Method for determining rotational spring characteristics of joint

Abstract

To provide a method for determining rotational spring characteristics of a joint that can acquire the rotational spring characteristics of a joint provided between segments using a simple method.SOLUTION: A method for determining rotational spring characteristics of a joint includes a gap measurement step of measuring a circumferential gap between a first segment S1 and a second segment S2 through a preliminary experiment, a first acquisition step of acquiring the rotational spring characteristics of a joint 1 including a joint hardware consisting of a male member 10 provided on the first segment S1 and a female member 20 provided on the second segment S2 through a joint bending test, a first analysis step of performing a numerical analysis under the same conditions as the joint bending test using the gap measured in the preliminary experiment and contact spring characteristics between the first segment S1 and the second segment S2 acquired in advance, and a confirmation step of confirming that the rotational spring characteristics obtained in the joint bending test are equivalent to the rotational spring characteristics determined by the analysis.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a method for determining the rotational spring characteristics of a joint. [Background technology]

[0002] A shield tunnel consists of a primary lining and a secondary lining that is installed inside the primary lining. In the design of a shield tunnel, it is common to use a "beam-spring model" in which the multiple segments that make up the primary lining are modeled as beams, the joints (segment joints) installed between the segments are modeled as rotational springs, and the joints (ring joints) installed between the rings along the axial direction of the tunnel are modeled as shear springs.

[0003] For example, Patent Document 1 discloses an invention related to the shape of segments that form shield tunnels. Based on the "beam-spring model" described above, this invention finely divides the weight of the segment and external working forces, performs a step analysis in which each divided force acts sequentially, and evaluates the behavior of the segment, which changes depending on the load acting at that time, by superimposing the generated cross-sectional forces. This method makes it possible to use segments manufactured using a design that faithfully models actual behavior. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2001-032692 Summary of the Invention [Problem to be solved by the invention]

[0005] In general beam-spring models, it is important to determine the rotational spring characteristics of segment joints. To determine the rotational spring characteristics, it is desirable to conduct joint bending tests using full-scale segments. However, conducting tests using full-scale segments has drawbacks, such as the time-consuming preparation and high costs involved. Furthermore, because the rotational spring characteristics of segment joints vary depending on factors such as segment thickness, joint type, and axial force, multiple tests are required. However, attempting to achieve all of these through experiments would result in enormous design costs.

[0006] Therefore, an object of the present invention is to provide a method for determining the rotational spring characteristics of a joint that can obtain the rotational spring characteristics of a joint provided between segments using a simple technique. [Means for solving the problem]

[0007] In response to the above-mentioned problems, the method for determining the rotational spring characteristics of a joint of the present invention is a method for determining the rotational spring characteristics of a joint in which a first segment and a second segment that constitute a shield tunnel are arranged circumferentially and joined by a joint, and is characterized by comprising: a gap measurement step of measuring the circumferential gap between the first segment and the second segment through a preliminary experiment; a first acquisition step of acquiring the rotational spring characteristics of a joint including a joint hardware composed of a male member provided on the first segment and a female member provided on the second segment through a joint bending test; a first analysis step of performing a numerical analysis under the same conditions as the joint bending test using the gap measured in the preliminary experiment and the contact spring characteristics between the first segment and the second segment that were acquired in advance; and a confirmation step of confirming that the rotational spring characteristics obtained in the joint bending test are equivalent to the rotational spring characteristics determined by the analysis.

[0008] Here, in the gap measuring step, it is preferable that the gap be measured based on a relative displacement occurring between the first segment and the second segment measured by a π gauge provided between the inner peripheral surface of the first segment and the inner peripheral surface of the second segment and a π gauge provided between the outer peripheral surface of the first segment and the outer peripheral surface of the second segment. Also, it is preferable that the male member be connected to the female member in a loose-fit state.

