Deformation Characteristics of Pipelines Due to Adjacent Excavation in Riprap Reclamation Strata

Abstract

The Shenzhen Ma Wan area has special geotechnical conditions, with more than 50% of the area being reclaimed rock formations. Riprap reclamation strata are particularly susceptible to significant deformation upon stress release. To comprehensively comprehend the reaction of existing pipelines to the excavation of an adjacent deep foundation pit within the riprap reclamation strata, an interaction of the soil–pipeline was conducted by encompassing both scaled model tests and numerical simulations based on a cross-sea channel project. Firstly, scaled model tests were performed on a soil–pipeline interaction caused by excavation. Subsequently, the numerical model was verified by comparing the numerical simulation results with the scaled model test results. Then, the internal force, strain of the pipeline, and soil surface deformation under the conditions of a soil layer with riprap were analyzed, and the results were compared with the case without riprap. Finally, the influence of the support structures was analyzed. The results indicated that the presence of the riprap in strata led to a 19% increase in vertical displacement of the ground surface and a 35% increase in the pipeline bending moment compared with the case without riprap in the same strata. The maximum internal force and strain occurred at an inclined angle of 45° in the pipeline section. Furthermore, it was found that the first lateral support after excavation played a pivotal role in controlling the overall deformation of the foundation pit. The changes in stiffness in the lateral support were more sensitive to the horizontal displacement than the vertical displacement of the pipeline. The results provide valuable insights for the design and safety evaluation of engineering projects in riprap reclamation strata.

1. Introduction

In light of the escalating requirement for subterranean space utilization in recent years, excavation projects face increasing risks and challenges. Especially in coastal cities, some land is formed via reclamation from the sea, which poses significant risks to engineering construction. This surge in activity is marked by a trend towards deeper and more extensive diggings [1,2,3]. Consequently, the excavation of foundation pits unavoidably brings safety risks to neighboring pipelines. This includes the induction of soil and pipeline deformation and potential pipeline impairment, which could culminate in substantial property loss. As a result, an imperative emerges to delve into the intricacies of the forces and deformation behaviors experienced by buried pipelines amid excavation in reclaimed strata [4,5,6].

Previous studies have shown [7,8,9,10] that the excavation of foundation pits disrupts the inherent stress equilibrium of the original soil, triggering deformations with the adjacent soil. This transformative process is intricately linked to various factors such as soil properties, excavation techniques, the rate of precipitation, pit dimensions, the depth of excavation, and the presence of supportive structures [11,12,13,14,15]. Negligent pit excavation could pose substantial threats to surrounding strata and structures. In addressing this excavation quandary, four methodologies have emerged: theoretical analysis, field monitoring, model testing, and numerical simulation. Li et al. [16] pioneered an approach by formulating a horizontal displacement deformation equation based on the Pasternak foundation model. Their study delved into the impact of lateral unloading stress paths on model parameters, consequently deriving an analytical solution for pipeline horizontal deformation. However, such an approach’s applicability is limited within complex stratigraphic contexts. Hsieh et al. [17] augmented accuracy by statistically analyzing surface settlement functions for foundation excavation. Zeng et al. [18] conducted model tests to decipher the mechanisms underpinning pit deformation resulting from pre-excavation precipitation, subsequently refining these insights through scaled simulations. While theoretical analyses and model tests offer practicable methods, comprehending the cumulative influence of diverse horizontal parameters on pipeline internal forces proves challenging. Herein, numerical simulation is an effective means to analyze the impact of foundation excavation works on the surrounding environment under complex strata.

Extensive research has been conducted on the impact of excavation on adjacent pipelines [19,20,21,22]. Zhang et al. [23] established a soil–pipeline interaction model through numerical simulation and analyzed the effects of pipelines, soil and foundation pit parameters, pipeline internal pressure, and lateral support of the excavation on pipeline internal forces and deformation. The findings illuminated that the effect of pipeline internal pressure on pipeline deformation characteristics is small and negligible. Zhang et al. [24] analyzed the method of pit excavation on the change in the internal force of the adjacent pipeline, and the results showed that stress concentration would occur on the upper and lower surfaces of the central part of the pipeline after the excavation was completed. Niu et al. [25] studied the excavation of a foundation pit in loose soil, and it was found that the reasonable design of the support structure could effectively reduce soil deformation during the excavation.

