Calculation method, equipment and storage medium for bending bearing capacity of core-filled composite pipe piles

Abstract

The present application discloses a method, device and storage medium for calculating the bending bearing capacity of a core-filled composite pipe pile, and relates to the field of bending bearing capacity calculation. The method includes: calculating the first equivalent stress diagram coefficient of the inner circle concrete and the second equivalent stress diagram coefficient of the outer circle concrete according to the rectangular stress diagram of the inner and outer ring concrete of the core-filled composite pipe pile; calculating the axial force and bending moment provided by the inner and outer ring concrete and the inner and outer ring steel bars in the core-filled composite pipe pile respectively, and obtaining the calculation model of the axial force and bending moment of the positive section of the core-filled composite pipe pile according to the internal force of the pile cross section satisfying the static equilibrium and strain coordination conditions; calculating the center angle coefficient of the outer ring concrete in the stress area with the axial force of the calculation model of the axial force being zero as a constraint condition; substituting the center angle coefficient into the calculation model of the bending moment to calculate the bending bearing capacity of the core-filled composite pipe pile. The present application solves the problem that there is a large deviation between the calculation result of the bending bearing capacity and the measured result.

Description

Technical Field

[0001] The present application relates to the field of calculation of the bending bearing capacity of reinforced concrete pipe pile structures, and more specifically, to a method, device and storage medium for calculating the bending bearing capacity of core-filled composite pipe piles. Background Art

[0002] Prestressed high-strength concrete pipe piles are prefabricated high-strength concrete piles made by pre-tensioning and prestressing centrifugal forming technology. Core-filled composite pipe piles are made by filling ordinary reinforced concrete into the hollow part of the prestressed high-strength concrete pipe piles, thereby forming a composite pipe pile structure composed of four materials: high-strength concrete (C80) in the outer circle, prestressed tendons, ordinary concrete (C40 or C30) in the inner circle, and ordinary steel bars. Prestressed high-strength concrete pipe piles can be used in slope reinforcement projects. As a reinforcement structure for prestressed high-strength concrete pipe piles, core-filled composite pipe piles can further improve the bending bearing capacity of the pipe piles, and are particularly suitable for the reinforcement and rescue of natural slopes or landslides, excavation slopes, and fill slopes.

[0003] For traditional non-core-filled prestressed high-strength concrete pipe piles, the prestressed tendons were previously equivalent to annular steel rings, and the corresponding bending bearing capacity calculation formula was obtained based on the plane section assumption and static equilibrium equation. For reinforced core-filled composite pipe piles, their bending bearing capacity was also derived based on this assumption model.

[0004] However, there are many problems with the calculation method provided by the prior art. There are time and space differences between the prefabricated outer ring part and the later cast inner ring part. Especially for the core filling part of the inner ring of the pile, due to the constraints of the outer ring concrete, the compressive strain distribution of the inner concrete is not 0~ε cu (ε cu is the ultimate compressive strain). Therefore, the existing calculation formula for the bending bearing capacity of the core-filled composite pipe pile is a simple superposition calculation formula based on the non-core-filled prestressed high-strength concrete pipe pile. The calculation formula, first of all, does not specify the coefficients in the formula (such as the stress diagram coefficient and the center angle coefficient). Secondly, the calculation formula is complicated, which affects the calculation efficiency. Finally, the calculation formula does not analyze the stress conditions of the outer ring prefabricated part and the inner ring core-filled part of the pile structure of the core-filled composite pipe pile, which leads to a large deviation between the calculation result of the bending bearing capacity of the core-filled composite pipe pile and the measured result, and cannot provide a theoretical basis for the reinforcement and rescue of actual projects. Summary of the invention

[0005] The purpose of this application is to provide a method, device and storage medium for calculating the bending bearing capacity of core-filled composite pipe piles, so as to solve the problem that there is a large deviation between the bending bearing capacity calculation results provided by the prior art and the measured results.

[0006] In a first aspect of the present application, a method for calculating the bending bearing capacity of a core-filled composite pipe pile is provided, the method comprising:

[0007] According to the rectangular stress diagrams of the inner and outer ring concrete of the core-filled composite pipe pile, the first equivalent stress diagram coefficient of the inner ring concrete and the second equivalent stress diagram coefficient of the outer ring concrete are calculated respectively;

[0008] Obtaining a first parameter of the inner ring concrete and a second parameter of the outer ring concrete, constructing a first model for calculating the axial force of the inner ring concrete and a second model for the bending moment according to the first equivalent stress diagram coefficient and the first parameter, and constructing a third model for calculating the axial force of the outer ring concrete and a fourth model for the bending moment according to the second equivalent stress diagram coefficient and the second parameter;

[0009] Obtaining a third parameter of the inner ring steel bar under tension and compression and a fourth parameter of the outer ring steel bar under tension and compression, constructing a fifth model for calculating the axial force of the inner ring steel bar and a sixth model for calculating the bending moment according to the first parameter and the third parameter, and constructing a seventh model for calculating the axial force of the outer ring steel bar and an eighth model for calculating the bending moment according to the second parameter and the fourth parameter;

[0010] The first model, the third model, the fifth model and the seventh model are summed to obtain an axial force calculation model of the positive section of the core-filled composite pipe pile; the second model, the fourth model, the sixth model and the eighth model are summed to obtain a bending moment calculation model of the positive section of the core-filled composite pipe pile;

[0011] Taking the axial force of the axial force calculation model as zero as the constraint condition, calculate the central angle coefficient of the outer ring concrete in the stress area;

[0012] Substitute the center angle coefficient into the bending moment calculation model to calculate the bending bearing capacity of the core-filled composite pipe pile.

[0013] In one implementation, the first equivalent stress diagram coefficient includes a strength factor and a depth factor of the inner ring concrete;

[0014] The first equivalent stress diagram coefficient of the inner ring concrete of the core-filled composite pipe pile is calculated by the following method: taking the inner ring neutral axis of the rectangular stress diagram as the origin and the compressive upper edge as the positive direction, the inner ring circular cross-section strip is divided into a plurality of rectangular strips;

[0015] Integrating and solving multiple rectangular strips to calculate the first resultant force and first resultant moment of the inner circle concrete;

[0016] The inner radius of the pipe pile is obtained, and the first central angle coefficient corresponding to the rectangular stress diagram of the inner circle concrete is calculated according to the inner radius of the pipe pile, the first resultant force and the first resultant moment;

[0017] Obtain the distance from the neutral axis of the inner circle to the wall of the inner circle, and calculate the depth factor of the inner circle concrete according to the first central angle coefficient, the distance from the neutral axis of the inner circle to the wall of the inner circle and the inner radius of the pile;

[0018] According to the depth factor of the inner circle concrete, the distance from the inner circle neutral axis to the inner circle wall and the inner radius of the pile, the first equivalent area of ​​the inner circle circular cross-section compression concrete is calculated;

[0019] The strength factor of the inner circle concrete is calculated according to the first resultant force, the first equivalent area and the axial compressive strength of the inner circle concrete.

[0020] In one implementation, the first parameter of the inner ring concrete includes the inner ring neutral axis and the central angle coefficient corresponding to the inner ring concrete equivalent compression zone.

[0021] The mathematical expression of the first model is: The mathematical expression of the second model is: Among them, N c1 、M c1 are the axial force and bending moment of the inner ring concrete, α 1 is the intensity factor of the first equivalent stress diagram coefficient, f c1 A is the axial compressive strength of the inner ring concrete, 1 is the cross-sectional area of ​​the inner circle, r 1 is the inner radius of the pile, α 4 is the central angle coefficient of the neutral axis of the inner circle, and θ is the central angle coefficient of the infinitesimal element.

[0022] In one implementation, the third parameter of the inner ring steel bar under tension and compression includes the compressive yield point of the inner ring steel bar equivalent steel ring, the central angle coefficient corresponding to the tensile yield point, the compressive strength and tensile strength of the inner ring steel bar, and the stress function of the inner ring steel bar in the unyielded triangle area;

[0023] The mathematical expression of the fifth model is:

[0024] The mathematical expression of the sixth model is:

[0025]

[0026] Among them, N sc 、N st are the axial forces of the inner ring steel bars under compression and tension, respectively. sc 、M st are the bending moments of the inner ring steel bars under compression and tension, respectively, and f' y 、f y are the compressive and tensile strengths of the inner ring steel bars, A sis the cross-sectional area of ​​the inner ring steel bar, α 5 is the central angle coefficient of the equivalent compression zone of the inner circle concrete, α 3 is the central angle coefficient of the neutral axis of the outer ring, r s is the radius of the distribution circle of the inner ring reinforcement, σ si is the stress function of the inner ring reinforcement in the unyielded triangle area, α 8 is the central angle coefficient of the equivalent steel ring under compression yield point of the inner steel ring, α 9 It is the central angle coefficient of the tensile yield point of the equivalent steel ring of the inner ring reinforcement.

