Analysis of the Impact of the Former Abandoned Dregs of Mountain Highways on the Construction and Safety of New Bridge Pile Foundations

Abstract

In highway reconstruction and expansion projects, the impact of the abandoned dreg body produced by the original highway on the new bridge project cannot be ignored. If the abandoned dregs are not handled properly, they will cause great threat to the operation of the new highway as well as to the safety of the surrounding environment and personnel. In this paper, based on a South China highway reconstruction and expansion project, a model of the abandoned dreg body, bridge pile and anti-slide pile is established with the help of finite difference software FLAC3D 5.0. The calculation results show that compared with burying the anti-slide pile, slope cutting is more effective for improving the stability of the abandoned dreg body. Under the action of vertical force intensity, the displacement of the top of the pile increases continuously, and the maximum bending moment of the pile body increases firstly and then decreases. The pile displacement and bending moment of the bridge pile increase significantly in the storm condition compared with the normal condition. In addition, the abandoned dreg body hazard prevention and control technical measures are studied. The impacts of different locations of anti-slide pile burial on bridge piles are analyzed and compared, and it is determined that the optimal location of anti-slide pile burial is the middle of the secondary slope.

1. Introduction

With the social and economic development of the new era, the highway has become an important pillar of China’s economic development. However, its scale is still unable to meet the growing economic demand, so China has begun a series of highway reconstruction and expansion projects. By the end of 2021, China’s highway mileage reached 5,280,700 km, and the mileage of high-speed grade road highway reached 169,100 km. The huge amount of waste slag is limited by high cost, low availability and construction difficulty, so it may not have secondary utilization and can only be deposited nearby. However, affected by the geological conditions of the abandoned dregs site, the construction process of the accumulation process, and the meteorological conditions [1], the slopes of artificial abandoned dreg body may be subject to damage such as sliding and collapsing. This causes lateral loading of new bridge piles, which in turn leads to the development of deflection and bending moments in the piles [2,3,4], posing a great threat to new bridge projects.

In recent years, accidents of destabilization of abandoned dregs have occurred from time to time. On 20 December 2015, a landslide occurred at the Hong Au abandoned dreg site in Shenzhen’s Guangming New District. The original plan was that the abandoned dreg site had a capacity of 4 million cubic meters and a closure elevation of 95 m. The results of the investigation showed that at the time of the accident, the actual volume of the site had exceeded 5.83 million cubic meters, and the actual height of the abandoned dreg body reached 160 m. The capacity and height were grossly excessive. The excessive and ultra-high abandoned dreg body led to increased sliding forces and reduced stability. Eventually, the slag became unstable and slid out. A landslide accident occurred on 16 September 2014 at the north entrance of the Angou Tunnel in the Xiaohe to Ankang section of the Xikang Expressway. Continuous heavy rainfall led to a serious landslide accident in the area. A 30-metre-long portion of the left bridge at the tunnel entrance broke and collapsed.

Scholars’ research and analysis of pile foundation force and deformation under pile–soil interaction are mainly carried out from the aspects of vertical load, lateral load and combined load. Rathod [5] conducted a series of indoor model experiments with varying slope angles and pile embedment length-to-diameter ratios. He used the curve fitting method to obtain the soil resistance and deflection, and established the p-s curve of soft clay slope piles under lateral loading. Zhang [6] proposed a new dimensionless embedded ratio for the study of c-φ soils, obtaining exact solutions for the dimensionless ultimate lateral bearing capacity and rotation center for three different soil types. The results indicate that both the dimensionless ultimate lateral bearing capacity and the dimensionless rotation center are linear functions of the new embedded ratio. Jian [7] conducted centrifuge tests in clay, establishing an upper-bound velocity field to illustrate the influence of progressive rotation on the ultimate load. Finite element modeling was employed to validate and analyze the findings. Nimityongskul [8] conducted comprehensive lateral loading tests on piles embedded near cohesive soil slopes. Normalizing the p-y curves of slope-adjacent piles with those of flat-ground piles, a p-multiplier was derived to account for the slope effect under lateral loading. Stewart [9] developed a new analytical approach based on a simple deformation mechanism. The main features of the problem are described by approximating the embankment–soil–pile interaction. Poulos [10] identified key parameters affecting the maximum bending moment within a pile at a certain soil density, including the pile head fixation conditions, the ratio of the embedment depth to the pile length, pile diameter, and pile stiffness. Luamba [11] proposed a formula that integrates the boundary element method and finite element method for analyzing the interaction between piles and soil under horizontal loading. The formula was validated through analysis of a single pile case. Cai [12] employed numerical simulation to investigate the lateral displacement of pile foundations under surcharge loading, identifying variations in the impact of different factors. Ashour [13], after modifying and improving the conventional strain wedge method, eliminated the need for a constant multiplier. The lateral behavior of piles and p-y curves can be predicted solely based on the pile inclination, soil properties, and pile–soil interaction. Peng [14] revised the conventional strain wedge model, incorporating both the upper soil wedge and lower strain wedge, making it applicable for the analysis of piles under lateral loads on slopes. This expansion broadened the scope of applicability of previous strain wedge models. Zhang [15] conducted long-term monitoring of bridge structures and employed numerical simulation to study the impact of steep slopes on the stress and deformation of bridge piles. Wang [16] designed model tests for rock-socketed piles subjected to axial and inclined tension. The uplift resistance of the piles significantly decreased under inclined loading compared to vertical uplift. Wang [17], through model experiments, investigated the influence of slope angle, pile location, and load on the vertical bearing characteristics of bridge piles.

