Box arch bearing capacity simplified calculation method and system considering UHPC reinforcing layer, storage medium and computer equipment

Abstract

The invention discloses a box arch bearing capacity simplified calculation method and system considering a UHPC reinforcing layer, a storage medium and computer equipment, and the calculation method comprises the following steps: S1, reinforcing an original concrete box arch by adopting UHPC, regarding the UHPC reinforcing layer and the original concrete box arch as a unified section, and calculating the equivalent strength grade C of section concrete; s2, moving longitudinal bars in the UHPC layer and longitudinal bars of an original structure to the position of a resultant force point, merging and calculating the areas of the longitudinal bars in the two layers, and calculating the equivalent areas of the newly-added longitudinal bars on the side with smaller tension or compression and the side with larger compression of the UHPC reinforcing layer; and S3, calculating the bearing capacity value of the box arch reinforced by the UHPC according to an existing box arch bearing capacity formula. The invention further provides a system, a storage medium and computer equipment capable of realizing the calculation method. After the simplified method provided by the invention is adopted, the bearing capacity of the reinforced box arch can be checked by using the existing software for calculating the bearing capacity of the arch bridge without additionally programming, so that the calculation time is greatly shortened.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge engineering reinforcement, in particular to a simplified calculation method, system, storage medium and computer device for the bearing capacity of a box arch considering a UHPC reinforcement layer. Background Technique

[0002] Reinforced concrete box arch bridges have the advantages of large torsional stiffness and good overall performance, and were widely used in the western regions of China in the 1980s. Prefabricated box arches generally have a high hollow ratio and thin top and bottom plates. In recent years, with the increasing traffic flow and the rapid increase in heavy vehicles in China, most box arch bridges are prone to problems such as insufficient bearing capacity and rapid development of diseases.

[0003] The conventional reinforcement methods for box arch bridges are generally to increase the cross-section or paste steel plates at the bottom surface of the arch rib. The method of increasing the cross-section at the bottom surface of the arch rib has a simple process and strong adaptability. However, for large-span box arches with a high hollow ratio and large span of the arch rib cross-section, the self-weight of the self-compacting concrete reinforcement layer is large, and the wet weight of the concrete during construction is directly borne by the original arch rib, resulting in a large construction risk. The method of pasting steel plates has a simple construction and less wet work, but the steel plates need to be anti-corrosive, and it is not easy to bond on the arc surface of the arch rib. The compatibility between the steel plate and the matrix is poor, and it is easy to be delaminated. When the applicant was engaged in bridge inspection and reinforcement work, it was found that after 5 years of pasting steel plates for reinforcement of a box arch bridge, the delamination rate of the steel plates reached 32% of the total number of samples, and 10 of the steel plates were completely delaminated; in addition, after 10 years of operation of another bridge, the bonding glue of the steel plates aged seriously, the delamination rate exceeded 50%, and the steel plates were severely corroded. The above two bridge reinforcement cases are individual cases but also reflect common problems. In addition, due to the high hollow ratio of the box cross-section and the small cross-section of the arch rib, even after pasting steel plates on the bottom surface of the arch rib of the box arch bridge, its bearing capacity may still not meet the requirements. Therefore, it is of great value to explore a reinforcement scheme suitable for large-span box arch bridges.

[0004] Ultra-high performance concrete (UHPC) has the advantages of high strength, high toughness, high durability, etc., and is very suitable for the reinforcement of long-span arch bridges. However, it has inherent defects such as high price and the need for steam curing in the strength formation process, which limits the wide application of UHPC. In recent years, with the emergence of UHPC steam-curing-free technology, the construction complexity of UHPC has been greatly reduced, and UHPC is expected to be widely used in the field of arch bridge reinforcement. At present, there are no engineering examples of using UHPC to reinforce long-span reinforced concrete arch bridges, and the technology is not yet mature. Therefore, whether the box arch design with UHPC can meet the load-bearing capacity requirements of the arch bridge remains to be further studied. During the research process, due to the high strength of UHPC and many reinforcement parameters, the calculation of the load-bearing capacity of the reinforced box arch is very complex, and each parameter is very easy to be confused, resulting in calculation errors. In addition, the accurate calculation formula needs to be calculated by compiling a program and cannot be directly calculated by existing software, which takes a long time. How to quickly calculate the load-bearing capacity of the box arch after UHPC reinforcement is also an important part of exploring the optimal reinforcement plan for box arch bridges. Summary of the Invention

[0005] The present invention provides a simplified calculation method, system, storage medium and computer device for the load-bearing capacity of a box arch considering the UHPC reinforcement layer, which can quickly calculate the load-bearing capacity of the reinforced box arch bridge and provide an important reference for exploring the optimal reinforcement plan for box arch bridges.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] A simplified calculation method for the load-bearing capacity of a box arch considering the UHPC reinforcement layer includes the following steps:

[0008] S1. The original concrete arch rib is reinforced with UHPC, and the UHPC reinforcement layer and the original concrete arch rib are regarded as a unified section. The calculation method of the equivalent strength grade C of the concrete of this section is:

[0009] C = [C p ×A p + 0.5C u ×A u / (A p + A u ) (1)

[0010] In the formula: C p , C u are the strength grade values of the original structure concrete and UHPC respectively, and A p , A u are the cross-sectional areas of the original structure and the UHPC cross-section respectively;