[0027] In one implementation, the second equivalent stress diagram coefficient includes a strength factor and a depth factor of the outer ring concrete;

[0028] The second equivalent stress diagram coefficient of the outer ring concrete of the core-filled composite pipe pile is calculated in the following way: taking the outer ring neutral axis of the rectangular stress diagram as the origin and the positive direction toward the upper edge of the compression, the outer ring section strip is divided into multiple rectangular strips; wherein, the outer ring section is obtained by subtracting the inner small circle from the outer large circle;

[0029] Integrating and solving multiple rectangular strips to calculate the second resultant force and second resultant moment of the outer ring concrete;

[0030] The inner radius and the outer radius of the pipe pile are obtained, and the second central angle coefficient corresponding to the rectangular stress diagram of the outer circle concrete is calculated according to the inner radius and the outer radius of the pipe pile, the second resultant force and the second resultant moment;

[0031] Obtain the distance from the neutral axis of the outer ring to the outer edge of the outer ring compression area, and calculate the depth factor of the outer ring concrete according to the second central angle coefficient, the distance from the neutral axis of the outer ring to the outer edge of the outer ring compression area and the outer radius of the pile;

[0032] According to the depth factor of the outer ring concrete, the inner radius of the pipe pile and the outer radius of the pipe pile, the second equivalent area of ​​the outer ring section compressed concrete is calculated;

[0033] The strength factor of the outer ring concrete is calculated based on the second resultant force, the second equivalent area and the axial compressive strength of the outer ring concrete.

[0034] In one implementation, the second parameter of the outer ring concrete includes the outer ring neutral axis and the center angle coefficient corresponding to the outer ring concrete equivalent compression zone;

[0035] The mathematical expression of the third model is: The mathematical expression of the fourth model is: Among them, N c2 、M c2 are the axial force and bending moment of the outer ring concrete, α 2is the intensity factor of the second equivalent stress diagram coefficient, f c2 A is the axial compressive strength of the outer ring concrete, 2 is the cross-sectional area of ​​the outer ring, r 1 is the inner radius of the pile, r 2 is the outer radius of the pile, α is the central angle coefficient of the equivalent compression zone of the outer circle concrete, and θ is the central angle coefficient of the microelement.

[0036] In one implementation, the fourth parameter of the outer ring steel bar under tension and compression includes the compressive yield point of the outer ring steel bar equivalent steel ring, the central angle coefficient corresponding to the tensile yield point, the compressive strength and tensile strength of the outer ring steel bar, and the stress function of the outer ring steel bar in the unyielded triangle area;

[0037] The mathematical expression of the seventh model is:

[0038] The mathematical expression of the eighth model is:

[0039]

[0040] Among them, N pc 、N pt are the axial forces of the outer ring steel bars in compression and tension respectively, M pc 、M pt are the bending moments of the outer ring steel bars under compression and tension, respectively. s is the cross-sectional area of ​​the inner ring of ordinary steel bars, f' py 、f py are the compressive strength and tensile strength of the prestressed tendons, r p A is the radius of the distribution circle of the outer ring reinforcement. p is the cross-sectional area of ​​the outer ring steel bars, σ pi is the stress of the outer ring reinforcement in the unyielded triangle area, σ p0 is the axial stress of the outer ring steel bar, α 6 is the central angle coefficient of the equivalent steel ring under compression yield point of the outer ring reinforcement, α 7 is the central angle coefficient of the tensile yield point of the equivalent steel ring of the outer ring reinforcement, α 3 is the central angle coefficient of the neutral axis of the outer ring.

[0041] In one implementation scheme, before calculating the center angle coefficient of the outer ring concrete in the stress area with the axial force of the axial force calculation model being zero as a constraint condition, the method also includes: fitting the center angle coefficients of the inner ring concrete, the tensile outer ring steel bars, the compressive outer ring steel bars, the tensile inner ring steel bars and the compressive inner ring steel bars included in the axial force calculation model and the bending moment calculation model, and obtaining the fitting results of the center angle coefficients of the inner ring concrete, the tensile outer ring steel bars, the compressive outer ring steel bars, the tensile inner ring steel bars and the compressive inner ring steel bars.

[0042] In one implementation, the fitting method includes trigonometric function fitting and linear correlation fitting.

[0043] In one implementation, the center angle coefficient is substituted into the bending moment calculation model to calculate the bending bearing capacity of the core-filled composite pipe pile, including:

[0044] Substituting the center angle coefficient into the fitting results of the center angle coefficient of the inner ring concrete, the outer ring steel bar under tension, the outer ring steel bar under compression, the inner ring steel bar under tension and the inner ring steel bar under compression, the center angle coefficient of the inner ring concrete, the outer ring steel bar under tension, the outer ring steel bar under compression, the inner ring steel bar under tension and the inner ring steel bar under compression are calculated respectively;

[0045] The calculated central angle coefficients of the inner ring concrete, the tensile outer ring steel bars, the compressive outer ring steel bars, the tensile inner ring steel bars and the compressive inner ring steel bars are substituted into the bending moment calculation model to calculate the bending bearing capacity of the core-filled composite pipe pile.

[0046] In one implementation, the method further includes:

[0047] Eliminate the first model used to calculate the axial force of the inner ring concrete and the fifth model used to calculate the axial force of the inner ring steel bar in the axial force calculation model to obtain a model used to calculate the axial force of the non-core-filled composite pipe pile;

[0048] Eliminate the second model for calculating the inner ring concrete bending moment and the sixth model for calculating the inner ring steel bar bending moment in the bending moment calculation model to obtain a model for calculating the non-core-filled composite pipe pile bending moment;

[0049] Taking the axial force of the model used to calculate the axial force of the non-core-filled composite pipe pile as zero as the constraint condition, the central angle coefficient of the outer ring concrete in the stress area is calculated;

[0050] The central angle coefficient is substituted into the model used to calculate the bending moment of non-core-filled composite pipe piles, and the bending bearing capacity of non-core-filled composite pipe piles is calculated.

[0051] The second aspect of the present application provides an electronic device, which includes a processor, a memory, and a computer program stored in the memory and executable by the processor, wherein when the computer program is executed by the processor, the steps of a method for calculating the bending bearing capacity of a core-filled composite pipe pile provided in the first aspect of the present application are implemented.

[0052] According to a third aspect of the present application, a computer-readable storage medium is provided, wherein the computer-readable storage medium includes a computer program, and when the computer program is executed by one or more processors, the computer program implements a method for calculating the bending bearing capacity of a core-filled composite pipe pile as provided in the first aspect of the present application.

[0053] Compared with the prior art, this application has the following beneficial effects:

[0054] In a method for calculating the flexural bearing capacity of a core-filled composite pipe pile provided in an embodiment of the present application, the method takes into account the initial strain difference between the post-cast concrete at the inner wall of the outer ring of the core-filled composite pipe pile and the outer ring concrete. Therefore, the first equivalent stress diagram coefficient and the second equivalent stress diagram coefficient of the inner and outer ring concrete are calculated respectively based on the rectangular stress diagrams of the inner and outer ring concretes. Then, the respective parameters of the inner and outer ring concretes are combined to construct a model for calculating the axial force and bending moment of the inner ring concrete and a model for calculating the axial force and bending moment of the outer ring concrete. Secondly, the parameters of the inner and outer ring steel bars under tension and compression are combined to construct a model for calculating the axial force and bending moment of the inner ring concrete. A model for calculating the axial force and bending moment of the reinforcement and a model for calculating the axial force and bending moment of the outer ring reinforcement are developed, and then, based on the internal force of the pile cross section satisfying the static equilibrium and strain coordination conditions, the above-mentioned models for calculating the axial force and bending moment are added and summed to obtain the axial force calculation model and bending moment calculation model of the positive section of the core-filled composite pipe pile. The axial force calculation model and the bending moment calculation model analyze the deformation coordination mechanism of the outer ring prefabricated part and the inner ring core-filled part of the pile structure. Therefore, the calculation model clarifies the definition of each coefficient, making the calculation result closer to the measured result, thereby solving the problem that there is a large deviation between the calculation result of the bending bearing capacity provided by the prior art and the measured result.