[0009] Furthermore, after the first analysis step, it is desirable to execute a second analysis step in which a numerical analysis is performed by applying different axial forces to the joint using the gap measured in the preliminary experiment and the contact spring characteristics obtained in advance. Furthermore, it is desirable that the numerical analysis be an FEM analysis. [Effects of the Invention]

[0010] The method of determining the rotational spring characteristics of a joint of the present invention involves obtaining the rotational spring characteristics of a joint including a joint hardware consisting of a male member provided on a first segment and a female member provided on a second segment through a joint bending test, and then performing a numerical analysis under the same conditions as the joint bending test using the gap measured in a preliminary experiment and the contact spring characteristics between the segments obtained in advance.

[0011] This eliminates the need to conduct experiments using full-scale segments each time to determine the rotational spring characteristics of the joints provided between the segments, and allows the rotational spring characteristics to be obtained using a simple method.

[0012] In particular, when the gap is measured based on the relative displacement between the first and second segments using a π gauge installed across the inner circumferential surface of the first segment and the inner or outer circumferential surface of the second segment, the rotational spring characteristics can be calculated taking into account the amount of mesh opening between the first and second segments, making it possible to calculate the rotational spring characteristics of the joint in accordance with actual conditions.

[0013] Furthermore, when the male member is connected to the female member in a loose fit state, a gap can be created between the first segment and the second segment, making it possible to reproduce with high accuracy a state in which there is a gap between the segments.

[0014] Furthermore, after the first analysis step, a second analysis step is performed in which numerical analysis is performed by applying different axial forces to the joint using the gap and the contact spring characteristics between the segments that have been obtained in advance. This allows for the introduction of multiple levels of axial force, making it possible to more accurately understand the effect of axial force on rotational spring characteristics.

[0015] Furthermore, the numerical analysis in the first or second analysis step is an FEM analysis. Therefore, by using FEM analysis, which is a finite element method, it is possible to more accurately grasp the influence on the rotational spring characteristics. [Brief explanation of the drawings]

[0016] [Figure 1] 1 is an explanatory diagram showing a shield tunnel cut away at the center to which a method for determining the rotational spring characteristics of a joint according to an embodiment of the present invention is applied. FIG. [Figure 2] This is an oblique view of a segment of a shield tunnel viewed from the joint surface side. [Figure 3] FIG. 1(a) is an enlarged view of a portion of a segment where a male member is provided, and FIG. 1(b) is an enlarged view of a portion of a segment where a female member is provided. [Figure 4] FIG. 4 is an enlarged side view showing a joint portion between segments. [Figure 5] FIG. 2 is an enlarged view showing a connecting portion between a male member and a female member. [Figure 6] FIG. 1 is a diagram showing a schematic diagram of a beam-spring model of a shield tunnel. [Figure 7] 10A and 10B are diagrams showing a schematic diagram of a case of positive bending in a preliminary experiment, in which FIG. 10A is a diagram before a load is applied, and FIG. 10B is a diagram after a load is applied. [Figure 8]10A and 10B are diagrams showing a schematic diagram of a case of negative bending in a preliminary experiment, in which FIG. 10A is a diagram before a load is applied, and FIG. 10B is a diagram after a load is applied. [Figure 9] FIG. 1 is a diagram schematically illustrating an outline of a joint bending test. [Figure 10] FIG. 1 is a diagram showing an analytical model for FEM analysis. [Figure 11] FIG. 10 is a diagram showing the relationship between bending moment and rotation angle when an axial force is applied in a joint bending test. DETAILED DESCRIPTION OF THE INVENTION

[0017] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. Figure 1 is an explanatory diagram showing a shield tunnel cut at the center to explain the configuration of a tunnel structure to which a method for determining the rotational spring characteristics of a joint (segment joint) according to an embodiment of the present invention is applied.

[0018] As shown in Fig. 1, the shield tunnel T is configured to have a primary lining and a secondary lining provided inside the primary lining. Note that, in the following, only the primary lining will be described, and the description and illustration of the secondary lining will be omitted.

[0019] As shown in Fig. 1, the shield tunnel T is composed of multiple rings R formed in an annular shape. The lining of the shield tunnel T is assembled by joining the rings R together along the axial direction D2 of the shield tunnel T.

[0020] Each ring R is configured to have a plurality of arc-shaped segments S. The segments S are arranged adjacent to each other along the circumferential direction D1.

