Rigid pavement vulnerability analysis method considering foundation performance degradation under wheel load action

Abstract

The invention discloses a rigid pavement vulnerability analysis method considering foundation performance degradation under a wheel load effect. The method comprises the following steps: establishing an airport rigid pavement simplified analysis model; determining the maximum tensile strain value range of the bottom of the critical pavement slab corresponding to each damage grade; introducing a foundation support stiffness degradation coefficient; calculating the actually generated maximum tensile strain of the bottom of the pavement slab; constructing a vulnerability function in a standard normal distribution accumulation function form; and calculating a comprehensive failure probability and the like. According to the method, by introducing the foundation support stiffness degradation coefficient and combining the reliability theory, an airport rigid pavement vulnerability analysis framework considering foundation performance degradation is established, and quantitative calculation of the pavement failure probability under different degradation degrees is achieved. The foundation support stiffness space variability and the structural performance degradation rule can be comprehensively reflected, and the analysis result is closer to the actual operation condition. The calculation process is simple and efficient, the precision is high, the applicability is high, and scientific and reliable technical support can be provided for structural safety evaluation, operation maintenance and service life prediction of the airport rigid pavement.

Description

Technical Field

[0001] This invention belongs to the field of airport engineering technology, and specifically relates to a method for analyzing the vulnerability of rigid pavement under wheel loads that takes into account the deterioration of foundation performance. Background Technology

[0002] Cement concrete pavements, due to their high strength and durability, have become the mainstream rigid pavement structure for civil airports in my country. However, during service, they are affected by repeated aircraft wheel loads, base erosion, and rainwater infiltration, leading to a decrease in the strength of the base layer and subgrade beneath the pavement slab. This results in reduced foundation support stiffness and even voids at the bottom of the slab, significantly increasing the risk of pavement cracking and affecting pavement safety and service life.

[0003] Existing simplified finite element methods for airport pavements generally assume that the base layer in the delamination zone at the bottom of the slab is unsupported, ignoring its residual support and the spatially uneven degradation characteristics of the foundation stiffness. This makes it difficult to reflect the gradual characteristics of foundation performance deterioration in actual service, resulting in a large deviation in the assessment of pavement failure probability.

[0004] In addition, existing methods for analyzing the vulnerability of rigid pavements focus on the functional vulnerability of airport pavement systems under military strikes and extreme weather conditions, and lack methods that consider the degradation of pavement foundation performance and the vulnerability of rigid pavements under daily aircraft wheel loads. Summary of the Invention

[0005] To address the aforementioned problems, the present invention aims to provide a method for analyzing the vulnerability of rigid pavements under wheel loads that takes into account the deterioration of foundation performance.

[0006] To achieve the above objectives, the present invention provides a method for analyzing the vulnerability of rigid pavements under wheel loads, taking into account the deterioration of foundation performance. This method comprises the following steps performed sequentially:

[0007] S1. Establish a simplified analysis model for rigid pavement of the airport. This model simplifies the three-dimensional pavement structure into a longitudinal two-dimensional section. The base layer and the subgrade within a finite depth range are equivalent to a series of independent spring elements. The pavement panel adopts the plastic damage constitutive model of concrete and sets the pavement panel parameters, aircraft wheel load parameters and wheel load taxiing path.

[0008] S2, with the maximum tensile strain ε at the bottom of the critical runner panel. i As a damage index, the damage level of the pavement panel is classified into four categories: minor damage, moderate damage, severe damage, and complete failure. The corresponding critical maximum tensile strain ε at the bottom of the pavement panel is determined for each damage level. i The range of values ​​for which the damage level is determined is used to quantify the damage level.

[0009] S3. Introduce the foundation support stiffness degradation coefficient η to characterize the degree of foundation support stiffness degradation, and set the foundation support stiffness as uniform or non-uniform degradation.

[0010] S4. Considering the uniform and non-uniform degradation of the foundation support stiffness mentioned above, based on the simplified analysis model of the airport rigid pavement established in step S1 and the foundation support stiffness degradation coefficient η introduced in step S3, calculate the actual maximum tensile strain at the bottom of the pavement slab.

[0011] S5. Define the vulnerability of rigid pavement under aircraft wheel loads as the failure probability of the pavement panel reaching a specific failure state under aircraft wheel loads under conditions of degraded foundation support stiffness; based on the maximum tensile strain ε at the bottom of the critical pavement panel obtained in step S2. i The actual maximum tensile strain ε on the bottom of the track panel obtained in step S4 ten Construct a vulnerability function in the form of a standard normal cumulative function, which represents the probability of damage when the response requirement of the track panel reaches a specified damage level j.

