A bridge engineering vulnerability assessment method based on static analysis of debris flow disasters

Abstract

The invention discloses a bridge engineering vulnerability assessment method based on static analysis of debris flow disasters, and relates to the technical field of debris flow damage monitoring. The method comprises: based on an improved bridge vulnerability assessment model in the earthquake field, and using finite element analysis to obtain a fitting relationship between debris flow intensity and pier top displacement, assuming that a response probability function and a component bearing capacity probability function are log-normal distributions, a failure probability function is obtained, and a vulnerability curve is drawn according to the failure probability function. The method of the invention can timely grasp the probability of different degrees of damage to the bridge under the impact of debris flows of different intensities, so as to timely carry out disaster prevention and mitigation work.

Description

Technical Field

[0001] The invention relates to the technical field of debris flow monitoring, and in particular to a bridge engineering vulnerability assessment method based on static analysis of debris flow disasters. Background Art

[0002] In the early studies on debris flow vulnerability, due to the lack of disaster history data and insufficient understanding of the structural damage mechanism, people did not have a clear understanding of the damage status of debris flow. Therefore, scholars established a vulnerability matrix based on a small number of field observation samples, that is, a corresponding relationship table between the degree of building loss and the intensity of debris flow. Fell and Hartford established a vulnerability matrix based on the relationship between debris flow properties (flow velocity, flow depth) and building damage by analyzing the disaster history data of rock collapse, landslide and debris flow. Zanchetta et al. used the debris flow data of Sarno Volcano in Italy to deduce the impact pressure of debris flow on the structure and established a matrix relationship (semi-quantitative) between damage level and debris flow impact force. Based on Zanchetta et al., Hu et al. established a vulnerability matrix of the degree of damage to different types of buildings and the impact pressure of debris flow based on the 8.7 Zhouqu debris flow survey data. Kang, Kim and others analyzed the relationship between the degree of building damage and the intensity of debris flow through field survey data, remote sensing interpretation and empirical formulas, and established empirical vulnerability curves for debris flow depth, flow velocity and impact pressure. At the same time, they divided the degree of building damage into four categories and established a matrix relationship between impact pressure and damage degree.

[0003] With the continuous improvement of field data, scholars have fitted the debris flow vulnerability experience curve based on disaster history data, which is more applicable. Fuchs et al. conducted statistics on the damage of 15 buildings in the 1997 Austrian debris flow disaster, using mud depth as the debris flow intensity and the ratio of building loss and building value as the vulnerability, established the debris flow building vulnerability curve, and organized it into a piecewise function. Akbas et al. investigated 35 buildings damaged by the debris flow in the Alps in 2008, and compared the established vulnerability curve with the research of Fell, Hartford, and Fuchs. The results showed that the vulnerability obtained by Akbas et al. was slightly higher than that obtained by Fuchs at the same debris flow intensity. The analysis showed that the personal judgment of building loss and debris flow intensity led to the difference in vulnerability curves. Subsequently, Totschnig et al. proposed that the depth of debris flow divided by the building height be used as the relative intensity of debris flow, and replaced the polynomial function proposed by Fuchs with the cumulative distribution function, and compared the established vulnerability curve with the depth-vulnerability curve. The results showed that the vulnerability curve established by relative intensity has better fitting properties. Totschnig et al. and Fuchs established vulnerability curves for different degrees of sand-laden water flow and different types of buildings, respectively, and fitted them to establish a joint vulnerability curve, which was tested using Italian disaster history data. Papathoma-Köhle et al. calculated the vulnerability curve between the degree of loss and flow depth of 51 buildings through photos, and then developed it into software for predicting debris flow disaster losses.

[0004] However, these technologies currently have the following problems: although regional and single-channel models and methods have been initially formed, the dynamic performance of debris flows on bridges has not been studied in depth, so the assignment of model weights and parameters is still subjective. Therefore, current research rarely establishes vulnerability assessment models based on mechanical mechanisms. Summary of the invention

[0005] The present invention aims to provide a bridge engineering vulnerability assessment method based on static analysis of debris flow disasters, so as to accurately grasp the probability of different degrees of damage to the bridge under the impact of debris flows of different intensities, and to carry out disaster prevention and mitigation work in a timely manner.

