A discrete element-based method for simulating the crack propagation behavior of steel bridge deck pavement under dynamic water pressure

Abstract

The present invention provides a method for simulating the surface crack expansion behavior of a steel bridge deck pavement layer under the action of dynamic water pressure based on discrete elements. The specific steps of the method are: first, a discrete element model of an asphalt pavement layer of corresponding size and gradation is generated according to the research objective; second, corresponding micromechanical parameters are assigned to the generated coarse aggregate particle clusters and asphalt mortar particles according to the macroscopic mechanical properties; next, based on Darcy's law, the Fish language is used in PFC2D to realize the coupling effect between the fluid and the asphalt pavement layer, and the number of dynamic water scouring, the number and development path of crack development, and the number of normal and tangential damages of particle bonding are collected in real time during the simulation process. When the number of dynamic water scouring actions reaches the target value, the simulation is terminated and the data results are exported to analyze the micromechanism of the surface crack expansion of the steel bridge deck pavement layer under the action of dynamic water pressure.

Description

Technical Field

[0001] The invention belongs to the technical field of steel bridge deck pavement engineering, and in particular relates to a method for simulating the surface crack expansion behavior of a steel bridge deck pavement layer under the action of dynamic water pressure based on discrete elements. Background Art

[0002] Bridge deck crack disease is a typical disease form of steel bridge deck pavement at home and abroad. It destroys the integrity and continuity of the pavement structure, reduces the service life of the bridge, and causes adverse social and economic impacts. Especially in the rainy season in the south, rainwater enters through the cracks and accumulates in the pavement layer. Under the action of traffic load, dynamic water pressure is formed to scour the pavement layer, causing the asphalt mixture to peel off, the surface cracks to continue to expand, and even destroy the bridge deck waterproof bonding layer, causing external water to enter the steel plate surface layer, causing corrosion damage to the steel bridge deck. Therefore, it is very necessary to study the mesoscopic mechanism of surface crack expansion of steel bridge deck pavement under the action of dynamic water pressure.

[0003] At present, the finite element method is used to simulate the dynamic water pressure of steel bridge deck pavement. However, according to the mortar theory, the asphalt concrete pavement can be regarded as a three-phase composite material composed of asphalt mortar, aggregate and voids. The finite element method is difficult to simulate the interface shape of coarse aggregate and asphalt mortar in asphalt mixture, and is not suitable for dealing with rigid-flexible contact problems and simulating large deformation of materials. When using field tests or indoor tests for research, only macroscopic mechanical properties can be obtained, but it is impossible to deeply reveal the process of "cracking-extension-destruction" of surface cracks in the steel bridge deck pavement under the action of dynamic water pressure. The particle flow software PFC2D can not only present the trend and distribution of crack expansion, but also present the microscopic deformation inside the pavement material, and accurately study the influence of different microscopic structural characteristics on crack expansion. Therefore, PFC2D is more suitable for simulating the expansion process of surface cracks in the steel bridge deck pavement under the action of dynamic water scouring. Summary of the invention

[0004] Purpose of the invention: In view of the above problems, the present invention provides a method for simulating the surface crack propagation behavior of steel bridge deck pavement under dynamic water pressure based on discrete elements. In view of the shortcomings of existing macro-scale research on dynamic water pressure of steel bridge deck pavement, a method for studying the influence of dynamic water scouring on steel bridge deck pavement from a micro-scale is provided.

