Analytical solution for vacuum preloading considering the nonlinear distribution of horizontal permeability within the smear zone

<div><p>The vacuum preloading is an effective method which is widely used in ground treatment. In consolidation analysis, the soil around prefabricated vertical drain (PVD) is traditionally divided into smear zone and undisturbed zone, both with constant permeability. In reality, the permeability of soil changes continuously within the smear zone. In this study, the horizontal permeability coefficient of soil within the smear zone is described by an exponential function of radial distance. A solution for vacuum preloading consolidation considers the nonlinear distribution of horizontal permeability within the smear zone is presented and compared with previous analytical results as well as a numerical solution, the results show that the presented solution correlates well with the numerical solution, and is more precise than previous analytical solution.</p></div

Schematic diagram of the vacuum preloading method with a PVD.

<p>Schematic diagram of the vacuum preloading method with a PVD.</p

Permeability coefficient of the present model and the numerical analysis when δ = 0.55.

<p>Permeability coefficient of the present model and the numerical analysis when δ = 0.55.</p

Solutions of Rujikiatkamjorn et al.[11], the present model, and the numerical analysis.

<p>Solutions of Rujikiatkamjorn et al.[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139660#pone.0139660.ref011" target="_blank">11</a>], the present model, and the numerical analysis.</p

Smear zone permeability coefficient curve based on data from Iyathurai et al.[24] and the proposed model.

<p>Smear zone permeability coefficient curve based on data from Iyathurai et al.[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139660#pone.0139660.ref024" target="_blank">24</a>] and the proposed model.</p

Parameters used in the analytical solution and the numerical model.

<p>Parameters used in the analytical solution and the numerical model.</p

Permeability coefficients of the present model and numerical analysis (δ = 0.45) and of the study by Rujikiatkamjorn et al.[11].

<p>Permeability coefficients of the present model and numerical analysis (δ = 0.45) and of the study by Rujikiatkamjorn et al.[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139660#pone.0139660.ref011" target="_blank">11</a>].</p

Cordycepin (10 μg/ml) inhibited NF-кB signaling pathway activated by LPS treatment.

<p>(A) The p65, IкBα and p-IкBα protein expression in the cytoplasm in the cultures under cordycepin treatment with or without LPS stimulation. (B-D) The relative optical densities of p65, IкBα and p-IкBα protein bands to control, normalized to β-actin. (E) The p65 expression in the nucleus in the experimental groups. (F) The relative optical densities of p65 protein bands to control, normalized to HDAC1. Data were presented by mean ± SEM. *p < 0.05, #p < 0.01.</p

Cordycepin treatment (10 μg/ml) could repair the LPS-induced injuries of neurite sprouting and outgrowth.

<p>The hippocampal neurons were cultured for 7 day in the different conditioned mediums of the experimental groups. (A) Typical hippocampal neurons with extending neurites in the culture in different experimental groups, stained for MAP-2. The neurite sprouting and outgrowth were characterized by the number of primary dendrites per cell (B), number of dendritic end tips (C) and the average neurite length (D) in the experimental groups. (E) Western blot analysis of GAP-43 expression in the cultures of different groups. (F) Relative optical densities of GAP-43 show in (E) (n = 3/group). Data were presented by mean ± SEM. * p < 0.05, #p < 0.01.</p

Cordycepin (10 μg/ml) rescued the LPS-induced impairments of GCs.

<p>The hippocampal neurons were cultured for 1 day in the different conditioned mediums of the experimental groups. (A) Representative fluorescence images of the hippocampal GC stained for actin, tubulin and merge of the two staining. Scale bar = 20 μm. (B) Relative area of GCs to control. (C) Average number of filopodia emerging from GCs. (D) Average filopodium lengths from the tip of each filopodia to the edge of the GCs. (E) Ratio of number of filopodia and area of GC in GCs. Data were presented by mean ± SEM. * p < 0.05.</p