CN102704947B - Method for designing thickness of underwater tunnel subsurface excavated construction grouting reinforcement ring - Google Patents

Abstract

The invention discloses a method for designing the thickness of an underwater tunnel subsurface excavated construction grouting reinforcement ring. The method is characterized by comprising the following steps of: 1, selecting a group of reinforcement ring thickness parameters, and calculating the stability factors of a tunnel construction working surface under different reinforcement ring thickness conditions; 2, obtaining a reinforcement ring thickness-stability factor regression curve according to a least squares method based on different reinforcement ring thicknesses and corresponding stability factors; and 3, obtaining a reinforcement ring thickness required by a tunnel under a certain designed stability factor condition according to the reinforcement ring thickness-stability factor regression curve. A reinforcement ring thickness is obtained with the method for designing the thickness of the underwater tunnel subsurface excavated construction grouting reinforcement ring, so the field engineering construction requirements can be met, the construction safety of the tunnel can be ensured, and the engineering cost can be reduced.

Description

A kind of method for designing of submerged tunnel tunneling construction grouting and reinforcing circle thickness

Technical field

The present invention relates to a kind of method for designing of submerged tunnel tunneling construction grouting and reinforcing circle thickness.

Background technology

When submerged tunnel adopts Mining Method to construct; for preventing that the engineering accidents such as gushing water caves in from appearring in excavation face; in construction, conventionally adopt pre-grouting to carry out pre-reinforcement, then under the protection of grouting and reinforcing circle, carry out tunnel excavation, to guarantee the construction safety of submerged tunnel.But, for the design of submerged tunnel pre-grouting reinforcing parameter, mainly still on the basis of experience, by engineering analog method, undertaken both at home and abroad at present, relevant highway and railway Tunnel Design standard does not relate to completely to submerged tunnel grouting and reinforcing circle thickness how to confirm.In actual submerged tunnel engineering design, determining of grouting and reinforcing parameter often judged according to design engineer's personal experience, for the grouting design parameter adopting, whether can guarantee the needs of tunnel safety construction completely, or whether definite grouting parameter is too conservative, its safety factor has much, comprises that design engineer oneself cannot determine.Therefore, on the one hand in design for guaranteeing safety, design engineer is the thickness of increasing grouting and reinforcing circle simply often, to guarantee the construction safety in tunnel, thereby has increased the construction costs in tunnel; On the other hand, owing to lacking effective analysis and design method, cannot design targetedly according to the geological conditions in tunnel, bed rearrangement tunnel often adopts identical grouting and reinforcing design parameters, makes submerged tunnel have again certain construction risk in geology weak location such as fault belt.

On the whole, the design of submerged tunnel grouting and reinforcing circle thickness also rests on the basis of experience at present, cannot meet China's submerged tunnel and build fast-developing needs.

Therefore, develop a kind of novel quantification submerged tunnel grouting and reinforcing circle thickness method for designing for be badly in need of.

Summary of the invention

Technical problem to be solved by this invention is to provide a kind of method for designing of submerged tunnel tunneling construction grouting and reinforcing circle thickness, the fixing collar thickness that adopts the method for designing of this submerged tunnel tunneling construction grouting and reinforcing circle thickness to obtain more can meet field engineering construction requirement, thereby the construction safety that can guarantee on the one hand tunnel, also can reduce construction costs on the other hand.

The technical solution of invention is as follows:

A method for designing for submerged tunnel tunneling construction grouting and reinforcing circle thickness, comprises the following steps:

Step 1: choose one group of fixing collar thickness parameter, calculate the coefficient of stability of constructing tunnel work plane under different fixing collar thickness condition;

Step 2: based on different fixing collar thickness and the corresponding coefficient of stability, according to least square method, obtain fixing collar thickness-coefficient of stability regression curve;

Step 3: according to this fixing collar thickness-coefficient of stability regression curve, can obtain the required fixing collar thickness in tunnel under the coefficient of stability condition of a certain design.

In step 1, the coefficient of stability that a certain fixing collar thickness is corresponding adopts following methods to calculate:

(1) calculate pressure from surrounding rock q;

1. H≤equivalent load height h _qtime,

q=γ·H；

In formula: γ is tunnel above rock severe; H is edpth of tunnel, refers to the distance of tunnel vault to ground;

2. equivalent load height h _q< H < is dark, shallow tunnel boundary depth H _ptime,

$q=\mathrm{\&gamma;H}(1-\frac{H}{2B}\mathrm{\&lambda;tg\&theta;}),$

$\mathrm{\&lambda;}=\frac{\mathrm{tg\&beta;}-\mathrm{tg\&phi;}}{\mathrm{tg\&beta;}[1+\mathrm{tg\&beta;}(\mathrm{tg\&phi;}-\mathrm{tg\&theta;})+\mathrm{tg\&phi;tg\&theta;}]};$

In formula: λ is lateral pressure coefficient; β is the angle of the plane of fracture and horizontal plane; φ is that θ is frictional resistance angle like angle of friction.

3. H)>=dark, shallow tunnel boundary depth H _ptime,

q=γ·h _q；

(2) adopt following formula to calculate the hydrostatic pressure acting on outside grouting and reinforcing circle:

$u={\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="0"\; label="w\; k"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">w</figure-callout>}}\frac{k_{}}{}\frac{{}_0\ln \frac{D/2+h}{D/2}}{{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">k</figure-callout>}}_0\ln \frac{D/2+h}{D/2}+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00001711299200011.png,HDA00001711299200022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\ln \frac{D/2+H}{D/2+\mathrm{<figure-callout\; id="0"\; label="h\; h"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">h</figure-callout>}}}{h}_{}{}_0;$

In formula: u is the hydrostatic pressure on grouting and reinforcing circle external surface; h ₀for the degree of depth of water; k ₀for the original transmission coefficient of ground around; k ₁for the transmission coefficient of Grouting Circle; H is edpth of tunnel; H is grouting and reinforcing circle thickness; D is tunnel span; γ _wfor the unit weight of water.

(3) calculate the total load acting on grouting and reinforcing circle, total load q ₀for pressure from surrounding rock q and hydrostatic pressure u sum;

(4) the deflection equation ω (x) of acquisition fixing collar;

By total load q ₀ substitution $\mathrm{EI}\frac{d^{}}{}$ $\frac{{}^4\mathrm{\&omega;}\left(x\right)}{{\mathrm{dx}}^4}-G_{p}b*\frac{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">d</figure-callout>}}^2\mathrm{\&omega;}\left(x\right)}{{\mathrm{<figure-callout\; id="2"\; label="dx"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">dx</figure-callout>}}^2}+\mathrm{kb}*\mathrm{\&omega;}\left(x\right)={\mathrm{<figure-callout\; id="0"\; label="bq"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">bq</figure-callout>}}_0$ And substitution fringe conditions solves above formula, obtain the deflection equation ω (x) of fixing collar;

In formula: G _pfor ground modulus of shearing, k is coefficient of subgrade reaction, (G _p, k all can obtain according to geological exploration data), b ^*for considering Two_Parameter Foundation continuity finite width beam equivalent width, have

e, I are modulus of elasticity and the moment of inertia of Grouting Circle, wherein

b is the width of beam, is the span in tunnel herein; H is the thickness of grouting and reinforcing circle.

(5) the deflection equation ω based on fixing collar (x), calculates and acts on the break total force P of body end face of wedge shape;

P=σ S, wherein, σ is the mean stress that acts on voussoir top,

integrating range (0, Dcot α), L=Dcot α;

s is the wedge shape body top surface area of breaking;

(6) calculate wedge shape break the head value h (y) of the inner centre of form of body place horizontal direction and the head value h (z) of vertical direction;

(7) act on the horizontal component F of penetration on sphenoid _y, vertical component F _z:

F _y=2γ _wD ²h(y)；

F _z=2γ _wD ²cosαh(z)；

Wherein, D is tunnel span; α is the break angle of the body plane of fracture and horizontal plane of wedge shape, and h (y) is the head of the inner centre of form of sphenoid place along continuous straight runs, and h (z) be centre of form place, sphenoid inside head vertically;

(8) calculate the skid resistance and the sliding force that act on sphenoid;

Skid resistance F _{skid resistance}=T _g+ T,

Sliding force F _{sliding force}=(P+G+F _z) sin α+F _ycos α;

In formula: T _gfor voussoir both sides side direction frictional resistance, $T_g={\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">D</figure-callout>}}^2\cot \mathrm{\&alpha;}(c+{\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">K</figure-callout>}}_0\tan \mathrm{\&phi;}\frac{2\mathrm{\&sigma;}+\mathrm{D\&gamma;}}{3});$

T is the frictional resistance in inclined slide,

n is the normal force that acts on the body that breaks,

N=(P+G+F _z) cos α-F _ysin α; P acts on the break total force (specifically calculate calculated by step (5)) of body end face of wedge shape, and G is voussoir deadweight,

α is the break angle of rupture of body of wedge shape, i.e. the wedge shape angle of the body plane of fracture and horizontal plane that breaks,

for the angle of internal friction of work plane country rock; γ is country rock unit weight; C is the cohesion of country rock;

K ₀for lateral pressure coefficient, μ is the poisson's ratio of country rock; [for concrete construction of tunnel, c,

γ, μ can choose according to geology prospecting report, also can according to Tunnel Design standard, choose according to the concrete Grades of Surrounding Rock in tunnel; ]

(9) calculate the coefficient of stability K of tunnel tunnel face:

Fixing collar thickness parameter is at least five, arranges from big to small or from small to large, and the difference of adjacent fixing collar thickness parameter value is 1m.

The method for designing of submerged tunnel tunneling construction grouting and reinforcing circle thickness provided by the invention, think that submerged tunnel construction working face can produce the potential wedge shape as shown in Figure 2 body that breaks under pressure from surrounding rock, hydrostatic pressure and penetration acting in conjunction, thereby by guaranteeing that the break stability of body of potential wedge shape carries out the design of grouting and reinforcing circle thickness.

The pressure from surrounding rock acting on grouting and reinforcing circle described in the present invention is also is calculated by associated tunnel design specifications according to the difference of edpth of tunnel.

