Large-span prestressed concrete box girder haunch cracking traceability method

Abstract

The invention belongs to the field of bridge structure health detection, and discloses a large-span prestressed concrete box girder haunch cracking tracing method which comprises the following steps: (1) establishing a three-dimensional splitting stress model; (2) the rule that the direction of the maximum splitting stress changes along with the steel beam anchoring mode is clarified; (3) qualitatively judging whether the splitting stress is a main factor of cracking or not by combining the stem and haunch crack trend and steel beam anchoring; and (4) solving the maximum three-dimensional splitting stress value, comparing the maximum three-dimensional splitting stress value with the tensile strength of the concrete, and quantitatively identifying whether the splitting stress is the main cause of cracking or not. According to the large-span prestressed concrete box girder haunch cracking traceability method, for the problem of large-span prestressed concrete box girder haunch cracking, qualitative judgment of main causes is rapidly completed in combination with the crack form and the steel beam anchoring mode, verification is conducted through three-dimensional splitting stress calculation, a traceability system with qualitative and quantitative double criteria is constructed, and the traceability accuracy is improved. And the method has a wide engineering application prospect.

Description

Technical Field

[0001] This invention belongs to the field of bridge structural health detection and relates to a method for tracing the source of cracks in the axle of a large-span prestressed concrete box girder. Background Technology

[0002] Long-span prestressed concrete box girder bridges play a crucial role in modern bridge engineering. However, during long-term operation, prestressed concrete box girders commonly exhibit numerous cracks. The presence of cracks accelerates the corrosion of internal steel reinforcement, significantly weakening the durability of prestressed concrete structures. The axles of prestressed concrete box girders, as critical connections between the top slab and web, frequently experience cracking in practical engineering. However, current analyses of the cracking mechanism in prestressed box girders primarily focus on the top slab, web, and bottom slab regions, while the causes and evolution mechanisms of cracks in the axle region have not been systematically revealed. Therefore, it is necessary to systematically study the cracking mechanism in this area to provide theoretical support for the durability design and maintenance of prestressed concrete box girder bridges.

[0003] Although existing studies have suggested that excessive splitting stress can lead to cracking in prestressed concrete structures—for example, Linyun Zhou and Shui Wan, in their paper "Full-range nonlinear analysis of post-tensioned anchorage zones based on modified strut-and-tie model," argue that excessive splitting stress is one of the main causes of cracking in the anchorage zone of post-tensioned prestressed concrete—there are still two major challenges in determining whether cracking in the axle area of ​​prestressed concrete box girders is caused by splitting stress: 1) The lack of a three-dimensional splitting stress calculation method for the axle area. Existing splitting stress calculation models have significant limitations: First, in terms of analytical dimensions, they are mostly limited to considering the two-dimensional distribution of vertical (along beam height) splitting stress along the beam length, failing to truly reflect the three-dimensional spatial distribution of vertical and transverse (along beam width) splitting stress along the longitudinal (along beam length) direction. For example, Zhiqi He and Zhao Liu studied a solution method for the distribution of vertical splitting stress along the longitudinal direction in two-dimensional prestressed concrete structures in their paper "Investigation of Bursting Forces in Anchorage Zones: Compression-Dispersion Models and Unified Design Equation". Second, in terms of application scenarios, existing methods mainly target the anchorage of prestressed steel strands along the section height direction, but fail to consider the characteristics of anchorage along the section width direction commonly found in the axle area. For example, Zhiqi He, Jiatong Chen, Zhao Liu, and Zhongguo John Ma studied a method for calculating splitting stress under steel strand anchorage along the beam height in their paper "Analytical approach for bursting cracking analysis of post-tensioned anchorage zone". This dual limitation makes it difficult to accurately obtain the actual splitting stress amplitude in the axle area, thus making it impossible to quantitatively determine whether cracking is dominated by splitting stress. 2) The direction of the maximum splitting stress under different steel strand anchorage methods is still unclear. For example, although Joung Rae Kim, Hyo-Gyoung Kwak and Byung-Suk Kim have confirmed in "Design equation to evaluate bursting forces at the end zone of post-tensioned members" that splitting stress is distributed in both beam height and beam width directions, they have not yet established a correspondence between the direction of splitting stress and the steel strand anchorage method.Existing research has failed to fully consider the influence of different anchorage arrangements on the direction of maximum splitting stress, resulting in the inability to effectively determine at the qualitative level whether the cracking at the haunch of the box girder is attributable to the action of splitting stress.

