Design method of UHPC (Ultra High Performance Concrete) hollow top plate for culvert

Abstract

The invention discloses a design method of a UHPC hollow top plate for a culvert, and relates to the technical field of constructional engineering, and the method comprises the steps: obtaining the size parameters of a to-be-optimized solid UHPC top plate; dividing the solid UHPC top plate into a plurality of bending units along the transverse direction, and calculating the width and the thickness of a simplified calculation section corresponding to the bending units; establishing a total constraint equation; the size parameters of the simplified calculation section and the set material saving proportion are substituted into the total constraint equation, the initial size of the optimized hollow section and the initial size of the hollowed-out groove of the optimized hollow section are set and input into the total constraint equation for iterative solution, a parameter set of the optimized hollow section of the optimized UHPC hollow top plate is obtained, rounding is carried out, and the optimal solution is screened out. According to the design method of the UHPC hollow top plate, on the premise that the bearing capacity of the structure is guaranteed, the using amount of UHPC materials is saved, the self weight and the manufacturing cost are reduced, an optimization method with complete logic is provided, and the design method has the advantages that needed parameters are few, and calculation is simple and efficient.

Description

Technical Field

[0001] The present application relates to the field of construction engineering technology, and in particular to a design method for a UHPC hollow top plate for a culvert. Background Art

[0002] Currently, concrete slab structures are a common structural form widely used in construction engineering. Ultra-High Performance Concrete (UHPC), thanks to its excellent mechanical properties and durability, has seen widespread adoption in lightweight and prefabricated construction in recent years. Compared to conventional concrete, UHPC offers significantly higher compressive and tensile strengths. This significantly improves UHPC slab construction in thickness, weight, durability, and other aspects under the same design load. However, the price of UHPC is over eight times that of conventional C50 concrete, so economical improvements are often achieved through structural optimization and volume reduction.

[0003] In the relevant technology, the existing UHPC top plate for culverts is directly subjected to soil pressure load and vehicle load, and is a typical bending plate component. The UHPC top plate for culverts is entirely solid, and when subjected to bending moment load, the positive stress level of the concrete near the neutral axis of the plate section is low. Therefore, the volume of UHPC material can be appropriately reduced near the neutral axis of the plate section (i.e., the height centerline), and the material utilization rate can be improved by hollowing out.

[0004] However, the cross-sectional optimization of existing technologies is mostly seen in UHPC columns and UHPC-NC composite column structures, while the cross-sectional optimization of UHPC top plates for culverts has never been involved. In addition, the current optimization design lacks a logically complete calculation method and current specifications. Summary of the Invention

[0005] The present application provides a design method for UHPC hollow roof panels for culverts. Under the premise of ensuring the structural bearing capacity, a logically complete optimization method is provided to reduce the material consumption of UHPC roof panels for culverts and reduce the construction cost.

[0006] This application discloses an embodiment of a design method for a UHPC hollow roof for a culvert, comprising the following steps:

[0007] Obtaining the dimensional parameters of the solid UHPC top plate to be optimized;

[0008] The solid UHPC top slab is divided into multiple bending units along the transverse direction. Based on the dimensional parameters of the solid UHPC top slab, the longitudinal reinforcement is equivalent to concrete, and the width and thickness of the simplified calculation section corresponding to the bending unit are calculated.

[0009] Based on the simplified calculation section and the corresponding optimized hollow section with hollowed-out slots, the total constraint equation was established with the goal of optimizing the UHPC dosage, while meeting the mechanical indicators of strength and stiffness and combining the structural requirements.

[0010] The dimensional parameters of the simplified calculated section and the set material saving ratio are substituted into the total constraint equation. The initial dimensions of the optimized hollow section and its hollowed-out groove are set and input into the total constraint equation for iterative solution. The parameter set of the optimized hollow section of the optimized UHPC hollow top plate is obtained, and the optimal solution is rounded and screened.

[0011] On the basis of the above technical solution, the width and thickness of the simplified calculation section corresponding to the bending unit are calculated, including:

[0012] For solid UHPC top slabs with uniform adjacent spacing of longitudinal reinforcements, the width of the simplified calculation section is equal to the spacing between adjacent longitudinal reinforcements; for solid UHPC top slabs with non-uniform adjacent spacing of longitudinal reinforcements, the width of the simplified calculation section is equal to the average value of the adjacent spacing of all longitudinal reinforcements;

[0013] The longitudinal reinforcement is equivalent to concrete and used in the calculation of section mechanical indicators to obtain the width and thickness of the simplified calculation section corresponding to the bending unit.

[0014] On the basis of the above technical solution, the dimensional parameters of the simplified calculation section, the set width of the optimized hollow section, and the set material saving ratio are used as known quantities of the total constraint equation, and the height of the optimized hollow section and the size of the hollowed groove are used as unknown quantities of the total constraint equation; the total constraint equation includes:

[0015] Based on the stiffness index requirements, the constraint equation is established according to the principle that the moment of inertia of the bending section does not decrease;

[0016] Based on the strength index requirements, the constraint equation is established according to the principle that the strain at the lower edge of the plate does not increase under the ultimate load condition;

[0017] Based on the UHPC construction requirements, the constraint equation is established according to the principle of constant plate thickness;

[0018] A constraint equation is established based on the principle of optimal material usage of the UHPC hollow top plate; the total constraint equation consists of four constraint equations.

