CN114398699A - Grouting pipe curtain deformation calculation method based on inter-pipe soil arch characteristics - Google Patents

Grouting pipe curtain deformation calculation method based on inter-pipe soil arch characteristics Download PDF

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CN114398699A
CN114398699A CN202111602961.6A CN202111602961A CN114398699A CN 114398699 A CN114398699 A CN 114398699A CN 202111602961 A CN202111602961 A CN 202111602961A CN 114398699 A CN114398699 A CN 114398699A
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grouting pipe
pipe curtain
section
curtain
load
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李然
王圣涛
申志军
潘红桂
艾鹏鹏
周云飞
徐洪强
方伏浪
张伟
李奥
罗基伟
徐曈
齐伟伟
李建业
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China Tiesiju Civil Engineering Group Co Ltd CTCE Group
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China Tiesiju Civil Engineering Group Co Ltd CTCE Group
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
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Abstract

The invention provides a grouting pipe curtain deformation calculation method based on the characteristics of soil arches among pipes, which comprises the steps of firstly analyzing the transverse soil arch characteristics of a grouting pipe curtain to determine a supporting load; analyzing the axial beam forming effect of the grouting pipe curtain to determine a control equation; then establishing a grouting pipe curtain long beam theoretical model to determine load distribution; and then solving the flexural deformation by a slip casting pipe curtain difference calculation method. The invention provides a calculation theory of the deflection deformation of the grouting pipe curtain, can quantitatively analyze the mechanical response of the grouting pipe curtain in the actual working state, has less dependence on engineering experience, has good universality and provides scientific basis for design and construction; a grouting pipe curtain stress calculation method considering soil arch characteristics is established, the inter-pipe soil arch bearing span reduction effect is mathematically analyzed and expressed, the existing design concept deviating from danger is avoided, and the construction safety is guaranteed; meanwhile, a double-parameter Passternak model is adopted, the transverse shearing action of a foundation spring, the foundation bed coefficient difference, the load release sectionalization and the foundation elastoplasticity are considered more reasonably, so that the grouting pipe curtain is continuously deformed, the distribution and release of tunnel excavation loads are simulated more reliably, the pipe body deformation of the tunnel grouting pipe curtain at a certain position is predicted, and a theoretical basis is provided for the design and construction of the grouting pipe curtain.

Description

Grouting pipe curtain deformation calculation method based on inter-pipe soil arch characteristics
Technical Field
The invention relates to the technical field of tunnels and underground engineering, in particular to a grouting pipe curtain deformation calculation method based on the characteristics of soil arches between pipes.
Background
When a large-span tunnel passes through a bad stratum or passes through an existing building, if effective engineering protection measures are not taken, serious accidents such as extrusion instability of a tunnel face, collapse damage of the tunnel and the like are easily caused. Therefore, in specific construction, in order to guarantee engineering safety, the grouting pipe curtain is generally adopted to pre-reinforce the front rock-soil body, namely, the grouting pipe curtain is supported in advance, the grouting pipe curtain bears the load of loose rock-soil, and the excessive deformation of surrounding rock is prevented, so that the risk potential is reduced.
In the prior art, the action mode and the deformation mechanism of a large grouting pipe curtain are not completely clear, the design and construction still excessively depend on engineering experience, and the engineering quality is difficult to ensure. For the law of deformation of grouting pipe curtain, some studies have been carried out in the academic world: in the aspect of theoretical derivation, an elastic foundation beam model is generally adopted to analyze a single grouting pipe curtain, and the grouting pipe curtain is considered to act on beams of mutually independent Winkler springs, so that the loaded deformation of the grouting pipe curtain is researched; in the aspect of field actual measurement, a steel bar strain gauge or an inclinometer is generally utilized to obtain real-time data of grouting pipe curtain deformation in the excavation process; in the aspect of numerical simulation, conventionally, a grouting pipe curtain is simulated by means of an entity unit, a grouting stratum is equivalently reinforced, and the space-time displacement of the grouting pipe curtain under three-dimensional excavation is analyzed.
However, most of the existing researches only qualitatively describe the supporting effect of the grouting pipe curtain, and the quantitative analysis of the stress mechanism and the deflection distribution of the grouting pipe curtain is less involved. In addition, in the past, the deformation calculation theory of the grouting pipe curtain considers that the bearing range of the grouting pipe curtain is only the upper area of the pipe diameter projection, and the soil arch characteristic between adjacent grouting pipe curtains is not considered, so that the obvious limitation is caused, and the difference from the actual situation is large.
Disclosure of Invention
The invention aims to provide a grouting pipe curtain deformation calculation method based on the characteristics of soil arches between pipes, so as to solve the problems in the background technology.
In order to achieve the purpose, the invention adopts the following technical scheme:
a grouting pipe curtain deformation calculation method based on the characteristics of soil arches between pipes comprises the following steps:
s1, analyzing the transverse soil arch characteristic of the grouting pipe curtain and determining a supporting load;
s2, analyzing the axial beam forming effect of the grouting pipe curtain, and determining a control equation;
s3, establishing a grouting pipe curtain long beam theoretical model, and determining load distribution;
and S4, solving the flexural deformation through a slip casting tube curtain difference calculation method.
