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Mechanical response analysis of the buried pipeline due to adjacent foundation pit excavation
Tunnelling and Underground Space Technology 78 (2018) 135–145
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Mechanical response analysis of the buried pipeline due to adjacent foundation pit excavation
T
⁎
Jie Zhanga,b, , Rui Xiea, Han Zhanga a b
School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Buried pipeline Foundation pit FEM Stress Deformation
Foundation pit is one of the most factors that threaten the safe operations of buried pipeline. In order to study the effect of foundation pit excavation on the buried pipeline, a three-dimensional model of pipeline and foundation pit was established, and the variation regulations of pipeline’s deformation under the foundation pit excavation were investigated. Effects of pipeline parameters, foundation pit parameters, soil parameters and underground continuous wall on the stress, strain and deformation of the pipeline were studied. The results show that the underground continuous wall can effectively reduce the pipeline deformation. After the foundation pit excavation, the upper surface of the pipeline’s middle section is pressed, and the lower surface is pulled, but the strain distribution of the pipeline at the edge of the pit is opposite. Horizontal and vertical displacements occurs on the pipeline, horizontal displacement moves to the inside of the pit, and vertical displacement moves to the bottom of the pit. The pipeline deformation decreases with the increasing of pipeline’s radius-thickness ratio, but it increases with the increasing of the distance between the pipeline and foundation pit. The internal pressure has a small effect on the pipeline deformation. Pipeline deformation increases with increasing of the foundation pit’s width and depth. However, the length of the foundation pit has no effect on the pipeline. The pipeline deformation increases with the soil’s Poisson’s ratio increases, and it decreases with the increasing of soil’s cohesion and elastic modulus. With the increasing of thickness and elastic modulus of the underground continuous wall, the pipeline deformation decreases. Those results can be used for pipeline laying, construction, maintenance and safety evaluation.
1. Introduction Compared to roads, rail transport, pipelines are the safest and most economical way to transport flammable substances. With the increasing of infrastructure construction, buried pipelines may be affected by other projects, such as various urban underground constructions, which may cause pipeline failure and leakage (Shen and Xu, 2011). The foundation pit excavation will change the initial stress state of the soil, thus resulting in the surrounding soil deformation. That mainly includes the uplift at the bottom of the foundation pit, the displacement of the underground continuous wall and the soil settlement after the wall. The soil deformation will lead to segment leakage or local damage of the pipelines. Longitudinal distortion is a fatal threat to the structural safety and normal operations of buried pipelines. Therefore, mechanical behavior analysis of buried pipelines affected by foundation pit excavation is very important for its safety evaluation. In recent years, many researches on the pipeline deformation caused by the foundation pit excavation were carried out. Zhang et al. (2012) ⁎
provides a continuous elastic analysis to simulate the responses of the pipelines subjected to tunnel-induced soil movement in multi-layered soils. Klar and Marshall (2007) analyzed the effect of tunneling on the pipeline by using Euler-Bernoulli simple beam theory and shell element theory. Zhang et al. (2015) presented a simplified method to determ the mechanical behavior of buried pipeline induced by foundation pit excavation by using Winkler foundation model. Li et al. (1999) used Winker theory to establish the vertical displacement and horizontal displacement equations of the pipeline affected by the foundation pit excavation. Jiang (2014) derived the deformation and internal force of the pipeline by the elastic foundation beam. Yang et al. (2011) studied the pipeline response by the finite element model. In addition, Shi et al. (2016) study the effects of the lateral unloading caused by foundation pit excavation on the existing shield tunnels based on nonlinear contact theory. Chen et al. (2016) studied the influence of a nearby large excavation on existing twin tunnels in soft soils by FEM. However, they did not pay attention to the effect of foundation pit excavation on buried pipelines. Li et al. (2016) presents an analytical solution for the
Corresponding author at: School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China. E-mail address: [email protected] (J. Zhang).
https://doi.org/10.1016/j.tust.2018.04.026 Received 7 July 2017; Received in revised form 3 March 2018; Accepted 11 April 2018 Available online 27 April 2018 0886-7798/ © 2018 Elsevier Ltd. All rights reserved.
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θ0 M0 Q0 ϕ (βx )
Nomenclature u(x) umax x i K0 D E I y a, b, c δ L y0
ground settlement the maximum ground settlement horizontal distance from the foundation pit axis width coefficient of the ground settlement the subgrade modulus outer diameter of the buried pipeline elasticity modulus inertia moment of the pipeline section displacement of the pipeline constant the maximum ground settlement deformation length of the pipeline displacement of the pipeline at O point
β=4 V W H t ρ μ σy Pmax l
rotation of the pipeline at O point bending moment of the pipeline at O point shear force of the pipeline at O point Krylov’s function K 4EI
– pit length pit width excavation depth wall thickness density Poisson’s ratio yield stress the maximum operating pressure distance between pipeline and foundation pit
θ0 M Q ϕ (βx )− 02 ϕ3 (βx )− 0 3 ϕ4 (βx ) β 2 EIβ EIβ
deflection and the internal forces of an existing tunnel. Li et al. (2014) carried out a centrifuge model test to investigate the effect of new shield tunnelling on an existing underlying large-diameter tunnel. Despite the contributions of these researches are inordinately valuable, but most researches assumed that the pipeline is in close contact with the soil when it is deformed, and analyzed the pipeline as a beam. In real working condition, the buried pipeline and surrounding soil affect each other, the pipelines and soil will not contact with each other along the axial direction. In this paper, a pipeline-soil interaction model was established to analyze mechanical behavior of the buried pipeline under the influence of foundation pit excavation, which can provide a reference for the design, laying and maintenance of the buried pipeline.
θ = −4βy0 ϕ4 (βx ) + θ0 ϕ1 (βx )−
2. Analytical model of the buried pipeline
f=−
y = y0 ϕ1 (βx ) +
whereϕ1 (βx ) , ϕ2 (βx ) , ϕ3 (βx ) , ϕ4 (βx ) is Krylov’s function. Eq. (6) is differentiated to get the rotation equation as follows:
f=
d 4y + Ky = q (x ) dx 4
∫0
x
Ku(z ) ϕ4[β (x −z )]dz
4δ 2 4δ 8δ 4δ x + x − 2 2 ϕ3(βx )− ϕ2(βx ) L2 L Lβ Lβ
y = y0 ϕ1 (βx ) +
θ0 M Q ϕ (βx )− 02 ϕ3 (βx )− 0 3 ϕ4 (βx ) + f β 2 EIβ EIβ
(9)
(10)
(1)
(2)
M0 Q0 8δ 4δ ϕ (βL) + ϕ (βL) + 2 2 ϕ3(βL) + ϕ (βL) = 0 EIβ 2 3 EIβ 3 4 Lβ Lβ 2
(11)
M0 Q0 8δ 8δ 4δ 4δ ϕ (βL) + ϕ (βL) + − ϕ (βL) + ϕ (βL)− =0 EIβ 2 EIβ 2 3 L L2β 2 L 1 L
(12)
Then the vertical displacement equation can be expressed as follows:
(3)
y=−
4δ 8δ 4δ 4δ M Q ϕ (βx )−⎡ 02 + 2 2 ϕ3⎤ (βx )− 0 3 ϕ4 (βx )− 2 x 2 + x ⎢ ⎥ Lβ 2 EIβ L β EIβ L L ⎣ ⎦ (13)
The horizontal displacement of the pipeline can be obtained by the
(4)
where a, b and c can be obtained by boundary conditions: u(0) = 0, u L (L) = 0, u 2 = δ . Then Eq. (4) can be written as follows:
()
4δ 4δ u(x ) = − 2 x 2 + x L L
(8)
The initial parameters are determined by the boundary conditions. At the O point, y(0) = 0. So, y0 = 0, θ0 = 0. At the L point, y(L) = 0. So, M0 and Q0 can be obtained by displacement equation and rotation equation as follows:
The solution of Eq. (3) consists of general solution and particular solution, but the particular solution is difficult to find out. Therefore, the ground settlement curve can be approximated as a quadratic function curve (Li et al., 1999). The pipeline under the load is shown in Fig. 1, the ground settlement curve is:
u(x ) = ax 2 + bx + c
1 EIβ 3
So, the vertical displacement equation of the pipeline can be obtained by initial parameter:
where K = K0D. Then the differential equation for the pipeline displacement induced by foundation pit excavation can be obtained:
EI
(7)
And the particular solution of Eq. (3) is:
According to Winker assumptions, the load on the pipeline is:
q(x ) = K ·u(x )
M0 Q ϕ (βx )− 0 2 ϕ3 (βx ) EIβ 2 EIβ
The particular solution of Eq. (3) can be obtained:
In the current theoretical calculations, the pipeline is usually analyzed as an elastic foundation beam to solve the displacement after pit excavation (Shen et al., 2013). The load on the pipeline due to foundation pit excavation is determined by the ground settlement. The ground settlement curve can be expressed by the Peck formula (Peck, 1969): 2 −x u(x )=u max e 2i2
(6)
(5)
The general solution of Eq. (3) can be obtained by using the initial parameter method of short beam (Li et al., 1999); the general solution is:
Fig. 1. Schematic diagram of a pipeline under the load. 136
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on the top surface of model, and normal constraint is applied to the rest surfaces.
same method. The horizontal load of the pipeline can be determined by the horizontal displacement of the soil. 3. Finite element model
4. Result analysis
3.1. Example validation
4.1. Underground continuous wall effect
In Ji (2013), a three-dimensional finite element model of a foundation pit project in Tianjin was established, actual measured and simulated values of surface settlement were compared. The same numerical model was established to simulate the excavation process. The length of foundation pit is 150 m, the width is 60 m, and the depth is 8 m. The thickness of underground continuous wall is 0.85 m, the total length is 18 m, and depth under the pit is 10 m. The distance between support center and surface is 2.65 m, and support cross-sectional size is 0.7 m × 0.7 m. According to the structural symmetry to simplify the calculation, the entire model size is 124 m × 107 m × 36 m. The eight-node reduced-integration elements are used to simulate soil and enclosure structure. Fig. 2 shows the surface settlement values at 1 m and 3 m from the foundation pit. The settlement trend is basically the same as the actual measured value. When the distance from the foundation pit is 1 m, the maximum settlement of the surface is 39.9 mm. When the distance is 3 m, the maximum settlement is 34.5 mm. The error is less than 10%. Obviously, the numerical simulation results are in good agreement with the actual values, which proved that the finite element model is reliable.
When the soil is silty clay, whether there is an underground continuous wall, the pipeline displacement is shown in Fig. 4. The underground continuous wall can greatly reduce the deformation of the buried pipeline. Under the action of the underground continuous wall, the pipeline displacement is small, and the overall displacement is not more than 5 mm. Therefore, the underground diaphragm wall can effectively reduce the effect of the foundation pit. 4.2. Numerical simulation result After foundation pit excavation, the deformation of the silty clay is smaller, while the deformation of the soft soil is larger. When the size of foundation pit is 30 m × 30 m×8m, Fig. 5 shows the stress-strain responses of the buried pipeline after the foundation pit excavation in soft soil. As seen in Fig. 5(a), the maximum von Mises stress appears on the upper surface of the middle part of the pipeline after foundation pit excavation, and the high stress distribution is narrow oval. The maximum stress is 150 MPa, the stress on the lower surface of the middle part of the pipeline is smaller than the upper surface. In addition, high stress area also appears on the pipeline at the edge of the pit. But the maximum stress of the pipeline’s lower surface is 120 MPa, which is greater than 100 MPa on the upper surface. As shown in Fig. 5(b), the high strain area of the pipeline corresponds to the high stress area, and the high strain area appears on both the upper and lower surfaces of the pipeline. Axial strain of the upper surface on the pipeline’s middle part is negative strain, while the lower surface is positive strain. It indicates that the upper surface of the pipeline’s middle part is pressed and the lower surface is pulled. But the strain distribution of the pipeline at the edge of the pit is opposite. Stress on the high strain area is greater than other section. Fig. 5(c) shows the displacement of buried pipeline. The vertical displacement appears on the top surface of the pipeline, it extends in z direction. The horizontal displacement appears on the side surface of the pipeline, it moves in the x direction toward the inside of the pit. Overall, the vertical displacement is bigger than the horizontal displacement. Because after the pit excavation, the soil settlement appears around the foundation pit, and it also moves to the inside of the pit.
3.2. Finite element model Removal of the soil within the foundation pit is accompanied by the release of the in-situ stress, and a large part of the earth pressure generated by the perturbation of the surrounding soil acts on the underground continuous wall, which greatly reduces the load on the buried pipeline. Fig. 3 shows the schematic diagram of the pipeline and the foundation pit. To save computation time, 1/2 model was established for the symmetry of the model structure, so the whole model size is 100 m × 50 m × 40 m (Zhang et al., 2015). The pit shape is rectangular, v = 30 m, w = 15 m, and H = 8 m. Gravity loading and internal pressure were applied first and subsequently foundation pit was excavated. Take X65 steel pipeline as an example in all cases. For the pipeline, D = 660 mm, t = 8 mm, ρ = 7800 kg/m3, E = 210GPa, μ = 0.3, and σy = 448.5 MPa (Zhang et al., 2018). Buried depth of the pipeline is 2 m, the pipeline is parallel to one side of the foundation pit, and the distance between the pipeline and the underground continuous wall l is 4 m. The material of underground continuous wall is concrete C20, the density is 2500 kg/m3, the elastic modulus is 25 GPa, the Poisson ratio is 0.2, the thickness of the wall is 0.6 m, and the depth is 16 m (Ji, 2013). Mechanical behavior of soil material is described through an elastic-perfectly plastic Mohr-Coulomb constitutive model (Zhang et al., 2018). The density of silty clay is 1980 kg/m3, the elastic modulus is 25 MPa, the Poisson’s ratio is 0.3, the cohesion is 22 kPa, and the friction angle is 15° (Jia, 2007). The density of the soft soil is 1760 kg/m3, the elastic modulus is 10.5 MPa, the Poisson’s ratio is 0.36, the cohesion is 12 kPa, and the friction angle is 7.1° (Ji, 2013). For pipeline-soil interaction, the outer surface of the pipeline and the soil are simulated with a contact algorithm, which allows for the separation of the pipeline and soil (Zhang et al., 2014). The friction coefficient is 0.3 (Shen et al., 2017). For the whole model, the soil is isotropic, homogeneous and continuous, regardless of groundwater. Pipeline extends along x-axis direction is horizontal, the y-axis direction for the axial direction, the zaxis direction for the vertical. Eight-node reduced-integration elements are used to simulate the soil and pipelines. The symmetry constraint is applied to the symmetry plane of the model, no constraint is imposed
Fig. 2. Surface settlement of the example. 137
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Fig. 3. Schematic diagram of the pipeline and the foundation pit.
gradually increases, and the high stress area extends along the pipeline axial direction. The pipeline is easily deformed when its thickness decreases. The axial strain on the upper surface of symmetrical section of the pipeline is shown in Fig. 6(b). As the radius-thickness ratio increasing, the maximum axial strain on the upper surface of the pipeline increases, but the change regulation of the lower surface of the pipeline is opposite to the upper surface. Fig. 7 shows the maximum displacement of the pipeline with different radius-thickness ratios. Under the action of pit excavation, horizontal and vertical displacements appears on the pipeline. The horizontal displacement is to the inside of the foundation pit, and the vertical displacement is to the bottom of the foundation pit. With the increasing of the radius-thickness ratio, the horizontal displacement of the pipeline increases gradually, and the variation is about 17 mm. At the same time, the vertical displacement of the pipeline increases, but the variation is more than 20 mm. It indicates that the vertical displacement of the pipeline is more sensitive, because the vertical displacement is bigger than the horizontal displacement. The change rates of horizontal displacement and vertical displacement reduce with the radius-thickness ratios increases. In general, the foundation pit excavation has a great effect on thin wall pipeline.
Fig. 4. Displacements of the pipeline in different directions.
However, due to the function of underground continuous wall, the soil’s horizontal displacement reduces. In Li et al. (1999), the value of some parameters have been provided. The theoretical vertical displacement of the pipeline can be obtained by Eq. (13). The curves show that the theoretical model is consistent with the numerical model, and the error is small at the maximum vertical displacement. It indicates that the numerical model is reasonable. Pipeline is a thin structure, and there may be residual stress and stress concentration for the pipeline. Therefore, the finite element method is more suitable.
5.2. Internal pressure effect For gas transmission pipeline, considering a safety factor equal to 0.72, and the maximum operating pressure can be given by the expression Pmax = 0.72 × (2σy/D) (Zhang et al., 2014). The maximum displacement of the pipeline with different internal pressures are shown in Fig. 8. With the increasing of the internal pressure, the horizontal and vertical displacement of the pipeline changes very little. It indicates that the pipeline deformation is mainly affected by the earth pressure accompanied with the foundation pit excavation. The effect of internal pressure on pipeline deformation and axial stress is very small, it only affect its circumferential stress.
5. Effect of pipeline parameters 5.1. Radius-thickness ratio effect
5.3. Distance effect
The existing results show that the radius-thickness ratio of the pipeline will directly affect the stability of the buried pipeline (Wu and Shen, 2017). When the diameter of the pipeline is 660 mm, the stressstrain responses of the pipeline with different radius-thickness ratios are shown in Fig. 6. In Fig. 6(a), when the radius-thickness ratio is 83, the thickness is 8 mm, the maximum stress of the pipeline is 152 MPa. When the thickness is 18 mm, the maximum stress of the pipeline is 100 MPa, the change rate is more obvious. With the radius-thickness ratio increasing, the maximum von Mises stress of the pipeline
When the radius-thickness ratio is 83, the stress-strain responses of the pipeline under different distances between pipeline and underground continuous wall are shown in Fig. 9. As shown in Fig. 9(a), the high stress area and the maximum von Mises stress decrease as the distance increases. When the distance is 10 m, the maximum stress of the pipeline is about 50 MPa, the change is very obvious. At the same time, the stress area of the pipeline at the edge of the foundation pit is 138
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(a) Von Mises stress (a) Von Mises stress
(b) Axial strain of xz plane (b) Axial strain
Fig. 6. Stress-strain responses of the pipeline with different radius-thickness ratios.
(c) Displacement Fig. 5. Stress-strain responses of the buried pipeline in soft soil. Fig. 7. Displacements of the pipeline with different radius-thickness ratios.
obviously decreases. In Fig. 9(b), the maximum axial strain of the pipeline decreases with the distance increases. When pipeline is far away from the pit, the soil displacement due to excavation is small. The maximum displacement of the pipeline under different distances are shown in Fig. 10. With the increasing of the distance, the pipeline displacement decreases. The change of the horizontal
displacement of the pipeline is about 50 mm. The change of the vertical displacement is about 80 mm, it is much larger than the horizontal displacement. Therefore, the actual construction should considering the distance between the foundation pit and the adjacent pipeline. 139
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Fig. 8. Displacements of the pipeline under different internal pressures.
Fig. 10. Displacements of the pipeline under different distances.
Mises stress increase with the pit width increases. This is because the pit width can resulting in the increasing of soil deformation’s area, that make the influence area of the pipeline becomes larger. In Fig. 11(b), the pit width not only affects the deformation of the pipeline but also affects the axial deformation range. With the increasing of the pit width, the deformation range of soil around the
(a) Von Mises stress
(a) Von Mises stress
(b) Axial strain of xz plane Fig. 9. Stress-strain responses of the pipeline under different distances.
6. Effect of foundation pit parameters 6.1. Pit width effect Fig. 11 shows the stress–strain responses of the pipeline under different widths of foundation pit. In Fig. 11(a), effect of the pit width on the pipeline is more obvious, the high stress area and the maximum von
(b) Axial strain of xz plane Fig. 11. Stress-strain responses of the pipeline under different pit widths. 140
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cohesion of the soil is 10 kPa, the maximum stress of the pipeline reaches 217 MPa, which is very large compared with 54 MPa when the cohesion is 18 kPa. In Fig. 17(b), the maximum axial strain of the pipeline decreases as cohesion increases, but the change rate decreases. According to common sense, the soft clay is prone to deform, so the deformation of the buried pipeline in the soft clay is more obvious after foundation pit excavation. In Fig. 18, the horizontal vertical displacements decrease with the increasing of the soil’s cohesion. The difference between them also decreases. In engineering practice, the property of the soil in the excavation area is critical for the engineering construction.
foundation pit gradually increases, the range of pipeline’s deformation also increases. Then, the maximum axial strain of the pipeline is increases. In Fig. 12, with the pit width increasing, the maximum displacement of the pipeline increases, but the change is not entirely linear. The difference between the horizontal displacement and the vertical displacement gradually increases. 6.2. Pit length effect According to the stress and strain responses of the pipeline under different pit lengths, there is a little change of the pipeline’s high stress area. And the maximum stress change of the pipeline is not obvious. The difference between the strain curves of the pipeline’s symmetrical section under different pit lengths is very small. It indicates that the length of the foundation pit has a little effect on the pipeline.
7.3. Elastic modulus of the soil effect When the Poisson’s ratio of the soil is 0.35, the cohesion is 12 kPa, the stress-strain responses of the pipeline under different elastic modulus of the soil are shown in Fig. 19. The maximum von Mises stress and high stress area decrease with the elastic modulus increasing. But the change of the pipeline at the edge of the foundation pit is not obvious. This is because the deformation of the soil with a small elastic modulus is bigger, then the force act on the pipeline is greater. The strain curve of symmetrical section shows that the maximum axial strain of the pipeline decreases with the increasing of the elastic modulus, but the change of the axial strain is small. In Fig. 20, the change of the horizontal displacement is very small, but the change of the vertical displacement more obvious. In general, the deformation of the pipeline decreases with the elastic modulus increasing, but the effect is not very obvious.
6.3. Pit depth effect Fig. 13 shows the stress-strain responses of the pipeline under different depths of foundation pit. In Fig. 13(a), the pit depth has an obvious effect on the pipeline’s stress, which increases with the increasing of the pit depth. When the pit depth is 9 m, the maximum stress of the pipeline is 285 MPa, which is very large compared with 150 MPa when the depth is 8 m. When the pit depth is 6 m, the stress of the pipeline is very small, there is only a high stress are at the edge of the pit. From the strain curves of symmetrical section Fig. 13(b)), the maximum axial strain of the pipeline gradually increases with the increasing of the pit depth. When the pit depth is 6 m, the axial strain of the pipeline is about zero. Fig. 14 shows the maximum displacement of the pipeline under different pit depths. The horizontal and vertical displacements and their difference increase with the increasing of the pit depth. When the depth is 6 m, the difference between horizontal displacement and vertical displacement is less than 5 mm, and the difference gradually increases. When the depth is larger, the soil’s displacement is larger, and there is a large settlement on the ground. Therefore, a bigger the deformation of buried pipeline occurs.
8. Effect of the underground continuous wall parameters 8.1. Wall thickness effect Define r is thickness of underground continuous wall. The underground continuous wall can withstand a lot of earth pressure in the process of foundation pit excavation. It has become an indispensable structure for deep foundation pit support works. When the distance between the pipeline and the underground continuous wall is 4 m, the stress-strain responses of the pipeline under different thicknesses of the underground continuous wall are shown in Fig. 21. The maximum von Mises stress and high stress area decrease as the thickness increases. The strain curves of symmetrical section show that the maximum axial strain of the pipeline decreases with the increasing of the wall’s thickness. Underground continuous wall can reduce the displacement of soil around the foundation pit, so the effect of underground continuous wall
7. Effect of soil parameters 7.1. Poisson’s ratio of the soil effect Surrounding soil is the media between the foundation pit and the buried pipeline. The earth pressure caused by foundation pit acts on the pipeline by surrounding soil. Therefore, surrounding soil parameters have a great effect on the buried pipeline. Fig. 15 shows the stress-strain responses of the pipeline under different Poisson’s ratios of the soil. In Fig. 15(a), the maximum von Mises stress and high stress area increase as the Poisson's ratio of the soil increases. But it has a small effect on the stress area. In Fig. 15(b), with the increasing of the Poisson’s ratio, the maximum axial strain of the pipeline increases, and the change rate also increases. In Fig. 16, the maximum displacement of the pipeline increases as the Poisson’s ratio increases. Both the change of the horizontal and the vertical displacement are small. But the change rate of vertical displacement gradually decreases while the change rate of horizontal displacement increases. 7.2. Cohesion of the soil effect Cohesion is the mutual attraction between adjacent parts in same material. When the soil’s Poisson’s ratio is 0.35, the stress-strain responses of the pipeline under different cohesions of the soil are shown in Fig. 17. In Fig. 17(a), the maximum von Mises stress and high stress area decrease with the increasing of the soil’s cohesion. When the
Fig. 12. Displacements of the pipeline under different pit widths. 141
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(a) Von Mises stress
(a) Von Mises stress
(b) Axial strain of xz plane
(b) Axial strain of xz plane Fig. 13. Stress and strain responses of the pipeline under different pit depths.
Fig. 15. Stress-strain responses of the pipeline under different soil’s Poisson’s ratios.
Fig. 14. Displacements of the pipeline under different pit depths.
Fig. 16. Displacements of the pipeline under different soil’s Poisson’s ratios.
on the pipeline is more serious when the thickness is smaller In Fig. 22, the change rules of the horizontal and the vertical displacement are similar. The pipeline deformation decreases with increasing of the wall thickness, and the change rate also decreases.
8.2. Wall material effect At present, the material of the underground continuous wall is concrete in foundation pit engineering. The main difference between the different types of the concrete is the elastic modulus. When the 142
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(a) Von Mises stress (a) Von Mises stress
(b) Axial strain of xz plane
(b) Axial strain of xz plane
Fig. 17. Stress-strain responses of the pipeline under different soil’s cohesions.
Fig. 19. Stress-strain responses of the pipeline under different soil’s elastic modulus.
Fig. 18. Displacements of the pipeline under different soil’s cohesions. Fig. 20. Displacements of the pipeline under different soil’s elastic modulus.
density of the concrete is 2500 kg/m3, the Poisson’s ratio of the concrete is 0.2, elastic modulus of the different concretes are shown in Table 1. The stress-strain responses of the pipeline under different concretes of the underground continuous wall are shown in Fig. 23. The maximum von Mises stress and high stress area decrease with the increasing
of the concrete’s elastic modulus, but the change is less than 25 MPa. The strain curves of symmetrical section show that the maximum axial strain of the pipeline decreases as the elastic modulus increases, but the change is small. The elastic modulus of underground continuous wall
143
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Table 1 Elastic modulus of different concretes. Concrete
C20
C25
C30
C35
C40
Elastic modulus (GPa)
25
28
30
31.5
32.5
(a) Von Mises stress
(a) Von Mises stress
(b) Axial strain of xz plane Fig. 21. Stress-strain responses of the pipeline under different wall thicknesses.
(b) Axial strain of xz plane Fig. 23. Stress-strain responses of the pipeline under different concretes.
Fig. 22. Displacements of the pipeline under different wall thicknesses.
reflects its deformability. When the elastic modulus of underground continuous wall is larger, the deformation capacity is larger. It can reduce soil displacement, and then the pipeline deformation is small. In Fig. 24, the changes of the horizontal and the vertical displacements are small, the difference between them is more than 45 mm. The
Fig. 24. Displacements of the pipeline under different wall materials. 144
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pipeline displacement decreases as the wall’s elastic modulus increases, and the curve is approximately linear. The effect of wall material on the pipeline is greater. Its choice should be decided according to the actual situation.
metro tunnels due to adjacent large excavation and protective measure in soft soil. Tunn. Undergr. Space Technol. 58, 224–235. Ji, K.X., 2013. Numerical Analysis of Effects of Excavation on Deformation of the Adjacent Pipeline Based on ABAQUS. M.S Thesis, Tianjin Chengjian University, Tianjin, China (in Chinese). Jia, H.B., 2007. The Effectiveness Analysis of Deep Excavation to Adjacent Underground Utilities. M.S Thesis, Tongji Univesity, Shanghai, China (in Chinese). Jiang, Z., 2014. Theoretical analysis on deformation of pipeline caused by adjacent foundation pit excavation. Chin. J. Undergr. Space Eng. 10 (2), 362–368 (in Chinese). Klar, A., Marshall, A.M., 2007. Shell versus beam representation of pipes in the evaluation of tunneling effects on pipelines. Tunnel. Undergr. Space Technol. Incorporat. Trench. Technol. Res. 23 (4), 431–437. Li, P., Du, S.J., Ma, X.F., Yin, Z.Y., Shen, S.L., 2014. Centrifuge investigation into the effect of new shield tunnelling on an existing underlying large-diameter tunnel. Tunn. Undergr. Space Technol. 42, 59–66. Li, P., Du, S.J., Shen, S.L., Wang, Y.H., Zhao, H.H., 2016. Timoshenko beam solution for the response of existing tunnels because of tunneling underneath. Int. J. Numer. Anal. Meth. Geomech. 40 (5), 766–784. Li, D.Y., Zhang, T.Q., Gong, X.N., 1999. Analysis of the displacements of buried pipelines caused by deep excavations. Indus. Constr. 29 (11), 36–42 (in Chinese). Peck, R.B., 1969. Deep Excavations and Tunneling in Soft Ground. ICSMFE, State of the Art Volume, pp. 225–290. Shen, S.L., Ma, L., Xu, Y.S., Yin, Z.Y., 2013. Interpretation of increased deformation rate in aquifer IV due to groundwater pumping in Shanghai. Can. Geotech. J. 50 (11), 1129–1142. Shen, S.L., Wu, Y.X., Misra, A., 2017. Calculation of head difference at two sides of a cutoff barrier during excavation dewatering. Comput. Geotech. 91 (9), 192–202. Shen, S.L., Xu, Y.S., 2011. Numerical evaluation of land subsidence induced by groundwater pumping in Shanghai. Can. Geotech. J. 48 (9), 1378–1392. Shi, C.H., Cao, C.Y., Lei, M.F., Peng, L.M., Ai, H.J., 2016. Effect of lateral unloading on the mechanical and deformation performance of shield tunnel segment joint. Tunn. Undergr. Space Technol. 51, 175–188. Wu, Y.X., Shen, J.S., Cheng, W.C., Hino, T., 2017. Semi-analytical solution to pumping test data with barrier, wellbore storage, and partial penetration effects. Eng. Geol. 226, 44–51. Yang, X., Song, H.W., Qin, Y.M., 2011. Numerical analysis for influence of deep excavation on adjacent unprotected underground pipelines. J. Water Resour. Archit. Eng. 9 (3), 19–24 (in Chinese). Zhang, J., Liang, Z., Han, C.J., 2014. Buckling behavior analysis of buried gas pipeline under strike-slip fault displacement. J. Nat. Gas Sci. Eng. 21, 921–928. Zhang, J., Liang, Z., Han, C.J., 2015. Effects of ellipsoidal corrosion defects on failure pressure of corroded pipelines based on finite element analysis. Int. J. Electrochem. Sci. 10, 5036–5047. Zhang, C.R., Yu, J., Huang, M.S., 2012. Effects of tunnelling on existing pipelines in layered soils. Comput. Geotech. 43, 12–25. Zhang, Z.G., Zhang, M.X., Zhao, Q.H., 2015. A simplified analysis for deformation behavior of buried pipelines considering disturbance effects of underground excavation in soft clays. Arab. J. Geosci. 8 (10), 7771–7785. Zhang, J., Zhang, L., Liang, Z., 2018. Buckling failure of a buried pipeline subjected to ground explosions. Process Saf. Environ. Prot. 114, 36–47.
9. Summary and conclusions (1) After the foundation pit excavation. Both the upper and lower surfaces of the pipeline have high stress area. The maximum von Mises stress appears on the upper surface of the middle part of the pipeline, the high stress distribution is narrow oval. The upper surface of the middle part the pipeline is pressed and the lower surface is pulled, but it is opposite at edge of the pit. The vertical displacement of the pipeline is bigger than the horizontal displacement. The underground continuous wall can effectively reduce the pipeline displacement. (2) Von Mises stress, axial strain and displacement of the buried pipeline increase with increasing of the radius-thickness ratio, pit width, pit depth and the soil’s Poisson’s ratio. They decrease with the increasing of distance between pipeline and foundation pit, soil’s cohesion, soil’s elastic modulus, underground continuous wall’s thickness and elastic modulus. The internal pressure has a small effect on the pipeline deformation. And the effect of foundation pit’s length on the deformation pit is not obvious. Acknowledgements This paper is supported by Scientific Research Starting Project of SWPU (No. 2017QHZ011), State Key Laboratory for Strength and Vibration of Mechanical Structures (No. SV2017-KF-08), Chengdu Science and Technology Project (No. 2016-HM01-00306-SF) and Nanchong Science and Technology Project (No. NC17SY4018). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.tust.2018.04.026. References Chen, R.P., Meng, F.Y., Li, Z.H., Ye, Y.H., Ye, J.N., 2016. Investigation of response of
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Mechanical response analysis of the buried pipeline due to adjacent foundation pit excavation
T
⁎
Jie Zhanga,b, , Rui Xiea, Han Zhanga a b
School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Buried pipeline Foundation pit FEM Stress Deformation
Foundation pit is one of the most factors that threaten the safe operations of buried pipeline. In order to study the effect of foundation pit excavation on the buried pipeline, a three-dimensional model of pipeline and foundation pit was established, and the variation regulations of pipeline’s deformation under the foundation pit excavation were investigated. Effects of pipeline parameters, foundation pit parameters, soil parameters and underground continuous wall on the stress, strain and deformation of the pipeline were studied. The results show that the underground continuous wall can effectively reduce the pipeline deformation. After the foundation pit excavation, the upper surface of the pipeline’s middle section is pressed, and the lower surface is pulled, but the strain distribution of the pipeline at the edge of the pit is opposite. Horizontal and vertical displacements occurs on the pipeline, horizontal displacement moves to the inside of the pit, and vertical displacement moves to the bottom of the pit. The pipeline deformation decreases with the increasing of pipeline’s radius-thickness ratio, but it increases with the increasing of the distance between the pipeline and foundation pit. The internal pressure has a small effect on the pipeline deformation. Pipeline deformation increases with increasing of the foundation pit’s width and depth. However, the length of the foundation pit has no effect on the pipeline. The pipeline deformation increases with the soil’s Poisson’s ratio increases, and it decreases with the increasing of soil’s cohesion and elastic modulus. With the increasing of thickness and elastic modulus of the underground continuous wall, the pipeline deformation decreases. Those results can be used for pipeline laying, construction, maintenance and safety evaluation.
1. Introduction Compared to roads, rail transport, pipelines are the safest and most economical way to transport flammable substances. With the increasing of infrastructure construction, buried pipelines may be affected by other projects, such as various urban underground constructions, which may cause pipeline failure and leakage (Shen and Xu, 2011). The foundation pit excavation will change the initial stress state of the soil, thus resulting in the surrounding soil deformation. That mainly includes the uplift at the bottom of the foundation pit, the displacement of the underground continuous wall and the soil settlement after the wall. The soil deformation will lead to segment leakage or local damage of the pipelines. Longitudinal distortion is a fatal threat to the structural safety and normal operations of buried pipelines. Therefore, mechanical behavior analysis of buried pipelines affected by foundation pit excavation is very important for its safety evaluation. In recent years, many researches on the pipeline deformation caused by the foundation pit excavation were carried out. Zhang et al. (2012) ⁎
provides a continuous elastic analysis to simulate the responses of the pipelines subjected to tunnel-induced soil movement in multi-layered soils. Klar and Marshall (2007) analyzed the effect of tunneling on the pipeline by using Euler-Bernoulli simple beam theory and shell element theory. Zhang et al. (2015) presented a simplified method to determ the mechanical behavior of buried pipeline induced by foundation pit excavation by using Winkler foundation model. Li et al. (1999) used Winker theory to establish the vertical displacement and horizontal displacement equations of the pipeline affected by the foundation pit excavation. Jiang (2014) derived the deformation and internal force of the pipeline by the elastic foundation beam. Yang et al. (2011) studied the pipeline response by the finite element model. In addition, Shi et al. (2016) study the effects of the lateral unloading caused by foundation pit excavation on the existing shield tunnels based on nonlinear contact theory. Chen et al. (2016) studied the influence of a nearby large excavation on existing twin tunnels in soft soils by FEM. However, they did not pay attention to the effect of foundation pit excavation on buried pipelines. Li et al. (2016) presents an analytical solution for the
Corresponding author at: School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China. E-mail address: [email protected] (J. Zhang).
https://doi.org/10.1016/j.tust.2018.04.026 Received 7 July 2017; Received in revised form 3 March 2018; Accepted 11 April 2018 Available online 27 April 2018 0886-7798/ © 2018 Elsevier Ltd. All rights reserved.
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θ0 M0 Q0 ϕ (βx )
Nomenclature u(x) umax x i K0 D E I y a, b, c δ L y0
ground settlement the maximum ground settlement horizontal distance from the foundation pit axis width coefficient of the ground settlement the subgrade modulus outer diameter of the buried pipeline elasticity modulus inertia moment of the pipeline section displacement of the pipeline constant the maximum ground settlement deformation length of the pipeline displacement of the pipeline at O point
β=4 V W H t ρ μ σy Pmax l
rotation of the pipeline at O point bending moment of the pipeline at O point shear force of the pipeline at O point Krylov’s function K 4EI
– pit length pit width excavation depth wall thickness density Poisson’s ratio yield stress the maximum operating pressure distance between pipeline and foundation pit
θ0 M Q ϕ (βx )− 02 ϕ3 (βx )− 0 3 ϕ4 (βx ) β 2 EIβ EIβ
deflection and the internal forces of an existing tunnel. Li et al. (2014) carried out a centrifuge model test to investigate the effect of new shield tunnelling on an existing underlying large-diameter tunnel. Despite the contributions of these researches are inordinately valuable, but most researches assumed that the pipeline is in close contact with the soil when it is deformed, and analyzed the pipeline as a beam. In real working condition, the buried pipeline and surrounding soil affect each other, the pipelines and soil will not contact with each other along the axial direction. In this paper, a pipeline-soil interaction model was established to analyze mechanical behavior of the buried pipeline under the influence of foundation pit excavation, which can provide a reference for the design, laying and maintenance of the buried pipeline.
