CN102704947B

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

Info

Publication number: CN102704947B
Application number: CN201210176528.5A
Authority: CN
Inventors: 施成华; 彭立敏; 雷明锋; 杨伟超; 曹成勇
Original assignee: Central South University
Current assignee: Central South University
Priority date: 2012-05-31
Filing date: 2012-05-31
Publication date: 2014-04-30
Anticipated expiration: 2032-05-31
Also published as: CN102704947A

Abstract

The invention discloses a method for designing the thickness of a grouting reinforcement circle in underground excavation construction of an underwater tunnel. The stability coefficient of the surface; Step 2: Based on the thickness of different reinforcement rings and the corresponding stability coefficients, according to the least squares method, obtain the thickness of the reinforcement ring-stability coefficient regression curve; Step 3: According to the thickness of the reinforcement ring-stability coefficient regression curve, you can The thickness of the reinforcement ring required by the tunnel under the condition of a certain designed stability coefficient is obtained. The thickness of the reinforcement ring obtained by adopting the design method of the thickness of the grouting reinforcement ring in the underground excavation construction of the underwater tunnel can better meet the construction requirements of the site engineering, so that on the one hand, the construction safety of the tunnel can be ensured, and on the other hand, the construction cost can also be reduced.

Description

A Design Method for the Thickness of Grouting Reinforcement Circle in Underwater Tunnel Underground Excavation Construction

技术领域 technical field

本发明涉及一种水下隧道暗挖施工注浆加固圈厚度的设计方法。The invention relates to a design method for the thickness of a grouting reinforcement ring in underground excavation construction of an underwater tunnel.

背景技术 Background technique

水下隧道采用矿山法进行施工时，为防止开挖面出现突水坍塌等工程事故，施工中通常采用超前注浆进行预加固，而后在注浆加固圈的保护下进行隧道开挖，以保证水下隧道的施工安全。然而，目前国内外对于水下隧道超前注浆加固参数的设计主要还是在经验的基础上按工程类比法进行，相关的公路和铁路隧道设计规范对水下隧道注浆加固圈厚度如何确定完全没有涉及。实际水下隧道工程设计中，注浆加固参数的确定往往根据设计工程师的个人经验进行判定，对于采用的注浆设计参数是否完全能够保证隧道安全施工的需要，或者确定的注浆参数是否过于保守，其安全系数有多大，包括设计工程师自己都无法确定。因此，一方面设计中为保证安全，设计工程师往往一味的加大注浆加固圈的厚度，以保证隧道的施工安全，从而增加了隧道的工程造价；另一方面，由于缺乏有效的分析和设计方法，无法根据隧道的地质条件进行针对性的设计，整座隧道往往采用完全相同的注浆加固设计参数，使得水下隧道在断层破碎带等地质薄弱位置又存在一定的施工风险。When underwater tunnels are constructed using the mining method, in order to prevent engineering accidents such as water inrush and collapse on the excavation surface, advance grouting is usually used for pre-reinforcement during construction, and then the tunnel is excavated under the protection of the grouting reinforcement ring to ensure Construction safety of underwater tunnels. However, at present, the design of advanced grouting reinforcement parameters for underwater tunnels at home and abroad is mainly carried out on the basis of experience and according to the engineering analogy method. The relevant highway and railway tunnel design codes have no idea how to determine the thickness of the underwater tunnel grouting reinforcement ring. involves. In the actual engineering design of underwater tunnels, the determination of grouting reinforcement parameters is often judged according to the personal experience of the design engineer. Whether the adopted grouting design parameters can fully meet the needs of safe tunnel construction, or whether the determined grouting parameters are too conservative , How big its safety factor is, even the design engineers themselves cannot be sure. Therefore, on the one hand, in order to ensure safety in the design, design engineers often blindly increase the thickness of the grouting reinforcement ring to ensure the construction safety of the tunnel, thereby increasing the engineering cost of the tunnel; on the other hand, due to the lack of effective analysis and design method, it is impossible to carry out targeted design according to the geological conditions of the tunnel, and the entire tunnel often adopts exactly the same grouting reinforcement design parameters, so that underwater tunnels have certain construction risks in geologically weak positions such as fault fracture zones.

总体来说，水下隧道注浆加固圈厚度的设计目前还停留在经验的基础上，无法满足我国水下隧道建设快速发展的需要。Generally speaking, the design of the thickness of the grouting reinforcement ring for underwater tunnels is still based on experience and cannot meet the needs of the rapid development of underwater tunnel construction in my country.

因此，研制一种新型的定量化的水下隧道注浆加固圈厚度的设计方法已为急需。Therefore, it is urgent to develop a new quantitative design method for the thickness of the grouting reinforcement ring in underwater tunnels.

发明内容 Contents of the invention

本发明所要解决的技术问题是提供一种水下隧道暗挖施工注浆加固圈厚度的设计方法，采用该水下隧道暗挖施工注浆加固圈厚度的设计方法得到的加固圈厚度更能满足现场工程施工要求，从而一方面可保证隧道的施工安全，另一方面也可降低工程造价。The technical problem to be solved by the present invention is to provide a design method for the thickness of the grouting reinforcement ring in the underwater tunnel excavation construction. On the one hand, it can ensure the construction safety of the tunnel, and on the other hand, it can also reduce the construction cost.

发明的技术解决方案如下：The technical solution of the invention is as follows:

一种水下隧道暗挖施工注浆加固圈厚度的设计方法，包括以下步骤：A method for designing the thickness of a grouting reinforcement circle in underground excavation construction of an underwater tunnel, comprising the following steps:

步骤1：选取一组加固圈厚度参数，计算不同加固圈厚度条件下隧道施工工作面的稳定系数；Step 1: Select a set of reinforcement ring thickness parameters, and calculate the stability coefficient of the tunnel construction face under different reinforcement ring thickness conditions;

步骤2：基于不同加固圈厚度以及对应的稳定系数，根据最小二乘法，获得加固圈厚度-稳定系数回归曲线；Step 2: Based on the thickness of different reinforcement rings and the corresponding stability coefficients, according to the least square method, obtain the regression curve of reinforcement ring thickness-stability coefficient;

步骤3：根据该加固圈厚度-稳定系数回归曲线，即可得到某一设计的稳定系数条件下隧道所需的加固圈厚度。Step 3: According to the thickness-stability coefficient regression curve of the reinforcement ring, the thickness of the reinforcement ring required for the tunnel under a certain designed stability coefficient can be obtained.

在步骤1，某一加固圈厚度对应的稳定系数采用以下方法计算：In step 1, the stability coefficient corresponding to a certain thickness of the reinforcement ring is calculated by the following method:

（1）计算围岩压力q；(1) Calculate the surrounding rock pressure q;

①H≤等效荷载高度h_q时，① When H≤equivalent load height h _q ,

q=γ·H；q=γ·H;

式中：γ为隧道上覆围岩重度；H为隧道埋深，指隧道拱顶至地面的距离；In the formula: γ is the weight of the overlying surrounding rock of the tunnel; H is the buried depth of the tunnel, which refers to the distance from the tunnel vault to the ground;

②等效荷载高度h_q＜H＜深、浅埋隧道分界深度H_p时，② When the equivalent load height h _q < H < the boundary depth H _p of deep and shallow buried tunnels,

$q q = = γH γH ((11 - - \frac{H h}{22 B B} λtgθ λtgθ)),,$

$λ λ = = \frac{tgβ tgβ - - tgφ tgφ}{tgβ tgβ [[11 + + tgβ tgβ ((tgφ tgφ - - tgθ tgθ)) + + tgφtgθ tgφtgθ]]};;$

式中：λ为侧压力系数；β为破裂面与水平面的夹角；φ为似摩擦角，θ为摩阻角。In the formula: λ is the lateral pressure coefficient; β is the angle between the rupture surface and the horizontal plane; φ is the approximate friction angle, and θ is the friction angle.

