A grouting structure with formwork for tunnel vault construction

Abstract

The present invention relates to the technical field of tunnel crown grouting, and specifically relates to a formwork grouting structure for tunnel crown construction, which includes a material injection cylinder. Inside the material injection cylinder, there are a guide cylinder and a fixing plate. The fixing plate is fixedly connected to the inner side wall of the material injection cylinder. At the center of the fixing plate, a fixing groove is fixedly opened. The outer side wall of the guide cylinder is fixedly connected to the inner wall of the fixing groove. A guide rod is slidably connected inside the guide cylinder. At the top of the guide rod, a conical pressure plate is sleeved and fixed. A diversion component is arranged outside the conical pressure plate. The diversion component includes a push rod and a conical connection block. A through groove is opened through the top of the guide rod. The push rod is slidably connected in the through groove. The conical connection block is fixedly connected to the top of the push rod. Compared with the prior art, the present invention can effectively improve the flow rate and impact force of concrete and enhance the filling effect on the crown through the coordinated action of the conical pressure plate and the second connecting plate, avoiding problems such as cavities during the grouting process.

Description

Technical Field

[0001] The present invention relates to the technical field of tunnel vault grouting, and specifically relates to a formwork grouting structure for tunnel vault construction. Background Technique

[0002] In tunnel vault construction, formwork grouting is to perform grouting operations inside the lining formwork, and the principle is to inject a slurry with specific properties into the gap between the lining and the primary support through the grouting holes reserved on the formwork, so as to achieve the purposes of filling, reinforcement, and waterproofing.

[0003] The traditional formwork grouting method for tunnel vault construction relies on the self-flow of concrete. However, it is difficult for the concrete to completely fill the vault by itself, and it is easy to generate voids and void areas. Moreover, it is easy to form accumulations near the grouting holes, further reducing the flow rate of the concrete slurry. Due to the change in flow resistance, the concrete may not reach fully, resulting in voids, greatly reducing the integrity and bearing capacity of the lining structure, adding safety risks during the use of the tunnel, and relying solely on the self-flow of concrete to complete filling is slow and greatly prolongs the construction time.

[0004] In view of the above technical defects, a solution is proposed now. Summary of the Invention

[0005] The purpose of the present invention is to provide a formwork grouting structure for tunnel vault construction to solve the technical defects proposed in the background technique.

[0006] To achieve the above purpose, the present invention provides the following technical solution: A formwork grouting structure for tunnel vault construction, including a material injection cylinder, wherein a guiding cylinder and a fixing plate are arranged inside the material injection cylinder, the fixing plate is fixedly connected to the inner side wall of the material injection cylinder, a fixing groove is fixedly opened at the center of the fixing plate, the outer side wall of the guiding cylinder is fixedly connected to the inner wall of the fixing groove, a guiding rod is slidably connected inside the guiding cylinder, a conical pressing plate is sleeved and fixed at the top end of the guiding rod, and a diversion assembly is arranged outside the conical pressing plate.

[0007] Further, the diversion assembly includes a push rod and a conical connecting block. A through groove is opened at the top end of the guiding rod, the push rod is slidably connected in the through groove, the conical connecting block is fixedly connected to the top end of the push rod, a plurality of groups of connecting plates one are arranged in an annular array at the bottom of the conical connecting block, a plurality of groups of connecting plates two are arranged in an annular array at the top of the conical pressing plate, the bottom of the conical connecting block is rotationally connected to the connecting plates one through corresponding brackets, the top of the conical pressing plate is rotationally connected to the connecting plates two through corresponding brackets, and the adjacent ends of the connecting plates one and the connecting plates two are rotationally connected.

[0008] Furthermore, a plurality of cushion sleeves are fixedly connected to the top of the conical pressure plate in an annular array. A first cushion block is slidably connected inside the cushion sleeve. A first compression spring is fixedly connected inside the cushion sleeve. The first cushion block is fixedly connected to the first compression spring. The top of the first cushion block is provided with an inclined surface that cooperates with the first connecting plate. A second cushion block is fixedly connected to one side wall of the second connecting plate.