[0019] On the basis of the above technical solution, the constraint equation is established based on the stiffness index requirement and the principle that the moment of inertia of the bending section does not decrease, including:

[0020] Calculate the section inertia moment I of the simplified calculation section separately s , and optimize the section moment of inertia of the hollow section I k :

[0021]

[0022] Where: h sj 、h k are the plate thickness of simplified calculation section and optimized hollow section respectively; I s1 , I s2 are the equivalent concrete section inertia moments of the simplified calculation section and the optimized hollow section; I w To optimize the hollow section moment of inertia of the hollow slot; w sj To simplify the calculation of the width of the section; w k To optimize the width of the hollow section;

[0023] If the hollowed-out groove is rectangular, m and n are the length and width of the rectangular hollowing slot respectively; if the hollowing slot is circular, d is the diameter of the circular hollowed slot;

[0024] The constraint conditions are set based on the principle that the bending inertia moment of the optimized hollow section does not decrease relative to the simplified calculation section, which can be expressed as:

[0025] I s ≤I k .

[0026] On the basis of the above technical solution, the constraint equation is established based on the strength index requirements and the principle that the strain at the lower edge of the plate does not increase under the ultimate load condition, including:

[0027] Calculate the strain ε of the lower edge of the plate at the simplified calculation section s and the strain ε of the lower edge of the plate of the optimized hollow section k They are:

[0028]

[0029] Where: M is the cracking moment of the simplified calculation section, E is the Young's modulus of elasticity of the UHPC material;

[0030] According to the principle that the strain at the bottom edge of the plate does not increase under the ultimate load condition, the constraint condition is set. Under the same load, the strain at the bottom edge of the plate of the simplified calculation section is greater than or equal to the strain at the bottom edge of the plate of the optimized hollow section, which can be expressed as:

[0031] ε s ≥ε k .

[0032] On the basis of the above technical solution, the constraint equation is established based on the UHPC construction requirements and the principle of constant plate thickness, including:

[0033] The structural requirements are that the upper and lower edge wall thicknesses of the hollowed-out grooves containing steel bars should be no less than 4 cm; the structural requirements are that the horizontal spacing between two adjacent hollowed-out grooves should be no less than 5 cm; the plate thickness of the optimized hollow section should be no less than the simplified calculated section;

[0034] The constraint equation corresponding to the optimization of the hollow section with a rectangular hollow groove is:

[0035]

[0036] wk-m≥5;

[0037] The constraint equation corresponding to the circular hollowing groove optimization of the hollow section is:

[0038]

[0039] w k -d≥5;

[0040] Optimizing hollow sections with circular hollowing slots or circular hollowing slots must meet the following requirements:

[0041] h k ≥h sj .

[0042] On the basis of the above technical solution, the constraint equation is established according to the optimal principle of the amount of UHPC hollow top material, including:

[0043] Calculate the cross-sectional area S of the simplified calculation section separately s and the optimized hollow section area S k ,

[0044] S s =w sj h sj ;

[0045] S k =w k h k -S w ;

[0046] Where: S w is the area of the hollowed-out slot. If it is a rectangular hollowed-out slot, then S w =mn, if it is a circular hollow groove,

[0047] The optimal material usage is expressed as:

[0048] (1-α)S s ≥S k ;

[0049] S k ={S k,i} min ;

[0050] Where: α is the set material saving ratio, {S k,i} is the set of cross-sectional areas of multiple solutions that satisfy the constraints, and i is the number of the solution.

[0051] On the basis of the above technical solution, after the total constraint equation is determined, the set initial dimensions of the optimized hollow section and its hollowed-out groove are used as initial data, and the total constraint equation is iteratively solved to obtain a solution set of the optimized hollow section with optimal material usage, unchanged plate thickness, unchanged strain at the lower edge of the plate, and unchanged section inertia moment. The optimal solution is then rounded and screened out.

[0052] On the basis of the above technical solution, after the total constraint equation is determined, when the design target is an optimized hollow section with a rectangular hollowed slot, the design method includes the following steps:

[0053] S101: Simplify the calculation of the width w of the section sj and thickness h sj , set material saving ratio α, set width w of optimized hollow section k =w sj These four known quantities are substituted into the total constraint equation; the initial thickness h of the optimized hollow section is input into the total constraint equation k =h sj and the initial length and width m0 and n0 of the rectangular hollowing slot;

[0054] S102: Let h k =h k +1, m=m0, and n=n0;

[0055] S103: Determine whether the total constraint equation is satisfied. If so, go to S106; if not, go to S104;

[0056] S104: Determine whether n reaches the limit value h k -5, if not, set n=n+1 and return to S103; if yes, go to S105;

[0057] S105: Determine whether m reaches the limit value w k -5, if yes, return to S102; if no, set m=m+1 and n=n0, return to S102;

[0058] S106: Get h k , m and n, round up and select the optimal solution for output.

[0059] On the basis of the above technical solution, when multiple rounds of calculations are performed and no solution is found, the process returns to S101 and sets α=α-5%, and performs iterative calculations again.

[0060] The beneficial effects of the technical solutions provided in the embodiments of the present application include at least:

[0061] The design method of the UHPC hollow top plate of the present application first obtains the dimensional parameters of the solid UHPC top plate 1 to be optimized, then divides the solid UHPC top plate into multiple bending units along the transverse direction, and obtains a simplified calculation section after the bending units are equivalent. Based on the simplified calculation section, a total constraint equation is established from four aspects, namely stiffness, strength, structure and material. Then, with the set initial size of the optimized hollow section and its hollowed-out groove, the dimensional parameters of the simplified calculation section and the set material saving ratio are used as initial inputs. After iterative solution, the parameter set of the optimized hollow section of the optimized UHPC hollow top plate can be obtained, and the optimal solution is rounded and screened. The design method of the UHPC hollow top plate of the present application can effectively save the amount of UHPC materials and reduce engineering costs under the premise of ensuring the bearing capacity of the structure. Under the same bearing requirements, the weight of the UHPC hollow top plate can be significantly reduced, which improves the installation and transportation efficiency. The entire design method is logically complete and efficient.

