CN112597674B - Method for determining lateral pipeline transverse additional internal force caused by foundation pit excavation - Google Patents
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Abstract
The invention relates to a method for determining lateral pipeline transverse additional internal force caused by foundation pit excavation, which comprises the following steps: step S1: acquiring information of a pipeline buried soil layer, and information related to design and construction of a pipeline and a foundation pit; step S2: determining a horizontal displacement curve of the enclosure structure caused by excavation construction of the foundation pit; step S3: obtaining a stress change value of the soil outside the pit under the excavation action of the foundation pit according to the horizontal displacement curve of the enclosure structure caused by the foundation pit excavation construction determined in the step S2; step S4: determining the additional load of the existing pipeline beside the foundation pit under the excavation effect according to the obtained stress change value; step S5: and determining the additional internal force of the existing pipeline beside the foundation pit under the excavation action according to the additional load. The invention can more conveniently determine the transverse additional internal force of the side pipeline under the excavation action of the foundation pit and provides a basis for the design of the foundation pit support of the adjacent pipeline.
Description
Technical Field
The invention relates to the technical field of building engineering, in particular to a method for determining lateral additional internal force of a side pipeline caused by foundation pit excavation.
Background
The rapid development of urban rail transit construction drives the construction of projects such as businesses, real estate and the like along the line and in the protection area. The projects for excavating foundation pits around the existing pipelines are more and more frequent and closer. Under the influence of excavation and unloading of the foundation pit, the enclosure structure moves towards the inner direction of the pit under the action of the pressure difference between water and soil inside and outside the pit, so that the soil pressure around the adjacent existing pipeline changes, the pipeline generates additional internal force, and the operation safety of the pipeline is seriously threatened.
At present, many analytical researches are carried out on the longitudinal influence of foundation pit excavation on the existing tunnel, and the researches show that most of the defects of the subway shield tunnel in the soft soil stratum are caused by transverse deformation; but at present, the research on the transverse influence of foundation pit excavation on the existing tunnel is less, and the method is mainly a numerical simulation method (for example, under the conditions of different building envelope deformation modes and deformation amounts, the cross section displacement of the tunnel at different positions is analyzed by adopting a finite element method such as Zhenggang, and the like, and the influence area division is carried out); in addition, when the additional stress field of the soil outside the pit under the action of foundation pit excavation is calculated through the theoretical analysis research, the unloading effect of the foundation pit excavation is mostly simplified into horizontal loads distributed on the side wall and towards the inner side of the foundation pit, and then the stress of the surrounding soil induced by the foundation pit excavation is solved according to Mindlin stress. However, the displacement change of the soil outside the foundation pit is influenced by a plurality of factors, including the excavation depth of the foundation pit, the support form, the on-site soil condition, the construction method and the like.
Disclosure of Invention
In view of the above, the present invention provides a method for determining a lateral additional internal force of a lateral pipeline caused by excavation of a foundation pit, which can more conveniently and accurately determine the lateral additional internal force of the lateral pipeline under the excavation action of the foundation pit, and provide a basis for design of a foundation pit support of an adjacent pipeline.
The invention is realized by adopting the following scheme: a method for determining lateral pipeline lateral additional internal force caused by foundation pit excavation mainly comprises two stages, wherein in the first stage, an additional stress field of soil outside a pit caused by foundation pit excavation is deduced by adopting an elastic mechanics method; and in the second stage, an additional soil pressure redistribution model in the tunnel stress-displacement-rebalancing process is established, and the transverse stress change of the adjacent existing pipeline under the action of the additional soil pressure is solved by adopting a modified inertial method. The method specifically comprises the following steps:
step S1: acquiring information of a pipeline buried soil layer, and information related to design and construction of a pipeline and a foundation pit;
step S2: determining a horizontal displacement curve of the enclosure structure caused by excavation construction of the foundation pit;
step S3: obtaining a stress change value of the soil outside the pit under the excavation action of the foundation pit according to the horizontal displacement curve of the enclosure structure caused by the foundation pit excavation construction determined in the step S2;
step S4: determining the additional load of the existing pipeline beside the foundation pit under the excavation effect according to the obtained stress change value;
step S5: and determining the additional internal force of the existing pipeline beside the foundation pit under the excavation action according to the additional load.
