CN111695186A - Method for calculating ultimate supporting force of circumferential excavation surface of shield tunnel without considering earth surface overload working condition - Google Patents

Method for calculating ultimate supporting force of circumferential excavation surface of shield tunnel without considering earth surface overload working condition Download PDF

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CN111695186A
CN111695186A CN202010534607.3A CN202010534607A CN111695186A CN 111695186 A CN111695186 A CN 111695186A CN 202010534607 A CN202010534607 A CN 202010534607A CN 111695186 A CN111695186 A CN 111695186A
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tunnel
supporting force
excavation surface
shield tunnel
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CN111695186B (en
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张箭
丰土根
宗晶瑶
张坤勇
钟小春
张福海
孔纲强
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Hohai University HHU
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Abstract

The invention discloses a method for calculating the ultimate supporting force of an annular excavation surface of a shield tunnel without considering the earth surface overload condition, which comprises the following steps of S1: constructing a soil body rigid sliding block damage theoretical model of the circumferential excavation surface of the shield tunnel, and confirming key parameters influencing the ultimate supporting force of the circumferential excavation surface of the shield tunnel; step S2: deducing key intermediate indexes based on the theoretical model and the key parameters in the step S1; step S3: constructing a model core formula, substituting the model core formula into the key intermediate index in the step S2, and solving the ultimate supporting force; step S4: and circularly optimizing the key parameters in the step S1, and solving the optimal upper limit solution of the ultimate supporting force of the shield tunnel annular excavation surface. The invention creatively provides that the rigid slide block of the soil body of the circumferential excavation surface of the shield tunnel destroys the theoretical model under the condition of ground surface level and no overload, has higher precision and is suitable for the working condition without ground surface overload, thereby reducing the tunneling construction cost of the shield tunnel and meeting the development requirement of tunnel construction.

Description

Method for calculating ultimate supporting force of circumferential excavation surface of shield tunnel without considering earth surface overload working condition
Technical Field
The invention relates to a method for analyzing the stability of a circumferential excavation surface of a shield tunnel, in particular to a method for calculating the ultimate supporting force of the circumferential excavation surface of the shield tunnel under the condition of not considering earth surface overload, and belongs to the technical field of shield construction.
Background
In the construction of the traffic infrastructure field, underground traffic infrastructures such as tunnels and subways have the advantages of road surface land resource saving, large transportation volume, high efficiency, environmental protection, capability of relieving urban traffic transportation pressure due to three-dimensional construction and the like, and become a preferred scheme for solving the problems of traffic deterioration and the like in each big city, so the tunnel engineering construction becomes a key component of the traffic infrastructure construction, and the generated tunnel engineering construction safety problem becomes a key problem of the infrastructure construction. In the tunneling construction in the tunnel construction process, reasonable supporting pressure needs to be timely provided for the surrounding ground layer of the tunnel excavation, so that the problems of tunnel working face collapse, ground surface settlement and the like are prevented, and serious accidents such as damage of underground and overground structures, vehicle collapse, damage of surrounding pipelines and the like are avoided. Therefore, reasonably determining the supporting pressure of the tunnel excavation face in the tunneling process is a key technology in construction, and has important practical significance for tunnel construction.
The limit analysis method is based on a plastic limit analysis theory, constructs a speed field allowed by movement and a static allowable stress field, determines the upper limit and the lower limit of a limit load by utilizing an upper limit theorem and a lower limit theorem according to an associated flow rule and a virtual work principle, considers the stress-strain relation of rock and soil body materials, has a stricter theoretical basis, is more accurate in solving result, and is an effective method for researching tunnel excavation stability analysis. On the basis of the assumed damage mode limit analysis method, a scholars considers the actual settlement of the unstable ground surface of the tunnel according to the ground surface overload construction working condition (such AS Mao pine, Songchun, Lu Rong. heterogeneous clay foundation tunnel annular excavation surface stability upper limit analysis [ J ]. geotechnical engineering report, 2013,35(08): 1504) and the actual settlement of the unstable ground surface of the tunnel (such AS Osman AS, Mair J, Bolton M D. On the mechanics of 2D tunnel collagen in undrainedclay [ J ]. G ethhnique, 2006,56(9): 585-, a series of research works are carried out on different conditions of introducing a soil body non-associative flow rule (such as Zhao Jiheng, Sun autumn red, yellow funus, Zhoujin Feng. non-associative flow rule, upper limit analysis [ J ] on stability influence of shallow tunnel, highway traffic science and technology, 2012,29(12): 101-. But the problem of stability of the circumferential excavation surface of the shield tunnel without considering the earth surface overload condition under the drainage condition is solved less.