[0062] The design method for the UHPC hollow roof in this application uses the known dimensional parameters of the simplified calculation section and the set width of the optimized hollow section as known quantities, and the height of the optimized hollow section and the size of the hollowed-out slot as unknown quantities. Constraint equations are constructed one by one from four dimensions, namely, stiffness index requirements, strength index requirements, UHPC construction requirements, and optimal material usage requirements, and a total constraint equation is formed. This lays the foundation for subsequent iterative calculations, provides clear mechanical concepts, and can achieve efficient iterative calculations.

[0063] The design method of the UHPC hollow top slab in this application simplifies the calculation of the width w of the cross section by inputting known quantities into the total constraint equation. sj and thickness h sj , input the set material saving ratio α, input the set width w of the optimized hollow section k ; Input the initial thickness h of the optimized hollow section into the total constraint equation k =h sj After determining the initial length and width m0 and n0 of the rectangular hollowing slot, iterative calculations are performed according to the set rules, which will gradually converge and obtain multiple sets of solutions. The optimal solution is rounded and screened for output, and the optimal solution for the optimized hollow section is obtained, which satisfies the requirements of optimal material usage, unchanged plate thickness, no increase in strain at the lower edge of the plate, and no decrease in the moment of inertia of the section. The design method of the UHPC hollow top slab in this application provides a fast, efficient, and logically complete optimization method while ensuring the structural bearing capacity, thereby reducing the material consumption of the UHPC hollow top slab used in culverts and lowering the construction cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1A flow chart of the design method of the UHPC hollow roof for the culvert of this application;

[0065] Figure 2 This is a schematic diagram of the assembled UHPC prefabricated culvert;

[0066] Figure 3 Schematic diagram of the cross section of the solid UHPC top plate to be optimized;

[0067] Figure 4 Schematic diagram of simplified calculation section and optimized section of solid UHPC top plate;

[0068] Figure 5 The cross-sectional diagram of the optimized UHPC square hollow top plate;

[0069] Figure 6 Schematic diagram of the cross section of the optimized UHPC hollow top plate;

[0070] Figure 7 Flow chart of iterative solution for optimization calculation of UHPC square hollow top slab;

[0071] Reference numerals:

[0072] 1. Solid UHPC roof slab; 2. Longitudinal reinforcement; 3. Stirrups; 4. UHPC square hollow roof slab; 5. Rectangular hollow channel; 6. Bending element; 7. Simplified calculation section; 8. Optimized hollow section; 9. UHPC circular hollow roof slab; 10. Circular hollow channel; 11. Culvert main structure. DETAILED DESCRIPTION

[0073] In order to enable those skilled in the art to better understand the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0074] The terms "including" and "having" and any variations thereof in the specification and claims of this application and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units that are not listed, or optionally includes other steps or units inherent to these processes, methods, products or devices. The terms "first", "second" and "third" are used to distinguish different objects, etc., and do not represent a sequence, nor do they limit the "first", "second" and "third" to different types.

[0075] In the description of the embodiments of the present application, the words "exemplary", "for example" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or device described as "exemplary", "for example" or "for example" in the embodiments of the present application is

[0076] The embodiment or design should not be interpreted as being more preferred or advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary", "for example" or "for example" is intended to present the relevant concepts in a specific way.

[0077] In the description of the embodiments of the present application, unless otherwise specified, “ / ” means or, for example, A / B can mean A or B; “and / or” in the text is merely a description of the association relationship of associated objects, indicating that three relationships may exist, for example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, in the description of the embodiments of the present application, “multiple” refers to two or more than two.

[0078] In some processes described in the embodiments of the present application, multiple operations or steps are included that appear in a specific order. However, it should be understood that these operations or steps may not be performed in the order in which they appear in the embodiments of the present application or may be performed in parallel. The sequence numbers of the operations are only used to distinguish between different operations, and the sequence numbers themselves do not represent any order of execution. In addition, these processes may include more or fewer operations, and these operations or steps may be performed in sequence or in parallel, and these operations or steps may be combined.

[0079] At present, the prefabricated UHPC prefabricated culvert has excellent structural performance. However, the large-scale promotion of prefabricated UHPC prefabricated culvert still has the following problems:

[0080] First, the price of the solid UHPC top plate 1 of the prefabricated UHPC culvert is relatively expensive;

[0081] Second, the UHPC material near the neutral axis of the solid UHPC top plate 1 (in the middle of the height direction) cannot exert its performance advantages, resulting in a large performance waste;

[0082] 3. The current codes, standards and technical specifications are still blank in the field of UHPC plate cross-section optimization, lacking reasonable guidance methods;

[0083] The design method of the UHPC hollow roof for culverts in this application addresses the first problem by effectively saving material usage and reducing application costs without affecting the bearing capacity; addresses the second problem by minimizing the material redundancy near the neutral axis (middle in the height direction) of the solid UHPC roof 1 without affecting the bearing capacity, thereby fully utilizing the performance of the UHPC material; and addresses the third problem by providing a logically complete and reasonable optimization method for optimizing the solid UHPC roof 1 to obtain a UHPC hollow roof (i.e., a UHPC square hollow roof 4 or a UHPC circular hollow roof 9).

[0084] like Figures 1 to 6 As shown, the present application discloses a design method for a UHPC hollow roof for a culvert, comprising the following steps:

[0085] S1: Obtain the dimensional parameters of the solid UHPC roof slab 1 to be optimized. Specifically, the dimensional parameters of the solid UHPC roof slab 1 include width, thickness, and spacing between adjacent longitudinal reinforcements 2. Specifically, the longitudinal reinforcements 2 within the solid UHPC roof slab 1 may be arranged at equal or unequal spacings.

