CN114417454B - Method for predicting deep soil displacement field of overlapping tunnel based on different excavation paths - Google Patents
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- 239000002689 soil Substances 0.000 title claims abstract description 145
- 238000006073 displacement reaction Methods 0.000 title claims abstract description 90
- 238000009412 basement excavation Methods 0.000 title claims abstract description 39
- 238000000034 method Methods 0.000 title claims abstract description 21
- 230000005641 tunneling Effects 0.000 claims description 35
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Abstract
The invention discloses a method for predicting a deep soil displacement field of an overlap tunnel based on different excavation paths, which comprises the following steps: establishing a three-dimensional model of an overlap tunnel, wherein the overlap tunnel comprises an uplink curve tunnel and a downlink straight line tunnel; determining standard equations of the shield machine and the outer ring surfaces of the segments of the uplink curve tunnel and the downlink straight tunnel according to the space positions of the uplink curve tunnel and the downlink straight tunnel; calculating deep soil displacement field caused by excavation of uplink curve tunnelThe method comprises the steps of carrying out a first treatment on the surface of the Calculating deep soil displacement field caused by excavation of downlink linear tunnelThe method comprises the steps of carrying out a first treatment on the surface of the For deep soil displacement field caused by excavationAndoverlapping to obtain deep soil displacement fields of overlapping tunnels under different excavation paths. The invention has the advantages that: the method can accurately predict deep soil displacement fields caused by stratum loss and friction force between the shield shell and soil in construction periods of overlapping tunnels of different excavation paths, and has higher popularization and application values.
Description
Technical Field
The invention relates to the technical field of tunnel engineering, in particular to a method for predicting a deep soil displacement field of a stacked tunnel based on different excavation paths.
Background
In the process of building urban subway tunnels, subway lines are not limited to an excavation path, the number of tunnels also tends to increase, and when a plurality of tunnels are excavated along different paths, displacement fields around the tunnels and even the whole deep soil body are difficult to grasp.
At present, the prediction method and the storage medium for predicting soil displacement caused by multi-line tunnel excavation only give out a transverse subsider curve of the earth surface caused by stratum loss, and deep soil displacement solution caused by shield construction load in the excavation period cannot be obtained. In addition, the line shape of the considered tunnel is single, and a deep soil displacement field prediction method for predicting the deep soil displacement field caused by excavation under the spatial complex overlapping position relationship of the curve tunnel and the straight tunnel is not found.
Disclosure of Invention
According to the defects of the prior art, the invention provides a method for predicting the displacement field of deep soil bodies of overlapping tunnels based on different excavation paths, which is used for deducing the sedimentation curves of the deep soil bodies under the different excavation paths by establishing a three-dimensional model of an uplink curve tunnel and a downlink straight line tunnel based on the assumption that a curve with infinite curvature radius can be approximated as a straight line.
The invention is realized by the following technical scheme:
the method for predicting the displacement field of the deep soil body of the overlapping tunnel based on different excavation paths is characterized by comprising the following steps of:
(S1) establishing a three-dimensional model of an overlap tunnel, wherein the overlap tunnel comprises an uplink curve tunnel and a downlink straight line tunnel; determining standard equations of the shield tunneling machine and the outer ring surfaces of the uplink curve tunnel and the downlink straight tunnel segment according to the space positions of the uplink curve tunnel and the downlink straight tunnel;
(S2) deducing a deep soil displacement field S of the uplink curve tunnel caused by soil loss based on a three-dimensional random medium theory c1 The method comprises the steps of carrying out a first treatment on the surface of the Deducing vertical deformation of a deep soil body of the uplink curve tunnel caused by friction force between a shield machine and the soil body based on a Mindlin formula; deep soil displacement field S caused by soil loss for uplink curve tunnel c1 And the vertical deformation of the deep soil body caused by the friction force between the shield tunneling machine and the soil body of the uplink curve tunnel is overlapped to obtain a deep soil body displacement field U caused by excavation of the uplink curve tunnel c ；
(S3) deducing a deep soil displacement field S of the downlink linear tunnel caused by soil loss based on a three-dimensional random medium theory s1 The method comprises the steps of carrying out a first treatment on the surface of the Deducing vertical deformation of a deep soil body of the downlink linear tunnel caused by friction force between a shield machine and the soil body based on a Mindlin formula; deep soil displacement field S caused by soil loss for downlink linear tunnel s1 And the vertical deformation of the deep soil body caused by the friction force between the shield tunneling machine and the soil body of the downlink linear tunnel is overlapped to obtain a deep soil body displacement field U caused by excavation of the downlink linear tunnel s ；。
(S4) for deep soil displacement field U caused by excavation c And U s And superposing to obtain the deep soil displacement field U of the superposed tunnel under different excavation paths.
