A method for predicting dynamic response of a lower structure of a long bridge over sea under ship collision

Abstract

The embodiment of the application discloses a method for predicting the dynamic response of a long bridge under a ship collision, comprising: obtaining a time-varying curve of a ship collision force to be evaluated and a bridge unit to be predicted; dividing a pier into a plurality of pier units of a set length along the vertical direction, and determining a stiffness matrix and a mass matrix of each pier unit according to the length of each pier unit; in each time step of the time-varying curve: determining a first shear stiffness between the pier and the pile cap and a second shear stiffness between the pile cap and the pile in the current time step; determining a global stiffness matrix and a global mass matrix of the bridge unit in the current time step; solving the lateral displacement state of the bridge unit in the current time step; and jointly forming the dynamic response of the bridge unit under the time-varying curve of the ship collision force from the lateral displacement state of each time step. The embodiment can determine the dynamic response of the flexible bridge section to the ship collision, and improve the resistance to the ship collision.

Description

Technical Field

[0001] This invention relates to the field of bridge-ship collision technology, and in particular to a method for predicting the dynamic response of the substructure of a long cross-sea bridge to a ship collision. Background Technology

[0002] As man-made structures spanning waterways, bridges undoubtedly pose an obstacle to ships navigating within them. With increasingly busy and diverse shipping traffic in bridge-adjacent waters, the problem of ship collisions with bridges has become more frequent, posing a risk of structural damage and collapse. In the event of a collision, the bridge will bear enormous lateral impact loads. The resulting transient high impact force is transmitted according to the characteristics of different structural systems, leading to a decrease in the resistance or breakage of various vulnerable components, or even collapse. Therefore, it is essential for bridge engineers to deeply understand the collision process between ships and bridge structures and to propose methods to improve bridge safety performance.

[0003] In existing technologies, the understanding of the dynamic characteristics of long-span bridges under ship collisions is insufficient, mainly focusing on anti-ship collision devices and early warning systems. However, these methods are only applicable to collision avoidance and general collisions between large ships and sturdy bridge piers, and are not universally applicable to situations where a ship yaws and then impacts a flexible bridge pier segment. For example, patent CN117888505B, by setting up a buffer connection mechanism, a rotational force-dissipating mechanism, an elastic guiding mechanism, and an energy-absorbing mechanism, causes the ship's impact part to deflect after an impact, thereby reducing the impact force generated by the ship collision and guiding the ship to turn, thus mitigating the damage caused by the ship collision. Patent CN117721766B utilizes water resistance to dissipate the kinetic energy generated when the ship impacts the bridge, and increases water flow resistance through a drag plate to prevent damage to the bridge, thereby avoiding the transmission of the ship's impact force to the bridge and thus preventing damage to the bridge. Patent CN117576951B proposes a ship collision risk probability that encompasses the probability of bridge collapse, the probability of a ship colliding with a bridge, and the risk level of the waterway. It comprehensively considers these three aspects of ship-bridge collision risk research and quantitatively calculates the risk of a ship colliding with a bridge. Patent CN117554964B proposes a bridge collision avoidance early warning method and system based on computer vision. This method filters dangerous targets from multiple ship targets and acquires their movement trajectory information in real time, thereby determining whether the target poses a risk of colliding with a bridge pier.

[0004] In summary, due to the slender pile foundations and beams of non-navigable sections of long cross-sea bridges, which possess a certain degree of flexibility, previous methods for determining dynamic response may no longer be applicable. Therefore, this invention is proposed to improve the resistance of flexible bridge sections to ship collisions. Summary of the Invention

[0005] This invention provides a method for predicting the dynamic response of the substructure of a long cross-sea bridge to a ship collision, in order to solve the above-mentioned technical problems.

[0006] In a first aspect, embodiments of the present invention provide a method for predicting the dynamic response of the substructure of a long cross-sea bridge to a ship collision, including:

[0007] The time-varying curve of the ship impact force to be evaluated and the bridge unit to be predicted are obtained, wherein the bridge unit is obtained by dividing the bridge along the transverse direction and the bridge unit includes beams, piers, abutments and piles.