Although the present studies provide valuable contributions, most studies have been conducted in land soil strata, with few cases of excavation adjacent to pipelines in riprap reclamation strata. In comparison with land soil strata, riprap reclamation strata exhibit diminished cohesion, heightened porosity, and an irregular distribution of sedimentary constituents. Due to the unique characteristics of riprap reclamation strata, the soil–pipeline interaction in riprap reclamation strata plays an important role for marine engineering safety. There is still a gap in the study of the influence of foundation pit excavation on the stress and deformation of adjacent pipelines under the geological background of riprap reclamation strata. In this study, a combination of model tests and the finite difference method was used to investigate the effects of foundation pit excavation adjacent to pipelines in reclaimed strata with riprap. Firstly, the correctness of the numerical simulation is verified via model tests. The internal force, strain of the pipeline, and soil surface deformation under the conditions of a soil layer with riprap are analyzed, and the results are compared with the case without riprap. The effect of a lateral support cross-sectional area on the internal force and deformation of pipelines is also discussed. This study can provide a valuable reference for the design and optimization of excavation projects in riprap reclamation strata.

2. Project Overview

The Ma wan cross-sea tunnel, the first undersea tunnel in Shenzhen, commences at the convergence of Moon Bay Avenue and Ma Wan Avenue in the south, and extends to Xixiang Avenue in the north, as depicted in Figure 1. This study focuses primarily on the open excavation section of the tunnel using the cut and cover method at Ma Wan Avenue in the south, as shown in Figure 1 marked with a red line. The excavation of the foundation pit had a width of 60 m and a depth of 30 m that the strata reclaimed with muddy soil and riprap. This riprap was characterized by haphazard distribution in soil, with void spaces interspersed among the loose riprap fragments, thereby amplifying the geological complexity. The geological configuration and excavation area is illustrated in Figure 2. Notably, a high-pressure gas pipeline was situated at a distance of 5.5–12 m from the outer edge of the foundation pit, and the direction of this gas pipeline was parallel to the longitudinal axis of the foundation pit. The plane arrangement is elucidated in Figure 3. The pipelines had a diameter of 0.61 m and were buried at a depth of 1.5–2.0 m.

3. Model Test

3.1. Design of Model Test

The purpose of this study is to examine the influence of riprap in soil on the adjacent pipeline deformation caused by deep excavation. Considering the symmetry of the foundation pit, only half of the excavation was taken for the scaled model test. According to the Buckingham π theorem, the geometric similarity ratio was determined as 1/30 (model/prototype) considering the actual engineering condition and model condition. The dimensions of the rigid container were 2.5 m (length) × 2.5 m (width) × 2.0 m (height) filled with clay. The depth of soil fill was 1.8 m. The excavation dimensions were 0.5 m (length) × 1.0 cm (width) × 1.0 cm (height). The depth of the pipeline was 0.05 m, and 0.18 m from the underground diaphragm wall was used for excavation support, as shown in Figure 4. Two cases are studied to examine the influence of riprap, which are Case 1 with a riprap layer and Case 2 without a riprap layer, and all the other conditions of the two cases are the same in the tests.

3.2. Materials of Soils and Structures

Since this study focuses on the influence of riprap layers on pipelines during foundation pit excavation, the original complex strata are simplified. The soil used in the model tests is only clay soil excavated from the project site. Building gravels with a particle size of 1–3 cm, selected according to the scaled ratio, were distributed in the upper clay layer to simulate a riprap layer. The thickness of the riprap layer was 0.2 m and the lower clay layer was 1.6 m, as shown in Figure 4c. The key parameters of the soil are shown in

Table 1. Soil parameters.

