Method for predicting soil body vertical deformation caused by space curve shield excavation face thrust

Abstract

The invention discloses a method for predicting soil body vertical deformation caused by space curve shield excavation face thrust, which comprises the following steps: 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, analyzing the influence of horizontal yawing, vertical pitching and curvature radius change on the termination surface of the abnormal tunneling section, determining the center coordinate C = (a, b, c) of the termination surface of the abnormal tunneling section and an excavation surface direction vector # imgabs0 #, and obtaining a circular surface space parameter equation; and S3, according to the tunnel face direction vector, the shield excavation face thrust f1 is decomposed, and vertical soil mass loss WAT caused by the fact that all component forces of the shield excavation face thrust f1 act on the tunnel face is obtained. The method has the advantages that the prediction of the vertical deformation of the soil body caused by the thrust of the space curve shield excavation face is realized, and a 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 thrust of an excavation face of a space curved 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 additional frontal thrust, a method for predicting the vertical deformation of soil caused by the thrust of the excavation face of a spatial curved 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 thrust of the excavation face of a spatial curved shield machine based on the above-mentioned deficiencies in the prior art. By analyzing the influence of the horizontal yaw, vertical pitch and curvature radius changes on the termination surface of the abnormal excavation section, the vertical soil loss caused by the various components of the thrust of the excavation face of the shield machine acting on the heading face is obtained, thereby realizing the prediction of the vertical deformation of soil caused by the thrust of the excavation face of the spatial curved shield machine, 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 soil vertical deformation caused by thrust of a space curved shield excavation face, 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: Analyze the influence of horizontal yaw, vertical pitch and curvature radius change on the termination surface of abnormal excavation section, and determine the center coordinates C = (a, b, c) of the termination surface of abnormal excavation section and the excavation surface direction vector And obtain the spatial parameter equation of the circular surface;

[0012] Among them, the coordinates of the center of the termination surface C = (a, b, c) are:

[0013]

[0014] In the formula, 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 of the abnormal excavation section, and β is the pitch angle of the shield machine;

[0015] Excavation face direction vector for:

[0016]

[0017] The spatial parameter equation of the circular surface is:

[0018]

[0019] Where r is the distance between point (x, y, z) and point (x0, y0, z0), point (x0, y0, z0) is the modified coordinate of the point (0, 0, c) where the concentrated force F acts; t is the arc of the circular surface;

[0020] S3: Decompose the thrust f1 of the shield excavation face according to the direction vector of the tunnel face to obtain the vertical soil loss W caused by the components of the thrust f1 of the shield excavation face acting on the tunnel face AT ;

[0021] Among them, the tunnel face direction vector decomposes the shield excavation face thrust f1 into:

[0022]

[0023] In the formula, f 1x 、f 1y and f 1z represents the components of f1 in the x, y and z directions;

[0024] The vertical soil loss W caused by the thrust f1 components of the shield excavation face acting on the tunnel face AT :

[0025]

[0026] Where:

[0027] 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;

[0028]

[0029] The position change of the center of the termination surface after horizontal yaw is as follows:

[0030] Horizontal yaw only affects the x and y values ​​of the center of the termination surface. The coordinates of the predetermined center C are known to be (Q·cosθ s ,Q·sinθ s ,h), take point O'=(0,0,h), then Rotate the vector around the z axis by an angle of α. The rotation axis point of the abnormal excavation section after horizontal deviation is P = (QQ·cosα,Q·sinα,h). The starting point is translated to point P, and the center position of the end surface after horizontal yaw is (QQ·cosα+Q·cos(θ s -α),Q·sinα+Q·sin(θ s -α),h).

[0031] The position change of the center of the termination surface after vertical pitch is as follows:

[0032] Horizontal pitching will only cause the center of the end surface to change in the vertical direction; in the abnormal excavation section, the shield machine has a pitch of β, and every rotation of θ around the rotation axis s , that is, dig forward θ s The distance Q will cause the center of the termination surface to change in the vertical direction by θ s ·Q·sinβ.

[0033] After the radius of curvature changes, the position of the center of the termination surface changes as follows:

[0034] The change in the curvature radius only affects the x and y values ​​of the center of the termination surface. When the curvature radius changes, the center of the termination surface after the curvature radius changes is translated to the origin, and the rotation θ is calculated. s After the center of the terminal surface reaches the point, the center of the terminal surface is restored, and the coordinates of the center of the terminal surface after the curvature radius changes are obtained as (Qyaw ·cosθ s +QQ yaw ,Q yaw sinθ s ,h).

[0035] When horizontal yaw and curvature radius change simultaneously, the position of the center of the termination surface changes as follows:

[0036] Translate the rotation axis after the curvature radius changes to the origin, and then calculate the rotation θ s The center of the final surface reaches the point, and the center of the final surface after the curvature radius changes is I. The specific coordinates of I are (Q yaw ·cosθ s ,Q yaw sinθ s ,h), then Rotate the vector around the z axis by an angle of α.