[0004] Therefore, how to establish a three-dimensional splitting stress calculation method applicable to the haunch region of box girders to determine its stress amplitude, and to reveal the intrinsic relationship between different steel strand anchorage methods and the direction of maximum splitting stress, so as to construct a crack source tracing judgment criterion that combines qualitative and quantitative methods, has become a technical bottleneck that urgently needs to be overcome. Summary of the Invention

[0005] This invention provides a method for tracing the source of haunch cracks in large-span prestressed concrete box girders. This method can accurately calculate the three-dimensional splitting stress in the haunch region of the box girder, clarify the stress distribution patterns under different anchorage methods, thereby achieving qualitative tracing and quantitative assessment of haunch cracking problems, and providing guidance for structural optimization and targeted reinforcement of the box girder.

[0006] The technical solution of the present invention:

[0007] A method for tracing the source of cracks in the haunches of large-span prestressed concrete box girders, comprising the following steps:

[0008] Step 1: Establish a three-dimensional splitting stress calculation model for post-tensioned prestressed concrete structures based on the compression-diffusion model;

[0009] Assume the anchorage zone of the post-tensioned prestressed concrete structure is filled with multiple longitudinal compressive stress contour lines, each representing a force flow; the compressive stress contour line along the vertical (beam height) direction is y(x), and the compressive stress contour line along the transverse (beam width) direction is z(x), where y(x) and z(x) are fourth-order polynomials containing x; in the three-dimensional splitting stress model, the coordinate directions are as follows: x, y, and z represent the longitudinal (beam length), vertical (beam height), and transverse (beam width) directions of the post-tensioned prestressed concrete structure, respectively; the three-dimensional splitting stress calculation model adopts the following three basic assumptions:

[0010] (1.1) Geometric distribution assumption: The force flow distribution below the anchor plate and in the stress uniform zone at the anchorage section of the post-tensioned prestressed concrete structure follows a linear relationship; if the longitudinal compressive stress contour lines have y-coordinates in the beam height and beam width directions at the stress uniform distribution zone section. i z i Then the starting coordinates y0, z0 of the longitudinal compressive stress contour lines at the cross section of the uniformly stress-distributed region satisfy:

[0011]

[0012] Where a represents the length of the anchor plate along the beam height, g represents the length of the anchor plate along the beam width, c represents the height of the anchor section of the post-tensioned prestressed concrete structure, and d represents the width of the anchor section of the post-tensioned prestressed concrete structure.

[0013] (1.2) Assumption of force flow direction: At the anchorage section and the section of uniform stress distribution area of ​​the post-tensioned prestressed concrete structure, the direction of the principal compressive stress (prestress) is perpendicular to the above two sections. Therefore, the slope of the tangent line of the longitudinal compressive stress contour line at the anchorage section and the section of uniform stress distribution area of ​​the post-tensioned prestressed concrete structure is zero.

[0014]

[0015] (1.3) Assumption of transverse stress boundary: In the section of the uniform stress distribution region, the stress is uniformly distributed, and the transverse stress σ b The curvature d of the contour lines of transverse stress and longitudinal compressive stress is zero. 2 y / d 2 x, d 2 z / d 2 x is directly proportional, therefore:

[0016]

[0017] (1.4) Formulas (1), (3), (5), (6), and (7) represent five boundary conditions, determining the expression for y(x); formulas (2), (4), (5), (6), and (7) determine the expression for z(x); at any position x in the longitudinal direction of the post-tensioned prestressed concrete structure, the vertical and transverse splitting stress σ b,h (x), σ b,t (x) is obtained by integrating the contributions of all longitudinal compressive stress contour lines passing through the cross section of the uniformly distributed stress region; σ b,h (x), σ b,t (x) is solved as follows:

[0018]

[0019] in, The stress is located at the cross-section of the region with uniform stress distribution. P represents the anchoring force; finally, the calculation models for the maximum splitting stress in the vertical and horizontal directions of the post-tensioned prestressed concrete structure are as follows:

[0020]

[0021] Step 2: Using finite element analysis, determine the direction of the maximum splitting stress when the prestressed steel strands are anchored along the beam height and width, specifically:

[0022] (2.1) Establish a three-dimensional finite element model of the post-tensioned prestressed concrete structure and anchor plate; considering the geometric size effect of the post-tensioned prestressed concrete structure and anchor plate, set multiple sets of size parameters, and simulate different arrangement conditions of the anchor plate along the beam height direction and beam width direction in the finite element model.

