CN113405908A - Shallow shield tunnel roof stability judgment method - Google Patents

Shallow shield tunnel roof stability judgment method Download PDF

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CN113405908A
CN113405908A CN202110843766.6A CN202110843766A CN113405908A CN 113405908 A CN113405908 A CN 113405908A CN 202110843766 A CN202110843766 A CN 202110843766A CN 113405908 A CN113405908 A CN 113405908A
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tunnel
excavation width
limit value
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CN113405908B (en
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曹勇
衣利伟
唐福源
黄小城
陈秋南
石红兵
李振宇
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China Construction Fifth Engineering Bureau Co Ltd
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Abstract

The invention provides a method for judging stability of a top plate of a shallow shield tunnel, which comprises the steps of determining parameters according to preset conditions and setting a preset value of half-excavation width of the tunnel; establishing an expression of a molar strength envelope curve based on parameters, establishing a shearing strength expression of a generalized HockBrownian rule according to a limit analysis principle, further establishing an expression of the tunnel semi-excavation width, calculating a limit value range of the tunnel semi-excavation width, and determining the limit value range of the tunnel semi-excavation width by combining each expression and each parameter; and finally, comparing the predicted value with the limit value range, and if the predicted value is within the limit value range, determining that the tunnel top plate is stable. The potential collapse criterion formula of the shallow tunnel shield is solved according to rigorous mathematical formula derivation, accurate reference is provided for preventing tunnel collapse, a simple, convenient and practical method for determining the limit width of the top plate of the shallow tunnel is provided, and related parameters are easy to determine.

Description

Shallow shield tunnel roof stability judgment method
Technical Field
The invention relates to the technical field of disaster prevention and control of geotechnical and urban underground engineering, in particular to a method for judging stability of a shallow shield tunnel roof.
Background
In the past decades, China has a large number of subways and tunnel constructions, wherein the construction of the subway projects can not avoid the shallow address section. However, accidents such as tunnel collapse are caused, and the tunnel collapse is mostly generated before the tunnel is built, so that stability analysis is necessary before excavation is performed to reduce the risk of safety accidents, prevent the accidents in the future, and have important significance for ensuring the sustainable development of economy and society in China.
The most critical issue for tunnel roof stability analysis is determining its excavation width. The existing patents or other achievements mostly adopt the HockBrownian criterion to analyze the tunnel instability mechanism, but the HockBrownian parameter is difficult to determine in the actual engineering, and the problem still cannot be solved well at present.
Disclosure of Invention
In view of the above, it is necessary to provide a method for determining stability of a top plate of a shallow shield tunnel.
A shallow shield tunnel roof stability judgment method comprises the following steps: according to preset conditions, specific parameters of shield surrounding rocks are determined, and the value of the half-excavation width of the tunnel is preset as a preset value, wherein the parameters comprise uniaxial compressive strength of a rock mass, uniaxial tensile strength of the rock mass and volume weight of the rock mass; establishing an expression of a molar strength envelope curve according to the parameters; establishing a shearing strength expression of a generalized HockBrown criterion according to a limit analysis principle, and further establishing an expression of tunnel half-excavation width; determining a limit value range of the tunnel half-excavation width according to the expression of the tunnel half-excavation width based on the expression of the molar strength envelope curve and the shear strength expression of the generalized HockBrown criterion; and comparing the preset value of the tunnel half-excavation width with the limit value range of the tunnel half-excavation width, and determining that the tunnel top plate is stable when the preset value belongs to the limit value range.
In one embodiment, the expression of the molar intensity envelope is specifically:
τ2＝n(σ+σt)； (1)
wherein, tau represents the shear strength shear stress of rock-soil body, sigma is positive stress, sigmatThe uniaxial tensile strength of the rock mass is shown, n is a coefficient, and the expression of n is as follows:
Figure BDA0003179779420000021
wherein σcThe uniaxial compressive strength of the rock mass.
In one embodiment, the shear strength expression of the generalized hockbron criterion is specifically:
τ＝±Aσc[(σt+σ)σc -1]B； (3)
wherein A and B are HockBrown parameters respectively.
In one embodiment, the expression of the tunnel half-excavation width specifically includes:
Lu＝AB-B(1+B)B(γ)-1σc 1-Bσt B； (4)
wherein L isuThe critical width of the tunnel half excavation, namely the limit value range, and gamma is the volume weight of the rock mass.
