Calculation method, device and medium for ultimate support pressure of ground uplift in shallow tunnels

Abstract

The invention discloses a method, device and medium for calculating the ultimate support pressure of surface uplift of a shallow tunnel. Based on the existing model test and numerical simulation results, the invention mainly divides the proposed model into a rigid rotation zone and a rigid translation zone, namely, zones I and II. Through the principle of virtual work, the external power Pe and the internal energy dissipation rate Pv on the sliding surface are made equal, and then the ultimate support pressure of surface uplift under the condition of a longitudinal inclined tunnel is obtained, thereby solving the problem that it is difficult to achieve the balance of shield soil chamber pressure in the existing shield tunneling technology, and the current soil chamber pressure calculation theory is only applicable to the prediction analysis of horizontal tunnels, while for longitudinal inclined tunnels, the critical point technical problem of surface uplift damage of shallow tunnels is still blank.

Description

Technical Field

[0001] The present invention belongs to the technical field of shield tunnel construction, and more specifically, relates to a method, a device and a medium for calculating the ultimate support pressure of surface uplift of a shallow tunnel. Background Art

[0002] In recent years, with the vigorous development of underground infrastructure construction, shield tunnels have played an important role in alleviating urban traffic congestion. Face stability has always been one of the main problems in shield tunnel construction, especially for shallow buried tunnels. If the face support pressure is too small, active instability is likely to occur, and if it is too large, passive instability is likely to occur. However, due to the complexity of the underground pipeline network and the influence of the existing riverbed, it is difficult to excavate in the ideal horizontal direction in actual tunnel construction, and a certain longitudinal inclination angle is required for crossing. A large longitudinal inclination angle can easily lead to a sudden change in the coverage depth. If the face support pressure is not adjusted in time, instability and failure are more likely to occur. In previous studies, the instability and failure of the tunnel face involving longitudinal inclination angles mainly focused on active instability, while studies considering passive instability were rarely mentioned. For shallow buried tunnels, the existence of longitudinal inclination angles makes passive failure more likely to occur. Therefore, exploring the influence of longitudinal inclination angles on surface uplift failure has important theoretical value for the design and construction of longitudinal inclined shield tunnels.

[0003] In the past few decades, the study of passive instability failure of soil in front of the tunnel face has received extensive attention. In terms of theory, the limit equilibrium method and limit analysis method have been applied to the study of passive instability of the tunnel face. The literature "Chen W F. Limit Analysis by the Upper-Bound Method [M] / / Developments in Geotechnical Engineering. Elsevier, 1975: 47-106." proposed a modified silo-wedge model based on the limit equilibrium framework and analyzed the passive failure mode of soil in front of the tunnel face in sandy soil. The literature "Leca E, Dormieux L. Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material [J]. Géotechnique, 1990, 40 (4): 581-606." considered the passive failure zone as a single rigid truncated cone translation block and solved the ultimate support pressure of the tunnel face based on the limit analysis upper limit method. Some scholars further optimized the failure contour by changing the number of rigid truncated cone translation blocks to obtain a more accurate solution. The experiments in the literature "Mollon G, Dias D, Soubra A H. Rotational failure mechanisms for the facestability analysis of tunnels driven by a pressurized shield[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2011, 35(12): 1363-1388" and the literature "Takano, D., Otani, J., Nagatani, H., Mukunoki, T., 2006. Application of x-ray CT on boundary value problems in geotechnical engineering: research on tunnel face failure. In: GeoCongress 2006: Geotechnical Engineering in the Information Technology Age. pp. 1–6." proposed two classic passive rotational failure mechanisms.However, existing passive centrifuge tests have shown that the soil in front of the tunnel face is not completely rotating, but also has some translational movement. On this basis, the literature "Liu W, Shi P, Chen L, Tang Q. Analytical analysis of working face passive stability during shield tunneling in friction alsoils. Acta Geotech 2020; 15: 781–94. " and the literature "Liu W, Wu B, Shi P, Cai G. Upper bound analysis of working face passive failure in large-diameter shield tunneling based on a composite mechanism. Comput Geotech 2021; 138: 104362. " consider the passive failure zone as a failure mechanism of lower rotation + upper translation from a two-dimensional perspective. In terms of longitudinally inclined tunnels, Lei Mingfeng et al. considered the influence of the longitudinal inclination of the shield tunnel excavation face on the support force, introduced the line slope angle into the collapse failure model based on the limit equilibrium analysis method, and derived the calculation formula through case analysis. The research results show that the increase in the line slope leads to a linear increase in the ultimate collapse support pressure. The paper "Cheng C, Jia P, Zhao W, et al. Experimental and analytical study of shield tunnel face in dense sand strata considering different longitudinal inclination [J]. Tunnelling and Underground Space Technology, 2021, 113: 103950." conducted experimental and analytical studies on the excavation face support pressure and collapse failure mode of shield tunnels with different longitudinal inclination angles (-15° to 15°) in dense sand layers. The experimental results show that the failure contours under the three longitudinal inclination angles are all "chimney-shaped", and the area of ​​the damaged area increases with the increase of the longitudinal inclination angle. At the same time, based on theoretical prediction results, the larger the longitudinal inclination angle, the higher the excavation face support pressure.

