A method for establishing a simplified equivalent model of pile-soil interaction under near-fault ground motion with multiple support excitations

Abstract

The application discloses a kind of near-cross-fault earthquake multi-point excitation pile soil action simplified equivalent model establishment method, the model depth fusion is the spatial non-uniformity characteristics of seismic wave propagation, complex dynamic interaction mechanism of pile-soil interface, and the amplification effect of far-field soil to seismic response, realize the accurate characterization of the dynamic response of bridge structure close to or across fault under strong earthquake action.This model not only greatly improves the simulation efficiency, but also significantly enhances the accuracy of the prediction results, provides a scientific basis and practical tool for bridge engineers in seismic design and performance evaluation, effectively promotes the improvement of the earthquake disaster prevention ability in bridge engineering field.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of civil engineering and geotechnical engineering, and particularly relates to a method for establishing a simplified equivalent model of pile-soil interaction under near-fault earthquake multi-point excitation. BACKGROUND

[0002] In regions with frequent geological activities, bridge construction faces severe challenges, especially when the bridge needs to be built near or across an active fault. The influence of ground motion on bridge structures becomes particularly complex and difficult to predict. Although the existing highway and railway seismic codes recommend avoiding fault construction, in actual engineering, due to the complexity of topography and the urgency of construction needs, it is often difficult to completely avoid active faults, so building bridges near or across faults becomes a necessary choice.

[0003] However, the current technical system has significant shortcomings in dealing with the seismic design of such bridges. First, near-fault and cross-fault ground motion has strong spatial variability, and traditional single-point excitation models cannot accurately simulate this ground motion characteristic, leading to deviations in the evaluation of the seismic performance of bridge structures. Second, the simulation of pile-soil interaction under seismic action is extremely complex, involving nonlinear behavior of soil, dynamic boundary conditions, and far-field soil dynamic effects. Existing models often fail to fully consider these factors, affecting the accuracy and reliability of the simulation results. In addition, although pile-soil interaction models have been widely applied and developed in recent years, comprehensive mechanical models for near-fault or cross-fault bridges are still lacking. These models need to consider the spatial variability of ground motion, accurately simulate pile-soil interaction and far-field soil dynamic effects, while existing models mostly focus on one aspect and cannot meet the comprehensive simulation needs.

[0004] Therefore, a method for establishing a simplified model of pile-soil interaction under cross-fault earthquake multi-point excitation is needed to solve the above technical problems. SUMMARY

[0005] To solve the above technical problems, the application designs a simplified equivalent model of pile-soil interaction under cross-fault earthquake multi-point excitation and a parameter determination method. This model comprehensively considers the spatial variability of ground motion, the complexity of pile-soil interaction, and the far-field soil dynamic effect, achieving comprehensive simulation of near-fault / cross-fault bridges under seismic action, improving simulation efficiency and accuracy, and providing strong support for bridge seismic design and performance evaluation.

[0006] In order to achieve the above technical effects, on the one hand, the application provides a cross-fault earthquake multi-point excitation pile-soil interaction simplified model, comprising: a main beam, a pier, a group pile, a foundation spring, a viscoelastic boundary, and a large mass point; the lower end of the main beam is fixedly connected with a plurality of piers, the lower part of the pier is connected with the group pile, the group pile is composed of a middle pile foundation and surrounding pile foundations, the surrounding pile foundations are connected to the outer side of the middle pile foundation and are connected by soil springs, the surrounding pile foundations are connected by the foundation spring to the viscous boundary, and the bottom of the group pile is the large mass point.

[0007] Further, the foundation spring is a near-field soil spring and a far-field soil spring connected in series.

[0008] On the other hand, the application discloses a method for establishing a cross-fault earthquake multi-point excitation pile-soil interaction simplified model, comprising the following steps:

[0009] S1: a bridge-pile foundation integrated finite element model located in a near / cross-fault region is established;

[0010] S2: the pile-soil interaction of the near-field soil body is equivalent to a spring connected group pile, and the group pile effect is ignored;

[0011] S3: the pile-soil interaction of the far-field soil body is equivalent to a spring connected surrounding group pile spring, and a far-field soil spring-near-field soil spring connected in series is formed;

[0012] S4: the bottom of the group pile is coupled to a large mass point;

[0013] Thirdly, the application provides a method for determining parameters of a cross-fault earthquake multi-point excitation pile-soil interaction simplified model, comprising the following steps:

[0014] S11: based on the established excitation pile-soil interaction simplified model, the stiffness of the near-field soil body is set as k ps , the stiffness of the far-field soil body is set as k s , and the equivalent stiffness k of the group pile is:

[0015]

[0016] In the formula, k ps is the stiffness of the near-field soil body, and k s is the stiffness of the far-field soil body.

