CN102704947A - 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 Mine Method to construct; For preventing that engineering accidents such as gushing water caves in from appearring in the excavation face; Usually adopt pre-grouting to reinforce in advance in the construction, then under the protection of grouting and reinforcing circle, carry out tunnel excavation, to guarantee the construction safety of submerged tunnel.Yet; Mainly still on the basis of experience, undertaken by engineering analog method for the design of submerged tunnel pre-grouting reinforcing parameter both at home and abroad at present, how relevant highway and Design of Railway Tunnel standard are confirmed not relate to fully to submerged tunnel grouting and reinforcing circle thickness.In the actual submerged tunnel engineering design; The grouting and reinforcing Determination of Parameters is often judged according to design engineer's personal experience; Whether can guarantee the needs of tunnel safety construction fully for the slip casting design parameters that adopts; Whether the grouting parameter of perhaps confirming is too conservative, and its safety factor has much, comprises that design engineer oneself can't confirm.Therefore, on the one hand in the design for guaranteeing safety, the design engineer is simply the thickness of increasing grouting and reinforcing circle often, guaranteeing the construction safety in tunnel, thereby has increased the construction costs in tunnel; On the other hand; Effectively analyze and method for designing owing to lack; Can't design targetedly according to the geological conditions in tunnel; The bed rearrangement tunnel often adopts identical grouting and reinforcing design parameters, makes submerged tunnel have certain construction risk again 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, can't satisfy China's submerged tunnel and build fast-developing needs.

Therefore, the method for designing of submerged tunnel grouting and reinforcing circle thickness of developing a kind of novel quantification is for being badly in need of.

Summary of the invention

Technical problem to be solved by this invention provides 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 satisfy the field engineering construction requirement; Thereby can guarantee the construction safety in tunnel on the one hand, also can reduce construction costs on the other hand.

The technical solution of invention is following:

A kind of method for designing of submerged tunnel tunneling construction grouting and reinforcing circle thickness may further comprise the steps:

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

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

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

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

(1) calculates pressure from surrounding rock q;

1. H≤equivalent load height h _qThe time,

q=γ·H；

In the formula: γ covers country rock severe on the tunnel; H is an edpth of tunnel, refers to the distance on tunnel vault to ground;

2. equivalent load height h _q＜H＜dark, shallow tunnel boundary depth H _pThe time,

$q=\mathrm{\γH}(1-\frac{H}{2B}\mathrm{\λtg\θ}),$

$\mathrm{\λ}=\frac{\mathrm{tg\β}-\mathrm{tg\φ}}{\mathrm{tg\β}[1+\mathrm{tg\β}(\mathrm{tg\φ}-\mathrm{tg\θ})+\mathrm{tg\φtg\θ}]};$

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

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

q=γ·h _q；

(2) adopt following formula to calculate and act on the outer hydrostatic pressure of 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 the formula: u is the hydrostatic pressure on the grouting and reinforcing circle external surface; h ₀The degree of depth for water; k ₀Be the original transmission coefficient of ground on every side; k ₁Transmission coefficient for the slip casting circle; H is an edpth of tunnel; H is a grouting and reinforcing circle thickness; D is the tunnel span; γ _wUnit weight for water.

(3) calculating acts on the total load on the grouting and reinforcing circle, total load q ₀Be pressure from surrounding rock q and hydrostatic pressure u sum;

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

With 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 the substitution fringe conditions finds the solution following formula, obtains the deflection equation ω (x) of fixing collar;

In the formula: G _pBe the ground modulus of shearing, k is a coefficient of subgrade reaction, (G _p, k all can obtain according to geological exploration data), b ^*For considering two-parameter ground continuity finite width beam equivalent width, have

E, I are the modulus of elasticity and the moment of inertia of slip casting circle, wherein B is the width of beam, is the span in tunnel here; H is the thickness of grouting and reinforcing circle.

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

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 the sphenoid _y, vertical component F _z:

F _y=2γ _wD ²h(y)；

F _z=2γ _wD ²cosαh(z)；

Wherein, D is the 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 sphenoid centre of form place, an inside head vertically;

(8) calculating acts on skid resistance and the sliding force on the sphenoid;

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

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

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

T is the frictional resistance on the 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 the voussoir deadweight,

α is the break angle of rupture of body of wedge shape; Be the break angle of the body plane of fracture and horizontal plane of wedge shape,

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

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

γ, μ can choose according to the geology prospecting report, also can choose according to the Tunnel Design standard according to the concrete country rock rank in tunnel; ]

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

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

1. buried depth (H)≤equivalent load height (h _q) time, load is regarded as being uniformly distributed with pressure at right angle:

q=γ·H （1）

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

2. equivalent load height (h _q)＜buried depth (H)＜dark, the shallow tunnel boundary degree of depth (H _p), the evenly distributed load that acts on the 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 following formula: B is the tunnel excavation width, β be the plane of fracture and horizontal plane angle (°); φ is that θ is the frictional resistance angle like angle of friction, chooses by " highway tunnel relates to standard " according to the country rock level is different.H _pFor the tunnel is dark, the shallow tunnel boundary degree of depth, H _p=(2 ~ 2.5) h _q,, country rock gets 2 when being I ~ III level, get 2.5 during IV ~ VI level, and λ is a 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 that also the described outer hydrostatic pressure of slip casting circle that acts on according to grouting and reinforcing circle thickness and transmission coefficient, finds the solution according to the correlation theory of seepage action of ground water.

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

In the formula: u is the hydrostatic pressure on the grouting and reinforcing circle external surface; h ₀The degree of depth for water; k ₀Be the original transmission coefficient of ground on every side; k ₁Transmission coefficient for the slip casting circle; H is an edpth of tunnel; H is a grouting and reinforcing circle thickness; D is the tunnel span; γ _wUnit weight for water.

(4) the present invention is that also described grouting and reinforcing circle carries out computational analysis according to the finite length beam on elastic foundation, and then calculates and act on the active force that potential wedge shape breaks on the 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 the formula, G _pBe the ground modulus of shearing, k is a coefficient of subgrade reaction.ω (x) is the deflection equation of slip casting circle, and its governing equation does $\mathrm{<figure-callout\; id="4"\; label="EI\; d"\; filenames="HDA00001711299200011.png,HDA00001711299200022.png"\; state="\{\{state\}\}">EI</figure-callout>}\frac{d^{}}{}\frac{{}^4\mathrm{\&omega;}\left(x\right)}{{\mathrm{Dx}}^4}-G_{p}b*\frac{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">d</figure-callout>}}^2\mathrm{\&omega;}\left(x\right)}{{\mathrm{<figure-callout\; id="2"\; label="Dx"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">Dx</figure-callout>}}^2}+\mathrm{Kb}*\mathrm{\&omega;}\left(x\right)={\mathrm{<figure-callout\; id="0"\; label="Bq"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">Bq</figure-callout>}}_0,$ The substitution fringe conditions can be found the solution.Wherein for to act on the load (comprising pressure from surrounding rock, hydrostatic pressure) on the grouting and reinforcing circle, p (x) is an elastic resistance to q (x), also promptly acts on the wedge shape active force on the body that breaks.E, I are the modulus of elasticity and the moment of inertia of slip casting circle.Wherein

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

(5) the present invention is that also 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 finds the solution according to seepage theory.Use Gauss theory, as shown in Figure 2, obtain acting on the horizontal component of the penetration on the 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 the formula: α is the break angle of rupture of body of wedge shape, γ _wBe the unit weight of water, h ^*For the average water head of sphenoid inside, have along the x direction

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

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

(6) the present invention also is describedly to act on sliding force and the skid resistance that potential wedge shape breaks on the 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 the formula: T _gBe voussoir both sides side direction frictional resistance, $T_g={\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">D</figure-callout>}}^2\mathrm{Cot}\mathrm{\&alpha;}(c+{\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="HDA00001711299200031.png"\; state="\{\{state\}\}">K</figure-callout>}}_0\mathrm{Tan}\mathrm{\&phi;}\frac{2\mathrm{\&sigma;}+\mathrm{D\&gamma;}}{3});$ T is the frictional resistance on the 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 the voussoir deadweight,

F _y, F _zBe horizontal component and the vertical component that acts on the penetration on the sphenoid, calculate by (11) and (12) formula; α is the break angle of rupture of body of wedge shape,

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

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

γ, μ can choose according to the geology prospecting report, also can choose according to the Tunnel Design standard according to the concrete country rock rank in tunnel; All the other symbolic significances are the same.

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

In the formula: each symbolic significance is the same.

(7) the present invention also is the grouting and reinforcing circle thickness of described the best; The coefficient of stability to tunnel construction tunnel face under the different grouting and reinforcing circle thickness condition is found the solution; Draw the relation curve of the fixing collar thickness and the face coefficient of stability, can try to achieve the grouting and reinforcing circle thickness of the best that satisfies 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; Compare with existing tunneling construction tunnel grouting and reinforcing method for designing under water; 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 the definite of thickness and obtains through Theoretical Calculation fully; Little with designer's design experiences relation; The fixing collar thickness that obtains more can satisfy the field engineering construction requirement, thereby can guarantee the construction safety of submerged tunnel on the one hand, also can reduce construction costs on the other hand.

Description of drawings

Fig. 1 is submerged tunnel tunneling construction grouting and reinforcing sketch map of the present invention

Fig. 2 is the face wedge shape of the present invention body sketch map that breaks

Fig. 3 is a hydrostatic pressure computation model sketch map of the present invention

Fig. 4 is slip casting circle Force Calculation model sketch map in the 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 sketch map

Among the figure: 1-preliminary bracing, 2-steel bow member, 3-face, 4-plane of fracture; 5-country rock, 6-grouting and reinforcing circle, at the bottom of 7-river the position, 8-river position; 9-tunnel, the 10-wedge shape body that breaks, H-edpth of tunnel, D-tunnel height; P slip casting circle is delivered to wedge shape and breaks making a concerted effort on the body, the deadweight of G voussoir, T _gBe voussoir both sides side direction frictional resistance, F _y-act on the horizontal component of the penetration on the sphenoid, F _z-act on the vertical component of the penetration on the sphenoid, the frictional resistance on 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 slip casting circle, the coefficient of stability of K-tunnel front, the break position on each summit of body of A, B, C, E, F, J-wedge shape.

The specific embodiment

Below will combine accompanying drawing and specific embodiment that the present invention is explained further details:

A kind of method for designing of submerged tunnel tunneling construction grouting and reinforcing parameter; Referring to Fig. 1; Behind the 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, through the analysis of face stabilizer property; By guaranteeing that the break stability of body of potential wedge shape carries out the grouting and reinforcing design, the concrete design parameters of grouting and reinforcing comprises transmission coefficient and the mechanics parameter after slip casting circle thickness, the slip casting.Pressure from surrounding rock is calculated by the associated tunnel design specifications according to the difference of edpth of tunnel; The grouting and reinforcing circle carries out computational analysis according to the finite length beam on elastic foundation; Act on the outer hydrostatic pressure of slip casting circle according to grouting and reinforcing circle thickness and transmission coefficient, find the solution, act on the break penetration of body of wedge shape and adopt method for numerical simulation to obtain the head of each point according to the correlation theory of phreatic seepage flow; Then find the solution according to seepage theory; Calculate respectively and act on potential wedge shape break sliding force and skid resistance on the body,, finally confirm to guarantee the break grouting and reinforcing circle thickness of body stability of potential wedge shape based on limit equilibrium theory.

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

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

h _q=0.45×2 ^S-1·ω （1）

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

1. buried depth (H)≤equivalent load height (h _q) time, load is regarded as being uniformly distributed with pressure at right angle:

q=γ·H （2）

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

2. equivalent load height (h _q)＜buried depth (H)＜dark, the shallow tunnel boundary degree of depth (H _p), the evenly distributed load that acts on the 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 the formula: λ is a lateral pressure coefficient; φ is like angle of friction; θ is the frictional resistance angle; β be the plane of fracture and horizontal plane angle (°);

φ wherein, θ chooses by the Tunnel Design standard according to country rock rank 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 outer hydrostatic pressure of slip casting circle.

Referring to Fig. 3, can get:

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

In the formula: u is the hydrostatic pressure on the grouting and reinforcing circle external surface; h ₀The degree of depth for water; k ₀Be the original transmission coefficient of ground on every side; (can obtain) k by geological prospecting survey data ₁Transmission coefficient (can obtain) for the slip casting circle through sampling test; H is an edpth of tunnel; H is a grouting and reinforcing circle thickness; D is the tunnel span; γ _wBe the unit weight of water, be 10kN/m ³(H, D confirms that according to the Tunnel Design drawing h is the design parameters that this method need be confirmed.）

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

The beam on elastic foundation mechanical model of grouting and reinforcing circle can see to have certain initial displacement ω with supporting section referring to Fig. 4 ₀With initial rotational angle theta ₀Elastic Fixed Ends, the initial displacement ω of slip casting circle ₀Existing displacement for preliminary bracing; The slip casting circle is regarded as the beam on elastic foundation of finite length, and the amount of deflection differential equation ω (x) that can get 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 the formula: for to act on the load (comprising pressure from surrounding rock, hydrostatic pressure, flowing pressure) on the grouting and reinforcing circle, p (x) is an elastic resistance to q (x), also promptly acts on the wedge shape active force on the body that breaks.E, I are the modulus of elasticity and the moment of inertia of slip casting circle.

