CN105787193A - Method for calculating triangular resistance loads of shield tunnel model structure - Google Patents

Abstract

The invention discloses a method for calculating triangular resistance loads of a shield tunnel model structure.The method comprises the steps that S1, due to the fact that a pipe sheet structure calculating model belongs to a small-deformation linear elasticity problem, resistance displacement y at the horizontal diameter position of a tunnel ring can be regarded as superposition of horizontal deformation caused by loads except for triangular deformation and horizontal deformation caused by the triangular resistance loads, y is set to be equal to U(q1, qG, e1, e2, g, qw)-U(ky), all the parameter are substituted into the formula, and a correlation coefficient determined by back arch soil pressure qG is 0.3145; S2, based on correct arc-shaped back arch soil pressure derivation, the coefficient 0.3145 is substituted to the formula, and the set resistance displacement (see the formula in the description) at the horizontal diameter position of the tunnel ring can be obtained.Based on correct arc-shaped back arch soil pressure, the precise triangular resistance displacement calculating formula is derived, a basis is provided for correct calculation of the internal force of the shield tunnel model structure, and the technical problem that an existing triangular resistance displacement calculating formula does not conform to the tunnel back arch soil pressure shape is solved.

Description

The triangle drag load computational methods of shield tunnel model structure

Technical field

The present invention relates to the triangle drag load computational methods of a kind of shield tunnel model structure.

Background technology

Along with computer technology and the development of Computational Mechanics, current shield tunnel tunnel segment structure internal force calculates big Use modified routine method more.Modified routine method is a kind of two-dimensional structure computation model, and physical model can be flat Face two dimensional model or threedimensional model.

Modified routine method hypothetical model structure is elastic uniform plastid, it is considered to girth joint exists, annulus entirety Bending stiffness reduces, and taking annulus bending rigidity is η EI.The lotus that in modified routine method, tunnel model structure is subject to Carry as it is shown in figure 1, include top vertical earth pressure q₁, hogback soil pressure q_G, top/bottom part level is to soil pressure e₁With, lining cutting deadweight g, hydrostatic pressure q_w, vertical counter-force q in bottom₂, level is to triangle drag pp.

In above-mentioned load, level belongs to tunnel model structure by other active load actions to triangle drag PP Under be deformed and by the soil body produce by power, with other actively loads all have relation.Triangle drag pair The impact of shield tunnel model structure internal force is very big, and therefore the accurately calculating of triangle drag load is to shield The determination of tunnel duct piece internal force has important meaning.

Triangle drag PP is assumed in isosceles triangle, in the range from the upper and lower 45 ° of folders of tunnel horizontal axis Within angular region, power is calculated as follows:

$PP=ky(1-\sqrt{2}|cos\mathrm{\α}\left|\right)$

Wherein k is the resistance coefficient (kN/m of Tunnel Passing soil layer³), y is to become at tunnel annulus horizontal diameter Shape (m).

The calculating deforming y at tunnel annulus horizontal diameter is most important.Being given of existing specification and document Y computing formula is as follows:

$y=\frac{(2q_1+0.4292{\mathrm{\γ}}_t^{\′}{R}_H+{\mathrm{\π\γ}}_{c}t-e_1-e_2-\frac{\mathrm{\π}}{2}{\mathrm{\γ}}_w{R}_H)R_H^4}{24(\mathrm{\η}EI+0.0454{\mathrm{kR}}_H^4)}$

Whereinq₀For overcharge on ground standard value (kPa), γ_iWeight for each layer in top, tunnel soil Degree standard value (kN/m³), the above soil layer of level of ground water takes natural density, level of ground water following soil layer water and soil Divide and take buoyant weight degree, h when calculating_iThickness (m) for each layer in top, tunnel soil；

γ_t' for more than horizontal axis in Tunnel Passing soil layer each layer soil weighted average buoyant weight degree (kN/m³)；

R_HFor tunnel radius (m)；

γ_cFor section of jurisdiction material severe (kN/m³)；T is section of jurisdiction thickness (m)；

e₁=q₁tg²(45 ° of-φ/2)-2Ctg (45 ° of-φ/2), e₂=e₁+2γ’_t1R_Htg²(45 ° of-φ/2), γ '_t1For tunnel institute Pass through the weighted average severe standard value (kN/m of soil layer³), the above soil layer of level of ground water takes natural density, underground water The following soil layer in position takes buoyant weight degree；Weighted average cohesive strength standard value (kPa) of the passed through soil layer in C, φ respectively tunnel, Weighted average internal friction angle standard value (°)；

γ_wSevere (kN/m for water³)；

η is section of jurisdiction bending rigidity reduction coefficient；E is the elastic modelling quantity (kPa) of section of jurisdiction material；I is tunnel The moment of inertia (the m of section⁴)；

K is the resistance coefficient (kN/m of Tunnel Passing soil layer³)。

0.4292 γ in above-mentioned formula denominator_tR_HFor hogback soil pressure q_GCaused, δ coefficient 0.4292 therein Derivation be based on by arc hogback soil pressure equivalence rectangular load form principle draw.But, this The actual loading form of the load form that δ coefficient 0.4292 that sample is derived calculates and hogback soil pressure also differs Cause.

Therefore, the drag load computational methods of existing shield tunnel model structure can not reflect pipe exactly Sheet deformation and stressing conditions.

Summary of the invention

Because the drawbacks described above of prior art, the present invention provide one can reflect more accurately segment deformation and The triangle drag load computational methods of the shield tunnel model structure of force-bearing situation, comprising:

S1, the load that drag displacement y at tunnel annulus horizontal diameter is considered as in addition to triangle drag is caused Horizontal distortion and the superposition of horizontal distortion that causes of triangle drag load (due to tunnel segment structure computation model Belong to small deformation Linear Elasticity Problem, therefore can so set), i.e. set:

Y=U (q₁,q_G,e₁,e₂,g,q_w)-U (ky)-----formula (1)

Wherein, U (q₁,q_G,e₁,e₂,g,q_w) horizontal distortion that causes for load in addition to triangle drag, U (ky) The horizontal distortion caused for triangle drag load；q₁For top vertical earth pressure, q_GFor hogback soil pressure, e₁For top/bottom part level to soil pressure and, g be lining cutting deadweight, q_wFor hydrostatic pressure, bring each parameter into public affairs Formula (1), obtains hogback soil pressure q_GThe coefficient correlation determined is 0.3145；

S2, based on arc hogback soil pressure accurately derive, coefficient 0.3145 is brought into the tunnel annulus of setting Drag displacement y at horizontal diameter, obtains:

Whereinq₀For overcharge on ground standard value (kPa), γ_iSevere for each layer in top, tunnel soil Standard value (kN/m³), the above soil layer of level of ground water takes natural density, and level of ground water following soil layer water and soil takes when dividing calculation Buoyant weight degree, h_iThickness (m) for each layer in top, tunnel soil；

γ_t' for more than horizontal axis in Tunnel Passing soil layer each layer soil reinforcement average buoyant weight degree (kN/m³)；

R_HFor tunnel radius (m)；

γ_cFor section of jurisdiction material severe (kN/m³)；T is section of jurisdiction thickness (m)；

e₁=q₁tg²(45 ° of-φ/2)-2Ctg (45 ° of-φ/2), e₂=e₁+2γ’_t1R_Htg²(45 ° of-φ/2), γ '_t1For tunnel institute Pass through the weighted average severe standard value (kN/m of soil layer³), the above soil layer of level of ground water takes natural density, underground water The following soil layer in position takes buoyant weight degree；Weighted average cohesive strength standard value (kPa) of the passed through soil layer in C, φ respectively tunnel, Weighted average internal friction angle standard value (°)；

γ_wSevere (kN/m for water³)；

η is section of jurisdiction bending rigidity reduction coefficient；E is the elastic modelling quantity (kPa) of section of jurisdiction material；I is tunnel The moment of inertia (the m of section⁴)；

K is the resistance coefficient (kN/m of Tunnel Passing soil layer³)。

It is preferred that set: q₀=20kPa, h₀=0.5m, h=18m, and h_i=h-h₀；Substitute into

(in the present embodiment, according in computation model figure it can be seen that h_iRepresent water level Hereinafter arriving the thickness of tunnel top soil, possible soil layer property is different produces layering, false in the present embodiment If soil layer is uniform, being no longer layered, the above unit weight of level of ground water takes 18, and the following unit weight of level of ground water takes 10, Therefore substitute intoAvailable q₁=20+18 × 0.5+10 × (18-0.5)=204kPa)；

γ_i=18kN/m³(more than water level)；

γ_t'=10kN/m³,

R_H=6.95m,

γ_c=25kN/m³,

T=0.6m,

C=19.8kPa, φ=17.7 °,

γ’_t1=10kN/m³,

γ_w=10kN/m³,

η=0.7, E=3.6e7kPa, I=0.018m⁴,

K=6200kN/m³,

The occurrence of above-mentioned parameter is substituted into the based on the derivation of arc hogback soil pressure accurately anti-of above-mentioned setting In the computing formula (2) of power displacement y, draw: y=11.8mm.