Further, the step S1 is specifically implemented by the following method:
s11, according to the Purchase pressure arch theory, considering the soil arch characteristic between adjacent grouting pipe curtains, and establishing a corresponding mechanical model: the grouting pipe curtains are regarded as cylindrical steel pipes and are distributed in the circumferential direction of the outer ring of the tunnel arch part at equal intervals; htAnd BtThe height and the span of the excavated tunnel are respectively, the outer diameter of the tunnel is R, the gravity of the surrounding rock is gamma, the outer diameter of the grouting pipe curtain is D, and the distance between two adjacent grouting pipe curtains is D1A clear spacing of D2The included angle between two adjacent grouting pipe curtains is alpha,
Figure BDA0003432572170000021
the friction angle of the surrounding rock is R + g, and the radius of the circular arc of the grouting pipe curtain is R + g;
s12, numbering each grouting pipe curtain from the vault to two sides in sequence, and regarding the gravity of the loose rock mass in the pressure arch area as the load of the grouting pipe curtains, wherein any one number is CnThe corresponding load height of the grouting pipe curtain is HdnAnd C isnThe serial numbers of two adjacent grouting pipe curtains are marked as Cn-1And Cn+1And with CnThe horizontal included angle of the grouting pipe curtain is recorded as thetan-1And thetan+1；
S13, in the mechanical model of grouting pipe curtains, defining the central connecting line of two adjacent grouting pipe curtains as an x axis, defining the vertical central line of two adjacent grouting pipe curtains as a y axis, establishing a plurality of rectangular coordinate systems, analyzing the load height corresponding to the grouting pipe curtains by establishing a soil arch axis in each coordinate system, and analyzing the soil arch axis by the equation y-mx without considering the tensile strength of rock mass2A parabola denoted by + n;
s14 grouting pipe curtain Cn-1And CnIn a rectangular coordinate system, the soil arch axis and the grouting pipe curtain Cn-1And CnHas a crossing point of V1And V2Are each independently of V1And grouting pipe curtain Cn-1Line connecting the centers of circles, V2And grouting pipe curtain CnThe intersection points of the segment perpendicular to the connecting line of the circle centers and the x axis are respectively M1And M2Suppose line segment V1Cn-1、V2CnAre all tangent with the soil arch axis and have included angles with the x axis
Figure BDA0003432572170000022
Then line segment V1M1、V2M2At an angle to the x-axis of
Figure BDA0003432572170000023
Then V2The coordinates of the points can be expressed as
Figure BDA0003432572170000024
Figure BDA0003432572170000025
S15, mixing V2The coordinates of the points are brought into the soil arch axis equation, and the following are obtained by solution:
Figure BDA0003432572170000026
Figure BDA0003432572170000031
uniform load q above the earth arch axisn-1And q isn-1Obtained by the following analytical formula:
Figure BDA0003432572170000032
Figure BDA0003432572170000033
vertical concentrated load p of soil arch axisn-1And pn+1Can be expressed as:
Figure BDA0003432572170000034
Figure BDA0003432572170000035
averaging the two to obtain a grouting pipe curtain CnVertical load p aboven：
Figure BDA0003432572170000036
Further, the step S2 is specifically implemented by the following method:
s21, regarding the surrounding rock as a homogeneous and continuous elastic-plastic entity, wherein the flexural deformation of the grouting pipe curtain has the mechanical characteristics of a Bernoulli-Euler beam, so that a grouting pipe curtain mechanical model based on the Passternak elastic-plastic foundation beam is obtained, and the grouting pipe curtain mechanical model is obtained according to the reaction analytical formula of the Passternak foundation beam by the following formula:
Figure BDA0003432572170000037
wherein: p (x) is the resistance of the surrounding rock foundation, k is the coefficient of the surrounding rock bed, w (x) is the flexural deformation of the grouting pipe curtain, GpIs the shear modulus of the surrounding rock foundation;
s22, considering tunnel support hysteresis, foundation bed coefficient change, stress release and stratum elastoplasticity factors, and sequentially dividing the grouting pipe curtain into a support closed section OA, a support non-closed section AB, a non-support section BC, a plastic disturbance section CD, an elastic disturbance section DE and a non-disturbance section EF from back to front along the advancing direction of the excavation face;
s23, obtaining the following results due to the balanced stress of the units:
Figure BDA0003432572170000038
wherein V (x) is shearing force of grouting pipe curtain, M (x) is bending moment of grouting pipe curtain, q (x) is load borne by grouting pipe curtain, b is width of surrounding rock foundation beam, b*Is equivalent surrounding rock foundationWidth, b*＝b[1+(Gp/k)1/2/b]；
S24, based on Bernoulli-Euler beam theory, the mechanical response of the grouting pipe curtain can be obtained, including the differential analytic formula of grouting pipe curtain deflection angle theta (x), longitudinal strain epsilon (x), grouting pipe curtain shear force V (x), grouting pipe curtain bending moment M (x) and grouting pipe curtain deflection deformation W (x):
Figure BDA0003432572170000041
Figure BDA0003432572170000042
Figure BDA0003432572170000043
Figure BDA0003432572170000044
solving a differential balance equation for controlling the deformation of the grouting pipe curtain through the formulas (9) to (13):
Figure BDA0003432572170000045
further, the step S3 is specifically implemented by the following method:
the mechanical model of the grouting pipe curtain of the Passternak foundation beam is obtained by considering the soil arch characteristic of the grouting pipe curtain and the space-time effect of stratum load:
the primary support closed section OA has a length of a, and the load borne by the grouting pipe curtain in the section is static load, namely q (x) q0，q0Calculating values according to a Prov theory formula; resistance of the zone surrounding rock foundation
Figure BDA0003432572170000046
The differential balance of the control in this section is formulated as
Figure BDA0003432572170000047
The initial branch unblocked section AB has the length of b, and the external load q (x) borne by the grouting pipe curtain of the section is [1+ (eta)1-1)(x-a)/(b+s)]q0Time-space coefficient eta of stress release of surrounding rock load1Taking 0.5; resistance of the primary support surrounding rock foundation of the section