[0004] In summary, the face support pressure is the key factor causing the surface uplift of shallow tunnels. However, existing research mainly focuses on horizontal tunnels, and there is a lack of research on tunnels that consider the longitudinal inclination. Summary of the invention

[0005] The present invention is provided to solve the above problems existing in the prior art. Therefore, a method, device and medium for calculating the ultimate support pressure of the surface uplift of a shallow tunnel are needed to solve the problem that it is difficult to achieve the balance of the shield soil compartment pressure in the existing shield tunneling technology, and the current soil compartment pressure calculation theory is only applicable to the prediction analysis of horizontal tunnels, while for longitudinal inclined tunnels, the critical point technical problem of the surface uplift failure of the shallow tunnel is still blank.

[0006] According to a first solution of the present invention, a method for calculating the ultimate support pressure of surface uplift of a shallow tunnel is provided, the method comprising:

[0007] The soil at the front end of the tunnel face is simplified into an arc rotation area as area I, the center point of the circle is point A at the top of the tunnel face, the starting end of the arc is tangent to point B at the bottom of the tunnel face, and the entire arc rotation area is controlled by the rotation angle θ;

[0008] Constructing the velocity field of the arc rotation area based on the determined area I;

[0009] The power caused by the external load and the internal energy dissipation power corresponding to the area I are calculated based on the velocity field of the arc rotation area. The power caused by the external load includes the power caused by the gravity of the area I. The internal energy dissipation power includes the energy dissipation at the arc failure surface BE and the radial discontinuity line inside the region I;

[0010] Construct area II, the starting point of area II is the end point E of the arc rotation area I and is tangent to point E, and the velocity vector direction of area II is in a positive direction with the boundaries AM and EN. Angular relationship, where is the friction angle within the soil;

[0011] Calculate the power of external load and internal energy dissipation corresponding to area II;

[0012] Calculate the tunnel face support pressure and the power exerted by the additional surface load;

[0013] Determine the stability condition of the tunnel face as P e ≤P v , where P e is the power of the external load, P v is the internal energy dissipation power, where the power of the external load is the sum of the power of the external load corresponding to area I, the power of the external load corresponding to area II, the tunnel surface support pressure, and the power of the additional surface load. The internal energy dissipation power is the sum of the internal energy dissipation power corresponding to area I and area II;

[0014] According to the power of external load and internal energy dissipation, the ultimate support pressure of the tunnel surface when the ground surface rises is obtained. The calculation formula is:

[0015]

[0016] Among them, P CI-BE and P CI-ABE represents the energy dissipation at the arc failure surface BE and the radial discontinuity line inside region I, P CII-AM and P CII-EN represents the internal energy dissipation power corresponding to region II, represents the additional surface load σ s Power produced, P γ-I represents the power of the external load corresponding to area I, P γ-II represents the power of the external load corresponding to region II, v I represents the velocity vector of region I, and D represents the tunnel diameter.

[0017] Further, the constructing of the arc rotation area velocity field based on the determined area I includes:

[0018] Discretize area I into numerous triangular areas, each of which is measured by a set velocity vector (ν0, ν1, ν2…ν n ) moves as a whole, and the velocity vectors on the discontinuity surfaces of each block are (dν0, dν1, dν2…dν n-1 ), the angle between the velocity direction and the failure contour is the friction angle of the soil The velocity vector in region I is ν Ⅰ , the construction of the velocity field satisfies the following formula:

[0019] l AB =r0=D

[0020]

[0021]

[0022] Among them l AB represents the length of line segment AB, r0 represents the starting radius of arc ABE, r represents the ending radius of arc ABE, exp represents the exponential function e, v n represents the velocity vector corresponding to the nth triangle area, v n-1 represents the velocity vector corresponding to the n-1th triangle area, n represents the number of discrete triangle areas, and i represents the maximum value range of n;

[0023] When the number of rigid sliding triangles approaches infinity, the velocity vector ν(θ) at any angle θ in region I is set as:

[0024]

[0025] Furthermore, the power of the external load corresponding to the area I is calculated based on the velocity field of the circular arc rotation area, specifically including:

[0026] The area of ​​the arc diameter break line and the arc surface ABE is calculated using the following formula:

[0027] AB=AB1=AB n =D

[0028] BB1=B n-1 B n

[0029] ∠BAE=θ=α

[0030]

[0031] Among them, B1 represents the first dividing point of the arc rotation area, B n-1 Indicates the n-1th segmentation point of the arc rotation area, B n represents the nth segmentation point of the arc rotation zone, α represents the failure mechanism angle parameter, δ represents the tunnel inclination, S ABE represents the area of ​​the arc surface ABE;

[0032] The power exerted by gravity in area I is calculated by the following formula

[0033]

[0034] Where γ represents the unit weight of soil and α represents the failure mechanism angle parameter.

[0035] Furthermore, the internal energy dissipation power of region I is calculated by the following formula:

[0036]

[0037] in, and represents the energy dissipation at the arc failure surface BE and the radial discontinuity line inside area I, c represents the soil cohesion, and e represents the natural constant.