[0005] Technical solution: To achieve the purpose of the present invention, the technical solution adopted by the present invention is: a method for simulating the surface crack propagation behavior of a steel bridge deck pavement layer under the action of dynamic water pressure based on discrete elements, the method comprising the following steps:

[0006] Step 1: According to the gradation composition of the asphalt mixture, the Fish language is used to generate an irregular N-gon aggregate template with gradation characteristics, and the template is randomly placed in the preset steel bridge deck asphalt pavement layer discrete element model size area according to the gradation;

[0007] Step 2: Generate spherical particles of preset size arranged regularly and covering the entire area within the preset discrete element model size area of ​​the asphalt pavement layer, and determine the positional relationship between the spherical particles and the coarse aggregate template generated in step 1. If the center of the spherical particle is inside the coarse aggregate template, the spherical particle is regarded as a coarse aggregate particle, otherwise it is regarded as an asphalt mortar particle;

[0008] Step 3: According to the void ratio of the asphalt mixture, randomly delete the corresponding number of asphalt mortar particles as voids, delete a certain number of asphalt mortar particles on the upper surface to achieve surface cracks, and complete the establishment of the discrete element model of the asphalt pavement layer;

[0009] Step 4: For the asphalt pavement model generated in step 3, assign corresponding micromechanical parameters between the coarse aggregate particles and the asphalt mortar particles therein;

[0010] Step 5: Based on Darcy's law, the fluid-solid coupling algorithm is written in PFC2D using the Fish language to realize the interaction between the fluid and the asphalt mixture and simulate the dynamic water scouring behavior;

[0011] Step 6: During the simulation, the number of dynamic water scouring times, the number and path of crack development, and the number of normal and tangential damages of particle bonding are collected in real time. When the number of dynamic water scouring actions reaches the target value, the simulation is terminated and the data results are exported.

[0012] Furthermore, in step 1, first, the number of edges and the number of nodes N of the aggregate template are controlled by formula (1):

[0013] N=N mean +(2∈-1)×N increase (1)

[0014] Where N mean is the median of the number of edges of the aggregate; ∈ is a random number on (0, 1); N increase is the fluctuation range of the number of aggregate edges;

[0015] Secondly, the “ring method” and “extreme radius method” are used to construct irregular shaped aggregate templates. When generating aggregate templates of corresponding sizes according to the target gradation, the median R between the maximum and minimum values ​​of the gradation is mean As the reference radius, the difference between the maximum and minimum values ​​R increase As the basic radius fluctuation range, in order to avoid the generation of needle-like aggregates, the fluctuation range of aggregate particle size is constrained by formula (2), Rinner and R outer are the inner and outer radii of the “ring method”, and the radius R corresponding to the i-th node i The following equations (3) to (6) are used to achieve:

[0016]

[0017] R outer =R mean +R increase-half (3)

[0018] R inner =R mean -R increase-half (4)

[0019] ΔR=R outer -R inner (5)

[0020] R i =R inner +γ×ΔR (6)

[0021] Among them, λ and γ are random numbers on (0, 1); R increase-half is the fluctuation range of aggregate particle size after constraint, in m; ΔR is the difference between the inner and outer radii of the “ring method”, in m;

[0022] The angle θ between the polar radii i It is realized by formula (7):

[0023]

[0024] Where η is a random number on (0, 1); δ is the degree of fluctuation of the angle, which is no greater than 1;

[0025] The position of the centroid of a certain aggregate is controlled by the center of the ring, and the position of the center of the ring is determined by formula (8):

[0026]

[0027] Where (x0, y0) is the coordinate of the center of the ring; h and w are the height and width of the discrete element model of the asphalt pavement layer, respectively, in meters; ζ is a random number on (0,1);

[0028] The coordinates of the i-th vertex of a random N polygon (x i ,y i ) is determined by formula (9):

[0029]

[0030] Furthermore, in step 2, the radius of the generated spherical particles is a mm. According to the positional relationship between the spherical particles and the aggregate template in the region, the spherical particles whose center is located inside the template are regarded as coarse aggregate particles, and the spherical particles whose center is located outside the template are regarded as asphalt mortar particles.

[0031] Furthermore, in step 4, the contact constitutive models inside the coarse aggregate particles, inside the asphalt mortar particles, and between the coarse aggregate particles and the asphalt mortar particles all adopt the parallel bonding model.

