## Abstract

As time goes by in deep silt, the water in the shallow layers of the soil and the water pressure will both dissipate, causing greater deformation of the soil structure. Based on the analysis of the new pipeline in Zhuhai, the post-settlement of the existing pipeline in the silt is calculated by theoretical analysis and simulation. It is concluded that the displacement deformation of the water supply pipeline after 400 days of sediment consolidation is still in safety control and puts forward some optimization methods to ensure the safety and function of the pipeline and provide the guidance basis for the follow-up maintenance and construction. It has a certain practical value.

## HIGHLIGHT

This paper calculates the late settlement of existing pipelines in the silt through theoretical analysis and simulation calculation and proposes corresponding treatment methods to provide guidance for subsequent maintenance and construction, ensure the structural safety and functional integrity of pipelines, and provide practical reference cases for similar projects in the future.

## INTRODUCTION

Zhuhai, being one of the central cities in the Pearl River Delta, is situated in a coastal area with deep silt. Due to the influence of silt consolidation, local structures are susceptible to uneven settlement, leading to structural damage. Under drainage conditions, the excess pore water pressure generated by the load in the soft soil gradually dissipates over time as the water in the soil is discharged, and the process of increasing effective stress in the soil continues until the excess pore pressure completely dissipates. This phenomenon is known as consolidation (Zhang 2009; Hong 2010; Fuhe). The consolidation settlement of silt soil results in the settlement of the existing pipeline within this stratum. Over the long term, excessive settlement and differential settlement of the pipeline can have adverse effects on its structure. This can lead to the expansion of existing structural cracks or the formation of new cracks, causing and worsening pipeline leakage. Furthermore, it will significantly impact the durability of the pipeline structure and reduce the waterproof performance of the settlement joint. In more severe cases, it may even alter the pipeline's geometry, affecting parameters such as curvature radius, slope, and slope length, which could pose safety risks during use.

In the context of the special soft soil layer in the Pearl River Delta region, Jiangfu River conducted a systematic study on the engineering properties of coastal soft soil through experiments. They analyzed the characteristics of coastal soft soil from both macro and micro perspectives (Lin 2000; Guo 2012). Kang Hong performed an extensive analysis and study of the soft soil in the Nansha Area using static penetrating tests, cross-plate shear tests, and geotechnical test data. They summarized the mechanical and engineering characteristics of the soft soil in Nansha area and proposed a modified exponential curve model based on multi-level analysis and a comprehensive fuzzy evaluation model to address the issue of settlement curves exhibiting a ‘step shape’ during hierarchical loading (Xiaoqing 2008).

Besides theoretical research, Guo Min, Zeng Xiaoqing, Wu Zhaoqiang, and others analyzed the deformation and displacement trends of pipelines or buildings in deep silt over time through practical engineering cases. They suggested targeted improvement measures, such as adding reinforcing plates, to mitigate potential issues (Wu 2015).

Building upon this research, with the new water supply pipeline from Zhuhai to Macao as the background, this paper calculates the late settlement of existing pipelines in the silt through theoretical analysis and simulation calculations. The study proposes corresponding treatment methods to guide subsequent maintenance and construction efforts, ensuring the structural safety and functional integrity of pipelines. Furthermore, the findings offer practical reference cases for similar projects in the future.

The provided research paper focuses on the consolidation and settlement of deep silt soil. The method described in the paper is specifically tailored for analyzing and simulating consolidation settlement in silt soil, considering its unique properties and behavior. It is important to note that different types of soils have varying engineering properties and behaviors, which may require specific analysis methods.

While the method described in the paper is suitable for silt soil, it may not be directly applicable to all types of soils. The consolidation behavior of different soils varies based on factors such as grain size, permeability, compressibility, and other geotechnical properties. For instance, clay soils, sandy soils, and peat soils will have different consolidation behaviors compared to silt soils.

To analyze consolidation and settlement for other types of soils, researchers and engineers would need to use appropriate methods and models specific to the soil type being studied. Each soil type may require its own set of laboratory tests, empirical correlations, and numerical modeling techniques to accurately assess its consolidation behavior.

The research primarily focuses on the influence of consolidation and settlement of deep silt soil on existing pipelines, the method described in the research is related to numerical simulations and finite element analysis for analyzing settlement and displacement of pipelines in silt soil. To compute the water content of soil, standard laboratory tests like the gravimetric method or using specialized instruments like moisture meters are commonly employed.