[0009] Furthermore, a positioning block is sleeved and fixed on the outer circumference of the guide rod near the bottom end. Threads are provided on the outer side of the positioning block. A cap nut is threadedly connected to the outer side of the positioning block. A plurality of positioning grooves and positioning holes are provided on the side wall of the positioning block. The bottom end of the push rod is fixedly connected to a base. A limiting rod corresponding to the number of positioning grooves is rotatably connected to the outer side of the base. A plug block that cooperates with the positioning groove is fixedly connected to the outer side of the top end of the limiting rod.

[0010] Furthermore, a plurality of through cylinders are fixedly connected to the side wall of the injection barrel in an annular array. The through cylinders communicate with the side wall of the injection barrel. A rotating rod is rotatably connected inside the through cylinder. A stirring frame is fixedly connected to the outer side of the rotating rod located outside the injection barrel. A gear is fixedly connected to one end of the rotating rod located inside the injection barrel.

[0011] Furthermore, a plurality of sliding grooves are provided on the side wall of the guide cylinder in an annular array. A rack is slidably connected inside the sliding groove. One end of the rack is fixedly connected to the side wall of the guide rod. The rack is meshed with the gear.

[0012] Furthermore, a flange is fixed to the outer circumferential side wall of the injection barrel by electric welding. A plurality of connectors are communicated with the side wall of the injection barrel. The connectors are arranged in an annular shape with the center of the injection barrel as the center.

[0013] Furthermore, the bottom of the injection barrel is fixedly connected to a frame by bolts. A driving block is slidably connected inside the frame. The driving block is fixedly connected to the bottom of the side wall of the guide rod. A turntable is rotatably connected to the side wall of the frame through a bearing. A motor for driving the turntable to rotate is fixedly installed on the other side wall of the frame. One end of the driving block is rotatably connected to a driving rod. The other end of the driving rod away from the driving block is rotatably connected to the side wall of the turntable.

[0014] Compared with the prior art, the beneficial effects of the present invention are:

[0015] 1. When dealing with the thorny problem of narrow grouting holes, the present invention gives full play to the remarkable feature of flexible folding of connecting plate one and connecting plate two, enabling the diversion component to smoothly enter the interior of the vault. By virtue of the close cooperation among the limiting rod, the insertion block, and the screw cap, the fixed states of folding and unfolding of connecting plate one and connecting plate two are firmly fixed. In addition, relying on the unique property that the guiding rod can reciprocate, the conical pressing plate and connecting plate two cooperate, which not only greatly increases the contact area with the concrete, significantly improves the amount of concrete processed at one time, but also effectively enhances the flowing ability of the concrete, meaning that the flowing speed and impact force of the concrete slurry are significantly increased, and its flowing range is also greatly expanded.

[0016] 2. The present invention replaces the "traditional flowing and stirring" method with an innovative "extrusion and pushing" method for filling. Through such an innovative measure, a series of thorny problems such as voids and cavities in the vault concrete can be more effectively solved. Moreover, by using the reciprocating meshing transmission between the rack and the gear, the rotating rod is powerfully driven to rotate, and during the rotation process of the rotating rod, the stirring frame is driven to rotate synchronously. The stirring frame further stirs and conveys the concrete slurry during this process, thus successfully avoiding the bad phenomenon of the concrete slurry accumulating near the injection barrel. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] For the convenience of those skilled in the art to understand, the present invention will be further described below in conjunction with the drawings;

[0018] Figure 1 is a three-dimensional view of the overall structure of the present invention;

[0019] Figure 2 is a sectional view of the overall structure of the present invention;

[0020] Figure 3 is Figure 1 an enlarged structural schematic diagram of area A of

[0021] Figure 4 is a top view of the internal structure of the injection barrel in the present invention;

[0022] Figure 5 is a schematic diagram of the diversion component in the present invention;

[0023] Figure 6 is a schematic diagram of the frame structure in the present invention.