Soil Layer	$\mathbf{Natural}\mathbf{Density}\mathit{\rho }$ (kg/m3)	Cohesion c (kPa)	Friction f (°)	Poisson Ratio µ	$\mathbf{Moisture}\mathbf{Content}\mathit{\omega }$ (%)	Elastic Modulus E (MPa)
Riprap layer	2100	4.5	35.0	0.2	0	40
Clay layer	1850	18.8	20.0	0.35	72.5	18.5

. Considering the long-term consolidation and settlement of the soil layer on site, the soil in the container was compacted layer by layer with a thickness of 10 cm for each layer when preparing the model strata.

Aligned with the principles of the similarity ratio, a PVC pipeline with an outer diameter of 2 cm and an inner diameter of 1.8 cm was employed to replicate the pipeline conditions. The underground diaphragm wall was emulated using acrylic glass. The specific parameters for PVC and acrylic glass are listed in

Table 2. Parameters of pipeline and diaphragm wall materials.

Materials	$\mathbf{Density}\mathit{\rho }$ (kg/m3)	Poisson Ratio µ	Elastic Modulus E (MPa)
PVC	1400	0.42	3200
Acrylic glass	1200	0.3	3500

.

3.3. Case Procedure

In the model tests, the bending moment within the pipeline section was monitored through strain gauges. The vertical displacement of the ground surface along the pipeline’s longitudinal axis is tracked via a tie-rod displacement sensor, denoted as S 1–S 5, as depicted in Figure 5. In the configuration of the tie-rod displacement sensor, a 5 cm side-length iron sheet is positioned horizontally on the soil surface, serving as a reference point. The displacement sensor probe is then placed in close contact with this iron sheet. Meanwhile, the fluctuation in the bending moment within the pipeline is captured by strain gauges affixed to the pipeline’s exterior surface. Within the foundation pit’s excavation zone, a network of 18 strain measurement points is uniformly distributed along the pipeline’s longitudinal axis. This arrangement is illustrated in Figure 5. Subsequent to the initial soil equilibrium, the excavation progressed step by step with each layer dug to a depth of 20 cm.

3.4. Analysis of Case Results

The settlement trend of the soil surface directly above the pipeline is shown in Figure 6a,b. It can be seen that the settlement increased with the depth of excavation. The maximum vertical displacement of the soil above the pipeline at each excavation stage under the case with a riprap layer was 0.11 mm, 0.32 mm, 0.66 mm, 1.03 mm, and 1.32 mm, respectively, while the maximum vertical displacement of the soil above the pipeline at each excavation stage under the case without a riprap layer was 0.09 mm, 0.21 mm, 0.47 mm, 0.79 mm, and 1.11 mm, respectively. Remarkably, the maximum value of vertical displacement increases by 19% when the riprap layer is considered. This is because the density of the riprap reclamation strata is greater than that of clayey strata, resulting in higher lateral pressure. As the strata is excavated and unloaded, the resulting settlement at the ground surface is also relatively significant.

Figure 7 shows the bending moment value of the pipeline according to the measured strain when excavated to the bottom of the foundation pit. The convention for bending moment notation is as follows: one sees a negative bending moment when the outer surface of the pipeline near the middle of pit is tensioned, and one sees a positive bending moment when the outer surface of the pipeline away from the middle of pit is tensioned. It can be seen that the pipeline near the foundation pit’s sides exhibits a bending behavior opposing its direction, becoming progressively closer to the middle line of the foundation pit. This transformation is indicated by the pipeline’s bending moment changing from positive to negative. In the case with a riprap layer, the pipeline’s bending moments surpass those recorded in the condition without a riprap layer. Specifically, the case with a riprap layer yields a maximum negative bending moment of −0.165 N·m and a positive bending moment of 0.068 N·m. In contrast, in the case without a riprap layer, the maximum negative bending moment is −0.122 N·m, with a positive bending moment of 0.05 N·m. The maximum longitudinal bending moment of the pipeline at the middle line of the foundation pit increases by 35% when considering the riprap layer. The presence of a riprap layer caused more risk during excavation, necessitating reinforcement measures to ensure pipeline safety.

