A high-sediment mountain torrent bridge damage evaluation method based on water-sand dynamics-finite element coupling

Abstract

The application discloses a high-silt mountain torrent bridge damage evaluation method based on water-sand dynamics-finite element coupling, which comprises the following steps: step 1, a water-sand water dynamics simulation model is established; step 2, the load time history acting on the bridge is calculated; step 3, a bridge finite element model is established; step 4, a damage evaluation index is calculated; and step 5, a damage grade is determined and the result is evaluated. The method realizes time-history coupling analysis of the water-sand dynamics model and the finite element model, accurately simulates time-varying characteristics of the mountain torrent load and cumulative effects of structural responses, comprehensively considers special action mechanisms of the high-silt mountain torrent, significantly improves load calculation precision, establishes a multi-dimensional damage evaluation index system comprising displacement, strength and stability, can comprehensively identify various damage modes, proposes a damage grade classification standard based on multi-index comprehensive determination, realizes scientific conversion from quantitative evaluation to qualitative classification, and provides definite basis for engineering decision-making.

Description

Technical Field

[0001] This invention belongs to the field of disaster prevention and mitigation engineering technology, and in particular relates to a method for assessing the damage of bridges with high sediment loads caused by mountain torrents based on hydrodynamic-finite element coupling. Background Technology

[0002] In recent years, influenced by global climate change, extreme rainfall events have become more frequent, and flash floods have become one of the major natural disasters threatening the safety of infrastructure in mountainous areas. Mountain floods are characterized by their sudden onset, high flow velocity, and high sediment content, often causing catastrophic damage to bridge structures. As a critical node in transportation networks, the safety of bridges under flash flood conditions directly affects the smooth flow of post-disaster rescue channels and regional economic losses. Existing methods for assessing bridge flood losses have the following main shortcomings:

[0003] (1) Most methods only consider hydrostatic pressure and ignore the dynamic effect of the high flow velocity and strong impact characteristics of flash floods on bridge structures.

[0004] (2) Most methods only consider the effect of clear water and ignore the high sediment content of mountain torrents, making it impossible to accurately assess the force of wide-grade sediment on bridge structures.

[0005] (3) The lack of probabilistic analysis of the bridge structure response, the failure to fully consider the impact of uncertainties such as material parameters, geometric dimensions, and boundary conditions on bridge damage, and the inability to accurately reflect the probability of bridge damage under different intensities of flash floods;

[0006] (4) Existing methods mostly use empirical formulas or simplified models, which are difficult to reflect the complex mechanical mechanism of the interaction between mountain torrents and bridges;

[0007] (5) Existing methods are difficult to give the probability of bridge failure under the action of flash floods of different intensities, and cannot provide probabilistic assessment results for risk decision-making.

[0008] Therefore, there is an urgent need to develop a loss assessment method that comprehensively considers the characteristics of flash floods, the response of bridge structures, and the probability of failure, in order to improve the accuracy and scientific nature of flash flood disaster risk assessment. Summary of the Invention

[0009] The purpose of this invention is to provide a method for assessing the damage of bridges with high sediment loads caused by mountain torrents based on hydrodynamic-finite element coupling. By coupling the hydrodynamic model and the finite element model, the method can accurately assess the damage level of the bridge.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] This invention discloses a method for assessing the damage of bridges with high sediment loads caused by mountain torrents based on hydrodynamic-finite element coupling. The method includes the following steps:

[0012] Step 1: Establish a hydrodynamic simulation model for water and sediment: Obtain topographic data, land use data, historical rainfall data, and sediment characteristic parameters of the target watershed; establish a hydrodynamic simulation model for water and sediment based on the shallow water equation and sediment transport equation; the shallow water equation includes the flow continuity equation and the flow momentum equation; set the parameters of the established hydrodynamic simulation model and solve it;

[0013] Step 2: Calculate the time history of loads acting on the bridge: Obtain bridge foundation data, including geometric dimensions, material properties, and pile depth; Based on the output of the hydrodynamic simulation model, extract the time history data of water depth, flow velocity, and sediment concentration at the bridge location, and calculate the time history of various loads acting on the bridge structure, including hydrostatic pressure, hydrodynamic pressure, sediment force, total horizontal load, and the height of the point of application of the total horizontal load;

[0014] The formula for calculating the hydrostatic pressure is:

[0015] (5)

[0016] In the formula: This refers to hydrostatic pressure, expressed in kN. ρ is the density of the water; h(t) is the water depth at the bridge location, in units of t / t. B represents the width of the pier body, in units of... ;

[0017] The formula for calculating the dynamic water pressure is:

[0018] (6)

[0019] In the formula: This refers to the dynamic water pressure, expressed in kN. The drag coefficient is 0.7 for circular piers and 1.4 for rectangular piers; The effective water-facing area is expressed in units of... ; , The locations of the bridges , directional flow velocity, in units of ;

[0020] The formula for calculating the sediment interaction force is:

[0021] (7)

[0022] in:

[0023] (8)

[0024] (9)

[0025] In the formula: This represents the force exerted by sediment, measured in kN. This represents the static pressure increment, in kN. This refers to the dynamic impact force, measured in kN. For the density of the mixed fluid; The concentration of sediment; The impact coefficient is determined based on the shape of the pier: 0.1 to 0.15 for circular or elliptical piers, 0.25 to 0.3 for rectangular piers, and 0.05 to 0.1 for pointed piers. The density of the sediment is taken as 2650 kg / m³.