[0023] (2.2) Apply prestressed load to the anchor plate and investigate the direction of maximum splitting stress in the anchorage zone of the post-tensioned prestressed concrete structure when the prestressed steel strands are anchored along the beam height and beam width directions through numerical simulation calculation.

[0024] Step 3: Based on the actual direction of the axle crack and the anchoring method of the prestressed steel strand, qualitatively determine whether the maximum splitting stress is the dominant factor leading to cracking.

[0025] (3.1) Cracks in the axilla area are divided into horizontal cracks and oblique cracks;

[0026] When a horizontal crack appears in the axle area and the prestressed steel strands in the axle area are anchored along the beam width direction, based on the consistency between the crack morphology and the spatial stress direction, it is presumed that the maximum splitting stress along the beam height direction is the dominant factor causing cracking.

[0027] (3.2) When a diagonal crack appears in the axle area, its morphological characteristics indicate the superposition of multidimensional stress fields; based on this, it is inferred that the diagonal crack is dominated by splitting stress along the beam height direction and along the beam width direction.

[0028] Step 4: Based on the qualitative judgment results, calculate the maximum splitting stress and compare it with the tensile strength of concrete to quantitatively determine whether the cracking is caused by the maximum splitting stress.

[0029] (4.1) In the modeling and analysis, the axle area is simplified into a regular cube structure, and the prestressed steel strand anchoring effect therein is equivalent to the concentric anchoring load acting on the cube structure.

[0030] (4.2) For the case of horizontal cracks appearing in the axle area and the prestressed steel strands being anchored along the beam width direction, the maximum splitting stress is calculated using formula (9) and compared with the tensile strength of concrete; if the maximum splitting stress is greater than the tensile strength of concrete, it proves that there is a risk of cracking.

[0031] (4.3) For the diagonal cracks that appear in the haunch area, it is necessary to calculate the maximum splitting stress along the beam height and beam width directions at the same time, and then calculate the principal tensile stress and compare it with the tensile strength of the concrete; if the principal tensile stress is greater than the tensile strength of the concrete, it proves that there is a risk of cracking.

[0032] The beneficial effects of this invention are:

[0033] 1) This invention establishes a three-dimensional splitting stress analysis model, which can simultaneously calculate the maximum splitting stress along both the beam height and beam width directions, thereby achieving a comprehensive assessment of the stress state. More importantly, this model clarifies the intrinsic relationship between the prestressed steel strand anchorage method and the maximum splitting stress.

[0034] 2) Based on the established three-dimensional splitting stress model, this invention proposes a method for tracing the source of cracks in the axle of large-span prestressed concrete box girders. This method first comprehensively considers the crack direction and the anchorage method of the prestressed steel strands to qualitatively determine whether the cracks are dominated by splitting stress. If so, the maximum splitting stress in the region is then quantitatively calculated using a three-dimensional model, and verified by comparing it with the tensile strength of the concrete. This achieves both qualitative and quantitative analysis of the cracking mechanism in the axle of prestressed concrete box girders. Attached Figure Description

[0035] Figure 1 This is a flowchart of the method of the present invention.

[0036] Figure 2 This is a schematic diagram of the prestressed concrete box girder haunch in a calculation example of the implementation of the method of the present invention.

[0037] Figure 3 This is a schematic diagram of cracking in a calculation example of the method of the present invention.

[0038] Figure 4 The diagram shows the three-dimensional splitting stress amplitude in a calculation example of the method of the present invention, where (a) is the maximum splitting stress along the beam height and beam width, and (b) is a comparison of the errors between the finite element simulation and the formula calculation.

[0039] Figure 5 The results of quantitative analysis of cracking in the implementation examples of the method of the present invention are shown, including (a) comparison of maximum splitting stress with concrete tensile strength, and (b) the proportion of maximum splitting stress exceeding the limit. Detailed Implementation

[0040] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0041] This invention proposes a method for tracing the source of haunch cracks in large-span prestressed concrete box girders, comprising four steps: "establishing a three-dimensional splitting stress model," "determining the relationship between the direction of the maximum splitting stress and the anchorage method of the prestressed steel strands," "qualitatively determining whether splitting stress is the dominant factor causing cracking based on the actual direction of the haunch crack and the anchorage method of the prestressed steel strands," and "calculating the three-dimensional splitting stress amplitude and comparing it with the tensile strength of the concrete to quantitatively determine whether the cracking is caused by splitting stress."