[0086] S2: Divide the solid UHPC top plate 1 into multiple bending units 6 along the transverse direction. Based on the dimensional parameters of the solid UHPC top plate 1, the longitudinal reinforcement is equivalent to concrete, and the width and thickness of the simplified calculation section 7 corresponding to the bending unit 6 are calculated.

[0087] S3: Based on the simplified calculation section 7 and its corresponding optimized hollow section 8 with a hollowed-out groove, while meeting strength and stiffness mechanical indicators, and in combination with structural construction requirements, a total constraint equation is established with the goal of optimizing UHPC usage. Specifically, the total constraint equation is established based on the principles of maintaining a constant section moment of inertia (meeting stiffness requirements), maintaining constant strain at the lower edge of the plate (meeting strength requirements), maintaining constant plate thickness (meeting structural requirements), and minimizing material usage (meeting optimal material usage).

[0088] S4: Substitute the dimensional parameters of the simplified calculation section 7 and the set material saving ratio into the total constraint equation, set the initial dimensions of the optimized hollow section 8 and its hollowed groove, and input them into the total constraint equation for iterative solution to obtain the parameter set of the optimized hollow section 8 of the optimized UHPC hollow top plate, round up and screen out the optimal solution.

[0089] Specifically, in step S1, the solid UHPC top plate 1 to be optimized is a normal load-bearing load-bearing component, and is regarded as a one-way bending plate in terms of load-bearing form. The load acts on the top surface of the solid UHPC top plate 1, and there is no load on the bottom surface of the solid UHPC top plate 1; the boundary condition of the solid UHPC top plate 1 is simply supported. In the plate thickness direction of the solid UHPC top plate 1, it contains at least two layers of steel mesh, and the three dimensional data of the plate width, plate thickness, and the spacing between adjacent longitudinal bars 2 are known. The overall plate width of the solid UHPC top plate 1 is obtained as w s , plate thickness is h s .

[0090] The design method of the UHPC hollow top plate of the present application first obtains the dimensional parameters of the solid UHPC top plate 1 to be optimized, then divides the solid UHPC top plate 1 into multiple bending units 6 along the horizontal direction, and obtains a simplified calculation section 7 after equivalent bending units 6. Based on the simplified calculation section 7, a total constraint equation is established from four aspects, namely stiffness, strength, structure and material. Then, with the set initial size of the optimized hollow section 8 and its hollowed groove, the dimensional parameters of the simplified calculation section 7 and the set material saving ratio are used as initial inputs. After iterative solution, the parameter set of the optimized hollow section 8 of the optimized UHPC hollow top plate can be obtained, and the optimal solution is rounded and screened. The design method of the UHPC hollow top plate of the present application can effectively save UHPC material consumption and reduce engineering costs under the premise of ensuring the structural bearing capacity. Under the same bearing requirements, the weight of the UHPC hollow top plate can be significantly reduced, which improves the installation and transportation efficiency. The entire design method is logically complete and efficient.

[0091] Furthermore, in one embodiment, in step S2, the solid UHPC top plate 1 is divided into a plurality of bending units 6 along the transverse direction. Based on the dimensional parameters of the solid UHPC top plate 1, the longitudinal reinforcement is equivalent to concrete, and the width and thickness of the simplified calculation section 7 corresponding to the bending unit 6 are calculated, which includes:

[0092] For a solid UHPC top slab 1 in which adjacent spacings of several longitudinal reinforcements 2 are uniform, the width of the simplified calculation section 7 is equal to the spacing between adjacent longitudinal reinforcements 2; for a solid UHPC top slab 1 in which adjacent spacings of several longitudinal reinforcements 2 are non-uniform, the width of the simplified calculation section 7 is equal to the average value of the adjacent spacings of all longitudinal reinforcements 2.

[0093] The longitudinal reinforcement is equivalent to concrete and used in the calculation of section mechanical indexes to obtain the width w of the simplified calculation section 7 corresponding to the bending unit 6. sj and thickness h sj .

[0094] Specifically, the dimensional parameters of the solid UHPC top plate 1 include the plate width w s , plate thickness is h s .

[0095] Specifically, the solid UHPC top plate 1 can be equally divided in this way because the earth pressure load on the top of the culvert and the vehicle load can be regarded as uniformly distributed loads after being distributed by the soil. The stress condition of the top plate can be regarded as uniform stress, so the top plate can be regarded as a combination of multiple bending units in the transverse direction.

[0096] The design method of the UHPC hollow top slab in this application divides the solid UHPC top slab 1 into equal parts, then equates the longitudinal reinforcement to concrete, participates in the calculation of cross-sectional mechanical indicators, and obtains the dimensional parameters of the simplified calculation section 7 corresponding to the bending unit 6, laying the foundation for subsequent calculations.

[0097] Furthermore, in one embodiment, in step S3, based on the simplified calculation section 7 and the corresponding optimized hollow section 8 with a hollowed-out slot, a total constraint equation is established with the goal of optimizing the UHPC usage, while satisfying strength and stiffness mechanical indicators and in combination with structural construction requirements. The dimensional parameters of the simplified calculation section 7, the set width of the optimized hollow section 8, and the set material savings ratio are used as known quantities in the total constraint equation, while the height of the optimized hollow section 8 and the dimensions of the hollowed-out slot (the length and width of a rectangular hollowed-out slot or the diameter of a circular hollowed-out slot) are used as unknown quantities in the total constraint equation.

