JPH03148037A - Method for analyzing stress in segment ring for shield tunnel - Google Patents

Abstract

PURPOSE:To make it possible to perform accurate analysis by assuming resistance earth pressure as spring force, analyzing the stress in a segment ring by a finite element method, releasing the spring force in a range wherein the radius after the deformation becomes smaller than the radius before the deformation, and analyzing angle stress. CONSTITUTION:An analyzing apparatus 1 comprises both means of an input means 2 and an output means 3, an interface 4, an element dividing means 5, a data forming means 5 and a FET computing means 7. The input comprises initial structure data and initial load data. As the structure data, the joint number, the coordinate values and the like of each element in a finite element method are obtained as the joint structure data through the means 5. The joint load data are obtained through the means 6 based on the structure data and the initial load data. Then both node data undergo FEM analysis in the means 7. When the radius R' after the deformation becomes smaller than that of the initial radius Rc, it is assumed that the ground spring does not act on that part. The spring is removed, and the computation is performed again. Thus the accurate analysis can be performed.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a stress analysis method for a segment ring for a shield tunnel.

(Prior Art) For example, when designing a segment ring 12 for a shield tunnel as shown in FIG. 13, stress analysis of the segment ring is performed. This stress analysis refers to obtaining the cross-sectional view shown in FIG. 15 from the load diagram shown in FIG. 14.

The limited element method is well known as a stress analysis method for such segment rings. As a solution method of this finite element method, for example, the one described in Japanese Patent Publication No. 10771/1983 is known.

This conventional analysis method divides the object to be analyzed into multiple micro-rigid elements of arbitrary shapes, and considers them as a collection of rigid body-spring system models that are connected by springs distributed on the interface between the elements. It was an attempt to solve the problem.

(Problem to be Solved by the Invention) By the way, one of the external forces that acts on the tunnel segment ring is resistance earth pressure. Do you think of this resisting earth pressure as a force similar to water pressure (does the pressure not change even if the ring deforms), or do you think of it as a force similar to the reaction force of a solid wall (because the soil and ring When they are in contact, a reaction force acts, but when they deform, a gap is created between the soil and the ring.
There was a very difficult question as to whether to think that there was no external force acting on them, or whether to think that it was some other force.

The analysis results differ depending on what kind of force is considered resistive earth pressure, and the handling of resistive earth pressure has been an extremely important issue in stress analysis.

Therefore, the present invention is inspired by the conventional solution method in which a rigid body model is regarded as an aggregate of rigid body-spring system models, and the present invention provides a segment ring for shield tunnels in which resistance earth pressure is regarded as spring force and solved. The purpose of this study is to provide a stress analysis method.

(Means for Solving the Problems) In order to achieve the above object, the present invention takes the following measures. That is, the feature of the stress analysis method for a segment ring for a shield tunnel of the present invention is that the stress of a segment ring for a shield tunnel is analyzed by the finite element method assuming that resistive earth pressure (ground reaction force) is a spring force. As a result, with respect to the radius Rc of the segment ring before deformation, the spring force in the range where the radius R'' after deformation is R′<Rc is released, and the stress analysis is performed again.

(Example) Embodiments of the present invention will be described below based on the drawings.

What is shown in FIG. 1 is a stress analysis device 1 for circular and occluded circular structures, and the device 1 includes an input means 2, an output means 3,
It consists of an interface 4 for connecting these to a computer, an element division means 5, a data generation means 6, an FEM calculation means 7, etc. inside the computer. The element dividing means 5 divides the structure into elements and calculates node numbers and coordinate values. The data generation means 6 distributes the input original data to each node. The FEM calculation means 7 performs stress analysis using the finite element method.

The stress analysis device 1 includes a structure 8 as shown in FIG.
Alternatively, the omitted circular structures 9 and 10 as shown in FIGS. 3(a) and 3(b) are targeted for analysis. (Note that the constraint conditions for the notched ends of the structures 9 and 10 in FIGS. 3(a) and 3(b) are different, such as whether the notched ends are hinged or fixed.) Such circular or broken circular structures A specific example of the object is a segment ring of a shield tunnel shown in FIG. 13.

The stress analysis device 1 analyzes the stress of a structure using the finite element method, and considers the following five load conditions acting on the structure.