Beneficial effects of the present invention:

1, use the calculated structural internal force of drag displacement accurately more accurate, and make model structure design Safer.

2, the present invention based on arc hogback soil pressure accurately derived accurate triangle drag displacement calculate Formula, provides the foundation for accurately calculating of shield tunnel model structure internal force, solves existing triangle The technical barrier that shape drag displacement computing formula is not inconsistent with tunnel hogback soil pressure shape.

3. the present invention provides the foundation for accurately solving shield tunnel segment inner force.

Below with reference to accompanying drawing, the technique effect of design, concrete structure and the generation of the present invention is made furtherly Bright, to be fully understood from the purpose of the present invention, feature and effect.

Accompanying drawing explanation

Fig. 1 is the computation model figure of modified routine method.

Detailed description of the invention

Enumerate preferred embodiment below, and combine accompanying drawing and become apparent from intactly illustrating the present invention.

Embodiment

The triangle drag load computational methods of the shield tunnel model structure that the present embodiment provides, including following Step:

S1, belong to small deformation Linear Elasticity Problem due to tunnel segment structure computation model, therefore can be by tunnel annulus level Horizontal distortion that the load that at diameter, drag displacement y is considered as in addition to triangle drag causes and triangle drag The superposition of the horizontal distortion that load causes, it may be assumed that

Y=U (q₁,q_G,e₁,e₂,g,q_w)-U (ky)-----formula (1)

Wherein, U (q₁,q_G,e₁,e₂,g,q_w) horizontal distortion that causes for load in addition to triangle drag, U (k δ) is the horizontal distortion that triangle drag load causes；q₁For top vertical earth pressure, q_GFor hogback soil Pressure, e₁For top/bottom part level to soil pressure and, g be lining cutting deadweight, q_wFor hydrostatic pressure, by each parameter Bring formula (1) into, obtain hogback soil pressure q_GThe coefficient correlation determined is 0.3145；

S2, based on arc hogback soil pressure accurately derive, coefficient 0.3145 is brought into the tunnel annulus of setting Drag displacement y at horizontal diameter, obtains:

Whereinq₀For overcharge on ground standard value (kPa), γ_iSevere for each layer in top, tunnel soil Standard value (kN/m³), the above soil layer of level of ground water takes natural density, and level of ground water following soil layer water and soil takes when dividing calculation Buoyant weight degree, h_iThickness (m) for each layer in top, tunnel soil；

γ_t' for more than horizontal axis in Tunnel Passing soil layer each layer soil reinforcement average buoyant weight degree (kN/m³)；

R_HFor tunnel radius (m)；

γ_cFor section of jurisdiction material severe (kN/m³)；T is section of jurisdiction thickness (m)；

e₁=q₁tg²(45 ° of-φ/2)-2Ctg (45 ° of-φ/2), e₂=e₁+2γ’_t1R_Htg²(45 ° of-φ/2), γ '_t1For tunnel institute Pass through the weighted average severe standard value (kN/m of soil layer³), the above soil layer of level of ground water takes natural density, underground water The following soil layer in position takes buoyant weight degree；Weighted average cohesive strength standard value (kPa) of the passed through soil layer in C, φ respectively tunnel, Weighted average internal friction angle standard value (°)；

γ_wSevere (kN/m for water³)；

η is section of jurisdiction bending rigidity reduction coefficient；E is the elastic modelling quantity (kPa) of section of jurisdiction material；I is tunnel The moment of inertia (the m of section⁴)；

K is the resistance coefficient (kN/m of Tunnel Passing soil layer³)。

Below in conjunction with concrete calculating parameter, the invention will be further described:

Set a certain shield tunnel model structure calculating parameter as follows:

q₀=20kPa, h₀=0.5m, h=18m, and h_i=h-h₀；

In the present embodiment, according in computation model figure it can be seen that h_iRepresent below water level to tunnel top The thickness of the layer, possible soil layer property is different produces layering, assumes that soil layer is uniform, no in the present embodiment Being layered, the above unit weight of level of ground water takes 18 again, and the following unit weight of level of ground water takes 10,

Therefore substitute intoAvailable

q₁=20+18 × 0.5+10 × (18-0.5)=204kPa；

γ_i=18kN/m³(more than water level)；

γ_t'=10kN/m³,

R_H=6.95m,

γ_c=25kN/m³,

T=0.6m,

C=19.8kPa, φ=17.7 °

γ’_t1=10kN/m³,

γ_w=10kN/m³,

η=0.7, E=3.6e7kPa, I=0.018m⁴,

K=6200kN/m³,

The occurrence of above-mentioned parameter is substituted in the formula (2) that the above-mentioned drag displacement y of the present invention calculates, Arrive: y=11.8mm, and use the drag displacement y formula calculated drag displacement in traditional literature Y=12.4mm.