Wherein

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

Subgrade reaction adopts the Pasternak model of two-parameter model to find the solution, and can get

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

In the formula: G _pBe the ground modulus of shearing, k is a coefficient of subgrade reaction, b ^*---consider two-parameter ground continuity finite width beam equivalent width, promptly

(initial displacement is ω to the substitution fringe conditions ₀, initial corner is θ ₀, ω ₀=2mm, θ ₀=1 ⁰) find the solution the deflection equation ω (x) that obtains the slip casting circle after, 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 the 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

Unit volume penetration on the sphenoid is used Gauss theory, obtains acting on the horizontal component of the penetration on the sphenoid and the expression formula of vertical component:

F _y=2γ _wD ²h(y) （11）

F _z=2γ _wD ²cosαh(z) （12）

In the formula: γ _wUnit weight for water; D is the 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, and h (z) is the inner centre of form place of a sphenoid head vertically, and it (is prior art that h (y), h (z) can obtain through numerical computation method; According to actual engineering; Actual parameter utilizes numerical simulation, sets up model analysis, obtains h (y), h (z)).

(5), act on sliding force and the skid resistance that potential wedge shape breaks on the body and adopt following method to calculate referring to Fig. 5.

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

In the formula: T _gBe voussoir both sides side direction frictional resistance, $T_g=D^2\mathrm{Cot}\mathrm{\&alpha;}(c+K_0\mathrm{Tan}\mathrm{\&phi;}\frac{2\mathrm{\&sigma;}+\mathrm{D\&gamma;}}{3});$ T is the frictional resistance on the 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 the voussoir deadweight,

F _y, F _zBe horizontal component and the vertical component that acts on the penetration on the sphenoid, calculate by (11) and (12) formula; α is the break angle of rupture of body of wedge shape,

Angle of internal friction for the work plane country rock; γ is a country rock unit weight; C is the cohesion of country rock; ( γ, c can both obtain according to the geologic parameter that the engineer geological prospecting report records) K ₀Be lateral pressure coefficient, μ is the poisson's ratio of country rock; For concrete construction of tunnel, c,

γ, μ can choose according to the geology prospecting report, also can choose according to the Tunnel Design standard according to the concrete country rock rank in tunnel; All the other symbolic significances are the same.

F _{Sliding force}=(P+G+F _z) sin α+F _yCos α (14)

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

F _y, F _zBe horizontal component and the vertical component that acts on the penetration on the sphenoid, calculate by (11) and (12) formula.

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

In the formula: each symbolic significance is the same.

(7) according to concrete engineering specifications; The coefficient of stability to tunnel construction tunnel face under the different grouting and reinforcing circle thickness condition is found the solution; Can obtain curve as shown in Figure 6; According to the Tunnel Design standard, the coefficient of stability of getting tunnel construction tunnel face is 2.0, and this moment, corresponding grouting and reinforcing circle thickness was best grouting and reinforcing circle thickness.

Below in conjunction with instance the present invention is further specified.

Certain submerged tunnel rock crusher is weak, particularly is communicated with river in fault belt section tunnel, and mud, water burst, sillar avalanche even construction risk such as cave in very easily take place in the constructing tunnel process to dash forward.This section edpth of tunnel is 24m, and top, the riverbed depth of water is 21m, and stratum osmotic coefficient is 0.89m/d, be to guarantee the construction safety in tunnel, has adopted 6.0 thick grouting and reinforcing circles according to engineering experience in the Tunnel Design, and the transmission coefficient on stratum is 10 after the slip casting ^-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 that the tunnel is passed through the fault belt section calculates, and its concrete design calculation process is following:

(1) at first calculates the coefficient of stability of constructing tunnel work plane under the different grouting and reinforcing circle thickness condition.6m is an example with grouting and reinforcing circle thickness, and its computational process is following:

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

2) calculate the hydrostatic pressure that acts on outside the grouting and reinforcing circle by formula (6), 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 on every side, k ₁Be transmission coefficient 10 after the grouting and reinforcing ^-6M/d, h ₀Be 15m;

3) calculating acts on the total load on the grouting and reinforcing circle, and above two pressure that calculate are superposeed to get final product, and its value is 506.5kN/m ²

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

In the formula: the ground shear modulus G _pBe 1.8 * 10 ⁴KN/m, k are 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 the deflection equation of slip casting circle after, 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, be 65.43m according to the area S at sphenoid top 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 inner centre of form place's horizontal direction of body and vertical direction of wedge shape _y, F _zBe 4.56m.

