Method for estimating vertical loads when shield tunnels pass through inclined composite strata

Abstract

The present invention discloses a method for estimating the vertical load of a shield tunnel passing through an inclined composite stratum, comprising the following steps: 1. constructing a database based on the basic parameters of the shield tunnel and the geometric parameters and physical and mechanical property parameters of the inclined composite stratum; 2. calculating the initial stress and principal stress deflection angle of the inclined subsurface stratum when subjected only to gravity, and calculating the inclination angle after the slip surface above the tunnel is deflected; 3. establishing a geometric model, importing the geometric model into the excavation influence width of the shield tunnel, and then calculating the excavation influence width of the shield tunnel based on the broken line slip surface method; 4. initializing the geometric model to form a calculation model; 5. solving the vertical stress in the upper half of the calculation model; and solving the vertical load on the vault of the tunnel in the inclined homogeneous stratum in the lower half of the calculation model. The present invention incorporates the properties of the principal stress deflection of the inclined stratum and the differences in the slip surface morphology in the composite stratum into the vertical load estimation of the shield tunnel, thereby overcoming the shortcomings of the existing technology.

Description

Technical Field

[0001] The invention relates to the technical field of computer-aided design, and in particular to a method for estimating vertical load when a shield tunnel passes through an inclined composite stratum. Background Art

[0002] Composite strata refer to a special stratum condition formed by the staggered distribution of different strata with large differences in physical and mechanical properties. It is more common in South China, Southwest my country, Southeast China and other regions. Currently, the number of ultra-large diameter shield tunnels passing through composite strata with soft upper part and hard lower part is gradually increasing.

[0003] Due to the different sliding surface morphology, the external load distribution of shield tunnels in composite strata is quite different from that of shield tunnels in homogeneous strata, which leads to different stress and deformation laws of tunnel structures from those in homogeneous strata.

[0004] Therefore, establishing an external load estimation model is of great significance to the design and construction of ultra-large diameter shield tunnels in composite strata.

[0005] Existing models mainly study the shape of the slip surface above the tunnel excavation surface, but there is relatively little research on the slip surfaces on both sides of the tunnel section.

[0006] Moreover, the traditional tunnel load calculation model is mainly aimed at homogeneous strata and horizontal strata. For composite strata, the stratum parameters are directly weighted averaged, which makes it difficult to reflect the differences in the physical and mechanical properties of different strata in the composite strata.

[0007] Therefore, how to incorporate the properties of the principal stress deflection of the inclined strata and the differences in the slip surface morphology in the composite strata into the vertical load estimation when the shield tunnel passes through the inclined composite strata has become a technical problem that technicians in this field urgently need to solve. Summary of the Invention

[0008] In view of the above-mentioned defects of the prior art, the present invention provides a method for estimating the vertical load when a shield tunnel passes through an inclined composite stratum. The purpose of the present invention is to incorporate the properties of the principal stress deflection of the inclined stratum and the differences in the slip surface morphology in the composite stratum into the vertical load estimation when the shield tunnel passes through the inclined composite stratum, so as to provide a reference for the design and construction of ultra-large diameter shield tunnels passing through the upper soft and lower hard composite stratum.

[0009] To achieve the above object, the present invention discloses a method for estimating vertical load when a shield tunnel passes through an inclined composite stratum; the method is characterized by comprising the following steps:

[0010] Step 1: Based on the survey data of the shield tunnel passing through the inclined composite stratum, the basic parameters of the shield tunnel and the geometric parameters and physical and mechanical property parameters of the inclined composite stratum are extracted, and after data standardization, a database is constructed in the shield machine PLC system;

[0011] Step 2: In the shield machine PLC system, the deflection angle calculation module is used to calculate the initial stress and principal stress deflection angle of the stratum under the inclined surface when it is only subjected to gravity, and the inclination angle of the slip surface above the tunnel after deflection is calculated;

[0012] Step 3: After establishing a geometric model of the shield tunnel passing through the inclined composite stratum, the geometric model is imported into the excavation influence width of the shield tunnel, and then the excavation influence width of the shield tunnel is calculated based on the broken line slip surface method;

[0013] Step 4: Import the standard data in the database and the geometric model into the model initialization module in the shield machine PLC system to initialize and form a calculation model;

[0014] Step 5: For the upper half of the calculation model, a differential equation for vertical stress is established using equilibrium conditions, and the boundary conditions are substituted to solve the vertical stress; for the lower half of the calculation model, the vertical load on the vault of the tunnel in inclined homogeneous strata is solved according to the vertical force balance.

