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 X 40 X 40 mm3, the minimum distance for accurate four-probe resistivity measurement is 5 mm for surface contacts (at the end surfaces), 5 mm for loop contacts (around the perimeter) and 40 mm 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 X 92 X 76 mm3, the minimum distance between the adjacent current and voltage contacts for accurate four-probe resistivity measurement is 50 mm for loop contacts and 400 mm for line contacts. For a slab of size 9.75 X 4.88 X 0.30 m3, the minimum distance for accurate four-probe resistivity measurement along the 9.75 m length is 250 mm for line contacts.