Shallow-buried tunnel vault confining pressure calculation method

Abstract

The invention relates to the field of theoretical calculation of geotechnical engineering tunnel confining pressure, in particular to a tunnel vault confining pressure calculation method. Comprising the steps of 1, obtaining a tunnel top surrounding rock pressure calculation model, and performing related assumption; 2, calculating an equilibrium equation of any point in the soil body, wherein the yield criterion meets the Mohr-Coulomb criterion, the boundary condition, the stress equation on the fracture surface and the moment equilibrium equation; 3, calculating corresponding soil pressure parameters Kq, Kgamma and Kc according to a fracture surface calculation mode; and 4, calculating according to a tunnel top confining pressure calculation formula to obtain a tunnel confining pressure value. The tunnel vault surrounding rock pressure obtained through the calculation method is larger than the vault surrounding rock pressure of the Rankine soil pressure calculation theory, so that stress calculation of a tunnel vault supporting structure is more reasonable; the fracture surface selected by the calculation method considers the extreme value condition of the yield function, the extreme value is not required, and the calculation is simpler and more convenient.

Description

Technical Field

[0001] The invention relates to the field of theoretical calculation of confining pressure of geotechnical engineering tunnels, and in particular to a method for calculating the confining pressure of a shallow tunnel vault. Background Art

[0002] At present, the calculation of the confining pressure of the shallow tunnel vault mainly adopts two methods: numerical simulation and theoretical calculation. The numerical calculation mainly adopts the stratum structure method, which is complex and the result is greatly affected by the experience of the calculator. The theoretical calculation mainly adopts the limit analysis and limit equilibrium methods. The limit analysis is divided into the upper limit method and the lower limit method. Since the solution obtained by the lower limit method is generally smaller than the true solution, it is rarely used in general engineering calculations. The upper limit method is more studied. Since the upper limit method needs to construct a velocity field, its limit value is greater than the true load, which is more conservative and beneficial to engineering safety, but it will inevitably cause waste in engineering. The limit equilibrium method usually assumes a sliding surface (or failure surface) and gives the stress along this sliding surface. The static equilibrium method is used to compare and find the most dangerous sliding surface to obtain the limit load. It does not meet the requirements of establishing a static field in the limit analysis method, so the limit equilibrium method solution is not a lower limit solution. It also does not meet the requirements of establishing a mobile field in the limit analysis method, so it is not an upper limit solution. At present, most of the limit equilibrium research is based on the modified soil column theory, mainly for different soil pressure coefficients and failure surface modes. The modified soil column theory introduces Rankine's earth pressure theory. In the derivation of his basic theory, Rankine made the following assumptions: the wall is rigid and the wall back is vertical; the surface of the backfill behind the wall is horizontal; the wall back is smooth and there is no friction between the wall back and the backfill. Since Rankine's theory ignores the fact that the actual wall back is not smooth and there is friction, the calculated active earth pressure is too large, which ultimately makes the confining pressure on the top of the tunnel too small, making the tunnel top structure support dangerous.

[0003] Therefore, in order to solve the above technical problems, make the construction of shallow tunnels reasonable and ensure safety, it is necessary to further study the stress conditions of the shallow tunnel vault confining pressure. Summary of the invention

[0004] The invention aims to provide a shallow buried tunnel vault confining pressure calculation method which is applicable to shallow buried tunnels, has simple calculation and more reasonable tunnel vault support structure force calculation.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] A method for calculating tunnel vault confining pressure, characterized in that it specifically comprises the following steps:

[0007] Step 1, obtain the calculation model of the surrounding rock pressure at the top of the tunnel and make relevant assumptions;

[0008] Step 2, calculate the equilibrium equation and yield criterion of any point in the soil to satisfy the Mohr-Coulomb criterion, boundary conditions, stress equation on the fracture surface, and moment equilibrium equation;

[0009] Step 3: Take the fracture surface calculation mode and calculate the corresponding earth pressure parameter K q , K γ , K c ;

[0010] Step 4: Calculate the tunnel confining pressure value according to the confining pressure calculation formula at the top of the tunnel.