Further, in step S1, the information on the pipeline buried soil layer, the pipeline and the information on the design and construction of the foundation pit include: elastic modulus, poisson's ratio of the soil layer; the buried depth of the pipeline and the inner and outer diameters of the pipeline; the excavation depth and width of the foundation pit, and the horizontal distance between the pipeline and the foundation pit.
Further, step S2 is specifically to predict the horizontal displacement curve of the enclosure structure in the foundation pit construction process by using the following formula:
in the formula umaxRepresents the maximum value of horizontal deformation of the building envelope, zIndicating the vertical distance of the calculated position from the ground, HmaxThe vertical distance from the maximum horizontal displacement of the enclosure structure to the ground is represented, and L represents the length of the enclosure structure; or acquiring a horizontal displacement curve of the enclosure structure through field monitoring; or simulating the excavation process of the foundation pit by adopting finite element software, and extracting a horizontal displacement curve of the edge of the foundation pit in the final excavation state of the foundation pit.
Further, step S3 is specifically: dividing the horizontal displacement curve of the enclosure structure into a plurality of equal segments, and regarding deformation of any infinitesimal segment as translation approximately; and calculating the additional stress of the soil outside the pit under the influence of the translation of the enclosure structure of each infinitesimal section by adopting an elastic mechanics method, and then summing the additional stresses generated by the deformation of each infinitesimal section within the length range of the whole enclosure structure to obtain the additional stress of the soil at any point outside the pit when the enclosure structure is deformed.
Further, when the enclosure structure deforms, the additional stress of the soil outside the foundation pit meets the following formula:
in the formula, σxRepresenting horizontal additional stress, σzRepresenting vertical additional stress, n being an equal number, HiIs the vertical distance to the ground at the ith bisecting point, x represents the horizontal distance from the calculated position to the building envelope, Δ σx(Hi)、Δσz(Hi) Respectively satisfying the following formulas for horizontal and vertical additional stress generated when the envelope structure above the depth of the ith division point translates:
wherein G represents the shear modulus of the soil body, v represents the Poisson's ratio of the soil body, and diDenotes the ithAnd (4) a horizontal displacement value of the infinitesimal section enclosure structure.
Further, step S4 is specifically: 1/2 of the difference between the additional soil pressures on the upper side and the lower side of the pipeline, the left side and the right side of the pipeline is used as an additional load acting on the pipeline, and the additional soil pressure is fitted by adopting a broken line segment. Wherein the additional load satisfies the following formula:
wherein q represents the vertical additional soil pressure borne by the pipeline, p represents the horizontal additional soil pressure borne by the pipeline, S represents the minimum horizontal distance between the tunnel and the foundation pit support structure, D represents the vertical distance from the top of the tunnel to the ground, and R represents the calculated radius of the tunnel.
Further, step S5 is specifically: the method comprises the following steps of dividing the additional load of the pipeline beside the foundation pit into four working conditions, respectively calculating the additional internal force generated under various working conditions by adopting an elastic center method, and obtaining the final additional internal force of the pipeline by using an overlap method; the four working conditions are respectively as follows: the additional internal force under the action of the vertically uniformly distributed load, the additional internal force under the action of the vertically triangular load, the additional internal force under the action of the horizontally uniformly distributed load and the additional internal force under the action of the horizontally triangular load.
Further, the final additional internal force of the pipe satisfies the following formula:
where ξ is the bending moment increasing rate, M is the additional bending moment of the pipeline, N is the additional axial force of the pipeline, Q is the additional shearing force of the pipeline, M is the additional shearing force of the pipelineiRepresents the additional bending moment of the pipeline under the i-th working condition, NiRepresents the additional axial force, Q, of the pipeline under the i-th working conditioniIndicating the added shear of the pipe in condition i.
Compared with the prior art, the invention has the following beneficial effects: the invention provides a two-stage analysis method for predicting lateral shield tunnel lateral stress based on supporting structure deformation, which can better reflect the influences of foundation pit excavation depth, supporting form, field soil condition and construction method, thereby more conveniently and accurately determining lateral pipeline lateral additional internal force under the foundation pit excavation effect and providing basis for the foundation pit supporting design of adjacent pipelines.