[0055] It can be understood that the embodiment of the present application also provides an electronic device and a storage medium, which have the technical effects corresponding to the above-mentioned method for calculating the bending bearing capacity of a core-filled composite pipe pile, and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The drawings described herein are used to provide a further understanding of the embodiments of the present application, constitute a part of the present application, and do not constitute a limitation on the embodiments of the present application. In the drawings:

[0057] Figure 1 A schematic diagram of a flow chart of a method for calculating the bending bearing capacity of a core-filled composite pipe pile provided in an embodiment of the present application;

[0058] Figure 2 A schematic diagram of an analysis model for the initial strain difference at the interface between the inner and outer concrete rings of a core-filled composite pipe pile provided in an embodiment of the present application;

[0059] Figure 3 A schematic diagram of equivalent stress of the inner ring concrete cross section provided in an embodiment of the present application;

[0060] Figure 4 A schematic diagram of equivalent stress of the outer ring concrete cross section provided in an embodiment of the present application;

[0061] Figure 5A curve diagram showing the variation of the equivalent coefficient of the outer ring concrete provided in the embodiment of the present application;

[0062] Figure 6 A curve diagram showing a change in the equivalent coefficient of the inner ring concrete provided in an embodiment of the present application;

[0063] Figure 7 A schematic diagram of stress and strain distribution of the inner circle concrete and the outer circle concrete provided in the embodiment of the present application;

[0064] Figure 8 A schematic diagram of stress and strain distribution of the inner ring steel bars and the outer ring steel bars provided in the embodiment of the present application;

[0065] Fig. 9 A schematic diagram of a curve showing the relationship between the central angle coefficient of the tensile prestressed tendons in the outer ring concrete and the central angle coefficient of the equivalent compressive area of ​​the outer ring concrete provided in an embodiment of the present application;

[0066] Fig.10 A schematic diagram of a curve showing the relationship between the central angle coefficient of the compressive prestressed tendons in the outer ring concrete and the central angle coefficient of the equivalent compressive area of ​​the outer ring concrete provided in an embodiment of the present application;

[0067] Fig.11 A schematic diagram of a curve showing the relationship between the central angle coefficients of the equivalent compressive areas of the inner ring steel bars and the outer ring concrete under compression and tension in the inner ring concrete provided in the embodiment of the present application;

[0068] Fig.12 A schematic diagram of a curve showing the relationship between the central angle coefficient of the inner circle of compressed concrete and the central angle coefficient of the equivalent compressed area of ​​the outer circle of concrete provided in an embodiment of the present application. DETAILED DESCRIPTION

[0069] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with examples and drawings. The illustrative implementation scheme of the present application and its description are only used to explain the present application and are not intended to limit the present application.

[0070] It should be noted that the terms "include" or "may include" used in various embodiments of the present application indicate the presence of the function, operation or element applied for, and do not limit the addition of one or more functions, operations or elements. In addition, as used in various embodiments of the present application, the terms "include", "have" and their cognates are only intended to indicate specific features, numbers, steps, operations, elements, components or a combination of the foregoing items, and should not be understood as first excluding the presence of one or more other features, numbers, steps, operations, elements, components or a combination of the foregoing items or the possibility of adding one or more features, numbers, steps, operations, elements, components or a combination of the foregoing items.

[0071] It should be understood that the orientation or position relationship indicated by terms such as "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside" and "outside" are based on the orientation or position relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present application.

[0072] In addition, terms such as "first", "second", "third", etc. are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, features defined as "first", "second", "third", etc. may explicitly or implicitly include one or more of the features. In the description of this application, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0073] Please refer to 1, Figure 1 A schematic diagram of a method for calculating the bending bearing capacity of a core-filled composite pipe pile provided in an embodiment of the present application is shown in FIG. Figure 1 As shown, the method includes:

[0074] S101, according to the rectangular stress diagrams of the inner and outer ring concrete of the core-filled composite pipe pile, respectively calculating the first equivalent stress diagram coefficient of the inner ring concrete and the second equivalent stress diagram coefficient of the outer ring concrete.

[0075] In this embodiment, compared with the hollow prestressed high-strength concrete pipe pile structure, the core-filled composite pipe pile structure is a structure formed by pouring ordinary concrete after placing a steel cage inside the prefabricated PHC pipe pile. The structure consists of four parts: steel bars and concrete in the outer ring part and steel bars and concrete in the inner ring part. It can be understood that the outer ring steel bars are prestressed bars, the outer ring concrete is high-strength concrete, the inner ring steel bars are ordinary steel bars, and the inner ring concrete is ordinary concrete. The bending bearing capacity of the PHC pipe pile is often obtained by superimposing the bending bearing capacity contributed by each part of the material. The core-filled composite pipe pile is its reinforcement structure, and the bending bearing capacity calculation principle is similar. However, since the new and old concrete of the inner and outer circles are formed by prefabrication and post-casting respectively, there are time and space differences between the prefabricated non-core-filled PHC pipe piles in the outer circle and the core-filled reinforced concrete in the inner circle. Therefore, for the core-filled composite pipe pile, the outer ring prefabricated non-core-filled PHC pipe pile and the inner ring core-filled reinforced concrete are distinguished, and the bending bearing capacity of the pipe pile is composed of four materials: prestressed tendons and high-strength concrete in the outer ring and ordinary steel bars and ordinary concrete in the inner ring. It should be noted that the inner ring concrete described in this application refers to ordinary concrete, the outer ring concrete refers to high-strength concrete, the inner ring steel bars refer to ordinary steel bars, and the outer ring steel bars are prestressed tendons.

[0076] Further, such as Figure 2 As shown in the figure, the PHC pile is made by prestressing the tendons first and then pouring high-strength concrete at high temperature centrifugation. con Under the action of pc and the steel stress σ after removing the prestress loss p0 At this time, the high-strength concrete and prestressed tendons produce initial compressive strains ε pc and tensile strain ε p0 ; For the core filling part of the pipe pile, since it is composed of ordinary steel bars and ordinary concrete poured later, there is no initial strain for ordinary concrete and ordinary steel bars, but there is an initial strain difference between the concrete of the inner and outer rings of the pipe pile at their interface. Therefore, it is necessary to establish the strength factor α included in the first equivalent stress diagram coefficient suitable for the outer ring high-strength concrete and the inner ring ordinary concrete in the core filling composite pipe pile 1 , depth factor β 1 and the second equivalent stress diagram coefficients including the intensity factor α 2 , depth factor β 2 The calculation method of .

[0077] The following will be combined Figure 3 and Figure 4 The first equivalent stress coefficient α of the inner ring concrete 1 , β 1 and the second equivalent stress coefficient α of the outer ring concrete 2 , β 2 The specific calculation process of is described in detail. It should be noted that the first equivalent stress diagram coefficient α 1 , β 1 and the second equivalent stress diagram coefficient α 2 , β 2 It can also be referred to as the equivalent coefficient.

[0078] (1) Inner ring concrete

[0079] like Figure 5 and Figure 6 As shown in the figure, for the ordinary concrete in the inner ring filling part, the compressive strain range of the concrete in the outer ring of the core-filled pipe pile is 0~ε cu , the compressive strain range of the inner ring concrete is 0~ε tu , where ε tu , ε cu The inner circle concrete compressive strain at the wall and the outer circle upper edge concrete compressive strain are respectively. The inner circle circular section should meet the deformation coordination, but the initial strain difference ε between the post-cast concrete at the inner wall of the outer circle and the prestressed concrete of the outer circle needs to be taken into account. pcTherefore, the equivalent rectangular stress diagram coefficient of the current standard cannot be simply adopted, and the stress diagram coefficient of the inner circle needs to be converted.

[0080] In some embodiments, the first equivalent stress diagram coefficient of the inner ring concrete of the core-filled composite pipe pile is calculated in the following manner: taking the inner ring neutral axis of the rectangular stress diagram as the origin and the inner ring circular cross-section strip as the positive direction toward the upper compressed edge; integrating and solving the multiple rectangular strips to calculate the first resultant force and the first resultant moment of the inner ring concrete; obtaining the inner radius of the pipe pile, and calculating the first center angle coefficient corresponding to the rectangular stress diagram of the inner ring concrete according to the inner radius of the pipe pile, the first resultant force and the first resultant moment; obtaining the distance from the inner ring neutral axis to the inner ring wall, and calculating the depth factor of the inner ring concrete according to the first center angle coefficient, the distance from the inner ring neutral axis to the inner ring wall and the inner radius of the pipe pile; calculating the first equivalent area of ​​the inner ring circular cross-section compressed concrete according to the depth factor of the inner ring concrete, the distance from the inner ring neutral axis to the inner ring wall and the inner radius of the pipe pile; calculating the strength factor of the inner ring concrete according to the first resultant force, the first equivalent area and the axial compressive strength of the inner ring concrete.