## PROJECT OVERVIEW

Zhuhai currently supplies water to Macao through three pipelines, consisting of two DN1000 pipelines and one DN1600 pipeline, running from Zhuxiandong Reservoir (South Bay of Zhuhai) to Qingzhou (Macau Peninsula). The combined water transmission capacity of these pipelines is 500,000 tons per day. However, due to the reclamation plan for Macao's Taipa New Urban Area and the development of new land in Cotai District, the total water consumption in Macao is expected to increase further. The current water supply layout in Macao lacks sufficient anti-risk capability, prompting the construction of four additional water supply pipeline projects dedicated to Macao (Wang *et al.* 2022a, 2023; Zhou *et al.* 2022).

The object of this study is No. C water supply pipeline: The newly built pipeline passes through the Cross-men Central Business District and crosses the Cross-men Waterway to Dangcheng District, Macao. The pipe diameter is D1600 (D1800 is taken from the sea section), and the length of the pipeline is about 3.84 km. The length of the pipeline undertakes Section B, starting from Bk7 + 810 and ending from Bk11 + 655. Cross-Men Central Business section (mileage Bk7 + 810–Bk8 + 970) is proposed to adopt open excavation construction, the buried depth of the pipeline is about 2.50–5.00 m, through the cross-men inland flood section (mileage Bk8 + 970–Bk9 + 257) is proposed to adopt immersed pipe construction, the buried depth of pipeline is about 7.00–8.00 m; pipe jacking is planned for the section from Cross-Men Waterway to Macao Taipa Area (mileage Bk11 + 070–Bk11 + 655), and the buried depth of the pipe is about 22.00–29.00 m.

### Geotechnical geology and hydrology

The overlying soil layer in the site area is mainly composed of sea-land intersedimentary layers and fluvial alluvial layers. The lithology primarily consists of silt, silty fine sand, clay, silty clay, sandy clayey soil, etc. The quality of concrete can be enhanced by using higher-grade sand. The grade of sand refers to its particle size distribution and shape. Higher-grade sand generally has more uniform particles and fewer impurities, which can lead to improved workability and strength of the concrete. Properly graded and clean sand ensures better bonding with cement and aggregates, reducing the risk of voids and weak spots in the concrete. High-quality sand also contributes to the overall durability and long-term performance of the concrete.

*et al.*2021). The groundwater types mainly include upper stagnant water and pore diving, as well as confined water and water within bedrock pore fissures. The typical geological section is shown in Figure 2.

## ANALYSIS THEORY OF SILT CONSOLIDATION SETTLEMENT

Consolidation deformation mechanism: According to consolidation deformation theory, soil particles have very small compressibility and are generally considered incompressible. Therefore, soil deformation occurs due to the loss of pore fluid, reduction of gas volume, rearrangement of particles, shortening of distances between particles, and movement of the soil skeleton. In the case of two-phase saturated soil, the pore water compression volume is small, and the change in pore volume is mainly due to the discharge of pore water. On the other hand, for three-phase unsaturated soil, the primary reason is the discharge of gas in the soil skeleton pores, leading to soil volume compression (Afzal *et al.* 2018; Dayarathne 2021; Ajay *et al.* 2022a, 2022b).

The order of density from maximum to minimum is as follows:

Saturated density > Wet density > Dry density

Saturated density: The density of the soil when all pore spaces are filled with water. It is the maximum density because water fills all available voids.

Wet density: The density of the soil when it contains the maximum amount of water that can be retained without excess water drainage. It is less than saturated density because some pore spaces are still filled with air.

Dry density: The density of the soil when all moisture is removed. It is the minimum density because all pore spaces are filled with air.

The relationship between dry density (*ρ*_{d}) and known moisture content (*w*) can be described using the Compaction Curve. The compaction curve shows the relationship between the dry density and moisture content achieved during the compaction process of a soil sample. As the moisture content increases, the dry density initially increases to reach the maximum dry density (MDD) at optimal moisture content. Beyond the MDD, if the moisture content continues to increase, the dry density decreases. The point on the compaction curve where the MDD is achieved is called the ‘optimum moisture content’ (OMC).

### Basic assumption

The pipeline is infinitely long along its direction, which satisfies the plane strain condition.

The soil surrounding the hole can be treated as a semi-infinite plane with a circular hole.

The silty soil beneath the pipeline is an isotropic medium, and its stress-strain relationship can be described using the rheological model of four elements, with all viscoelastic parameters being constant.

The soil is saturated, and both soil particles and pore water are incompressible. Pour water flow follows Darcy's law, and the permeability coefficient remains constant during the consolidation process.

