# Datasets for validity of a vertical drain system as a lumped model

## Description

The dual-porosity medium includes the natural/irregular and the artificial/regular (figure 1), and latter is applied more and more in our engineering practice, e.g. a vertical drain system. Figure 2 shows that the structure of the drain system and their terminology. Based on heat-conduction theory, the lumped model was applied to a derivation process in order to acquire a quasi-thermodynamics solution involving some parameters such as Biot number (BiV) and Fourier number (FoV). The universality of the solution make it also applicable to the dual-porosity medium problem. An analogy graph to the vertical drain system was shown in Figure 3. In order to further analysis, the deconstruction of the vertical drain system is performed to divide the system into both parts of an external convective environment (drain wells) and an internal conductive medium (soil matrix) as shown in figure 4. The effective permeability coefficient keff(s), relevant to the drainage behavior of external expel facility, was derived and analyzed based on the graph of deconstruction (figure 5a). Comparing it with the equivalent permeability coefficient keq, which is represented the hydraulic conductive behavior of internal soil matrix, was performed. The convergent relationship between both of permeability coefficients was evaluated through the ratio of keff(s) and keq. A further analysis was carried out to the equivalent permeability keq under consideration of the effects of curvature and divergence, respectively, as shown in figure 6. Figure 7 shows the variation of BiV number with drain spacing ratio n-value to indicate the validity of a vertical drain system as a lumped model. All of above data were calculated through software of Matlab R2015a before they were made the series of graphs. A series of discussion was performed to demonstrate graphically the dissipation process of excess pore pressure of a drain well solved by analytical solution (figure 8) and a comparison between analytical solution and numerical was given in figure 9. Finally, a numerical simulation (figures 10 and 11) by use of FLAC3D5.0 software was carried out for visualizing the process of excess pore pressure dissipation better. The raw data for all above figures produced by aid of calculation software are listed in the dataset specified in the next section of this article. For convenient indexing, they are named in the form of ×××.data_for_fig.number with the ＊.csv file type.