Figure BDA0003432572170000048
Surrounding rock foundation coefficient k in formulac(x)＝-kcx/b+(a+b)kcB, and k at point B cmin0; the differential balance of control for that segment is formulated as
Figure BDA0003432572170000049
For the unsupported section BC with the length of c, the distribution form of external load borne by the grouting pipe curtain of the section is the same as that of the section AB, and because the initial support of the section BC is not applied, the load p (x) is also taken to be 0, the differential balance formula controlled by the section is as follows
Figure BDA0003432572170000051
Plastic perturbation zone CD of length
Figure BDA0003432572170000052
Wherein h isuIs the height of the tunnel step,
Figure BDA0003432572170000053
the friction angle is calculated for the surrounding rock. In addition, the front of the excavation surface has a remarkable stress concentration phenomenon, and the space-time coefficient eta of the release of the load stress of the surrounding rock at the D point is taken2Take 1.2, the section bears the external load q (x) ═ η2-η1)[x-(a+b+c)]q0/d+η1q0(ii) a Resistance of the zone surrounding rock foundation
Figure BDA0003432572170000054
k0(x)＝[x-(a+b+c+d)](k0-k0min)/s+k0minWhere s is the length of the rock mass before the excavation face, k0Constant coefficient of rock mass bed, k, without disturbance0minIs a ground reduction factor, and k0min＝0.6k0(ii) a The differential balance of the control in this section is formulated as
Figure BDA0003432572170000055
The elastic disturbance section DE is of length e, and the total length of the elastic disturbance section and the undisturbed section of the large-span tunnel grouting pipe curtain is taken as 2huThe segment slip casting tube bears the load q (x) ═ η2[x-(a+b+c+d)]q0/s+η2q0The resistance of the surrounding rock foundation of the section is consistent with the CD section, and the section is taken
Figure BDA0003432572170000056
The differential balance of the control in this section is formulated as
Figure BDA0003432572170000057
An undisturbed section EF with the length f, which is the length of the residual grouting pipe curtain after deducting each section in front; the section grouting pipe curtain is not subjected to any external load, and if q (x) is 0, the resistance of the section surrounding rock foundation is obtained
Figure BDA0003432572170000058
The differential balance of the control in this section is formulated as
Figure BDA0003432572170000059
Further, the step S4 is specifically implemented by the following method:
s41, equally dividing the grouting pipe curtain with the length of L into n sections, and according to the sequence from left to right, each node is compiled into 0, 1 … i … n-1, n, and the length of each section is divided into L0The deflection deformation of the grouting pipe curtain of the node i is wi, and in order to adapt to the analytic degree of freedom of the grouting pipe curtain, two different virtual nodes-2, -1, n +1 and n +2 are respectively arranged on the left side and the right side;
and S42, carrying out Taylor formula expansion on the deformation of the left and right adjacent nodes of the node i, and taking the four polynomials in front of the Taylor expansion formula to ensure the analysis accuracy.
Figure BDA00034325721700000510
Figure BDA0003432572170000061
Figure BDA0003432572170000062
This enables the derivation of the various derivatives:
Figure BDA0003432572170000063
Figure BDA0003432572170000064
Figure BDA0003432572170000065
Figure BDA0003432572170000066
s43, combining the above formulas to solve the grouting tube curtain deflection difference formula:
Figure BDA0003432572170000067
order to
Figure BDA0003432572170000068
The formula is simplified as:
Ci(wi-2-4wi-1+6wi-4wi+1+wi+2)+Biwi-Di(-wi-2+16wi-1-30wi+16wi+1-wi+2)＝qi (23)
analyzing and expressing mechanical boundary conditions on two sides of the grouting pipe curtain:
Figure BDA0003432572170000069
Figure BDA00034325721700000610
Figure BDA00034325721700000611
Figure BDA00034325721700000612
simultaneous implementation of the above formula yields:
Figure BDA00034325721700000613
Figure BDA00034325721700000614
when i is 0, 1, n-1, n, the simplified slip casting curtain deflection difference formula can be converted into:
C0(w-2-4w-1+6w0-4w1+w2)+B0w0-D0(-w-2+16w-1-30w0+16w1-w2)＝q0
C1(w-1-4w0+6w1-4w2+w3)+B1w1-D1(-w-1+16w0-30w1+16w2-w3)＝q1
Cn-1(wn-3-4wn-2+6wn-1-4wn+wn+1)+Dn-1wn-1
-Dn-1(-wn-3+16wn-2-30wn-1+16wn-wn+1)＝qn-1
Cn(wn-2-4wn-1+6wn-4wn+1+wn+2)+Bnwn-Dn(-wn-2+16wn-1-30wn+16wn+1-wn+2)＝qn
handle w-2、w-1、w1、w2Substituting, one can get:
Figure BDA0003432572170000071
Figure BDA0003432572170000072
Figure BDA0003432572170000073
Figure BDA0003432572170000074
s44, the above equation is expressed in a matrix form to obtain:
{[B]+[C]-[D]}{w}＝{p}
wherein the matrix dimensions of [ B ], [ C ] and [ D ] are all N +1, and the expression is as follows:
Figure BDA0003432572170000075
Figure BDA0003432572170000081
Figure BDA0003432572170000082
in addition, the grouting pipe curtain bears the expression of the load matrix { p }:
{p}＝{p0 p1 p2 … pn-1 pn}T
and then the expression of the grouting pipe screen deflection matrix { w } can be obtained:
{w}＝{w0 w1 w2 … wn-1 wn}T
and S45, writing a Matlab program, and solving the flexural deformation wi of each node of the grouting pipe curtain.
According to the technical scheme, the invention provides a calculation theory of the deflection deformation of the grouting pipe curtain, can quantitatively analyze the mechanical response of the grouting pipe curtain in the actual working state, is less dependent on engineering experience, has good universality and provides scientific basis for design and construction; a grouting pipe curtain stress calculation method considering soil arch characteristics is established, the inter-pipe soil arch bearing span reduction effect is mathematically analyzed and expressed, the existing design concept deviating from danger is avoided, and the construction safety is guaranteed; meanwhile, a double-parameter Passternak model is adopted, the transverse shearing action of a foundation spring, the foundation bed coefficient difference, the load release sectionalization and the foundation elastoplasticity are considered more reasonably, so that the grouting pipe curtain is continuously deformed, the distribution and release of tunnel excavation loads are simulated more reliably, the pipe body deformation of the tunnel grouting pipe curtain at a certain position is predicted, and a theoretical basis is provided for the design and construction of the grouting pipe curtain.