[0012] S6. Introduce the aircraft main landing gear wheel track distribution model, assuming that the wheel tracks follow a standard normal distribution in the transverse direction of the pavement panel. Discretize the cross-section of the pavement panel into multiple strips of equal width, calculate the wheel load distribution probability of each strip, and then combine the foundation support stiffness degradation coefficient η and the mean μ calculated in step S5. j and standard deviation σ j The overall failure probability P is calculated using a probability weighting method. f .

[0013] In step S1, a simplified analysis model for the rigid pavement of the airport is established. This model simplifies the three-dimensional pavement structure into a longitudinal two-dimensional section. The base course and the subgrade within a finite depth range are equivalent to a series of independent spring elements. The pavement panel adopts a concrete plastic damage constitutive model. The specific methods for setting the pavement panel parameters, aircraft wheel load parameters, and wheel load taxiing paths are as follows:

[0014] S1.1. A simplified analysis model of the rigid pavement of the airport is established using the finite element software ABAQUS. The model takes a unit width section along the transverse direction of the three-dimensional pavement structure and approximates it as a longitudinal two-dimensional section for analysis. The base course and the subgrade within a finite depth range are equivalent to a series of mutually independent spring elements.

[0015] S1.2 The pavement panel is a 5m×5m cement concrete pavement panel, and the concrete plastic damage constitutive model built into the finite element software ABAQUS is selected.

[0016] S1.3. The equivalent single wheel load of the aircraft's main landing gear is used as the aircraft wheel load value. The wheel load taxiing path includes three typical paths: the longitudinal centerline of the runway panel, the transverse 1 / 4 position of the runway panel, and the longitudinal joint of the runway panel.

[0017] In step S2, the maximum tensile strain ε of the critical duct panel bottom corresponding to each damage level is... i The range of values ​​for is as follows:

[0018] The critical maximum tensile strain ε on the bottom of the runner plate corresponding to minor damage, moderate damage, severe damage, and complete failure is described. i The range of values ​​for ε is: 0.00008 ≤ ε t <0.0001, 0.0001≤ε t <0.00016, 0.00016≤ε t <0.0003 and ε t ≥0.0003.

[0019] In step S3, the formula for the foundation support stiffness degradation coefficient η is as follows:

[0020]

[0021] In the formula: K j K0 and K0 are the reaction moduli of the top surface of the base course with and without deterioration, respectively, in MN / m. 3 According to the "Design Specification for Cement Concrete Pavement of Civil Airports" (MH / T5004-2010), the reaction modulus K0 of the top surface of the base course where the subgrade performance has not deteriorated is taken as 150MN / m. 3 The reaction modulus K of the top surface of the base course where the foundation performance deteriorates j The value range is 30-150 MN / m 3 .

[0022] In step S4, considering the uniform and non-uniform degradation of the foundation support stiffness, the specific method for calculating the actual maximum tensile strain at the bottom of the pavement, based on the simplified analysis model of the airport rigid pavement established in step S1 and the foundation support stiffness degradation coefficient η introduced in step S3, is as follows:

[0023] S4.1 When the stiffness of the foundation support degrades uniformly, select 30-150 MN / m. 3 The reaction modulus K of the top surface of the base course, where multiple foundation properties deteriorate within the range. jAccording to equation (1) in step S3, a set of foundation support stiffness degradation coefficients η are calculated. Then, the simplified analysis model of the airport rigid pavement established in step S1 is used for analysis. According to the three wheel-load taxiing paths set in step S1.3, the maximum tensile strain ε of the pavement slab under each foundation support stiffness degradation coefficient η is obtained. ten ;

[0024] S4.2 When the stiffness of the foundation support degrades unevenly, select 30-150 MN / m. 3 The reaction modulus K of the top surface of the base course, where multiple foundation properties deteriorate within the range. j According to equation (1) in step S3, calculate the corresponding set of foundation support stiffness degradation coefficients η; assuming that the foundation support stiffness follows a normal distribution along the longitudinal direction, use the mean μ to characterize the overall foundation support stiffness level, and use the coefficient of variation CV to characterize the stiffness dispersion. The expression of the coefficient of variation CV is shown in equation (2).

[0025]

[0026] In the formula, σ represents the standard deviation of the normal distribution function of the foundation support stiffness;

[0027] Then, based on the mean μ and coefficient of variation CV, a set of foundation support stiffness values ​​under each foundation support stiffness degradation coefficient η is randomly generated. These generated foundation support stiffness values ​​are then randomly assigned to the spring elements below the pavement panel in the simplified analysis model of the airport rigid pavement established in step S1. The simplified analysis model of the airport rigid pavement is then used for analysis, and according to the three wheel-load taxiing paths set in step S1.3, the actual maximum tensile strain ε at the bottom of the pavement panel corresponding to each set of foundation support stiffness values ​​under each foundation support stiffness degradation coefficient η is calculated. ten .

