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

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

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CN115114692A
CN115114692A CN202110286618.9A CN202110286618A CN115114692A CN 115114692 A CN115114692 A CN 115114692A CN 202110286618 A CN202110286618 A CN 202110286618A CN 115114692 A CN115114692 A CN 115114692A
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吕洋
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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

一种摇摆型自复位独立基础的地震响应简化计算方法A Simplified Calculation Method for Seismic Response of Swing Type Self-resetting Independent Foundation

技术领域technical field

本发明属于土与结构相互作用地震反应分析技术领域,具体涉及一种摇摆型自复位独立基础的地震响应简化计算方法。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.

背景技术Background technique

传统抗震设计要求地基具备足够承载力以满足稳定性与变形要求,通过上部结构的延性变形来消耗地震能量。但由于强震幅值大、持续时间长,结构中累积的损伤程度重而可能导致其在震后不可修或存在稳定性等安全隐患。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.

摇摆型自复位独立基础结构系统是以基础摇摆为主导运动模式的新型震后可恢复功能结构系统。这类系统利用基础摇摆过程中的提离与地基土塑性变形限制地基对基础底部的反力,从而减小上部结构的损伤;并借助结构自重使系统回复原位,将结构震后残余位移控制在一个较小的范围内,降低地震损失。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.

为设计合理的摇摆型自复位独立基础结构系统,需要进行地震响应分析。常规做法是对整个结构、基础、地基系统进行有限元建模;但由于涉及结构与地基土弹塑性变形、重力二阶效应、基础提离等非线性行为,对工程人员来说是一个很大的挑战。美国建筑抗震设计标准提供了一种三折线骨架曲线用以描述摇摆基础在单轴静力荷载作用下的基底弯矩—基础转角关系,但因其缺少卸载—再加载关系,无法用于地震响应计算。因此,有必要提出摇摆型自复位独立基础的地震响应简化计算方法,为工程人员提供一个高效、便捷的地震响应分析工具。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.

综上所述,现有技术存在的问题为:摇摆基础结构系统地震响应分析亟需简化计算方法以便于工程人员对此类结构进行抗震设计,而目前建筑抗震设计标准采用的摇摆基础响应简化计算方法仅适用于单轴静力加载工况,无法考虑地震引起的真实动态响应,因此不能应用于摇摆基础结构系统地震响应分析。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.

现有技术中解决这一技术问题的技术方案:采用弹性弹簧与线性阻尼壶的组合系统近似考虑基础摇摆响应的非线性行为与耗能,包括两种方法。方法一采用多折线弹性弹簧并联线性阻尼壶系统;方法二采用线性弹簧串联一个由线性弹簧与线性阻尼壶并联组成的系统。这两种计算方法本质上将摇摆基础响应看成是一种非线性弹性行为,虽然可以通过优化阻尼系数使计算摇摆响应幅值接近真实情况,但无法得到结构抗震设计所需的基础摇摆残余转角,也无法反映基础摇摆响应的物理机制。实际上,在基础摇摆运动过程中,位于基础两端下部土体的塑性压缩变形持续累积,导致摇摆滞回曲线的卸载刚度与再加载刚度随转角幅值持续变化。因此,采用弹性计算方法无法得到地基土塑性变形引起的基础残余转角,也不能得到基础摇摆运动的实际滞回曲线。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.

发明内容SUMMARY OF THE INVENTION

本发明的目的是为方便工程人员对新型摇摆自复位独立基础结构系统进行地震响应分析,提供了一种摇摆型自复位独立基础的地震响应简化计算方法。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.

本发明是这样实现的,一种考虑压剪耦合的温克尔黏土地基地震反应计算方法,实现步骤包括: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:

(1)获取地基土体的基本力学性能参数,包括密度ρ、剪切模量G、泊松比ν、内摩擦角

Figure BDA0002980727570000026
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
Figure BDA0002980727570000026
and cohesion c, given the side length B of the independent foundation and the design value N of the vertical gravity load;

(2)根据第(1)步获得的参数计算地基摇摆刚度KR、竖向承载力qu和基础摇摆复位系数Fsc(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)根据第(2)步得到的地基刚度和竖向承载力,建立基底弯矩M和基础转角θ关系的双线性骨架曲线;(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)确定M—θ关系的卸载—再加载滞回规则,结合第(3)步的双线性骨架曲线,建立M—θ恢复力模型;(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)根据第(4)步得到的M—θ恢复力模型,列出基础摇摆运动的动力控制方程,计算基础在地震作用下的动力摇摆响应。(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.

进一步地,第(2)步所述的地基摇摆刚度KR、竖向承载力qu可根据地基土参数和基础尺寸查地基基础设计手册得到,基础摇摆复位系数Fsc计算如公式(1):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) :

Figure BDA0002980727570000021
Figure BDA0002980727570000021

进一步地,第(3)步所述的基底弯矩M和基础转角θ关系的双线性骨架曲线计算公式如公式(2):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):

Figure BDA0002980727570000022
Figure BDA0002980727570000022

进一步地,第(4)步所述的M—θ关系的卸载—再加载滞回规则如下:卸载、再加载均采用基于初始刚度k=3/5KR的线性关系假设,当荷载反向且仅当该反向点位于M—θ骨架曲线平台段时,对刚度k进行更新,计算如公式(3):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):

Figure BDA0002980727570000023
Figure BDA0002980727570000023

进一步地,第(5)步所述的基础摇摆运动的动力控制方程如公式(4):Further, the dynamic control equation of the basic rocking motion described in step (5) is as formula (4):

Figure BDA0002980727570000024
Figure BDA0002980727570000024

公式(4)中J为基础绕其中心水平转轴的转动惯量,üg为地震地表面水平加速度,M(θ)为M—θ恢复力模型;采用纽马克积分法求解该动力方程即得基础在地震作用下的动力摇摆响应θ。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.