Step S1 comprises the steps of:
establishing an uplink curve tunnel model with a curvature radius Q and longitudinal, transverse and vertical distances D respectively x 、D y 、D z A downlink straight line tunnel model of (a);
the outer ring surface and the pipe of the shield machine during the tunneling of the uplink curve tunnelOuter annular surface C (x) 0 ，y 0 ，z 0 ) Standard equations for (2) are:
the standard equations of the shield machine outer ring surface and the segment outer ring surface during the downstream linear tunnel tunneling are respectively as follows:
wherein: h is the axial line burial depth of the uplink curve tunnel; r is R c And R is s The outer diameters of the shield machine in the uplink curve tunnel and the shield machine in the downlink straight line tunnel are respectively; r is (r) 1 And r 2 The outer diameters of the duct piece in the uplink curve tunnel and the duct piece in the downlink linear tunnel are respectively; u (u) z1 And u z2 And the displacement parameters are respectively the vertical downward movement of the duct piece in the uplink curve tunnel and the vertical downward movement of the duct piece in the downlink linear tunnel.
Step S2 comprises the steps of:
(S21) deducing a deep soil displacement field S of the uplink curve tunnel caused by soil loss based on a three-dimensional random medium theory c1 Comprises the following steps:
in a three-dimensional rectangular coordinate system, points (x 0 ，y 0 ，z 0 ) The void per unit volume at the point causes a vertical displacement at any point (x, y, z) in the deep soil mass of:
wherein r (z) is the main influence radius of the void of unit volume in the z direction, and r (z) =z/tan beta, wherein beta is the main influence angle of surrounding rock at the upper part of the tunnel, and can be selected according to geological survey data;
summarizing the three-dimensional gap at the tail of the shield tunneling machine into theoretical gap parameters in a two-dimensional model perpendicular to the axis of the uplink curve tunnel, wherein the gap parameters of the tail of the uplink curve tunnel and the tail of the downlink straight line tunnel are G respectively under the condition of synchronous grouting at the tail of the shield tunneling machine without consideration of the synchronous grouting p1 ＝2(R c -r 1 )、G p2 ＝2(R s -r 2 )；
The tunneling length of the shield tunneling machine along the axis of the uplink curve tunnel is l c Triple integration is carried out on a unit volume gap in a three-dimensional gap volume domain at the shield shell of the shield machine, wherein the three-dimensional gap volume domain is G in thickness p1 Along the curve l c The space volume enclosed by the length is used for obtaining a deep soil displacement field S for predicting the uplink curve tunnel caused by soil loss c1 Solution:
wherein: q and theta are function independent variables; l (L) 1 The length of the shield machine in the uplink curve tunnel is set;
(S22) friction force f between the shield shell and the soil body 1 Decomposing along the directions of the x axis and the y axis of the three-dimensional rectangular coordinate system to obtain the horizontal component of the surface distribution force acting on the space curved surface: f (f) x1 ＝f 1 cos(θ+π/2)、f y1 ＝f 1 sin(θ+π/2)；
The concentration forces of the horizontal component along the coordinate axis on the unit area are respectively as follows:
the vertical displacement of the midpoint (x, y, z) of the deep soil caused by the concentrated force along the directions of the x axis and the y axis is respectively as follows:
wherein:is a function argument;
when the semi-infinite in-vivo point (x 0 ，y 0 ，z 0 ) When a unit concentrated force in the positive direction of the x-axis and the y-axis acts, the sedimentation value w of any point (x, y, z) in the deep soil is caused x 、w y Can be solved by the modified Mindlin formula:
wherein: g is soil shear elastic modulus; μ is poisson's ratio;
(S23) for the deep soil displacement field S of the uplink curve tunnel caused by soil loss c1 Vertical displacement W of midpoint (x, y, z) of deep soil body caused by concentrated force along x-axis direction x1 And the vertical displacement W of the midpoint (x, y, z) of the deep soil body is caused by the concentrated force along the y-axis direction y1 Overlapping to obtain a deep soil displacement field U caused by excavation of the uplink curve tunnel c The calculation formula is: u (U) c ＝S c1 +W x1 +W y1 。
Step S3 comprises the steps of:
(S31) deducing a deep soil displacement field S of the downlink linear tunnel caused by soil loss based on a three-dimensional random medium theory s1 Comprises the following steps:
the tunneling length of the shield tunneling machine along the axis of the downlink linear tunnel is l s Triple integration is carried out on a unit volume gap in a three-dimensional gap volume domain at the shield shell of the shield machine, wherein the three-dimensional gap volume domain is G in thickness p2 Along the curve l s The space volume enclosed by the length is used for obtaining a deep soil displacement field S for predicting the loss of soil of the downlink linear tunnel s1 Solution:
wherein: l (L) 2 The length of the shield tunneling machine in the downlink linear tunnel is set;
(S32) friction force f between the shield shell and the soil body 2 Decomposing along the directions of the x axis and the y axis of the three-dimensional rectangular coordinate system to obtain the horizontal component of the surface distribution force acting on the space curved surface: f (f) x2 ＝f 2 cos(θ+π/2)、f y2 ＝f 2 sin(θ+π/2)；
The concentration forces of the horizontal component along the coordinate axis on the unit area are respectively as follows:
the vertical displacement of the midpoint (x, y, z) of the deep soil caused by the concentrated force along the directions of the x axis and the y axis is respectively as follows:
(S33) for the deep soil displacement field S of the downlink linear tunnel caused by soil loss s1 Vertical displacement W of midpoint (x, y, z) of deep soil body caused by concentrated force along x-axis direction x2 And the vertical displacement W of the midpoint (x, y, z) of the deep soil body is caused by the concentrated force along the y-axis direction y2 Overlapping to obtain a deep soil displacement field U caused by excavation of the downlink linear tunnel s The calculation formula is: u (U) s ＝S s1 +W x2 +W y2 。
Step S4 comprises the steps of:
for deep soil displacement field U caused by excavation c And U s Superposing to obtain the deep soil displacement field U of the overlap tunnel under different excavation paths, wherein the calculation formula is as follows: u=u c +U s 。
The invention has the advantages that: the method fully considers the different tunneling paths of the multi-line shield tunnel, the spatial position relation of the multi-line shield tunnel and the load characteristics of the shield construction period, can solve the problem that the existing two-dimensional theoretical analysis can not accurately reflect the non-earth settlement of the three-dimensional soil caused by the shield tunnel construction, can accurately predict the deep soil displacement field caused by stratum loss and friction between the shield shell and the soil in the construction period of the overlap tunnel of different tunneling paths, and has higher popularization and application values.
Drawings
FIG. 1 is a flow chart of a method for predicting a deep soil displacement field of an overlap tunnel based on different excavation paths;
FIG. 2 is a schematic representation of the stacked tunneling model of the present invention.
