# A Siphon Drainage Method for Consolidation of Soft Soil Foundation
## 3 Numerical Simulation of Feasibility of Siphon Drainage in Soft Soil Consolidation  
### Numerical Models  
In order to verify the feasibility of siphon drainage in soft soil consolidation, numerical simulations are conducted. The software ABAQUS is used to simulate the siphon drainage to deal with the water level change. The water-soil coupling finite element model of soft soil foundation drainage is established based on [PERSON]'s consolidation theory. In addition, the influences of drain spacing \(d\) and soil permeability on the effect of siphon drainage are also studied. Siphon pipes are the main tools for siphon drainage, and will be arranged with a large amount in a soft soil foundation. In the numerical model, it is assumed that the siphon drainage holes are arranged in a square form, and the drawdown of the water head in each siphon hole is the same. When solving the groundwater level, according to the mirror image method and the superposition principle of the planar seepage theory, for the problem of equal-flow group wells working at the same time in an infinite aquifer, it can be equivalent to a single well in a rectangular aquifer whose boundary is a water-resistant boundary question. Therefore, a single drainage element whose side length is the well spacing can be used to simulate the situation of large-scale precipitation after setting the boundary as an  
Figure 2: Schematic diagram of siphon drainage profile structure in soft soil. impermeable boundary (see Figure 3). According to the principle of symmetry, the seepage field between adjacent drainage holes has a symmetrical distribution in the homogeneous soft layer, which means that the flow at the middle of each drainage hole does not flow horizontally. Therefore, with respect to a single siphon drainage hole, the position of the midpoint between holes can be regarded as an impermeable boundary, and the area within the boundary range is the corresponding influence range of the drainage hole. Thus, when the drainage holes are arranged in a square, the analyzed zone of the numerical model can be set as the square columnar area around the drainage hole with a distance d between two adjacent holes. The mesh schematic of the model is shown in Figure 4.  
The conditions of the numerical model are set as follows: (a) The surrounding sides of the model constrain the movement in the horizontal direction; (b) The bottom of the model constrains the movement in both horizontal and vertical directions; (c) The side walls of the drainage holes constrain the movement in the horizontal direction; (d) The bottom and the surroundings of the model are impermeable boundaries, through which the flow rate equals zero; (e) The side walls of the drainage holes are drainage boundaries. Considering  
Figure 4: Mesh schematic of the model. Figure 3: Square arrangement of siphon drainage holes. that the siphon lift is limited by atmospheric pressure, the water level drop in the drainage holes is set to 10 m.  
In the numerical model, the vertical thickness of the aquifer, that is, the vertical height of the model, is taken as 20 m. The horizontal direction of the model is a square whose side length is the drainage well spacing \(d\). The drainage hole is located in the middle, and the radius is 0.03 m. The analysis step is taken in 1 day, and there are 100 days in total. Different drain spacing (0.8 m, 1 m, 1.5 m, and 2 m) and soil permeability (\(1\times 10^{-7}\) cm/s, \(2\times 10^{-7}\) cm/s, \(5\times 10^{-7}\) cm/s, and \(1\times 10^{-6}\) cm/s) are adopted in the numerical simulations. The soil model adopts the modified Cambridge model. Due to symmetry, there is no water flow on the side of the model, which is set as an undrained boundary. The bottom of the model is considered to be an impermeable layer, which is also set as an undrained boundary. Since the flow velocity of the siphon is much greater than the speed at which water collects into the siphon drainage hole, the side wall of the siphon drainage hole is a free drainage boundary.