[0015] Preferably, in step 1, the basic parameters of the shield tunnel in the database include the outer diameter of the lining, the buried depth of the arch and the ground overload, the geometric parameters of the inclined composite stratum include the stratum inclination angle and the thickness of each stratum, and the physical and mechanical property parameters of the inclined composite stratum include the density, internal friction angle, cohesion and Poisson's ratio of each stratum.

[0016] Preferably, in step 2, the working steps of the deflection angle calculation module are as follows:

[0017] Step 2.1, initial stress calculation: Specifically, calculate the initial stress of the inclined subsurface stratum of the inclined composite stratum when it is subjected only to gravity, and the calculation formula is as follows:

[0018]

[0019] Among them, σ x , σ y and τ xy are the horizontal stress, vertical stress, and shear stress of the point in the soil where the initial stress needs to be calculated, γ is the soil density, β is the stratum inclination, μ is the Poisson's ratio of the soil, and y is the vertical distance from the point in the soil where the initial stress needs to be calculated to the inclined surface;

[0020] Step 2.2, principal stress deflection angle calculation: Specifically, calculate the principal stress deflection angle of the inclined composite formation, and the calculation formula is as follows:

[0021]

[0022] Among them, α0 is the principal stress deflection angle;

[0023] Step 2.3, calculation of deflection inclination angle: specifically, calculating the inclination angle of the upper sliding surface of the shield tunnel after deflection, the calculation formula is as follows:

[0024]

[0025] Among them, θ1 and θ2 are the angles between the slip plane on one side and the slip plane on the other side and the vertical plane, is the internal friction angle of the soil.

[0026] More preferably, step 3 is as follows:

[0027] Step 3.1, calculation of the inclination angle of the slip surface; specifically, calculating the inclination angle of each segment of the broken line slip surface on both sides of the shield tunnel, the specific formula is as follows:

[0028]

[0029] Among them, α1, α2 and α3 are the inclination angles of each segment of the broken line slip surface on one side of the shield tunnel, and α1', α'2 and α3' are the inclination angles of each segment of the broken line slip surface on the other side of the tunnel. and is the internal friction angle of each stratum;

[0030] Step 3.2, calculate the position of the sliding surface on one side; specifically, calculate the distance B from the sliding surface on one side of the shield tunnel to the tunnel centerline after it extends to the ground surface. tR , the specific formula is as follows:

[0031] B tR =L0+L1+L2+L3;

[0032] in,

[0033]

[0034] Among them, B tR is the distance from the tunnel centerline after the sliding surface on one side of the shield tunnel extends to the ground surface, h1, h2 and h3 are the thickness of each layer at the tunnel centerline, H0, L0, L1, L2 and L3 are all geometric quantities in the calculation process, and R is the outer radius of the lining;

[0035] Step 3.3, calculate the position of the other side slip surface; specifically: calculate the distance B from the other side slip surface of the shield tunnel to the tunnel centerline after it extends to the ground surface tL ;

[0036] Step 3.4, calculating the width affected by the shield tunnel excavation; specifically, calculating the width affected by the shield tunnel excavation when passing through the inclined composite stratum, the specific formula is as follows:

[0037] 2B t =B tL +B tR

[0038] Among them, B t It is half of the affected width of the tunnel excavation.

[0039] More preferably, in step 4, during the initialization process by the model initialization module, the following initial boundary conditions are set: the shield tunnel is a shallow buried tunnel, the soil sliding surface is an inclined plane and extends to the ground surface, the sliding body is a rigid body and moves as a whole, and only moves within the plane; the ground surface is an inclined plane; there is no horizontal shear stress on the section parallel to the ground surface.

