In actual engineering practice,the stress increment within a composite foundation caused by external loads may vary simultaneously with depth and time.In addition,column installation always leads to a decay of soil permeability towards the column.However,almost none of the consolidation theories for composite foundation comprehensively consider these factors until now.For this reason,a stress increment due to external loads changing simultaneously with time and depth was incorporated into the analysis,and three possible variation patterns of soil’s horizontal permeability coefficient were considered to account for the detrimental influence of column installation.These three patterns included a constant distribution pattern(Pattern I),a linear distribution pattern(Pattern II),and a parabolic distribution pattern(Pattern III).Solutions were obtained for the average excess pore water pressures and the average degree of consolidation respectively.Then several special cases were discussed in detail based on the general solution obtained.Finally,comparisons were made,and the results show that the present solution is the most general rigorous solution in the literature,and it can be broken down into a number of previous solutions.The consolidation rate is accelerated with the increase in the value of the top to the bottom stress ratio.The consolidation rate calculated by the solution for Pattern I is less than that for Pattern II,which in turn is less than that for Pattern III. In actual engineering practice, the stress increment within a composite foundation caused by external load may vary with with depth and time. In addition, column installation always leads to a decay of soil permeability towards the column. However, almost none of the consolidation theories for composite foundation comprehensively comprehensively consider these factors until incorporated into the analysis, and three possible variation patterns of soil’s horizontal permeability coefficient were considered to account for the detrimental influence of column installation.These three patterns included a constant distribution pattern (Pattern I), a linear distribution pattern (Pattern II), and a parabolic distribution pattern (Pattern III) .Solutions were obtained for the average excess pore water pressures and the average degree of consolidating.Then several special cases were discussed i n detail based on the general solution obtained. Finaally, comparisons were made, and the results show that the present solution is the most general rigorous solution in the literature, and it can be broken down into a number of previous solutions. consolidation rate is accelerated with the increase in the value of the top to the bottom stress ratio. The consolidation rate calculated by the solution for Pattern I is less than that for Pattern II, which in turn is less than that for Pattern III.