Detailed Description
The features of the invention and other related features are described in further detail below by way of example in conjunction with the following figures to facilitate understanding by those skilled in the art:
as shown in fig. 1-2, reference numerals 1-2 are respectively represented as: an uplink curve tunnel 1 and a downlink straight tunnel 2.
Examples: 1-2, the embodiment relates to a method for predicting a deep soil displacement field of an overlap tunnel based on different excavation paths, which comprises the steps of firstly establishing a three-dimensional rectangular coordinate system, wherein a O, x axis and a y axis of a coordinate origin are both positioned on the ground surface, and a z axis is vertically downward as shown in FIG. 2; the prediction method specifically comprises the following steps:
(S1) establishing an uplink curve tunnel model with a curvature radius Q and longitudinal, transverse and vertical distances between the model and the model being D x 、D y 、D z A downlink straight line tunnel model of (a);
when the curvature radius of the tunnel axis is large enough, the axis of the uplink curve tunnel 1 can be approximated to a straight line, so that the axes of the uplink curve tunnel 1 and the downlink straight line tunnel 2 can be assumed to be curved for easy analysis.
Wherein, the shield machine outer ring surface and the segment outer ring surface C (x) during the tunneling of the ascending curve tunnel 1 0 ，y 0 ，z 0 ) Standard equation (C (x) 0 ，y 0 ，z 0 ) Any point on the curved surface C) are:
the standard equations of the shield machine outer ring surface and the segment outer ring surface during the tunneling of the downlink linear tunnel 2 are respectively as follows:
wherein: h is the axial line burial depth of the uplink curve tunnel 1; r is R c And R is s The outer diameters of the shield machine in the uplink curve tunnel 1 and the shield machine in the downlink straight line tunnel 2 are respectively; r is (r) 1 And r 2 The outer diameters of the duct piece in the uplink curve tunnel 1 and the duct piece in the downlink straight tunnel 2 are respectively; u (u) z1 And u z2 And the displacement parameters are respectively the displacement parameters of the vertical downward movement of the duct piece in the upward curve tunnel 1 and the duct piece in the downward straight line tunnel 2.
(S2) deducing a deep soil displacement field S of the uplink curve tunnel 1 caused by soil loss based on a three-dimensional random medium theory proposed by Litwiniszyn c1 Comprises the following steps:
in a three-dimensional rectangular coordinate system, points (x 0 ，y 0 ，z 0 ) The void per unit volume at the point causes a vertical displacement at any point (x, y, z) in the deep soil mass of:
wherein r (z) is the main influence radius of the void of unit volume in the z direction, and r (z) =z/tan beta, wherein beta is the main influence angle of surrounding rock at the upper part of the tunnel, and can be selected according to geological survey data;
the three-dimensional gap at the shield tail of the shield tunneling machine is generalized to be theoretical gap parameters in a two-dimensional model perpendicular to the axis of the uplink curve tunnel 1, and under the condition that synchronous grouting at the shield tail of the shield tunneling machine is not considered, the gap parameters of the shield tail of the uplink curve tunnel 1 and the downlink straight line tunnel 2 are G respectively p1 ＝2(R c -r 1 )、G p2 ＝2(R s -r 2 )；
The tunneling length of the shield tunneling machine along the axis of the uplink curve tunnel 1 is l c Triple integration is carried out on the gap with unit volume in a three-dimensional gap volume domain at the shield shell of the shield machine, wherein the three-dimensional gap volume domain is G in thickness p1 Is a ring of (2)Travel along a curve l c The space volume enclosed by the length is used for obtaining a deep soil displacement field S for predicting the soil loss of the uplink curve tunnel 1 c1 Solution:
wherein: q and theta are function independent variables; l (L) 1 The length of the shield machine in the uplink curve tunnel 1;
(S22) friction force f between the shield shell and the soil body 1 Decomposing along the directions of the x axis and the y axis of the three-dimensional rectangular coordinate system to obtain the horizontal component of the surface distribution force acting on the space curved surface: f (f) x1 ＝f 1 cos(θ+π/2)、f y1 ＝f 1 sin(θ+π/2)；
The concentration forces of the horizontal component along the coordinate axis on the unit area are respectively as follows:
the vertical displacement of the midpoint (x, y, z) of the deep soil caused by the concentrated force along the directions of the x axis and the y axis is respectively as follows:
wherein:is a function argument;
when the semi-infinite in-vivo point (x 0 ，y 0 ，z 0 ) When a unit concentrated force in the positive direction of the x-axis and the y-axis acts, any point in the deep soil body is causedSedimentation value w of (x, y, z) x 、w y Can be solved by the modified Mindlin formula:
wherein: g is soil shear elastic modulus; μ is poisson's ratio;
deep soil displacement field S caused by soil loss for ascending curve tunnel 1 c1 Vertical displacement W of midpoint (x, y, z) of deep soil body caused by concentrated force along x-axis direction x1 And the vertical displacement W of the midpoint (x, y, z) of the deep soil body is caused by the concentrated force along the y-axis direction y1 Overlapping to obtain a deep soil displacement field U of the uplink curve tunnel 1 caused by excavation c The calculation formula is: u (U) c ＝S c1 +W x1 +W y1 。
(S3) deducing a deep soil displacement field S of the downlink linear tunnel 2 caused by soil loss based on a three-dimensional random medium theory proposed by Litwiniszyn s1 Comprises the following steps:
the tunneling length of the shield tunneling machine along the axis of the downlink linear tunnel 2 is l s Triple integration is carried out on the gap with unit volume in a three-dimensional gap volume domain at the shield shell of the shield machine, wherein the three-dimensional gap volume domain is G in thickness p2 Is routed along a curve s The space volume enclosed by the length is used for obtaining a deep soil displacement field S for predicting the loss of the soil of the downlink linear tunnel 2 s1 Solution:
wherein: l (L) 2 The length of the shield machine in the downlink linear tunnel 2;
friction force f between shield shell and soil body 2 Decomposing along the directions of the x axis and the y axis of the three-dimensional rectangular coordinate system to obtain the horizontal component of the surface distribution force acting on the space curved surface: f (f) x2 ＝f 2 cos(θ+π/2)、f y2 ＝f 2 sin(θ+π/2)；
The concentration forces of the horizontal component along the coordinate axis on the unit area are respectively as follows:
the vertical displacement of the midpoint (x, y, z) of the deep soil caused by the concentrated force along the directions of the x axis and the y axis is respectively as follows:
deep soil displacement field S caused by soil loss for descending straight line tunnel 2 s1 Vertical displacement W of midpoint (x, y, z) of deep soil body caused by concentrated force along x-axis direction x2 And the vertical displacement W of the midpoint (x, y, z) of the deep soil body is caused by the concentrated force along the y-axis direction y2 Overlapping to obtain a deep soil displacement field U of the downlink linear tunnel 2 caused by excavation s The calculation formula is: u (U) s ＝S s1 +W x2 +W y2 。
(S4) for deep soil displacement field U caused by excavation c And U s Overlapping to obtain deep soil bodies of overlapping tunnels under different excavation pathsThe displacement field U is calculated as: u=u c +U s 。
Although the foregoing embodiments have been described in some detail with reference to the accompanying drawings, it will be appreciated by those skilled in the art that various modifications and changes may be made thereto without departing from the scope of the invention as defined in the appended claims, and thus are not repeated herein.
