A dimensional analysis method for seismic response of adjacent building impact systems

Abstract

A dimensional analysis method for the seismic response of adjacent building collision system is proposed, and the intrinsic length scale is proposed, including: using an improved linear viscoelastic contact unit model to simulate the collision process, using MP pulses to characterize near-fault ground motions, obtaining the dynamic equations of adjacent buildings under earthquake action, and considering the influence of structure-soil-structure interaction. This method uses the Newmark method to solve the dynamic response of the building, performs dimensional analysis on the adjacent building collision system based on the intrinsic length scale, and obtains the parameter influence law of the collision response.

Description

Technical Field

[0001] The invention relates to a new method for dimensional analysis of earthquake responses of adjacent building collision systems, which is applicable to the technical field of earthquake resistance of building engineering. Background Art

[0002] There are usually significant differences between seismic records. For example, the vertical fault component of near-fault seismic records usually contains significant velocity pulses, while the parallel fault component has no velocity pulses. The differences in seismic records lead to a large discreteness in seismic responses. Moreover, with the substantial improvement in computer performance, it is becoming increasingly convenient to obtain linear and nonlinear structural response solutions. The task of researchers has become how to correctly and reasonably present a large number of structural response solutions and explain the laws they contain.

[0003] The research on the engineering characteristics and structural effects of near-fault ground motions has been an important topic in the field of earthquake engineering in recent years. A large number of earthquake disaster surveys have shown that collisions between adjacent buildings are one of the important causes of structural damage. In order to reduce the losses caused by structural collisions, it is essential to conduct dynamic response analysis of collisions between adjacent buildings, which is also a requirement for preventing earthquake disasters. Research on earthquake collision damage between adjacent buildings has high theoretical significance and engineering application value. Due to the high nonlinearity of the problem of adjacent building collisions, a large number of influencing parameters have led to the one-sidedness of many research results. The dimensional analysis method can effectively reduce the parameter complexity in the problem of adjacent building collisions, use fewer dimensionless parameters to characterize the collision response law of building structures under earthquake action, and provide a basic theory for the interaction problem of structural groups composed of multiple buildings. Summary of the invention

[0004] This method proposes an intrinsic length scale representing the static displacement of the structure to analyze the dimensional response of the adjacent building collision system under near-fault seismic motion. The intrinsic length scale is a parameter related to the structure and has a clear physical meaning. The dynamic equation of the multi-degree-of-freedom adjacent inelastic building collision system is derived, and the influence of the structure-soil-structure interaction is considered, revealing the impact law of the collision response of each parameter of the collision system. The new dimensional analysis method for structural seismic analysis can reduce the discreteness of the seismic response and discover a completely self-similar law.

[0005] The present invention adopts a new method for analyzing the dimensional response of the adjacent building collision system under the action of near-fault earthquake, which comprises the following steps:

[0006] (1) An intrinsic length scale for dimensional analysis in earthquake engineering is proposed, which is related to structural properties and has clear physical meaning;

[0007] (2) The dynamic equations of the multi-degree-of-freedom adjacent inelastic building collision system were established, the collision process was simulated with the improved Kelvin contact element model, the MP pulse was used to characterize the near-fault ground motion, and the influence of structure-soil-structure interaction was considered;

[0008] (3) Based on the intrinsic length scale, a dimensional analysis of the collision system of adjacent buildings is carried out to study the influence of parameters on the collision response.

[0009] The specific steps are as follows:

[0010] Step (1): The structural parameters of the excitation energy length scale are all derived from pulse excitation and are non-structure related parameters. Studies have shown that the structure-related strength parameters have a stronger correlation with the structural response. Therefore, when conducting dimensional analysis on the seismic response of buildings and exploring the laws of seismic response of building structures, the excitation energy length scale may not be the most appropriate choice.

[0011] Principles that should be followed in parameter selection in the field of earthquake engineering: (1) Structural response cannot be selected as the basic quantity; (2) To satisfy the principle of dimensional harmony, the selected parameters need to contain two basic dimensions, [L] and [T]; (3) The length scale should be linearly related to the excitation amplitude; (4) The selected parameters should have clear physical meanings and be easy to estimate.

