Mathematical Problems in Engineering

Volume 2018, Article ID 9714901, 10 pages

https://doi.org/10.1155/2018/9714901

## Seepage Flow Model and Deformation Properties of Coastal Deep Foundation Pit under Tidal Influence

Geotechnical and Structural Engineering Research Center, Shandong University, Shandong, China

Correspondence should be addressed to Can Xie; moc.361@udsnaceix

Received 6 January 2018; Revised 12 February 2018; Accepted 11 March 2018; Published 16 April 2018

Academic Editor: Qin Yuming

Copyright © 2018 Shu-chen Li 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

As the coastal region is the most developed region in China, an increasing number of engineering projects are under construction in it in recent years. However, the quality of these projects is significantly affected by groundwater, which is influenced by tidal variations. Therefore, the regional groundwater dynamic characteristics under tidal impact and the spatiotemporal evolution of the seepage field must be considered in the construction of the projects. Then, Boussinesq function was introduced into the research to deduce the seepage equation under tidal influence for the coastal area. To determine the spatiotemporal evolution of the deep foundation pit seepage field and the coastal seepage field evolution model, numerical calculations based on changes in the tidal water level and seepage equation were performed using MATLAB. According to the developed model, the influence of the seepage field on the foundation pit supporting structure in the excavation process was analyzed through numerical simulations. The results of this research could be considered in design and engineering practice.

#### 1. Introduction

Groundwater seepage significantly impacts the stability of foundation pit engineering and the deformation of the foundation pit support structure and, hence, is a major factor in several foundation pit engineering accidents [1–3]. Based on the generalized Darcy law, Atangana and Vermeulen [4] derived a new equation for groundwater flow and obtained an asymptotic analytical solution of the generalized groundwater flow equation by the Frobenius and Adomian decomposition method. And the feasibility of the solution was verified through comparisons with field test results. Finally, Atangana and Vermeulen further presented a proposition for reducing uncertainties in groundwater study. In order to investigate the influences of seepage field on mechanical property, Wang [5] developed a 3-Dimensional Stochastic Seepage finite element model and proposed a more comprehensive stochastic algorithm to analyze seepage field problems. Qiu et al. [6] established a statistical model and an artificial wavelet neural network model so as to improve predication accuracy.

To explore the impact of changes in seawater tides on variations in groundwater levels, Jacob [7] first established a one-dimensional tidal seepage equation. The equation could be used to fit the movement of seawater by using the sine trigonometric function or cosine trigonometric function. Jeng et al. [8] established a new groundwater seepage model by considering the dynamic effects of the phreatic aquifer on the head fluctuations in the confined aquifer and accordingly derived a closed-form analytical solution. In contrast to the previous solutions, the newly developed solution could describe the interaction effect between tidal oscillations and semiconfined/phreatic coastal aquifers. Li et al. [9] constructed a two-dimensional permeability model of coastal tides by using the boundary element method. They demonstrated that the groundwater amplitude decreased compared with the tide amplitude and the vibration phase was also deferred. Zhang et al. [10] considered the mechanical properties and seepage characteristics of aquifers to explore the interaction between the water level and seepage flow and to express the relationship between confined groundwater and tides using a mathematical equation. Numerous theories exist to describe the seepage of water. Guo [11] investigated a multilayer aquifer system comprising an upper weak permeable layer, a lower weak permeable layer, and a confined aquifer. According to the premise that the boundary between the sea and land is vertical, a mathematic model of groundwater level fluctuation with tides was established and an analytical solution was determined.

Numerous theories exist to describe the seepage of water. In particular, the Boussinesq equation has been widely employed [12–17]. Nielsen [12] analyzed the relationship between the inland average water table and tidal amplitude and solved the question of tidal dynamics on a sloping beach on the basis of the Boussinesq equation and a field monitoring test. A new Boussinesq equation was proposed and a set of formulae for groundwater recession was derived to use for groundwater flow in confined and unconfined aquifers [14]. Li et al. [15] presented a new method to improve the discontinuous boundary condition of the Boussinesq equation. The method is useful for handling the moving boundary condition by replacing the Boussinesq equation with an advection–diffusion equation with an oscillation velocity. Teo et al. [17] analyzed the effect of tidal fluctuation on the groundwater level and developed a new parameter to replace the factor of tilted shores.

It is suffice to note that foundation pit engineering in coastal areas and inland areas significantly differs in the influence of groundwater levels. In coastal areas, the groundwater level is directly affected by the tidal properties outside the pit. Because seepage characteristics may be different from the steady supply of the groundwater level, it is crucial to explore the seepage characteristics around a deep foundation pit under a tidal dynamic cycle. Therefore, this research proposes a seepage equation under tidal influence according to the Boussinesq function. To explore the deformation properties of the supporting structure in a deep foundation pit under tidal impact, a spatiotemporal evolution model of the seepage field was established in accordance with the onsite water level monitoring results of a deep foundation pit in a coastal area. In addition, a finite difference simulation software program was used to simulate the excavation process of the pit.

#### 2. Seepage Flow Model

##### 2.1. Seepage Equation

A side of a deep foundation pit near the coast was chosen because of its significant tidal impact. The following assumptions were made: (1) the seepage field has a gradually varied horizontal flow; (2) changes in the vertical seepage velocity are ignored because the vertical seepage velocity is much smaller than the horizontal seepage velocity; (3) the external precipitation recharge on the free surface is ignored. Because the tide level changes over time, the partial derivative with respect to time should be preserved in the study to explore the time–space evolution characteristics of the seepage field under tidal influence. It is supposed that the bottom bedrock of the pit is impermeable and no water-resisting layer exists among the backfill layers above the bedrock. The normal direction of the pit is the -axis, the coastline is set as the origin of the -axis, and the direction from the coastline to foundation pit is the positive direction of the -axis. An unstable flow has been previously introduced [18–20]:

Here, is the permeability coefficient, is the gravitational specific yield and empirical value of is 0.23, is the seepage time, is the seepage distance, and is a function of the seepage field free surface.

According to assumptions that (1) the distance from the foundation pit boundary to coastline is meters; (2) the function is introduced to calculate the tide accords; and (3) on the impermeable plane, as shown in Figure 1, since there are water-stop curtains around the foundation pit and the support structure is impermeable, the boundary condition at is obtained. That is, . Then, the boundary conditions of the seepage model can be expressed as follows: