CN106372292A - Calculation method for building settlement caused by shield tunnel construction - Google Patents

Abstract

The invention provides a calculation method for building settlement caused by shield tunnel construction. The method comprises the following steps of firstly calculating ground surface settlement caused by the shield tunnel construction without consideration of a building, and calculating displacements of points in the position of the building and in a certain range around the building; calculating a foundation reverse force of a Winkler elastic foundation beam; drawing ground surface settlement curve in consideration of the building; drawing the calculated ground surface settlement without consideration of the building and the calculated ground surface settlement in consideration of the building on a same graph, so that the influence of consideration of building rigidity on the building settlement caused by a shield tunnel is reflected in a calculated ground surface settlement calculation result; and comparing the calculation result with settlement reference to judge the safety of the building. Therefore, the method is used for predicting an additional settlement amount of the building under the influence of shield tunnel excavation, and is of important significance for safety assessment of the building.

Description

Method for calculating building settlement caused by shield tunnel construction

Technical Field

The invention relates to a method for calculating building settlement caused by shield tunnel construction, and belongs to the technical field of underground engineering.

Background

Ouyangwenbiao, etc^[1]Based on Verruijt and Booker solutions, and in combination with an equivalent stiffness principle, a calculation formula of surface subsidence caused by the fact that single-line and double-line shield tunnels penetrate through a building is given in consideration of the stiffness of the building. And by combining the example that the 11 # line of the Shanghai rail transit passes through Xuhui Zhongji Chong building, the calculation formula of the surface subsidence caused by the double-line shield tunnel passing through the building and the subsidence of the existing building are used for prediction, the comparison with the detection result shows that the coincidence is better, and the applicability of the formula is verified. The method has the following defects:

1) the basic Verruijt and Booker solutions of the article assume that the soil around the tunnel uniformly shrinks towards the center of the tunnel, which can cause the calculated maximum value of surface subsidence to be smaller and the scope of a subsider to be larger;

2) there is some deviation from the original interpretation of the parameters;

the main problems in the prior art are found by the investigation of the document [1] and other searched documents, in addition to the above disadvantages:

1) the theoretical research on the influence of the shield tunnel construction on the building settlement curve is relatively few;

2) the parameter values adopted by the building in the theoretical calculation have not been studied in detail and have not been defined

3) Generally, influence of structural rigidity on deformation of the structure is neglected in engineering practice, and a structural deformation prediction result is greatly conservative.

Wherein:

[1] ouyangwen Biao, Dingwen, Xieastern Wu. Shield construction induced settlement calculation method considering building rigidity [ J ]. Underground Space and Engineering report, 2013,9(1):155-

Disclosure of Invention

In recent decades, subways develop rapidly in China, and all major cities build subways near urban mass-flow central areas to relieve ground traffic. However, most of the existing and constructed subway tunnels in China are located below urban main roads or directly pass through buildings above the urban main roads, and particularly in urban centers with relatively congested traffic, frequent passing of the buildings by shield tunnel construction is a normal state. At present, a large number of shield methods are adopted to construct subway tunnels, and in the construction process of shield tunnels, soil bodies are inevitably disturbed to cause settlement of building foundations, possibly resulting in a series of problems of inclination, cracking, even collapse and the like of buildings, and affecting the normal use and safety of the buildings. Therefore, the method has important research value for researching the building settlement caused by shield tunnel construction.

By the method, the additional settlement of the building under the influence of shield tunnel excavation can be predicted according to conditions such as the upper load of the building, the foundation burial depth of the building, the soil condition of the position where the building is located, the wall length of the building, the diameter of the shield tunnel, the burial depth of the shield tunnel, the position relation between the shield tunnel and the building and the like, and the method has important significance for safety evaluation of the building.

The invention aims to overcome the defects in the prior art and provides a method for calculating the building settlement caused by shield tunnel construction, which comprises the following 5 steps:

step 1: and (4) not considering the building, firstly calculating the ground surface settlement caused by the shield tunnel construction, and calculating the displacement of each point in the position where the building is located and a certain range around the building.