[0012] The motion equation of the elastic SDOF pendulum under the action of simple harmonic pulse is:

[0013]

[0014] The maximum displacement x can be obtained from the equation max With the damping ratio ξ and natural angular frequency ω of the simple pendulum 1 , simple harmonic pulse amplitude a p and pulse angular frequency ω p about, that is

[0015] x max =f(ξ,ω 1 ,a p ,ω p )(2)

[0016] The number of variables in the above formula is 5, including two basic dimensions [L] and [T]. According to the П theorem, there are two basic quantities in this formula, and the remaining 5-2=3 physical quantities can be expressed by these two basic quantities. Excitation energy length scale in earthquake engineering (a p ,ω p ) is a fundamental quantity. In contrast, the intrinsic length scale The structural natural angular frequency ω 1It is a basic quantity of time dimension and depends on the characteristics of the structure itself. The maximum steady-state response of the pendulum is normalized at two length scales and solved as follows:

[0017]

[0018]

[0019] In the above formula, the normalized maximum steady-state response solution obtained by the intrinsic length scale is consistent with the expression in the textbook, and the frequency ratio involved is ω p / ω 1 , but when the excitation energy length scale is used, the normalized maximum steady-state response solution is different from the textbook, involving a frequency ratio of ω 1 / ω p .

[0020] Step (2): Discretize the adjacent building collision system considering the foundation effect into a multi-mass point model, and use the Bouc-Wen model to characterize the inelastic characteristics of the adjacent buildings. The foundation soil layer of each building contains two degrees of freedom: translation and rotation, and shear force and bending moment can be transmitted between the foundations. Under the action of seismic excitation, the dynamic equation of the adjacent buildings considering the SSSI effect can be written as

[0021]

[0022] Among them, M bsb ,C bsb ,K bsb are the mass matrix, damping matrix and stiffness matrix of the SSSI system, U bsb , are the displacement, velocity, and acceleration column vectors for each degree of freedom, respectively. p is the collision force vector during the motion, is the ground acceleration, v bsb ,v fbsb are the influence vectors of building and foundation on external excitation respectively.

[0023] The matrix equation (4.1) consists of equations corresponding to two buildings. The first group contains n+2 coupled equations, where n is the number of floors of the building on the left and 2 is the two degrees of freedom of the foundation soil layer. Similarly, the second group contains m+2 coupled equations, where m is the number of floors of the building on the right. Here, n≥m is assumed.

[0024] Further expand formula (5)

[0025]

[0026] The matrices and vectors corresponding to the building structure on the left are expanded as follows (the matrices and vectors corresponding to the building on the right are similar to the left, just replace l and n with r and m respectively):

[0027]

[0028] u lb T = {u l1 u l2 … u ln} (8)

[0029] v lb T ={1 … 1} (9)

[0030] Among them, m li , k li are the floor mass and lateral bending stiffness of the i-th floor of the left building respectively. lb is the Rayleigh damping matrix of the left structure, which can be obtained from the mass matrix and stiffness matrix.

[0031] The matrices and vectors corresponding to the left foundation are as follows:

[0032]

[0033]

[0034]

[0035]

[0036] u ls T = {u lφ u lf} (14)

[0037] v ls T ={0 m lf} (15)

[0038] Among them, H i is the height of the i-th floor from the ground. The subscripts φ and f correspond to the sway deformation and horizontal deformation of the foundation, respectively. lφ ,c lφ are the spring and damping parameters corresponding to the foundation rocking motion, k lf ,c lf are the spring and damping parameters corresponding to the horizontal movement of the foundation, and their values ​​are determined by the material and geometric properties of the foundation.

[0039] When studying the interaction between soil and structure, most scholars only consider the interaction between the building and its underlying foundation. However, under the action of an earthquake, since the foundations of adjacent buildings are close to each other, the movement and deformation of one side will inevitably be transmitted to the other side through the intermediate soil layer, thereby affecting the seismic response of the buildings above each other. In this chapter, it is considered that the shear force and bending moment can be transmitted between the foundations, that is, the intermediate soil layer has swaying motion and horizontal motion. The corresponding coupling term in the dynamic equation is

[0040]

[0041]

[0042] Among them, k bsbφ ,c bsbφ are the spring and damping parameters corresponding to the swaying motion of the middle soil layer, k bsbf ,c bsbf are the spring and damping parameters corresponding to the horizontal movement of the middle soil layer.

[0043] In this chapter, a discrete element model is used to simulate the dynamic characteristics of a circular rigid foundation on a homogeneous soil half-space. The model is based on an idealization of the homogeneous soil under the foundation using a semi-infinite truncated cone. Studies have shown that its accuracy is sufficient for practical applications compared to more rigorous solutions. The motion of the foundation is simulated using a swing and sway model, whose parameter values ​​are given by empirical formulas:

[0044]

[0045] Among them, m f ,c f ,k f and m φ ,c φ ,k φ are the mass, damping and stiffness corresponding to the horizontal motion and rocking motion in the discrete model, respectively.

