Method for predicting vertical deformation of soil body caused by axial friction force of shield shell

Abstract

The invention discloses a method for predicting vertical deformation of a soil body caused by axial friction force of a shield shell, which comprises the following steps of: S1, establishing a space rectangular coordinate system, and constructing a space curve shield tunnel calculation model according to the tunneling attitude of a shield tunneling machine; s2, assuming that the shield tunneling machine has pitching with an angle of beta, and obtaining a space parameter equation of a contact surface of a shield shell and a soil body; and S3, calculating the axial friction force f2 of the shield shell, the direction vector # imgabs0 # of the excavation face and the direction vector # imgabs1 # of the plane where the shield tail rear outlet is located, and decomposing the axial friction force f2 of the shield shell according to the shield head direction vector and the shield tail direction vector to obtain the vertical soil body loss WAT caused by the fact that each component force of the axial friction force f2 of the shield shell acts on the shield shell rear soil body. The method has the advantages that the vertical deformation of the soil body caused by the axial friction force of the shield shell is predicted, and reference is provided for actual tunnel construction.

Description

Technical Field

[0001] The invention belongs to the technical field of tunnel engineering, and in particular relates to a method for predicting vertical deformation of soil caused by axial friction of a shield. Background Art

[0002] Shield construction has the advantages of little interference with urban ground traffic, short construction period, and adaptability to complex and changeable underground environments. It is currently the preferred construction method for urban tunnels. With the continuous development of underground space and the further improvement of tunnel selection requirements, more and more space arc shield tunnels are designed and constructed. The construction of space line shield tunnels is more difficult and the impact on the ground is more complicated. In order to ensure that the shield machine excavates according to the predetermined space axis, the attitude control requirements of the shield machine are also relatively high. These are the main problems in space line shield construction.

[0003] The main factors that affect soil settlement during shield construction are soil loss and construction load. Soil loss mainly comes from the integration gap at the shield tail, and there is also an over-excavation gap in the small radius turning section. The construction loads with greater influence include: additional front thrust, axial friction of the shield shell on the soil, and grouting pressure at the shield tail.

[0004] In view of the axial friction force of the shield on the soil, a method for predicting the vertical deformation of the soil caused by the axial friction force of the shield is needed. Summary of the invention

[0005] The purpose of the present invention is to provide a method for predicting the vertical deformation of soil caused by the axial friction of the shield based on the deficiencies of the above-mentioned prior art. By analyzing the influence of horizontal yaw, vertical pitch and curvature radius changes on the termination surface of the abnormal excavation section, the vertical soil loss caused by the components of the axial friction of the shield acting on the soil behind the shield is obtained, thereby realizing the prediction of the vertical deformation of the soil caused by the axial friction of the shield and providing a reference for actual tunnel construction.

[0006] The purpose of the present invention is achieved by the following technical solutions:

[0007] A method for predicting vertical deformation of soil caused by axial friction of a shield shell, the method comprising the following steps:

[0008] S1: Establish a spatial rectangular coordinate system and construct a spatial curved shield tunnel calculation model based on the tunneling posture of the shield machine;

[0009] The coordinate origin O, the x-axis and the y-axis in the spatial rectangular coordinate system are all located on the surface of the earth, and the z-axis is vertically downward;

[0010] Assume that the shield machine is located at a depth of h underground, starts from the negative half-axis of the y-axis, and turns right with a curvature radius of Q to excavate; the shield machine excavates to the xOz surface, at which time the horizontal yaw, vertical pitch and curvature radius change, and the shield machine enters the abnormal excavation section from the normal excavation section;

[0011] S2: Assuming that the shield machine has a pitch angle of β, obtain the spatial parameter equation of the contact surface between the shield shell and the soil;

[0012] Among them, the spatial parameter equation of the contact surface between the shield and the soil is:

[0013]

[0014] Where R is the radius of the shield machine;

[0015] It is the angle between any point on the shield shell of the shield machine and the vertical line connecting the central axis of the shield machine and the x-axis;

[0016] φ is the angle range of the shield machine in the tunnel, and its value is:

[0017] φ∈[θ s -α-θ L ,θ s -α];

[0018] Among them, the length occupied by the shield machine is converted into an angle θ L for: L is the length of the shield machine, Q yaw is the curvature radius of the shield machine during the excavation process of the abnormal excavation section; α is the yaw angle of the shield machine; θ s is the rotation angle of the shield machine during the excavation process of the abnormal excavation section;