[0006] The present invention provides a bridge engineering vulnerability assessment method based on static analysis of debris flow disasters, comprising:

[0007] By using a nonlinear finite element analysis method, a bridge dynamic response value under different debris flow intensity variables is obtained, and the bridge dynamic response value is used as the pier top displacement;

[0008] By establishing a fitting relationship between each debris flow intensity variable and the pier top displacement, a debris flow intensity variable that meets the debris flow intensity index is selected, and the debris flow intensity variable that meets the debris flow intensity index is used to determine a fitting expression for different debris flow intensity variables that meet the debris flow intensity index and the pier top displacement;

[0009] Calculating a bending moment-curvature curve of a pier section, and determining a vulnerability index classification using the bending moment-curvature curve of the pier section;

[0010] The bridge failure probability function is obtained by using the fitting expressions of the debris flow intensity variables and pier top displacement that meet the debris flow intensity index and the vulnerability index classification, and the bridge failure probability function is used to perform bridge engineering vulnerability assessment.

[0011] Preferably, the debris flow intensity variables include: flow velocity v, flow depth h, relative intensity h / l, flow velocity and flow depth squared vh 2 , momentum flux hv 2 , overturning bending moment vh, mud impact force P, stone impact force F.

[0012] Preferably, the selecting of debris flow intensity variables that meet the debris flow intensity index by establishing a fitting relationship between each debris flow intensity variable and the pier top displacement comprises:

[0013] By establishing a fitting relationship between each debris flow intensity variable and the pier top displacement, a fitting result between each debris flow intensity variable and the pier top displacement is obtained;

[0014] According to the fitting result between each debris flow intensity variable and the pier top displacement, a debris flow intensity variable that meets the debris flow intensity index is selected.

[0015] Preferably, when the debris flow intensity variables are flow velocity and flow depth squared vh 2 , momentum flux hv 2 , when the overturning moment vh is , the fitting result between each debris flow intensity variable and the pier top displacement is obtained by establishing a fitting relationship between each debris flow intensity variable and the pier top displacement, including:

[0016] By establishing a fitting relationship between each debris flow intensity variable and the pier top displacement, a first determination coefficient is calculated;

[0017] The second coefficient of determination is calculated by taking the logarithm of each debris flow intensity variable and the pier top displacement and then fitting them with a linear function;

[0018] The first coefficient of determination and the second coefficient of determination are used as fitting results between each debris flow intensity variable and the pier top displacement.

[0019] Preferably, the selecting of the debris flow intensity variable that meets the debris flow intensity index according to the fitting result between each debris flow intensity variable and the pier top displacement comprises:

[0020] comparing the first coefficient of determination and the second coefficient of determination with a preset coefficient of determination threshold;

[0021] When the first coefficient of determination and the second coefficient of determination are both greater than a preset coefficient of determination threshold, the debris flow intensity variables corresponding to the first coefficient of determination and the second coefficient of determination are used as debris flow intensity variables that meet the debris flow intensity index;

[0022] When one of the first coefficient of determination and the second coefficient of determination is not greater than a preset coefficient of determination threshold, the debris flow intensity variables corresponding to the first coefficient of determination and the second coefficient of determination are taken as debris flow intensity variables that do not meet the debris flow intensity index.

[0023] Preferably, the fitting expressions of the debris flow intensity variables and the pier top displacement that meet the debris flow intensity index include:

[0024]

[0025] Among them, D S is the debris flow intensity, Δ is the pier top displacement, k and b are constants.

[0026] Preferably, the calculating the moment-curvature curve of the pier cross section and determining the vulnerability index classification using the moment-curvature curve of the pier cross section comprises:

[0027] By calculating the resistance of the pier concrete structure, the moment-curvature relationship of the pier section is established;

[0028] The moment-curvature relationship of the pier cross section is fitted into a bilinear curve, and the vulnerability index classification is determined using the bilinear curve.