[0046] For the coupling effect between foundations, we have

[0047]

[0048] The collision force between adjacent building floors is still calculated using the improved Kelvin model. It is worth noting that due to the coupling between the foundations, the displacement responses of the left and right building foundations are not necessarily the same. At this time, the condition for the collision to occur should be that the relative displacement of the adjacent floors is greater than the initial spacing. The collision force calculation formula is:

[0049]

[0050]

[0051] δ=(u li +u lf +H i u lφ )-(u ri +u rf +H i u rφ )-d (22)

[0052] It is generally believed that near-fault ground motion refers to ground motion within 20 km of the fault rupture surface, which is strongly dependent on the fault rupture mechanism and contains obvious rupture directionality effect and slip effect. The MP pulse model fully describes the pulse characteristics of near-fault ground motion from both qualitative and quantitative aspects, and has only one mathematical expression, and the input parameters also have clear physical meanings. The MP pulse mathematical expression is as follows:

[0053]

[0054] Among them, γ and are the velocity pulse vibration characteristic parameter and the phase angle of the amplitude modulation simple harmonic function, both are dimensionless constants, v 0 Control pulse velocity amplitude, T p is the dominant period of earthquake motion. By adjusting γ and Different types of MP pulses are available: γ = 1.01 and Corresponding to the sliding pulse, the acceleration pulse amplitude is approximately equal to 0.879ω p v 0 ; γ = 1.01 and Corresponding to the forward directional pulse, the acceleration pulse amplitude is approximately equal to ω p v 0 . Note that γ and are dimensionless constants, so they can be used in dimensional analysis. to represent the near-fault MP pulse.

[0055] Step (3): Based on the derived dynamic equation, the peak response of the adjacent building can be expressed as follows:

[0056]

[0057] The left side of formula (22) is the peak displacement and peak shear force of the building floor, and the right side is the 18 influencing parameters of the peak response, which are the pulse earthquake excitation acceleration amplitude a p and angular frequency ω p , the natural angular frequency of the right floor Left and right building floor mass m L and m R , floor stiffness ratio μ = k L / k R, structural damping ratio ξ, floor stiffness ratio after yield α, yield displacement of left and right floors Contact unit angular frequency ω con , contact unit energy recovery coefficient r, initial distance between adjacent buildings d, floor height H, soil shear modulus G and Poisson's ratio ν, circular foundation equivalent radius a, soil shear wave velocity V s .

[0058] Based on the intrinsic length scale, the adjacent building collision system considering SSSI is analyzed dimensionally, and the pulse excitation acceleration amplitude a is selected. p 、The natural angular frequency of the right structure ω R and the mass of the right structural floor m R As the basic quantity, the variables in formula (22) are dimensionless, and we get

[0059]

[0060]

[0061] Substitute the above dimensionless parameters into the dynamic equation, control the input variables, and calculate the time-history responses of adjacent building floors under different frequency ratios based on Newmark, so as to obtain the parameter influence law of the collision response.

[0062] This application proposes an intrinsic length scale with clear physical meaning and establishes a new method for dimensional analysis of seismic response of adjacent building collision system. It is a general and simple method system that can be used to solve the dynamic response of adjacent building structures under various near-fault earthquake excitations. This method uses the intrinsic length scale related to the structural characteristics and has a clear physical meaning to normalize the displacement response, which can clearly obtain the collision response law of adjacent buildings, discover the complete self-similar phenomenon, and provide a theoretical basis for the seismic design of building structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 A schematic diagram showing the dimensional response analysis method of the adjacent building collision system under the action of near-fault ground motion of the present application is shown.

[0064] Figure 2 A schematic diagram of the adjacent building model considering the influence of foundations is shown.

[0065] Figure 3 Response spectrum curves of the top floor on the left side of the adjacent building under different post-yield stiffness ratios.

[0066] Figure 4 Response spectrum curves of the top floor on the right side of the adjacent building under different post-yield stiffness ratios. DETAILED DESCRIPTION

[0067] The specific embodiments of the present invention are described in detail below in combination with the technical solutions and the accompanying drawings.

[0068] Reference example: Dimensional analysis of the impact response of adjacent 15-story and 8-story buildings under near-fault ground motion.

[0069] Based on the intrinsic length scale given in this project, a dimensional analysis of the adjacent building collision system is carried out, the relevant influencing parameters are non-dimensionalized, the dimensionless dynamic equation is solved, and the changing parameters are input to obtain the peak response of the building floors at different frequency ratios, so as to study the influence of parameters on the collision response.

[0070] Taking the adjacent 15-story and 8-story buildings considering structure-soil-structure interaction (SSSI) as an example, the specific calculation steps are as follows:

[0071] Figure 2 To consider the adjacent building dynamic analysis model of SSSI, (such as Figure 3 As shown), the system's equation of motion is obtained

[0072]

[0073] Among them, M bsb ,C bsb ,K bsb are the mass matrix, damping matrix and stiffness matrix of the SSSI system, U bsb , are the displacement, velocity, and acceleration column vectors for each degree of freedom, respectively. p is the collision force vector during the motion, is the ground acceleration, v bsb ,v fbsb are the influence vectors of building and foundation on external excitation respectively.