[0037] The rotation axis point after horizontal yaw is P'=(Q yaw -Q yaw ·cosα,Q yaw ·sinα,h), then the coordinate position of the center of the termination surface after horizontal yaw is:

[0038] (Q yaw -Q yaw ·cosα+Q yaw ·cos(θ s -α),Q yaw ·sinα+Q yaw ·sin(θ s -α),h);

[0039] The center of the termination surface after horizontal yaw is translated to the origin, and the coordinates of the center of the termination surface after translation to the origin are:

[0040] (Q yaw -Q yaw ·cosα+Q yaw ·cos(θ s -α)+QQ yaw ,Q yaw ·sinα+Q yaw ·sin(θ s -α),h).

[0041] ω x ,ω y and ω zThis 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:

[0042]

[0043]

[0044] 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).

[0045] 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 thrust components of the shield excavation face acting on the heading face is obtained, and the vertical deformation of the soil caused by the thrust of the spatial curved shield excavation face is predicted, providing a reference for actual tunnel construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a schematic diagram of the position change of the center of the termination surface after horizontal yaw in the present invention;

[0047] Figure 2 It is a schematic diagram of the position change of the center of the termination surface after the radius of curvature is changed in the present invention;

[0048] Figure 3 It is a schematic diagram of the position change of the center of the termination surface when the horizontal yaw and the change of the curvature radius occur simultaneously in the present invention. DETAILED DESCRIPTION

[0049] 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:

[0050] Example: Figure 1-3 As shown, this embodiment specifically relates to a method for predicting the vertical deformation of soil caused by the thrust of the excavation face of a space curved shield, and the prediction method mainly includes the following steps:

[0051] 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.

[0052] 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.

[0053] S2: Analyze the influence of horizontal yaw, vertical pitch and curvature radius change on the termination surface of abnormal excavation section, and determine the center coordinates C = (a, b, c) of the termination surface of abnormal excavation section and the excavation surface direction vector And obtain the spatial parameter equation of the circular surface.

[0054] Among them, Figure 1 As shown in the figure, the position change of the center of the termination surface after horizontal yaw is as follows:

[0055] Horizontal yaw only affects the x and y values ​​of the center of the termination surface. The coordinates of the predetermined center C are known to be (Q·cosθ s ,Q·sinθ s ,h), take point O'=(0,0,h), then Rotate the vector around the z axis by an angle of α. The rotation axis point of the abnormal excavation section after horizontal deviation is P = (QQ·cosα,Q·sinα,h). The starting point is translated to point P, and the center position of the end surface after horizontal yaw is (QQ·cosα+Q·cos(θ s -α),Q·sinα+Q·sin(θ s -α),h).

[0056] The position change of the center of the termination surface after vertical pitch is as follows:

[0057] Horizontal pitching will only cause the center of the end surface to change in the vertical direction; in the abnormal excavation section, the shield machine has a pitch of β, and every rotation of θ around the rotation axis s , that is, dig forward θ s The distance Q will cause the center of the termination surface to change in the vertical direction by θ s ·Q·sinβ.

[0058] like Figure 2 As shown in the figure, the position of the center of the termination surface changes as follows after the radius of curvature changes:

[0059] The change in the curvature radius only affects the x and y values ​​of the center of the termination surface. When the curvature radius changes, the center of the termination surface after the curvature radius changes is translated to the origin, and the rotation θ is calculated. sAfter the center of the terminal surface reaches the point, the center of the terminal surface is restored, and the coordinates of the center of the terminal surface after the curvature radius changes are obtained as (Q yaw ·cosθ s +QQ yaw ,Q yaw sinθ s ,h).

[0060] like Figure 3 As shown in the figure, when the horizontal yaw and the curvature radius change simultaneously, the position of the center of the termination surface changes as follows:

[0061] Translate the rotation axis after the curvature radius changes to the origin, and then calculate the rotation θ s The center of the final surface reaches the point, and the center of the final surface after the curvature radius changes is I. The specific coordinates of I are (Q yaw ·cosθ s ,Q yaw sinθ s ,h), then Rotate the vector around the z axis by an angle of α.

[0062] The coordinates of the center of the termination surface C = (a, b, c) are:

[0063]

[0064] In the formula, 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 of the abnormal excavation section, and β is the pitch angle of the shield machine.

[0065] Excavation face direction vector for:

[0066]

[0067] The spatial parameter equation of the circular surface is:

[0068]

[0069] In the formula, r is the distance between point (x, y, z) and point (x0, y0, z0), point (x0, y0, z0) is the modified coordinate of the point (0, 0, c) where the concentrated force F acts; t is the arc of the circular surface;

[0070] S3: Decompose the thrust f1 of the shield excavation face according to the direction vector of the tunnel face to obtain the vertical soil loss W caused by the components of the thrust f1 of the shield excavation face acting on the tunnel face AT ;

[0071] Among them, the tunnel face direction vector decomposes the shield excavation face thrust f1 into:

[0072]

[0073] In the formula, f 1x 、f 1y and f 1z represents the components of f1 in the x, y and z directions;

[0074] The vertical soil loss W caused by the thrust f1 components of the shield excavation face acting on the tunnel face AT :

[0075]

[0076] Where:

[0077] 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:

[0078]

[0079] 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 point (x,y,z) and point (x0,y0,–z0);

[0080]

[0081] 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 thrust components of the shield excavation face acting on the heading face is obtained, and the vertical deformation of the soil caused by the thrust of the spatial curved shield excavation face is predicted, which provides a reference for actual tunnel construction.

