CN116341067A - Method for analyzing influence of foundation pit precipitation on adjacent tunnels under action of lateral soil - Google Patents

Method for analyzing influence of foundation pit precipitation on adjacent tunnels under action of lateral soil Download PDF

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CN116341067A
CN116341067A CN202310291712.2A CN202310291712A CN116341067A CN 116341067 A CN116341067 A CN 116341067A CN 202310291712 A CN202310291712 A CN 202310291712A CN 116341067 A CN116341067 A CN 116341067A
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tunnel
precipitation
water level
displacement
foundation pit
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徐长节
管凌霄
王雪鹏
王小兵
丁海滨
胡晖
秦金龙
刘洪河
刘昆
夏雪勤
李懿娴
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Nuclear Industry East China Construction Engineering Group Co ltd
East China Jiaotong University
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East China Jiaotong University
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Abstract

The invention discloses a method for analyzing influence of foundation pit dewatering on adjacent tunnels under the action of lateral soil bodies, which comprises the following steps: establishing and solving a tunnel control equation, regarding the tunnel as an Euler-Bernoulli beam resting on a Vlasov foundation to simulate the interaction between the tunnel and soil, and obtaining a displacement control equation of the tunnel according to a stress balance relation of the tunnel under the influence of foundation pit dewatering; establishing a tunnel displacement control equation under the action of a lateral soil body; solving a tunnel displacement control equation; and calculating the additional load caused by the precipitation, and obtaining the additional stress generated by the foundation pit precipitation on the adjacent existing tunnel. The method disclosed by the invention has higher accuracy and adaptability, and can derive and analyze the osmotic coefficient k t Distance d between tunnel and dewatering well and water level lowering depth s w Relation to tunnel stress deformation, canAnd the tunnel stress deformation condition caused by foundation pit pre-precipitation is analyzed more accurately and comprehensively.

Description

Method for analyzing influence of foundation pit precipitation on adjacent tunnels under action of lateral soil
Technical Field
The invention discloses a method for analyzing influence of foundation pit dewatering on adjacent tunnels under the action of lateral soil bodies, and relates to the technical field of constructional engineering.
Background
Foundation pit engineering in water-rich stratum has to be performed to pre-dewatering foundation pit for excavation, and pre-dewatering foundation pit can result in lowered water level in surrounding stratum and increased effective stress in soil. When the existing shield tunnel exists nearby the engineering, the water level is lowered to cause effective stress increment in the soil, so that the additional load born by the tunnel is increased, and the tunnel is adversely affected.
The subway shield tunnel is used as a life line of urban traffic, and the maintenance and protection work of the subway shield tunnel in service state is slightly neglected, so that huge economic property loss can be caused. Therefore, the method analyzes the stress deformation condition of the tunnel caused by foundation pit pre-precipitation, and is important to strengthen the control and protection of the tunnel deformation.
In the prior art, many scholars have studied the stress deformation of the tunnel caused by foundation pit precipitation, for example Zheng Gang and the like, and have performed finite element simulation of the influence of pressure-bearing layer pressure-reducing precipitation on the existing shield tunnel. Liu Yunsheng in combination with Tianjin western station foundation pit engineering, a numerical model is built to study the influence of precipitation on adjacent subway tunnels. Wu Huaina and the like are based on engineering practice, and the influence of foundation pit precipitation above the river-crossing tunnel on the structure of the river-crossing tunnel is analyzed by adopting a finite element method. Li Wenan the influence of precipitation in the adjacent foundation pit on the longitudinal deformation of the operating subway tunnel is analyzed according to the water level geology of the Shanghai region. Li Heng the deformation stress rule of the existing tunnel under different precipitation conditions is analyzed and researched by adopting numerical calculation. Nie Xuehui the influence of foundation pit precipitation on adjacent underground pipelines is researched by combining theoretical analysis, on-site actual measurement and numerical calculation. Xu Changjie et al use a two-stage analysis to derive an analytical solution for deformation of adjacent lines caused by precipitation in a single well. Based on the Pasternak foundation Liang Moxing, the European snow peak and the like analyze the deformation of the tunnel under the foundation pit caused by excavation and precipitation, and the result shows that the influence of the precipitation on the underlying tunnel is not neglected.
In theoretical research aiming at shield tunnel deformation, an interaction between a simulated tunnel and a soil body is often simulated by adopting an elastic foundation beam. The Vlasov foundation beam model not only can consider the continuity of foundation soil deformation, but also can well solve the determination of model parameters in theory, and has good calculation accuracy. However, the interaction of the subsurface structure with the soil is essentially a three-dimensional problem, which is analyzed not only by considering the effect of the foundation beneath the structure, but also by considering the constraints of the lateral soil of the structure on its deformation.
In the prior art, an analysis method is lacking, and the influence of foundation pit pre-precipitation on an adjacent tunnel under the action of a lateral soil body can be comprehensively considered.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the method for analyzing the influence of foundation pit dewatering on the adjacent tunnel under the action of the lateral soil body is provided, a Vlasov foundation beam model is adopted, the lateral soil body action is considered at the same time, and deformation analysis solutions of the adjacent shield tunnel under the action of the foundation pit dewatering are deduced. "
The technical scheme disclosed by the invention is as follows:
the method for analyzing influence of foundation pit precipitation on adjacent tunnels under the action of lateral soil bodies comprises the following steps:
step one, establishing and solving a tunnel control equation, wherein the step specifically comprises the following steps:
101. considering the tunnel as an Euler-Bernoulli beam placed on a Vlasov foundation to simulate the interaction of the tunnel and soil, and obtaining a displacement control equation of the tunnel according to the stress balance relation of the tunnel under the influence of foundation pit precipitation; in the Vlasov foundation model, the relation between the foundation reaction force p (x) and the tunnel displacement u (x) is:
Figure BDA0004141805920000021
wherein: k is foundation reaction coefficient, t is soil layer shearing coefficient;
the calculation formula of k and t in the Vlasov foundation model is as follows:
Figure BDA0004141805920000022
Figure BDA0004141805920000023
E s the soil body elastic modulus; v is the poisson ratio of soil; t is the foundation elastic layer thickness, taking t=2.5d, d is the tunnel diameter; h (z) is an attenuation function in the Vlasov foundation model, and the function obtains the values of k and T by considering the attenuation of foundation soil along the deformation direction, which can be a linear or exponential function generally, where h (z) = (T-z)/z is taken as the coordinate of the depth direction of the foundation soil.
