Prediction method for stratum settlement caused by vertical pitching of space curve shield

Abstract

The invention discloses a method for predicting stratum settlement caused by vertical pitching of a space curve shield, and the method comprises the following steps: S1, building a space rectangular coordinate system, and constructing a space curve shield tunnel calculation model according to the tunneling posture of a shield tunneling machine; the shield tunneling machine enters the abnormal tunneling section from the normal tunneling section and turns right around the new rotating shaft l1 with the curvature radius Q for tunneling, the tunneling distance is converted into the angle formed by rotating around the new rotating shaft l1 by theta s, and a pitch angle beta is formed between the new rotating shaft l1 and the z axis; s2, projection processing is conducted on the excavation face of the shield tunneling machine of the abnormal tunneling section, and the pitching height of the shield tunneling machine is determined; and S3, on the basis of three-dimensional space column coordinate transformation, soil body settlement caused by various soil body losses under the vertical pitching condition can be obtained. The method has the advantages that the stratum settlement caused by vertical pitching of the space curve shield 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 ground settlement caused by vertical pitch 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] The shield tunneling deviation will separate an originally complete tunnel section into a normal excavation section and an abnormal excavation section, and the front and rear separation may also occur in vertical pitch. Summary of the invention

[0005] The purpose of the present invention is to provide a prediction method for ground settlement caused by vertical pitch of a space curved shield machine based on the above-mentioned deficiencies in the prior art, to project the excavation surface of the shield machine in the abnormal excavation section, and to obtain the soil settlement caused by various types of soil losses under vertical pitch conditions based on the three-dimensional spatial cylindrical coordinate transformation, thereby realizing the prediction of ground settlement caused by vertical pitch of a space 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 ground settlement caused by vertical pitch of a space curved shield, involving a large-scale, long-distance, large-section shield tunnel, the prediction 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, starting from the negative half-axis of the y-axis, turning right with a curvature radius Q, and the excavation distance is converted into an angle of rotation θ around the z-axis; the shield machine excavates to the xOz surface, at which time an instantaneous vertical pitch occurs. The shield machine enters the abnormal excavation section from the normal excavation section, and excavates around the new rotation axis l1 with a curvature radius Q to turn right, and the excavation distance is converted into a rotation θ around the new rotation axis l1 s The new rotation axis l1 and the z-axis are in the same plane but not parallel, and both pass through the point (0, 0, h). A pitch angle β is formed between the new rotation axis l1 and the z-axis. The shield machine advances θ in the abnormal excavation section. s ·Q's distance ends;

[0011] S2: Project the excavation surface of the shield machine in the abnormal excavation section and determine the shield machine's elevation and pitch height;

[0012] S3: Based on the three-dimensional cylindrical coordinate transformation, the soil settlement caused by various soil losses in vertical pitch conditions can be obtained as:

[0013] The calculation formula for over-excavation clearance is:

[0014]

[0015] The calculation formula of the shield tail integration gap is:

[0016]

[0017] In the formula, G t is the shield tail integration gap; ω is the calculated over-excavation layer thickness, which is calculated by the theoretical over-excavation volume G a Multiply by the reduction factor 1 / 3 to get G a It is determined by the curvature radius Q and the shield machine excavation radius R; L is the length of the shield machine; q is the change value of the curvature radius; s z is the vertical displacement of any point in the half space caused by the spherical void with a radius of 1 at the midpoint (x0, y0, z0) of the elastic semi-infinite body.

[0018] Theoretical overexcavation G a The calculation formula is:

[0019]

[0020] Where, L tail =2D, D is the width of the segment.

[0021] Based on the three-dimensional mirror theory and the three-dimensional space integration method, the vertical displacement s of any point in the half space caused by the spherical gap with a radius of 1 at the midpoint (x0, y0, z0) of the elastic semi-infinite body is obtained. z The calculation formula is:

[0022]

[0023] in:

[0024]

[0025] Where s is the variable on the x-axis, t is the variable on the y-axis, b and c are the upper and lower limit variables of integration, and μ is Poisson's ratio.

[0026] The method for projecting the shield machine excavation face in the abnormal excavation section is as follows:

[0027] Project the excavation surface of the shield machine after pitching onto the xOz plane, and the rectangular coordinate equation is:

[0028]

[0029] Where R0 is the radius of the interface of the shield machine excavation face.

[0030] The method for determining the pitch height of the shield machine is as follows:

[0031] According to the geometric relationship, the forward distance of the shield machine in the cylindrical coordinates and the actual excavation distance have the following relationship:

[0032] d pitch =θ s Q.cosβ;

[0033] The value range of the cylindrical coordinate integral parameter θ in the abnormal excavation section is: θ∈[0,θ s ·cosβ];

[0034] When the shield machine rotates θ around the z-axis, that is, when the shield machine advances θ·Q in the abnormal excavation section, the shield machine will pitch to a height of -θ·Q·sinβ.