[0028] In step S5, the specific method for constructing the vulnerability function in the form of the standard normal distribution cumulative function is as follows:

[0029] The expression for the vulnerability function in the form of the standard normal cumulative function is:

[0030]

[0031] In the formula, S d In response to demand S d Take the actual maximum tensile strain ε at the bottom of the track panel obtained in step S4. ten ; For responsiveness Take the maximum tensile strain ε at the bottom of the critical channel panel obtained in step S2. t ; Response demand S d With responsiveness The ratio is used to quantify the safety margin of pavement panels under aircraft wheel loads;

[0032] Response demand S d and responsiveness Assuming it follows a log-normal distribution, for equation (3) Perform a univariate linear regression fit to obtain the mean μ. j and standard deviation σ j The expressions are as follows:

[0033] μ j =aln(η)+b (4);

[0034]

[0035] In the formula, a and b are the slope and intercept in the univariate linear regression fitting expression, respectively; S r This is the sum of squared residuals at each calculation point in the univariate linear regression fitting expression;

[0036] Based on the above mean μ j and standard deviation σ j The probability P of the damage to the track panel that meets the specified damage level j, as shown in equation (3). f The cumulative distribution function of the standard normal distribution shown in Equation (6) is converted into the form of the standard normal distribution. Then, based on Equation (6), the vulnerability function expression of the pavement panel under each damage level j is obtained, which represents the failure probability of the pavement panel under the degree of foundation performance deterioration.

[0037]

[0038] In the formula, Φ is the cumulative distribution function of the standard normal distribution.

[0039] In step S6, the aircraft main landing gear wheel track distribution model is introduced. It is assumed that the wheel tracks follow a standard normal distribution laterally on the pavement panel. The cross-section of the pavement panel is discretized into multiple strips of equal width. The wheel load distribution probability of each strip is calculated, and then combined with the foundation support stiffness degradation coefficient η and the mean μ calculated in step S5, the model is applied. j and standard deviation σ j The overall failure probability P is calculated using a probability weighting method. f The specific methods are as follows:

[0040] S6.1. Discretize the cross-section of the pavement panel into e strips of equal width, each strip having a width of f meters. The width of the strips is approximately consistent with the lateral dimension of the simplified wheel mark of the aircraft's main landing gear. Based on the pavement panel dimensions of 5m × 5m set in step S1.2, the relationship between e and f satisfies the following formula:

[0041] e*f=5 (7);

[0042] The wheel load distribution probability of strip i is calculated using the cumulative probability expression of the standard normal distribution shown in equation (8). The wheel load distribution probability of the symmetrical strip is twice that of the single strip.

[0043]

[0044] In the formula, a i and b i Let represent the lower and upper limits of the lateral coordinates of strip i, respectively; μ is the mean of the lateral distribution of the wheel tracks; σ is the standard deviation of the lateral distribution of the wheel tracks; and Φ is the cumulative distribution function of the standard normal distribution, expressed as:

[0045]

[0046] S6.2. Based on the wheel load distribution probability of the above strip i and the mean value μ of the corresponding vulnerability function calculated by equations (4) and (5) in step S5. j and standard deviation σ j The probability weighted method was used to calculate the comprehensive failure probability of the pavement panel reaching damage level j under aircraft wheel load. For the foundation support stiffness degradation coefficient η, the comprehensive failure probability P of the pavement panel reaching damage level j was calculated. f The calculation formula is shown in equation (10):

[0047]

[0048] In the formula, Φ is the cumulative distribution function of the standard normal distribution; p i Let be the probability distribution of wheel load for strip i.

[0049] The vulnerability analysis method for rigid pavements under wheel loads considering foundation performance degradation provided by this invention has the following advantages: By introducing a foundation support stiffness degradation coefficient and combining it with reliability theory, a vulnerability analysis framework for airport rigid pavements considering foundation performance degradation is established, enabling quantitative calculation of pavement failure probabilities under different degrees of degradation. This method can comprehensively reflect the spatial variability of foundation support stiffness and the degradation law of structural performance, and the analysis results are closer to actual operating conditions. This invention effectively overcomes the shortcomings of traditional pavement structural analysis in considering the effects of foundation degradation and randomness. The calculation process is simple, efficient, accurate, and highly applicable, providing scientific and reliable technical support for the structural safety assessment, operation and maintenance, and life prediction of airport rigid pavements. Attached Figure Description

[0050] Figure 1 The flowchart of the method for analyzing the vulnerability of rigid pavement under wheel load considering the deterioration of foundation performance provided by the present invention is shown.

[0051] Figure 2This is a schematic diagram of the simplified analysis model of airport rigid pavement in this invention.

[0052] Figure 3 This is a schematic diagram of three wheel-mounted sliding paths in this invention.

[0053] Figure 4 This is a comparison of pavement vulnerability curves under various damage states with uniform degradation of foundation support stiffness.

