CN114398698A - Method for evaluating support effect of deep-buried pipe curtain based on inter-pipe soil arch characteristics - Google Patents

Method for evaluating support effect of deep-buried pipe curtain based on inter-pipe soil arch characteristics Download PDF

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CN114398698A
CN114398698A CN202111601128.XA CN202111601128A CN114398698A CN 114398698 A CN114398698 A CN 114398698A CN 202111601128 A CN202111601128 A CN 202111601128A CN 114398698 A CN114398698 A CN 114398698A
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curtain
pipe curtain
pipe
section
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
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Abstract

The invention provides a deep buried pipe curtain supporting effect evaluation method based on inter-pipe soil arch characteristics, which comprises the steps of firstly analyzing transverse soil arch characteristics of a pipe curtain and determining the load borne by the pipe curtain; then, building a vertical pipe curtain two-parameter elastic-plastic Passternak foundation beam mechanical model to obtain an analytical expression of pipe curtain deformation and internal force; then extracting a calculation formula of the ratio of the surrounding rock to the initial support load under the action of the pipe curtain, and obtaining the maximum deformation of the pipe curtain and the ratio of the surrounding rock to the initial support load under a specific working condition; and determining the allowable maximum deformation and the allowable minimum surrounding rock-to-primary support load ratio of the pipe curtain, comparing and evaluating the supporting effect of the pipe curtain under a specific working condition, and optimizing the design. The stress of the pipe curtain advance support is obtained through scientific quantification, the method has universality and is easy to understand and accept by designers, the stress of the pipe curtain with the soil arch characteristic between adjacent pipe curtains is considered, the tunnel excavation safety is obviously improved, the bearing span reduction and load transmission effects of the pipe curtain are reasonably evaluated through two index parameters of the maximum deformation of the pipe curtain and the bearing ratio of surrounding rocks to primary supports, the design and construction parameters of the tunnel pipe curtain can be optimized, the overall performance of the pipe curtain support is fully exerted, and the scientificity and the economy of the design of the tunnel pipe curtain are improved.

Description

Method for evaluating support effect of deep-buried pipe curtain 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 method for evaluating the supporting effect of a deep-buried pipe curtain based on the characteristics of an inter-pipe soil arch.
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, for guaranteeing engineering safety, the pipe curtain is generally adopted to pre-reinforce the front rock-soil body, namely, the pipe curtain is supported in advance, the load of loose rock-soil is borne through the pipe curtain, 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 the large 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 tube curtain deformation, the academia has carried out some studies: in the aspect of theoretical derivation, an elastic foundation beam model is generally adopted to analyze a single pipe curtain, and the pipe curtain is considered to act on beams of mutually independent Winkler springs, so that the loaded deformation of the pipe curtain is researched; in the field actual measurement aspect, a steel bar strain gauge or an inclinometer is usually utilized to obtain real-time data of pipe curtain deformation in the excavation process; in the aspect of numerical simulation, the pipe curtain is simulated conventionally by means of a solid unit, a grouting stratum is equivalently reinforced, and the space-time displacement of the pipe curtain under three-dimensional excavation is analyzed.
However, most of the existing researches only qualitatively describe the supporting effect of the pipe curtain, and the existing researches are less related to quantitative analysis of the stress mechanism and the deflection distribution of the pipe curtain. In addition, the traditional pipe curtain deformation calculation theory considers that the bearing range of the pipe curtain is only the area above the pipe diameter projection, and the soil arch characteristic between adjacent pipe curtains is not considered, so that the obvious limitation is caused, and the difference from the actual situation is larger.
Disclosure of Invention
The invention aims to provide a method for evaluating the supporting effect of a deep-buried pipe curtain based on the characteristics of an inter-pipe soil arch, which aims to solve the problems in the background art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a deep-buried pipe curtain supporting effect evaluation method based on inter-pipe soil arch characteristics is characterized by comprising the following steps:
s1, analyzing the transverse soil arch characteristic of the pipe curtain, and determining the load borne by the pipe curtain;
s2, establishing a pipe curtain two-parameter elastic-plastic Passternak foundation beam model to obtain an analytical expression of pipe curtain deformation and internal force;
s3, providing a calculation formula of the ratio of the surrounding rock to the initial support load under the action of the pipe curtain, and obtaining the maximum deformation of the pipe curtain and the ratio of the surrounding rock to the initial support load under a specific working condition;
and S4, determining the allowable maximum deformation and the allowable minimum surrounding rock-to-primary support load ratio of the pipe curtain, comparing and evaluating the pipe curtain support effect under a specific working condition, and optimizing the design.
