CN115168952B - TBM tunnel primary support stress calculation method considering time effect - Google Patents

TBM tunnel primary support stress calculation method considering time effect Download PDF

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CN115168952B
CN115168952B CN202210808289.4A CN202210808289A CN115168952B CN 115168952 B CN115168952 B CN 115168952B CN 202210808289 A CN202210808289 A CN 202210808289A CN 115168952 B CN115168952 B CN 115168952B
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吴圣智
赵洪海
王晨光
王浩爽
刘秀芝
李晓静
谢宏强
刘越
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Shandong Jianzhu University Engineering Appraisal And Reinforcement Research Institute Co ltd
Shandong Jianzhu University
China Railway 14th Bureau Group Co Ltd
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Abstract

The invention discloses a TBM tunnel primary support stress calculation method considering time effect; in the TBM construction process, the stress state of each time stage is different under the influence of surrounding rock release and support material performance change, and the stress analysis in the TBM construction process needs to find out the surrounding rock pressure and the initial support material performance of the primary support at each time stage. Firstly, a surrounding rock pressure correction coefficient considering time effect is provided, a surrounding rock pressure correction coefficient calculation method is established according to a surrounding rock pressure release rule, and a surrounding rock pressure gauge algorithm method considering time effect is formed. And then, considering the change rule of the mechanical property of the primary support sprayed concrete along with time, and establishing a method for calculating the bending rigidity of the primary support. And finally, establishing a load structure calculation model by integrating a surrounding rock load calculation method and a primary support rigidity calculation method, and analyzing the stress state of the primary support in each time period.

Description

TBM tunnel primary support stress calculation method considering time effect
Technical Field
The invention belongs to the field of primary support of TBM tunnels, and particularly relates to a method for calculating the stress of the primary support of a TBM tunnel by considering a time effect.
Background
In the TBM construction process, the safety performance of the primary support in the tunnel composite lining needs to be evaluated, however, the safety evaluation of the primary support at present is based on the final stress state after the tunnel is built, and the dynamic evaluation in the construction process is lacked. In the TBM construction process, the stress states of all time stages are different under the influence of surrounding rock release and support material performance change, and the final stress state is adopted to evaluate the safety existence of primary support, so that the risks of large deformation and the like are gradually increased in the TBM tunnel construction process, and the TBM popularization is seriously restricted.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a time effect-considered TBM tunnel primary support stress calculation method, which can reflect the TBM stress characteristics in the whole construction process and provide support for the evaluation of the primary support safety, thereby promoting the application of high-end equipment such as TBM and the like in tunnel engineering.
In order to achieve the purpose, the invention is realized by the following technical scheme:
the embodiment of the invention provides a TBM tunnel primary support stress calculation method considering time effect, which comprises the following steps:
(1) Collecting tunnel design parameters and geological parameters;
(2) Determining a time node t needing to calculate primary support;
(3) Determining a surrounding rock pressure correction coefficient k according to a tunnel longitudinal deformation curve, and calculating surrounding rock pressures q (t) and e (t) at the time node t;
(4) Determining the elastic modulus E of the sprayed concrete under the time node t according to the test or the specification c (t), determining the bending rigidity E (t) I of the primary support section considering the aging characteristic of the sprayed concrete;
(5) Establishing a load-structure numerical model, and inputting the surrounding rock pressure and the bending rigidity of the primary support section under a time node t;
(6) And calculating to obtain the primary support bending moment and the axial force.
The beneficial effects of the above-mentioned embodiment of the present invention are as follows:
in the TBM construction process, the stress state of each time stage is different under the influence of surrounding rock release and support material performance change. In order to calculate the stress characteristic of the primary support at any moment, the invention establishes a surrounding rock pressure correction coefficient calculation method according to the surrounding rock pressure release rule, can calculate the surrounding rock pressure at any moment in the construction process, and simultaneously establishes a primary support bending rigidity calculation method at any moment by considering the change rule of the mechanical property of the primary support sprayed concrete along with the time. According to the method for calculating the pressure correction coefficient of the surrounding rock and the method for calculating the bending rigidity of the primary support at any moment, the stress characteristic of the primary support at any moment can be calculated, the stress state of the primary support at the whole construction stage can be shown, a foundation is laid for accurately evaluating the safety performance of the primary support, the safety and the reliability of the primary support in the using process are further guaranteed, the risk occurrence probability is reduced, and the application of TBM in various stratums is favorably promoted.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are included to illustrate an exemplary embodiment of the invention and not to limit the invention.