[0081] Specifically, this embodiment uses the inner ring equivalent stress diagram with the inner ring neutral axis as the origin and the upper edge of the compression as the positive direction to divide the circular cross-section strip into several rectangular strips for integration and solution. Based on the ideal elastic-plastic stress distribution mode, the first resultant force F of the ordinary concrete in the inner ring can be calculated by multiplying the cross-sectional stress and the cross-sectional area and integrating them. 1 By multiplying and integrating the cross-sectional stress, cross-sectional area, and force arm, the first resultant moment M can be calculated. 1 , the calculation expressions of the two are as follows:

[0082]

[0083]

[0084] In the formula, ε 01 It represents the compressive strain of the inner ring concrete when the compressive stress of the inner ring concrete just reaches the axial compressive strength of the inner ring concrete, which can be taken as 0.002; ε x represents the compressive strain at any cross-sectional position of the inner circle concrete, k represents the cross-sectional curvature, and n 1 Represents the coefficient in the specification.

[0085] Combined with the first resultant force and the first resultant moment, since the cross-sectional stress diagram of the inner circle concrete elastoplastic constitutive law is equivalent to a rectangular stress diagram, the inner circle concrete before and after the equivalence satisfies the force balance and moment balance, and the position of the concrete resultant force action point remains unchanged. Therefore, the position of the resultant force action point of the inner circle circular cross-section concrete is: Among them, x 1is the distance between the inner ring concrete force action point and the upper edge of the outer ring compression zone, r 1 is the inner radius of the pile, i.e. the radius at the interface between the inner and outer rings of the core-filled composite pile. From this, the first central angle coefficient θ corresponding to the rectangular stress diagram of the inner ring concrete can be obtained: 1 .

[0086] Based on the determined position of the equivalent rectangular stress diagram of the inner ring concrete, the depth factor β of the first equivalent stress diagram of the inner ring concrete can be obtained: 1 =(r 1 -r 1 cosπθ 1 ) / x tu , and the equivalent area of ​​the circular cross-section compressed concrete Among them, x tu is the distance from the neutral axis of the inner ring to the inner ring wall; according to the static equilibrium, the strength factor α of the first equivalent stress diagram of the inner ring concrete is obtained 1 =F 1 / (S 1 f c1 ), where f c1 is the axial compressive strength of the inner ring concrete. Thus, the strength factor α included in the equivalent first stress diagram coefficient of the inner ring concrete is 1 , depth factor β 1 can be obtained, it can be seen that α 1 and β 1 The distance x from the inner ring neutral axis to the inner ring wall is tu is the only variable.

[0087] (2) Outer ring concrete

[0088] like Figure 4 As shown in the figure, for PHC piles made of C80 high-strength concrete, the current standard specifies the α 1 , β 1 They are taken as 0.94 and 0.74 respectively for approximate calculation, but this is not true for the actual annular section. For the annular section, the strain and stress of the concrete far from the neutral axis are large, but the stress area is small, while the strain and stress of the concrete close to the neutral axis are small, but the stress area is large. The correlation coefficient is greatly affected by the position of the neutral axis.

[0089] In some embodiments, the second equivalent stress diagram coefficient of the outer ring concrete of the core-filled composite pipe pile is calculated in the following manner: taking the outer ring neutral axis of the rectangular stress diagram as the origin and the compressive upper edge as the positive direction, the outer ring cross-section strip is divided into a plurality of rectangular strips; wherein the outer ring cross-section is obtained by subtracting the inner ring small circle from the outer ring large circle; integrating and solving the plurality of rectangular strips to calculate the second resultant force and the second resultant moment of the outer ring concrete; obtaining the inner radius and the outer radius of the pipe pile, and calculating according to the inner radius of the pipe pile, the outer radius of the pipe pile, the second resultant force and the second resultant moment Calculate the second central angle coefficient corresponding to the rectangular stress diagram of the outer ring concrete; obtain the distance from the neutral axis of the outer ring to the outer edge of the outer ring compression area, and calculate the depth factor of the outer ring concrete according to the second central angle coefficient, the distance from the neutral axis of the outer ring to the outer edge of the outer ring compression area and the outer radius of the pipe pile; calculate the second equivalent area of ​​the outer ring annular cross-section compression concrete according to the depth factor of the outer ring concrete, the inner radius of the pipe pile and the outer radius of the pipe pile; calculate the strength factor of the outer ring concrete according to the second resultant force, the second equivalent area and the axial compressive strength of the outer ring concrete.

[0090] Therefore, in this embodiment, the neutral axis of the outer circle of the rectangular stress diagram is taken as the origin, and the positive direction is taken as the upper edge of the compression. The circular cross-sectional strip is divided into several rectangular strips for integration and solution. The annular cross-sectional area is obtained by subtracting the inner circle from the outer circle. Based on the ideal elastic-plastic stress distribution mode, the second resultant force F of the outer circle high-strength concrete can also be calculated. 2 With the second resultant moment M 2 , the calculation expressions for both are:

[0091]

[0092] In the formula, ε 02 It represents the compressive strain of the outer ring concrete when the compressive stress of the outer ring concrete just reaches the axial compressive strength of the outer ring concrete, which can also be taken as 0.002; n 2 represents the coefficient in the specification, ε c It indicates the compressive strain at the distance from the neutral axis of the outer ring to the inner wall of the outer ring; the section curvature k is equal to the compressive strain at the distance from the neutral axis of the outer ring to the inner wall of the outer ring divided by the distance from the neutral axis of the outer ring to the inner wall of the outer ring.

[0093] The concrete of the outer ring section also satisfies the force balance and moment balance before and after the equivalence, and the position of the resultant force application point of the outer ring concrete remains unchanged. Therefore, the position of the resultant force application point of the outer ring section concrete is: Among them, x 2 is the distance between the point of action of the combined force of the outer ring high-strength concrete and the upper edge of the outer ring compression zone, r 2 is the outer radius of the pile, that is, the radius at the outer edge of the outer ring of the core-filled composite pile. From this, the central angle coefficient θ corresponding to the equivalent rectangular stress diagram of the outer ring concrete can be obtained:2 .

[0094] Based on the determined position of the equivalent rectangular stress diagram of the outer ring concrete, the depth factor β of the second equivalent stress diagram of the outer ring concrete can be obtained: 2 =(r 2 -r 2 cosπθ 2 ) / x cu , where x cu is the distance from the neutral axis of the outer ring to the outer edge of the outer ring compression area, and the equivalent area of ​​the outer ring cross section under compression concrete According to the static equilibrium, the intensity factor α of the second stress diagram coefficient can be obtained: 2 =F 2 / (S 2 f c2 ), where f c2 is the axial compressive strength of the outer ring concrete. Thus, the strength factor α included in the equivalent second stress diagram coefficient of the outer ring concrete is 2 , depth factor β 2 can be found, α 2 and β 2 The distance x is from the neutral axis of the outer ring to the outer edge of the pressure zone. cu is the only variable.

[0095] It should also be noted here that the equivalent rectangular stress diagram coefficient used in the past is based on the rectangular pile section, and the tensile yield strain of ordinary steel bars is 0.0018 as the critical value of proper reinforcement failure. However, for the core-filled composite pipe piles targeted by this embodiment, the tensile yield strain of the outer ring steel bars should be used as the critical value to calculate the equivalent coefficient. In actual engineering, the outer ring steel bars are generally prestressed rods, prestressed threaded steel bars, steel strands, etc., and their tensile yield strain ranges from 0.003 to 0.007. Based on the assumption of the plane section, it can be obtained that the distance x from the neutral axis of the inner ring to its ring wall is tu The distance x from the neutral axis of the outer ring to the outer edge of the pressure zone cu The variation curve of the prestressed tendon yield strain under tension can be used to obtain α 1 , β 1 and α 2 , β 2 The variation curve of the yield strain of the prestressed tendons under tension only depends on the strength grade of the outer ring concrete and the strength grade of the inner ring concrete.

[0096] like Figure 5 and Figure 6 As shown in the figure, according to the calculation method of the equivalent stress diagram coefficients of the inner and outer ring concrete provided above, the equivalent rectangular stress diagram coefficients α of the outer and inner ring concrete can be obtained. 1 , β 1 and α2 , β 2 With the change curve of the prestressed tendon tensile yield strain, in order to give a modified equivalent rectangular stress diagram coefficient suitable for the core-filled composite pipe pile structure and convenient for engineering application, the median of the change curve is taken as α 1 , β 1 and α 2 , β 2 Preferably, for the outer ring concrete with strength grade C80 and the inner ring concrete with strength grade C30 or C40, the strength factor α of the inner ring concrete can be approximated as 1 =0.8, depth factor β 1 =0.95; strength factor of outer ring concrete α 2 =0.72, depth factor β 2 =0.86.

[0097] S102, obtaining the first parameter of the inner ring concrete and the second parameter of the outer ring concrete, constructing a first model for calculating the axial force of the inner ring concrete and a second model for the bending moment according to the first equivalent stress diagram coefficient and the first parameter, and constructing a third model for calculating the axial force of the outer ring concrete and a fourth model for the bending moment according to the second equivalent stress diagram coefficient and the second parameter.