[0024] Reference numerals: 1, material injection cylinder; 2, flange; 3, connector; 4, guide cylinder; 5, fixing plate; 6, guide rod; 7, conical pressure plate; 8, diversion assembly; 801, push rod; 802, conical connection block; 803, connecting plate I; 804, connecting plate II; 805, cushion sleeve; 806, cushion block I; 807, cushion block II; 9, positioning block; 10, screw cap; 11, positioning groove; 12, positioning hole; 13, base; 14, limiting rod; 15, plug-in block; 16, through cylinder; 17, rotating rod; 18, stirring frame; 19, gear; 20, chute; 21, rack; 22, frame; 23, driving block; 24, turntable; 25, motor; 26, driving rod. Detailed implementation mode

[0025] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work shall fall within the protection scope of the present invention.

[0026] Embodiment 1: As Figures 1-6 shown, a formwork grouting structure for tunnel vault construction includes a material injection cylinder 1. A guide cylinder 4 and a fixing plate 5 are arranged inside the material injection cylinder 1. The fixing plate 5 is fixedly connected to the inner side wall of the material injection cylinder 1. A fixing groove is fixedly opened at the center of the fixing plate 5. The outer side wall of the guide cylinder 4 is fixedly connected to the inner wall of the fixing groove. A guide rod 6 is slidably connected inside the guide cylinder 4. The top of the guide rod 6 is sleeved and fixed with a conical pressure plate 7. A diversion assembly 8 is arranged outside the conical pressure plate 7;

[0027] The outer circumferential side wall of the material injection cylinder 1 is fixed with a flange 2 by electric welding. A plurality of groups of connectors 3 are communicated with the side wall of the material injection cylinder 1. The connectors 3 are arranged in a ring with the center of the material injection cylinder 1 as the center. A positioning block 9 is sleeved and fixed on the outer circumference of the guide rod 6 near the bottom end. Threads are opened on the outer side of the positioning block 9. A screw cap 10 is threadedly connected to the outer side of the positioning block 9. A plurality of groups of positioning grooves 11 and positioning holes 12 are opened on the side wall of the positioning block 9. The bottom end of the push rod 801 is fixedly connected with a base 13. The outer side of the base 13 is rotatably connected with a limiting rod 14 corresponding to the number of the positioning grooves 11. The outer side of the top end of the limiting rod 14 is fixedly connected with a plug-in block 15 matching the positioning groove 11.

[0028] During specific installation, the connecting plate one 803 and the connecting plate two 804 in the diversion component 8 are folded so that they can smoothly enter the grouting area through the grouting hole. The feeding cylinder 1 vertically passes through the grouting hole and is fixed to the positioning flange at the masonry area by using the flange 2. The grouting pipeline is hermetically connected to the connector 3 so that the slurry can be injected into the feeding cylinder 1 from the connector 3. It should be noted here that the discharge channel of the feeding cylinder 1 is composed of the inner side wall of the feeding cylinder 1 and the outer side wall of the guiding cylinder 4;

[0029] A plurality of sets of cushion sleeves 805 are fixedly connected to the top of the conical pressure plate 7 in an annular array. A first cushion block 806 is slidably connected inside the cushion sleeve 805. A first compression spring is fixedly connected inside the cushion sleeve 805. The first cushion block 806 is fixedly connected to the first compression spring. The top of the first cushion block 806 is arranged as an inclined surface that matches the connecting plate one 803. One side wall of the connecting plate two 804 is fixedly connected to a second cushion block 807.

[0030] Restricted by the diameter of the grouting hole, it is impossible to install an auxiliary stirring or auxiliary slurry conveying mechanism inside the arch crown. Coupled with the low fluidity of the grouting slurry itself, problems such as concrete voids and cavities in the arch crown are likely to occur. To solve this problem, the specific improvements are as follows:

[0031] By setting the foldable connecting plate one 803 and connecting plate two 804, the connecting plate one 803 and the connecting plate two 804 are folded so that they can smoothly pass through the grouting hole and be unfolded inside the arch crown. The steps for unfolding and fixing the connecting plate one 803 and the connecting plate two 804 are as follows:

[0032] As Figure 2 shown, when the overall structure of the feeding cylinder 1 is fixed at the grouting hole position through the flange 2, at this time, the push rod 801 is vertically pulled downward. The push rod 801 drives the connecting plate one 803 and the connecting plate two 804 to rotate synchronously through the conical connection block 802. It should be noted here that torsion springs are provided at the rotational connection points of the connecting plate one 803, the connecting plate two 804, and the corresponding brackets to assist the smooth rotation of the connecting plate one 803 and the connecting plate two 804. During the relative rotation of the connecting plate one 803 and the connecting plate two 804, when the inner side wall of the connecting plate one 803 contacts and abuts against the first cushion block 806 and the second cushion block 807, at this time, the connecting plate one 803 and the connecting plate two 804 can no longer continue to rotate, that is, the push rod 801 can no longer be pulled downward in the vertical direction;

[0033] At this time, the limiting rod 14 is rotated to make the plug-in block 15 at the top of the limiting rod 14 snap into the positioning groove 11. Then the cap 10 is rotated. The cap 10 rotates downward and positions the plug-in block 15 to prevent the push rod 801 from sliding by itself and affecting the unfolding effect of the connecting plate one 803 and the connecting plate two 804. As Figure 3As shown, the outer side of the plug-in block 15 is also provided with a thread that matches the internal thread of the rotary cap 10 to further fix the push rod 801. Moreover, a plug-in hole that matches the positioning hole 12 is opened on the outer side of the rotary cap 10. The plug-in hole and the positioning hole 12 are positioned by using a nut, so as to effectively avoid the problem that the rotary cap 10 rotates by itself.

[0034] The first connecting plate 803 and the second connecting plate 804 are made of high-strength alloy, such as alloy steel, etc., and have the characteristics of corrosion resistance and high strength. By setting the first cushion block 806 and the second cushion block 807, the first connecting plate 803 and the second connecting plate 804 after folding are further strengthened during the reciprocating movement in the vertical direction, that is, the impact resistance to concrete is increased, and the problem that the first connecting plate 803 and the second connecting plate 804 are broken during the continuous reciprocating sports process is avoided. At the same time, the top of the conical connecting block 802 is conical, which can further increase the smoothness of the reciprocating movement of the first connecting plate 803 and the second connecting plate 804.

[0035] Embodiment 2: As Figure 1 、 Figure 2 、 Figure 4 、 Figure 5 and Figure 6 As shown, the diversion assembly 8 includes a push rod 801 and a conical connecting block 802. A through groove is opened through the top end of the guide rod 6, and the push rod 801 is slidably connected in the through groove. The conical connecting block 802 is fixedly connected to the top end of the push rod 801. A plurality of groups of the first connecting plates 803 are arranged in an annular array at the bottom of the conical connecting block 802. A plurality of groups of the second connecting plates 804 are arranged in an annular array at the top of the conical pressing plate 7. The bottom of the conical connecting block 802 is rotatably connected to the first connecting plate 803 through a corresponding bracket. The top of the conical pressing plate 7 is rotatably connected to the second connecting plate 804 through a corresponding bracket. The adjacent ends of the first connecting plate 803 and the second connecting plate 804 are rotatably connected.

[0036] The bottom of the injection cylinder 1 is fixedly connected to the frame 22 by bolts. A driving block 23 is slidably connected in the frame 22. The driving block 23 is fixedly connected to the bottom side wall of the guide rod 6. The side wall of the frame 22 is rotatably connected to a turntable 24 through a bearing. A motor 25 for driving the turntable 24 to rotate is fixedly installed on the other side wall of the frame 22. One end of the driving block 23 is rotatably connected to a driving rod 26. The end of the driving rod 26 away from the driving block 23 is rotatably connected to the side wall of the turntable 24.

[0037] A plurality of through cylinders 16 are fixedly connected to the side wall of the charging cylinder 1 in an annular array. The through cylinders 16 communicate with the side wall of the charging cylinder 1. A rotating rod 17 is rotatably connected inside the through cylinder 16. A stirring frame 18 is fixedly connected to the outer side of the rotating rod 17 located outside the charging cylinder 1. A gear 19 is fixedly connected to one end of the rotating rod 17 located inside the charging cylinder 1. A plurality of sliding grooves 20 are formed in the side wall of the guiding cylinder 4 in an annular array. A rack 21 is slidably connected inside the sliding groove 20. One end of the rack 21 is fixedly connected to the side wall of the guiding rod 6. The rack 21 is meshed with the gear 19.