The deformation is small, and the influence of deformation on the sitting mark is not considered (Liu

*et al.*2022).The uniform load on the ground will not be redistributed due to differential settlement, and the total stress borne by the soil at each point of the underlying layer does not change over time.

The soil at each point of the underlying bed remains free from deformation and is not affected by the arch action caused by the soil itself or the pipeline.

### Fundamental equation

*s* is the Laplace transformation parameter.

Before providing the basic equation for the definite solution of the problem, the positive and negative deformations in the soil are defined. The radial displacement *ur* is considered positive when it is far away from the centerline of the pipeline, and negative when it is close to the centerline. The tangential displacement *uθ* is positive when it is in the same direction as the variable *θ*, and negative when it is in the opposite direction (Xie *et al.* 2020; O'Beirne *et al.* 2021; Wang *et al.* 2022b).

In order to facilitate the analysis of the problem, the above constitutive equation adopts the original equation in. The stress is positive in tension, negative in compression, and the total stress is *σ _{ij}*. The relationship between

*p*and pore water pressure is as follows: , this formula is Biot's ‘effective stress’ expression. The Terazghi principle of effective stress is generally adopted in soil mechanics: , in this formula, the stress is positive with compression and negative with tension. Obviously, the form of Biot's ‘effective stress’ expression is different from Terzaghi's effective stress principle, but if the stress is considered as positive in compression and negative in tension, Biot's ‘effective stress’ expression becomes: , this formula is consistent with Terazghi's formula of effective stress principle in the mechanical sense.

### Model building and solving

*U*(

*z*) at the top of the soil block is evenly distributed at a certain depth and varies with different depths (Gao

*et al.*2023); (3) the initial excess pore water pressure at each point in the soil body changes radially, and the main transmission of the initial excess pore water pressure at each point is through the adjacent soil's initial excess pore water pressure

*U*0, regardless of the influence of

*U*0 from other locations on the soil force as shown in Figure 3.

*Z*is transferred to a depth of

*z*, as shown in Figure 4. The formula is derived as follows:

By using the above formula, assuming the unit width of the soil block and the distribution range of the initial excess pore water pressure, the initial excess pore water pressure at each point in the soil body can be determined.

(11)

(12)

In the formula, the bottom represents the range of the initial excess pore water pressure boundary line at the bottom of the pipeline, and the top represents the distribution range from the top of the pipeline to the surface. *H*_{1} is the distance between the soil at the top of the pipeline and the initial excess pore water pressure boundary of the corresponding soil at this position (i.e., the surface); *z*_{1} is the distance from the soil at the top of the pipeline to the top of the pipeline; *H*_{2} is the distance between the soil at the bottom of the pipeline and the initial excess pore water pressure boundary of the corresponding soil at this position. *Z*_{2} is the distance from the soil at the bottom of the pipe to the bottom of the pipe.

## THREE-DIMENSIONAL FINITE ELEMENT NUMERICAL SIMULATION ANALYSES

In this paper, the construction of a new water supply pipeline project from Zhuhai to Macao is taken as the background, and two-dimensional and three-dimensional finite element analysis models are established for analysis and comparison.

In the analysis process, the mesh refinement is carried out to improve the calculation accuracy, and the influence of silt consolidation and settlement on the pipeline over time is considered. The parameters of geotechnical layer and structural material are shown in Table 1.

Geotechnical designation . | Heavy γ (kN/m^{3})
. | Angle of internal friction φ (°)
. _{q} | Cohesion C (kPa)
. _{q} | Modulus of elasticity E_{s} (MPa)
. | Poisson's ratio/u
. |
---|---|---|---|---|---|

Miscellaneous fill | 19.5 | 20.0 | 5.0 | 3.27 | 0.38 |

Silt (after treatment) | 19.0 | 6.0 | 8.0 | 3.60 | 0.36 |

Medium and coarse sand | 20.0 | 25.0 | 0.0 | 6.00 | 0.33 |

Silty clay | 19.6 | 11.0 | 20.0 | 4.95 | 0.32 |

Granite | 19.0 | 28.0 | 20.0 | 50.00 | 0.28 |

Steel pipe | 78.5 | – | – | 200,000 | 0.24 |

Geotechnical designation . | Heavy γ (kN/m^{3})
. | Angle of internal friction φ (°)
. _{q} | Cohesion C (kPa)
. _{q} | Modulus of elasticity E_{s} (MPa)
. | Poisson's ratio/u
. |
---|---|---|---|---|---|