[0008] The pier is divided vertically into multiple pier units of a set length, and the stiffness matrix and mass matrix of each pier unit are determined according to the length of each pier unit.

[0009] The following operations are performed at each time step of the time-varying curve:

[0010] S1-1. Based on the mechanical parameters of the bridge and the impact stage in the time-varying curve of the ship impact force at the current time step, determine the first shear stiffness between the pier and the abutment and the second shear stiffness between the abutment and the pile at the current time step.

[0011] S1-2. Based on the first shear stiffness, the second shear stiffness, and the stiffness matrix and mass matrix of each pier element, determine the global stiffness matrix and global mass matrix of the bridge element at the current time step.

[0012] S1-3. Based on the global stiffness matrix and global mass matrix, solve for the lateral displacement state of the bridge element at the current time step;

[0013] The lateral displacement state at each time step constitutes the dynamic response of the bridge unit under the time-varying curve of the ship impact force.

[0014] In a second aspect, embodiments of the present invention provide an electronic device, the electronic device comprising:

[0015] One or more processors;

[0016] Memory, used to store one or more programs.

[0017] When the one or more programs are executed by the one or more processors, the one or more processors implement the method for predicting the dynamic response of the substructure of a cross-sea long bridge under ship collision as described in any embodiment.

[0018] Thirdly, embodiments of the present invention also provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for predicting the dynamic response of the substructure of a cross-sea long bridge to a ship collision as described in any embodiment.

[0019] In summary, this invention provides a method for predicting the dynamic response of the substructure of a long cross-sea bridge under ship collision. First, the collision process is simplified and the bridge piers are divided into elements, and the dynamic response of each pier element is determined. Then, a state-space equation for the key bridge components under shear failure conditions is established. Finally, the time-varying ship collision force is input into the state-space equation, and the dynamic response data of the key components is iteratively calculated based on a three-segmented line model describing the shear-displacement relationship of reinforced concrete. This method achieves the following beneficial effects:

[0020] 1) Existing dynamic response determination methods are not applicable to the current situation of ship collisions with bridges with flexible piers. The method in this embodiment proposes a simplified bridge system (i.e., bridge unit) based on the characteristics of flexible piers, and effectively integrates the refined flexible pier unit division strategy with the efficient state space solution method to build an efficient solution for dynamic response analysis of complex bridge components such as slender flexible piers.

[0021] 2) The method in this embodiment combines the Euler-Bernoulli beam free vibration theory and the state-space iterative calculation model, which can quickly obtain the dynamic response of key bridge components, requiring only the following: Figure 3 The analysis process and derivation formulas shown can achieve accurate calculations without the need for time-consuming and labor-intensive simulation software, and the calculation accuracy is high.

[0022] 3) The method in this embodiment establishes a state-space equation that considers the flexible characteristics of bridge piers and incorporates the time-varying stiffness of the connection of key bridge components into the calculation process. Compared with the traditional dynamic response calculation method, this method considers the collision characteristics of non-navigable sections under ship yaw conditions, and provides data support for the protection measures of flexible bridge piers that are more prone to collapse. Attached Figure Description

[0023] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0024] Figure 1 This is a schematic diagram of a ship-bridge collision model provided in an embodiment of the present invention;

[0025] Figure 2 This is a flowchart of a method for predicting the dynamic response of the substructure of a long cross-sea bridge under ship collision, provided by an embodiment of the present invention.

[0026] Figure 3This is a flowchart of another method for predicting the dynamic response of the substructure of a long cross-sea bridge under ship collision, provided by an embodiment of the present invention;

[0027] Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0029] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0030] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0031] This invention provides a method for predicting the dynamic response of the substructure of a long cross-sea bridge to a ship collision. To illustrate this method, the ship-bridge collision model and state-space equations on which this method is based will be introduced first.