On the other hand, as the development of the calculation software matures, a numerical simulation method is adopted to solve the tunnel stability problem (such as Qin construction, Egyueju. shield tunnel excavation surface stability numerical simulation research [ J ]. Proc. mining and safety Engineering, 2005,22(1): 27-30; Ukriston B, Keawsawasvong S, Yingchankikkajorn K. Undrainequality stability of tunnels in Bangkok subsolides [ J ]. International Journal of Geotechnical Engineering,2016:1-16.) also obtains a plurality of research results. However, when the stability problem is solved by adopting a numerical simulation means, analysis mostly needs to be performed by trial calculation for many times, and no clear instability criterion exists at present, that is, the instability critical state of the tunnel is difficult to find accurately, and the numerical simulation means often cannot obtain the limit supporting force with higher precision.
Disclosure of Invention
The invention aims to provide a method for calculating the ultimate supporting force of the circumferential excavation surface of the shield tunnel without considering the earth surface overload working condition, which has higher precision and is suitable for the earth surface overload-free working condition so as to reduce the tunneling construction cost of the shield tunnel and meet the development requirement of tunnel construction.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method for calculating the ultimate supporting force of the circumferential excavation surface of a shield tunnel without considering the earth surface overload working condition is characterized by comprising the following steps of:
step S1: constructing a soil body rigid sliding block damage theoretical model of the circumferential excavation surface of the shield tunnel, and confirming key parameters influencing the ultimate supporting force of the circumferential excavation surface of the shield tunnel;
step S2: deducing key intermediate indexes based on the theoretical model and the key parameters in the step S1;
step S3: constructing a model core formula, substituting the model core formula into the key intermediate index in the step S2, and solving the ultimate supporting force;
step S4: and circularly optimizing the key parameters in the step S3, and solving the optimal upper limit solution of the ultimate supporting force of the shield tunnel annular excavation surface.
Wherein the theoretical model in step S1 includes:
model conditions: the earth surface is horizontal and has no overload, and supporting force loads are uniformly distributed only on the inner contour of the tunnel;
the damage area is composed of n convex rigid sliding blocks on the lateral direction of the tunnel axis and above the tunnel top plate, the contact edge of the rigid sliding blocks and the tunnel is an arc edge, the 1 st rigid sliding block is a trilateral sliding block on the lateral bottom of the tunnel axis, the ith sliding block is a convex quadrilateral sliding block on the lateral direction of the tunnel axis, i is 2,3,4,5, n-1, and the nth sliding block is a sliding block above the tunnel top plate.
Preferably, the number n of the convex rigid sliders is 7
Further, the first assumed module mode, i.e. in general, the nth slider is a pentagonal slider above the tunnel ceiling.
And in the second assumed module mode, namely, in the case of the damage condition that the plastic damage of the unstable stratum of the tunnel excavation does not extend to the ground surface, the nth sliding block is a quadrangle.
In step S2, the key intermediate indicators include: side length, area, absolute speed and relative speed of the slider.
In step S3, the core formula is:
pr+pw＝pc(1)
wherein p isrIs the system gravity power, pwIs that the inner contour of the tunnel acts on the uniformly distributed supporting force load sigmaTPower of operation, pcIs to destroy the energy dissipated power inside the area,
Figure BDA0002536571260000031
wherein, ξiIs the angle between the speed of the ith rigid slide block and the vertical direction, viIs the absolute velocity of the ith rigid slide, SiThe area of the ith rigid slide block is shown, and gamma is the volume weight of the soil body.