1. buried depth (H)≤equivalent load height (h _q) time, load is considered as uniform pressure at right angle:

q=γ·H （1）

In formula: q is vertical well-distributed pressure (kN/m ²); γ is tunnel above rock severe (kN/m ³); H is edpth of tunnel, refers to the distance (m) of tunnel vault to ground.Wherein h _qfor equivalent load height (m), h _q=0.45 × 2 ^s-1ω, S is Grades of Surrounding Rock; ω is width influence coefficient, i.e. ω=1+i (B-5), and wherein B is tunnel width (m), pressure from surrounding rock gradient when i is the every increase and decrease of tunnel width B 1m, the vertical well-distributed pressure of country rock with B=5m is as the criterion, and when B<5m, gets i=0.2; During B=5 ~ 15m, get i=0.1.

2. equivalent load height (h _q) < buried depth (H) < is dark, the shallow tunnel boundary degree of depth (H _p), the evenly distributed load acting on grouting and reinforcing circle is:

$q=\mathrm{\&gamma;H}(1-\frac{H}{2B}\mathrm{\&lambda;tg\&theta;})---\left(2\right)$

$\mathrm{\&lambda;}=\frac{\mathrm{tg\&beta;}-\mathrm{tg\&phi;}}{\mathrm{tg\&beta;}[1+\mathrm{tg\&beta;}(\mathrm{tg\&phi;}-\mathrm{tg\&theta;})+\mathrm{tg\&phi;tg\&theta;}]}---\left(3\right)$

In above formula: B is tunnel excavation width, β be the plane of fracture and horizontal plane angle (°); φ is that θ is frictional resistance angle, relates to standard > > choose according to country rock level difference by < < highway tunnel like angle of friction.H _pfor tunnel is dark, the shallow tunnel boundary degree of depth, H _p=(2 ~ 2.5) h _q, when being I ~ III level, country rock gets 2, and during IV ~ VI level, getting 2.5, λ is lateral pressure coefficient, is calculated as follows.

3. buried depth (H)>=dark, the shallow tunnel boundary degree of depth (H _p)

q=γ·h _q （4）

(3) the present invention is also described to act on hydrostatic pressure outside Grouting Circle according to grouting and reinforcing circle thickness and transmission coefficient, according to the correlation theory of seepage action of ground water, solves.

$u={\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="0"\; label="w\; k"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">w</figure-callout>}}\frac{k_{}}{}\frac{{}_0\ln \frac{D/2+h}{D/2}}{{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">k</figure-callout>}}_0\ln \frac{D/2+h}{D/2}+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00001711299200011.png,HDA00001711299200022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\ln \frac{D/2+H}{D/2+h}}{h}_0---\left(5\right)$

In formula: u is the hydrostatic pressure on grouting and reinforcing circle external surface; h ₀for the degree of depth of water; k ₀for the original transmission coefficient of ground around; k ₁for the transmission coefficient of Grouting Circle; H is edpth of tunnel; H is grouting and reinforcing circle thickness; D is tunnel span; γ _wfor the unit weight of water.

(4) the present invention is also that described grouting and reinforcing circle carries out computational analysis according to finite length beam on elastic foundation, and then calculates and act on the active force that potential wedge shape breaks on body and be:

$p\left(x\right)=\mathrm{k\&omega;}\left(w\right)-G_p\frac{d{\mathrm{\&omega;}}^2\left(x\right)}{{\mathrm{dx}}^2}---\left(6\right)$

In formula, G _pfor ground modulus of shearing, k is coefficient of subgrade reaction.The deflection equation that ω (x) is Grouting Circle, its governing equation is $\mathrm{<figure-callout\; id="4"\; label="EI\; d"\; filenames="HDA00001711299200011.png,HDA00001711299200022.png"\; state="\{\{state\}\}">EI</figure-callout>}\frac{d^{}}{}\frac{{}^4\mathrm{\&omega;}\left(x\right)}{{\mathrm{dx}}^4}-G_{p}b*\frac{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">d</figure-callout>}}^2\mathrm{\&omega;}\left(x\right)}{{\mathrm{<figure-callout\; id="2"\; label="dx"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">dx</figure-callout>}}^2}+\mathrm{kb}*\mathrm{\&omega;}\left(x\right)={\mathrm{<figure-callout\; id="0"\; label="bq"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">bq</figure-callout>}}_0,$ Substitution fringe conditions can solve.Wherein q (x) is for acting on the load (comprising pressure from surrounding rock, hydrostatic pressure) on grouting and reinforcing circle, and p (x) is elastic resistance, also acts on the active force that wedge shape is broken on body.E, I are modulus of elasticity and the moment of inertia of Grouting Circle.Wherein

b is the width of beam, is the span in tunnel herein; H is the thickness of grouting and reinforcing circle.

(5) the present invention is also that described the break penetration of body of wedge shape that acts on adopts method for numerical simulation to obtain the head of each point, then solves according to seepage theory.Application Gauss theory, as shown in Figure 2, obtains acting on the horizontal component of the penetration on sphenoid and the expression formula of vertical component:

F _y(α)=γ _w(-sinα∫ _ABEFh ^*dA+∫A _BCJh ^*dA) （7）

F _z(α)=γ _w(cosα∫ _ABEFh ^*dA-∫C _JEFh ^*dA) （8）

In formula: α is the break angle of rupture of body of wedge shape, γ _wfor the unit weight of water, h ^*for sphenoid inside average water head in the x-direction, have

$h^{*}=h^{*}(y,z)=\frac{1}{D}{\&Integral;}_{-D/2}^{D/2}h(x,y,z)\mathrm{dx}---\left(9\right)$

In formula: D is tunnel span; The head value of the each point that h (x, y, z) obtains for numerical simulation.

(6) the present invention is also described act on sliding force and the skid resistance that potential wedge shape breaks on body and be respectively:

F _{skid resistance}=T _g+ T (10)

F _{sliding force}=(P+G+F _z) sin α+F _ycos α (11)

In formula: T _gfor voussoir both sides side direction frictional resistance, $T_g={\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">D</figure-callout>}}^2\cot \mathrm{\&alpha;}(c+{\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">K</figure-callout>}}_0\tan \mathrm{\&phi;}\frac{2\mathrm{\&sigma;}+\mathrm{D\&gamma;}}{3});$ T is the frictional resistance in inclined slide,

n is the normal force that acts on the body that breaks, N=(P+G+F _z) cos α-F _ysin α; P is the break total force of body end face of wedge shape, and G is voussoir deadweight, f _y, F _zfor acting on horizontal component and the vertical component of the penetration on sphenoid, by (11) and (12) formula, calculate; α is the break angle of rupture of body of wedge shape,

for the angle of internal friction of work plane country rock; γ is country rock unit weight; C is the cohesion of country rock; K ₀for lateral pressure coefficient,

μ is the poisson's ratio of country rock; For concrete construction of tunnel, c,

γ, μ can choose according to geology prospecting report, also can according to Tunnel Design standard, choose according to the concrete Grades of Surrounding Rock in tunnel; All the other symbolic significances are the same.

(7) the present invention is also the coefficient of stability of described tunnel construction tunnel face, calculates and acts on sliding force and the skid resistance that potential wedge shape is broken on body respectively, can obtain the coefficient of stability of submerged tunnel construction face, specifically by following formula, solves.

In formula: each symbolic significance is the same.

(7) the present invention is also described best grouting and reinforcing circle thickness, the coefficient of stability to tunnel construction tunnel face under different grouting and reinforcing circle thickness condition solves, draw the relation curve of fixing collar thickness and the face coefficient of stability, can try to achieve the best grouting and reinforcing circle thickness that meets the requirement of face stabilizer coefficient.

Beneficial effect:

The method for designing of submerged tunnel tunneling construction grouting and reinforcing circle thickness of the present invention, compared with the existing construction tunnel of tunneling under water grouting and reinforcing method for designing, its advantage is: the method for designing of traditional submerged tunnel grouting and reinforcing circle thickness based on standard and experience, the reasonability that its design thickness is selected place one's entire reliance upon designer's itself design experiences and field experience, and the Quantitative design method of the submerged tunnel grouting and reinforcing circle thickness that the present invention proposes, it is reinforced determining of thickness and by theory, calculates completely, little with designer's design experiences relation, make the fixing collar thickness obtaining more can meet field engineering construction requirement, thereby can guarantee on the one hand the construction safety of submerged tunnel, also can reduce on the other hand construction costs.

Accompanying drawing explanation

Fig. 1 is submerged tunnel tunneling construction grouting and reinforcing schematic diagram of the present invention

Fig. 2 is the face wedge shape of the present invention body schematic diagram that breaks

Fig. 3 is hydrostatic pressure computation model schematic diagram of the present invention

Fig. 4 is Grouting Circle Force Calculation model schematic diagram in tunnel excavation process of the present invention

Fig. 5 is the face wedge shape of the present invention body force diagram that breaks

Fig. 6 is grouting and reinforcing circle thickness of the present invention and tunnel tunnel face coefficient of stability relation curve schematic diagram

In figure: 1-preliminary bracing, 2-steel arch frame, 3-face, 4-plane of fracture, 5-country rock, 6-grouting and reinforcing circle, position at the bottom of 7-river, 8-river position, 9-tunnel, 10-wedge shape body that breaks, H-edpth of tunnel, D-tunnel height, P Grouting Circle is delivered to wedge shape and breaks making a concerted effort on body, the deadweight of G voussoir, T _gfor voussoir both sides side direction frictional resistance, F _y-act on the horizontal component of the penetration on sphenoid, F _z-act on the vertical component of the penetration on sphenoid, the frictional resistance in T-inclined slide, N-the act on normal force of the body that breaks, h ₀the water level depth of-tunnel vault, the thickness of h Grouting Circle, the coefficient of stability of K-tunnel front, the break position on the each summit of body of A, B, C, E, F, J-wedge shape.

The specific embodiment

Below with reference to the drawings and specific embodiments, the present invention is described in further details:

A kind of method for designing of submerged tunnel tunneling construction grouting and reinforcing parameter, referring to Fig. 1, after tunnel excavation, submerged tunnel construction working face can produce the potential wedge shape body (Fig. 2) that breaks under pressure from surrounding rock, hydrostatic pressure and penetration acting in conjunction, by face stabilizer, analyze, by guaranteeing that the break stability of body of potential wedge shape carries out grouting and reinforcing design, the specific design parameter of grouting and reinforcing comprises transmission coefficient and the mechanics parameter after Grouting Circle thickness, slip casting.Pressure from surrounding rock is calculated by associated tunnel design specifications according to the difference of edpth of tunnel, grouting and reinforcing circle carries out computational analysis according to finite length beam on elastic foundation, act on hydrostatic pressure outside Grouting Circle according to grouting and reinforcing circle thickness and transmission coefficient, correlation theory according to the seepage flow of underground water solves, acting on the break penetration of body of wedge shape adopts method for numerical simulation to obtain the head of each point, then according to seepage theory, solve, calculate and act on sliding force and the skid resistance that potential wedge shape is broken on body respectively, based on limit equilibrium theory, final determine guarantee the break grouting and reinforcing circle thickness of body stability of potential wedge shape.

(1) act on the calculating of the pressure from surrounding rock on grouting and reinforcing circle

According to highway in China or Design of Railway Tunnel standard, can obtain tunnel surrounding equivalent load height h _qfor:

h _q=0.45×2 ^S-1·ω （1）

In formula: h _qfor equivalent load height (m); S is Grades of Surrounding Rock; ω is width influence coefficient, i.e. ω=1+i (B-5), and wherein B is tunnel width (m), pressure from surrounding rock gradient when i is the every increase and decrease of tunnel width B 1m, the vertical well-distributed pressure of country rock with B=5m is as the criterion, and when B<5m, gets i=0.2; During B=5～15m, get i=0.1.

1. buried depth (H)≤equivalent load height (h _q) time, load is considered as uniform pressure at right angle:

q=γ·H （2）

In formula: q is vertical well-distributed pressure (kN/m ²); γ is tunnel above rock severe (kN/m ³); H is edpth of tunnel, refers to the distance (m) of tunnel vault to ground.

2. equivalent load height (h _q) < buried depth (H) < is dark, the shallow tunnel boundary degree of depth (H _p), the evenly distributed load acting on grouting and reinforcing circle is:

$q=\mathrm{\&gamma;H}(1-\frac{H}{2B}\mathrm{\&lambda;tg\&theta;})---\left(3\right)$

$\mathrm{\&lambda;}=\frac{\mathrm{tg\&beta;}-\mathrm{tg\&phi;}}{\mathrm{tg\&beta;}[1+\mathrm{tg\&beta;}(\mathrm{tg\&phi;}-\mathrm{tg\&theta;})+\mathrm{tg\&phi;tg\&theta;}]}---\left(4\right)$

In formula: λ is lateral pressure coefficient; φ is like angle of friction, and θ is frictional resistance angle, β be the plane of fracture and horizontal plane angle (°), wherein φ, θ chooses by Tunnel Design standard according to Grades of Surrounding Rock difference, and all the other symbolic significances are the same.

3. buried depth (H)>=dark, the shallow tunnel boundary degree of depth (H _p)

q=γ·h _q （5）

(2) act on the calculating of the hydrostatic pressure outside Grouting Circle.

Referring to Fig. 3, can obtain:

$u={\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="0"\; label="w\; k"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">w</figure-callout>}}\frac{k_{}}{}\frac{{}_0\ln \frac{D/2+h}{D/2}}{{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">k</figure-callout>}}_0\ln \frac{D/2+h}{D/2}+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00001711299200011.png,HDA00001711299200022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\ln \frac{D/2+H}{D/2+h}}{h}_0---\left(6\right)$

In formula: u is the hydrostatic pressure on grouting and reinforcing circle external surface; h ₀for the degree of depth of water; k ₀for the original transmission coefficient of ground around; (can be obtained by geological prospecting survey data) k ₁for the transmission coefficient (can obtain by sampling test) of Grouting Circle; H is edpth of tunnel; H is grouting and reinforcing circle thickness; D is tunnel span; γ _wfor the unit weight of water, be 10kN/m ³(H, D is definite according to Tunnel Design drawing, and h is the design parameters that this method need to be definite.）

(3) by grouting and reinforcing circle, act on the break calculating of the active force on body of potential wedge shape.

The beam on elastic foundation mechanical model of grouting and reinforcing circle, referring to Fig. 4, can seen supporting section and have certain initial displacement ω ₀with initial rotational angle theta ₀elastic Fixed Ends, the initial displacement ω of Grouting Circle ₀for the existing displacement of preliminary bracing; Grouting Circle is considered as to the beam on elastic foundation of finite length, the Deflection Differential Equation ω (x) that can obtain beam is:

$\mathrm{EI}\frac{{\mathrm{d\&omega;}}^4\left(x\right)}{{\mathrm{<figure-callout\; id="4"\; label="dx"\; filenames="HDA00001711299200011.png,HDA00001711299200022.png"\; state="\{\{state\}\}">dx</figure-callout>}}^4}=b[q\left(x\right)-p\left(x\right)]---\left(7\right)$

In formula: q (x) is for acting on the load (comprising pressure from surrounding rock, hydrostatic pressure, flowing pressure) on grouting and reinforcing circle, and p (x) is elastic resistance, also acts on the active force that wedge shape is broken on body.E, I are modulus of elasticity and the moment of inertia of Grouting Circle.