In one embodiment, according to the expression (1) and the expression (3), B may be equal to 0.5, so the expression (4) is:
Figure BDA0003179779420000022
where γ is ρ g, ρ is density, g is gravitational acceleration.
In one embodiment, when B is 0.5, the expression (1) and the expression (3) are squared simultaneously, and then:
Figure BDA0003179779420000023
on the basis of the expression (6), and in combination with the expression (5), the range of the limit value of the tunnel half excavation is obtained as follows:
Figure BDA0003179779420000024
where γ is ρ g, ρ is density, g is gravitational acceleration.
In one embodiment, the establishing of the shear strength expression of the generalized hockbron criterion according to the limit analysis principle further establishes an expression of the tunnel half-excavation width, specifically: establishing a shearing strength expression of a generalized HockBrown criterion according to a limit analysis principle; and establishing an expression of the tunnel half-excavation width according to the shearing strength expression of the generalized HockBrownian criterion based on the limit analysis principle.
In one embodiment, the comparing the preset value of the tunnel half-cut width with the limit value range of the tunnel half-cut width, and when the preset value falls within the limit value range, after the tunnel roof is determined to be stable, the method further includes: and when the preset value exceeds the limit value range, resetting the preset value of the tunnel half-excavation width, so that the preset value belongs to the limit value range.
The invention has the beneficial effects that: according to the method for judging the stability of the top plate of the shallow shield tunnel, parameters are determined according to preset conditions, and the preset value of the half-excavation width of the tunnel is set; establishing an expression of a molar strength envelope curve based on parameters, establishing a shearing strength expression of a generalized HockBrownian rule according to a limit analysis principle, further establishing an expression of the tunnel semi-excavation width, calculating a limit value range of the tunnel semi-excavation width, and determining the limit value range of the tunnel semi-excavation width by combining each expression and each parameter; and finally, comparing the predicted value with the limit value range, and if the predicted value is within the limit value range, determining that the tunnel top plate is stable. The potential collapse criterion formula of the shallow tunnel shield is solved according to rigorous mathematical formula derivation, accurate reference is provided for preventing tunnel collapse, a simple, convenient and practical method for determining the limit width of the top plate of the shallow tunnel is provided, and related parameters are easy to determine.
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Fig. 1 is a scene model diagram of a shallow tunnel shield roof stability determination method in an embodiment;
fig. 2 is a schematic flow chart of a method for determining stability of a top plate of a shallow shield tunnel according to an embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings by way of specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The method for judging the stability of the top plate of the shallow shield tunnel can be applied to a scene model diagram shown in figure 1. Wherein, 1-a collapse zone; 2-a rectangular tunnel; 3-circular tunnel; l isu-the critical width of the tunnel half excavation, i.e. the limit value range of the tunnel half excavation; the actual half-excavation width of the L-tunnel is a preset value in the following; h is the collapse zone height; xoy is as shown to establish a coordinate system(ii) a (x) is the tunnel roof collapse curve; h is the tunnel burial depth, (here, the rectangular tunnel burial depth).
In one embodiment, as shown in fig. 2, a method for determining stability of a shallow shield tunnel roof is provided, which includes the following steps:
s110, specific parameters of shield surrounding rocks are determined according to preset conditions, and the value of the half-excavation width of the tunnel is preset as a preset value, wherein the parameters comprise uniaxial compressive strength of a rock mass, uniaxial tensile strength of the rock mass and volume weight of the rock mass.
Specifically, the preset conditions are that specific parameters of the shield surrounding rock, including uniaxial compressive strength sigma of the rock mass, are determined according to construction drawings and other datacUniaxial tensile strength of rock masstThe volume weight γ of the rock mass.
S120, establishing an expression of the molar strength envelope curve according to the parameters.
In one embodiment, the expression of the molar intensity envelope in step S120 is specifically:
τ2＝n(σ+σt)； (1)
wherein, tau represents the shear strength shear stress of rock-soil body, sigma is positive stress, sigmatThe uniaxial tensile strength of the rock mass is shown, n is a coefficient, and the expression of n is as follows:
Figure BDA0003179779420000041
wherein σcThe uniaxial compressive strength of the rock mass.
S130, according to the limit analysis principle, a shearing strength expression of the generalized HockBrownian rule is established, and an expression of the tunnel half-excavation width is further established.