[0038] Furthermore, the power P of the external load corresponding to area II is calculated by the following formula: γ-Ⅱ And the internal energy dissipation power

[0039]

[0040] l EN =(Dcosα+C) / sinα

[0041]

[0042] Among them, l AM represents the length of the line segment AM in area II, C represents the thickness of the tunnel cover, α represents the failure mechanism angle parameter, γ represents the unit weight of the soil, and v II represents the velocity vector of region II, e represents a natural constant, l EN Represents the length of line segment EN in area II.

[0043] Furthermore, the tunnel face support pressure and the power of the additional surface load are calculated by the following formula:

[0044]

[0045] Among them, v I and v II denote the velocity vectors of region I and region II, σ t represents the tunnel face support pressure, σ s represents the additional surface load, l MN represents the length of the line segment MN in region II, α represents the failure mechanism angle parameter, and δ represents the tunnel inclination.

[0046] Furthermore, the method further comprises:

[0047] The calculation formula of the tunnel face ultimate support pressure when the ground surface rises is simplified by the following formula:

[0048]

[0049] in:

[0050]

[0051]

[0052] Among them, η γ , η c , R A , R B , R C and R D All represent dimensionless parameters.

[0053] Furthermore, after simplifying the calculation formula of the tunnel face limit support pressure when the ground surface rises, the method further includes:

[0054] According to the failure mechanism angle parameter α and the tunnel inclination angle δ, the excavation face limit support pressure σ is adjusted T, where α∈[0,π / 2], and the longitudinal inclination angle δ ranges from [-10° to 10°].

[0055] According to a second technical solution of the present invention, a device for calculating the ultimate support pressure of surface uplift of a shallow tunnel is provided, the device comprising:

[0056] The first area construction module is configured to simplify the soil at the front end of the tunnel face into an arc rotation area as area I, the center point of the circle is point A at the top of the tunnel face, the starting end of the arc is tangent to point B at the bottom of the tunnel face, and the entire arc rotation area is controlled by a rotation angle θ;

[0057] A velocity field construction module is configured to construct a velocity field of the arc rotation area based on the determined area I;

[0058] The first power calculation module is configured to calculate the power of the external load and the internal energy dissipation power corresponding to the area I based on the velocity field of the arc rotation area, wherein the power of the external load includes the power of the gravity of the area I. The internal energy dissipation power includes the energy dissipation at the arc failure surface BE and the radial discontinuity line inside the region I;

[0059] The second area construction module is configured to construct area II, the starting point of area II is the end point E of the arc rotation area I and is tangent to point E, and the velocity vector direction of area II is in a straight line with the boundaries AM and EN. Angular relationship, where is the friction angle within the soil;

[0060] The second power calculation module is configured to calculate the power of the external load and the internal energy dissipation power corresponding to the area II;

[0061] A third power calculation module is configured to calculate the power produced by the tunnel face support pressure and the additional surface load;

[0062] The stability condition determination module is configured to determine the stability condition of the tunnel face as P e ≤P v , where P e is the power of the external load, P v is the internal energy dissipation power, where the power of the external load is the sum of the power of the external load corresponding to area I, the power of the external load corresponding to area II, the tunnel surface support pressure, and the power of the additional surface load. The internal energy dissipation power is the sum of the internal energy dissipation power corresponding to area I and area II;

[0063] The ultimate pressure calculation module is configured to obtain the ultimate support pressure of the tunnel surface when the ground surface rises based on the power produced by the external load and the internal energy dissipation power being equal. The calculation formula is:

[0064]

[0065] Among them, P CI-BE and P CI-ABE represents the energy dissipation at the arc failure surface BE and the radial discontinuity line inside region I, P CII-AM and P CII-EN represents the internal energy dissipation power corresponding to region II, represents the additional surface load σ s Power produced, P γ-I represents the power of the external load corresponding to area I, P γ-II represents the power of the external load corresponding to region II, v I represents the velocity vector of region I, and D represents the tunnel diameter.

[0066] According to a third technical solution of the present invention, a readable storage medium is provided, wherein the readable storage medium stores one or more programs, and the one or more programs can be executed by one or more processors to implement the method as described above.

[0067] The present invention has at least the following beneficial effects:

[0068] This paper proposes a new type of two-dimensional rotation-translation failure mechanism, which takes into account the longitudinal inclination of the tunnel. The model consists of a rigid translation block and a rigid rotation block, which is more in line with the failure contour of the soil in front of the tunnel face under the actual condition of excessive support pressure causing surface uplift. The proposed two-dimensional mechanism is simple and efficient to calculate, and is convenient for engineering application. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 A schematic diagram of a model according to an embodiment of the present invention is shown.

[0070] Figure 2 A schematic diagram of the velocity field in region I according to an embodiment of the present invention is shown.

[0071] Figure 3 A schematic diagram of the velocity field in region I at the radial break line AB1 according to an embodiment of the present invention is shown.

[0072] Figure 4 A schematic diagram of the velocity field in region II according to an embodiment of the present invention is shown.

[0073] Figure 5 It shows that when C / D=0.5, the normalized ultimate support pressure (σ T / γD) changes with the longitudinal inclination angle δ of the tunnel.

[0074] Figure 6A schematic diagram of a three-dimensional numerical model considering the longitudinal inclination of a tunnel according to an embodiment of the present invention is shown.