Wherein b is the width of beam, is the span in tunnel herein; H is the thickness of grouting and reinforcing circle.

Subgrade reaction adopts the Pasternak model of two-parameter model to solve, and can obtain

$\mathrm{<figure-callout\; id="4"\; label="EI\; d"\; filenames="HDA00001711299200011.png,HDA00001711299200022.png"\; state="\{\{state\}\}">EI</figure-callout>}\frac{d^{}}{}\frac{{}^4\mathrm{\&omega;}\left(x\right)}{{\mathrm{dx}}^4}-G_{p}b*\frac{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">d</figure-callout>}}^2\mathrm{\&omega;}\left(x\right)}{{\mathrm{<figure-callout\; id="2"\; label="dx"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">dx</figure-callout>}}^2}+\mathrm{kb}*\mathrm{\&omega;}\left(x\right)={\mathrm{bq}}_0---\left(8\right)$

In formula: G _pfor ground modulus of shearing, k is coefficient of subgrade reaction, b ^*---consider Two_Parameter Foundation continuity finite width beam equivalent width,

(initial displacement is ω to substitution fringe conditions ₀, initial corner is θ ₀, ω ₀=2mm, θ ₀=1 ⁰) solve after the deflection equation ω (x) that obtains Grouting Circle, can try to achieve and act on the break active force of body end face of wedge shape and be:

$p\left(x\right)=\mathrm{k\&omega;}\left(x\right)-G_p\frac{{\mathrm{d\&omega;}}^2\left(x\right)}{{\mathrm{dx}}^2}---\left(9\right)$

Obtain acting on the mean stress σ on voussoir top simultaneously,

(integrating range (0, Dcot α), L=Dcot α)

Further try to achieve and act on the wedge shape total active force of body end face that breaks and be:

P=σ·S （10）

In formula: S is the wedge shape body top surface area of breaking.

(4) act on the break calculating of penetration of body of wedge shape

To unit volume penetration application Gauss theory on sphenoid, obtain acting on the horizontal component of the penetration on sphenoid and the expression formula of vertical component:

F _y=2γ _wD ²h(y) （11）

F _z=2γ _wD ²cosαh(z) （12）

In formula: γ _wfor the unit weight of water; D is tunnel span; α is the break angle of the body plane of fracture and horizontal plane of wedge shape, h (y) is the head of the inner centre of form of sphenoid place along continuous straight runs, h (z) is the inner centre of form of sphenoid place head vertically, it (is prior art that h (y), h (z) can obtain by numerical computation method, according to Practical Project, actual parameter, utilizes numerical simulation, sets up model analysis, obtains h (y), h (z)).

(5), referring to Fig. 5, act on break sliding force on body and skid resistance of potential wedge shape and adopt following methods to calculate.

F _{skid resistance}=T _g+ T (13)

In formula: T _gfor voussoir both sides side direction frictional resistance, $T_g={\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">D</figure-callout>}}^2\cot \mathrm{\&alpha;}(c+{\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">K</figure-callout>}}_0\tan \mathrm{\&phi;}\frac{2\mathrm{\&sigma;}+\mathrm{D\&gamma;}}{3});$ T is the frictional resistance in inclined slide,

n is the normal force that acts on the body that breaks, N=(P+G+F _z) cos α-F _ysin α; P is the break total force of body end face of wedge shape, and G is voussoir deadweight, f _y, F _zfor acting on horizontal component and the vertical component of the penetration on sphenoid, by (11) and (12) formula, calculate; α is the break angle of rupture of body of wedge shape,

for the angle of internal friction of work plane country rock; γ is country rock unit weight; C is the cohesion of country rock; ( the geologic parameter that γ, c can record according to engineer geological prospecting report can obtain) K ₀for lateral pressure coefficient,

μ is the poisson's ratio of country rock; For concrete construction of tunnel, c,

γ, μ can choose according to geology prospecting report, also can according to Tunnel Design standard, choose according to the concrete Grades of Surrounding Rock in tunnel; All the other symbolic significances are the same.

F _{sliding force}=(P+G+F _z) sin α+F _ycos α (14)

In formula: P is the break total force of body end face of wedge shape, and G is voussoir deadweight,

f _y, F _zfor acting on horizontal component and the vertical component of the penetration on sphenoid, by (11) and (12) formula, calculate.

(6), referring to Fig. 5, according to formula (13) and (14), the coefficient of stability of tunnel construction tunnel face can solve by following formula

In formula: each symbolic significance is the same.

(7) according to concrete engineering specifications, the coefficient of stability to tunnel construction tunnel face under different grouting and reinforcing circle thickness condition solves, can obtain curve as shown in Figure 6, according to Tunnel Design standard, the coefficient of stability of getting tunnel construction tunnel face is 2.0, and now corresponding grouting and reinforcing circle thickness is best grouting and reinforcing circle thickness.

