A construction method for prestressed aqueduct that speeds up construction progress and reduces the number of post-cast strips

Abstract

The present invention belongs to the field of prestressed aqueducts, and in particular relates to a construction method for a prestressed aqueduct that accelerates construction progress and reduces the number of post-cast strips. The method includes the arrangement of prestressed steel bar tensioning process, the arrangement of aqueduct span structure, and the selection of different lower structures for support corresponding to different span connection methods. Compared with traditional prestressed aqueducts, the present invention can greatly reduce the number of post-cast strips of the trough, avoid safety hazards in weak links, and has high construction flexibility. The number of working surfaces can be set according to engineering requirements, thereby achieving the purpose of accelerating engineering construction.

Description

Technical Field

[0001] The invention belongs to the field of prestressed aqueducts, and in particular relates to a construction method for a prestressed aqueduct which can accelerate construction progress and reduce the number of post-cast strips. Background Art

[0002] There are generally two structures and tensioning arrangements for prestressed aqueducts. One is unidirectional progressive tensioning without post-cast strips; the other is to have post-cast strips at both ends of the trough body, and bidirectional or unidirectional tensioning can be used.

[0003] One-way progressive tensioning, that is, tensioning from one end of the upstream or downstream to the other side or from the middle of multiple spans to both sides. The advantage of this method is that there is no post-casting strip between different spans, which avoids shrinkage and cracking of the post-casting strip and the weak anti-seepage link adjacent to the main structure; the disadvantage is that it is necessary to wait until one span is tensioned and anchored before connecting the water stop to the next span. There are only two working surfaces at most, which cannot meet the construction needs of aqueducts with a tight schedule and a large number of spans.

[0004] A post-cast strip is set up in each span. In theory, one working surface can be achieved in each span. However, when constructing multiple spans, the number of working surfaces is mainly related to the number of formworks invested by the construction unit. Generally, one formwork is not used for each span, as the investment is too large and the adjacent spans will affect each other during tensioning. Although the post-cast strip is set up in each span, the construction progress is accelerated, the advantage of more working surfaces is not fully utilized, and the weak link between the post-cast strip and the main structure of the aqueduct is increased. Therefore, unless two-way tensioning is required, it is not recommended to lay post-cast strips on the aqueduct body of each span.

[0005] In general, large-scale aqueduct projects on trunk lines have large longitudinal beams and prestressed steel strands with large bending angles. To reduce prestress loss, bidirectional tensioning is used, and each span is equipped with a post-casting strip. The left bank drainage aqueduct project generally uses unidirectional tensioning. Both tensioning and structural layout forms have certain limitations. Summary of the invention

[0006] The purpose of the present invention is to provide a construction method for a prestressed aqueduct which can accelerate the construction progress and reduce the number of post-casting strips.

[0007] The present invention adopts the following technical solution:

[0008] A construction method for prestressed aqueduct that speeds up construction progress and reduces the number of post-cast strips. All aqueduct spans are designed to be unidirectional tensioned. The prestressed tensioning construction of the aqueduct is carried out by adopting unidirectional progressive tensioning and opposite tensioning of the spans, thereby increasing the prestressed tensioning construction working surface and improving the construction progress. Post-cast strips are only required to be poured at the tensioning and closing positions, thereby reducing the number of post-cast strips.

[0009] Furthermore, according to the needs of the prestressed tensioning work space of the aqueduct, post-cast strips are left in both spans of the aqueduct body at the tensioning and closing position, and the combined width of the two groups of post-cast strips meets the needs of the prestressed tensioning work space.

[0010] Furthermore, the aqueduct span is a simply supported beam structure. To ensure the symmetry of the aqueduct force, after the post-cast strip is set at the end of the tensioned and closed span, the width of the aqueduct bottom plate outside the end bottom rib should meet the requirement that the arrangement of the spiral reinforcement of the anchor does not conflict with the main reinforcement of the end bottom rib. For the end structure without the post-cast strip side, the end bottom rib should be arranged appropriately to the outside while considering the effective flange width of the T-beam to meet the spacing of the prestressed anchor and spiral reinforcement arrangement and help reduce the spacing between the adjacent span supports, thereby reducing the size of the lower pier cap. If a post-cast strip is set at one end to close, the bottom ribs and side bottom ribs should also be arranged symmetrically with the closed end to ensure the symmetry of the longitudinal beam force at the other end.

