CN107657091A - The computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement - Google Patents

The computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement Download PDF

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CN107657091A
CN107657091A CN201710821034.0A CN201710821034A CN107657091A CN 107657091 A CN107657091 A CN 107657091A CN 201710821034 A CN201710821034 A CN 201710821034A CN 107657091 A CN107657091 A CN 107657091A
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CN107657091B (en
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王海龙
武志辉
董捷
杨越
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Hebei University of Architecture
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Abstract

The invention discloses a kind of computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement, comprise the following steps：（ⅰ）Calculate heavy haul train operation and act on the vertical concentrated force of tunnel railway roadbed；（ⅱ）Calculate tunnel bottom displacement under High-speed Train Loads；（ⅲ）It is determined that influenceed newly-built Under-cross tunnel edge stress state by train load；（ⅳ）Calculate existing tunnel tunnel bottom displacement caused by Under-cross tunnel excavation；（ⅴ）Calculate and consider existing tunnel tunnel bottom displacement under train load influence and Under-cross tunnel excavation effect.The present invention to transposition section country rock by carrying out force analysis, consider heavy haul train additional load, existing tunnel structural strength, rock mass strength characteristic, cross tunnel buried depth, cross tunnel interlayer rock pillar height, analysis calculates small interval heavy haul railway cross tunnel tunnel bottom shift value, the consolidating settlement amount of established tunnel in Tunnel Passing engineering can be better anticipated, so as to meet the needs of existing tunnel normal operation and newly built tunnels safe construction.

Description

The computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement
Technical field
The invention belongs to a kind of computational methods of tunnel tunnel bottom displacement, and in particular to a kind of small interval heavy haul railway intersects tunnel The computational methods of road tunnel bottom displacement.
Background technology
With the increase year by year of China's transit's routes density, all kinds of excessive risk cross tunnels increase year by year.Wherein, small interval It is new to intersect pars infrasegmentalis because of the influence of the factors such as top heavy haul train axle is great, impact load amplitude height for heavy haul railway cross tunnel Built tunnel construction will produce greater risk to the existing heavy haul railway safe operation in top.Generally, by studying existing tunnel The displacement deformation rule of road structure can effectively judge tunnel overall security with objective.At present, it is heavy on existing tunnel deformation The main influence for considering the factors such as newly built tunnels construction, edpth of tunnel and periphery ground formation parameter of research of drop prediction, Draw the tunnel deformation settlement prediction formula by the amendment of empirical parameter.It is pointed out that in Under-cross tunnel neighboring tunneling During, influenceed by top tunnel heavy haul train load, transposition section force-bearing of surrounding rock mass state settles complex, tunnel deformation Amount can be further exacerbated by.Therefore, if consider that heavy haul train additional load will directly affect and existing tunnel displacement structure is deformed The accuracy of predicted value, it is related to the security of cross tunnel crossing project.Because existing research is handed over small interval heavy haul railway Fork tunnel tunnel bottom displacement does not provide simple, fast Forecasting Methodology, and the calculating of existing tunnel structure sediment is not examined mostly at present Consider the heavy haul train additional load that tunnel intersection is subject to, cause existing tunnel displacement settling amount to calculate reliability deficiency, it is existing The safe construction of the normal operation in tunnel and newly-built Under-cross tunnel cannot get effective guarantee.
The content of the invention
The present invention proposes that the purpose is to provide a kind of small interval weight in order to overcome shortcoming present in prior art Carry the computational methods of railway cross tunnel tunnel bottom displacement.
The technical scheme is that：
A kind of computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement, comprise the following steps：
(I) calculates heavy haul train operation and acts on the vertical concentrated force F of tunnel railway roadbedt(S1)；
(II) calculates tunnel bottom displacement components u under High-speed Train Loads1(S2)；
(III) determines to be influenceed newly-built Under-cross tunnel edge stress state (S3) by train load；
(IV) calculates existing tunnel tunnel bottom displacement components u caused by Under-cross tunnel excavation2(S4)；
(V), which calculates, considers existing tunnel tunnel bottom displacement components u under train load influence and Under-cross tunnel excavation effectd(S5)。
The vertical concentrated force FtCalculation formula be：
Ft=γ1·a·b
In formula：γ1For the earth pillar severe that converts；A is conversion earth pillar height；B is conversion earth pillar width.