Drawings
Fig. 1 is a schematic view of mechanical calculation of a lateral pipeline under the excavation effect of a foundation pit according to an embodiment of the invention.
FIG. 2 is a schematic diagram of a mechanical model of a circular pipeline under the action of additional soil pressure according to an embodiment of the present invention.
FIG. 3 is a schematic diagram of the calculation of the mechanical response of the circular pipeline under the action of the additional soil pressure according to the embodiment of the invention.
Fig. 4 is a schematic diagram of a horizontal displacement curve of a soil body after the building envelope of the embodiment of the invention.
Fig. 5 is a schematic view of the pressure curve of the additional soil around the existing tunnel under the excavation effect of the foundation pit according to the embodiment of the invention.
Fig. 6 is a schematic diagram of additional loads of the shield tunnel according to the embodiment of the present invention.
Fig. 7 is a schematic diagram of additional internal force of the shield tunnel under the excavation effect of the foundation pit according to the embodiment of the invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The embodiment provides a method for determining lateral pipeline transverse additional internal force caused by foundation pit excavation, which mainly comprises two stages, wherein in the first stage, an additional stress field of soil outside a pit caused by foundation pit excavation is deduced by adopting an elastic mechanics method; and in the second stage, an additional soil pressure redistribution model in the tunnel stress-displacement-rebalancing process is established, and the transverse stress change of the adjacent existing pipeline under the action of the additional soil pressure is solved by adopting a modified inertial method. The method specifically comprises the following steps:
step S1: acquiring information of a pipeline buried soil layer, and information related to design and construction of a pipeline and a foundation pit;
step S2: determining a horizontal displacement curve of the enclosure structure caused by excavation construction of the foundation pit;
step S3: obtaining a stress change value of the soil outside the pit under the excavation action of the foundation pit according to the horizontal displacement curve of the enclosure structure caused by the foundation pit excavation construction determined in the step S2;
step S4: determining the additional load of the existing pipeline beside the foundation pit under the excavation effect according to the obtained stress change value;
step S5: and determining the additional internal force of the existing pipeline beside the foundation pit under the excavation action according to the additional load.
In this embodiment, in step S1, the information on the pipeline buried soil layer, the pipeline and the information on the design and construction of the foundation pit include: elastic modulus, poisson's ratio of the soil layer; the buried depth of the pipeline and the inner and outer diameters of the pipeline; the excavation depth and width of the foundation pit, and the horizontal distance between the pipeline and the foundation pit.
In this embodiment, step S2 may be implemented by field monitoring or finite element simulation to obtain a horizontal displacement curve of the enclosure structure; and predicting the horizontal displacement deformation mode and the horizontal displacement deformation curve of the enclosure structure in the excavation process of the foundation pit by adopting an empirical formula. The solution in this implementation is that finite element software is adopted to simulate the excavation process of the foundation pit, a numerical simulation value of the horizontal displacement of the edge of the foundation pit in the final state of the excavation of the foundation pit is extracted, and then the following formula is adopted to fit the numerical simulation value, so that a horizontal displacement curve of the enclosure structure in the construction process of the foundation pit is obtained:
in the formula umaxRepresents the maximum horizontal deformation of the building envelope, z represents the vertical distance from the calculated position to the ground, HmaxAnd the vertical distance from the maximum value of the horizontal displacement of the building envelope to the ground is represented, and L represents the length of the building envelope.
In this embodiment, step S3 specifically includes: as shown in fig. 1 (H in the figure represents the excavation depth of the foundation pit, L represents the length of the enclosure structure, HmaxRepresenting the vertical distance from the maximum value of the horizontal displacement of the enclosure structure to the ground, dh representing the length of the infinitesimal section, S representing the minimum horizontal distance between the tunnel and the enclosure structure of the foundation pit, D representing the vertical distance from the top of the tunnel to the ground, and R representing the calculated radius of the tunnel), dividing the horizontal displacement curve of the enclosure structure into a plurality of equal sections, and approximately regarding the deformation of any infinitesimal section as translation; and calculating the additional stress of the soil outside the pit under the influence of the translation of the enclosure structure of each infinitesimal section by adopting an elastic mechanics method, and then summing the additional stresses generated by the deformation of each infinitesimal section within the length range of the whole enclosure structure to obtain the additional stress of the soil at any point outside the pit when the enclosure structure is deformed.