[0035] The pitch angle β is defined as follows:

[0036] The excavation face of the shield machine rotates along the x-axis by a certain angle, which is recorded as β. When the z-axis component is negative, β is a negative value, and when the z-axis component is positive, β is a positive value.

[0037] The advantages of the present invention are: projection processing is performed on the excavation surface of the shield machine in the abnormal excavation section, and based on the three-dimensional space cylindrical coordinate transformation, the soil settlement caused by various soil losses under vertical pitch conditions is obtained, thereby realizing the prediction of the stratum settlement caused by the vertical pitch of the space curved shield, and providing a reference for actual tunnel construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic diagram of a calculation model of a space curved shield tunnel with vertical pitch in a space rectangular coordinate system in the present invention;

[0039] Figure 2 It is a schematic diagram of a calculation model of a space curved shield tunnel with vertical pitch at an x-axis viewing angle in the present invention;

[0040] Figure 3 It is the projection diagram of the excavation face of the shield machine on xOz in the present invention;

[0041] Figure 4 It is a geometric relationship diagram of z and θ in the present invention. DETAILED DESCRIPTION

[0042] 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:

[0043] Example: Figure 1-4 As shown, this embodiment specifically relates to a prediction method for ground settlement caused by vertical pitch of a space curved shield, involving a large-scale, long-distance, large-section shield tunnel, which passes through a soil body under homogeneous multi-layer geological conditions with an arbitrary excavation axis. The prediction method mainly includes the following steps:

[0044] 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.

[0045] Among them, Figure 1 and Figure 2 As shown, the coordinate origin O, the x-axis and the y-axis in the spatial rectangular coordinate system are all located on the surface, while the z-axis is vertically downward. Assuming 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), turning right with a curvature radius Q, the excavation distance is converted into an angle of rotation θ around the z-axis; 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 an instantaneous vertical pitch occurs, and the shield machine enters the abnormal excavation section from the normal excavation section, and turns right around the new rotation axis l1 with a curvature radius Q. The excavation distance is converted into a rotation of θ around the new rotation axis l1 s The new rotation axis l1 and the z-axis are in the same plane but not parallel, and both pass through the point (0, 0, h). A pitch angle β is formed between the new rotation axis l1 and the z-axis. The shield machine advances θ in the abnormal excavation section. s ·Q's distance ends.

[0046] In addition, the pitch angle β is defined as follows:

[0047] The essence of the pitch action of the shield machine is that the z-axis component of the excavation direction vector is no longer 0, that is, the excavation face of the shield machine rotates along the x-axis by a certain angle, which is denoted as β; when the z-axis component is negative, β is a negative value, and when the z-axis component is positive, β is a positive value.

[0048] S2: Project the excavation surface of the shield machine in the abnormal excavation section and determine the pitch height of the shield machine.

[0049] Among them, Figure 3 As shown in the figure, in order to ensure that the interfaces of the excavation surface remain circular and satisfy the integral transformation of cylindrical coordinates, the shield excavation surface is processed as follows:

[0050] Project the excavation surface of the shield machine after pitching onto the xOz plane, and the rectangular coordinate equation is:

[0051]

[0052] Where R0 is the radius of the interface of the shield machine excavation face.

[0053] like Figure 4 As shown, in the abnormal excavation section, the advance was θ s Q, the distance actually projected onto the xOy plane is smaller. According to the geometric relationship, the forward distance of the shield machine in the cylindrical coordinates and the actual excavation distance have the following relationship:

[0054] d pitch =θ s Q.cosβ;

[0055] The value range of the cylindrical coordinate integral parameter θ in the abnormal excavation section is: θ∈[0,θ s ·cosβ];

[0056] When the shield machine rotates θ around the z-axis, that is, when the shield machine advances θ·Q in the abnormal excavation section, the shield machine will pitch to a height of -θ·Q·sinβ.

[0057] S3: Based on the three-dimensional cylindrical coordinate transformation, the soil settlement caused by various types of soil losses in the vertical pitch condition can be obtained, which are the over-excavation gap and the shield tail integration gap.

[0058] The calculation formula for over-excavation clearance is:

[0059]

[0060] The calculation formula of the shield tail integration gap is:

[0061]

[0062] In the formula, G t is the shield tail integration gap; ω is the calculated over-excavation layer thickness, which is calculated by the theoretical over-excavation volume G a Multiply by the reduction factor 1 / 3 to get G a It is determined by the curvature radius Q and the shield machine excavation radius R; L is the length of the shield machine; q is the change value of the curvature radius; s zis the vertical displacement of any point in the half space caused by the spherical void with a radius of 1 at the midpoint (x0, y0, z0) of the elastic semi-infinite body.