[0026] The formula for calculating the total horizontal load is as follows:

[0027] (10)

[0028] In the formula: Total horizontal load, in kN;

[0029] The formula for calculating the height of the total horizontal load is:

[0030] (11)

[0031] In the formula: The height of the point of application of the total horizontal load, in meters; , is the height of the point of application of hydrostatic pressure; , is the height of the point of application of dynamic water pressure and sediment impact force;

[0032] Step 3: Establish the bridge finite element model: Based on the obtained bridge foundation data, establish the bridge finite element model and extract the finite element analysis results, including displacement results, internal force results, stress results, and support reactions.

[0033] The displacement results include the horizontal displacement of the pier top node. Vertical displacement The internal force results include the bending moment at the pier bottom section. pier bottom shear force Axial force at the bottom of the pier The stress results include the maximum compressive stress in the concrete. Reinforcing steel stress The support reaction forces include the vertical reaction forces of each support. , i is the support variable, and m is the number of supports;

[0034] Step 4: Calculate failure evaluation indices: Based on the finite element output results and load information, calculate the failure indices at each time point, including displacement indices, strength indices, and stability indices.

[0035] The displacement indicators include the pier top displacement angle. The calculation formula is as follows:

[0036] (12)

[0037] In the formula: H is the pier height;

[0038] The strength indicators include the cross-sectional bearing capacity ratio. Concrete stress ratio Reinforcing steel stress ratio ;

[0039] The formula for calculating the cross-sectional bearing capacity ratio is:

[0040] (13)

[0041] In the formula: The ultimate bending moment bearing capacity is calculated according to the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG 3362).

[0042] The formula for calculating the concrete stress ratio is:

[0043] (14)

[0044] In the formula: The design value of the axial compressive strength of concrete, in MPa, is determined according to the concrete strength grade in the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG 3362).

[0045] The formula for calculating the stress ratio of steel reinforcement is:

[0046] (15)

[0047] In the formula: This is the design value of the tensile strength of the reinforcing steel, in MPa. For HRB400 reinforcing steel, the value is... MPa;

[0048] The stability index includes the overturning stability coefficient. , minimum support reaction force ;

[0049] The formula for calculating the overturning stability coefficient is:

[0050] (16)

[0051] (17)

[0052] (18)

[0053] In the formula: The overturning stability coefficient is dimensionless. The overturning moment is expressed in kN·m. G is the overturning moment, in kN·m; G is the self-weight of the superstructure, in kN. The horizontal distance from the center of gravity of the superstructure to the overturning point at the bottom of the pier, in meters; The axial force at the bottom of the pier is expressed in kN.

[0054] The formula for calculating the minimum support reaction force is:

[0055] (19)

[0056] when When the support is dislodged, it indicates that the support has come out of place.

[0057] Step 5: Determine the damage level and evaluate the results: First, determine the instantaneous damage level, that is, for time t, determine the instantaneous damage level corresponding to each indicator based on the judgment criteria according to the value of each indicator.

[0058] Then, a comprehensive damage level assessment is performed, that is, the worst-case scenario principle is adopted, and the maximum instantaneous damage level corresponding to each index at time t is taken as the damage level at that time. :

[0059] (20)

[0060] Finally, the final damage level is determined by taking the maximum damage level at all times throughout the entire flood event. :

[0061] (twenty one)

[0062] Based on the final damage level The safety status of the bridge is assessed and corresponding engineering solutions are proposed.

[0063] Furthermore, the water flow continuity equation mentioned in step 1 is:

[0064] (1)

[0065] The water flow equation is:

[0066] (2)

[0067] (3)

[0068] The sediment transport equation is as follows:

[0069] Considering the wide gradation characteristics of mountain torrent sediment, the sediment is divided into different categories according to particle size. Particle size groups ( Sediment transport equations for each particle size group were established respectively:

[0070] (4)

[0071] In the formula: For water depth, in units ; , They are respectively , Directional flow velocity, unit ; It is the acceleration due to gravity; Riverbed elevation, unit: , They are respectively , Shear stress on the bed surface in the direction of the stress, in units ρ is the density of water, in units of... ; For the first Sediment concentration in particle size group, dimensionless; , The first Particle size group scour and sedimentation rate, in units .

[0072] Furthermore, the specific process of setting parameters and solving the established hydrodynamic simulation model in step 1 is as follows:

[0073] (1) Computational area and grid division: The computational area is determined according to the target watershed range. Unstructured triangular grids or structured rectangular grids are used for spatial discretization. The grid size is determined according to the complexity of the terrain and the accuracy requirements of the calculation, and is taken as 5 to 20m.

[0074] (2) Roughness parameter setting: Determine the Manning roughness coefficient according to the land use type. The main channel should be 0.03–0.05, the beach area 0.05–0.08, and the building area 0.08–0.15.

[0075] (3) Sediment particle size grouping: Determine the representative particle size of each particle size group based on the characteristics of sediment in the watershed. It is divided into clay ( mm), silt ( mm), fine sand ( mm), gravel ( mm) group;

[0076] (4) Boundary condition setting: The upstream boundary input is based on the inflow process line derived from the measured or designed rainfall process, and the downstream boundary is set as a water level boundary or a free outflow boundary according to the actual situation;

[0077] (5) Simulation duration setting: Covers the entire process from the rise of the flood to its receding;

[0078] Then, by numerically solving the system of equations, the spatiotemporal distribution of various physical quantities under flash flood conditions with different return periods is obtained, including water depth, flow velocity, and sediment concentration.