Under the influence of surrounding soil surcharge, the damage to bridge pile foundations directly impacts the safety of both the bridge itself and the surrounding slopes or other facilities. Research on safety control measures primarily focuses on two aspects: support for the slopes and reinforcement of the bridge pile foundations. In terms of slope support, Zou [18] devised vibration table tests for slope–bridge pile reinforcement using front and rear rows of anti-slide piles. Loading with varying peak EI Centeo waves revealed that the front row of anti-slide piles had an adverse effect on bridge pile deformation, while the rear row of anti-sliding piles played a seismic reinforcement role. In terms of bridge pile reinforcement, Huang [19] implemented pile repair measures on both sides of piles eroded by water flow. The reinforcement was found to meet the load-bearing requirements and stabilize under strong seismic conditions. Shen [20] initially removed the additional loads causing tilting and then employed lateral pushing methods to correct the displacement of some bridge piers and expansion joints that exceeded displacement limits. Hu [21], based on bridge pier displacement monitoring and subgrade settlement observation data, established a relationship curve between pier displacement and settlement. The recommendation was made to unload piers with rapid displacement development, but analysis of the pile displacement mechanism was not provided.

Previous studies have provided comprehensive analyses of the force distribution in bridge pile foundations. However, there is a paucity of research on the practical engineering aspects of constructing new piles on abandoned dreg body. This study, conducted in conjunction with a highway reconstruction and expansion project in South China, employs numerical simulation to investigate the stability of the original abandoned dreg body. This study also explores the influence of residue on the mechanical behavior of bridge pile foundations and addresses strategies for the prevention and mitigation of potential hazards. This paper aims to serve as a practical reference for similar abandoned dregs engineering projects during the construction phase.

2. Investigation and Characterization of Former Abandoned Dreg Sites on Mountain Highways

2.1. Engineering Background

The highway from Guilin to Quanzhou adopts the standard of a two-way eight-lane highway, and the designed traffic speed is 100 km/h. The width of the old road on both sides of the whole splicing and the whole of the new roadbed is 41 m; the width of the old road on one side of the splicing roadbed (excluding pavement) is 20.25 m; the width of the new four-lane separated roadbed is 20.5 m; and the width of the new two-lane separated roadbed is 13 m. The design loading level of the bridges and culverts adopts the Highway Grade I.

The slope of this paper is the original abandoned dregs slope in the location of the route alignment of the new Lanma Bridge (YK1179 + 550). The design of this expansion will require the upper portion of the abandoned dreg stockpile to be removed the remaining abandoned dreg to be force-rammed, and the slope to be leveled after force-ramming. Then, the interceptor ditch and hardening layer must be addressed. The lower part of the slope is protected by an inundation berm between the standing water level and the 100-year flood level. The impact of the original abandoned dregs on the bridge foundation, the impact of the disturbance from the bridge pile construction on the stability of the existing line bridge and the original abandoned dregs, and the impact of the instability of the original abandoned dregs on the highway after disturbance may all be critical factors in determining the safe construction and structural stability of the structure in this area.

The contract section YK1179 + 210 ~ YK1179 + 235 landslide body is located on the left side of the old motorway. The planar morphology is horseshoe-shaped. Shallow slides are caused mainly by heavy rainfall, as shown in Figure 1. It is now in an unstable state. In Figure 1, the original spoil is located next to the existing roads and the new roads are built on the spoil.

For YK1179 + 260 ~ YK1179 + 370, the right 70 m of the accumulation body is an artificial accumulation body. It is due to artificial filling during the construction of the original highway, filling the original surface of the gully, as shown in Figure 2. The body is about 150 m long and 70 m wide, with a thickness of 4.8–25.6 m. The main component is sandstone gravel, which is now in a stable state.

2.2. Engineering Geological Conditions of the Abandoned Dreg Site

2.2.1. Meteorology and Hydrology

The project area is located at a low latitude, belonging to the transition zone from the southern subtropical zone to the central Asian zone, and is more obviously influenced by the monsoon circulation. It is characterized by a mild climate and abundant rainfall. However, the seasonal and regional distribution is uneven, so it is susceptible to flooding and drought. According to the meteorological records of Luzhai county town from 1960 to 1980 and Luo Rong farm from 1957 to 1980, the annual sunshine hours are from 1531 to 1672 h. The average annual sunshine percentage is 35–37.4%, with the highest being 59% in July and the lowest being 15–18% in March. The average annual temperature is 20.2 °C, with a maximum of 28.5 °C in July and a minimum of 10.1 °C in January. The rainy season usually starts in mid-April and ends in late August, totaling more than 140 days. Rainfall during this period ranges from 974 to 1300 mm, accounting for 71 to 78 per cent of the annual rainfall. May to June is the peak of the annual rainfall, with an average monthly rainfall of 250 to 300 mm, with a maximum of 915.7 mm.