θ = −4βy0 ϕ4 (βx ) + θ0 ϕ1 (βx )−
2. Analytical model of the buried pipeline
f=−
y = y0 ϕ1 (βx ) +
whereϕ1 (βx ) , ϕ2 (βx ) , ϕ3 (βx ) , ϕ4 (βx ) is Krylov’s function. Eq. (6) is differentiated to get the rotation equation as follows:
f=
d 4y + Ky = q (x ) dx 4
∫0
x
Ku(z ) ϕ4[β (x −z )]dz
4δ 2 4δ 8δ 4δ x + x − 2 2 ϕ3(βx )− ϕ2(βx ) L2 L Lβ Lβ
y = y0 ϕ1 (βx ) +
θ0 M Q ϕ (βx )− 02 ϕ3 (βx )− 0 3 ϕ4 (βx ) + f β 2 EIβ EIβ
(9)
(10)
(1)
(2)
M0 Q0 8δ 4δ ϕ (βL) + ϕ (βL) + 2 2 ϕ3(βL) + ϕ (βL) = 0 EIβ 2 3 EIβ 3 4 Lβ Lβ 2
(11)
M0 Q0 8δ 8δ 4δ 4δ ϕ (βL) + ϕ (βL) + − ϕ (βL) + ϕ (βL)− =0 EIβ 2 EIβ 2 3 L L2β 2 L 1 L
(12)
Then the vertical displacement equation can be expressed as follows:
(3)
y=−
4δ 8δ 4δ 4δ M Q ϕ (βx )−⎡ 02 + 2 2 ϕ3⎤ (βx )− 0 3 ϕ4 (βx )− 2 x 2 + x ⎢ ⎥ Lβ 2 EIβ L β EIβ L L ⎣ ⎦ (13)
The horizontal displacement of the pipeline can be obtained by the
(4)
where a, b and c can be obtained by boundary conditions: u(0) = 0, u L (L) = 0, u 2 = δ . Then Eq. (4) can be written as follows:
()
4δ 4δ u(x ) = − 2 x 2 + x L L
(8)
The initial parameters are determined by the boundary conditions. At the O point, y(0) = 0. So, y0 = 0, θ0 = 0. At the L point, y(L) = 0. So, M0 and Q0 can be obtained by displacement equation and rotation equation as follows:
The solution of Eq. (3) consists of general solution and particular solution, but the particular solution is difficult to find out. Therefore, the ground settlement curve can be approximated as a quadratic function curve (Li et al., 1999). The pipeline under the load is shown in Fig. 1, the ground settlement curve is:
u(x ) = ax 2 + bx + c
1 EIβ 3
So, the vertical displacement equation of the pipeline can be obtained by initial parameter:
where K = K0D. Then the differential equation for the pipeline displacement induced by foundation pit excavation can be obtained:
EI
(7)
And the particular solution of Eq. (3) is:
According to Winker assumptions, the load on the pipeline is:
q(x ) = K ·u(x )
M0 Q ϕ (βx )− 0 2 ϕ3 (βx ) EIβ 2 EIβ
The particular solution of Eq. (3) can be obtained:
In the current theoretical calculations, the pipeline is usually analyzed as an elastic foundation beam to solve the displacement after pit excavation (Shen et al., 2013). The load on the pipeline due to foundation pit excavation is determined by the ground settlement. The ground settlement curve can be expressed by the Peck formula (Peck, 1969): 2 −x u(x )=u max e 2i2
(6)
(5)
The general solution of Eq. (3) can be obtained by using the initial parameter method of short beam (Li et al., 1999); the general solution is:
Fig. 1. Schematic diagram of a pipeline under the load. 136
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on the top surface of model, and normal constraint is applied to the rest surfaces.
same method. The horizontal load of the pipeline can be determined by the horizontal displacement of the soil. 3. Finite element model
4. Result analysis
3.1. Example validation
4.1. Underground continuous wall effect
In Ji (2013), a three-dimensional finite element model of a foundation pit project in Tianjin was established, actual measured and simulated values of surface settlement were compared. The same numerical model was established to simulate the excavation process. The length of foundation pit is 150 m, the width is 60 m, and the depth is 8 m. The thickness of underground continuous wall is 0.85 m, the total length is 18 m, and depth under the pit is 10 m. The distance between support center and surface is 2.65 m, and support cross-sectional size is 0.7 m × 0.7 m. According to the structural symmetry to simplify the calculation, the entire model size is 124 m × 107 m × 36 m. The eight-node reduced-integration elements are used to simulate soil and enclosure structure. Fig. 2 shows the surface settlement values at 1 m and 3 m from the foundation pit. The settlement trend is basically the same as the actual measured value. When the distance from the foundation pit is 1 m, the maximum settlement of the surface is 39.9 mm. When the distance is 3 m, the maximum settlement is 34.5 mm. The error is less than 10%. Obviously, the numerical simulation results are in good agreement with the actual values, which proved that the finite element model is reliable.
When the soil is silty clay, whether there is an underground continuous wall, the pipeline displacement is shown in Fig. 4. The underground continuous wall can greatly reduce the deformation of the buried pipeline. Under the action of the underground continuous wall, the pipeline displacement is small, and the overall displacement is not more than 5 mm. Therefore, the underground diaphragm wall can effectively reduce the effect of the foundation pit. 4.2. Numerical simulation result After foundation pit excavation, the deformation of the silty clay is smaller, while the deformation of the soft soil is larger. When the size of foundation pit is 30 m × 30 m×8m, Fig. 5 shows the stress-strain responses of the buried pipeline after the foundation pit excavation in soft soil. As seen in Fig. 5(a), the maximum von Mises stress appears on the upper surface of the middle part of the pipeline after foundation pit excavation, and the high stress distribution is narrow oval. The maximum stress is 150 MPa, the stress on the lower surface of the middle part of the pipeline is smaller than the upper surface. In addition, high stress area also appears on the pipeline at the edge of the pit. But the maximum stress of the pipeline’s lower surface is 120 MPa, which is greater than 100 MPa on the upper surface. As shown in Fig. 5(b), the high strain area of the pipeline corresponds to the high stress area, and the high strain area appears on both the upper and lower surfaces of the pipeline. Axial strain of the upper surface on the pipeline’s middle part is negative strain, while the lower surface is positive strain. It indicates that the upper surface of the pipeline’s middle part is pressed and the lower surface is pulled. But the strain distribution of the pipeline at the edge of the pit is opposite. Stress on the high strain area is greater than other section. Fig. 5(c) shows the displacement of buried pipeline. The vertical displacement appears on the top surface of the pipeline, it extends in z direction. The horizontal displacement appears on the side surface of the pipeline, it moves in the x direction toward the inside of the pit. Overall, the vertical displacement is bigger than the horizontal displacement. Because after the pit excavation, the soil settlement appears around the foundation pit, and it also moves to the inside of the pit.
