Method for defining near fault bridge and application thereof

Abstract

The invention relates to the technical field of bridge aseismic design, in particular to a method for defining a near-adjacent fault bridge and application thereof, and the method comprises the following steps: S1, collecting seismic records and geological data of a bridge position; s2, drawing a near fault ground motion fault fracture permanent displacement attenuation relation curve based on the data collected in the step S1; and S3, determining the displacement response in the transverse bridge direction, the longitudinal bridge direction or the vertical bridge direction caused by the permanent displacement. S4, deriving a displacement reaction formula acting on the bridge; and S5, when the static displacement of the bridge structure caused by the fracture displacement of the fault exceeds half of the dynamic effect reservation (expansion joint) D, judging that the bridge is a near fault bridge. According to the method, the possible displacement and position of the bridge under the specific seismic condition can be accurately calculated, and the specific influence of different types of faults (such as strike-slip faults and tilt-slip faults) on the bridge can be predicted, so that a tool with high predictability is provided for design.

Description

Technical Field

[0001] The invention relates to the technical field of bridge seismic design, and in particular to a method for defining a bridge close to a fault and an application thereof. Background Art

[0002] There are far-field and near-field earthquakes. Far-field earthquakes are generally within 20 km of the earthquake source, while near-field earthquakes are within less than 20 km. Near-fault earthquakes are a very special type of near-field earthquake, which not only has ground vibrations but also permanent displacements of surface ruptures. Bridge structures are subject to dual rupture factors of ground vibrations and surface ruptures. The definition of near-fault bridges must consider the permanent displacements of surface ruptures in addition to the strong ground vibrations of near-fault earthquakes. The attenuation of the rupture displacements of near-fault earthquakes causes inconsistent displacements between bridge piers, thereby destroying the bridge structure. The definition of near-fault bridges must consider the impact of permanent displacements of surface ruptures on the mechanical behavior of bridges. Permanent displacements of surface ruptures are related to factors such as magnitude and source mechanism (strike-slip faults and dip-slip faults). Bridge damage is also related to the design parameters of the structure itself (main span length, pier and support stiffness). On the basis of considering the above two factors, the distance of near-fault bridges from the fault is comprehensively determined, thereby defining the concept of near-fault bridges. Only after the concept is clear can we adopt special anti-seismic and shock-absorbing measures for bridges near faults to reduce the destructive effects of near-fault earthquakes on bridge structures. To this end, the present invention proposes to define the concept of near-fault bridges based on the dual factors of earthquake characteristics (magnitude, source mechanism, and permanent displacement attenuation relationship of surface rupture) and bridge structure design parameters (main span length, pier and support stiffness). Summary of the invention

[0003] The purpose of the present invention is to provide a method for defining a bridge close to a fault and its application, a method based on the dual factors of earthquake motion characteristics and bridge structure design parameters to define and identify a bridge close to a fault.

[0004] In order to achieve the above technical objectives and the above technical effects, the present invention is implemented through the following technical solutions:

[0005] A method for defining a bridge proximate to a fault comprises the following steps:

[0006] S1: Collect seismic records and geological data at the bridge location;

[0007] S2: Based on the data collected in step S1, a permanent displacement attenuation curve of the fault rupture near the fault is drawn to describe the relationship between the permanent displacement and the fault distance under different earthquake magnitude conditions.

[0008] S3: According to the attenuation curve obtained in step S2, combined with the fault type analysis and the main span length L of the bridge, the size of the permanent displacement and its action position on the bridge are estimated to determine the displacement response in the transverse, longitudinal or vertical direction of the bridge caused by the permanent displacement.

[0009] S4: Based on the principles of structural mechanics, combined with the stiffness parameters (K1 and K2) and permanent displacement values ​​of the bridge, the displacement response formula acting on the bridge is derived. The displacement response of the bridge under the influence of permanent displacement is calculated in the case of strike-slip faults and dip-slip faults.

[0010] S5: Compare the displacement along the bridge calculated using the formula derived in step S4 with half of the dynamic effect reserve D. If the static displacement of the structure caused by the permanent displacement exceeds half of the dynamic effect reserve, the bridge is determined to be a near-fault bridge.