The rivers in the project area are mainly the Luoqing River system, with more developed tributaries. The rivers in the area are the Luoqing River, Shijuan River, Luo River, Guzao River, and so on. The route scope is in the east wing of the Liuzhou mountain forearc and the oblique joint compound part of the Guidong north–south tectonic belt through each tectonic system, and the tectonic trajectory is from south to north. The main tectonic structures include the Suqiao dorsal slope, Dashitun dorsal slope–Guangfu dorsal slope, and Yongfu reverse fault. The faults in the above mentioned tectonics have not been found to show signs of new activity since the Late Tertiary. Surface water in this section is mainly water of the Luoching River; groundwater mainly consists of pore water from loose layers of the Tertiary system, bedrock fissure water, and carbonate karst water. Groundwater is mainly stored in bedrock fissures and karst fissures. The main sources of recharge are atmospheric rainfall recharge and lateral recharge of groundwater. The overall runoff is to the west and eventually discharges to the surface water body, the Luoqing River.

2.2.2. Earthquake Conditions

According to the “China Earthquake Parameter Zoning Map” GB18306-2015 [22], the “China Earthquake Peak Acceleration Zoning Map”, and the “China Earthquake Response Spectrum Characteristic Cycle Zoning Map”, the peak acceleration of earthquakes in the project area is less than 0.05 g. The characteristic cycle of the response spectrum is 0.35 s. The corresponding seismic intensity is VI, and the seismic fortification level is VII.

2.3. Types of Abandoned Dreg Site Damage and Trigger Conditions

2.3.1. Types of Damage

Through on-site research, combined with other slope damage types in China, the type of damage to the abandoned dreg site is mainly as follows:

(1) Erosion: Under rainfall conditions, loose soil layers on the slopes of the abandoned dregs are washed away by concentrated water flows from surface runoff [23,24]. Part of the soil in the water flows to the bottom of the slope. The original slag body slope forms a gully. According to the site investigation, the abandoned dreg body is mostly a loose accumulation body. It does not perform well in terms of viscosity and permeability. And in the face of precipitation, the body is easy to relax and slide, and part of the discarded debris will form a small mudslide with the surface runoff.

(2) Collapse: When the self-gravitational stress exceeds the strength of the geotechnical body due to the irrational design of the abandoned dregs, collapse damage occurs. A collapse does not have a fixed damage surface; each time a collapse appears after a new damage surface, it continues to collapse until it reaches natural stability.

(3) Spalling: When large rocks are piled up on the slope, they will naturally decompose into small rock and soil blocks with the application of weathering, expansion, and contraction. Under the action of self-weight, they roll downwards from the slope face [25], until they roll down to the bottom of the slope or are stabilized prematurely due to resistance. This type of damage occurs in almost every abandoned dreg body. However, it needs to be controlled by safe techniques, especially in the case of dumps with a high rock content and steep slopes.

(4) Landslide: A phenomenon in which soil, rock, debris, and other materials on the ground surface or on a slope move down the slope due to gravity. It can be classified into four types: landslides on internal minimum slip-resistant surfaces, landslides along bedrock contact surfaces, landslides along weak foundations, and landslides causing debris flows.

2.3.2. Trigger Conditions

(1) Effects of water

The location of the site is in a low-latitude, subtropical monsoon climate, where the monsoon circulation influence is more obvious. Although the site is east of Luoching River, the relevant slope section is at the bottom of the construction of gabions, so the main consideration is the impact of the infiltration of abundant precipitation. The slopes of the abandoned dregs are manmade slopes with a low degree of consolidation, and the whole body is loose and has the characteristic of strong water permeability. Precipitation can infiltrate into the body from the slope surface faster. On the one hand, it makes the self-weight of the soil body increase, and the downward trend increases. On the other hand, it causes the cohesion and friction angle to decrease [26,27]. The anti-slide ability decreases.

(2) Elements of the abandoned dreg stockpile

The main elements of the abandoned dreg stockpile are slope height, square footage, and slope. The calculation of slope height is based on the location of the abandoned dreg stockpile, the square volume requirement, and the topography. If the height is too low, it may be difficult to meet the square volume requirements or the slope ratio may be too large. If the height is too high, it will increase the internal stress and reduce the safety factor. Abandoned dreg stockpile volume requirements are determined by the designer. If the volume exceeds the limit, the internal stress of the body increases, which may also cause foundation damage and trigger slope failure. The slope of the abandoned dregs needs to be determined by considering the requirement of the volume and the stability requirement of the abandoned dregs. If the slope is too low, then the volume will be reduced, and if the slope is too high, it will lead to an increase in the slip force.

(3) Soil properties

The composition of the abandoned dregs is complex, with different properties of the soils that make up the abandoned dreg body. These undoubtedly include hydrophilic soils such as clay, which significantly reduces the overall hydrophobicity. The soil layer on the slope of the abandoned dregs has a short cycle of wet and dry cycles, and becomes looser and softer under the influence of a monsoon climate. If strong precipitation is encountered, erosion, spalling, mudslides, and other damage are likely to occur, threatening the stability of the slope.