FIG. 1 is a computational model on which the computational method proposed by the present invention is based;
FIG. 2 is a flow chart of a calculation method proposed by the present invention;
FIG. 3 is a graph of the change in modulus of elasticity of shotcrete over time;
FIG. 4 load-structure numerical model;
FIG. 5 calculation of bending moment (N m);
FIG. 6 axial force calculation (N);
in the figure: 1-vertical pressure of surrounding rock, 2-horizontal pressure of surrounding rock, 3-formation resistance and 4-primary support.
1-1 primary support simulation unit, giving bending rigidity at time t; 1-2 formation springs; 1-3-constraint; the vertical pressure of surrounding rock is 1-4 t; and 5-surrounding rock horizontal pressure at time t.
Detailed Description
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an", and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof;
as introduced by the background technology, the defects in the prior art are that in order to solve the technical problems, the invention provides a method for calculating the primary support stress of a TBM tunnel by considering the time effect.
In a typical embodiment of the invention, in the TBM construction process, the stress state of each time stage is different under the influence of surrounding rock release and support material performance change, and the stress analysis in the TBM construction process needs to ascertain surrounding rock pressure and primary support material performance of primary support at each time stage. Firstly, a surrounding rock pressure correction coefficient considering time effect is provided, a surrounding rock pressure correction coefficient calculation method is established according to a surrounding rock pressure release rule, and a surrounding rock pressure gauge algorithm method considering time effect is formed. And then, considering the change rule of the mechanical property of the primary support sprayed concrete along with time, and establishing a method for calculating the bending rigidity of the primary support. And finally, establishing a load structure calculation model by integrating a surrounding rock load calculation method and a primary support rigidity calculation method, and analyzing the stress state of each time period of the primary support.
The method comprises the following specific steps:
(1) Collecting tunnel design parameters and geological parameters, and determining tunnel excavation span, radius, surrounding rock grade, weight, internal friction angle, cohesive force, poisson, resistance coefficient, original rock stress and other parameters.
(2) And determining the time node t needing to calculate the preliminary bracing.
(3) Determining a surrounding rock pressure correction coefficient k according to a tunnel longitudinal deformation curve, and calculating surrounding rock pressures q (t) and e (t) at the time node t;
(4) Determining the elastic modulus E of the sprayed concrete under the time node t according to the test or the specification c (t), and determining the flexural rigidity E (t) I of the primary bracing section in consideration of the aging characteristics of the shotcrete.
(5) And (3) establishing a load-structure numerical model, and inputting the surrounding rock pressure and the bending rigidity of the primary support section under the time node t.
(6) And calculating to obtain the primary support bending moment and the primary support axial force.
Further, the method for calculating the surrounding rock pressure considering the time effect comprises the following steps:
the calculation method for the deeply buried tunnel surrounding rock provided by TB 10003-2016 railway tunnel design Specification is based on construction actual measurement landslide height statistical analysis, can calculate surrounding rock pressures corresponding to different tunnel spans and different surrounding rock grades, is used for a plurality of years along a railway tunnel, and achieves a good design effect; the surrounding rock pressure calculation formula is expressed by formula (1):
Figure BDA0003739235960000041
in the formula, q is the vertical pressure of surrounding rock, kPa; e is the horizontal pressure of the surrounding rock, kPa and gamma are the volume weight of the surrounding rock, kN/m 3 (ii) a s is the grade of surrounding rock; w is the width impact coefficient, w =1+ i (B-5), where B is the tunnel width, m; i is the surrounding rock pressure increase and decrease rate when B increases or decreases by 1m, B<5m, i =0.2,B>At 5m, i =0.1 can be selected; λ is the lateral pressure coefficient, taken as in table 1.