Tunnel bottom, which is displaced through, under the High-speed Train Loads calculates vertical concentrated force FtAct on lower tunnel bottom stress state and hang down Straight concentrated force FtThe lower tunnel bottom displacement components u of effect1Obtain.
Tunnel bottom stress state is under the vertical concentrated force effect：
The lower tunnel bottom displacement components u of vertical concentrated force effect1Calculation formula be：
In formula：EtFor existing tunnel structure modulus of elasticity；d1Under being acted on for concentrated force no displacement point and concentrated force it is vertical away from From；r1Existing tunnel railway roadbed top layer and tunnel dolly are taken to distance l1。
The determination is influenceed newly-built Under-cross tunnel edge stress state by train load includes vertical stress and lateral stress, Obtained especially by following steps：
(a) train load is calculated to Under-cross tunnel country rock vertical attached power
In formula：r1By way of bed top layer and the vertical distance l in interlayer center2；
(b) newly-built Under-cross tunnel buried depth is calculated
H=h1+h2+h3+R0
In formula：h1For existing tunnel buried depth；h2For existing tunnel height；h3For cross tunnel country rock band height；R0To be new Built tunnel radius；
(c) Under-cross tunnel country rock stress of primary rock state is calculated
P0=γ2·H
In formula：γ2For country rock severe；
(d) newly-built Under-cross tunnel periphery vertical stress is calculated
(e) newly-built Under-cross tunnel periphery lateral stress is calculated
In formula：λ is rock static lateral pressure coefficient.
The existing tunnel tunnel bottom is displaced through following steps acquisition：
(a) existing tunnel tunnel bottom stress state under Under-cross tunnel excavation effect is calculated
(b) calculate and lower existing tunnel tunnel bottom displacement components u is acted under Under-cross tunnel excavation effect2
In formula：EsFor elastic modulus of rock；υ is Rock Poisson Ratio Using；d2No displacement point and tunnel under being acted on for tunnel excavation Centre distance；r2Under-cross tunnel center and existing tunnel tunnel dolly are taken to distance l3。
The calculation formula of the existing tunnel tunnel bottom displacement is：ud=u1+u2；
Calculated value udAs consider that heavy haul train load influences existing tunnel tunnel bottom total displacement caused by Under-cross tunnel excavation Value.
The beneficial effects of the invention are as follows：
The invention provides a kind of computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement, heavy haul train is established Load action lower plane analysis model and newly built tunnels excavate coffer mechanics analysis model；By carrying out stress to transposition section country rock Analysis, consider heavy haul train additional load, existing tunnel structural strength, rock mass strength characteristic, cross tunnel buried depth, cross tunnel Interlayer rock pillar height, more comprehensively, more reasonably considers heavy haul train load and newly built tunnels excavate transposition section under collective effect Force-bearing of surrounding rock mass deformation characteristicses, analysis calculates small interval heavy haul railway cross tunnel tunnel bottom shift value, to meet small interval heavy duty iron The needs of road cross tunnel normal operation.The consolidating settlement of established tunnel in Tunnel Passing engineering can be better anticipated in the present invention Amount, so as to meet the needs of existing tunnel normal operation and newly built tunnels safe construction.
Brief description of the drawings
Fig. 1 is that the displacement of small interval heavy haul railway cross tunnel tunnel bottom calculates method flow schematic diagram.
Fig. 2 is the equivalent concentrated force two dimensional analysis model of heavy haul train conversion.
Fig. 3 is train Concentrated load tunnel bottom displacement computation model.
Fig. 4 is that Under-cross tunnel excavation causes existing tunnel tunnel bottom displacement plane computation model.
