A Multi-Field Coordinated Similarity Design Method for Curved Anchorless Floating Bridges under Seismic-Wave Coupling

Abstract

This invention discloses a design method for seismic-wave multi-field coordinated similarity criteria for deep-water floating bridges, belonging to the technical field of bridge safe service. It involves dimensional analysis of physical quantities in the multi-physics field under seismic-wave coupling: establishing physical quantity relationships under the elastic similarity criterion for the design of the superstructure of the floating bridge, and establishing physical quantity relationships under the gravity similarity criterion for the design of the substructure of the floating bridge. When the geometric quantities of the elastic and gravity similarity criteria are consistent, the time fields are not unified. Therefore, the cross-sectional area of ​​the main beam is corrected to maintain elastic force similarity, and the bending stiffness is corrected to ensure that the dynamic response of the model is consistent with the prototype, thus realizing the similarity criterion design of deep-water floating bridges under seismic-wave multi-field coupling. This invention is simple to operate and can be effectively used for service performance evaluation of large floating bridge structures under seismic-wave multi-field coupling.

Description

Technical Field

[0001] This invention belongs to the field of safe service technology for near-sea and cross-sea bridges, and specifically relates to a multi-field coordinated similarity criterion design method for curved cable-free floating bridges under seismic-wave coupling. Background Technology

[0002] In deep-water floating bridges constructed in marine seismic zones, the structural motion and deformation caused by seismic forces transmitted from the fixed foundations at the bridge's shore-connecting end will lead to significant fluid-structure interaction between the floating foundations and the water body. Considering the characteristics of large floating bridges—large spans, flexible systems, weak lateral resistance, and significant spatial differences in seismic response—the coupling and dynamic effects under multiple seismic and wave-induced hazards will be even more pronounced. The complex environment of extreme seismic-wave coupling can lead to extreme responses in floating bridges, and even local instability of the floating foundations, resulting in the failure of the entire floating bridge structure.

[0003] In multiphysics model testing, accurately reproducing the complex multi-hazard service environment of a target engineering structure within a laboratory scale is a primary scientific challenge for studying the dynamic response evolution mechanism and disaster-causing mechanism of the target structure in extreme environments. Similarity theory is relatively mature in single-physics dynamic model testing, with established model scaling design schemes. However, for multi-hazard coupled model testing of large floating bridges, the incompatibility of multiphysics similarity criteria arises due to their long, flexible structural characteristics and significant multi-field coupling effects. For example, the incompatibility between elastic similarity criteria and Froude similarity criteria in earthquake-wave coupled effects prevents a true reflection of the load characteristics and structural dynamic behavior of the prototype structure under multi-hazard environments. Therefore, research is urgently needed on the design theory and technology of coordinated similarity criteria for floating bridge structures under earthquake-wave multiphysics effects. Summary of the Invention

[0004] Based on the above shortcomings, the purpose of this invention is to provide a multi-field coordinated similarity criterion design method for curved cable-free floating bridges under earthquake-wave coupling, so as to solve the problem that earthquake-wave coupling cannot be accurately realized on a laboratory scale.

[0005] The technical solution adopted in this application is as follows: a design method for seismic-wave multi-field coordinated similarity criteria for deep-water floating bridges, the steps of which are as follows:

[0006] S1: Dimensional analysis of multiphysics physical quantities in earthquake-wave coupling:

[0007] S11: Design of the superstructure of the floating bridge based on the elastic similarity criterion: Under seismic action, the restoring force of the superstructure of the floating bridge, namely the main beam, is mainly elastic force. It is necessary to ensure that the inertial force FI and the elastic force F of the prototype and the scaled model are similar, and to establish the physical quantity relationship under the elastic similarity criterion.

[0008] S12: Design of the substructure based on gravity similarity criterion: The substructure of the floating bridge under wave action, namely the piers and floating foundation, is based on gravity similarity to ensure that the gravity G of the prototype and the model is similar, and to establish the physical quantity relationship under the gravity similarity criterion.

