The electrical resistance R of a conductor of length L and uniform cross-sectional area A is given by the equation shown in the figure to the right. The quantity ρ is the electrical resistivity and is a material property, with units of resistance multiplied by length, such as ohm·m. If the electrical resistance R of a specimen of length L and area A is measured, the resistivity can be calculated from the relationship ρ = R A/L. The inverse of electrical resistivity is the electrical conductivity, σ. The inverse of ohms is a unit called siemens (S). Therefore, electrical conductivity has units of S/m. For concrete, it is convenient to express electrical conductivity in millisiemens per meter or mS/m.
In assessing the ability of a concrete mixture to resist penetration of a particular type of ion, one of the key properties is the diffusivity, which defines how readily the given type of ion will migrate through saturated concrete in the presence of a concentration gradient. For a saturated porous material, such as hardened concrete, the diffusion coefficient of a give type of ion can be related to electrical conductivity through the Nernst-Einstein equation as follows (Snyder et al. 2000; Nokken and Hooton 2006):
where σ = bulk electrical conductivity of the saturated porous material
σp = conductivity of the pore fluid
D = bulk diffusion coefficient of the specific type of ion through the porous material, and
Dw = diffusion coefficient of the specific ion through water (Mills and Lobo 1989).
If the conductivity of the pore fluid is assumed to be similar among different concretes, the measured bulk electrical conductivity is related directly to the bulk diffusion coefficient (Berke and Hicks 1992). Measurement of the bulk diffusion coefficient of a particular type of ion through concrete is a time consuming process, while electrical conductivity can be measured in a matter of seconds.
The electrical conductivity of saturated cement paste is related to the volume of pores and how they are connected within the paste. The paste porosity is related to the water-cementitious materials (w/cm) ratio, the types of supplementary cementitious materials (SCMs), and the degree of hydration. For the same w/cm and degree of hydration, the use SCMs reduces pore size and increases the tortuosity of the pores and, thereby, reduces electrical conductivity and the ease of fluid penetration.
Method of Operation
The following is a schematic of the measurement method incorporated in Merlin. The four-point measurement method that is used provides an accurate measure of specimen resistance by minimizing the effects of the conductive sponges and the pressure applied to the electrodes. The specimen must be in a water-saturated condition to obtain a meaningful measurement.
An alternating current source (325 Hz) is used to apply current through the saturated cylinder or core. A voltmeter measures the voltage drop across the specimen, and an ammeter measures the current through the specimen. From the measured current I and voltage V, the bulk conductivity is calculated as follows:
where, L is the specimen length and A is the specimen cross-sectional area. The bulk resistivity is the inverse of the bulk conductivity, that is, ρ = 1/σ .
A 100 by 200 mm verification cylinder is provided to check that the Merlin system is operating correctly. The cylinder includes a push button switch than can be used to select one of several precision resistor from 10Ω to 1 MΩ. For example, if the 1000 Ω resistor is selected and the system is functioning correctly, the displayed conductivity of the verification cylinder should be 25.46 mS/m and the resistivity should be 39.27 Ω•m.
From the theoretical basis of the Merlin, it can be seen that measurement of the bulk electrical conductivity of a saturated concrete specimen also provides an indication of the diffusivity properties of the concrete. If the test is conducted at a consistent degree of hydration for a given combination of cementitious materials, the variation in measured bulk electrical conductivity can be used as an indicator of variation of w/cm using a pre-established correlation. If the bulk electrical conductivity of the approved concrete mixture for a project is known, that value can be used for quality control and quality assurance. Thus Merlin has the potential to be considered as a surrogate test to verify the w/cm of a specimen.
The bulk conductivity measured with Merlin is related directly to the charge passed through a specimen as measured by ASTM C1202 using the PROOVE’it system, provided that the current remains constant during the 6 h test duration. This is typically not the case for highly conductive concretes due to electrical heating of the specimen, which increases the pore fluid conductivity and the current. If we assume, however, that current is constant during a PROOVE’it test, we can convert the ASTM C1202 coulomb limits for the different categories of “chloride ion penetrability” into bulk conductivity limits using the following relationship:
The bulk resistivity limits can also be calculated by taking the inverse of the above equation.
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