Drawings
FIG. 1 is a schematic flow chart of the steps of the present invention;
FIG. 2 is a schematic diagram of the mechanical model of step S1 according to the present invention;
FIG. 3 is a schematic sectional view of the grouting pipe curtain of the present invention;
FIG. 4 is a schematic view of the nodal division of the grouting pipe curtain of the present invention;
FIG. 5 is a comparison graph of the measured distribution and the theoretical distribution of the measured deflection deformation of the grouting pipe curtain of the present invention.
Detailed Description
A preferred embodiment of the present invention will be described in detail below with reference to the accompanying drawings.
As shown in fig. 1, a grouting pipe curtain deformation calculation method based on characteristics of soil arches between pipes includes the following steps:
s1, analyzing the transverse soil arch characteristic of the grouting pipe curtain and determining a supporting load;
the method is realized by the following steps:
s11, according to the Purchase pressure arch theory, considering the soil arch characteristic between adjacent grouting pipe curtains, and establishing a corresponding mechanical model: the grouting pipe curtains are regarded as cylindrical steel pipes and are distributed in the circumferential direction of the outer ring of the tunnel arch part at equal intervals; htAnd BtThe height and the span of the excavated tunnel are respectively, the outer diameter of the tunnel is R, the gravity of the surrounding rock is gamma, the outer diameter of the grouting pipe curtain is D, and the distance between two adjacent grouting pipe curtains is D1A clear spacing of D2The included angle between two adjacent grouting pipe curtains is alpha,
Figure BDA0003432572170000091
the friction angle of the surrounding rock is R + g, and the radius of the circular arc of the grouting pipe curtain is R + g;
s12, numbering each grouting pipe curtain from the vault to two sides in sequence, and regarding the gravity of the loose rock mass in the pressure arch area as the load of the grouting pipe curtains, wherein any one number is CnThe corresponding load height of the grouting pipe curtain is HdnAnd C isnThe serial numbers of two adjacent grouting pipe curtains are marked as Cn-1And Cn+1And with CnThe horizontal included angle of the grouting pipe curtain is recorded as thetam-1And thetan+1；
S13, in the mechanical model of the grouting pipe curtains, the central connecting line of two adjacent grouting pipe curtains is defined as an x axis, and two adjacent grouting pipe curtains are connectedThe vertical center line of the pipe curtain is defined as a y axis, a plurality of rectangular coordinate systems are established, the load height corresponding to the grouting pipe curtain is analyzed by establishing a soil arch axis in each coordinate system, and the soil arch axis is formed by the equation y-mx without considering the tensile strength of the rock mass2A parabola denoted by + n;
s14 grouting pipe curtain Cn-1And CnIn a rectangular coordinate system, the soil arch axis and the grouting pipe curtain Cn-1And CnHas a crossing point of V1And V2Are each independently of V1And grouting pipe curtain Cn-1Line connecting the centers of circles, V2And grouting pipe curtain CnThe intersection points of the segment perpendicular to the connecting line of the circle centers and the x axis are respectively M1And M2Suppose line segment V1Cn-1、V2CnAre all tangent with the soil arch axis and have included angles with the x axis
Figure BDA0003432572170000092
Then line segment V1M1、V2M2At an angle to the x-axis of
Figure BDA0003432572170000101
Then V2The coordinates of the points can be expressed as
Figure BDA0003432572170000102
Figure BDA0003432572170000103
S15, mixing V2The coordinates of the points are brought into the soil arch axis equation, and the following are obtained by solution:
Figure BDA0003432572170000104
Figure BDA0003432572170000105
uniform load q above the earth arch axisn-1And q isn-1Analysis was conducted byThe formula is obtained:
Figure BDA0003432572170000106
Figure BDA0003432572170000107
vertical concentrated load p of soil arch axisn-1And pn+1Can be expressed as:
Figure BDA0003432572170000108
Figure BDA0003432572170000109
averaging the two to obtain a grouting pipe curtain CnVertical load p aboven：
Figure BDA00034325721700001010
S2, analyzing the axial beam forming effect of the grouting pipe curtain, and determining a control equation;
the method is realized by the following steps:
s21, regarding the surrounding rock as a homogeneous and continuous elastic-plastic entity, wherein the flexural deformation of the grouting pipe curtain has the mechanical characteristics of a Bernoulli-Euler beam, so that a grouting pipe curtain mechanical model based on the Passternak elastic-plastic foundation beam is obtained, and the grouting pipe curtain mechanical model is obtained according to the reaction analytical formula of the Passternak foundation beam by the following formula:
Figure BDA00034325721700001011
wherein: p (x) is the resistance of the surrounding rock foundation, k is the coefficient of the surrounding rock bed, w (x) is the flexural deformation of the grouting pipe curtain, GpShear modulus of the surrounding rock foundation；
S22, as shown in figure 3, considering factors such as tunnel support hysteresis, foundation bed coefficient change, stress release and stratum elastoplasticity, sequentially dividing the grouting pipe curtain into a support closed section OA, a support non-closed section AB, a non-support section BC, a plastic disturbance section CD, an elastic disturbance section DE and a non-disturbance section EF from back to front along the advancing direction of the excavation face;
s23, obtaining the following results due to the balanced stress of the units:
Figure BDA0003432572170000111
wherein V (x) is shearing force of grouting pipe curtain, M (x) is bending moment of grouting pipe curtain, q (x) is load borne by grouting pipe curtain, b is width of surrounding rock foundation beam, b*Is equivalent to the width of the surrounding rock foundation, b*＝b[1+(Gp/k)1/2/b]；
S24, based on Bernoulli-Euler beam theory, the mechanical response of the grouting pipe curtain can be obtained, including the differential analytic formula of grouting pipe curtain deflection angle theta (x), longitudinal strain epsilon (x), grouting pipe curtain shear force V (x), grouting pipe curtain bending moment M (x) and grouting pipe curtain deflection deformation W (x):
Figure BDA0003432572170000112
Figure BDA0003432572170000113
Figure BDA0003432572170000114