[0009] S2: Earthquake-Wave Multi-Field Coordinated Similarity: When the geometric quantities of the elastic similarity criterion and the gravity similarity criterion are consistent, the time field is not unified. Therefore, the cross-sectional area of ​​the main beam is modified to maintain the similarity of elastic force, and the bending stiffness is modified to ensure that the dynamic response of the model is consistent with the prototype. This realizes the similarity criterion design of the deep-water floating bridge under the coupling effect of earthquake-wave multi-field, and ensures the effective reproduction of the dynamic response of the prototype at the laboratory scale.

[0010] Furthermore, the specific steps of the seismic-wave multi-field coordinated similarity criterion design method for deep-water floating bridges, as described above, are as follows:

[0011] S1: Dimensional analysis of multiphysics physical quantities in earthquake-wave coupling:

[0012] S11: Under earthquake action, the restoring force of the superstructure of the floating bridge, namely the main beam, is mainly elastic force. Based on the elastic similarity criterion, a scaled-down test design was carried out on the main beam. The inertial force and elastic force between the prototype structure and the scaled-down model are kept similar, as shown in formulas (1)-(2).

[0013] λ FI =λ F (1)

[0014] λ ρ ·λ L 3 ·λ a =λ E ·λ L 2 ·λ ε (2)

[0015] In the formula, FI and F are the inertial force and elastic force, respectively; ρ and L are the density and length, respectively; a is the acceleration; E and ε are the elastic modulus and strain, respectively; λ ε =1.0; λ X The physical quantity X in the scaled-down model m Physical quantity X of the prototype structure p The ratio;

[0016] From formula (2):

[0017]

[0018] Where, λ a Represented as:

[0019]

[0020] Therefore, the time term λ t Represented as:

[0021]

[0022] Formula (3) can be rewritten as the velocity term λ. v The function yields:

[0023]

[0024] Considering the speed of sound in a fluid:

[0025]

[0026] In the formula, c is the speed at which sound travels in three dimensions;

[0027] Therefore, formulas (5)-(6) can be further expressed as:

[0028]

[0029] In the formula, v 2 / c 2 M is the Cauchy number; const is a constant; M a It is the Mach number;

[0030] S12: When the substructure of the floating bridge is subjected to wave action, the scaled-down test design of the substructure of the floating bridge, namely the piers and floating foundation, is carried out based on the gravity similarity criterion between the prototype structure and the scaled-down model, as shown in formulas (9)-(11).

[0031] λ FI =λ G (9)

[0032] λ ρ ·λ L 3 ·λ a =λ ρ ·λ L 3 ·λ g (10)

[0033] λ a =λ g (11)

[0034] In the formula, G and g are gravity and gravitational acceleration, respectively;

[0035] Since the prototype structure and the scaled-down model are in the same gravitational field, λ g It is 1.0;

[0036] Formula (11) can be further rewritten as:

[0037] λ t =λ L 1 / 2 (12)

[0038] Formula (10) can be rewritten as the velocity term λ. v The function yields:

[0039]

[0040] In the formula, v 2 / (g·L) is a Froude number;

[0041] This leads to the similarity relationship of the target physical quantities of the corresponding structures under seismic and wave action.

[0042] S2: Earthquake-Wave Multifield Coordination Similarity:

[0043] When the geometric quantities of the elastic similarity criterion and the gravitational similarity criterion are consistent, they are difficult to exist in the same time field. In order to achieve the mutual unification of the elastic similarity criterion and the Froude similarity criterion, for the main beam based on the elastic similarity criterion, let λ E =λ L The duration of the earthquake is amplified, which leads to a change in the velocity term in the scaled model of the actual main beam. According to formula (8), the Cauchy number of the prototype structure and the scaled model will no longer remain unchanged. That is, the elastic force and the inertial force cannot maintain the original similarity relationship. Considering that the change of parameter E has the greatest impact on the elastic force of the section, the scaled criterion of the cross-sectional area of ​​the main beam is modified to be equivalent to the scaled effect of parameter E. As shown in formula (14), the coordinated similarity relationship of each physical quantity under the two similarity criteria under the combined action of earthquake and wave is obtained.

