Quantifying the effects of crack width, tortuosity, and roughness on water permeability of cracked mortars

Abstract

The existing service-life prediction models rarely account for the effect of cracks on mass transport and durability of concrete. To correct this deficiency, transport in fractured porous media must be studied. The objective of this paper is to quantify the water permeability of localized cracks as a function of crack geometry (i.e., width, tortuosity, and surface roughness). Plain and fiber-reinforced mortar disk specimens were cracked by splitting tension; and the crack profile was digitized by image analysis and translated into crack geometric properties. Crack permeability was measured using a Darcian flow-thru cell. The results show that permeability is a function of crack width square. Crack tortuosity and roughness reduce the permeability by a factor of 4 to 6 below what is predicted by the theory for smooth parallel plate cracks. Although tortuosity and roughness exhibit fractal behavior, their proper measurement is possible and results in correct estimation of crack permeability.

Introduction

The permeability of concrete has an important impact on its durability since permeability controls the rate of penetration of moisture that may contain aggressive solutes and also controls moisture movement during heating and cooling or freezing and thawing [1]. While permeability of concrete is commonly measured using uncracked laboratory specimens [2], [3], in real structures, the existence of cracks (induced by restrained shrinkage or mechanical loading) can significantly increase the penetration of moisture and salts into concrete. This can especially be significant for high strength concretes which are known to have a higher tendency for cracking due to a larger autogenous and thermal shrinkage and a lower capacity for stress relaxation [4], [5], [6]. As such, for service-life predictions, it is important to account for the effect of cracks on accelerating the transport of moisture and aggressive agents inside concrete. Unfortunately, the present generation of service-life models largely overlooks the effect of cracks on durability.

Research on the water permeability of crack-free concrete has been extensive [7], [8], [9], [10], [11], [12] and has led to a general understanding that the saturated water permeability of concrete is a function of its porosity, pore connectivity, and the square of a threshold pore diameter [10], [11], [12]. In addition to the classical flow-thru permeability measurements [2], [3], new methods (e.g., thermal expansion kinetics [13], beam bending [14], and dynamic pressurization [15]) have been offered that allow a more rapid and repeatable measurement of the saturated permeability.

In comparison, research on the permeability of cracked concrete has been limited. The pioneering works of Kermani [16], Tsukamoto and Wörner [17], and Gérard et al. [18] explored changes in permeability of concrete caused by the application of compressive or tensile stress. Wang et al. [19] measured the permeability of concrete disks fractured using a splitting tensile test, and correlated the crack opening displacement (COD) with the permeability coefficient of a crack. Their results suggested that for COD smaller than 25 μm, there is no significant increase in permeability beyond the matrix permeability. For larger cracks, permeability increases exponentially. It should be noted that in this study (as well as some future studies [20], [21], [22]), crack width was not directly measured; but assumed to be equal to the lateral displacement of the disk specimen which was measured using an LVDT setup (Fig. 1). This assumption could result in inaccuracies due to crack branching, variability of crack width along its length, and inelastic deformation of the matrix; as discussed later in this paper.

For use in service-life prediction models, it is important to establish a quantitative correlation between crack geometry and its permeability. Using the theory of laminar flow of incompressible Newtonian fluids inside a smooth parallel-plate gap, Eq. (1), often referred to as the Poiseuille law, can be derived showing that the water flow rate through a crack, Q (m³/s), is related to the cube of crack width, b (m) [23]:

$$Q=\xi \frac{L{b}^3}{12\eta }\left[\frac{dP}{dx}\right]$$

where Lb (m²) is the crack cross sectional area perpendicular to the direction of flow, η (Pa·s) is dynamic viscosity of fluid, and $\left[\frac{dP}{dx}\right]$ (Pa/m) is the pressure gradient that drives the flow. This equation can be combined with Darcy's law:

$$J=\frac{Q}{Lb}=\frac{\kappa }{\eta }\left[\frac{dP}{dx}\right]$$

and alternatively presented in terms of the permeability coefficient of a crack κ (m²), as a function of crack width square [24]:

$$\kappa =\xi \frac{b^2}{12}\text{.}$$

Eqs. (1), (3) are strictly valid for a smooth, straight, and parallel plate crack. Real cracks in concrete never have such characteristics. As shown in Fig. 2, the crack width often varies along the length of a crack; cracks are tortuous meaning their actual length is larger than their nominal length; and crack wall surfaces are rough. These features reduce the permeability of a crack, sometimes significantly. To account for this reduction in permeability, in Eqs. (1), (3), an empirical reduction factor ξ has been included; the values of ξ = 0.001 to 0.1 have been reported for plain and fiber reinforced concrete [21], [25]. Unfortunately, these values are uncertain (vary several orders of magnitude), purely empirical, and have not been correlated to the geometric properties of cracks. For implementation in service-life models, it is important to improve the estimation of crack permeability (and other transport properties) as a function of crack geometric parameters; i.e., average or effective width, tortuosity, and roughness. The present paper pursues this objective.