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 tube curtains, establishing a corresponding mechanical model: the pipe curtains are cylindrical steel pipes and are circumferentially distributed at equal intervals on the outer ring of the tunnel arch part; htAnd BtThe height and the span of the excavated tunnel are respectively, the outer diameter of the tunnel is R, the weight of the surrounding rock is gamma, the outer diameter of the pipe curtain is D, and the distance between two adjacent pipe curtains is D1A clear spacing of D2The included angle between two adjacent tube curtains is alpha,
Figure BDA0003431819200000026
the friction angle of the surrounding rock is R + g, and the radius of the circular arc of the pipe curtain is R + g;
s12, numbering each 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 pipe curtain load, wherein any one of the numbers is CnThe corresponding load height of the tube curtain is HdnAnd C isnThe serial numbers of two adjacent tube screens of the tube screen are marked as Cn-1And Cn+1And with CnThe horizontal included angle of the number tube screen is marked as thetan-1And thetan+1；
S13, in the pipe curtain mechanical model, defining the central connecting line of two adjacent pipe curtains as an x axis, defining the vertical central line of two adjacent pipe curtains as a y axis, establishing a plurality of rectangular coordinate systems, analyzing the load height corresponding to the 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, tube curtain Cn-1And CnIn a rectangular coordinate system, the soil arch axis and the pipe screen Cn-1And CnHas a crossing point of V1And V2Are each independently of V1And tube screen Cn-1Line connecting the centers of circles, V2And tube screen 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、V2CnAll-in-one arch shaftThe line is tangent and has an included angle with the x axis
Figure BDA0003431819200000021
Then line segment V1M1、V2M2At an angle to the x-axis of
Figure BDA0003431819200000022
Then V2The coordinates of the points can be expressed as
Figure BDA0003431819200000023
Figure BDA0003431819200000024
S15, mixing V2The coordinates of the points are brought into the soil arch axis equation, and the following are obtained by solution:
Figure BDA0003431819200000025
Figure BDA0003431819200000031
uniform load q above the earth arch axisn-1And q isn-1Obtained by the following analytical formula:
Figure BDA0003431819200000032
Figure BDA0003431819200000033
vertical concentrated load p of soil arch axisn-1And pn+1Can be expressed as:
Figure BDA0003431819200000034
Figure BDA0003431819200000035
averaging the two to obtain a tube curtain CnVertical load p aboven：
Figure BDA0003431819200000036
Further, the step S2 is specifically implemented by the following method:
s21, regarding the surrounding rock as a homogeneous and continuous elastic-plastic solid, wherein the flexural deformation of the tube curtain has the mechanical characteristics of a Bernoulli-Euler beam, so that a tube curtain mechanical model based on the Pastnak elastic-plastic foundation beam is obtained, and the tube curtain mechanical model is obtained according to the reaction analytical expression of the Pastnak foundation beam by the following formula:
Figure BDA0003431819200000037
wherein: p (x) is the resistance of the surrounding rock foundation, k is the surrounding rock bedspread coefficient, w (x) is the deflection of the pipe curtain, GpIs the shear modulus of the surrounding rock foundation;
s22, considering factors such as tunnel support hysteresis, foundation bed coefficient change, stress release and stratum elastoplasticity, and sequentially dividing the 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 BDA0003431819200000038
wherein V (x) is shearing force of the pipe curtain, M (x) is bending moment of the pipe curtain, q (x) is load borne by the pipe curtain, b is width of the wall 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 tube curtain can be obtained, and the mechanical response comprises a differential analytic formula of tube curtain deflection angle theta (x), longitudinal strain epsilon (x), tube curtain shear force V (x), tube curtain bending moment M (x) and tube curtain deflection deformation W (x):
Figure BDA0003431819200000041
Figure BDA0003431819200000042
Figure BDA0003431819200000043
Figure BDA0003431819200000044
through the above equations (9) - (13), the differential balance equation for controlling the deformation of the tube curtain is solved:
Figure BDA0003431819200000045
s25, obtaining a pipe curtain mechanical model of the Passternak foundation beam by considering the pipe curtain soil arch characteristic and the stratum load space-time effect:
the primary support closed section OA has a length of a, and the load borne by the tube curtain of the section is static load, i.e. q (x) q0，q0Calculating values according to a Prov theory formula; resistance of the zone surrounding rock foundation
Figure BDA0003431819200000046
The differential balance of the control in this section is formulated as
Figure BDA0003431819200000047
The initial unblocked section AB has the length of b, and the external load borne by the tube curtain of the sectionq(x)＝[1+(η1-1)(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 BDA0003431819200000048
Figure BDA0003431819200000049
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 BDA00034318192000000410