[0011] S2. Move the longitudinal reinforcement in the UHPC layer and the original structural longitudinal reinforcement to the position of the resultant force point, combine the areas of the two layers of longitudinal reinforcement, take the strength of the new longitudinal reinforcement as the strength of the old longitudinal reinforcement, and adjust the cross-sectional area of ​​the new longitudinal reinforcement accordingly:

[0012]

[0013] f sd 、f' sd are the design values ​​of tensile and compressive strength of the original box arch reinforcement, f sdu 、f' sdu are the design values ​​of tensile and compressive strength of new longitudinal reinforcement in UHPC reinforcement layer, A su , A' su The longitudinal reinforcement area is added to the UHPC reinforcement layer on the side with smaller tension or compression and the side with larger compression. sue , A' sue The equivalent area of ​​the longitudinal reinforcement added to the UHPC reinforcement layer on the side with smaller tension or compression and the side with larger compression;

[0014] S3. Use formulas (3) and (4) to calculate the bearing capacity values ​​Mn1uz and Mn2uz:

[0015] γ0N du ≤f cdz [bx+(b' f -b)h' fz ]+f s ' d A' z -σ sz A z =Mn1uz (3)

[0016]

[0017] Where: N du is the axial force of the box arch after reinforcement, γ0 is the structural importance factor, which is 1.1 for the bridge; b is the sum of the thickness of the box arch slats; f cdz is the design value of compressive strength corresponding to the equivalent concrete strength C; x is the height of the compression zone, which can be used to calculate N du The distance between the action point and the target point can also be calculated by combining equation (3) and equation (4); b f , b' f h is the flange width of the side with smaller tension or compression and the side with larger compression respectively; u is the thickness of the UHPC layer on the side with smaller tension or compression, h' u is the thickness of the UHPC layer on the side with greater pressure, h fz 、h' fz are the thickness of the flange plate on the side with smaller tension or compression and the side with larger compression after reinforcement, respectively. fz =h f +hu , h’ fz = h’ f + h’ u , that is, the flange height of the unified cross-section is the sum of the thicknesses of the UHPC reinforcement layer and the original concrete flange; f sd , f’ sd are the design values of the tensile and compressive strengths of the steel bars respectively, and the design values of the tensile and compressive strengths of the old longitudinal bars are uniformly taken; A s , A’ s are the areas of the longitudinal bars in the original box arch on the smaller tension or compression side and the larger compression side respectively; A z , A’ z are the equivalent areas of the longitudinal bars on the smaller tension or compression side and the larger compression side of the unified cross-section respectively, Az = As + Asue, A’z = A’s + A’sue; a z , a’ z are the distances from the resultant force points of the longitudinal bars on the smaller tension or compression side and the larger compression side after reinforcement to the near side of the cross-section respectively, and are obtained from Equations (5) and (6); h is the total height of the cross-section before reinforcement, h z is the total height of the cross-section after reinforcement, h z = h + h u + h’ u , h z0 = h z - a z , h’ z0 = h z - a’ z ;

[0018] a z = [A s × (a s + h u ) + A sue × a su / A z (5)

[0019] a' z = [A s ' × (a' s + h' u ) + A s ' ue × a' su / A z ' (6)

[0020] In the formula: a s , a’ s are the distances from the resultant force points of the longitudinal bars on the smaller tension or compression side and the larger compression side of the original box arch before reinforcement to the near side of the cross-section respectively; a su , a’ suThey are the distances from the resultant force points of the newly added longitudinal bars in the UHPC on the smaller tension or compression side and the larger compression side after strengthening to the near side of the section, respectively.

[0021] σ sz It is the equivalent stress after combining the original longitudinal bars and the newly added longitudinal bars on the smaller tension or compression side of the unified section, obtained from Equation (7). σ sz It should be within the range of the design value of the steel bar strength. For the steel bar stress value calculated by Equation (7), when it exceeds the design value, it needs to be further taken as the design value:

[0022]

[0023] In the formula: ε cu It is the ultimate strain corresponding to the equivalent concrete type obtained from Equation (1). The ratio of the height of the rectangular stress diagram to the actual compression zone height β = 0.8; E s It is the elastic modulus of the steel bar;

[0024] e u It is the distance from the action point of the axial force after strengthening to the resultant force point of the longitudinal bars on the smaller tension or compression side of the unified section; obtained from Equation (8):

[0025] e u = η u e 0u + h z / 2 - a z (8)

[0026] In the formula: η u It is the eccentricity amplification factor of the axial force of the eccentric compression member after strengthening, obtained from Equation (9); the eccentricity of the axial force to the centroid axis of the section after strengthening e 0u = M du / N du ,M du It is the bending moment value of the box arch after strengthening;

[0027]

[0028] The calculated length l0 of the member = 0.36 times the length of the arch rib; ζ 1u It is the influence coefficient of the load eccentricity ratio on the section curvature after strengthening, obtained from Equation (10); ζ 2u It is the influence coefficient of the slenderness ratio of the member after strengthening on the section curvature, obtained from Equation (11):

[0029]

[0030] The present invention further provides an arch rib bearing capacity calculation system considering the UHPC strengthening layer. The system applies the simplified calculation method for the box arch bearing capacity considering the UHPC strengthening layer described above.

[0031] The present invention further provides a storage medium storing a computer program, which, when executed by a processor, can implement the above-mentioned simplified calculation method for the load-bearing capacity of a box arch considering the UHPC strengthening layer.