4. 3D Numerical Simulation

To further explore the influence of excavation on adjacent pipelines in riprap reclamation strata, a soil–structure model through the finite difference program Flac 3D was established. First, a model with the same dimensions as the experimental model was created to validate the rationality of the numerical simulation method. Subsequently, a full-scale numerical model was developed based on the actual project dimensions. It should be noted that the clay used in the experiment was unsaturated clay with a high moisture content, but in the numerical calculation, it was assumed to be saturated clay based on the ground water condition in the project site.

4.1. Fluid–Solid Coupling Method

For the problem of soil excavation, the analysis is performed using a fluid–solid coupling method through the finite difference software. The relationship between pore water pressure and soil stress strain can be solved based on the following four equations.

Small deformation was assumed; the equilibrium equation is

$$\frac{\partial {\sigma }_{ij}}{\partial x_j}+\rho g_i=\rho \frac{d{u}_i}{dt},$$

(1)

where $\rho$ is the soil density, $\partial {\sigma }_{ij}$ is the stress, $u_i$ is the velocity component, and $t$ is the time, where $\rho =\left(1-n\right){\rho }_s+n{\rho }_w$, ${\rho }_s$ is the density of the solid phase, ${\rho }_w$ is the density of the liquid phase, and $n$ is the porosity.

The variation in pore pressure at the node with time should satisfy:

$$\frac{\partial P}{\partial t}=\frac{K_w}{-nV}\left(Q+\frac{\partial V}{\partial t}\right),$$

(2)

where $P$ is the pore pressure, $K_w$ is the fluid bulk modulus, $V$ is the total volume, and $Q$ is the total flow rate at the node.

The fluid conduction conforms to Darcy’s law,

$$q_i=-k_{ij}\frac{\partial }{\partial x_j}\left(P-{\rho }_w{g}_k{x}_k\right),$$

(3)

where $q_i$ is the flow rate and ${\rho }_w$ is the permeability coefficient.

The fluid balance equation is given by

$$\frac{\partial \varsigma }{\partial t}=-\frac{\partial q_i}{\partial x_j}+q_v,$$

(4)

where $\varsigma$ is the variable of fluid volume per unit volume and $q_v$ is the intensity of the volumetric flow source.

$$\frac{\partial P}{\partial t}=M\left(\frac{\partial \varsigma }{\partial t}-\alpha \frac{\partial \epsilon }{\partial t}\right),$$

(5)

where $M$ is the Biot modulus, $\alpha$ is the Biot coefficient, and $\epsilon$ is the volume strain.

The phase capacity equation is

$$\stackrel{·}{\epsilon }=\frac{1}{2}(\frac{\partial {\stackrel{·}{u}}_i}{\partial x_j}+\frac{\partial {\stackrel{·}{u}}_j}{\partial x_i}),$$

(6)

where $\stackrel{·}{\epsilon }$ is the strain rate component and ${\stackrel{·}{u}}_i$ is the velocity component.

4.2. 3D Numerical Model and Verification

The dimensions of the numerical model are exactly the same as those of the test model, and the length, width, and height are 2.5 m, 2.5 m, and 1.8 m, respectively, as shown in Figure 8. The simulated soil, underground diaphragm wall, and pipeline models were all built using 8-node solid elements, with a total of 45,884 elements and 53,791 nodes. The fluid was set to be isotropic, and the soil was assumed to be saturated.

For the boundary condition, the surfaces of the bottom (z = 0) and four sides of the model are constrained in their normal directions, and the top surface of the model (z = 1.8) is a free surface. The bottom surface and four sides are set as an impermeable boundary, and the top surface is set as a permeable boundary. The excavation face is not set to mechanical constraints and is considered to be a permeable boundary. The pipeline and underground diaphragm wall are set to be impermeable.

In the numerical analysis, the pipeline and the underground diaphragm wall are modeled as an elastic structure, and the soils are calculated with the Mohr–Coulomb model. All the parameters are taken according to the parameters used in the model tests. Equal thickness of the pipeline is assumed. The internal pressure and joints of the pipeline are not considered. The Coulomb friction is used to describe the soil–structure interaction, and the Coulomb friction angle is 30°.

A total of six stages in the numerical calculation were carried out, starting with the initial geostatic conditions, followed by five stages of excavations for the pit, with each stage at a depth of 0.2 m.