③H)≥深、浅埋隧道分界深度H_p时，③H)≥deep and shallow tunnel boundary depth _Hp ,

q=γ·h_q；q=γ h _q ;

（2）采用以下公式计算作用于注浆加固圈外的静水压力：(2) Use the following formula to calculate the hydrostatic pressure acting on the outside of the grouting reinforcement circle:

$u u = = {γ γ}_{w w} \frac{{k k}_{00} ln ln \frac{D D. / / 22 + + h h}{D D. / / 22}}{{k k}_{00} ln ln \frac{D D. / / 22 + + h h}{D D. / / 22} + + {k k}_{11} ln ln \frac{D D. / / 22 + + H h}{D D. / / 22 + + h h}} {h h}_{00};;$

式中：u为注浆加固圈外表面上的静水压力；h₀为水的深度；k₀为周围岩土原有的渗透系数；k₁为注浆圈的渗透系数；H为隧道埋深；h为注浆加固圈厚度；D为隧道跨度；γ_w为水的容重。In the formula: u is the hydrostatic pressure on the outer surface of the grouting ring; _h0 is the depth of water; _k0 is the original permeability coefficient of the surrounding rock and soil; _k1 is the permeability coefficient of the grouting ring; H is the buried depth of the tunnel ; h is the thickness of the grouting reinforcement ring; D is the tunnel span; γ _w is the bulk density of water.

（3）计算作用于注浆加固圈上的总荷载，总荷载q₀为围岩压力q与静水压力u之和；(3) Calculate the total load acting on the grouting reinforcement ring, the total load _q0 is the sum of surrounding rock pressure q and hydrostatic pressure u;

(4)获得加固圈的挠度方程ω(x)；(4) Obtain the deflection equation ω(x) of the reinforcement ring;

将总荷载q₀代入 $EI \frac{d^{4} ω (x)}{{dx}^{4}} - G_{p} b * \frac{d^{2} ω (x)}{{dx}^{2}} + kb * ω (x) = {bq}_{0}$ 并代入边界条件对上式求解，得到加固圈的挠度方程ω(x)；Substitute the total load q ₀ into $EI d \frac{^{4} ω (x)}{{dx}^{4}} - G_{p} b * \frac{d^{2} ω (x)}{{dx}^{2}} + kb * ω (x) = {bq}_{0}$ And substituting the boundary conditions to solve the above formula, the deflection equation ω(x) of the reinforcement ring is obtained;

式中：G_p为地基剪切模量，k为基床系数，（G_p、k均能根据地质勘探资料得到），b^*为考虑双参数地基连续性有限宽度梁等效宽度，有

E、I为注浆圈的弹性模量和惯性矩，其中

b为梁的宽度，此处即为隧道的跨度；h为注浆加固圈的厚度。In the formula: G _p is the shear modulus of the foundation, k is the subgrade coefficient, (G _p and k can be obtained according to the geological exploration data), b ^* is the equivalent width of the finite-width beam considering the continuity of the two-parameter foundation,

E and I are the elastic modulus and moment of inertia of the grouting ring, where

b is the width of the beam, here is the span of the tunnel; h is the thickness of the grouting reinforcement ring.

(5)基于加固圈的挠度方程ω(x)，计算作用于楔形破裂体顶面的总作用力P；(5) Based on the deflection equation ω(x) of the reinforcement ring, calculate the total force P acting on the top surface of the wedge-shaped rupture body;

P=σ·S，其中，σ为作用在楔块上部的平均应力，

积分区间（0，Dcotα），L=Dcotα；

S为楔形破裂体顶面面积；P=σ·S, where σ is the average stress acting on the upper part of the wedge,

Integral interval (0, Dcotα), L=Dcotα;

S is the area of the top surface of the wedge-shaped rupture body;

(6)计算楔形破裂体内部形心处水平方向的水头值h(y)和竖直方向的水头值h(z)；(6) Calculate the hydraulic head value h(y) in the horizontal direction and the hydraulic head value h(z) in the vertical direction at the centroid inside the wedge-shaped rupture body;

(7)作用于楔形体上渗透力的水平分量F_y，竖直分量F_z：(7) Horizontal component F _y and vertical component F _z of seepage force acting on the wedge:

F_y=2γ_wD²h(y)；F _y =2γ _w D ² h(y);

F_z=2γ_wD²cosαh(z)；F _z =2γ _w D ² cosαh(z);

其中，D为隧道跨度；α为楔形破裂体破裂面与水平面的夹角，h(y)为楔形体内部形心处沿水平方向的水头，h(z)为楔形体内部形心处沿竖直方向的水头；Among them, D is the span of the tunnel; α is the angle between the fracture surface of the wedge-shaped rupture body and the horizontal plane, h(y) is the water head along the horizontal direction at the centroid inside the wedge-shaped body, and h(z) is the water head along the vertical direction at the centroid inside the wedge-shaped body. vertical head of water;

(8)计算作用于楔形体上的抗滑力和下滑力；(8) Calculate the anti-slip force and the sliding force acting on the wedge;

抗滑力F_抗滑力=T_g+T，Anti-slip force F _{Anti-slip force} = T _g + T,

下滑力F_下滑力=(P+G+F_z)sinα+F_ycosα；Sliding force F _{sliding force} = (P+G+F _z ) sinα+F _y cosα;

式中：T_g为楔块两侧侧向摩阻力， $T_{g} = D^{2} \cot α (c + K_{0} \tan φ \frac{2 σ + Dγ}{3});$ In the formula: T _g is the lateral friction resistance on both sides of the wedge, $T_{g} = {D.}^{2} \cot α (c + K_{0} the tan φ \frac{2 σ + Dγ}{3});$

T为倾斜滑动面上的摩阻力，

N为作用于破裂体的法向力，T is the frictional resistance on the inclined sliding surface,

N is the normal force acting on the rupture body,

N=(P+G+F_z)cosα-F_ysinα；P为作用于楔形破裂体顶面的总作用力（具体计算由步骤（5）算得），G为楔块自重，

N=(P+G+F _z )cosα-F _y sinα; P is the total force acting on the top surface of the wedge-shaped broken body (the specific calculation is calculated in step (5)), G is the self-weight of the wedge,

α为楔形破裂体的破裂角，即楔形破裂体破裂面与水平面的夹角， α is the rupture angle of the wedge-shaped rupture body, that is, the angle between the rupture surface of the wedge-shaped rupture body and the horizontal plane,

为工作面围岩的内摩擦角；γ为围岩容重；c为围岩的粘聚力；

is the internal friction angle of the surrounding rock of the working face; γ is the bulk density of the surrounding rock; c is the cohesion of the surrounding rock;

K₀为侧压力系数，μ为围岩的泊松比；【对于具体的隧道工程，c、

γ、μ可根据地质勘探报告选取，也可根据隧道具体的围岩级别根据隧道设计规范选取；】K ₀ is the lateral pressure coefficient, μ is the Poisson's ratio of the surrounding rock; [for specific tunnel engineering, c,

γ and μ can be selected according to the geological exploration report, or can be selected according to the specific surrounding rock level of the tunnel according to the tunnel design specification;]

(9)计算得到隧道掌子面的稳定系数K：(9) Calculate the stability factor K of the tunnel face:

加固圈厚度参数为至少五个，从大到小或从小到大排列，相邻的加固圈厚度参数值的差值为1m。The thickness parameters of the reinforcement rings are at least five, arranged from large to small or from small to large, and the difference between the thickness parameters of adjacent reinforcement rings is 1m.

