Clay-based materials are widely used in practice of contaminant control. Diffusion coefficient is one of the most important parameters of clay. It is usually determined by fitting the data of one-dimensional convection-diffusion soil column tests. Zero concentration boundary, zero concentration-gradient boundary and semi-infinite boundary are discussed. A unified boundary condition is proposed. By transforming and introducing auxiliary problems, unified convection-diffusion-adsorption analytical solutions for three boundary conditions are acquired. Both difference between these analytical solutions and data-fitting errors are investigated. The results show that different boundaries should correspond to different conditions in the bottom of a column test. Cauchy boundary can be regarded as an unified form of all these boundaries. The calculated results corresponding to these boundaries are equivalent before breakthrough, however, the results become quite different in the bottom of the column after breakthrough. The concentration decreases as Cauchy parameter increases. The bigger the Cauchy parameter is, the more dominant role the diffusion effect plays in the solute transport process, at the same time, the bigger the concentration gradient at the bottom is. Fitting the data of a semi-infinite boundary test using analytical solutions of zero concentration boundary and zero concentration-gradient boundary will overestimate 15% and underestimate 9% of the result, respectively. It is essential for data fitting to choose an analytical solution according to convection-diffusion proportion and concentration-gradient at the bottom of a soil column.