[0054] Figure 5 This is a comparison of vulnerability curves for moderate damage to pavement under different wheel-load skid paths under uniform degradation of foundation support stiffness.

[0055] Figure 6 This is a comparison of pavement vulnerability curves under moderate damage conditions when the foundation support stiffness deteriorates unevenly.

[0056] Figure 7 This is a schematic diagram of the lateral wheel track distribution of the main landing gear wheels of an aircraft.

[0057] Figure 8 A comparison of pavement vulnerability curves taking into account wheel track distribution. Detailed Implementation

[0058] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0059] like Figure 1 As shown, the method for analyzing the vulnerability of rigid pavement under wheel load considering the deterioration of foundation performance provided by the present invention includes the following steps performed in sequence:

[0060] S1. Establish a simplified analysis model for rigid pavement of the airport. This model simplifies the three-dimensional pavement structure into a longitudinal two-dimensional section. The base layer and the subgrade within a finite depth range are equivalent to a series of independent spring elements. The pavement panel adopts the plastic damage constitutive model of concrete and sets the pavement panel parameters, aircraft wheel load parameters and wheel load taxiing path.

[0061] The specific method is as follows:

[0062] S1.1, Using the finite element software ABAQUS, establish as follows: Figure 2 The simplified analysis model of the rigid pavement of the airport shown is used to analyze the three-dimensional pavement structure by taking a unit width section in the transverse direction and approximating it as a longitudinal two-dimensional section. The base course and the subgrade within a finite depth range are treated as a series of independent spring elements.

[0063] S1.2 The pavement panel is a 5m×5m cement concrete pavement panel, and the concrete plastic damage constitutive model built into the finite element software ABAQUS is selected.

[0064] S1.3, The equivalent single wheel load of the aircraft's main landing gear is used as the aircraft wheel load value, such as... Figure 3 As shown, the wheel-borne sliding path includes three typical paths: the longitudinal centerline of the track panel, the transverse 1 / 4 position of the track panel, and the longitudinal joint of the track panel.

[0065] S2, with the maximum tensile strain ε at the bottom of the critical runner panel. i As a damage index, the damage level of the pavement panel is classified into four categories: minor damage, moderate damage, severe damage, and complete failure. The corresponding critical maximum tensile strain ε at the bottom of the pavement panel is determined for each damage level. i The range of values ​​is used to quantify the damage level, as shown in Table 1.

[0066] Table 1. Damage levels and value ranges of pavement panels

[0067]

[0068] S3. Introduce the foundation support stiffness degradation coefficient η to characterize the degree of foundation support stiffness degradation, as shown in Equation (1), and set the foundation support stiffness to be uniform or non-uniform degradation.

[0069]

[0070] In the formula: K j K0 and K0 are the reaction moduli of the top surface of the base course with and without deterioration, respectively, in MN / m. 3 According to the "Design Specification for Cement Concrete Pavement of Civil Airports" (MH / T5004-2010), the reaction modulus K0 of the top surface of the base course where the subgrade performance has not deteriorated is taken as 150MN / m. 3 The reaction modulus K of the top surface of the base course where the foundation performance deteriorates j The value range is 30-150 MN / m 3 ;

[0071] S4. Considering the uniform and non-uniform degradation of the foundation support stiffness mentioned above, based on the simplified analysis model of the airport rigid pavement established in step S1 and the foundation support stiffness degradation coefficient η introduced in step S3, calculate the actual maximum tensile strain at the bottom of the pavement slab.

[0072] The specific method is as follows:

[0073] S4.1 When the stiffness of the foundation support degrades uniformly, select 30-150 MN / m. 3 The reaction modulus K of the top surface of the base course, where multiple foundation properties deteriorate within the range. jAccording to equation (1) in step S3, a set of foundation support stiffness degradation coefficients η are calculated, as shown in Table 2. Then, the simplified analysis model of the airport rigid pavement established in step S1 is used for analysis, and the maximum tensile strain ε of the pavement slab under each foundation support stiffness degradation coefficient η is obtained according to the three wheel-load taxiing paths set in step S1.3. ten ;

[0074] Table 2. Support Stiffness Degradation Coefficient

[0075]

[0076] S4.2 When the stiffness of the foundation support degrades unevenly, select 30-150 MN / m. 3 The reaction modulus K of the top surface of the base course, where multiple foundation properties deteriorate within the range. j According to equation (1) in step S3, the corresponding set of foundation support stiffness degradation coefficients η are calculated as shown in Table 2. It is assumed that the foundation support stiffness follows a normal distribution along the longitudinal direction. The mean value μ is used to characterize the overall foundation support stiffness level, and the coefficient of variation CV is used to characterize the stiffness dispersion. The expression of the coefficient of variation CV is shown in equation (2).

