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

A kind of shield tunnel construction causes the computational methods of building settlement

Technical field

The present invention relates to a kind of shield tunnel construction causes the computational methods of building settlement, belong to underground engineering technology neck Domain.

Background technology

Ou Yangwenbiao etc.^[1]Based on verruijt and booker solution, in conjunction with equivalent stiffness principle, give consideration building The calculation of ground surface settlement formula that during rigidity, single line and two-wire shield driven tunnel crossing building cause.And combine Shanghai rail transit 11 Number line passes through the example in Xuhui middle school Chong Si building, the calculation of ground surface settlement formula causing with two-wire shield driven tunnel crossing building It is predicted with existing building sedimentation, coincide preferably with testing result contrast display, demonstrate the suitability of this formula.The party The weak point of method has:

1) the basic verruijt and booker solution of article assumes that tunnel surrounding soil to tunnel center uniform shrinkage, this Can lead to the ground settlement maximum tried to achieve can less than normal, subsider scope bigger than normal；

2) there is certain deviation for the explanation for parameter δ in original text；

By to document [1] and other searching documents investigation find, the subject matter in existing technology except more than Weak point outside, still suffered from:

1) theoretical research building settlement curve being affected with regard to shield tunnel construction is relatively fewer；

2) parameter value being adopted in Theoretical Calculation for building has no detailed research and clear and definite standard

3) typically all have ignored, in engineering practice, the influence that the rigidity of structure deforms to it, make malformation predict knot Fruit is significantly relatively conservative.

Wherein:

[1] Ou Yangwenbiao, Ding Wenqi, Xie Dongwu. consider that the shield-tunneling construction of building rigidity is led to settlement calculation method [j]. The underground space and engineering journal, 2013,9 (1): 155-160. (ouyang wenbiao, ding wenqi, xie dongwu.calculation method for settlement due to shield tunnelling considering structure stiffness[j].chinese journal of underground space and engineering, 2013,9(1):155-160.(in chinese))

Content of the invention

Recent decades, China's Development of underground railway is rapid, and each big city is all built in the crowded near central regions in city Subway is alleviating traffic above-ground.But China existing and be all in below major urban arterial highway in the subway tunnel overwhelming majority making or Person directly passes through top building, especially in the downtown of traffic more congestion, the frequent passing through building of shield tunnel construction It has been normality.In a large number subway tunnel is built using shield method at present, in the work progress of shield tunnel, the soil body is inevitably Can be disturbed, cause building foundation settlement, a series of problems, such as building inclination may being led to, ftractures or even cave in, shadow Ring the normal of building to use and safety.Therefore, shield tunnel construction is caused with the research of building settlement, has important Researching value.

By the method for this patent, can be according to building upper load, building embedded depth of foundation, building present position Soil condition, building wall body length, the position of shield tunnel diameter, shield tunnel buried depth and shield tunnel and building The conditions such as relation, predict subsequent settlement under the influence of Shield Tunneling for the building, the security evaluation to building Have great significance.

The purpose of the present invention is to overcome deficiency in prior art, provides a kind of shield tunnel construction to cause building settlement Computational methods, including following 5 steps:

Step 1: do not consider building, first the ground settlement that shield tunnel construction causes is calculated, calculate building At thing place and about in certain limit each point displacement.

Using unified ground movement pattern solution, the ground settlement that shield-tunneling construction causes is counted without exception in this computational methods Calculate, this computational methods adopts the two tangent ground loss models of circle, the moving focal point of tunnel surrounding soil tunnel central point with Change between tunnel bottom position.Single line shield tunnel construction causes the computing formula of vertical vibration:

$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 formula:

R is tunnel excavation radius, and unit symbol is m；

H is tunnel axis distance from the ground, and unit symbol is m；

D is the distance of soil body moving focal point to tunnel central point, and unit symbol is m；

D=β r, unit symbol is m, and wherein β is the calculating parameter (for dimensionless group) relevant with soil condition, value Scope is (0,1), and the better β value of soil property is bigger, and the poorer β value of soil property is less, and according to the soil property of China different regions, d has different Recommended value^[2], can be calculated with reference to the value of recommended value according to the soil condition of Practical Project；

Y is the transverse horizontal distance apart from tunnel axis, and unit symbol is m；

Z is vertical distance from the ground, is faced down as just, unit symbol is m by ground；

_ηFor ground loss percentage rate, dimensionless；

G is equivalent ground loss parameter,Unit symbol is mm.

