Simplified equivalent model for multipoint excitation pile-soil action of near-span fault earthquake

Abstract

The invention discloses a near-span fault earthquake multipoint excitation pile-soil effect simplified equivalent model, which deeply integrates spatial non-uniformity characteristics of seismic wave propagation, a pile-soil interface complex dynamic interaction mechanism and an amplification effect of far-field soil on earthquake response. Accurate description of the dynamic response of a bridge structure adjacent to or crossing a fault under the action of a strong earthquake is realized. According to the model, the simulation efficiency is greatly improved, the accuracy of a prediction result is remarkably enhanced, a scientific basis and a practical tool are provided for bridge engineers in aseismic design and performance evaluation, and improvement of the earthquake disaster defense capability in the bridge engineering field is effectively promoted.

Description

Technical Field

[0001] The invention belongs to the technical field of civil engineering and geotechnical engineering, and in particular relates to a simplified equivalent model of pile-soil action for near-fault earthquake multi-point excitation. Background Art

[0002] In areas with frequent geological activities, bridge construction faces severe challenges, especially when bridges need to be close to or cross active faults. The impact of earthquake motion on bridge structures becomes particularly complex and difficult to predict. Although existing highway and railway seismic codes recommend avoiding faults when building bridges, in actual projects, due to the complexity of the topography and the urgency of construction needs, it is often difficult to completely avoid active faults. Therefore, building bridges close to and across faults has become an inevitable choice.

[0003] However, the current technical system has significant deficiencies in dealing with the seismic design of such bridges. First, the ground motion near and across faults has strong spatial variability, and the traditional single-point excitation model cannot accurately simulate this ground motion characteristic, resulting in deviations in the seismic performance evaluation of bridge structures. Second, the simulation of pile-soil interaction under earthquake action is extremely complex, involving multiple aspects such as nonlinear behavior of soil, dynamic boundary conditions, and far-field soil dynamic effects. Existing models often find it difficult to fully consider these factors, thus affecting the accuracy and reliability of the simulation results. In addition, although the pile-soil interaction model has been widely used and developed in recent years, there is still a lack of comprehensive mechanical models for bridges near or across faults. These models need to consider the spatial variability of ground motions and accurately simulate pile-soil interaction and far-field soil dynamic effects. However, most existing models focus on one aspect and cannot meet the needs of comprehensive simulation.

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

[0005] In order to solve the above technical problems, the present invention designs a simplified model of pile-soil interaction under cross-fault earthquake multi-point excitation and a parameter determination method. The model realizes a comprehensive simulation of near / cross-fault bridges under earthquake action by comprehensively considering the spatial variability of seismic motion, the complexity of pile-soil interaction and far-field soil dynamic effects, thereby improving the simulation efficiency and accuracy, and providing strong support for the seismic design and performance evaluation of bridges.

[0006] In order to achieve the above technical effects, on the one hand, the present invention provides a simplified model of pile-soil interaction under cross-fault earthquake multi-point excitation, including: a main beam, a bridge pier, a pile group, a foundation spring, a viscoelastic boundary, and a large mass point; the lower end of the main beam is fixedly connected to a plurality of bridge piers, and the lower part of the bridge piers is connected to the pile group, the pile group is composed of an intermediate pile foundation and surrounding pile foundations, the surrounding pile foundations are connected to the outside of the intermediate pile foundation and are connected by soil springs, the surrounding pile foundations are connected to the viscous boundary by the foundation spring, and the bottom of the pile group is the maximum mass point;

[0007] Furthermore, the foundation spring is composed of a near-field soil spring and a far-field soil spring connected in series;

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

[0009] S1: Establish an integrated finite element model of bridge-pile foundation located near / across fault areas;

[0010] S2: The pile-soil interaction in the near-field soil is equivalent to a group of piles connected by springs, and the pile group effect is ignored;

[0011] S3: The pile-soil interaction of the far-field soil is equivalent to a spring connecting the springs of the surrounding pile groups, forming a far-field soil spring-near-field soil spring series connection;

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

[0013] In a third aspect, the present invention provides a method for determining parameters of a simplified model of pile-soil interaction under cross-fault earthquake multi-point excitation, comprising the following steps:

[0014] S11: Based on the established simplified model of excitation pile-soil interaction, the near-field soil stiffness is set to k ps , far-field soil stiffness k s , then the equivalent stiffness k is:

[0015]

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

[0017] S22: Determine the mechanical parameters of the spring unit and the damping unit at the tangential boundary. The calculation formula is:

[0018]

