CN111985028B - Calculation method for cross section deformation of adjacent tunnel segment caused by engineering precipitation - Google Patents
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- 238000001556 precipitation Methods 0.000 title claims abstract description 95
- 238000004364 calculation method Methods 0.000 title claims abstract description 37
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 77
- 238000000034 method Methods 0.000 claims description 17
- 239000002689 soil Substances 0.000 claims description 12
- 230000015572 biosynthetic process Effects 0.000 claims description 6
- 238000005086 pumping Methods 0.000 claims description 4
- 230000005251 gamma ray Effects 0.000 claims description 3
- 230000005484 gravity Effects 0.000 claims description 3
- 230000035699 permeability Effects 0.000 claims description 3
- 238000012360 testing method Methods 0.000 claims description 3
- 238000011156 evaluation Methods 0.000 abstract description 3
- 230000009286 beneficial effect Effects 0.000 abstract description 2
- 238000000247 postprecipitation Methods 0.000 description 9
- 239000003673 groundwater Substances 0.000 description 7
- 238000010586 diagram Methods 0.000 description 6
- 238000009412 basement excavation Methods 0.000 description 3
- 238000011160 research Methods 0.000 description 3
- 238000004458 analytical method Methods 0.000 description 2
- 230000007547 defect Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 239000002349 well water Substances 0.000 description 1
- 235000020681 well water Nutrition 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Abstract
The invention discloses a calculation method for deformation of a cross section of an adjacent tunnel segment caused by engineering precipitation, which comprises the steps of calculating an additional load increment at a position adjacent to a tunnel caused by engineering precipitation, and then calculating the deformation of the cross section of the tunnel under a total stress increment based on structural mechanics. The beneficial effects of the invention are as follows: the efficiency of foundation pit dewatering scheme evaluation is greatly improved, the calculation time is shortened, the manual investment is reduced, and a quick and reasonable reference is provided for the comparison and selection of the foundation pit dewatering scheme.
Description
Technical Field
The invention relates to an analytical calculation method suitable for deformation of an adjacent tunnel caused by engineering precipitation, in particular to a calculation method for deformation of a cross section of an adjacent tunnel segment caused by engineering precipitation, and belongs to the technical field of engineering precipitation.
Background
Due to the increasingly compact utilization of urban space, a great number of foundation pit projects are occurring which are tightly built along subway lines and around subway stations. Meanwhile, the excavation depth of the foundation pit engineering is gradually increased, and in areas with higher underground water levels, the depth of foundation pit precipitation is increased, so that influence on surrounding running subways is inevitably caused, and subway deceleration and even shutdown can be caused when the underground is serious.
At present, many researches on the influence of engineering precipitation on the surrounding environment at home and abroad are carried out, but most of the researches are focused on the problem of surface subsidence caused by precipitation, and a small number of students study the problem of deformation of adjacent existing tunnels caused by engineering precipitation. The numerical calculation method is widely applied to engineering precipitation, and the response rule of adjacent tunnel deformation to different engineering precipitation conditions can be obtained on the basis of considering factors such as precipitation water level, water pumping level, precipitation time and mode. However, the numerical calculation method has obvious defects that a great deal of effort and time are required for modeling and calculation, and proper constitutive relation and other factors are required to be considered. The analysis and calculation method is quicker, and the result can be obtained only by simply adjusting corresponding parameter parameters for a few minutes when other conditions are changed except for time for the first time (but still faster than numerical simulation). For the conventional use method of the calculation method of the tunnel cross section deformation, only natural load conditions can be considered, but calculation under additional load conditions cannot be considered, and no research on the calculation method of the adjacent tunnel cross section deformation caused by engineering precipitation is seen.
Disclosure of Invention
The invention aims to solve the problems that the numerical calculation method needs to consume a great deal of effort and time to carry out modeling and calculation and the analysis calculation method for the deformation of the cross section of the adjacent tunnel segment caused by engineering precipitation is still lacked.
The invention realizes the above purpose through the following technical scheme: a calculation method for deformation of a cross section of an adjacent tunnel segment caused by engineering precipitation comprises the following steps:
step one, calculating an additional load increment at a position adjacent to a tunnel due to engineering precipitation;
and secondly, calculating the deformation of the cross section of the tunnel under the total stress increment based on structural mechanics.