[0075] Figure 7 A schematic diagram showing the comparison between the proposed model solution and the existing horizontal mechanism and numerical simulation when C / D=0.5 according to an embodiment of the present invention is shown.

[0076] Figure 8 A schematic diagram showing the comparison between the proposed model solution and the existing horizontal mechanism and numerical simulation when C / D=1 according to an embodiment of the present invention is shown.

[0077] Fig. 9 It shows that when the Schematic diagram of the comparison between the proposed model solution and the existing horizontal mechanism and numerical simulation.

[0078] Fig.10 A structural diagram of a device for calculating the ultimate support pressure of surface uplift of a shallow tunnel according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0079] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings and specific embodiments, but are not intended to limit the present invention. For the various steps described herein, if there is no necessity for a causal relationship between each other, the order in which they are described as examples herein should not be regarded as a limitation, and those skilled in the art should know that they can be adjusted in order, as long as the logic between them is not destroyed, resulting in the inability to implement the entire process.

[0080] In the existing shield tunneling technology, it is difficult to achieve the balance of shield soil compartment pressure, and the current soil compartment pressure calculation theory is only applicable to the prediction and analysis of horizontal tunnels. For longitudinally inclined tunnels, the critical point technical problem of shallow tunnel surface uplift failure is still blank. Based on this, an embodiment of the present invention provides a method for calculating the ultimate support pressure of shallow tunnel surface uplift, which takes into account the longitudinal inclination of the tunnel.

[0081] like Figure 1 As shown, based on the existing model test and numerical simulation results, the present invention mainly divides the proposed model into a rigid rotation zone and a rigid translation zone, namely, zones I and II. Through the principle of virtual work, the external power Pe on the sliding surface and the internal energy dissipation rate Pv are equal, and then the surface uplift limit support pressure under the longitudinal inclined tunnel working condition is obtained. The tunnel inclination conditions corresponding to the three α angles, namely, α = α1 for upward tilt, α = α2 for horizontal tilt and α = α3 for downward tilt, are specifically represented by the symbol δ.

[0082] Specifically, the method comprises the following steps:

[0083] Step 1: Figure 2 As shown in the figure, the soil near the front end of the tunnel face is simplified into an arc rotation zone, the center point of the circle is point A at the top of the tunnel face, the starting end of the arc (close to the end of the tunnel face) is tangent to point B at the bottom of the tunnel face, and the entire arc rotation zone is controlled by the rotation angle θ.

[0084] Step 2: Figure 2 and Figure 3 The velocity field of the arc rotation zone constructed by the limit upper bound analysis method is given. The arc rotation zone I is discretized into countless triangles. Each triangle block is centered at a certain velocity vector (ν0, ν1, ν2…ν n ) moves as a whole, and the velocity vectors on the discontinuity surfaces of each block are (dν0, dν1, dν2…dν n-1 ), under the condition of meeting the associated flow criterion, the angle between the velocity direction and the failure contour is is the internal friction angle of the soil, and the velocity vector of region I is ν Ⅰ , the construction of the specific velocity field needs to satisfy the following formula:

[0085] l AB =r0=D

[0086]

[0087]

[0088] Among them l AB represents the length of line segment AB, r0 represents the starting radius of arc ABE, r represents the ending radius of arc ABE, exp represents the exponential function e, v n represents the velocity vector corresponding to the nth triangle area, v n-1 represents the velocity vector corresponding to the n-1th triangle area, n represents the number of discrete triangle areas, and i represents the maximum value range of n;

[0089] When the number of rigid sliding triangles approaches infinity, the velocity vector ν(θ) at any angle θ in the arc rotation zone I is set as:

[0090]

[0091] Step 3: Calculate the power of external load and internal energy dissipation power of the rotating area based on the constructed velocity field of the circular arc rotating area.

[0092] The calculation formula for the area of ​​the arc diameter break line and the arc surface ABE is as follows:

[0093] AB=AB1=AB n =D

[0094] BB1=B n-1 B n

[0095] ∠BAE=θ=α

[0096]

[0097] Among them, B1 represents the first dividing point of the arc rotation area, B n-1 Indicates the n-1th segmentation point of the arc rotation area, B n represents the nth segmentation point of the arc rotation zone, α represents the failure mechanism angle parameter, δ represents the tunnel inclination, S ABE represents the area of ​​the arc surface ABE,

[0098] Power due to gravity in arc rotation zone I

[0099]

[0100] Where γ represents the unit weight of soil and α represents the failure mechanism angle parameter.

[0101] Energy dissipation power in area I It mainly includes the energy dissipation on the arc failure surface BE and the radial discontinuity line inside area I. and

[0102]

[0103] in, and represents the energy dissipation at the arc failure surface BE and the radial discontinuity line inside area I, c represents the soil cohesion, and e represents the natural constant.

