Due to its importance to the durability assessment and design of reinforced concrete structures located in a marine or deicing salt environment, it is essential to determine the chloride diffusivity of hardened cement paste. This paper presents an analytical solution for the chloride diffusivity of hardened cement paste. By modeling hardened cement paste as a two-phase composite material, composed of gel and capillary pores and solid cement gel, an analytical solution is derived for the chloride diffusivity of hardened cement paste based on the general effective medium theory. A parameter involved in the analytical solution is then determined by experimental calibration. After verifying the analytical solution with experimental results obtained from the literature, the effects of the water/cement ratio and the degree of hydration on the chloride diffusivity of hardened cement paste are evaluated in a quantitative manner. It is found that the chloride diffusivity of hardened cement paste with a water/cemen...

Fiber-reinforced plastic (FRP) tendons have been widely used for ground anchors in civil engineering. Although various pull-out tests of FRP rods from grout-filled steel tubes have been conducted to simulate ground anchors in rock, there are relatively few theoretical studies reported in the literature for this type of bonded anchorages. The intention of this paper is to present an analytical solution for predicting the maximum pull-out load of FRP rods embedded in steel tubes filled with cement grout. First, the expression of the shear stress along the thickness direction of the grout layer is obtained analytically. The tensile stress in the rod and the interfacial shear stress at the rod–grout interface are formulated at different loading stages. By modeling interfacial debonding as an interfacial shear crack, the pull-out load is then expressed as a function of the interfacial crack length. Finally, based on the Lagrange multiplier method, the maximum pull-out load and the critical crack length are determined. The validity of the proposed analytical solution is verified with the experimental results obtained from literature. It can be concluded that the proposed analytical solution can predict the maximum pull-out load of spiral wound and indented rods embedded in steel tubes filled with cement grout with reasonable accuracy. The proposed solution can be also applied in predicting the pull-out capacity of steel bars from concrete.

In view of the importance of percolation of the interfacial transition zones (ITZs) in concrete to its transport properties, it is necessary to determine the ITZ percolation threshold for any aggregate gradation and ITZ thickness. This paper presents a numerical method for predicting the ITZ percolation threshold of concrete. To represent the mesostructure of concrete as realistically as possible, a simulation algorithm for the distribution of aggregate particles and ITZs in concrete with periodic boundary conditions is proposed. By analyzing and studying the numerical results, it is shown in this paper that, for a given aggregate volume fraction and element size, the ITZ percolation probability tends to be a constant for a sufficient number of simulations and that the slope of the ITZ percolation probability curve becomes vertical as the element size increases. Finally the results produced by the proposed numerical method are verified by experimental results obtained from the research literature. Based o...

Owing to its importance in evaluating the fracture behavior of concrete, the crack extension resistance curve of concrete has been widely studied, both experimentally and theoretically. In this paper, a numerical approach is developed for the crack extension resistance curve of concrete by considering the variation of the fracture process zone (FPZ) length during the whole fracture process. In this approach, the FPZ length is determined by using the linear asymptotic superposition assumption. Dividing the whole fracture process into three different stages of the cohesive stress distribution within the FPZ, the crack extension resistance curve is formulated by superposition of the intrinsic fracture toughness of concrete and the fracture toughness caused by the cohesive stress within the FPZ. The developed numerical approach is applied to the tested and simulated standard three-point bending notched concrete beams. The effect of the variation of the FPZ length on the crack extension resistance curve is eva...

In predicting the chloride diffusivity of concrete as a three-phase material, the morphological characteristics of the three phases, the physical properties of each phase constituent material, and the interactions of the three phases in the concrete matrix should all be taken into account. The present paper attempts to develop an analytical method to achieve this. A three-phase composite sphere model for the concrete matrix is proposed to represent the heterogeneous nature of concrete and a closed form solution for the chloride diffusivity of concrete is derived. After verifying the derived closed form solution with experimental results, the effects of key factors that affect the chloride diffusivity of concrete, namely the chloride diffusivity and thickness of the interfacial transition zone (ITZ), the maximum aggregate diameter, and the aggregate gradation are examined in a quantitative manner. It is found in the paper that the most important factor influencing the chloride diffusivity of concrete is the chloride diffusivity of ITZ. When the aggregate volume fraction is equal to 0.8, the relative chloride diffusivity of concrete to cement paste for a given relative chloride diffusivity of ITZ to cement paste at 10 is almost four times that for a given relative chloride diffusivity of ITZ to cement paste at 2. The second most important factor is the thickness of ITZ. When the aggregate volume fraction is equal to 0.8, the relative chloride diffusivity of concrete to cement paste for a given ITZ thickness at $0.05\mathrm{mm}$ increases by 76% as compared to that for a given ITZ thickness at $0.02\mathrm{mm}$ . The least important factors are the maximum aggregate diameter and aggregate gradation. The extent to which they influence the chloride diffusivity of concrete is in the range of 10–55%. The paper concludes that the closed form solution derived here can predict the chloride diffusivity of concrete with reasonable accuracy.