The calculation method uniformly adopts a unified soil body movement model solution to calculate the ground surface settlement caused by shield construction, the calculation method adopts a soil body loss model with two tangent circles, and the movement focus of the soil body around the tunnel changes between the center point of the tunnel and the bottom position of the tunnel. The calculation formula of the vertical displacement of the earth surface caused by the construction of the single shield tunnel is as follows:

$U_{z\sin gle}=\frac{R^2}{2}\·\{\frac{h-z}{y^2+{(h-z)}^2}+\frac{h+z}{y^2+{(h+z)}^2}-\frac{2z\[y^2-{(h+z)}^2\]}{{\[y^2+{(h+z)}^2\]}^2}\}\·\frac{4Rg-g^2}{4R^2}\·B\·\exp \[\frac{y^{2}ln\mathrm{\λ}}{{(h+R)}^2}+\frac{z^2(ln\mathrm{\λ}-ln\mathrm{\δ})}{{(h+d)}^2}\]---\left(1\right)$

wherein,

$\mathrm{\λ}=\frac{1}{4}-\frac{g}{\mathrm{\π}g\mathrm{\η}}\[arcsin\left(\frac{d}{R-g/2}\right)+\sqrt{1-{\left(\frac{d}{R-g/2}\right)}^2}-1\];$

$\mathrm{\δ}=\frac{1}{2}-\frac{g}{{\mathrm{\πR}}^2\mathrm{\η}}(R-g/4)arcsin\left(\frac{d}{R-g/4}\right);$

in the formula:

r is the tunnel excavation radius, and the unit symbol is m;

h is the distance between the axis of the tunnel and the ground, and the unit symbol is m;

d is the distance from the moving focus of the soil body to the center point of the tunnel, and the unit symbol is m;

β R, wherein the unit symbol is m, wherein β is a calculation parameter(s) related to soil conditionsIs a dimensionless parameter), the value range is (0, 1), the better the soil quality is, the β value is larger, the worse the soil quality is, the β value is smaller, and d has different suggested values according to the soil quality of different regions in China^[2]Calculating according to the soil condition of the actual engineering by referring to the value of the suggested value;

y is the horizontal distance from the axis of the tunnel, and the unit symbol is m;

z is the vertical distance from the ground, is positive from the ground to the bottom, and the unit symbol is m;

_ηthe loss percentage of the soil body is dimensionless;

g is an equivalent soil mass loss parameter,the unit symbol is mm.

Assuming that the right side tunnel of the double-line shield tunnel is excavated first, the calculation formula of the vertical displacement of the earth surface caused by the construction of the double-line shield tunnel is as follows:

$\begin{array}{c}{U}_{zDouble}=U_{zSingle}(y-L/2,z)+U_{zSingle}(y+L/2+b,z)\\ =\frac{R^2}{2}\·\{\frac{h-z}{{(y-L/2)}^2+{(h-z)}^2}+\frac{h+z}{{(y-L/2)}^2+{(h+z)}^2}-\frac{2z\[{(y-L/2)}^2-{(h+z)}^2\]}{{\[{(y-L/2)}^2+{(h+z)}^2\]}^2}\·\frac{4{\mathrm{Rg}}_f-{g_f}^2}{4R^2}{B}_f\exp \[\frac{{(y-L/2)}^2{\mathrm{ln\λ}}_f}{{(h+R)}^2}+\frac{z^2(ln\mathrm{\λ}{f}_{}-{\mathrm{ln\δ}}_f)}{{(h+d_f)}^2}\]+\\ \frac{R^2}{2}\{\frac{h-z}{{(y+L/2+b)}^2+{(h-z)}^2}+\frac{h+z}{{(y+L/2+b)}^2+{(h+z)}^2}-\frac{2z\[{(y+L/2+b)}^2-{(h+z)}^2\]}{{\[{(y+L/2+b)}^2+{(h+z)}^2\]}^2}\·\frac{4{\mathrm{Rg}}_s-{g_s}^2}{4R^2}{B}_s\exp \[\frac{{(y+L/2+b)}^2{\mathrm{ln\λ}}_s}{{(h+R)}^2}+\frac{z^2({\mathrm{ln\λ}}_s-{\mathrm{ln\δ}}_s)}{{(h+d_s)}^2}\]\end{array}---\left(2\right)$