[0098] The total constraint equation contains:

[0099] Step S31: Based on the stiffness index requirement, a constraint equation is established according to the principle that the moment of inertia of the bending section does not decrease;

[0100] Step S32: Based on the strength index requirements, a constraint equation is established according to the principle that the strain at the lower edge of the plate does not increase under the ultimate load condition;

[0101] Step S33: Based on the UHPC construction requirements, a constraint equation is established according to the principle that the plate thickness does not decrease;

[0102] Step S34: Establish a constraint equation based on the optimal principle of the amount of UHPC hollow top material. The total constraint equation consists of four constraint equations.

[0103] The design method for the UHPC hollow roof of the present application uses the known dimensional parameters of the simplified calculation section 7 and the set width of the optimized hollow section 8 as known quantities, and the height of the optimized hollow section 8 and the size of the hollowed-out slot as unknown quantities. Constraint equations are constructed one by one from four dimensions, namely, stiffness index requirements, strength index requirements, UHPC construction requirements, and optimal material usage requirements. This lays the foundation for subsequent iterative calculations, provides clear mechanical concepts, and enables efficient iterative calculations.

[0104] Furthermore, in one embodiment, in step S31, based on the stiffness index requirement, a constraint equation is established according to the principle that the moment of inertia of the section against bending does not decrease, including:

[0105] According to the size of the simplified calculation section 7 and the size of the optimized hollow section 8, the section inertia moment I of the simplified calculation section 7 is calculated respectively. s , and optimize the section moment of inertia I of the hollow section 8 k :

[0106]

[0107] Where: h sj 、h k are the plate thicknesses of the simplified calculated section 7 and the optimized hollow section 8; s1 , I s2 I are the equivalent concrete section moments of inertia of the simplified calculated section 7 and the optimized hollow section 8; w To optimize the moment of inertia of the hollow section 8; w sj To simplify the calculation of the width of section 7; w k To optimize the width of the hollow section 8;

[0108] If the hollowed-out groove is rectangular, m, n are the length and width of the rectangular hollowed-out groove 5 respectively; if the hollowed-out groove is circular, d is the diameter of the circular hollowed-out groove 5;

[0109] The constraint conditions are set based on the principle that the bending inertia moment of the optimized hollow section 8 does not decrease relative to the simplified calculation section 7, which can be expressed as:

[0110] I s ≤I k .

[0111] The design method of the UHPC hollow top plate of this application first calculates the cross-sectional inertia moment I of the solid UHPC top plate 1 s and the section inertia moment I of the UHPC hollow top plate k , then through I s ≤I k , a constraint equation is established that complies with the principle that the moment of inertia of the bending section does not decrease, which can ensure the stiffness index requirements from the simplified calculation section 7 to the optimized hollow section 8 and provide a basis for iterative calculation.

[0112] Furthermore, in one embodiment, in step S32, based on the strength index requirement, a constraint equation is established according to the principle that the strain at the lower edge of the plate does not increase under the ultimate load condition, including:

[0113] Calculate the strain ε of the lower edge of the plate at the simplified calculation section 7 s The strain ε of the lower edge of the plate of the optimized hollow section 8 k They are:

[0114]

[0115] Where: M is the cracking moment of the simplified calculation section 7, E is the Young's modulus of elasticity of the UHPC material;

[0116] According to the principle that the strain at the lower edge of the plate does not increase under the ultimate load condition, the constraint condition is set. That is, under the same load, the strain at the lower edge of the plate of the simplified calculation section 7 is greater than or equal to the strain at the lower edge of the plate of the optimized hollow section 8, which can be expressed as:

[0117] ε s ≥ε k .

[0118] The design method of the UHPC hollow top plate in this application first calculates the strain ε of the lower edge of the simplified calculation section 7. s The strain ε of the lower edge of the plate of the optimized hollow section 8 k , then through ε s ≥ε k Establishing a constraint equation that complies with the principle that the strain at the lower edge of the plate does not increase under the ultimate load condition can ensure the strength index requirements from the simplified calculation section 7 to the optimized hollow section 8, providing a basis for iterative calculation; ε s ≥ε k Combined I s ≤I k It can ensure that the structural bearing capacity does not decrease during the optimization process from the simplified calculation section 7 to the optimized hollow section 8, and fully guarantee the mechanical properties of the UHPC hollow top plate.

[0119] Furthermore, in one embodiment, in step S33, based on the UHPC construction requirements and in accordance with the principle of constant plate thickness, a constraint equation is established to control indicators such as the protective layer thickness, the wall thickness, and the plate thickness, specifically including:

[0120] The thickness of the protective layer on the surface of the steel bars in the optimized hollow section (8) is not less than 1.5 cm. The diameter of the steel bars on both sides is added to the diameter of the steel bars themselves (generally 1 cm steel bars are used). The resulting wall thickness of the hollowed-out part is not less than 1.5 + 1.5 + 1 = 4 cm. The structural requirement is that the upper and lower edge wall thickness of the hollowed-out groove containing the steel bars is not less than 4 cm. Considering the casting quality and structural requirements, the horizontal spacing between two adjacent hollowed-out grooves is not less than 5 cm. At the same time, the plate thickness of the optimized hollow section 8 is not less than that of the simplified calculation section 7.

[0121] The constraint equation corresponding to the optimization of the hollow section 8 with the rectangular hollowing groove 5 is:

[0122]

[0123] wk-m≥5;

[0124] The corresponding constraint equation when optimizing the hollow section 8 with a circular hollowing groove 10 is:

[0125]

[0126] w k -d≥5;

[0127] The optimized hollow section 8 with a circular hollow groove 10 or the circular hollow groove 10 must meet the following requirements:

[0128] h k ≥h sj .

