A generalized Archie’s law for n phases

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A new theoretical interpretation of Archie’s saturation exponent (2017, methodology): “…to the original Archie’s law have allowed it to be used when both the pore fill and the matrix have significant electrical conductivities (Glover et al., 2000a; Glover, 2009), such as the case when a rock melt occupies spaces between a solid matrix in the lower crust (Glover et al., 2000b).”
Geophysical Properties of the Near Surface Earth: Electrical Properties (2015, methodology): “sites on the quartz being negative (the situation in the previous theory by Glover et al., 1994), which is shown by the dotted line, and the more sophisticated Revil and Glover (1997)”
Archie's law – a reappraisal (2016, background): “Archie’s law is given by the equation where  o is the resistivity of the fully water-saturated rock sample,  f is the resistivity of the water saturating the pores,  is the porosity of the rock, m is the cementation exponent (Glover, 2009), and the ratio  o /  f is called the formation factor.”