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In this paper, the seepage finite element method (FEM) is used to simulate the transient seepage of Beijiang Dike, and antiseepage solutions are designed and discussed. By comparing the measured data of a piezometer with the steady-state calculation model, the calculated results are compatible very well with the measured data. Aiming to improve the ability to respond in extreme weather conditions, we calculate the transient seepage field after the water level suddenly rises in a short time and then select the relief well as the antiseepage measure and optimize it. The results show that when the water level is 15.78 m, the slope reaches 0.5, and the embankment is damaged. With the increase of penetration depth, the effect of drainage and decompression in the depth of 3/5 and 4/5 is relatively small due to geological strips. Due to different geological conditions, the same relief wells are placed in different positions with a wide gap in effect, the antiseepage effect is the best when the horizontal distance is 95 m, and the effect is the best when the depth is 16.5 m. The research results can be used to guide the seepage prevention and control design of Beijiang Dike.

Embankment engineering is the foundation of the flood control engineering system and an important barrier against flood [

Seepage analysis is a study of fluid mechanics, geotechnical mechanics, and other interdisciplinary fields. In 1856, French scholar Henry Darcy used a vertical circular pipe to conduct sand seepage experiment, which was the first seepage analysis method. Then, he proposed Darcy’s law [

The seepage analysis method of dike engineering mainly includes model experiment, numerical simulation, and data analysis [

Many scholars use the finite element analysis (FEA) method to simulate seepage in dike engineering. Moran [

In the simulation study of the antiseepage effect of the relief well, Zhang[

Located in the lower reaches of the Beijiang River, Beijiang Dike is an important barrier for the defence of the Xijiang and Beijiang floods in Guangzhou and is also a national first-class dike. The total population of the dike area is more than 5 million, and the cultivated land is 44.66 million square meters. It is one of the seven significant embankments in China. However, there are few safety analyses for it, especially in extreme weather. Therefore, this paper will adopt seepage finite element software to simulate the seepage field of Beijiang embankment instantaneously and verify it by comparing with the measured value of the pressure pipe.

As mentioned in the literature above, most of the current simulation analysis of relief wells is based on steady seepage field, which lacks the support for analysis of transient behaviour. Few studies have been carried out to calculate the change of seepage control effect of relief wells in the case of short-term water level surges. For the study of transient seepage fields, the dangerous water level at which the dike is about to be destroyed can be calculated. At the same time, the choice of the best relief wells also provides an excellent reference value for the difficult-to-test wells in practical engineering. Based on the transient seepage field, the influence of various design schemes of relief wells on the phreatic line and seepage flow rate is studied, and the optimal seepage control scheme of relief wells under the transient seepage field is obtained.

According to Darcy’s law, the seepage equation of porous media can be expressed as follows [

The differential formula of Darcy’s law is as follows:

According to the law of conservation of mass, it is generally believed that the mass of the fluid does not increase or decrease when it moves in the seepage field. It is assumed that there is fluid inflow in all directions of the unit body. The inflow rate is assumed to be

Velocity vector diagram and flow diagram of seepage unit.

The total seepage quantity in the cell can be calculated by superposition of the seepage quantity in

The change rate of a point with mass

According to the law of conservation of mass, formula (

Equation (

Equation (

Richard extended Darcy’s law to unsaturated seepage in 1931 and obtained the fundamental differential equation of unsaturated seepage：

When the hydraulic conductivity in the

If the permeability coefficient is isotropic and equal, equation (

Combining the continuity equation with Darcy’ law results in Poisson’s equation:

Although equations (

When the fluid is in turbulence, according to formula (_{s} is the unit storage capacity (1/

When the permeability coefficient is assumed to be isotropic, formula (

The gradient of homogeneous soil on permeable foundation can be calculated by the following formula.

Along the exudate,

This paper takes the Beijiang Dike as the research object and analyses the seepage field of the dike and the optimization of the antiseepage scheme of the relief well. The Beijiang Dike in Guangdong Province is located on the left bank of the lower reaches of the Beijiang River, with a total length of 63.346 km. It is a flood control barrier for Guangzhou and the Pearl River Delta. It belongs to the first-class levee of the China and is one of the seven levees guaranteed by the whole country. More than 90% of piping effect of Beijiang Dike is caused by seepage of embankment foundation. Flood hazards are mainly concentrated in the area of the pile number 7 + 000 – 10 + 980. In case of large floods, there are many dangers such as piping and sand bursting in pits, lowlands, ditches, and wells behind dikes. Some of them are very serious and need to be vigorously rescued to survive the floods. Therefore, seepage analysis is needed to solve related problems.