Figure BDA0002536571260000032
Wherein c is soil cohesion, virIs the relative speed of the ith rigid slide block and the (i + 1) th rigid slide block, ai+1biLength of the base side of the (i + 1) th rigid slider, bibi+1Is the side edge of the (i + 1) th rigid sliding block, phi is an internal friction angle,
Figure BDA0002536571260000033
wherein σTUniformly distributing supporting force loads on the inner contour of the tunnel,
Figure BDA0002536571260000034
a speed field for the slide block of the tunnel excavation surface to collapse towards the inside of the tunnel under the action of the supporting force,
Figure BDA0002536571260000035
the speed of the tunnel excavation surface in the normal direction is the speed of the circumferential supporting force action direction, and S represents the plastic deformation area of the tunnel excavation surface, namely the total area of the rigid sliding blocks.
In step S3, the key parameters include a circle center angle α corresponding to the arc edge of the ith rigid slideriAnd two opposite corners β2i-1,β2i。
The upper limit of the ultimate supporting force of the annular excavation surface of the tunnel is defined as follows:
Figure BDA0002536571260000036
compared with the prior art, the invention has the following beneficial effects:
the invention provides a method for calculating the ultimate supporting force of the circumferential excavation surface of the shield tunnel without considering the earth surface overload working condition, which has higher precision and is suitable for the earth surface overload-free working condition, so that the tunneling construction cost of the shield tunnel is reduced, and the development requirement of tunnel construction is met.
1. The theoretical model of the ultimate supporting force of the shield tunnel circumferential excavation surface is creatively provided under the condition that the earth surface is horizontal and no overload exists, and the theoretical model is used for researching the supporting effect of shield segments on the surrounding strata of the tunnel.
2. The rigid sliding block failure mode of the soil body of the circumferential excavation surface of the shield tunnel under the drainage condition is creatively provided, and the gap of the existing research on the drainage condition is filled.
3. The solved limit load is optimized through the optimization variables, so that the limit load is continuously close to the real limit load, and the instability critical state can be found better theoretically.
4. The invention considers the no-overload working condition, the solving result under the no-drainage condition is equivalent to the solving result under the existing consideration of the earth surface overload working condition, and the experimental data proves that the invention has higher precision compared with the existing consideration of the research of the earth surface overload working condition under the no-drainage condition.
Drawings
Fig. 1(a) is a diagram of a failure mode region of a presumed rigid sliding block of a first proposed type of shield tunnel instability, and fig. 1(b) is a diagram of a corresponding angle variable;
fig. 2(a) is a diagram of a second proposed area of the shield tunnel instability assuming a rigid slider failure mode, and fig. 2(b) is a diagram of a corresponding angle variable;
FIG. 3 is a diagram of the geometry of the proposed two proposed postulated failure modes respectively;
FIG. 4(a) is a lateral slider velocity field relationship for two failure modes, and FIG. 4(b) is a top slider velocity field relationship for two failure modes;
FIG. 5 is a diagram of a numerical model used in numerical simulation;
FIG. 6 is a comparison between the tunnel instability destruction state solving and the numerical simulation solving under the typical working condition without water drainage;
FIG. 7 is a comparison between the tunnel instability destruction state solved by the present invention and the numerical simulation solution under typical conditions under drainage conditions;
FIG. 8 is a comparison of the present invention calculation method with a prior art calculation method; (a) H/D ═ 1, (b) H/D ═ 2, (c) H/D ═ 3, and (D) H/D ═ 4.
Detailed Description
1. Firstly, proposing a theoretical model assumption, and constructing the theoretical model damaged by the rigid sliding blocks of the soil body of the circumferential excavation surface of the shield tunnel under the condition that the earth surface is horizontal and no overload exists.
The damage area is composed of 7 convex rigid sliding blocks on the lateral direction of the tunnel axis and above the tunnel top plate, the contact edge of the rigid sliding blocks and the tunnel is an arc edge, the 1 st rigid sliding block is a trilateral sliding block on the lateral bottom of the tunnel axis, the ith sliding block is a convex quadrilateral sliding block on the lateral direction of the tunnel axis, and i is 2,3,4,5 and 6.
The first hypothetical module mode, as shown in fig. 1, is typically a pentagonal slider above the tunnel ceiling.