本发明提供的水下隧道暗挖施工注浆加固圈厚度的设计方法，认为水下隧道施工工作面在围岩压力、静水压力和渗透力共同作用下会产生如图2所示的潜在楔形破裂体，从而按保证潜在楔形破裂体的稳定性进行注浆加固圈厚度的设计。The design method for the thickness of the grouting reinforcement ring in the underwater tunnel excavation construction provided by the present invention considers that the underwater tunnel construction face will produce a potential wedge-shaped fracture as shown in Figure 2 under the joint action of surrounding rock pressure, hydrostatic pressure and seepage force body, so as to ensure the stability of the potential wedge-shaped fractured body, the thickness of the grouting reinforcement ring is designed.

本发明还在于所述的作用于注浆加固圈上的围岩压力根据隧道埋深的不同按相关隧道设计规范进行计算。The present invention also lies in that the surrounding rock pressure acting on the grouting reinforcement ring is calculated according to the relevant tunnel design specifications according to the difference in the buried depth of the tunnel.

①埋深(H)≤等效荷载高度(h_q)时，荷载视为均布垂直压力：① When buried depth (H) ≤ equivalent load height (h _q ), the load is regarded as uniform vertical pressure:

q=γ·H （1）q=γ·H （1）

式中：q为垂直均布压力(kN/m²)；γ为隧道上覆围岩重度（kN/m³）；H为隧道埋深，指隧道拱顶至地面的距离(m)。其中h_q为等效荷载高度（m），h_q=0.45×2^S-1·ω，S为围岩级别；ω为宽度影响系数，即ω=1+i(B-5)，其中B为隧道宽度(m)，i为隧道宽度B每增减1m时的围岩压力增减率，以B=5m的围岩垂直均布压力为准，当B<5m时，取i＝0.2；B=5~15m时，取i＝0.1。In the formula: q is the vertical uniform pressure (kN/m ² ); γ is the weight of the surrounding rock above the tunnel (kN/m ³ ); H is the buried depth of the tunnel, which refers to the distance from the tunnel vault to the ground (m). where h _q is the equivalent load height (m), h _q =0.45×2 ^S-1 ω, S is the grade of surrounding rock; ω is the width influence coefficient, that is, ω=1+i(B-5), where B is the tunnel width (m), i is the increase or decrease rate of the surrounding rock pressure when the tunnel width B increases or decreases by 1m, taking the vertical uniform pressure of the surrounding rock as B=5m as the criterion, when B<5m, take i=0.2; When B=5~15m, take i=0.1.

②等效荷载高度(h_q)＜埋深(H)＜深、浅埋隧道分界深度(H_p)，作用在注浆加固圈上的均布荷载为：② Equivalent load height (h _q ) < buried depth (H) < deep and shallow tunnel boundary depth (H _p ), the uniform load acting on the grouting reinforcement ring is:

$q q = = γH γH ((11 - - \frac{H h}{22 B B} λtgθ λtgθ)) - - - - - - ((22))$

$λ λ = = \frac{tgβ tgβ - - tgφ tgφ}{tgβ tgβ [[11 + + tgβ tgβ ((tgφ tgφ - - tgθ tgθ)) + + tgφtgθ tgφtgθ]]} - - - - - - ((33))$

以上式中：B为隧道开挖宽度，β为破裂面与水平面的夹角(°)；φ为似摩擦角，θ为摩阻角，根据围岩级不同按《公路隧道涉及规范》选取。H_p为隧道深、浅埋隧道分界深度，H_p=(2~2.5)h_q，当围岩为Ⅰ~Ⅲ级时取2，Ⅳ~Ⅵ级时取2.5，λ为侧压力系数，按下式计算。In the above formula: B is the excavation width of the tunnel, β is the angle between the rupture surface and the horizontal plane (°); φ is the friction angle, and θ is the friction angle, which is selected according to the "Code for Highway Tunnels" according to the different grades of surrounding rocks. H _p is the depth of the tunnel depth and the boundary depth of the shallow buried tunnel, H _p = (2~2.5)h _q , when the surrounding rock is grade I~III, take 2, and when the surrounding rock is grade IV~VI, take 2.5, λ is the lateral pressure coefficient, according to Calculated with the following formula.

③埋深(H)≥深、浅埋隧道分界深度(H_p)③ Burial depth (H) ≥ Deep and shallow buried tunnel boundary depth (H _p )

q=γ·h_q （4）q=γ h _q (4)

（3）本发明还在于所述的作用于注浆圈外的静水压力根据注浆加固圈厚度及渗透系数，按照地下水渗流的相关理论进行求解。(3) The present invention also lies in that the hydrostatic pressure acting on the outside of the grouting ring is solved according to the relevant theory of groundwater seepage according to the thickness of the grouting reinforcement ring and the permeability coefficient.

$u u = = {γ γ}_{w w} \frac{{k k}_{00} ln ln \frac{D D. / / 22 + + h h}{D D. / / 22}}{{k k}_{00} ln ln \frac{D D. / / 22 + + h h}{D D. / / 22} + + {k k}_{11} ln ln \frac{D D. / / 22 + + H h}{D D. / / 22 + + h h}} {h h}_{00} - - - - - - ((55))$

（4）本发明还在于所述的注浆加固圈按照有限长度弹性地基梁进行计算分析，进而计算得到作用于潜在楔形破裂体上的作用力为：(4) The present invention also lies in the fact that the grouting reinforcement ring is calculated and analyzed according to the finite length of the elastic foundation beam, and then the calculated force acting on the potential wedge-shaped fracture body is:

$p p ((x x)) = = kω kω ((w w)) - - {G G}_{p p} \frac{d d {ω ω}^{22} ((x x))}{{dx dx}^{22}} - - - - - - ((66))$

式中，G_p为地基剪切模量，k为基床系数。ω(x)为注浆圈的挠度方程，其控制方程为 $EI \frac{d^{4} ω (x)}{{dx}^{4}} - G_{p} b * \frac{d^{2} ω (x)}{{dx}^{2}} + kb * ω (x) = {bq}_{0},$ 代入边界条件即可进行求解。其中q(x)为作用于注浆加固圈上的荷载（包括围岩压力、静水压力），p(x)为弹性抗力，也即作用于楔形破裂体上的作用力。E、I为注浆圈的弹性模量和惯性矩。其中

b为梁的宽度，此处即为隧道的跨度；h为注浆加固圈的厚度。In the formula, G _p is the shear modulus of the foundation, and k is the coefficient of the subgrade bed. ω(x) is the deflection equation of the grouting ring, and its governing equation is

EI d \frac{^{4} ω (x)}{{dx}^{4}} - G_{p} b * \frac{d^{2} ω (x)}{{dx}^{2}} + kb * ω (x) = {bq}_{0},

It can be solved by substituting boundary conditions. Among them, q(x) is the load acting on the grouting reinforcement ring (including surrounding rock pressure and hydrostatic pressure), and p(x) is the elastic resistance, that is, the force acting on the wedge-shaped fractured body. E and I are the elastic modulus and moment of inertia of the grouting ring. in

（5）本发明还在于所述的作用于楔形破裂体的渗透力采用数值模拟方法求出各点的水头，而后根据渗流理论进行求解。应用高斯理论，如图2所示，得到作用在楔形体上的渗透力的水平分量和垂直分量的表达式：(5) The present invention also lies in that the seepage force acting on the wedge-shaped fractured body adopts the numerical simulation method to obtain the water head at each point, and then solves it according to the seepage theory. Applying the Gaussian theory, as shown in Fig. 2, the expressions of the horizontal and vertical components of the seepage force acting on the wedge are obtained:

F_y(α)=γ_w(-sinα∫_ABEFh^*dA+∫A_BCJh ^*dA) （7）F _y (α)= _γw (-sinα∫ _ABEF h ^* dA+∫A _BCJh ^* dA) (7)

F_z(α)=γ_w(cosα∫_ABEFh^*dA-∫C_JEFh ^*dA) （8）F _z (α)=γ _w (cosα∫ _ABEF h ^* dA-∫C _JEFh ^* dA) (8)

式中：α为楔形破裂体的破裂角，γ_w为水的容重，h^*为楔形体内部沿x方向的平均水头，有In the formula: α is the rupture angle of the wedge-shaped rupture body, γ _w is the bulk density of water, h ^* is the average water head along the x direction inside the wedge-shaped body, and

${h h}^{* *} = = {h h}^{* *} ((y the y,, z z)) = = \frac{11}{D D.} {&Integral; &Integral;}_{- - D D. / / 22}^{D D. / / 22} h h ((x x,, y the y,, z z)) dx dx - - - - - - ((99))$

式中：D为隧道跨度；h(x,y,z)为数值模拟得到的各点的水头值。In the formula: D is the span of the tunnel; h(x, y, z) is the head value of each point obtained by numerical simulation.

（6）本发明还在于所述的作用于潜在楔形破裂体上的下滑力和抗滑力分别为：(6) The present invention also lies in that the sliding force and anti-sliding force acting on the potential wedge-shaped broken body are respectively:

F_抗滑力=T_g+T （10）F _{Anti-slip force} = T _g + T (10)

F_下滑力=(P+G+F_z)sinα+F_ycosα （11）F _{sliding force} =(P+G+F _z ) sinα+F _y cosα (11)

式中：T_g为楔块两侧侧向摩阻力， $T_{g} = D^{2} \cot α (c + K_{0} \tan φ \frac{2 σ + Dγ}{3});$ T为倾斜滑动面上的摩阻力，

N为作用于破裂体的法向力，N=(P+G+F_z)cosα-F_ysinα；P为楔形破裂体顶面的总作用力，G为楔块自重，F_y、F_z为作用在楔形体上的渗透力的水平分量和垂直分量，按（11）和（12）式进行计算；α为楔形破裂体的破裂角，

为工作面围岩的内摩擦角；γ为围岩容重；c为围岩的粘聚力；K₀为侧压力系数，

μ为围岩的泊松比；对于具体的隧道工程，c、

γ、μ可根据地质勘探报告选取，也可根据隧道具体的围岩级别根据隧道设计规范选取；其余符号意义同前。In the formula: T _g is the lateral friction resistance on both sides of the wedge,

T_{g} = {D.}^{2} \cot α (c + K_{0} the tan φ \frac{2 σ + Dγ}{3});

T is the frictional resistance on the inclined sliding surface,

N is the normal force acting on the rupture body, N=(P+G+F _z )cosα-F _y sinα; P is the total force on the top surface of the wedge-shaped rupture body, G is the self-weight of the wedge, F _y and F _z are the horizontal and vertical components of the seepage force acting on the wedge, calculated according to formulas (11) and (12); α is the rupture angle of the wedge-shaped rupture,

is the internal friction angle of the surrounding rock in the working face; γ is the bulk density of the surrounding rock; c is the cohesion of the surrounding rock; K ₀ is the lateral pressure coefficient,

μ is Poisson's ratio of surrounding rock; for specific tunnel engineering, c,

γ and μ can be selected according to the geological exploration report, or can be selected according to the specific surrounding rock grade of the tunnel according to the tunnel design specification; the meanings of other symbols are the same as before.

（7）本发明还在于所述的隧道施工掌子面的稳定系数，分别计算作用于潜在楔形破裂体上的下滑力和抗滑力，即可得到水下隧道施工掌子面的稳定系数，具体按下式求解。(7) The present invention also lies in the stability coefficient of the tunnel construction face, and the stability coefficient of the underwater tunnel construction face can be obtained by calculating the sliding force and the anti-sliding force acting on the potential wedge-shaped rupture body respectively, Specifically, solve it according to the formula.

式中：各符号意义同前。In the formula: the meanings of the symbols are the same as before.

（7）本发明还在于所述的最佳的注浆加固圈厚度，对不同注浆加固圈厚度条件下隧道施工掌子面的稳定系数进行求解，绘制加固圈厚度与掌子面稳定系数的关系曲线，即可求得满足工作面稳定系数要求的最佳的注浆加固圈厚度。(7) The present invention also lies in the optimal thickness of the grouting reinforcement ring, and solves the stability coefficient of the tunnel construction tunnel face under the condition of different grouting reinforcement ring thicknesses, and draws the relationship between the thickness of the reinforcement ring and the stability coefficient of the tunnel face The relationship curve can be used to obtain the optimal thickness of the grouting reinforcement ring that meets the requirements of the stability coefficient of the working face.

有益效果：Beneficial effect:

本发明的水下隧道暗挖施工注浆加固圈厚度的设计方法，与现有水下暗挖施工隧道注浆加固设计方法相比，其优点在于：传统的基于规范和经验的水下隧道注浆加固圈厚度的设计方法，其设计厚度选择的合理性完全依赖于设计人员本身的设计经验和现场经验，而本发明提出的水下隧道注浆加固圈厚度的定量化设计方法，其加固厚度的确定完全通过理论计算得到，和设计人员的设计经验关系不大，使得得到的加固圈厚度更能满足现场工程施工要求，从而一方面可保证水下隧道的施工安全，另一方面也可降低工程造价。The method for designing the thickness of the grouting reinforcement ring for underwater tunnel excavation construction of the present invention, compared with the existing design method for underwater tunnel construction grouting reinforcement, has the advantage that the traditional underwater tunnel grouting method based on norms and experiences The design method of the thickness of the grouting reinforcement ring, the rationality of its design thickness selection completely depends on the design experience and field experience of the designer itself, and the quantitative design method of the thickness of the underwater tunnel grouting reinforcement ring proposed by the present invention, the reinforcement thickness The determination of is completely obtained through theoretical calculation, and has little to do with the design experience of the designer, so that the thickness of the reinforcement ring obtained can better meet the construction requirements of the site engineering, so that on the one hand, the construction safety of the underwater tunnel can be ensured, and on the other hand, it can also be reduced. project costs.

附图说明 Description of drawings

图1为本发明水下隧道暗挖施工注浆加固示意图Fig. 1 is a schematic diagram of grouting reinforcement for underwater tunnel excavation construction of the present invention

图2为本发明掌子面楔形破裂体示意图Fig. 2 is a schematic diagram of a wedge-shaped rupture body of the face of the present invention

图3为本发明静水压力计算模型示意图Fig. 3 is the schematic diagram of hydrostatic pressure calculation model of the present invention

图4为本发明隧道开挖过程中注浆圈受力计算模型示意图Fig. 4 is a schematic diagram of the force calculation model of the grouting ring during the tunnel excavation process of the present invention

图5为本发明掌子面楔形破裂体作用力示意图Figure 5 is a schematic diagram of the force of the wedge-shaped rupture body on the face of the face of the present invention

图6为本发明注浆加固圈厚度与隧道掌子面稳定系数关系曲线示意图Fig. 6 is a schematic diagram of the relationship curve between the thickness of the grouting reinforcement ring and the stability coefficient of the tunnel face according to the present invention