TABLE 1 side pressure coefficient value-taking table
Figure BDA0003739235960000051
However, the existing more actual measurement data of the surrounding rock pressure show that the surrounding rock pressure has a certain space-time effect, and the time effect is not considered in the formula (1), namely the calculation result is the final value. The release of the surrounding rock pressure is not completed instantly, but gradually released along with the approaching and the moving away of the excavation surface until the space effect of the excavation surface is completely disappeared. The surrounding rock pressure is different along with the change of the excavation face space effect, and the accurate expression of the excavation face space effect has important significance for the determination of the surrounding rock pressure. Representing the space-time change characteristic of the surrounding rock pressure by using a surrounding rock pressure correction coefficient k, wherein the surrounding rock pressures of different time nodes are represented as follows:
Figure BDA0003739235960000052
further, when determining the surrounding rock pressure correction coefficient k, a longitudinal deformation curve of the tunnel is needed, and for this purpose, different tunnel deformation curves can be adopted. The longitudinal deformation curve of the tunnel can describe the relaxation release of surrounding rocks in the tunnel excavation process, and the longitudinal deformation curve of the tunnel is represented by formula (3):
Figure BDA0003739235960000053
wherein R is tunnelTrack radius, m; and x is the distance from the excavation surface, and m is the distance from the excavation surface. Wherein R is * ＝R p /R，x * ＝x/R，u ∞ 、R p The maximum deformation value (m) and the maximum plastic zone radius (m) of the surrounding rock under the condition of no supporting force are respectively. u. of 0 *、u * (x) And representing the deformation release coefficient of the excavation position and the rear deformation release coefficient of the excavation surface. Regarding the calculation of the radius of the plastic zone of the surrounding rock and the maximum deformation value of the surrounding rock, a related elastic-plastic analytic solution can be selected for calculation:
Figure BDA0003739235960000061
in the formula p 0 Is the stress of the original rock, kPa, and can be obtained through testing; c is cohesive force of surrounding rock, kPa;
Figure BDA0003739235960000062
the internal friction angle of the surrounding rock.
The pressure release coefficient of the surrounding rock is closely related to the relaxation release of the surrounding rock, and the pressure correction coefficient k of the surrounding rock can be used as u in the formula (3) * (x) In that respect x is the distance from the excavation surface, in actual engineering, the distance can be determined according to the excavation rate v (m/d) and the construction time t (d), and the distance is expressed by the formula (6):
x＝vt (5)
further, the method for determining the parameters of the primary support material comprises the following steps:
the primary supporting structure is composed of a sprayed concrete and arch (steel arch, grid arch and the like) structure, and is a combined structure, so that equivalent analysis needs to be carried out on the bending rigidity of the section of the primary supporting structure in the calculation process, and the specific equivalent method is represented by formula (7):
E h I＝E c I c +E a I a (6)
in the formula E h I is the bending rigidity of the section of the primary support structure, GPa.m 4 ；I c Is the section moment of inertia, m, of the sprayed concrete 4 ；E c I c Bending-resistant steel for sprayed concrete partial sectionDegree, GPa.m 4 ；I a Is the section moment of inertia, m, of the steel arch 4 ；E a I a Is the bending rigidity of partial section of the arch frame structure, and is GPa.m 4 。
The mechanical property of the sprayed concrete has certain timeliness due to the hardening property of the sprayed concrete. Modulus of elasticity E of shotcrete c The relation with time t is expressed by equation (8):
E c (t)＝E c,0 (1-e -αt ) (7)
in the formula E c (t) the elastic modulus, GPa, of the sprayed concrete at time node t; e c,0 The final elastic modulus, GPa, of the sprayed concrete can be obtained according to specifications; t is the concrete spraying time, d; α is a time constant. In actual engineering, alpha can be determined according to an actual material selection test of the engineering, and if no field test data exists, parameters are selected according to relevant concrete material specifications.
The calculation result of the formula (8) is carried into the formula (7), and the flexural rigidity E of the primary support section considering the aging characteristic of the sprayed concrete can be obtained h (t)I：
E h (t)I＝E c (t)I c +E a I a (8)
Further, the method for calculating the stress of the primary support comprises the following steps:
and selecting time nodes t to be calculated, calculating the surrounding rock pressure and the bending rigidity of the primary support on the primary support at the moment respectively, and calculating the stress of the primary support by adopting a load-structure model.