Wherein, when the envelope warp, the additional stress of the soil body outside the foundation pit satisfies the following formula:
in the formula, σxRepresenting horizontal additional stress, σzRepresenting vertical additional stress, n being an equal number, HiFor the depth at the ith bisection point, x represents the horizontal distance of the computed position from the enclosure, Δ σx(Hi)、Δσz(Hi) Respectively satisfying the following formulas for horizontal and vertical additional stress generated when the foundation pit above the depth of the ith division point is translated:
wherein G represents the shear modulus of the soil body, v represents the Poisson's ratio of the soil body, and diAnd representing the horizontal displacement value of the building envelope of the ith infinitesimal section.
In this embodiment, step S4 specifically includes: 1/2 of the difference between the additional soil pressures on the upper side and the lower side of the pipeline, the left side and the right side of the pipeline is used as an additional load, and the additional soil pressure is fitted by adopting a broken line segment. In this embodiment, the pipeline is regarded as a free deformation homogeneous circular ring model, and the width is 1m for analysis, as shown in FIG. 2, wherein q is1Represents the vertical additional load applied to the left end of the pipeline, q2Represents the difference value of the vertical additional loads of the left end and the right end of the pipeline, P1Indicating horizontal additional load, P, on the upper end of the pipe2Representing the difference value of the horizontal additional loads of the upper end and the lower end of the pipeline;
wherein, the vertical additional load q that the pipeline receives satisfies following formula:
the horizontal additional load P borne by the pipeline meets the following formula:
in this embodiment, step S5 specifically includes: dividing the additional load of the pipeline beside the foundation pit into four working conditions, respectively calculating the additional internal force generated under various working conditions by adopting an elastic center method, and then obtaining the final additional internal force of the pipeline by using an superposition method; four working conditions are shown in fig. 3, which are respectively: an additional internal force by a vertically uniform load ((a) in fig. 3), an additional internal force by a vertically triangular load ((b) in fig. 3), an additional internal force by a horizontally uniform load ((c) in fig. 3), and an additional internal force by a horizontally triangular load ((d) in fig. 3).
In this embodiment, the final additional internal force of the pipe satisfies the following formula:
where ξ is the bending moment increasing rate, M is the additional bending moment of the pipeline, N is the additional axial force of the pipeline, Q is the additional shearing force of the pipeline, M is the additional shearing force of the pipelineiRepresents the additional bending moment of the pipeline under the i-th working condition, NiRepresents the additional axial force, Q, of the pipeline under the i-th working conditioniIndicating the added shear of the pipe in condition i.
The working condition corresponding to i ═ 1 is the additional internal force under the action of the vertically uniformly distributed load, the working condition corresponding to i ═ 2 is the additional internal force under the action of the vertically triangular load, the working condition corresponding to i ═ 3 is the additional internal force under the action of the horizontally uniformly distributed load, and the working condition corresponding to i ═ 4 is the additional internal force under the action of the horizontally triangular load. Then:
the additional internal force under the action of the vertically and uniformly distributed load meets the following formula
The additional internal force under the action of the vertical triangular load meets the following formula
The additional internal force under the action of the horizontally uniformly distributed load meets the following formula
The additional internal force under the action of horizontal triangular load meets the following formula
In the formula, φ represents an angle (with the tunnel vertex as a starting point and clockwise as a positive direction).
Specifically, the present embodiment further describes the above process with a specific embodiment.
The first step is as follows: acquiring information of a pipeline buried soil layer, pipeline and information related to design and construction of a foundation pit, and determining the transverse bending rigidity of the pipeline.