Wherein：
1st, existing tunnel inverted arch structure 2, existing tunnel railway roadbed top layer
3rd, tunnel bottom displacement prediction line 4, newly-built Under-cross tunnel
5th, transposition section country rock interlayer center line 6, existing tunnel vault hatching
Embodiment
Meter with reference to Figure of description and embodiment to small interval heavy haul railway cross tunnel tunnel bottom displacement of the present invention Calculation method is described in detail：
As shown in figure 1, a kind of computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement, comprise the following steps：
(I) calculates heavy haul train operation and acts on the vertical concentrated force F of tunnel railway roadbedt(S1)；
(II) calculates tunnel bottom displacement components u under High-speed Train Loads1(S2)；
(III) determines to be influenceed newly-built Under-cross tunnel edge stress state (S3) by train load；
(IV) calculates existing tunnel tunnel bottom displacement components u caused by Under-cross tunnel excavation2(S4)；
(V), which calculates, considers existing tunnel tunnel bottom displacement components u under train load influence and Under-cross tunnel excavation effectd(S5)。
The vertical concentrated force FtCalculation formula be：
Ft=γ1·a·b
In formula：γ1For the earth pillar severe that converts；A is conversion earth pillar height；B is conversion earth pillar width.
Tunnel bottom, which is displaced through, under the High-speed Train Loads calculates vertical concentrated force FtAct on lower tunnel bottom stress state and hang down Straight concentrated force FtThe lower tunnel bottom displacement components u of effect1Obtain.
Tunnel bottom stress state is under the vertical concentrated force effect：
The lower tunnel bottom displacement components u of vertical concentrated force effect1Calculation formula be：
In formula：EtFor existing tunnel structure modulus of elasticity；d1Under being acted on for concentrated force no displacement point and concentrated force it is vertical away from From；r1Existing tunnel railway roadbed top layer and tunnel dolly are taken to distance l1。
The determination is influenceed newly-built Under-cross tunnel edge stress state by train load includes vertical stress and lateral stress, Obtained especially by following steps：
(a) train load is calculated to Under-cross tunnel country rock vertical attached power
In formula：r1By way of bed top layer and the vertical distance l in interlayer center2；
(b) newly-built Under-cross tunnel buried depth is calculated
H=h1+h2+h3+R0
In formula：h1For existing tunnel buried depth；h2For existing tunnel height；h3For cross tunnel country rock band height；R0To be new Built tunnel radius；
(c) Under-cross tunnel country rock stress of primary rock state is calculated
P0=γ2·H
In formula：γ2For country rock severe；
(d) newly-built Under-cross tunnel periphery vertical stress is calculated
(e) newly-built Under-cross tunnel periphery lateral stress is calculated
In formula：λ is rock static lateral pressure coefficient.
The existing tunnel tunnel bottom is displaced through following steps acquisition：
(a) existing tunnel tunnel bottom stress state under Under-cross tunnel excavation effect is calculated
(b) calculate and lower existing tunnel tunnel bottom displacement components u is acted under Under-cross tunnel excavation effect2
In formula：EsFor elastic modulus of rock；υ is Rock Poisson Ratio Using；d2No displacement point and tunnel under being acted on for tunnel excavation Centre distance；r2Under-cross tunnel center and existing tunnel tunnel dolly are taken to distance l3。
The calculation formula of the existing tunnel tunnel bottom displacement is：ud=u1+u2；
Calculated value udAs consider that heavy haul train load influences existing tunnel tunnel bottom total displacement caused by Under-cross tunnel excavation Value.
Embodiment 1
The basic parameter of example sets as follows：
30t heavy haul train loads earth pillar conversion severe γ1=18kN/m3, earth pillar reduced height a=4.1m, soil
Post conversion width b=5.0m
Existing tunnel structure modulus of elasticity Et=3.0 × 107kPa
No displacement point and the vertical distance d in railway roadbed top layer under the effect of train concentrated force1=26m
Existing tunnel railway roadbed top layer and tunnel dolly are to distance l1=2m
Existing tunnel railway roadbed top layer and the vertical distance l in country rock interlayer center2=10.20m.