Below in conjunction with example, the present invention is further described.

Certain submerged tunnel rock crusher weakness, is particularly communicated with at fault belt section tunnel and river, and prominent mud, water burst, the sillar avalanche construction risk such as even cave in very easily occurs in constructing tunnel process.This section of edpth of tunnel is 24m, and top, the riverbed depth of water is 21m, and stratum osmotic coefficient is 0.89m/d, is to guarantee the construction safety in tunnel, in Tunnel Design, according to engineering experience, adopted 6.0 thick grouting and reinforcing circles, and after slip casting, the transmission coefficient on stratum is 10 ^-6m/d.

Adopt the method for designing of submerged tunnel tunneling construction grouting and reinforcing circle thickness of the present invention, the grouting and reinforcing circle thickness of Tunnel Passing fault belt section is calculated, its specific design computational process is as follows:

(1) first calculate the coefficient of stability of constructing tunnel work plane under different grouting and reinforcing circle thickness condition.Take grouting and reinforcing circle thickness 6m as example, its computational process is as follows:

1) according to the difference of edpth of tunnel situation, by formula (2), (3) or (5), calculate the pressure from surrounding rock acting on grouting and reinforcing circle, for this example, by formula (3), calculating pressure from surrounding rock is 356.5kN/m ².

2) by formula (6), calculate the hydrostatic pressure acting on outside grouting and reinforcing circle, its value is 150.0kN/m ².

Edpth of tunnel H21m, grouting and reinforcing circle thickness h 6m, span D is 10m, γ _w=10kN/m ³, k ₀the original transmission coefficient 0.89m/d of ground around, k ₁for transmission coefficient 10 after grouting and reinforcing ^-6m/d, h ₀for 15m;

3) calculate the total load acting on grouting and reinforcing circle, above two pressure that calculate are superposeed, its value is 506.5kN/m ².

4) by the total load q calculating ₀substitution formula (8), and solving equation formula (8), according to fringe conditions, as shown in Figure 4, have certain initial displacement ω at B end ₀with initial rotational angle theta ₀, at C point, Grouting Circle must meet the condition of continuity, at D end, is free end, can obtain thus the deflection equation ω (x) of fixing collar.Separate the fringe conditions of the differential equation: ω ₀=2mm, θ ₀=1 ⁰)

In formula: ground shear modulus G _pbe 1.8 × 10 ⁴kN/m, k is that coefficient of subgrade reaction k is 4.0 × 10 ⁴kN/m ³, grouting and reinforcing ring cross-section rigidity EI is 8.4 × 10 ⁵kN/m ², the width b of beam is 10m.

5) try to achieve after the deflection equation of Grouting Circle, further according to formula (9) and (10), can try to achieve and act on the break average of body end face active force of wedge shape is 320.56kN/m ², according to the area S at sphenoid top, be 65.43m ², can obtain acting on the break total force P of body end face of wedge shape is 20974kN.σ=320.56kN/m ²，S=65.43m ²。

6) adopt numerical computation method, calculate the break head value F of the inner centre of form place's horizontal direction of body and vertical direction of wedge shape _y, F _zbe 4.56m.

7) employing formula (11) and (12), try to achieve the horizontal component F that acts on penetration on sphenoid _yfor 9120kN, vertical component F _zfor 5055.3kN.Wherein, α is 56.3 °, γ _wbe 10 ⁴kN/m ³, D is 10m.

8) according to formula (13) and (14), calculate respectively the skid resistance and the sliding force that act on sphenoid, be respectively 76791.7kN and 32279kN.

9) coefficient of stability K that calculates tunnel tunnel face according to formula (15) is 2.379, and this is grouting and reinforcing circle thickness is the coefficient of stability of tunnel tunnel face under 6m condition.

10) according to above identical computational methods and computational process can in the hope of under grouting and reinforcing condition not and grouting and reinforcing circle thickness be respectively 1.0m, 2.0m, 3.0m, 4.0m, 5.0m, 6.0m, 7.0m, during 8.0m, the coefficient of stability of tunnel tunnel face is respectively 0.41,1.126,1.523,1.853,2.062,2.251,2.379,2.445,2.492.

(2) by face safety factor corresponding under different grouting and reinforcing circle thickness condition, according to least square method drafting pattern, (be the accuracy of assurance graphing, generally at least needing to get 5 above fixing collar thickness calculates, calculate the desirable 1m of step-length), can obtain regression curve as shown in Figure 6.

(3), according to regression curve, can obtain the required fixing collar thickness in tunnel under a certain design face safety factor condition;

According to Tunnel Design standard, tunnel safety coefficient generally gets 2.0, now guarantees that the minimum Grouting Circle thickness of this tunnel construction tunnel face stability is 3.8m, and the grouting and reinforcing circle thickness definite compared with empirical method reduces 2.2m.