[0104] Step 4: Figure 4 The velocity field diagram corresponding to region II is given, where the starting point of region II is the end point E of the arc rotation region I and is tangent to point E. According to the associated flow criterion, the direction of its velocity vector is in a positive direction with respect to the boundaries AM and EN. The specific area calculation formula of region II is as follows:

[0105]

[0106] Step 5: Based on Figure 4 We can further calculate the power P of the external load corresponding to area II. γ-Ⅱ And the internal energy dissipation power The specific calculation results must satisfy the following derivation formula:

[0107]

[0108] l EN =(Dcosα+C) / sinα

[0109]

[0110] Among them, l AM represents the length of the line segment AM in area II, C represents the thickness of the tunnel cover, α represents the failure mechanism angle parameter, γ represents the unit weight of the soil, and v II represents the velocity vector of region II, e represents a natural constant, l EN Represents the length of line segment EN in area II.

[0111] Step 6: According to Figure 1 As shown in Figure 2, the tunnel face support pressure σ t and possible additional surface load σ s It is also necessary to calculate the power it produces, which is specifically attributed to the power produced by the external load. The power derivation formula is as follows:

[0112]

[0113]

[0114] Among them, v I and v II denote the velocity vectors of region I and region II, σ t represents the tunnel face support pressure, σ s represents the additional surface load, l MN represents the length of the line segment MN in region II, α represents the failure mechanism angle parameter, and δ represents the tunnel inclination.

[0115] Step 7: According to the upper limit theorem of limit analysis, the stability condition of the tunnel face is:

[0116] P e ≤P v

[0117] Where P e is the power of the external load, P v Then it is the internal energy dissipation power, the specific formula is as follows:

[0118]

[0119]

[0120] Step 8: According to the proposed mechanism, the power produced by the external load is equal to the internal energy dissipation power, and the ultimate support pressure of the tunnel surface when the ground surface rises can be obtained. The specific formula is derived as follows:

[0121]

[0122] Step 9: To facilitate the subsequent calculation of the scheme and the application of the model, the formula derived in step 8 is simplified as follows:

[0123]

[0124] in:

[0125]

[0126] Among them, η γ , η c , R A , R B , R C and R D All represent dimensionless parameters.

[0127] Step 10: Based on the simplified formula in step 9, the excavation face ultimate support pressure σ T Under the control of the proposed failure mechanism angle parameter α and the tunnel inclination δ, where α∈[0,π / 2], some scholars summarized the existing cases based on the actual construction environment and gave that the maximum longitudinal inclination of shield tunneling should not exceed 10°. Therefore, the present invention stipulates that the value range of the longitudinal inclination δ is [-10°~10°]. Therefore, the optimal failure mechanism is sought with the help of MATLAB software, so as to calculate the optimal solution of the tunnel face limit support pressure when the surface rises.

[0128] The feasibility and advancement of the present invention will be further illustrated below with reference to specific examples.

[0129] Taking the shield construction in sandy soil as an example, the specific analysis parameters are shown in Table 1.

[0130] Table 1 Analysis parameters

[0131]

[0132] Figure 5 The normalized ultimate support pressure (σ) of five soil internal friction angles when C / D = 0.5 is given. T The normalized ultimate support pressures obtained under the five internal friction angles all decrease gradually with the increase of the tunnel longitudinal inclination angle in the range of [-10°, 10°], and the influence of the tunnel longitudinal inclination angle on the ultimate support pressure becomes more significant when the friction angle is larger.

[0133] Figure 6In order to combine the parameters in Table 1 and the three-dimensional numerical model considering the longitudinal inclination of the tunnel established by the finite difference software FLAC3D 7.0, in order to verify the effectiveness of the proposed model in studying the stability of the longitudinal inclined tunnel face, considering the symmetry of the tunnel along the longitudinal direction, the model only uses half of the area for calculation, the tunnel diameter is 6m, and the model size is 60m (length) * 30m (width) * 45m (height) to avoid the influence of boundary factors on the numerical results. The boundary conditions of the model are set as follows: the bottom surface is completely fixed in three directions, all vertical boundaries are fixed along the normal direction, and the top surface is free. The soil properties are characterized by the ideal elastic-plastic constitutive Mohr-coulomb, and the influence of the sand cohesion c′ is ignored.

[0134] Figure 7 and Figure 8 When C / D = 0.5 and C / D = 1, the analytical solution of the proposed model is compared with the existing horizontal mechanism and the numerical simulation of this paper. It can be found that no matter the numerical scheme or the proposed scheme, the tunnel face support pressure ratio and the soil friction angle The relationship between σ and T / γD When When is small, the three theoretical solutions are close to the numerical solution, which further verifies the rationality and effectiveness of the model proposed in this invention.

[0135] Fig. 9 for When δ = 0°, the analytical solution of the proposed model is compared with the existing horizontal mechanism and the numerical simulation of this paper. It can be found that the prediction results of the proposed model are relatively close to the numerical solution, and with the increase of the tunnel coverage depth ratio, the maximum difference between the model solution and the numerical solution does not change suddenly.