Figure 9a shows the comparison of the bending moment distribution of the pipeline between the numerical simulation and model test. It can be found that the change trend of the bending moment is the same. For the simulation results, the maximum positive bending moment is 0.101 N·m, which is about 56% of the maximum negative bending moment. Figure 9b shows the vertical displacement of the ground surface obtained from the numerical simulation and the model test, respectively. The maximum settlement appears in the middle of the pit and the values are −1.32 mm and −2.04 mm for the model test and numerical simulation, respectively. The maximum land subsidence error is 54%. The difference between the numerical simulation and the model test is related to the basic assumptions made in the numerical calculations. When the clay layer is considered to be saturated, the surface settlement due to drainage consolidation is relatively large. Therefore, it can be considered that the results of the numerical simulation are credible.

5. Numerical Simulation

Through the results from the above model test and numerical simulation, it can be concluded that the presence of the riprap layer leads to greater pipeline bending moments and ground surface settlements compared with the case without the riprap layer. A 3D numerical model in the real scale size is constructed. In the numerical simulation, Case 1 is the working condition without lateral support, and Case 2 is the working condition considering lateral support.

Figure 10 shows the numerical model. To save computational costs, a symmetric 1/2 model was created. The whole model size is 90 m × 90 m × 60 m in length (X direction), width (Y direction), and depth (Z direction), respectively. The pit size is 30 m length × 13 m width × 30 m depth. The thickness of the underground diaphragm wall is 1 m and the height is 40 m. The radius of the pipeline is 0.305 m, and the buried depth is 2 m, which is located at a distance of 5 m from the underground diaphragm wall. The simulated soil, underground diaphragm wall, and pipeline models were all built using 8-node solid elements, with a total of 28,444 elements and 32,710 nodes.

The strata consist of riprap, mud, sand, clay, completely weathered granite, strongly weathered granite, and moderately weathered granite from the surface to the bottom. The used soil parameters are listed in

Table 3. Parameters of soil.

Soil Layer	Height h (m)	$\mathbf{Natural}\mathbf{Density}\mathit{\rho }$(kg/m3)	Permeability (cm/s) k	Porosity n	Cohesion c (kPa)	Friction f (°)	Poisson Ratio µ	Elastic Modulus E (MPa)
Riprap	8.5	2200	3 × 10−2	0.45	0	37.0	0.25	40.4
Mud	7.5	1650	1.6 × 10−4	0.39	10.0	25.0	0.4	2.5
Sand	11.0	2000	1 × 10−3	0.50	0	33.0	0.3	50.0
Clay	8.0	1900	1.05 × 10−4	0.37	20.0	20.0	0.35	19.6
Completely weathered granite	3.0	1950	5.2 × 10−5	0.28	35.0	22.0	0.38	61.4
Strongly weathered granite	10.0	2200	3 × 10−5	0.25	134.0	28.0	0.35	100.0
Moderately weathered granite	12.0	2700	3.3 × 10−6	0.20	500.0	40.0	0.3	92.6

, and the Mohr–Coulomb damage criterion is assumed for the soil. The lateral supports of excavation are 0.32 m in diameter and are assumed to be elastic models. The underground diaphragm wall is made of C 35 concrete and is assumed to be elastic material. The structure parameters are listed in

Table 4. Parameters of structure.

Type of Structure	$\mathbf{Density}\mathit{\rho }$	Elastic Modulus E (MPa)	Poisson Ratio µ	Diameter D (mm)	Thickness t (mm)
Reinforced concrete lateral support	2600	3.13 × 104	0.30	610	-
Underground diaphragm wall	2300	3.2 × 104	0.2	-	1000
Pipeline	7800	2.1 × 1011	0.3	-	110

. Coulomb friction was assumed to describe the soil–pipeline interaction, and the Coulomb friction angle is 30°. Normal displacements are constrained on four sides of the model and the bottom of the model and are set to impermeable boundaries. The top of the model and the face of the excavation are not mechanically or fluidly constrained. The numerical calculation commences with establishing the initial geostatic conditions, followed by five successive excavation stages, each stage with a depth of 6 m.

