Advances in Civil Engineering

Volume 2019, Article ID 5329795, 7 pages

https://doi.org/10.1155/2019/5329795

## The Settlement Models of Deep Vacuum Dewatering Method

School of Engineering & Technology, China University of Geosciences, Beijing 100083, China

Correspondence should be addressed to Jianguo Lyu; nc.ude.bguc@gjl

Received 4 July 2018; Revised 21 November 2018; Accepted 4 December 2018; Published 14 March 2019

Academic Editor: Emilio García-Taengua

Copyright © 2019 Feng Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The deep vacuum dewatering method is effective for groundwater control in projects. By now, although the vacuum consolidation in soft soil foundation treatment has been analyzed much, the settlement of deep vacuum dewatering has not been researched sufficiently. Because of the extra vacuum pressure, the settlement should be analyzed further. In this paper, the settlement models are derived and analyzed based on the 2 vacuum pressure distribution models (plane seepage model and Johnson’s model), Imai and Chai’s vacuum consolidation models, and elastic model of traditional soil mechanics. And then a project case is provided to verify the theoretical models. The results show that the proposed model is suitable to predict the settlement and provide new references for vacuum dewatering engineering.

#### 1. Introduction

Vacuum consolidation has been extensively applied [1–6] and proved very effective in improving soft ground [7, 8]. Vacuum consolidation usually applies a vacuum pressure into soil and a sealing membrane at the surface of the ground. It is very different from Terzaghi’s consolidation theory for the isotropic additional stress caused by vacuum pressure. Therefore, the settlement of soft soil foundation caused by vacuum pressure has been researched in theoretical, numerical, laboratorial, and practical ways. Chai et al. [9] proposed a method of determining the vacuum-drain consolidation based on unit cell finite element analysis results and proved the method at Tokyo Bay in Japan. Chai et al. [10] also developed a method for the consolidation of dredged mud or clayey soil deposits containing prefabricated horizontal drains (PHDs). Chen and Xiang [11] carried out a theoretical analysis of the settlement of the piles caused by vacuum treatment of the submerged layer, which indicated that the settlement caused by dewatering increased the negative frictional resistance of the pile and increased the settlement. Robinson et al. [12] studied the influence of lateral displacement of soil volumetric strain under vacuum preloading. Then, the lateral displacements of soil under different stress states were analyzed, and the prediction model of volume strain and lateral displacement was proposed, which was validated by 2 projects in China.

Rujikiatkamjorn et al. [13] presented numerical analysis of a combined vacuum and surcharge preloading project in China. The simulation analyzed the settlement of the soil by modified Cam-clay model. Indraratna et al. [14] carried out the simulation of vacuum consolidation using finite element. Subsequently, the vertical displacements were predicted by the 2D and 3D numerical multidrain model. Ji et al. [15] analyzed the surface settlement of vacuum preloading of reclamation sludge foundation by using the finite difference method.

Saowapakpiboon et al. [16] conducted large-scale consolidation experiments on soil samples with and without vacuum pressure, and then the geotechnical parameters of the soil were analyzed. Kianfar et al. [17] investigated the influences of the duration of application and removal of vacuum pressures on radial consolidation by using excess pore-water pressure, axial strain, and over consolidation ratio. Long et al. [18] conducted trial sections to investigate the soft ground improvement performance using different vacuum consolidation methods. Sun et al. [19] analyzed a site trial of vacuum preloading and vacuum preloading in combination with electro-osmotic. The physical mechanical properties and bearing capacity of soil after treatment were tested, which revealed the consolidation law of vacuum preloading and the combination method.

Many results have been obtained and some of them were used in practice. However, the thickness of soil needs to be considered in deep well dewatering project since it is usually larger than in foundation treatment project because the dewatering wells are deep in tunnel excavation. Thus, there is a need to investigate the suitable consolidation model to predict the surface settlement of deep vacuum dewatering method. Because of the capillary force in silty and clay soil, there is still much water that cannot be drained out by the nonvacuum dewatering method. As a result, the deep vacuum dewatering wells are usually applied in tunnel and deep foundation pit excavation. However, there is no specific consolidation model by now to calculate the settlement in the deep vacuum dewatering method. In this paper, 3 methods are proposed based on Imai’s model, Chai’s model, and elastic model. Then, a project case is provided to verify the theoretical models.