Contrast understands, and is respectively adopted in the drag displacement calculating tunnel model structure that above-mentioned different formulas obtains Power, when using drag displacement accurately, calculated structure Maximum bending moment calculates than traditional formula It is worth big 5.6%.Therefore use the calculated structural internal force of drag displacement accurately more accurate, and make structure set Count safer.

Additionally, use the calculated structural internal force of drag displacement accurately more accurate, and structure is made to design more Content to retain sovereignty over a part of the country entirely.

Further, this invention also solves triangle drag displacement computing formula and tunnel hogback soil pressure shape The contradiction that shape is not inconsistent, provides stronger basis for accurately solving shield tunnel segment inner force.

The preferred embodiment of the present invention described in detail above.Should be appreciated that the ordinary skill of this area Personnel just can make many modifications and variations according to the design of the present invention without creative work.Therefore, all Technical staff passes through logic analysis the most on the basis of existing technology, pushes away in the art Reason or the limited available technical scheme of experiment, all should be at the protection model being defined in the patent claims In enclosing.

Claims (2)

1. the triangle drag load computational methods of a shield tunnel model structure, it is characterised in that its Including:

S1, the load that drag displacement y at tunnel annulus horizontal diameter is considered as in addition to triangle drag is caused Horizontal distortion and the superposition of horizontal distortion that causes of triangle drag load, i.e. set:

Y=U (q₁,q_G,e₁,e₂,g,q_w)-U (ky),

Wherein, U (q₁,q_G,e₁,e₂,g,q_w) horizontal distortion that causes for load in addition to triangle drag, U (ky) is the horizontal distortion that triangle drag load causes；q₁For top vertical earth pressure, q_GFor hogback soil pressure Power, e₁For top/bottom part level to soil pressure and, g be lining cutting deadweight, q_wFor hydrostatic pressure；Each parameter is brought into Formula 1, obtains hogback soil pressure q_GThe coefficient correlation determined is 0.3145；

S2, based on arc hogback soil pressure accurately derive, coefficient 0.3145 is brought into the tunnel annulus of setting Drag displacement y at horizontal diameter, obtains:

$y=\frac{(2q_1+0.3145{\mathrm{\γ}}_t^{\′}{R}_H+{\mathrm{\π\γ}}_{c}t-e_1-e_2-\frac{\mathrm{\π}}{2}{\mathrm{\γ}}_w{R}_H)R_H^4}{24(\mathrm{\η}EI+0.0454{\mathrm{kR}}_H^4)},$

Whereinq₀For overcharge on ground standard value, γ_iFor each layer in top, tunnel soil severe standard value, The above soil layer of level of ground water takes natural density, and level of ground water following soil layer water and soil takes buoyant weight degree, h when dividing calculation_iFor top, tunnel The thickness of each layer soil；

γ′_tReinforcement average buoyant weight degree for more than horizontal axis in Tunnel Passing soil layer each layer soil；

R_HFor tunnel radius；

γ_cFor section of jurisdiction material severe；T is section of jurisdiction thickness；

e₁=q₁tg²(45 ° of-φ/2)-2Ctg (45 ° of-φ/2), e₂=e₁+2γ′_t1R_Htg²(45 ° of-φ/2), γ '_t1For tunnel institute Passing through the weighted average severe standard value of soil layer, the above soil layer of level of ground water takes natural density, the following soil layer of level of ground water Take buoyant weight degree；Friction in the weighted average cohesive strength standard value of the passed through soil layer in C, φ respectively tunnel, weighted average Angle standard value；

γ_wSevere for water；

η is section of jurisdiction bending rigidity reduction coefficient；E is the elastic modelling quantity of section of jurisdiction material；I is the used of tunnel cross-section Property square；

K is the resistance coefficient of Tunnel Passing soil layer.

2. the triangle drag load computational methods of shield tunnel model structure as claimed in claim 1, It is characterized in that, set: q₀=20kPa, h₀=0.5m, h=18m, and h_i=h-h₀, substitute into

γ_i=18kN/m³,

γ′_t=10kN/m³,

R_H=6.95m,

γ_c=25kN/m³,

T=0.6m,

C=19.8kPa, φ=17.7 °,

γ′_t1=10kN/m³,

γ_w=10kN/m³,

η=0.7, E=3.6e7kPa, I=0.018m⁴,

K=6200kN/m³,

The occurrence of above-mentioned parameter is substituted into the based on the derivation of arc hogback soil pressure accurately anti-of above-mentioned setting Power displacement computing formula, draws: y=11.8mm.