JPH0468512B2 - - Google Patents

Description

[Detailed description of the invention]

[Industrial Field of Application] The present invention relates to a piping design method for a buried conduit formed to be connected to a structure in the ground that is expected to subside. [Prior art] The ground in which the pipe is buried is either (1) extremely strong and there is no need to consider subsidence under normal conditions, or (2) contrary to the above, it is considered to be highly susceptible to subsidence. There may be cases where In the latter case, ground improvement work or reinforcement piles may be driven in advance of piping, but these measures may not completely eliminate the risk of subsidence, and if no special measures are taken. It is often piped. Therefore, when installing piping in such subsidence-prone ground, it is necessary to design highly safe pipelines by assuming that ground subsidence after piping is unavoidable, regardless of whether the above-mentioned precautions are taken or not. It's coming. However, when we talk about ground subsidence, we can think of two types: uniform subsidence, in which the piping subsides entirely, and uneven subsidence, in which local subsidence occurs. However, in the former case of uniform settlement, there is no serious problem because the entire pipe is affected equally, and even in uneven settlement, the amount of subsidence when viewed in the length direction of the pipe changes gradually. If there is, there are few problems. In other words, a big problem with uneven settlement is when an unsettled part and a submerged part exist next to each other, and in general, various structures (buildings, etc.) and buried objects (manholes, etc.) become unsettled parts. , the piping that is joined to these and further extended becomes the submerged part. By the way, the settlement situation in the uneven settlement section piping where the non-subsidence section and subsidence section are adjacent to each other is not fully understood, and common sense suggests that
It was thought that it would be something like the one shown in the figure. In the figure, M indicates a manhole, G indicates subsidence ground (hereinafter simply referred to as ground), and in order from the pipe directly connected to manhole M, the first pipe 1, the second pipe 2, and the third pipe
Number pipe 3, . . . will be referred to as number N pipe N. As for the joints that connect the pipes, use No. 1 joint 1.
j, the second joint 2j, the third joint 3j,..., and the N-th joint Nj. The joint R between the manhole M and the first pipe 1 is completely fixed (non-bending and non-stretchable), but the other joints 1j, 2j, 3j,...Nj are all flexible and non-stretchable. shall have a gender. Therefore, under the conventionally imagined uneven settlement situation as shown in FIG. It is assumed that the entire structure is bent, and the more pipes that participate in this bending (3 pipes No. 2 to 4 in Figure 2), the more stable the uneven settlement situation is. It was thought that In other words, it has been common practice to use tubes with short effective lengths for use in such areas, and to connect many tubes to accommodate the above-mentioned flexure. However, according to the research conducted by the present inventors, it has become clear that there is a need to be concerned about the occurrence of breakaway accidents at the first joint 1j and the second joint 2j in the event of actual uneven settlement. [Problems to be Solved by the Invention] The present applicant has been conducting various researches for some time from the viewpoint of forming pipe joints with a large allowable limit for bending angles, and has developed a multi-stage structure with wide internal pockets for synthetic resin pipe sockets. A version with an expanded diameter is being developed (see Figure 3).
In a conduit in which synthetic resin pipes with single-sided sockets and one-sided sockets with multi-stage enlarged diameter sockets are joined together, the bending angle at the joint can be made large, as shown by the dashed-dotted line in Fig. 3, so that the ground It is expected that it will be highly adaptable to the above-mentioned uneven subsidence caused by weak soils and earthquakes. Therefore, when we investigated the behavior against uneven settlement using a pipe body with a joint with a large allowable bending angle as described above for a pipe directly connected to a manhole where there is a strong risk of uneven settlement, we found the following. Divided. That is, in actual uneven settlement, instead of the situation shown in FIG. 2, where each pipe gradually sinks as it moves away from the manhole M, the second pipe 2 as shown in FIG. There was a tendency for the pipe body beyond No. 3 pipe 3 to maintain a nearly concentric state and eventually undergo equal subsidence. Under such subsidence conditions, the bending angle at the first joint 1j and the second joint 2j becomes extremely large, and the inlet pipe first bends over the open end of the socket pipe as shown by the dashed line in Figure 3. The tube comes into contact with the edge, and the tube continues to bend while being deformed to the extent permitted by the tube characteristics (characteristics of the tube material, diameter, wall thickness, etc.). When such a large bending angle is formed, (1) stress increases at the pipe joint, (2) compression of the packing becomes uneven in the circumferential direction, leading to the risk of water leakage, and (3) power pipes and When inserting cables such as telegraph tubes, there are inconveniences such as reduced insertion workability, etc.