[0040] More preferably, step 5 is as follows:

[0041] Step 5.1, equation establishment; specifically, taking a differential thin layer in the upper half of the calculation model to establish the equilibrium equation;

[0042] Step 5.2, solving the equations; specifically, simplifying the equilibrium equations to obtain differential equations, substituting the boundary conditions into the equations, and solving for the vertical stress;

[0043] Step 5.3, vertical load calculation; specifically: according to the vertical balance of the lower half of the calculation model, solve the vertical load of the tunnel vault in inclined homogeneous strata.

[0044] More preferably, the vertical load on the vault of a tunnel in inclined homogeneous strata in step 5.3 is calculated as follows:

[0045]

[0046] Among them, q y is the vertical load on the tunnel vault, σ yGI is the vertical stress on the GI surface, w is the gravity of the lower half of the calculation model, σ bIJ and τ bIJ are the normal stress and shear stress on the IJ surface of the lower half of the calculation model, and c is the cohesion of the soil.

[0047] More preferably, if the vertical load on the top of the shield tunnel is linearly distributed in the horizontal direction and the distribution slope is the same as the surface slope, the vertical loads at the intermediate points are calculated by interpolation in step 5.3.

[0048] More preferably, the vertical loads at the intermediate points are calculated by interpolation using the following formula:

[0049]

[0050] Among them, q1 and q2 are the vertical loads on the left and right sides of the shield tunnel vault respectively.

[0051] Beneficial effects of the present invention:

[0052] The present invention incorporates the properties of the principal stress deflection of the inclined strata and the differences in the slip surface morphology in the composite strata into the vertical load estimation when the shield tunnel passes through the inclined composite strata, providing a reference for the design and construction of ultra-large diameter shield tunnels passing through the upper soft and lower hard composite strata.

[0053] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A schematic diagram of calculating the tunnel excavation-affected width according to an embodiment of the present invention is shown.

[0055] Figure 2 The figure shows a tunnel load calculation model in one embodiment of the present invention.

[0056] Figure 3 A schematic diagram of force analysis of the upper half of the model in one embodiment of the present invention is shown.

[0057] Figure 4 A schematic diagram of the force analysis of the lower half of the model in one embodiment of the present invention is shown.

[0058] Figure 5 A schematic diagram of the horizontal distribution of vertical load on the top of a tunnel in one embodiment of the present invention is shown.

[0059] Figure 6 A schematic cross-sectional view of a tunnel passing through an inclined composite stratum in one embodiment of the present invention is shown. DETAILED DESCRIPTION

[0060] Example

[0061] like Figures 1 to 6 As shown in FIG, a method for estimating vertical load when a shield tunnel passes through an inclined composite stratum is characterized by comprising the following steps:

[0062] Step 1: Based on the survey data of the shield tunnel passing through the inclined composite stratum, the basic parameters of the shield tunnel and the geometric parameters and physical and mechanical property parameters of the inclined composite stratum are extracted. After data standardization, a database is constructed in the shield machine PLC system;

[0063] Step 2: Calculate the initial stress and principal stress deflection angle of the stratum under the inclined surface when it is only subjected to gravity through the deflection angle calculation module, and calculate the inclination angle of the slip surface above the tunnel after deflection;

[0064] Step 3: After establishing a geometric model of the shield tunnel passing through the inclined composite stratum in the shield machine PLC system, the geometric model is imported into the shield tunnel excavation influence width, and then the shield tunnel excavation influence width is calculated based on the broken line sliding surface method;

[0065] Step 4: Import the standard data and geometric model in the database into the model initialization module in the shield machine PLC system to initialize and form a calculation model;

[0066] Step 5: For the upper part of the calculation model, use the equilibrium condition to establish the differential equation for vertical stress, and substitute the boundary conditions to solve the vertical stress; for the lower part of the calculation model, solve the vertical load of the tunnel vault in inclined homogeneous strata based on the vertical force balance.