Through investigation, the stratum where the foundation pit is located is mainly soft soil, and the average value of the compression modulus is 10Mpa and the Poisson ratio is 0.4999 after unloading. The excavation width B of the foundation pit is 60m, and the excavation depth H is 18 m; the underground continuous wall penetrates into a foundation pit below the ground to an excavation depth L of 18m, four horizontal supports are arranged, and the elevations are sequentially-1 m, -5.5m, -10m and-14.5 m; the side of the foundation pit is provided with a shield tunnel approximately parallel to the foundation pit, the minimum clear distance S between the tunnel and the side line of the foundation pit enclosure structure is 8m, the tunnel burial depth D is 8m, C50 concrete pipe pieces are adopted, the outer diameter R is 3.1m, the thickness t is 0.35m, the ring width delta is 1.2m, and the bending moment increase rate xi is 1.25.
The second step: and determining a horizontal displacement curve of the enclosure structure in the excavation construction process of the foundation pit. Firstly, finite element software is adopted to simulate the excavation process of the foundation pit, the numerical simulation value of the horizontal displacement of the side of the foundation pit in the final state of the excavation of the foundation pit is extracted, an empirical formula is adopted to fit the numerical simulation value, and the numerical simulation result and the empirical result are drawn in a graph 4. Wherein u is the deformation of the enclosure.
And thirdly, determining the stress change value of the soil outside the pit under the excavation action of the foundation pit. Dividing the horizontal displacement curve of the soil body behind the building enclosure into 60 equal segments, calculating the additional stress of the soil body outside the foundation pit under the influence of the translation of the building enclosure of each micro-element segment by segment, and summing the additional stresses generated by the deformation of each micro-segment to obtain the additional stress of the soil body around the tunnel outside the foundation pit when the building enclosure is deformed, as shown in fig. 5. In fig. 5, (a) is a horizontal additional stress curve, and (b) is a vertical additional stress curve.
And fourthly, determining the additional load of the existing pipeline beside the foundation pit under the excavation effect. 1/2 of the difference of the additional soil pressure on the upper side, the lower side, the left side and the right side of the pipeline is used as an additional load acting on the pipeline, and a broken line segment is adopted to fit the additional soil pressure; the pipe was considered as a free-form homogeneous torus model, and 1m wide was taken for analysis, as shown in fig. 6.
And fifthly, determining that the existing pipeline at the side has additional internal force under the excavation action of the foundation pit. The additional load of the pipeline beside the foundation pit is divided into four working conditions, the additional internal force generated by the shield tunnel under the action of the additional soil pressure is respectively calculated by adopting a formula, and then the additional internal force is superposed to obtain the final additional internal force, wherein the result is shown in figure 7, wherein (a) in figure 7 is an axial diagram, (b) is a bending moment diagram, and (c) is a shear diagram.
Therefore, the embodiment can better reflect the influences of the excavation depth of the foundation pit, the supporting form, the field soil condition and the construction method, thereby more conveniently determining the transverse additional internal force of the side pipeline under the excavation action of the foundation pit and providing a basis for the supporting design of the foundation pit of the adjacent pipeline.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
Claims (7)
1. A method for determining lateral additional internal force of a side pipeline caused by excavation of a foundation pit is characterized by comprising the following steps of:
step S1: acquiring information of a pipeline buried soil layer, and information related to design and construction of a pipeline and a foundation pit;
step S2: determining a horizontal displacement curve of the enclosure structure caused by excavation construction of the foundation pit;
step S3: obtaining a stress change value of the soil outside the pit under the excavation action of the foundation pit according to the horizontal displacement curve of the enclosure structure caused by the foundation pit excavation construction determined in the step S2;
step S4: determining the additional load of the existing pipeline beside the foundation pit under the excavation effect according to the obtained stress change value;
step S5: determining the additional internal force of the existing pipeline beside the foundation pit under the excavation action according to the additional load;
step S3 specifically includes: dividing the horizontal displacement curve of the enclosure structure into a plurality of equal segments, and regarding the deformation of any infinitesimal segment as translation; calculating the additional stress of the soil outside the pit under the influence of the translation of the enclosure structure of each infinitesimal section by adopting an elastic mechanics method, and then summing the additional stresses generated by the deformation of each infinitesimal section within the length range of the whole enclosure structure to obtain the additional stress of the soil at any point outside the pit when the enclosure structure is deformed;
when the enclosure structure deforms, the additional stress of the soil outside the foundation pit meets the following formula:
in the formula, σxRepresenting horizontal additional stress, σzRepresenting vertical additional stress, n being an equal number, HiIs the vertical distance from the ith bisecting point to the ground, delta sigmax(Hi)、Δσz(Hi) Respectively horizontal and vertical additional stress generated when the envelope structure above the ith equal division point is translated, wherein z represents the vertical distance from the calculated position to the ground; respectively satisfy the following formulas:
wherein G represents the shear modulus of the soil body, v represents the Poisson's ratio of the soil body, and diRepresenting the i-th infinitesimal section building envelope horizontal displacement value and x representing the horizontal distance from the calculated position to the building envelope.