[0032] Specifically, in this embodiment, the direction of bridge extension is referred to as the transverse direction, and the direction perpendicular to both the transverse direction and the ground is referred to as the vertical direction. For example... Figure 1As shown, this embodiment divides the entire bridge into multiple units along the transverse direction. Each unit is centered on a pier in the transverse direction and includes, from top to bottom, the beam, pier, abutment, and piles in the vertical direction. These units are referred to as bridge units or simplified bridge systems in this embodiment. The simplified bridge system connected to the ship impact system can be used to simulate the ship-bridge collision process. Under the condition that the bridge does not rotate around its vertical axis and the ship collides with the abutment at a specified speed, the impact of the ship impact system on the simplified bridge system is represented by the time-varying impact force. Since shear failure at the interface of bridge components is a common failure mode for bridges subjected to ship collisions, this embodiment simplifies the form of the connection between the upper and lower abutments, and denotes the shear stiffness and damping of the connection between the abutment and the piles as k. a and c a The shear stiffness and damping of connecting the pier cap to the bridge pier are k, respectively. b and c b The foundation is considered to have a mass of m. a The mass block, the bridge pier is considered to have a mass of m. b The mass block.

[0033] Furthermore, in this embodiment, the piers with large displacement responses are divided vertically into multiple pier units, such as... Figure 1 As shown, the vertical lengths of each pier element are l1, l2…l n Where n is the number of pier elements. Each pier element is described by nodes at both ends, resulting in a total of n+1 nodes. The vertical positions of each node are p1, p2, ..., p1. n p n+1 The lateral displacements of each node are w1, w2...w n w n+1 The rotation angles of each node are θ1, θ2…θ n θ n+1 Based on the Euler-Bernoulli theory of free vibration of beams, the lateral displacement w(x,t) of a single pier element can be obtained by interpolating the displacement and rotation angle of each node using a cubic polynomial function:

[0034] w(x,t)=[N1(x),N2(x),N3(x),N4(x)][w e1 (t),θ e1 (t),w e2 (t),θ e2 (t)] T (1)

[0036] Where x represents the vertical position, w represents the horizontal displacement, and w(x,t) represents the horizontal displacement at the vertical position x at time t; e1 (t) and θ e1(t) represents the lateral displacement and rotation angle of a single pier element at node e1 at time t, respectively. e2 (t) and θ e2 (t) represents the lateral displacement and rotation angle of a single pier element at another node e2 at time t; N1(x), N2(x), N3(x) and N4(x) represent four shape functions, which correspond to the lateral displacement and rotation angle at e1 and the lateral displacement and rotation angle at e2, respectively.

[0037] Integrating the second derivative of the shape function yields the stiffness matrix [K] of a single pier element. e The mass matrix [M] of a single pier element can be obtained by integrating the cross terms of the sum of squares of the shape functions themselves. e ]:

[0038]

[0039] Where l, E, I, and ρA represent the vertical length, elastic modulus, moment of inertia, and mass of a single pier element, respectively.

[0040] Based on the position of each pier element's degree of freedom, the [K] of each pier element is superimposed. e ] and [M e From this, we can obtain the stiffness matrix [K] of the entire bridge pier. pier ] and the mass matrix [M pier Specifically, taking the stiffness matrix as an example, the [K] of the stiffness matrix of each pier element is... e ] superimposed on [K pier At the location corresponding to the pier element, the formula for superimposing the pier stiffness of the n pier elements is:

[0041]

[0042] Among them, [K e ] i,j The stiffness matrix [K] of the bridge pier element e The element in the i-th row and j-th column of ], dof e [K] is the global array of degrees of freedom for the bridge piers. dofe(i),dofe(j) It is the dof of the global stiffness matrix of the bridge pier. e (i) row and the dof e (j) is the element in column (j). Equation (3) is for the pier element, where j = 1, 2, 3, 4, which correspond to the four variables of displacement and rotation angle of two nodes in an element, respectively. The matrix superposition method is equivalent to placing each element in [K pier In the corresponding position of ], since each pier unit is connected to each other through nodes, the common nodes are superimposed.

[0043] Using the same method, the mass matrix [M] of the bridge piers can be obtained. pier ].

[0044] Then, according to the Rayleigh damping calculation formula, the damping matrix of the pier [C] can be obtained. pier ]:

[0045] [C pier ]=α[M pier ]+β[K pier (4)

[0046] Where α and β are proportionality coefficients.