(4) Effects of fissures

Under the action of external forces as well as self-weight, the abandoned dregs are deformed, thus expanding cracks on the surface. Especially at the top of slopes subjected to tensile stresses, atmospheric precipitation can more easily penetrate into the abandoned dregs from the cracks. And the internal moisture is also more likely to evaporate from the cracks. The shear strength of the abandoned dregs is significantly reduced under the wet–dry cycle [28].

3. Computational Principle and Numerical Model

3.1. Computational Principle

In this paper, a numerical model of the disposal body is established with the help of FLAC3D based on the finite difference method. The finite difference method is a commonly used numerical computation method. By discretizing continuous differential equations into difference equations, the numerical solution of complex geological and engineering problems can be achieved on a computer. As shown in Figure 3, the bridge pile in the slope section of this paper is divided into the free section and the loaded section. The top of the pile may be subjected to vertical load P₀, horizontal load Q₀, and bending moment M₀. The following assumptions are made to establish the differential equations: (1) the pile is in an elastic working condition; (2) the soil resistance around the pile adopts the general equation $q\left(x,z\right)=k{z}^{n}x$; (3) the soil thrust around the pile adopts the general equation $p\left(z\right)=a{z}^2+bz+c$, where a, b, and c are determined by test or on-site monitoring; (4) the axial force distribution of the pile body is $P\left(z\right)=P_0+fz$, where $f$ is the self-weight along the pile body as well as the lateral friction resistance.

3.1.1. Differential Equation Establishment

We take a section of the free section and the loaded section of the bridge pile to analyze the force, as shown in Figure 4.

Taking the moments at the midpoint of the lower edge of the micrometric body and simplifying them gives the differential equations for the free and loaded segments:

$$EI\frac{d^{3}x}{d^{3}z}+\left(P_0+f_{1}z\right)\frac{dx}{dz}=Q$$

(1)

$$EI\frac{d^{4}x}{d^{4}z}+\left(P_0+f_{2}z\right)\frac{d^{2}x}{d^{2}z}+f_2\frac{dx}{dz}+k{z}^{n}x=a{z}^2+bz+c$$

(2)

The pile top and pile bottom boundary conditions are free. Equations (3) and (4) are the differential equations for the boundary conditions at the top and bottom of the pile, and H is the length of the pile.

$$\left\{\begin{array}{c}EI\frac{d^{2}x}{d^{2}z}{|}_{Z=0}=M_0\\ \left[EI\frac{d^{3}x}{d^{3}z}+(P_0+f_{1}z)\frac{dx}{dz}\right]{|}_{z=0}=Q_0\end{array}\right.$$

(3)

$$\left\{\begin{array}{c}EI\frac{d^{2}x}{d^{2}z}{|}_{Z=H}=0\\ \left[EI\frac{d^{3}x}{d^{3}z}+(P_0+f_{2}z)\frac{dx}{dz}\right]{|}_{z=H}=0\end{array}\right.$$

(4)

3.1.2. Finite Difference Forms of Differential Equations

We discretize the bridge piles from top to bottom [29,30], as shown in Figure 5. In the figure, the discretization points 0 and N are the top and bottom of the pile, respectively, and the discretization points K and K + 5 are the junction points of the free section and the loaded section.

Equations (5)–(9) are finite difference equations.

$$z=ih$$

(5)

$$\frac{dx}{dz}=\frac{x_{i+1}-x_i}{h}$$

(6)

$$\frac{d^{2}x}{d^{2}z}=\frac{x_{i+1}-2x_i+x_{i-1}}{h^2}$$

(7)

$$\frac{d^{3}x}{d^{3}z}=\frac{x_{i+2}-2x_{i+1}+2x_{i-1}-x_{i-2}}{2h^3}$$

(8)

$$\frac{d^{4}x}{d^{4}z}=\frac{x_{i+2}-4x_{i+1}+6x_i-4x_{i-1}+x_{i-2}}{h^4}$$

(9)

The finite difference equations for the free and loaded segments are expressed as Equations (10) and (11) by inserting Equations (5)~(9) into Equations (1) and (2).

$$EI{x}_{i+2}+\left(-2EI+P_0{h}^2+f_{1}i{h}^3\right)x_{i+1}-(-2EI+P_0{h}^2+f_{1}i{h}^3)x_{i-1}-EI{x}_{i-2}=2h^{3}Q$$

(10)

$$\begin{gathered} EI{x}_{i+2}+\left(-4EI+{P_{0}h}^2+f_{2}i{h}^3+f_2{h}^3\right)x_{i+1} \\ +\left(6EI-2P_0{h}^2-2f_{2}i{h}^3-f_2{h}^3+k{i}^n{h}^{n+4}\right)x_i \\ +(-4EI+{P_{0}h}^2+f_{2}i{h}^3)x_{i-1}+EI{x}_{i-2}=a{i}^2{h}^6+bi{h}^5+c{h}^4 \end{gathered}$$

(11)