[0098] In this embodiment, the first parameter of the inner ring concrete includes the neutral axis of the inner ring and the central angle coefficient corresponding to the equivalent compression zone of the inner ring concrete.

[0099] like Figure 7 As shown in the figure, based on the constitutive model of the inner and outer ring concrete and the inner and outer ring cross-section analysis model, the stress and strain distribution of the outer and inner ring concrete on the cross-section of the pile is given. The concrete stress diagram includes a parabolic area and a rectangular area. For the convenience of analysis, it is equivalent to a rectangular stress diagram. Figure 7 In, α 1 f c1 is the stress value of the inner circle concrete rectangular stress diagram, β 1 x tu is the stress distribution height; α 2 f c2 is the stress value of the outer circle concrete rectangular stress diagram, β 2 x cu is the height of the stress distribution diagram; t is the wall thickness of the pile (outer ring thickness), x u It is the distance from the neutral axis of the inner ring to the upper edge of the pressure zone.

[0100] like Figure 7 As shown, α, α 3 , α 4 , α 5They are the central angle coefficients corresponding to the outer circle concrete equivalent compression zone, the outer circle neutral axis, the inner circle neutral axis, and the inner circle concrete equivalent compression zone. They are dimensionless coefficients corresponding to the corresponding stress areas of concrete and can be obtained through the trigonometric transformation of the central angle, where the central angle is the angle formed by rotating around the center of the pile cross section from the radius of the left or right end of the compression zone to the left and right symmetry axes of the compression zone.

[0101] Without considering the tensile effect of concrete, only the axial force and bending moment of the outer ring high-strength concrete and the inner ring ordinary concrete compression zone are calculated. The annular cross-sectional area of ​​the outer ring concrete is A. 2 , the area of ​​the compression zone of the concrete annular section is approximated as a sector area, and the area increment corresponding to the central angle d(πθ) of the sector microelement is Among them, θ is the central angle coefficient of the microelement, which is a dimensionless coefficient. The inner circle circular cross-sectional area uses several strips, and the circular cross-sectional area of ​​the inner circle concrete is A 1 , then the area increment corresponding to the inner circular cross section is dA 1 =2r 1 2 sin 2 (πθ)d(πθ).

[0102] Therefore, the first model and the second model are constructed by combining the first equivalent stress diagram coefficient and the first parameter described above, and their mathematical expressions are: Among them, N c1 、M c1 are the axial force and bending moment of the inner ring concrete, α 1 is the intensity factor of the first equivalent stress diagram coefficient, f c1 A is the axial compressive strength of the inner ring concrete, 1 is the cross-sectional area of ​​the inner circle, r 1 is the inner radius of the pile, α 4 is the central angle coefficient of the neutral axis of the inner circle, and θ is the central angle coefficient of the infinitesimal element.

[0103] Since the axial compressive strength, central angle coefficient and cross-sectional area increment of the inner ring concrete stress area are all determined, the specific results of the axial force and bending moment of the inner ring concrete can be obtained by solving the corresponding model through integration.

[0104] In some embodiments, the second parameter of the outer ring concrete includes the neutral axis of the outer ring and the central angle coefficient corresponding to the equivalent compression zone of the outer ring concrete.

[0105] The third model and the fourth model are constructed by combining the second equivalent stress diagram coefficient and the second parameter described above. The mathematical expressions of the third model are: The mathematical expression of the fourth model is: Among them, Nc2 、M c2 are the axial force and bending moment of the outer ring concrete, α 2 is the intensity factor of the second equivalent stress diagram coefficient, f c2 A is the axial compressive strength of the outer ring concrete, 2 is the cross-sectional area of ​​the outer ring, r 1 is the inner radius of the pile, r 2 is the outer radius of the pile, α is the central angle coefficient of the equivalent compression zone of the outer circle concrete, and θ is the central angle coefficient of the microelement.

[0106] S103, obtaining a third parameter of the inner ring steel bar under tension and compression and a fourth parameter of the outer ring steel bar under tension and compression, constructing a fifth model for calculating the axial force of the inner ring steel bar and a sixth model for calculating the bending moment according to the first parameter and the third parameter, and constructing a seventh model for calculating the axial force of the outer ring steel bar and an eighth model for calculating the bending moment according to the second parameter and the fourth parameter.

[0107] In this embodiment, the third parameter of the inner ring steel bar under tension and compression states includes the central angle coefficient corresponding to the compressive yield point and tensile yield point of the equivalent steel ring of the inner ring steel bar, the compressive strength and tensile strength of the inner ring steel bar, and the stress function of the inner ring steel bar in the unyielded triangular area.

[0108] like Figure 8 As shown in the figure, based on the constitutive model of the inner and outer ring steel bars and the inner and outer ring cross-section analysis model, the stress and strain distribution of the outer and inner ring steel bars on the cross section of the pile are given. Figure 8 The rectangular stress distribution in the yield zone and the triangular stress distribution in the unyielded zone are considered for both the outer and inner rings of steel bars. The outer ring of steel bars is in a decompressed state, and the internal force of the outer ring of steel bars is equal to the axial stress σ p0 Multiply by the cross-sectional area A of the prestressing tendon p , the axial force and bending moment are presented in the internal force equilibrium equation of the entire pile cross section. The steel bar strain is represented by ε.

[0109] like Figure 8 As shown, α 6 , α 7 , α 8 , α 9 They represent the central angle coefficients corresponding to the compressive yield point and tensile yield point of the outer ring reinforcement and the compressive yield point and tensile yield point of the inner ring reinforcement respectively. They are dimensionless coefficients, corresponding to the corresponding stress areas of the longitudinal reinforcement respectively, and can be obtained by trigonometric transformation of the central angle.

[0110] like Figure 8As shown in the figure, the longitudinal reinforcement is equivalent to a steel ring with a circular cross-section. Different from the concrete equivalent rectangular stress diagram, the stress area of ​​the reinforcement is divided into a yielded rectangular area and an unyielded triangular area. The stress values ​​of the outer and inner ring reinforcements in the yielded rectangular area are the compressive and tensile strength values ​​of the reinforcement; the unyielded triangular area is located between the compressive yield section and the tensile yield section. The stresses of the prestressed tendons and ordinary reinforcements in the unyielded triangular area are linear functions, respectively expressed as σ pi , σ si .

[0111] Based on the central angle coefficient, cross-sectional area increment and stress function of the longitudinal reinforcement stress area, the axial force and bending moment of the longitudinal reinforcement can be obtained by integral solution. Different from the calculation method of concrete only for the compression zone, the axial force and bending moment of the longitudinal reinforcement need to be calculated in both the compression zone and the tension zone.

[0112] Therefore, the mathematical expression of the fifth model is:

[0113] The mathematical expression of the sixth model is:

[0114]

[0115] Among them, N sc 、N st are the axial forces of the inner ring steel bars under compression and tension, respectively. sc 、M st are the bending moments of the inner ring steel bars under compression and tension, respectively, and f' y 、f y are the compressive and tensile strengths of the inner ring steel bars, A s is the cross-sectional area of ​​the inner ring steel bar, α 5 is the central angle coefficient of the equivalent compression zone of the inner circle concrete, α 3 is the central angle coefficient of the neutral axis of the outer ring, r s is the radius of the distribution circle of the inner ring reinforcement, σ si is the stress of the inner ring reinforcement in the unyielded triangle area, α 8 is the central angle coefficient of the equivalent steel ring under compression yield point of the inner steel ring, α 9 It is the central angle coefficient of the tensile yield point of the equivalent steel ring of the inner ring reinforcement.

[0116] In some embodiments, the fourth parameter of the outer ring steel bars under tension and compression states includes the central angle coefficient corresponding to the compressive yield point and tensile yield point of the equivalent steel ring of the outer ring steel bars, the compressive strength and tensile strength of the outer ring steel bars, and the stress function of the outer ring steel bars in the unyielded triangular area.

[0117] The mathematical expression of the seventh model is:

[0118] The mathematical expression of the eighth model is:

[0119]

[0120] Among them, N pc 、N pt are the axial forces of the outer ring steel bars in compression and tension respectively, M pc 、M pt are the bending moments of the outer ring steel bars under compression and tension, respectively. s is the cross-sectional area of ​​the inner ring of ordinary steel bars, f' py 、f py are the compressive strength and tensile strength of the prestressed tendons, r p A is the radius of the distribution circle of the outer ring reinforcement. p is the cross-sectional area of ​​the outer ring steel bars, σ pi is the stress of the outer ring reinforcement in the unyielded triangle area, σ p0 is the axial stress of the outer ring steel bar, α 6 is the central angle coefficient of the equivalent steel ring under compression yield point of the outer ring reinforcement, α 7 is the central angle coefficient of the tensile yield point of the equivalent steel ring of the outer ring reinforcement, α 3 is the central angle coefficient of the neutral axis of the outer ring.