The second assumed module mode is shown in fig. 2, namely, when the plastic damage of the unstable stratum of tunnel excavation does not extend to the damage condition of the ground surface, the 7 th sliding block is a quadrangle.
2. Based on a theoretical model, deducing a shield tunnel circumferential excavation face ultimate supporting force calculation formula, wherein the deduction process is as follows:
in the model, the diameter of ① tunnel is D, the buried depth is H, the load of ② tunnel inner contour evenly distributed supporting force is sigma T③ the volume weight of soil is gamma, the cohesive force of soil is c, the internal friction angle is phi,
assuming that the rigid slider angle variable in failure mode is α1,α2,α3.....,α7,β1,β2,β3,.....,β12Determination, wherein 2 α is assumed1,2α2,2α3.....,2α6The angle of the circle center corresponding to the arc edge of the lateral rigid slide block of each tunnel axis is α7The arc edge of the slide block at the top of the tunnel corresponds to the angle of the circle center β2i-1,β2iTwo of the ith rigid slide blockDiagonal, i-1, 2,3,4,5, 6; the included angle between the relative speed direction of each rigid sliding block and the direction of the discontinuous surface is phi.
According to the geometric relationship, firstly, the relationship between the geometric parameters and the velocity field of each rigid slide block is calculated,
as shown in FIGS. 3-4, assume that the length of the base of the ith rigid slider is aibi-1I is 2,3,4,5,6,7, wherein a1b1The bottom edge of the 1 st trilateral slide block at the lateral bottom of the tunnel; bibi+1The side of the (i + 1) th rigid slider is, i is 1,2,3,4,5, 6.
The recursion formula of the side length of the trilateral rigid sliding block at the lateral bottom of the tunnel axis is as follows:
Figure BDA0002536571260000051
Figure BDA0002536571260000052
the side length recurrence formula of the lateral quadrilateral rigid sliding block of the tunnel axis is as follows:
Figure BDA0002536571260000053
Figure BDA0002536571260000054
(i ═ 1,2,3,4,5) the recursive formula for the tunnel roof rigid slider side length is:
Figure BDA0002536571260000055
Figure BDA0002536571260000056
wherein, the equation (10) is the side length of the pentagonal rigid sliding block at the top of the tunnel in the first assumed failure mode, and the equation (11) is the side length of the quadrangular rigid sliding block at the top of the tunnel in the second assumed failure mode after correction.
Deriving the area S of each rigid slider from the geometrical propertiesiThe calculation formula is as follows:
the area calculation formula of the triangular rigid sliding block at the lateral bottom of the tunnel is as follows:
Figure BDA0002536571260000061
for the area of the tunnel lateral quadrilateral rigid slide block, the area of three triangles is correspondingly subtracted by the area of a fan, and the area calculation formula is as follows:
Figure BDA0002536571260000062
the area formula of the rigid slide block above the top of the tunnel is as follows:
Figure BDA0002536571260000063
Figure BDA0002536571260000064
the formula (14) is a formula of the area of the pentagonal rigid sliding block at the top of the tunnel in the first assumed failure mode, and the formula (15) is a formula of the area of the quadrilateral rigid sliding block at the top of the tunnel in the second assumed failure mode after correction.
Suppose the absolute velocity of the ith rigid slider is viThe relative speed of the ith rigid slide block and the (i + 1) th rigid slide block is virAccording to the velocity vector diagram, the numerical recursion relation between the absolute velocity and the relative velocity is as follows:
the recursion formula of the speed variable of the trilateral rigid sliding block at the lateral bottom of the tunnel axis is as follows:
Figure BDA0002536571260000065
Figure BDA0002536571260000066
the recursion formula of the speed variable of the tunnel axis lateral quadrilateral rigid sliding block is as follows:
Figure BDA0002536571260000071
Figure BDA0002536571260000072
the recursion formula of the side length speed variable of the rigid sliding block at the top of the tunnel is as follows:
Figure BDA0002536571260000073
Figure BDA0002536571260000074
the upper limit theorem of the limit analysis applied to solving the upper limit solution of the objective function is expressed as follows: permitting plastic strain rate fields for arbitrary motion
Figure BDA0002536571260000075
Velocity field
Figure BDA0002536571260000076
And the limit load determined by the imaginary power equation is greater than or equal to the real limit load, so that the upper limit solution of the objective function is solved. Then, an imaginary power equation is established according to the limit analysis upper limit theorem to solve the upper limit solution of the annular limit supporting force of the tunnel, namely:
pr+pw＝pc(22)
wherein p isrIs the system gravity power, pwIs that the inner contour of the tunnel acts on the uniformly distributed supporting force load sigmaTPower of operation, pcIs the energy dissipated power inside the damage area.