[0067] The present invention takes into account the properties of principal stress deflection in inclined strata and the differences in slip surface morphology in composite strata, providing a reference for the design and construction of ultra-large diameter shield tunnels passing through composite strata with soft upper layers and hard lower layers.

[0068] In certain embodiments, in step 1, the basic parameters of the shield tunnel in the database include the outer diameter of the lining, the buried depth of the vault, and the ground overload; the geometric parameters of the inclined composite stratum include the inclination angle of the stratum and the thickness of each stratum; and the physical and mechanical property parameters of the inclined composite stratum include the density, internal friction angle, cohesion, and Poisson's ratio of each stratum.

[0069] In some embodiments, in step 2, the deflection angle calculation module operates as follows:

[0070] Step 2.1, initial stress calculation: Specifically, calculate the initial stress of the inclined subsurface stratum of the inclined composite stratum when it is subjected only to gravity. The calculation formula is as follows:

[0071]

[0072] Among them, σ x , σ y and τ xy are the horizontal stress, vertical stress, and shear stress of the point in the soil where the initial stress needs to be calculated, γ is the soil density, β is the stratum inclination, μ is the Poisson's ratio of the soil, and y is the vertical distance from the point in the soil where the initial stress needs to be calculated to the inclined surface;

[0073] Step 2.2: Calculate the principal stress deflection angle. Specifically, calculate the principal stress deflection angle of the inclined composite formation using the following formula:

[0074]

[0075] Among them, α0 is the principal stress deflection angle;

[0076] Step 2.3: Calculate the deflection inclination angle. Specifically, calculate the inclination angle of the upper sliding surface of the shield tunnel after deflection. The calculation formula is as follows:

[0077]

[0078] Among them, θ1 and θ2 are the angles between the slip plane on one side and the slip plane on the other side and the vertical plane, is the internal friction angle of the soil.

[0079] In some embodiments, step 3 is as follows:

[0080] Step 3.1: Calculate the inclination angle of the slip surface. Specifically, calculate the inclination angle of each segment of the broken-line slip surface on both sides of the shield tunnel. The specific formula is as follows:

[0081]

[0082] Among them, α1, α2 and α3 are the inclination angles of each segment of the broken line slip surface on one side of the shield tunnel (the right or left side in the figure), α1', α'2 and α3' are the inclination angles of each segment of the broken line slip surface on one side of the tunnel (the right or left side in the figure), and is the internal friction angle of each stratum;

[0083] Step 3.2: Calculate the position of the slip surface on one side of the shield tunnel (the right or left side in the figure) to calculate the distance B from the tunnel centerline after the slip surface on one side of the shield tunnel (the right or left side in the figure) extends to the ground surface. tR , the specific formula is as follows:

[0084] B tR =L0+L1+L2+L3;

[0085] in,

[0086]

[0087] Among them, B tR is the distance from the tunnel centerline after the sliding surface on one side of the shield tunnel (the right or left side in the figure) extends to the ground surface. h1, h2, and h3 are the thicknesses of the strata at the tunnel centerline. H0, L0, L1, L2, and L3 are all geometric quantities used in the calculation process. R is the outer radius of the lining.

[0088] Step 3.3: Calculate the position of the sliding surface on the other side of the shield tunnel (the left or right side in the figure) to calculate the distance B from the tunnel centerline after the sliding surface on the other side of the shield tunnel (the left or right side in the figure) extends to the ground surface. tL ;

[0089] Step 3.4: Calculate the affected width of shield tunnel excavation. Specifically, calculate the affected width of shield tunnel excavation when it passes through inclined composite strata. The specific formula is as follows:

[0090] 2B t =B tL +B tR

[0091] Among them, B t It is half of the affected width of the tunnel excavation.

[0092] In some embodiments, in step 4, during the initialization process by the model initialization module, the following initial boundary conditions are set: the shield tunnel is a shallow tunnel, the soil sliding surface is an inclined plane and extends to the ground surface, the sliding body is a rigid body and moves as a whole, and only moves within the plane; the ground surface is an inclined plane; and there is no horizontal shear stress on the section parallel to the ground surface.