[0017] S22: the mechanical parameters of the spring unit and the damping unit at the tangential boundary are determined, and the calculation formula is:

[0018]

[0019] In the formula, K BT is the stiffness coefficient of the tangential spring, C BT is the damping coefficient of the tangential damper, and a Tis the correction coefficient of the viscoelastic boundary, and the value range is [0.5, 1.0]; G is the shear modulus of the foundation, R is the distance from the wave source to the viscoelastic artificial boundary, p is the density of the foundation, c s is the shear wave velocity of the foundation;

[0020] S33: Determine the mechanical parameters of the spring unit and the damping unit at the normal boundary, and the calculation formula is:

[0021]

[0022] In the formula, K BN is the stiffness coefficient of the normal spring, C BN is the damping coefficient of the normal damper, a N is the correction coefficient of the viscoelastic boundary, and the value range is [1.0, 2.0]; G is the shear modulus of the foundation, R is the distance from the wave source to the viscoelastic artificial boundary, p is the density of the foundation, c s is the longitudinal wave velocity of the foundation;

[0023] S44: Coupling all the group piles at the bottom to a large mass point, facilitating multi-point excitation, and the motion equation is:

[0024]

[0025] In the formula, X t and U s respectively represent the absolute displacement vectors of the upper structure and the seismic excitation point; M, C, and K respectively represent the mass, damping and stiffness matrices; the subscripts nn, ss and ns respectively represent the degrees of freedom of the upper structure, the support and the coupling term; R m represents the reaction force vector at the support point.

[0026] The beneficial effects of the present application are:

[0027] Firstly, the present application establishes a multi-point excitation model based on the interaction between pile foundation and soil, comprehensively considers the spatial variability of seismic motion, and overcomes the shortcomings of the traditional single-point excitation model. The model can more accurately reflect the complex seismic motion suffered by the cross-fault bridge, and improves the accuracy of bridge seismic analysis. In the existing model, the complex pile-soil interaction often leads to huge calculation amount and difficulty in convergence. The present application equivalent the interaction between near-field soil and far-field soil into a series spring model, which significantly simplifies the calculation process. At the same time, the large mass point coupling model is adopted, which makes the multi-point excitation calculation more efficient and reduces the occupation of calculation resources.

[0028] In addition, the model of the application is not only suitable for general sites, but also specially considers the special geological environment of bridges near faults or across fault regions. The parameter determination method of the model can adaptively adjust according to the characteristics of the site soil and the propagation path of the seismic wave, ensuring the wide applicability of the model. By accurately calculating the equivalent stiffness of the near-field soil stiffness and the far-field soil stiffness, and correcting the boundary spring and damping using the viscoelastic boundary correction coefficient, the application realizes accurate simulation of the dynamic behavior of complex soil. These improvements improve the reliability of the simulation results, providing more robust technical support for bridge seismic design.

[0029] The motion equation of the application comprehensively considers the interaction between the superstructure, pile foundation and seismic excitation point, ensuring the system integrity of the model. This method can not only be used for seismic analysis of overall bridges, but also for fine design of local structures, meeting the needs of seismic design of different scales. The application reduces the dependence on high-cost sensor equipment and complex field tests through simplified models and optimized calculation methods, providing a cost-effective solution for bridge seismic design in engineering practice. At the same time, the standardization method of model parameters enables engineers to quickly determine design parameters, improving engineering efficiency.

[0030] In summary, the simplified equivalent model of cross-fault seismic multi-point excitation pile-soil interaction and the parameter determination method of the application significantly improve the accuracy, efficiency and reliability of bridge seismic analysis, have important theoretical value and engineering application prospect, and provide an innovative solution for bridge cross-fault seismic design field. BRIEF DESCRIPTION OF DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the embodiments of the application, the following will briefly introduce the drawings needed for the embodiment description.

[0032] Figure 1 is a side view of the simplified model of cross-fault seismic multi-point excitation pile-soil interaction;

[0033] Figure 2 is a top view of the simplified model of cross-fault seismic multi-point excitation pile-soil interaction.