As still further aspects of the invention: the step oneIn which first the vertical total stress delta sigma at the position adjacent to the tunnel axis due to engineering precipitation is calculated V And a horizontal total stress delta sigma H ：
Δσ V ＝ΔH W (γ-γ sat )
Wherein, gamma is the natural gravity of soil; gamma ray sat The soil body saturation is severe; gamma' is the soil body floating degree; k (K) 0 Is the side pressure coefficient; when the water line is above the tunnel vault, ΔH W Is the lowering of the central axis position of the tunnel; when the water line is below the tunnel vault, ΔH W ΔH is the distance from the initial water line to the tunnel vault W The calculation method of (1) is as follows:
ΔH W ＝H 0 -H x 。
wherein H is 0 For the thickness of the aquifer, H x For the water level at the tunnel position, H x The calculation method of (1) is as follows:
wherein H is w The water level in the dewatering well is the water level in the dewatering well; h 0 Is the thickness of the aquifer; r is (r) w Is the radius of the dewatering well; r is the radius of influence of precipitation; r is (r) x Is the distance from any point of the longitudinal direction (parallel to the Y axis) of the tunnel to the dewatering well.
Wherein r is x The calculation method of (1) is as follows:
the intersection point of the X axis and the axis (parallel to the Y axis) of any point of the tunnel is O, and L is the distance between the central axis of the precipitation well and the O point; y is the distance between any point of the tunnel and the point O.
Wherein, the precipitation influence radius R can be obtained according to a water pumping test; when the conditions are insufficient, the method can be expressed according to an empirical formulaAnd (5) calculating. Wherein S is w For lowering the depth of the dewatering well, when the lowering depth is smaller than 10m, S is taken out w =10m, k is soil permeability coefficient, H 0 Is the thickness of the aquifer.
As still further aspects of the invention: in the first step, when the cross section is calculated, the distributed load formed by the additional stress combination of any point on the cross section is the additional load. Because the external loads of the tunnel before and after the excavation of the foundation pit are balanced, the additional loads are balanced, so that the additional loads on the horizontal and vertical axes of the cross section of the tunnel can be calculated, namely the vertical additional load and the horizontal additional load are respectively applied to the tunnel structure.
Wherein, vertical additional load is equipartition load, and horizontal additional load falls into three types:
(1) The water level is still above the tunnel after precipitation, and the horizontal additional load is an even load;
(2) The water level after precipitation is in the section range of the tunnel, the horizontal additional load above the water level line of the underground water is a trapezoid load, and the horizontal additional load below the water level line is an even load;
(3) The water level is below the tunnel after precipitation, and the horizontal additional load is a trapezoidal load.
As still further aspects of the invention: in the second step, the calculation method of the vertical deformation of any point of the cross section of the tunnel comprises the following steps:
wherein,vertical deformation of the tunnel cross section caused by horizontal additional load, < >>Vertical deformation of the tunnel cross section caused by vertical additional loads, +.>Vertical deformation of the tunnel cross section caused by additional load for stratum resistance.
Wherein when the water level is still above the tunnel after precipitation, the cross section of the tunnel is vertically deformed due to horizontal additional load
Wherein when the water level after precipitation is within the range of the tunnel cross section, the tunnel cross section is deformed vertically due to horizontal additional load
Wherein when the water level after precipitation is below the tunnel, the vertical deformation of the cross section of the tunnel is caused by the horizontal additional load
Wherein DeltaP h1 Is a horizontal trapezoid with an additional load delta P h Is equal to the uniformly distributed load part delta P h2 Is a horizontal trapezoid with an additional load delta P h Is provided.
Wherein the vertical deformation of the tunnel cross section caused by the vertical additional load
Wherein the vertical deformation of the tunnel cross section caused by stratum resistance
When θ is more than or equal to 0 and less than pi/4:
pi/4 is less than or equal to theta and less than pi/2:
wherein DeltaP r For formation resistance, R 0 And the radius of the tunnel is the included angle formed by any point of the cross section of the tunnel around the circle center, and the vault is taken as the starting point.