[0011] Furthermore, the data collection in step S1 specifically includes:

[0012] Magnitude (M w ): The moment magnitude of an earthquake, which represents the total amount of energy released by the earthquake.

[0013] Source mechanism: including fault type, which is mainly divided into strike-slip faults and dip-slip faults.

[0014] Earthquake fault rupture permanent displacement attenuation relationship: This is a curve that characterizes the change of fault rupture permanent displacement with fault distance, usually derived from seismological models.

[0015] Bridge design parameters: including main span (L), pier stiffness (K1), support stiffness (K2), and dynamic effect reserve (D, equal to half the width of the expansion joint).

[0016] Furthermore, the step S2 specifically includes: collecting statistics of seismic data in the earthquake event, drawing a scatter plot of seismic displacement attenuation of the upper and lower plates, and fitting a curve of seismic permanent displacement versus fault distance based on the scatter plot, which is expressed as:

[0017] GSRPD=f(R rup , M w )

[0018] Furthermore, the step S3 specifically includes:

[0019] The main span of the bridge is calibrated at the fault distance, and the permanent displacement ΔP acting on the bridge pier is found on the curve according to the main span. D , the permanent displacement ΔP obtained under the strike-slip fault condition D Acting on the transverse and longitudinal directions of the bridge, the permanent displacement ΔP D Acts on the vertical and longitudinal directions of the bridge.

[0020] Furthermore, the step S4 specifically includes:

[0021] The stiffness of the pier is K1, and the height is H1. According to structural mechanics, we can get

[0022]

[0023] Similarly, the support stiffness can be obtained as EI is the bending stiffness; then the equivalent stiffness of the pier and support is

[0024]

[0025] Obtain

[0026]

[0027] K 11 is the stiffness coefficient caused by unit displacement ΔX;

[0028] The permanent displacement ΔP DX Under the effect

[0029] R=-3K eff ×ΔP DX

[0030] R is the reaction force on the additional chain rod;

[0031] According to the basic equation of displacement method, we can get:

[0032] K 11 ΔX+R=0

[0033] Obtain

[0034]

[0035] In summary, it can be concluded that the bridge is in permanent displacement ΔP DX The displacement along the bridge under the action is

[0036]

[0037] Furthermore, the step S5 specifically includes:

[0038] When the static displacement of the bridge structure caused by the fault rupture displacement exceeds half of the dynamic effect reserve (expansion joint) D, the bridge can be determined to be a near-fault bridge.

[0039] Right now That is, ΔP DX When ≥D, the bridge is a bridge close to the fault;

[0040] ΔP DX With the main span L and fault distance Rrup According to the actual main span L and fault distance R rup Calibrate ΔP DX , determine ΔP DX Is it greater than the dynamic effect reserved D? If so, it means that the bridge is a near-fault bridge, otherwise it is not.

[0041] The criteria for judging the adjacent fault bridge of a dip-slip fault are the same as those for a strike-slip fault, which are:

[0042] When the static displacement of the bridge structure caused by the fault rupture displacement exceeds half of the dynamic effect reserve (expansion joint) D, the bridge can be determined to be a near-fault bridge.

[0043] Right now That is, ΔP DX When ≥D, the bridge is a bridge close to the fault;

[0044] ΔP DX With the main span L, fault distance R rup And the relationship curve between the permanent displacement of the rupture fault and the fault distance changes. According to the actual main span L and fault distance R rup The relationship curve between the permanent displacement of the rupture fault and the fault distance is used to calibrate ΔP DX , determine ΔP DX Is it greater than the dynamic effect reserved D? If so, it means that the bridge is a near-fault bridge, otherwise it is not.

[0045] On the other hand, the present invention proposes the application of the above method in the study of defining the concept of near-fault bridges.