[0079] Furthermore, the specific process of establishing the bridge finite element model described in step 3 includes:

[0080] (1) Model building: A numerical model of the bridge was built using commercial finite element software:

[0081] Main beam: Beam element, defining section properties and prestress;

[0082] Bridge piers: fiber beam units or solid units, with reinforcement considered;

[0083] Pile foundation: Beam unit combined with soil spring;

[0084] Support: Nonlinear connection element, defining friction and separation characteristics - Material constitutive model: Concrete adopts a nonlinear model considering cracking and crushing, and steel reinforcement adopts a bilinear elastoplastic model;

[0085] (2) Model input parameter settings:

[0086] Geometric parameters: bridge span L, pier height H, pier diameter D or pier width B, wall thickness;

[0087] Material parameters: Concrete strength grade C30~C50, steel reinforcement HRB400;

[0088] Load input: The load calculated in step 2 According to the height of action Applied to bridge piers;

[0089] Boundary conditions: Pier base consolidation or pile-soil interaction considerations;

[0090] (3) Analysis settings:

[0091] Analysis type: Nonlinear time history analysis;

[0092] Step size: Determined based on the rate of load change, ranging from 10 to 60 seconds;

[0093] Total duration: t ∈ [0, tf ], covering the entire flood process, including This represents the total duration of the flood event.

[0094] Solution settings: Enable large deformation and consider the P-Δ effect; the P-Δ effect refers to the additional bending moment effect of the vertical load on the structure after the structure has undergone lateral displacement under horizontal load.

[0095] The extraction of finite element analysis results specifically involves the finite element software automatically calculating the structural response at each time step by solving the structural dynamics equations based on the input load time history and structural model.

[0096] Furthermore, the judgment criteria mentioned in step 5 are as follows:

[0097] For the pier top displacement angle :when At that time, Level I; when At that time, Level II; when At that time, Level III; when At that time, it was Level IV;

[0098] For the cross-sectional bearing capacity ratio :when At that time, Level I; when At that time, Level II; when At that time, Level III; when At that time, it was Level IV;

[0099] For concrete stress ratio :when At that time, Level I; when At that time, Level II; when At that time, Level III; when At that time, it was Level IV;

[0100] For steel reinforcement stress ratio :when At that time, Level I; when At that time, Level II; when At that time, Level III; when At that time, it was Level IV;

[0101] For overturning stability coefficient :when At that time, Level I; when At that time, Level II; when At that time, Level III; when At that time, it was Level IV;

[0102] For the minimum support reaction force :when At that time, Level I; when At that time, it was classified as Level IV.

[0103] The beneficial effects of this invention are as follows: The method described in this invention realizes the time-history coupling analysis of the hydrodynamic model and the finite element model, accurately simulating the time-varying characteristics of flash flood loads and the cumulative effect of structural response; it comprehensively considers the special action mechanism of high sediment load flash floods, including the additional static pressure and dynamic impact effect caused by sediment, significantly improving the accuracy of load calculation; it establishes a multi-dimensional failure evaluation index system including displacement, strength, and stability, especially the overturning stability coefficient and support reaction force index, which can comprehensively identify various failure modes; it proposes a failure level classification standard based on multi-index comprehensive judgment, realizing the scientific transformation from quantitative assessment to qualitative classification, providing a clear basis for engineering decision-making; it has strong operability, is easy to promote and apply in actual engineering, and provides a scientific reference for post-disaster emergency response and bridge repair decision-making.

[0104] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0105] Figure 1 This is a schematic diagram of the method flow described in this invention. Detailed Implementation

[0106] This invention discloses a method for assessing the damage of bridges with high sediment loads caused by mountain torrents based on hydrodynamic-finite element coupling, such as... Figure 1 As shown, the method includes the following steps:

[0107] Step 1: Establish a hydrodynamic simulation model of water and sediment: Obtain topographic data, land use data, historical rainfall data, and sediment characteristic parameters of the target watershed; establish a hydrodynamic simulation model of water and sediment based on shallow water equations (including the continuity equation of water flow and the flow momentum equation) and sediment transport equation; then set the parameters of the established hydrodynamic simulation model of water and sediment and solve it.

[0108] The continuity equation for water flow is:

[0109] (1)

[0110] The equation for water flow is:

[0111] (2)

[0112] (3)

[0113] The sediment transport equation is as follows: Considering the wide gradation characteristics of mountain torrent sediment, the sediment is divided into different particle sizes. Particle size groups ( Sediment transport equations for each particle size group were established respectively:

[0114] (4)

[0115] In the formula: For water depth, in units ; , They are respectively , Directional flow velocity, unit ; It is the acceleration due to gravity; Riverbed elevation, unit: , They are respectively , Shear stress on the bed surface in the direction of the stress, in units ρ is the density of water, in units of... ; For the first Sediment concentration in particle size group, dimensionless; , The first Particle size group scour and sedimentation rate, in units .

[0116] Parameter settings are configured for the established hydrodynamic simulation model of water and sediment:

[0117] (1) Computational area and grid division: The computational area is determined according to the target watershed range. Unstructured triangular grids or structured rectangular grids are used for spatial discretization. The grid size is determined according to the complexity of the terrain and the accuracy requirements of the calculation, and is generally 5 to 20 m.