Eventually, this will lead to the joint becoming detached or damaged. That is, it was confirmed that the limit of the pipe as a whole that can withstand uneven settlement is controlled by the joint maintenance limit of the first joint 1j and the second joint 2j. Furthermore, under the condition of uneven settlement as shown in Fig. 1, a situation occurs in which the No. 1 pipe 1 shows significant flexure and responds to the subsidence of the No. 1 joint 1j, causing damage at the joint. It was also confirmed that the root joint R of No. 1 pipe 1 may receive excessive stress and break before an accident occurs. Therefore, we investigated the factors that influence the above-mentioned joint maintenance limit, but since there are restrictions on the allowable bending angle of the joint itself due to the characteristics of the pipe itself or the shape of the joint, no improvement beyond a certain level can be expected. . It was also thought that damage at the joint R with a structure etc. would be greatly influenced by factors other than the allowable bending angle. Therefore, it is thought that it is necessary to deal with this by adding design or improvement to factors other than those mentioned above, and as a result of various studies, the present invention has been completed. In other words, in the ground where uneven settlement is likely to occur, the joints of each pipe maintain the joint function as described above under the assumed amount of subsidence, do not dislodge, and prevent damage to the pipe. In order to design a conduit that can prevent damage (mainly damage at joints with structures, etc.), we conducted research to provide a method that can contribute to this, and arrived at the present invention. [Means for Solving the Problems] The present invention that achieves the above object includes
A buried pipe is constructed by permanently connecting the pipe, and sequentially connecting the pipes from No. 2, No. 3, etc. that are expected to sink relative to the structure to the No. 1 pipe. In forming the formation, in addition to calculating the expected amount of ground subsidence, we also calculate the pipe properties such as the shape and material of the pipe, the joint properties determined by the shape and packing of the joint, and the ground properties given as the ground spring constant. By conducting a response analysis of the pipe based on the above, we can calculate the stress generated in the pipe body that makes up the pipe and the bending at the joint when the length of the first pipe or the second pipe is fixed. Find the allowable range of the length of the second pipe or the first pipe such that the angle and the amount of expansion/contraction satisfy the respective tolerance values, and calculate the effective length of the first pipe and the second pipe from within the permissible range. The purpose of this project is to select and design optimal pipelines to prevent ground subsidence. [Operation] The design procedure of the present invention will be explained below based on FIG. 19. Note that the following description includes related items in addition to the above-mentioned essential constituent elements of the present invention. [] First, we will obtain input data that will be the basis for various analyzes when designing buried pipelines in unevenly settled ground. These basic data can be roughly divided into (A) pipe characteristics, (B) joint characteristics, and (C)
It can be classified into ground characteristics. (A) Pipe characteristics When uneven settlement occurs, external forces are applied to buried pipes from various directions, so it is necessary to be aware of the following characteristic values. Shape: Outer diameter, wall thickness, length, etc. Material: Young's modulus, Poisson's ratio, etc. (B) Joint properties Characteristics determined by the shape of the joint and the characteristics of the attached packing, i.e., bending properties, elastic properties, etc. can be obtained. It is essential. Bending characteristics Bending characteristics are expressed by the relationship between the bending angle of the joint and the rotational moment acting in the bending direction, and are generally as shown in Figure 4, where the bending angle θ at the joint is