For the unsupported section BC with the length of c, the distribution form of the external load born by the tube screen 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 of the section control is as follows
Figure BDA00034318192000000411
Plastic perturbation zone CD of length
Figure BDA00034318192000000412
Wherein h isuIs the height of the tunnel step,
Figure BDA00034318192000000413
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 BDA0003431819200000051
k0(x)＝[x-(a+b+c+d)](k0-k0min)/s+k0minWhere s is the length of the rock mass before the excavation face, k0Is notConstant coefficient of rock mass bed, k, under disturbance0minIs a ground reduction factor, and k0min＝0.6k0(ii) a The differential balance of the control in this section is formulated as
Figure BDA0003431819200000052
The length of the elastic disturbance section DE is e, and the total length of the elastic disturbance section and the undisturbed section of the large-span tunnel pipe curtain is taken as 2huThe segment tube sheet 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 BDA0003431819200000053
The differential balance of the control in this section is formulated as
Figure BDA0003431819200000054
Figure BDA0003431819200000055
The undisturbed section EF is the length f of the residual pipe screen after deducting each section in front; the section 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 BDA0003431819200000056
The differential balance of the control in this section is formulated as
Figure BDA0003431819200000057
S26, equally dividing the tube curtain with the length of L into n segments, 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 segment is divided into L0The pipe curtain deflection deformation of the node i is wi;
s27, carrying out Taylor formula expansion on the deflection of the node i to obtain a tube curtain deflection difference formula:
Figure BDA0003431819200000058
order to
Figure BDA0003431819200000059
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 (16)
substituting the boundary conditions of the two sides of the tube curtain, and performing matrixing expression on the equation:
{[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 BDA0003431819200000061
Figure BDA0003431819200000062
Figure BDA0003431819200000063
in addition, the tube sheet bears the expression of the load matrix { p }:
{p}＝{p0 p1 p2…pn-1 pn}T (17)
and then the expression of the pipe curtain deflection matrix { w } can be obtained:
{w}＝{w0 w1 w2…wn-1 wn}T (18)
s28, writing a Matlab program, solving the flexural deformation wi of each node of the tube curtain, and solving the simultaneous equations (8) - (13) to obtain the substrate reaction force R of the tube curtainiAngle of rotation thetaiAxial strain epsiloniBending moment MiAnd shear force Vi：
Figure BDA0003431819200000064
Figure BDA0003431819200000071
Figure BDA0003431819200000072
Figure BDA0003431819200000073
Figure BDA0003431819200000074
Further, the step S3 is specifically implemented by the following method:
s31, respectively evaluating and analyzing the circumferential direction and the axial direction of the pipe curtain, and obtaining the bearing ratio of the surrounding rock and the primary support under the working condition of the pipe curtain without construction according to the load distribution mode of the tunnel
Figure BDA0003431819200000075
In the formula, PrIs the load of surrounding rock in the section 3m ahead of the excavation face, PcThe load borne by the primary support in a section 3m behind the excavation face is measured;
s32, combined with the theoretical derivation above, yields:
Figure BDA0003431819200000076
further, the step S4 is specifically implemented by the following method:
s41, consulting the specifications, and determining the allowable maximum deformation w of the pipe curtain by combining the stratum settlement control standard and the excavation reserved deformation0And allowable minimum wall rock to primary support bearing ratio eta0。
S42, obtaining the maximum deformation w of the pipe curtain under the specific working condition through the theoretical calculationmaxAnd the ratio eta of surrounding rock to primary bearing loadpAnd the maximum deformation w allowed for the tube curtain0And allowable minimum wall rock to primary support bearing ratio eta0And (3) comparison:
if wmax>w0Adjusting the maximum deformation of the tube curtain to wmax≤w0And through ηpAnd η0Comparing to evaluate the load transmission effect of the pipe curtain;
and S43, optimizing the design parameters of the pipe curtain by combining the load transmission effect evaluation of the pipe curtain.
According to the technical scheme, the stress of the pipe curtain advance support is obtained through scientific quantification, the method has universality and is easy to understand and accept by designers, the stress of the pipe curtain with the soil arch characteristic between adjacent pipe curtains is considered, the tunnel excavation safety is obviously improved, the bearing span reduction and the load transmission effect of the pipe curtain are reasonably evaluated through the maximum deformation of the pipe curtain and the bearing ratio of surrounding rocks to primary supports, the design and construction parameters of the tunnel pipe curtain can be optimized, the overall performance of the pipe curtain support is fully exerted, and the scientificity and the economy of the design of the tunnel pipe curtain are improved.