[0118] (2) Roughness parameter setting: Determine the Manning roughness coefficient according to the land use type. The main channel is generally 0.03 to 0.05, the beach area is generally 0.05 to 0.08, and the construction area is 0.08 to 0.15.

[0119] (3) Sediment particle size grouping: Determine the representative particle size of each particle size group based on the characteristics of sediment in the watershed. Generally, it can be divided into clay ( mm), silt ( mm), fine sand ( mm), gravel ( Groups such as mm);

[0120] (4) Boundary condition setting: The upstream boundary input is based on the inflow process line derived from the measured or designed rainfall process, and the downstream boundary is set as a water level boundary or a free outflow boundary according to the actual situation;

[0121] (5) Simulation duration setting: It should cover the entire process from the rise of the flood to the receding of the flood.

[0122] By numerically solving the above set of equations, the spatiotemporal distributions of various physical quantities under flash flood conditions with different return periods were obtained. Since the above set of equations describes a two-dimensional unsteady flow problem, the water depth in the solution results is... Flow rate and Sediment concentration Both are spatial coordinates (x, y) and time. The function, i.e. , , , .

[0123] Step 2: Calculate the time history of loads acting on the bridge: Obtain bridge foundation data, including geometric dimensions, material properties, pile depth, etc. Based on the output of the hydrodynamic simulation model, extract the location of the bridge. Time-history data of water depth, flow velocity, and sediment concentration at the location. Since the bridge site coordinates are already determined, they will be abbreviated below. , , , Then, calculate the time histories of various loads acting on the bridge structure, including hydrostatic pressure, hydrodynamic pressure, sediment force, total horizontal load, and the height of the point of application of the total horizontal load.

[0124] (1) The formula for calculating hydrostatic pressure is:

[0125] (5)

[0126] In the formula: This refers to hydrostatic pressure, expressed in kN. ρ is the density of the water; h(t) is the water depth at the bridge location, in units of t / t. B represents the width of the pier body, in units of... .

[0127] (2) The formula for calculating dynamic water pressure is:

[0128] (6)

[0129] In the formula: This refers to the dynamic water pressure, expressed in kN. The drag coefficient is 0.7 for circular piers and 1.4 for rectangular piers; The effective water-facing area is expressed in units of... ; , The locations of the bridges , directional flow velocity, in units of .

[0130] (3) The formula for calculating the force of sediment is:

[0131] (7)

[0132] In the formula: This represents the force exerted by sediment, measured in kN. This represents the static pressure increment, in kN. This refers to the dynamic impact force, measured in kN.

[0133] The formula for calculating the static pressure increment is:

[0134] (8)

[0135] The formula for calculating dynamic impact force is:

[0136] (9)

[0137] In the formula: For the density of the mixed fluid; The concentration of sediment; The impact coefficient is determined based on the shape of the pier: 0.1 to 0.15 for circular or elliptical piers, 0.25 to 0.3 for rectangular piers, and 0.05 to 0.1 for pointed piers. The density of the sediment is taken as 2650 kg / m³.

[0138] (4) The formula for calculating the total horizontal load is:

[0139] (10)

[0140] In the formula: This represents the total horizontal load, expressed in kN.

[0141] (5) The height of the total horizontal load application point is: the height of the hydrostatic pressure application point. Height of the point of application of hydrodynamic pressure and sediment impact force The height of the resultant force's point of application, which is also the height of the total horizontal load's point of application, is:

[0142] (11)

[0143] In the formula: The height of the point of application of the total horizontal load is in meters (m).

[0144] Step 3: Establish the bridge finite element model: Based on the acquired bridge foundation data, establish the bridge finite element model and extract the finite element analysis results. This specifically includes the following steps:

[0145] (1) Model building: A numerical model of the bridge was built using commercial finite element software (MIDAS Civil, SAP2000 or ABAQUS):

[0146] Main beam: Beam element, defining section properties and prestress;

[0147] Bridge piers: fiber beam units or solid units, with reinforcement considered;

[0148] Pile foundation: Beam element combined with soil spring (py curve method);

[0149] Support: Nonlinear connection element, defining friction and separation characteristics - Material constitutive model: Concrete adopts a nonlinear model considering cracking and crushing, and steel reinforcement adopts a bilinear elastoplastic model.

[0150] (2) Model input parameters:

[0151] Geometric parameters: bridge span L, pier height H, pier diameter D or pier width B, wall thickness (for hollow piers).

[0152] Material parameters: Concrete strength grade C30~C50, steel reinforcement HRB400;

[0153] Load input: The load calculated in step 2 According to the height of action Applied to bridge piers;

[0154] Boundary conditions: pier base consolidation or pile-soil interaction considerations.

[0155] (3) Analysis settings:

[0156] Analysis type: Nonlinear time history analysis;

[0157] Step size: The value is determined based on the rate of change of the load, and is generally taken as 10 to 60 seconds.

[0158] Total duration: t ∈ [0, t f ], covering the entire flood process, including The total duration of the flood event is expressed in seconds (s).

[0159] Solution settings: Enable large deformation and consider the P-Δ effect. The P-Δ effect refers to the additional bending moment effect of the vertical load on the structure after the structure has undergone lateral displacement under horizontal load. It has an important impact on the response analysis of high-pier bridges under flash floods.