One specific example is given below:
(1) Collecting tunnel design parameters and geological parameters, for example, the collected parameters are as follows:
the tunnel excavation span is 12m, the tunnel radius is 6m, the surrounding rock grade is IV grade, and the gravity is 22kN/m 3 The internal friction angle is 40 degrees, the cohesive force is 100kPa, the Poisson ratio is 0.4, the elastic resistance coefficient is 500MPa/m, the original rock stress is 1000kPa, and the excavation rate is 2m/d. The tunnel design parameter C30 is sprayed with concrete, the thickness is 25cm, and the distance between the I18 steel arches is 1m.
(2) Determining time nodes needing to calculate primary support: t =2d.
(3) Solving a surrounding rock pressure correction coefficient and a surrounding rock pressure: solving Rp =8.4m according to formula 4, solving the distance 4m from the excavation surface according to formula 5, and solving u according to formula 3 * (x) At 0.64, a surrounding rock pressure correction coefficient k =0.64 is determined. Solving for q (t) =122.2kPa according to equation 2; e (t) =36.7kPa.
(4) Determining the elastic modulus of the sprayed concrete at t and the bending rigidity E (t) I of the tunnel at the time: determining the relation between the C30 sprayed concrete elastic modulus and the time by the concrete, and determining the elastic modulus E of the sprayed concrete when t =2d c (t) =17.9GPa, and the bending rigidity of the tunnel E (t) I =0.0266GPa.m is determined according to the formula 8 4 。
(5) Establishing a load-structure numerical model, wherein the model comprises a primary support simulation unit and is required to be endowed with bending rigidity at time t as shown in figure 4; the stratum spring is used for simulating the stratum constraint force and needs to be endowed with an elastic resistance coefficient; meanwhile, horizontal and vertical surrounding rock pressure at the time t needs to be exerted on the primary support simulation unit.
(6) After the model is established and assigned, the model is solved, and the primary support bending moment and the axial force are calculated, as shown in fig. 5 and 6, the bending moment and the axial force of each position of the tunnel at the time node t are respectively displayed on the primary support simulation unit in a cloud picture mode, and the darker the color of the cloud picture of the bending moment and the axial force represents that the bending moment value and the axial force value are larger. When the bending moment value is positioned in the primary support unit, the bending moment represents that the inner side of the primary support is pulled and the outer side is pressed; when the bending moment value is positioned outside the primary support unit, the inner side of the primary support is pressed and the outer side is pulled due to the bending moment. When the axial force value is positioned outside the primary support unit, the axial force of the primary support is reflected as pressure; and when the axial force value is positioned at the inner part of the primary support unit, the axial force of the primary support is reflected as a tensile force.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. A TBM tunnel primary support stress calculation method considering time effect is characterized by comprising the following steps:
(1) Collecting tunnel design parameters and geological parameters;
(2) Determining time nodes for which preliminary bracing needs to be calculatedt；
(3) Determining surrounding rock pressure correction coefficient according to tunnel longitudinal deformation curvekThe pressure correction coefficient of the surrounding rockkTaking the rear deformation release coefficient of the excavation surfaceu * (x) The coefficient of releasing the rear deformation of the excavated surfaceu * (x) The calculation formula is as follows:
Figure 276789DEST_PATH_IMAGE001
；
in the formulau 0 * In order to release the deformation coefficient of the excavated part,u * (x) In order to release the coefficient of the rear deformation of the excavation face,Ris the tunnel radius, in units of: m;xthe unit of the distance from the excavation surface is as follows: m; wherein the content of the first and second substances,R * =R p /R，x * =x/R，u ∞ 、R p respectively the maximum deformation value and the maximum plastic zone radius of the surrounding rock without supporting force; saidx Is calculated as follows:
Figure 503371DEST_PATH_IMAGE002
；
wherein, the first and the second end of the pipe are connected with each other,vthe excavation rate is determined;tthe construction time is set; at this time nodetCalculating the vertical pressure and the horizontal pressure of the surrounding rock pressure; the surrounding rock pressures at different time nodes are expressed as:
Figure 72892DEST_PATH_IMAGE003
；
q(t) The unit of the surrounding rock vertical pressure of different time nodes is as follows: kPa; e (t) is the surrounding rock horizontal pressure of different time nodes, and the unit is as follows: kPa;Kis a correction coefficient of the pressure of the surrounding rock,γthe unit is the volume weight of the surrounding rock: kN/m 3 ；sIs the grade of the surrounding rock;wis the width influence coefficient;λis a lateral pressure coefficient;
(4) Determining time nodes from trial or specificationtThe elastic modulus of the lower sprayed concrete and the bending rigidity of the primary support section considering the ageing characteristic of the sprayed concrete are determined;
(5) Establishing a load-structure numerical model and inputting time nodestThe pressure of the lower surrounding rock and the bending rigidity of the section of the primary support;
(6) And calculating to obtain the primary support bending moment and the primary support axial force.