#### 2. Vacuum Pressure and Water Level Distribution in Vacuum Dewatering

It is needful to use the vacuum pressure distribution laws in deriving the theoretical settlement model. Therefore, 2 models of air pressure distribution in soil are proposed. One is the plane seepage model [20] and the other one is Johnson’s model [21], which are shown as equations (1) and (2), respectively:where = distance from the well, = air pressure at distance of , = measured air pressure at the known distance of , = the radius of the well, = air pressure of the well, = absolute ambient pressure, and = largest influence distance of vacuum pressure.

The water level, *h*_{vac} (equation (3)), in flow boundary condition has been established by the author [20]:where *h*_{phreatic} = water head, *R* = influence radius of dewatering, = atmosphere pressure, and = thickness of aquifer.

The water level distribution law under the vacuum pressure derived by the authors was used to calculate the final draw down of the groundwater in this paper. Then, the water level distribution models were combined to three existing consolidation models to analyze the vacuum settlement.

#### 3. Modified Imai’s Method

Imai [22] proposed a method of calculating the final settlement and lateral displacement in vacuum consolidation. It is assumed that the vacuum pressure *p*_{vac} keeps stable in soil and affects the active earth pressure. The increase of effective stress, Δ*σ*_{vac}, is equal to vacuum pressure in both vertical and horizontal directions. At this time, the effective stress in horizontal direction will be reduced to (*K*_{a} is active earth pressure coefficient) from . The effective stresses in vacuum condition are shown as follows:where = vertical effective stress without vacuum pressure, = vertical effective stress in vacuum field, and = horizontal effective stress in vacuum field.

Equations (6) and (7) present the changes of effective stress:

*I* is defined as the ratio of the change of effective stress in horizontal and vertical direction in the following equation:

The vertical and horizontal strains in consolidation area are shown in the following equations:where, *a*_{v}, *a*_{h,} and *m*_{v} are presented in the following equations:where *E* = elastic modulus.

It is also proposed that the lateral displacement will not happen when *I* *=* *K*_{0}. Equation (14) can be obtained at the depth where there is no lateral displacement:

If the depth calculated from equation (14) is larger than the well’s depth, *I* can be changed into the following equation:where *z* = distance from ground surface and *H* = consolidation depth of vacuum well.

Based on the groundwater distribution in flow boundary condition, the thickness of the consolidation (*H*_{Imai}) after draw down will be

Thus, the vertical displacement of the soil above the water surface in vacuum dewatering method can be derived based on Imai’s method. Imai’s solution is proposed in equations (17) and (18) based on plane seepage model and Johnson’s model, respectively:where = vacuum pressure of plane seepage model and = vacuum pressure of Johnson’s model.

#### 4. Modified Chai’s Method

Chai and Carter [22] believed that when the vacuum pressure is larger than the stress needed to keep *K*_{0} status, the lateral displacement will happen and the vertical displacement will be less than that without vacuum. Otherwise, there is no lateral displacement and the settlement will not be affected. The vertical strain of vacuum consolidation model is shown as follows:where *λ* = compression index, *e* = porosity ratio, and *p* = consolidation stress. *α* = *α*_{min} at the ground surface and *α* = 1 when (*z*_{l} is the depth where there is no lateral displacement) or . However, ifwhere , *ϕ* = effective friction angle, OCR = over consolidation ratio, and *α*_{min} = *α*_{min−T} or *α*_{min} = *α*_{min−P} in triaxial stress condition and plane strain condition. *α*_{min−T} = 0.8 and proposed by experimental results.

#### 5. Elastic Method

Soil is assumed elastic in the elastic method. When the air extraction is performed in the dewatering well, the air pressure in the pores of the soil will be reduced. At this time, the pressure difference between the atmospheric pressure at the ground surface and the pressure in the soil leads to a compression, resulting in settlement. The soil above the original phreatic water surface can be considered as a sealing layer. Boussinesq [23] used the elastic theory to derive the analytical solution of the stress at any point *M* (shown in Figure 1) when the vertical concentrated force (*P*) acts on the surface of the semi-infinite space elastomer.