راه حل کلی برای تثبیت خاک چند طبقه با سیستم زهکشی عمودی

ABSTRACT General solutions for consolidation of multilayered soil with a vertical drain system

Preloading is widely used to improve soft ground, and vertical drains are usually installed to accelerate the consolidation of soils in preloading (Artidteang et al., 2011; Cascone and Biondi, 2013; Chai et al., 2008, 2010; Indraratna et al., 2010, 2011, 2012; Karunaratne, 2011; Lin and Chang, 2009; Lo et al., 2008; Saowapakpiboon et al., 2009, 2010, 2011). The shear strength of soil can be increased and the post-construction foundation settlement can be eliminated significantly due to consolidation (Almeida et al., 2013; Chai and Duy, 2013; Dash and Bora, 2013; Elsawy, 2013; Rowe and Li, 2005; Rowe and Taechakumthorn, 2008). For consolidation of a homogeneous soil with a vertical drain, many analytical solutions have been proposed based on various assumptions and considerations (Abuel-Naga et al., 2012; Bari and Shahin, 2014; Barron, 1948; Castro and Sagaseta, 2013; Chai et al., 2001; Conte and Troncone, 2009; Deng et al., 2013; Geng et al., 2011, 2012; Indraratna et al., 2011; Hansbo, 1981; Hu et al., 2014; Leo, 2004; Ong et al., 2012; Onoue, 1988b; Rujikiatkamjorn and Indraratna, 2009; Tang and Onitsuka, 2000; Yoshikuni and Nakanodo, 1974; Zeng and Xie, 1989; Zhu and Yin, 2001, 2004; among others). However, natural sediments are rarely homogeneous and usually consist of several different soil layers.

For consolidation of layered soil with a vertical drain, only a limited number of analytical solutions are available in literature. Xie (1995) proposed a solution for consolidation of two-layered soil with an ideal drain (i.e., without drain resistance and smear actions) by using the method of separation of variables. Tang and Onitsuka (2001) and Wang and Jiao (2004) extended this solution to include drain resistance and smear effects. On this basis, Tang et al. (2013) have recently proposed a solution for consolidation of threelayered soil. Although the solution is precise, it has been proven to have some convergence problems (Tang et al., 2013). By simply using the method of separation of variables, it is difficult to extend the solution to consolidation of soils of four or more layers. For arbitrarily multilayered soil, Rujikiatkamjorn and Indraratna (2010) proposed a solution for purely radial consolidation based on the soil slice (instead of soil element) flow continuity equations, which are similar to that developed by Hansbo (1981). Vertical drainage conditions were neglected. Nogami and Li (2003) used the matrix transfer method to formulate the consolidation behavior of soil with a system of horizontal thin drains and a vertical drain. However, smear effect and drain resistance were not considered in their solution. Walker and Indraratna (2009) and Walker et al. (2009) used the spectral method to obtain a solution for consolidation of multilayered soil based on a lumped governing equation derived from the soil slice flow continuity, but drain resistance was ignored. Moreover, a transcendental equation is usually involved in the available analytical solutions for consolidation of layered soil. The most difficult part of the solutions is calculating, without missing, eigenvalues or eigenvectors from the zeros of transcendental equation.

In this note, a powerful Laplace transform and its numerical inverse technique is used to formulate the consolidation behavior of arbitrarily multilayered soil with a vertical drain. The assumptions and flow continuity conditions involved are same as those applied to two-layered soil by Tang and Onitsuka (2001) and threelayered soil by Tang et al. (2013). Radial and vertical drainage conditions, as well as drain resistance and smear effects, are considered. An explicit quasi-analytical solution is derived for calculating excess pore-water pressure and the degree of consolidation. The validity and accuracy of this solution are verified against a finite-element solution for two-layered soil, and an analytical solution derived for single-layered soil by Tang and Onitsuka (2000). Moreover, the consolidation behavior of a fourlayered soil with a vertical drain system is investigated.