[0011] In step 1, it is assumed that the width of the tunnel is 2a. When the soil layer ABCD of the arch sinks, it is squeezed by the soil blocks ADEF and BCE'F' on both sides. Assuming that the ground surface is horizontal, the soil blocks ADEF and BCE'F' are symmetrical. The soil block ADEF is analyzed in detail below. The soil block ADEF is divided into two areas a and b for consideration. The fracture surface is taken as plane~plane, and the slope of the surface AF is h' b , the slope of surface FE is h′ a The model needs to find out the corresponding soil pressure on the AD surface when x=0 and at any depth h, and then find out the surrounding rock pressure of the tunnel vault.

[0012] In step 2, the equilibrium equation is considered as a plane strain problem, and the stress component σ x , σ z , τ xz Satisfies the equilibrium equation:

[0013]

[0014] In the formula, γ is the soil weight;

[0015] Yield criterion, define f as the Coulomb yield function:

[0016]

[0017] In the formula, σ is the normal stress, τ is the tangential shear stress, c and φ are the soil cohesion and internal friction angle;

[0018] The stress relationship in statics is:

[0019]

[0020] Where h′ is the slope of the tangent line of the surface;

[0021] Substituting formula (3) into formula (2), we have:

[0022]

[0023] The Mohr-Coulomb yield criterion for soil in the limit state along the fracture surface and in the stable state along other surfaces satisfies:

[0024]

[0025] The above formula is called the yield function. When taking the extreme value of formula (5), we have:

[0026]

[0027] Then equation (6) is the extreme value condition of the yield function;

[0028] Rewritten as stress component relations are as follows:

[0029]

[0030] In the formula, λ=tanφ, c and φ are soil cohesion and internal friction angle respectively; σ is the normal stress on the curved surface; is the tangent slope of the fracture surface;

[0031] Boundary conditions, for soil pressure: At the soil surface z = 0, given the surface load σ z =q,τ xz =0; Substituting into formula (6), we have:

[0032]

[0033] On the straight wall AD: x = 0, the shear stress at any point between the wall and the soil is the shear strength reduction value, that is:

[0034] From formula (7), we have:

[0035]

[0036] Force and moment equilibrium equation, from the equilibrium equation, we have:

[0037]

[0038] By calculating the above three equations, the stress relationship can be obtained:

[0039] Where:

[0040] Formulas (10) and (11) are the differential equations of the horizontal force and vertical force on the vertical plane 0≤z≤h, respectively, and formula (12) is the differential equation of the moment of the horizontal force on this vertical plane with respect to z=h;

[0041] For any point (x R , z R ), multiply both sides of formula (10) by (hz R), multiply both sides of formula (11) by (xx R ) and according to formula (12), we can get:

[0042]

[0043] Formula (17) is the force on the vertical plane 0≤z≤h on the point (x R , z R ) in general form;

[0044] If z=0 and z=h are the soil surface and sliding surface respectively, from equations (10), (11), and the yield condition τ-σλ-c=0, we can obtain:

[0045]

[0046] Formula (18) is the equation for the force on the vertical surface 0≤z≤h;

[0047] According to the yield condition, the moment equilibrium equation (17) is:

[0048]

[0049] In step 3, when the open-cut method is used to construct a tunnel with a shallow burial depth, that is, a tunnel with a top cover close to the ground surface, the fracture surface is a plane-to-plane calculation mode. In order to meet the straight wall boundary condition (9), the soil behind the wall is divided into two areas a and b for consideration. The fracture surface is taken as plane-to-plane. In area a, the fracture surface is: z = h′ a (x+b), from formula (7) we have T1=0, so from formula (18) we have:

[0050]

[0051] In area b, the fracture surface is: z = h + h' b x, and in order to make the fracture surface of zone b close to the real fracture surface, it is advisable to:

[0052] h′ b =0.5(h′ a +h′0), from formula (18):

[0053]

[0054] Substitute equation (21) and the wall boundary condition into the equation, and obtain The total earth pressure at any height h on the vertical wall AD is obtained as:

[0055]

[0056] The earth pressure at any height h on the vertical wall AD is:

[0057] e h =γhK γ -2cK t +qK q (23)Where:

[0058] According to formula (26) and formula (25), the Rankine earth pressure coefficient K is calculated respectively: γ , K c .

