CN115114692A - A Simplified Calculation Method for Seismic Response of Swing Type Self-resetting Independent Foundation - Google Patents

Abstract

The invention belongs to the technical field of soil and structure interaction seismic response analysis, and discloses a seismic response simplified calculation method of a swinging type self-resetting independent foundation, which comprises the steps of firstly obtaining basic mechanical property parameters of a foundation soil body, the size of the independent foundation and a vertical gravity load design value, and calculating foundation swinging rigidity, vertical bearing capacity and foundation swinging resetting coefficient; then establishing a bilinear framework curve of a foundation bending moment-foundation corner relation and an unloading-reloading hysteresis rule, and further establishing a foundation bending moment-foundation corner restoring force model; finally, a dynamic control equation of the foundation swing motion is listed, and dynamic swing response of the foundation under the action of the earthquake is calculated. The invention provides an efficient and convenient calculation tool for the seismic response analysis of the novel swing self-reset independent infrastructure system.

Description

A Simplified Calculation Method for Seismic Response of Swing Type Self-resetting Independent Foundation

technical field

The invention belongs to the technical field of seismic response analysis of the interaction between soil and structure, and particularly relates to a simplified calculation method of seismic response of a rocking self-resetting independent foundation.

Background technique

The traditional seismic design requires the foundation to have sufficient bearing capacity to meet the stability and deformation requirements, and the seismic energy is consumed by the ductile deformation of the superstructure. However, due to the large amplitude and long duration of the strong earthquake, the accumulated damage in the structure is heavy, which may cause it to be unrepairable after the earthquake or have potential safety hazards such as stability.

The rocking self-resetting independent foundation structure system is a new post-earthquake recoverable functional structure system with foundation rocking as the dominant movement mode. This type of system uses the lift-off and the plastic deformation of the foundation soil during the foundation rocking process to limit the reaction force of the foundation to the bottom of the foundation, thereby reducing the damage of the superstructure; On a smaller scale, earthquake damage is reduced.

In order to design a reasonable rocking self-resetting independent base structure system, seismic response analysis is required. The conventional practice is to carry out finite element modeling of the entire structure, foundation and foundation system; however, due to nonlinear behaviors such as the elastic-plastic deformation of the structure and foundation soil, the second-order gravity effect, and the foundation lift-off, it is a big problem for engineers. challenge. The American Standard for Seismic Design of Buildings provides a three-line skeleton curve to describe the base moment-base rotation relationship of a rocking foundation under uniaxial static load, but it cannot be used for seismic response due to the lack of unloading-reloading relationship. calculate. Therefore, it is necessary to propose a simplified seismic response calculation method for a rocking self-resetting independent foundation, which provides an efficient and convenient seismic response analysis tool for engineers.

To sum up, the problems existing in the existing technology are: the seismic response analysis of the rocking foundation structure system urgently needs to simplify the calculation method to facilitate the seismic design of such structures by engineers, and the current seismic design standards for buildings adopt the simplified calculation of the response of the rocking foundation. The method is only suitable for uniaxial static loading conditions, and cannot consider the real dynamic response caused by earthquakes, so it cannot be applied to the seismic response analysis of rocking foundation structure systems.

The technical solution for solving this technical problem in the prior art is: adopting the combined system of elastic spring and linear damping pot to approximately consider the nonlinear behavior and energy consumption of the basic rocking response, including two methods. Method 1 uses a multi-polyline elastic spring in parallel with a linear damping pot system; These two calculation methods essentially regard the rocking foundation response as a kind of nonlinear elastic behavior. Although the amplitude of the calculated rocking response can be close to the real situation by optimizing the damping coefficient, the residual rotation angle of the foundation rocking required for the seismic design of the structure cannot be obtained. , also cannot reflect the physical mechanism of the underlying rocking response. In fact, during the rocking motion of the foundation, the plastic compressive deformation of the soil below both ends of the foundation continues to accumulate, resulting in the unloading stiffness and reloading stiffness of the rocking hysteresis curve changing continuously with the amplitude of the rotation angle. Therefore, the elastic calculation method cannot obtain the foundation residual rotation angle caused by the plastic deformation of the foundation soil, nor can the actual hysteresis curve of the foundation rocking motion be obtained.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a simplified calculation method of the seismic response of the rocking self-resetting independent foundation for the convenience of engineering personnel to analyze the seismic response of the new rocking self-resetting independent foundation structure system.

The present invention is realized in this way, a method for calculating the earthquake response of Winkel clay foundation considering compression-shear coupling, and the realization steps include:

和粘聚力c，给定独立基础的边长B和竖向重力荷载设计值N；(1) Obtain the basic mechanical performance parameters of the foundation soil, including density ρ, shear modulus G, Poisson's ratio ν, internal friction angle

and cohesion c, given the side length B of the independent foundation and the design value N of the vertical gravity load;

(2) Calculate the foundation rocking stiffness K _R , the vertical bearing capacity q _u and the foundation rocking reset coefficient F _sc according to the parameters obtained in step (1);

(3) According to the foundation stiffness and vertical bearing capacity obtained in step (2), establish a bilinear skeleton curve of the relationship between the foundation bending moment M and the foundation rotation angle θ;

(4) Determine the unloading-reloading hysteresis rule of the M-θ relationship, and combine the bilinear skeleton curve in step (3) to establish the M-θ restoring force model;

(5) According to the M-θ restoring force model obtained in step (4), the dynamic control equation of the foundation rocking motion is listed, and the dynamic rocking response of the foundation under the action of earthquake is calculated.