102. Establishing a tunnel displacement control equation under the action of a lateral soil body;
according to the stress balance relation of the tunnel under the influence of foundation pit precipitation, a displacement control equation of the tunnel is obtained:
Figure BDA0004141805920000031
wherein: EI is tunnel bending stiffness, wherein E is tunnel elastic modulus, and I is tunnel cross-sectional moment of inertia; q (x) is the additional load caused by precipitation;
substitution of formula (1) into formula (3) yields:
Figure BDA0004141805920000032
when analyzing the influence of the lateral soil body of the tunnel on the deformation of the tunnel, setting the following conditions:
(1) The parameters of the lateral soil body of the tunnel are consistent with those of the soil body below the tunnel;
(2) The acting force of the lateral soil body to the tunnel is TI and T2, and the acting force is transmitted to the two sides of the tunnel through the soil body shearing layer;
for any plane with x=x0, the deformation balance equation of the lateral soil body of the tunnel is as follows:
Figure BDA0004141805920000033
wherein:
Figure BDA0004141805920000034
deformation of a lateral soil shear layer of the tunnel along the y-axis direction is realized;
the general solution of soil displacement is as follows:
Figure BDA0004141805920000035
when y is more than or equal to D/2, the lateral soil displacement is equal to the tunnel displacement:
Figure BDA0004141805920000036
and lateral soil displacement far enough from the tunnel y=y is:
Figure BDA0004141805920000041
from the above boundary conditions, c1=u (x) can be found, so the displacement of the lateral mass is:
Figure BDA0004141805920000042
the acting force of the lateral soil body to the tunnel is as follows:
Figure BDA0004141805920000043
under the constraint action of the lateral soil body, the tunnel deformation control equation is as follows:
Figure BDA0004141805920000044
103. solving a tunnel displacement control equation;
under the combined action of soil below the tunnel and lateral soil, the displacement control equation of the tunnel is as follows:
Figure BDA0004141805920000045
wherein: γ=2 tD/EI;
Figure BDA0004141805920000046
let q (x) =0 find its general solution, yielding:
u(x)＝e αx [A 1 cos(βx)+A 2 sin(βx)]+e -αx [A 3 cos(βx)+A 4 sin(βx)]； (11)
wherein: a is that 1 、A 2 、A 3 、A 4 Is a coefficient to be determined;
Figure BDA0004141805920000047
Figure BDA0004141805920000048
assuming that an infinitely long tunnel receives concentrated load Q at a point of x=0, firstly solving tunnel displacement under the action of concentrated force, and at the moment, the boundary conditions of the tunnel are as follows:
u(±∞)＝0； (12)
Figure BDA0004141805920000051
Figure BDA0004141805920000052
substituting the boundary conditions into the formula (11), and solving a displacement equation of the tunnel under the action of concentrated load, wherein the displacement equation is as follows:
Figure BDA0004141805920000053
assuming that an additional load q=q (η) dη caused by precipitation is received at an arbitrary point η on the tunnel axis, according to equation (15), a displacement du (x) of the tunnel caused by this load is obtained:
Figure BDA0004141805920000054
integrating the formula (16) in the precipitation additional load distribution range to obtain tunnel displacement caused by foundation pit precipitation:
Figure BDA0004141805920000055
further tunnel bending moment can be obtained:
Figure BDA0004141805920000056
and step two, calculating additional load caused by precipitation, and obtaining additional stress generated by foundation pit precipitation on adjacent existing tunnels.
In a specific preferred embodiment, setting r as the horizontal distance between a certain point and a precipitation well, and setting h as the water level height of the position; h 0 To the initial water level of the submerged aquifer, H t The water level in the well after precipitation; r is R 0 For dewatering well radius, based on Dupuit assumption, the distribution h (r) of groundwater level around dewatering well is:
Figure BDA0004141805920000057
wherein: r is the radius of the precipitation influence range, according to sakur Jin Gongshi, the radius R of the precipitation influence range is:
Figure BDA0004141805920000061
wherein: k (k) t Is the permeability coefficient of the soil body; s is S w S is the water level of the dewatering well to be reduced w ＝H 0 -H t ；
The existing tunnel exists in the influence range of precipitation, the effective stress in the soil is increased due to the decrease of the water level of the soil body above the tunnel, additional stress is generated on the tunnel, the vertical horizontal distance between a precipitation well and the existing tunnel is d, an O point closest to the precipitation well on the axis of the tunnel is taken as an origin, an x axis is established along the direction of the tunnel, the A point, the A' point is the intersection point of the influence range of precipitation and the tunnel, and the B point is 1 Point and B 2 The effective stress increment delta of the two points are respectively positioned above and below the water level after precipitation σ1 ，Δ σ2 The calculation formula is as follows:
Δσ 1 ＝h 1 (γ-γ s +γ w )； (21a)
Figure BDA0004141805920000062
wherein: h is a 1 Is B 1 The height difference between the point and the initial water level; h (r) B2 ) Is B 2 The ground water level of the point; gamma, gamma s And gamma w The soil body weight, the soil body saturation weight and the water weight are respectively.