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 in step S1 according to the present invention;
FIG. 3 is a schematic sectional view of the tube sheet according to the present invention;
FIG. 4 is a schematic view of node division of the pipe screen according to the present invention;
FIG. 5 is a graph of the tube curtain deflection distribution of an embodiment of the present invention;
FIG. 6 is a graph of the load ratio of the surrounding rock to the primary support according to an embodiment 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, the method for evaluating the supporting effect of the deep-buried pipe curtain based on the characteristics of the soil arch between pipes comprises the following steps:
s1, analyzing the transverse soil arch characteristic of the pipe curtain, and determining the load borne by the pipe curtain;
the step provides a tube curtain mechanical calculation method considering the characteristics of the inter-tube soil arch, the inter-tube soil arch is considered to be an important means for the tube curtain to exert bearing and span reduction, and the consistency of the gravity of the rock and soil mass in the soil arch loosening area and the actual situation is better; the method is realized by the following steps:
s11, according to the Purchase pressure arch theory, considering the soil arch characteristics between adjacent pipe curtains, and establishing a corresponding mechanical model, as shown in figure 2: the pipe curtains are cylindrical steel pipes and are circumferentially distributed at equal intervals on the outer ring of the tunnel arch part; htAnd BtThe height and the span of the excavated tunnel are respectively, the outer diameter of the tunnel is R, the weight of the surrounding rock is gamma, the outer diameter of the pipe curtain is D, and the distance between two adjacent pipe curtains is D1A clear spacing of D2The included angle between two adjacent tube curtains is alpha,
Figure BDA0003431819200000081
the friction angle of the surrounding rock is R + g, and the radius of the circular arc of the pipe curtain is R + g;
s12, numbering each 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 pipe curtain load, wherein any one of the numbers is CnThe corresponding load height of the tube curtain is HdnAnd C isnThe serial numbers of two adjacent tube screens of the tube screen are marked as Cn-1And Cn+1And with CnThe horizontal included angle of the number tube screen is marked as thetan-1And thetan+1；
S13, in the pipe curtain mechanical model, defining the central connecting line of two adjacent pipe curtains as an x axis, defining the vertical central line of two adjacent pipe curtains as a y axis, establishing a plurality of rectangular coordinate systems, analyzing the load height corresponding to the 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, tube curtain Cn-1And CnAt right angle to each otherIn the coordinate system, the earth arch axis and the pipe screen Cn-1And CnHas a crossing point of V1And V2Are each independently of V1And tube screen Cn-1Line connecting the centers of circles, V2And tube screen 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 BDA0003431819200000091
Then line segment V1M1、V2M2At an angle to the x-axis of
Figure BDA0003431819200000092
Then V2The coordinates of the points can be expressed as
Figure BDA0003431819200000093
Figure BDA0003431819200000094
S15, mixing V2The coordinates of the points are brought into the soil arch axis equation, and the following are obtained by solution:
Figure BDA0003431819200000095
Figure BDA0003431819200000096
uniform load q above the earth arch axisn-1And q isn-1Obtained by the following analytical formula:
Figure BDA0003431819200000097
Figure BDA0003431819200000098
vertical concentrated load p of soil arch axisn-1And pn+1Can be expressed as:
Figure BDA0003431819200000099
Figure BDA00034318192000000910
averaging the two to obtain a tube curtain CnVertical load p aboven：
Figure BDA00034318192000000911
S2, establishing a pipe curtain two-parameter elastic-plastic Passternak foundation beam model to obtain an analytical expression of pipe curtain deformation and internal force;
the method is realized by the following steps:
s21, regarding the surrounding rock as a homogeneous and continuous elastic-plastic solid, wherein the flexural deformation of the tube curtain has the mechanical characteristics of a Bernoulli-Euler beam, so that a tube curtain mechanical model based on the Pastnak elastic-plastic foundation beam is obtained, and the tube curtain mechanical model is obtained according to the reaction analytical expression of the Pastnak foundation beam by the following formula:
Figure BDA0003431819200000101
wherein: p (x) is the resistance of the surrounding rock foundation, k is the surrounding rock bedspread coefficient, w (x) is the deflection of the pipe curtain, GpIs the shear modulus of the surrounding rock foundation;
s22, as shown in figure 3, considering factors of tunnel support hysteresis, foundation bed coefficient change, stress release and stratum elastoplasticity, dividing the 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 in sequence along the advancing direction of the excavation surface;
s23, obtaining the following results due to the balanced stress of the units:
Figure BDA0003431819200000102
wherein V (x) is shearing force of the pipe curtain, M (x) is bending moment of the pipe curtain, q (x) is load borne by the pipe curtain, b is width of the wall 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 tube curtain can be obtained, and the mechanical response comprises a differential analytic formula of tube curtain deflection angle theta (x), longitudinal strain epsilon (x), tube curtain shear force V (x), tube curtain bending moment M (x) and tube curtain deflection deformation W (x):
Figure BDA0003431819200000103
Figure BDA0003431819200000104
Figure BDA0003431819200000105
Figure BDA0003431819200000106
through the above equations (9) - (13), the differential balance equation for controlling the deformation of the tube curtain is solved:
Figure BDA0003431819200000107
s25, obtaining a pipe curtain mechanical model of the Passternak foundation beam by considering the pipe curtain soil arch characteristic and the stratum load space-time effect:
the primary support closed section OA has the length of a, the load borne by the tube curtain of the section is static load,i.e. q (x) q0，q0Calculating values according to a Prov theory formula; resistance of the zone surrounding rock foundation
Figure BDA0003431819200000108
The differential balance of the control in this section is formulated as
Figure BDA0003431819200000111