The method for calculating the horizontal deformation of any point of the tunnel cross section comprises the following steps:
wherein when the water level is still above the tunnel after precipitation, the horizontal deformation of the cross section of the tunnel is caused by horizontal additional load
Wherein when the water level after precipitation is within the range of the tunnel cross section, the horizontal deformation of the tunnel cross section caused by the horizontal additional load
Wherein when the water level after precipitation is below the tunnel, the horizontal deformation of the cross section of the tunnel caused by horizontal additional load
Wherein DeltaP h1 Is a horizontal trapezoid with an additional load delta P h Is equal to the uniformly distributed load part delta P h2 Is a horizontal trapezoid with an additional load delta P h Is provided.
Wherein the horizontal deformation of the tunnel cross section caused by the vertical additional load
Wherein the horizontal deformation of the tunnel cross section caused by formation resistance
When θ is more than or equal to 0 and less than pi/4,
when pi/4 is less than or equal to theta and less than pi/2,
the beneficial effects of the invention are as follows: the calculation method for the cross section deformation of the adjacent tunnel duct piece caused by engineering precipitation is reasonable in design, the evaluation efficiency of the foundation pit precipitation scheme is greatly improved, the calculation time is shortened, the labor investment is reduced, and a quick and reasonable reference is provided for comparison and selection of the foundation pit precipitation scheme.
Drawings
FIG. 1 is a schematic view of calculated points at different positions before and after precipitation according to the present invention;
FIG. 2 is a schematic diagram of the calculation of the additional load of the tunnel according to the present invention;
FIG. 3 is a schematic view of a tunnel cross-sectional structure according to the present invention;
FIG. 4 is a schematic diagram of a cross-sectional structure of a tunnel according to the present invention;
FIG. 5 is a schematic view of a tunnel cross-section split structure of the present invention;
FIG. 6 is a schematic diagram of a cross-sectional structure of a tunnel with water level after precipitation according to the present invention;
FIG. 7 is a schematic diagram of a cross-sectional split structure of a tunnel with water level after precipitation according to the present invention;
FIG. 8 is a schematic diagram of a cross-sectional structure of a tunnel caused by engineering precipitation below the tunnel at a water level after precipitation according to the invention;
FIG. 9 is a schematic diagram of a cross-sectional split structure of a tunnel caused by engineering precipitation below the tunnel at a water level after precipitation.
In the figure: 1. dewatering well, 2, tunnel, 3, initial ground water line, 4, ground water line after dewatering, 5, distance Z from ground surface to initial ground water line 1 6, calculating the distance Z between the initial ground water line and the ground water line after precipitation on the vertical axis of the point 2 7, the vertical distance Z between the ground water line and the calculated point B after precipitation 3 8, vertical distance Z from initial ground water line to calculation point A x 9, calculating points A,10, calculating points B,11 and lowering the depth S of the precipitation well w 12, dewatering well water level H w 13, water level height H at tunnel position after precipitation x 14, water-bearing layer height H0, 15, dewatering well radius r w Distance r between dewatering well and tunnel x 17, the precipitation influence radius R,18, the X axis, 19, the Y axis, 20, any point on the tunnel, 21, the intersection point O of the axis where the X axis and any point on the tunnel are located, 22, the distance L between the center of a precipitation well and the O point, 23, the horizontal additional load calculation point of the cross section of the tunnel, 24, the vertical additional load calculation point of the cross section of the tunnel, 25, when the water level is still above the tunnel after precipitationThe engineering precipitation causes vertical additional load of the tunnel cross section, 26, the engineering precipitation causes horizontal additional load of the tunnel cross section when the post-precipitation water level is still above the tunnel, 27, the engineering precipitation causes stratum resistance of the tunnel cross section when the post-precipitation water level is still above the tunnel, 28, the tunnel radius, 29, 45 DEG angle, 30, the trapezoid load part of the horizontal additional load of the tunnel cross section when the post-precipitation water level is within the tunnel cross section range, 31, the uniform load part of the horizontal additional load of the tunnel cross section when the post-precipitation water level is within the tunnel cross section range, 32, the vertical additional load of the tunnel cross section when the post-precipitation water level is within the tunnel cross section range, 33, the horizontal additional load of the tunnel cross section when the post-precipitation water level is within the tunnel cross section range, 34, the post-precipitation water level causes the horizontal additional load of the tunnel cross section below the engineering precipitation, 35, the post-precipitation water level causes the vertical additional load of the tunnel cross section below the tunnel, 36, the post-precipitation level causes stratum resistance of the tunnel cross section below the engineering precipitation below the tunnel.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1 to 9, a calculation method for deformation of a cross section of an adjacent tunnel segment caused by engineering precipitation includes the following steps:
step one, calculating an additional load increment at a position adjacent to a tunnel due to engineering precipitation;
and secondly, calculating the deformation of the cross section of the tunnel under the total stress increment based on structural mechanics.