[0129] The design method for the UHPC hollow roof slab of this application is based on structural requirements to ensure the strength of the concrete around the embedded steel bars, the strength between adjacent hollowed-out slots, and the overall strength. Three structural requirements are set: the structural requirement that the upper and lower edge wall thicknesses of the hollowed-out slots containing steel bars be no less than 4 cm, the structural requirement that the lateral spacing between two adjacent hollowed-out slots be no less than 5 cm; the structural requirement that the plate thickness of the optimized hollow section 8 be no less than the simplified calculated section 7, further ensuring the mechanical properties during the optimization process from the simplified calculated section 7 to the optimized hollow section 8. In one embodiment, in step S34, a constraint equation is established based on the principle of optimal material usage for the UHPC hollow roof slab, including:

[0130] Based on the principle of optimal material usage of the plate, the cross-sectional area of the hollow section 8 is controlled and optimized; the cross-sectional area S of the simplified calculation section 7 is calculated respectively. s And optimize the cross-sectional area S of the hollow section 8 k .

[0131] S s =w sj h sj ;

[0132] S k =w k h k -S w ;

[0133] Where: S w is the area of the hollowed-out groove. If it is a rectangular hollowed-out groove (5), then S w =mn, if it is a circular hollow groove,

[0134] The material consumption of the panel is the volume requirement. Under the condition that the panel span remains unchanged, the volume ratio of the solid UHPC top panel and the UHPC hollow top panel is consistent with the area ratio.

[0135] The optimal material usage is expressed as:

[0136] (1-α)S s ≥S k ;

[0137] Where: α is the set material saving ratio, which serves as an additional constraint to further control the material usage.

[0138] Finally, the constraints for optimal material usage are established:

[0139] S k ={S k,i} min ;

[0140] Where: {S k,i} is the set of cross-sectional areas of multiple solutions that satisfy the constraints, and i is the number of the solution. k,i} min It means to select the optimal solution with the least material consumption from multiple solutions.

[0141] The design method of the UHPC hollow top plate in this application uses (1-α)S s ≥S k As an additional constraint to further control the material usage, and use S k ={S k,i} min By screening out the optimal solution with the least material usage from multiple solutions, we can obtain the optimal solution that meets the strength requirements, stiffness requirements, and structural requirements, and uses the least material, thus saving UHPC materials and reducing construction costs.

[0142] Furthermore, in step S4, the plate thickness, plate width, and set material saving ratio of the simplified calculation section are used as known quantities, and the set initial size of the optimized hollow section 8 and its hollowed groove are used as initial data to start iterative calculation, and the total constraint equation related to the four dimensions is iterated and solved iteratively to obtain a hollow top plate with optimal material usage, no reduction in structural bearing capacity, and meeting the construction and construction requirements.

[0143] Specifically, all calculations in this application are performed in the controller.

[0144] Furthermore, in one embodiment, after the total constraint equation is determined, the set initial dimensions of the optimized hollow section 8 and its hollowed-out groove are used as initial data, and the total constraint equation is iteratively solved to obtain a solution set of the optimized hollow section 8 with optimal material usage, unchanged plate thickness, unchanged strain at the lower edge of the plate, and unchanged section inertia moment, and the optimal solution is rounded and screened out.

[0145] like Figure 7 As shown, further, in one embodiment, in step S4, the width and thickness of the simplified calculated cross section 7 and the width of the set optimized hollow cross section 8 are used as known quantities, and the height of the optimized hollow cross section 8 and the size of the hollowed groove are used as unknown quantities;

[0146] After the total constraint equation is determined, when the design target is an optimized hollow section 8 with a rectangular hollowed-out groove 5, the design method includes the following steps:

[0147] S101: Simplify the calculation of the width w of section (7) sj and thickness h sj , the set material saving ratio α, the set width w of the optimized hollow section (8) k =w sj These four known quantities are substituted into the total constraint equation; the initial thickness h of the optimized hollow section 8 is input into the total constraint equation. k =h sj and the initial length and width m0 and n0 of the rectangular hollowed-out groove 5;

[0148] S102: Let h k =h k +1, m=m0, n=n0;

[0149] S103: Determine whether the total constraint equation is satisfied. If so, go to S106; if not, go to S104;

[0150] S104: Determine whether n reaches the limit value h k -5, if not, set n=n+1 and return to S103; if yes, go to S105;

[0151] S105: Determine whether m reaches the limit value w k -5, if yes, return to S102; if no, set m=m+1 and n=n0, return to S102;

[0152] S106: Get h k , m and n, round up and select the optimal solution for output.

[0153] The design method of the UHPC hollow top plate in this application simplifies the calculation of the width w of section 7 by inputting known quantities into the total constraint equation. sj and thickness h sj , input the set material saving ratio α, input the set width w of the optimized hollow section 8 k ; Input the initial thickness h of the optimized hollow section 8 into the total constraint equation k =h sjAfter determining the initial length and width m0 and n0 of the rectangular hollowed-out groove 5, iterative calculations are performed according to the set rules, which will gradually converge and obtain multiple sets of solutions. The optimal solution is rounded and screened for output, and the optimal solution of the optimized hollow section 8 is obtained, which satisfies the requirements of optimal material usage, unchanged plate thickness, no increase in strain at the lower edge of the plate, and no decrease in the moment of inertia of the section. The design method of the UHPC hollow top slab of the present application provides a fast, efficient, and logically complete optimization method while ensuring the structural bearing capacity, thereby reducing the material usage of the UHPC hollow top slab used in the culvert and lowering the construction cost.

[0154] After the total constraint equation is determined, when the design goal is to optimize the design steps of the hollow section 8 with the circular hollow groove 10, this application will not repeat them.

[0155] Furthermore, in one embodiment, when multiple rounds of calculations are performed, no solution is found, indicating that the iteration has not converged, indicating that the material saving ratio is set too large, and the process returns to S101 and sets α=α-5%, while keeping all other parameters unchanged, and iterates again until the material saving ratio is obtained.

