Numerical assessment of the methods of measurement of the electrical resistance in carbon fiber reinforced cement

Carbon fiber reinforced cement is a smart material due to its sensing ability, which is based on piezoresistivity. A finite element model for simulating the measurement of electrical resistance in this material is provided. The measured four-probe resistance decreases with increasing distance between the adjacent voltage and current contacts. For a beam of size 320 × 40 × 40mm³, the minimum distance for accurate four-probe resistivity measurement is 5mm for surface contacts (at the end surfaces), 5mm for loop contacts (around the perimeter) and 40mm for line contacts (on one surface). The two-probe resistivity is most inaccurate for the line contacts. For loop contacts, the two-probe resistivity is accurate when the aspect ratio exceeds 8, and the four-probe resistivity is accurate when the aspect ratio exceeds 1.5. For a column of size 426 × 92 × 76mm ³, the minimum distance between the adjacent current and voltage contacts for accurate four-probe resistivity measurement is 50mm for loop contacts and 400mm for line contacts. For a slab of size 9.75 × 4.88 × 0.30m³, the minimum distance for accurate four-probe resistivity measurement along the 9.75m length is 250mm for line contacts.