[0032] Furthermore, in step 5, first, a fluid network is constructed inside the discrete element model of the asphalt pavement layer of the steel bridge deck, and the fluid network includes a flow domain and a fluid pipeline. The area surrounded by asphalt mortar particles and the area surrounded by asphalt mortar particles and coarse aggregate particles in the model are defined as a flow domain, and the fluid pipeline is the flow channel between two adjacent flow domains. Assuming that the fluid pipeline is perpendicular to the particle contact force line, the flow between them is expressed by formula (10):

[0033]

[0034] Where: q is the flow rate, unit is m 3 / s; a is the fluid pipeline opening, unit is m; k is the permeability coefficient, unit is m / s; Δp is the pressure difference between two adjacent basins, unit is MPa; L is the fluid pipeline length, unit is m;

[0035] Secondly, it is assumed that there is an initial fluid pipeline opening a0 between the two flow basins, so that fluid can still pass through when no microscopic cracks are generated in the model. When the contact force between particles on both sides of the fluid pipeline is compressive stress, the fluid pipeline opening a is determined by formula (11):

[0036]

[0037] Where, F is the compressive stress between particles on both sides of the fluid pipeline, unit N; F0 is the compressive stress when a0 is reduced to half, unit N;

[0038] When the particles on both sides of the fluid pipeline are subjected to tensile stress, or the bonding between the particles is broken, resulting in cracks, the fluid pipeline a is determined by formula (12):

[0039] a=a0+λ(d-R1-R2) (12)

[0040] Where, d is the distance between the centers of the two particles, in m; R1 and R2 are the radii of the two particles, in m; λ is a constant not greater than 1;

[0041] Next, assuming that there are n fluid pipelines around a flow area, the fluid pressure in the flow area is affected by the total flow rate of fluid exchange generated by the n fluid pipelines. In the Δt time step, the internal fluid pressure is determined by formula (13):

[0042]

[0043] In the formula, K f V is the fluid compression modulus, in MPa; d is the basin volume, in m 3 ; ΔV d is the change in basin volume, in m 3 ;∑q is the total flow rate of fluid in n pipelines, unit is m 3 / s.

[0044] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0045] The present invention provides a method for simulating the expansion behavior of surface cracks on the pavement layer of a steel bridge deck under the action of dynamic water pressure based on discrete elements. The influence of dynamic water pressure on the expansion of surface cracks on the pavement layer of a steel bridge deck under factors such as vehicle speeds and crack morphology is considered, and the expansion mechanism of surface cracks on the pavement layer is analyzed from a microscopic perspective, so as to track the development of damage more clearly. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flow chart for simulating the crack propagation behavior of the steel bridge deck pavement surface under the action of dynamic water pressure in an embodiment of the present invention;

[0047] Figure 2 Schematic diagram of an irregular N-sided aggregate template in an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of a template for generating coarse aggregates of different particle sizes in a given area in an embodiment of the present invention;

[0049] Figure 4 This is a schematic diagram of a cracked steel bridge deck pavement layer in an embodiment of the present invention;

[0050] Figure 5 Schematic diagram of fluid action in an embodiment of the present invention;

[0051] Figure 6 It is a schematic diagram of the expansion of surface cracks of the steel bridge deck pavement layer under the action of dynamic water pressure in an embodiment of the present invention;

[0052] Explanation of the reference numerals: 1-wall; 2-coarse aggregate formwork; 3-coarse aggregate particles; 4-asphalt mortar particles; 5-micro cracks. DETAILED DESCRIPTION

[0053] The present invention is further described in detail below through specific examples. The following examples are only illustrative and not restrictive, and the protection scope of the present invention cannot be limited thereto.

