CN111859553B - Method for manufacturing combined material pipe gallery model in geotechnical centrifuge - Google Patents
Method for manufacturing combined material pipe gallery model in geotechnical centrifuge Download PDFInfo
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- CN111859553B CN111859553B CN202010486075.0A CN202010486075A CN111859553B CN 111859553 B CN111859553 B CN 111859553B CN 202010486075 A CN202010486075 A CN 202010486075A CN 111859553 B CN111859553 B CN 111859553B
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- G06F30/10—Geometric CAD
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Abstract
The invention belongs to the technical field of geotechnical engineering experiments, and discloses a method for manufacturing a combined material pipe gallery model in a geotechnical centrifuge, wherein a material A with the elastic modulus larger than that of concrete used by a solid pipe joint is selected to be manufactured into a sheet body; selecting a material B with the elasticity modulus smaller than that of concrete used by the solid pipe joint as a main body; the sizes of the main body and the sheet body are determined and corrected, so that the sum of the bending rigidity of the centering neutral shaft of the main body and the sheet body is equal to the section bending equivalent rigidity of the reduced-scale pipe joint; the sheet body is attached to the main body to manufacture a reduced-scale pipe joint; a plurality of reduced scale tube joints are connected to be model piping lane to at the junction installation rubber pad of reduced scale tube joint. According to the invention, through the rigidity equivalence principle, the ratio of the section bending equivalent rigidity of the manufactured pipe gallery model to the section bending rigidity of the prototype pipe gallery is 1/N4Therefore, the deformation field in the geotechnical centrifuge test is similar to the actual situation.
Description
Technical Field
The invention belongs to the technical field of geotechnical engineering experiments, and particularly relates to a method for manufacturing a pipe gallery reduced scale model under the condition of equivalent rigidity, which is suitable for being applied to a narrow space in a centrifugal machine.
Background
The basic principle of the centrifugal machine model test is that a reduced scale model is manufactured by a prototype structure or a component according to a certain proportion and is placed in a high centrifugal stress field generated by the high-speed rotation of a centrifugal machine main shaft, the physical force borne by the reduced scale model is increased, the physical force borne by the reduced scale model and the surface force borne by the reduced scale model are increased by a certain factor, and the deformation process similar to that of the prototype structure or the component is shown. Wherein the conversion relation between the expansion factor N and the rotating speed rpm is as follows:
N=1.11×10-5×R×(rpm)2/g (1)
in the formula:
n-the stress expansion multiple of the model;
r-rotational radius of geotechnical centrifuge (cm);
rpm-geotechnical centrifuge rotational speed (r/min);
g-acceleration of gravity (m/s)2)。
TABLE 1 geotechnical centrifuge model test similarity relationship
And applying a rotating speed to the reduced scale model through the centrifugal machine to enable the external force borne by the reduced scale model to be equivalent to the actual situation. In order to make the strain state of the reduced scale model similar to the actual situation, the bending rigidity ratio of the reduced scale model to the prototype pipe gallery/tunnel needs to be ensured to be 1/n. However, it is difficult to find a material that is easy to process, has a certain strength, and has an elastic modulus exactly the same as that of the prototype structural concrete.
Disclosure of Invention
The invention aims to solve the problem of equivalent rigidity of the model under the condition of reducing the scale in the centrifuge, provides a method for manufacturing a combined material pipe gallery model in a geotechnical centrifuge, and can realize the similarity of the deformation conditions of the reducing scale model and a prototype pipe gallery in a centrifuge test as far as possible.
In order to solve the technical problems, the invention is realized by the following technical scheme:
method for manufacturing combined material pipe gallery model in geotechnical centrifuge
The pipe gallery model is formed by connecting a plurality of reduced scale pipe joints, and the reduced scale pipe joints are manufactured according to the following steps:
(1) according to the size of the solid pipe joint of the prototype pipe gallery, obtaining the section bending rigidity of the solid pipe joint and obtaining the size of the outer frame of the reduced pipe joint;
(2) obtaining the section bending equivalent stiffness of the reduced pipe joint according to the section bending stiffness of the solid pipe joint and the model stress expansion multiple;
(3) selecting a material A with the elastic modulus larger than that of concrete used by the solid pipe joint, manufacturing the material A into one or two sheet bodies with the length and width dimensions same as those of the upper surface and/or the lower surface of the reduced pipe joint, and correcting the thickness of the sheet bodies to enable the bending rigidity of a centering neutral shaft of the sheet bodies to reach 80-95% of the bending equivalent rigidity of the section of the reduced pipe joint;
(4) selecting a material B with the elastic modulus smaller than that of concrete used by the solid pipe joint, and manufacturing the material B into a main body, wherein the length and width of the main body are the same as those of the outer frame of the reduced pipe joint, and the height of the main body is equal to the difference between the height of the outer frame of the reduced pipe joint and the thickness of the sheet body;
(5) correcting the size of an inner frame of the main body to enable the sum of the bending rigidity of the centering neutral shaft of the main body and the sheet body to be equal to the section bending equivalent rigidity of the reduced pipe joint;
(6) and (4) laminating and fixedly connecting the sheet body obtained in the step (3) with the upper surface and/or the lower surface of the main body obtained in the step (4) to manufacture the reduced-scale pipe joint.