[0034] In the drawings, the components represented by each reference number are listed as follows:

[0035] Main girder 1, pier 2, group pile 3, near-field soil spring 4, far-field soil spring 5, viscoelastic boundary 6, large mass point 7. DETAILED DESCRIPTION

[0036] EMBODIMENT

[0037] The application discloses a simplified equivalent model of cross-fault seismic multi-point excitation pile-soil interaction, which comprises: a main girder, a pier, a group pile, a near-field soil stiffness k ps, far-field soil stiffness k s , viscoelastic boundary, large mass point; the lower end of the main beam is fixedly connected with several bridge piers, the bridge piers are connected with pile groups below, the pile groups are composed of middle pile foundations and surrounding pile foundations, the surrounding pile foundations are connected outside the middle pile foundations and are connected by using soil springs, the spring stiffness of the middle pile foundation is near-field soil stiffness k ps , the surrounding pile foundations are connected by foundation springs, and the bottom of the pile group is a maximum mass point; and the foundation spring is a series connection of near-field soil springs and far-field soil springs;

[0038] Meanwhile, the establishment method of the simplified model is provided in the embodiment, and specifically includes the following steps:

[0039] S1: establishing a bridge-pile foundation integrated finite element model located in a near / far-fault region;

[0040] S2: the pile-soil interaction of the near-field soil is equivalent to a spring connected pile group, the pile group effect is ignored, and the pile-soil interaction is simulated;

[0041] S3: the pile-soil interaction of the far-field soil is equivalent to a spring connected surrounding pile group spring, forming a series connection of far-field soil springs and near-field soil springs;

[0042] S4: the bottom of the pile group is coupled to a large mass point;

[0043] In order to verify the feasibility and superiority of the simplified model of the cross-fault seismic multi-point excitation pile-soil interaction, the following will demonstrate the establishment and parameter determination process of the model in detail through specific cases:

[0044] A certain highway cross-fault bridge seismic performance simulation, site and model setting: the bridge crosses the fault region, the total length is 80 meters, and two bridge piers are provided. The bridge pier height is 20 meters, the foundation form is a pile group foundation. The fault distance: one bridge pier is 10 meters away from the fault, and the other bridge pier is 50 meters away from the fault.

[0045] Parameter setting (hypothetical and experienced value assignment): near-field soil stiffness k ps : 3000 kN / m, far-field soil stiffness k s : 1000 kN / m; viscoelastic boundary coefficient α T : 0.8 (tangential), α N : 1.2 (normal); foundation shear modulus G: 50 MPa; foundation density ρ: 1800 kg / m 3 ; shear wave velocity c s : 200 m / s, longitudinal wave velocity c p : 400 m / s; large mass point: the mass of the pile group bottom is about 1000 tons.

[0046] According to the above parameter setting, the specific establishment process is as follows:

[0047] S1: Establish finite element model: The bridge superstructure, piers and pile group foundation are coupled into an integrated finite element model.

[0048] S2: Near-field pile-soil interaction modeling: The interaction between pile foundation and near-field soil is simulated by spring, and the stiffness k ps = 3000 kN / m.

[0049] S3: Far-field pile-soil interaction in series: The near-field soil spring is connected in series with the far-field soil spring, and the equivalent stiffness is calculated:

[0050]

[0051] S4: Viscoelastic boundary condition setting: Tangential spring stiffness Normal spring stiffness Assuming the distance between the wave source and the boundary is R = 10 m, the calculation can obtain:

[0052] k BT = 4 MN / m, k BT = 6 MN / m

[0053] S5: Large mass point coupling: The bottom of the pile group is coupled to a large mass point to simplify the calculation of multi-point excitation.

[0054] Simulation results and analysis: The displacement of the near-fault pier is the largest, reaching 15 cm, while the displacement of the pier far from the fault is only 6 cm, indicating that the response of the pier under multi-point excitation is significantly different.

[0055] After coupling with the large mass point, the model calculation time is shortened by 30%, and the simulation results have an error of less than 10% compared with the actual seismic monitoring data. This case verifies that the model of the present application can accurately simulate the seismic response of the bridge under multi-point excitation, providing reliable support for bridge seismic design. The viscoelastic boundary effectively reduces the boundary reflection and improves the accuracy of the simulation.