[0029] Preferably, the obtaining of the bridge failure probability function by using the fitting expressions of the debris flow intensity variables and the pier top displacement that meet the debris flow intensity index and the vulnerability index classification comprises:

[0030] A bridge failure probability model is established, and a bridge failure probability function is obtained by substituting the fitting expressions of the debris flow intensity variables and pier top displacements that meet the debris flow intensity index and the vulnerability index into the bridge failure probability model in a graded manner.

[0031] Preferably, the use of the bridge failure probability function to perform bridge engineering vulnerability assessment includes:

[0032] A fragility curve is drawn according to the bridge failure probability function, and the fragility curve is used to perform bridge engineering fragility assessment.

[0033] In summary, the beneficial effects of the present invention are as follows: a vulnerability assessment model based on mechanical analysis is established, which can quickly realize regional-scale bridge vulnerability assessment and contribute to the debris flow disaster risk analysis of bridges in mountainous areas of my country. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a flow chart provided by an embodiment of the present invention;

[0035] Figure 2 is a fitting curve diagram of the overturning bending moment vh and the pier top displacement Δ provided in an embodiment of the present invention;

[0036] Figure 3 is vh provided by the embodiment of the present invention 2 Fitting curve diagram of Δ with pier top displacement;

[0037] Figure 4 is the momentum flux hv provided by the embodiment of the present invention 2 Fitting curve diagram of Δ with pier top displacement;

[0038] Figure 5 is a scatter plot of stone impact force-pier top displacement provided by an embodiment of the present invention;

[0039] Figure 6 is a scatter diagram of slurry impact force-pier top displacement provided by an embodiment of the present invention;

[0040] Figure 7 is a moment-curvature curve diagram of a bridge pier cross section provided by an embodiment of the present invention;

[0041] Figure 8 is the debris flow intensity vh provided by the embodiment of the present invention 2 Vulnerability curve diagram;

[0042] Fig. 9 is a vulnerability curve diagram of debris flow intensity vh provided by an embodiment of the present invention;

[0043] Fig.10 It is a flow chart of a bridge engineering vulnerability assessment method based on static analysis of debris flow disasters provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described below are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0045] Embodiment 1:

[0046] Fig.10 is a flow chart of a bridge engineering vulnerability assessment method based on static analysis of debris flow disasters provided by an embodiment of the present invention, such as Fig.10 As shown, including:

[0047] Step S101: obtaining the dynamic response value of the bridge under different debris flow intensity variables by nonlinear finite element analysis method, and using the dynamic response value of the bridge as the pier top displacement;

[0048] Step S102: by establishing a fitting relationship between each debris flow intensity variable and the pier top displacement, a debris flow intensity variable that meets the debris flow intensity index is selected, and the debris flow intensity variable that meets the debris flow intensity index is used to determine a fitting expression for different debris flow intensity variables that meet the debris flow intensity index and the pier top displacement;

[0049] Step S103: calculating the bending moment-curvature curve of the pier cross section, and determining the vulnerability index classification using the bending moment-curvature curve of the pier cross section;

[0050] Step S104: using the fitting expressions of the debris flow intensity variables and pier top displacements that meet the debris flow intensity index and the vulnerability index classification, a bridge failure probability function is obtained, and the bridge engineering vulnerability assessment is performed using the bridge failure probability function.

[0051] The debris flow intensity variables include: velocity v, flow depth h, relative intensity h / l, velocity and flow depth squared vh 2 , momentum flux hv 2 , overturning bending moment vh, mud impact force P, stone impact force F.

[0052] Among them, the method of selecting a debris flow intensity variable that meets the debris flow intensity index by establishing a fitting relationship between each debris flow intensity variable and the pier top displacement includes: obtaining a fitting result between each debris flow intensity variable and the pier top displacement by establishing a fitting relationship between each debris flow intensity variable and the pier top displacement; and selecting a debris flow intensity variable that meets the debris flow intensity index according to the fitting result between each debris flow intensity variable and the pier top displacement.