Miscellaneous fill | 19.5 | 20.0 | 5.0 | 3.27 | 0.38 |

Silt (after treatment) | 19.0 | 6.0 | 8.0 | 3.60 | 0.36 |

Medium and coarse sand | 20.0 | 25.0 | 0.0 | 6.00 | 0.33 |

Silty clay | 19.6 | 11.0 | 20.0 | 4.95 | 0.32 |

Granite | 19.0 | 28.0 | 20.0 | 50.00 | 0.28 |

Steel pipe | 78.5 | – | – | 200,000 | 0.24 |

### Establishment of two-dimensional finite element analysis model

The need to conduct this test depends on the specific context and objectives of the project. If the project involves construction or infrastructure development in areas with deep silt soil, and if there are existing pipelines or structures that could be affected by consolidation settlement, then conducting this test could be crucial to ensure the safety and integrity of the pipelines and structures. The test provides valuable insights into the settlement behavior and potential displacements, helping engineers and planners to make informed decisions and implement appropriate reinforcement measures.

*X*and

*Y*directions at the bottom of the model, while only horizontal constraints in the

*X*direction are applied on the left and right sides to ensure the stress and strain of the soil mass align as closely as possible with the actual situation. The finite element analysis model accounts for an active ground load of 20 (KN·m

^{−2}), as shown in Figure 5.

^{−2}) live load, respectively, calculating the displacement and deformation of the stratum and pipeline after 30, 100 and 400 days. The data summary is shown in Table 1. After 400 days, soil consolidation settlement deformation and pipeline displacement deformation are shown in Figures 6–11.

As can be seen from the figure above, after 400 days of consolidation settlement, vertical settlement displacement occurs mainly in the soil layer, showing an obvious stratified settlement trend, which is distributed along the pipeline in some parts. The horizontal displacement of soil layer is small, which mainly occurs in the middle of an inclined section of pipeline. The total displacement of soil layer is mainly vertical displacement, and the trend is similar to vertical subsidence displacement. At the same time, the settlement of the topsoil near the surface of the pipeline is large, and the vertical settlement decreases with the increase of the depth. The horizontal displacement of the tunnel is small and mainly occurs in the middle of the inclined section of the pipeline. Tunnel displacement is mainly vertical displacement, so the trend is similar to vertical settlement displacement.

### Establishment of three-dimensional finite element analysis models

*X*direction,

*Y*direction and

*Z*direction are applied, while horizontal constraints in the

*X*direction and

*Y*direction are applied on the left and right sides of the model to ensure that the stress and strain of the soil mass are as consistent as possible with the actual situation. Considering the active load of 20 KN/m

^{2}on the ground, the established finite element analysis model is shown in Figure 12.

^{2}, the displacement and deformation of the stratum and pipeline in 30, 100 and 400 days are calculated, respectively. The data summary is shown in Table 2 and Figures 13–17. After 400 days, soil consolidation settlement deformation and pipeline displacement deformation are shown in Figures 13 and 18–24.

Model . | Displacement direction . | Soil layer (mm) . | Pipeline (mm) . | ||||
---|---|---|---|---|---|---|---|

30 days . | 100 days . | 400 days . | 30 days . | 100 days . | 400 days . | ||

Two-dimensional finite element analysis model | Horizontal displacement | −0.02 | −0.13 | 0.85 | −0.01 | −0.78 | −0.51 |

Vertical displacement | −0.74 | −4.05 | −26.48 | −0.68 | −3.76 | −24.66 | |

Total displacement | 0.75 | 4.09 | 26.50 | 0.69 | 3.79 | 24.72 | |

Three-dimensional finite element analysis model | Horizontal X displacement | 0.01 | 0.04 | 1.87 | 0.01 | 0.25 | 1.87 |

Horizontal Y displacement | −0.01 | −0.09 | −3.48 | −0.01 | −0.56 | −0.07 | |

Vertical displacement | −0.53 | −2.92 | −19.28 | −0.49 | −2.71 | −19.28 | |

Total displacement | 0.54 | 2.94 | 19.29 | 0.50 | 2.73 | 19.29 |

Model . | Displacement direction . | Soil layer (mm) . | Pipeline (mm) . | ||||
---|---|---|---|---|---|---|---|

30 days . | 100 days . | 400 days . | 30 days . | 100 days . | 400 days . | ||

Two-dimensional finite element analysis model | Horizontal displacement | −0.02 | −0.13 | 0.85 | −0.01 | −0.78 | −0.51 |