Similarly, the boundary conditions can be simplified as follows:

$$\left\{\begin{array}{c}EI\frac{x_{i+1}-2x_i+x_{i-1}}{h^2}{|}_{i=0}=M_0\\ \left[EI\frac{x_{i+2}-2x_{i+1}+2x_{i-1}-x_{i-2}}{2h^3}+(P_0+f_{1}ih)\frac{x_{i+1}-x_{i-1}}{2h}\right]{|}_{i=0}=Q_0\end{array}\right.$$

(12)

$$\left\{\begin{array}{c}EI\frac{x_{i+1}-2x_i+x_{i-1}}{h^2}{|}_{i=bottom}=0\\ \left[EI\frac{x_{i+2}-2x_{i+1}+2x_{i-1}-x_{i-2}}{2h^3}+(P_0+f_{2}ih)\frac{x_{i+1}-x_{i-1}}{2h}\right]{|}_{i=bottom}=0\end{array}\right.$$

(13)

The displacement, corner, shear force, and bending moment continuity conditions at the junction of the free and loaded sections of the pile are as follows:

$$\left\{\begin{array}{c}{x}_K=x_{K+5}\\ x_{K+1}-x_{K-1}=x_{K+4}-x_{K+6}\\ {2x}_{K+2}-x_{K+1}+2x_{K-1}-x_{K-2}=-2x_{K+7}+x_{K+6}-2x_{K+4}+x_{K+3}\\ x_{K+1}-2x_K+x_{K-1}=x_{K+6}-2x_{K+5}+x_{K+4}\end{array}\right.$$

(14)

According to the above, the finite difference equations can be solved jointly for each node displacement. Then, the peripile soil resistance, pile bending moment, and pile shear force can be solved according to the following equations:

$$\left\{\begin{array}{c}{\sigma }_i=-k{\left(ih\right)}^n{x}_i\\ M_i=\frac{EI}{h^2}(x_{i+1}+x_{i-1}-2x_i)\\ Q_i=\frac{EI}{{2h}^3}(-x_{i-2}+{2x}_{i-1}-2x_{i+1}+x_{i+2})\end{array}\right.$$

(15)

3.2. Numerical Model

3.2.1. Simulation Scheme

There are various types of abandoned dregs in the abandoned dregs project. There are both small abandoned dreg bodies piled up on bedrock surfaces and large abandoned dreg body with typical double-sided openings. The former slag sliding type is sliding along the bedrock. This study focuses on the latter and uses FLAC3D to model the abandoned dregs. The stability of the abandoned dreg body was analyzed under heavy rainfall conditions for three scenarios: the original condition, a cut slope, and a buried anti-slide pile. We establish the bridge pile model under the best stability condition and further analyze the influence of the abandoned dreg body on bridge piles. Finally, the preventive and control measures for the abandoned dreg body on the bridge pile are studied, and the program of burying the anti-slide pile in the secondary slope is determined.

3.2.2. Model Building

Figure 6 shows the model dimensions. The overall dimensions of the model are 152 m in the x-direction, 60 m in the z-direction, and 9 m in the y-direction. Horizontal velocities are constrained on the left and right sides of the model, vertical velocities are constrained at the bottom of the model, and the top is a free boundary. For the slope of the original abandoned dregs and the cut slope, the model is built by command flow, and a total of 2500 units and 3324 nodes are generated. The same command flow is used for modeling the abandoned dreg body with the buried anti-slide pile, with hexahedral block mesh and uniform wedge mesh. The length of the anti-slide pile is 20 m, and the cross-section size is 2 m × 1.8 m. According to engineering experience, the anti-slide pile is buried in the middle and lower position of the primary slope. The upper 5 m of the anti-slide pile is constrained by x-, y-, and z-direction velocity, and the grid is encrypted for the anti-slide pile and the surrounding soil. The total length of the bridge pile is 45.5 m, and the cross-section is 1.8 m × 1.8 m. The pile body is not constrained.

The ontological model of the abandoned dreg body was set as a Mohr–Coulomb plastic model. The anti-slide pile and bridge pile were modeled with reference to Won [31], where the pile was treated as a solid unit and set up as an elastic model. This can simulate the pile relatively realistically. However, since the strength discount method does not support the elastic model, the anti-slide pile is set as a Mohr–Coulomb plastic model when calculating the slope safety factor. The elastic model is still used in other cases. Considering the large difference in pile–soil properties, there is also a contact surface between the pile and soil in order to better simulate the actual situation.

3.2.3. Model Parameters

For the selection of physical and mechanical parameters of the soil and pile in the site, they are determined mainly based on engineering data and combined with relevant research findings. The ontological model of the anti-slide pile is set as a Mohr–Coulomb plastic model when calculating the slope safety factor. Cohesion $c$ and the friction angle $\phi$ can be calculated according to Equations (16) and (17).

$$tan\phi =\frac{{\sigma }_c-{\sigma }_t}{2\sqrt{{\sigma }_c{\sigma }_t}}$$

(16)

$$c=\frac{1}{2}\sqrt{{\sigma }_c{\sigma }_t}$$

(17)

We estimate the parameters of the anti-slide pile with reference to C30 concrete strength. It is known that its standard value of compressive strength is ${\sigma }_c=20.1 \mathrm{N}/\mathrm{m}{\mathrm{m}}^2$ and the standard value of tensile strength is ${\sigma }_t=2.01 \mathrm{N}/\mathrm{m}{\mathrm{m}}^2$. Inserting these strength values into Equations (16) and (17) can allow us to calculate the cohesive force $c$ and friction angle $\phi$.