[0046] Beneficial effects of the present invention:

[0047] Traditionally, the seismic design of bridges often only considers the intensity of earthquake motion and rarely considers the permanent displacement of the ground surface. This technical solution collects detailed earthquake records and geological data, and draws a permanent displacement attenuation relationship curve based on these data. This method can accurately calculate the displacement size and position that the bridge may experience under specific earthquake conditions. This analysis is based on the principles of seismology and structural dynamics, and can predict the specific impact of different types of faults (such as strike-slip faults and dip-slip faults) on bridges, thereby providing a highly predictive tool for design. It can assist in predicting the behavior of bridges in actual earthquakes during the design stage, so that the seismic design not only relies on general design standards, but is based on a detailed analysis of specific earthquake motion characteristics and bridge responses, thereby improving the pertinence and adaptability of the design.

[0048] The definition method described in the present invention takes into account the following influencing factors: magnitude, source mechanism (fault type: strike-slip fault and dip-slip fault) and the permanent displacement attenuation relationship curve of the near-fault seismic motion fault rupture, structural design parameters: main span, stiffness parameters of piers and supports, dynamic effect reserve (half the width of the expansion joint). The criteria for near-fault bridges defined in this way are more reasonable and the accuracy is greatly improved.

[0049] In addition, based on the aforementioned influencing factors, the present invention also proposes a determination formula, which comprehensively considers the fault mechanism, bridge span, pier support stiffness, and dynamic effect reservation, thereby reducing the calculation complexity and improving the determination accuracy.

[0050] The determination of bridges close to faults will be conducive to the rational design of bridges, avoid collision damage, and improve the seismic performance and safety of bridges. It is also of great significance for improving the corresponding seismic design standards.

[0051] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0053] Figure 1 The relationship between the permanent displacement of the fault rupture caused by the earthquake near the fault and the fault distance of the present invention;

[0054] Figure 2 This is a front view and parameter description of the simply supported bridge of the present invention; the main span of the bridge L, the stiffness of the pier K1, the stiffness of the support K2, the permanent displacement of the fault transmitted to the bottom of the pier ΔP D , dynamic effect reserved D;

[0055] Figure 3 This is a schematic diagram of the permanent displacement of the bridge pier calibrated in the present invention; the main span L is calibrated on the horizontal coordinate axis, and the permanent displacement ΔP is calibrated on the vertical coordinate axis D ;

[0056] Figure 4 It is a schematic diagram of the permanent displacement in the transverse direction and the longitudinal direction of the bridge acted on by the present invention;

[0057] Figure 5 It is a schematic diagram of the permanent displacement in the vertical and longitudinal directions of the bridge acting on the bridge according to the present invention;

[0058] Figure 6is a bending moment diagram under unit displacement in Example 2 of the present invention;

[0059] Figure 7 is a bending moment diagram of the reaction force of the additional chain rod in Example 2 of the present invention;

[0060] Figure 8 It is the scatter plot of earthquake displacement attenuation of upper and lower plates;

[0061] Fig. 9 It is a schematic diagram of the curve of fitting the permanent displacement of ground motion with fault distance;

[0062] In the attached figure:

[0063] 1. Simplified main span of the bridge, 2. Bridge piers, 3. Bridge side spans, 4. Abutments, 5. Supports, 6. Strike-slip faults, 7. Dip-slip faults. DETAILED DESCRIPTION

[0064] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0065] Example 1

[0066] A method for defining a bridge adjacent to a fault described in this embodiment includes the following steps:

[0067] S1: Collect seismic records and geological data at the bridge location;

[0068] S2: Based on the data collected in step S1, a permanent displacement attenuation curve of the fault rupture near the fault is drawn to describe the relationship between the permanent displacement and the fault distance under different earthquake magnitude conditions.

[0069] S3: According to the attenuation curve obtained in step S2, combined with the fault type analysis and the main span length L of the bridge, the size of the permanent displacement and its action position on the bridge are estimated to determine the displacement response in the transverse, longitudinal or vertical direction of the bridge caused by the permanent displacement.

[0070] S4: Based on the principles of structural mechanics, combined with the stiffness parameters (K1 and K2) and permanent displacement values ​​of the bridge, the displacement response formula acting on the bridge is derived. The displacement response of the bridge under the influence of permanent displacement is calculated in the case of strike-slip faults and dip-slip faults.