An initial unblocked section AB of length b, the section bearing an external load q (x) ([ 1+ (. eta ])) on the tube sheet1-1)(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 BDA0003431819200000112
Figure BDA0003431819200000113
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 BDA0003431819200000114
For the unsupported section BC with the length of c, the distribution form of the external load born by the tube screen 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 of the section control is as follows
Figure BDA0003431819200000115
Plastic perturbation zone CD of length
Figure BDA0003431819200000116
Wherein h isuIs the height of the tunnel step,
Figure BDA0003431819200000117
the friction angle is calculated for the surrounding rock. In addition, the front of the excavation surface has obvious stress concentrationTaking the space-time coefficient eta of the stress release of the surrounding rock load at the D point2Take 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 BDA0003431819200000118
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 BDA0003431819200000119
The length of the elastic disturbance section DE is e, and the total length of the elastic disturbance section and the undisturbed section of the large-span tunnel pipe curtain is taken as 2huThe segment tube sheet 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 BDA00034318192000001110
The differential balance of the control in this section is formulated as
Figure BDA00034318192000001111
Figure BDA00034318192000001112
The undisturbed section EF is the length f of the residual pipe screen after deducting each section in front; the section 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 BDA00034318192000001113
The differential balance of the control in this section is formulated as
Figure BDA00034318192000001114
S26, as shown in FIG. 4, equally dividing the tube sheet with the length L into n segments, 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 segment is divided into L0The pipe curtain deflection deformation of the node i is wi;
s27, carrying out Taylor formula expansion on the deflection of the node i to obtain a tube curtain deflection difference formula:
Figure BDA0003431819200000121
order to
Figure BDA0003431819200000122
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 (16)
substituting the boundary conditions of the two sides of the tube curtain, and performing matrixing expression on the equation:
{[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 BDA0003431819200000123
Figure BDA0003431819200000124
Figure BDA0003431819200000131
in addition, the tube sheet bears the expression of the load matrix { p }:
{p}＝{p0 p1 p2 …pn-1 pn}T (17)
and then the expression of the pipe curtain deflection matrix { w } can be obtained:
{w}＝{w0 w1 w2…wn-1 wn}T (18)
s28, solving the flexural deformation wi of each node of the tube curtain by writing a Matlab program and solving the simultaneous equations (8) - (13) to obtain the base reaction force R of the tube curtainiAngle of rotation thetaiAxial strain epsiloniBending moment MiAnd shear force Vi：
Figure BDA0003431819200000132
Figure BDA0003431819200000133
Figure BDA0003431819200000134
Figure BDA0003431819200000135
Figure BDA0003431819200000136
S3, providing a calculation formula of the ratio of the surrounding rock to the initial support load under the action of the pipe curtain, and obtaining the maximum deformation of the pipe curtain and the ratio of the surrounding rock to the initial support load under a specific working condition;
the step is based on an elastic-plastic Passternak foundation beam model, a mathematical expression of the bearing ratio of the surrounding rock to the primary support is provided, and the advantage and the disadvantage of the load transmission effect of the pipe curtain can be evaluated more scientifically and reasonably; the method is realized by the following steps:
s31, evaluating and analyzing the circumferential direction and the axial direction of the pipe curtain respectively;in the circumferential direction, due to the existence of the soil arch characteristic, the pipe curtain can be subjected to load deflection by virtue of the high-strength pipe section material, so that the span-reducing bearing effect is effectively achieved, the bearing performance of the pipe curtain is reasonably predicted, the maximum deformation of the pipe curtain is determined to serve as an evaluation index, and the effect of the pipe curtain is further characterized; in the axial aspect, due to the existence of the beam forming effect, the tube curtain can transmit the load in front of the tunnel to the rear primary support through the tube body, and the obvious load transmission effect is achieved. Determining foundation resistance of a section 3m in front of or behind a tunnel face to represent the bearing quantity value of the surrounding rock and the primary support, and quantitatively evaluating the quality of the load transfer effect of the pipe curtain through the bearing ratio of the surrounding rock to the primary support; obtaining the bearing ratio of the surrounding rock to the primary support under the working condition of the non-applied pipe curtain by the tunnel load distribution mode
Figure BDA0003431819200000141
In the formula PrIs the load of surrounding rock in the section 3m ahead of the excavation face, PcThe load borne by the primary support in a section 3m behind the excavation face.
S32, combined with the theoretical derivation above, yields:
Figure BDA0003431819200000142
s4, determining the allowable maximum deformation and the allowable minimum surrounding rock-to-primary support load ratio of the pipe curtain, comparing and evaluating the pipe curtain support effect under a specific working condition, and performing design optimization;
the method is realized by the following steps:
s41, consulting the specifications, and determining the allowable maximum deformation w of the pipe curtain by combining the stratum settlement control standard and the excavation reserved deformation0And allowable minimum wall rock to primary support bearing ratio eta0。
S42, obtaining the maximum deformation w of the pipe curtain under the specific working condition through the theoretical calculationmaxAnd the ratio eta of surrounding rock to primary bearing loadpAnd the maximum deformation w allowed for the tube curtain0And allowable minimum wall rock to primary support bearing ratio eta0And (3) comparison:
if wmax>w0Adjusting the maximum deformation of the tube curtain to wmax≤w0And through ηpAnd η0Comparing to evaluate the load transmission effect of the pipe curtain;
and S43, optimizing the design parameters of the pipe curtain by combining the load transmission effect evaluation of the pipe curtain.