in the formula:

r is the tunnel excavation radius, and the unit symbol is m;

h is the distance between the axis of the tunnel and the ground, and the unit symbol is m;

y is the horizontal distance from the axis of the tunnel, and the unit symbol is m;

z is the vertical distance from the ground, is positive from the ground to the bottom, and the unit symbol is m;

g_f、η_f、d_frespectively the equivalent soil loss parameter, the soil loss percentage and the distance from the soil moving focus to the center point of the tunnel of the preceding tunnel, η_fIs a dimensionless parameter, gf, d_fThe unit symbols are mm, m,

g_s、η_s、d_srespectively the equivalent soil loss parameter, the soil loss percentage and the distance from the soil moving focus to the center point of the tunnel of the back tunnel η_sAs a dimensionless parameter, g_s、d_sThe unit symbols are mm, m,

λ_f、_f、B_fthe calculation parameters are respectively the calculation parameters of the advanced tunnel and satisfy the following formula:

${\mathrm{\λ}}_f=\frac{1}{4}-\frac{g_f}{{\mathrm{\πR\η}}_f}\[arcsin\left(\frac{d_f}{R-g_f/2}\right)+\sqrt{1-{\left(\frac{d_f}{R-g_f/2}\right)}^2}-1\];$

${\mathrm{\δ}}_f=\frac{1}{2}-\frac{g_f}{{\mathrm{\πR}}^2{\mathrm{\η}}_f}(R-g_f/4)arcsin\left(\frac{d_f}{R-g_f/4}\right);$

$B_f=\frac{4h\[h+d_f-\sqrt{{(h+d_f)}^2-{\mathrm{\η}}_f{(R+d_f)}^2}\]}{{\mathrm{f\η}}_f(R+d_f)};$

λ_s、_s、B_srespectively are calculation parameters of the backward tunnel, and satisfy the following formula:

${\mathrm{\λ}}_s=\frac{1}{4}-\frac{g_s}{{\mathrm{\πR\η}}_s}\[arcsin\left(\frac{d_s}{R-g_s/2}\right)+\sqrt{1-{\left(\frac{d_s}{R-g_s/2}\right)}^2}-1\];$

${\mathrm{\δ}}_s=\frac{1}{2}-\frac{g_s}{{\mathrm{\πR}}^2{\mathrm{\η}}_s}(R-g_s/4)arcsin\left(\frac{d_s}{R-g_s/4}\right);$

$B_s=\frac{4h\[h+d_s-\sqrt{{(h+d_s)}^2-{\mathrm{\η}}_s{(R+d_s)}^2}\]}{{\mathrm{R\η}}_s(R+d_s)};$

b is the offset of the soil body settlement axis caused by the backward tunnel, and the unit symbol is m on the assumption that the side of the deviation tunnel is positive.

Step 2: through a calculation formula of the reaction force of the Weckel elastic foundation beam foundation:

F＝kU_z(3)

f is foundation reaction force, and the unit symbol is kN/m;

k-bed coefficient in kN/m²；

U_ZThe unit symbol of the vertical displacement of the earth surface caused by shield construction is m;

the aim of the step is to convert the ground surface settlement caused by shield tunnel excavation into settlement counter force to be applied to the building simplified into the elastic foundation beam.

And step 3: when the MIDAS-GTS is used for calculation, the section of the beam is selected to be a solid groove rectangular section, and the length-width ratio is 1.5: 1. The bed coefficient k was taken to be 15000kN/m³. After dividing the model of the beam into 20 equal parts, settling reaction force (constant load) is established. And calculating the building settlement caused by the settlement counter force by using MIDAS-GTS software to obtain the building settlement value caused by the settlement counter force, and drawing a ground surface settlement curve when the building is considered.

And 4, step 4: the ground surface subsidence calculated in step 1 without considering the building and the ground surface subsidence calculated in step 3 with considering the building are plotted on the same graph, and as shown in fig. 1, it can be understood that the influence of the method herein on the shield tunnel-induced building subsidence in consideration of the rigidity of the building is reflected in the ground surface subsidence calculation result calculated in step 3.