[0071] S5: Compare the displacement along the bridge calculated using the formula derived in step S4 with half of the dynamic effect reserve D. If the static displacement of the structure caused by the permanent displacement exceeds half of the dynamic effect reserve, the bridge is determined to be a near-fault bridge.

[0072] The main span of the bridge near the fault is L;

[0073] The stiffness of the bridge pier and support are defined as K1 and K2 respectively;

[0074] The heights of the pier and support are defined as H1 and H2 respectively;

[0075] The dynamic effect reserved parameter is D.

[0076] In this embodiment, collecting data in step S1 specifically includes:

[0077] Magnitude (M w ): The moment magnitude of an earthquake, which represents the total amount of energy released by the earthquake.

[0078] Source mechanism: including fault type, which is mainly divided into strike-slip faults and dip-slip faults.

[0079] Earthquake fault rupture permanent displacement attenuation relationship: This is a curve that characterizes the change of fault rupture permanent displacement with fault distance, usually derived from seismological models.

[0080] Bridge design parameters: including main span (L), pier stiffness (K1), support stiffness (K2), and dynamic effect reserve (D, equal to half the width of the expansion joint).

[0081] In this embodiment, the permanent displacement attenuation relationship curve of the fault rupture in step S2 is expressed as:

[0082] GSRPD=f(R rup , M w )

[0083] The statistics of 80 sets of seismic data in the Chi-Chi earthquake event show that the long-period component shows the relationship between permanent displacement and fault distance attenuation. The scatter plot of earthquake displacement attenuation of the upper and lower plates is shown in the figure below. Figure 8 As shown:

[0084] Based on the scatter plot, the approximate curve of the permanent displacement of the earthquake motion changing with the fault distance is fitted, such as Fig. 9 As shown:

[0085] In this embodiment, step S3 specifically includes:

[0086] The main span of the bridge is calibrated at the fault distance, and the permanent displacement ΔP acting on the bridge pier is found on the curve according to the main span. D, the permanent displacement ΔP obtained under the strike-slip fault condition D Acting on the transverse and longitudinal directions of the bridge, the permanent displacement ΔP D Acts on the vertical and longitudinal directions of the bridge.

[0087] In this embodiment, step S4 specifically includes:

[0088] The stiffness of the pier is K1, and the height is H1. According to structural mechanics, we can get

[0089]

[0090] Similarly, the support stiffness can be obtained as EI is the bending stiffness; then the equivalent stiffness of the pier and support is

[0091]

[0092] Obtain

[0093]

[0094] K 11 is the stiffness coefficient caused by unit displacement ΔX;

[0095] The permanent displacement ΔP DX Under the effect

[0096] R=-3K eff ×ΔP DX

[0097] R is the reaction force on the additional chain rod;

[0098] According to the basic equation of displacement method, we can get:

[0099] K 11 ΔX+R=0

[0100] Obtain

[0101]

[0102] In summary, it can be concluded that the bridge is in permanent displacement ΔP DX The displacement along the bridge under the action is

[0103]

[0104] In this embodiment, step S5 specifically includes:

[0105] When the static displacement of the bridge structure caused by the fault rupture displacement exceeds half of the dynamic effect reserve (expansion joint) D, the bridge can be determined to be a near-fault bridge.

[0106] Right now That is, ΔP DX When ≥D, the bridge is a bridge close to the fault;

[0107] ΔP DX With the main span L and fault distance R rup According to the actual main span L and fault distance R rup Calibrate ΔP DX , determine ΔP DX Is it greater than the dynamic effect reserved D? If so, it means that the bridge is a near-fault bridge, otherwise it is not.

[0108] The criteria for judging the adjacent fault bridge of a dip-slip fault are the same as those for a strike-slip fault, which are:

[0109] When the static displacement of the bridge structure caused by the fault rupture displacement exceeds half of the dynamic effect reserve (expansion joint) D, the bridge can be determined to be a near-fault bridge.

[0110] Right now That is, ΔP DX When ≥D, the bridge is a bridge close to the fault;

[0111] ΔP DX With the main span L, fault distance R rup And the relationship curve between the permanent displacement of the rupture fault and the fault distance changes. According to the actual main span L and fault distance R rup The relationship curve between the permanent displacement of the rupture fault and the fault distance is used to calibrate ΔP DX , determine ΔP DX Is it greater than the dynamic effect reserved D? If so, it means that the bridge is a near-fault bridge, otherwise it is not.