[0156] The design method of the UHPC hollow top plate of the present application further iterates the material saving ratio α, which can ensure that the iterative calculation will gradually converge and obtain multiple sets of solutions that meet the total constraint equations, thereby obtaining the target design parameters for optimizing the hollow section 8.

[0157] In one example, the design method of the UHPC hollow roof of the present application aims to design a UHPC hollow roof 9 with an optimized hollow section 8 and a rectangular hollow slot 5 .

[0158] In step S1, the cross-sectional width w of the solid top plate is determined s =180cm, plate thickness h s =15cm, horizontal spacing of longitudinal reinforcement is 20cm.

[0159] In step S2, the solid UHPC top plate 1 to be optimized is regarded as a combination of multiple bending units 6, and the width w of the simplified calculation section 7 is determined based on the transverse spacing of the longitudinal reinforcement. sj =20cm, calculate the section thickness h sj =15cm.

[0160] In step S3, a total constraint equation is established for optimizing the solid UHPC top plate 1 toward the optimized hollow section 8 based on the simplified calculated section 7. The constraint equation is set based on the principle that the strain at the lower edge of the plate does not increase under ultimate load conditions; the constraint equation is set based on the principle that the section moment of inertia of the bending plate does not decrease; based on the UHPC construction requirements, the constraint equation is established based on the principle that the plate thickness does not decrease; the constraint equation is set based on the principle of optimizing the plate material usage, here setting the UHPC material saving ratio α to 0.25; and the constraint equation is set based on the construction requirements of the UHPC specification. These four constraint equations constitute the total constraint equation.

[0161] In step S4, the solid UHPC top plate 1 is optimized based on the total constraint equation. The width w of the cross section 7 is simplified by inputting the known quantity into the total constraint equation. sj =20cm and thickness h sj =15cm, input the set material saving ratio α=0.25, input the set width w of the optimized hollow section 8 k =

[0162] w sj = 20cm; input the initial thickness h of the optimized hollow section 8 into the total constraint equation k =h sj =15cm and the initial length and width of the rectangular hollowed-out groove (5) are m0=0, n0=0.

[0163] Iterative solution is performed based on the total constraint equation, and the results are rounded and output considering engineering practicality to obtain several available solutions. After multiple iterations, solution 1 is obtained: h k =18cm, m=14cm, n=10cm; Solution 2: h k =19cm, m=14cm, n=11cm; Solution 3: h k =20cm, m=15cm, n=12cm.

[0164] Among them, the moment of inertia of solution 1 increased by about 52%, the strain at the lower edge of the plate decreased by about 21%, and the amount of UHPC was saved by about 27%; the moment of inertia of solution 2 increased by about 75%, the strain at the lower edge of the plate decreased by about 28%, and the amount of UHPC was saved by about 25%; the moment of inertia of solution 3 increased by about 100%, the strain at the lower edge of the plate decreased by about 33%, and the amount of UHPC was saved by about 27%. After comprehensive comparison, solution 3 with the best calculation result was selected as the optimized result, and the optimized section thickness h was obtained. k = 20 cm, hollow width m = 15 cm, hollow height n = 12 cm. The optimized hollow section 8 and the UHPC hollow top 4 for the culvert are obtained.

[0165] It should be noted that the serial numbers of the above-mentioned embodiments of the present application are for description only and do not represent the advantages or disadvantages of the embodiments.

[0166] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus the necessary general hardware platform, of course, it can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes a number of instructions for enabling a terminal device to execute the methods described in each embodiment of the present application.

[0167] The above are only preferred embodiments of the present application and do not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A design method for UHPC hollow roof for culvert, characterized by: The following steps are involved: Obtaining dimensional parameters of a solid UHPC top plate (1) to be optimized; The solid UHPC top plate (1) is divided into a plurality of bending units (6) along the transverse direction. Based on the size parameters of the solid UHPC top plate (1), the longitudinal reinforcement is equivalent to concrete, and the width and thickness of the simplified calculation section (7) corresponding to the bending unit (6) are calculated; Based on the simplified calculation section (7) and the corresponding optimized hollow section with hollowed-out groove (8), the total constraint equation is established with the goal of optimizing the amount of UHPC, while meeting the mechanical indicators of strength and stiffness and combining the structural requirements. The size parameters of the simplified calculation section (7) and the set material saving ratio are substituted into the total constraint equation, the initial size of the optimized hollow section (8) and its hollowed groove is set, and input into the total constraint equation for iterative solution, and the parameter set of the optimized hollow section (8) of the optimized UHPC hollow top plate is obtained, and the optimal solution is rounded and screened.

2. The design method of UHPC hollow roof for culvert according to claim 1, characterized in that: The width and thickness of the simplified calculation section (7) corresponding to the bending unit (6) are calculated, including: For a solid UHPC top slab (1) with uniform adjacent spacing of a plurality of longitudinal reinforcements (2), the width of the simplified calculation section (7) is equal to the spacing between adjacent longitudinal reinforcements (2); for a solid UHPC top slab (1) with non-uniform adjacent spacing of a plurality of longitudinal reinforcements (2), the width of the simplified calculation section (7) is equal to the average value of the adjacent spacing of all longitudinal reinforcements (2); The longitudinal reinforcement is equivalent to concrete and used in the calculation of section mechanical indexes to obtain the width and thickness of the simplified calculation section (7) corresponding to the bending unit (6).