[0032] A computer device includes a memory and a processor, the processor is coupled to the memory, reads and executes instructions in the memory to implement the above-mentioned simplified calculation method for the load-bearing capacity of a box arch considering the UHPC strengthening layer.

[0033] The above-mentioned simplified calculation method for the load-bearing capacity of a box arch considering the UHPC strengthening layer simplifies the accurate calculation method for the load-bearing capacity of the strengthened arch rib. The simplified formula has a simple form and is easier to be accepted and understood. Moreover, existing software for calculating the load-bearing capacity of an arch rib can be used to check the load-bearing capacity of the strengthened arch rib, without the need to separately compile a program, greatly shortening the calculation time and being able to provide an important reference for exploring the optimal strengthening plan of a box arch bridge in a timely manner. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1a is the cross-section a of the unstrengthened arch rib s , a’ s and other related parameter diagrams.

[0035] Figure 1b is the cross-section A of the unstrengthened arch rib s , A’ s , h fz , h’ fz and other related parameter diagrams.

[0036] Figure 2a is the cross-section a of the strengthened arch rib in the accurate calculation method su , a’ su and other related parameter diagrams.

[0037] Figure 2b is the cross-section A of the strengthened arch rib in the accurate calculation method su , A’ su , h u , h’ u and other related parameter diagrams.

[0038] Figure 3 is the simplified calculation diagram of the eccentric compression load-bearing capacity of the cross-section after UHPC strengthening.

[0039] Figure 4 is the comparison diagram of the load-bearing capacity between the simplified calculation method and the accurate calculation method of the present invention.

[0040] Figure 5 is the elevation structure diagram of a case of the present invention.

[0041] Figure 6 It is a schematic cross-sectional structure diagram (the upper-column on the arch is omitted) of a case of the present invention.

[0042] Figure 7 It is a schematic structure diagram of the longitudinal stressed reinforcement on the top surface at the connection position between the top-surface UHPC reinforcement layer and the upper-column on the arch.

[0043] Figure 8 It is Figure 7 A-A schematic structure diagram of

[0044] In the figure, the original concrete box arch 1, the bottom-surface UHPC reinforcement layer 2, the top-surface UHPC reinforcement layer 3, the connection position 301 between the top-surface UHPC reinforcement layer and the upper-column on the arch, the upper-column on the arch 4, the fill on the arch 5, the longitudinal stressed reinforcement on the top surface 6, the first longitudinal stressed reinforcement on the top surface 601, the second longitudinal stressed reinforcement on the top surface 602, and the longitudinal stressed reinforcement on the bottom surface 7. Specific implementation manners

[0045] The present invention will be further described below in conjunction with the accompanying drawings and embodiments, but the protection scope of the present invention is not limited to the following embodiments.

[0046] I. The calculation method of the bearing capacity of the arch rib before UHPC reinforcement is as follows:

[0047] According to the provisions of the "Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG 3362-2018), long-span arch bridges should check four sections: the crown, 3 / 8 of the arch span, 1 / 4 of the arch span, and the arch foot. The box arch is an eccentric compression member. As Figure 1a and Figure 1b described, the box section can be simplified into an I-shaped section, and the ultimate bearing capacity Mn1 and Mn2 can be calculated according to the following formulas:

[0048] γ0N d ≤f cd [bx+(b' f -b)h' f +f s ' d A s '-σ s A s =Mn1 (12)

[0049]

[0050] e=ηe0+h / 2-a s (15)

[0051]

[0052] In the formula: N dis the axial force value of the box arch, γ0 is the structural importance coefficient, taking 1.1 for large bridges; f cd is the design value of concrete strength; b is the sum of the thicknesses of the box arch web; x is the height of the compression zone, which can be obtained by taking the distance from the action point of N d , or can be obtained by combining Equation (12) and Equation (13); b f , b’ f are the flange widths of the smaller tension or compression side and the larger compression side respectively; h f , h’ f are the flange plate thicknesses of the smaller tension or compression side and the larger compression side respectively; f sd , f’ sd are the design values of the tensile and compressive strengths of the steel bars respectively; A s , A’ s are the longitudinal bar areas of the smaller tension or compression side and the larger compression side respectively; a s , a’ s are the distances from the resultant force points of the longitudinal bars on the smaller tension or compression side and the larger compression side to the near side of the section respectively; h is the section height, h0 = h - a s , h’0 = h - a’ s .

[0053] σ s is the stress of the longitudinal bars on the smaller tension or compression side, obtained from Equation (14), σ s needs to be within the range of the design value of the steel bar strength. For the steel bar stress value calculated by Equation (14), when it exceeds the design value, it needs to be further taken as the design value; ε cu is the ultimate strain of the concrete; the ratio of the height of the rectangular stress diagram to the actual compression zone height β = 0.8; E s is the elastic modulus of the steel bar.

[0054] M d is the bending moment value of the box arch, and the eccentricity of the axial force with respect to the centroid axis of the section e0 = M d / N d ; e is the distance from the action point of the axial force to the resultant force point of the longitudinal bars on the smaller tension or compression side of the section, obtained from Equation (15).

[0055] η is the eccentricity amplification coefficient of the axial force of the eccentric compression member, obtained from Equation (16); the calculated length l0 of the member = 0.36 times the length of the arch rib.

[0056] ζ1 is the influence coefficient of the load eccentricity on the section curvature, obtained from Equation (17); ζ2 is the influence coefficient of the slenderness ratio of the member on the section curvature, obtained from Equation (18).