It is assumed that the right side tunnel of two-wire shield tunnel first excavates, then two-wire shield tunnel construction causes vertical vibration Computing formula is:

$\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 formula:

R is tunnel excavation radius, and unit symbol is m；

H is tunnel axis distance from the ground, and unit symbol is m；

Y is the transverse horizontal distance apart from tunnel axis, and unit symbol is m；

Z is vertical distance from the ground, is faced down as just, unit symbol is m by ground；

g_f、η_f、d_fIt is respectively equivalent ground loss parameter, ground loss percentage rate and the soil body moving focal point in leading tunnel To the distance of tunnel central point, η_fFor dimensionless group, gf, d_fUnit symbol is respectively mm, m,

g_s、η_s、d_sThe equivalent ground loss parameter in row tunnel, ground loss percentage rate and soil body moving focal point after being respectively To the distance of tunnel central point, η_sFor dimensionless group, g_s、d_sUnit symbol is respectively mm, m,

λ_f、δ_f、b_fIt is respectively the calculating parameter in leading tunnel, and meet below equation:

${\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、δ_s、b_sThe calculating parameter in row tunnel after being respectively, and meet below equation:

${\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 be after row tunnel cause the soil body sedimentation axis deviant it is assumed that deflection leading tunnel side be just, unit symbol is m.

Step 2: by the computing formula of Wen Keer beam on elastic foundation subgrade reaction:

F=ku_z(3)

F subgrade reaction, unit symbol is kn/m；

K bedding value, unit symbol is kn/m²；

u_zThe vertical vibration that shield-tunneling construction causes, unit symbol is m；

The purpose of this step is that the ground settlement causing Shield Tunneling is converted into sedimentation counter-force and is added in and is simplified to bullet On the building of property grade beam.

Step 3: when being calculated with midas-gts, the section of beam is chosen for real flute length square-section, length-width ratio is 1.5:1.Base Bed coefficient k is taken as 15000kn/m³.The model of built beam is divided into after 20 equal portions, sets up sedimentation counter-force (dead load).Using The building settlement that midas-gts software causes to sedimentation counter-force calculates, and draws the building settlement that sedimentation counter-force causes Value, and draw out ground settlement curve when considering building.

Step 4: the consideration building that the ground settlement not considered during building that step 1 is calculated is calculated with step 3 Ground settlement during thing is plotted on same figure, see Fig. 1 it is known that context of methods for consider building rigidity to shield tunnel The impact of the building settlement that road causes has been reflected in the calculation of ground surface settlement result that step 3 calculates.

Step 5: surface subsidence reaches the safety that can endanger building to a certain degree, therefore China determines urban ground and becomes Shape is that "+10mm～-30mm " sinks grand benchmark to guarantee the safety of above ground structure, by this paper result of calculation compared with sedimentation benchmark Relatively may determine that the safety of building.

This patent computational methods simple it is contemplated that soil condition causes the impact of building settlement to shield tunnel construction, Have wide range of applications it is adaptable to Shield Tunneling causes the calculating of close to buildings sedimentation, and can be used for shield tunnel to building Build the security evaluation that thing impacts.

Brief description

Fig. 1 is the consideration that the ground settlement not considered during building that in the present invention, step 1 calculates is calculated with step 3 Ground settlement schematic diagram during building；

The comparison schematic diagram of the ground settlement that Fig. 2 is the present invention to be calculated after considering building and measured value.

Specific embodiment

With reference to Figure of description, technical scheme is described further:

As shown in Fig. 1～2, a kind of present invention shield tunnel construction of proposition causes the concrete of the computational methods of building settlement Embodiment, including following 5 steps:

Step 1: do not consider building, first the ground settlement that shield tunnel construction causes is calculated, calculate building At thing place and about in certain limit each point displacement.

Using unified ground movement pattern solution, the ground settlement that shield-tunneling construction causes is counted without exception in this computational methods Calculate, this computational methods adopts the two tangent ground loss models of circle, the moving focal point of tunnel surrounding soil tunnel central point with Change between tunnel bottom position.Single line shield tunnel construction causes the computing formula of vertical vibration:

$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 formula:

R is tunnel excavation radius, and unit symbol is m；

H is tunnel axis distance from the ground, and unit symbol is m；

D is the distance of soil body moving focal point to tunnel central point, and unit symbol is m；

D=β r, unit symbol is m, and wherein β is the calculating parameter (for dimensionless group) relevant with soil condition, value Scope is (0,1), and the better β value of soil property is bigger, and the poorer β value of soil property is less, and according to the soil property of China different regions, d has different Recommended value^[2], can be calculated with reference to the value of recommended value according to the soil condition of Practical Project；

Y is the transverse horizontal distance apart from tunnel axis, and unit symbol is m；

Z is vertical distance from the ground, is faced down as just, unit symbol is m by ground；

η is ground loss percentage rate, dimensionless；

G is equivalent ground loss parameter,Unit symbol is mm.