[0011] Furthermore, the arrangement of one-way progressive and closing spans involves three types of adjacent slot spans, namely, one-way progressive adjacency, tensioned closing span connection, and one-way progressive and closing span connection.

[0012] Furthermore, the support center of the end of the longitudinal beam of the trough body should generally be arranged at the center of the intersection of the longitudinal beam and the end bottom rib. Different support and pier cap structures are used for different trough span connection methods. It should be noted that due to the arrangement of the end bottom rib, the aqueduct structure seam is not aligned with the center of the lower structure. It is only necessary to ensure that the support centers of the two trough spans are symmetrical to the axis of the lower structure.

[0013] The adjacent one-way progressive spans use pier caps with smaller structures than those of the closing spans and corresponding supports to provide lower support; the connection between the one-way progressive and closing spans uses pier caps with pier cap axes that are not aligned with the structural seams of the aqueduct to provide lower support, and the centers of the two supports are symmetrical to the pier cap axes; the connection between the tensioned closing spans uses pier caps with larger structures and corresponding supports to provide lower support.

[0014] Furthermore, the pier cap size model is the smallest in the thrust span, and the thrust closing connection is medium in size with the largest closing span.

[0015] Further, specifically including A one-way tension span aqueduct, including the following steps:

[0016] (1) Determine the number of working surfaces B;

[0017] (2) Determine the number of closing units C based on the determined number of working surfaces B;

[0018] (3) Each closing unit needs to be connected with a back-to-back tie-groove span group, and the number of the tie-groove span groups is C-1; the back-to-back tie-groove span groups are provided with lower support in the form of support arrangements, and pier caps are also selected to cooperate with them.

[0019] Furthermore, the number of the one-way tensioned span aqueducts A is no less than 8; and the number of the working surfaces B is no less than 4.

[0020] Furthermore, one of the closing units includes D tensioning advancement spans with the tensioning direction being right, one tensioning closing span with the tensioning direction being right, and E tensioning advancement spans with the tensioning direction being left, and one tensioning closing span with the tensioning direction being left; one of the closing units provides two tensioning working surfaces for simultaneous tensioning construction, that is, B=2×C, C≥2; within a single closing unit, the number of slot spans included is D+E+2, that is, A=C×(D+E+2), D≥1, E≥1.

[0021] (1) Span arrangement: All aqueduct spans are designed to be tensioned in one direction, and tensioning is carried out from the upstream and downstream ends to the middle. The tensioning direction is fixed by setting up back-to-back tension span groups, and back-to-back tensioning is carried out from this position to the upstream and downstream. Post-casting strips are only required at the tensioning closure position.

[0022] (2) Increase the working surface: According to the configuration of construction personnel and mechanical equipment, the number of scaffolding and formwork, the construction period requirements, etc., by increasing the number of tension groove spans, increasing the prestressing tensioning construction working surface, and improving the construction progress.

[0023] (3) Span of the trough at the closing position: According to the requirements of the prestressing working space of the aqueduct, post-cast strips are left on both spans of the trough at the closing position, and the combined width of the two groups of post-cast strips is used to meet the requirements of the prestressing working space.

[0024] (4) Arrangement of the trough body in the closed span: Since the longitudinal direction of the aqueduct is a simply supported beam structure, it is necessary to ensure that the aqueduct is symmetrically stressed. At one end of the closed span where a post-cast strip is required, a certain length of the aqueduct bottom plate must be reserved between the post-cast strip and the end bottom rib to ensure that the width of the aqueduct bottom plate outside the end bottom rib is sufficient to ensure that the spiral reinforcement arrangement of the anchor does not conflict with the main reinforcement of the end bottom rib. ① To ensure the longitudinal symmetry of the aqueduct, ② consider the effective flange width of the T-beam, ③ meet the spacing of the prestressed anchor and spiral reinforcement arrangement, ④ arrange the end bottom rib as far out as possible to reduce the spacing between the adjacent span supports. Taking the above factors into consideration, even if a post-cast strip is set at one end to close the span, the bottom ribs and side bottom ribs should be arranged symmetrically with the closed end to ensure the symmetry of the longitudinal beam stress at the other end.