Further, the material A is one of stainless steel, iron, zinc and tin.
Further, the material B is one of photosensitive resin, plastic and epoxy resin.
Further, in step (5): when the size of the inner frame of the main body is corrected, the sum of the bending rigidity of the centering shaft of the main body and the sheet body cannot be equal to the section bending equivalent rigidity of the reduced pipe joint, the size of the inner frame of the main body meeting the strength requirement is determined, and then the length of the sheet body is corrected, so that the bending rigidity of the centering shaft of the sheet body is equal to the difference between the section bending equivalent rigidity of the reduced pipe joint and the bending rigidity of the centering shaft of the main body.
Further, in step (6): and (4) attaching and fixedly connecting one sheet body obtained in the step (3) to the upper surface or the lower surface of the main body obtained in the step (4).
Further, in step (6): and (4) respectively attaching and fixedly connecting the two sheet bodies obtained in the step (3) to the upper surface and the lower surface of the main body obtained in the step (4).
Further, a plurality of the reduced pipe joints obtained in the step (6) are connected into a model pipe gallery, a rubber pad is installed at the joint of the reduced pipe joints, and the rubber pad is used for simulating a water stop pad of the entity pipe gallery.
The invention has the beneficial effects that:
the invention relates to a pipe gallery model manufactured by a rigidity equivalence principleThe ratio of the cross-section bending equivalent stiffness to the cross-section bending stiffness of the prototype pipe gallery is 1/N4The method has a similar deformation field with the actual situation in the geotechnical centrifuge test, and provides a reliable model manufacturing method for exploring the model deformation test in the geotechnical centrifuge;
according to the invention, two materials with different rigidity are combined to manufacture the reduced pipe joint, the processing process is simple and controllable, and the pipe gallery model can be quickly and efficiently manufactured;
the invention has the advantages that the two materials with different rigidities are selected to be combined to manufacture the reduced-scale pipe joint, the material selection range is wide, different materials can adapt to different soil quality and water quality conditions, and the reduced-scale pipe joint can be well coupled with the geotechnical centrifuge environment.
Drawings
Fig. 1 is a schematic structural diagram of a solid pipe joint of a prototype pipe gallery in this embodiment;
FIG. 2 is a front view of a reduced scale pipe section of the pipe gallery model in this embodiment;
FIG. 3 is a reduced scale pipe section side view of the pipe gallery model in this embodiment;
in the above figures: 1-a body; 2-tablet.
Detailed Description
In order to further understand the contents, features and effects of the present invention, the following embodiments are illustrated and described in detail with reference to the accompanying drawings:
the embodiment provides a method for manufacturing a combined material pipe gallery model in a geotechnical centrifuge, which comprises the steps of calculating and determining the section size of a pipe gallery model after being reduced in size according to a rigidity equivalence principle, and then manufacturing the combined material pipe gallery model by combining two materials; the large-scale pipe gallery test bench mainly solves the problems that in a geotechnical centrifuge test, a prototype pipe gallery is too large in size and cannot be directly tested, a common scale model is not easy to machine, and rigidity equivalence and deformation similarity of the prototype pipe gallery are difficult to achieve.
The pipe gallery model is formed by connecting a plurality of reduced pipe joints, each reduced pipe joint is generally a cuboid frame-shaped structure, the reduced pipe joints are made by combining a material A and a material B, the material A is a material with the elasticity modulus larger than that of concrete used by a solid pipe joint, and specifically, stainless steel, iron, zinc, tin and the like can be adopted; the material B is selected from the materials with the elastic modulus smaller than that of the material BConcrete materials used for the pipe joints can be photosensitive resin, plastic, epoxy resin and the like. The material A is made into one or two sheet bodies 2, the material B is made into a main body 1, the sheet bodies 2 are fixedly connected to the upper surface and/or the lower surface of the main body 1 in an attaching mode to make a reduced pipe joint, and the ratio of the bending equivalent stiffness of the section of a reduced pipe gallery model to the bending equivalent stiffness of the section of a prototype pipe gallery is 1/N4。
According to the rigidity equivalence principle, the formula is obtained:
(E1I1+E2I2)×1/N4=ECIC (2)
in formula (2): e1Elastic modulus (kPa), E of Material A used for sheet 22The modulus of elasticity (kPa), E of the material B of the body 1C-modulus of elasticity (kPa), I of concrete selected for solid pipe section1The central neutral moment of inertia (m) of the plate 24),I2Centering axial moment of inertia (m) of body 14),ICSection moment of inertia (m) of a solid pipe section4) And N is the stress expansion multiple of the model.