Further, according to the relative position of the ground water level after precipitation and the existing tunnel, the tunnel receives additional stress and is divided into two cases for calculation:
1. after precipitation, the groundwater level is located above the tunnel:
when the ground water level is higher than the tunnel after precipitation, the horizontal distance between any point x on the tunnel and the precipitation well is as follows:
Figure BDA0004141805920000063
the ground water level at the position of the tunnel after precipitation can be calculated by substituting the ground water level into the formula (19), and the additional stress to be applied to the tunnel can be obtained by substituting the ground water level into the formula (21 b):
Figure BDA0004141805920000064
2. after precipitation, part of water level drops to the tunnel below:
when part of water level drops below the tunnel: at this time, the additional stress received by the tunnel is calculated in two parts, and the additional stress received by the tunnel above the water level is the same, and is a certain value:
σ＝h 1 (γ-γ s +γ w )； (23)
secondly, the additional stress to which the tunnel below the water level is subjected can be calculated according to equation (22);
when H (r) =h 0 -h 1 In this case, the intersection point of the water level and the tunnel is exactly the point, so that the coordinates of the point can be obtained as follows:
Figure BDA0004141805920000071
the calculation formula of the additional stress generated by foundation pit precipitation on the adjacent existing tunnel is obtained as follows:
Figure BDA0004141805920000072
in a further preferred embodiment of the present invention, consideration may be given to adding important relevant factors of influence of precipitation on the tunnel in the analysis method, the important relevant factors including: permeability coefficient k t Distance d between tunnel and dewatering well and water level lowering S w 。
With the soil permeability coefficient k t When the displacement of the adjacent tunnel is increased due to precipitation, the change of the bending moment of the tunnel is small;
the influence of the distance d between the tunnel and the dewatering well on the stress deformation of the tunnel is that the displacement and the bending moment generated by the tunnel are reduced along with the increase of the distance d;
water level lowering S w The increase of the water level in the surrounding stratum is caused to wholly decrease, and the additional stress and the generated displacement of the tunnel are increased;
when the water level falls below the tunnel axis, the maximum value of the additional stress suffered by the tunnel is not increased any more, but the range is enlarged; at this point, the maximum bending moment generated by the tunnel begins to decrease and occurs at the intersection of the tunnel and the water level. The beneficial effects of the invention are as follows: the method of the invention verifies the accuracy of calculation after comparing with the finite element result and the measured data, and can deduce and analyze to obtain the permeability coefficient k t Distance d between tunnel and dewatering well and water level lowering depth s w The relation with the tunnel stress deformation can more accurately and comprehensively analyze the tunnel stress deformation condition caused by foundation pit pre-precipitation.
Drawings
FIG. 1 is a front view of a simplified schematic of a computational model.
FIG. 2 is a side view of a simplified schematic of a computational model.
Fig. 3 is a schematic diagram of lateral soil deformation.
Fig. 4 is a schematic representation of precipitation curves.
Fig. 5 is a schematic drawing of precipitation radius.
FIG. 6 is a schematic diagram showing the distribution of additional load along the length of a tunnel when the water level is higher than that of the tunnel after precipitation.
FIG. 7 is a schematic diagram showing the distribution of additional load along the length of a tunnel when the partial water level is lower than the water level of the tunnel after precipitation.
FIG. 8 is a graphical representation of the results of the protocol described herein compared to the calculations performed in the prior art.
FIG. 9 is a schematic diagram comparing the protocol described herein with the methods used in the prior art literature under precipitation test results.
FIG. 10 is a graph of different permeability coefficients k t The tunnel displacement curve below.
FIG. 11 is a graph of different permeability coefficients k t Lower tunnel bending moment curve.
Fig. 12 is a graph of tunnel displacement at different spacings d.
Fig. 13 is a tunnel bending moment curve at different spacings d.
FIG. 14 is a graph showing different water depths s w A lower ground water level curve.
FIG. 15 is a graph of different water depths s w Additional stress curves below.
FIG. 16 is a graph showing different water depths s w The tunnel displacement curve below.
FIG. 17 is a graph of different water depths s w Lower tunnel bending moment curve.
Detailed Description
The method for analyzing the influence of foundation pit dewatering on the adjacent tunnels under the action of the lateral soil bodies provided by the invention is further described below with reference to specific embodiments and drawings thereof. It should be noted that the embodiments of the present invention are not intended to limit the present invention in any form. The technical features or combinations of technical features described in the embodiments of the present invention should not be regarded as isolated, and they may be combined with each other to achieve a better technical effect.
Additional implementations are also included within the scope of the preferred embodiments of the present invention and should be understood by those skilled in the art to which the embodiments of the present invention pertain. Techniques, methods, and apparatus known to one of ordinary skill in the relevant art may not be discussed in detail, but should be considered part of the specification where appropriate. In all examples shown and discussed herein, any specific values should be construed as merely illustrative and not limitative. Thus, other examples of the exemplary embodiments may have different values.
The drawings of the invention are in a very simplified form and are not to scale precisely, but are for the purpose of illustrating embodiments of the invention conveniently and clearly, and are not intended to limit the scope of the invention. Any structural modification, proportional change or size adjustment should fall within the scope of the technical disclosure without affecting the effects and the achieved objects of the present invention. And the same reference numbers appearing in the figures represent the same features or elements, as may be used in different embodiments.
The invention discloses a method for analyzing influence of foundation pit dewatering on adjacent tunnels under the action of lateral soil bodies, which comprises the following steps:
step one, establishing and solving a tunnel control equation.