[0053] Furthermore, when the debris flow intensity variables are flow velocity and flow depth squared vh 2 , momentum flux hv 2, when the overturning bending moment vh is obtained, the fitting result between each debris flow intensity variable and the pier top displacement is obtained by establishing a fitting relationship between each debris flow intensity variable and the pier top displacement, including: calculating a first determination coefficient by establishing a fitting relationship between each debris flow intensity variable and the pier top displacement; calculating a second determination coefficient by taking the logarithm of each debris flow intensity variable and the pier top displacement and fitting them with a linear function; and using the first determination coefficient and the second determination coefficient as the fitting result between each debris flow intensity variable and the pier top displacement.

[0054] Specifically, the selection of debris flow intensity variables that meet the debris flow intensity index based on the fitting results between each debris flow intensity variable and the pier top displacement includes: comparing the first determination coefficient and the second determination coefficient with a preset determination coefficient threshold; when the first determination coefficient and the second determination coefficient are both greater than the preset determination coefficient threshold, the debris flow intensity variables corresponding to the first determination coefficient and the second determination coefficient are used as debris flow intensity variables that meet the debris flow intensity index; when one of the first determination coefficient and the second determination coefficient is not greater than the preset determination coefficient threshold, the debris flow intensity variables corresponding to the first determination coefficient and the second determination coefficient are used as debris flow intensity variables that do not meet the debris flow intensity index.

[0055] Furthermore, the fitting expressions of the debris flow intensity variables and the pier top displacement that meet the debris flow intensity index include:

[0056]

[0057] Among them, D S is the debris flow intensity, Δ is the pier top displacement, k and b are constants.

[0058] The method of calculating the moment-curvature curve of the pier cross section and determining the vulnerability index classification using the moment-curvature curve of the pier cross section includes: establishing the moment-curvature relationship of the pier cross section by calculating the resistance of the pier concrete structure; fitting the moment-curvature relationship of the pier cross section into a bilinear curve, and determining the vulnerability index classification using the bilinear curve.

[0059] Among them, the method of obtaining the bridge failure probability function by using the fitting expressions of the debris flow intensity variables and pier top displacements that meet the debris flow intensity index and the vulnerability index classification includes: establishing a bridge failure probability model, and obtaining the bridge failure probability function by substituting the fitting expressions of the debris flow intensity variables and pier top displacements that meet the debris flow intensity index and the vulnerability index classification into the bridge failure probability model.

[0060] Wherein, the use of the bridge failure probability function to perform bridge engineering vulnerability assessment includes: drawing a vulnerability curve according to the bridge failure probability function, and using the vulnerability curve to perform bridge engineering vulnerability assessment.

[0061] Embodiment 2

[0062] The flowchart of this embodiment is as follows Figure 1 As shown, the specific implementation steps are as follows:

[0063] S1: Taking debris flow intensity as the independent variable and bridge dynamic response as the dependent variable, the bridge dynamic response value under different debris flow intensities is obtained by nonlinear finite element analysis method;

[0064] S2: Establish the fitting relationship between each debris flow intensity variable and the dynamic response of the bridge pier;

[0065] S3: screening debris flow intensity indexes according to the fitting effect, and obtaining fitting expressions for fitting debris flow intensity and pier top displacement;

[0066] S4: Establish the moment-curvature relationship of the pier section;

[0067] S5: Determine the vulnerability index μ and the index classification standard;

[0068] S6: Substitute the fitting expression of S3 and the vulnerability index classification of S5 into the failure probability model to obtain the bridge failure probability equation;

[0069] S7: Draw a fragility curve based on the failure probability equation;

[0070] Specifically, a finite element model of debris flow impacting a bridge pier is first established. The impact of rocks is equivalent to a concentrated load calculated by the rock impact force, the mud load is a uniformly distributed load calculated by the slurry dynamic pressure, and the load on the top of the pier is a uniformly distributed load of 4500 kN.

[0071] The mud impact force can be included in the hydrodynamic pressure and hydrostatic pressure. Since the hydrostatic pressure of the mud is very small, the hydrostatic pressure of the mud can be ignored and the hydrodynamic pressure formula (10) is used to calculate the mud impact force. Where P is the debris flow pressure (Pa), is the dynamic pressure coefficient, and ρ is the debris flow density (kg / m 3 ), v is the flow velocity.