[0025] (5) Support arrangement type: The present invention involves three types of slot span adjacency, namely, one-way progressive adjacency, tensioned and closed span adjacency, and one-way progressive and closed span adjacency, involving three types of support arrangement types.

[0026] The support center of the one-way progressive adjacent and tensioned closure span should generally be arranged at the center of the intersection of the longitudinal beam and the end bottom rib. The support of the one-way progressive and closure span adjacent to the span is affected by the arrangement of the end bottom rib. The aqueduct structure seam is not aligned with the center of the lower structure, but the support center of the two spans is symmetrical with the axis of the lower structure.

[0027] (6) Pier cap structure: The present invention involves three types of adjacent slot spans. Since the ends of different slot spans are arranged differently, the distances between the supports and the ends of the slot spans are different. Therefore, three types of pier cap structures need to be set to meet the requirements of structural safety and economy.

[0028] Beneficial effects of the present invention:

[0029] The present invention designs all aqueduct spans to be unidirectional tensioned. The prestressed tensioning construction of the aqueduct is carried out by adopting unidirectional progressive tensioning and the opposite tensioning of the spans, thereby increasing the prestressed tensioning construction work surface, improving the construction progress, and only requiring the casting of post-cast strips at the tensioning and closing positions, thereby reducing the number of post-cast strips. The present invention leaves post-cast strips on both spans of the trough body at the tensioning and closing positions, and the combined width of the two groups of post-cast strips meets the needs of the prestressed tensioning work space. Compared with the traditional prestressed aqueduct, the present invention can greatly reduce the number of post-cast strips of the trough body, avoid safety hazards in weak links, and has high construction flexibility. The number of working surfaces can be set according to engineering requirements, thereby achieving the purpose of speeding up engineering construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a layout diagram of the aqueduct tensioning process according to the first embodiment of the present invention;

[0031] Figure 2 This is a diagram of the aqueduct body structure and the trough span adjacency of the first embodiment of the present invention;

[0032] Figure 3 This is a layout diagram of the aqueduct tensioning process according to the second embodiment of the present invention;

[0033] Figure 4 This is a diagram of the aqueduct body structure and the trough span adjacency of the second embodiment of the present invention;

[0034] Figure 5 This is a diagram of the structure of the traditional aqueduct and the adjacent spans of the aqueduct.

[0035] In the figure: 1. Tensioning advancement span 2. Tensioning closing span 3. Tensioning direction → 4. Tensioning direction ← 5. Back-to-back tensioning slot span group 6. One-way progressive slot span group 7. One-way progressive and closing slot span group 8. Tensioning closing slot span group 9. Post-cast strip 10.1# end bottom rib 11.2# end bottom rib 12.1# end bottom plate 13.2# end bottom plate 14.1# support arrangement form 15.2# support arrangement form 16.3# support arrangement form 17.1# pier cap 18.2# pier cap 19.3# pier cap. DETAILED DESCRIPTION

[0036] The method of the present invention is applicable to multiple one-way tension span A aqueducts. To better illustrate the present invention, a one-way tension span A aqueduct is taken as an example, A≥8. First, the number of working surfaces B is determined according to the configuration of construction personnel and mechanical equipment, the number of scaffolds and templates, and the construction period requirements, B≥4.

[0037] According to the determined number of working surfaces B, the number of closing units C can be determined. A single closing unit is composed of D tensioning advancing spans 1 with tensioning direction →3, one tensioning closing span 2 with tensioning direction →3, and E tensioning advancing spans 1 with tensioning direction ←4, and one tensioning closing span 2 with tensioning direction ←4. A closing unit provides two tensioning working surfaces for simultaneous tensioning construction, that is, B=2×C, C≥2. In a single closing unit, the number of slot spans is (D+E+2), that is, A=C×(D+E+2), D≥1, E≥1.

[0038] Each closing unit needs to be connected with a back-to-back groove span group 5, and the number of the back-to-back groove span group 5 is (C-1). The back-to-back groove span group 5 is provided with a 1# support arrangement form 14 to provide lower support, and the 1# pier cap 17 is also selected to cooperate.