The shear normal stiffness of the contact surface is approximately the same and can be calculated according to Equations (18)–(20), where E is the modulus of elasticity, $\mu$ is Poisson’s ratio, and $K$ and $G$ are the shear modulus and bulk modulus of the abandoned dreg body around the anti-slide pile. $\Delta z_{min}$ is the minimum size of the mesh in the normal direction of the contact surface. The contact surface cohesion and friction angle are taken as 80% of the surrounding soil body.

$$K=E/3(1-2\mu )$$

(18)

$$G=E/2(1+\mu )$$

(19)

$$K_n{=K}_s=10 \mathrm{m}\mathrm{a}\mathrm{x}\left[\frac{K+\frac{4}{3}G}{\Delta z_{min}}\right]$$

(20)

The final selected physical–mechanical parameters of each part are shown in

Table 1. Physical–mechanical parameters of model.

Materials	Working Condition	Severe (kN/m3)	E/ (GPa)	$\mathit{\mu }$	C/ (kPa)	$\mathit{\phi }$/ (°)	${\mathit{K}}_{\mathit{n}}$/ (GPa)	${\mathit{K}}_{\mathit{s}}$/ (GPa)
Abandoned dregs	Normal	19.0	0.12	0.35	43	30.0	/	/
	Storm	19.7	0.12	0.35	42	27.0	/	/
Bridge pile	Normal and storm	25	30	0.20	/	/	/	/
Anti-slide pile	Normal and storm	25	30	0.20	3178	54.9	/	/
Contact surface	Normal	/	/	/	34.4	24.0	0.88	0.88
	Storm	/	/	/	33.6	21.6	0.88	0.88

.

4. Results and Discussion

4.1. Stability Analysis of Abandoned Dreg Body

We model the spoil pile according to the above description and assign mechanical parameters. We analyze the stability of three states: the original slope, cut slope, and buried anti-slip pile.

4.1.1. Analysis of Original Slope Calculation Results

After the original slope modeling is completed and its mechanical parameters are assigned to obtain the solution, the maximum principal stress and minimum principal stress diagrams can be obtained from the solution, as shown in Figure 7 and Figure 8. From the maximum principal stress and minimum principal stress cloud diagrams, it can be seen that the maximum principal stress and minimum principal stress of the abandoned dreg body are less than 0, so the original slope is in a state of compression as a whole.

The strength reduction method is used to solve for the factor of safety, and the resulting factor of safety, shear strain maps, and velocity vector maps are shown in Figure 9. From the figure, it can be seen that the factor of safety of the original slope is 1.95. The factor of safety is greater than the standard value of 1.35 specified in the Technical Specification for Construction Slope Engineering (GB50330-2013), so the slope is in a stable condition. From the figure, it is obvious that there is a wider potential slip surface, which runs through the abandoned dreg body from the foot of the slope to the top of the slope. The maximum shear strain is located close to the foot of the slope. The velocity of each grid node in the region above the potential slip surface is significantly larger compared to the other regions, indicating that slip damage has occurred in this region at the current time step.

4.1.2. Analysis of Calculation Results after Slope Cutting

Slope cutting is a treatment method that reduces the height and gradient of a slope by removing part of the slope [32]. The simulation of slope cutting is carried out by zeroing out the displacements and velocities on the basis of the initial stress equilibrium. The subgroups that acted as cut-off slopes set during the initial meshing are set as empty models. The original slope angle of the secondary slope was 27°, which is reduced to 26° after cutting. The factor of safety, shear strain cloud, and velocity vector diagrams obtained by using the strength discount method are shown in Figure 10. From the figure, it can be seen that the factor of safety is increased from 1.95 to 2.28 after slope cutting, and the stability is significantly improved, which meets the relevant norms. Although the shear strain at the foot of the primary slope is larger compared with the surrounding soil, the maximum shear strain is located at the foot of the secondary slope. And the potential slip surface from the foot of the primary slope to the top of the slope does not span completely through the slope. After cutting the slope, the potential slip surface is shifted upward from the original surface through the abandoned dreg side slope to the secondary slope body. The velocity vectors show that only the secondary slope is undermined at the current time step. In the event of a landslide, the primary slope area acts as a buffer zone and the severity of the accident is reduced.

4.1.3. Analysis of Calculation Results after Burying Anti-Slide Pile

The displacement and velocity of each node are cleared to zero after the initial stress of the original abandonment body reaches equilibrium, and the anti-slide pile unit is activated. The mechanical parameters of the abandoned dregs initially set by the anti-slide pile group are modified to the mechanical parameters of the anti-slide pile in Table 1, and then, the factor of safety is solved. The calculated safety factor, shear strain cloud, and velocity vector diagram are shown in Figure 11. Compared with the original slope safety coefficient, there is a certain improvement after burying the anti-slide pile, from 1.95 to 2.11, but the effect of stability improvement is obviously poorer than that of slope cutting. From the shear strain map, it can be seen that after burying the anti-slide pile, the potential slip surface spans from the soil around the anti-slide pile to the top of the slope. From the velocity vector diagram, it can be seen that the abandoned dreg body above the potential slip surface is unstable, and the damage area is also larger compared with the cut slope.