[0047] like Figure 1 As shown, the bridge pier has (n+1) nodes, and the stiffness matrix of the bridge pier has a dimension of (n+1)×(n+1) (in this case, the stiffness matrix eliminates the rotation angle of each node, retaining only the (n+1)×(n+1) node displacements). This embodiment uses the state-space method to obtain the dynamic response of the pier cap and the top of the bridge pier under the action of a ship collision, and needs to consider the k-axis of the pile foundation. a and c a And k acting at the junction of the pier and the pile cap b and c b Therefore, the global mass matrix [M] of the bridge system is simplified. total ] and global stiffness matrix [K total ] can be represented as follows:

[0048]

[0049] Based on the above, the simplified bridge system can be regarded as a response system, with the time-varying curve f(t) of the ship impact force as the system input and the lateral displacement state of the simplified bridge system as the system output. Then, the system matrix [A] and the input matrix [B] can be represented as follows:

[0050]

[0051] Where [I] represents the identity matrix, with 1s on the main diagonal and 0s on the rest.

[0052] The corresponding state equation is:

[0053]

[0054] Where f(t) can be the historical data of the impact force of the ship collision; {w} represents the lateral displacement of the simplified bridge system. {w} is a vector formed by arranging the lateral displacements of each node in the simplified bridge system in order of the position of each node, with a dimension of (n+2)×1. This represents the simplified lateral velocity of the bridge system, which is the first derivative of the lateral displacement with respect to time. It is a vector composed of the lateral velocities of each node in a simplified bridge system arranged in order of their positions, with a dimension of (n+2)×1. This represents the simplified lateral acceleration of the bridge system, which is the second derivative of the lateral displacement with respect to time. It is a vector composed of the lateral accelerations of each node in a simplified bridge system arranged in order of the position of each node, with a dimension of (n+2)×1; The vector represents the lateral displacement state of the bridge unit, with a dimension of (2n+4)×1.

[0055] In the aforementioned state equations, neither the system matrix [A] nor the input matrix [B] reflects the time-varying characteristics of the ship collision process. However, in reality, reinforced concrete components may experience crack propagation, steel yielding and reinforcement, localized concrete cracking and spalling, and even component failure. Therefore, during a ship collision with a non-navigable section of a bridge, the stiffness at the connection between the abutment, pile foundation, and pier is not constant but dynamically changes with time. Therefore, this embodiment divides the ship collision time into multiple time intervals Δt. For any time t... i =iΔt (i = 1, 2, 3, ...), the state equation (9) can be transformed into the following form.

[0056]

[0057] The state equation is a non-homogeneous linear equation with constant coefficients, over a sampling period t. i -Δt≤t≤t i The solution is:

[0058]

[0059] Where τ represents the time variable, and These respectively represent the bridge unit at t i The lateral velocity and lateral acceleration at time t. and These respectively represent the bridge unit at t i -Δt represents the lateral velocity and lateral acceleration.

[0060] The second term on the right side of the above equation can be transformed using Simpson's integral method:

[0061]

[0062] Based on the above ship-bridge collision model and state-space equations Figure 2This is a flowchart illustrating a method for predicting the dynamic response of a long cross-sea bridge substructure to a ship collision, as provided in an embodiment of the present invention. This method is applicable to flexible bridge piers and is executed by electronic equipment. Figure 2 As shown, the method specifically includes:

[0063] S110. Obtain the time-varying curve of the ship impact force to be evaluated, and the bridge unit to be predicted, wherein the bridge unit is obtained by dividing the bridge along the transverse direction, and the bridge unit includes beams, piers, abutments and piles.

[0064] The bridge unit to be predicted can be a simplified bridge system centered on a flexible pier. The time-varying curve of the ship impact force to be evaluated can be the time-varying curve of the ship impact force when a ship of a specific tonnage and speed impacts the simplified bridge system. Optionally, the time-varying curve of the ship impact force can be observed during bridge maintenance. After obtaining the curve, this embodiment will predict in advance the response process of the simplified bridge system to the impact of the ship of the specific tonnage and speed, providing data support for beam collapse risk, bridge design and maintenance, etc.