[0019] S3: Calculate the axial friction force f2 of the shield and the direction vector of the excavation surface and the direction vector of the plane where the shield tail exit is located The shield axial friction force f2 is decomposed according to the shield head direction vector and the shield tail direction vector, and the vertical soil loss W caused by the components of the shield axial friction force f2 acting on the soil behind the shield is obtained. AT ;

[0020] Among them, according to engineering experience, the axial friction force of the shield shell should take into account the softening effect of the soil interface caused by the shield excavation of the soil. The actual f2 calculation formula is:

[0021]

[0022] In the formula, β s It represents the soil softening coefficient; represents the radial normal stress acting on the shield; δ is the friction angle between the shield and the soil interface;

[0023] Calculate the excavation face direction vector for:

[0024]

[0025] The calculated direction vector of the plane where the shield tail rear exit is located is:

[0026]

[0027] The shield shell axial friction force f2 is decomposed according to the shield head direction vector and the shield tail direction vector:

[0028]

[0029] In the formula, f 2，head，x 、f 2，head，y and f 2，head，z represents the components of f2 in the x, y and z directions when the central section of the shield head is taken as the control section, f 2，tail，x 、f 2，tail，y and f 2，tail，z It represents the components of f2 in the x, y and z directions when the central section of the shield tail is taken as the control section;

[0030] The vertical soil loss caused by the components of the shield axial friction force f2 acting on the soil behind the shield is:

[0031]

[0032] Where:

[0033] ω x is the thickness of the over-excavation layer in the x-axis direction, ω y is the thickness of the over-excavation layer in the y-axis direction, ω z is the thickness of the over-excavation layer in the z-axis direction;

[0034]

[0035] Soil softening coefficient β s The value of is between 0.83 and 0.97; the radial normal stress acting on the shield In the formula, horizontal earth pressure σ h =K0σ v , vertical earth pressure K0 is the lateral static earth pressure coefficient, γ is the soil bulk density; the value of δ is between 6.5° and 9°.

[0036] ω x ,ω y and ωz This is a rewrite of the classic Mindlin displacement solution, that is, the point of action of the concentrated force F (0,0,c) is changed to an arbitrary point (x0,y0,z0), and the vertical displacement calculation formula of a point (x,y,z) in the soil body caused by a unit force acting on an arbitrary point (x0,y0,z0) in the semi-infinite elastic body along the positive direction of the x,y and z axes is obtained:

[0037]

[0038] In the formula, G is the shear elastic modulus, μ is the Poisson's ratio, r is the distance between point (x, y, z) and point (x0, y0, z0), is the distance between the point (x,y,z) and the point (x0,y0,–z0).

[0039] The advantages of the present invention are as follows: by analyzing the influence of horizontal yaw, vertical pitch and curvature radius change on the termination surface of the abnormal excavation section, the vertical soil loss caused by the components of the axial friction force of the shield acting on the soil behind the shield is obtained, the vertical deformation of the soil caused by the axial friction force of the shield is predicted, and a reference is provided for actual tunnel construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a simplified schematic diagram of the axial friction force of the shield shell in the present invention. DETAILED DESCRIPTION

[0041] The features of the present invention and other related features are further described in detail below through embodiments in conjunction with the accompanying drawings to facilitate understanding by those skilled in the art:

[0042] Example: Figure 1 As shown, this embodiment specifically relates to a method for predicting the vertical deformation of soil caused by the axial friction of the shield, and the prediction method mainly includes the following steps:

[0043] S1: Establish a spatial rectangular coordinate system and construct a spatial curved shield tunnel calculation model based on the tunneling posture of the shield machine.

[0044] Among them, the coordinate origin O, the x-axis and the y-axis in the spatial rectangular coordinate system are all located on the surface, and the z-axis is vertically downward. Assume that the shield machine is located at a depth of h underground, starting from the negative half-axis part of the y-axis (normal excavation section), and excavating with a curvature radius Q to the right; the shield machine excavates to the xOz surface, that is, when y=0, it reaches the end point of the normal excavation surface, at which time the horizontal yaw, vertical pitch and curvature radius change, and the shield machine enters the abnormal excavation section from the normal excavation section.