[0039] Taking a single closing unit as an example to describe the present invention, it is assumed that the number D of the tensioning advancement span 1 with the tensioning direction of →3 is 2, and the number E of the tensioning advancement span 1 with the tensioning direction of ←4 is 3, that is, the arrangement of the single closing unit is ①→, ②→, ③→, ←→, ←④, ←⑤, ←⑥, ←⑦. Among them, the slot spans ①, ②, ⑤, ⑥, ⑥, ⑦ are connected to form a one-way progressive slot span group 6, and the 1# support arrangement form 14 is used to provide lower support for it, and the 1# pier cap 17 is also selected to cooperate. The slot spans ②, ③, ④, ⑤ are connected to form a one-way progressive and closing slot span group 7, and the 2# support arrangement form 15 is used to provide lower support for it, and the 2# pier cap 18 is also selected to cooperate. The slot spans ③ and ④ are connected to form a tensioning and closing slot span group 8, and the 3# support arrangement form 16 is used to provide lower support for it, and the 3# pier cap 19 is also selected to cooperate.

[0040] The number of slot spans in each closing unit can vary according to the project layout. The pier cap size model is the smallest push span, and the push closing connection is medium and the closing span is the largest.

[0041] Example 1

[0042] In conjunction with the accompanying drawings, the specific implementation of the present invention is further described:

[0043] It should be noted that a set of construction methods for prestressed aqueducts that speed up construction progress and reduce the number of post-cast strips includes a prestressed aqueduct tensioning process, a trough span structure arrangement, and a trough span connection arrangement. The following only takes an 18-span aqueduct as an example to specifically illustrate the characteristics, features, and advantages of the aqueduct structure and tensioning process of the present invention. However, all descriptions are only for illustration and should not be understood as limiting the present invention in any way.

[0044] Figure 1 The aqueduct tensioning process layout of the present invention is given, and by Figure 2 It shows three structural arrangements of the aqueduct body structure and the connection between the trough spans, as well as the different support and pier cap structure arrangements required for different trough span connections.

[0045] First, the present invention Figure 1 Two types of slot span arrangements are shown, namely, tensioning advancement span 1, tensioning closing span 2, and prestressed slot span tensioning direction arrangement. The aqueduct slot spans are all designed as unidirectional tensioning types, and the tensioning direction is only →3 or ←4.

[0046] Further, two slot spans are selected as the back-to-back pulling slot group, that is, Figure 1 The 9th and 10th trough spans in the middle have fixed tensioning directions, effectively dividing the 18-span aqueduct into two working surfaces, and the aqueduct prestressing tensioning construction can be carried out simultaneously. It should be noted that after the opposite tensioning trough span groups are set, the aqueduct structure and tensioning arrangement of the front and rear working surfaces are exactly the same, and the present invention is continued to be described based on the 1st to 9th trough spans.

[0047] Further, the slot spans ⑤ and ⑥ are set as tension closing span 2, that is, the slot spans ①, ②, ③, ④, ⑦, ⑧, and ⑨ are all tension advancing span 1. The tensioning direction of slot spans ①, ②, ③, ④, and ⑤ is →3; the tensioning direction of slot spans ⑥, ⑦, ⑧, and ⑨ is ←4.

[0048] Furthermore, by arranging a group of back-to-back tension slot groups 5 and two groups of tensioning and closing slot span groups 8, the aqueduct with a total of 18 slot spans can be arranged as four working surfaces for simultaneous construction operations, and only the post-casting strips 9 need to be arranged at the tensioning and closing locations 8. Compared with the usual arrangement of setting post-casting strips for each span of the aqueduct body, the number of post-casting strips is greatly reduced.

[0049] Furthermore, according to the configuration of construction personnel and mechanical equipment, the number of scaffolding and formwork, construction period requirements, etc., the number of tensioning trough spans and tensioning and closing trough spans can be increased to increase the prestressing tensioning construction working surface and improve the construction progress.

[0050] Furthermore, Figure 1 The tensioning arrangement shown involves three types of slot span adjacency forms, namely, connection of one-way progressive slot span group 6, connection of one-way progressive and closing slot span group 7, and connection of tensioned and closed slot span group 8.

[0051] Furthermore, in order to meet the needs of prestressing tensioning working space, a post-cast strip 9 is reserved at one end of the tensioning closure span 2. In order to prevent the anchor spiral reinforcement arrangement from conflicting with the end bottom rib main reinforcement, an aqueduct bottom plate 12 needs to be arranged outside the end bottom rib 11.