And 5: the ground settlement harms the safety of buildings to a certain degree, so that China determines that the urban ground deformation is a settlement standard of between +10mm and-30 mm so as to ensure the safety of the buildings on the ground, and the safety of the buildings can be judged by comparing the calculation result with the settlement standard.

The calculation method is simple, considers the influence of soil conditions on the building settlement caused by the shield tunnel construction, has wide application range, is suitable for calculating the settlement of the adjacent building caused by the shield tunnel excavation, and can be used for safety evaluation of the influence of the shield tunnel on the building.

Drawings

FIG. 1 is a schematic diagram of the surface subsidence calculated in step 1 without regard to the building and the surface subsidence calculated in step 3 with regard to the building according to the present invention;

fig. 2 is a schematic diagram comparing the calculated surface subsidence with the measured value after considering the building according to the present invention.

Detailed Description

The technical scheme of the invention is further explained by combining the attached drawings of the specification:

as shown in fig. 1-2, the present invention provides a specific embodiment of a method for calculating building settlement caused by shield tunnel construction, which includes the following 5 steps:

step 1: and (4) not considering the building, firstly calculating the ground surface settlement caused by the shield tunnel construction, and calculating the displacement of each point in the position where the building is located and a certain range around the building.

The calculation method uniformly adopts a unified soil body movement model solution to calculate the ground surface settlement caused by shield construction, the calculation method adopts a soil body loss model with two tangent circles, and the movement focus of the soil body around the tunnel changes between the center point of the tunnel and the bottom position of the tunnel. The calculation formula of the vertical displacement of the earth surface caused by the construction of the single shield tunnel is as follows:

$U_{z\sin gle}=\frac{R^2}{2}\·\{\frac{h-z}{y^2+{(h-z)}^2}+\frac{h+z}{y^2+{(h+z)}^2}-\frac{2z\[y^2-{(h+z)}^2\]}{{\[y^2+{(h+z)}^2\]}^2}\}\·\frac{4Rg-g^2}{4R^2}\·B\·\exp \[\frac{y^{2}ln\mathrm{\λ}}{{(h+R)}^2}+\frac{z^2(ln\mathrm{\λ}-ln\mathrm{\δ})}{{(h+d)}^2}\]---\left(1\right)$

wherein,

$\mathrm{\λ}=\frac{1}{4}-\frac{g}{\mathrm{\π}g\mathrm{\η}}\[arcsin\left(\frac{d}{R-g/2}\right)+\sqrt{1-{\left(\frac{d}{R-g/2}\right)}^2}-1\];$

$\mathrm{\δ}=\frac{1}{2}-\frac{g}{{\mathrm{\πR}}^2\mathrm{\η}}(R-g/4)arcsin\left(\frac{d}{R-g/4}\right);$

in the formula:

r is the tunnel excavation radius, and the unit symbol is m;

h is the distance between the axis of the tunnel and the ground, and the unit symbol is m;

d is the distance from the moving focus of the soil body to the center point of the tunnel, and the unit symbol is m;

d is β R, the unit symbol is m, wherein β is a calculation parameter (dimensionless parameter) related to soil conditions, the value range is (0, 1), the better the soil is, the β value is larger, the worse the soil is, the β value is smaller, and d has different suggested values according to the soil in different regions of China^[2]Calculating according to the soil condition of the actual engineering by referring to the value of the suggested value;

y is the horizontal distance from the axis of the tunnel, and the unit symbol is m;

z is the vertical distance from the ground, is positive from the ground to the bottom, and the unit symbol is m;

eta is the soil mass loss percentage and has no dimension;

g is an equivalent soil mass loss parameter,the unit symbol is mm.