When is in the range up to the one-dot chain line state in FIG. 3 (-θ ₁ ≦θ≦θ ₁ ), the joint function is fully exerted and the rotational moment is small. However, when this state is exceeded, stress is generated in the tube body (the tip of the socket and the socket that comes into contact with it), and the rotational moment required for bending increases rapidly. The change in rotational moment during this period should be expressed as a multidimensional function, but for convenience of analysis, it can be expressed as a nonlinear first-order function including a displacement point (allowable bending angle taking into account the safety factor) as shown in Figure 4. It is recommended to use a function. However, if necessary, it can also be grasped and analyzed as a quadratic or cubic function. Stretching characteristics Stretching characteristics are determined by the relationship between the external force acting in the axial direction of the joint and the resulting expansion and contraction [elongation in the direction of withdrawal (plus direction) and contraction in the direction of insertion (minus direction)]. It is generally shown as shown in Figure 5. In the figure, the amount of expansion and contraction (−A ₁ ) ~
The range between (A ₁ ) is the allowable expansion and contraction range that takes into account the safety factor, and if you try to insert it beyond the amount of expansion and contraction (-A ₁ ), an excessive external force will be required and large stress will occur in the pipe body. . On the other hand, if an attempt is made to extend it beyond the amount of expansion/contraction (A ₁ ), it will be pulled out by a slight external force, and if it further exceeds the amount of expansion/contraction (A ₂ ), so-called detachment of the joint will occur. (C) Ground characteristics On the other hand, it is also necessary to be aware of the characteristics of the ground, such as the following. Ground spring constant k ₁ (Kgf/cm ³ ) Relative displacement between the pipe and the soil at the bending point of the nonlinear linear function Δ ₁ (cm) This state can be expressed as shown in Figure 6, and is shown on the vertical axis. What is unit friction force τ (Kgf/cm ² )?
This is the frictional force between soil and soil, and corresponds to the force when the soil begins to slide against each other and collapse. As shown in the figure, until the relative displacement Δ (cm) between the pipe and the soil reaches a certain value (Δ ₁ ), there is a proportional relationship between the unit frictional force and the spring constant k ₁ , but when Δ ₁ It is known that the spring constant k ₂ after the soil begins to collapse is approximately 1/100 of the above spring constant k ₁ . [] The next step is to assume the amount of uneven settlement in the ground where the piping is planned, based on Terzagy's theory [Reference: Latest Soft Ground Handbook for Civil Engineers and Architectural Engineers, published by Construction Industry Research Group Co., Ltd. pp. 134-136 (1981)
(10th day of the month)]. [] Furthermore, we will set the allowable bending angle and allowable amount of expansion/contraction at the pipe joint, as well as the allowable stress of the pipe body, but here we will discuss the above-mentioned pipe body characteristics and joint characteristics (bending characteristics, expansion/contraction characteristics, etc.) using study materials and study results. is used. [] The pipe properties and joint properties given in this way,
By inputting ground characteristics and estimated settlement amounts, response analysis is performed for pipelines using pipes of various shapes and lengths. [] Find a value that satisfies each allowable value for all response values, such as stress joint bending angles, and use this as the allowable amount of settlement of the pipeline. The outline of the analysis method is as follows. (a) Analysis model The following model is the subject of analysis. (1) Consider the buried pipe as a beam on an elastic floor. (2) Ground motion acts only as forced deformation;
Ground displacement at that point acts on the pipe via the ground spring. (3) The spring between the buried pipe and the ground has nonlinear characteristics. In other words, in the direction of the pipe axis, the pipe follows the movement of the ground due to the frictional force acting between the pipe and the soil, but when the maximum frictional force is exceeded, slippage occurs between the pipe and the soil, and the pipe moves in the direction perpendicular to the pipe axis. Now, consider that when a certain value is exceeded, the soil changes from an elastic state to a plastic state. It is assumed that the spring in any direction has completely elastic-plastic nonlinear characteristics. (4) Buried pipelines are intended for those with joints, and the pipe bodies are connected by joints using expansion and contraction springs and rotation springs. At the joint position, axial force is transmitted in the direction of the pipe axis, and axial force is transmitted in the direction perpendicular to the pipe axis. For convey the shear force. The bending moment is also transmitted via the rotation spring. Furthermore, the spring of the joint has nonlinear characteristics depending on the characteristics of the joint.