[0021] Figure 2 is an oblique view of the segment S as seen from the side of the joint surface Sa that appears in the circumferential direction D1, Figure 3(a) is an enlarged view of the portion of the segment where the male member 10 is provided, Figure 3(b) is an enlarged view of the portion of the segment where the female member 20 is provided, and Figure 4 is an enlarged side view of the joint portion between the segments.

[0022] The joint 1 is configured to have a male member 10 and a female member 20 as joint hardware. Specifically, as shown in FIG. 2, the male member 10 and the female member 20 are arranged side by side along the width direction W (axial direction D2) on the joint surface Sa of the segment S. Specifically, a pair of male members 10 are provided on one side of the joint surface Sa in the width direction W, spaced apart in the tunnel interior / exterior direction. On the other side of the joint surface Sa in the width direction W, a pair of recesses C extending along the width direction W are formed, spaced apart in the tunnel interior / exterior direction. Each recess C is formed in a groove shape extending to the end face Sb, and a female member 20 is housed in the recess C.

[0023] As shown in Figures 3(a) and 4, male member 10 is comprised of male main body 11 and male shank 12. Male main body 11 has fitting portion 11a at its tip. Male shank 12 is a reinforcing bar that protrudes from male main body 11.

[0024] As shown in Figures 3(b) and 4, the female member 20 is configured to have a female main body portion 21 and a female shaft portion 22. A fitting hole 21a is formed in the female main body portion 21. The female shaft portion 22 is a reinforcing bar that protrudes from the female main body portion 21.

[0025] Adjacent segments S are joined by sliding the male member 10 and the female member 20 relative to one another along the width direction W. The segments S are joined by connecting the male member 10 provided on the segment S on one side (first segment S1) with the female member 20 provided on the segment S on the other side (second segment S2). The first segment S1 and the second segment S2 are arranged along the circumferential direction D1 and joined by a joint 1, and the male-side shank 12 and the female-side shank 22 extend along the circumferential direction D1.

[0026] As shown in Figure 5, in joint 1, male member 10 is connected to female member 20 in a loose fit state. That is, mating portion 11a of male member 10 is connected to mating hole 21a of female member 20 in a state with some play (gap indicated by arrow in the figure). Due to the play occurring within joint 1, when segments S are joined together, a gap can be generated between adjacent segments S. The male-side shank 12 and female-side shank 22 are arranged as a pair with a gap between them along the depth direction of the page.

[0027] When segments S are joined together using the above-described joint 1, a gap G is generally formed between adjacent segments S along the circumferential direction D1, as shown in Figure 4. Therefore, as will be explained below, it is important to obtain the rotational spring characteristics of the joint 1 taking into account the gap G that occurs between the segments S.

[0028] To obtain the rotational spring characteristics of joint 1 of a shield tunnel, an analysis method is used that uses a structural model called a beam-spring model, in which the segment is modeled as a beam, the interaction with the ground is modeled as a ground spring, and joint 1 is modeled as a rotational spring, as shown in Figure 6.

[0029] A specific method for determining the rotational spring characteristics of the joint 1 will be described. When determining the rotational spring characteristics, a joint bending test is generally performed. A specific method will be described below.

[0030] <Condition determination> First, when conducting a joint bending test, the conditions for the joint bending test are determined. Specifically, the information necessary for conducting the joint bending test, such as the dimensions, weight, shape, and material strength of the segment S to be tested, and the dimensions and axial force of the joint 1, is obtained in advance.

[0031] <Gap measurement step> Next, before the joint bending test, a preliminary experiment is conducted, which is the gap measurement step. In the preliminary experiment, the gap between the segments S is measured. Specifically, with the joints between the segments S supported by support jacks, the strain of the segments S when no weight is acting on them and the gap between the segments S are measured.

[0032] As shown in Figures 7(a) and 7(b), the joint between the first segment S1 and the second segment S2 is supported by a support jack 100, a π gauge 101 is placed on the outer peripheral surface side with the joint surface Sa sandwiched between them, and the support jack 100 is gradually lowered to apply its own weight. Then, the relative displacement (first change amount) that occurs between the segments S when the first segment S1 and the second segment S2 tilt and the segments S come into contact on the side where the π gauge 101 is placed is obtained (positive bending).