Load condition j-1;-1; Vertical condition j-2;-2; Horizontal condition j-3; Own weight/self-weight reaction load condition j-4; Internal pressure load condition j-5; Nodal concentrated load/reaction force As shown in FIG. 2, the horizontal and vertical loads can be input even if the horizontal and vertical loads are asymmetrical. It is also possible to perform an analysis using any combination of the five load conditions. For example, if the load condition is set as j = 1.2.3, (vertical load) + (
The analysis is performed assuming that horizontal load) + (self-weight/self-weight reaction force) acts.

Furthermore, the stress analysis device 1 considers resistance earth pressure (ground reaction force) as a spring 11, as shown in FIG. The strength k of the ground spring 11 can be arbitrarily changed depending on the case where the ground layer changes in the middle of the segment ring.

Data input to the stress analysis bag W1 is performed in an interactive manner via the input means 2, and the original input data is
As shown in the figure, structural data consisting of load conditions j, physical properties such as the structure's elastic modulus, centroid radius Re, node division angle θ, restraint conditions (fixed contact or hinges, etc.), etc., and the ground reaction force coefficient It consists of load data consisting of K, vertical load P, horizontal load T, nodal load (concentrated load), own weight, internal pressure, etc.

The primitive structure data is processed by the element dividing means 5. That is, the element dividing means 5 divides the structure into elements according to the finite element method, and determines the node number and coordinate value of each element.

That is, in the case of the same structure 8 shown in FIG. 5, the input items are the centroid radius Rc, (division angle θ or number of nodes n),
For the input item, the element dividing means 5 determines the node number!
and the angle θt of the node is θi = (360”/n)
X (1-IJ!=(θi/θ)+1, and the coordinate values xi and yi of each node 2 are x
It is calculated as i-Rcxsinθt yi = Rc X cosθ1.

In the case of the missing circular structure 9 shown in FIG. 6, opening angles A and B are additionally input in addition to the above input items.

Then, the node numbers a and b of the hesitation opening are a = -int (-A/θ)+1 b-t (B/θ)+1 However, 1nt(r) represents the largest integer that does not exceed X. .

It is obtained by calculating.

The node number 1, coordinate values xi, yi, etc. obtained by the element dividing means 5 are hereinafter referred to as node structure data in order to distinguish them from the initially input original data.

Next, the nodal load data acting on each node is determined by the data generating means 6 from the nodal structure data and the original load data.

First, the data generation means 6 calculates a spring constant.

That is, as shown in Fig. 7, the load range of the spring attached to node 1 is from (θ1-θ/2) to (θ1+θ/2).
For the horizontal ground spring, find the projected length in the X direction (L+-+1), and for the vertical ground spring, find the projected length in the y direction (Li), and calculate the respective projections to the ground reaction force coefficient. Let the product of the length be the spring constant.

In other words, the horizontal ground reaction force coefficient k of the input item of the original load data
Hi(L/n() and vertical ground reaction force coefficient kvi(t
/m), the horizontal spring constant k acting on each node i
Hf (t/m) and vertical spring constant kvi (t/m)
is calculated using the following formula. (However, the spring constant is straight per 1.0m depth.) L, 11-2×Rcxsin(θ/2)X, stnθi
(m) L, vi= 2 ×Rcxsin(θ/;l
) X cosθ! (m) kH1=kHiXL, l1
X1.0 (t/m)kv1=kvtxLvt×
1.0 (t/m) Furthermore, data generation means 6
The load acting on each node i is calculated by That is,
The vertical load P and horizontal load T of the original load data are distributed to each node.

The shield top horizontal load T (t/t/
This is an explanation for finding the load ti at each node l when the shield bottom horizontal load T, (t/m) is input, and the load t1 at each node is as follows: tt=TI+((Tz T+)X Iyt y+
I/(2xRc)).

Furthermore, the data generation means 6 calculates the self-weight reaction force. Figure 9 shows the case where the self-weight reaction force for a perfectly circular structure is considered to be equally distributed, and the input items are the self-weight of the ring,
That is, it is the weight g (t/m) per unit length of the material. From this weight g, the weight W of the entire ring is determined by the following formula.

j2 i = 2 x Rc/n And the reaction force IIR=R, is It is required as.

FIG. 10 shows a case where the self-weight reaction force in the case of a missing circular structure is considered as a scalene distribution, and in this case, the self-weight reaction force is obtained by the following equation.

ei; Center of gravity distance of the fourth member.