Existing tunnel buried depth h1=70m；Existing tunnel height h2=11.2m；Cross tunnel country rock band height
h3=16.39m；Newly built tunnels radius R0=7.04m
Country rock severe γ2=25kN/m3
Rock static lateral pressure coefficient λ=1.0
Elastic modulus of rock Es=2.5 × 107kPa
Rock Poisson Ratio Using υ=0.3
No displacement point and tunnel centre distance d under tunnel excavation effect2=6R0=42.24m
Under-cross tunnel center and existing tunnel tunnel dolly are to distance l3=R0+h3=23.43m
Specific calculating analytical procedure is as follows：
S1：Calculate heavy haul train operation and act on the vertical concentrated force F of tunnel railway roadbedt, analysis model is as shown in Figure 2；
Determine that heavy haul train acts on vertical concentrated force Ft=γ1Ab=18 × 4.1 × 5=369kN/m
S2：Calculate existing tunnel tunnel bottom displacement μ under High-speed Train Loads1
Calculate the vertical lower existing tunnel tunnel bottom stress state of concentrated force effect
Calculate the vertical lower existing tunnel tunnel bottom displacement components u of concentrated force effect1
S3：It is determined that being influenceed newly-built Under-cross tunnel edge stress state by train load, computation model is as shown in Figure 3；
Train load is calculated to Under-cross tunnel country rock vertical attached power
Calculate newly-built Under-cross tunnel buried depth
H=h1+h2+h3+R0=70+11.2+16.39+7.04=104.63m
Calculate Under-cross tunnel country rock stress of primary rock state
P0=γ2H=25 × 104.63=2620kPa
Calculate newly-built Under-cross tunnel periphery vertical stress
Calculate newly-built Under-cross tunnel periphery lateral stress
S4:Calculate existing tunnel tunnel bottom displacement components u caused by Under-cross tunnel excavation2, computation model is as shown in Figure 4；
Calculate existing tunnel tunnel bottom stress state under Under-cross tunnel excavation effect
Calculate existing tunnel tunnel bottom displacement components u under Under-cross tunnel excavation effect2
S5:Calculate and consider existing tunnel tunnel bottom displacement under train load influence and Under-cross tunnel excavation effect
ud=u1+u2=2.0 × 10-5+1.21×10-4=1.41 × 10-4m
It is 1.41 to consider heavy haul train load to influence across existing tunnel tunnel bottom total displacement value on caused by Under-cross tunnel excavation ×10-4m。

Claims (8)

  1. A kind of 1. computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement, it is characterised in that：Comprise the following steps：
    (I) calculates heavy haul train operation and acts on the vertical concentrated force F of tunnel railway roadbedt(S1)；
    (II) calculates tunnel bottom displacement components u under High-speed Train Loads1(S2)；
    (III) determines to be influenceed newly-built Under-cross tunnel edge stress state (S3) by train load；
    (IV) calculates existing tunnel tunnel bottom displacement components u caused by Under-cross tunnel excavation2(S4)；
    (V), which calculates, considers existing tunnel tunnel bottom displacement components u under train load influence and Under-cross tunnel excavation effectd(S5)。
  2. 2. a kind of computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement according to claim 1, its feature It is：The vertical concentrated force FtCalculation formula be：
    Ft=γ1·a·b
    In formula：γ1For the earth pillar severe that converts；A is conversion earth pillar height；B is conversion earth pillar width.
  3. 3. a kind of computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement according to claim 1, its feature It is：Tunnel bottom, which is displaced through, under the High-speed Train Loads calculates vertical concentrated force FtThe lower tunnel bottom stress state of effect and vertical collection Middle power FtThe lower tunnel bottom displacement components u of effect1Obtain.