[0045] S2: Since the horizontal yaw and the change of curvature radius have no effect on the excavation posture in the vertical direction, only the translation action in the three-dimensional rectangular coordinate system is required, so only the shield shell and soil contact surface equation in the pitch state is analyzed. When the pitch action occurs, the contact surface between the shield shell and the soil can actually be regarded as a space circle doing a stable spiral motion around the z-axis. Assuming that the shield machine pitches at an angle of β, the spatial parameter equation of the contact surface between the shield shell and the soil is obtained.

[0046] Among them, the spatial parameter equation of the contact surface between the shield and the soil is:

[0047]

[0048] Where R is the radius of the shield machine;

[0049] It is the angle between any point on the shield shell of the shield machine and the vertical line connecting the central axis of the shield machine and the x-axis;

[0050] φ is the angle range of the shield machine in the tunnel, and its value is:

[0051] φ∈[θ s -α-θ L ,θ s -α];

[0052] Among them, the length occupied by the shield machine is converted into an angle θ L for: L is the length of the shield machine, Q yaw is the curvature radius of the shield machine during the excavation process of the abnormal excavation section; α is the yaw angle of the shield machine; θ s It is the rotation angle of the shield machine during the excavation process in the abnormal excavation section.

[0053] S3: Calculate the axial friction force f2 of the shield and the direction vector of the excavation surface and the direction vector of the plane where the shield tail exit is located The shield axial friction force f2 is decomposed according to the shield head direction vector and the shield tail direction vector, and the vertical soil loss W caused by the components of the shield axial friction force f2 acting on the soil behind the shield is obtained. AT .

[0054] Among them, according to engineering experience, the axial friction force of the shield shell should take into account the softening effect of the soil interface caused by the shield excavation of the soil. The actual f2 calculation formula is:

[0055]

[0056] In the formula, β s Indicates the soil softening coefficient, soil softening coefficient β s The values ​​of range from 0.83 to 0.97; Represents the radial normal stress acting on the shield shell. In the formula, horizontal earth pressure σ h =K0σ v , vertical earth pressure K0 is the lateral static earth pressure coefficient, γ is the soil bulk density; δ is the friction angle between the shield and the soil, and the value of δ is between 6.5° and 9°.

[0057] like Figure 1 As shown in the figure, since the normal vector of the excavation face is constantly changing during the shield tunneling process, a simplified calculation is performed, and the friction force of the shield machine on the soil behind the shield shell wall is considered to be completely generated by the entire shield shell. The following assumptions are made: the length of the shield machine is L, and the shield machine is divided into a shield head and a shield tail with equal lengths. Both sections are right cylinders. Due to the existence of the connection device, there is a certain angle deviation between the shield head and the shield tail during the curved shield process. The direction vector of the shield head is controlled by the abnormal shield end surface, and the direction vector of the shield tail is determined by the direction vector of the plane where the rear exit of the shield tail is located.

[0058] Calculate the excavation face direction vector for:

[0059]

[0060] The calculated direction vector of the plane where the shield tail rear exit is located is:

[0061]

[0062] The shield shell axial friction force f2 is decomposed according to the shield head direction vector and the shield tail direction vector:

[0063]

[0064]

[0065] In the formula, f 2，head，x 、f 2，head，y and f 2，head，z represents the components of f2 in the x, y and z directions when the central section of the shield head is taken as the control section, f 2，tail，x 、f 2，tail，y and f 2，tail，z It represents the components of f2 in the x, y and z directions when the central section of the shield tail is taken as the control section;

[0066] The vertical soil loss caused by the components of the shield axial friction force f2 acting on the soil behind the shield is:

[0067]

[0068] Where:

[0069]

[0070] ω x is the thickness of the over-excavation layer in the x-axis direction, ω y is the thickness of the over-excavation layer in the y-axis direction, ω z is the thickness of the over-excavation layer in the z-axis direction; ω x ,ω y and ω z This is a rewrite of the classic Mindlin displacement solution, that is, the point of action of the concentrated force F (0,0,c) is changed to an arbitrary point (x0,y0,z0), and the vertical displacement calculation formula of a point (x,y,z) in the soil body caused by a unit force acting on an arbitrary point (x0,y0,z0) in the semi-infinite elastic body along the positive direction of the x,y and z axes is obtained:

[0071]

[0072]

[0073] In the formula, G is the shear elastic modulus, μ is the Poisson's ratio, r is the distance between point (x, y, z) and point (x0, y0, z0), is the distance between the point (x,y,z) and the point (x0,y0,–z0).