[0077]

[0078] In the formula, σ represents the standard deviation of the normal distribution function of the foundation support stiffness;

[0079] Then, based on the mean μ and coefficient of variation CV, a set of foundation support stiffness values ​​under each foundation support stiffness degradation coefficient η is randomly generated. These generated foundation support stiffness values ​​are then randomly assigned to the spring elements below the pavement panel in the simplified analysis model of the airport rigid pavement established in step S1. The simplified analysis model of the airport rigid pavement is then used for analysis, and according to the three wheel-load taxiing paths set in step S1.3, the actual maximum tensile strain ε at the bottom of the pavement panel corresponding to each set of foundation support stiffness values ​​under each foundation support stiffness degradation coefficient η is calculated. ten ;

[0080] S5. Define the vulnerability of rigid pavement under aircraft wheel loads as the failure probability of the pavement panel reaching a specific failure state under aircraft wheel loads under conditions of degraded foundation support stiffness; based on the maximum tensile strain ε at the bottom of the critical pavement panel obtained in step S2. i The actual maximum tensile strain ε on the bottom of the track panel obtained in step S4 ten Construct a vulnerability function in the form of a standard normal cumulative function, which represents the probability of damage to the track panel when the response demand reaches a specified damage level j, expressed as:

[0081]

[0082] In the formula, S d In response to demand S d Take the actual maximum tensile strain ε at the bottom of the track panel obtained in step S4. ten ; For responsiveness Take the maximum tensile strain ε at the bottom of the critical channel panel obtained in step S2. i ; Response demand S d With responsiveness The ratio is used to quantify the safety margin of pavement panels under aircraft wheel loads;

[0083] Response demand S d and responsiveness Assuming it follows a log-normal distribution, for equation (3) Perform a univariate linear regression fit to obtain the mean μ. j and standard deviation σ j The expressions are as follows:

[0084] μ j =aln(η)+b (4)

[0085]

[0086] In the formula, a and b are the slope and intercept in the univariate linear regression fitting expression, respectively; S r This is the sum of squared residuals at each calculation point in the univariate linear regression fitting expression;

[0087] Based on the above mean μ j and standard deviation σ j The probability P of the damage to the track panel that meets the specified damage level j, as shown in equation (3). f The cumulative distribution function of the standard normal distribution, as shown in Equation (6), is converted. Then, based on Equation (6), the vulnerability function expression of the pavement panel corresponding to each damage level j is obtained, as follows:

[0088] Table 3 shows the failure probability of the pavement panel under the degree of foundation performance degradation;

[0089]

[0090] In the formula, Φ is the cumulative distribution function of the standard normal distribution.

[0091] Table 3. Vulnerability Function of Track Panel

[0092]

[0093] S6. Introduce the aircraft main landing gear wheel track distribution model, assuming that the wheel tracks follow a standard normal distribution in the transverse direction of the pavement panel. Discretize the cross-section of the pavement panel into multiple strips of equal width, calculate the wheel load distribution probability of each strip, and then combine the foundation support stiffness degradation coefficient η and the mean μ calculated in step S5. j and standard deviation σ j The overall failure probability P is calculated using a probability weighting method. f ;

[0094] The specific steps are as follows:

[0095] S6.1. Discretize the cross-section of the pavement panel into e strips of equal width, each strip having a width of f meters. In this invention, there are 17 strips, each 0.3 meters wide. The width of the strips is approximately consistent with the lateral dimension of the simplified wheel mark of the aircraft's main landing gear. Based on the pavement panel dimensions of 5m × 5m set in step S1.2, the relationship between e and f satisfies the following formula:

[0096] e*f=5 (7)

[0097] The wheel load distribution probability of strip i is calculated using the cumulative probability expression of the standard normal distribution shown in equation (8). The wheel load distribution probability of the symmetrical strip is twice that of the single strip.

[0098]

[0099] In the formula, a i and b i Let represent the lower and upper limits of the lateral coordinates of strip i, respectively; μ is the mean of the lateral distribution of the wheel tracks; σ is the standard deviation of the lateral distribution of the wheel tracks; and Φ is the cumulative distribution function of the standard normal distribution, expressed as:

[0100]

[0101] The probability statistics of wheel load distribution for each strip are shown in Table 4.