Figure BDA0003432572170000115
solving a differential balance equation for controlling the deformation of the grouting pipe curtain through the formulas (9) to (13):
Figure BDA0003432572170000116
s3, establishing a grouting pipe curtain long beam theoretical model, and determining load distribution;
specifically, the mechanical model of the grouting pipe curtain of the Passternak foundation beam is obtained by considering the soil arch characteristic of the grouting pipe curtain and the stratum load space-time effect:
the primary support closed section OA has a length of a, and the load borne by the grouting pipe curtain in the section is static load, namely q (x) q0，q0Calculating values according to a Prov theory formula; resistance of the zone surrounding rock foundation
Figure BDA0003432572170000117
The differential balance of the control in this section is formulated as
Figure BDA0003432572170000118
The initial branch unblocked section AB has the length of b, and the external load q (x) borne by the grouting pipe curtain of the section is [1+ (eta)1-1)(x-a)/(b+s)]q0Time-space coefficient eta of stress release of surrounding rock load1Taking 0.5; resistance of the primary support surrounding rock foundation of the section
Figure BDA0003432572170000121
Surrounding rock foundation coefficient k in formulac(x)＝-kcx/b+(a+b)kcB, and k at point B cmin0; the differential balance of control for that segment is formulated as
Figure BDA0003432572170000122
For the unsupported section BC with the length of c, the distribution form of external load borne by the grouting pipe curtain of the section is the same as that of the section AB, and because the initial support of the section BC is not applied, the load p (x) is also taken to be 0, the differential balance formula controlled by the section is as follows
Figure BDA0003432572170000123
Plasticity ofA perturbation zone CD of length
Figure BDA0003432572170000124
Wherein h isuIs the height of the tunnel step,
Figure BDA0003432572170000125
the friction angle is calculated for the surrounding rock. In addition, the front of the excavation surface has a remarkable stress concentration phenomenon, and the space-time coefficient eta of the release of the load stress of the surrounding rock at the D point is taken2Take 1.2, the section bears the external load q (x) ═ η2-η1)[x-(a+b+c)]q0/d+η1q0(ii) a Resistance of the zone surrounding rock foundation
Figure BDA0003432572170000126
k0(x)＝[x-(a+b+c+d)](k0-k0min)/+k0minWhere s is the length of the rock mass before the excavation face, k0Constant coefficient of rock mass bed, k, without disturbance0minIs a ground reduction factor, and k0min＝0.6k0(ii) a The differential balance of the control in this section is formulated as
Figure BDA0003432572170000127
The elastic disturbance section DE is of length e, and the total length of the elastic disturbance section and the undisturbed section of the large-span tunnel grouting pipe curtain is taken as 2huThe segment slip casting tube bears the load q (x) ═ η2[x-(a+b+c+d)]q0/s+η2q0The resistance of the surrounding rock foundation of the section is consistent with the CD section, and the section is taken
Figure BDA0003432572170000128
The differential balance of the control in this section is formulated as
Figure BDA0003432572170000129
An undisturbed section EF with the length f, which is the length of the residual grouting pipe curtain after deducting each section in front; the section grouting pipe curtain is not subjected to any external load, and q (x) is 0, thenResistance of the zone surrounding rock foundation
Figure BDA00034325721700001210
The differential balance of the control in this section is formulated as
Figure BDA00034325721700001211
And S4, solving the flexural deformation through a slip casting tube curtain difference calculation method.
The method is realized by the following steps:
s41, as shown in FIG. 4, equally dividing the grouting pipe curtain with the length of L into n sections, and according to the sequence from left to right, each node is coded into 0, 1 … i … n-1, n, and the length of each section is divided into L0The deflection deformation of the grouting pipe curtain of the node i is wi, and in order to adapt to the analytic degree of freedom of the grouting pipe curtain, two different virtual nodes-2, -1, n +1 and n +2 are respectively arranged on the left side and the right side;
and S42, carrying out Taylor formula expansion on the deformation of the left and right adjacent nodes of the node i, and taking the four polynomials in front of the Taylor expansion formula to ensure the analysis accuracy.
Figure BDA0003432572170000131
Figure BDA0003432572170000132
Figure BDA0003432572170000133
This enables the derivation of the various derivatives:
Figure BDA0003432572170000134
Figure BDA0003432572170000135
Figure BDA0003432572170000136
Figure BDA0003432572170000137
s43, combining the above formulas to solve the grouting tube curtain deflection difference formula:
Figure BDA0003432572170000138
order to
Figure BDA0003432572170000139
The formula is simplified as:
Ci(wi-2-4wi-1+6wi-4wi+1+wi+2)+Biwi-Di(-wi-2+16wi-1-30wi+16wi+1-wi+2)＝qi (23)
analyzing and expressing mechanical boundary conditions on two sides of the grouting pipe curtain:
Figure BDA00034325721700001310
Figure BDA00034325721700001311
Figure BDA0003432572170000141
Figure BDA0003432572170000142
simultaneous implementation of the above formula yields:
Figure BDA0003432572170000143
Figure BDA0003432572170000144
when i is 0, 1, n-1, n, the simplified slip casting curtain deflection difference formula can be converted into:
C0(w-2-4w-1+6w0-4w1+w2)+B0w0-D0(-w-2+16w-1-30w0+16w1-w2)＝q0
C1(w-1-4w0+6w1-4w2+w3)+B1w1-D1(-w-1+16w0-30w1+16w2-w3)＝q1
Cn-1(wn-3-4wn-2+6wn-1-4wn+wn+1)+Bn-1wn-1
-Dn-1(-wn-3+16wn-2-30wn-1+16wn-wn+1)＝qn-1
Cn(wn-2-4wn-1+6wn-4wn+1+wn+2)+B2wn-n(-wn-2+16wn-1-30wn+16wn+1-wn+2)＝qn
handle w-2、w-1、w1、w2Substituting, one can get:
Figure BDA0003432572170000145
Figure BDA0003432572170000146
Figure BDA0003432572170000147
Figure BDA0003432572170000148
s44, the above equation is expressed in a matrix form to obtain:
{[B]+[C]-[D]}{w}＝{p}
wherein the matrix dimensions of [ B ], [ C ] and [ D ] are all N +1, and the expression is as follows:
Figure BDA0003432572170000151
Figure BDA0003432572170000152
Figure BDA0003432572170000153
in addition, the grouting pipe curtain bears the expression of the load matrix { p }:
{p}＝{p0 p1 p2 … pn-1 pn}T
and then the expression of the grouting pipe screen deflection matrix { w } can be obtained:
{w}＝{w0 w1 w2 … wn-1 wn}T
and S45, writing a Matlab program, and solving the flexural deformation wi of each node of the grouting pipe curtain.