Further, the foundation rocking stiffness K _R and the vertical bearing capacity q _u described in step (2) can be obtained from the foundation soil parameters and foundation size by checking the foundation design manual, and the foundation rocking reset coefficient F _sc is calculated as formula (1) :

Further, the bilinear skeleton curve calculation formula of the relationship between the base bending moment M and the base rotation angle θ described in step (3) is as formula (2):

Further, the unloading-reloading hysteresis rule of the M-θ relationship described in step (4) is as follows: unloading and reloading are assumed to be linear relations based on the initial stiffness k=3/5K _R. When the load is reversed and Only when the reverse point is located in the platform segment of the M-θ skeleton curve, the stiffness k is updated, and the calculation is as formula (3):

Further, the dynamic control equation of the basic rocking motion described in step (5) is as formula (4):

In formula (4), J is the moment of inertia of the foundation around its center horizontal axis, ü _g is the horizontal acceleration of the earthquake ground surface, and M(θ) is the M-θ restoring force model; the Newmark integration method is used to solve the dynamic equation to obtain the foundation Dynamic rocking response θ under seismic action.

To sum up, the advantages and positive effects of the present invention are:

(1) The simplified calculation method of the rocking foundation response adopted in the current building seismic design standard is only applicable to the uniaxial static loading condition, and cannot consider the real dynamic response caused by the earthquake, so it cannot be applied to the seismic response analysis of the rocking foundation structure system. The invention proposes an M-θ restoring force model suitable for any loading path, so that the simplified calculation of the response of the rocking foundation can be applied to the real dynamic situation.

(2) The present invention describes the actual situation that the unloading stiffness and the reloading stiffness of the rocking continuously change with the amplitude of the rotation angle by establishing a complete set of basic rocking skeleton curves and unloading-reloading hysteresis rules. Compared with the existing simplified calculation methods based on linear or nonlinear viscoelastic models, which can only estimate the peak rotation angle demand, it can also obtain the foundation rocking residual rotation angle required for the seismic design of the structure, which can well reflect the physical mechanism of the foundation rocking response.

Description of drawings

Fig. 1 is a calculation step diagram of the present invention.

FIG. 2 is a comparison diagram of the calculation results of the present invention and the fine finite element calculation results.

Detailed ways

In order to make the problems, technical solutions and advantages to be solved by the present invention clearer, further detailed description will be given below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the application of the present invention.

Applications:

According to the steps of the simplified calculation method of the seismic response of the rocking self-resetting independent foundation shown in Fig. 1, the rocking response of the independent foundation subjected to the horizontal cyclic reciprocating earthquake under the foundation conditions of the two clay sites is analyzed. The site soil parameters, foundation size, The parameters such as foundation rocking stiffness K _R , vertical bearing capacity _qu and foundation rocking reset coefficient F _sc are shown in Table 1.

Table 1 Site soil, foundation and foundation parameters

Using displacement-controlled cyclic loading, the foundation rocking response can be obtained. Compared with the ABAQUS fine finite element calculation results, the calculation results of this method are basically consistent with the accurate finite element results, as shown in Figure 2. Compared with the fine finite element modeling calculation, the present invention greatly reduces the modeling difficulty while ensuring the calculation accuracy, and the calculation efficiency is also significantly improved.

Claims (5)

1. the seismic response simplification calculation method of a rocking type self-resetting independent foundation, is characterized in that, this method comprises the following steps: (1) Obtain the basic mechanical performance parameters of the foundation soil, including density ρ, shear modulus G, Poisson's ratio ν, internal friction angle

and cohesion c, given the side length B of the independent foundation and the design value N of the vertical gravity load; (2) Calculate the foundation rocking stiffness K _R , the vertical bearing capacity q _u and the foundation rocking reset coefficient F _sc according to the parameters obtained in step (1); (3) According to the foundation stiffness and vertical bearing capacity obtained in step (2), establish a bilinear skeleton curve of the relationship between the foundation bending moment M and the foundation rotation angle θ; (4) Determine the unloading-reloading hysteresis rule of the M-θ relationship, and combine the bilinear skeleton curve in step (3) to establish the M-θ restoring force model; (5) According to the M-θ restoring force model obtained in step (4), the dynamic control equation of the foundation rocking motion is listed, and the dynamic rocking response of the foundation under the action of earthquake is calculated. 2. The seismic response simplified calculation method of the rocking self-resetting independent foundation described in claim 1, characterized in that: the foundation rocking stiffness K _R and the vertical bearing capacity q _u described in the step (2) can be calculated according to the foundation The soil parameters and foundation dimensions are obtained from the foundation design manual, and the calculation formula of the foundation rocking reset coefficient F _sc is as follows:

3. according to the seismic response simplification calculation method of the rocking type self-resetting independent foundation described in claim 1, it is characterized in that: the bilinear skeleton curve of the relationship between the foundation bending moment M and foundation rotation angle θ described in the (3) step Calculated as follows:

4. according to the seismic response simplification calculation method of the rocking type self-resetting independent foundation described in claim 1, it is characterized in that: the unloading-reloading hysteresis rule of the M-θ relation described in the (4) step is as follows: The linear relationship assumption based on the initial stiffness k=3/5K _R is used for reloading. When the load is reversed and only when the reverse point is located in the platform section of the M-θ skeleton curve, the stiffness k is updated. The calculation formula is as follows:

5. according to the seismic response simplified calculation method of the rocking type self-resetting independent foundation described in claim 1, it is characterized in that: the dynamic control equation of the foundation rocking motion described in the (5) step is as follows:

where J is the moment of inertia of the foundation around its central horizontal axis,

is the horizontal acceleration of the earthquake surface, and M(θ) is the M-θ restoring force model; The dynamic rocking response θ of the foundation under earthquake is obtained by solving the dynamic equation by the Newmark integral method.

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