101. The tunnel control equations are established irrespective of the lateral soil effects, and figures 1 and 2 are front and side views, respectively, of a simplified schematic of the computational model herein, with the tunnel being considered as an Euler-Bernoulli beam resting on a Vlasov foundation to simulate the tunnel-soil interactions.
In the Vlasov foundation model, the relation between the foundation reaction force p (x) and the tunnel displacement u (x) is:
Figure BDA0004141805920000101
wherein: k is foundation reaction coefficient, t is soil layer shearing coefficient.
The calculation formula of k and t in the Vlasov foundation model is as follows:
Figure BDA0004141805920000102
Figure BDA0004141805920000103
wherein: e (E) s The soil body elastic modulus; v is the poisson ratio of soil; t is the foundation elastic layer thickness, taking t=2.5d, d is the tunnel diameter; h (z) is an attenuation function in the Vlasov foundation model, and the function obtains the values of k and T by considering the attenuation of foundation soil along the deformation direction, which can be a linear or exponential function generally, where h (z) = (T-z)/z is taken as the coordinate of the depth direction of the foundation soil.
At this time, according to the stress balance relation of the tunnel under the influence of foundation pit precipitation, the displacement control equation of the tunnel can be obtained:
Figure BDA0004141805920000104
wherein: EI is tunnel bending stiffness, wherein E is tunnel elastic modulus, and I is tunnel cross-sectional moment of inertia; q (x) is the additional load caused by precipitation. Substitution of formula (1) into formula (3) yields:
Figure BDA0004141805920000105
102. when the tunnel is subjected to additional load to generate settlement deformation, the tunnel control equation under the action of the lateral soil body is established, and the tunnel is subjected to foundation counterforce of the soil body below the tunnel, and the lateral soil body also has a constraint function on the deformation of the tunnel, as shown in fig. 2.
When analyzing the influence of the lateral soil body of the tunnel on the deformation of the tunnel, the following assumption is made:
(1) The parameters of the lateral soil body of the tunnel are consistent with those of the soil body below the tunnel;
(2) The acting force of the lateral soil body on the tunnel is T I And T is 2 And the soil body shear layer is used for transmitting and acting on two sides of the tunnel. For any x=x 0 The deformation balance equation of the lateral soil body of the tunnel is as follows:
Figure BDA0004141805920000111
wherein:
Figure BDA0004141805920000112
is the deformation of the lateral soil shear layer of the tunnel along the y-axis direction.
The general solution of soil displacement is as follows:
Figure BDA0004141805920000113
as shown in FIG. 3, when y is equal to or greater than D/2, the lateral soil displacement is equal to the tunnel displacement
Figure BDA0004141805920000114
And lateral soil displacement y=y far enough from the tunnel is +.>
Figure BDA0004141805920000115
C can be obtained from the boundary conditions 1 =u (x), so the displacement of the lateral mass is:
Figure BDA0004141805920000116
further, the acting force of the lateral soil body on the tunnel is calculated as follows:
Figure BDA0004141805920000117
through analysis, under the constraint action of the lateral soil body, the tunnel deformation control equation is as follows:
Figure BDA0004141805920000118
103. solving a tunnel displacement control equation, in summary, under the combined action of soil below the tunnel and lateral soil, the tunnel displacement control equation is as follows:
Figure BDA0004141805920000119
wherein: γ=2 tD/EI;
Figure BDA00041418059200001110
to solve equation (10), we can first let q (x) =0 solve for its general solution, to obtain:
u(x)＝e αx [A 1 cos(βx)+A 2 sin(βx)]+e -αx [A 3 cos(βx)+A 4 sin(βx)]； (11)
wherein: a is that 1 、A 2 、A 3 、A 4 Is a coefficient to be determined;
Figure BDA0004141805920000121
further, assuming that the infinitely long tunnel receives a concentrated load Q at a point where x=0, firstly solving a tunnel displacement under the action of a concentrated force, wherein the boundary condition of the tunnel is as follows:
u(±∞)＝0； (12)
Figure BDA0004141805920000122
Figure BDA0004141805920000123
substituting the boundary conditions into the formula (11), and solving a displacement equation of the tunnel under the action of concentrated load, wherein the displacement equation is as follows:
Figure BDA0004141805920000124
assuming that an additional load q=q (η) dη caused by precipitation is received at an arbitrary point η on the tunnel axis, according to equation (15), a displacement du (x) of the tunnel caused by this load is obtained:
Figure BDA0004141805920000125
integrating the formula (16) in the precipitation additional load distribution range to obtain the tunnel displacement caused by foundation pit precipitation:
Figure BDA0004141805920000126
further tunnel bending moment can be obtained:
Figure BDA0004141805920000127
and step two, calculating additional load caused by precipitation.
201. The precipitation curve is calculated, the foundation pit precipitation will inevitably cause the surrounding ground water level to change, and after long-time precipitation in the infinite diving aquifer, the ground water level around the precipitation well will form a stable precipitation curve, as shown in fig. 4. In fig. 4, r is the horizontal distance between a certain point and a precipitation well, and h is the water level at the position; h 0 To the initial water level of the submerged aquifer, H t The water level in the well after precipitation; r is R 0 Is the radius of the dewatering well.
Based on Dupuit assumption, the distribution h (r) of groundwater level around dewatering wells (foundation pit can be considered as a large well) is:
Figure BDA0004141805920000131
wherein: r is the radius of the influence range of precipitation, which is abbreviated as precipitation radius, according to salsa Jin Gongshi, the precipitation radius R is:
Figure BDA0004141805920000132
wherein: k (k) t Is the permeability coefficient of the soil body; s is(s) w For lowering the water level of the dewatering well, s w ＝H 0 -H t 。
As shown in fig. 5, an existing tunnel exists in the influence range of precipitation, and at the moment, the effective stress in soil above the tunnel is increased due to the fact that the water level is lowered, and additional stress is generated on the tunnel. In fig. 5, the vertical and horizontal distance between the dewatering well and the existing tunnel is d, and the x-axis is established along the tunnel direction by taking the O point closest to the dewatering well on the tunnel axis as the origin. And the point A' is the intersection point of the precipitation influence range and the tunnel.