[0112] On the other hand, the present invention proposes the application of the above method in the study of defining the concept of near-fault bridges.

[0113] Example 2

[0114] Definition and formula of near-fault bridge under strike-slip fault

[0115] Permanent displacement and magnitude of fault rupture near fault ground motion (M w ), fault distance (R rup ) and the fault dip angle (δ), the present invention provides a fault rupture permanent displacement attenuation relationship curve that is more in line with the actual situation. The curve describes the relationship between the permanent displacement and the fault distance, such as Figure 1 shown.

[0116] Combination Figure 2 Some parameters of the simply supported bridge include: the main span of the bridge L, the stiffness of the pier K1, the stiffness of the support K2, the permanent displacement of the fault transmitted to the bottom of the pier ΔPD , reserve D for dynamic effect (half of the width of the expansion joint), etc., and derive the specific formula;

[0117] In this embodiment, Figure 1 The main span of the bridge is calibrated by the fault distance in the curve, and the permanent displacement ΔP acting on the bridge pier is found on the curve according to the main span. D ,like Figure 3 As shown;

[0118] The resulting permanent displacement ΔP D Acting on the transverse and longitudinal directions of the bridge, such as Figure 4 As shown;

[0119] According to the relevant knowledge of structural mechanics, the calculation formula is derived as follows:

[0120] The stiffness of the pier is K1, and the height is H1. According to the knowledge of structural mechanics, we can get

[0121]

[0122] Similarly, the support stiffness can be obtained as The equivalent stiffness of the pier and support is

[0123]

[0124] exist Figure 6 middle

[0125] Obtain

[0126]

[0127] In Figure 7 The permanent displacement ΔP is obtained from DX Under the effect

[0128] R1=-3K eff ×ΔP DX

[0129] According to the basic equation of displacement method, we can get:

[0130] K 11 ΔX+R=0

[0131] Obtain

[0132]

[0133] In summary, it can be concluded that the bridge is in permanent displacement ΔP DX The displacement along the bridge under the action is

[0134]

[0135] Judgment conditions: When the static displacement of the bridge structure caused by the fault rupture displacement exceeds half of the dynamic effect reserve (expansion joint) D, the bridge can be determined to be a near-fault bridge.

[0136] Right now That is, ΔP DX When ≥D, the bridge is a bridge close to the fault.

[0137] ΔP DX With the main span L and fault distance R rup According to the actual main span L and fault distance R rup Calibrate ΔP DX , determine ΔP DX Is it greater than the dynamic effect reserved D? If so, it means that the bridge is a near-fault bridge, otherwise it is not.

[0138] Example 3

[0139] Definition and formula of near-fault bridge under dip-slip fault

[0140] In Example 2, the definition method and formula derivation process of the near-fault bridge of a strike-slip fault are given. In this example, the definition and formula of the near-fault bridge under a dip-slip fault will be studied.

[0141] In this embodiment, the difference from Embodiment 2 is that the permanent displacement ΔP of the dip-slip fault is D To act on the vertical and longitudinal directions of the bridge, such as Figure 5 As shown in the figure, the other parameters do not change. The formula derivation proves that the longitudinal displacement of the bridge is only related to the permanent displacement of the ruptured fault ΔP DX Therefore, the criteria for judging the adjacent fault bridge of a dip-slip fault are consistent with those of a strike-slip fault, which are:

[0142] When the static displacement of the bridge structure caused by the fault rupture displacement exceeds half of the dynamic effect reserve (expansion joint) D, the bridge can be determined to be a near-fault bridge.

[0143] Right now That is, ΔP DX When ≥D, the bridge is a bridge close to the fault.

[0144] ΔP DX With the main span L, fault distance R rup And the relationship curve between the permanent displacement of the rupture fault and the fault distance changes. According to the actual main span L and fault distance R rup The relationship curve between the permanent displacement of the rupture fault and the fault distance is used to calibrate ΔP DX , determine ΔP DX Is it greater than the dynamic effect reserved D? If so, it means that the bridge is a near-fault bridge, otherwise it is not.