5.1. Result Analysis

Figure 11 shows the displacement of the pipeline at the location of the middle line of the excavation pit. The results indicate that in Case 1, the horizontal displacement of the pipeline is consistently greater than the vertical displacement during the first four stages of excavation. In Case 2, the horizontal displacement of the pipeline is greater than the vertical displacement in all excavation stages. It is noteworthy that, whether considering lateral support or not, the maximum increase in horizontal displacement occurs during the first stage of excavation, while the maximum increase in vertical displacement occurs during the fifth stage of excavation. This is because the shallow soil layers consist of riprap. The higher density of the riprap layer leads to relatively greater lateral pressure, resulting in greater horizontal displacement of the pipeline compared with its vertical displacement. Due to the influence of the riprap layer, the greatest impact on the horizontal displacement of the pipeline occurs in the first excavation stage, accounting for 42% of the cumulative horizontal displacement value in Case 1. Therefore, the first lateral support plays a crucial role during pit excavation, especially in strata consisting of riprap.

Figure 12 illustrates the horizontal and vertical displacements of the entire pipeline at the end of the excavation. From the figure, it can be observed that in Case 2, both the horizontal and vertical displacements are well controlled due to the presence of lateral support. When increasing lateral support, the vertical displacement of the pipeline is reduced by 43.7%, and the horizontal displacement is reduced by 28.2%.

Figure 13 shows the results of surface settlement after the completion of the excavation. As depicted in Figure 13, in Case 1, the maximum settlement at measuring line A is −23.7 mm, while the surface settlement farther away from the excavation edge approaches −7.7 mm. In Case 2, the maximum settlement at measuring line A reaches −12.4 mm, with soil settlement on the side farther from the excavation at −7.3 mm. This indicates that the lateral support of the excavation can only constrain the settlement of the surrounding soil within a certain range. At positions A in both Case 1 and Case 2, the surface settlement significantly exceeds that on the side adjacent to the underground diaphragm wall. This is because the diaphragm wall generates upward frictional forces on the soil, restricting the spread of soil settlement. In both Case 1 and Case 2, position B of the surface settlement above the pipeline exhibits a similar trend. In Case 2, with lateral support, the surface settlement is reduced by 54.4%.

Figure 14 displays the distribution of Von Mises stress of the pipeline. When excavating the foundation pit in the riprap reclamation strata, whether considering lateral support or not, the maximum Von Mises stress always occurs at a 45° angle from the cross-section. As the excavation of the foundation pit progresses in both Case 1 and Case 2, the high-stress areas and the maximum Von Mises stress continually increase. The maximum Von Mises stress in Case 1 and Case 2 is 11.57 MPa and 8.038 MPa, respectively.

Figure 15 illustrates the axial strain distribution of the pipeline at the middle line and the corner of the foundation pit, respectively. Here, positive values indicate tension, while negative values indicate compression. It can be observed that in both Case 1 and Case 2, the deformations in the middle section of the pipeline and in the corner of the foundation pit are opposite in direction. In Case 2, due to the presence of lateral support, the internal forces and deformations in the pipeline are much smaller. Furthermore, whether lateral support is considered or not, the peak stress and axial strain at the central position of the pipeline are larger than at other locations. Therefore, this section should receive greater attention and protection. Specifically, the maximum stress of the pipeline is reduced by 30.5%. The maximum axial strain of the pipeline in the middle and corner of the foundation pit is reduced by 30.9% and 34.8%, respectively. It can be seen that setting lateral support is more beneficial for reducing pipeline deformation at the corner of the foundation pit.