[0054] The present invention provides a method for simulating the surface crack propagation behavior of a steel bridge deck pavement layer under the action of dynamic water pressure based on discrete elements. The specific calculation steps are as follows:

[0055] Step 1: According to the gradation composition of asphalt mixture, aggregates with a particle size greater than 2.36 mm are regarded as coarse aggregates, and fine aggregates and asphalt with a particle size less than 2.36 mm are uniformly regarded as asphalt mortar. Fish language is used to generate irregular N-gon aggregate templates with gradation characteristics, and they are randomly generated in an area with a size of 200 mm × 60 mm;

[0056] Step 2: Generate spherical particles with a radius of 0.5 mm that are regularly arranged and spread over the entire area in the asphalt pavement area model of the coarse aggregate template, and determine the positional relationship between the spherical particles and the coarse aggregate template. If the center of the spherical particle is inside the coarse aggregate template, the spherical particle is regarded as a coarse aggregate particle, otherwise it is regarded as an asphalt mortar particle.

[0057] Step 3: According to the void ratio of the asphalt mixture, 206 asphalt mortar particles are randomly deleted as voids, and asphalt mortar particles within the range of 10 mm in length and 2 mm in width on the upper surface are deleted to realize surface cracks, thus completing the establishment of the discrete element model of the asphalt pavement layer;

[0058] Step 4: The contact constitutive model inside the coarse aggregate particles, inside the asphalt mortar particles, and between the coarse aggregate particles and the asphalt mortar particles all adopts the parallel bonding model;

[0059] Step 5: Based on Darcy's law, the fluid-solid coupling algorithm is written in PFC2D using the FISH language to realize the interaction between the fluid and the asphalt mixture. The initial fluid pressure is set according to the driving speed to simulate the dynamic water scouring behavior.

[0060] Step 6: During the simulation, the number of dynamic water scouring times, the number and path of crack development, and the number of normal and tangential damages of particle bonding are collected in real time. When the number of dynamic water scouring actions reaches the target value, the simulation is terminated and the data results are exported.

Claims

1. A method for simulating the surface crack propagation behavior of steel bridge deck pavement under dynamic water pressure based on discrete elements, characterized in that: The method comprises the following steps: Step 1: According to the gradation composition of the asphalt mixture, the Fish language is used to generate an irregular N-gon aggregate template with gradation characteristics, and the template is randomly placed in the preset steel bridge deck asphalt pavement layer discrete element model size area according to the gradation; Step 2: Generate spherical particles of preset size in a regularly arranged area within the preset discrete element model size area of ​​the asphalt pavement layer, and determine the positional relationship between the spherical particles and the coarse aggregate template generated in step 1. If the center of the spherical particle is inside the coarse aggregate template, the spherical particle is regarded as a coarse aggregate particle; otherwise, it is regarded as an asphalt mortar particle. Step 3: According to the void ratio of the asphalt mixture, randomly delete the corresponding number of asphalt mortar particles as voids, delete a certain number of asphalt mortar particles on the upper surface to achieve surface cracks, and complete the establishment of the discrete element model of the asphalt pavement layer; Step 4: For the asphalt pavement model generated in step 3, assign corresponding micromechanical parameters between the coarse aggregate particles and the asphalt mortar particles therein; Step 5: Based on Darcy's law, the fluid-solid coupling algorithm is written in PFC2D using the Fish language to realize the interaction between the fluid and the asphalt mixture and simulate the dynamic water scouring behavior; Step 6: During the simulation, the number of dynamic water scouring, the number and path of crack development, and the number of normal and tangential damages of particle bonding are collected in real time. When the number of dynamic water scouring reaches the target value, the simulation is terminated and the data results are exported; In step 5, first, a fluid network is constructed inside the discrete element model of the asphalt pavement layer of the steel bridge deck. The fluid network includes a flow domain and a fluid pipeline. The area surrounded by asphalt mortar particles and the area surrounded by asphalt mortar particles and coarse aggregate particles in the model are defined as a flow domain. The fluid pipeline is the flow channel between two adjacent flow domains. Assuming that the fluid pipeline is perpendicular to the particle contact force line, the flow rate between them is expressed by formula (10): Where: q is the flow rate, unit is m 3 / s; a is the fluid pipeline opening, unit is m; k is the permeability coefficient, unit is m / s; Δp is the pressure difference between two adjacent basins, unit is MPa; L is the fluid pipeline length, unit is m; Secondly, it is assumed that there is an initial fluid pipeline opening a0 between the two flow basins, so that fluid can still pass through when no micro-cracks are generated in the model. When the contact force between particles on both sides of the fluid pipeline is compressive stress, the fluid pipeline opening a is determined by formula (11): Where, F is the compressive stress between particles on both sides of the fluid pipeline, unit N; F0 is the compressive stress when a0 is reduced to half, unit N; When the particles on both sides of the fluid pipeline are subjected to tensile stress, or the bonding between the particles is broken, resulting in cracks, the fluid pipeline a is determined by formula (12): a=a0+λ(d-R1-R2) (12) Where, d is the distance between the centers of the two particles, in m; y1 and R2 are the radii of the two particles, in m; λ is a constant not greater than 1; Assuming that there are n fluid pipelines around a certain flow area, the fluid pressure in the flow area is affected by the total flow rate of fluid exchange generated by the n fluid pipelines. In the Δt time step, the internal fluid pressure is determined by formula (13): In the formula, K f V is the fluid compression modulus, in MPa; d is the basin volume, in m 3 ; ΔV d is the change in basin volume, in m 3 ;∑q is the total flow rate of fluid in n pipelines, unit is m 3 / s.