It goes without saying that by considering the cross-sectional force at the joint position as continuous, it is possible to analyze welding without a joint. (5) The tube remains within its elastic range even after deformation. Figure 7 shows an analytical model diagram. (b) Balance equation for pipes Based on the above assumptions, the basic equations for buried pipes in the elastic region are the following two equations. Tube axis direction (axial strain) -EAd ² U/dx ² +k _sx・U=k _sx・U _sx ……(1) Tube axis perpendicular direction (bending strain) EId ⁴ V/dx ⁴ +k _sy・V=k _sy・V _sy ...(2) Where, U: Displacement of the tube in the tube axis direction (cm), V: Displacement of the tube in the direction perpendicular to the tube axis (cm), E: Elastic constant of the tube body (Kg/cm ² ), I: Moment of inertia of the pipe body (cm
⁴ ), A: Cross-sectional area of the pipe (cm ² ) k _sx : Spring coefficient per unit length of the ground in the direction of the pipe axis (Kg/cm ² ) k _sy : Spring per unit length of the ground in the direction perpendicular to the pipe axis Coefficient (Kg/cm ² ) U _sx : Ground change in the direction of the pipe axis (cm) V _sy : Ground change in the direction perpendicular to the pipe axis (cm) (c) Balance equation of joints Consider the balance of joints of buried pipes . The buried pipes are connected at the joint by an axial spring (spring constant k _T ) and a rotational spring (spring constant k _R ). Figure 8 shows the balance between stress and deformation in the joint. From FIG. 8, the continuity condition at the joint is as follows. U V Φ _L ^k+1 = U V Φ _R ^k +−N/k _T −M/k _R 0 _R ^k ……(3) N M Q _R ^k =N M Q _L ^k+1 ……(4) Here, U, V, Φ, N, M, and Q are the axial direction, axis-perpendicular direction displacement, and deflection angle of the tube, respectively.
It represents axial force, moment, and shear force. (d) Transfer matrix method From equations (1) and (2), the following equation holds between the state quantity vectors V ^L _k and V ^R _k at both ends of the tube l _k . V ^R _k =F _k ·V ^L _k (5) Furthermore, from equations (3) and (4), the following equation holds true between the state quantity vectors on the left and right sides of joint k point. V ^L _k+1 =P _k ·V ^R _k (6) In equations (5) and (6), F _k and P _k are called case and case transfer matrices. Substituting equation (5) into equation (6) yields the following equation. V ^L _k+1 = P _k・F _k・V ^L _k ……(7) Equation (7) shows that the state quantity vector V on the left side of beam l _k is
By apron of case transfer matrix F _k and case transfer matrix P _k , beams l _k = l ₁ , l ₂ ...