202. The additional stress of the tunnel caused by the lowering of the ground water level can be calculated in two cases according to the relative positions of the ground water level and the calculation points.
B in FIG. 4 1 Point and B 2 The effective stress increment delta sigma of the two points respectively at the position of the precipitation and above and below the water level 1 ，Δσ 2 The calculation formula is as follows:
Δσ 1 ＝h 1 (γ-γ s +γ w )； (21a)
Figure BDA0004141805920000133
wherein: h is a 1 Is B 1 The height difference between the point and the initial water level; h (r) B2 ) Is B 2 The ground water level of the point. Gamma, gamma s And gamma w The soil body weight, the soil body saturation weight and the water weight are respectively. Therefore, according to the relative position of the ground water level after precipitation and the existing tunnel, the additional stress applied to the tunnel can be calculated in two cases:
1. after precipitation, the ground water levels are all above the tunnel, as shown in fig. 6;
2. after precipitation, part of the water level drops below the tunnel, as shown in fig. 7.
When the ground water level is higher than the tunnel after precipitation: the horizontal distance between any point x on the tunnel and the precipitation well is as follows:
Figure BDA0004141805920000141
the ground water level at the position of the tunnel after precipitation can be calculated by substituting the ground water level into the formula (19), and the additional stress to be applied to the tunnel can be obtained by substituting the ground water level into the formula (21 b):
Figure BDA0004141805920000142
and when part of the water level drops below the tunnel: the additional stress to which the tunnel is subjected is calculated in two parts. The additional stress to be applied to the tunnel above the water level is the same, and is a certain value:
σ＝h 1 (γ-γ s +γ w )； (23)
second, the additional stress experienced by the tunnel below the water level can be calculated according to equation (22). When H (r) =h 0 -h 1 In this case, the intersection point of the water level and the tunnel is exactly the point, so that the coordinates of the point can be obtained as follows:
Figure BDA0004141805920000143
in summary, an additional stress calculation formula generated by foundation pit precipitation on the adjacent existing tunnel can be obtained as follows:
Figure BDA0004141805920000144
the accuracy and rationality of the comparison of the present method with the prior art is calculated by means of the specific examples below.
1. Comparison was performed by three-dimensional finite element numerical analysis.
In order to study the influence of foundation pit precipitation on the adjacent existing tunnels, in the prior art, sun Dongyu adopts ABAQUS finite element software to establish a numerical model. The size of the numerical model is 240 multiplied by 200 multiplied by 60m, the non-excavated foundation pit is positioned in the center of the model, the size is 40 multiplied by 45m, the dewatering well is arranged along the outer side of the foundation pit by 2m, and meanwhile, the model is provided with the water level which is 100m away from the foundation pit and does not change along with dewatering. An existing tunnel exists near the foundation pit, the depth of burial is h 2 =21m, outer diameter d=6m, wall thickness 0.5m, elastic modulus e=19gpa. The soil layer of the tunnel is loess, and the elastic modulus E s =33.1 MPa, poisson ratio v s =0.32, soil density 1650kg/m above water level 3 The soil body floating density below the water level is 650kg/m 3 Coefficient of soil permeability k t =0.8m/d, initial water level burial depth h 0 Because the design depth of the non-excavated foundation pit is 22m and the design water level is 2m below the foundation pit surface, the water level is reduced by s in the numerical analysis w ＝21m。
FIG. 8 is a schematic diagram of the results of the method herein, numerical model analysis and comparison of tunnel displacements obtained by ignoring lateral soil effects. Fig. 8 shows displacement curves of the tunnel under the conditions of 13m and 25m of the distance d between the tunnel and the dewatering well, and it can be seen that the calculation result of the method has better consistency with the result of the numerical model, and the calculation result has larger deviation due to the method of neglecting the lateral soil body effect. The method and the three-dimensional numerical model can consider the constraint effect of the lateral soil body on tunnel displacement, and the situation that the effect of the lateral soil body is ignored is not consistent with the actual situation, so that a larger deviation of a calculation result can occur. By comparing the method with a three-dimensional numerical model, the method has certain accuracy and rationality.
2. And (5) comparing the single well precipitation tests.
Because no detailed foundation pit precipitation causes the literature of the deformation measured data of the adjacent tunnels, the method is verified by adopting the monitoring data of the adjacent existing pipelines under the single well precipitation test. In the in-situ single well precipitation test case, the thickness of the aquifer of the test site is 20.0-26.4 m, and the water levelThe initial water level height H can be obtained by averaging 1.3-2 m below the ground surface 0 =23.2m, initial water level burial depth h 0 =1.65m. Disposable water level drop s in precipitation test w An existing pipeline exists at the position with the vertical horizontal distance d=10m from the precipitation well and the pipeline burial depth z 0 =6m, diameter d=1m, wall thickness 0.1m, elastic modulus E t =30gpa. The specific parameter values are shown in table 1.
Table 1 calculation parameters
Table1 Calculation parameters
Figure BDA0004141805920000161
FIG. 9 is a comparison of the results of the method calculations herein with the actual measurement of precipitation tests. As can be seen from fig. 9, the calculated result without considering the lateral soil body has a large deviation from the measured value. The method considers the influence of the lateral soil body, and the calculated result is more consistent with the precipitation test result. By comparison with the measured data of the in situ test, the method has better rationality.
The analysis method of the invention also carries out special analysis aiming at various parameters.