Further, in the embodiment of the present invention, in the first step, first, the vertical total stress at the position adjacent to the tunnel axis due to the engineering precipitation is calculatedDelta sigma V And a horizontal total stress delta sigma H : for the point A above the water level after precipitation, the vertical total stress is: z is Z 1 γ+Z x γ sat After precipitation, the method comprises the following steps: (Z) 1 +Z x ) Gamma, delta is Z x (γ-γ sat ) The method comprises the steps of carrying out a first treatment on the surface of the The horizontal total stress is: k (K) 0 Z 1 γ+K 0 Z x γ′+Z x γ w After precipitation, the method comprises the following steps: k (K) 0 (Z 1 +Z x ) Gamma, increment is:for the point B below the water level line after precipitation, the vertical total stress before precipitation is: z is Z 1 +(Z 2 +Z 3 )γ sat After precipitation, the method comprises the following steps: (Z) 1 +Z 2 )γ+Z 3 γ sat Increment of Z 2 (γ-γ sat ) The method comprises the steps of carrying out a first treatment on the surface of the The horizontal total stress is: k (K) 0 Z 1 γ+K 0 (Z 2 +Z 3 )γ′+(Z 2 +Z 3 )γ w After precipitation, the method comprises the following steps: k (K) 0 (Z 1 +Z 2 )γ+K 0 Z 3 γ′+Z 3 γ w The increment is: />The vertical total stress delta sigma at any point adjacent to the tunnel location due to engineering precipitation V And a horizontal total stress delta sigma H ：
Δσ V ＝ΔH W (γ-γ sat )
Wherein, gamma is the natural gravity of soil; gamma ray sat The soil body saturation is severe; gamma' is the soil body floating degree; k (K) 0 Is the side pressure coefficient; when the water line is above the tunnel vault, ΔH W Is the lowering of the central axis position of the tunnel; when the water line is below the tunnel vault, ΔH W ΔH is the distance from the initial water line to the tunnel vault W Is calculated by the method of (a)The method comprises the following steps:
ΔH W ＝H 0 -H x 。
wherein H is 0 For the thickness of the aquifer, H x For the water level at the tunnel position, H x The calculation method of (1) is as follows:
wherein H is w The water level in the dewatering well is the water level in the dewatering well; h 0 Is the thickness of the aquifer; r is (r) w Is the radius of the dewatering well; r is the radius of influence of precipitation; r is (r) x Is the distance from any point of the longitudinal direction (parallel to the Y axis) of the tunnel to the dewatering well.
Wherein r is x The calculation method of (1) is as follows:
the intersection point of the X axis and the axis (parallel to the Y axis) of any point of the tunnel is O, and L is the distance between the central axis of the precipitation well and the O point; y is the distance between any point of the tunnel and the point O.
Wherein, the precipitation influence radius R can be obtained according to a water pumping test; when the conditions are insufficient, the method can be expressed according to an empirical formulaAnd (5) calculating. Wherein S is w For lowering the depth of the dewatering well, when the lowering depth is smaller than 10m, S is taken out w =10m, k is soil permeability coefficient, H 0 Is the thickness of the aquifer.
Further, in the embodiment of the present invention, in the step one, when the cross section is calculated, the distributed load formed by combining the additional stresses at any point on the cross section is the additional load. Because the external loads of the tunnel before and after the excavation of the foundation pit are balanced, the additional loads are balanced, so that the additional loads on the horizontal and vertical axes of the cross section of the tunnel can be calculated, namely the vertical additional load and the horizontal additional load are respectively applied to the tunnel structure.