Since the case transfer matrix and the case transfer matrix are found for ..., repeating the transfer calculation shown in equation (7) in order from beam l ₁ , we get
The state quantity vector at the left end of the continuous beam is transmitted to the right end. In other words, V ^R _N =F _N・P _N-1 …P ₂・F ₂・P ₁・F ₁・V ^L ₁ …(8) Equation (8) is related only to the physical quantities at both ends of the continuous beam. It is a linear equation. By substituting the boundary conditions at both ends into this equation (8), the following equation is obtained. R′・F _N・P _N-1・F _N-1 …P ₁・F ₁・R・A ^L ₁ = 0
...(9) By solving Equation (9), the unknown quantity at the left end is found, and by repeatedly using the case transfer formula and case transfer formula from beam l ₁ , the state quantities of the beams in all spans are calculated. A vector is calculated. By the way, the transfer matrix method repeats matrix multiplication as described above. Therefore, it is expected that a loss of digits will occur in numerical calculations. Therefore, in order to avoid this problem of dropped digits, it is necessary to make the numerical elements of the transfer matrix dimensionless and convert them into numerical values close to 1 using an arbitrary reference constant. By analyzing equation (9) using the load increment method, nonlinear characteristics of the ground spring and joint spring are introduced. According to the above analysis, for a pipeline with a certain shape and pipe length, the relationship between the joint bending angle (θ) and the amount of settlement (δ) [Figure 9a], the amount of expansion and contraction of the joint (Δ) and the amount of settlement (δ) ) [Figure 9b] and the relationship between the maximum stress (σ) generated in the pipe body and the amount of settlement (Figure 10)
are obtained as shown in the figure. From these figures, the amount of settlement when the joint bending angle reaches its allowable bending angle (hereinafter referred to as allowable settlement amount δ ^B _cri ), and the amount of settlement when the amount of joint expansion and contraction reaches its allowable amount of expansion and contraction (hereinafter referred to as allowable settlement amount) (referred to as δ ^E _cri ) and the amount of settlement when the stress generated in the tube reaches its maximum stress (hereinafter referred to as allowable amount of settlement δ ^S _cri ). Such calculations are performed by varying the pipe length to determine the pipe length that maximizes the allowable sinkage amount. for example,
If the lengths of the second and subsequent pipes are fixed and the length of the first pipe is varied, the relationship between the length of the first pipe and the allowable settlement amount is obtained as shown in FIG. 11. Based on the idea that the allowable sinkage amount of the pipe is controlled by the lowest value among δ ^B _cri , δ ^E _cri and δ ^S _cri , the optimum length of the first pipe in FIG. 11 is lop. Similarly, if the length of the second pipe is fixed to an arbitrary value and the length of the first pipe is varied for each of the second pipe lengths, for example,
As shown in the figure, the allowable range of the length of the first pipe that can be adapted to the allowable settlement amounts δ ^B _cri , δ ^E _cri , and δ ^S _cri can be determined. In addition, in the above explanation, the length of the second pipe was fixed and the allowable range of the length of the first pipe was determined, but the length of the first pipe was fixed to an arbitrary value, and the length of the first pipe was When the length of the second pipe is varied, for example, in a graph in which the horizontal axis is the fixed length of the first pipe and the vertical axis is the fixed length of the second pipe in Fig. 20, the allowable range of the length of the second pipe is similarly shown. Desired. That is, in the present invention, after determining the allowable range of the length of the second pipe or the first pipe when the length of the first pipe or the second pipe is fixed, The effective length of the pipe and/or the second pipe is selected from within the above-mentioned allowable range. [Effects of the Invention] Since the present invention is configured as described above, it is possible to appropriately design piping in the ground where uneven settlement occurs, contributing to safe and efficient piping formation. [Example] In the description of the following examples, all calculations are performed by an electronic computer (not shown) unless otherwise specified. In the pipeline shown in FIG. 12, the length _l1 of the first pipe shall be determined so that the allowable amount of subsidence of the conduit is greater than or equal to the expected amount of ground subsidence. In this example, the length of the pipes after the second pipe was fixed at 2 m. Also, the estimated amount of subsidence is assumed to be 15cm. Table 1 shows the pipe characteristics as input data necessary for response analysis, and Fig. 13 shows the joint characteristics. Based on the experimental results of the present inventors, the ground spring constant and the slip limit displacement of the ground spring as ground characteristics are as follows.
The soil cover was set at 1.2m as shown in Figure 14.

[Table] Figure 15 shows the relationship between the length of the first pipe: l ₁ and the allowable settlement amounts δ ^B _cri and δ ^S _cri obtained from the response analysis results.
The amount of joint expansion and contraction was omitted in this example because the response value was well below the allowable value and it was judged to be sufficiently safe. From this figure, we obtained the result that by setting l ₁ to 50 to 70 cm, a pipe can be formed in which the allowable amount of subsidence of the pipe is 15 cm or more, which is the expected amount of ground subsidence. In the above example, the length of the second pipe is fixed at 2 m, but the length of the second pipe is set to 1 m.