When tunnel grouting fixing collar thickness is 6.0m, the slip casting expense of its every linear meter(lin.m.) is about 1.5 ten thousand yuan, when the thickness of grouting and reinforcing circle is reduced to 3.8m, the slip casting expense of its every linear meter(lin.m.) is about 0.7 ten thousand yuan, compared with 6.0m Grouting Circle, reduce expense more than 50%, for general submerged tunnel, its length is generally more than 2km, and the construction costs that adopts the present invention to reduce will be more than 1,600 ten thousand yuan.

In addition, adopt definite method of grouting and reinforcing circle thickness of the present invention, owing to having reduced the thickness of grouting and reinforcing circle, reduced the difficulty of mortar depositing construction, accelerated the construction speed in tunnel, can effectively shorten the construction period in tunnel, the economic benefit that it produces and social benefit are also highly significants.

Claims (2)

1. a method for designing for submerged tunnel tunneling construction grouting and reinforcing circle thickness, is characterized in that, comprises the following steps:

Step 1: choose one group of fixing collar thickness parameter, calculate the coefficient of stability of constructing tunnel work plane under different fixing collar thickness condition;

Step 2: based on different fixing collar thickness and the corresponding coefficient of stability, according to least square method, obtain fixing collar thickness-coefficient of stability regression curve;

Step 3: according to this fixing collar thickness-coefficient of stability regression curve, can obtain the required fixing collar thickness in tunnel under the coefficient of stability condition of a certain design;

In step 1, the coefficient of stability that a certain fixing collar thickness is corresponding adopts following methods to calculate:

(1) calculate pressure from surrounding rock q;

1. H≤equivalent load height h _qtime,

q=γ·H；

In formula: γ is tunnel above rock severe; H is edpth of tunnel, refers to the distance of tunnel vault to ground;

2. equivalent load height h _q< H < is dark, shallow tunnel boundary depth H _ptime,

In formula: λ is lateral pressure coefficient; B is tunnel excavation width, and β is the angle of the plane of fracture and horizontal plane; φ is that θ is frictional resistance angle like angle of friction;

3. H>=dark, shallow tunnel boundary depth H _ptime,

q=γ·h _q；

(2) adopt following formula to calculate the hydrostatic pressure acting on outside grouting and reinforcing circle:

In formula: u is the hydrostatic pressure on grouting and reinforcing circle external surface; h ₀for the degree of depth of water; k ₀for the original transmission coefficient of ground around; k ₁for the transmission coefficient of Grouting Circle; H is edpth of tunnel; H is grouting and reinforcing circle thickness; D is tunnel span; γ _wfor the unit weight of water;

(3) calculate the total load acting on grouting and reinforcing circle, total load q ₀for pressure from surrounding rock q and hydrostatic pressure u sum;

(4) the deflection equation ω (x) of acquisition fixing collar;

By total load q ₀substitution

and substitution fringe conditions solves above formula, obtain the deflection equation ω (x) of fixing collar;

In formula: G _pfor ground modulus of shearing, k is coefficient of subgrade reaction, b ^*for considering Two_Parameter Foundation continuity finite width beam equivalent width, have

e, I are modulus of elasticity and the moment of inertia of Grouting Circle, wherein

b is the width of beam, is the span in tunnel herein; H is the thickness of grouting and reinforcing circle;

(5) the deflection equation ω based on fixing collar (x), calculates and acts on the break total force P of body end face of wedge shape; P=σ S, wherein, σ is the mean stress that acts on voussoir top,

integrating range (0, Dcot α), L=Dcot α;

s is the wedge shape body top surface area of breaking;

(6) calculate wedge shape break the head value h (y) of the inner centre of form of body place horizontal direction and the head value h (z) of vertical direction;

(7) act on the horizontal component F of penetration on sphenoid _y, vertical component F _z:

F _y=2γ _wD ²h(y)；

F _z=2γ _wD ²cosαh(z)；

Wherein, D is tunnel span; α is the break angle of the body plane of fracture and horizontal plane of wedge shape, and h (y) is the head of the inner centre of form of sphenoid place along continuous straight runs, and h (z) be centre of form place, sphenoid inside head vertically;

(8) calculate the skid resistance and the sliding force that act on sphenoid;

Skid resistance F _{skid resistance}=T _g+ T,

Sliding force F _{sliding force}=(P+G+F _z) sin α+F _ycos α;

In formula: T _gfor voussoir both sides side direction frictional resistance,

T is the frictional resistance in inclined slide,

n is the normal force that acts on the body that breaks,

N=(P+G+F _z) cos α-F _ysin α; P acts on the break total force (specifically calculate calculated by step (5)) of body end face of wedge shape, and G is voussoir deadweight,

α is the break angle of rupture of body of wedge shape, i.e. the wedge shape angle of the body plane of fracture and horizontal plane that breaks,

for the angle of internal friction of work plane country rock; γ is country rock unit weight; C is the cohesion of country rock;

K ₀for lateral pressure coefficient,

μ is the poisson's ratio of country rock;

(9) calculate the coefficient of stability K of tunnel tunnel face:

2. the method for designing of submerged tunnel tunneling construction grouting and reinforcing circle thickness according to claim 1, is characterized in that, fixing collar thickness parameter is at least five, arranges from big to small or from small to large, and the difference of adjacent fixing collar thickness parameter value is 1m.

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