The invention provides a calculation theory of the deflection deformation of the grouting pipe curtain, can quantitatively analyze the mechanical response of the grouting pipe curtain in the actual working state, has less dependence on engineering experience, has good universality and provides scientific basis for design and construction; a grouting pipe curtain stress calculation method considering soil arch characteristics is established, the inter-pipe soil arch bearing span reduction effect is mathematically analyzed and expressed, the existing design concept deviating from danger is avoided, and the construction safety is guaranteed; meanwhile, a double-parameter Passternak model is adopted, and the transverse shearing action of a foundation spring, the foundation bed coefficient difference, the load release sectionalization and the foundation elastoplasticity are considered more reasonably, so that the grouting pipe curtain deformation is continuous, and the distribution release of the tunnel excavation load can be simulated more reliably.
The calculation method of the present invention is explained below by specific examples:
a certain mountain tunnel adopts a grouting pipe curtain advanced support; according to geological survey data, the surrounding rock foundation coefficient k of the tunnel engineering045MPa/m, shear modulus Grp2.5kN/m, primary bedding coefficient kc150MPa/m, shear modulus Gcp5kN/m, the weight of the surrounding rock is 18.5kN/m3Width of tunnel Bt15.15m, tunnel height Ht12.78m, angle of friction of surrounding rock
Figure BDA0003432572170000161
Cohesive force c of surrounding rockn50 kPa. The total length L of the grouting pipe curtain is 30m, the outer diameter D of the steel pipe is 0.089m, the wall thickness t of the steel pipe is 0.006m, and the grouting pipe curtain is equally spaced by a distance D10.4 m. Dividing according to theoretical sections to obtain a grouting pipe curtain support unsealed section b being 5m, an unbuttled section c being 1.6m and a plastic disturbance section
Figure BDA0003432572170000162
At the same time, the elastic disturbance section e can be obtained as 2.0hu-c；
By adopting the method steps, a matlab program is compiled, stratum and grouting pipe curtain parameters are substituted, and an analytic solution of the flexural deformation of the grouting pipe curtain is solved; comparing and analyzing the calculated deformation value of the grouting pipe curtain with the existing theoretical value and the field measured value according to the actually measured distribution and the theoretical distribution comparison diagram of the actually measured deflection deformation of the grouting pipe curtain shown in fig. 5;
according to the theoretical curve and the on-site actual measurement scatter points, the grouting pipe curtain deflection deformation distribution obtained by the calculation method is basically consistent with the actual measurement result, the reliable prediction performance is displayed, and guidance can be provided for design and construction; in addition, the invention reasonably considers the distribution change characteristic of the stratum foundation bed coefficient along with excavation, and can more accurately reflect the axial beam forming effect of the grouting pipe curtain.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements made to the technical solution of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims (5)

1. A grouting pipe curtain deformation calculation method based on the characteristics of soil arches between pipes is characterized by comprising the following steps:
s1, analyzing the transverse soil arch characteristic of the grouting pipe curtain and determining a supporting load;
s2, analyzing the axial beam forming effect of the grouting pipe curtain, and determining a control equation;
s3, establishing a grouting pipe curtain long beam theoretical model, and determining load distribution;
and S4, solving the flexural deformation through a slip casting tube curtain difference calculation method.