[0044]

[0045] In the formula, A is the cross-sectional area of ​​the main beam;

[0046] Thus, by making a virtual scaling assumption on E, we obtain the modified elastic similarity criterion after magnifying the time field;

[0047] Since the parameter E of the actual model test material cannot be scaled down, the bending stiffness of the prototype structure is similarly modified; let the scaled design of EI be modified to: λ L 5 As shown in formula (15),

[0048] λ EI ′=λ E ·λ I ′=λ L 5(15)

[0049] In the formula, I is the moment of inertia of the main beam section;

[0050] The cross-section design of the main beam is based on the modified bending stiffness, which can reproduce the dynamic response of the prototype structure at the laboratory scale.

[0051] This invention is based on the following principle: To achieve the unification of the elastic similarity criterion and the Froude similarity criterion, this invention diffuses the instantaneous seismic energy over a wider time range, while simultaneously changing the dynamically related physical quantities. Although the accurate simulation of the cross-sectional shape is sacrificed, the time scale under seismic action is magnified, and the geometric scaling ratio remains unchanged. The key to the multiphysics coordinated similarity design of the elastic similarity criterion and the Froude similarity criterion lies in the unification of equations (14) and (15).

[0052] Compared with existing technologies, the advantages and beneficial effects of this invention are as follows: This invention abandons the concept of multi-field model testing based on the Froude similarity criterion in traditional experimental methods. Instead, it establishes dimensional analysis models for each target physical quantity in both the elastic similarity criterion and the Froude similarity criterion for earthquake-wave multi-hazard field effects. The method proposed in this invention is applicable to the dynamic response calculation of earthquake-wave coupling based on displacement, and also ensures that the earthquake field and the wave field are in the same time field, the same acceleration field, and the same gravity field. Thus, by introducing a correction term caused by the dissimilarity of the time term, the incompatibility problem of similarity criteria in the floating bridge structure system under earthquake-wave coupling is solved. This invention is simple to operate and can be effectively used for the service performance evaluation of large floating bridge structures under earthquake-wave multi-field coupling. Attached Figure Description

[0053] Figure 1 A schematic diagram of time field correction for the multi-field similarity criterion between earthquakes and waves; Detailed implementation method:

[0054] The present invention will be further described below with reference to the accompanying drawings. The steps of the multi-field coordinated similarity criterion design method for a curved cable-free floating bridge under seismic-wave coupling action provided by the present invention are as follows:

[0055] Example 1

[0056] A multi-field coordinated similarity criterion design method for a curved, anchorless floating bridge under seismic-wave coupling, comprising the following steps: S1: Dimensional analysis of physical quantities in the multi-physics field under seismic-wave coupling:

[0057] S11: Under earthquake action, the restoring force of the superstructure of the pontoon bridge, i.e., the main beam, is mainly elastic force. When designing scaled-down tests, the dynamic similarity between the prototype and model structures should be based on the elastic force similarity criterion. The inertial force and elastic force between the prototype structure and the scaled-down model should remain similar, as shown in formula (1-2).

[0058] λ FI =λ F (1)

[0059] λ ρ ·λ L 3 ·λ a =λ E ·λ L 2 ·λ ε (2)

[0060] In the formula, FI and F are the inertial force and elastic force, respectively; ρ and L are the density and length, respectively; a is the acceleration; E and ε are the elastic modulus and strain, respectively; λ ε Typically 1.0; λ X The physical quantity X in the scaled-down model m Physical quantity X of the prototype structure p The ratio;

[0061] From formula (2), we can obtain:

[0062]

[0063] Where, λ a Represented as:

[0064]

[0065] Therefore, the time term λ t Represented as:

[0066]

[0067] Formula (3) can be rewritten as the velocity term λ. v The function yields:

[0068]

[0069] Considering the speed of sound in a fluid:

[0070]

[0071] In the formula, c is the speed at which sound travels in three dimensions;

[0072] Therefore, formulas (5)-(6) can be further expressed as:

[0073]

[0074] In the formula, v 2 / c 2 M is the Cauchy number, and const is a constant; a It is the Mach number;

[0075] S12: In model test studies of marine engineering, the motion characteristics of structures are usually dominated by gravity. To satisfy gravity similarity, the substructure of the floating bridge is subjected to wave action. Therefore, based on the gravity similarity criterion, a scaled-down model design of the substructure of the floating bridge, namely the piers and floating foundation, is carried out. The inertial force and gravity between the prototype structure and the scaled-down model are kept similar. See formulas (9)-(11) for details.