[0065] S120. Divide the pier vertically into multiple pier units of a set length, and determine the stiffness matrix and mass matrix of each pier unit according to the length of each pier unit.

[0066] The specific process is as described in the ship-bridge collision model above, and the stiffness matrix and mass matrix of each pier element are shown in equation (2).

[0067] S130. Perform the following operations at each time step of the time-varying curve:

[0068] S1-1. Based on the mechanical parameters of the bridge and the impact stage in the time-varying curve of the ship impact force at the current time step, determine the shear stiffness between the pier and the abutment, and the shear stiffness between the abutment and the pile at the current time step.

[0069] For ease of distinction and description, this embodiment refers to the shear stiffness between the pier and the abutment as the first shear stiffness, and the shear stiffness between the abutment and the pile as the second shear stiffness. This step fully considers the time-varying characteristics of the two shear stiffnesses, recalculating the current shear stiffness value in each time step.

[0070] In one specific embodiment, the process may include the following steps:

[0071] Step 1: Based on the mechanical parameters of the pier, calculate the impact force that causes shear cracking and the impact force that causes shear failure between the pier and the abutment. These two impact forces are key parameters between the various components of the bridge and are used to determine the impact stage at the current time step. Specifically, the skeleton curve describing the shear-displacement relationship of reinforced concrete columns currently typically uses a trilinear model. Concrete cracking significantly reduces the shear stiffness of the pier. Furthermore, even after reaching its shear bearing capacity, the pier can still maintain a certain degree of ductility and will not immediately fail. Optionally, based on existing US standards and widely accepted empirical formulas, the following formulas can be used to obtain several key parameters of the pier:

[0072]

[0073]

[0074] Where K1 is the initial shear stiffness, A g ρ is the cross-sectional area of ​​the pier or pile, G is the shear modulus of concrete, H is the height of the pier or pile, K2 is the shear stiffness of the concrete after cracking, η is the axial compression ratio, E is the elastic modulus of concrete, S1 is the impact force that causes shear cracking, S2 is the impact force that causes shear failure, and ρ is the shear stiffness of the concrete after cracking. s It is the reinforcement ratio of the longitudinal bars, f c P is the compressive strength of concrete, λ is the axial force, λ is the shear span ratio of the pier or pile, and S is the shear strength of concrete. c S p and S s These represent the shear capacity, axial force, and circumferential reinforcement of the concrete, respectively; r is the degradation coefficient of the concrete shear strength; h is the cross-sectional width along the loading direction; c is the height of the compression zone within the cross-section; and A... sh It is the total area of ​​the stirrups, f yt θ is the yield strength of the stirrups, s is the stirrup spacing, and θ is the angle between the shear crack and the longitudinal axis of the pier or pile.

[0075] According to the AASHTO American standard, the residual stiffness K3 can be taken as 0.2 times K1.

[0076] K1, K2, K3, S1, and S2 in the above calculations are all key parameters required in subsequent operations. In the calculation, substituting the mechanical parameters of the pier into equations (13) to (16) yields five key parameters between the pier and the abutment; substituting the mechanical parameters of the pile into equations (13) to (16) yields five key parameters between the abutment and the pile. Of course, in addition to calculation based on empirical formulas, shear stiffness can also be determined by fitting the data to existing experimental results; this embodiment does not impose specific limitations.

[0077] Step 2: Determine the ship impact force f(t) at the current time step based on the time-varying curve of the ship impact force.i ), where t i This represents the end time of the current time step.

[0078] Step 3: Solve for the first shear stiffness. In this step, K1, K2, K3, S1, and S2 are all key parameters between the pier and the abutment. Specifically, based on the maximum ship impact force f in the time-varying curve of the ship impact force... max and f(t) i The relationship between S1 and S2 is used to determine the impact stage between the pier and the abutment at the current time step; based on the impact stage, the first shear stiffness within the current time step is determined.