综上所述,本发明的优点及积极效果为:To sum up, the advantages and positive effects of the present invention are:

(1)目前建筑抗震设计标准采用的摇摆基础响应简化计算方法仅适用于单轴静力加载工况,无法考虑地震引起的真实动态响应,因此不能应用于摇摆基础结构系统地震响应分析。本发明提出适用于任意加载路径的M—θ恢复力模型,使得摇摆基础响应简化计算能够应用于真实动态情况。(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)本发明通过建立一套完整的基础摇摆骨架曲线和卸载—再加载滞回规则来描述摇摆卸载刚度与再加载刚度随转角幅值持续变化的实际情况。相比现有基于线性或非线性粘弹性模型而仅能估计峰值转角需求的简化计算方法,还能得到结构抗震设计所需的基础摇摆残余转角,很好地反映基础摇摆响应的物理机制。(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.

附图说明Description of drawings

图1为本发明的计算步骤图。Fig. 1 is a calculation step diagram of the present invention.

图2为本发明计算结果与精细有限元计算结果对比图。FIG. 2 is a comparison diagram of the calculation results of the present invention and the fine finite element calculation results.

具体实施方式Detailed ways

为了使本发明所要解决的问题、技术方案和优点更加清楚,以下将结合附图及具体实施例进行进一步详细说明。应当理解,此处所描述的具体施例仅用于解释本发明,并不用于限定本发明的应用。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.

应用实例:Applications:

根据图1所示摇摆型自复位独立基础的地震响应简化计算方法的步骤,对受水平循环往复地震作用的独立基础在两种黏土场地地基条件的摇摆响应进行分析,场地土参数、基础尺寸、地基摇摆刚度KR、竖向承载力qu和基础摇摆复位系数Fsc等参数如表1所示。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.

表1场地土、基础以及地基参数Table 1 Site soil, foundation and foundation parameters

Figure BDA0002980727570000031
Figure BDA0002980727570000031

采用位移控制循环加载,可以求得基础摇摆响应,与ABAQUS精细有限元计算结果进行对比,该方法计算结果与精细有限元准确结果基本吻合,如图2所示。相较于精细有限元建模计算,本发明在保证计算精度的同时极大降低了建模难度,计算效率也得到了显著提高。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)

1.一种摇摆型自复位独立基础的地震响应简化计算方法,其特征在于,该方法包括以下步骤: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)获取地基土体的基本力学性能参数,包括密度ρ、剪切模量G、泊松比ν、内摩擦角
Figure FDA0002980727560000016
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
Figure FDA0002980727560000016
and cohesion c, given the side length B of the independent foundation and the design value N of the vertical gravity load;
(2)根据第(1)步获得的参数计算地基摇摆刚度KR、竖向承载力qu和基础摇摆复位系数Fsc(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)根据第(2)步得到的地基刚度和竖向承载力,建立基底弯矩M和基础转角θ关系的双线性骨架曲线;(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)确定M—θ关系的卸载—再加载滞回规则,结合第(3)步的双线性骨架曲线,建立M—θ恢复力模型;(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)根据第(4)步得到的M—θ恢复力模型,列出基础摇摆运动的动力控制方程,计算基础在地震作用下的动力摇摆响应。(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.根据权利要求1中所述的摇摆型自复位独立基础的地震响应简化计算方法,其特征在于:第(2)步所述的地基摇摆刚度KR、竖向承载力qu可根据地基土参数和基础尺寸查地基基础设计手册得到,基础摇摆复位系数Fsc计算公式如下: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:
Figure FDA0002980727560000011
Figure FDA0002980727560000011
3.根据权利要求1中所述的摇摆型自复位独立基础的地震响应简化计算方法,其特征在于:第(3)步所述的基底弯矩M和基础转角θ关系的双线性骨架曲线计算公式如下: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:
Figure FDA0002980727560000012
Figure FDA0002980727560000012
4.根据权利要求1中所述的摇摆型自复位独立基础的地震响应简化计算方法,其特征在于:第(4)步所述的M—θ关系的卸载—再加载滞回规则如下:卸载、再加载均采用基于初始刚度k=3/5KR的线性关系假设,当荷载反向且仅当该反向点位于M—θ骨架曲线平台段时,对刚度k进行更新,计算公式如下: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:
Figure FDA0002980727560000013
Figure FDA0002980727560000013
5.根据权利要求1中所述的摇摆型自复位独立基础的地震响应简化计算方法,其特征在于:第(5)步所述的基础摇摆运动的动力控制方程如下: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:
Figure FDA0002980727560000014
Figure FDA0002980727560000014
式中J为基础绕其中心水平转轴的转动惯量,
Figure FDA0002980727560000015
为地震地表面水平加速度,M(θ)为M—θ恢复力模型;
where J is the moment of inertia of the foundation around its central horizontal axis,
Figure FDA0002980727560000015
is the horizontal acceleration of the earthquake surface, and M(θ) is the M-θ restoring force model;
采用纽马克积分法求解该动力方程即得基础在地震作用下的动力摇摆响应θ。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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