[0076] λ FI =λ G (9)

[0077] λ ρ ·λ L 3 ·λ a =λ ρ ·λ L 3 ·λ g (10)

[0078] λ a =λ g (11)

[0079] In the formula, G and g are gravity and gravitational acceleration, respectively;

[0080] Since the prototype structure and the scaled-down model are in the same gravitational field, λ g The value is usually 1.0, resulting in formulas (12)-(13).

[0081] λ t =λ L 1 / 2 (12)

[0082]

[0083] In the formula, v 2 / (g·L) is the Froude number, and the gravity similarity criterion is also known as the Froude similarity criterion;

[0084] In summary, the multi-field similarity criteria for floating bridges under earthquake-wave coupling can be summarized as follows: (1) When the superstructure is subjected to earthquake action, model test design is based on the elastic similarity criterion; (2) When the substructure is subjected to wave action, model test design is based on the gravity similarity criterion. The similarity relationships of the target physical quantities of the structures corresponding to the two disaster field similarity criteria are detailed in Table 1.

[0085] Table 1. Similarity Design of Different Parts of Floating Bridges

[0086]

[0087] S2: Earthquake-Wave Multifield Coordination Similarity:

[0088] It is assumed that the material of the scaled-down model is the same as that of the prototype structure, λ ρ =λ E =1, and based on this, the actual similarity relationship of different parts of the pontoon bridge under different loads is obtained, as shown in Table 2.

[0089] Table 2. Actual similarity design of different parts of floating bridges

[0090]

[0091] When the geometric quantities of the elastic similarity criterion and the gravitational similarity criterion are consistent, they are unlikely to exist in the same time field. The difference in time quantities further leads to inconsistencies in physical quantities such as velocity, acceleration, force, bending moment, elastic modulus, and bending stiffness. Let the elastic similarity criterion and the Froude similarity criterion have the same geometric scaling ratio, i.e., λ. L1 =λ L2 Based on the assumption of the same geometric scaling ratio, dimensional models of motion and dynamic quantities corresponding to the elastic similarity criterion and the Froude similarity criterion under the combined action of earthquake and wave are obtained. See details. Figure 1 .

[0092] To achieve the unification of the elastic similarity criterion and the Froude similarity criterion, for the main beam based on the elastic similarity criterion, let λ E =λ L The duration of the earthquake is amplified, which leads to a change in the velocity term in the scaled-down model of the actual main beam. As shown in Equation (8), the Cauchy number of the prototype pontoon bridge and the scaled-down model will no longer remain unchanged, that is, the elastic force and the inertial force cannot maintain the original similarity relationship. Considering that the change of E has the greatest impact on the elastic force of the section, the scaled-down criterion of the main beam is modified to be equivalent to the scaled-down effect of E, as detailed in Equation (14). The coordinated similarity relationship of each physical quantity under the two similarity criteria under the combined action of earthquake and wave after the update is shown in Table 3.

[0093]

[0094] In the formula, A is the cross-sectional area of ​​the main beam;

[0095] Thus, by making a virtual scaling assumption on E, we obtain the modified elastic similarity criterion after magnifying the time field.

[0096] According to the Freud similarity criterion, E also needs to be scaled down. Since the actual model test material's E cannot be scaled down, similarly, the flexural stiffness of its target structure needs to be modified. Let the scaled-down design of EI be modified to: λ L 5 For details, see formula (15).

[0097] λ EI ′=λ E ·λ I ′=λ L 5 (15)

[0098] In the formula, I is the moment of inertia of the main beam section;

[0099] By designing the cross-section of the main beam based on the modified bending stiffness, the dynamic response of the prototype structure at the laboratory scale can be reproduced.