[0052] Furthermore, an end bottom plate 13 is arranged at one end of the tensioning and closing span 2 where no post-cast strip is set, in order to ensure the effective flange width of the T-beam while appropriately arranging the end bottom ribs to the outside to meet the spacing of the prestressed anchors and spiral reinforcement and to reduce the spacing of the end bottom ribs of adjacent slot spans as much as possible. The length of the end bottom plate 13 is the sum of the length of the end bottom plate 12 and the length of the post-cast strip 9.

[0053] Furthermore, three support arrangements are provided, namely 14, 15, and 16, to satisfy the three trough span adjacency modes 6, 7, and 8. The support center at the end of the trough body longitudinal beam should generally be arranged at the center position where the longitudinal beam intersects the end bottom rib. Support arrangement form 14 is that two supports are symmetrically arranged under the end bottom rib 10, and the center of the trough span adjacency 6 is aligned with the axis of the pier cap 17. Support arrangement form 15 is that one support is arranged under the end bottom rib 10, and the other support is arranged under the end bottom rib 11. The center of the trough span adjacency 7 is not aligned with the axis of the pier cap 18. It is only necessary to ensure that the support centers of the two trough spans are aligned with the axis of the lower pier cap 18. Support arrangement form 16 is that two supports are symmetrically arranged under the end bottom rib 11, and the center of the trough span adjacency 8 is aligned with the axis of the pier cap 19.

[0054] Furthermore, the support arrangement between spans ④ and ⑤ is 15, the support arrangement between spans ⑤ and ⑥ is 16, and the rest are 14.

[0055] Furthermore, in order to meet the three support arrangement forms, three pier caps with different structures, namely 17, 18, and 19, are set. The 1# pier cap 17 is used for the connection of the one-way progressive slot span group 6; the 2# pier cap 18 is used for the connection of the one-way progressive and closing slot span group 7; and the 3# pier cap is used for the connection of the tensioned closing slot span group 8.

[0056] Example 2

[0057] It should be noted that a set of construction methods for prestressed aqueducts that speed up construction progress and reduce the number of post-cast strips includes a prestressed aqueduct tensioning process, a trough span structure arrangement, and a trough span connection arrangement. The following only takes an eight-span aqueduct as an example to specifically illustrate the characteristics, features, and advantages of the aqueduct structure and tensioning process of the present invention. However, all descriptions are only used for illustration and should not be understood as forming any limitation on the present invention.

[0058] like Figure 3-4 As shown, the present invention is described by taking the minimum span number A=8 and B=4 as an example. The basic arrangement is as follows: ①→, ②→, ←→, ③, ←④, ⑤→, ⑥→, ←→, ⑦, ←⑧. This combination constitutes the minimum closing unit of the present invention, namely ①→, ②→, ←→, ③, ←④ (⑥→, ←→, ⑦, ←⑧). ①, ④, ⑤, ⑧ are tensioning advancement spans 1, and ②, ③, ⑥, ⑦ are tensioning closing spans 2. Among them, the two spans ④ and ⑤ form the only group of back-to-back tensioning slot span group 5 in this example. The back-to-back tensioning slot span group 5 uses the 1# support arrangement form 14 to provide lower support for it, and the 1# pier cap 17 is also selected to cooperate. The connection mode of the two (③, ④, ⑤, ⑥, ⑦, ⑧) slot spans ① and ② is a one-way progressive and closing slot span group 7, and the 2# support arrangement form 15 is used to provide lower support for it, and the 2# pier cap 18 is also selected to cooperate. The two groups of trough spans ②, ③, ⑥, and ⑦ are set as tensioning and closing trough span groups 8, and only 4 post-cast strips 10 are required to be set at the closing position. The tensioning and closing trough span group 8 uses the 3# support arrangement form 16 to provide lower support for it, and the 3# pier cap 19 is also selected to cooperate with it.

[0059] It should be noted that when the present invention is applied to the design and construction of aqueducts with a large number of trough spans, its high flexibility can be better utilized according to the construction party's requirements for the working surface.