[0038] During specific setting, when the first connecting plate 803 and the second connecting plate 804 are unfolded and fixed, at this time, the slurry is injected into the charging cylinder 1 from the connecting head 3. It should be noted here that a housing for isolating the concrete is provided outside the rack 21 and the gear 19 to avoid the problem that the concrete adheres to the surfaces of the gear 19 and the rack 21 and affects the relative rotation of the two.

[0039] As Figure 1 shown, a plurality of overflow grooves are also formed at the top of the charging cylinder 1 to assist the flow of the concrete. In order to improve the grouting effect of the concrete, the present invention uses the method of reciprocating extrusion and combined stirring and conveying to replace the traditional grouting method that utilizes the self-flow of the concrete, that is, the motor 25 is started, the motor 25 drives the turntable 24 to rotate, and the turntable 24 drives the driving block 23 to reciprocate inside the frame 22 through the driving rod 26. During the reciprocating sliding process of the driving block 23, the guiding rod 6 is driven to reciprocate inside the guiding cylinder 4.

[0040] During the reciprocating sliding process of the guiding rod 6, the conical pressure plate 7 and the second connecting plate 804 are driven to move vertically in a reciprocating manner. By arranging a plurality of second connecting plates 804 in an annular array on the top of the conical pressure plate 7, the plurality of second connecting plates 804 cooperate with the conical pressure plate 7 to increase the contact area with the concrete, increase the single processing amount of the concrete, and improve the flow ability of the concrete. When the concrete slurry gushes out from the top of the charging cylinder 1, by setting the cross-section of the second connecting plate 804 as an inverted triangle and the cross-section of the first connecting plate 803 as an equilateral triangle, the purpose of further reducing the resistance of the first connecting plate 803 and the second connecting plate 804 during the reciprocating movement is achieved.

[0041] During the process of the concrete slurry gushing out from the charging cylinder 1, the conical connecting block 802 cooperates with the second connecting plate 804 to further press down the concrete slurry. At the same time, the conical connecting block 802 uses the inclined surface at its bottom to further press down the concrete slurry, thereby accelerating the diffusion speed of the concrete slurry in all directions. At the same time, when the conical connecting block 802 cooperates with the second connecting plate 804 to press down the concrete, the flow speed and impact force of the concrete slurry can also be increased, and the flow range of the concrete slurry can be expanded, thereby effectively solving problems such as concrete voids and cavities in the arch top.

[0042] During the reciprocating sliding process of the guide rod 6, the rack 21 is also driven to move reciprocally. The rack 21 meshes with the gear 19 for transmission, thereby driving the rotating rod 17 to rotate. During the rotation of the rotating rod 17, the stirring frame 18 is driven to rotate synchronously. The stirring frame 18 further stirs and conveys the concrete slurry, preventing the concrete slurry from accumulating near the injection cylinder 1.

[0043] After the grouting of the concrete slurry is completed, the first connecting plate 803 and the second connecting plate 804 are folded and stored to facilitate the disassembly of the entire device.

[0044] The above content is only an example and description of the structure of the present invention. Those skilled in the art of this technology can make various modifications or supplements to the described specific embodiments or use similar ways to replace them. As long as it does not deviate from the structure of the invention or exceed the scope defined by this claim book, it shall fall within the protection scope of the present invention.

[0045] In the description of this specification, the description with reference to terms such as "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0046] The preferred embodiments of the present invention disclosed above are only used to help explain the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to only the specific implementation manners. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments to better explain the principle and practical application of the present invention, so that those skilled in the art of this technology can understand and utilize the present invention well. The present invention is only limited by the claim book and its full scope and equivalents.