[0072] (10)

[0073] The calculation of the impact force of large rocks is mostly based on the theory of perfectly elastic sphere assumption and the beam deformation theory of material mechanics, and then corrected using field data and experimental data. The calculation formula for the impact force of large rocks based on the perfectly elastic sphere assumption is shown in formula (1), and is corrected with indoor experimental data. This formula is widely used in static analysis.

[0074] (1)

[0075] Where v is the velocity (m / s), R is the radius of the stone (m), and g is the acceleration due to gravity (m / s 2 ) According to field survey data, when the debris flow is a dilute debris flow, the height of the large rocks is 2 / 5 of the height of the debris flow; when the debris flow is a viscous debris flow, the height of the large rocks is 3 / 5 of the height of the debris flow.

[0076] Analysis settings and simulation conditions. Debris flow intensity variables include flow velocity v, flow depth h, relative intensity h / l, vh 2 , momentum flux hv 2 , overturning bending moment vh, mud impact force P, rock impact force F. There are 15 groups of flow velocities ranging from 1m / s to 15m / s, and 10 groups of flow depths ranging from 1m / s to 10m / s. The flow velocities and flow depths are arranged and combined to obtain 150 groups of debris flow intensity values. 150 groups of mud impact force P and rock impact force F are input into the impact model.

[0077] The RHT model is used for the pier concrete, and the bilinear elastic-plastic hardening model is used for the steel bar. The connection between the steel bar and the concrete is based on the strengthening algorithm, which is suitable for the rubber and steel bar contact setting. Based on the above material and parameter settings, nonlinear finite element analysis is performed to obtain the maximum displacement of the top of the pier center, and the results are shown in Table 1.

[0078]

[0079] Next, a fitting relationship is established for the pier top displacement Δ based on different strength indicators.

[0080] (1) Relationship between overturning moment vh and pier top displacement Δ

[0081] The debris flow velocity multiplied by the flow depth is the overturning moment of the debris flow on the structure. The overturning moment is used as the debris flow strength, and the fitting relationship between the debris flow strength and the pier top displacement is established ( Figure 2 The quadratic function relationship between the overturning moment and the pier top displacement is shown in formula (11), and the coefficient of determination R 2 The logarithm of the lateral displacement of the pier top and vh is taken respectively, and then a linear function is used for fitting. The fitting relationship is shown in formula (12). The coefficient of determination r 2 It is 0.952, indicating that the dynamic response caused by debris flow impacting bridge piers is similar to that of earthquake disasters, and both satisfy the linear function relationship between the intensity and the logarithm of the response.

[0082] (11)

[0083] (12)

[0084] (2) Flow velocity multiplied by the square of flow depth vh 2 Relationship with pier top displacement Δ

[0085] The flow velocity multiplied by the square of the flow depth is taken as the debris flow intensity, and the fitting relationship between the debris flow intensity and the pier top displacement is established ( Figure 3 The debris flow intensity and the pier top displacement still satisfy the quadratic function relationship as shown in formula (13), and the coefficient of determination R 2 is 0.988. For the lateral displacement of the pier top and vh 2 Take the logarithm respectively, and then use the linear function to fit. The fitting relationship is shown in formula (14). The coefficient of determination r 2 is 0.979. The fitting effect shows that the use of vh 2 It is more suitable as an indicator of debris flow intensity.

[0086] (13)

[0087] (14)

[0088] (3) Relationship between momentum flux hv2 and pier top displacement Δ

[0089] The momentum flux is the flow depth multiplied by the square of the flow velocity. The fitting effect between the lateral displacement and the momentum flux is relatively discrete, and the two satisfy a linear function relationship with a determination coefficient R2 of 0.853. When the logarithm of the lateral displacement of the pier top and hv2 is taken respectively, the debris flow intensity and the lateral displacement are still fitted by a linear function, and the determination coefficient r2 is 0.752. The fitting effect shows that the use of hv2 as a debris flow intensity indicator is weaker than vh and vh2. Figure 4 shown.