[0121] S104, summing the first model, the third model, the fifth model and the seventh model to obtain an axial force calculation model of the core-filled composite pipe pile cross section, and summing the second model, the fourth model, the sixth model and the eighth model to obtain a bending moment calculation model of the core-filled composite pipe pile cross section.

[0122] In this embodiment, the internal force of the core-filled composite pipe pile is provided by the four materials it contains. According to the internal force of the cross-section of the core-filled composite pipe pile should satisfy the static equilibrium and strain coordination conditions, the calculation expressions of the axial force and bending moment of the cross-section of the core-filled composite pipe pile are: N = N c1 +N c2 +N pc +N pt +N sc +N st ;

[0123] M=M c1 +M c2 +M pc +M pt +M sc +M st Where N is the axial force of the core-filled composite pipe pile's positive section, and M is the bending moment of the core-filled composite pipe pile's positive section.

[0124] In this embodiment, for the first to eighth models, the specific contents of the mathematical expressions are integrated and solved, and then the corresponding sums are obtained to obtain the specific calculation expressions of the axial force and bending moment of the positive section of the core-filled composite pipe pile:

[0125] In the formula, α, α c , α pt , α pc , α st , α sc They are the central angle coefficients of the stress-bearing areas of the outer ring concrete, inner ring concrete, tensile outer ring steel bars, compressive outer ring steel bars, tensile inner ring steel bars, and compressive inner ring steel bars.

[0126] In a further embodiment, the first model for calculating the axial force of the inner circle concrete and the fifth model for calculating the axial force of the inner circle steel bar are eliminated from the axial force calculation model to obtain a model for calculating the axial force of the non-core-filled composite pipe pile; the second model for calculating the bending moment of the inner circle concrete and the sixth model for calculating the bending moment of the inner circle steel bar are eliminated from the bending moment calculation model to obtain a model for calculating the bending moment of the non-core-filled composite pipe pile; the axial force of the model for calculating the axial force of the non-core-filled composite pipe pile is zero as a constraint condition to calculate the central angle coefficient of the outer circle concrete in the stress area; the central angle coefficient is substituted into the model for calculating the bending moment of the non-core-filled composite pipe pile to calculate the bending bearing capacity of the non-core-filled composite pipe pile.

[0127] Specifically, after removing the model, the specific calculation expressions of the axial force and bending moment of the positive section of the non-core-filled PHC pile are:

[0128] N=αα 2 f c2 A 2 +α pc f′ py A p -α pt (f py -σ p0 )A p -σ p0 A p ;

[0129]

[0130] In some embodiments, before executing step S104, the method also includes: fitting the central angle coefficients of the inner ring concrete, the tensile outer ring steel bars, the compressive outer ring steel bars, the tensile inner ring steel bars and the compressive inner ring steel bars included in the axial force calculation model and the bending moment calculation model, and obtaining the fitting results of the central angle coefficients of the inner ring concrete, the tensile outer ring steel bars, the compressive outer ring steel bars, the tensile inner ring steel bars and the compressive inner ring steel bars.

[0131] Specifically, the center angle coefficients in the axial force calculation model and the bending moment calculation model of the core-filled composite pipe pile cross section are fitted and simplified, and the center angle coefficients of the inner ring concrete, the tensile outer ring steel bars, the compressive outer ring steel bars, the tensile inner ring steel bars and the compressive inner ring steel bars in the calculation expressions are fitted by trigonometric function fitting and linear correlation fitting, so as to obtain simplified calculation expressions of the center angle coefficients of the inner ring concrete, the tensile outer ring steel bars, the compressive outer ring steel bars, the tensile inner ring steel bars and the compressive inner ring steel bars, and the simplified expressions of the center angle coefficients can be replaced accordingly, so as to obtain simplified calculation expressions of the axial force and bending moment of the core-filled composite pipe pile cross section.

[0132] Specifically, Fig. 9 and Fig.10 As shown in the figure, the distribution of the central angle coefficient in the axial force formula of the tensile and compressive pre-external reinforcement in the outer ring concrete is approximately linearly related to α, and the fitting expressions are α pc =α 6 +n pc =0.85α,α pt =1-α 7 +n pt =0.93-1.5α; the distribution of the central angle coefficient in the bending moment formula of the outer ring steel bar under tension and compression is close to the sine curve of α, and the fitting expressions are sinπα 6 +m pc =0.95sinπα pc , sinπα 7 -m pt = sinπα pt .

[0133] like Fig.11 and Fig.12 As shown in the figure, considering three kinds of ordinary steel bars, HRB335, HRB400 and HRB500, the expressions of the central angle coefficients in the axial force formulas of the inner ring steel bars under compression and tension and the inner ring concrete under compression are α sc =α 8 +n sc =1.35α-0.35,α st =1-α 9 +n st =1.3-2α,α c =1.5–0.25α; the expressions of the central angle coefficients in the bending moment formulas for the inner ring of compression and tension reinforcement are sinπα respectively. 8 +m sc =0.9sinπα sc , sinπα 9 -m st = sinπα st Among them, n pc 、npt 、n sc 、n st are the dimensionless coefficients related to the axial forces of the outer ring of compression steel bars, the outer ring of tension steel bars, the inner ring of compression steel bars, and the inner ring of tension steel bars, respectively. pc 、m pt 、m sc 、m st are dimensionless coefficients related to the bending moment.

[0134] Therefore, the relevant central angle coefficient in the specific calculation expression of the axial force and bending moment of the positive section of the core-filled composite pipe pile can be fitted and simplified, and the expression of the fitting result is as follows:

[0135] Substituting the expression of the fitting result into the specific calculation expression of the axial force and bending moment of the positive section of the core-filled composite pipe pile, the simplified calculation expression of the axial force and bending moment of the positive section of the core-filled composite pipe pile can be obtained.

[0136] In particular, for non-core filled PHC piles, the central angle coefficient α pc , α pt The simplified calculation expression is as follows:

[0137]

[0138] Accordingly, the simplified calculation formula of the central angle coefficient of the non-core-filled PHC pile is substituted into the specific calculation expressions of the axial force and bending moment of the positive section of the non-core-filled PHC pile, and the simplified calculation expressions of the axial force and bending moment of the positive section of the non-core-filled PHC pile can be obtained.

[0139] It can be seen that the simplified center angle coefficient makes the center angle coefficient in the calculation formula of axial force and bending moment simplified and no longer complicated, so there is no need for corresponding calculation software or solver to solve the calculation moment of axial force and bending moment. Only simple calculation tools need to be introduced to realize the calculation of axial force and bending moment, thereby improving the calculation efficiency of axial force and bending moment of core-filled composite pipe piles or non-core-filled PHC pipe piles.

[0140] S105, taking the axial force of the axial force calculation model as zero as a constraint condition, calculating the center angle coefficient of the outer ring concrete in the stress area.

[0141] In this embodiment, based on the axial force calculation model described above, when the axial force is zero, there is:

[0142]

[0143] ; In the formula, α 0 It is the central angle coefficient of the outer ring concrete stress zone when the axial force is zero.

[0144] Depend on Available

[0145] Then, combined The two conditions of zero axial force can be used to calculate the central angle coefficient α of the outer ring concrete stress zone. 0 .

[0146] S106, substituting the center angle coefficient into the bending moment calculation model to calculate the bending bearing capacity of the core-filled composite pipe pile.

[0147] The central angle coefficient α of the outer ring concrete stress zone 0 Substitute , calculate the center angle coefficients of the stress-bearing areas of the inner ring concrete, the outer ring tensile steel bars, the outer ring compressive steel bars, the inner ring tensile steel bars, and the inner ring compressive steel bars. Then substitute the center angle coefficients of the stress-bearing areas of the inner ring concrete, the outer ring tensile steel bars, the outer ring compressive steel bars, the inner ring tensile steel bars, and the inner ring compressive steel bars into the specific calculation expression of the bending moment of the positive section of the core-filled composite pipe pile, and the bending bearing capacity of the core-filled composite pipe pile can be calculated. It should be noted that if the value of the center angle coefficient of the stress-bearing areas of the inner ring concrete, the outer ring tensile steel bars, the outer ring compressive steel bars, the inner ring tensile steel bars, and the inner ring compressive steel bars is negative, then take its value as 0.

[0148] Accordingly, the calculation process for the flexural bearing capacity of the cross section of the non-core-filled PHC pile is consistent with the calculation process for the flexural bearing capacity of the core-filled composite pile described above, and will not be repeated in this embodiment.