The embodiment provides a method for manufacturing a combined material pipe gallery model in a geotechnical centrifuge, which comprises the following specific steps:
as shown in fig. 1, determining the size of the solid pipe joint of the prototype pipe gallery, selecting an outer frame of the solid pipe joint with the length of 6.75m, the height of 3.5m, the width of 2m and the wall thickness of 0.25 m; each bin of the solid pipe joint inner frame is 3m by 3m in size, and a chamfer is arranged. The solid pipe joint is made of concrete with the mark C50 and the elastic modulus EC35.5 GPa. According to the inertia moment formula, calculating the section inertia moment Ic of the solid pipe section to be 1.112e13mm4Section bending stiffness Ecic of 3.9476e14kPa x mm4。
And (3) setting the rotating speed rpm according to the geotechnical centrifuge model test, and obtaining the stress expansion factor N of the model as 100 by converting the relation formula (1). And reducing the size of the outer frame of the solid pipe joint by N which is 100 times, so that the load borne by the reduced pipe joint in the geotechnical centrifuge test process is equivalent to the load borne by the solid pipe joint. Determining the external dimensions of the reduced pipe section as follows: the length is 6.75cm, the width is 2cm and the height is 3.5 cm.
According to Ecic of 3.9476e14kPa x mm4And N is 100, calculating the section bending equivalent stiffness of the reduced-scale pipe joint equivalent to the stiffness of the solid pipe joint by the formula (2) (E)1I1+E2I2) 394.76kPa x mm4. In this embodiment, stainless steel with a modulus of elasticity greater than that of concrete used for the solid pipe joint is selected, and the modulus of elasticity E of stainless steel1Is 206 GPa. Stainless steel was made as two sheets 2 by laser cutting. The length and width of the sheet body 2 are consistent with the length and width of the upper surface and the lower surface of the reduced-scale pipe joint obtained by calculation, and are determined as 6.75cm in length and 2cm in width.
In order to ensure that the bending stiffness of the sheet body 2 accounts for 80% -95% of the equivalent bending stiffness of the section of the reduced pipe joint, the bending stiffness of the sheet body 2 accounts for 95% in the embodiment. To ensure the machining accuracy, the decimal place is discarded, and according to the formula of the moment of inertia, two sheets 2 with the thickness h equal to 0.45mm are selected for the present embodiment. The central neutral axis inertia moment I of each sheet 2 according to the formula of inertia moment1/2=0.906mm4Centering neutral axis bending stiffness E of the two sheet bodies 21I1=373.2kPa×mm4And the equivalent bending rigidity accounts for 94.54% of the section bending equivalent rigidity of the reduced-scale pipe joint.
In this embodiment, a photosensitive resin is selected as the main body 1, and the elastic modulus of the photosensitive resin is smaller than that of concrete used for the solid pipe joint. The material properties of the inlet 9400 photosensitive resin are shown in table 2.
TABLE 2
The photosensitive resin was 3D printed into a body 1 having a length and width identical to those of the reduced-scale pipe section, 6.75cm in length and 2cm in width. In order to ensure that the load borne by the reduced-scale pipe joint is equivalent, the height H of the photosensitive resin 3D printing main body 1 is calculated according to the following formula, and H is calculated to be 34.1 mm.
H=H1-2*h (3)
In formula (3), H-height (mm) of the body 1, H1-height of reduced pipe section (mm)And h-thickness (mm) of each sheet 2.
Elastic modulus E of photosensitive resin2Is 2 GPa. The embodiment selects the photosensitive resin 3D printing main body 1, and the cross-sectional dimension of the main body is 6.75cm long, 2cm wide and 3.41cm high. For the inner frame size, the size of each inner bin and the size of the solid pipe joint are reduced according to the stress expansion multiple N of the model, namely 100, according to the formula (3), the cross section size of each bin is calculated to be 2.91cm by 2.91cm, and chamfers are arranged. Calculating the section inertia moment I of the photosensitive resin 3D printing main body 1 according to an inertia moment formula2=17.089mm4Cross-sectional bending stiffness E2I2=34.176kPa×mm4。
According to the formula (E)1I1+E2I2)×1/N4=ECICThe equivalent rigidity (E) of the bending resistance of the section of the reduced pipe section designed at present can be known1I1+E2I2) 394.7952kPa x mm4And the completely equivalent section bending rigidity is 394.76kPa x mm4The relative error is 8.9e-5, and the error is less than 1 percent, thereby meeting the test requirements.