[0074] The beneficial effect of this embodiment is that by analyzing the influence of horizontal yaw, vertical pitch and curvature radius changes on the termination surface of the abnormal excavation section, the vertical soil loss caused by the components of the axial friction force of the shield acting on the soil behind the shield is obtained, and the vertical deformation of the soil caused by the axial friction force of the shield is predicted, which provides a reference for actual tunnel construction.

Claims

1. A method for predicting the vertical deformation of soil caused by the axial friction of the shield, characterized in that The prediction method comprises the following steps: S1: Establish a spatial rectangular coordinate system and construct a spatial curved shield tunnel calculation model based on the tunneling posture of the shield machine; The coordinate origin O, the x-axis and the y-axis in the spatial rectangular coordinate system are all located on the surface of the earth, and the z-axis is vertically downward; Assume that the shield machine is located at a depth of h underground, starts from the negative half-axis of the y-axis, and turns right with a curvature radius of Q to excavate; the shield machine excavates to the xOz surface, at which time the horizontal yaw, vertical pitch and curvature radius change, and the shield machine enters the abnormal excavation section from the normal excavation section; S2: Assuming that the shield machine has a pitch angle of β, obtain the spatial parameter equation of the contact surface between the shield shell and the soil; Among them, the spatial parameter equation of the contact surface between the shield and the soil is: Where R is the radius of the shield machine; It is the angle between any point on the shield shell of the shield machine and the vertical line connecting the central axis of the shield machine and the x-axis; φ is the angle range of the shield machine in the tunnel, and its value is: φ∈[θ s -a-i L ,i s -a]; Among them, the length occupied by the shield machine is converted into an angle θ L for: L is the length of the shield machine, Q yaw is the curvature radius of the shield machine during the excavation process of the abnormal excavation section; α is the yaw angle of the shield machine; θ s is the rotation angle of the shield machine during the excavation process of the abnormal excavation section; S3: Calculate the axial friction force f2 of the shield and the direction vector of the excavation surface and the direction vector of the plane where the shield tail exit is located The shield axial friction force f2 is decomposed according to the shield head direction vector and the shield tail direction vector, and the vertical soil loss W caused by the components of the shield axial friction force f2 acting on the soil behind the shield is obtained. AT ; Among them, according to engineering experience, the axial friction force of the shield shell should take into account the softening effect of the soil interface caused by the shield excavation of the soil. The actual f2 calculation formula is: In the formula, β s It represents the soil softening coefficient; represents the radial normal stress acting on the shield; δ is the friction angle between the shield and the soil interface; Calculate the excavation face direction vector for: The calculated direction vector of the plane where the shield tail rear exit is located is: The shield shell axial friction force f2 is decomposed according to the shield head direction vector and the shield tail direction vector: In the formula, f 2，head，x 、f 2，head，y and f 2，head，z represents the components of f2 in the x, y and z directions when the central section of the shield head is taken as the control section, f 2，tail，x 、f 2，tail，y and f 2，tail，z It represents the components of f2 in the x, y and z directions when the central section of the shield tail is taken as the control section; The vertical soil loss caused by the components of the shield axial friction force f2 acting on the soil behind the shield is: Where: ω x is the thickness of the over-excavation layer in the x-axis direction, ω y is the thickness of the over-excavation layer in the y-axis direction, ω z is the thickness of the over-excavation layer in the z-axis direction; 2. The method for predicting the vertical deformation of soil caused by the axial friction of the shield according to claim 1 is characterized in that Soil softening coefficient β s The value of is between 0.83 and 0.97; the radial normal stress acting on the shield In the formula, horizontal earth pressure σ h =K0σ v , vertical earth pressure K0 is the lateral static earth pressure coefficient, γ is the soil bulk density; the value of δ is between 6.5° and 9°.

3. The method for predicting the vertical deformation of soil caused by the axial friction of the shield according to claim 1 is characterized in that ω x ,ω y and ω z This is a rewrite of the classic Mindlin displacement solution, that is, the point of action of the concentrated force F (0,0,c) is changed to an arbitrary point (x0,y0,z0), and the vertical displacement calculation formula of a point (x,y,z) in the soil body caused by a unit force acting on an arbitrary point (x0,y0,z0) in the semi-infinite elastic body along the positive direction of the x,y and z axes is obtained: In the formula, G is the shear elastic modulus, μ is the Poisson's ratio, r is the distance between the point (x, y, z) and the point (x0, y0, z0), is the distance between the point (x,y,z) and the point (x0,y0,–z0).

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