[0136] The embodiment of the present invention provides a device for calculating the ultimate support pressure of the ground uplift of a shallow tunnel. Fig.10 As shown, the device 1000 includes:

[0137] The first region construction module 1001 is configured to simplify the soil at the front end of the tunnel face into an arc rotation region as region I, the center point of the circle is point A at the top of the tunnel face, the starting end of the arc is tangent to point B at the bottom of the tunnel face, and the entire arc rotation region is controlled by a rotation angle θ;

[0138] The velocity field construction module 1002 is configured to construct a circular arc rotation area velocity field based on the determined area I;

[0139] The first power calculation module 1003 is configured to calculate the power of the external load and the internal energy dissipation power corresponding to the area I based on the velocity field of the arc rotation area, wherein the power of the external load includes the power of the gravity of the area I. The internal energy dissipation power includes the energy dissipation at the arc failure surface BE and the radial discontinuity line inside area I;

[0140] The second region construction module 1004 is configured to construct region II, wherein the starting point of region II is the end point E of arc rotation region I and is tangent to point E, and the velocity vector direction of region II is in a straight line with the boundaries AM and EN. Angular relationship, where is the friction angle within the soil;

[0141] The second power calculation module 1005 is configured to calculate the power of the external load and the internal energy dissipation power corresponding to the area II;

[0142] The third power calculation module 1006 is configured to calculate the power of the tunnel face support pressure and the additional surface load;

[0143] The stability condition determination module 1007 is configured to determine the stability condition of the tunnel face as P e ≤P v , where P e is the power of the external load, P v is the internal energy dissipation power, where the power of the external load is the sum of the power of the external load corresponding to area I, the power of the external load corresponding to area II, the tunnel surface support pressure, and the power of the additional surface load. The internal energy dissipation power is the sum of the internal energy dissipation power corresponding to area I and area II;

[0144] The ultimate pressure calculation module 1008 is configured to obtain the ultimate support pressure of the tunnel surface when the ground surface rises based on the power produced by the external load and the internal energy dissipation power being equal. The calculation formula is:

[0145]

[0146] Among them, P CI-BE and P CI-ABE represents the energy dissipation at the arc failure surface BE and the radial discontinuity line inside region I, P CII-AM and P CII-EN represents the internal energy dissipation power corresponding to region II, represents the additional surface load σ s Power produced, P γ-I represents the power of the external load corresponding to area I, P γ-II represents the power of the external load corresponding to region II, v I represents the velocity vector of region I, and D represents the tunnel diameter.

[0147] In some embodiments, the velocity field construction module is further configured to:

[0148] Discretize area I into numerous triangular areas, each of which is measured with a set velocity vector (ν0, ν1, ν2…ν n ) moves as a whole, and the velocity vectors on the discontinuity surfaces of each block are (dν0, dν1, dν2…dν n-1 ), the angle between the velocity direction and the failure contour is the friction angle of the soil The velocity vector in region I is ν Ⅰ , the construction of the velocity field satisfies the following formula:

[0149] l AB =r0=D

[0150]

[0151]

[0152] Among them l AB represents the length of line segment AB, r0 represents the starting radius of arc ABE, r represents the ending radius of arc ABE, exp represents the exponential function e, v n represents the velocity vector corresponding to the nth triangle area, v n-1 represents the velocity vector corresponding to the n-1th triangle area, n represents the number of discrete triangle areas, and i represents the maximum value range of n;

[0153] When the number of rigid sliding triangles approaches infinity, the velocity vector ν(θ) at any angle θ in region I is set as:

[0154]

[0155] In some embodiments, the first power calculation module is further configured to:

[0156] The area of ​​the arc diameter break line and the arc surface ABE is calculated using the following formula:

[0157] AB=AB1=AB n =D

[0158] BB1=B n-1 B n

[0159] ∠BAE=θ=α

[0160]

[0161] Among them, B1 represents the first dividing point of the arc rotation area, B n-1 Indicates the n-1th segmentation point of the arc rotation area, B nrepresents the nth segmentation point of the arc rotation zone, α represents the failure mechanism angle parameter, δ represents the tunnel inclination, S ABE represents the area of ​​the arc surface ABE;

[0162] The power exerted by gravity in area I is calculated by the following formula

[0163]

[0164] Where γ represents the unit weight of soil and α represents the failure mechanism angle parameter.

[0165] In some embodiments, the first power calculation module is further configured to calculate the internal energy dissipation power of region I by the following formula:

[0166]

[0167] in, and represents the energy dissipation at the arc failure surface BE and the radial discontinuity line inside area I, c represents the soil cohesion, and e represents the natural constant.

[0168] In some embodiments, the second power calculation module is further configured to calculate the power P of the external load corresponding to the region II by the following formula: γ-Ⅱ And the internal energy dissipation power

[0169]

[0170] l EN =(Dcosα+C) / sinα

[0171]

[0172]

[0173] Among them, l AM represents the length of the line segment AM in area II, C represents the thickness of the tunnel cover, α represents the failure mechanism angle parameter, γ represents the unit weight of the soil, and v II represents the velocity vector of region II, e represents a natural constant, l EN Represents the length of line segment EN in area II.

[0174] In some embodiments, the third power calculation module is further configured to calculate the power of the tunnel face support pressure and the additional surface load by the following formula:

[0175]

[0176]

[0177] Among them, v I and v II denote the velocity vectors of region I and region II, σ t represents the tunnel face support pressure, σ s represents the additional surface load, l MN represents the length of the line segment MN in region II, α represents the failure mechanism angle parameter, and δ represents the tunnel inclination.