The seepage finite element analysis (FEA) method is used to model and analyze the 8 + 230 section of the Shijiao segment of Beijiang Dike. The height of the dike section is 17.85 m, the total length of the section is 181 m, the width of the top of the dike is 8.0 m, the ratio of the upstream batter is 1 : 3, the ratio of the downstream slope above the original road surface is 1 : 3, and the ratio of the downstream slope below the original road surface is 1 : 38. The Shijiao segment is built on a robust permeable layer about 15∼25 m thick. The cross section of the embankment is approximately trapezoidal, and the materials of the embankment body include silt, clay, silty clay, and artificial fill.

The upper layer of dike foundation is clay, and the lower is a strong permeable layer, which mainly includes fine sand layer, medium-coarse sand layer, and gravel layer. Assuming that the permeability of soil in the same region is uniform, it is an isotropic medium [

Model hydraulic conductivity table.

Material | Dam body | Fine sand layer | Medium-coarse sand layer | Gravel layer |
---|---|---|---|---|

Hydraulic conductivity K (cm/s) | 1.94 × 10^{−4} | 5.7 × 10^{−2} | 2.2 × 10^{−1} | 1.3 × 10^{−1} |

Schematic diagram of the embankment (unit: m). (a) Three-dimensional dike. (b) Typical section diagram of Shijiao segment.

For numerical simulation, it is necessary to determine the independence between the number of meshes used in the calculation and the results obtained, that is, to verify the grid independence. The outer river level is 11.38 meters, and the global element size of the grid is set to 0.7 m, 1 m, and 1.3 m. The measured value of the water head is provided by the Beijiang Dike administration department.

From Table

Grid independence validation (unit: m).

Pressure tube head | 0.7 m grid | 1 m grid | 1.3 m grid | Measured value |
---|---|---|---|---|

B0 | 11.38 | 11.38 | 11.38 | 11.38 |

B1 | 10.86 | 10.82 | 10.88 | 10.71 |

B2 | 10.24 | 10.2 | 10.18 | 10.17 |

B3 | 9.76 | 9.74 | 9.75 | 9.76 |

The validation of the model is mainly based on the comparison between the numerical simulation of the water head of the phreatic line and the actually measured water head of the piezometric pipe under four working conditions. It is known that three pressure measuring pipes are located at horizontal distances of 48 m, 134 m, and 181 m under the conditions of water level of 8.7 m, 9.54 m, 10.56 m, and 11.38 m in the outer river. The measured values of water head are shown in Table

Measured water level of the 8 + 232 piezometric pipe (unit: m).

Manometer number | 8.7 outer river level | 9.54 outer river level | 11.38 outer river level | 10.56 outer river level |
---|---|---|---|---|

B1 | 8.69 | 9.02 | 10.71 | 9.92 |

B2 | 8.53 | 8.99 | 10.17 | 9.76 |

B3 | 8.36 | 9.02 | 9.76 | 9.32 |

The boundary conditions of numerical simulation are as follows: the upstream water level is in the outer river, and the downstream water level is in the measured value of a B3 piezometer. The simulation results are shown in Figure

After obtaining the specific numerical simulation data, we compare the numerical simulation data with the actual value of the pressure tube and show it in the form of a graph. Figure

Numerical simulation results where the outer river water level is (a) 8.7 m, (b) 9.54 m, (c) 10.56 m, and (d) 11.38 m.

Through the analysis and comparison of Figure

Comparison between calculated head value and measured head value where the outer river water level is (a) 8.7 m, (b) 9.54 m, (c) 10.56 m, and (d) 11.38 m.

In this section, the transient state of Shijiao segment is simulated numerically. Then, the antiseepage measures and optimization of the use of the relief well are proposed for the dike. Through numerical simulation, we can analyze various embankment conditions including steady state, transient state, and antiseepage measures with relief wells, including phreatic line, seepage quantity, and gradient. The boundary conditions of the outer river level (upstream water level) are set in Table

Boundary conditions of the transient upstream water level.