  4. 4. a kind of computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement according to claim 3, its feature It is：Tunnel bottom stress state is under the vertical concentrated force effect：
    <mrow> <msub> <mi>&amp;sigma;</mi> <msub> <mi>r</mi> <mn>1</mn> </msub> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>F</mi> <mi>t</mi> </msub> </mrow> <mrow> <msub> <mi>&amp;pi;r</mi> <mn>1</mn> </msub> </mrow> </mfrac> <mo>.</mo> </mrow>
    <mrow> <msub> <mi>&amp;sigma;</mi> <msub> <mi>h</mi> <mn>1</mn> </msub> </msub> <mo>=</mo> <mn>0</mn> </mrow>
  5. 5. a kind of computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement according to claim 3, its feature It is：The lower tunnel bottom displacement components u of vertical concentrated force effect1Calculation formula be：
    <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>F</mi> <mi>t</mi> </msub> </mrow> <mrow> <msub> <mi>&amp;pi;E</mi> <mi>t</mi> </msub> </mrow> </mfrac> <mi>ln</mi> <mfrac> <msub> <mi>d</mi> <mn>1</mn> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> </mfrac> </mrow>
    In formula：EtFor existing tunnel structure modulus of elasticity；d1No displacement point and the vertical distance of concentrated force under being acted on for concentrated force； r1Existing tunnel railway roadbed top layer and tunnel dolly are taken to distance l1。
  6. 6. a kind of computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement according to claim 1, its feature It is：The determination is influenceed newly-built Under-cross tunnel edge stress state by train load includes vertical stress and lateral stress, has Body is obtained by following steps：
    (a) train load is calculated to Under-cross tunnel country rock vertical attached power
    <mrow> <msub> <mi>&amp;sigma;</mi> <msub> <mi>r</mi> <mn>1</mn> </msub> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>F</mi> <mi>t</mi> </msub> </mrow> <mrow> <msub> <mi>&amp;pi;r</mi> <mn>1</mn> </msub> </mrow> </mfrac> </mrow>
    In formula：r1By way of bed top layer and the vertical distance l in interlayer center2；
    (b) newly-built Under-cross tunnel buried depth is calculated
    H=h1+h2+h3+R0
    In formula：h1For existing tunnel buried depth；h2For existing tunnel height；h3For cross tunnel country rock band height；R0For newly-built tunnel Road radius；
    (c) Under-cross tunnel country rock stress of primary rock state is calculated
    P0=γ2·H
    In formula：γ2For country rock severe；
    (d) newly-built Under-cross tunnel periphery vertical stress is calculated
    <mrow> <msub> <mi>P</mi> <mi>z</mi> </msub> <mo>=</mo> <msub> <mi>P</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>&amp;sigma;</mi> <msub> <mi>r</mi> <mn>1</mn> </msub> </msub> </mrow>
    (e) newly-built Under-cross tunnel periphery lateral stress is calculated
    <mrow> <msub> <mi>P</mi> <msub> <mi>h</mi> <mn>2</mn> </msub> </msub> <mo>=</mo> <msub> <mi>&amp;lambda;P</mi> <mi>z</mi> </msub> </mrow>
    In formula：λ is rock static lateral pressure coefficient.