It is assumed that the right side tunnel of two-wire shield tunnel first excavates, then two-wire shield tunnel construction causes vertical vibration Computing formula is:

$\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 formula:

R is tunnel excavation radius, and unit symbol is m；

H is tunnel axis distance from the ground, and unit symbol is m；

Y is the transverse horizontal distance apart from tunnel axis, and unit symbol is m；

Z is vertical distance from the ground, is faced down as just, unit symbol is m by ground；

g_f、η_f、d_fIt is respectively equivalent ground loss parameter, ground loss percentage rate and the soil body moving focal point in leading tunnel To the distance of tunnel central point, η_fFor dimensionless group, g_f、d_fUnit symbol is respectively mm, m,

g_s、η_s、d_sThe equivalent ground loss parameter in row tunnel, ground loss percentage rate and soil body moving focal point after being respectively To the distance of tunnel central point, η_sFor dimensionless group, g_s、d_sUnit symbol is respectively mm, m,

λ_f、δ_f、b_fIt is respectively the calculating parameter in leading tunnel, and meet below equation:

${\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、δ_s、b_sThe calculating parameter in row tunnel after being respectively, and meet below equation:

${\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 be after row tunnel cause the soil body sedimentation axis deviant it is assumed that deflection leading tunnel side be just, unit symbol is m.

Step 2: by the computing formula of Wen Keer beam on elastic foundation subgrade reaction:

F=ku_z(3)

F subgrade reaction, unit symbol is kn/m；

K bedding value, unit symbol is kn/m²；

u_zThe vertical vibration that shield-tunneling construction causes, unit symbol is m；

The purpose of this step is that the ground settlement causing Shield Tunneling is converted into sedimentation counter-force and is added in and is simplified to bullet On the building of property grade beam.

Step 3: when being calculated with midas-gts, the section of beam is chosen for real flute length square-section, length-width ratio is 1.5:1.Base Bed coefficient k is taken as 15000kn/m³.The model of built beam is divided into after 20 equal portions, sets up sedimentation counter-force (dead load).Using The building settlement that midas-gts software causes to sedimentation counter-force calculates, and draws the building settlement that sedimentation counter-force causes Value, and draw out ground settlement curve when considering building.

Step 4: the consideration building that the ground settlement not considered during building that step 1 is calculated is calculated with step 3 Ground settlement during thing is plotted on same figure, see Fig. 1 it is known that context of methods for consider building rigidity to shield tunnel The impact of the building settlement that road causes has been reflected in the calculation of ground surface settlement result that step 3 calculates.

Step 5: surface subsidence reaches the safety that can endanger building to a certain degree, therefore China determines urban ground and becomes Shape is that "+10mm～-30mm " sinks grand benchmark to guarantee the safety of above ground structure, by this paper result of calculation compared with sedimentation benchmark Relatively may determine that the safety of building.

This patent computational methods simple it is contemplated that soil condition causes the impact of building settlement to shield tunnel construction, Have wide range of applications it is adaptable to Shield Tunneling causes the calculating of close to buildings sedimentation, and can be used for shield tunnel to building Build the security evaluation that thing impacts.

In conjunction with Fig. 2: No. 11 lines of Shanghai rail transit pass through immediately below Xuhui middle school Chong Si building, tunnel diameter 6.2m, axle Line buried depth about 22.7m, two tunnel axis spacing about 16.5m^[1].Chong Silou is about 66m, high 4 layers of about 23m.During constructing tunnel Lay subsidence survey point in Chong Silou, the measured value of each measuring point is shown in Fig. 2.Left side tunnel is leading tunnel, and leading tunnel soil body is damaged Mistake rate is η_fFor 1.24%, rear row tunnel soil body loss rate η_sFor 1.25%.Leading tunnel moving focal point to tunnel central point away from From d_fFor 0.45r, rear row tunnel moving focal point is to tunnel central point apart from d_sFor 0.04r.The soil body sedimentation that row tunnel causes afterwards Axis deviant b is 4m.