[0079] Optionally, based on the maximum impact force and key control nodes of the trilinear model, this embodiment divides the impact process into 3 stages and 6 cases to determine the shear stiffness, such as... Figure 3 As shown:

[0080] Phase 1: Elastic Impact Phase, including the following two scenarios:

[0081] 1)f max ≤S2 and f(t) i )≤S1

[0082] 2)f max ≥S2 and And f(t) i ) <S1

[0083] In this stage, the first shear stiffness k(i) is taken as the initial shear stiffness K1.

[0084] The second stage: the plastic impact stage, includes the following two situations:

[0085] 3)f max ≤S2 and S1 <f(t i )≤S2

[0086] 4)f max ≥S2 and And S1 <f(t i )≤S2

[0087] In this stage, the first shear stiffness k(i) is taken as the shear stiffness K2 of the concrete after cracking.

[0088] Phase Three: The destructive impact phase, which includes the following two scenarios:

[0089] 5)f max ≥S2 and f(t) i )≥S1

[0090] 6)f max ≥S2 and

[0091] In this stage, the first shear stiffness k(i) is taken as the residual stiffness K3.

[0092] Step 4: Solve for the second shear stiffness. In this step, K1, K2, K3, S1, and S2 are all key parameters between the pile cap and the pile. Similarly, based on the maximum ship impact force f in the time-varying curve of the ship impact force... max and f(t) i The relationship between k(i) and S1 and S2 is used to determine the impact stage between the pier and the abutment at the current time step; based on the impact stage, the second shear stiffness within the current time step is determined. The specific process is similar to step three, except that k(i) represents the second shear stiffness at this time.

[0093] S1-2. Based on the first shear stiffness, the second shear stiffness, and the stiffness matrix and mass matrix of each pier element, determine the global stiffness matrix and global mass matrix of the bridge element at the current time step.

[0094] Corresponding to the stiffness matrix, the first shear stiffness is k in equation (6). b The second shear stiffness is k in equation (6). a The [K] obtained in S120 e [K] generated by superposition pier ], and k obtained in S1-1 a and k b Substituting into equation (6), we can obtain [K] for the current time step. total (i)].

[0095] Similarly, the [M] obtained in S120 e [M] generated by superposition pier ] and m a Substituting into equation (5), we can obtain [M] for the current time step. total ].

[0096] S1-3. Based on the global stiffness matrix and global mass matrix, solve for the lateral displacement state of the bridge element at the current time step.

[0097] Specifically, firstly, based on the global stiffness matrix [K] total (i)] and global quality matrix [M total ], thus obtaining the global damping matrix [C] of the bridge element at the current time step. total (i)]. The calculation method is the same as that in equation (4).

[0098] Then, based on the global stiffness matrix, global mass matrix, and global damping matrix, the system matrix [A] and input matrix [B] of the bridge element at the current time step are determined. Specifically, [K] total (i)]、[M total ] and [C total Substituting (i) into equation (10), we get [A]; [M] total Substituting into equation (8), we get [B].

[0099] Finally, the state equations of the system are solved based on the system matrix and the input matrix to obtain the lateral displacement state of the bridge unit at the current time step. Specifically, substituting [A] and [B] obtained in the previous step into equations (11) and (12) yields the lateral displacement state at the current time step.

[0100] S140. The lateral displacement state at each time step constitutes the dynamic response of the bridge unit under the time-varying curve of the ship impact force.

[0101] Performing operations S1-1 to S1-3 at each time step yields the lateral displacement state at each time step. The lateral displacement states at each time step collectively constitute the dynamic response of the bridge unit under the time-varying curve of the ship impact force, such as... Figure 3 As shown in the figure, t all This indicates the total duration covered by the time-varying curve of the ship's impact force.