[0090] (15)

[0091] (16)

[0092] (4) Relationship between rock impact force F and mud impact force P and pier top displacement Δ

[0093] Draw the scatter plots of the rock impact force F and mud impact force P against the pier top displacement Δ, respectively, as shown in Figure 5 , Figure 6 As shown in the figure, when the rock impact force F and the mud impact force P are used as debris flow intensity indicators, the scatter plot is relatively discrete because the intensity indicators have not yet taken the impact height of the debris flow into consideration, that is, the effect of using the rock impact force F or the mud impact force P as debris flow intensity indicators is poor.

[0094] In summary, the debris flow intensity and the pier top displacement satisfy the quadratic function relationship, and the debris flow intensity and the pier top displacement satisfy the linear function relationship after taking the logarithm. The coefficient of determination shows that vh, vh 2 Better than hv 2 Therefore, the earthquake-bridge vulnerability assessment model can be used in debris flow disaster assessment, but the debris flow intensity index should be selected using vh and vh 2 More suitable.

[0095] The bridge vulnerability index is graded. There are many indicators used to define the ultimate state of bridge piers. The commonly used pier damage indicators are: material strain, pier top displacement, curvature ductility ratio, displacement ductility ratio, and structural demand ratio. Considering that the damage of debris flow to bridge piers is mainly bending damage, and the displacement ductility ratio is based on the moment-curvature curve of the steel-concrete section when it is bent, it is derived by selecting different damage stages of the control section. Therefore, this study uses the displacement ductility ratio as an indicator to establish the structural damage level.

[0096] Before classifying the structural damage index, it is necessary to calculate the resistance of the concrete structure and obtain the moment-curvature relationship of the reinforced concrete column section. The reinforced concrete pier is regarded as a compression-bending member under the upper load, and it is assumed that the axial pressure remains unchanged during the deformation of the pier. The section pressure and moment balance are shown in formulas (17) and (18). In order to balance the upper load given on the pier section, the material needs to produce the corresponding section curvature, and the section moment can be calculated from the section curvature. Therefore, a moment-curvature relationship curve is established, namely the M-ϕ curve. This embodiment uses XTRACT to calculate the moment-curvature curve of the pier section and fits it to a bilinear curve ( Figure 7 ), the initial elastic stage is the line connecting the origin and the first yield point of the tensile steel bar, and the plastic stage is the line connecting the equivalent yield point and the limit curvature point. The equivalent yield point is calculated by the equality of the area of ​​the first straight line of the bilinear curve and the area of ​​the original curve.

[0097] (17)

[0098] (18)

[0099] , is the concrete cross-sectional area and concrete stress in the compression zone of the jth layer (Pa), , is the cross-sectional area and stress of the steel bars in the i-th layer (Pa).

[0100] A grading standard for vulnerability indicators is established, and the displacement-ductility ratio is used to grade the pier damage. The main grading methods and related descriptions are shown in Table 2.

[0101]

[0102] in , , , They are first yield displacement ductility ratio, equivalent yield displacement ductility ratio, displacement ductility ratio at concrete compressive strain and maximum displacement ductility ratio. The calculation method is shown in the following formula.

[0103] (19)

[0104] (20)

[0105] (twenty one)

[0106] (twenty two)

[0107] (twenty three)

[0108] In the formula , , , are the first yielding time of steel bar, equivalent yield point and concrete compressive strain respectively. The corresponding pier top displacement (m) and the maximum pier top displacement (m) are is the displacement of the pier top under the lateral load (m). Concrete compressive strain The corresponding top displacement Displacement by elastic deformation and plastic hinge displacement Composition, each parameter is calculated as follows.

[0109] (twenty four)

[0110] (25)

[0111] (26)

[0112] (27)

[0113] (28)

[0114] In the formula According to the load combination, take 1 / 3, plastic hinge length Calculate according to formula (29). , , are the first yield curvature, equivalent yield curvature, and concrete compressive strain in cross-section analysis. The corresponding curvature.