To study the effect of precipitation on the tunnel and the relationship between factors, we assume the following engineering profile to analyze: underground initial water level H 0 =40m, initial water level burial depth h 0 =3m, post-precipitation well water level H t =25m, water level drop s w =15m; soil parameters: permeability coefficient k t =1m/d, modulus of elasticity E s Poisson ratio v=0.3, soil body weight γ=18 kN/m =30 MPa 2 Saturation gravity gamma s ＝19kN/m 2 The method comprises the steps of carrying out a first treatment on the surface of the Tunnel parameters: the distance d=12m between the tunnel and the dewatering well, the burial depth z=10m, h 2 =9m, diameter d=6m, wall thickness 0.3m, flexural rigidity ei= 7.548 ×10 5 MN·m 2 . The remaining parameters are unchanged when analyzing for a certain parameter.
Parameter 1, permeability coefficient k t 。
Taking 5 groups of permeability coefficients k t The effect of the material on the deformation stress of the tunnel was studied and was 0.5m/d, 1m/d, 1.5m/d, 2m/d and 2.5m/d, respectively. At 5 groups of permeability coefficients k t And the curve of the tunnel displacement and the bending moment caused by the foundation pit dewatering calculated by the method is shown in fig. 10 and 11. It can be seen from fig. 10 that as the permeability coefficient increases, the vertical displacement of the tunnel and the range of displacement increase. When the permeability coefficient k t Increasing from 0.5m/d to 2.5m/d, the maximum vertical displacement of the tunnel increases from 5.79mm to 7.07mm. This is because the increase in permeability coefficient increases the extent and extent to which the foundation pit precipitation affects the surrounding water level, and thus the extent and extent of the tunnel. It can be seen from fig. 11 that as the permeability coefficient increases, the tunnel bending moment slightly decreases, indicating that the permeability coefficient has less influence on the tunnel bending moment, and that the portion of the tunnel where the bending moment occurs is mainly within ±100deg.m, which is smaller than the displacement range.
Parameter 2, the distance d between the tunnel and the dewatering well.
5 groups of different intervals are adopted to study the influence of the intervals on the deformation stress of the tunnel, wherein the influence is respectively 10m, 15m, 20m, 25m and 30m. The curves of tunnel displacement and bending moment caused by foundation pit dewatering calculated by the method are shown in fig. 12 and 13. It can be seen from fig. 12 and 13 that as the distance d increases, both the vertical displacement and the bending moment generated by the tunnel decrease. When the distance d is increased from 10m to 30m, the maximum vertical displacement of the tunnel is reduced from 6.37mm to 4.28mm, and the maximum bending moment value is reduced from 4.63 Mn.m to 1.44 Mn.m, so that the influence degree is more remarkable. This is because the lower the water level change at a position farther from the dewatering well in the foundation pit dewatering, the lower the stress in the vicinity of the tunnel, that is, the weaker the influence on the tunnel is with the further the dewatering well is.
Parameter 3 Water level Depression s w 。
Taking 5 groups of water level lowering s in well w Study the influence of the water level falling depth s of 5 groups on the deformation stress of the tunnel w 10m, 15m, 20m, 25m and 30m respectively, corresponding to the water level H in the well t 30m, 25m, 20m, 15m and 10m, respectively.
FIG. 14 is a 5-group water level fall s w And (5) a curve of the groundwater level in the ground. It can be seen from FIG. 14 that the water level in the well decreases as s w Is increased, the water level in the surrounding formation is lowered as a whole. And when precipitation s w At 10m and 15m, the tunnel axis burial depth is still below the groundwater level. However, as the water level drops s w Reaching below 20m, the nearest part of the tunnel from the dewatering well is already above the water level. FIG. 15 is a 5-group water level fall s w An additional stress profile experienced by the tunnel below. It can be seen from fig. 15 that the additional stress to which the tunnel is subjected decreases with the water level s w Is increased due to the increase in total effective stress of the soil body above the tunnel with the increase in water level drop. However, after the water level drops below the tunnel, the additional stress to which the tunnel is subjected is not increased any more, as shown in FIG. 15, when the water level in the well drops by s w When reaching below 20m, the maximum value of the additional stress to which the tunnel is subjected is unchanged, while the range of the maximum values increases.
The curve of the tunnel displacement and bending moment caused by the pre-precipitation calculated by the method is shown in fig. 16 and 17. As can be seen from FIG. 16, as the water level depth increases, the vertical displacement of the tunnel and the range of displacement increase, and the water level depth s increases w As one increases from 10 to 30m, the maximum vertical displacement of the tunnel increases from 4.01mm to 9.12mm. At the same time, when the water level in the well is reduced by s w When the maximum displacement of the tunnel is below 20m, the increase amount of the maximum displacement of the tunnel is obviously reduced. Combining different water level depths s w The underground water level curve and the effective stress curve are not difficult to analyze, and the influence of precipitation on the surrounding water level is along with the water level falling depth s w As the number of tunnels increases, the additional load induced on the tunnels increases, resulting in greater displacement of the tunnels. It can be seen from FIG. 17 that as the water level decreases s w When the tunnel is increased from 10m to 20m, the maximum bending moment of the tunnel is increased from 3.37 Mn.m to 5.06 Mn.m. However, the water level is lowered by s w When the tunnel bending moment maximum value is increased from 20m to 30m, the maximum bending moment position starts to shift from the position of x=0 to two sides, and two symmetrical bending moment peaks appear. At the same time, the peak position corresponds to the range of the maximum value of the additional stress in FIG. 15, which shows that the peak position is the intersection point of the ground water level and the tunnel and can be used for dewateringIn the process, the point closest to the water level on the tunnel is focused.