The evaluation method according to the invention is illustrated below by means of specific examples:
the pipe curtain of the double-line deep-buried tunnel is adopted for a certain high-speed rail tunnel; based on the early-stage survey data of the tunnel, inquiring relevant tunnel design specifications to obtain necessary calculation parameters: the length a of the primary support closed section is 3m, the length b of the non-closed section is 15m, the length c of the non-supported section is 1m, and the length of the plastic disturbance section is deduced by analysis
Figure BDA0003431819200000143
And the length e of the elastic disturbance section is 2.0hu-c. At the same time, the Purchase arch load height Hdn24.05m, total length L of tube screen 30m, and distance D between tube screens10.4m, 108mm of pipe screen diameter D, 6mm of pipe wall thickness t, and surrounding rock bed coefficient k045MPa/m, the primary foundation bed coefficient kc 90MPa/m, the primary shear modulus Gcp5kN/m, shear modulus G of surrounding rockrp2.5kN/m, step excavation height hu7m, angle of friction of surrounding rock
Figure BDA0003431819200000151
Presetting the maximum deformation w allowed for the tube curtain0And allowable minimum wall rock to primary support bearing ratio eta0The method steps are adopted by combining the design parameters to calculate the actual maximum deformation w of the pipe curtainmaxAnd the ratio eta of surrounding rock to primary bearing loadpComparing, evaluating and analyzing, and specifically:
(1) consulting the standard, combining the stratum settlement control standard and the reserved deformation amount, and determining the allowable maximum deformation w of the pipe curtain0150mm, a minimum surrounding rock to primary support bearing ratio eta of0Is 3.0;
(2) when other parameters are not changedThe excavation footage is sequentially 0.50m, 0.75m, … m and 3.00m, and the maximum deformation w of the pipe curtain under different excavation footages is obtained through the theoretical calculation as shown in fig. 5 and 6maxAnd the bearing ratio eta of the surrounding rock to the primary supportp. Combining it with the tube curtain to allow maximum deformation w0And allowable minimum wall rock to primary support bearing ratio eta0And (3) comparison: if wmax>w0Adjusting the maximum deformation of the tube curtain to wmax≤w0And through ηpAnd η0And (3) comparing to evaluate the load transmission effect of the pipe curtain:
as can be seen from the pipe curtain deflection distribution curves of different excavation footings in the figure 5, the deflection curves are obviously concave downward, and the deformation value in the front and rear 3m sections of the excavation surface is the largest. Along with the increasing of the excavation footage s, the deflection of the pipe curtain is increased rapidly in a nonlinear way, the larger the sinking amplitude is, the excavation footage is increased from 0.75m to 2.50m and is only increased by 3.3 times, but the maximum deformation value of the pipe curtain is increased rapidly from 31.5mm to 7.2 times and is up to 225.9mm, and the maximum deformation value exceeds the preset allowable maximum deformation w of the pipe curtain0(ii) a Through comparative analysis, when the excavation footage s is less than 2m, the allowable maximum deformation w of the pipe curtain is less than the preset value0Therefore, the excavation footage is strictly controlled within 2 m;
as can be seen from the curve of the ratio of the surrounding rock to the initial bearing load of different excavation footage in the figure 6, when no construction pipe curtain is constructed, the ratio eta of the surrounding rock to the initial bearing load is obtainedpIs obvious and large, and the surrounding rock load in front of the excavation surface is also increased continuously along with the increase of the excavation footage. This means that in the interval of 3m before or after the excavation face, the surrounding rock is the main bearing body compared with the supporting secondary bearing body, and the surrounding rock itself bears most of the load. And after pipe-curtain advance support, etapThe speed increase is remarkably slowed down, and when the excavation footage is equal to 2m, the eta of the pipe curtain advanced support is arrangedpIs 2.08, without η of pipe curtain advance supportpA 3.94, a significant reduction of 47.2%. The pipe curtain can obviously improve the load distribution between the surrounding rock and the primary support, timely transmits the disturbance load in front of the excavation face to the primary support at the rear, and obviously reduces the advanced influence area. When the excavation footage is more than or equal to 1.75m, the ratio eta of the surrounding rock to the initial bearing loadpMore than 3.0, greater than a predetermined toleranceMinimum wall rock to primary support bearing ratio eta0It shows that the excavation footage should be greater than 1.75 m.
In conclusion, although the excavation footage is increased, the tunneling efficiency can be obviously improved, and the pipe curtain can also ensure the excavation safety to a certain extent, the excavation footage cannot be too large, otherwise, the bending displacement of the pipe body and the ratio of the surrounding rock to the primary support load are rapidly increased, and the risk of the sliding damage of the surrounding rock of the tunnel on the excavation face is rapidly increased; therefore, in order to ensure the excavation safety, the excavation footage should be reasonably determined, and finally the excavation footage is optimized to be 2 m. Similarly, according to the evaluation method provided by the invention, design parameters such as the pipe curtain distance, the pipe curtain diameter, the step height and the like can be optimized.