[0059] In step 3, when the open-cut method is used for construction and the buried depth is deep, that is, the top cover is far from the ground surface, the fracture surface is a plane-helical calculation mode. In order to make the fracture surface smooth, the soil behind the wall is divided into two areas a and b for consideration, and the fracture surface is a plane-helical;

[0060] because The formula (19) can also be written as:

[0061]

[0062] Integrating the moment equation (27) along the fracture surface gives the overall moment equilibrium equation on the entire fracture surface; on the plane segment EF: have In the helical segment AF:

[0063] (hz R )(h′-λ)+(1+λh′)(xx R )=0

[0064] so:

[0065]

[0066] After integral operation, we get:

[0067]

[0068] in:

[0069] Solving this integral equation, we can obtain the earth pressure at any height h on the vertical wall AD:

[0070] e h =γhK γ -2cK c +qK q (29)

[0071] Where:

[0072]

[0073]

[0074]

[0075] According to equations (29) to (32), the earth pressure coefficient can be obtained when the failure surface is in the form of a plane or a spiral surface.

[0076] In step 4, the vertical confining pressure Q acting on the tunnel is equal to the weight G of the soil column minus the lateral force T on both sides, that is,

[0077] Q=G-2T (33)

[0078] The lateral force T is the sum of friction and adhesion. The lateral stress acting on any point on the side of the soil column is:

[0079]

[0080] Where: e h —lateral pressure at a point at a depth h from the ground;

[0081] e h =γhK γ -2cK c +qK q (35)

[0082] K γ is the self-weight earth pressure coefficient, K c is the cohesive earth pressure coefficient, K q is the earth pressure coefficient of surface load;

[0083] From formula (33), the total value of the vertical confining pressure acting on the tunnel can be obtained as:

[0084]

[0085] in:

[0086] If the confining pressure at the top of the tunnel is assumed to be uniformly distributed, then:

[0087]

[0088] Formula (37) is used to calculate the confining pressure at the top of the tunnel.

[0089] In step 4, when the open-cut method is used for construction and the buried depth is shallow, that is, the top cover is close to the ground surface, when the overburden layer on the tunnel slides vertically downward, two sliding surfaces AB and CD are generated on both sides of the soil column, and the starting points are at the wall foundation, and the soil column above the cavern is GJKH; when the open-cut method is used for construction and the buried depth is deep, that is, the top cover is far from the ground surface, when the overburden layer on the tunnel slides vertically downward, two sliding surfaces AD and BC are generated on both sides of the soil column, and the starting points are at the wall foundation, and the soil column above the cavern is ABCD.

[0090] The advantages and positive effects of the present invention are:

[0091] 1. The tunnel vault surrounding rock pressure obtained by the calculation method is greater than the vault surrounding rock pressure calculated by the Rankine earth pressure theory, which makes the force calculation of the tunnel vault support structure more reasonable.

[0092] 2. The fracture surface selected by the calculation method takes into account the extreme value conditions of the yield function, so there is no need to find the extreme value, and the calculation is simpler. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 is a calculation flow chart of the present invention;

[0094] Figure 2 is the modified soil column theory diagram;

[0095] Figure 3 It is the plane-to-plane rupture surface calculation model for shallow buried tunnels;

[0096] Figure 4 It is a calculation model of plane-spiral fracture surface of deep buried tunnel. DETAILED DESCRIPTION

[0097] The present invention is further described in detail below in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention, and in no way limit the protection scope of the present invention.