7) the horizontal component F that acts on penetration on the sphenoid is tried to achieve in employing formula (11) and (12) _yBe 9120kN, vertical component F _zBe 5055.3kN.Wherein, α is 56.3 °, γ _wBe 10 ⁴KN/m ³, D is 10m.

8) calculate skid resistance and the sliding force that acts on the sphenoid respectively according to formula (13) and (14), 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 the 6m condition.

10) according to more than identical computational methods and computational process can in the hope of under the 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, the coefficient of stability of tunnel tunnel face is respectively 0.41 during 8.0m; 1.126,1.523,1.853,2.062; 2.251,2.379,2.445,2.492.

(2) face safety factor corresponding under the different grouting and reinforcing circle thickness condition (is the accuracy of assurance graphing according to the least square method drafting pattern; The general fixing collar thickness that need get at least more than 5 calculates; Calculate the desirable 1m of step-length), can obtain regression curve as shown in Figure 6.

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

According to the Tunnel Design standard, the tunnel safety coefficient generally gets 2.0, guarantees that the minimum slip casting circle thickness of this tunnel construction tunnel face stability is 3.8m this moment, and the grouting and reinforcing circle thickness of confirming than empirical method reduces 2.2m.

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

In addition; Adopt definite method of grouting and reinforcing circle thickness of the present invention; Owing to 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, economic benefit that it produced and social benefit also are very remarkable.

Claims (3)

1. the method for designing of a submerged tunnel tunneling construction grouting and reinforcing circle thickness is characterized in that, may further comprise the steps:

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

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

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

2. the method for designing of submerged tunnel tunneling construction grouting and reinforcing circle thickness according to claim 1 is characterized in that in step 1, the coefficient of stability that a certain fixing collar thickness is corresponding adopts following method to calculate:

(1) calculates pressure from surrounding rock q;

1. H≤equivalent load height h _qThe time,

q=γ·H；

In the formula: γ covers country rock severe on the tunnel; H is an edpth of tunnel, refers to the distance on tunnel vault to ground;

2. equivalent load height h _q＜H＜dark, shallow tunnel boundary depth H _pThe time,

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

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

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

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

q=γ·h _q；

(2) adopt following formula to calculate and act on the outer hydrostatic pressure of grouting and reinforcing circle:

$u={\mathrm{\&gamma;}}_w\frac{k_0\ln \frac{D/2+h}{D/2}}{k_0\ln \frac{D/2+h}{D/2}+k_1\ln \frac{D/2+H}{D/2+h}}{h}_0;$

In the formula: u is the hydrostatic pressure on the grouting and reinforcing circle external surface; h ₀The degree of depth for water; k ₀Be the original transmission coefficient of ground on every side; k ₁Transmission coefficient for the slip casting circle; H is an edpth of tunnel; H is a grouting and reinforcing circle thickness; D is the tunnel span; γ _wUnit weight for water.

(3) calculating acts on the total load on the grouting and reinforcing circle, total load q ₀Be pressure from surrounding rock q and hydrostatic pressure u sum;

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

With total load q ₀Substitution And the substitution fringe conditions finds the solution following formula, obtains the deflection equation ω (x) of fixing collar; In the formula: G _pBe the ground modulus of shearing, k is a coefficient of subgrade reaction, b ^*For considering two-parameter ground continuity finite width beam equivalent width, have E, I are the modulus of elasticity and the moment of inertia of slip casting circle, wherein

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

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

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 the sphenoid _y, vertical component F _z:

F _y=2γ _wD ²h(y)；

F _z=2γ _wD ²cosαh(z)；

Wherein, D is the 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 sphenoid centre of form place, an inside head vertically;

(8) calculating acts on skid resistance and the sliding force on the sphenoid;

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

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

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

T is the frictional resistance on the 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 the voussoir deadweight,

α is the break angle of rupture of body of wedge shape; Be the break angle of the body plane of fracture and horizontal plane of wedge shape,

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

K ₀Be lateral pressure coefficient,

μ is the poisson's ratio of country rock;

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

3. the method for designing of submerged tunnel tunneling construction grouting and reinforcing circle thickness according to claim 1 and 2 is characterized in that the 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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