[0145] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific implementation methods described. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for defining a bridge adjacent to a fault, characterized in that: The following steps are involved: S1: Collect seismic records and geological data at the bridge location; S2: based on the data collected in step S1, a permanent displacement attenuation curve of the fault rupture near the fault is drawn to describe the relationship between the permanent displacement and the fault distance under different earthquake magnitude conditions; S3: according to the attenuation curve obtained in step S2, combined with the fault type analysis and the main span length L of the bridge, the size of the permanent displacement and its action position on the bridge are estimated to determine the displacement response in the transverse direction, longitudinal direction or vertical direction caused by the permanent displacement; S4: Based on the principles of structural mechanics, combined with the stiffness parameters and permanent displacement values ​​of the bridge, the displacement response formula acting on the bridge is derived; the displacement response of the bridge under the influence of permanent displacement in the case of strike-slip faults and dip-slip faults is calculated; S5: Compare the displacement along the bridge calculated using the formula derived in step S4 with half of the dynamic effect reserve D; if the static displacement of the structure caused by the permanent displacement exceeds half of the dynamic effect reserve, the bridge is determined to be a near-fault bridge.

2. The method for defining a bridge adjacent to a fault according to claim 1, characterized in that: The data collection in step S1 specifically includes: Magnitude: The moment magnitude of an earthquake, which represents the total amount of energy released by the earthquake; Source mechanism: including fault type, which is divided into strike-slip fault and dip-slip fault; Attenuation relationship of permanent displacement of fault rupture due to earthquake motion: a curve that characterizes the change of permanent displacement of fault rupture with distance from the fault; Bridge design parameters: including main span, pier stiffness, support stiffness, and dynamic effect reserve.

3. The method for defining a bridge adjacent to a fault according to claim 1, characterized in that: The step S2 specifically includes: collecting statistics of seismic data in earthquake events, drawing a scatter plot of earthquake displacement attenuation between the upper and lower plates, and fitting a curve of seismic permanent displacement versus fault distance based on the scatter plot, which is expressed as: GSRPD=f(R rup ,M w )。 4. The method for defining a bridge adjacent to a fault according to claim 1, wherein: The step S3 specifically includes: The main span of the bridge is calibrated at the fault distance, and the permanent displacement ΔP acting on the bridge pier is found on the curve according to the main span. D , the permanent displacement ΔP obtained under the strike-slip fault condition D Acting on the transverse and longitudinal directions of the bridge, the permanent displacement ΔP D Acts on the vertical and longitudinal directions of the bridge.

5. The method for defining a bridge adjacent to a fault according to claim 1, characterized in that: The step S4 specifically includes: The stiffness of the pier is K1, and the height is H1. According to structural mechanics, we can get Similarly, the support stiffness can be obtained as EI is the bending stiffness; then the equivalent stiffness of the pier and support is Obtain K 11 is the stiffness coefficient caused by unit displacement ΔX; The permanent displacement ΔP DX R = -3K under action eff ×ΔP DX R is the reaction force on the additional chain rod; According to the basic equation of displacement method, we can get: K 11 ΔX+R=0 Obtain In summary, it is concluded that the bridge is in permanent displacement ΔP DX The displacement along the bridge under the action is 6. The method for defining a bridge adjacent to a fault according to claim 1, characterized in that: The step S5 specifically includes: When the static displacement of the bridge structure caused by the fault rupture displacement exceeds half of the dynamic effect reserve D, the bridge can be determined to be a near-fault bridge; Right now That is, ΔP DX When ≥D, the bridge is a bridge close to the fault; The criteria for judging the adjacent fault bridge of a dip-slip fault are the same as those for a strike-slip fault, which are: When the static displacement of the bridge structure caused by the fault rupture displacement exceeds half of the dynamic effect reserve D, the bridge can be determined to be a near-fault bridge; Right now That is, ΔP DX When ≥D, the bridge is a near-fault bridge.

7. Application of the method as claimed in any one of claims 1 to 6 in a conceptual study of defining a near-fault bridge.

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