3.2. Finite element model Removal of the soil within the foundation pit is accompanied by the release of the in-situ stress, and a large part of the earth pressure generated by the perturbation of the surrounding soil acts on the underground continuous wall, which greatly reduces the load on the buried pipeline. Fig. 3 shows the schematic diagram of the pipeline and the foundation pit. To save computation time, 1/2 model was established for the symmetry of the model structure, so the whole model size is 100 m × 50 m × 40 m (Zhang et al., 2015). The pit shape is rectangular, v = 30 m, w = 15 m, and H = 8 m. Gravity loading and internal pressure were applied first and subsequently foundation pit was excavated. Take X65 steel pipeline as an example in all cases. For the pipeline, D = 660 mm, t = 8 mm, ρ = 7800 kg/m3, E = 210GPa, μ = 0.3, and σy = 448.5 MPa (Zhang et al., 2018). Buried depth of the pipeline is 2 m, the pipeline is parallel to one side of the foundation pit, and the distance between the pipeline and the underground continuous wall l is 4 m. The material of underground continuous wall is concrete C20, the density is 2500 kg/m3, the elastic modulus is 25 GPa, the Poisson ratio is 0.2, the thickness of the wall is 0.6 m, and the depth is 16 m (Ji, 2013). Mechanical behavior of soil material is described through an elastic-perfectly plastic Mohr-Coulomb constitutive model (Zhang et al., 2018). The density of silty clay is 1980 kg/m3, the elastic modulus is 25 MPa, the Poisson’s ratio is 0.3, the cohesion is 22 kPa, and the friction angle is 15° (Jia, 2007). The density of the soft soil is 1760 kg/m3, the elastic modulus is 10.5 MPa, the Poisson’s ratio is 0.36, the cohesion is 12 kPa, and the friction angle is 7.1° (Ji, 2013). For pipeline-soil interaction, the outer surface of the pipeline and the soil are simulated with a contact algorithm, which allows for the separation of the pipeline and soil (Zhang et al., 2014). The friction coefficient is 0.3 (Shen et al., 2017). For the whole model, the soil is isotropic, homogeneous and continuous, regardless of groundwater. Pipeline extends along x-axis direction is horizontal, the y-axis direction for the axial direction, the zaxis direction for the vertical. Eight-node reduced-integration elements are used to simulate the soil and pipelines. The symmetry constraint is applied to the symmetry plane of the model, no constraint is imposed
Fig. 2. Surface settlement of the example. 137
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Fig. 3. Schematic diagram of the pipeline and the foundation pit.
gradually increases, and the high stress area extends along the pipeline axial direction. The pipeline is easily deformed when its thickness decreases. The axial strain on the upper surface of symmetrical section of the pipeline is shown in Fig. 6(b). As the radius-thickness ratio increasing, the maximum axial strain on the upper surface of the pipeline increases, but the change regulation of the lower surface of the pipeline is opposite to the upper surface. Fig. 7 shows the maximum displacement of the pipeline with different radius-thickness ratios. Under the action of pit excavation, horizontal and vertical displacements appears on the pipeline. The horizontal displacement is to the inside of the foundation pit, and the vertical displacement is to the bottom of the foundation pit. With the increasing of the radius-thickness ratio, the horizontal displacement of the pipeline increases gradually, and the variation is about 17 mm. At the same time, the vertical displacement of the pipeline increases, but the variation is more than 20 mm. It indicates that the vertical displacement of the pipeline is more sensitive, because the vertical displacement is bigger than the horizontal displacement. The change rates of horizontal displacement and vertical displacement reduce with the radius-thickness ratios increases. In general, the foundation pit excavation has a great effect on thin wall pipeline.
Fig. 4. Displacements of the pipeline in different directions.
However, due to the function of underground continuous wall, the soil’s horizontal displacement reduces. In Li et al. (1999), the value of some parameters have been provided. The theoretical vertical displacement of the pipeline can be obtained by Eq. (13). The curves show that the theoretical model is consistent with the numerical model, and the error is small at the maximum vertical displacement. It indicates that the numerical model is reasonable. Pipeline is a thin structure, and there may be residual stress and stress concentration for the pipeline. Therefore, the finite element method is more suitable.
5.2. Internal pressure effect For gas transmission pipeline, considering a safety factor equal to 0.72, and the maximum operating pressure can be given by the expression Pmax = 0.72 × (2σy/D) (Zhang et al., 2014). The maximum displacement of the pipeline with different internal pressures are shown in Fig. 8. With the increasing of the internal pressure, the horizontal and vertical displacement of the pipeline changes very little. It indicates that the pipeline deformation is mainly affected by the earth pressure accompanied with the foundation pit excavation. The effect of internal pressure on pipeline deformation and axial stress is very small, it only affect its circumferential stress.
5. Effect of pipeline parameters 5.1. Radius-thickness ratio effect
5.3. Distance effect
The existing results show that the radius-thickness ratio of the pipeline will directly affect the stability of the buried pipeline (Wu and Shen, 2017). When the diameter of the pipeline is 660 mm, the stressstrain responses of the pipeline with different radius-thickness ratios are shown in Fig. 6. In Fig. 6(a), when the radius-thickness ratio is 83, the thickness is 8 mm, the maximum stress of the pipeline is 152 MPa. When the thickness is 18 mm, the maximum stress of the pipeline is 100 MPa, the change rate is more obvious. With the radius-thickness ratio increasing, the maximum von Mises stress of the pipeline
When the radius-thickness ratio is 83, the stress-strain responses of the pipeline under different distances between pipeline and underground continuous wall are shown in Fig. 9. As shown in Fig. 9(a), the high stress area and the maximum von Mises stress decrease as the distance increases. When the distance is 10 m, the maximum stress of the pipeline is about 50 MPa, the change is very obvious. At the same time, the stress area of the pipeline at the edge of the foundation pit is 138
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(a) Von Mises stress (a) Von Mises stress
(b) Axial strain of xz plane (b) Axial strain
Fig. 6. Stress-strain responses of the pipeline with different radius-thickness ratios.
(c) Displacement Fig. 5. Stress-strain responses of the buried pipeline in soft soil. Fig. 7. Displacements of the pipeline with different radius-thickness ratios.
obviously decreases. In Fig. 9(b), the maximum axial strain of the pipeline decreases with the distance increases. When pipeline is far away from the pit, the soil displacement due to excavation is small. The maximum displacement of the pipeline under different distances are shown in Fig. 10. With the increasing of the distance, the pipeline displacement decreases. The change of the horizontal
displacement of the pipeline is about 50 mm. The change of the vertical displacement is about 80 mm, it is much larger than the horizontal displacement. Therefore, the actual construction should considering the distance between the foundation pit and the adjacent pipeline. 139
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Fig. 8. Displacements of the pipeline under different internal pressures.
Fig. 10. Displacements of the pipeline under different distances.
Mises stress increase with the pit width increases. This is because the pit width can resulting in the increasing of soil deformation’s area, that make the influence area of the pipeline becomes larger. In Fig. 11(b), the pit width not only affects the deformation of the pipeline but also affects the axial deformation range. With the increasing of the pit width, the deformation range of soil around the
(a) Von Mises stress
(a) Von Mises stress
(b) Axial strain of xz plane Fig. 9. Stress-strain responses of the pipeline under different distances.
6. Effect of foundation pit parameters 6.1. Pit width effect Fig. 11 shows the stress–strain responses of the pipeline under different widths of foundation pit. In Fig. 11(a), effect of the pit width on the pipeline is more obvious, the high stress area and the maximum von
(b) Axial strain of xz plane Fig. 11. Stress-strain responses of the pipeline under different pit widths. 140
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cohesion of the soil is 10 kPa, the maximum stress of the pipeline reaches 217 MPa, which is very large compared with 54 MPa when the cohesion is 18 kPa. In Fig. 17(b), the maximum axial strain of the pipeline decreases as cohesion increases, but the change rate decreases. According to common sense, the soft clay is prone to deform, so the deformation of the buried pipeline in the soft clay is more obvious after foundation pit excavation. In Fig. 18, the horizontal vertical displacements decrease with the increasing of the soil’s cohesion. The difference between them also decreases. In engineering practice, the property of the soil in the excavation area is critical for the engineering construction.
foundation pit gradually increases, the range of pipeline’s deformation also increases. Then, the maximum axial strain of the pipeline is increases. In Fig. 12, with the pit width increasing, the maximum displacement of the pipeline increases, but the change is not entirely linear. The difference between the horizontal displacement and the vertical displacement gradually increases. 6.2. Pit length effect According to the stress and strain responses of the pipeline under different pit lengths, there is a little change of the pipeline’s high stress area. And the maximum stress change of the pipeline is not obvious. The difference between the strain curves of the pipeline’s symmetrical section under different pit lengths is very small. It indicates that the length of the foundation pit has a little effect on the pipeline.