2. The method for simulating the surface crack propagation behavior of a steel bridge deck pavement under dynamic water pressure based on discrete elements according to claim 1 is characterized in that: In step 1, first, the number of edges and nodes N of the aggregate template is controlled by formula (1): N=N mean +(2∈-1)×N increase (1) Where N mean is the median of the number of edges of the aggregate; ∈ is a random number on (0,1); N increase is the fluctuation range of the number of aggregate edges; Secondly, the circular ring method and the polar radius method are used to construct the irregular shaped aggregate template. When the aggregate template of the corresponding size is generated according to the target gradation, the median value R between the maximum and minimum values ​​of the gradation is calculated. mean As the reference radius, the difference between the maximum and minimum values ​​R increase As the basic radius fluctuation range, in order to avoid the generation of needle-like aggregates, the fluctuation range of aggregate particle size is constrained by formula (2), R inner and R outer are the inner and outer radii of the ring method, and the radius R corresponding to the i-th node o The following equations (3) to (6) are used to achieve: R outer =R mean +R increase-half (3) R inner =R mean -R increase-half (4) ΔR= R outer -R inner (5) R i =R inner +γ×ΔR (6) Among them, λ and γ are random numbers on (0,1); R increase-half is the fluctuation range of aggregate particle size after constraint, in m; ΔR is the difference between the inner and outer radii of the ring method, in m; The angle θ between the polar radii i It is realized by formula (7): Where η is a random number on (0,1); δ is the degree of fluctuation of the angle, which is no greater than 1; The position of the centroid of a certain aggregate is controlled by the center of the ring, and the position of the center of the ring is determined by formula (8): Where (x0, y0) is the coordinate of the center of the ring; h and w are the height and width of the discrete element model of the asphalt pavement layer, respectively, in meters; ζ is a random number on (0,1); The coordinates of the i-th vertex of a random N polygon (x i ,y i ) is determined by formula (9):

3. The method for simulating the surface crack propagation behavior of a steel bridge deck pavement under dynamic water pressure based on discrete elements according to claim 1 is characterized in that: In step 2, the radius of the generated spherical particles is amm. According to the positional relationship between the spherical particles and the aggregate template in the region, the spherical particles whose center is located inside the template are regarded as coarse aggregate particles, and the spherical particles whose center is located outside the template are regarded as asphalt mortar particles.

4. The method for simulating the surface crack propagation behavior of a steel bridge deck pavement layer under dynamic water pressure based on discrete elements according to claim 1 is characterized in that: In step 4, the contact constitutive models inside the coarse aggregate particles, inside the asphalt mortar particles, and between the coarse aggregate particles and the asphalt mortar particles all adopt the parallel bonding model.

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