[0098] Example 1

[0099] In this embodiment, the tunnel depth is H = 10m, which is a shallow tunnel. The tunnel span 2a = 10m, the soil layer weight is 20kN / m3, the surface is horizontal, the surface load q = 0, the soil cohesion C = 10kPa / 50kPa / 100kPa, and the internal friction angle φ = 5°

[0100] / 10° / 15° / 20° / 25° / 30° / 35° / 45°. Figure 1 A method for calculating the confining pressure of a tunnel vault is shown, and the confining pressure of the tunnel vault is calculated. The specific steps are as follows:

[0101] Step 1: Obtain the calculation model of the surrounding rock pressure at the top of the tunnel and make relevant assumptions; Figure 2 As shown in the figure, assuming that the tunnel width is 2a, when the soil layer ABCD of the arch sinks, it is squeezed by the soil blocks ADEF and BCE'F' on both sides; assuming that the ground surface is horizontal, the soil blocks ADEF and BCE'F' are symmetrical. The soil block ADEF is analyzed in detail below. The soil block ADEF is divided into two areas a and b. The fracture surface is taken as plane~plane, and the slope of surface AF is h' b , the slope of surface FE is h′ a The model needs to find out the corresponding soil pressure on the AD surface when x=0 and at any depth h, and then find out the surrounding rock pressure of the tunnel vault.

[0102] What is known at present is that the equilibrium equation and yield criterion of any point in the soil satisfy the Mohr-Coulomb criterion, boundary conditions, stress equation on the fracture surface, boundary conditions, and moment equilibrium equation.

[0103] Step 2, calculate the equilibrium equation and yield criterion of any point in the soil to satisfy the Mohr-Coulomb criterion, boundary conditions, stress equation on the fracture surface, and moment equilibrium equation;

[0104] The equilibrium equation is considered as a plane strain problem, and the stress component σ x , σ z , τ xz Satisfies the equilibrium equation:

[0105]

[0106] In the formula, γ is the soil weight;

[0107] Yield criterion, define f as the Coulomb yield function:

[0108]

[0109] In the formula, σ is the normal stress, τ is the tangential shear stress, c and φ are the soil cohesion and internal friction angle;

[0110] The stress relationship in statics is:

[0111]

[0112] Where h′ is the slope of the tangent line of the surface;

[0113] Substituting formula (3) into formula (2), we have:

[0114]

[0115] The Mohr-Coulomb yield criterion for soil in the limit state along the fracture surface and in the stable state along other surfaces satisfies:

[0116]

[0117] The above formula is called the yield function. When taking the extreme value of formula (5), we have:

[0118]

[0119] Then equation (6) is the extreme value condition of the yield function;

[0120] Rewritten as stress component relations are as follows:

[0121]

[0122] In the formula, λ=tan φ, c and φ are soil cohesion and internal friction angle respectively; σ is the normal stress on the curved surface; is the tangent slope of the fracture surface;

[0123] Boundary conditions, for soil pressure: At the soil surface z = 0, given the surface load σ z =q,τ xz =0; Substituting into formula (6), we have:

[0124]

[0125] On the straight wall AD: x = 0, the shear stress at any point between the wall and the soil is the shear strength reduction value, that is:

[0126] From formula (7), we have:

[0127]

[0128] Force and moment equilibrium equation, from the equilibrium equation, we have:

[0129]

[0130] By calculating the above three equations, the stress relationship can be obtained:

[0131] Where:

[0132] Formulas (10) and (11) are the differential equations of the horizontal force and vertical force on the vertical plane 0≤z≤h, respectively, and formula (12) is the differential equation of the moment of the horizontal force on this vertical plane with respect to z=h;

[0133] For any point (x R , z R ), multiply both sides of formula (10) by (hz R ), multiply both sides of formula (11) by (xx R ) and according to formula (12), we can get:

[0134]

[0135] Formula (17) is the force on the vertical plane 0≤z≤h on the point (x R , z R ) in general form;

[0136] If z=0 and z=h are the soil surface and sliding surface respectively, from equations (10), (11), and the yield condition τ-σλ-c=0, we can obtain:

[0137]

[0138] Formula (18) is the equation for the force on the vertical surface 0≤z≤h;

[0139] According to the yield condition, the moment equilibrium equation (17) is:

[0140]