[0093] In some embodiments, step 5 is as follows:

[0094] Step 5.1: Equation establishment: Specifically, take a differential thin layer in the upper half of the calculation model and establish the equilibrium equation;

[0095] Step 5.2: Solve the equations. Specifically, simplify the equilibrium equations to obtain differential equations, then substitute the boundary conditions to solve for the vertical stress.

[0096] Step 5.3: Calculate the vertical load. Specifically, calculate the vertical load on the vault of the tunnel in inclined homogeneous strata based on the vertical equilibrium of the lower half of the calculation model.

[0097] In some embodiments, the vertical load on the vault of a tunnel in inclined homogeneous strata in step 5.3 is calculated as follows:

[0098]

[0099] Among them, q y is the vertical load on the tunnel vault, σ yGI is the vertical stress on the GI surface, w is the gravity of the lower half of the calculation model, σ bIJ and τ bIJ is the normal stress and shear stress on the IJ surface of the lower half of the calculation model, and c is the cohesion of the soil.

[0100] In some embodiments, if the vertical load on the top of the shield tunnel is linearly distributed in the horizontal direction and the distribution slope is the same as the surface slope, the vertical loads at the intermediate points are calculated by interpolation in step 5.3.

[0101] In some embodiments, the formula for calculating the vertical load at each intermediate point by interpolation is as follows:

[0102]

[0103] Among them, q1 and q2 are the vertical loads on the left and right sides of the shield tunnel vault, respectively.

[0104] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A method for estimating vertical loads when a shield tunnel passes through inclined composite strata; characterized in that: The steps include: Step 1: Based on the survey data of the shield tunnel passing through the inclined composite stratum, the basic parameters of the shield tunnel and the geometric parameters and physical and mechanical property parameters of the inclined composite stratum are extracted, and after data standardization, a database is constructed in the shield machine PLC system; Step 2: Calculate the initial stress and principal stress deflection angle of the stratum under the inclined surface when it is only subjected to gravity through the deflection angle calculation module, and calculate the inclination angle of the slip surface above the tunnel after deflection; The working steps of the deflection angle calculation module are as follows: Step 2.1, initial stress calculation: Specifically, calculate the initial stress of the inclined subsurface stratum of the inclined composite stratum when it is subjected only to gravity, and the calculation formula is as follows: Among them, σ x , σ y and τ xy are the horizontal stress, vertical stress, and shear stress of the point in the soil where the initial stress needs to be calculated, γ is the soil density, β is the stratum inclination, μ is the Poisson's ratio of the soil, and y is the vertical distance from the point in the soil where the initial stress needs to be calculated to the inclined surface; Step 2.2, principal stress deflection angle calculation: Specifically, calculate the principal stress deflection angle of the inclined composite formation, and the calculation formula is as follows: Among them, α0 is the principal stress deflection angle; Step 2.3, calculation of deflection inclination angle: specifically, calculating the inclination angle of the upper sliding surface of the shield tunnel after deflection, the calculation formula is as follows: Among them, θ1 and θ2 are the angles between the slip plane on one side and the slip plane on the other side and the vertical plane, is the internal friction angle of the soil; Step 3: After establishing a geometric model of the shield tunnel passing through the inclined composite stratum in the shield machine PLC system, the geometric model is imported into the excavation influence width of the shield tunnel, and then the excavation influence width of the shield tunnel is calculated based on the broken line slip surface method; The specific steps are as follows: Step 3.1, calculation of the inclination angle of the slip surface; specifically, calculating the inclination angle of each segment of the broken line slip surface on both sides of the shield tunnel, the specific formula is as follows: Among them, α1, α2 and α3 are the inclination angles of each segment of the broken line slip surface on one side of the shield tunnel, α1', α'2 and α3' are the inclination angles of each segment of the broken line slip surface on one side of the tunnel, and is the internal friction angle of each stratum; Step 3.2, calculate the position of the sliding surface on one side; specifically, calculate the distance B from the sliding surface on one side of the shield tunnel to the tunnel centerline after it extends to the ground surface. tR , the specific formula is as follows: <h2 style=";text-align:left;direction:ltr">B<h2 style=";text-align:left;direction:ltr"> tR <h2 style=";text-align:left;direction:ltr"> =L0+L1+L2+L3; in, Among them, B tR is the distance from the tunnel centerline after the sliding surface on one side of the shield tunnel extends to the ground surface, h1, h2 and h3 are the thickness of each layer at the tunnel centerline, H0, L0, L1, L2 and L3 are all geometric quantities in the calculation process, and R is the outer radius of the lining; Step 3.3, calculate the position of the other side slip surface; specifically: calculate the distance B from the other side slip surface of the shield tunnel to the tunnel centerline after it extends to the ground surface tL ; Step 3.4, calculating the width affected by the shield tunnel excavation; specifically, calculating the width affected by the shield tunnel excavation when passing through the inclined composite stratum, the specific formula is as follows: 2B t =B tL +B tR Among them, B t half of the affected width of the tunnel excavation; Step 4: Import the standard data in the database and the geometric model into the model initialization module in the shield machine PLC system to initialize and form a calculation model; Step 5: For the upper half of the calculation model, establish a differential equation for vertical stress using equilibrium conditions, and substitute the boundary conditions to solve for the vertical stress; for the lower half of the calculation model, solve the vertical load on the vault of the tunnel in inclined homogeneous strata based on vertical force balance; The specific steps are as follows: Step 5.1, equation establishment; specifically, taking a differential thin layer in the upper half of the calculation model to establish the equilibrium equation; Step 5.2, solving the equations; specifically, simplifying the equilibrium equations to obtain differential equations, substituting the boundary conditions into the equations, and solving for the vertical stress; Step 5.3, vertical load calculation; specifically: according to the vertical balance of the lower half of the calculation model, solve the vertical load of the tunnel vault in inclined homogeneous strata.