Figure BDA0002536571260000077
ξi: the included angle between the speed of the ith rigid slide block and the vertical direction (the gravity action direction);
Figure BDA0002536571260000078
uniform supporting force load sigma under action of inner contour of tunnelTThe work is expressed as:
Figure BDA0002536571260000079
wherein the content of the first and second substances,
Figure BDA0002536571260000081
representing the speed field of the tunnel excavation face slide block collapsing into the tunnel under the action of the supporting force, and supposing that the supporting force load sigma is uniformly distributed under the action of the inner contour of the tunnelT，
Figure BDA0002536571260000082
The power is the supporting force of the excavation face.
Figure BDA0002536571260000083
The speed of the tunnel excavation surface in the normal direction is the speed of the circumferential supporting force action direction, and S represents the plastic deformation area of the tunnel excavation surface, namely the total area of the rigid sliding blocks.
Establishing an imaginary power equation, and taking an angle variable α of the rigid slide block1,α2,α3.....,α7,β1,β2,β3,.....,β12For optimizing variables, solving the upper limit of the ultimate supporting force of the annular excavation surface of the tunnel as follows:
Figure BDA0002536571260000084
determining an angle variable α based on compatible velocity and geometry constraints of the failure mode1,α2,α3.....,α7,β1,β2,β3,.....,β12And (3) performing variable optimization by using an MATLAB software Fmincon nonlinear programming function, and solving an optimal upper limit solution of the ultimate supporting force of the circumferential excavation surface of the shield tunnel.
3. The specific experimental conditions were:
(1) establishing a numerical model
A plane strain tunnel mechanical model is established by using ABAQUS software, as shown in figure 5, the diameter of a calculation model tunnel is 6m, and 3-5 times of the diameter D of the tunnel is taken as the range of the calculation model according to the modeling experience of relevant scholars, so that the size of the numerical model determined by the method is as follows: the X direction (the width direction of the model) was 48m, and the Y direction (the vertical depth direction) was 30m and 48m, respectively. The boundary conditions of the model are: the ground surface is a free surface and is not constrained, and the boundary around the soil body is constrained by deformation. Under the condition of not considering the earth surface overload condition, the supporting load sigma is uniformly distributed only on the inner contour of the tunnelTThe soil body adopts a Moire-Coulomb mechanical model. And when the stability problem of the excavation surface is solved through numerical simulation, the instability limit state of the tunnel is solved by adopting a trial calculation method. In the simulation, a certain supporting pressure is applied to an excavation surface, the supporting force applied to the excavation surface is continuously reduced, and when the displacement mutation of a soil body near the excavation surface of a tunnel is caused by the minimum change of the supporting force, the tunnel instability limit state is obtained.
(2) Method for solving tunnel instability failure form through numerical simulation
The numerical model modeling process is as follows: firstly, establishing a stratum analysis model, setting boundary and load conditions, carrying out initial ground stress balance, simulating an initial state of a stratum, and eliminating the influence of initial stress on model establishment; simulating tunnel excavation by adopting a living and dead unit method, applying tunnel excavation surface supporting force, then gradually reducing the applied excavation surface supporting force, and recording the applied supporting force and the displacement of soil bodies near the excavation surface; and thirdly, continuously reducing the applied tunnel excavation face supporting force until the displacement value changes suddenly, and stopping calculation, wherein the tunnel instability critical state is obtained at the moment.