2. The grouting pipe curtain deformation calculation method based on the characteristics of the soil arch between pipes as claimed in claim 1, wherein the step S1 is specifically realized by the following method:
s11, according to the Purchase pressure arch theory, considering the soil arch characteristic between adjacent grouting pipe curtains, and establishing a corresponding mechanical model: the grouting pipe curtains are regarded as cylindrical steel pipes and are distributed in the circumferential direction of the outer ring of the tunnel arch part at equal intervals; htAnd BtRespectively the height and the span of the excavated tunnel, the outer diameter of the tunnel is R, the gravity of the surrounding rock is gamma, and the outer diameter of the grouting pipe curtainD, the distance between two adjacent grouting pipe curtains is D1A clear spacing of D2The included angle between two adjacent grouting pipe curtains is alpha,
Figure FDA0003432572160000011
the friction angle of the surrounding rock is R + g, and the radius of the circular arc of the grouting pipe curtain is R + g;
s12, numbering each grouting pipe curtain from the vault to two sides in sequence, and regarding the gravity of the loose rock mass in the pressure arch area as the load of the grouting pipe curtains, wherein any one number is CnThe corresponding load height of the grouting pipe curtain is HdnAnd C isnThe serial numbers of two adjacent grouting pipe curtains are marked as Cn-1And Cn+1And with CnThe horizontal included angle of the grouting pipe curtain is recorded as thetan-1And thetan+1；
S13, in the mechanical model of grouting pipe curtains, defining the central connecting line of two adjacent grouting pipe curtains as an x axis, defining the vertical central line of two adjacent grouting pipe curtains as a y axis, establishing a plurality of rectangular coordinate systems, analyzing the load height corresponding to the grouting pipe curtains by establishing a soil arch axis in each coordinate system, and analyzing the soil arch axis by the equation y-mx without considering the tensile strength of rock mass2A parabola denoted by + n;
s14 grouting pipe curtain Cn-1And CnIn a rectangular coordinate system, the soil arch axis and the grouting pipe curtain Cn-1And CnHas a crossing point of V1And V2Are each independently of V1And grouting pipe curtain Cn-1Line connecting the centers of circles, V2And grouting pipe curtain CnThe intersection points of the segment perpendicular to the connecting line of the circle centers and the x axis are respectively M1And M2Suppose line segment V1Cn-1、V2CnAre all tangent with the soil arch axis and have included angles with the x axis
Figure FDA0003432572160000016
Then line segment V1M1、V2M2At an angle to the x-axis of
Figure FDA0003432572160000015
Then V2The coordinates of the points can be expressed as
Figure FDA0003432572160000013
Figure FDA0003432572160000014
S15, mixing V2The coordinates of the points are brought into the soil arch axis equation, and the following are obtained by solution:
Figure FDA0003432572160000021
Figure FDA0003432572160000022
uniform load q above the earth arch axisn-1And q isn-1Obtained by the following analytical formula:
Figure FDA0003432572160000023
Figure FDA0003432572160000024
vertical concentrated load p of soil arch axisn-1And pn+1Can be expressed as:
Figure FDA0003432572160000025
Figure FDA0003432572160000026
averaging the two to obtain a grouting pipe curtain CnUpper side ofVertical load p ofn：
Figure FDA0003432572160000027
3. The grouting pipe curtain deformation calculation method based on the characteristics of the soil arch between pipes as claimed in claim 1, wherein the step S2 is specifically realized by the following method:
s21, regarding the surrounding rock as a homogeneous and continuous elastic-plastic entity, so that the flexural deformation of the grouting pipe curtain has the mechanical characteristics of Bernoulli-Euler beam, thereby obtaining a grouting pipe curtain mechanical model based on the Pasternak elastic-plastic foundation beam, and obtaining the grouting pipe curtain mechanical model according to the reaction analytical formula of the Pastemak foundation beam by the following formula:
Figure FDA0003432572160000028
wherein: p (x) is the resistance of the surrounding rock foundation, k is the coefficient of the surrounding rock bed, w (x) is the flexural deformation of the grouting pipe curtain, GpIs the shear modulus of the surrounding rock foundation;
s22, considering tunnel support hysteresis, foundation bed coefficient change, stress release and stratum elastoplasticity factors, and sequentially dividing the grouting pipe curtain into a support closed section OA, a support non-closed section AB, a non-support section BC, a plastic disturbance section CD, an elastic disturbance section DE and a non-disturbance section EF from back to front along the advancing direction of the excavation face;
s23, obtaining the following results due to the balanced stress of the units:
Figure FDA0003432572160000031
wherein V (x) is shearing force of grouting pipe curtain, M (x) is bending moment of grouting pipe curtain, q (x) is load borne by grouting pipe curtain, b is width of surrounding rock foundation beam, b*Is equivalent to the width of the surrounding rock foundation, b*＝b[1+(Gp/k)1/2/b]；
S24, based on Bernoulli-Euler beam theory, the mechanical response of the grouting pipe curtain can be obtained, including the differential analytic formula of grouting pipe curtain deflection angle theta (x), longitudinal strain epsilon (x), grouting pipe curtain shear force V (x), grouting pipe curtain bending moment M (x) and grouting pipe curtain deflection deformation W (x):
Figure FDA0003432572160000032
Figure FDA0003432572160000033
Figure FDA0003432572160000034
Figure FDA0003432572160000035
solving a differential balance equation for controlling the deformation of the grouting pipe curtain through the formulas (9) to (13):
Figure FDA0003432572160000036
4. the grouting pipe curtain deformation calculation method based on the characteristics of the soil arch between pipes as claimed in claim 1, wherein the step S3 is specifically realized by the following method:
and (3) obtaining a grouting pipe curtain mechanical model of the Pastemak foundation beam by considering the soil arch characteristic of the grouting pipe curtain and the space-time effect of stratum load:
the primary support closed section OA has a length of a, and the load borne by the grouting pipe curtain in the section is static load, namely q (x) q0，q0Calculating values according to a Prov theory formula; resistance of the zone surrounding rock foundation
Figure FDA0003432572160000037
The differential balance of the control in this section is formulated as
Figure FDA0003432572160000038
The initial branch unblocked section AB has the length of b, and the external load q (x) borne by the grouting pipe curtain of the section is [1+ (eta)1-1)(x-a)/(b+s)]q0Time-space coefficient eta of stress release of surrounding rock load1Taking 0.5; resistance of the primary support surrounding rock foundation of the section