图中：1—初期支护，2—钢拱架，3—掌子面，4—破裂面，5—围岩，6—注浆加固圈，7—江底位置，8—江水位，9—隧道，10—楔形破裂体，H—隧道埋深，D-隧道高度，P注浆圈传递到楔形破裂体上的合力，G楔块自重，T_g为楔块两侧侧向摩阻力，F_y-作用在楔形体上的渗透力的水平分量，F_z-作用在楔形体上的渗透力的垂直分量，T—倾斜滑动面上的摩阻力，N—作用于破裂体的法向力，h₀-隧道拱顶的水位深度，h注浆圈的厚度，K-隧道工作面的稳定系数，A、B、C、E、F、J-楔形破裂体各顶点的位置。In the figure: 1—initial support, 2—steel arch, 3—face of tunnel, 4—fracture surface, 5—surrounding rock, 6—ring of grouting reinforcement, 7—position of river bottom, 8—water level of river, 9 —Tunnel, 10—Wedge-shaped rupture body, H—Tunnel burial depth, D—Tunnel height, P The resultant force transmitted from the grouting ring to the wedge-shaped rupture body, G The self-weight of the wedge, T _g is the lateral friction resistance on both sides of the wedge, F _y -horizontal component of seepage force acting on the wedge, F _z -vertical component of seepage force acting on the wedge, T—frictional resistance on the inclined sliding surface, N—normal force acting on the fractured body , h ₀ - the water level depth of the tunnel vault, h the thickness of the grouting ring, K - the stability coefficient of the tunnel working face, A, B, C, E, F, J - the positions of the vertices of the wedge-shaped fracture body.

具体实施方式 Detailed ways

以下将结合附图和具体实施例对本发明做进一步详细说明：The present invention will be described in further detail below in conjunction with accompanying drawing and specific embodiment:

一种水下隧道暗挖施工注浆加固参数的设计方法，参见图1，隧道开挖后,水下隧道施工工作面在围岩压力、静水压力和渗透力共同作用下会产生潜在的楔形破裂体（图2），通过工作面稳定性分析，按保证潜在楔形破裂体的稳定性进行注浆加固设计，注浆加固的具体设计参数包括注浆圈厚度、注浆后的渗透系数和力学参数。围岩压力根据隧道埋深的不同按相关隧道设计规范进行计算，注浆加固圈按照有限长度弹性地基梁进行计算分析，作用于注浆圈外的静水压力根据注浆加固圈厚度及渗透系数，按照地下水的渗流的相关理论进行求解，作用于楔形破裂体的渗透力采用数值模拟方法求出各点的水头，而后根据渗流理论进行求解，分别计算作用于潜在楔形破裂体上的下滑力和抗滑力，基于极限平衡理论，最终确定保证潜在楔形破裂体稳定性的注浆加固圈厚度。A design method of grouting reinforcement parameters for underwater tunnel excavation construction, see Figure 1. After the tunnel is excavated, the underwater tunnel construction face will produce potential wedge-shaped fractures under the combined action of surrounding rock pressure, hydrostatic pressure and seepage force body (Fig. 2), through the stability analysis of the working face, the grouting reinforcement design is carried out to ensure the stability of the potential wedge-shaped fractured body. The specific design parameters of the grouting reinforcement include the thickness of the grouting ring, the permeability coefficient after grouting, and the mechanical parameters. . The surrounding rock pressure is calculated according to the relevant tunnel design codes according to the different buried depths of the tunnel. The grouting reinforcement ring is calculated and analyzed according to the finite length elastic foundation beam. The hydrostatic pressure acting on the outside of the grouting ring is based on the thickness and permeability coefficient of the grouting reinforcement ring. According to the relevant theory of groundwater seepage, the seepage force acting on the wedge-shaped rupture body is calculated by numerical simulation method to obtain the water head at each point, and then the solution is carried out according to the seepage theory, and the sliding force and resistance acting on the potential wedge-shaped rupture body are respectively calculated. Sliding force, based on the limit equilibrium theory, finally determines the thickness of the grouting reinforcement ring to ensure the stability of the potential wedge-shaped fractured body.

（1）作用于注浆加固圈上的围岩压力的计算(1) Calculation of surrounding rock pressure acting on the grouting reinforcement circle

根据我国公路或铁路隧道设计规范，可得隧道围岩等效荷载高度h_q为：According to the design specification of road or railway tunnel in China, the equivalent load height _hq of the surrounding rock of the tunnel can be obtained as:

h_q=0.45×2^S-1·ω （1）h _q =0.45×2 ^S-1 ω (1)

式中：h_q为等效荷载高度（m）；S为围岩级别；ω为宽度影响系数，即ω=1+i(B-5)，其中B为隧道宽度(m)，i为隧道宽度B每增减1m时的围岩压力增减率，以B=5m的围岩垂直均布压力为准，当B<5m时，取i=0.2；B=5～15m时，取i=0.1。In the formula: h _q is the equivalent load height (m); S is the grade of surrounding rock; ω is the width influence coefficient, that is, ω=1+i(B-5), where B is the tunnel width (m), and i is the tunnel width The increase or decrease rate of the surrounding rock pressure when the width B is increased or decreased by 1m is based on the vertical uniform pressure of the surrounding rock with B=5m. When B<5m, take i=0.2; when B=5～15m, take i= 0.1.

q=γ·H （2）q=γ·H （2）

式中：q为垂直均布压力(kN/m²)；γ为隧道上覆围岩重度（kN/m³）；H为隧道埋深，指隧道拱顶至地面的距离(m)。In the formula: q is the vertical uniform pressure (kN/m ² ); γ is the weight of the surrounding rock above the tunnel (kN/m ³ ); H is the buried depth of the tunnel, which refers to the distance from the tunnel vault to the ground (m).

$q q = = γH γH ((11 - - \frac{H h}{22 B B} λtgθ λtgθ)) - - - - - - ((33))$

$λ λ = = \frac{tgβ tgβ - - tgφ tgφ}{tgβ tgβ [[11 + + tgβ tgβ ((tgφ tgφ - - tgθ tgθ)) + + tgφtgθ tgφtgθ]]} - - - - - - ((44))$

式中：λ为侧压力系数；φ为似摩擦角，θ为摩阻角，β为破裂面与水平面的夹角(°)，其中φ，θ根据围岩级别不同按隧道设计规范选取，其余符号意义同前。In the formula: λ is the lateral pressure coefficient; φ is the apparent friction angle, θ is the friction angle, and β is the angle (°) between the rupture surface and the horizontal plane, where φ, θ are selected according to the tunnel design code according to the different grades of surrounding rock, and the meanings of other symbols are the same as before.

q=γ·h_q （5）q=γ h _q (5)

（2）作用于注浆圈外的静水压力的计算。(2) Calculation of the hydrostatic pressure acting on the outside of the grouting circle.

参见图3，可得：Referring to Figure 3, we can get:

$u u = = {γ γ}_{w w} \frac{{k k}_{00} ln ln \frac{D D. / / 22 + + h h}{D D. / / 22}}{{k k}_{00} ln ln \frac{D D. / / 22 + + h h}{D D. / / 22} + + {k k}_{11} ln ln \frac{D D. / / 22 + + H h}{D D. / / 22 + + h h}} {h h}_{00} - - - - - - ((66))$

式中：u为注浆加固圈外表面上的静水压力；h₀为水的深度；k₀为周围岩土原有的渗透系数；（可由地质勘探测资料得到）k₁为注浆圈的渗透系数（可通过取样试验得到）；H为隧道埋深；h为注浆加固圈厚度；D为隧道跨度；γ_w为水的容重，为10kN/m³（H，D根据隧道设计图纸确定，h为本方法需要确定的设计参数。）In the formula: u is the hydrostatic pressure on the outer surface of the grouting reinforcement ring; h ₀ is the depth of water; k ₀ is the original permeability coefficient of the surrounding rock and soil; (obtained from geological survey data) k ₁ is the grouting ring Permeability coefficient (can _be obtained by sampling test); H is the depth of the tunnel; h is the thickness of the grouting reinforcement circle; D is the ^span of the tunnel; , h is the design parameter that needs to be determined by this method.)