[0149] The following will combine the specific parameters of the core-filled composite pipe pile to calculate the bending bearing capacity of the core-filled composite pipe pile, as follows:

[0150] For the core-filled composite pipe pile, the outer diameter is 400mm, the inner diameter is 270mm, the outer ring reinforcement is 7 prestressed steel bars with a diameter of 7.1mm, abbreviated as 7Φ7.1, and the inner ring reinforcement is 6 ordinary steel bars with a diameter of 16mm, abbreviated as 6Φ16. The strength grade of the outer ring concrete is C80, the axial compressive strength of the outer ring concrete is 46.21MPa, the strength grade of the inner ring concrete is C30, the axial compressive strength of the inner ring concrete is 26.5MPa, the tensile strength of the outer ring steel bar is 1463MPa, the tensile strength of the inner ring steel bar is 335MPa, and the compressive strength of the outer ring steel bar and the inner ring steel bar are 400MPa and 335Mpa respectively.

[0151] In this embodiment, the outer ring concrete is of C80 strength grade, and the inner ring concrete is of C30 strength grade. Therefore, the strength factor α of the inner ring concrete can be approximately taken as 1 =0.8, depth factor β 1 =0.95; strength factor of outer ring concrete α 2=0.72, depth factor β 2 =0.86.

[0152] Secondly, the relevant parameters for calculating the bending bearing capacity of the core-filled composite pipe piles are given as follows:

[0153] r 1 =135mm, r 2 =200mm, r p =7.1mm, r s =16mm, f c1 =26.5MPa, f c2 =46.21MPa, f y =f' y =335MPa,

[0154] f py =400MPa, f' py =1463MPa, α 1 =0.8,β 1 =0.95,α 2 =0.72, β 2 =0.86.

[0155] Substituting the relevant parameters into the specific calculation expressions of the axial force and bending moment of the positive section of the core-filled composite pipe pile described above, the calculation expressions corresponding to the axial force and bending moment are obtained, respectively:

[0156]

[0157] Then, the fitting results of the central angle coefficients of the inner ring concrete, the tensile outer ring steel bars, the compressive outer ring steel bars, the tensile inner ring steel bars and the compressive inner ring steel bars are substituted into the corresponding calculation expressions of the axial force and the bending moment, and the simplified calculation expressions of the axial force and the bending moment of the positive section of the core-filled composite pipe pile can be obtained, which are:

[0158]

[0159]

[0160] Under the condition of zero axial force, the corresponding central angle coefficient α of the stress zone containing high-strength concrete can be obtained: 0 The equation is:

[0161] Solving this equation, we can obtain the central angle coefficient α of the outer ring concrete stress zone: 0 = 0.2618, substitute it into It can be calculated that α c =01427, α pt =0.5373, α pc =0.2225, αst =0.7764, α sc =0; then substitute the relevant parameters into the bending moment calculation expression The bending bearing capacity M of the core-filled composite pipe pile can be calculated. 0 =114.49kN·m.

[0162] Secondly, the measured result of the bending bearing capacity of the core-filled composite pipe pile obtained by the loading test is 126 kN·m. It can be seen that the absolute value of the relative error between the calculation result of the bending bearing capacity calculation method provided in this embodiment and the measured result is (126-114.49) / 126=9.1%, and the two are relatively close, with a small deviation, indicating that the bending bearing capacity calculation method of the core-filled composite pipe pile provided in this embodiment has good rationality and solves the problem of large deviation between the bending bearing capacity calculation result and the measured result.

[0163] The embodiment of the present application also provides an electronic device, which includes a processor, a memory, a communication interface and at least one communication bus for connecting the processor, the memory and the communication interface. The memory includes but is not limited to a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (PROM) or a portable CD-ROM, and the memory is used for related instructions and data.

[0164] The communication interface is used to receive and send data. The processor may be one or more CPUs. When the processor is a CPU, the CPU may be a single-core CPU or a multi-core CPU. The processor in the electronic device is used to read one or more programs stored in the memory and perform the following operations: according to the rectangular stress diagrams of the inner and outer ring concrete of the core-filled composite pipe pile, respectively calculate the first equivalent stress diagram coefficient of the inner ring concrete and the second equivalent stress diagram coefficient of the outer ring concrete; obtain the first parameter of the inner ring concrete and the second parameter of the outer ring concrete, and construct a first model for calculating the axial force of the inner ring concrete and a second model for the bending moment according to the first equivalent stress diagram coefficient and the first parameter; and construct a third model for calculating the axial force of the outer ring concrete and a fourth model for the bending moment according to the second equivalent stress diagram coefficient and the second parameter; obtain the third parameter of the inner ring steel bar under tension and compression and the fourth model of the outer ring steel bar under tension and compression. According to the fourth parameter of the state, a fifth model for calculating the axial force of the inner ring steel bar and a sixth model for the bending moment are constructed according to the first parameter and the third parameter; according to the second parameter and the fourth parameter, a seventh model for calculating the axial force of the outer ring steel bar and an eighth model for the bending moment are constructed; the first model, the third model, the fifth model and the seventh model are summed to obtain the axial force calculation model of the positive section of the core-filled composite pipe pile; the second model, the fourth model, the sixth model and the eighth model are summed to obtain the bending moment calculation model of the positive section of the core-filled composite pipe pile; with the axial force of the axial force calculation model being zero as a constraint condition, the center angle coefficient of the outer ring concrete in the stress area is calculated; the center angle coefficient is substituted into the bending moment calculation model to calculate the bending bearing capacity of the core-filled composite pipe pile.

[0165] It should be noted that the specific implementation of each operation can be Figure 1 The corresponding description of the method embodiment shown, the electronic device can be used to execute a method for calculating the bending bearing capacity of a core-filled composite pipe pile in the above method embodiment, which will not be described in detail here.

[0166] In the embodiments of the present disclosure, a computer-readable storage medium is also provided, and the computer-readable storage medium is a memory device in a computer device for storing programs and data. It is understandable that the computer-readable storage medium here can include both the built-in storage medium in the computer device and the extended storage medium supported by the computer device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory (non-volatile memory), such as at least one disk memory. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the method for calculating the bending bearing capacity of a core-filled composite pipe pile in the above embodiment. Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0167] The specific implementation methods described above further illustrate the purpose, technical solutions and beneficial effects of the present application in detail. It should be understood that the above description is only the specific implementation method of the present application and is not intended to limit the scope of protection of the present application. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A method for calculating the bending bearing capacity of a core-filled composite pipe pile, characterized in that the method include: According to the rectangular stress diagrams of the inner and outer ring concrete of the core-filled composite pipe pile, the first equivalent stress diagram coefficient of the inner ring concrete and the second equivalent stress diagram coefficient of the outer ring concrete are calculated respectively; wherein the first equivalent stress diagram coefficient includes the strength factor and depth factor of the inner ring concrete; and the second equivalent stress diagram coefficient includes the strength factor and depth factor of the outer ring concrete; The first parameter of the inner ring concrete and the second parameter of the outer ring concrete are obtained, and according to the first equivalent stress diagram coefficient and the first parameter, a first model for calculating the axial force of the inner ring concrete and a second model for the bending moment are constructed, and according to the second equivalent stress diagram coefficient and the second parameter, a third model for calculating the axial force of the outer ring concrete and a fourth model for the bending moment are constructed; wherein the first parameter of the inner ring concrete includes the neutral axis of the inner ring and the center angle coefficient corresponding to the equivalent compression zone of the inner ring concrete; the second parameter of the outer ring concrete includes the neutral axis of the outer ring and the center angle coefficient corresponding to the equivalent compression zone of the outer ring concrete; the mathematical expression of the first model is: ; The mathematical expression of the second model: ;in, N c1 , M c1 are the axial force and bending moment of the inner ring concrete, α 1 is the intensity factor of the first equivalent stress diagram coefficient, f c1 is the axial compressive strength of the inner ring concrete, A 1 is the cross-sectional area of ​​the inner circle, r 1 is the inner radius of the pile, α 4 is the central angle coefficient of the neutral axis of the inner ring, θ is the central angle coefficient of the microelement; the mathematical expression of the third model is: ; The mathematical expression of the fourth model is: ;in, N c2 , M c2 are the axial force and bending moment of the outer ring concrete, α 2 is the intensity factor of the second equivalent stress diagram coefficient, f c2 is the axial compressive strength of the outer ring concrete, A 2 is the cross-sectional area of ​​the outer ring, r 1 is the inner radius of the pile, r 2 is the outer radius of the pile, α is the central angle coefficient of the equivalent compression zone of the outer ring concrete, θ is the central angle coefficient of the differential element; Obtain the third parameter of the inner ring steel bar under tension and compression and the fourth parameter of the outer ring steel bar under tension and compression, and construct a fifth model for calculating the axial force of the inner ring steel bar and a sixth model for the bending moment according to the first parameter and the third parameter, and construct a seventh model for calculating the axial force of the outer ring steel bar and an eighth model for the bending moment according to the second parameter and the fourth parameter; wherein the third parameter of the inner ring steel bar under tension and compression includes the central angle coefficient corresponding to the compressive yield point and the tensile yield point of the equivalent steel ring of the inner ring steel bar, the compressive strength and the tensile strength of the inner ring steel bar, and the stress function of the inner ring steel bar in the unyielded triangular area; the fourth parameter of the outer ring steel bar under tension and compression includes the central angle coefficient corresponding to the compressive yield point and the tensile yield point of the equivalent steel ring of the outer ring steel bar, the compressive strength and the tensile strength of the outer ring steel bar, and the stress function of the outer ring steel bar in the unyielded triangular area; wherein the mathematical expression of the fifth model is: ; The mathematical expression of the sixth model is: ； in, N sc , N st are the axial forces of the inner ring steel bars under compression and tension, respectively. M sc , M st are the bending moments of the inner ring steel bars under compression and tension, respectively. f’ y , f y are the compressive and tensile strengths of the inner ring steel bars, A s is the cross-sectional area of ​​the inner ring steel bar, α 5 is the central angle coefficient of the equivalent compression zone of the inner circle concrete, r s is the radius of the distribution circle for the inner ring reinforcement, σ si is the stress of the inner ring reinforcement in the unyielded triangle area, α 8 is the central angle coefficient of the equivalent steel ring compression yield point of the inner steel ring, α 9 is the central angle coefficient of the tensile yield point of the equivalent steel ring of the inner steel ring; The mathematical expression of the seventh model is: ; The mathematical expression of the eighth model is: ； in, N pc , N pt are the axial forces of the outer ring steel bars in compression and tension, respectively. M pc , M pt are the bending moments of the outer ring steel bars under compression and tension, respectively. f’ py , f py are the compressive strength and tensile strength of the prestressed tendons, r p is the radius of the distribution circle for the outer ring reinforcement, A p is the cross-sectional area of ​​the outer ring steel bars, σ pi is the stress of the outer ring reinforcement in the unyielded triangle area, σ p0 is the axial stress of the outer ring reinforcement, α 6 is the central angle coefficient of the compression yield point of the equivalent steel ring of the outer ring reinforcement, α 7 is the central angle coefficient of the tensile yield point of the equivalent steel ring of the outer ring reinforcement, α 3 is the central angle coefficient of the neutral axis of the outer ring; The first model, the third model, the fifth model and the seventh model are summed to obtain an axial force calculation model of the positive section of the core-filled composite pipe pile; the second model, the fourth model, the sixth model and the eighth model are summed to obtain a bending moment calculation model of the positive section of the core-filled composite pipe pile; Taking the axial force of the axial force calculation model as zero as the constraint condition, calculate the central angle coefficient of the outer ring concrete in the stress area; Substitute the center angle coefficient into the bending moment calculation model to calculate the bending bearing capacity of the core-filled composite pipe pile.