As can be seen from Figure 2, the ground settlement that this patent method calculates after considering building is substantially identical with measured value, and phase In the situation not considering building, the curve that this patent method calculates embodies the stiffness characteristics of building to ratio.Due to earth's surface Sedimentation is less than 30mm, so Chong Silou is safe during constructing tunnel.

Above-described embodiment is the description of the invention, is not limitation of the invention, any to simple transformation of the present invention after Scheme belong to protection scope of the present invention.

Claims (1)

1. a kind of shield tunnel construction causes the computational methods of building settlement it is characterised in that including following 5 steps:

Step 1: do not consider building, first the ground settlement that shield tunnel construction causes is calculated, calculate building institute The displacement of each point in place and about certain limit；

Using unified ground movement pattern solution, the ground settlement that shield-tunneling construction causes is calculated, this computational methods adopts two circles Tangent ground loss model, the moving focal point of tunnel surrounding soil changes between tunnel central point and tunnel bottom position； Single line shield tunnel construction causes the computing formula of vertical vibration:

$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 formula:

R is tunnel excavation radius, and unit symbol is m；

H is tunnel axis distance from the ground, and unit symbol is m；

D is the distance of soil body moving focal point to tunnel central point, and unit symbol is m；

D=β r, unit symbol is m, and wherein β is the calculating parameter relevant with soil condition, and span is (0,1)；

Y is the transverse horizontal distance apart from tunnel axis, and unit symbol is m；

Z is vertical distance from the ground, is faced down as just, unit symbol is m by ground；

η is ground loss percentage rate, dimensionless；

G is equivalent ground loss parameter,Unit symbol is mm；

It is assumed that the right side tunnel of two-wire shield tunnel first excavates, then two-wire shield tunnel construction causes the calculating of vertical vibration Formula is:

$u_{zdouble}=u_{zsingle}(y-l/2,z)+u_{zsingle}(y+l/2+b,z)$

$\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 formula:

R is tunnel excavation radius, and unit symbol is m；

H is tunnel axis distance from the ground, and unit symbol is m；

Y is the transverse horizontal distance apart from tunnel axis, and unit symbol is m；

Z is vertical distance from the ground, is faced down as just, unit symbol is m by ground；

g_f、η_f、d_fThe equivalent ground loss parameter, ground loss percentage rate and the soil body moving focal point that are respectively leading tunnel are to tunnel The distance of road central point, η_fFor dimensionless group, g_f、d_fUnit symbol is respectively mm, m,

g_s、η_s、d_sAfter being respectively, the equivalent ground loss parameter in row tunnel, ground loss percentage rate and soil body moving focal point are to tunnel The distance of road central point, η_sFor dimensionless group, g_s、d_sUnit symbol is respectively mm, m,

λ_f、δ_f、b_fIt is respectively the calculating parameter in leading tunnel, and meet below equation:

${\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、δ_s、b_sThe calculating parameter in row tunnel after being respectively, and meet below equation:

${\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 be after row tunnel cause the soil body sedimentation axis deviant it is assumed that deflection leading tunnel side be just, unit symbol be m；

Step 2: by the computing formula of Wen Keer beam on elastic foundation subgrade reaction:

F=ku_z(3)；

In formula:

F subgrade reaction, unit symbol is kn/m；

K bedding value, unit symbol is kn/m²；

u_zThe vertical vibration that shield-tunneling construction causes, unit symbol is m；

The purpose of this step is that the ground settlement causing Shield Tunneling is converted into sedimentation counter-force and is added in and is simplified to flexibly On the building of Ji Liang；

Step 3: when being calculated with midas-gts, the section of beam is chosen for real flute length square-section, length-width ratio is 1.5:1；Bedding system Number k is taken as 15000kn/m³；The model of built beam is divided into after 20 equal portions, sets up sedimentation counter-force (dead load)；Using midas- The building settlement that gts software causes to sedimentation counter-force calculates, and draws the building settlement value that sedimentation counter-force causes, and paints Make ground settlement curve when considering building；

Step 4: during the consideration building that the ground settlement not considered during building that step 1 is calculated is calculated with step 3 Ground settlement be plotted in same figure upper it is known that what this computational methods caused to shield tunnel for the rigidity considering building The impact of building settlement has been reflected in the calculation of ground surface settlement result that step 3 calculates；

Step 5: above-mentioned result of calculation is compared with sedimentation benchmark, thus judging the safety of building.