Assuming that the right side tunnel of the double-line shield tunnel is excavated first, the calculation formula of the vertical displacement of the earth surface caused by the construction of the double-line shield tunnel is as follows:

$\begin{array}{c}{U}_{zDouble}=U_{zSingle}(y-L/2,z)+U_{zSingle}(y+L/2+b,z)\\ =\frac{R^2}{2}\·\{\frac{h-z}{{(y-L/2)}^2+{(h-z)}^2}+\frac{h+z}{{(y-L/2)}^2+{(h+z)}^2}-\frac{2z\[{(y-L/2)}^2-{(h+z)}^2\]}{{\[{(y-L/2)}^2+{(h+z)}^2\]}^2}\·\frac{4{\mathrm{Rg}}_f-{g_f}^2}{4R^2}{B}_f\exp \[\frac{{(y-L/2)}^2{\mathrm{ln\λ}}_f}{{(h+R)}^2}+\frac{z^2(ln\mathrm{\λ}{f}_{}-{\mathrm{ln\δ}}_f)}{{(h+d_f)}^2}\]+\\ \frac{R^2}{2}\{\frac{h-z}{{(y+L/2+b)}^2+{(h-z)}^2}+\frac{h+z}{{(y+L/2+b)}^2+{(h+z)}^2}-\frac{2z\[{(y+L/2+b)}^2-{(h+z)}^2\]}{{\[{(y+L/2+b)}^2+{(h+z)}^2\]}^2}\·\frac{4{\mathrm{Rg}}_s-{g_s}^2}{4R^2}{B}_s\exp \[\frac{{(y+L/2+b)}^2{\mathrm{ln\λ}}_s}{{(h+R)}^2}+\frac{z^2({\mathrm{ln\λ}}_s-{\mathrm{ln\δ}}_s)}{{(h+d_s)}^2}\]\end{array}---\left(2\right)$

in the formula:

r is the tunnel excavation radius, and the unit symbol is m;

h is the distance between the axis of the tunnel and the ground, and the unit symbol is m;

y is the horizontal distance from the axis of the tunnel, and the unit symbol is m;

z is the vertical distance from the ground, is positive from the ground to the bottom, and the unit symbol is m;

g_f、η_f、d_frespectively the equivalent soil loss parameter, the soil loss percentage and the distance from the soil moving focus to the center point of the tunnel of the preceding tunnel, η_fAs a dimensionless parameter, g_f、d_fThe unit symbols are mm, m,

g_s、η_s、d_srespectively the equivalent soil loss parameter, the soil loss percentage and the distance from the soil moving focus to the center point of the tunnel of the back tunnel η_sAs a dimensionless parameter, g_s、d_sThe unit symbols are mm, m,

λ_f、_f、B_fthe calculation parameters are respectively the calculation parameters of the advanced tunnel and satisfy the following formula:

${\mathrm{\λ}}_f=\frac{1}{4}-\frac{g_f}{{\mathrm{\πR\η}}_f}\[arcsin\left(\frac{d_f}{R-g_f/2}\right)+\sqrt{1-{\left(\frac{d_f}{R-g_f/2}\right)}^2}-1\];$

${\mathrm{\δ}}_f=\frac{1}{2}-\frac{g_f}{{\mathrm{\πR}}^2{\mathrm{\η}}_f}(R-g_f/4)arcsin\left(\frac{d_f}{R-g_f/4}\right);$

$B_f=\frac{4h\[h+d_f-\sqrt{{(h+d_f)}^2-{\mathrm{\η}}_f{(R+d_f)}^2}\]}{{\mathrm{f\η}}_f(R+d_f)};$

λ_s、_s、B_srespectively are calculation parameters of the backward tunnel, and satisfy the following formula:

${\mathrm{\λ}}_s=\frac{1}{4}-\frac{g_s}{{\mathrm{\πR\η}}_s}\[arcsin\left(\frac{d_s}{R-g_s/2}\right)+\sqrt{1-{\left(\frac{d_s}{R-g_s/2}\right)}^2}-1\];$

${\mathrm{\δ}}_s=\frac{1}{2}-\frac{g_s}{{\mathrm{\πR}}^2{\mathrm{\η}}_s}(R-g_s/4)arcsin\left(\frac{d_s}{R-g_s/4}\right);$

$B_s=\frac{4h\[h+d_s-\sqrt{{(h+d_s)}^2-{\mathrm{\η}}_s{(R+d_s)}^2}\]}{{\mathrm{R\η}}_s(R+d_s)};$

b is the offset of the soil body settlement axis caused by the backward tunnel, and the unit symbol is m on the assumption that the side of the deviation tunnel is positive.