（3）通过注浆加固圈作用于潜在楔形破裂体上的作用力的计算。(3) Calculation of the force acting on the potential wedge-shaped fracture body through the grouting reinforcement ring.

注浆加固圈的弹性地基梁力学模型参见图4，可将已支护段看着具有一定初始位移ω₀和初始转角θ₀的弹性固定端，注浆圈的初始位移ω₀为初期支护的既有位移；将注浆圈视为有限长度的弹性地基梁，可得梁的挠度微分方程ω(x)为：See Figure 4 for the mechanical model of the elastic foundation beam of the grouting reinforcement circle. The supported section can be regarded as the elastic fixed end with a certain initial displacement ω ₀ and an initial rotation angle θ _0. The initial displacement ω ₀ of the grouting circle is the initial support The existing displacement of the grouting ring is regarded as a finite length elastic foundation beam, and the deflection differential equation ω(x) of the beam can be obtained as:

$EI EI \frac{{dω dω}^{44} ((x x))}{{dx dx}^{44}} = = b b [[q q ((x x)) - - p p ((x x))]] - - - - - - ((77))$

式中：q(x)为作用于注浆加固圈上的荷载（包括围岩压力、静水压力、动水压力），p(x)为弹性抗力，也即作用于楔形破裂体上的作用力。E、I为注浆圈的弹性模量和惯性矩。In the formula: q(x) is the load acting on the grouting reinforcement ring (including surrounding rock pressure, hydrostatic pressure, and hydrodynamic pressure), p(x) is the elastic resistance, that is, the force acting on the wedge-shaped fractured body . E and I are the elastic modulus and moment of inertia of the grouting ring.

其中b为梁的宽度，此处即为隧道的跨度；h为注浆加固圈的厚度。in b is the width of the beam, here is the span of the tunnel; h is the thickness of the grouting reinforcement ring.

地基反力采用双参数模型的Pasternak模型进行求解，可得The foundation reaction force is solved by the Pasternak model of the two-parameter model, which can be obtained

$EI EI \frac{{d d}^{44} ω ω ((x x))}{{dx dx}^{44}} - - {G G}_{p p} b b * * \frac{{d d}^{22} ω ω ((x x))}{{dx dx}^{22}} + + kb kb * * ω ω ((x x)) = = {bq bq}_{00} - - - - - - ((88))$

式中：G_p为地基剪切模量，k为基床系数，b^*——考虑双参数地基连续性有限宽度梁等效宽度，即

In the formula: G _p is the shear modulus of the foundation, k is the coefficient of the subgrade bed, b ^* ——the equivalent width of the finite-width beam considering the continuity of the double-parameter foundation, that is

代入边界条件（初始位移为ω₀，初始转角为θ₀,ω₀=2mm，θ₀=1⁰）进行求解得到注浆圈的挠度方程ω(x)后，即可求得作用于楔形破裂体顶面的作用力为：Substituting the boundary conditions (the initial displacement is ω ₀ , the initial rotation angle is θ ₀ , ω ₀ =2mm, θ ₀ =1 ⁰ ) to solve the deflection equation ω(x) of the grouting ring, and then the wedge-shaped fracture can be obtained The force acting on the top surface of the body is:

$p p ((x x)) = = kω kω ((x x)) - - {G G}_{p p} \frac{{dω dω}^{22} ((x x))}{{dx dx}^{22}} - - - - - - ((99))$

同时得到作用在楔块上部的平均应力σ，

（积分区间（0，Dcotα），L=Dcotα）At the same time, the average stress σ acting on the upper part of the wedge is obtained,

(integration interval (0, Dcotα), L=Dcotα)

进一步求得作用于楔形破裂体顶面总的作用力为：Further obtain the total force acting on the top surface of the wedge-shaped rupture body as:

P=σ·S （10）P=σ·S （10）

式中：S为楔形破裂体顶面面积。In the formula: S is the area of the top surface of the wedge-shaped rupture body.

（4）作用于楔形破裂体的渗透力的计算(4) Calculation of seepage force acting on the wedge-shaped fracture body

对楔形体上单位体积渗透力应用高斯理论，得到作用在楔形体上的渗透力的水平分量和垂直分量的表达式：Applying the Gaussian theory to the permeation force per unit volume on the wedge, the expressions of the horizontal and vertical components of the permeation force acting on the wedge are obtained:

F_y=2γ_wD²h(y) （11）F _y =2γ _w D ² h(y) (11)

F_z=2γ_wD²cosαh(z) （12）F _z =2γ _w D ² cosαh(z) (12)

式中：γ_w为水的容重；D为隧道跨度；α为楔形破裂体破裂面与水平面的夹角，h(y)为楔形体内部形心处沿水平方向的水头，h(z)为楔形体内部形心处沿竖直方向的水头，h(y)、h(z)可通过数值计算方法得到(是现有技术，根据实际工程，实际参数，利用数值模拟、建立模型分析，得到h(y)、h(z))。In the formula: γ _w is the bulk density of water; D is the span of the tunnel; α is the angle between the fracture surface of the wedge-shaped fracture body and the horizontal plane, h(y) is the water head along the horizontal direction at the centroid inside the wedge-shaped body, and h(z) is The water head along the vertical direction at the centroid inside the wedge-shaped body, h(y), h(z) can be obtained by numerical calculation method (it is the prior art, according to the actual project, actual parameters, using numerical simulation and model analysis, it can be obtained h(y), h(z)).

（5）参见图5，作用于潜在楔形破裂体上的下滑力和抗滑力采用以下方法进行计算。(5) Referring to Figure 5, the sliding force and anti-sliding force acting on the potential wedge-shaped rupture body are calculated by the following methods.

F_抗滑力=T_g+T （13）F _{Anti-slip force} = T _g + T (13)

为工作面围岩的内摩擦角；γ为围岩容重；c为围岩的粘聚力；（γ、c可根据工程地质勘探报告测得的地质参数都能得到）K₀为侧压力系数，

μ为围岩的泊松比；对于具体的隧道工程，c、

T_{g} = {D.}^{2} \cot α (c + K_{0} the tan φ \frac{2 σ + Dγ}{3});

T is the frictional resistance on the inclined sliding surface,

is the internal friction angle of the surrounding rock of the working face; γ is the bulk density of the surrounding rock; c is the cohesion of the surrounding rock; ( γ and c can be obtained from the geological parameters measured in the engineering geological exploration report) K ₀ is the lateral pressure coefficient,

μ is Poisson's ratio of surrounding rock; for specific tunnel engineering, c,

F_下滑力=(P+G+F_z)sinα+F_ycosα （14）F _{sliding force} =(P+G+F _z ) sinα+F _y cosα (14)

式中：P为楔形破裂体顶面的总作用力，G为楔块自重，

F_y、F_z为作用在楔形体上的渗透力的水平分量和垂直分量，按（11）和（12）式进行计算。In the formula: P is the total force on the top surface of the wedge-shaped broken body, G is the self-weight of the wedge,

F _y and F _z are the horizontal and vertical components of the seepage force acting on the wedge, calculated according to (11) and (12).