[0063] Theoretical overexcavation G a The calculation formula is:

[0064]

[0065] Where, L tail =2D, D is the segment width, in other words, the theoretical overbreak G a It is sufficient to cover the tail of the shield machine with 2 rings of segments.

[0066] Based on the three-dimensional mirror theory and the three-dimensional space integration method, the vertical displacement s of any point in the half space caused by the spherical gap with a radius of 1 at the midpoint (x0, y0, z0) of the elastic semi-infinite body is obtained. z The calculation formula is:

[0067]

[0068] in:

[0069]

[0070] Where s is the variable on the x-axis, t is the variable on the y-axis, b and c are the upper and lower limit variables of integration, and μ is Poisson's ratio.

[0071] The beneficial effects of this embodiment are: projection processing is performed on the excavation surface of the shield machine in the abnormal excavation section, and based on the three-dimensional space cylindrical coordinate transformation, the soil settlement caused by various soil losses under vertical pitch conditions is obtained, thereby realizing the prediction of the stratum settlement caused by the vertical pitch of the space curved shield, and providing a reference for actual tunnel construction.

Claims

1. A method for predicting ground settlement caused by vertical pitch of a space curved shield, involving a large-scale, long-distance, large-section shield tunnel, 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, starting from the negative half-axis of the y-axis, turning right with a curvature radius Q, and the excavation distance is converted into an angle of rotation θ around the z-axis; the shield machine excavates to the xOz surface, at which time an instantaneous vertical pitch occurs. The shield machine enters the abnormal excavation section from the normal excavation section, and excavates around the new rotation axis l1 with a curvature radius Q to turn right, and the excavation distance is converted into a rotation θ around the new rotation axis l1 s The new rotation axis l1 and the z-axis are in the same plane but not parallel, and both pass through the point (0, 0, h). A pitch angle β is formed between the new rotation axis l1 and the z-axis. The shield machine advances θ in the abnormal excavation section. s ·Q's distance ends; S2: Project the excavation surface of the shield machine in the abnormal excavation section and determine the shield machine's elevation and pitch height; S3: Based on the three-dimensional cylindrical coordinate transformation, the soil settlement caused by various soil losses in vertical pitch conditions can be obtained as: The calculation formula for over-excavation clearance is: The calculation formula of the shield tail integration gap is: In the formula, G t is the shield tail integration gap; ω is the calculated over-excavation layer thickness, which is calculated by the theoretical over-excavation volume G a Multiply by the reduction factor 1 / 3 to get G a It is determined by the curvature radius Q and the shield machine excavation radius R; L is the length of the shield machine; q is the change value of the curvature radius; s z is the vertical displacement of any point in the half space caused by the spherical void with a radius of 1 at the midpoint (x0, y0, z0) of the elastic semi-infinite body.

2. A method for predicting ground settlement caused by vertical pitch of a space curved shield according to claim 1, characterized in that Theoretical over-excavation G a The calculation formula is: Where, L tail =2D, D is the width of the segment.

3. The method for predicting ground settlement caused by vertical pitch of a space curved shield according to claim 1 is characterized in that Based on the three-dimensional mirror theory and the three-dimensional space integration method, the vertical displacement s of any point in the half space caused by the spherical gap with a radius of 1 at the midpoint (x0, y0, z0) of the elastic semi-infinite body is obtained. z The calculation formula is: in: Where s is the variable on the x-axis, t is the variable on the y-axis, b and c are the upper and lower limit variables of integration, and μ is Poisson's ratio.

4. The method for predicting ground settlement caused by vertical pitch of a space curved shield according to claim 1 is characterized in that The method for projecting the shield machine excavation face in the abnormal excavation section is as follows: Project the excavation surface of the shield machine after pitching onto the xOz plane, and the rectangular coordinate equation is: Where R0 is the radius of the interface of the shield machine excavation face.

5. The method for predicting ground settlement caused by vertical pitch of a space curved shield according to claim 1 is characterized in that The method for determining the pitch height of the shield machine is as follows: According to the geometric relationship, the forward distance of the shield machine in the cylindrical coordinates and the actual excavation distance have the following relationship: d pitch =θ s ·Q.cosβ; The value range of the cylindrical coordinate integral parameter θ in the abnormal excavation section is: θ∈[0,θ s ·cosβ]; When the shield machine rotates θ around the z-axis, that is, when the shield machine advances θ·Q in the abnormal excavation section, the shield machine will pitch to a height of -θ·Q·sinβ.

6. The method for predicting ground settlement caused by vertical pitch of a space curved shield according to claim 1 is characterized in that The pitch angle β is defined as follows: The excavation face of the shield machine rotates along the x-axis by a certain angle, which is recorded as β. When the z-axis component is negative, β is a negative value, and when the z-axis component is positive, β is a positive value.

Images