability of these theories are drawn. Subsequently, the article discusses the application of the known size effect law for the measurement of material fracture properties, and the modeling of the size effect by the cohesive crack model, non local finite element models and discrete element models. Extensions to com­ pression failure and to the rate-dependent material behavior are also outlined. The damage con­ stitutive law needed for describing a microcracked material in the fracture process zone is dis­ cussed. Various applications to quasibrittle materials, including concrete, sea ice, fiber compos­ ites, rocks and ceramics are presented. There are 377 references included in this article.

Microprestress-solidification theory for concrete creep. ii: algorithm and verification

Abstract: This paper presents a numerical algorithm for the microprestress-solidification theory developed in a companion paper and verifies this theory by comparisons with typical test data from the literature. A model for cracking is incorporated in the algorithm.

Scaling of quasibrittle fracture : hypotheses of invasive and lacunar fractality, their critique and weibull connection

Abstract: Considerable progress has been achieved in fractal characterization of the properties of crack surfaces in quasibrittle materials such as concrete, rock, ice, ceramics and composites. Recently, fractality of cracks or microcracks was proposed as the explanation of the observed size effect on the nominal strength of structures. This explanation, though, has rested merely on intuitive analogy and geometric reasoning, and did not take into account the mechanics of crack propagation. In this paper, the energy-based asymptotic analysis of scaling presented in the preceding companion paper in this issue [1] is extended to the effect of fractality on scaling. First, attention is focused on the propagation of fractal crack curves (invasive fractals). The modifications of the scaling law caused by crack fractality are derived, both for quasibrittle failures after large stable crack growth and for failures at the initiation of a fractal crack in the boundary layer near the surface. Second, attention is focused on discrete fractal distribution of microcracks (lacunar fractals), which is shown to lead to an analogy with Weibull's statistical theory of size effect due to material strength randomness. The predictions ensuing from the fractal hypothesis, either invasive or lacunar, disagree with the experimentally confirmed asymptotic characteristics of the size effect in quasibrittle structures. It is also pointed out that considering the crack curve as a self-similar fractal conflicts with kinematics. This can be remedied by considering the crack to be an affine fractal. It is concluded that the fractal characteristics of either the fracture surface or the microcracking at the fracture front cannot have a significant influence on the law of scaling of failure loads, although they can affect the fracture characteristics.

Scaling of structural failure

Abstract: This article attempts to review the progress achieved in the understanding of scaling and size effect in the failure of structures. Particular emphasis is placed on quasibrittle materials for which the size effect is complicated. Attention is focused on three main types of size effects, namely the statistical size effect due to randomness of strength, the energy release size effect, and the possible size effect due to fractality of fracture or microcracks. Definitive conclusions on the applicability of these theories are drawn. Subsequently, the article discusses the application of the known size effect law for the measurement of material fracture properties, and the modeling of the size effect by the cohesive crack model, nonlocal finite element models and discrete element models. Extensions to compression failure and to the rate-dependent material behavior are also outlined. The damage constitutive law needed for describing a microcracked material in the fracture process zone is discussed. Various applications to quasibrittle materials, including concrete, sea ice, fiber composites, rocks and ceramics are presented.

Crack Growth and Lifetime of Concrete under Long Time Loading

Abstract: Edge-notched eccentrically compressed fracture specimens made of aggregate of reduced size are loaded in standard creep test frames. Measurements of the time rate of crack mouth opening in notched concrete specimens subjected to constant load of almost one month duration are reported and analyzed. To reveal the size effect, geometrically similar specimens of four sizes in the ratio I :2:4:8 are tested. The results are success­ fully described by a previously proposed time-dependent generalization of the R-curve model, in which the rate of crack growth is a function of the ratio of the stress intensity factor to the R-curve, and linear aging viscoelastic creep in the bulk of the specimen is treated according to the operator method. Good predictions are also obtained with a simplified method in which the R-curve is replaced by a constant asymptotic value of the critical stress intensity factor and creep is handled in similarity to the effective modulus method, neglecting the history effect. The time curves of crack opening terminate with an infinite slope, indicating the lifetime. The finiteness of the lifetime is not caused by creep, but by time-dependent crack growth, which dominates the final stage of crack opening. The initial stage of crack opening, on the other hand, is dominated by creep. Tests are conducted both for concretes of normal strength of 33.4 MPa (4,847 psi) in compression and relatively high strength of 46.4 MPa (6,442 psi). For the stronger concrete, the lifetimes are found to be longer. An increase of specimen size is found to decrease the lifetime. Since the same type of model was previously shown capable of describing all other known time-dependent fracture phenomena in concrete, a rather general applicability may be expected.

Fracturing truss model: size effect in shear failure of reinforced concrete

Abstract: The classical truss model (or strut-and-tie model) for shear failure of reinforced concrete beans is modified to describe fracture phenomena during failure. The failure is assumed to be caused by propagation of a compression fracture across the concrete strut during the portion of the loading history in which the maximum load is reached. The compression fracture may consist of a band of splitting cracks that later interconnect to form a shear crack or a shear fracture band inclined to the strut. The width of the fracture band is assumed to occupy only a portion of the strut length and to represent a fixed material property independent of the beam depth. The energy release from the truss is calculated using two alternative approximate methods: (1) using the potential energy change deduced from the concept of stress relief zones; and (2) using the complementary energy change due to stress redistribution caused by propagation of the fracture band across the compressed concrete strut. Both approaches show that a size effect on the nominal strength of shear failure must exist and that it should approximately follow the size effect law proposed by Bazant in 1984. The physical mechanism of the size effect is also explained in a clear and simple intuitive manner. Finally, it is shown that the applied nominal shear stress that causes large initial diagonal cracks to form also exhibits a size effect.

Inelastic Buckling of Concrete Column in Braced Frame

Abstract: The paper proposes an improved method of analysis of reinforced concrete columns in braced (no-sway) frames, which is suitable as a simple computer solution for design practice and is more realistic than the existing ACI and CBB methods. The elastic restraint provided by beams adjacent to columns is described by rotational springs. The inelastic behavior of concrete is defined by a uniaxial stress-strain curve with postpeak softening in compression and a zero strength in tension. Plasticity of reinforcement is also considered. The deflection curve is assumed to be a sine curve. The improvement consists in considering the wavelength as unknown and variable during loading. The problem is reduced to a system of seven nonlinear algebraic equations, which are easily solved for small increments of axial displacement by a standard library optimization algorithm. The convergence always occurs and is fast if the increments are small enough. The influence of various param­ eters on the load-deflection curve, the path in the diagram of axial load P versus moment M, and the failure envelope are studied. Various phenomena, such as the possibility of a concave P(M) path at constant load eccentricity, are explained. It is shown that the ACI approach is slightly conservative in most cases, although situations exist in which the ACI approach is either grossly overconservative or slightly unconservative.