[0141] Step 3: Take the fracture surface calculation mode and calculate the corresponding earth pressure parameter K q , K γ , K c ;

[0142] In this embodiment, the fracture surface is as follows Figure 3 In the plane-to-plane calculation mode shown in FIG. 1 , in order to satisfy the straight wall boundary condition (9), the soil behind the wall is divided into two regions, a and b, and the fracture surface is taken as plane-to-plane. In region a, the fracture surface is: z = h′ a (x+b), from formula (7) we have i, so from formula (18) we have:

[0143]

[0144] In area b, the fracture surface is: z = h + h' b x, and in order to make the fracture surface of zone b close to the real fracture surface, it is possible to:

[0145] h′ b =0.5(h′ a +h′0), from formula (18):

[0146]

[0147] Substitute equation (21) and the wall boundary condition into the equation, and obtain The total earth pressure at any height h on the vertical wall AD is obtained as:

[0148]

[0149] The earth pressure at any height h on the vertical wall AD is:

[0150] e h =γhK γ -2ck c +qK q (23)Where:

[0151] According to formula (26) and formula (25), the Rankine earth pressure coefficient K is calculated respectively: γ , K c .

[0152] Step 4: Calculate the tunnel confining pressure value according to the confining pressure calculation formula at the top of the tunnel.

[0153] When the overburden of the tunnel slides vertically downward, two sliding surfaces AB and CD are generated on both sides of the soil column. The starting point of the sliding surface is at the wall foundation, and the soil column above the cavern is "GJKH". Therefore, it can be considered that the vertical confining pressure Q (total pressure) acting on the tunnel is equal to the weight G of the soil column GJKH minus the lateral force T on the GJ and KH surfaces on both sides, that is,

[0154] Q=G-2T (33)

[0155] The lateral force T is the sum of friction and adhesion. The lateral stress acting on any point on the side of the soil column is:

[0156]

[0157] Where: e h —lateral pressure at a point at a depth h from the ground;

[0158] e h =γhK γ -2cK c +qK q (35)

[0159] K γ is the self-weight earth pressure coefficient, K c is the cohesive earth pressure coefficient, K q is the earth pressure coefficient of surface load;

[0160] From formula (33), the total value of the vertical confining pressure acting on the tunnel can be obtained as:

[0161]

[0162] in: If the confining pressure at the top of the tunnel is assumed to be uniformly distributed, then:

[0163]

[0164] Formula (37) is used to calculate the confining pressure at the top of the tunnel.

[0165] Table 1 Comparison of the calculation results of this embodiment with the calculation results of Rankine earth pressure theory

[0166]

[0167] Example 2

[0168] The tunnel described in this embodiment is a deep buried tunnel. It is known that the tunnel depth is H = 100m, the tunnel span 2a = 10m, and the soil layer weight is 20kN / m 3 , the ground surface is horizontal, the ground load q = 0, the soil cohesion C = 10 kPa / 50 kPa / 100 kPa, and the internal friction angle φ = 5° / 10° / 15° / 20° / 25° / 30° / 35° / 45°. The confining pressure of the tunnel vault is calculated using the same method as in Example 1.

[0169] The differences are:

[0170] In this embodiment, the fracture surface is as follows Figure 4 The calculation mode of plane-helical surface shown in the figure, in order to make the fracture surface smooth, the soil behind the wall is divided into two areas a and b, and the fracture surface is plane-helical surface;

[0171] because The formula (19) can also be written as:

[0172]

[0173] Integrating the moment equation (27) along the fracture surface gives the overall moment equilibrium equation on the entire fracture surface; on the plane segment EF: have In the helical segment AF:

[0174] (hz R )(h′-2)+(1+λh′)(xx R )=0

[0175] so:

[0176]

[0177] After integral operation, we get:

[0178]

[0179] in:

[0180] Solving this integral equation, we can obtain the earth pressure at any height h on the vertical wall AD:

[0181] e h =γhK γ -2cK c +qK q (29)

[0182] Where:

[0183]

[0184]

[0185]

[0186] According to equations (29) to (32), the earth pressure coefficient can be obtained when the failure surface is in the form of a plane or a spiral surface.