2. The vertical load estimation method for a shield tunnel passing through an inclined composite stratum according to claim 1 is characterized in that: In step 1, the basic parameters of the shield tunnel in the database include the outer diameter of the lining, the buried depth of the vault and the ground overload, the geometric parameters of the inclined composite stratum include the stratum inclination angle and the thickness of each stratum, and the physical and mechanical property parameters of the inclined composite stratum include the density, internal friction angle, cohesion and Poisson's ratio of each stratum.

3. The method for estimating vertical load when a shield tunnel passes through an inclined composite stratum according to claim 1 is characterized in that: In step 4, during the initialization process by the model initialization module, the following initial boundary conditions are set: the shield tunnel is a shallow tunnel, the soil slip surface is an inclined plane and extends to the ground surface, the sliding body is a rigid body and moves as a whole, and only moves within the plane; the ground surface is an inclined plane; and there is no horizontal shear stress on the section parallel to the ground surface.

4. The method for estimating vertical load when a shield tunnel passes through an inclined composite stratum according to claim 1 is characterized in that: The calculation method for the vertical load on the vault of a tunnel in inclined homogeneous strata in step 5.3 is as follows: Among them, q y is the vertical load on the tunnel vault, σ yGI is the vertical stress on the GI surface, w is the gravity of the lower half of the calculation model, σ bIJ and τ bIJ are the normal stress and shear stress on the IJ surface of the lower half of the calculation model, and c is the cohesion of the soil.

5. The method for estimating vertical load when a shield tunnel passes through an inclined composite stratum according to claim 4 is characterized in that: If the vertical load on the top of the shield tunnel is linearly distributed in the horizontal direction and the distribution slope is the same as the surface slope, the vertical loads at the intermediate points are calculated by interpolation in step 5.

3.

6. The method for estimating vertical load when a shield tunnel passes through an inclined composite stratum according to claim 5 is characterized in that: The formula for calculating the vertical load at each intermediate point by interpolation is as follows: Among them, q1 and q2 are the vertical loads on the left and right sides of the shield tunnel vault respectively.

Images