Claims

1. A grouting structure with formwork for tunnel vault construction, including a grout injection cylinder (1), characterized in that, Inside the charging cylinder (1), a guiding cylinder (4) and a fixing plate (5) are provided. The fixing plate (5) is fixedly connected to the inner side wall of the charging cylinder (1). At the center of the fixing plate (5), a fixing groove is fixedly opened. The outer side wall of the guiding cylinder (4) is fixedly connected to the inner wall of the fixing groove. A guiding rod (6) is slidably connected inside the guiding cylinder (4). At the top of the guiding rod (6), a conical pressing plate (7) is sleeved and fixed. Outside the conical pressing plate (7), a flow guiding assembly (8) is provided. The flow guiding assembly (8) includes a push rod (801) and a conical connecting block (802). A through groove is opened at the top of the guiding rod (6). The push rod (801) is slidably connected inside the through groove. The conical connecting block (802) is fixedly connected to the top of the push rod (801). At the bottom of the conical connecting block (802), a plurality of groups of connecting plates one (803) are arranged in a circular array. At the top of the conical pressing plate (7), a plurality of groups of connecting plates two (804) are arranged in a circular array. The cross section of the connecting plate two (804) is an inverted triangle, and the cross section of the connecting plate one (803) is an equilateral triangle. The bottom of the conical connecting block (802) is rotatably connected to the connecting plate one (803) through a corresponding support. The top of the conical pressing plate (7) is rotatably connected to the connecting plate two (804) through a corresponding support. The adjacent ends of the connecting plate one (803) and the connecting plate two (804) are rotatably connected. At the top of the conical pressing plate (7), a plurality of groups of cushion sleeves (805) are fixedly connected in a circular array. A cushion block one (806) is slidably connected inside the cushion sleeve (805). A first compression spring is fixedly connected inside the cushion sleeve (805). The cushion block one (806) is fixedly connected to the first compression spring. The top of the cushion block one (806) is arranged as an inclined surface that cooperates with the connecting plate one (803). On one side wall of the connecting plate two (804), a cushion block two (807) is fixedly connected. The bottom of the charging cylinder (1) is fixedly connected to a frame (22) through bolts. A driving block (23) is slidably connected inside the frame (22). The driving block (23) is fixedly connected to the bottom of the side wall of the guiding rod (6). The side wall of the frame (22) is rotatably connected to a turntable (24) through a bearing. On the other side wall of the frame (22), a motor (25) for driving the turntable (24) to rotate is fixedly installed. One end of the driving block (23) is rotatably connected to a driving rod (26). The end of the driving rod (26) far from the driving block (23) is rotatably connected to the side wall of the turntable (24).

2. The grouting structure with formwork for tunnel crown construction according to claim 1, characterized in that, A positioning block (9) is sleeved and fixed on the outer circumference of the guide rod (6) near the bottom end. Threads are provided on the outer side of the positioning block (9). A cap nut (10) is threadedly connected to the outer side of the positioning block (9). A plurality of positioning grooves (11) and positioning holes (12) are provided on the side wall of the positioning block (9). The bottom end of the push rod (801) is fixedly connected to a base (13). A limiting rod (14) corresponding to the number of the positioning grooves (11) is rotatably connected to the outer side of the base (13). An insertion block (15) matched with the positioning groove (11) is fixedly connected to the outer side of the top end of the limiting rod (14).

3. The grouting structure with formwork for tunnel vault construction according to claim 1, characterized in that, A plurality of through cylinders (16) are fixedly connected to the side wall of the injection cylinder (1) in an annular array. The through cylinders (16) communicate with the side wall of the injection cylinder (1). A rotating rod (17) is rotatably connected in the through cylinder (16). A stirring frame (18) is fixedly connected to the outer side of the rotating rod (17) located outside the injection cylinder (1). A gear (19) is fixedly connected to one end of the rotating rod (17) located inside the injection cylinder (1).

4. A grouting structure with formwork for tunnel vault construction according to claim 1, characterized in that, A plurality of sliding grooves (20) are provided on the side wall of the guide cylinder (4) in an annular array. A rack (21) is slidably connected in the sliding groove (20). One end of the rack (21) is fixedly connected to the side wall of the guide rod (6). The rack (21) is meshed with the gear (19).

5. The grouting structure with formwork for tunnel vault construction according to claim 1, characterized in that, A flange plate (2) is fixed to the outer circumferential side wall of the injection cylinder (1) by electric welding. A plurality of connectors (3) communicate with the side wall of the injection cylinder (1). The connectors (3) are arranged in an annular shape with the center of the injection cylinder (1) as the center.

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