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This paper presents the useful equations for the estimation of apparent resistivity with depth and layer thickness in a multi-layer earth structure for geotechnical investigations. In recent advances of soil characterization with soil resistivity measurements, a two-layer soil model is implemented for obtaining near surface soil profile. Although geo-electric techniques offer an improvement to traditional soil sampling methods, the resulting data are still often misinterpreted for two-layer soil model, especially in terms of the interrelationships between soil apparent electrical resistivity and several soil physical or chemical properties. In this study, the soil electrical properties are measured along the depth for geotechnical characterizations. Moreover, the theoretical relationships of the electric field density and voltage difference with the thickness of soil layer are revealed in this study. The equations and relationship for multi-layer soil resistivity profile are validated with the numerical formulations and fundamental electromagnetic equations of electrical and electronics engineering. The crucial equations based on the layered earth model can significantly reduce the complexity of estimation of depth and thickness corresponding soil resistivity profile. The nobility of the research is obtaining the simple equations and providing the easy means of soil resistivity measurements with depth and layer thickness in multi-layer soil characterizations.