[0102] Table 4. Wheel load distribution probability for each strip

[0103]

[0104] S6.2. Based on the wheel load distribution probability of the above strip i and the mean value μ of the corresponding vulnerability function calculated by equations (4) and (5) in step S5. j and standard deviation σ j The probability weighted method was used to calculate the comprehensive failure probability of the pavement panel reaching damage level j under aircraft wheel load. For the foundation support stiffness degradation coefficient η, the comprehensive failure probability P of the pavement panel reaching damage level j was calculated. f The calculation formula is shown in equation (10):

[0105]

[0106] In the formula, Φ is the cumulative distribution function of the standard normal distribution; p i Let be the probability distribution of wheel load for strip i. Specific implementation examples:

[0108] Please see Figures 2-3 Establish such a finite element method in the ABAQUS software Figure 2 The simplified analysis model of the rigid pavement of the airport is shown. This model takes a unit width section along the transverse direction of the three-dimensional pavement structure and approximates it as a longitudinal two-dimensional section for analysis, and treats the base course and the subgrade within a finite depth range as a series of independent spring elements. Figure 3 This diagram illustrates three wheel-load taxiing paths. In the model, the longitudinal dimension of the pavement surface layer is set to 5m, the mesh size to 0.1m, the elastic modulus of the concrete surface layer to be 34.5GPa, and the surface layer thickness to range from 0.24 to 0.40m. Using the equivalent single-wheel load of the Boeing 737-800 main landing gear as the wheel load value, three typical wheel-load taxiing paths are selected. In the diagram, L represents the lateral dimension of the pavement surface layer, which is taken as 5m.

[0109] Please see Figures 4-5 With a pavement thickness of 0.36m and a wheel-loaded sliding path as the reference, Figure 3 Taking the second path as an example, numerical calculations of the pavement under uniform degradation conditions of different foundation support stiffness were carried out. The maximum tensile strain at the bottom of the pavement slab under each working condition was extracted. Based on the pavement slab damage levels classified in Table 1, univariate linear regression analysis was performed to establish regression analysis models for minor damage, moderate damage, severe damage, and complete failure. Figure 4 This is a comparison of pavement vulnerability curves under different damage states with uniform degradation of foundation support stiffness. Based on this, the failure probability of pavement panels considering different degradation of foundation support stiffness under aircraft wheel loads can be determined. Figure 5 This is a comparison of vulnerability curves for pavement under moderate damage in different wheel-load skid paths under uniform degradation of foundation support stiffness. The selection was made under a fixed pavement thickness of 0.36m. Figure 3 The three typical wheel-mounted taxiing paths shown are analyzed to examine the influence of aircraft wheel-mounted taxiing paths on the failure probability of moderate damage to the pavement.

[0110] Please see Figure 6 The coefficients of variation (CV) were selected as 0, 0.2, and 0.5, corresponding to the degree of dispersion of the spring element stiffness relative to the mean of 0%, 20%, and 50%, respectively. Based on the normal distribution, the foundation support stiffness data were randomly generated as the foundation support stiffness values ​​at each node at the bottom of the pavement panel. Figure 6 This is a comparison of pavement vulnerability curves under moderate damage conditions when the foundation support stiffness deteriorates unevenly.

[0111] Please see Figures 7-8 A lateral wheel track distribution model of the aircraft main landing gear wheels on the pavement is introduced. It is assumed that the taxiing wheel track of a single aircraft main landing gear wheel follows a standard normal distribution with a standard deviation of 1.0 on the cross section of the pavement panel relative to the centerline. The vulnerability function of different wheel load taxiing paths is calculated by probability weighting, thereby obtaining a more reasonable comprehensive failure probability of the pavement panel. Figure 7 This is a schematic diagram of the lateral wheel track distribution of the main landing gear wheels of an aircraft. To discretize the wheel track distribution characteristics, the cross section of the pavement panel is divided into 17 strips of equal width, with each strip having a width of 0.3m. Figure 8 To compare pavement vulnerability curves that take into account wheel track distribution, a pavement analysis model with a surface layer thickness of 0.3m and a coefficient of variation of support stiffness degradation of 0.5 was selected.

[0112] In summary, the method of this invention can accurately reflect the impact of foundation performance degradation on the vulnerability of rigid airport pavements, and can provide a scientific basis for pavement structure safety assessment and operation and maintenance.