[0042] Example: Case study of source analysis of axle cracking in large-span prestressed concrete structures;

[0043] To fully verify the effectiveness and engineering applicability of the proposed method, a large-span prestressed concrete continuous rigid frame bridge exhibiting typical axle cracking was selected as a case study. The main girder of this bridge adopts a single-box, single-cell cross-section. The selected analysis object is a standard cantilevered segment, with a total width of 15 m for each segment. During construction, the prestressed steel strands were tensioned after the concrete in the corresponding beam segment reached its design strength, with their anchorage ends located in the axle region at the junction of the top slab and web of the box girder. Due to the abrupt change in geometry and complex stress in this region, a huge localized concentrated force (splitting stress) was generated when the prestressed steel strands were anchored along the beam height. Details of the anchorage section are provided in [link to relevant documentation]. Figure 2 On-site investigation revealed varying degrees of cracking in multiple beam segments after prestressing tensioning. The segment with the most significant and typical crack development in the axle area was selected as the research focus. This area primarily exhibits cracks along the direction of the prestressing duct (crack morphology see...). Figure 3 This seriously affects the durability and safety of the structure.

[0044] Detailed on-site investigation and crack morphology tracing of the actual bridge revealed that the cracks in the axle area of ​​the box girder exhibited significant directional characteristics, primarily manifesting as multiple parallel horizontal cracks. Considering the bridge's prestressed steel strand arrangement, the strands were anchored transversely (width direction) along the box girder. Analysis using a three-dimensional splitting stress model showed that when the prestressed steel strands were anchored transversely, the maximum splitting stress was concentrated in the vertical (beam height direction) tensile stress due to the diffusion effect of the concentrated force under the anchor. According to the failure criteria of mechanics of materials, the cracking direction of concrete is usually orthogonal to the direction of the principal tensile stress. Therefore, the high-amplitude splitting stress distributed along the beam height direction analyzed by the model corresponds precisely to the horizontal cracks observed on-site. This consistency between analysis and measurement strongly demonstrates that the vertical splitting effect caused by prestressed anchorage is the main mechanical cause of horizontal cracking in the axle area.

[0045] To accurately quantify the splitting stress level in the haunch region of a prestressed box girder, a three-dimensional finite element model was established based on a real bridge project. For the critical condition of prestressed tendons anchored along the beam width, its complex stress state was analyzed in detail, and the calculated splitting stress cloud diagram is shown below. Figure 4As shown. From the stress distribution pattern, the splitting stress component along the beam height (vertical) is significantly larger than the component along the beam width (transverse), indicating that under the current anchorage arrangement, vertical tensile stress is the key factor controlling the section design. Regarding the comparison of values: the maximum splitting stress peak value obtained from the finite element simulation is 2.32 MPa; meanwhile, the splitting stress value calculated using the theoretical formula is 2.17 MPa. Error analysis shows that the theoretical formula value and the finite element simulation value agree well, with a relative error of only 6%. This not only verifies the accuracy of the finite element model in this paper but also indicates that the theoretical formula can reflect the stress characteristics of this region to a certain extent. Safety verification results (such as...) Figure 5 The figure (shown) illustrates the grim reality: both finite element simulation values ​​and formula calculation values ​​exceed the standard value for the tensile strength of concrete. Specifically, the maximum splitting stress calculated by the finite element method exceeds the tensile strength by approximately 24%, while the theoretical formula calculation value also exceeds the limit by 16%.

[0046] In conclusion, this vertical splitting stress, which far exceeds the tensile strength of the material, is the root cause of the horizontal cracks in the axle area of ​​the bridge pier.