[0102] In summary, this embodiment provides a method for predicting the dynamic response of the substructure of a long cross-sea bridge under ship collision. First, the ship-bridge collision process is simplified and the bridge piers are divided into elements. The dynamic response of each pier element is calculated based on the Euler-Bernoulli beam free vibration theory. Then, a state-space equation for the key bridge components under shear failure conditions is established. Finally, the time-varying ship collision force is input into the state-space equation, and the dynamic response data of the key components is iteratively calculated based on a three-segmented line model describing the shear-displacement relationship of reinforced concrete. The method of this embodiment can achieve the following beneficial effects:

[0103] 1) Existing dynamic response determination methods are not applicable to the current situation of ship collisions with bridges with flexible piers. The method in this embodiment proposes a simplified bridge system (i.e., bridge unit) based on the characteristics of flexible piers, and effectively integrates the refined flexible pier unit division strategy with the efficient state space solution method to build an efficient solution for dynamic response analysis of complex bridge components such as slender flexible piers.

[0104] 2) The method in this embodiment combines the Euler-Bernoulli beam free vibration theory and the state-space iterative calculation model, which can quickly obtain the dynamic response of key bridge components, requiring only the following: Figure 3 The analysis process and derivation formulas shown can achieve accurate calculations without the need for time-consuming and labor-intensive simulation software, and the calculation accuracy is high.

[0105] 3) The method in this embodiment establishes a state-space equation considering the flexible characteristics of bridge piers and incorporates the time-varying stiffness at the connection points of key bridge components into the calculation process. Compared with traditional dynamic response calculation methods, this method considers the collision characteristics of non-navigable sections under ship yaw conditions, providing data support for protective measures for flexible bridge piers that are more prone to collapse.

[0106] 4) The method in this embodiment divides the ship-bridge collision impact process into 6 cases to determine the shear stiffness. This method provides a reasonable basis for judging the time-varying shear stiffness in the state-space iterative calculation process, which will help improve the dynamic response calculation accuracy of key bridge components and provide support for the time history analysis of the collision energy dissipation process of the entire bridge structure.

[0107] Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention, such as... Figure 4 As shown, the device includes a processor 60, a memory 61, an input device 62, and an output device 63; the number of processors 60 in the device can be one or more. Figure 4 Taking a processor 60 as an example; the processor 60, memory 61, input device 62, and output device 63 in the device can be connected via a bus or other means. Figure 4 Taking the example of a connection between China and Israel via a bus.

[0108] The memory 61, as a computer-readable storage medium, can be used to store software programs, computer-executable programs, and modules, such as the program instructions / modules corresponding to the method for predicting the dynamic response of the substructure of a long-distance bridge under ship collision in this embodiment of the invention. The processor 60 executes various functional applications and data processing of the device by running the software programs, instructions, and modules stored in the memory 61, thereby realizing the aforementioned method for predicting the dynamic response of the substructure of a long-distance bridge under ship collision.

[0109] The memory 61 may primarily include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a given function; the data storage area may store data created based on terminal usage. Furthermore, the memory 61 may include high-speed random access memory and non-volatile memory, such as at least one disk storage device, flash memory, or other non-volatile solid-state storage device. In some instances, the memory 61 may further include memory remotely located relative to the processor 60, which can be connected to the device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0110] Input device 62 can be used to receive input digital or character information, and to generate key signal inputs related to user settings and function control of the device. Output device 63 may include display devices such as a display screen.

[0111] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for predicting the dynamic response of the substructure of a cross-sea long bridge under ship collision according to any embodiment.

[0112] The computer storage medium of this invention can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0113] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of sending, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device.

[0114] Program code contained on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0115] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof. Programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—as well as conventional procedural programming languages—such as C or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the dynamic response of the substructure of a long cross-sea bridge under ship collision, characterized in that, include: The time-varying curve of the ship impact force to be evaluated and the bridge unit to be predicted are obtained, wherein the bridge unit is obtained by dividing the bridge along the transverse direction, and the bridge unit includes beams, piers, abutments and piles. The pier is divided vertically into multiple pier units of a set length, and the stiffness matrix and mass matrix of each pier unit are determined according to the length of each pier unit. The following operations are performed at each time step of the time-varying curve: S1-1. Based on the mechanical parameters of the pier, calculate the first impact force between the pier and the abutment that causes shear cracking. and the second impact force that caused shear failure. According to the maximum ship impact force in the time-varying curve of the ship impact force. The impact force of the ship at the current time step and and The relationship between the pier and the abutment is used to determine the impact stage between the pier and the abutment at the current time step; based on the impact stage, the first shear stiffness between the pier and the abutment and the second shear stiffness between the abutment and the pile are determined at the current time step. S1-2. Based on the first shear stiffness, the second shear stiffness, and the stiffness matrix and mass matrix of each pier element, determine the global stiffness matrix and global mass matrix of the bridge element at the current time step. S1-3. Based on the global stiffness matrix and global mass matrix, solve for the lateral displacement state of the bridge element at the current time step; The lateral displacement state at each time step constitutes the dynamic response of the bridge unit under the time-varying curve of the ship impact force.