The effective length of the first pipe when the fixed length is changed to m, 3 m, and 4 m is as shown in Figure 20, and the allowable range of the first pipe length according to the second pipe length is Desired. Similarly, by fixing the length of the first pipe to an arbitrary length, the allowable range of the length of the second pipe can be determined. However, even greater ground subsidence may be expected. For example, if the expected amount of subsidence is 30 cm, as shown in Figure 15, it is impossible to counter ground subsidence by modifying the length of the first pipe _l1 .
The present inventors have developed the 16th tube body with excellent stress resistance.
We are developing pipes with different wall thicknesses as shown in the figure. FIG. 18 shows the relationship between the first pipe length l ₁ and the allowable settlement amounts δ ^B _cri and δ ^S _cri for this pipe with different wall thicknesses, obtained by the same analysis as described above. From this figure, we obtained the result that by setting _l1 to 95 to 100 cm, a conduit can be formed in which the allowable amount of ground subsidence for the conduit is at least 30 cm.
The characteristics of the main pipe body are shown in Table 2.

[Table] When a pipe of different wall thickness as described above is used as the first pipe, the maximum stress may be observed in the second pipe. However, from the perspective of piping safety, it is best to generate the maximum stress in the first pipe fixed to a structure, etc. In this case, as shown in Figure 17, it is better to generate the maximum stress in the first pipe with a different wall thickness. Adopted as the second pipe, the first and second
It is recommended that both pipes be of different wall thickness.

[Brief explanation of drawings]

Figure 1 is an explanatory diagram of the unequal settlement situation that the inventors were able to clarify, Figure 2 is an explanatory diagram of the unequal settlement situation that was conventionally considered, and Figure 3 is the allowable bending according to the development of the inventors. Explanatory diagram showing a pipe body with a large angle, 4th and 5th
The figure is a graph showing the bending and expansion characteristics of the joint, Figure 6 is a graph showing the ground characteristics, Figures 7 and 8 are analysis model diagrams based on beam theory on an elastic floor, and Figures 9 and 10 are settlement amount and pipe response. Fig. 11 is a graph showing the relationship between allowable settlement amount and pipe length, Fig. 12 is a schematic explanatory diagram showing the pipe line adopted in the example, Fig. 1
Figure 3 is a graph showing the joint characteristics used in the response analysis in the example, Figure 14 is a graph showing the ground characteristics used in the response analysis in the example, and Figure 15.
Figures 7 and 18 are graphs showing the relationship between the allowable settlement amount and the length of the first pipe obtained by the response analysis in the example,
FIG. 16 is a partially cutaway side view of a tube of different wall thickness. FIG. 19 is an explanatory diagram showing the design procedure according to the present invention, and FIG. 20 is a graph showing the relationship between the length of the second pipe and the effective length of the first pipe in the embodiment of the present invention.

Claims (1)

[Claims] 1. A first pipe is fixedly connected to a structure, and a second pipe is fixedly connected to a structure, and a second pipe is expected to sink relative to the structure.
When forming a buried pipeline by sequentially connecting the pipes from No. 3 to the No. 1 pipe, we calculate the expected amount of subsidence of the ground, and also determine the pipe characteristics such as the shape and material of the pipe. The length of the first or second pipe can be determined by analyzing the response of the pipe based on the joint characteristics determined by the joint shape and packing, and the ground characteristics given as the ground spring constant. The second pipe is such that the stress generated in the pipe body constituting the pipe line and the bending angle and expansion/contraction amount at the joint part satisfy the respective allowable values when fixed.
Find the allowable range of the effective length of the first pipe or the first pipe,
A piping design method for a buried pipeline, characterized by designing an optimal pipeline for ground subsidence, characterized by selecting effective lengths of the first pipe and the second pipe from the range.