The invention is based on a Vlasov foundation model, and adopts a theoretical method to research the influence of foundation pit dewatering on adjacent existing tunnels under the action of lateral soil mass. The rationality and accuracy of the method are verified through three-dimensional finite element and in-situ test results, and the influence of each factor on the stress deformation of the tunnel is studied in parameter analysis. By adopting the analysis method disclosed by the invention, the following analysis conclusion can be obtained.
1) Considering the fact that the constraint effect of the lateral soil body on tunnel deformation is more fit, neglecting the lateral soil body effect may lead to larger calculation result and insufficient accuracy.
2) With the soil permeability coefficient k t When the displacement of the adjacent tunnel is increased due to precipitation, the bending moment of the tunnel is not changed greatly; the distance d between the tunnel and the dewatering well has a larger influence on the stress deformation of the tunnel, and the displacement and the bending moment generated by the tunnel are reduced along with the increase of the distance d.
3) Water level lowering s w The increase in (2) may result in an overall drop in the water level in the surrounding formation, with increased additional stress and resultant displacement to the tunnel. However, when the water level falls below the tunnel axis, the maximum value of the additional stress to which the tunnel is subjected is not increasing, but the range is enlarged; the maximum value of the bending moment generated by the tunnel starts to be reduced and appears at the intersection point of the tunnel and the water level; therefore, important attention should be paid to the part of the tunnel closest to the water level during precipitation.
The analysis method disclosed by the invention provides a new calculation method for the stress deformation of the adjacent tunnel under the effect of foundation pit pre-precipitation, and the conclusion obtained by research can provide advice for the prevention and control of tunnel deformation under similar working conditions, and has certain reference value and engineering significance.
The above example represents only one embodiment of the present invention, which is described in more detail and is not to be construed as limiting the scope of the invention. It should be noted that it would be apparent to those skilled in the art that several variations and modifications could be made without departing from the spirit of the invention, which would fall within the scope of the invention. Accordingly, the protection scope of the present invention should be mainly determined by the appended claims.

Claims (8)

1. The method for analyzing the influence of foundation pit precipitation on adjacent tunnels under the action of lateral soil bodies is characterized by comprising the following steps:
step one, establishing and solving a tunnel control equation;
101. considering the tunnel as an Euler-Bernoulli beam placed on a Vlasov foundation to simulate the interaction of the tunnel and soil, and obtaining a displacement control equation of the tunnel according to the stress balance relation of the tunnel under the influence of foundation pit precipitation;
102. establishing a tunnel displacement control equation under the action of a lateral soil body;
103. solving a tunnel displacement control equation;
and step two, calculating additional load caused by precipitation, and obtaining additional stress generated by foundation pit precipitation on adjacent existing tunnels.
2. The method for analyzing influence of foundation pit precipitation on adjacent tunnels under the action of lateral soil bodies as claimed in claim 1, wherein the method comprises the following steps: in the Vlasov foundation model of the first step, the relation between the foundation reaction force p (x) and the tunnel displacement u (x) is:
Figure FDA0004141805900000011
wherein: k is foundation reaction coefficient, t is soil layer shearing coefficient;
the calculation formula of k and t in the Vlasov foundation model is as follows:
Figure FDA0004141805900000012
Figure FDA0004141805900000013
E s the soil body elastic modulus; v is the poisson ratio of soil; t is the foundation elastic layer thickness, taking t=2.5d, d is the tunnel diameter; h (z) is an attenuation function in the Vlasov foundation model, h (z) = (T-z)/z, z being coordinates in the depth direction of the foundation soil.
3. The method for analyzing influence of foundation pit precipitation on adjacent tunnels under the action of lateral soil bodies as claimed in claim 2, wherein the method comprises the following steps of: in step 102, according to the stress balance relationship of the tunnel under the influence of foundation pit precipitation, a displacement control equation of the tunnel is obtained:
Figure FDA0004141805900000021
wherein: EI is tunnel bending stiffness, wherein E is tunnel elastic modulus, and I is tunnel cross-sectional moment of inertia; q (x) is the additional load caused by precipitation;
substitution of formula (1) into formula (3) yields:
Figure FDA0004141805900000022
4. a method for analyzing the influence of foundation pit dewatering on adjacent tunnels under the action of a lateral soil body as claimed in claim 3, wherein when the influence of the lateral soil body of the tunnel on the deformation of the tunnel is analyzed, the following conditions are set:
(1) The parameters of the lateral soil body of the tunnel are consistent with those of the soil body below the tunnel;
(2) The acting force of the lateral soil body to the tunnel is TI and T2, and the acting force is transmitted to the two sides of the tunnel through the soil body shearing layer;
for any plane with x=x0, the deformation balance equation of the lateral soil body of the tunnel is as follows:
Figure FDA0004141805900000023
wherein:
Figure FDA0004141805900000024
deformation of a lateral soil shear layer of the tunnel along the y-axis direction is realized;
the general solution of soil displacement is as follows:
Figure FDA0004141805900000025
when y is more than or equal to D/2, the lateral soil displacement is equal to the tunnel displacement:
Figure FDA0004141805900000026
and lateral soil displacement far enough from the tunnel y=y is:
Figure FDA0004141805900000031
from the above boundary conditions, c1=u (x) can be found, so the displacement of the lateral mass is:
Figure FDA0004141805900000032
the acting force of the lateral soil body to the tunnel is as follows:
Figure FDA0004141805900000033
under the constraint action of the lateral soil body, the tunnel deformation control equation is as follows:
Figure FDA0004141805900000034