In one embodiment, step S130 specifically includes: establishing a shearing strength expression of a generalized HockBrown criterion according to a limit analysis principle; based on the principle of limit analysis, an expression of the tunnel half-excavation width is established according to a shearing strength expression of the generalized HockBrown criterion.
In one embodiment, the shearing strength expression of the generalized hockbron criterion in step S130 is specifically:
τ＝±Aσc[(σt+σ)σc -1]B； (3)
wherein A and B are HockBrown parameters respectively.
In an embodiment, the expression of the tunnel half-excavation width in step S130 is specifically:
Lu＝AB-B(1+B)B(γ)-1σc 1-Bσt B； (4)
wherein L isuThe critical width of the tunnel half excavation, namely the limit value range, and gamma is the volume weight of the rock mass.
Specifically, a shearing strength expression of the generalized HockBrown criterion is established according to the limit analysis principle, and then checking calculation is carried out according to the shearing strength expression of the generalized HockBrown criterion, so that an expression of the tunnel half-excavation width can be obtained.
S140, determining the limit value range of the tunnel half-excavation width according to the expression of the tunnel half-excavation width based on the expression of the molar strength envelope curve and the shearing strength expression of the generalized HockBrown criterion.
In one embodiment, according to expression (1) and expression (3), B may be equal to 0.5, so expression (4) is:
Figure BDA0003179779420000051
where γ is ρ g, ρ is density, g is gravitational acceleration.
In one embodiment, when B is 0.5, expression (1) and expression (3) are squared simultaneously, which may result in:
Figure BDA0003179779420000052
on the basis of the expression (6) and in combination with the expression (5), the range of the limit value of the tunnel half excavation can be obtained as follows:
Figure BDA0003179779420000053
where γ is ρ g, ρ is density, g is gravitational acceleration. Specifically, based on the expression of the molar strength envelope and the shear strength expression of the generalized hockbron criterion, the molar strength envelope is obtained first, and the actual B is 0.5, so that substituting B into 0.5 can simplify the expression of the tunnel half-excavation width. And then, squaring two sides according to an expression of a molar strength envelope curve and a shearing strength expression of a generalized HockBrown criterion, combining the squaring two sides, and finally obtaining an expression of the tunnel half-excavation width without calculating HockBrown parameters by combining the simplified expression of the tunnel half-excavation width, and finally calculating the limit value range of the tunnel half-excavation width according to the parameters.
S150, comparing the preset value of the tunnel half-excavation width with the limit value range of the tunnel half-excavation width, and determining that the tunnel roof is stable when the preset value belongs to the limit value range.
Specifically, if the preset value falls within the limit value range, the tunnel corresponding to the preset value is stable and will not collapse.
In one embodiment, after step S150, the method further includes: and when the preset value exceeds the limit value range, resetting the preset value of the tunnel half excavation width, so that the preset value is within the limit value range. Specifically, if the preset value exceeds the limit value range, the preset value needs to be reset, and the limit value range is stable and cannot collapse for the tunnel corresponding to the half excavation width of the tunnel in the range, and if the preset value exceeds the limit value range, the corresponding tunnel is unstable and is likely to collapse.
In one embodiment, as shown in FIG. 1, the uniaxial compressive strength and tensile strength of the rock mass are respectively 0.5MPa, 0.06MPa and 26kN/m3. Then, according to the expression (7), the tunnel half-excavation limit width can be determined to be 6.71m, and the limit value range is<6.71 m. Based on the same parameter setting, calculating the obtained half-excavation width limit value by adopting an ANSYS numerical model, wherein the maximum value area of the plastic zone is 6.59 m; using FLAC numerical modulusThe maximum plastic zone area of the half-excavation width limit value obtained by the model calculation is 6.63 m. It can be seen that the calculation result of the method provided by the invention is close to the result obtained by the reliable method of the prior mature technology, which shows that the method of the invention is accurate and feasible.
In the embodiment, parameters are determined according to preset conditions, and the preset value of the tunnel half-excavation width is set; establishing an expression of a molar strength envelope curve based on parameters, establishing a shearing strength expression of a generalized HockBrownian rule according to a limit analysis principle, further establishing an expression of the tunnel semi-excavation width, calculating a limit value range of the tunnel semi-excavation width, and determining the limit value range of the tunnel semi-excavation width by combining each expression and each parameter; and finally, comparing the predicted value with the limit value range, and if the predicted value is within the limit value range, determining that the tunnel top plate is stable. The potential collapse criterion formula of the shallow tunnel shield is solved according to rigorous mathematical formula derivation, accurate reference is provided for preventing tunnel collapse, a simple, convenient and practical method for determining the limit width of the top plate of the shallow tunnel is provided, and related parameters are easy to determine.