[0057] The above formulas (12)-(18) are standard formulas, and most finite element software has embedded the bearing capacity method of the above formulas (12)-(18). After inputting the relevant cross-sectional dimensions and material information, the corresponding bearing capacity of the box arch can be obtained.

[0058] II. The precise calculation method for the bearing capacity of the arch rib after UHPC strengthening is as follows:

[0059] The UHPC strengthening layer is generally cast after roughening the top and bottom plates of the box arch and implanting shear reinforcement. Therefore, it can be considered to satisfy the plane section assumption. Since the UHPC layer is relatively thin, under normal circumstances, the compression zone height x is greater than the thickness of the UHPC layer. In addition, referring to the "Technical Guide for Strengthening Highway Bridges with Ultra-High Performance Concrete", the strength utilization coefficient of the newly added steel bars in the strengthening layer is taken as 0.8, and the strength utilization coefficient of the UHPC layer is taken as 0.5. For conservative calculation, the contribution of the UHPC tensile strength to the bearing capacity is not considered. Therefore, based on the design principle of concrete structures, as Figure 2a and Figure 2b shown, the precise calculation methods for the bearing capacities Mn1u and Mn2u of the box arch strengthened with UHPC are as follows:

[0060]

[0061] e u = η u e 0u + h z / 2 - a z (23)

[0062]

[0063] In the formula: N du is the axial force value of the box arch after UHPC strengthening, f cdu is the design value of the UHPC compressive strength; h’ u is the thickness of the UHPC layer on the larger compression side; h u is the thickness of the UHPC layer on the smaller tension or compression side; A su , A’ su are the areas of the newly added longitudinal bars on the smaller tension or compression side and the larger compression side of the strengthening layer respectively, f sdu , f’ sdu are the design values of the tensile and compressive strengths of the steel bars in the strengthening layer respectively; h z is the total height of the strengthened section; a z is the distance from the resultant force point of the longitudinal bars A s and A su on the smaller tension or compression side after strengthening to the near side of the section, a’ z is the distance from the resultant force point of the longitudinal bars A’ s and A’ su on the larger compression side after strengthening to the near side of the section; h z0= h z - a z 、h’ z0 = h’ z - a’ z 。

[0064] σ su is the stress of the longitudinal bars in the UHPC on the tension or compression smaller side, obtained from Equation (22); M du is the bending moment value after the box arch is strengthened with UHPC, N du is the axial force value of the box arch after the box arch is strengthened with UHPC, and the eccentricity e of the axial force with respect to the centroid axis of the cross-section 0u = M du / N du ; e u is the distance from the action point of the axial force to the resultant force point of the longitudinal bars on the tension or compression smaller side of the cross-section, obtained from Equation (23).

[0065] η u is the eccentricity amplification coefficient of the axial force of the eccentric compression member after strengthening, obtained from Equation (24).

[0066] ζ 1u is the influence coefficient of the load eccentricity ratio on the cross-section curvature after strengthening, obtained from Equation (25), and ζ 2u is the influence coefficient of the slenderness ratio of the member on the cross-section curvature after strengthening, obtained from Equation (26). The remaining parameters are the same as those in Equations (12) - (18).

[0067] III. The simplified calculation method for the bearing capacity of the arch rib after UHPC strengthening is as follows:

[0068] Compared with Equations (12) and (13), the design parameters in Equations (19) and (20) in the precise calculation method increase significantly, resulting in a very complex formula, and each parameter is very easy to confuse, leading to calculation errors. The difficulty of solving the compression zone height x also increases significantly.

[0069] In addition, the precise calculation formula needs to be calculated using a compiled program and cannot be directly calculated using existing software, which takes a long time. To facilitate the calculation and analysis using existing software such as Midas, this embodiment proposes a simplified calculation method, considering the UHPC strengthening layer and the original concrete structure as a unified cross-section, and the equivalent strength grade C of the concrete of this cross-section can be calculated according to Equation (1).

[0070] C = [C p × A p + 0.5C u × A u / (A p + A u ) (1)

[0071] Where C p 、Cu are the strength grade values of the original structure concrete and UHPC, respectively, A p and A u are the cross-sectional areas of the original structure and the UHPC cross-section, respectively. For example, substituting C p = 40, C u = 140 and the cross-sectional area into Equation (1), the calculated value of C = 44.8 MPa is obtained, that is, the equivalent strength grade of the new cross-section concrete can be taken as C45. The simplified formula has a simple form and is easier to be accepted and understood after being unified into a new cross-section.