（6）参见图5，根据式（13）和（14），隧道施工掌子面的稳定系数可按下式求解(6) Referring to Figure 5, according to formulas (13) and (14), the stability coefficient of the tunnel face can be solved by the following formula

（7）根据具体的工程条件，对不同注浆加固圈厚度条件下隧道施工掌子面的稳定系数进行求解，即可得到如图6所示的曲线，根据隧道设计规范，取隧道施工掌子面的稳定系数为2.0，此时对应的注浆加固圈厚度即为最佳的注浆加固圈厚度。(7) According to the specific engineering conditions, the stability coefficient of the tunnel construction face under the condition of different thicknesses of the grouting reinforcement ring is solved, and the curve shown in Figure 6 can be obtained. According to the tunnel design specification, the tunnel construction face is taken The stability coefficient of the surface is 2.0, and the thickness of the corresponding grouting reinforcement ring is the optimal thickness of the grouting reinforcement ring.

下面结合实例对本发明进行进一步说明。Below in conjunction with example the present invention is further described.

某水下隧道围岩破碎软弱，特别是在断层破碎带段隧道和江水连通，隧道施工过程中极易发生突泥、涌水、岩块崩落甚至坍塌等施工风险。该段隧道埋深为24m，河床顶部水深为21m，地层渗透系数为0.89m/d，为保证隧道的施工安全，隧道设计中按照工程经验采用了6.0厚的注浆加固圈，注浆后地层的渗透系数为10^-6m/d。The surrounding rock of an underwater tunnel is broken and weak, especially when the tunnel is connected to the river in the fault fracture zone, construction risks such as mud inrush, water gushing, rock collapse or even collapse are very likely to occur during tunnel construction. The buried depth of this section of the tunnel is 24m, the water depth at the top of the river bed is 21m, and the formation permeability coefficient is 0.89m/d. The permeability coefficient is 10 ^-6 m/d.

采用本发明的水下隧道暗挖施工注浆加固圈厚度的设计方法，对隧道穿越断层破碎带段的注浆加固圈厚度进行计算，其具体设计计算过程如下：Adopt the design method of the thickness of the grouting reinforcement ring for underwater tunnel excavation construction of the present invention to calculate the thickness of the grouting reinforcement ring for the tunnel passing through the fault broken zone section, the specific design and calculation process is as follows:

（1）首先计算不同注浆加固圈厚度条件下隧道施工工作面的稳定系数。以注浆加固圈厚度6m为例，其计算过程如下：(1) First, calculate the stability coefficient of the tunnel construction face under the condition of different grouting reinforcement circle thickness. Taking the grouting reinforcement ring with a thickness of 6m as an example, the calculation process is as follows:

1）根据隧道埋深情况的不同，按公式（2）、（3）或（5）计算作用于注浆加固圈上的围岩压力，对于本实例，按式（3）计算得到围岩压力为356.5kN/m²。1) According to the different buried depths of the tunnel, calculate the surrounding rock pressure acting on the grouting reinforcement ring according to the formula (2), (3) or (5). For this example, calculate the surrounding rock pressure according to the formula (3) It is 356.5kN/m ² .

2）按式（6）计算作用于注浆加固圈外的静水压力，其值为150.0kN/m²。2) Calculate the hydrostatic pressure acting on the outside of the grouting reinforcement circle according to formula (6), and its value is 150.0kN/m ² .

隧道埋深H21m，注浆加固圈厚度h6m，跨度D为10m，γ_w=10kN/m³，k₀周围岩土原有的渗透系数0.89m/d,k₁为注浆加固以后渗透系数10^-6m/d，h₀为15m；The buried depth of the tunnel is H21m, the thickness of the grouting reinforcement ring is h6m, the span D is 10m, γ _w =10kN/m ³ , the original permeability coefficient of the rock and soil around k ₀ is 0.89m/d, and k ₁ is the permeability coefficient after grouting reinforcement 10 ^-6 m/d, _h0 is 15m;

3）计算作用于注浆加固圈上的总荷载，将以上两项计算得到的压力进行叠加即可，其值为506.5kN/m²。3) To calculate the total load acting on the grouting reinforcement ring, the pressure obtained by the above two calculations can be superimposed, and the value is 506.5kN/m ² .

4）将计算得到的总荷载q₀代入式（8），并求解方程式（8），根据边界条件，如图4所示，在B端具有一定初始位移ω₀和初始转角θ₀，在C点，注浆圈必定满足连续性条件，在D端为自由端，由此即可得到加固圈的挠度方程ω(x)。解微分方程的边界条件：ω₀=2mm，θ₀=1⁰）4) Substitute the calculated total load q ₀ into Equation (8), and solve Equation (8). According to the boundary conditions, as shown in Figure 4, there is a certain initial displacement ω ₀ and initial rotation angle θ ₀ at B, and at C point, the grouting ring must satisfy the continuity condition, and the D end is a free end, so the deflection equation ω(x) of the reinforcement ring can be obtained. Boundary conditions for solving differential equations: ω ₀ =2mm, θ ₀ =1 ⁰ )

式中：地基剪切模量G_p为1.8×10⁴kN/m,k为，基床系数k为4.0×10⁴kN/m³，注浆加固圈截面刚度EI为8.4×10⁵kN/m²，梁的宽度b为10m。In the formula: the foundation shear modulus G _p is 1.8×10 ⁴ kN/m, k is , the bed coefficient k is 4.0×10 ⁴ kN/m ³ , the section stiffness EI of the grouting reinforcement ring is 8.4×10 ⁵ kN/m m ² , the width b of the beam is 10m.

5）求得注浆圈的挠度方程后，进一步根据式（9）和（10），即可求得作用于楔形破裂体顶面作用力的平均值为320.56kN/m²,根据楔形体顶部的面积S为65.43m²，即可得到作用于楔形破裂体顶面的总作用力P为20974kN。σ=320.56kN/m²，S=65.43m²。5) After obtaining the deflection equation of the grouting ring, further according to formulas (9) and (10), the average value of the force acting on the top surface of the wedge-shaped broken body can be obtained as 320.56kN/m ² , according to the top of the wedge-shaped body The area S of is 65.43m ² , and the total force P acting on the top surface of the wedge-shaped rupture body is 20974kN. σ=320.56kN/m ² , S=65.43m ² .

6）采用数值计算方法，计算得到楔形破裂体内部形心处水平方向和竖直方向的水头值F_y、F_z均为4.56m。6) Using the numerical calculation method, the water head values F _y and F _z in the horizontal and vertical directions at the centroid inside the wedge-shaped rupture body are calculated to be 4.56m.

7）采用式（11）和（12），求得作用于楔形体上渗透力的水平分量F_y为9120kN，竖直分量F_z为5055.3kN。其中，α为56.3°，γ_w为10⁴kN/m³,D为10m。7) Using formulas (11) and (12), the horizontal component F _y of the seepage force acting on the wedge is 9120kN, and the vertical component F _z is 5055.3kN. Among them, α is 56.3°, γ _w is 10 ⁴ kN/m ³ , and D is 10m.

8）根据式（13）和（14）分别计算作用于楔形体上的抗滑力和下滑力，分别为76791.7kN和32279kN。8) According to formulas (13) and (14), calculate the anti-sliding force and sliding force acting on the wedge body, which are 76791.7kN and 32279kN, respectively.

9）根据式（15）计算得到隧道掌子面的稳定系数K为2.379，此即为注浆加固圈厚度为6m条件下隧道掌子面的稳定系数。9) According to formula (15), the stability coefficient K of the tunnel face is 2.379, which is the stability coefficient of the tunnel face under the condition that the thickness of the grouting reinforcement circle is 6m.