Claims (1)
1. The method for predicting the displacement field of the deep soil body of the overlapping tunnel based on different excavation paths is characterized by comprising the following steps of:
(S1) establishing a three-dimensional model of an overlap tunnel, wherein the overlap tunnel comprises an uplink curve tunnel and a downlink straight line tunnel; determining standard equations of the shield tunneling machine and the outer ring surfaces of the uplink curve tunnel and the downlink straight tunnel segment according to the space positions of the uplink curve tunnel and the downlink straight tunnel;
step S1 comprises the steps of:
establishing an uplink curve tunnel model with a curvature radius Q and longitudinal, transverse and vertical distances D respectively x 、D y 、D z A downlink straight line tunnel model of (a);
the outer ring surface of the shield machine and the outer ring surface C (x) of the segment during the tunneling of the uplink curve tunnel 0 ,y 0 ,z 0 ) Standard equations for (2) are:
the standard equations of the shield machine outer ring surface and the segment outer ring surface during the downstream linear tunnel tunneling are respectively as follows:
wherein: h is the axial line burial depth of the uplink curve tunnel; r is R c And R is s The outer diameters of the shield machine in the uplink curve tunnel and the shield machine in the downlink straight line tunnel are respectively; r is (r) 1 And r 2 The outer diameters of the duct piece in the uplink curve tunnel and the duct piece in the downlink linear tunnel are respectively; u (u) z1 And u z2 Respectively obtaining displacement parameters of the vertical downward movement of the duct piece in the uplink curve tunnel and the duct piece in the downlink linear tunnel;
(S2) deducing a deep soil displacement field S of the uplink curve tunnel caused by soil loss based on a three-dimensional random medium theory c1 The method comprises the steps of carrying out a first treatment on the surface of the Deducing vertical deformation of a deep soil body of the uplink curve tunnel caused by friction force between a shield machine and the soil body based on a Mindlin formula; deep soil displacement field S caused by soil loss for uplink curve tunnel c1 And the vertical deformation of the deep soil body caused by the friction force between the shield tunneling machine and the soil body of the uplink curve tunnel is overlapped to obtain a deep soil body displacement field U caused by excavation of the uplink curve tunnel c ；
Step S2 comprises the steps of:
(S21) deducing a deep soil displacement field S of the uplink curve tunnel caused by soil loss based on a three-dimensional random medium theory c1 Comprises the following steps:
in a three-dimensional rectangular coordinate system, points (x 0 ,y 0 ,z 0 ) The void per unit volume at the point causes a vertical displacement at any point (x, y, z) in the deep soil mass of:
wherein r (z) is the main influence radius of the void of unit volume in the z direction, and r (z) =z/tan beta, wherein beta is the main influence angle of surrounding rock at the upper part of the tunnel, and can be selected according to geological survey data;
summarizing the three-dimensional gap at the tail of the shield tunneling machine into theoretical gap parameters in a two-dimensional model perpendicular to the axis of the uplink curve tunnel, wherein the gap parameters of the tail of the uplink curve tunnel and the tail of the downlink straight line tunnel are G respectively under the condition of synchronous grouting at the tail of the shield tunneling machine without consideration of the synchronous grouting p1 ＝2(R c –r 1 )、G p2 ＝2(R s –r 2 )；
The tunneling length of the shield tunneling machine along the axis of the uplink curve tunnel is l c Triple integration is carried out on a unit volume gap in a three-dimensional gap volume domain at the shield shell of the shield machine, wherein the three-dimensional gap volume domain is G in thickness p1 Along the curve l c The space volume enclosed by the length is used for obtaining a deep soil displacement field S for predicting the uplink curve tunnel caused by soil loss c1 Solution:
wherein: q and theta are function independent variables; l (L) 1 The length of the shield machine in the uplink curve tunnel is set;
(S22) friction force f between the shield shell and the soil body 1 Decomposing along the directions of the x axis and the y axis of the three-dimensional rectangular coordinate system to obtain the horizontal component of the surface distribution force acting on the space curved surface: f (f) x1 ＝f 1 cos(θ+π/2)、f y1 ＝f 1 sin(θ+π/2)；