[0115] (29)

[0116] Where f y is the design value of steel bar tensile strength (MPa), d s is the steel bar diameter (m), h is the distance from the dangerous section to the inflection point (m), and D is the pier diameter (m).

[0117] Calculate the failure probability of bridge engineering. The bridge response probability function and the component bearing capacity probability function are log-normal distributions as shown in formulas (4)-(5), where and are the mean and standard deviation of the corresponding probability functions, respectively.

[0118] (4)

[0119] (5)

[0120] When the dynamic response of the bridge pier under the action of debris flow exceeds the bearing capacity of the bridge pier, the bridge pier fails. Therefore, the failure probability of the structure is shown in formula (3). Through the probability calculation method, it is easy to know that when the bridge response probability function and the bridge bearing capacity probability function When the normal distribution is satisfied, formula (3) can be expressed as formula (6).

[0121] (3)

[0122] (6)

[0123] In the static equivalent model, the debris flow intensity D S The logarithm of the displacement at the pier top shows a linear relationship, and the fitting relationship between strength and pier top displacement is established as shown in formula (2). Substituting formula (2) into formula (6), the failure probability of the pier at each stage can be obtained as shown in formula (7).

[0124] (2)

[0125] (7)

[0126] Where Φ is the standard normal distribution function, D S is the debris flow intensity, b and k are the constants obtained by fitting the debris flow intensity and the top displacement. The logarithmic standard deviation of the bridge dynamic response to debris flow It can be estimated by formula (8); the logarithmic standard deviation of bridge bearing capacity is The uncertainty calculation of the ultimate failure state of components under seismic response conditions can be referred to, and the uncertainty of the ultimate failure state can be described by the coefficient of variation (COV). In addition, the coefficient of variation and the degree of damage to the pier have a direct correlation as shown in formula (9).

[0127] (8)

[0128] (9)

[0129] In the formula is the i-th structural displacement demand in the N-th nonlinear finite element analysis, is the i-th debris flow intensity. The value of the coefficient of variation COV is related to the degree of damage to the bridge components. COV is 0.25 for slight and moderate damage states, and 0.5 for severe and complete damage.

[0130] According to the failure probability, the debris flow intensity vh 2 and vh as independent variables, and draw the vulnerability curve of the bridge pier under the action of debris flow, such as Figure 8 and Fig. 9 As shown. Each vulnerability curve is a monotonically increasing "S" curve. As the debris flow intensity increases, the probability of pier damage gradually increases. The shapes of each curve are relatively consistent. The failure probability increases slowly at the front and rear ends, and the failure probability increases rapidly in the middle. As the damage level gradually increases, the required debris flow intensity gradually increases. For example, when the damage is slight, the debris flow intensity is [0,125], while when the damage is complete, the debris flow intensity is [0,400]. This shows that the debris flow intensity corresponding to the increase in the damage state of the pier is greater, which is consistent with the actual situation.

[0131] The physical meaning of the slope is the ability of the bridge pier to resist the impact of debris flow. The larger the slope of the vulnerability curve, the weaker the structure's ability to resist disasters. As the intensity of the debris flow gradually increases, the slope of the vulnerability curve suddenly increases, indicating that after the bridge pier encounters a critical intensity debris flow disaster, the ability of the structure to resist disasters decreases rapidly, resulting in a rapid increase in the probability of pier failure. Therefore, by obtaining the maximum value of the slope of the vulnerability curve, the position of the sudden change in the resistance of the bridge pier can be identified, as shown in Table 3. The impact resistance of the bridge pier can then be evaluated based on the critical strength of the control point, thereby providing a basis for risk prevention and control in engineering design.