Firstly, comparing the tunnel instability destruction form solved by the method under the typical parameters of the water non-drainage condition and the destruction mode diagram of the numerical simulation result, as shown in fig. 6, the tunnel instability destruction mode solved by the method and the surrounding stratum plastic destruction cloud diagram in the tunnel instability limit state obtained by numerical simulation are displayed. The comparison shows that the damage forms of the stratums around the instability of the tunnel solved by the two methods are both from the near bottom plate of the side wall of the tunnel and extend to the earth surface, and the damage forms are relatively close. Similarly, the failure modes under the typical parameter condition under the drainage condition are selected for comparison, as shown in fig. 7, it can be found that the failure modes of the stratum around the tunnel instability solved by the two methods are both shown that the failure occurs only along the periphery of the tunnel and does not extend to the ground surface, and the area with large plastic failure is concentrated at the top plate of the tunnel, which shows that the failure characteristics of the tunnel instability which does not extend to the ground surface working condition can be reflected to a certain extent by the solution of the method of the present invention.
(3) The calculation method proposed herein is further elaborated below in conjunction with a comparison of the calculation method of the present invention with existing calculation methods.
It should be noted that, at present, few studies are made on the circumferential ultimate supporting force of the tunnel under the condition without considering the surface overload, and when the surface overload σ is considered under the condition without draining water (Φ ═ 0)SUnder the working condition, the soil body does not change in volume at the moment according to the associated flow rule, and the power of the external load is expressed as
Figure BDA0002536571260000091
And the external power equivalent is not considered under the condition of earth surface overload, so that the solution of the method is compared and verified with the existing research method considering the condition of earth surface overload under the condition of selecting (phi is 0) without water drainage. The method is used for solving the working condition that the tunnel instability limit support force coefficient sigma is solved by using the working condition that the tunnel burial depth ratio H/D (ratio to depth) is 1-4, the soil mass severe cohesion parameter gamma D/c (ratio to gravity) is 0-4 and the soil mass internal friction angle phi is 0TAnd/c, and comparing the method of the invention with the existing research method. FIG. 8 shows the variation curve of the solution of the optimal ultimate supporting force coefficient of the ultimate supporting force solved by the invention along with the heavy cohesion parameter of the soil body and the buried depth ratio of the tunnel, and the solution result (such as Wilson D W, Abbo A J, Sloa) considering the overload conditionn S W,et al.Undrained stabilityof a circular tunnel where the shear strength increases linearly with depth[J]Canadian geomechnical Journal,2011,48(9): 1328-. FIG. 8 shows the ultimate support force coefficient σ of the tunnel obtained by the two methods after the dimensionless processingTThe value of/c is shown in fig. 8, the calculation result obtained by the method is greater than the Wilson (2011) upper limit solution, namely the method is high in precision, and the ultimate supporting force obtained by the two methods is consistent with the overall change of the soil mass severe cohesion parameter and the tunnel burial depth ratio.
In the description provided herein, numerous specific details are set forth. It is understood, however, that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.
In the description of the present invention, it is to be understood that the terms "upper", "lower", "front", "rear", "left", "right", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present invention. Similarly, it should be appreciated that in the foregoing description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. However, the disclosed method should not be interpreted as reflecting an intention that: that the invention as claimed requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this invention.
As used herein, unless otherwise specified the use of the ordinal adjectives "first", "second", "third", etc., to describe a common object, merely indicate that different instances of like objects are being referred to, and are not intended to imply that the objects so described must be in a given sequence, either temporally, spatially, in ranking, or in any other manner.
While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this description, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as described herein. Furthermore, it should be noted that the language used in the specification has been principally selected for readability and instructional purposes, and may not have been selected to delineate or circumscribe the inventive subject matter. Accordingly, many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the appended claims. The present invention has been disclosed in an illustrative rather than a restrictive sense, and the scope of the present invention is defined by the appended claims.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (8)

1. A method for calculating the ultimate supporting force of the circumferential excavation surface of a shield tunnel without considering the earth surface overload working condition is characterized by comprising the following steps of:
step S1: constructing a soil body rigid sliding block damage theoretical model of the circumferential excavation surface of the shield tunnel, and confirming key parameters influencing the ultimate supporting force of the circumferential excavation surface of the shield tunnel;
step S2: deducing key intermediate indexes based on the theoretical model and the key parameters in the step S1;
step S3: constructing a core formula of a theoretical model, substituting the core formula into the key intermediate index in the step S2, and solving the ultimate supporting force;
step S4: and circularly optimizing the key parameters in the step S1, and solving the optimal upper limit solution of the ultimate supporting force of the shield tunnel annular excavation surface.