Claims

1. A method for analyzing the vulnerability of rigid pavement under wheel loads considering the deterioration of foundation performance, characterized in that: The method for analyzing the vulnerability of rigid pavement under wheel loads that takes into account the deterioration of foundation performance includes the following steps performed in sequence: S1. Establish a simplified analysis model for rigid pavement of the airport. This model simplifies the three-dimensional pavement structure into a longitudinal two-dimensional section. The base layer and the subgrade within a finite depth range are equivalent to a series of independent spring elements. The pavement panel adopts the plastic damage constitutive model of concrete and sets the pavement panel parameters, aircraft wheel load parameters and wheel load taxiing path. S2, with the maximum tensile strain ε at the bottom of the critical runner panel. t As a damage index, the damage level of the pavement panel is classified into four categories: minor damage, moderate damage, severe damage, and complete failure. The corresponding critical maximum tensile strain ε at the bottom of the pavement panel is determined for each damage level. t The range of values ​​for which the damage level is determined is used to quantify the damage level. S3. Introduce the foundation support stiffness degradation coefficient η to characterize the degree of foundation support stiffness degradation, and set the foundation support stiffness as uniform or non-uniform degradation. S4. Considering the uniform and non-uniform degradation of the foundation support stiffness mentioned above, based on the simplified analysis model of the airport rigid pavement established in step S1 and the foundation support stiffness degradation coefficient η introduced in step S3, calculate the actual maximum tensile strain at the bottom of the pavement slab. S5. Define the vulnerability of rigid pavement under aircraft wheel loads as the failure probability of the pavement panel reaching a specific failure state under aircraft wheel loads under conditions of degraded foundation support stiffness; based on the maximum tensile strain ε at the bottom of the critical pavement panel obtained in step S2. t The actual maximum tensile strain ε on the bottom of the track panel obtained in step S4 ten Construct a vulnerability function in the form of a standard normal cumulative function, which represents the probability of damage when the response requirement of the track panel reaches a specified damage level j. S6. Introduce the aircraft main landing gear wheel track distribution model, assuming that the wheel tracks follow a standard normal distribution in the transverse direction of the pavement panel. Discretize the cross-section of the pavement panel into multiple strips of equal width, calculate the wheel load distribution probability of each strip, and then combine the foundation support stiffness degradation coefficient η and the mean μ calculated in step S5. j and standard deviation σ j The overall failure probability P is calculated using a probability weighting method. f .

2. The method for analyzing the vulnerability of rigid pavement under wheel load considering foundation performance degradation as described in claim 1, characterized in that: In step S1, a simplified analysis model for the rigid pavement of the airport is established. This model simplifies the three-dimensional pavement structure into a longitudinal two-dimensional section. The base course and the subgrade within a finite depth range are equivalent to a series of independent spring elements. The pavement panel adopts a concrete plastic damage constitutive model. The specific methods for setting the pavement panel parameters, aircraft wheel load parameters, and wheel load taxiing paths are as follows: S1.

1. A simplified analysis model of the rigid pavement of the airport is established using the finite element software ABAQUS. The model takes a unit width section along the transverse direction of the three-dimensional pavement structure and approximates it as a longitudinal two-dimensional section for analysis. The base course and the subgrade within a finite depth range are equivalent to a series of mutually independent spring elements. S1.2 The pavement panel is a 5m×5m cement concrete pavement panel, and the concrete plastic damage constitutive model built into the finite element software ABAQUS is selected. S1.

3. The equivalent single wheel load of the aircraft's main landing gear is used as the aircraft wheel load value. The wheel load taxiing path includes three typical paths: the longitudinal centerline of the runway panel, the transverse 1 / 4 position of the runway panel, and the longitudinal joint of the runway panel.

3. The method for analyzing the vulnerability of rigid pavement under wheel load considering foundation performance degradation as described in claim 1, characterized in that: In step S2, the maximum tensile strain ε of the critical duct panel bottom corresponding to each damage level is... t The range of values ​​for is as follows: The critical maximum tensile strain ε on the bottom of the runner plate corresponding to minor damage, moderate damage, severe damage, and complete failure is described. t The range of values ​​for ε is: 0.00008 ≤ ε t <0.0001, 0.0001≤ε t <0.00016, 0.00016≤ε t <0.0003 and ε t ≥0.0003.

4. The method for analyzing the vulnerability of rigid pavement under wheel load considering foundation performance degradation as described in claim 1, characterized in that: In step S3, the formula for the foundation support stiffness degradation coefficient η is as follows: Where: K j K0 and K0 are the reaction moduli of the top surface of the base course with and without deterioration, respectively, in MN / m. 3 According to the "Design Specification for Cement Concrete Pavement of Civil Airports" (MH / T5004-2010), the reaction modulus K0 of the top surface of the base course where the subgrade performance has not deteriorated is taken as 150MN / m. 3 The reaction modulus K of the top surface of the base course where the foundation performance deteriorates j The value range is 30-150 MN / m 3 .