[0187] In this embodiment, when the overlying soil layer of the tunnel slides vertically downward, two sliding surfaces AD and BC are generated on both sides of the soil column. The starting point of the sliding surface is at the wall foundation, and the soil column above the cavern is "ABCD". Therefore, it can be considered that the vertical confining pressure Q (total pressure) acting on the tunnel is equal to the weight G of the soil column ABCD minus the lateral force T on the AD and BC surfaces on both sides.

[0188] Table 2 is a comparison of the calculation results of this embodiment and the calculation results of the modified soil column crown confining pressure based on Rankine's earth pressure theory.

[0189] Table 2 Comparison of the calculation results of this embodiment with the calculation results of Rankine earth pressure theory

[0190]

[0191] The present invention is described above by way of example. It should be noted that, without departing from the core of the present invention, any simple deformation, modification or other equivalent replacement that can be made by those skilled in the art without inventive effort falls within the protection scope of the present invention.

Claims

1. A method for calculating tunnel vault confining pressure, characterized in that: The specific steps are as follows: Step 1, obtain the calculation model of the surrounding rock pressure at the top of the tunnel and make relevant assumptions; Step 2, calculate the equilibrium equation and yield criterion of any point in the soil to satisfy the Mohr-Coulomb criterion, boundary conditions, stress equation on the fracture surface, and moment equilibrium equation; Step 3: Take the fracture surface calculation mode and calculate the corresponding earth pressure parameter K q , K γ , K c ; Step 4: Calculate the tunnel confining pressure value according to the confining pressure calculation formula at the top of the tunnel.

2. A method for calculating tunnel vault confining pressure according to claim 1, characterized in that: In step 1, it is assumed that the width of the tunnel is 2a. When the soil layer ABCD of the arch sinks, it is squeezed by the soil blocks ADEF and BCE'F' on both sides. Assuming that the ground surface is horizontal, the soil blocks ADEF and BCE'F' are symmetrical. The soil block ADEF is analyzed in detail below. The soil block ADEF is divided into two areas a and b for consideration. The fracture surface is taken as plane~plane, and the slope of the surface AF is h' b , the slope of surface FE is h′ a The model needs to find out the corresponding soil pressure on the AD surface when x=0 and at any depth h, and then find out the surrounding rock pressure of the tunnel vault.

3. A method for calculating tunnel vault confining pressure according to claim 1, characterized in that: In step 2, the equilibrium equation is considered as a plane strain problem, and the stress component σ x , σ z , τ xz Satisfies the equilibrium equation: In the formula, γ is the soil weight; Yield criterion, define f as the Coulomb yield function: In the formula, σ is the normal stress, τ is the tangential shear stress, c and φ are the soil cohesion and internal friction angle; The stress relationship in statics is: Where h′ is the slope of the tangent line of the surface; Substituting formula (3) into formula (2), we have: The Mohr-Coulomb yield criterion for soil in the limit state along the fracture surface and in the stable state along other surfaces satisfies: The above formula is called the yield function. When taking the extreme value of formula (5), we have: Then equation (6) is the extreme value condition of the yield function; Rewritten as stress component relations are as follows: In the formula, λ=tanφ, c and φ are soil cohesion and internal friction angle respectively; σ is the normal stress on the curved surface; is the tangent slope of the fracture surface; Boundary conditions, for soil pressure: At the soil surface z = 0, given the surface load σ z =q,τ xz =0; Substituting into formula (6), we have: On the straight wall AD: x = 0, the shear stress at any point between the wall and the soil is the shear strength reduction value, that is: From formula (7), we have: Force and moment equilibrium equation, from the equilibrium equation, we have: By calculating the above three equations, the stress relationship can be obtained: Where: Formulas (10) and (11) are the differential equations of the horizontal force and vertical force on the vertical plane 0≤z≤h, respectively, and formula (12) is the differential equation of the moment of the horizontal force on this vertical plane with respect to z=h; For any point (x R , z R ), multiply both sides of formula (10) by (hz R ), multiply both sides of formula (11) by (xx R ) and according to formula (12), we can get: Formula (17) is the force on the vertical plane 0≤z≤h on the point (x R , z R ) in general form; If z = 0, z = h are the soil surface and sliding surface respectively, from equations (10), (11), and the yield condition τ-σλ-c = 0, we can obtain: Formula (18) is the equation for the force on the vertical surface 0≤z≤h; According to the yield condition, the moment equilibrium equation (17) is:

4. A method for calculating tunnel vault confining pressure according to claim 1, characterized in that: In step 3, when the open-cut method is used to construct a tunnel with a shallow burial depth, that is, a tunnel with a top cover close to the ground surface, the fracture surface is a plane-to-plane calculation mode. In order to meet the straight wall boundary condition (9), the soil behind the wall is divided into two areas a and b for consideration. The fracture surface is taken as plane-to-plane. In area a, the fracture surface is: z = h′ a (x+b), from formula (7) we have T1=0, so from formula (18) we have: In area b, the fracture surface is: z = h + h' b x, and in order to make the fracture surface of zone b close to the real fracture surface, it is possible to take: h′ b =0.5(h′ a +h′0), from formula (18): Substitute equation (21) and the wall boundary condition into the equation, and obtain The total earth pressure at any height h on the vertical wall AD is obtained as: The earth pressure at any height h on the vertical wall AD is: yes h =γhK γ –2cK c ++qK q (23) Where: According to formula (26) and formula (25), the Rankine earth pressure coefficient K is calculated respectively: γ , K c .

5. A method for calculating tunnel vault confining pressure according to claim 1, characterized in that: In step 3, when the open-cut method is used for construction and the buried depth is deep, that is, the top cover is far from the ground surface, the fracture surface is a plane-helical calculation mode. In order to make the fracture surface smooth, the soil behind the wall is divided into two areas a and b for consideration, and the fracture surface is a plane-helical; because The formula (19) can also be written as: Integrating the moment equation (27) along the fracture surface gives the overall moment equilibrium equation on the entire fracture surface; on the plane segment EF: have In the helical segment AF: (Hz R )(h′−λ)+(1+λh′)(xx R )=0, so: After integral operation, we get: in: Solving this integral equation, we can obtain the earth pressure at any height h on the vertical wall AD: yes h =γhK γ -2cK c +qK q (29) Where: According to equations (29) to (32), the earth pressure coefficient can be obtained when the failure surface is in the form of a plane or a spiral surface.

6. A method for calculating the confining pressure of a shallow tunnel vault according to claim 1, characterized in that: In step 4, the vertical confining pressure Q acting on the tunnel is equal to the weight G of the soil column minus the lateral force T on both sides, that is, Q=G-2T (33) The lateral force T is the sum of friction and adhesion. The lateral stress acting on any point on the side of the soil column is: Where: e h —lateral pressure at a point at a depth h from the ground; yes h =γhK γ -2cK c +qK q (35) K γ is the self-weight earth pressure coefficient, K c is the cohesive earth pressure coefficient, K q is the earth pressure coefficient of surface load; From formula (33), the total value of the vertical confining pressure acting on the tunnel can be obtained as: in: If the confining pressure at the top of the tunnel is assumed to be uniformly distributed, then: Formula (37) is used to calculate the confining pressure at the top of the tunnel.

7. A method for calculating the confining pressure of a shallow tunnel vault according to claim 6, characterized in that: In step 4, when the open-cut method is used for construction and the buried depth is shallow, that is, the top cover is close to the ground surface, when the overburden layer on the tunnel slides vertically downward, two sliding surfaces AB and CD are generated on both sides of the soil column, and the starting points are at the wall foundation, and the soil column above the cavern is GJKH; when the open-cut method is used for construction and the buried depth is deep, that is, the top cover is far from the ground surface, when the overburden layer on the tunnel slides vertically downward, two sliding surfaces AD and BC are generated on both sides of the soil column, and the starting points are at the wall foundation, and the soil column above the cavern is ABCD.

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