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 deep-buried pipe curtain supporting effect evaluation method based on inter-pipe soil arch characteristics is characterized by comprising the following steps:
s1, analyzing the transverse soil arch characteristic of the pipe curtain, and determining the load borne by the pipe curtain;
s2, establishing a pipe curtain two-parameter elastic-plastic Passternak foundation beam model to obtain an analytical expression of pipe curtain deformation and internal force;
s3, providing a calculation formula of the ratio of the surrounding rock to the initial support load under the action of the pipe curtain, and obtaining the maximum deformation of the pipe curtain and the ratio of the surrounding rock to the initial support load under a specific working condition;
and S4, determining the allowable maximum deformation and the allowable minimum surrounding rock-to-primary support load ratio of the pipe curtain, comparing and evaluating the pipe curtain support effect under a specific working condition, and optimizing the design.
2. The method for evaluating the supporting effect of the deeply buried pipe curtain based on the characteristics of the soil arch between the pipes according to 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 tube curtains, establishing a corresponding mechanical model: the pipe curtains are cylindrical steel pipes and are circumferentially distributed at equal intervals on the outer ring of the tunnel arch part; htAnd BtThe height and the span of the excavated tunnel are respectively, the outer diameter of the tunnel is R, the weight of the surrounding rock is gamma, the outer diameter of the pipe curtain is D, and the distance between two adjacent pipe curtains is D1A clear spacing of D2The included angle between two adjacent tube curtains is alpha,
Figure FDA0003431819190000011
the friction angle of the surrounding rock is R + g, and the radius of the circular arc of the pipe curtain is R + g;
s12, numbering each 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 pipe curtain load, wherein any one of the numbers is CnThe corresponding load height of the tube curtain is HdnAnd C isnThe serial numbers of two adjacent tube screens of the tube screen are marked as Cn-1And Cn+1And with CnThe horizontal included angle of the number tube screen is marked as thetan-1And thetan+1；
S13, in the pipe curtain mechanical model, defining the central connecting line of two adjacent pipe curtains as an x axis, defining the vertical central line of two adjacent pipe curtains as a y axis, establishing a plurality of rectangular coordinate systems, analyzing the load height corresponding to the 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, tube curtain Cn-1And CnIn a rectangular coordinate system, the soil arch axis and the pipe screen Cn-1And CnHas a crossing point of V1And V2Are each independently of V1And tube screen Cn-1Line connecting the centers of circles, V2And tube screen 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 FDA0003431819190000012
Then line segment V1M1、V2M2At an angle to the x-axis of
Figure FDA0003431819190000013
Then V2The coordinates of the points can be expressed as
Figure FDA0003431819190000014
Figure FDA0003431819190000015
S15, mixing V2The coordinates of the points are brought into the soil arch axis equation, and the following are obtained by solution:
Figure FDA0003431819190000021
Figure FDA0003431819190000022
uniform load q above the earth arch axisn-1And q isn-1Obtained by the following analytical formula:
Figure FDA0003431819190000023
Figure FDA0003431819190000024
vertical concentrated load p of soil arch axisn-1And pn+1Can be expressed as:
Figure FDA0003431819190000025
Figure FDA0003431819190000026
averaging the two to obtain a tube curtain CnVertical load p aboven：
Figure FDA0003431819190000027
3. The method for evaluating the supporting effect of the deeply buried pipe curtain based on the characteristics of the soil arch between the pipes according to 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 solid, wherein the flexural deformation of the tube curtain has the mechanical characteristics of a Bernoulli-Euler beam, so that a tube curtain mechanical model based on the Pastnak elastic-plastic foundation beam is obtained, and the tube curtain mechanical model is obtained according to the reaction analytical expression of the Pastnak foundation beam by the following formula:
Figure FDA0003431819190000028
wherein: p (x) is the resistance of the surrounding rock foundation, k is the surrounding rock bedspread coefficient, w (x) is the deflection of the pipe curtain, GpIs the shear modulus of the surrounding rock foundation;
s22, considering factors such as tunnel support hysteresis, foundation bed coefficient change, stress release and stratum elastoplasticity, and sequentially dividing the 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 FDA0003431819190000031
wherein V (x) is shearing force of the pipe curtain, M (x) is bending moment of the pipe curtain, q (x) is load borne by the pipe curtain, b is width of the wall 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 tube curtain can be obtained, and the mechanical response comprises a differential analytic formula of tube curtain deflection angle theta (x), longitudinal strain epsilon (x), tube curtain shear force V (x), tube curtain bending moment M (x) and tube curtain deflection deformation W (x):
Figure FDA0003431819190000032
Figure FDA0003431819190000033
Figure FDA0003431819190000034
Figure FDA0003431819190000035
through the above equations (9) - (13), the differential balance equation for controlling the deformation of the tube curtain is solved:
Figure FDA0003431819190000036
s25, obtaining a pipe curtain mechanical model of the Passternak foundation beam by considering the pipe curtain soil arch characteristic and the stratum load space-time effect:
the primary support closed section OA has a length of a, and the load borne by the tube curtain of the section is static load, i.e. q (x) q0，q0Calculating values according to a Prov theory formula; resistance of the zone surrounding rock foundation
Figure FDA0003431819190000037
The differential balance of the control in this section is formulated as
Figure FDA0003431819190000038
An initial unblocked section AB of length b, the section bearing an external load q (x) ([ 1+ (. eta ])) on the tube sheet1-1)(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 FDA0003431819190000039
Figure FDA00034318191900000310
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 FDA00034318191900000311
For the unsupported section BC with the length of c, the distribution form of the external load born by the tube screen 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 of the section control is as follows
Figure FDA0003431819190000041
Plastic perturbation zone CD of length
Figure FDA0003431819190000042
Wherein h isuIs the height of the tunnel step,
Figure FDA0003431819190000043
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 taken2Taking 1.2, this 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 FDA0003431819190000044
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 FDA0003431819190000045
The length of the elastic disturbance section DE is e, and the total length of the elastic disturbance section and the undisturbed section of the large-span tunnel pipe curtain is taken as 2huThe segment tube sheet 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 FDA0003431819190000046
The differential balance of the control in this section is formulated as
Figure FDA0003431819190000047
Figure FDA0003431819190000048
The undisturbed section EF is the length f of the residual pipe screen after deducting each section in front; the section 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 FDA0003431819190000049
The differential balance of the control in this section is formulated as
Figure FDA00034318191900000410
S26, equally dividing the 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 pipe curtain deflection deformation of the node i is wi;
s27, carrying out Taylor formula expansion on the deflection of the node i to obtain a tube curtain deflection difference formula:
Figure FDA00034318191900000411
order to
Figure FDA00034318191900000412
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 (16)
substituting the boundary conditions of the two sides of the tube curtain, and performing matrixing expression on the equation:
{[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 FDA0003431819190000051
Figure FDA0003431819190000052
Figure FDA0003431819190000053
in addition, the tube sheet bears the expression of the load matrix { p }:
{p}＝{p0 p1 p2 … pn-1 pn}T (17)
and then the expression of the pipe curtain deflection matrix { w } can be obtained:
{w}＝{w0 w1 w2 … wn-1 wn}T (18)
s28, writing a Matlab program, solving the flexural deformation wi of each node of the tube curtain, and solving the simultaneous equations (8) - (13) to obtain the substrate reaction force R of the tube curtainiAngle of rotation thetaiAxial strain epsiloniBending moment MiAnd shear force Vi：
Figure FDA0003431819190000061
Figure FDA0003431819190000062
Figure FDA0003431819190000063
Figure FDA0003431819190000064
Figure FDA0003431819190000065
4. The method for evaluating the supporting effect of the deeply buried pipe curtain based on the characteristics of the soil arch between the pipes according to claim 1, wherein the step S3 is specifically realized by the following method:
s31, respectively evaluating and analyzing the circumferential direction and the axial direction of the pipe curtain, and obtaining the surrounding rock and the primary support under the working condition of the pipe curtain without construction according to the tunnel load distribution modeBearing ratio
Figure FDA0003431819190000066
In the formula, PrIs the load of surrounding rock in the section 3m ahead of the excavation face, PcThe load borne by the primary support in a section 3m behind the excavation face is measured;
s32, combined with the theoretical derivation above, yields:
Figure FDA0003431819190000067
5. the method for evaluating the supporting effect of the deeply buried pipe curtain based on the characteristics of the soil arch between the pipes according to claim 1, wherein the step S4 is specifically realized by the following method:
s41, consulting the specifications, and determining the allowable maximum deformation w of the pipe curtain by combining the stratum settlement control standard and the excavation reserved deformation0And allowable minimum wall rock to primary support bearing ratio eta0。
S42, obtaining the maximum deformation w of the pipe curtain under the specific working condition through the theoretical calculationmaxAnd the ratio eta of surrounding rock to primary bearing loadpAnd the maximum deformation w allowed for the tube curtain0And allowable minimum wall rock to primary support bearing ratio eta0And (3) comparison:
if wmax＞w0Adjusting the maximum deformation of the tube curtain to wmax≤w0And through ηpAnd η0Comparing to evaluate the load transmission effect of the pipe curtain;
and S43, optimizing the design parameters of the pipe curtain by combining the load transmission effect evaluation of the pipe curtain.
CN202111601128.XA 2021-12-24 2021-12-24 Method for evaluating support effect of deep-buried pipe curtain based on inter-pipe soil arch characteristics Pending CN114398698A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116579150A (en) * 2023-04-26 2023-08-11 山东建筑大学 Full-stage ground surface subsidence prediction and control method
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

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
CN116579150A (en) * 2023-04-26 2023-08-11 山东建筑大学 Full-stage ground surface subsidence prediction and control method
CN116579150B (en) * 2023-04-26 2024-01-26 山东建筑大学 Full-stage ground surface subsidence prediction and control method

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