10）根据以上相同的计算方法和计算过程可以求得不注浆加固条件下以及注浆加固圈厚度分别是1.0m，2.0m，3.0m，4.0m，5.0m，6.0m，7.0m，8.0m时隧道掌子面的稳定系数分别为0.41，1.126，1.523，1.853，2.062，2.251，2.379，2.445，2.492。10) According to the same calculation method and calculation process as above, it can be obtained that under the condition of no grouting reinforcement and the thickness of the grouting reinforcement ring is 1.0m, 2.0m, 3.0m, 4.0m, 5.0m, 6.0m, 7.0m, 8.0 The stability coefficients of the tunnel face at m are 0.41, 1.126, 1.523, 1.853, 2.062, 2.251, 2.379, 2.445, and 2.492, respectively.

（2）将不同注浆加固圈厚度条件下对应的掌子面安全系数根据最小二乘法绘制成图（为保证绘制图形的准确性，一般至少需取5个以上的加固圈厚度进行计算，计算步长可取1m），即可得到如图6所示的回归曲线。(2) Draw the corresponding tunnel face safety factors under different grouting reinforcement ring thicknesses according to the least square method (in order to ensure the accuracy of drawing graphics, it is generally necessary to take at least 5 reinforcement ring thicknesses for calculation, and calculate The step length can be 1m), and the regression curve shown in Figure 6 can be obtained.

（3）根据回归曲线图，即可得到某一设计掌子面安全系数条件下隧道所需的加固圈厚度；(3) According to the regression curve, the thickness of the reinforcement ring required by the tunnel under the condition of a certain design tunnel face safety factor can be obtained;

根据隧道设计规范，隧道安全系数一般取2.0，此时保证该隧道施工掌子面稳定性的最小注浆圈厚度为3.8m，较经验法确定的注浆加固圈厚度减小2.2m。According to the tunnel design specification, the tunnel safety factor is generally taken as 2.0. At this time, the minimum thickness of the grouting ring to ensure the stability of the tunnel construction face is 3.8m, which is 2.2m smaller than the thickness of the grouting reinforcement ring determined by the empirical method.

当隧道注浆加固圈厚度为6.0m时，其每延米的注浆费用约为1.5万元，当注浆加固圈的厚度减小为3.8m时，其每延米的注浆费用约为0.7万元，较6.0m注浆圈减少费用50%以上，对于一般的水下隧道，其长度一般在2km以上，采用本发明降低的工程造价将在1600万元以上。When the thickness of the tunnel grouting reinforcement ring is 6.0m, the grouting cost per linear meter is about 15,000 yuan. When the thickness of the grouting reinforcement ring is reduced to 3.8m, the grouting cost per linear meter is about 07,000 yuan, more than 50% of the cost reduction compared with the 6.0m grouting circle. For general underwater tunnels, whose length is generally more than 2km, the project cost reduced by the present invention will be more than 16 million yuan.

此外，采用本发明的注浆加固圈厚度的确定方法，由于减小了注浆加固圈的厚度，降低了注浆施工的难度，加快了隧道的施工进度，可有效的缩短隧道的施工工期，其所产生的经济效益和社会效益也是非常显著。In addition, by adopting the method for determining the thickness of the grouting reinforcement ring of the present invention, since the thickness of the grouting reinforcement ring is reduced, the difficulty of grouting construction is reduced, the construction progress of the tunnel is accelerated, and the construction period of the tunnel can be effectively shortened. The economic and social benefits it produces are also very significant.

Claims

1. A design method for the thickness of an underwater tunnel construction grouting reinforcement ring is characterized in that, comprising the following steps:

Step 1: Select a set of reinforcement ring thickness parameters, and calculate the stability coefficient of the tunnel construction face under different reinforcement ring thickness conditions;

Step 2: Based on the thickness of different reinforcement rings and the corresponding stability coefficients, according to the least square method, obtain the regression curve of reinforcement ring thickness-stability coefficient;

Step 3: According to the regression curve of the reinforcement ring thickness-stability coefficient, the thickness of the reinforcement ring required by the tunnel under a certain designed stability coefficient can be obtained;

In step 1, the stability coefficient corresponding to a certain thickness of the reinforcement ring is calculated by the following method:

(1) Calculate surrounding rock pressure q;

① When H≤equivalent load height h _q ,

q=γ·H;

In the formula: γ is the weight of the overlying surrounding rock of the tunnel; H is the buried depth of the tunnel, which refers to the distance from the tunnel vault to the ground;

② When the equivalent load height h _q < H < the boundary depth H _p of deep and shallow buried tunnels,

In the formula: λ is the lateral pressure coefficient; B is the tunnel excavation width, β is the angle between the rupture surface and the horizontal plane; φ is the approximate friction angle, and θ is the friction angle;

③ When H ≥ deep and shallow buried tunnel depth H _p ,

q=γ h _q ;

(2) Use the following formula to calculate the hydrostatic pressure acting on the outside of the grouting reinforcement circle:

In the formula: u is the hydrostatic pressure on the outer surface of the grouting ring; _h0 is the depth of water; _k0 is the original permeability coefficient of the surrounding rock and soil; _k1 is the permeability coefficient of the grouting ring; H is the buried depth of the tunnel ; h is the thickness of the grouting reinforcement ring; D is the span of the tunnel; γ _w is the bulk density of water;

(3) Calculate the total load acting on the grouting reinforcement ring, the total load _q0 is the sum of surrounding rock pressure q and hydrostatic pressure u;

(4) Obtain the deflection equation ω(x) of the reinforcement ring;

Substitute the total load q ₀ into

And substituting the boundary conditions to solve the above formula, the deflection equation ω(x) of the reinforcement ring is obtained;

In the formula: G _p is the shear modulus of the foundation, k is the coefficient of the subgrade bed, b ^* is the equivalent width of the finite-width beam considering the continuity of the double-parameter foundation, and

b is the width of the beam, here is the span of the tunnel; h is the thickness of the grouting reinforcement ring;

(5) Based on the deflection equation ω(x) of the reinforcement ring, calculate the total force P acting on the top surface of the wedge-shaped broken body; P=σ·S, where σ is the average stress acting on the upper part of the wedge,

Integral interval (0, Dcotα), L=Dcotα;

S is the area of the top surface of the wedge-shaped rupture body;

(6) Calculate the water head value h(y) in the horizontal direction and the water head value h(z) in the vertical direction at the centroid inside the wedge-shaped rupture body;

(7) Horizontal component F _y and vertical component F _z of seepage force acting on the wedge:

F _y =2γ _w D ² h(y);

F _z =2γ _w D ² cosαh(z);

Among them, D is the span of the tunnel; α is the angle between the fracture surface of the wedge-shaped rupture body and the horizontal plane, h(y) is the water head along the horizontal direction at the centroid inside the wedge-shaped body, and h(z) is the water head along the vertical direction at the centroid inside the wedge-shaped body. water head in the vertical direction;

(8) Calculate the anti-sliding force and sliding force acting on the wedge;

Anti-slip force F _{Anti-slip force} = T _g + T,

Sliding force F _{sliding force} = (P+G+F _z ) sinα+F _y cosα;

In the formula: T _g is the lateral friction resistance on both sides of the wedge,

T is the frictional resistance on the inclined sliding surface,

N is the normal force acting on the rupture body,

α is the rupture angle of the wedge-shaped rupture body, that is, the angle between the rupture surface of the wedge-shaped rupture body and the horizontal plane,

K ₀ is the lateral pressure coefficient,

μ is the Poisson's ratio of the surrounding rock;

(9) Calculate the stability factor K of the tunnel face:

2. the method for designing the thickness of the grouting reinforcement ring for underwater tunnel excavation according to claim 1, characterized in that the thickness parameters of the reinforcement ring are at least five, arranged from large to small or small to large, adjacent The difference between the thickness parameter values of the reinforcement ring is 1m. the