  7. 7. a kind of computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement according to claim 1, its feature It is：The existing tunnel tunnel bottom is displaced through following steps acquisition：
    (a) existing tunnel tunnel bottom stress state under Under-cross tunnel excavation effect is calculated
    <mrow> <msub> <mi>&amp;sigma;</mi> <msub> <mi>r</mi> <mn>2</mn> </msub> </msub> <mo>=</mo> <mfrac> <msub> <mi>P</mi> <mi>z</mi> </msub> <mn>2</mn> </mfrac> <mo>&amp;lsqb;</mo> <mn>2</mn> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>-</mo> <mn>3</mn> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mfrac> <msubsup> <mi>R</mi> <mn>0</mn> <mn>2</mn> </msubsup> <msubsup> <mi>r</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mfrac> <mo>+</mo> <mn>3</mn> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mfrac> <msubsup> <mi>R</mi> <mn>0</mn> <mn>4</mn> </msubsup> <msubsup> <mi>r</mi> <mn>2</mn> <mn>4</mn> </msubsup> </mfrac> <mo>&amp;rsqb;</mo> </mrow>
    <mrow> <msub> <mi>&amp;sigma;</mi> <msub> <mi>h</mi> <mn>2</mn> </msub> </msub> <mo>=</mo> <mfrac> <msub> <mi>P</mi> <mi>z</mi> </msub> <mn>2</mn> </mfrac> <mo>&amp;lsqb;</mo> <mn>2</mn> <mi>&amp;lambda;</mi> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mfrac> <msubsup> <mi>R</mi> <mn>0</mn> <mn>2</mn> </msubsup> <msubsup> <mi>r</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mfrac> <mo>+</mo> <mn>3</mn> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mfrac> <msubsup> <mi>R</mi> <mn>0</mn> <mn>4</mn> </msubsup> <msubsup> <mi>r</mi> <mn>2</mn> <mn>4</mn> </msubsup> </mfrac> <mo>&amp;rsqb;</mo> </mrow>
    (b) calculate and lower existing tunnel tunnel bottom displacement components u is acted under Under-cross tunnel excavation effect2
    <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>&amp;upsi;</mi> <mo>)</mo> <msub> <mi>P</mi> <mi>z</mi> </msub> </mrow> <mrow> <mn>2</mn> <msub> <mi>E</mi> <mi>s</mi> </msub> </mrow> </mfrac> <mfenced open = "{" close = "}"> <mtable> <mtr> <mtd> <mo>&amp;lsqb;</mo> <mn>4</mn> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;lambda;</mi> <mo>)</mo> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;upsi;</mi> <mo>)</mo> <mo>+</mo> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>&amp;lambda;</mi> <mo>)</mo> <mo>&amp;rsqb;</mo> <mo>(</mo> <mfrac> <msubsup> <mi>R</mi> <mn>0</mn> <mn>2</mn> </msubsup> <msub> <mi>r</mi> <mn>2</mn> </msub> </mfrac> <mo>-</mo> <mfrac> <msubsup> <mi>R</mi> <mn>0</mn> <mn>2</mn> </msubsup> <msub> <mi>d</mi> <mn>2</mn> </msub> </mfrac> <mo>)</mo> <mo>-</mo> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;lambda;</mi> <mo>)</mo> <mo>(</mo> <mfrac> <msubsup> <mi>R</mi> <mn>0</mn> <mn>4</mn> </msubsup> <msubsup> <mi>r</mi> <mn>2</mn> <mn>3</mn> </msubsup> </mfrac> <mo>-</mo> <mfrac> <msubsup> <mi>R</mi> <mn>0</mn> <mn>4</mn> </msubsup> <msubsup> <mi>d</mi> <mn>2</mn> <mn>3</mn> </msubsup> </mfrac> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> <mn>2</mn> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;upsi;</mi> <mo>-</mo> <mi>&amp;lambda;</mi> <mi>&amp;upsi;</mi> <mo>+</mo> <mfrac> <msub> <mi>P</mi> <mn>0</mn> </msub> <msub> <mi>P</mi> <mi>z</mi> </msub> </mfrac> <mo>(</mo> <mn>2</mn> <mi>&amp;upsi;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> <mo>&amp;rsqb;</mo> <mo>(</mo> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> </mrow>
    In formula：EsFor elastic modulus of rock；υ is Rock Poisson Ratio Using；d2No displacement point and tunnel center under being acted on for tunnel excavation Distance；r2Under-cross tunnel center and existing tunnel tunnel dolly are taken to distance l3。
  8. 8. a kind of computational methods of small interval heavy haul railway cross tunnel tunnel bottom displacement according to claim 1, its feature It is：The calculation formula of the existing tunnel tunnel bottom displacement is：ud=u1+u2；
    Calculated value udAs consider that heavy haul train load influences existing tunnel tunnel bottom total displacement value caused by Under-cross tunnel excavation.
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