Claims

1. A method for tracing the source of haunch cracks in large-span prestressed concrete box girders, characterized in that, The steps are as follows: Step 1: Establish a three-dimensional splitting stress calculation model for post-tensioned prestressed concrete structures based on the compression-diffusion model; Assume the anchorage zone of the post-tensioned prestressed concrete structure is filled with multiple longitudinal compressive stress contour lines, each representing a force flow; the compressive stress contour line along the vertical direction (beam height) is y(x), and the compressive stress contour line along the transverse direction (beam width) is z(x), where y(x) and z(x) are fourth-order polynomials containing x; in the three-dimensional splitting stress model, the coordinate directions are as follows: x, y, and z represent the longitudinal direction (beam length), the vertical direction (beam height), and the transverse direction (beam width) of the post-tensioned prestressed concrete structure, respectively; the three-dimensional splitting stress calculation model adopts the following three basic assumptions: (1.1) Geometric distribution assumption: The force flow distribution below the anchor plate and in the stress uniform zone at the anchorage section of the post-tensioned prestressed concrete structure follows a linear relationship; if the longitudinal compressive stress contour lines have y-coordinates in the beam height and beam width directions at the stress uniform distribution zone section. i z i Then the starting coordinates y0, z0 of the longitudinal compressive stress contour lines at the cross section of the uniformly stress-distributed region satisfy: ； Where a represents the length of the anchor plate along the beam height, g represents the length of the anchor plate along the beam width, c represents the height of the anchor section of the post-tensioned prestressed concrete structure, and d represents the width of the anchor section of the post-tensioned prestressed concrete structure. (1.2) Assumption of force flow direction: At the anchorage section and the section of uniform stress distribution area of ​​the post-tensioned prestressed concrete structure, the direction of the principal compressive stress, i.e., the prestress, is perpendicular to the anchorage section and the section of uniform stress distribution area of ​​the post-tensioned prestressed concrete structure. Therefore, the slope of the tangent line of the longitudinal compressive stress contour line at the anchorage section and the section of uniform stress distribution area of ​​the post-tensioned prestressed concrete structure is zero. ； (1.3) Assumption of transverse stress boundary: In the section of the uniform stress distribution region, the stress is uniformly distributed, and the transverse stress σ b The curvature d of the contour lines of transverse stress and longitudinal compressive stress is zero. 2 y / d 2 x, d 2 z / d 2 x is directly proportional, therefore: ； (1.4) Formulas (1), (3), (5), (6), and (7) represent five boundary conditions, determining the expression for y(x); formulas (2), (4), (5), (6), and (7) determine the expression for z(x); at any position x in the longitudinal direction of the post-tensioned prestressed concrete structure, the vertical and transverse splitting stress σ b,h (x), σ b,t (x) is obtained by integrating the contributions of all longitudinal compressive stress contour lines passing through the cross section of the uniformly distributed stress region; σ b,h (x), σ b,t (x) is solved as follows: ； in, The stress is located at the cross-section of the region with uniform stress distribution. P represents the anchoring force; finally, the calculation models for the maximum splitting stress in the vertical and horizontal directions of the post-tensioned prestressed concrete structure are as follows: ； Step 2: Using finite element analysis, determine the direction of the maximum splitting stress when the prestressed steel strands are anchored along the beam height and width, specifically: (2.1) Establish a three-dimensional finite element model of the post-tensioned prestressed concrete structure and anchor plate; considering the geometric size effect of the post-tensioned prestressed concrete structure and anchor plate, set multiple sets of size parameters, and simulate different arrangement conditions of the anchor plate along the beam height direction and beam width direction in the finite element model. (2.2) Apply prestressed load to the anchor plate and investigate the direction of maximum splitting stress in the anchorage zone of the post-tensioned prestressed concrete structure when the prestressed steel strands are anchored along the beam height and beam width directions through numerical simulation calculation. Step 3: Based on the actual direction of the axle crack and the anchoring method of the prestressed steel strand, qualitatively determine whether the maximum splitting stress is the dominant factor leading to cracking. (3.1) Cracks in the axilla area are divided into horizontal cracks and oblique cracks; When a horizontal crack appears in the axle area and the prestressed steel strands in the axle area are anchored along the beam width direction, based on the consistency between the crack morphology and the spatial stress direction, it is presumed that the maximum splitting stress along the beam height direction is the dominant factor causing cracking. (3.2) When a diagonal crack appears in the axle area, its morphological characteristics indicate the superposition of multidimensional stress fields; based on this, it is inferred that the diagonal crack is dominated by splitting stress along the beam height direction and along the beam width direction. Step 4: Based on the qualitative judgment results, calculate the maximum splitting stress and compare it with the tensile strength of concrete to quantitatively determine whether the cracking is caused by the maximum splitting stress. (4.1) In the modeling and analysis, the axle area is simplified into a regular cube structure, and the prestressed steel strand anchoring effect therein is equivalent to the concentric anchoring load acting on the cube structure. (4.2) For the case of horizontal cracks appearing in the axle area and the prestressed steel strands being anchored along the beam width direction, the maximum splitting stress is calculated using formula (9) and compared with the tensile strength of concrete; if the maximum splitting stress is greater than the tensile strength of concrete, it proves that there is a risk of cracking. (4.3) For the diagonal cracks that appear in the haunch area, it is necessary to calculate the maximum splitting stress along the beam height and beam width directions at the same time, and then calculate the principal tensile stress and compare it with the tensile strength of the concrete; if the principal tensile stress is greater than the tensile strength of the concrete, it proves that there is a risk of cracking.

Images