[0100] To achieve the unification of the elastic similarity criterion and the Froude similarity criterion, this embodiment diffuses the instantaneous seismic energy over a wider time range, while the dynamic physical quantities also change accordingly. Although the accurate simulation of the cross-sectional shape is sacrificed, the time scale under seismic action is magnified, and the geometric scaling ratio remains unchanged. The proposed method is applicable to the dynamic response calculation of seismic-wave coupling based on displacement in this embodiment, and also ensures that the seismic field and the wave field are in the same time field, the same acceleration field, and the same gravity field. Thus, by introducing a correction term caused by the dissimilarity of the time term, the incompatibility of similarity criteria for various components under different loads in the floating bridge structure system under seismic-wave coupling action is solved. The key to the multi-physics field coordinated similarity design of the elastic similarity criterion and the Froude similarity criterion lies in the unification of equations (14) and (15).

[0101] Table 3. Design of Modified Coordination Similarity Relationships

[0102]

Claims

1. A multi-field coordinated similar design method for a curved anchor-cable-free floating bridge under the action of earthquake and wave, characterized in that, The steps are as follows: S1: Seismic-wave coupling multi-physical field physical quantity dimensional analysis: S11: Due to the elastic force of the restoring force of the superstructure of the floating bridge, i.e. the main beam, under the action of the earthquake, the main beam is designed for scale test based on the elastic similarity criterion, the inertia force and the elastic force between the prototype structure and the scale model are kept similar, as shown in formulas (1)-(2), (1) (2) where F and F are the inertial and elastic forces, respectively; p and L are the density and length, respectively; a is the acceleration; E and e are the elastic modulus and strain, respectively; and l ε is 1.0; and l X is the ratio of the physical quantity X m of the scaled model to the physical quantity X p of the prototype structure. From formula (2), we have: (3) where λ a is represented as: (4) Thus, the time term λ t is expressed as: (5) Rewriting equation (3) as a function of the velocity term λ v yields: (6) Considering the speed of sound propagation in fluid is: (7) In the formula, c is the speed of sound propagation in the three-dimensional space; Therefore, formulas (5)-(6) are further expressed as: (8) where v 2 / c 2 is the Cosserat number; const is a constant; is the Mach number; S12: The substructure of the floating bridge is subjected to wave action, and the substructure of the floating bridge, i.e. the pier and the floating foundation, is designed for scale test, and the model test design is based on the gravitational similarity criterion between the prototype structure and the scale model, as shown in formulas (9)-(11), (9) (10) (11) In the formula, G and g are the gravity and the acceleration of gravity, respectively; Since the prototype structure and the scaled model are in the same gravitational field, λ g is 1.0; Formula (11) is further rewritten as: (12) Rewriting equation (10) as a function of the velocity term λ v yields: (13) where v 2 (g-L) is the Froude number; Further, the similarity criterion corresponding to the target physical quantity of the structure under the action of the earthquake and the wave is obtained; S2: Seismic-wave multi-field coordination similarity: When the geometric quantities of elastic similarity criterion and gravity similarity criterion are consistent, they are difficult to be in the same time field. In order to realize the mutual unification of elastic similarity criterion and Froude similarity criterion, the main beam is set as the benchmark of elastic similarity criterion, and λ E = λ L The amplification of earthquake duration leads to the change of velocity term in the scale model of the actual main beam. According to formula (8), the Cauchy number of the prototype structure and the scale model will no longer remain unchanged, that is, the elastic force and the inertial force cannot maintain the original similarity relationship. Considering that the change of parameter E has the greatest impact on the cross-sectional elastic force, the cross-sectional area scale criterion of the main beam is modified to equivalent the scale effect of parameter E, as shown in formula (14). The modified coordination similarity relationship of each physical quantity under the combined action of earthquake and wave under two similarity criteria is obtained, (14) In the formula, A is the cross-sectional area of the main beam; At this point, by assuming a virtual scale of E, the modified elastic similarity criterion after amplifying the time field is obtained; Because the parameter E of the actual model test material cannot be scaled down, the bending stiffness of the prototype structure is corrected in the same way. The scaled-down design of EI is modified as follows: L 5 As shown in equation (15), (15) In the formula, I is the moment of inertia of the main beam section; Based on the modified bending stiffness, the cross-section design of the main beam is carried out, that is, the dynamic response of the prototype structure under the laboratory scale can be reproduced.

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