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

Changes in portlandite morphology with solvent composition: Atomistic simulations and experiment

Supplementary cementitious materials

Mechanisms of cement hydration

Influence of nano-SiO2 addition on properties of hardened cement paste as compared with silica fume

Mercury porosimetry: An inappropriate method for the measurement of pore size distributions in cement-based materials

Expression and analysis of pore fluids from hardened cement pastes and mortars

The traditional picture of the ITZ in concrete involves an approximately 30 μm zone around each aggregate, within which the porosity increases as the aggregate interface is approached. The results of the writers' extensive image analysis investigations, and examinations of SEM specimens from various concretes provide a very different picture. While the “wall effect” excluded much of the ground cement from the vicinity of the aggregates, the great increases in pore content within a few μm of the aggregate, up to approximately 30% porosity, that have been reported by others, are not found. On average, only modestly higher porosities are observed within the ITZ than in the bulk paste. This is true even in the innermost areas immediately adjacent to the aggregates. In part, the extra space produced by the wall effect is filled in by CH deposits, many of which are anchored directly on the surfaces of aggregates and are essentially non-porous. Strong indications exist that the ITZ contains as high a proportion of C–S–H per unit volume as the bulk paste; thus some of the extra space that was created by the wall effect is filled in by through-solution deposits of C–S–H derived from elsewhere in the system. It is considered that the structure of the ITZ in ordinary concretes is not different enough from that of the bulk cement paste to provide any basis for significant effects on permeance or mechanical properties.

The ITZ in concrete – a different view based on image analysis and SEM observations

Abstraet-A knowledge of the distribution of pore sizes in clay and soil bodies is a useful element in the microstructural characterization of such materials. Pore-size distributions and total porosity of a number of reference clays, naturally-occurring subsoils, and commercial clay samples prepared in various ways were determined by mercury porosimetry. The range of equivalent pore diameter explored covered almost five orders of magnitude, from several hundred microns down to approximately 150A. The method and its assumptions are critically evaluated, and measurements of the contact angle of mercury on clays yield values of 139 ~ for montmorillonite and 147 ~ for kaolinite and illite clays. The extent of shrinkage on oven-drying prior to mercury intrusion is assessed in each case and found to vary from insignificant to as much as 30 per cent of the pore space, depending on microstructural state and degree of initial saturation. The development of techniques for water removal which do not involve change in pore structure is explored. Some preliminary results for structurally weak saturated clays suggest that critical-region drying and perhaps freeze-drying procedures may be practical.

Pore Size Distributions in Clays

This paper represents an attempt to provide an introduction to the microstructure of cement paste and concrete as seen in backscatter-mode scanning electron microscopy (SEM). Illustrations are provided of the `internal architecture' underlying the microstructure of hardened cement paste and paste in concrete, at the size scales accessible to this instrument. Concrete is a uniquely complex engineering material. The aim of this paper is to provide researchers and practitioners who deal with it an acquaintance with its internal structure.

Sidney Diamond

Papers

Mercury porosimetry: An inappropriate method for the measurement of pore size distributions in cement-based materials

Expression and analysis of pore fluids from hardened cement pastes and mortars

The ITZ in concrete – a different view based on image analysis and SEM observations

Pore Size Distributions in Clays

The microstructure of cement paste and concrete - a visual primer