[0160] (4) Extracting Finite Element Analysis Results: Based on the input load time history and structural model, the finite element software automatically calculates the structural response at each time step by solving the structural dynamics equations. The following time history results are extracted from the finite element software:

[0161] Displacement results: Horizontal displacement of the pier top node Vertical displacement ;

[0162] Internal force results: Bending moment at the pier base section pier bottom shear force Axial force at the bottom of the pier ;

[0163] Stress results: Maximum compressive stress in concrete Reinforcing steel stress ;

[0164] Support reactions: Vertical reactions at each support , , where i is the support variable and m is the number of supports.

[0165] Step 4: Calculate the failure evaluation index: Based on the finite element output results and load information, calculate the failure index at each time step:

[0166] (1) Displacement indicators: including pier top displacement angle The calculation formula is:

[0167] (12)

[0168] In the formula: H is the pier height.

[0169] (2) Strength-related indicators: including the cross-sectional bearing capacity ratio Concrete stress ratio Reinforcing steel stress ratio ;

[0170] The formula for calculating the cross-sectional bearing capacity ratio is as follows:

[0171] (13)

[0172] In the formula: The ultimate bending moment bearing capacity is calculated according to the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG 3362).

[0173] The formula for calculating the concrete stress ratio is:

[0174] (14)

[0175] In the formula: This is the design value of the axial compressive strength of concrete, in MPa, determined according to the concrete strength grade in the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG 3362).

[0176] The formula for calculating the stress ratio of steel reinforcement is:

[0177] (15)

[0178] In the formula: This is the design value of the tensile strength of the reinforcing steel, in MPa. For HRB400 reinforcing steel, the value is... MPa.

[0179] (3) Stability indicators: including overturning stability coefficient , minimum support reaction force ;

[0180] The formula for calculating the overturning stability coefficient is as follows:

[0181] (16)

[0182] (17)

[0183] (18)

[0184] In the formula: The overturning stability coefficient is dimensionless. The overturning moment is expressed in kN·m. G is the overturning moment, in kN·m; G is the self-weight of the superstructure, in kN. The horizontal distance from the center of gravity of the superstructure to the overturning point at the bottom of the pier, in meters; This represents the axial force at the bottom of the pier, expressed in kN.

[0185] The formula for calculating the minimum support reaction force is:

[0186] (19)

[0187] when When the support is detached, it indicates that the support has come out of the air.

[0188] Step 5: Determine the level of damage and assess the results: This includes the following process:

[0189] (1) Instantaneous damage level determination: For time t, the instantaneous damage level corresponding to each index is determined based on the index value. The determination criteria are shown in the table below:

[0190] Table 1

[0191]

[0192] It should be noted that the minimum support reaction force As a binary state index, support detachment indicates severe structural failure; therefore, levels II and III are not specified. Additionally, when... At that time, although the indicator was judged as Level I, the final damage level of the structure was determined according to the comprehensive judgment principle, taking the maximum value of the corresponding levels of all indicators, which may be Level I, Level II, Level III or Level IV.

[0193] (2) Comprehensive determination of damage level: The worst-case scenario principle is adopted, and the maximum value of the instantaneous damage level corresponding to each index at time t is taken as the damage level at that time. :

[0194] (20)

[0195] For example, a bridge is classified as Class I (basically intact) only when all indicators meet the Class I standard; when any indicator reaches a higher level of damage, the overall damage level of the bridge is increased accordingly, reflecting the worst-case scenario principle of structural safety assessment.

[0196] (3) Determination of final damage level: The maximum value of the damage level at all times during the entire duration of the flood process shall be taken as the final damage level. :

[0197] (twenty one)

[0198] The threshold values ​​for each indicator in the above-mentioned damage level determination criteria (such as...) The threshold values ​​(1 / 250, 1 / 100, 1 / 50, etc.) can be adjusted according to the importance of the bridge: For Class I highway bridges, the threshold values ​​for each displacement and stress index are reduced by 20% (i.e., the safety requirements are more stringent, for example, the displacement angle boundary between Class I and Class II is adjusted from 1 / 250 to 1 / 312), and the threshold values ​​for stability indexes are increased by 20%; for Class IV highway bridges, the threshold values ​​for each displacement and stress index can be increased by 20%, and the threshold values ​​for stability indexes can be reduced by 20%.

[0199] Simultaneously record key moments:

[0200] The moment of first injury:

[0201] When the final destruction level is reached:

[0202] Destructive evolution timeline: .

[0203] (4) Result assessment: based on the final damage level The safety status of the bridge was assessed and corresponding engineering recommendations were proposed.

[0204] Level I: Continue monitoring and conduct routine inspections after the flood season;

[0205] Level II: Strengthen monitoring, conduct detailed inspections after the flood season, and implement necessary repairs;

[0206] Level III: Immediately close traffic, conduct a comprehensive inspection and assessment after the flood season, and formulate a reinforcement plan;

[0207] Level IV: Immediately close traffic and establish a warning zone; assess the necessity of demolition and reconstruction.

[0208] Example 1

[0209] This embodiment is an application example of the above method.