When the sum of the bending rigidity of the centering neutral axis of the main body 1 and the sheet bodies 2 cannot be equal to the section bending equivalent rigidity of the reduced pipe joint by correcting the size of the inner frame of the main body 1, the size of the inner frame of the main body 1 meeting the strength requirement is determined, and then the length of the sheet bodies 2 is corrected to enable the bending rigidity of the centering neutral axis of the main body 1 to be equal to the difference between the section bending equivalent rigidity of the reduced pipe joint and the bending rigidity of the centering neutral axis of one or two sheet bodies 2.
And step five, designing the size according to the step four, and manufacturing the main body 1 by adopting a photosensitive resin 3D printer.
And step six, respectively bonding the sheet body 2 with the upper surface and the lower surface of the main body 1 printed by the photosensitive resin 3D by using AB glue, manufacturing a reduced scale pipe joint, and bonding a water-stopping rubber pad at a socket of the reduced scale pipe joint. And after the bonding is finished, splicing the reduced pipe sections back and forth to manufacture a pipe gallery model.
Although the preferred embodiments of the present invention have been described with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, which are only illustrative and not restrictive, and those skilled in the art can make various changes and modifications within the scope of the present invention without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (7)
1. The utility model provides a combined material pipe gallery model manufacturing method in geotechnical centrifuge, this pipe gallery model is connected by a plurality of reduced scale tube joints and constitutes which characterized in that, the reduced scale tube joint is according to following step preparation:
(1) according to the size of the solid pipe joint of the prototype pipe gallery, obtaining the section bending rigidity of the solid pipe joint and obtaining the size of the outer frame of the reduced pipe joint;
(2) obtaining the section bending equivalent stiffness of the reduced pipe joint according to the section bending stiffness of the solid pipe joint and the model stress expansion multiple;
(3) selecting a material A with the elastic modulus larger than that of concrete used by the solid pipe joint, manufacturing the material A into one or two sheet bodies with the length and width dimension same as that of the upper surface and/or the lower surface of the reduced pipe joint, and correcting the thickness of the sheet bodies to enable the bending rigidity of a centering neutral axis of the sheet bodies to reach 80-95% of the section bending equivalent rigidity of the reduced pipe joint;
(4) selecting a material B with the elastic modulus smaller than that of concrete used by the solid pipe joint, and manufacturing the material B into a main body, wherein the length and width of the main body are the same as those of the outer frame of the reduced pipe joint, and the height of the main body is equal to the difference between the height of the outer frame of the reduced pipe joint and the thickness of the sheet body;
(5) correcting the size of an inner frame of the main body to enable the sum of the bending rigidity of the centering neutral shaft of the main body and the sheet body to be equal to the section bending equivalent rigidity of the reduced pipe joint;
(6) and (4) laminating and fixedly connecting the sheet body obtained in the step (3) with the upper surface and/or the lower surface of the main body obtained in the step (4) to manufacture the reduced-scale pipe joint.
2. The method for modeling a combined material pipe gallery in a centrifugal machine for earthwork according to claim 1, wherein the material A is one of stainless steel, iron, zinc and tin.
3. The method for modeling the combined material pipe gallery in the geotechnical centrifuge as claimed in claim 1, wherein said material B is one of photosensitive resin, plastic and epoxy resin.
4. The method for making a combined material pipe gallery model in a centrifugal machine for earthwork according to claim 1, wherein in the step (5): when the size of the inner frame of the main body is corrected, the sum of the bending rigidity of the centering shaft of the main body and the sheet body cannot be equal to the section bending equivalent rigidity of the reduced pipe joint, the size of the inner frame of the main body meeting the strength requirement is determined, and then the length of the sheet body is corrected, so that the bending rigidity of the centering shaft of the sheet body is equal to the difference between the section bending equivalent rigidity of the reduced pipe joint and the bending rigidity of the centering shaft of the main body.
5. The method for manufacturing the combined material pipe gallery model in the geotechnical centrifuge according to claim 1, wherein in the step (6): and (4) adhering and fixedly connecting one sheet body obtained in the step (3) to the upper surface or the lower surface of the main body obtained in the step (4).
6. The method for manufacturing the combined material pipe gallery model in the geotechnical centrifuge according to claim 1, wherein in the step (6): and (4) respectively attaching and fixedly connecting the two sheet bodies obtained in the step (3) to the upper surface and the lower surface of the main body obtained in the step (4).
7. The method for manufacturing the combined material pipe gallery model in the geotechnical centrifuge as claimed in claim 1, wherein the plurality of reduced pipe joints obtained in the step (6) are connected to form a model pipe gallery, and a rubber pad is installed at the joint of the reduced pipe joints and used for simulating a water stop pad of a solid pipe gallery.
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