3. The design method of UHPC hollow roof for culvert according to claim 1, characterized in that: The size parameters of the simplified calculation section (7), the width of the set optimized hollow section (8) and the set material saving ratio are used as known quantities of the total constraint equation, and the height of the optimized hollow section (8) and the size of the hollowed groove are used as unknown quantities of the total constraint equation; the total constraint equation includes: Based on the stiffness index requirements, the constraint equation is established according to the principle that the moment of inertia of the bending section does not decrease; Based on the strength index requirements, the constraint equation is established according to the principle that the strain at the lower edge of the plate does not increase under the ultimate load condition; Based on the UHPC construction requirements, the constraint equation is established according to the principle of constant plate thickness; Establish constraint equations based on the optimal material usage principle for UHPC hollow roof; The total constraint equation consists of four constraint equations.

4. The design method of UHPC hollow roof for culvert according to claim 3, characterized in that: Based on the stiffness index requirements, the constraint equation is established according to the principle that the moment of inertia of the bending section does not decrease, including: Calculate the section inertia I of the simplified calculation section (7) separately s , and the optimized section moment of inertia I of the hollow section (8) k : Where: h sj 、h k are the plate thicknesses of the simplified calculated section (7) and the optimized hollow section (8); I s1 , I s2 are the equivalent concrete section moments of inertia of the simplified calculation section (7) and the optimized hollow section (8); I w To optimize the hollow section (8) of the hollow slot section moment of inertia; w sj To simplify the calculation of the width of section (7); w k To optimize the width of the hollow section (8); If the hollowed-out groove is rectangular, m and n are the length and width of the rectangular hollowed-out groove (5) respectively; if the hollowed-out groove is circular, then d is the diameter of the circular hollowed-out groove (5); The constraint condition is set according to the principle that the bending moment of inertia of the optimized hollow section (8) does not decrease relative to the simplified calculation section (7), which is expressed as: I s ≤I k 。 5. The design method of UHPC hollow roof for culvert according to claim 4, characterized in that: Based on the strength index requirements, the constraint equation is established according to the principle that the strain at the lower edge of the plate does not increase under the ultimate load condition, including: Calculate the lower edge strain ε of the simplified calculation section (7) separately s and the lower edge strain ε of the optimized hollow section (8) k They are: Where: M is the cracking moment of the simplified calculation section (7), E is the Young's modulus of elasticity of the UHPC material; According to the principle that the strain at the bottom edge of the plate does not increase under the ultimate load condition, the constraint condition is set. Under the same load, the strain at the bottom edge of the plate of the simplified calculation section (7) is greater than or equal to the strain at the bottom edge of the plate of the optimized hollow section (8), which can be expressed as: e s ≥e k 。 6. The design method of UHPC hollow roof for culvert according to claim 4, characterized in that: Based on the UHPC construction requirements, the constraint equation is established according to the principle of constant plate thickness, including: The structural requirement is that the wall thickness of the upper and lower edges of the hollowed-out groove containing steel bars should be no less than 4 cm; the structural requirement is that the horizontal spacing between two adjacent hollowed-out grooves should be no less than 5 cm; the plate thickness of the optimized hollow section (8) should be no less than that of the simplified calculated section (7); The corresponding constraint equation when optimizing the hollow section (8) with a rectangular hollowing groove (5) is: wk-m≥5; The corresponding constraint equation when optimizing the hollow section (8) with a circular hollowing groove (10) is: In k -d≥5; The optimized hollow section (8) with a circular hollowed-out groove (10) or the circular hollowed-out groove (10) must satisfy the following conditions: h k ≥h sj 。 7. The design method of UHPC hollow roof for culvert according to claim 4, characterized in that: The constraint equation is established based on the optimal principle of the amount of UHPC hollow top material, including: Calculate the cross-sectional area S of the simplified calculation section (7) respectively s and the optimized hollow section area S k , S s =w sj h sj ; S k =w k h k -S w ; Where: S w is the area of the hollowed-out groove. If it is a rectangular hollowed-out groove (5), then S w =mn, if it is a circular hollow groove, The optimal material usage is expressed as: (1-a)S s ≥S k ; S k ={S k,i } min ; Where: α is the set material saving ratio, {S k,i } is the set of cross-sectional areas of multiple solutions that satisfy the constraints, and i is the number of the solution.

8. The design method of UHPC hollow roof for culvert according to claim 4, characterized in that: After the total constraint equation is determined, the set optimized hollow section (8) and the initial size of the hollowed groove thereof are used as initial data, and the total constraint equation is iteratively solved to obtain a solution set of the optimized hollow section (8) with the optimal material usage, unchanged plate thickness, unchanged plate lower edge strain, and unchanged section inertia moment. The optimal solution is rounded and screened out.

9. The design method of UHPC hollow roof for culvert according to claim 8, characterized in that: After the total constraint equation is determined, when the design target is an optimized hollow section (8) with a rectangular hollowed-out groove (5), the design method includes the following steps: S101: Simplify the calculation of the width w of section (7) sj and thickness h sj , the set material saving ratio α, the set width w of the optimized hollow section (8) k =w sj These four known quantities are substituted into the total constraint equation; the initial thickness h of the optimized hollow section (8) is input into the total constraint equation k =h sj and the initial length and width m0 and n0 of the rectangular hollowed-out groove (5); S102: Let h k =h k +1, m=m0, and n=n0; S103: Determine whether the total constraint equation is satisfied. If so, go to S106; if not, go to S104; S104: Determine whether n reaches the limit value h k -5, if not, set n=n+1 and return to S103; if yes, go to S105; S105: Determine whether m reaches the limit value w k -5, if yes, return to S102; if no, set m=m+1 and n=n0, return to S102; S106: Get h k , m and n, round up and select the optimal solution for output.

10. The design method of a UHPC hollow roof for a culvert according to claim 9, characterized in that: When multiple rounds of calculations are performed and no solution is found, the process returns to S101 and sets α=α-5%, and performs iterative calculations again.

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