5. the method for analyzing influence of foundation pit precipitation on adjacent tunnels under the action of lateral soil bodies as claimed in claim 4, wherein the method comprises the following steps: in step 103, under the combined action of the soil body below the tunnel and the lateral soil body, the displacement control equation of the tunnel is:
Figure FDA0004141805900000035
wherein: γ=2 tD/EI;
Figure FDA0004141805900000036
let q (x) =0 find its general solution, yielding:
u(x)＝e αx [A 1 cos(βx)+A 2 sin(βx)]+e -αx [A 3 cos(βx)+A 4 sin(βx)]； (11)
wherein: a is that 1 、A 2 、A 3 、A 4 Is a coefficient to be determined;
Figure FDA0004141805900000037
Figure FDA0004141805900000038
assuming that an infinitely long tunnel receives concentrated load Q at a point of x=0, firstly solving tunnel displacement under the action of concentrated force, and at the moment, the boundary conditions of the tunnel are as follows:
u(±∞)＝0； (12)
Figure FDA0004141805900000041
Figure FDA0004141805900000042
substituting the boundary conditions into the formula (11), and solving a displacement equation of the tunnel under the action of concentrated load, wherein the displacement equation is as follows:
Figure FDA0004141805900000043
assuming that an additional load q=q (η) dη caused by precipitation is received at an arbitrary point η on the tunnel axis, according to equation (15), a displacement du (x) of the tunnel caused by this load is obtained:
Figure FDA0004141805900000044
integrating the formula (16) in the precipitation additional load distribution range to obtain tunnel displacement caused by foundation pit precipitation:
Figure FDA0004141805900000045
further tunnel bending moment can be obtained:
Figure FDA0004141805900000046
6. the method for analyzing influence of foundation pit precipitation on adjacent tunnels under the action of lateral soil bodies as claimed in claim 5, wherein the method comprises the following steps: in the second step, setting r as the horizontal distance between a certain point and the precipitation well, and setting h as the water level height of the position; h 0 To the initial water level of the submerged aquifer, H t The water level in the well after precipitation; r is R 0 For dewatering well radius, based on Dupuit assumption, the distribution h (r) of groundwater level around dewatering well is:
Figure FDA0004141805900000051
wherein: r is the radius of the precipitation influence range, according to sakur Jin Gongshi, the radius R of the precipitation influence range is:
Figure FDA0004141805900000052
wherein: k (k) t Is the permeability coefficient of the soil body; s is S w S is the water level of the dewatering well to be reduced w ＝H 0 -H t ；
The existing tunnel exists in the influence range of precipitation, the effective stress in the soil is increased due to the decrease of the water level of the soil body above the tunnel, additional stress is generated on the tunnel, the vertical horizontal distance between a precipitation well and the existing tunnel is d, an O point closest to the precipitation well on the axis of the tunnel is taken as an origin, an x axis is established along the direction of the tunnel, the A point, the A' point is the intersection point of the influence range of precipitation and the tunnel, and the B point is 1 Point and B 2 The effective stress increment delta of the two points are respectively positioned above and below the water level after precipitation σ1 ，Δ σ2 The calculation formula is as follows:
Δσ 1 ＝h 1 (γ-γ s +γ w )； (21a)
Figure FDA0004141805900000053
wherein: h is a 1 Is B 1 The height difference between the point and the initial water level; h (r) B2 ) Is B 2 The ground water level of the point; gamma, gamma s And gamma w The soil body weight, the soil body saturation weight and the water weight are respectively.
7. The method for analyzing influence of foundation pit precipitation on adjacent tunnels under the action of lateral soil bodies as claimed in claim 6, wherein the method comprises the following steps: according to the relative position of the ground water level after precipitation and the existing tunnel, the tunnel receives additional stress and is divided into two cases for calculation:
1. after precipitation, the groundwater level is located above the tunnel:
when the ground water level is higher than the tunnel after precipitation, the horizontal distance between any point x on the tunnel and the precipitation well is as follows:
Figure FDA0004141805900000054
the ground water level at the position of the tunnel after precipitation can be calculated by substituting the ground water level into the formula (19), and the additional stress to be applied to the tunnel can be obtained by substituting the ground water level into the formula (21 b):
Figure FDA0004141805900000061
2. after precipitation, part of water level drops to the tunnel below:
when part of water level drops below the tunnel: at this time, the additional stress received by the tunnel is calculated in two parts, and the additional stress received by the tunnel above the water level is the same, and is a certain value:
σ＝h 1 (γ-γ s +γ w )； (23)
secondly, the additional stress to which the tunnel below the water level is subjected can be calculated according to equation (22);
when H (r) =h 0 -h 1 In this case, the intersection point of the water level and the tunnel is exactly the point, so that the coordinates of the point can be obtained as follows:
Figure FDA0004141805900000062
the calculation formula of the additional stress generated by foundation pit precipitation on the adjacent existing tunnel is obtained as follows:
Figure FDA0004141805900000063
8. the method for analyzing influence of foundation pit precipitation on adjacent tunnels under the action of lateral soil bodies as claimed in claim 1 or 7, wherein the method comprises the following steps of: in the analysis method, relevant factors influencing the tunnel by precipitation include: permeability coefficient k t Distance d between tunnel and dewatering well and water level lowering S w ；
With the soil permeability coefficient k t When the displacement of the adjacent tunnel is increased due to precipitation, the change of the bending moment of the tunnel is small;
the influence of the distance d between the tunnel and the dewatering well on the stress deformation of the tunnel is that the displacement and the bending moment generated by the tunnel are reduced along with the increase of the distance d;
water level lowering S w The increase of the water level in the surrounding stratum is caused to wholly decrease, and the additional stress and the generated displacement of the tunnel are increased;
when the water level falls below the tunnel axis, the maximum value of the additional stress suffered by the tunnel is not increased any more, but the range is enlarged; at this point, the maximum bending moment generated by the tunnel begins to decrease and occurs at the intersection of the tunnel and the water level.
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