[0033] 8(a) and 8(b), the joint between the first segment S1 and the second segment S2 is supported by a support jack 100, a π gauge 101 is placed on the inner circumferential surface with the joint surface Sa sandwiched between them, and a load equivalent to twice the weight of the segments is applied from below. Then, the first segment S1 and the second segment S2 tilt, causing the segments S to come into contact on the side where the π gauge 101 is placed. The relative displacement (second change amount) that occurs between the segments S is obtained (negative bending). The average of the first change amount and the second change amount is then calculated, and this value is used as the value of the gap that has occurred between the segments S.

[0034] <First acquisition step> In the first acquisition step, the rotational spring characteristics of the joint 1 including a joint hardware composed of a male member 10 provided on the first segment S1 and a female member 20 provided on the second segment S2 are acquired by a joint bending test.

[0035] Specifically, as shown in Figure 9, the joint bending test is performed by arranging full-scale first and second segments S1 and S2 facing each other. Note that Figure 9 is a diagram that shows a schematic overview of the joint bending test, and a detailed diagram of the entire equipment used in the joint bending test is omitted. Flat plate-shaped segments S are arranged side by side and joined together with their joint surfaces Sa butting against each other via joint 1. A load P is applied to the bending moment by two-point loading. An axial force D is also introduced by pressing the first and second segments S1 and S2 together horizontally with a jack.

[0036] In the first acquisition step, the rotational spring characteristics of the joint 1 composed of the male member 10 provided on the first segment S1 and the female member 20 provided on the second segment S2 are acquired by a joint bending test. That is, the rotational spring characteristics are obtained by taking into account the bending moment (load P) generated between the segments S and the amount of mesh between the segments S. In this way, by taking the gap between the segments S into account, it becomes possible to calculate the rotational spring characteristics of the joint 1 that are in line with the actual situation.

[0037] <First analysis step> Incidentally, in order to accurately calculate the rotational spring characteristics of joint 1, it is desirable to use a larger-scale device using full-scale segments, as in a joint bending test. However, when full-scale segments are used, the preparation for the test itself is time-consuming and requires a large amount of expense, which places restrictions on conducting the test. Therefore, we will conduct tests that minimize the number of times joint bending tests and the like are conducted, and that will enable the calculation of the rotational spring characteristics of joint 1 that match the actual situation.

[0038] In the first analysis step, a numerical analysis is performed under the same conditions as the joint bending test (first acquisition step), using the gap measured in the preliminary experiment and the contact spring characteristics between the segments S that were previously acquired. Specifically, using the analysis model shown in Figure 10, a load and axial force are applied under the same conditions as the joint bending test, and a numerical analysis is performed using FEM analysis. In the FEM analysis, a sufficient compressive force is set in the compression direction (circumferential direction D1) so that the end faces of the segments S do not interfere with each other, and settings are made so that almost no tensile force is applied.

[0039] Additionally, the gap between segments S is set to the same value as that obtained in the joint bending test. By performing numerical analysis using FEM analysis, the load and axial force can be applied to the elements with an equal distribution. This allows for a more accurate understanding of the effect on the rotational spring characteristics. Furthermore, the validity of the rotational spring characteristics of joint 1 can be repeatedly examined without using full-scale segments.

[0040] <Second analysis step> In the second analysis step after the first analysis step, numerical analysis is performed by applying different axial forces to the joint 1 using the gap between the segments S measured in the preliminary experiment and the contact spring characteristics obtained in advance. Specifically, three levels of axial force were used: no axial force, 600 kN axial force, and 1200 kN axial force.

[0041] As shown in Figure 11, the gradient increased as the axial force increased. In other words, it was found that the greater the axial force, the greater the rotational spring characteristics. By introducing multiple levels of axial force, it is possible to more accurately grasp the effect of axial force on the rotational spring characteristics. Note that the axial force introduced may be four or more levels.