Claims

1. A method for predicting the vertical deformation of soil caused by the thrust of the excavation face of a space curved shield machine, 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: Analyze the influence of horizontal yaw, vertical pitch and curvature radius change on the termination surface of abnormal excavation section, and determine the center coordinates C = (a, b, c) of the termination surface of abnormal excavation section and the excavation face direction vector And obtain the spatial parameter equation of the circular surface; Among them, the coordinates of the center of the termination surface C = (a, b, c) are: In the formula, 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, and θ s is the rotation angle of the shield machine during the excavation of the abnormal excavation section, and β is the pitch angle of the shield machine; Excavation face direction vector for: The spatial parameter equation of the circular surface is: Where r is the distance between point (x, y, z) and point (x0, y0, z0), point (x0, y0, z0) is the modified coordinate of the point (0, 0, c) where the concentrated force F acts; t is the arc of the circular surface; S3: Decompose the thrust f1 of the shield excavation face according to the direction vector of the tunnel face to obtain the vertical soil loss W caused by the components of the thrust f1 of the shield excavation face acting on the tunnel face AT ; Among them, the tunnel face direction vector decomposes the shield excavation face thrust f1 into: In the formula, f 1x 、f 1y and f 1z represents the components of f1 in the x, y and z directions; The vertical soil loss W caused by the thrust f1 components of the shield excavation face acting on the tunnel face AT : 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 soil vertical deformation caused by thrust of space curved shield excavation face according to claim 1 is characterized in that The position change of the center of the termination surface after horizontal yaw is as follows: Horizontal yaw only affects the x and y values ​​of the center of the termination surface. The coordinates of the predetermined center C are known to be (Q·cosθ s ,Q·sinθ s ,h), take point O'=(0,0,h), then Rotate the vector around the z axis by an angle of α. The rotation axis point of the abnormal excavation section after horizontal deviation is P = (QQ·cosα,Q·sinα,h). The starting point is translated to point P, and the center position of the end surface after horizontal yaw is (QQ·cosα+Q·cos(θ s -α),Q·sinα+Q·sin(θ s -α),h).

3. The method for predicting the vertical deformation of soil caused by the thrust of the excavation face of a space curved shield according to claim 1 is characterized in that The position change of the center of the termination surface after vertical pitch is as follows: Horizontal pitching will only cause the center of the end surface to change in the vertical direction; in the abnormal excavation section, the shield machine has a pitch of β, and every rotation of θ around the rotation axis s , that is, dig forward θ s The distance Q will cause the center of the end surface to change in the vertical direction by θ s ·Q·sinβ.

4. The method for predicting vertical deformation of soil caused by thrust of excavation face of space curved shield according to claim 2 is characterized in that After the radius of curvature changes, the position of the center of the termination surface changes as follows: The change in the radius of curvature only affects the x and y values ​​of the center of the end surface. When the radius of curvature changes, the center of the end surface after the radius of curvature changes is translated to the origin, and the rotation θ is calculated. s After the center of the terminal surface reaches the point, the center of the terminal surface is restored, and the coordinates of the center of the terminal surface after the curvature radius changes are obtained as (Q yaw ·cosθ s +QQ yaw ,Q yaw sinθ s ,h).

5. The method for predicting soil vertical deformation caused by thrust of space curved shield excavation face according to claim 4 is characterized in that When horizontal yaw and curvature radius change simultaneously, the position of the center of the termination surface changes as follows: Translate the rotation axis after the curvature radius changes to the origin, and then calculate the rotation θ s The center of the final surface reaches the point, and the center of the final surface after the curvature radius changes is I. The specific coordinates of I are (Q yaw ·cosθ s ,Q yaw sinθ s ,h), then Rotate the vector around the z axis by an angle of α. The rotation axis point after horizontal yaw is P'=(Q yaw -Q yaw ·cosα,Q yaw ·sinα,h), then the coordinate position of the center of the termination surface after horizontal yaw is: (Q yaw -Q yaw ·cosα+Q yaw ·cos(θ s -a),Q yaw ·sinα+Q yaw ·sin(θ s -a),h); The center of the termination surface after horizontal yaw is translated to the origin, and the coordinates of the center of the termination surface after translation to the origin are: (Q yaw -Q yaw ·cosα+Q yaw ·cos(θ s -α)+Q-Q yaw ,Q yaw ·sinα+Q yaw ·sin(θ s -α),h)。 6. The method for predicting the vertical deformation of soil caused by the thrust of the excavation face of a space curved 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 point (x, y, z) and point (x0, y0, z0), is the distance between the point (x,y,z) and the point (x0,y0,–z0).

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