[0072] For example Figure 3 , after calculating the strength grade of the new cross-section concrete according to Equation (1), at the same time, move the longitudinal bars in the UHPC layer and the longitudinal bars of the original structure to the position of the resultant force point, and calculate the combined area of the two layers of longitudinal bars. Since the strengths of the old and new longitudinal bars may be inconsistent, the strength of the new longitudinal bars can be uniformly taken as the strength of the old longitudinal bars, and only the cross-sectional area of the new longitudinal bars needs to be adjusted accordingly. For example, the equivalent areas A sue and A' sue of the newly added longitudinal bars on the smaller tension or compression side and the larger compression side of the UHPC reinforcement layer are calculated as shown in Equation (2):

[0073]

[0074] f sd and f' sd are the design values of the tensile and compressive strengths of the steel bars of the original box arch, respectively, and f sdu and f' sdu are the design values of the tensile and compressive strengths of the new longitudinal bars of the UHPC reinforcement layer, respectively. A su and A' su are the areas of the newly added longitudinal bars on the smaller tension or compression side and the larger compression side of the UHPC reinforcement layer, and A sue and A' sue are the equivalent areas of the newly added longitudinal bars on the smaller tension or compression side and the larger compression side of the UHPC reinforcement layer;

[0075] After the above simplification, the load-bearing capacity diagram after UHPC reinforcement is consistent with the conventional calculation diagram in Figure 1. Therefore, the form of the calculation formula is the same as that of Equations (12)-(13). The specific calculation formulas are as shown in Equations (3)-(4), and there is no need to use the long Equations (19)-(26) for calculation, which can simplify the calculation process; and because the formula forms are the same, the existing software can be used to directly check the bearing capacity of the formulas in Equations (3)-(4), and there is no need to compile another program. By inputting the parameters such as the dimensions of the unified cross-section and the equivalent material strength, the bearing capacity value can be easily calculated using the existing software, which greatly shortens the calculation time. The specific calculation formulas for the bearing capacities Mn1uz and Mn2uz are as follows:

[0076] γ0N du ≤fcdz [bx + (b' f - b)h' fz + f s ' d A' z - σ sz A z = Mn1uz (3)

[0077]

[0078] In the above formula, the bearing capacity values obtained by calculating the middle two formulas of formula (3) and formula (4) are Mn1uz and Mn2uz respectively, and both must be greater than γ0N du .

[0079] Where: f cdz is the design compressive strength value corresponding to the equivalent concrete strength C; A z , A’ z are the equivalent areas of the longitudinal reinforcement on the smaller tension or compression side and the larger compression side of the unified cross-section respectively; for the remaining parameters, refer to formula (12) - formula (26), specifically as follows:

[0080] N du is the axial force value of the box arch after reinforcement, γ0 is the structural importance coefficient, taking 1.1 for large bridges; b is the sum of the web thicknesses of the box arch; f cdz is the design compressive strength value corresponding to the equivalent concrete strength C; x is the height of the compression zone, which can be obtained by taking the distance from the action point of N du , or can be obtained by combining formula (3) and formula (4); b f , b’ f are the flange widths of the smaller tension or compression side and the larger compression side respectively; h u is the thickness of the UHPC layer on the smaller tension or compression side, h’ u is the thickness of the UHPC layer on the larger compression side, h fz , h’ fz are the thicknesses of the flange plates on the smaller tension or compression side and the larger compression side after reinforcement respectively, h fz = h f + h u , h’ fz = h’ f + h’ u , that is, the flange height of the unified cross-section is the sum of the UHPC reinforcement layer and the thickness of the original concrete flange plate; f sd , f’ sd are the design tensile and compressive strength values of the reinforcement respectively, uniformly taking the design tensile and compressive strength values of the old longitudinal reinforcement; A s , A’ s are the areas of the longitudinal reinforcement in the original box arch on the smaller tension or compression side and the larger compression side respectively; A z, A’ z They are the equivalent areas of longitudinal reinforcement at the smaller tension or compression side and the larger compression side of the unified cross-section respectively. Az = As + Asue, A’z = A’s + A’sue; a z , a’ z They are the distances from the resultant force points of longitudinal reinforcement at the smaller tension or compression side and the larger compression side after strengthening to the near side of the cross-section respectively, which are obtained from Equations (5) and (6); h is the total height of the cross-section before strengthening, h z is the total height of the cross-section after strengthening, h z = h + h u + h’ u , h z0 = h z - a z , h’ z0 = h z - a’ z ;

[0081] a z = [A s ×(a s + h u ) + A sue × a su / A z (5)

[0082] a' z = [A s '×(a' s + h' u ) + A s ' ue × a' su / A z ' (6)

[0083] In the formula: a s , a’ s They are the distances from the resultant force points of the original longitudinal reinforcement at the smaller tension or compression side and the larger compression side of the original box arch before strengthening to the near side of the cross-section respectively; a su , a’ su They are the distances from the resultant force points of the newly added longitudinal reinforcement in UHPC at the smaller tension or compression side and the larger compression side after strengthening to the near side of the cross-section respectively;

[0084] σ sz is the equivalent stress after combining the original longitudinal reinforcement and the newly added longitudinal reinforcement at the smaller tension or compression side of the unified cross-section. According to Equation (7), σ sz should be within the range of the design value of the steel bar strength. The steel bar stress value calculated by Equation (7), when exceeding the design value, needs to be further taken as the design value:

[0085]

[0086] In the formula: ε cuis the ultimate strain corresponding to the equivalent concrete type, and the ratio β of the height of the rectangular stress diagram to the actual height of the compression zone is 0.8; E s is the elastic modulus of the steel bar; the equivalent concrete mentioned here refers to obtaining the equivalent concrete type according to the equivalent strength grade C of the cross-section concrete calculated by formula (1), and then corresponding to ε cu .