4.2. Analysis of the Impacts of Abandoned Dregs on the Bridge Project in the Abandoned Dreg Site

From the analysis of the stability of the abandoned dreg body, it can be seen that slope cutting of the original abandoned dreg body is more able to improve the stability of the abandoned dreg body compared to burying the anti-slide pile. Therefore, the mechanical analysis model of the bridge pile was established after the original slope cutting measures were taken to analyze the impact of the abandoned dreg pile on the bridge pile.

4.2.1. Analysis of the Effect of Vertical Force Intensity on the Top of the Pile

Firstly, the calculation is carried out without vertical force intensity at the top of the pile. Then, a vertical force intensity of 4 MPa is loaded on the top of the pile in 10 stages, and the force intensity is increased by 0.4 MPa each time. The results of each calculation are analyzed and compared. The mechanical parameters are adopted from Table 1 for the storm condition. The lateral displacement of the pile top and the maximum bending moment of the pile body under different vertical force intensities are calculated and shown in Figure 12. The results of each calculation are compared and analyzed after applying vertical force intensity to the top of the pile hierarchically.

It can be seen from Figure 12a that the minimum lateral displacement of the top of the bridge pile is 3.91 cm when no vertical force intensity is applied. The displacement increases significantly after the force intensity is applied to the top of the pile. As the vertical force intensity is applied step by step, the inclination of the pile body is increasing, so the lateral displacement of the top of the pile shows an increasing trend. From Figure 12b, it can be seen that the maximum bending moment of the pile body increases continuously with the increase in vertical force intensity within a certain range. The maximum bending moment is 641.58318 kN·m when the vertical force intensity is 1.6 MPa, and the maximum bending moment of the pile body shows a decreasing trend after exceeding this range. Because of the loose nature of the abandoned dregs, initially, the bridge piles buckle to an increasing degree as the force intensity increases. When the vertical force intensity exceeds a certain range, the ultimate bearing capacity of the pile can be increased, and the influence of soil slip force is weakened. As a result, the bending moment of the bridge pile tends to decrease again.

4.2.2. Impact Analysis of Different Working Conditions

(1) Under normal conditions

The mechanical parameters of the model are taken from the normal working condition parameters in Table 1. The lateral displacement cloud and bending moment distribution of the pile obtained from the calculation in the case of no load at the top of the pile are shown in Figure 13 and Figure 14.

From Figure 13, it can be seen that the lateral displacement along the pile body from bottom to top decreases at first and then increases in the reverse direction. The maximum lateral displacement of the pile body is 11.13 cm, which occurred in the lowest part. The lateral displacement at the top is in the negative x-axis direction, which is 2.17 cm. It can be seen from Figure 14 that the distribution of the pile bending moment presents an inverse “S” shape. With the increase in pile height, the bending moment first increases to the first peak value of −261.37 kN·m. It then decreases to 0 and then increases reversely to a second, larger peak of 416.54 kN·m, and finally decreases continuously to 0.

(2) Under storm conditions

The mechanical parameters of the model are taken from the storm condition parameters in Table 1. The distribution of pile bending moments in the lateral displacement cloud of the pile calculated under storm conditions is shown in Figure 15 and Figure 16.

From Figure 15, it can be seen that the pile body is still tilted to the left in the storm condition, and the lateral displacement along the pile body from bottom to top decreases continuously to 0 and then increases in the reverse direction. The maximum displacement is 15.64 cm at the bottom of the pile, which is 40.52% higher than the maximum lateral displacement at the bottom of the pile under the normal condition. The lateral displacement at the top of the pile in the negative direction of the x-axis is 3.91 cm, which is 80.18% more than in the normal condition. From Figure 16, it can be seen that the bending moment of the pile body shows a trend of increasing and then decreasing with the increase in pile height. The peak value is 643.85 kN·m, which is 54.57% higher than the peak positive bending moment in the normal condition.

4.3. Hazard Prevention and Control Techniques for Bridge Engineering in Cases of Slipping of Abandoned Dreg Body

By comparing the normal condition and the storm condition, it can be seen that the maximum bending moment of the pile body increases significantly when the working condition becomes unfavorable. And the compressive strength of reinforced concrete is stronger and the tensile strength is weaker [33]. The tensile strength is about 1/10 to 1/8 of the compressive strength. Therefore, in order to prevent the bridge pile damage caused by the sliding of the abandoned dregs under more unfavorable conditions, it is necessary to strengthen the slope by adopting hazard prevention and control techniques.

4.3.1. Anti-Slide Pile Support Scheme

Nowadays, there are various techniques to prevent and control slope hazards, among which the buried anti-slide pile is more common and effective. Anti-slide piles embedded in the upper part of the slope have a shorter length through the slip zone due to the deeper potential slip zone. And there are more tension cracks on the upper slope. Therefore, the anti-slide pile is usually buried in the middle and lower part of the slope in the actual project [34,35,36]. The anti-slide pile model established in this paper is a rectangular pile with a cross-section size of 2 m × 1.8 m and a length of 25 m. There is no load at the top of the pile, and the top 5 m of the pile body is restrained in the x, y, and z directions. The mechanical parameters of the model are adopted from Table 1 for each parameter under the storm condition. It should be noted that at this time, the anti-slide pile is set as an elastic model, and there is no need to assign values to the cohesion and friction angle.