The concentration forces of the horizontal component along the coordinate axis on the unit area are respectively as follows:
the vertical displacement of the midpoint (x, y, z) of the deep soil caused by the concentrated force along the directions of the x axis and the y axis is respectively as follows:
wherein:is a function argument;
when the semi-infinite in-vivo point (x 0 ,y 0 ,z 0 ) When a unit concentrated force in the positive direction of the x-axis and the y-axis acts, the sedimentation value w of any point (x, y, z) in the deep soil is caused x 、w y Can be solved by the modified Mindlin formula:
wherein: g is soil shear elastic modulus; μ is poisson's ratio;
(S23) for the deep soil displacement field S of the uplink curve tunnel caused by soil loss c1 Vertical position of midpoint (x, y, z) of deep soil caused by concentrated force along x-axis directionMove W x1 And the vertical displacement W of the midpoint (x, y, z) of the deep soil body is caused by the concentrated force along the y-axis direction y1 Overlapping to obtain a deep soil displacement field U caused by excavation of the uplink curve tunnel c The calculation formula is: u (U) c ＝S c1 +W x1 +W y1 ；
(S3) deducing a deep soil displacement field S of the downlink linear tunnel caused by soil loss based on a three-dimensional random medium theory s1 The method comprises the steps of carrying out a first treatment on the surface of the Deducing vertical deformation of a deep soil body of the downlink linear tunnel caused by friction force between a shield machine and the soil body based on a Mindlin formula; deep soil displacement field S caused by soil loss for downlink linear tunnel s1 And the vertical deformation of the deep soil body caused by the friction force between the shield tunneling machine and the soil body of the downlink linear tunnel is overlapped to obtain a deep soil body displacement field U caused by excavation of the downlink linear tunnel s ；
Step S3 comprises the steps of:
(S31) deducing a deep soil displacement field S of the downlink linear tunnel caused by soil loss based on a three-dimensional random medium theory s1 Comprises the following steps:
the tunneling length of the shield tunneling machine along the axis of the downlink linear tunnel is l s Triple integration is carried out on a unit volume gap in a three-dimensional gap volume domain at the shield shell of the shield machine, wherein the three-dimensional gap volume domain is G in thickness p2 Along the curve l s The space volume enclosed by the length is used for obtaining a deep soil displacement field S for predicting the loss of soil of the downlink linear tunnel s1 Solution:
wherein: l (L) 2 The length of the shield tunneling machine in the downlink linear tunnel is set;
(S32) friction force f between the shield shell and the soil body 2 Decomposing along the directions of the x axis and the y axis of the three-dimensional rectangular coordinate system to obtain a space curved surfaceThe plane of action distributes the force horizontal component: f (f) x2 ＝f 2 cos(θ+π/2)、f y2 ＝f 2 sin(θ+π/2)；
The concentration forces of the horizontal component along the coordinate axis on the unit area are respectively as follows:
the vertical displacement of the midpoint (x, y, z) of the deep soil caused by the concentrated force along the directions of the x axis and the y axis is respectively as follows:
(S33) for the deep soil displacement field S of the downlink linear tunnel caused by soil loss s1 Vertical displacement W of midpoint (x, y, z) of deep soil body caused by concentrated force along x-axis direction x2 And the vertical displacement W of the midpoint (x, y, z) of the deep soil body is caused by the concentrated force along the y-axis direction y2 Overlapping to obtain a deep soil displacement field U caused by excavation of the downlink linear tunnel s The calculation formula is: u (U) s ＝S s1 +W x2 +W y2 ；
(S4) for deep soil displacement field U caused by excavation c And U s Overlapping to obtain deep soil displacement fields U of the overlapping tunnels under different excavation paths;
step S4 comprises the steps of:
for deep soil displacement field U caused by excavation c And U s Superposing to obtain the deep soil displacement field U of the overlap tunnel under different excavation paths, wherein the calculation formula is as follows: u=u c +U s 。
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