[0087] In the above calculation method, formula (7) calculates the equivalent stress after combining the original longitudinal reinforcement and the newly added longitudinal reinforcement on the smaller side of tension or compression of the unified cross-section. Since the relevant parameters change before and after UHPC strengthening, the x obtained before strengthening is different from the x obtained after strengthening. e u is the distance from the action point of the axial force after strengthening to the resultant force point of the longitudinal reinforcement on the smaller side of tension or compression of the cross-section; it is obtained from formula (8):

[0088] e u = η u e 0u + h z / 2 - a z (8)

[0089] In the formula: η u is the eccentricity magnification coefficient of the axial force of the eccentric compression member after strengthening, which is obtained from formula (9); the eccentricity e of the axial force after strengthening to the centroid axis of the cross-section 0u = M du / N du , M du is the bending moment value of the box arch after strengthening;

[0090]

[0091] The calculated length l0 of the member = 0.36 times the length of the arch rib; ζ 1u is the influence coefficient of the load eccentricity ratio on the cross-section curvature after strengthening, which is obtained from formula (10); ζ 2u is the influence coefficient of the slenderness ratio of the member after strengthening on the cross-section curvature, which is obtained from formula (11):

[0092]

[0093] The following provides a case:

[0094] A reinforced concrete box arch bridge was built in 1989, with a main span of 125m, a total bridge deck width of 11.5m, a rise-span ratio of 1 / 8, a rise of 15.68m, and the main bridge substructure is a gravity pier and an enlarged foundation. The width of the box arch is 9.6m, with 7 box chambers arranged transversely, a height of 1.85m, and the thickness of the top and bottom plates is 0.14m each. The technical condition grade of this bridge is rated as Class 3, and components such as the box arch and the deck slab have relatively serious diseases. After renovation, the design load grade of the bridge is Highway - II level.

[0095] According to Equations (13) - (19), when un-reinforced, the calculation results of the bearing capacity of each control section are shown in Table 1. The thickness of the upper and lower flange plates of the box arch of this bridge is only 14 cm, and the reinforcement is less. The arch foot section, 3 / 8 section, and arch crown section do not meet the requirements of Highway Class-II load level under the maximum bending moment load combination.

[0096] Table 1 Check Results of the Ultimate State of Un-reinforced Bearing Capacity

[0097]

[0098] Note: When ξ is less than the relative boundary compression zone height ξ b =0.53, it is large eccentricity failure, otherwise it is small eccentricity failure. In Equations (1) - (7), the parameters f cd =18.4 MPa; b = 2120 mm; h = 1850; a’ s =a s =40 mm; h0 = 1810 mm; b’ f =9600 mm; h f =h’ f =140 mm; f sd 、f’ sd =±330 MPa; The top and bottom plates of the box arch are symmetrically reinforced, A s =A’ s =22518 mm 2 ; ε cu =0.0033; E s =200000 MPa; β = 0.8, l0 = 47.228 m.

[0099] The following reinforcement methods are specifically adopted in this embodiment:

[0100] Combined with Figure 5 and Figure 6As shown in the figure, it includes the original concrete box arch 1 and the upper-arch columns 4, and also includes bottom shear reinforcement, bottom longitudinal stressed reinforcement 7, bottom UHPC reinforcement layer 2, top shear reinforcement, top longitudinal stressed reinforcement 6 and top UHPC reinforcement layer 3. Among them: The bottom shear reinforcement is implanted at intervals on the bottom surface of the original concrete box arch 1. Before implantation, the bottom surface of the original concrete box arch 1 is roughened, and then it is implanted according to the conventional construction method, so that the subsequently poured bottom UHPC reinforcement layer 2 can cooperate with the structural layer of the original concrete box arch 1. The bottom longitudinal stressed reinforcement 7 is longitudinally arranged at intervals on the bottom surface of the original concrete box arch 1 and is connected and fixed to the bottom shear reinforcement. The bottom longitudinal stressed reinforcement 7 is generally arranged longitudinally and continuously along the original concrete box arch 1. The bottom UHPC reinforcement layer 2 is arranged on the bottom surface of the original concrete box arch 1 to cover the bottom shear reinforcement and the bottom longitudinal stressed reinforcement. The top shear reinforcement is implanted at intervals on the top surface of the original concrete box arch 1. Before implantation, the top surface of the original concrete box arch 1 is roughened, and then it is implanted according to the conventional construction method, so that the subsequently poured top UHPC reinforcement layer 3 can cooperate with the structural layer of the original concrete box arch 1. The top longitudinal stressed reinforcement 6 is longitudinally arranged at intervals on the top surface of the original concrete box arch 1 and is connected and fixed to the top shear reinforcement. The top longitudinal stressed reinforcement 6 is generally arranged longitudinally and continuously along the original concrete box arch 1. However, due to the existence of the upper-arch columns 4, the top longitudinal stressed reinforcement 6 cannot pass through the upper-arch columns 4 directly in a continuous length and needs to drill holes in the upper-arch columns 4 to pass through the reinforcement. To prevent the concrete of the upper-arch columns 4 from being drilled and collapsed due to the too-dense drilling spacing, in this embodiment, a special design is made for the layout of the top longitudinal stressed reinforcement 6 passing through the upper-arch columns 4: Combining Figure 7 and Figure 8 As shown in the figure, the top longitudinal stressed reinforcement 6 includes a first top longitudinal stressed reinforcement 601 and a second top longitudinal stressed reinforcement 602. The first top longitudinal stressed reinforcement 601 and the second top longitudinal stressed reinforcement 602 are arranged alternately and equidistantly. At the connection position of the original concrete box arch 1 and the upper-arch columns 4, the first top longitudinal stressed reinforcement 601 passes through the upper-arch columns 4 at a distance d1 above the top surface of the original concrete box arch 1, and the second top longitudinal stressed reinforcement 602 passes through the upper-arch columns 4 at a distance d2 above the top surface of the original concrete box arch 1. d1 is 15 cm and d2 is 15 cm. In this embodiment, the top longitudinal stressed reinforcement 6 at the upper-arch columns 4 is arranged in two rows. In this way, the drilling spacing of each row of the upper-arch columns 4 is twice the spacing of the top longitudinal stressed reinforcement 6, which can better prevent the concrete of the upper-arch columns 4 from being drilled and collapsed and ensure the support strength of the upper-arch columns 4; The top UHPC reinforcement layer 3 is arranged on the top surface of the original concrete box arch 1 to cover the top shear reinforcement and the top longitudinal stressed reinforcement. There is also upper-arch filling 5 filled between the original concrete box arch 1, the bridge deck and the two middle upper-arch columns 4.