[0132]

[0133] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A bridge engineering vulnerability assessment method based on static analysis of debris flow disasters, characterized in that: The following steps are involved: By using a nonlinear finite element analysis method, the displacement of the bridge pier top under different debris flow intensity variables is obtained, and the displacement of the bridge pier top is used as the dynamic response value of the bridge; By establishing a fitting relationship between each debris flow intensity variable and the pier top displacement, a debris flow intensity variable that meets the debris flow intensity index is selected, and the debris flow intensity variable that meets the debris flow intensity index is used to determine a fitting expression for different debris flow intensity variables that meet the debris flow intensity index and the pier top displacement; Calculating a bending moment-curvature curve of a pier section, and determining a vulnerability index classification using the bending moment-curvature curve of the pier section; The bridge failure probability function is obtained by using the fitting expressions of the debris flow intensity variables and pier top displacement that meet the debris flow intensity index and the vulnerability index classification, and the bridge failure probability function is used to perform bridge engineering vulnerability assessment.

2. The method according to claim 1, characterized in that The debris flow intensity variables include: flow velocity v, flow depth h, relative intensity h / l, flow velocity and flow depth squared vh 2 , momentum flux hv 2 , overturning bending moment vh, mud impact force P, stone impact force F.

3. The method according to claim 2, characterized in that The debris flow intensity variable that meets the debris flow intensity index is selected by establishing a fitting relationship between each debris flow intensity variable and the pier top displacement, including: By establishing a fitting relationship between each debris flow intensity variable and the pier top displacement, a fitting result between each debris flow intensity variable and the pier top displacement is obtained; According to the fitting result between each debris flow intensity variable and the pier top displacement, a debris flow intensity variable that meets the debris flow intensity index is selected.

4. The method according to claim 3, characterized in that When the debris flow intensity variables are flow velocity and flow depth squared vh 2 , momentum flux hv 2 , when the overturning moment vh is , the fitting result between each debris flow intensity variable and the pier top displacement is obtained by establishing a fitting relationship between each debris flow intensity variable and the pier top displacement, including: By establishing a fitting relationship between each debris flow intensity variable and the pier top displacement, a first determination coefficient is calculated; The second coefficient of determination is calculated by taking the logarithm of each debris flow intensity variable and the pier top displacement and then fitting them with a linear function; The first coefficient of determination and the second coefficient of determination are used as fitting results between each debris flow intensity variable and the pier top displacement.

5. The method according to claim 4, characterized in that The selecting of the debris flow intensity variable that meets the debris flow intensity index according to the fitting result between each debris flow intensity variable and the pier top displacement comprises: comparing the first coefficient of determination and the second coefficient of determination with a preset coefficient of determination threshold; When the first coefficient of determination and the second coefficient of determination are both greater than a preset coefficient of determination threshold, the debris flow intensity variables corresponding to the first coefficient of determination and the second coefficient of determination are used as debris flow intensity variables that meet the debris flow intensity index; When one of the first coefficient of determination and the second coefficient of determination is not greater than a preset coefficient of determination threshold, the debris flow intensity variables corresponding to the first coefficient of determination and the second coefficient of determination are taken as debris flow intensity variables that do not meet the debris flow intensity index.

6. The method according to claim 5, characterized in that The fitting expressions of the debris flow intensity variables and the pier top displacement that meet the debris flow intensity index include: ln(Δ)=kln(D S )+lnb Among them, D S is the debris flow intensity, Δ is the pier top displacement, k and b are constants.

7. The method according to claim 6, characterized in that The calculating of the moment-curvature curve of the pier section and determining the vulnerability index classification using the moment-curvature curve of the pier section includes: By calculating the resistance of the pier concrete structure, the moment-curvature relationship of the pier section is established; The moment-curvature relationship of the pier cross section is fitted into a bilinear curve, and the vulnerability index classification is determined using the bilinear curve.

8. The method according to claim 7, characterized in that The bridge failure probability function is obtained by using the fitting expressions of the debris flow intensity variables and the pier top displacement that meet the debris flow intensity index and the vulnerability index classification, including: A bridge failure probability model is established, and a bridge failure probability function is obtained by substituting the fitting expressions of the debris flow intensity variables and pier top displacements that meet the debris flow intensity index and the vulnerability index into the bridge failure probability model in a graded manner.

9. The method according to claim 8, characterized in that The bridge engineering vulnerability assessment using the bridge failure probability function comprises: A fragility curve is drawn according to the bridge failure probability function, and the fragility curve is used to perform bridge engineering fragility assessment.

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