Time (hour) | Outer river level (meter) |
---|---|

0 | 9.5 |

6 | 10 |

12 | 10.5 |

18 | 11.5 |

24 | 12.5 |

30 | 13.5 |

36 | 14 |

42 | 14.5 |

48 | 15 |

60 | 16 |

72 | 17 |

The most probable cause of embankment failure in practical engineering is the seepage damage. Under the seepage action of the dike body and foundation, soil particles are lost and local damage is deformed (such as piping or flowing soil) due to its mechanical or chemical action. The seepage of water will increase the phreatic of soil and decrease the suction of the matrix in the unsaturated area, thus increasing the possibility of slope instability. Especially, when the water level changes, the sudden rise and fall of the water level in the dam body will make the seepage stress in the soil body larger, which is easier to destroy the slope soil body. Therefore, the transient analysis of the embankment can better predict the water level when the embankment is damaged, which has a strong guiding significance for the safe operation of the embankment. In Figure

Transient numerical simulation of phreatic line variation.

From Figure

From Figure ^{−5} m^{3}/d. Higher safety measures should be taken when the same water level falls in the rain. With the increase of the water level, the seepage of the dam body increases gradually, and the gradient of dam body increases in a curve. When the water level is 15.78 m, the gradient reaches 0.5 [

(a) Changes in transient and steady-state seepage quantity. (b) Changes in transient gradient.

As one of the primary seepage control means, relief wells are widely used in dike engineering. Relief wells are often used in dikes and dams. If the design and construction are unreasonable or the operation and management are not good, the output of water will be small, the effect of decompression will be poor, and the safety of dikes will be endangered. Therefore, it is of considerable significance to study the location and penetration depth of relief wells.

We analyzed the relief well depths of 10 m, 11 m, 12.5 m, and 16.5 m and analyzed the relief wells with a penetration depth of 12.5 m at horizontal distances of 84 m, 94 m, and 114 m.

The higher the water level of the outer river, the higher the height of the phreatic line and the greater the risk of breaking dikes. As shown in Figure

Variation diagram of the phreatic line in numerical simulation of relief wells.

Variation diagram of phreatic line in numerical simulation of relief wells.

As shown in Figure ^{−10} m^{3}/d, which is remarkable when the seepage quantity is 10^{−5} m^{3}/d compared with that without the relief wells. It can be seen that if comprehensive factors such as economy and technology are not considered, the deeper the penetration depth of relief wells in different permeability coefficients, the better.

Seepage quantity of added relief wells. (a) Seepage quantity of relief wells with different depths. (b) Seepage quantity of relief wells with different positions.

In Figure ^{−10} m^{3}/d.

The geological variation of embankment foundation is great, the terrain is complex, and a lot of data are difficult to observe. This paper calculates the transient seepage field of the embankment by numerical simulation and chooses appropriate antiseepage measures of relief wells. Finally, different antiseepage schemes are analyzed.

The average error value of model validation is 0.104 m, which is close to the actual situation. We can accurately and effectively simulate the seepage field and get the gradient, the phreatic line, and the seepage velocity. When the water level is 15.78 m, the gradient reaches 0.5 and the embankment is damaged. Accurate numerical simulation can provide sufficient support for the safety evaluation of embankment seepage.

As a seepage control measure, the effect of relief wells is significantly different from that of non-pressure-relief wells. The ^{−10} m^{3}/d and without a relief well is 1.65 × 10^{−5} m^{3}/d. The lowering of the water head of the phreatic line is up to 12 m, and the lowering of seepage quantity is beneficial to prevent piping, flowing soil, swamping, and other phenomena in the embankment, which plays an indispensable role in the safety of the embankment.

At the same water level, the transient seepage quantity is larger than the steady seepage quantity. Therefore, the safety hazards of dikes are greater when rapid rainfall occurs, and safer antiseepage measures should be taken.

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study.

The authors declare that they have no conflicts of interest.

Wenbing Xu, Chuan Xu, and Qinghe Yao contributed equally to this work.

This work was partly supported by the National Key R&D Program for HPC under grant no. 2016YFB0200603 and the National Key R&D Program for International Cooperation, grant no. 2018YFE9103900. The Guangdong MEPP Fund (no. GDOE[2019] A01), the project of the Guangzhou Science and Technology Program, grant no. 201704030089, and the NSFC project (grant no. 11972384) also supported this research.