Figure 16 displays the axial force distribution of lateral supports in Case 2. It can be observed from the figure that the maximum axial force of lateral supports occurs at the middle position of the first layer, measuring 3352 kN. At the end of the excavation, the axial forces of the five lateral supports in the first layer are greater than those at corresponding positions in other layers. This indicates that the lateral supports used after the first stage of excavation play a critical role in controlling the deformation of the excavation in riprap reclamation strata. Therefore, in engineering projects, it is advised to increase the lateral support stiffness in this area to ensure reasonable control of the excavation deformation. The axial forces of lateral supports at the two corners near the underground diaphragm wall are relatively low and the stiffness of the supports can be reduced. In addition, it is found that the axial force of lateral support in the middle position of each layer is greater than other lateral support in the same excavation layer. This is because the existence of the underground diaphragm wall shares the axial force of the surrounding lateral support. As the most common supporting structure in the foundation pit project, the underground diaphragm wall and lateral support should be used together to obtain their maximum performance. This can not only effectively maintain the stability of the foundation pit and the surrounding structure, but also reduce the cost.

5.2. Influence of Lateral Support Parameters

Generally, the influence of excavation on the stress and strain distribution of soil is intricately tied not only to the size and excavation method, but also to the support structures [26]. In the process of considering lateral support of the excavation in the foundation pit, the role of supports in controlling soil deformation is crucial. In the engineering described in this study, the top soil involves a riprap layer, which results in greater lateral displacement at the top of the underground diaphragm wall when the first stage of excavation is performed. The parameters of the lateral support are examined to explore the impact of different stiffness levels of lateral support of the excavation on pipeline force and deformation. Based on the above section, nine cases with a support radius R of 0.16 m, 0.20 m, 0.24 m, 0.28 m, 0.32 m, 0.36 m, 0.40 m, 0.44 m, and 0.48 m are considered to present different stiffness levels of the support, respectively.

Figure 17 shows the horizontal and vertical displacements of the pipeline at the end of the excavation. From the results, the horizontal and vertical displacements of the pipeline decrease with increasing radius, and the impact of changing the stiffness level of lateral support of the excavation on the pipeline horizontal displacement is obvious. When R = 0.2 m, the pipeline vertical displacement decreased by 18.15%, and the horizontal displacement decreased by 13.67%. Compared with R = 0.16 m, the vertical and horizontal displacements of the pipeline reduced by 39.75% and 39.68%, respectively, when R = 0.28 m and decreased by 69.9% and 74.3%, respectively, when R = 0.48 m. This trend indicated that high stiffness of lateral support of the excavation can effectively restrain the pipeline displacements in both the horizontal and vertical directions.

6. Conclusions

In this study, the displacement and internal force response of pit excavation adjacent to a pipeline in a riprap layer is analyzed through model tests and numerical analysis. The following conclusions are drawn.

(1)

In the presence of riprap reclamation strata, the maximum vertical displacement of the pipeline increased by 19% compared with the case without a riprap layer. The maximum negative moment of the pipeline in the middle of the foundation pit increased by 35%, and the maximum positive moment of the pipeline near the two corners of the foundation pit increased by 36%. The existence of a riprap layer greatly influences the pipeline safety.

(2)

During excavation of the foundation pit, the maximum change in horizontal displacement of the pipeline occurred during the first stage of excavation of the top soil, and the maximum change in vertical displacement occurred at the last stage of excavation. The maximum internal force and strain occurred at an inclined angle of 45° in the pipeline section, and the overall distribution was symmetric around the pipeline section.

(3)

The first layer of lateral support of the excavation plays a crucial role in controlling the deformation of the foundation pit, and increasing the stiffness of the lateral support of the excavation can be appropriated. For the lateral support with small axis force, the stiffness of excavation support can be relatively reduced.

(4)

When increasing the section area of the lateral support of the excavation, both the horizontal and vertical displacement of the pipeline showed a decreasing trend, but the decrease in the vertical displacement was smaller. The horizontal displacement of the pipeline was more sensitive to changes in the lateral support of the excavation than the vertical displacement.

(5)

An underground diaphragm wall can only limit further settlement of the ground within a certain spatial extent. The maximum ground settlement often occurs at the limit of this spatial extent. In real projects, underground diaphragm walls should be constructed at reasonable locations so that the maximum surface settlement occurs away from the location of pipelines.

It should be noted that for the soil–structure contact effect, Coulomb friction is used in this study. However, the soil–structure contact effects are much more complex in real engineering. This problem should be further studied in the future.