Vertical displacement | −0.74 | −4.05 | −26.48 | −0.68 | −3.76 | −24.66 | |

Total displacement | 0.75 | 4.09 | 26.50 | 0.69 | 3.79 | 24.72 | |

Three-dimensional finite element analysis model | Horizontal X displacement | 0.01 | 0.04 | 1.87 | 0.01 | 0.25 | 1.87 |

Horizontal Y displacement | −0.01 | −0.09 | −3.48 | −0.01 | −0.56 | −0.07 | |

Vertical displacement | −0.53 | −2.92 | −19.28 | −0.49 | −2.71 | −19.28 | |

Total displacement | 0.54 | 2.94 | 19.29 | 0.50 | 2.73 | 19.29 |

As can be seen from the figure above, after 400 days of consolidation settlement, the soil displacement is mainly manifested as vertical settlement displacement, which is most significant near the pipeline. It can be seen that pipeline construction changes the three-dimensional constraint effect of soil mass and reduces the strength of soil mass. The horizontal level of soil layer is small and mainly distributed around the pipeline. The overall displacement of soil layer is similar to the vertical displacement. Similar to the soil layer, the displacement of pipeline is mainly manifested in the vertical settlement, and the settlement of the pipeline near the surface is larger. With the increase of depth, the displacement of the pipeline gradually decreases. The horizontal displacement of the pipeline is small, and the general trend is close to the two-dimensional model. The total displacement of pipeline is dominated by vertical settlement, so the deformation trend is similar to that of vertical settlement.

After comparative analysis and calculation of two-dimensional finite element model and three-dimensional finite element model, the summary of results is shown in Table 2:

Based on the above analysis results, the maximum settlement of soil layer is 26.48 mm and that of pipeline is 24.72 mm. The three-dimensional model analysis shows that the maximum settlement of soil layer is 19.28 mm and that of pipeline is 19.28 mm. The analysis result of the three-dimensional model is smaller than that of the two-dimensional model, because the soil layer of the three-dimensional model has a spatial constraint effect, which improves the integrity and stability of the soil layer.

## CONCLUSION AND SUGGESTION

According to the results of calculation and analysis, it can be seen that even if large-diameter mixing piles are considered for foundation reinforcement, the silt will still inevitably consolidate and settle with the passage of time. However, after 400 days, the settlement of soil layer and pipeline is about 20 mm, which is less than the early-warning control value of water supply and drainage pipeline. This project pipeline is safe.

In the silt stratum, in order to avoid the uneven settlement of the pipeline, strengthening plates can be added on the pipeline to improve the bending performance and integrity of the pipeline, and the construction is simple and easy, greatly saving compared with other pipe rack forms;

Larsen steel sheet pile can be used to support open-cut ground, which can provide reliable support strength and effectively reduce project cost. Moreover, the surrounding vibration load can be reduced in the process of trench excavation. When conditions allow, the working face should be covered in the rainy season and dried in the sunny days to avoid the saturation of silt water content.

Formulate suitable construction scheme of water supply and drainage pipeline. In the construction process, the principle of avoiding or reducing interference with transport road should be adhered to, combined with earthwork construction water supply and drainage, and drainage dragon ditch network should be reasonably laid.

Pay attention to the treatment of the silt layer at the joint of the pipeline, and the large-diameter mixing pile can be used for strengthening in full hall to improve the bearing capacity of the formation, reduce the consolidation settlement of silt, and avoid the uneven settlement at the joint of the pipeline leading to structural damage.

Several sources of error could be present in this experiment, including:

Variability in soil properties: Silt soil can have varying properties across different locations, and obtaining accurate and representative data for all locations might be challenging.

Simplified assumptions: The research relies on certain assumptions and simplifications to model the behavior of the soil and pipeline. These assumptions may not perfectly reflect the real-world complexity, leading to some degree of error.

Model accuracy: The accuracy of the finite element models used in the simulations can impact the reliability of the results.

Uncertainty in parameters: The accuracy of the results may also depend on the accuracy of the input parameters used in the analysis, such as soil properties and construction details.

## ACKNOWLEDGEMENTS

The authors would like to show sincere thanks to those techniques who have contributed to this research.

## CONSENT FOR PUBLICATION

All authors reviewed the results, approved the final version of the manuscript, and agreed to publish it.

## FUNDING STATEMENT

There is no specific funding to support this research.

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

## REFERENCES

*Finite Element and Centrifuge Modeling of Frost Heave and Thaw Consolidation Settlement of Pipelines in Cold Regions*