[0210] In 2023, a mountainous area in a certain province experienced an exceptionally heavy rainstorm. Within a certain county, a river basin recorded a cumulative rainfall of 238 mm in 6 hours, triggering a major flash flood and debris flow disaster. This example selects a highway bridge within this river basin as the evaluation object. The bridge is a three-span continuous beam bridge spanning the river, and its basic parameters are as follows:

[0211] Table 2

[0212]

[0213] This embodiment discloses a method for assessing the damage of bridges with high sediment loads caused by mountain torrents based on hydrodynamic-finite element coupling, including the following steps:

[0214] Step 1: Establish a hydrodynamic simulation model for water and sediment: Based on the 30m resolution DEM data and land use data of the watershed, establish a two-dimensional coupled water and sediment model. The main parameters of the model are set as follows:

[0215] Calculation area: Upstream catchment area approximately 85 km²;

[0216] Mesh size: 10m × 10m unstructured triangular mesh;

[0217] Manning roughness coefficient: main channel n=0.035, beach n=0.06;

[0218] Sediment particle size group: d1=0.01mm (clay), d2=0.1mm (silt), d3=1mm (fine sand), d4=10mm (gravel);

[0219] Input boundary: Inflow process line based on measured rainfall events;

[0220] Simulation duration: 12 hours (07:00-19:00);

[0221] Simulation results show that the flood peak arrived at the bridge site at 14:30. The time histories of the main water and sediment characteristic parameters are shown in the table below:

[0222] Table 3

[0223]

[0224] Step 2: Calculate the load time history acting on the bridge: Taking the flood peak time (14:30) as an example, calculate the various loads acting on the bridge piers:

[0225] (1) Basic parameters:

[0226] , , ;

[0227] (Volume sand content);

[0228] (Drum width) = 1000 kg / m³, = 2650 kg / m³;

[0229] (Rectangular pier) = 0.3 (rectangular pier).

[0230] (2) Hydrostatic pressure:

[0231] .

[0232] (3) Dynamic water pressure:

[0233] ;

[0234] ;

[0235] .

[0236] (4) Sediment action force:

[0237] Mixed fluid density:

[0238] Static pressure increment:

[0239] Dynamic impact force: ;

[0240] Sediment force: .

[0241] (5) Total horizontal load:

[0242]

[0243] (6) Height of the point of application of the total horizontal load:

[0244]

[0245] .

[0246] Step 3: Establish the finite element model of the bridge:

[0247] Main girder: Simulated using beam elements, the section properties of the prestressed concrete box girder are defined as follows: section area A = 5.2 m², bending moment of inertia I = 3.8 m. 4 ;

[0248] Bridge piers: Utilize fiber beam elements, divided into 20 elements;

[0249] Pile foundation: Simulated using beam elements + m-method soil springs;

[0250] Support: Employs elastic connection units, taking frictional characteristics into account;

[0251] Material constitutive model: The Mander constitutive model was used for concrete, and the design value of the compressive strength of C40 concrete was [not specified]. =26.8 MPa; The reinforcement adopts a bilinear model, and the yield strength of HRB400 reinforcement is... =400 MPa;

[0252] Load application: Apply the load time history calculated in step 2. According to the height of action Applied to bridge piers;

[0253] Analysis settings: Time step =60s, analysis duration 12 hours (covering the entire flood process), enable the large deformation option, and consider the P-Δ effect.

[0254] Key output results of finite element analysis at the peak of the flood (14:30):

[0255] Table 4

[0256]

[0257] Step 4: Calculate the failure evaluation index: Calculate the bearing capacity parameters based on the specifications.

[0258] C40 concrete: =26.8 MPa; Reinforcing steel HRB400: =400 MPa;

[0259] Calculate the ultimate bending moment bearing capacity according to the "Design Specifications for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts":

[0260] Superstructure self-weight: The horizontal distance from the center of gravity to the overturning point at the bottom of the pier: ;

[0261] Calculation results of various destructive indicators at the peak of the flood:

[0262] Table 5

[0263]

[0264] The calculation process for the overturning stability coefficient is as follows:

[0265]

[0266]

[0267] .

[0268] Step 5: Determine the level of damage and assess the results:

[0269] (1) Instantaneous damage level determination: Based on the calculated values ​​of each indicator at the flood peak, the damage level corresponding to each indicator is determined according to the damage level determination criteria, as shown in the table below:

[0270] Table 6

[0271]

[0272] (2) Comprehensive determination of damage level: Based on the worst-case scenario principle, the maximum value of the corresponding level for each indicator is taken:

[0273] = max{II, III, III, III, I, I} = Level III.

[0274] (3) Final level of damage: Based on the full-time analysis, the maximum level of damage occurred at the peak of the flood at 14:30:

[0275] = Level III.

[0276] Record key moments:

[0277] The moment of first injury: = 13:15 );

[0278] When the final destruction level is reached: = 14:30;

[0279] Duration of destructive evolution: ΔT = 1 hour 15 minutes.

[0280] (4) Result assessment: The bridge reached a level III damage state under the impact of the "7.15" catastrophic flash flood, specifically manifested as follows:

[0281] The concrete stress ratio reached 0.851, close to the compressive strength limit, and crushing may occur in some areas; the steel reinforcement stress reached 96.3% of the yield strength, and was in the critical yield state; the pier top displacement angle reached 1 / 175, and there was obvious residual deformation; the overturning stability coefficient was 3.19, which met the stability requirements.

[0282] Recommendations for handling the project:

[0283] Immediately close traffic: prohibit all vehicles and pedestrians from passing through;

[0284] Comprehensive inspection: A detailed inspection will be conducted immediately after the flood recedes, with a focus on checking for cracks in the pier body, corrosion of the reinforcing bars, and the condition of the supports;

[0285] Develop a reinforcement plan: Based on the test results, measures such as pier reinforcement (increasing the cross-section or bonding carbon fiber) and bearing replacement may be required.

