Consolidation and Load Transfer Characteristics of Soft Ground Improved by Combined PVD-SC Column Method Considering Finite Discharge Capacity of PVDs

Abstract

Prefabricated vertical drains (PVDs) can be installed with soil cement (SC) columns to enhance the efficiency of soft soil improvement. In this combined method, PVDs are first installed and then SC columns are established between the PVDs; this enables a larger spacing between SC columns resulting in a lower construction cost. As an embankment load is applied on composite foundation, time-dependent behavior occurs in the soft soil due to consolidation according to the radial flow toward PVDs, while the corresponding stress transfer takes place between the SC columns and the soft soil. This paper develops an axisymmetric finite element model to analyze the consolidation and stress transfer behaviors of composite foundation, in which an equivalent permeability of subsoil is proposed considering the effects of finite discharge capacity of PVDs. The developed model is applied to an embankment located in China to estimate the settlement of soft ground improved by the combined method. Subsequently, the current numerical model is applied to investigate consolidation characteristics and the stress transfer mechanism of composite foundation. The results show that the consolidation of soils can cause significant effects on the stress transfer process and the stress concentration ratio of the composite ground. The stress concentration mobilizes with the depth over time and stabilizes around the middle of the treated soil when the consolidation time exceeds 50 days. The magnitude of drain discharge capacity also contributes significantly to mobilizing stress concentration in the composite foundation.

Appendix. Derivation of Eq. 3

Based on Barron’s solution [31], the average degree of consolidation of PVD-improved soft soil considering smear zone and well-resistance effects was developed by Yoshikuni and Nakanodo [47] as follows:

$$U = 1 - \sum\limits_{i = 1}^{\infty } {\frac{2}{{M^{2} }}} e^{{ - \beta_{i} t}}$$

(8)

where $\beta_{i}$ is expressed as:

$$\beta_{i} = \frac{{M^{2} }}{{H^{2} }}\frac{{k_{v} E_{s} }}{{\gamma_{w} }} + \frac{2}{{\mu r_{e}^{2} }}\frac{{k_{h} E_{s} }}{{\gamma_{w} }}$$

(9)

where

$$\mu = \ln \frac{n}{s} + \frac{{k_{h} }}{{k_{sm} }}\ln s - \frac{3}{4} + \pi z\left( {2H - z} \right)\frac{{k_{h} }}{{q_{w} }}$$

(10)

In the above equations, $\gamma_{w}$ is unit weight of water; $E_{s}$ is compression modulus of soil; k_v and k_h are permeability of subsoil in vertical and horizontal direction, respectively; k_sm is permeability coefficient of subsoil in disturbed zone due to PVD installation; $M = (i - 1{/}2)\pi$, i = 1, 2, 3, ….; $n = r_{e} {/}r_{w}$; $s = r_{s} {/}r_{w}$; r_e is radius of influence zone (unit cell); r_w is equivalent radius of vertical drain, r_s is radius of smear zone; H is drain length of PVD; z is a certain depth of soil; q_w is PVD discharge capacity.

Ye et al. [29] established the analysis unit cell of composite foundation, in which the zones were partitioned as shown in Fig. 1. The influence zone included a single SC column enclosed by surrounding soil and PVDs were converted in to drain wall. The overall average degree of consolidation of unit cell with drain wall was then obtained as follows:

$$U_{dwall} = 1 - \sum\limits_{i = 1}^{\infty } {\frac{2}{{M^{2} }}} e^{{ - \beta_{i} t}}$$

(11)

In Eq. (11),

$$\beta_{i} = \frac{{M^{2} }}{{H^{2} }}\frac{{k_{v} E_{s} }}{{\gamma_{w} }} + \frac{8}{{r_{e}^{2} }}\frac{{k_{h}^{{eq^{\prime}}} E_{s} }}{{\gamma_{w} }}$$

(12)

where $k_{h}^{{eq^{\prime}}}$ is equivalent horizontal permeability for the unit cell model considering the well resistance of PVD. In this paper, $k_{h}^{{eq^{\prime}}}$ is established to consider PVD discharge capacity and can obtained from making the same Eq. (8) with Eq. (11). Therefore, the equivalent permeability of subsoil in unit cell with equivalent drain zone can then be expressed as Eq. (3).