The nodal load data obtained by the data generation means 6 as described above and the nodal structure data obtained by the element division means 5 are edited so that they can be processed by the FEM calculation means 7,
FEM analysis is performed.

Details of the processing in this FEM calculation means 7 are shown in FIG.

First, based on the load condition setting values, processing is performed separately for the case of dead weight (j=3) and the case of load conditions other than dead weight (j-1, 2, 4, 5).

In the case of load conditions other than self-weight, the cross-sectional force is calculated using the finite element method from the nodal structure data, nodal load data, and restraint conditions (hinge or fixed, etc.), that is, the stiffness matrix K is created, and the simultaneous equation U= 1'F is required.

In this analysis, as shown in FIG. 11, when the radius R after deformation becomes smaller than the initial radius Re,
Assuming that the ground spring 11 does not act on that part, the ground spring 11 is removed and the calculation is performed again.

In other words, when considering the ground as a spring and evaluating the ground reaction force (resistance earth pressure), the ground reaction force (resistance earth pressure) is only when the shield tunnel segment ring 8 deforms toward the ground (outside). When the tensile force is applied and deforms inward, the ground does not resist the tensile force, so the ground spring 11 does not act.

Therefore, if node 2 is deformed by ΔX and Δy due to the load, R' = 4 (xi + Δx)" + (yi + Δy)" When R'> RcO, the spring 11 acts, and the spring reaction force acts as an external force. When R'<RcO, a tensile force is applied to the spring, so remove it and recalculate. This calculation is repeated until convergence.

Then, -U is calculated for the cross-sectional force f, =, and the displacement U1, moment Mi, axial force N1, and shearing force Qi of each node are determined.

When the load condition is self-weight with j=3, the ground spring may not be considered, so the processing is different from that for other load conditions. However, the analysis procedure is basically the same as in the previous case.

And as a result of automatic analysis, displacement U3, moment)
L, axial force N8, and shear force are determined, and then the values determined under the other load conditions are added to obtain the analysis results U=ΣUj M−ΣMj N−ΣNj Q=ΣQj.

As shown in FIG. 4, these results are outputted in a list format via the output means 3, and are also plotted and outputted as drawings.

1 Note that the present invention is not limited to the above embodiments.

(Effects of the Invention) According to the present invention, the stress of the segment ring for a shield tunnel is analyzed by the finite element method assuming that the ground reaction force is a spring force, and as a result, the radius Re of the segment ring before deformation is , the spring force in the range where the radius R'' after deformation is R'<Rc is released and the stress analysis is performed again, so that accurate stress analysis can be performed. became.

[Brief explanation of the drawing]

Fig. 1 is a block diagram showing the configuration of a stress analysis device showing an embodiment of the present invention, Fig. 2 is a model diagram of the same structure, Fig. 3 is a model diagram of a missing circular structure, and Fig. 4 is a diagram of the present implementation. A block diagram showing the functions of the example stress analysis device, FIGS. 5 and 6 are explanatory diagrams for explaining the functions of the element dividing means, and FIGS.
Figure 0 is a diagram for explaining the function of the data generation means, Figure 7 is an explanatory diagram of the calculation of the spring constant, Figure 8 is an explanatory diagram of the calculation of the load distribution, and Figures 9 and 10 are diagrams for explaining the calculation of the load distribution. FIG. 11 is an explanatory diagram of the calculation of self-weight reaction force. FIG. 11 is a diagram for explaining the function of the FEM calculation means and is an explanatory diagram of determining whether the spring is attached or detached. FIG. 12 is a flowchart for explaining the function of the FEM calculation means. , FIG. 13 is a sectional view of the shield tunnel, FIG. 14 is a load diagram, and FIG. 15 is a sectional view. 1... Stress analysis device, 5... Element division means, 6...
- Data generation means, 7... FEM calculation means, 8, 9.
10... Segment ring for shield tunnel. JP-A-3-148037 (6) -izu=shi b2

Claims (1)

[Claims] (1) Assuming that the ground reaction force is a spring force, the stress of the segment ring for a shield tunnel is analyzed using the finite element method, and as a result, the radius (Rc) of the segment ring before deformation is determined.
A stress analysis method for a segment ring for a shield tunnel, characterized in that the spring force in the range where the radius (R') after deformation satisfies R'<Rc is released and the stress analysis is performed again.