[0019] Where, K BT The stiffness coefficient of the tangential spring, C BT is the damping coefficient of the tangential damper, α Tis the correction coefficient of the viscoelastic boundary, and its value range is [0.5, 1.0]; G is the foundation shear modulus, R is the distance from the wave source to the viscoelastic artificial boundary, ρ is the foundation density, 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. 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, α N is the correction coefficient of the viscoelastic boundary, and its value range is [1.0, 2.0]; G is the foundation shear modulus, R is the distance from the wave source to the viscoelastic artificial boundary, ρ is the foundation density, c s is the longitudinal wave velocity of the foundation;

[0023] S44: The bottom of the pile group is coupled to a large mass point to facilitate multi-point excitation. The equation of motion is:

[0024]

[0025] Where, X t and U s denote the absolute displacement vectors of the superstructure and the seismic excitation point, respectively; M, C, and K denote the mass, damping, and stiffness matrices, respectively; the subscripts nn, ss, and ns denote the degrees of freedom of the superstructure, support, and their coupling terms, respectively; R m The vector representing the reaction force at the support point.

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

[0027] First, the present invention overcomes the shortcomings of the traditional single-point excitation model by establishing a multi-point excitation model based on the interaction between pile foundation and soil, taking into account the spatial variability of seismic motion. The model can more accurately reflect the complex seismic motions experienced by cross-fault bridges, thereby improving the accuracy of bridge seismic analysis. In existing models, complex pile-soil interactions often lead to huge amounts of calculations and difficulty in convergence. The present invention equates the interaction between the near-field soil and the far-field soil to a series spring model, significantly simplifying the calculation process. At the same time, the use of a large mass point coupling model makes multi-point excitation calculations more efficient and reduces the occupation of computing resources.

[0028] In addition, the model of the present invention is not only applicable to general sites, but also specifically considers the special geological environment of bridges near faults or across fault areas. The parameter determination method of the model can be adaptively adjusted according to the on-site soil characteristics and seismic wave propagation path to ensure 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 using the viscoelastic boundary correction coefficient to correct the boundary spring and damping, the present invention achieves accurate simulation of the dynamic behavior of complex soils. These improvements improve the reliability of the simulation results and provide more robust technical support for bridge seismic design.

[0029] The motion equation of the present invention 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 the seismic analysis of the entire bridge, but also for the fine design of local structures to meet the needs of seismic design of different scales. By simplifying the model and optimizing the calculation method, the present invention reduces the dependence on high-cost sensor equipment and complex field tests, and provides a cost-effective solution for the seismic design of bridges in engineering practice. At the same time, the standardized method of model parameters enables engineers to quickly determine the design parameters and improve engineering efficiency.

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

[0031] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for describing the embodiments are briefly introduced below.

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

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

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

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

[0036] Example

[0037] The invention discloses a simplified model of pile-soil interaction under cross-fault earthquake multi-point excitation, a main beam, a bridge pier, a pile group, and a near-field soil stiffness k ps , far-field soil stiffness ks , viscoelastic boundary, large mass point; the lower end of the main beam is fixedly connected to several bridge piers, and the lower part of the bridge piers is connected to the pile group, which is composed of the middle pile foundation and the surrounding pile foundation. The surrounding pile foundation is connected to the outside of the middle pile foundation and connected by soil springs. The spring stiffness of the middle pile foundation is the near-field soil stiffness k ps , the surrounding piles are connected to the viscous boundary through foundation springs, and the bottom of the pile group is the maximum mass point; and the foundation spring is a near-field soil spring and a far-field soil spring in series;

[0038] At the same time, a method for establishing the simplified model is provided in this embodiment, which specifically includes the following steps:

[0039] S1: Establish an integrated finite element model of bridge-pile foundation located near / across fault areas;

[0040] S2: The pile-soil interaction in the near-field soil is equivalent to a group of piles connected by springs, and the pile group effect is ignored to simulate the pile-soil interaction;

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

[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 pile-soil interaction for cross-fault earthquake multi-point excitation of the present invention, the model establishment and parameter determination process will be demonstrated in detail through a specific case:

[0044] Simulation of seismic performance of a highway bridge across a fault. Site and model settings: The bridge spans the fault area, with a total length of 80 meters and two piers. Pier height: 20 meters, foundation form: pile group foundation. Fault distance: one pier is 10 meters away from the fault, and the other pier is 50 meters away from the fault.

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

[0046] According to the above parameter settings, the specific establishment process is:

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

[0048] S2: Modeling of near-field pile-soil interaction: The interaction between the pile foundation and the near-field soil is simulated by a spring with a stiffness of kps = 3000 kN / m.

[0049] S3: Far-field pile-soil interaction series connection: The near-field soil spring is connected in series with the far-field soil spring to calculate the equivalent stiffness:

[0050]

[0051] S4: Viscoelastic boundary condition setting: tangential spring stiffness Normal spring rate Assuming that the distance between the wave source and the boundary is R = 10m, the calculation can be obtained:

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

[0053] S5: Large mass point coupling: Couple the bottom of the pile group to a large mass point to simplify multi-point excitation calculations.