Wherein, vertical additional load is equipartition load, and horizontal additional load falls into three types:
(1) The water level is still above the tunnel after precipitation, and the horizontal additional load is an even load;
(2) The water level after precipitation is in the section range of the tunnel, the horizontal additional load above the water level line of the underground water is a trapezoid load, and the horizontal additional load below the water level line is an even load;
(3) The water level is below the tunnel after precipitation, and the horizontal additional load is a trapezoidal load.
Further, in the embodiment of the present invention, in the second step, the method for calculating the vertical deformation of any point of the tunnel cross section includes:
wherein,vertical deformation of the tunnel cross section caused by horizontal additional load, < >>Vertical deformation of the tunnel cross section caused by vertical additional loads, +.>Vertical deformation of the tunnel cross section caused by additional load for stratum resistance.
Wherein when the water level is still above the tunnel after precipitation, the cross section of the tunnel is vertically deformed due to horizontal additional load
Wherein when the water level after precipitation is within the range of the tunnel cross section, the tunnel cross section is deformed vertically due to horizontal additional load
Wherein when the water level after precipitation is below the tunnel, the vertical deformation of the cross section of the tunnel is caused by the horizontal additional load
Wherein DeltaP h1 Is a horizontal trapezoid with an additional load delta P h Is equal to the uniformly distributed load part delta P h2 Is a horizontal trapezoid with an additional load delta P h Is provided.
Wherein the vertical deformation of the tunnel cross section caused by the vertical additional load
Wherein the vertical deformation of the tunnel cross section caused by stratum resistance
When θ is more than or equal to 0 and less than pi/4:
pi/4 is less than or equal to theta and less than pi/2:
wherein DeltaP r For formation resistance, R 0 And the radius of the tunnel is the included angle formed by any point of the cross section of the tunnel around the circle center, and the vault is taken as the starting point.
The method for calculating the horizontal deformation of any point of the tunnel cross section comprises the following steps:
wherein when the water level is still above the tunnel after precipitation, the horizontal deformation of the cross section of the tunnel is caused by horizontal additional load
Wherein when the water level after precipitation is within the range of the tunnel cross section, the horizontal deformation of the tunnel cross section caused by the horizontal additional load
Wherein when the water level after precipitation is below the tunnel, the horizontal deformation of the cross section of the tunnel caused by horizontal additional load
Wherein DeltaP h1 Is a horizontal trapezoid with an additional load delta P h Is equal to the uniformly distributed load part delta P h2 Is a horizontal trapezoid with an additional load delta P h Is provided.
Wherein, vertical is attachedHorizontal deformation of tunnel cross section caused by loading
Wherein the horizontal deformation of the tunnel cross section caused by formation resistance
When θ is more than or equal to 0 and less than pi/4,
when pi/4 is less than or equal to theta and less than pi/2,
working principle: when the calculation method for deformation of the cross section of the adjacent tunnel segment caused by engineering precipitation is used, the additional load increment at the position of the adjacent tunnel due to engineering precipitation is calculated, then the deformation of the cross section of the tunnel under the total stress increment is calculated based on structural mechanics, the evaluation efficiency of the foundation pit precipitation scheme is greatly improved, the calculation time is shortened, the labor investment is reduced, and a quick and reasonable reference is provided for comparison and selection of the foundation pit precipitation scheme.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (1)
1. A calculation method for deformation of the cross section of an adjacent tunnel segment caused by engineering precipitation is characterized by comprising the following steps: the method comprises the following steps:
step one, calculating an additional load increment at a position adjacent to a tunnel due to engineering precipitation;
in the first step, firstly, the vertical total stress increment delta sigma at the position adjacent to the tunnel axis caused by engineering precipitation is calculated V And a horizontal total stress delta sigma H ：
Δσ V ＝ΔH W (γ-γ sat )
Δσ H ＝ΔH q [K 0 (γ-γ′)-γ w ]
Wherein, gamma is the natural gravity of soil; gamma ray sat The soil body saturation is severe; gamma' is the soil body floating degree; k (K) 0 Is the side pressure coefficient; when the water line is above the tunnel vault, ΔH W Is the lowering of the central axis position of the tunnel; when the water line is below the tunnel vault, ΔH W ΔH is the distance from the initial water line to the tunnel vault W The calculation method of (1) is as follows:
ΔH W ＝H 0 -H x
wherein H is 0 For the thickness of the aquifer, H x For the water level at the tunnel position, H x The calculation method of (1) is as follows:
wherein H is w The water level in the dewatering well is the water level in the dewatering well; h 0 Is the thickness of the aquifer; r is (r) w Is the radius of the dewatering well; r is the radius of influence of precipitation; r is (r) x The distance from any point of the tunnel longitudinal direction parallel to the Y axis to the dewatering well;
wherein r is x The calculation method of (1) is as follows:
the intersection point of the axis of any point of the X axis and the tunnel, which is parallel to the Y axis, is O, and L is the distance between the central axis of the precipitation well and the O point; y is the distance between any point of the tunnel and the O point;
the precipitation influence radius R is obtained according to a water pumping test; when the conditions are insufficient, the method can be expressed according to an empirical formulaCalculating; wherein S is w For lowering the depth of the dewatering well, when the lowering depth is smaller than 10m, S is taken out w =10m, k is soil permeability coefficient, H 0 Is the thickness of the aquifer;
in the first step, when the cross section is calculated, the distributed load formed by the combination of the additional stress at any point on the cross section is the additional load;
wherein, vertical additional load is equipartition load, and horizontal additional load falls into three types:
(1) The water level is still above the tunnel after precipitation, and the horizontal additional load is an even load;
(2) The water level after precipitation is in the section range of the tunnel, the horizontal additional load above the water level line of the underground water is a trapezoid load, and the horizontal additional load below the water level line is an even load;
(3) The water level is below the tunnel after precipitation, and the horizontal additional load is a trapezoidal load;
calculating the deformation of the tunnel cross section under the total stress increment based on structural mechanics;
in the second step, the calculation method of the vertical deformation of any point of the cross section of the tunnel comprises the following steps:
wherein,vertical deformation of the tunnel cross section caused by horizontal additional load, < >>Vertical deformation of the tunnel cross section caused by vertical additional loads, +.>Vertical deformation of the cross section of the tunnel caused by additional load for stratum resistance;
wherein when the water level is still above the tunnel after precipitation, the cross section of the tunnel is vertically deformed due to horizontal additional load
Wherein when the water level after precipitation is within the range of the tunnel cross section, the tunnel cross section is deformed vertically due to horizontal additional load
Wherein when the water level after precipitation is below the tunnel, the vertical deformation of the cross section of the tunnel is caused by the horizontal additional load
Wherein DeltaP h1 Is a horizontal trapezoid with an additional load delta P h Is equal to the uniformly distributed load part delta P h2 Is a horizontal trapezoid with an additional load delta P h Is provided with a triangular load part;
wherein the vertical deformation of the tunnel cross section caused by the vertical additional load
Wherein the vertical deformation of the tunnel cross section caused by stratum resistance
When θ is more than or equal to 0 and less than pi/4:
pi/4 is less than or equal to theta and less than pi/2:
wherein DeltaP r For formation resistance, R 0 Is the radius of the tunnel, theta is any point of the cross section of the tunnelThe included angle formed by the circle centers takes the vault as a starting point;
the method for calculating the horizontal deformation of any point of the tunnel cross section comprises the following steps:
wherein when the water level is still above the tunnel after precipitation, the horizontal deformation of the cross section of the tunnel is caused by horizontal additional load
Wherein when the water level after precipitation is within the range of the tunnel cross section, the horizontal deformation of the tunnel cross section caused by the horizontal additional load
Wherein when the water level after precipitation is below the tunnel, the horizontal deformation of the cross section of the tunnel caused by horizontal additional load
Wherein DeltaP h1 Is a horizontal trapezoid with an additional load delta P h Is equal to the uniformly distributed load part delta P h2 Is a horizontal trapezoid with an additional load delta P h Is provided with a triangular load part;
wherein the horizontal deformation of the tunnel cross section caused by the vertical additional load
Wherein the horizontal deformation of the tunnel cross section caused by formation resistance
When θ is more than or equal to 0 and less than pi/4,
when pi/4 is less than or equal to theta and less than pi/2,
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