To investigate the impact of anti-slide piles at different embedment positions on the foundations of bridge piles and determine the optimal placement of anti-slide piles, five such piles are arranged from near to far in the lower section of a secondary slope. Taking the bottom of the secondary slope as the starting point, it is assumed that the horizontal distance between the anti-slide pile and the starting point is L_X, the projected length of the secondary slope in the horizontal plane is L = 48.39 m, and the anti-slide pile position is characterized by L_X/L. The five anti-slide piles are designed to be placed in the middle and lower parts of the secondary slope. The L_X/L of the five designed anti-slide pile locations is 0.17, 0.25, 0.33, 0.41, and 0.50, respectively. The grouping of the constructed model is shown in Figure 17. The five anti-slide pile groups are activated sequentially during the calculation, and the mechanical parameters of normal anti-slide piles are assigned.

4.3.2. Analysis of Support Effectiveness

The above scheme is adopted to protect the slopes of the abandoned dreg body. Under the action of anti-slide pile support at different locations, the lateral displacement values of the top and bottom of the bridge pile are shown in Figure 18. The top and bottom displacements of the piles after burying the anti-slide pile are significantly reduced compared with those without the anti-slide pile. The lateral displacement of the top of the pile decreases with the increase in L_X/L and reaches a minimum of 2.99 cm when L_X/L = 0.5. The lateral displacement of the bottom of the pile shows a fluctuating decreasing trend with the increase in L_X/L and reaches a minimum of 14.03 cm when L_X/L = 0.5.

Figure 19 and Figure 20 show the point line diagrams of the maximum compressive stress and the maximum tensile stress, respectively. The maximum compressive stress and the maximum tensile stress of the bridge pile body show an increasing trend at 0.17 < L_X/L < 0.25 and a decreasing trend at 0.25 < L_X/L < 0.5. The maximum compressive stress reaches a minimum value of 2 MPa and the maximum tensile stress reaches a minimum value of 1.34 MPa when L_X/L = 0.5.

The bending moments of bridge piles under different anti-slide pile support schemes are shown in Figure 21.

From the figure, it can be seen that under different schemes, the bending moment of the pile body shows a tendency to increase and then decrease with the increase in pile height. The bending moment of the pile body reaches the maximum value at a height of about 15 m. By comparing the different schemes, it is found that the maximum bending moment value of the pile is when L_X/L = 0.5, which is 3009.474 kN·m.

5. Summary

This paper takes a highway reconstruction and expansion project in South China as the background and analyzes the stability of the abandoned dreg body by using a numerical simulation method. The impact of the abandoned dregs on the new bridge and the hazard prevention and control measures are studied, and the following conclusions are drawn:

• Compared with burying the anti-slide pile, slope cutting is more conducive to improving the stability of the slopes of the abandoned dreg body. The calculation results show that the safety factor of the abandoned dreg body slopes in the original state, after slope cutting, and with a buried anti-slide pile is 1.95, 2.28, and 2.11. This shows that the original slope is in a stable state, and the cut slope and buried anti-slide pile improve the stability to different degrees, but the effect of slope cutting is more obvious.
• The bridge pile deflection increases with the increase in vertical force intensity, and the maximum bending moment of the pile body increases first and then decreases. The vertical force intensity of 4 MPa was loaded on the top of the pile in 10 stages, and the force intensity was increased by 0.4 MPa each time. The results show that the displacement of the pile top increases significantly after the vertical force intensity is applied, and the lateral displacement of the pile top shows an increasing trend as the vertical force intensity is applied step by step. The maximum bending moment of the pile body increases to 641.58318 kN·m with the increase in vertical force intensity within a certain range, and the maximum bending moment of the pile body tends to decrease after exceeding this range.
• The impact of the abandoned dregs on the bridge pile under the storm condition increases significantly. Under the normal condition, the lateral displacement of the pile body decreases from bottom to top, and the maximum lateral displacement of the pile body of 11.13 cm occurs in the lowest part. The lateral displacement at the top is 2.13 cm in the negative direction of the x-axis, and the bending moment distribution of the pile has an inverse “S” shape. The maximum displacement at the bottom of the pile in the storm condition increases by 40.52% compared to the normal condition. The value of lateral displacement at the top of the pile increases by 40.52% compared to the normal condition. The bending moment of the pile body shows a tendency to increase and then decrease with the increase in pile height, and the peak positive bending moment in the normal condition increases by 54.57%.
• The best protective effect is achieved when the anti-slide pile is buried in the middle of the secondary slope. By analyzing the lateral displacement, stress, and bending moment distribution of the bridge pile after the anti-slide pile is buried in different locations, it is determined that the anti-slide pile buried in the middle of the secondary slope has the best protective effect when it is buried at L_X/L = 0.5. However, this paper only establishes a single-pile model, and research on group piles needs to be further improved according to the actual project.