[0178] In some embodiments, the apparatus further comprises a formula simplification module, wherein the formula simplification module is configured to:

[0179] The calculation formula of the tunnel face ultimate support pressure when the ground surface rises is simplified by the following formula:

[0180]

[0181] in:

[0182]

[0183]

[0184] Among them, η γ , η c , R A , R B , R C and R D All represent dimensionless parameters.

[0185] In some embodiments, the apparatus further comprises a control module, wherein the control module is configured to:

[0186] According to the failure mechanism angle parameter α and the tunnel inclination angle δ, the excavation face limit support pressure σ is adjusted T , where α∈[0,π / 2], and the longitudinal inclination angle δ ranges from [-10° to 10°].

[0187] It should be noted that the device described in this embodiment belongs to the same technical concept as the method described previously, and can achieve the same technical effect, which will not be repeated here.

[0188] An embodiment of the present invention provides a readable storage medium, which stores one or more programs. The one or more programs can be executed by one or more processors to implement the methods described in the above embodiments.

[0189] The above description is intended to be illustrative rather than restrictive. For example, the above examples (or one or more of them) can be used in combination with each other. For example, those of ordinary skill in the art can use other embodiments when reading the above description. In addition, in the above-mentioned specific embodiments, various features can be grouped together to simplify the present invention. This should not be interpreted as a feature of an invention that is not claimed for protection being necessary for any claim. On the contrary, the subject matter of the present invention may be less than all the features of the embodiments of a specific invention. Thus, the following claims are incorporated into the specific embodiments as examples or embodiments, wherein each claim is independently used as a separate embodiment, and it is considered that these embodiments can be combined with each other in various combinations or arrangements. The scope of the present invention should be determined with reference to the full scope of the equivalent forms of the attached claims and these claims.

Claims

1. A method for calculating the ultimate support pressure of surface uplift in a shallow tunnel, characterized in that: The method comprises: The soil at the front end of the tunnel face is simplified into an arc rotation area as area I, the center point of the circle is point A at the top of the tunnel face, the starting end of the arc is tangent to point B at the bottom of the tunnel face, and the entire arc rotation area is controlled by the rotation angle θ; Constructing the velocity field of the arc rotation area based on the determined area I; Based on the velocity field of the arc rotation zone, the power of the external load and the internal energy dissipation power corresponding to the area I are calculated. The power of the external load includes the power P caused by the gravity of the area I. γⅠ , the internal energy dissipation power includes the energy dissipation at the arc failure surface BE and the radial discontinuity line inside area I; Construct area II, the starting point of area II is the end point E of the arc rotation area I and is tangent to point E, and the velocity vector direction of area II is in a positive direction with the boundaries AM and EN. Angular relationship, where is the friction angle within the soil; Calculate the power of external load and internal energy dissipation corresponding to area II; Calculate the tunnel face support pressure and the power exerted by the additional surface load; Determine the stability condition of the tunnel face as P e ≤P v , where P e is the power of the external load, P v is the internal energy dissipation power, where the power of the external load is the sum of the power of the external load corresponding to area I, the power of the external load corresponding to area II, the tunnel surface support pressure, and the power of the additional surface load. The internal energy dissipation power is the sum of the internal energy dissipation power corresponding to area I and area II; According to the power of external load and internal energy dissipation, the ultimate support pressure of the tunnel surface when the ground surface rises is obtained. The calculation formula is: Among them, P CI-BE and P CI-ABE represents the energy dissipation at the arc failure surface BE and the radial discontinuity line inside region I, P CII-AM and P CII-EN represents the internal energy dissipation power corresponding to region II, represents the additional surface load σ s Power produced, P γ-I represents the power of the external load corresponding to area I, P γ-II represents the power of the external load corresponding to region II, v I represents the velocity vector of region I, and D represents the tunnel diameter; The method of constructing the arc rotation area velocity field based on the determined area I includes: Discretize area I into numerous triangular areas, each of which is measured by a set velocity vector (ν0, ν1, ν2…ν n ) moves as a whole, and the velocity vectors on the discontinuity surfaces of each block are (dν0, dν1, dν2…dν n-1 ), the angle between the velocity direction and the failure contour is the friction angle of the soil The velocity vector in region I is ν Ⅰ , the construction of the velocity field satisfies the following formula: l AB ＝r0＝D Among them l AB represents the length of line segment AB, r0 represents the starting radius of arc ABE, r represents the ending radius of arc ABE, exp represents the exponential function e, v n represents the velocity vector corresponding to the nth triangle area, v n-1 represents the velocity vector corresponding to the n-1th triangle area, n represents the number of discrete triangle areas, and i represents the maximum value range of n; When the number of rigid sliding triangles approaches infinity, the velocity vector ν(θ) at any angle θ in region I is set as:

2. The method according to claim 1, characterized in that The power of the external load corresponding to the area I is calculated based on the velocity field of the circular arc rotation area, specifically including: The area of ​​the arc diameter break line and the arc surface ABE is calculated using the following formula: AB=AB1=AB n =D BB1=B n-1 B n ∠BAE=θ=α Where α represents the failure mechanism angle parameter, δ represents the tunnel inclination, S ABE represents the area of ​​the arc surface ABE; The power exerted by gravity in area I is calculated by the following formula Where γ represents the unit soil mass.