7.3. Elastic modulus of the soil effect When the Poisson’s ratio of the soil is 0.35, the cohesion is 12 kPa, the stress-strain responses of the pipeline under different elastic modulus of the soil are shown in Fig. 19. The maximum von Mises stress and high stress area decrease with the elastic modulus increasing. But the change of the pipeline at the edge of the foundation pit is not obvious. This is because the deformation of the soil with a small elastic modulus is bigger, then the force act on the pipeline is greater. The strain curve of symmetrical section shows that the maximum axial strain of the pipeline decreases with the increasing of the elastic modulus, but the change of the axial strain is small. In Fig. 20, the change of the horizontal displacement is very small, but the change of the vertical displacement more obvious. In general, the deformation of the pipeline decreases with the elastic modulus increasing, but the effect is not very obvious.
6.3. Pit depth effect Fig. 13 shows the stress-strain responses of the pipeline under different depths of foundation pit. In Fig. 13(a), the pit depth has an obvious effect on the pipeline’s stress, which increases with the increasing of the pit depth. When the pit depth is 9 m, the maximum stress of the pipeline is 285 MPa, which is very large compared with 150 MPa when the depth is 8 m. When the pit depth is 6 m, the stress of the pipeline is very small, there is only a high stress are at the edge of the pit. From the strain curves of symmetrical section Fig. 13(b)), the maximum axial strain of the pipeline gradually increases with the increasing of the pit depth. When the pit depth is 6 m, the axial strain of the pipeline is about zero. Fig. 14 shows the maximum displacement of the pipeline under different pit depths. The horizontal and vertical displacements and their difference increase with the increasing of the pit depth. When the depth is 6 m, the difference between horizontal displacement and vertical displacement is less than 5 mm, and the difference gradually increases. When the depth is larger, the soil’s displacement is larger, and there is a large settlement on the ground. Therefore, a bigger the deformation of buried pipeline occurs.
8. Effect of the underground continuous wall parameters 8.1. Wall thickness effect Define r is thickness of underground continuous wall. The underground continuous wall can withstand a lot of earth pressure in the process of foundation pit excavation. It has become an indispensable structure for deep foundation pit support works. When the distance between the pipeline and the underground continuous wall is 4 m, the stress-strain responses of the pipeline under different thicknesses of the underground continuous wall are shown in Fig. 21. The maximum von Mises stress and high stress area decrease as the thickness increases. The strain curves of symmetrical section show that the maximum axial strain of the pipeline decreases with the increasing of the wall’s thickness. Underground continuous wall can reduce the displacement of soil around the foundation pit, so the effect of underground continuous wall
7. Effect of soil parameters 7.1. Poisson’s ratio of the soil effect Surrounding soil is the media between the foundation pit and the buried pipeline. The earth pressure caused by foundation pit acts on the pipeline by surrounding soil. Therefore, surrounding soil parameters have a great effect on the buried pipeline. Fig. 15 shows the stress-strain responses of the pipeline under different Poisson’s ratios of the soil. In Fig. 15(a), the maximum von Mises stress and high stress area increase as the Poisson's ratio of the soil increases. But it has a small effect on the stress area. In Fig. 15(b), with the increasing of the Poisson’s ratio, the maximum axial strain of the pipeline increases, and the change rate also increases. In Fig. 16, the maximum displacement of the pipeline increases as the Poisson’s ratio increases. Both the change of the horizontal and the vertical displacement are small. But the change rate of vertical displacement gradually decreases while the change rate of horizontal displacement increases. 7.2. Cohesion of the soil effect Cohesion is the mutual attraction between adjacent parts in same material. When the soil’s Poisson’s ratio is 0.35, the stress-strain responses of the pipeline under different cohesions of the soil are shown in Fig. 17. In Fig. 17(a), the maximum von Mises stress and high stress area decrease with the increasing of the soil’s cohesion. When the
Fig. 12. Displacements of the pipeline under different pit widths. 141
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(a) Von Mises stress
(a) Von Mises stress
(b) Axial strain of xz plane
(b) Axial strain of xz plane Fig. 13. Stress and strain responses of the pipeline under different pit depths.
Fig. 15. Stress-strain responses of the pipeline under different soil’s Poisson’s ratios.
Fig. 14. Displacements of the pipeline under different pit depths.
Fig. 16. Displacements of the pipeline under different soil’s Poisson’s ratios.
on the pipeline is more serious when the thickness is smaller In Fig. 22, the change rules of the horizontal and the vertical displacement are similar. The pipeline deformation decreases with increasing of the wall thickness, and the change rate also decreases.
8.2. Wall material effect At present, the material of the underground continuous wall is concrete in foundation pit engineering. The main difference between the different types of the concrete is the elastic modulus. When the 142
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(a) Von Mises stress (a) Von Mises stress
(b) Axial strain of xz plane
(b) Axial strain of xz plane
Fig. 17. Stress-strain responses of the pipeline under different soil’s cohesions.
Fig. 19. Stress-strain responses of the pipeline under different soil’s elastic modulus.
Fig. 18. Displacements of the pipeline under different soil’s cohesions. Fig. 20. Displacements of the pipeline under different soil’s elastic modulus.
density of the concrete is 2500 kg/m3, the Poisson’s ratio of the concrete is 0.2, elastic modulus of the different concretes are shown in Table 1. The stress-strain responses of the pipeline under different concretes of the underground continuous wall are shown in Fig. 23. The maximum von Mises stress and high stress area decrease with the increasing
of the concrete’s elastic modulus, but the change is less than 25 MPa. The strain curves of symmetrical section show that the maximum axial strain of the pipeline decreases as the elastic modulus increases, but the change is small. The elastic modulus of underground continuous wall
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Table 1 Elastic modulus of different concretes. Concrete
C20
C25
C30
C35
C40
Elastic modulus (GPa)
25
28
30
31.5
32.5
(a) Von Mises stress
(a) Von Mises stress
(b) Axial strain of xz plane Fig. 21. Stress-strain responses of the pipeline under different wall thicknesses.
(b) Axial strain of xz plane Fig. 23. Stress-strain responses of the pipeline under different concretes.
Fig. 22. Displacements of the pipeline under different wall thicknesses.
reflects its deformability. When the elastic modulus of underground continuous wall is larger, the deformation capacity is larger. It can reduce soil displacement, and then the pipeline deformation is small. In Fig. 24, the changes of the horizontal and the vertical displacements are small, the difference between them is more than 45 mm. The
Fig. 24. Displacements of the pipeline under different wall materials. 144
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pipeline displacement decreases as the wall’s elastic modulus increases, and the curve is approximately linear. The effect of wall material on the pipeline is greater. Its choice should be decided according to the actual situation.
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9. Summary and conclusions (1) After the foundation pit excavation. Both the upper and lower surfaces of the pipeline have high stress area. The maximum von Mises stress appears on the upper surface of the middle part of the pipeline, the high stress distribution is narrow oval. The upper surface of the middle part the pipeline is pressed and the lower surface is pulled, but it is opposite at edge of the pit. The vertical displacement of the pipeline is bigger than the horizontal displacement. The underground continuous wall can effectively reduce the pipeline displacement. (2) Von Mises stress, axial strain and displacement of the buried pipeline increase with increasing of the radius-thickness ratio, pit width, pit depth and the soil’s Poisson’s ratio. They decrease with the increasing of distance between pipeline and foundation pit, soil’s cohesion, soil’s elastic modulus, underground continuous wall’s thickness and elastic modulus. The internal pressure has a small effect on the pipeline deformation. And the effect of foundation pit’s length on the deformation pit is not obvious. Acknowledgements This paper is supported by Scientific Research Starting Project of SWPU (No. 2017QHZ011), State Key Laboratory for Strength and Vibration of Mechanical Structures (No. SV2017-KF-08), Chengdu Science and Technology Project (No. 2016-HM01-00306-SF) and Nanchong Science and Technology Project (No. NC17SY4018). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.tust.2018.04.026. References Chen, R.P., Meng, F.Y., Li, Z.H., Ye, Y.H., Ye, J.N., 2016. Investigation of response of
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