Figure FDA0003432572160000041
Surrounding rock foundation coefficient k in formulac(x)＝-kcx/b+(a+b)kcB, and k at point Bcmin0; the differential balance of control for that segment is formulated as
Figure FDA0003432572160000042
For the unsupported section BC with the length of c, the distribution form of external load borne by the grouting pipe curtain of the section is the same as that of the section AB, and because the initial support of the section BC is not applied, the load p (x) is also taken to be 0, the differential balance formula controlled by the section is as follows
Figure FDA0003432572160000043
Plastic perturbation zone CD of length
Figure FDA00034325721600000410
Wherein h isuIs the height of the tunnel step,
Figure FDA00034325721600000411
the friction angle is calculated for the surrounding rock. In addition, the front of the excavation surface has a remarkable stress concentration phenomenon, and the space-time coefficient eta of the release of the load stress of the surrounding rock at the D point is taken2Take 1.2, the section bears the external load q (x) ═ η2-η1)[x-(a+b+c)]q0/d+η1q0(ii) a Resistance of the zone surrounding rock foundation
Figure FDA0003432572160000044
k0(x)＝[x-(a+b+c+d)](k0-k0min)/s+k0minWhere s is the length of the rock mass before the excavation face, k0Constant coefficient of rock mass bed, k, without disturbance0minIs a ground reduction factor, and k0min＝0.6k0(ii) a The differential balance of the control in this section is formulated as
Figure FDA0003432572160000045
The elastic disturbance section DE is of length e, and the total length of the elastic disturbance section and the undisturbed section of the large-span tunnel grouting pipe curtain is taken as 2huThe segment slip casting tube bears the load q (x) ═ η2[x-(a+b+c+d)]q0/s+η2q0The resistance of the surrounding rock foundation of the section is consistent with the CD section, and the section is taken
Figure FDA0003432572160000046
The differential balance of the control in this section is formulated as
Figure FDA0003432572160000047
An undisturbed section EF with the length f, which is the length of the residual grouting pipe curtain after deducting each section in front; the section grouting pipe curtain is not subjected to any external load, and if q (x) is 0, the resistance of the section surrounding rock foundation is obtained
Figure FDA0003432572160000048
The differential balance of the control in this section is formulated as
Figure FDA0003432572160000049
5. The grouting pipe curtain deformation calculation method based on the characteristics of the soil arch between pipes as claimed in claim 1, wherein the step S4 is specifically realized by the following method:
s41, equally dividing the grouting pipe curtain with the length of L into n sections, and according to the sequence from left to right, each node is compiled into 0, 10The deflection deformation of the grouting pipe curtain of the node i is wi, and in order to adapt to the analytic degree of freedom of the grouting pipe curtain, two different virtual nodes-2, -1, n +1 and n +2 are respectively arranged on the left side and the right side;
and S42, carrying out Taylor formula expansion on the deformation of the left and right adjacent nodes of the node i, and taking the four polynomials in front of the Taylor expansion formula to ensure the analysis accuracy.
Figure FDA0003432572160000051
Figure FDA0003432572160000052
Figure FDA0003432572160000053
This enables the derivation of the various derivatives:
Figure FDA0003432572160000054
Figure FDA0003432572160000055
Figure FDA0003432572160000056
Figure FDA0003432572160000057
s43, combining the above formulas to solve the grouting tube curtain deflection difference formula:
Figure FDA0003432572160000058
order to
Figure FDA0003432572160000059
The formula is simplified as:
Ci(wi-2-4wi-1+6wi-4wi+1+wi+2)+Biwi-Di(-wi-2+16wi-1-30wi+16wi+1-wi+2)＝qi (23)
analyzing and expressing mechanical boundary conditions on two sides of the grouting pipe curtain:
Figure FDA00034325721600000510
Figure FDA00034325721600000511
Figure FDA00034325721600000512
Figure FDA0003432572160000061
simultaneous implementation of the above formula yields:
Figure FDA0003432572160000062
Figure FDA0003432572160000063
when i is 0, 1, n-1, n, the simplified slip casting curtain deflection difference formula can be converted into:
C0(w-2-4w-1+6w0-4w1+w2)+B0w0-D0(-w-2+16w-1-30w0+16w1-w2)＝q0
C1(w-1-4w0+6w1-4w2+w3)+B1w1-D1(-w-1+16w0-30w1+16w2-w3)＝q1
Cn-1(wn-3-4wn-2+6wn-1-4wn+wn+1)+Bn-1wn-1-Dn-1(-wn-3+16wn-2-30wn-1+16wn-wn+1)＝qn-1
Cn(wn-2-4wn-1+6wn-4wn+1+wn+2)+Bnwn-Dn(-wn-2+16wn-1-30wn+16wn+1-wn+2)＝qn
handle w-2、w-1、w1、w2Substituting, one can get:
Figure FDA0003432572160000064
Figure FDA0003432572160000065
Figure FDA0003432572160000066
Figure FDA0003432572160000067
s44, the above equation is expressed in a matrix form to obtain:
{[B]+[C]-[D]}{w}＝{p}
wherein the matrix dimensions of [ B ], [ C ] and [ D ] are all N +1, and the expression is as follows:
Figure FDA0003432572160000071
Figure FDA0003432572160000072
Figure FDA0003432572160000073
in addition, the grouting pipe curtain bears the expression of the load matrix { p }:
{p}＝{p0 p1 p2…pn-1 pn}T
and then the expression of the grouting pipe screen deflection matrix { w } can be obtained:
{w}＝{w0 w1 w2…wn-1 wn}T
and S45, writing a Matlab program, and solving the flexural deformation wi of each node of the grouting pipe curtain.
CN202111602961.6A 2021-12-24 2021-12-24 Grouting pipe curtain deformation calculation method based on inter-pipe soil arch characteristics Pending CN114398699A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116579057A (en) * 2023-04-24 2023-08-11 山东建筑大学 Prediction and control method for deformation of transverse pipe curtain or pipe shed of pilot tunnel excavation
CN117852313A (en) * 2024-03-07 2024-04-09 山东大学 Advanced sectional pre-grouting rapid numerical simulation method and system for underground engineering
CN117852313B (en) * 2024-03-07 2024-05-10 山东大学 Advanced sectional pre-grouting rapid numerical simulation method and system for underground engineering

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116579057A (en) * 2023-04-24 2023-08-11 山东建筑大学 Prediction and control method for deformation of transverse pipe curtain or pipe shed of pilot tunnel excavation
CN116579057B (en) * 2023-04-24 2024-03-08 山东建筑大学 Prediction and control method for deformation of transverse pipe curtain or pipe shed of pilot tunnel excavation
CN117852313A (en) * 2024-03-07 2024-04-09 山东大学 Advanced sectional pre-grouting rapid numerical simulation method and system for underground engineering
CN117852313B (en) * 2024-03-07 2024-05-10 山东大学 Advanced sectional pre-grouting rapid numerical simulation method and system for underground engineering

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