2. The method for determining the lateral additional internal force of the side pipeline caused by excavation of the foundation pit as claimed in claim 1, wherein in step S1, the information of the pipeline buried soil layer, the information of the pipeline and the information related to design and construction of the foundation pit comprise: elastic modulus, poisson's ratio of the soil layer; the buried depth of the pipeline and the inner and outer diameters of the pipeline; the excavation depth and width of the foundation pit, and the horizontal distance between the pipeline and the foundation pit.
3. The method for determining the lateral additional internal force of the side pipeline caused by excavation of the foundation pit according to claim 1, wherein the step S2 is specifically to obtain a horizontal displacement curve of the enclosure structure through field monitoring; or simulating the excavation process of the foundation pit by adopting finite element software, extracting a numerical simulation value of the horizontal displacement of the edge of the foundation pit in the final state of excavation of the foundation pit, and fitting the numerical simulation value by adopting the following formula to obtain a horizontal displacement curve of the enclosure structure in the construction process of the foundation pit:
in the formula umaxRepresents the maximum horizontal deformation of the building envelope, z represents the vertical distance from the calculated position to the ground, HmaxAnd L represents the length of the enclosure structure.
4. The method for determining the lateral additional internal force of the side pipeline caused by excavation of the foundation pit as claimed in claim 1, wherein the step S4 is specifically as follows: 1/2 of the difference between the additional soil pressures on the upper side and the lower side of the pipeline and the left side and the right side of the pipeline is used as an additional load acting on the pipeline, and a broken line segment is adopted to fit the additional soil pressure.
5. The method for determining the lateral additional internal force of the side pipeline caused by excavation of the foundation pit as claimed in claim 4, wherein the additional load satisfies the following formula:
in the formula, q represents the vertical additional soil pressure borne by the pipeline, p represents the horizontal additional soil pressure borne by the pipeline, S represents the minimum horizontal distance between the tunnel and the foundation pit support structure, D represents the vertical distance between the top of the tunnel and the ground, and R represents the calculated radius of the tunnel.
6. The method for determining the lateral additional internal force of the side pipeline caused by excavation of the foundation pit as claimed in claim 1, wherein the step S5 is specifically as follows: dividing the additional load of the pipeline beside the foundation pit into four working conditions, respectively calculating the additional internal force generated under various working conditions by adopting an elastic center method, and then obtaining the final additional internal force of the pipeline by using an superposition method; the four working conditions are respectively as follows: the additional internal force under the action of the vertically uniformly distributed load, the additional internal force under the action of the vertically triangular load, the additional internal force under the action of the horizontally uniformly distributed load and the additional internal force under the action of the horizontally triangular load.
7. The method for determining the lateral additional internal force of the side pipeline caused by excavation of the foundation pit as claimed in claim 6, wherein the final additional internal force of the pipeline satisfies the following formula:
where ξ is the bending moment increasing rate, M is the additional bending moment of the pipeline, N is the additional axial force of the pipeline, Q is the additional shearing force of the pipeline, M is the additional shearing force of the pipelineiRepresents the additional bending moment of the pipeline under the i-th working condition, NiRepresents the additional axial force, Q, of the pipeline under the i-th working conditioniIndicating the added shear of the pipe in condition i.
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| CN202011409140.6A CN112597674B (en) | 2020-12-05 | 2020-12-05 | Method for determining lateral pipeline transverse additional internal force caused by foundation pit excavation |
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