[0286] Long-term monitoring: Deformation monitoring points are set up after reinforcement for long-term tracking and observation.

[0287] This embodiment fully demonstrates the entire process of assessing bridge damage under high-sediment-laden flash floods using a hydrodynamic-finite element coupled method. This method accurately simulates the spatiotemporal evolution characteristics of flash floods, obtaining the time histories of water depth, flow velocity, and sediment concentration at the bridge site; comprehensively considers the combined effects of hydrostatic pressure, hydrodynamic pressure, and sediment force, with the total horizontal load reaching 857.4 kN at the peak flood; obtains the dynamic evolution process of the structural response through finite element time history analysis; accurately identifies excessive concrete stress as the primary control failure mode based on a multi-dimensional failure index system; and ultimately determines the bridge failure level to be Level III, providing clear engineering treatment recommendations.

[0288] Finally, it should be noted that the above description is only used to illustrate the technical solution of the present invention and not to limit it. Although the present invention has been described in detail with reference to the preferred arrangement, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for assessing the damage of bridges with high sediment loads due to mountain torrents based on hydrodynamic-finite element coupling, characterized in that, The method includes the following steps: Step 1: Establish a hydrodynamic simulation model for water and sediment: Obtain topographic data, land use data, historical rainfall data, and sediment characteristic parameters of the target watershed; establish a hydrodynamic simulation model for water and sediment based on the shallow water equation and sediment transport equation; the shallow water equation includes the flow continuity equation and the flow momentum equation; set the parameters of the established hydrodynamic simulation model and solve it; Step 2: Calculate the time history of loads acting on the bridge: Obtain bridge foundation data, including geometric dimensions, material properties, and pile depth; Based on the output of the hydrodynamic simulation model, extract the time history data of water depth, flow velocity, and sediment concentration at the bridge location, and calculate the time history of various loads acting on the bridge structure, including hydrostatic pressure, hydrodynamic pressure, sediment force, total horizontal load, and the height of the point of application of the total horizontal load; The formula for calculating the hydrostatic pressure is: （5） In the formula: This refers to hydrostatic pressure, expressed in kN. ρ is the density of the water; h(t) is the water depth at the bridge location, in units of t / t. B represents the width of the pier body, in units of... ; The formula for calculating the dynamic water pressure is: （6） In the formula: This refers to the dynamic water pressure, expressed in kN. The drag coefficient is 0.7 for circular piers and 1.4 for rectangular piers; The effective water-facing area is expressed in units of... ; , The locations of the bridges , directional flow velocity, in units of ; The formula for calculating the sediment interaction force is: （7） in: （8） （9） In the formula: This represents the force exerted by sediment, measured in kN. This represents the static pressure increment, in kN. This refers to the dynamic impact force, measured in kN. For the density of the mixed fluid; The concentration of sediment; The impact coefficient is determined based on the shape of the pier: 0.1 to 0.15 for circular or elliptical piers, 0.25 to 0.3 for rectangular piers, and 0.05 to 0.1 for pointed piers. The density of the sediment is taken as 2650 kg / m³. The formula for calculating the total horizontal load is as follows: （10） In the formula: Total horizontal load, in kN; The formula for calculating the height of the total horizontal load is: （11） In the formula: The height of the point of application of the total horizontal load, in meters; , is the height of the point of application of hydrostatic pressure; , is the height of the point of application of dynamic water pressure and sediment impact force; Step 3: Establish the bridge finite element model: Based on the obtained bridge foundation data, establish the bridge finite element model and extract the finite element analysis results, including displacement results, internal force results, stress results, and support reactions. The displacement results include the horizontal displacement of the pier top node. Vertical displacement The internal force results include the bending moment at the pier bottom section. pier bottom shear force Axial force at the bottom of the pier The stress results include the maximum compressive stress in the concrete. Reinforcing steel stress The support reaction forces include the vertical reaction forces of each support. , i is the support variable, and m is the number of supports; Step 4: Calculate failure evaluation indices: Based on the finite element output results and load information, calculate the failure indices at each time point, including displacement indices, strength indices, and stability indices. The displacement indicators include the pier top displacement angle. The calculation formula is as follows: （12） In the formula: H is the pier height; The strength indicators include the cross-sectional bearing capacity ratio. Concrete stress ratio Reinforcing steel stress ratio ; The formula for calculating the cross-sectional bearing capacity ratio is: （13） In the formula: The ultimate bending moment bearing capacity is calculated according to the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG3362). The formula for calculating the concrete stress ratio is: （14） In the formula: The design value of the axial compressive strength of concrete, in MPa, is determined according to the concrete strength grade in the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG 3362). The formula for calculating the stress ratio of steel reinforcement is: （15） In the formula: This is the design value of the tensile strength of the reinforcing steel, in MPa. For HRB400 reinforcing steel, the value is... MPa; The stability index includes the overturning stability coefficient. , minimum support reaction force ; The formula for calculating the overturning stability coefficient is: （16） （17） （18） In the formula: The overturning stability coefficient is dimensionless. The overturning moment is expressed in kN·m. G is the overturning moment, in kN·m; G is the self-weight of the superstructure, in kN. The horizontal distance from the center of gravity of the superstructure to the overturning point at the bottom of the pier, in meters; The axial force at the bottom of the pier is expressed in kN. The formula for calculating the minimum support reaction force is: （19） when When the support is dislodged, it indicates that the support has come out of place. Step 5: Determine the damage level and evaluate the results: First, determine the instantaneous damage level, that is, for time t, determine the instantaneous damage level corresponding to each indicator based on the judgment criteria according to the value of each indicator. Then, a comprehensive damage level assessment is performed, that is, the worst-case scenario principle is adopted, and the maximum instantaneous damage level corresponding to each index at time t is taken as the damage level at that time. : （20） Finally, the final damage level is determined by taking the maximum damage level at all times throughout the entire flood event. : （21） Based on the final damage level The safety status of the bridge is assessed and corresponding engineering solutions are proposed.

