Analytical solutions for consolidation of composite foundation with multiple drains considering clogging effect

The composite foundation with multiple drains can be combined with different drainage bodies to accelerate the consolidation of foundation，and the multiple drains will clog inevitably during consolidation. However，there is no analytical consolidation theory of composite foundation with multiple drains that can consider the clogging effect. Based on this，the mathematical model with an exponentially decaying well resistance over time and four layout forms are introduced to establish the consolidation model of composite foundation with multiple drains combining stone columns with prefabricated vertical drains(PVDs). Considering the radial two-way seepage to stone columns and PVDs in the foundation soil and smear effect，based on the assumption of equal strain，the consolidation analytical solutions of composite foundation with multiple drains considering stone columns clogging and PVDs clogging are given respectively，using mathematical and physical methods such as the method of separated variables and the orthogonality of Fourier functions. The rationality and practicability of the solutions are verified by theoretical degradation and case comparison. The consolidation behavior is analyzed，and the following conclusions manifest：Considering the clogging effect will slow down the consolidation rate of the composite foundation，especially the clogging effect of the stone columns. If the final drainage capacity is reduced or the exponential attenuation factor of permeability coefficient is increased，the consolidation rate will slow down. The final drainage capacity has a great influence on the later stage of consolidation，with minimal influence on the early stages，while the influence of exponential attenuation factor on the whole stage of consolidation is relatively balanced. When the initial permeability coefficient of stone columns is low，the clogging effect exhibits a greater influence on consolidation，whereas when the initial permeability coefficient of PVDs is large，the clogging effect has a greater impact. Considering the clogging effect，the dissipation of soil pore pressure slows，and the influence of stone columns clogging on soil pore pressure is stronger than that of PVDs.