3. The method according to claim 2, characterized in that The internal energy dissipation power of area I is calculated by the following formula in, and represents the energy dissipation at the arc failure surface BE and the radial discontinuity line inside area I, c represents the soil cohesion, and e represents the natural constant.

4. The method according to claim 3, characterized in that The power P of the external load corresponding to area II is calculated by the following formula γ-Ⅱ And the internal energy dissipation power l EN =(Dcosα+C) / sinα Among them, l AM represents the length of the line segment AM in area II, C represents the thickness of the tunnel cover, α represents the failure mechanism angle parameter, γ represents the unit weight of the soil, and v II represents the velocity vector of region II, e represents a natural constant, l EN Represents the length of line segment EN in area II.

5. The method according to claim 1, characterized in that The tunnel face support pressure and the power of the additional surface load are calculated using the following formula: Among them, v I and v II denote the velocity vectors of region I and region II, σ t represents the tunnel face support pressure, σ s represents the additional surface load, l MN represents the length of the line segment MN in region II, α represents the failure mechanism angle parameter, δ represents the tunnel inclination, and C represents the tunnel cover thickness.

6. The method according to claim 1, characterized in that The method further comprises: The calculation formula of the tunnel face ultimate support pressure when the ground surface rises is simplified by the following formula: in: Among them, η γ , η c , R A , R B , R C and R D All represent dimensionless parameters; σ t represents the tunnel face support pressure, σ s represents the additional surface load, α represents the failure mechanism angle parameter, δ represents the tunnel inclination; C represents the tunnel cover thickness; c represents the soil cohesion; γ represents the unit soil weight.

7. The method according to claim 6, characterized in that After simplifying the calculation formula of the tunnel face limit support pressure when the ground surface rises, the method further includes: The ultimate support pressure σ of the excavation face is regulated according to the failure mechanism angle parameter α and the tunnel inclination angle δ T , where α∈[0,π / 2], and the longitudinal inclination angle δ ranges from [-10° to 10°].

8. A device for calculating the ultimate support pressure of surface uplift in a shallow tunnel, characterized in that: The device comprises: The first area construction module is configured to simplify the soil at the front end of the tunnel face into an arc rotation area as area I, the center point of the circle is point A at the top of the tunnel face, the starting end of the arc is tangent to point B at the bottom of the tunnel face, and the entire arc rotation area is controlled by a rotation angle θ; A velocity field construction module is configured to construct a velocity field of the arc rotation area based on the determined area I; The first power calculation module is configured to calculate the power of the external load and the internal energy dissipation power corresponding to the area I based on the velocity field of the arc rotation area, wherein the power of the external load includes the power of the gravity of the area I. The internal energy dissipation power includes the energy dissipation at the arc failure surface BE and the radial discontinuity line inside area I; The second area construction module is configured to construct area II, the starting point of area II is the end point E of the arc rotation area I and is tangent to point E, and the velocity vector direction of area II is in a straight line with the boundaries AM and EN. Angular relationship, where is the friction angle within the soil; The second power calculation module is configured to calculate the power of the external load and the internal energy dissipation power corresponding to the area II; A third power calculation module is configured to calculate the power produced by the tunnel face support pressure and the additional surface load; The stability condition determination module is configured to determine the stability condition of the tunnel face as P e ≤P v , where P e is the power of the external load, P v is the internal energy dissipation power, where the power of the external load is the sum of the power of the external load corresponding to area I, the power of the external load corresponding to area II, the tunnel surface support pressure, and the power of the additional surface load. The internal energy dissipation power is the sum of the internal energy dissipation power corresponding to area I and area II; The ultimate pressure calculation module is configured to obtain the ultimate support pressure of the tunnel surface when the ground surface rises based on the power produced by the external load and the internal energy dissipation power being equal. The calculation formula is: Among them, P CI-BE and P CI-ABE represents the energy dissipation at the arc failure surface BE and the radial discontinuity line inside region I, P CII-AM and P CII-EN represents the internal energy dissipation power corresponding to region II, represents the additional surface load σ s Power produced, P γ-I represents the power of the external load corresponding to area I, P γ-II represents the power of the external load corresponding to region II, v I represents the velocity vector of region I, and D represents the tunnel diameter; The velocity field building module is further configured as: Discretize area I into numerous triangular areas, each of which is measured by a set velocity vector (ν0, ν1, ν2…ν n ) moves as a whole, and the velocity vectors on the discontinuity surfaces of each block are (dν0, dν1, dν2…dν n-1 ), the angle between the velocity direction and the failure contour is the friction angle of the soil The velocity vector in region I is ν Ⅰ , the construction of the velocity field satisfies the following formula: l AB ＝r0＝D Among them l AB represents the length of line segment AB, r0 represents the starting radius of arc ABE, r represents the ending radius of arc ABE, exp represents the exponential function e, v n represents the velocity vector corresponding to the nth triangle area, v n-1 represents the velocity vector corresponding to the n-1th triangle area, n represents the number of discrete triangle areas, and i represents the maximum value range of n; When the number of rigid sliding triangles approaches infinity, the velocity vector ν(θ) at any angle θ in region I is set as:

9. A readable storage medium, characterized in that: The readable storage medium stores one or more programs, and the one or more programs can be executed by one or more processors to implement the method according to any one of claims 1 to 7.

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