Step 2: through a calculation formula of the reaction force of the Weckel elastic foundation beam foundation:

F＝kU_z(3)

f is foundation reaction force, and the unit symbol is kN/m;

k-bed coefficient in kN/m²；

U_ZThe unit symbol of the vertical displacement of the earth surface caused by shield construction is m;

the aim of the step is to convert the ground surface settlement caused by shield tunnel excavation into settlement counter force to be applied to the building simplified into the elastic foundation beam.

And step 3: when the MIDAS-GTS is used for calculation, the section of the beam is selected to be a solid groove rectangular section, and the length-width ratio is 1.5: 1. The bed coefficient k was taken to be 15000kN/m³. After dividing the model of the beam into 20 equal parts, settling reaction force (constant load) is established. And calculating the building settlement caused by the settlement counter force by using MIDAS-GTS software to obtain the building settlement value caused by the settlement counter force, and drawing a ground surface settlement curve when the building is considered.

And 4, step 4: the ground surface subsidence calculated in step 1 without considering the building and the ground surface subsidence calculated in step 3 with considering the building are plotted on the same graph, and as shown in fig. 1, it can be understood that the influence of the method herein on the shield tunnel-induced building subsidence in consideration of the rigidity of the building is reflected in the ground surface subsidence calculation result calculated in step 3.

And 5: the ground settlement harms the safety of buildings to a certain degree, so that China determines that the urban ground deformation is a settlement standard of between +10mm and-30 mm so as to ensure the safety of the buildings on the ground, and the safety of the buildings can be judged by comparing the calculation result with the settlement standard.

The calculation method is simple, considers the influence of soil conditions on the building settlement caused by the shield tunnel construction, has wide application range, is suitable for calculating the settlement of the adjacent building caused by the shield tunnel excavation, and can be used for safety evaluation of the influence of the shield tunnel on the building.

With reference to fig. 2: the Shanghai rail transit 11 number line passes through the position right below the Chongsi building in Xuhui Chinese school, the diameter of the tunnel is 6.2m, the axial burial depth is about 22.7m, and the axial distance between the two tunnels is about 16.5m^[1]The length of the Chongsi building is about 66m, the height of the tunnel is about 23m, settlement measuring points are distributed in the Chongsi building in the construction process, the actual measurement value of each measuring point is shown in figure 2, the tunnel on the left side is a prior tunnel, the soil loss rate of the prior tunnel is η_f1.24 percent, the soil loss rate of the backward tunnel η_sIt was 1.25%. Distance d from moving focus of preceding tunnel to center point of tunnel_f0.45R, the distance d from the moving focus of the backward tunnel to the center point of the tunnel_sIs 0.04R. The offset b of the soil body settlement axis caused by the backward tunnel is 4 m.

As can be seen from fig. 2, the ground surface subsidence calculated by the method of the present invention in consideration of the building substantially matches the measured value, and the curve calculated by the method of the present invention represents the rigidity characteristic of the building as compared with the case where the building is not considered. Because the ground surface settlement is not more than 30mm, the Chong building is safe in the tunnel construction process.

The above embodiments are illustrative of the present invention, and are not intended to limit the present invention, and any simple modifications of the present invention are within the scope of the present invention.

Claims (1)

1. A method for calculating building settlement caused by shield tunnel construction is characterized by comprising the following 5 steps:

step 1: the method comprises the following steps of (1) calculating the ground surface settlement caused by shield tunnel construction without considering a building, and calculating the displacement of each point in the position where the building is located and a certain range around the building;

calculating the ground surface settlement caused by shield construction by adopting a unified soil body movement model solution, wherein a soil body loss model with two tangent circles is adopted in the calculation method, and the movement focus of the soil body around the tunnel changes between the center point of the tunnel and the bottom position of the tunnel; the calculation formula of the vertical displacement of the earth surface caused by the construction of the single shield tunnel is as follows:

$U_{z\sin gle}=\frac{R^2}{2}\·\{\frac{h-z}{y^2+{(h-z)}^2}+\frac{h+z}{y^2+{(h+z)}^2}-\frac{2z\[y^2-{(h+z)}^2\]}{{\[y^2+{(h+z)}^2\]}^2}\}\·\frac{4Rg-g^2}{4R^2}\·B\·\exp \[\frac{y^{2}ln\mathrm{\λ}}{{(h+R)}^2}+\frac{z^2(ln\mathrm{\λ}-ln\mathrm{\δ})}{{(h+d)}^2}\]---\left(1\right)$

wherein:

$B=\frac{4h\[h+d-\sqrt{{(h+d)}^2-\mathrm{\η}{(R+d)}^2}\]}{R\mathrm{\η}(R+d)};$

$\mathrm{\λ}=\frac{1}{4}-\frac{g}{\mathrm{\π}R\mathrm{\η}}\[\arcsin \left(\frac{d}{R-g/2}\right)+\sqrt{1-{\left(\frac{d}{R-g/2}\right)}^2}-1\];$

$\mathrm{\δ}=\frac{1}{2}-\frac{g}{{\mathrm{\πR}}^2\mathrm{\η}}(R-g/4)\arcsin \left(\frac{d}{R-g/4}\right);$

in the formula:

r is the tunnel excavation radius, and the unit symbol is m;

h is the distance between the axis of the tunnel and the ground, and the unit symbol is m;

d is the distance from the moving focus of the soil body to the center point of the tunnel, and the unit symbol is m;

d is beta R, the unit symbol is m, wherein beta is a calculation parameter related to soil conditions, and the value range is (0, 1);

y is the horizontal distance from the axis of the tunnel, and the unit symbol is m;

z is the vertical distance from the ground, is positive from the ground to the bottom, and the unit symbol is m;

eta is the soil mass loss percentage and has no dimension;

g is an equivalent soil mass loss parameter,the unit symbol is mm;

assuming that the right side tunnel of the double-line shield tunnel is excavated first, the calculation formula of the vertical displacement of the earth surface caused by the construction of the double-line shield tunnel is as follows:

$U_{zDouble}=U_{zSingle}(y-L/2,z)+U_{zSingle}(y+L/2+b,z)$

$\begin{array}{c}=\frac{R^2}{2}\·\{\frac{h-z}{{\left(y-L/2\right)}^2+{\left(h-z\right)}^2}+\frac{h+z}{{\left(y-L/2\right)}^2+{\left(h+z\right)}^2}-\frac{2z\[{\left(y-L/2\right)}^2-{\left(h+z\right)}^2\]}{{\[{\left(y-L/2\right)}^2+{\left(h+z\right)}^2\]}^2}\·\frac{4{\mathrm{Rg}}_f-{g_f}^2}{4R^2}{B}_f\exp \[\frac{{\left(y-L/2\right)}^2{\mathrm{ln\λ}}_f}{{\left(h+R\right)}^2}+\frac{z^2\left({\mathrm{ln\λ}}_f-{\mathrm{ln\δ}}_f\right)}{{\left(h+d_f\right)}^2}\]+\\ \frac{R^2}{2}\{\frac{h-z}{{\left(y+L/2+b\right)}^2+{\left(h-z\right)}^2}+\frac{h+z}{{\left(y+L/2+b\right)}^2+{\left(h+z\right)}^2}-\frac{2z\[{\left(y+L/2+b\right)}^2-{\left(h+z\right)}^2\]}{\[{\left(y+L/2+b\right)}^2+{\left(h+z\right)}^2\]}\·\frac{4{\mathrm{Rg}}_s-{g_s}^2}{4R^2}{B}_s\exp \[\frac{{\left(y+L/2+b\right)}^2{\mathrm{ln\λ}}_s}{{\left(h+R\right)}^2}+\frac{z^2\left({\mathrm{ln\λ}}_s-{\mathrm{ln\δ}}_s\right)}{{\left(h+d_s\right)}^2}\]\end{array}---\left(2\right)$

in the formula:

r is the tunnel excavation radius, and the unit symbol is m;