It will be apparent to those skilled in the art that the modules or steps of the invention described above may be implemented in a general purpose computing device, they may be centralized on a single computing device or distributed across a network of computing devices, and optionally they may be implemented in program code executable by a computing device, such that they may be stored on a computer storage medium (ROM/RAM, magnetic disks, optical disks) and executed by a computing device, and in some cases, the steps shown or described may be performed in an order different than that described herein, or they may be separately fabricated into individual integrated circuit modules, or multiple ones of them may be fabricated into a single integrated circuit module. Thus, the present invention is not limited to any specific combination of hardware and software.
The foregoing is a more detailed description of the present invention that is presented in conjunction with specific embodiments, and the practice of the invention is not to be considered limited to those descriptions. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (8)

1. A shallow shield tunnel roof stability judgment method is characterized by comprising the following steps:
according to preset conditions, specific parameters of shield surrounding rocks are determined, and the value of the half-excavation width of the tunnel is preset as a preset value, wherein the parameters comprise uniaxial compressive strength of a rock mass, uniaxial tensile strength of the rock mass and volume weight of the rock mass;
establishing an expression of a molar strength envelope curve according to the parameters;
establishing a shearing strength expression of a generalized HockBrown criterion according to a limit analysis principle, and further establishing an expression of tunnel half-excavation width;
determining a limit value range of the tunnel half-excavation width according to the expression of the tunnel half-excavation width based on the expression of the molar strength envelope curve and the shear strength expression of the generalized HockBrown criterion;
and comparing the preset value of the tunnel half-excavation width with the limit value range of the tunnel half-excavation width, and determining that the tunnel top plate is stable when the preset value belongs to the limit value range.
2. The method of claim 1, wherein the molar intensity envelope is expressed by:
τ2＝n(σ+σt)； (1)
wherein, tau represents the shear strength shear stress of rock-soil body, sigma is positive stress, sigmatThe uniaxial tensile strength of the rock mass is shown, n is a coefficient, and the expression of n is as follows:
Figure FDA0003179779410000011
wherein σcThe uniaxial compressive strength of the rock mass.
3. The method according to claim 2, characterized in that the shear strength expression of the generalized HockBrownian criterion is in particular:
τ＝±Aσc[(σt+σ)σc -1]B； (3)
wherein A and B are HockBrown parameters respectively.
4. The method according to claim 3, wherein the expression of the tunnel half-excavation width is:
Lu＝AB-B(1+B)B(γ)-1σc 1-Bσt B； (4)
wherein L isuThe critical width of the tunnel half excavation, namely the limit value range, and gamma is the volume weight of the rock mass.
5. The method according to claim 4, wherein B is 0.5 according to the expression (1) and the expression (3), so that the expression (4) is:
Figure FDA0003179779410000021
where γ is ρ g, ρ is density, g is gravitational acceleration.
6. The method of claim 5, wherein when B is 0.5, the expression (1) and the expression (3) are squared simultaneously, resulting in:
Figure FDA0003179779410000022
on the basis of the expression (6), and in combination with the expression (5), the range of the limit value of the tunnel half excavation is obtained as follows:
Figure FDA0003179779410000023
where γ is ρ g, ρ is density, g is gravitational acceleration.
7. The method according to claim 1, wherein the shear strength expression of the generalized HockBrownian criterion is established according to the principle of limit analysis, and the expression of the tunnel half-excavation width is further established, specifically:
establishing a shearing strength expression of a generalized HockBrown criterion according to a limit analysis principle;
and establishing an expression of the tunnel half-excavation width according to the shearing strength expression of the generalized HockBrownian criterion based on the limit analysis principle.
8. The method of claim 1, wherein the comparing the preset value of the tunnel half-excavation width with a limit value range of the tunnel half-excavation width, and when the preset value falls within the limit value range, after the tunnel roof is determined to be stable, further comprises:
and when the preset value exceeds the limit value range, resetting the preset value of the tunnel half-excavation width, so that the preset value belongs to the limit value range.
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