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

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

[0056] In summary, the simplified model of pile-soil interaction of cross-fault earthquake multi-point excitation proposed by the present invention, by comprehensively considering the spatial variability of ground motion, the complexity of pile-soil interaction and the far-field soil dynamic effect, adopts a multi-point excitation model to simulate this spatial effect, breaking through the limitations of the traditional single-point excitation model. In the model, the seismic excitations received by different support points (bridge piers) are independently input, simulating the multi-point complex vibrations generated when the fault passes through the bridge, and considering the influence of the fault seismic pulse and the permanent displacement of the surface rupture. At the same time, the present invention equates the interaction between the near-field soil and the far-field soil to spring models respectively, and uses a series spring system 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. In addition, a viscoelastic boundary is designed in the model, and the mechanical properties of the tangential and normal springs and dampers are adjusted by correction coefficients to ensure the true propagation of seismic waves. Through the reasonable calculation of the stiffness coefficient and the damping coefficient, the boundary reflection and energy dissipation in the simulation are optimized. The bottom of the pile group is also coupled with a large mass point, which effectively simplifies 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 present invention establishes a coupled dynamic equation between the superstructure and the support system, comprehensively considers the interaction between the bridge structure, pile foundation and seismic excitation, and ensures the accuracy of the overall response of the model.

[0057] The preferred embodiments of the present invention disclosed above are only used to help explain the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to only the specific implementation methods described.

Claims

1. A simplified equivalent model of pile-soil interaction under multi-point earthquake excitation near fault, characterized in that: include: Main beam, bridge piers, pile groups, foundation springs, viscoelastic boundaries, and large mass points; the lower end of the main beam is fixedly connected to a number of bridge piers, and the lower part of the bridge piers is connected to the pile groups, the pile groups are composed of a middle pile foundation and surrounding pile foundations, the surrounding pile foundations are connected to the outside of the middle pile foundation and are connected by soil springs, the surrounding pile foundations are connected to the viscous boundary by the foundation springs, and the bottom of the pile group is the maximum mass point.

2. According to claim 1, a simplified equivalent model of pile-soil interaction under near-fault earthquake multi-point excitation, characterized in that: The foundation spring is composed of a near-field soil spring and a far-field soil spring connected in series.

3. The method for establishing a simplified model of pile-soil interaction under cross-fault earthquake multi-point excitation as claimed in any one of claims 1 to 2, characterized in that: The following steps are involved: S1: Establish an integrated finite element model of bridge-pile foundation located near / across fault areas; S2: The pile-soil interaction in the near-field soil is equivalent to a group of piles connected by springs, and the pile group effect is ignored; S3: The pile-soil interaction of the far-field soil is equivalent to a spring connecting the springs of the surrounding pile groups, forming a far-field soil spring-near-field soil spring series connection; S4: The bottom of the pile group is coupled to a large mass point.

4. The method for determining parameters of the simplified model of pile-soil interaction under cross-fault earthquake multi-point excitation as claimed in any one of claims 1 to 2, characterized in that: The following steps are involved: S11: Based on the established simplified model of excitation pile-soil interaction, the near-field soil stiffness is set to k ps , far-field soil stiffness k s , then the equivalent stiffness k is: In the formula, k ps is the near-field soil stiffness, k s is the far-field soil stiffness. S22: Determine the mechanical parameters of the spring unit and the damping unit at the tangential boundary. The calculation formula is: C BT =ρc s Where, K BT The stiffness coefficient of the tangential spring, C BT is the damping coefficient of the tangential damper, α T is the correction coefficient of the viscoelastic boundary, and its value range is [0.5, 1.0]; G is the foundation shear modulus, R is the distance from the wave source to the viscoelastic artificial boundary, ρ is the foundation density, c s is the shear wave velocity of the foundation; S33: Determine the mechanical parameters of the spring unit and the damping unit at the normal boundary. The calculation formula is: C BN =ρc p In the formula, K BN is the stiffness coefficient of the normal spring, C BN is the damping coefficient of the normal damper, α N is the correction coefficient of the viscoelastic boundary, and its value range is [1.0, 2.0]; G is the foundation shear modulus, R is the distance from the wave source to the viscoelastic artificial boundary, ρ is the foundation density, c s is 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. The equation of motion is: Where, X t and U s denote the absolute displacement vectors of the superstructure and the seismic excitation point, respectively; M, C, and K denote the mass, damping, and stiffness matrices, respectively; the subscripts nn, ss, and ns denote the degrees of freedom of the superstructure, support, and their coupling terms, respectively; R m The vector representing the reaction force at the support point.

Images