h is the distance between the axis of the tunnel and the ground, and the unit symbol is m;

y is the horizontal distance from the axis of the tunnel, and the unit symbol is m;

z is the vertical distance from the ground, is positive from the ground to the bottom, and the unit symbol is m;

g_f、η_f、d_frespectively the equivalent soil loss parameter, the soil loss percentage and the distance from the soil moving focus to the center point of the tunnel of the preceding tunnel, η_fAs a dimensionless parameter, g_f、d_fThe unit symbols are mm, m,

g_s、η_s、d_srespectively, the equivalent soil loss parameter, the soil loss percentage and the soil moving focus of the backward tunnel to the central point of the tunnelDistance, η_sAs a dimensionless parameter, g_s、d_sThe unit symbols are mm, m,

λ_f、_f、B_fthe calculation parameters are respectively the calculation parameters of the advanced tunnel and satisfy the following formula:

${\mathrm{\λ}}_f=\frac{1}{4}-\frac{g_f}{{\mathrm{\πR\η}}_f}\[\arcsin \left(\frac{d_f}{R-g_f/2}\right)+\sqrt{1-{\left(\frac{d_f}{R-g_f/2}\right)}^2}-1\];$

${\mathrm{\δ}}_f=\frac{1}{2}-\frac{g_f}{{\mathrm{\πR}}^2{\mathrm{\η}}_f}(R-g_f/4)arcsin\left(\frac{d_f}{R-g_f/4}\right);$

$B_f=\frac{4h\[h+d_f-\sqrt{{(h+d_f)}^2-{\mathrm{\η}}_f{(R+d_f)}^2}\]}{{\mathrm{R\η}}_f(R+d_f)};$

λ_s、_s、B_srespectively are calculation parameters of the backward tunnel, and satisfy the following formula:

${\mathrm{\λ}}_s=\frac{1}{4}-\frac{g_s}{{\mathrm{\πR\η}}_s}\[arcsin\left(\frac{d_s}{R-g_s/2}\right)+\sqrt{1-{\left(\frac{d_s}{R-g_s/2}\right)}^2}-1\];$

${\mathrm{\δ}}_s=\frac{1}{2}-\frac{g_s}{{\mathrm{\πR}}^2{\mathrm{\η}}_s}(R-g_s/4)\arcsin \left(\frac{d_s}{R-g_s/4}\right);$

$B_s=\frac{4h\[h+d_s-\sqrt{{(h+d_s)}^2-{\mathrm{\η}}_s{(R+d_s)}^2}\]}{{\mathrm{R\η}}_s(R+d_s)};$

b is the offset of the soil body settlement axis caused by the backward tunnel, the side of the deviation tunnel is assumed to be positive, and the unit symbol is m;

step 2: through a calculation formula of the reaction force of the Weckel elastic foundation beam foundation:

F＝kU_z(3)；

in the formula:

f is foundation reaction force, and the unit symbol is kN/m;

k-bed coefficient in kN/m²；

U_ZThe unit symbol of the vertical displacement of the earth surface caused by shield construction is m;

the method aims to convert the surface subsidence caused by shield tunnel excavation into subsidence counter-force to be added to a building simplified into an elastic foundation beam;

and step 3: when the MIDAS-GTS is used for calculation, the section of the beam is selected to be a solid groove rectangular section, and the length-width ratio is 1.5: 1; the bed coefficient k was taken to be 15000kN/m³(ii) a Dividing the model of the built beam into 20 equal parts, and then building a settlement counter force (constant load); calculating the building settlement caused by the settlement counter force by using MIDAS-GTS software to obtain the building settlement value caused by the settlement counter force and drawing a ground surface settlement curve when the building is considered;

and 4, step 4: the ground surface subsidence calculated in the step 1 without considering the building and the ground surface subsidence calculated in the step 3 with considering the building are drawn on the same graph, and it can be known that the influence of the calculation method on the shield tunnel caused by considering the rigidity of the building is reflected in the ground surface subsidence calculation result calculated in the step 3;

and 5: and comparing the calculation result with a settlement standard so as to judge the safety of the building.