2. The method for calculating the ultimate supporting force of the circumferential excavation surface of the shield tunnel without considering the earth surface overload condition according to claim 1, wherein the method comprises the following steps:
the theoretical model in step S1 includes:
theoretical model conditions: the earth surface is horizontal and has no overload, and supporting force loads are uniformly distributed only on the inner contour of the tunnel;
the damage area is composed of n rigid sliding blocks in the lateral direction of the tunnel axis and above the tunnel top plate, the contact edge of the rigid sliding blocks and the tunnel is an arc edge, the 1 st rigid sliding block is a trilateral sliding block at the lateral bottom of the tunnel axis, the ith sliding block is a convex quadrilateral sliding block in the lateral direction of the tunnel axis, i is 2,3,4,5, n-1, and the nth sliding block is a sliding block above the tunnel top plate.
3. The method for calculating the ultimate supporting force of the circumferential excavation surface of the shield tunnel without considering the earth surface overload condition according to claim 2, wherein the method comprises the following steps: the number n of the convex rigid sliding blocks is 7.
4. The method for calculating the ultimate supporting force of the circumferential excavation surface of the shield tunnel without considering the earth surface overload condition according to claim 3,
the first hypothetical mode, i.e., in general, the nth slider is a pentagonal slider above the tunnel ceiling.
In the second assumed mode, namely in the case of the damage condition that the plastic damage of the unstable stratum of the tunnel excavation does not extend to the ground surface, the nth sliding block is a quadrangle.
5. The method for calculating the ultimate supporting force of the circumferential excavation surface of the shield tunnel without considering the earth surface overload condition according to claim 1, wherein in the step S2, the key intermediate indexes comprise: side length, area, absolute speed and relative speed of the slider.
6. The method for calculating the ultimate supporting force of the circumferential excavation surface of the shield tunnel without considering the earth surface overload condition according to claim 1,
in step S3, the core formula is:
pr+pw＝pc(1)
wherein p isrIs the system gravity power, pwIs that the inner contour of the tunnel acts on the uniformly distributed supporting force load sigmaTPower of operation, pcIs to destroy the energy dissipated power inside the area,
Figure FDA0002536571250000021
wherein, ξiIs the angle between the absolute speed of the ith rigid slide block and the vertical direction, viIs the absolute velocity of the ith rigid slide, SiThe area of the ith rigid slide block is shown, and gamma is the volume weight of the soil body.
Figure FDA0002536571250000022
Wherein c is soil cohesion, virIs the relative speed of the ith rigid slide block and the (i + 1) th rigid slide block, ai+1biLength of the base side of the (i + 1) th rigid slider, bibi+1The length of the side edge of the (i + 1) th rigid sliding block, phi is an internal friction angle,
Figure FDA0002536571250000023
wherein σTUniformly distributing supporting force loads on the inner contour of the tunnel,
Figure FDA0002536571250000024
a speed field for the slide block of the tunnel excavation surface to collapse towards the inside of the tunnel under the action of the supporting force,
Figure FDA0002536571250000025
the speed of the tunnel excavation surface in the normal direction is the speed of the circumferential supporting force action direction, and S represents the total area of a plastic deformation area of the tunnel excavation surface, namely the total area of the rigid sliding block.
7. The method for calculating the ultimate supporting force of the circumferential excavation surface of the shield tunnel without considering the earth surface overload condition according to claim 1, wherein the method comprises the following steps:
in step S1, the key parameters include a circle center angle α corresponding to the arc edge of the ith rigid slideriAnd two opposite corners β2i-1,β2i。
8. The method for calculating the ultimate supporting force of the circumferential excavation surface of the shield tunnel without considering the earth surface overload condition according to claim 1,
the upper limit of the ultimate supporting force of the annular excavation surface of the tunnel is defined as follows:
Figure FDA0002536571250000026
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