2. The method according to claim 1, characterized in that, The process of determining the stiffness matrix and mass matrix of each pier element based on its length includes: According to the Euler-Bernoulli theory of free vibration of beams, the lateral displacement of each pier element is expressed as an equation of shape function related to the length l of the pier element; Based on the shape functions, determine the stiffness matrix and mass matrix of each pier element.

3. The method according to claim 2, characterized in that, Stiffness matrix of each pier element and They are respectively: ， Where E represents the elastic modulus of the pier element, I represents the moment of inertia of the pier element section, and ρA represents the mass of the pier element.

4. The method according to claim 1, characterized in that, The maximum ship impact force based on the time-varying curve of the ship impact force The impact force of the ship at the current time step and and The relationship between the bridge pier and the abutment is used to determine the impact stage between them at the current time step, including: if and ,or, and and The current time step determines that the bridge pier and abutment are in the elastic impact stage; if and ,or, and and The current time step determines that the bridge pier and abutment are in the plastic impact stage; if and ,or, and The current time step indicates that the bridge pier and abutment are in the stage of destructive impact; among which, Indicates the end time of the current time step; Accordingly, determining the first shear stiffness between the pier and the abutment in the current time step based on the impact stage includes: when the pier and the abutment are in the elastic impact stage, the first shear stiffness between the pier and the abutment in the current time step is the initial shear stiffness; when the pier and the abutment are in the plastic impact stage, the first shear stiffness between the pier and the abutment in the current time step is the shear stiffness of the cracked concrete; when the pier and the abutment are in the destructive impact stage, the first shear stiffness between the pier and the abutment in the current time step is the residual stiffness.

5. The method according to claim 1, characterized in that, S1-2 includes: Based on the positional relationship of each pier unit, the stiffness matrix and mass matrix of each pier unit are superimposed to form the stiffness matrix and mass matrix of the pier. Based on the stiffness matrix of the pier, and the first shear stiffness and the second shear stiffness, the global stiffness matrix of the bridge element at the current time step is generated. Based on the mass matrix of the piers and the mass of the abutments, the global mass matrix of the bridge unit at the current time step is generated.

6. The method according to claim 1, characterized in that, S1-3 includes: Based on the global stiffness matrix and the global mass matrix, the global damping matrix of the bridge element at the current time step is obtained; Time-varying curve of ship impact force As system input, the lateral displacement state of the bridge unit is taken as system output. Based on the global stiffness matrix, global mass matrix, and global damping matrix, the system matrix of the bridge unit at the current time step is determined. and input matrix The lateral displacement state includes lateral velocity. and lateral acceleration ; The system's state equations are solved using the system matrix and input matrix to obtain the lateral displacement state of the bridge unit at the current time step.

7. The method according to claim 6, characterized in that, The state equation is: ， in, This represents the lateral displacement of the bridge unit. This indicates the lateral displacement state of the bridge unit; Accordingly, the state equation at the end of the current time step The solution is: ， in, Indicates the duration of a time step. Represents a time variable. and These respectively represent the bridge units in The lateral velocity and lateral acceleration at time t. and These respectively represent the bridge units in The lateral velocity and lateral acceleration at time t.

8. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors implement the method for predicting the dynamic response of the substructure of a cross-sea long bridge under ship collision as described in any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the method for predicting the dynamic response of the substructure of a long cross-sea bridge under ship collision as described in any one of claims 1-7.

Images