5. The method for analyzing the vulnerability of rigid pavement under wheel load considering foundation performance degradation as described in claim 4, characterized in that: In step S4, considering the uniform and non-uniform degradation of the foundation support stiffness, the specific method for calculating the actual maximum tensile strain at the bottom of the pavement, based on the simplified analysis model of the airport rigid pavement established in step S1 and the foundation support stiffness degradation coefficient η introduced in step S3, is as follows: S4.1 When the stiffness of the foundation support degrades uniformly, select 30-150 MN / m. 3 The reaction modulus K of the top surface of the base course, where multiple foundation properties deteriorate within the range. j According to equation (1) in step S3, a set of foundation support stiffness degradation coefficients η are calculated. Then, the simplified analysis model of the airport rigid pavement established in step S1 is used for analysis. According to the three wheel-load taxiing paths set in step S1.3, the maximum tensile strain ε of the pavement slab under each foundation support stiffness degradation coefficient η is obtained. ten ; S4.2 When the stiffness of the foundation support degrades unevenly, select 30-150 MN / m. 3 The reaction modulus K of the top surface of the base course, where multiple foundation properties deteriorate within the range. j According to equation (1) in step S3, calculate the corresponding set of foundation support stiffness degradation coefficients η; assuming that the foundation support stiffness follows a normal distribution along the longitudinal direction, use the mean μ to characterize the overall foundation support stiffness level, and use the coefficient of variation CV to characterize the stiffness dispersion. The expression of the coefficient of variation CV is shown in equation (2). In the formula, σ represents the standard deviation of the normal distribution function of the foundation support stiffness; Then, based on the mean μ and coefficient of variation CV, a set of foundation support stiffness values ​​under each foundation support stiffness degradation coefficient η is randomly generated. These generated foundation support stiffness values ​​are then randomly assigned to the spring elements below the pavement panel in the simplified analysis model of the airport rigid pavement established in step S1. The simplified analysis model of the airport rigid pavement is then used for analysis, and according to the three wheel-load taxiing paths set in step S1.3, the actual maximum tensile strain ε at the bottom of the pavement panel corresponding to each set of foundation support stiffness values ​​under each foundation support stiffness degradation coefficient η is calculated. ten .

6. The method for analyzing the vulnerability of rigid pavement under wheel load considering foundation performance degradation as described in claim 5, characterized in that: In step S5, the specific method for constructing the vulnerability function in the form of the standard normal distribution cumulative function is as follows: The expression for the vulnerability function in the form of the standard normal cumulative function is: In the formula, S d In response to demand S d Take the actual maximum tensile strain ε at the bottom of the track panel obtained in step S4. ten ; For responsiveness Take the maximum tensile strain ε at the bottom of the critical channel panel obtained in step S2. t ; Response demand S d With responsiveness The ratio is used to quantify the safety margin of pavement panels under aircraft wheel loads; Response demand S d and responsiveness Assuming it follows a log-normal distribution, for equation (3) Perform a univariate linear regression fit to obtain the mean μ. j and standard deviation σ j The expressions are as follows: m j =a ln(η)+b (1); In the formula, a and b are the slope and intercept in the univariate linear regression fitting expression, respectively; S r This is the sum of squared residuals at each calculation point in the univariate linear regression fitting expression; Based on the above mean μ j and standard deviation σ j The probability P of the damage to the track panel that meets the specified damage level j, as shown in equation (3). f The cumulative distribution function of the standard normal distribution shown in Equation (6) is converted into the form of the standard normal distribution. Then, based on Equation (6), the vulnerability function expression of the pavement panel under each damage level j is obtained, which represents the failure probability of the pavement panel under the degree of foundation performance deterioration. In the formula, Φ is the cumulative distribution function of the standard normal distribution.

7. The method for analyzing the vulnerability of rigid pavement under wheel load considering foundation performance degradation as described in claim 6, characterized in that: In step S6, the aircraft main landing gear wheel track distribution model is introduced. It is assumed that the wheel tracks follow a standard normal distribution laterally on the pavement panel. The cross-section of the pavement panel is discretized into multiple strips of equal width. The wheel load distribution probability of each strip is calculated, and then combined with the foundation support stiffness degradation coefficient η and the mean μ calculated in step S5, the model is applied. j and standard deviation σ j The overall failure probability P is calculated using a probability weighting method. f The specific methods are as follows: S6.

1. Discretize the cross-section of the pavement panel into e strips of equal width, each strip having a width of f meters. The width of the strips is approximately consistent with the lateral dimension of the simplified wheel mark of the aircraft's main landing gear. Based on the pavement panel dimensions of 5m × 5m set in step S1.2, the relationship between e and f satisfies the following formula: e*f=5 (7); The wheel load distribution probability of strip i is calculated using the cumulative probability expression of the standard normal distribution shown in equation (8). The wheel load distribution probability of the symmetrical strip is twice that of the single strip. In the formula, a i and b i These represent the lower and upper limits of the horizontal coordinate of stripe i, respectively; μ is the mean of the lateral distribution of wheel tracks; σ is the standard deviation of the lateral distribution of wheel tracks; Φ is the cumulative distribution function of the standard normal distribution, and its expression is: S6.

2. Based on the wheel load distribution probability of the above strip i and the mean value μ of the corresponding vulnerability function calculated by equations (4) and (5) in step S5. j and standard deviation σ j The probability weighted method was used to calculate the overall failure probability of the pavement panel reaching damage level j under aircraft wheel load. For the foundation support stiffness degradation coefficient η, the overall failure probability P of the pavement panel reaching damage level j was calculated. f The calculation formula is shown in equation (10): In the formula, Φ is the cumulative distribution function of the standard normal distribution; p i Let be the probability distribution of wheel load for strip i.

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