2. The method for calculating the preliminary bracing stress of the TBM tunnel considering the time effect as claimed in claim 1, wherein the tunnel design parameters and the geological parameters comprise: the tunnel excavation method comprises the following steps of tunnel excavation span, radius, surrounding rock grade, weight, internal friction angle, cohesive force, poisson, resistance coefficient and original rock stress.
3. The method for calculating the primary support stress of the TBM tunnel considering the time effect as claimed in claim 1, wherein the method is characterized in thatR p Is calculated as follows:
Figure 144753DEST_PATH_IMAGE004
；
in the formulap 0 Is the stress of the original rock and has the unit: kPa, obtainable by testing;cthe cohesive force of the surrounding rock is shown in the unit: kPa;
Figure 116121DEST_PATH_IMAGE005
is the internal friction angle of the surrounding rock, and the unit is: and (4) degree.
4. The method for calculating the primary support stress of the TBM tunnel considering the time effect as claimed in claim 1, wherein the elastic modulus of the shotcrete isE c And withTimetThe relationship of (a) is as follows:
Figure 513604DEST_PATH_IMAGE006
；
in the formula
Figure 39263DEST_PATH_IMAGE007
As a time nodetThe elastic modulus of the sprayed concrete is as follows: GPa;E c,0 final modulus of elasticity for shotcrete, in units of: GPa;tthe unit is the concrete spraying time: day;αis a time constant.
5. The method for calculating the primary support stress of the TBM tunnel considering the time effect as claimed in claim 4, wherein the method is characterized in thatαAnd determining according to an engineering actual selected material test or selecting parameters according to concrete material specifications.
6. The method for calculating the primary support stress of the TBM tunnel considering the time effect as claimed in claim 4, wherein the flexural rigidity of the section of the primary support considering the aging characteristic of the shotcrete is
Figure 445974DEST_PATH_IMAGE008
The following:
Figure 6268DEST_PATH_IMAGE009
；
wherein the content of the first and second substances,
Figure 574653DEST_PATH_IMAGE010
the unit is the section inertia moment of the sprayed concrete, and is as follows: m is 4 ；
Figure 853187DEST_PATH_IMAGE011
Is the section moment of inertia of the steel arch frame, and the unit is: m is a unit of 4 ；
Figure 735693DEST_PATH_IMAGE012
The bending rigidity of the section of the arch structure part is expressed by the unit: GPa . m 4 。
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107917839A (en) * 2017-11-16 2018-04-17 山东建筑大学 Test evaluation tunnel anchors the pilot system and method for country rock composite bearing performance
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CN114607406A (en) * 2022-03-15 2022-06-10 沈阳工业大学 Weak surrounding rock open type TBM construction surrounding rock reinforcing device and construction method

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107917839A (en) * 2017-11-16 2018-04-17 山东建筑大学 Test evaluation tunnel anchors the pilot system and method for country rock composite bearing performance
CN114154211A (en) * 2021-11-10 2022-03-08 中南大学 Design method of high ground stress soft rock tunnel supporting structure, computer device and product
CN114607406A (en) * 2022-03-15 2022-06-10 沈阳工业大学 Weak surrounding rock open type TBM construction surrounding rock reinforcing device and construction method

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Title
TBM盾构施工斜井管片和锚喷衬砌结构力学特性研究;杨悦;《工程科技Ⅱ辑》;20180915;第13-14、21-23、75-79页 *
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