[0056] In summary, the application provides a method for establishing a simplified model of pile-soil interaction under cross-fault earthquake multi-point excitation, which breaks through the limitations of the traditional single-point excitation model by comprehensively considering the spatial variability of ground motion, the complexity of pile-soil interaction, and the far-field soil dynamic effect, and using a multi-point excitation model to simulate the spatial effect. In the model, the seismic excitation received by different support points (bridge piers) is independently input, simulating the multi-point complex vibration generated when the fault passes through the bridge, and considering the influence of fault earthquake pulse and surface rupture permanent displacement. At the same time, the interaction between the near-field soil and the far-field soil is equivalent to a spring model, and a series spring system is used to simulate the dynamic coupling relationship between the two. The near-field soil spring captures the subtle dynamic response around the pile foundation, and the far-field soil spring simulates the remote dynamic influence of the deep soil. And in the model, a viscoelastic boundary is designed, and a correction coefficient is used to adjust the mechanical properties of the tangential and normal springs and dampers, to ensure the real propagation of the seismic wave. Through reasonable calculation of the stiffness coefficient and the damping coefficient, the boundary reflection and energy dissipation in the simulation are optimized. Moreover, the group pile bottom is coupled with a large mass point, effectively simplifying the calculation process of multi-point excitation, making the response of the pile foundation under seismic excitation more accurate, and improving the calculation efficiency. The application establishes the coupling dynamics equation of the upper structure and the support system, comprehensively considers the interaction between the bridge structure, the pile foundation and the seismic excitation, and ensures the accuracy of the overall response of the model.

[0057] The above disclosed preferred embodiments of the application are only used to help illustrate the application, and the preferred embodiments do not describe all the details and do not limit the application to the specific embodiments described.

Claims

1. A method for establishing a simplified equivalent model of pile-soil interaction under multi-point excitation in near-span fault earthquakes, characterized in that, include: The main beam consists of a main beam, piers, pile groups, foundation springs, a viscoelastic boundary, and a large mass point. The lower end of the main beam is fixedly connected to several piers, and the pile groups are connected below the piers. The pile groups consist of a central pile foundation and surrounding pile foundations. The surrounding pile foundations are connected to the outside of the central pile foundations and are connected by soil springs. The surrounding pile foundations are connected to the viscoelastic boundary through foundation springs. The bottom of the pile groups is the large mass point. The basic spring is composed of a near-field soil spring and a far-field soil spring connected in series. The specific method includes the following steps: S1: Establish an integrated finite element model of bridge-pile foundation located near / across fault zones; S2: The pile-soil interaction of the near-field soil is equivalent to a group of piles connected by springs, and the group pile effect is ignored; S3: The pile-soil interaction of the far-field soil is equivalent to a spring connecting the surrounding pile group, forming a series of far-field soil springs and near-field soil springs. S4: The bottom of the pile group is coupled to the large mass point.

2. The parameter determination method for the simplified equivalent model of multi-point excitation pile-soil interaction across faults as described in claim 1, characterized in that, Includes the following steps: S11: Based on the established simplified model of the excitation pile-soil interaction, the near-field soil stiffness is set to k. ps Far-field soil stiffness k s Its equivalent stiffness k is: In the formula, k ps For near-field soil stiffness, k s For far-field soil stiffness; S22: Determine the mechanical parameters of the spring element and damping element at the tangential boundary. The calculation formula is as follows: C BT =ρc s In the formula, K BT C is the stiffness coefficient of the tangential spring. BT Let α be the damping coefficient of the tangential damper. T is the correction factor for the viscoelastic boundary, and its value ranges from [0.5, 1.0]; G is the shear modulus of the foundation, R is the distance from the wave source to the viscoelastic artificial boundary, ρ is the foundation density, and c s The shear wave velocity of the foundation; S33: Determine the mechanical parameters of the spring element and damping element at the normal boundary. The calculation formula is as follows: C BN =ρc p In the formula, K BN C is the stiffness coefficient of the normal spring. BN α is the damping coefficient of the normal damper. N is the correction factor for the viscoelastic boundary, and its value ranges from [1.0, 2.0]; G is the shear modulus of the foundation, R is the distance from the wave source to the viscoelastic artificial boundary, ρ is the foundation density, and c s The longitudinal wave velocity of the foundation; S44: The bottom of the pile group is coupled to a large mass point to facilitate multi-point excitation. Its equation of motion is: In the formula, X t and U s Let represent the absolute displacement vectors of the superstructure and the seismic excitation point, respectively; M, C, and K represent the mass, damping, and stiffness matrices, respectively; subscripts nn, ss, and ns represent the degrees of freedom of the superstructure, the support, and their coupling terms, respectively; R m This represents the vector of the reaction force at the support point.

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