[0060] The present invention is attached Figure 5 This is the traditional unidirectional prestressed aqueduct layout process. As shown in the figure, traditional aqueducts are equipped with post-cast strips in each span. In theory, one working surface can be achieved in each span. However, when constructing multiple spans, due to the configuration of construction personnel and mechanical equipment, the number of scaffolding and formwork, construction period requirements and other factors, generally one formwork will not be used for each span. The investment is too large, and adjacent spans will also affect each other during tensioning. Although the post-cast strips are set in each span to speed up the construction progress, it does not fully utilize the advantage of more working surfaces, and it will also increase the weak link between the post-cast strips and the main structure of the aqueduct.

[0061] By applying the method of the present invention, the number of post-cast strips can be greatly reduced, and the impact of weak links on the overall aqueduct can be reduced. At the same time, the tensioning sequence of the aqueduct can be arranged more flexibly, which can greatly reduce the number of post-cast strips of the trough and reduce the impact of weak links on the overall aqueduct. The construction flexibility is high, and the number of working surfaces can be set according to the project requirements, thereby achieving the purpose of speeding up the project construction. At the same time, different pier cap structural types are applied to reduce the amount of pier cap engineering.

Claims

1. A method for constructing a prestressed aqueduct that accelerates construction progress and reduces the number of post-cast strips, characterized in that: All aqueduct spans are of unidirectional tensioning type. The prestressing tensioning construction of the aqueduct is carried out by adopting unidirectional progressive tensioning and the tensioning of spans in opposite directions, thereby increasing the prestressing tensioning construction working surface, and only the post-casting strip needs to be cast at the tensioning and closing position, thereby reducing the number of post-casting strips; the aqueduct span is a simply supported beam structure. After the post-casting strip is set at the end of the tensioning and closing span, the width of the aqueduct bottom plate outside the end bottom rib meets the requirement that the arrangement of the spiral reinforcement of the anchor does not conflict with the main reinforcement of the end bottom rib; the end structure on the side of the post-casting strip is not set, and the end bottom rib is arranged outside while considering the effective flange width of the T-beam, so as to meet the spacing of the prestressed anchor and spiral reinforcement and reduce the spacing between the adjacent span supports, thereby reducing the size of the lower pier cap; a post-casting strip is set at one end for closing, and the bottom rib and the side bottom rib are arranged symmetrically with the closing end at the other end; The arrangement of one-way progressive spans and closing spans involves three adjacent ways of slot spans, namely, one-way progressive spans adjacent, tensioned closing span connection, and one-way progressive spans and closing spans connection; The support center of the end of the longitudinal beam of the trough body is arranged at the center position where the longitudinal beam and the end bottom rib intersect. Different support and pier cap structures are used for different trough span connection methods. The one-way progressive span is adjacent to the pier cap with a smaller structure than the pier cap of the closed span and the corresponding support to provide lower support; the one-way progressive span and the closed span are connected to the pier cap with the axis of the pier cap not aligned with the structural seam of the aqueduct to provide lower support, and the centers of the two supports are symmetrical to the axis of the pier cap; The tensioned closing span connection adopts a structural form that provides lower support for the pier cap and corresponding bearings that are larger than the closing span; Specifically, it includes A one-way tension span aqueduct, including the following steps: (1) Determine the number of working surfaces B; (2) Determine the number of closing units C based on the determined number of working surfaces B; (3) Each closing unit is connected with a back-to-back tie groove span group, and the number of the back-to-back tie groove span groups is C-1; the back-to-back tie groove span groups are provided with lower support in the form of support arrangement, and pier caps are also selected to cooperate; One of the closing units includes D tensioning advancement spans with the tensioning direction being right, one tensioning closing span with the tensioning direction being right, and E tensioning advancement spans with the tensioning direction being left, and one tensioning closing span with the tensioning direction being left; one of the closing units provides two tensioning working surfaces for simultaneous tensioning construction, that is, B=2×C, C≥2; a single closing unit includes D+E+2 slot spans, that is, A=C×(D+E+2), D≥1, E≥1.

2. The method for constructing a prestressed aqueduct according to claim 1, which is characterized in that: The connection between the one-way progressive span and the closing span is affected by the arrangement of the end bottom ribs. The structural seam of the aqueduct is not aligned with the center of the lower structure, and the support centers of the two spans are symmetrical to the axis of the lower structure.

3. The method for constructing a prestressed aqueduct according to claim 1, which is characterized in that: The number A of the one-way tensioned span aqueducts is no less than 8; the number B of the working surfaces is no less than 4.

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