[0042] <Confirmation step> In the confirmation step, the rotational spring characteristics obtained from the actual joint bending test are compared with the FEM analysis results to confirm the validity of the FEM analysis conditions (whether they are equivalent). In other words, the validity of the beam-spring model set for the shield tunnel is confirmed.

[0043] In this way, in the method of determining the rotational spring characteristics of a joint of this embodiment, the rotational spring characteristics of a joint 1 including a joint hardware composed of a male member 10 provided on the first segment S1 and a female member 20 provided on the second segment S2 are obtained by a joint bending test, and a numerical analysis is performed under the same conditions as the joint bending test using the gap measured in a preliminary experiment and the contact spring characteristics between the segments S obtained in advance.

[0044] Therefore, there is no need to conduct experiments using full-scale segments S each time to obtain the rotational spring characteristics of the joint 1 provided between the segments S. Therefore, the rotational spring characteristics can be obtained by a simple method.

[0045] In particular, when the gap is measured based on the relative displacement between the first segment S1 and the second segment S2 using a π gauge 101 provided across the inner circumferential surface of the first segment S1 and the inner or outer circumferential surface of the second segment S2, the rotational spring characteristics can be calculated taking into account the amount of mesh opening between the first segment S1 and the second segment S2. This makes it possible to calculate the rotational spring characteristics of the joint 1 in accordance with the actual situation.

[0046] Furthermore, when the male member 10 is connected to the female member 20 in a loosely fitted state, a gap can be generated between the first segment S1 and the second segment S2. Therefore, a state in which there is a gap between the segments can be reproduced with high accuracy.

[0047] Furthermore, after the first analysis step, a second analysis step is performed in which a numerical analysis is performed by applying different axial forces to the joint 1 using the gap and the contact spring characteristics obtained in advance. This makes it possible to introduce multiple levels of axial force, making it possible to more accurately understand the effect of the axial force on the rotational spring characteristics.

[0048] Furthermore, the numerical analysis in the first or second analysis step is an FEM analysis. Therefore, by using FEM analysis, which is a finite element method, it is possible to more accurately grasp the influence on the rotational spring characteristics.

[0049] Although an embodiment of the present invention has been described in detail above with reference to the drawings, the specific configuration is not limited to this embodiment, and design changes that do not deviate from the gist of the present invention are included in the present invention. [Explanation of symbols]

[0050] 1: Joint 10: Male member 20: Female member 101: π gauge D1: Circumferential direction D2: Axial direction G: Gap S: Segment S1: First segment S2: Second segment Sa: Joint surface T: Shield tunnel

Claims

1. A method for determining rotational spring characteristics of a joint in which a first segment and a second segment that constitute a shield tunnel are arranged along a circumferential direction and joined by a joint, comprising: a gap measuring step of measuring a circumferential gap between the first segment and the second segment through a preliminary experiment; a first acquisition step of acquiring the rotational spring characteristics of a joint including a joint hardware configured with a male member provided on the first segment and a female member provided on the second segment by a joint bending test; a first analysis step of performing a numerical analysis under the same conditions as the joint bending test using the gap measured in the preliminary experiment and the contact spring characteristics between the first segment and the second segment acquired in advance; a confirmation step of confirming that the rotational spring characteristics obtained in the joint bending test are equivalent to the rotational spring characteristics obtained by analysis.

2. A method for determining the rotational spring characteristics of a joint as described in claim 1, characterized in that in the gap measurement step, the gap is measured based on the relative displacement occurring between the first segment and the second segment measured by a π gauge installed across the inner surface of the first segment and the inner surface of the second segment and a π gauge installed across the outer surface of the first segment and the outer surface of the second segment.

3. 3. The method for determining the rotational spring characteristics of a joint according to claim 1, wherein the male member is connected to the female member in a loose fit state.

4. 3. A method for determining the rotational spring characteristics of a joint according to claim 1 or 2, characterized in that after the first analysis step, a second analysis step is carried out in which a numerical analysis is performed by applying different axial forces to the joint using the gap measured in the preliminary experiment and the contact spring characteristics obtained in advance.

5. 3. The method for determining the rotational spring characteristics of a joint according to claim 1, wherein the numerical analysis is an FEM analysis.

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