[0101] The spacing between the bottom shear reinforcement and the top shear reinforcement is 0.4 m, and they are arranged in a quincunx pattern. The diameter of the transverse reinforcement in the UHPC layer is not greater than 16 mm, and the spacing is 10 - 15 cm. The thickness of the UHPC strengthening layers 2 and 3 is generally 5 - 10 cm. At the connection position 301 between the top UHPC strengthening layer and the upper column on the arch, the thickness exceeds the highest height of the top longitudinal stressed reinforcement 6 by 3 - 10 cm. In addition, the thickness can be appropriately increased at the arch feet.

[0102] Using the strengthening method of the present invention, the top and bottom surfaces of the box arch are strengthened with UHPC with a strength of U140 and a thickness of 6 cm. Both the top longitudinal stressed reinforcement 6 and the bottom longitudinal stressed reinforcement 7 adopt 112 C16 steel bars.

[0103] According to Formulas (19) - (26), after the top and bottom surfaces of the box arch are heightened by 6 cm thick UHPC, the sectional load - bearing capacity is greatly improved, and both are greater than the internal - force design value γ0N du , the minimum safety factor is 1.07, meeting the requirements. From the calculation and analysis results, it can be seen that the load - bearing capacity at the L / 2 position of the arch crown before strengthening is only 53182 kN, while after UHPC strengthening, the load - bearing capacity reaches 77679 kN, which is greater than the internal - force design value γ0N du = 63657, the safety factor is 1.22, and the increase amplitude of the load - bearing capacity is 46%. In addition, the load - bearing capacities of the arch feet and the 3L / 8 positions are increased by 66% and 58% respectively, indicating that the method has a significant effect on strengthening box - type arch bridges. It is worth mentioning that the above - mentioned increase amplitude of the load - bearing capacity is the calculation result under the condition that the strength utilization coefficient of UHPC is only 0.5 and the strength utilization coefficient of steel bars is only 0.8. The calculation result is conservative and has a certain safety reserve, and the actual strengthening effect may be better. The UHPC strengthening method is reliable. The detailed calculation is shown in Table 2:

[0104] Table 2 Precise calculation table of the ultimate load - bearing capacity of UHPC strengthening

[0105]

[0106] Note: f cdu = 68 MPa; h u = h’ u = 60 mm; hz = 1970 mm; The UHPC layers on the top and bottom of the box arch are symmetrically reinforced, A su = A’ su = 22518 mm 2 , f sdu , f’ sdu = ±330 MPa; a’ su = a su = 30 mm; a’ z = a z= 65 mm, hz0 = h'z0 = 1905 mm; The other parameter values are the same as those in Table 1.

[0107] According to Formulas (1)-(11), after calculation, the concrete strength grade after unified section is C45. The calculation results of the bearing capacity strengthened by UHPC obtained by the simplified method are shown in Table 3. It can be analyzed that the bearing capacity values obtained by the simplified formula are in good agreement with the actual bearing capacity values, and the maximum deviation is within 4%. This indicates that the simplified method proposed in the present invention has good accuracy in calculating the bearing capacity of UHPC-strengthened box arches and effectively simplifies the calculation process. It is worth mentioning that, Figure 4 as can be seen, the bearing capacity obtained by the simplified method is less than that obtained by the exact method. This is because for eccentric compression members such as box arches, the parts with high material strength utilization rate are at the top and bottom plates. Formula (1) distributes the high-strength UHPC on the top and bottom plates to the entire section, resulting in lower and more conservative material utilization rate. Therefore, the simplified calculation method is on the safe side.

[0108] Table 3 Simplified calculation table of the ultimate bearing capacity strengthened by UHPC

[0109]

[0110]

[0111] Note: f cdz = 20.5 MPa; h' fz = h fz = 200 mm; A z = A' z = 22518 + 0.8×22518 = 40532 mm 2 ; a' z = a z = 65 mm, hz0 = h'z0 = 1905 mm; The other parameter values are the same as those in Table 1 and Table 2.