2. The method for assessing the damage of bridges with high sediment loads due to mountain torrents based on hydrodynamic-finite element coupling as described in claim 1, characterized in that, The continuity equation for the water flow mentioned in step 1 is: （1） The water flow equation is: （2） （3） The sediment transport equation is as follows: Considering the wide gradation characteristics of mountain torrent sediment, the sediment is divided into different categories according to particle size. Particle size groups ( Sediment transport equations for each particle size group were established respectively: （4） In the formula: For water depth, in units ; , They are respectively , Directional flow velocity, unit ; It is the acceleration due to gravity; Riverbed elevation, unit: , They are respectively , Shear stress on the bed surface in the direction of the stress, in units ρ is the density of water, in units of... ; For the first Sediment concentration in particle size group, dimensionless; , The first Particle size group scour and sedimentation rate, in units .

3. The method for assessing the damage of bridges with high sediment loads due to mountain torrents based on hydrodynamic-finite element coupling as described in claim 2, is characterized in that... The specific process of setting parameters and solving the established hydrodynamic simulation model in step 1 is as follows: (1) Computational area and grid division: The computational area is determined according to the target watershed range. Unstructured triangular grids or structured rectangular grids are used for spatial discretization. The grid size is determined according to the complexity of the terrain and the accuracy requirements of the calculation, and is taken as 5 to 20m. (2) Roughness parameter setting: Determine the Manning roughness coefficient according to the land use type. The main channel should be 0.03–0.05, the beach area 0.05–0.08, and the building area 0.08–0.

15. (3) Sediment particle size grouping: Determine the representative particle size of each particle size group based on the characteristics of sediment in the watershed. It is divided into clay ( mm), silt ( mm), fine sand ( mm), gravel ( mm) group; (4) Boundary condition setting: The upstream boundary input is based on the inflow process line derived from the measured or designed rainfall process, and the downstream boundary is set as a water level boundary or a free outflow boundary according to the actual situation; (5) Simulation duration setting: Covers the entire process from the rise of the flood to its receding; Then, by numerically solving the system of equations, the spatiotemporal distribution of various physical quantities under flash flood conditions with different return periods is obtained, including water depth, flow velocity, and sediment concentration.

4. The method for assessing the damage of bridges with high sediment loads due to mountain torrents based on hydrodynamic-finite element coupling as described in claim 1, characterized in that, The specific process of establishing the bridge finite element model described in step 3 includes: (1) Model building: A numerical model of the bridge was built using commercial finite element software: Main beam: Beam element, defining section properties and prestress; Bridge piers: fiber beam units or solid units, with reinforcement considered; Pile foundation: Beam unit combined with soil spring; Support: Nonlinear connection element, defining friction and separation characteristics - Material constitutive model: Concrete adopts a nonlinear model considering cracking and crushing, and steel reinforcement adopts a bilinear elastoplastic model; (2) Model input parameter settings: Geometric parameters: bridge span L, pier height H, pier diameter D or pier width B, wall thickness; Material parameters: Concrete strength grade C30~C50, steel reinforcement HRB400; Load input: The load calculated in step 2 According to the height of action Applied to bridge piers; Boundary conditions: Pier base consolidation or pile-soil interaction considerations; (3) Analysis settings: Analysis type: Nonlinear time history analysis; Step size: Determined based on the rate of load change, ranging from 10 to 60 seconds; Total duration: t ∈ [0, t f ], covering the entire flood process, including This represents the total duration of the flood event. Solution settings: Enable large deformation and consider the P-Δ effect; the P-Δ effect refers to the additional bending moment effect of the vertical load on the structure after the structure has undergone lateral displacement under horizontal load. The extraction of finite element analysis results specifically involves the finite element software automatically calculating the structural response at each time step by solving the structural dynamics equations based on the input load time history and structural model.

5. The method for assessing the damage of bridges with high sediment loads due to mountain torrents based on hydrodynamic-finite element coupling as described in claim 1, characterized in that, The specific judgment criteria mentioned in step 5 are as follows: For the pier top displacement angle :when At that time, Level I; when At that time, Level II; when At that time, Level III; when At that time, it was Level IV; For the cross-sectional bearing capacity ratio :when At that time, Level I; when At that time, Level II; when At that time, Level III; when At that time, it was Level IV; For concrete stress ratio :when At that time, Level I; when At that time, Level II; when At that time, Level III; when At that time, it was Level IV; For steel reinforcement stress ratio :when At that time, Level I; when At that time, Level II; when At that time, Level III; when At that time, it was Level IV; For overturning stability coefficient :when At that time, Level I; when At that time, Level II; when At that time, Level III; when At that time, it was Level IV; For the minimum support reaction force :when At that time, Level I; when At that time, it was classified as Level IV.

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