2. A method for calculating the bending bearing capacity of a core-filled composite pipe pile according to claim 1, characterized in that: The first equivalent stress diagram coefficient of the inner ring concrete of the core-filled composite pipe pile is calculated in the following way: Taking the neutral axis of the inner circle of the rectangular stress diagram as the origin and the positive direction toward the upper edge of the compression, the inner circle circular cross-section strip is divided into multiple rectangular strips; Integrating and solving multiple rectangular strips to calculate the first resultant force and first resultant moment of the inner circle concrete; The inner radius of the pipe pile is obtained, and the first central angle coefficient corresponding to the rectangular stress diagram of the inner circle concrete is calculated according to the inner radius of the pipe pile, the first resultant force and the first resultant moment; Obtain the distance from the neutral axis of the inner circle to the wall of the inner circle, and calculate the depth factor of the inner circle concrete according to the first central angle coefficient, the distance from the neutral axis of the inner circle to the wall of the inner circle and the inner radius of the pile; According to the depth factor of the inner circle concrete, the distance from the inner circle neutral axis to the inner circle wall and the inner radius of the pile, the first equivalent area of ​​the inner circle circular cross-section compression concrete is calculated; The strength factor of the inner circle concrete is calculated based on the first resultant force, the first equivalent area and the axial compressive strength of the inner circle concrete.

3. The method for calculating the bending bearing capacity of a core-filled composite pipe pile according to claim 1, characterized in that: The second equivalent stress diagram coefficient of the outer ring concrete of the core-filled composite pipe pile is calculated in the following way: Taking the neutral axis of the outer ring of the rectangular stress diagram as the origin and the positive direction toward the upper edge of the compression, the outer ring section strip is divided into multiple rectangular strips; wherein, the outer ring section is obtained by subtracting the inner ring small circle from the outer ring large circle; Integrating and solving multiple rectangular strips to calculate the second resultant force and second resultant moment of the outer ring concrete; The inner radius and the outer radius of the pipe pile are obtained, and the second central angle coefficient corresponding to the rectangular stress diagram of the outer circle concrete is calculated according to the inner radius and the outer radius of the pipe pile, the second resultant force and the second resultant moment; Obtain the distance from the neutral axis of the outer ring to the outer edge of the outer ring compression area, and calculate the depth factor of the outer ring concrete according to the second central angle coefficient, the distance from the neutral axis of the outer ring to the outer edge of the outer ring compression area and the outer radius of the pile; According to the depth factor of the outer ring concrete, the inner radius of the pipe pile and the outer radius of the pipe pile, the second equivalent area of ​​the outer ring section compressed concrete is calculated; The strength factor of the outer ring concrete is calculated based on the second resultant force, the second equivalent area and the axial compressive strength of the outer ring concrete.

4. The method for calculating the bending bearing capacity of a core-filled composite pipe pile according to claim 1, characterized in that: Before calculating the center angle coefficient of the outer ring concrete in the stress area with the axial force of the axial force calculation model being zero as a constraint condition, the method also includes: fitting the center angle coefficients of the inner ring concrete, the tensile outer ring steel bars, the compressive outer ring steel bars, the tensile inner ring steel bars and the compressive inner ring steel bars included in the axial force calculation model and the bending moment calculation model, and obtaining the fitting results of the center angle coefficients of the inner ring concrete, the tensile outer ring steel bars, the compressive outer ring steel bars, the tensile inner ring steel bars and the compressive inner ring steel bars.

5. A method for calculating the bending bearing capacity of a core-filled composite pipe pile according to claim 4, characterized in that: The fitting methods include trigonometric function fitting and linear correlation fitting.

6. The method for calculating the bending bearing capacity of a core-filled composite pipe pile according to claim 4, characterized in that: Substitute the center angle coefficient into the bending moment calculation model to calculate the bending bearing capacity of the core-filled composite pipe pile, including: Substituting the center angle coefficient into the fitting results of the center angle coefficient of the inner ring concrete, the outer ring steel bar under tension, the outer ring steel bar under compression, the inner ring steel bar under tension and the inner ring steel bar under compression, the center angle coefficient of the inner ring concrete, the outer ring steel bar under tension, the outer ring steel bar under compression, the inner ring steel bar under tension and the inner ring steel bar under compression are calculated respectively; The calculated central angle coefficients of the inner ring concrete, the tensile outer ring steel bars, the compressive outer ring steel bars, the tensile inner ring steel bars and the compressive inner ring steel bars are substituted into the bending moment calculation model to calculate the bending bearing capacity of the core-filled composite pipe pile.

7. The method for calculating the bending bearing capacity of a core-filled composite pipe pile according to claim 1, characterized in that: The method further comprises: Eliminate the first model used to calculate the axial force of the inner ring concrete and the fifth model used to calculate the axial force of the inner ring steel bar in the axial force calculation model to obtain a model used to calculate the axial force of the non-core-filled composite pipe pile; Eliminate the second model for calculating the inner ring concrete bending moment and the sixth model for calculating the inner ring steel bar bending moment in the bending moment calculation model to obtain a model for calculating the non-core-filled composite pipe pile bending moment; Taking the axial force of the model used to calculate the axial force of the non-core-filled composite pipe pile as zero as the constraint condition, the central angle coefficient of the outer ring concrete in the stress area is calculated; The central angle coefficient is substituted into the model used to calculate the bending moment of non-core-filled composite pipe piles, and the bending bearing capacity of non-core-filled composite pipe piles is calculated.

8. An electronic device, characterized in that: The electronic device includes a processor, a memory, and a computer program stored in the memory and executable by the processor, wherein when the computer program is executed by the processor, the steps of a method for calculating the bending bearing capacity of a core-filled composite pipe pile as described in any one of claims 1 to 7 are implemented.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium comprises a computer program, and when the computer program is executed by one or more processors, the computer program implements a method for calculating the bending bearing capacity of a core-filled composite pipe pile according to any one of claims 1 to 7.

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