Claims

1. A simplified calculation method for the bearing capacity of box arches considering the UHPC reinforcement layer, characterized in that The following steps are involved: S1.Use UHPC to reinforce the original concrete arch rib, and regard the UHPC reinforcement layer and the original concrete arch rib as a unified section. The calculation method of the equivalent strength grade C of the concrete in this section is: C=[C p ×A p +0.5C u ×A u ] / (AND p +A u ) (1) Where: C p , C u are the strength grade values ​​of the original structural concrete and UHPC, A p , A u are the original structure cross section and UHPC cross section area respectively; S2. Move the longitudinal reinforcement in the UHPC layer and the original structural longitudinal reinforcement to the position of the resultant force point, combine the areas of the two layers of longitudinal reinforcement, take the strength of the new longitudinal reinforcement as the strength of the old longitudinal reinforcement, and adjust the cross-sectional area of ​​the new longitudinal reinforcement accordingly: f sd 、f' sd are the design values ​​of tensile and compressive strength of the original box arch reinforcement, f sdu 、f' sdu are the design values ​​of tensile and compressive strength of new longitudinal reinforcement in UHPC reinforcement layer, A su , A' su The longitudinal reinforcement area is added to the UHPC reinforcement layer on the side with smaller tension or compression and the side with larger compression. sue , A' sue The equivalent area of ​​the longitudinal reinforcement added to the UHPC reinforcement layer on the side with smaller tension or compression and the side with larger compression; S3. Use formulas (3) and (4) to calculate the bearing capacity values ​​Mn1uz and Mn2uz: γ0N du ≤f cdz [bx+(b' f -b)h' fz ]+f s ' d A' z -s sz A z =Mn1uz (3) Where: N du is the axial force of the box arch after reinforcement, γ0 is the structural importance factor, which is 1.1 for the bridge; b is the sum of the thickness of the box arch slats; f cdz is the design value of compressive strength corresponding to the equivalent concrete strength C; x is the height of the compression zone, which can be used to calculate N du The distance between the action point and the target point can also be calculated by combining equation (3) and equation (4); b f , b' f h is the flange width of the side with smaller tension or compression and the side with larger compression respectively; u is the thickness of the UHPC layer on the side with smaller tension or compression, h' u is the thickness of the UHPC layer on the side with greater pressure, h fz 、h' fz are the thickness of the flange plate on the side with smaller tension or compression and the side with larger compression after reinforcement, respectively. fz =h f +h u , h' fz =h' f +h' u , that is, the uniform section flange height is the sum of the thickness of the UHPC reinforcement layer and the original concrete flange plate; f sd 、f' sd A is the design value of tensile and compressive strength of steel bars, and the design value of tensile and compressive strength of old longitudinal bars is used uniformly; s , A' s A is the longitudinal reinforcement area of ​​the original box arch on the side with smaller tension or compression and the side with larger compression respectively; z , A' z A is the equivalent area of ​​longitudinal reinforcement on the smaller side of tension or compression and the larger side of compression of the same section, respectively. z =A s +A sue , A' z =A' s +A' sue ; a z 、a' z are the distances from the longitudinal reinforcement resultant point to the near side of the section from the side with smaller tension or compression and the side with larger compression after reinforcement, respectively, and are obtained by equations (5) and (6); h is the total height of the section before reinforcement, h z is the total height of the section after reinforcement, h z =h+h u +h' u ,h z0 =h z -a z 、h' z0 =h z -a' z ; a z =[A s ×(a s +h u )+A sue ×a su ] / A z (5) a' z =[A s '×(a' s +h' u )+A s ' ue ×a' su ] / A z ' (6) Where: a s 、a' s are the distances from the longitudinal reinforcement resultant point to the near side of the section from the smaller tensile or compressive side and the larger compressive side of the original box arch before reinforcement; a su 、a' su They are the distances from the newly added longitudinal reinforcement resultant point to the near side of the section from the side with smaller tension or compression and the side with larger compression after reinforcement; σ sz To unify the equivalent stress of the original longitudinal reinforcement + the newly added longitudinal reinforcement on the smaller side of the section under tension or compression, σ sz The steel bar stress value calculated by formula (7) must be within the design value range of the steel bar strength. If it exceeds the design value, it must be further taken as the design value: Where: ε cu is the limit strain corresponding to the equivalent concrete model obtained by formula (1), the ratio of the height of the rectangular stress diagram to the height of the actual compression zone is β = 0.8; E s is the elastic modulus of the steel bar; e u is the distance from the point of action of the axial force after reinforcement to the resultant force point of the longitudinal reinforcement on the smaller side of tension or compression of the uniform section; obtained by formula (8): And u =η u And 0u +h z / 2-a z (8) Where: η u is the coefficient of eccentricity increase of the axial force of the eccentrically compressed member after reinforcement, which is obtained by formula (9); the eccentricity of the axial force to the centroidal axis of the cross section after reinforcement, e 0u =M du / N du , M du is the bending moment value of the box arch after reinforcement; The calculated length of the component l0 = 0.36 times the length of the arch rib; 1u is the influence coefficient of load eccentricity on section curvature after reinforcement, obtained by formula (10); ζ 2u is the influence coefficient of the slenderness ratio of the reinforced component on the cross-sectional curvature, which is obtained by formula (11):

2. A box arch bearing capacity calculation system considering the UHPC reinforcement layer, characterized by: The system uses the simplified calculation method of the box arch bearing capacity considering the UHPC reinforcement layer as described in claim 1.

3. A storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by the processor, the simplified calculation method of the box arch bearing capacity considering the UHPC reinforcement layer as claimed in claim 1 can be implemented.

4. A computer device, characterized in that: The invention comprises a memory and a processor, wherein the processor is coupled to the memory and reads and executes instructions in the memory to implement the simplified calculation method of the box arch bearing capacity considering the UHPC reinforcement layer as claimed in claim 1.

Images