[0074] Characterization of near-fault ground motions by MP pulses.

[0075] Based on the intrinsic length scale, the relevant influencing parameters are dimensionless, and the Newmark-β method is used to solve the dimensionless dynamic equation to obtain the dynamic response of the adjacent building collision system.

[0076] By controlling the variables, the influence of influencing parameters on the collision response of adjacent buildings is studied. Figure 3 and Figure 4 The response spectrum curves of the top floors of adjacent buildings under different post-yield stiffness values ​​are given.

Claims

1. A dimensional analysis method for the seismic response of adjacent building collision systems. It is characterized by the following steps: Step (1) proposes an intrinsic length scale for dimensional analysis in earthquake engineering, which is related to structural properties and has clear physical meaning; The motion equation of the elastic SDOF pendulum under the action of simple harmonic pulse is: The maximum displacement x can be obtained from the equation max With the damping ratio ξ and natural angular frequency ω of the simple pendulum 1 , simple harmonic pulse amplitude a p and pulse angular frequency ω p about, that is x max =f(ξ,ω 1 ,a p ,oh p ) (2) The number of variables in the above formula is 5, including two basic dimensions [L] and [T]. According to the П theorem, there are two basic quantities in this formula, and the remaining 5-2=3 physical quantities can be represented by these two basic quantities. The excitation energy length scale in the field of earthquake engineering (a p ,ω p ) is a fundamental quantity; in contrast, the intrinsic length scale The structural natural angular frequency ω 1 It is a basic quantity of time dimension, which depends on the characteristics of the structure itself; the maximum steady-state response of the pendulum is normalized at two length scales and solved as follows: In the above formula, the normalized maximum steady-state response solution obtained by the intrinsic length scale involves a frequency ratio of ω p / ω 1 , while when the excitation energy length scale is used, the normalized maximum steady-state response solution involves a frequency ratio of ω 1 / ω p ; Step (2) The dynamic equations of the multi-degree-of-freedom adjacent inelastic building collision system are established, the collision process is simulated with the improved Kelvin contact element model, the near-fault ground motion is characterized by MP pulse, and the influence of structure-soil-structure interaction is considered; The collision system of adjacent buildings considering the influence of foundation is discretized into a multi-mass point model, and the inelastic characteristics of adjacent buildings are characterized by the Bouc-Wen model; the foundation soil layer of each building contains two degrees of freedom, translation and rotation, and shear force and bending moment can be transmitted between foundations; under the action of seismic excitation, the dynamic equation of adjacent buildings considering the SSSI effect can be written as Among them, M bsb ,C bsb ,K bsb are the mass matrix, damping matrix and stiffness matrix of the SSSI system, U bsb , are the displacement, velocity, and acceleration column vectors for each degree of freedom, respectively. p is the collision force vector during the motion, is the ground acceleration, v bsb ,v fbsb are the influence vectors of building and foundation on external excitation respectively; The collision force between adjacent building floors is still calculated using the improved Kelvin model; the collision force calculation formula is: δ=(u li +u lf +H i u lφ )-(u ri +u rf +H i u rφ )-d(8) Step (3) Based on the newly proposed intrinsic length scale, the adjacent building collision system is dimensionally analyzed to study the influence of relevant parameters on the collision response; the established structural seismic analysis dimensional analysis method can reduce the discreteness of the seismic response and discover the completely self-similar law; According to the derived dynamic equation, the peak response of the adjacent building can be expressed as follows: The left side of formula (24) is the peak displacement and peak shear force of the building floor, and the right side is the 18 influencing parameters of the peak response, which are the pulse earthquake excitation acceleration amplitude a p and angular frequency ω p , the natural angular frequency of the right floor Left and right building floor mass m L and m R , floor stiffness ratio μ = k L / k R , structural damping ratio ξ, floor stiffness ratio after yield α, yield displacement of left and right floors Contact unit angular frequency ω con , contact unit energy recovery coefficient r, initial distance between adjacent buildings d, floor height H, soil shear modulus G and Poisson's ratio ν, circular foundation equivalent radius a, soil shear wave velocity V s .

2. According to claim 1, a dimensional analysis method for earthquake response of adjacent building collision system, It is characterized in that In step (1), the structural parameters of the excitation energy length scale are all derived from pulse excitation and are non-structure related parameters. Studies have shown that the structure-related strength parameters have a stronger correlation with the structural response; therefore, when conducting dimensional analysis on the seismic response of buildings and exploring the laws of seismic response of building structures, the excitation energy length scale may not be the most appropriate choice; Principles that should be followed in parameter selection in the field of earthquake engineering: (1) Structural response cannot be selected as the basic quantity; (2) To satisfy the principle of dimensional harmony, the selected parameters need to contain two basic dimensions, [L] and [T]; (3) The length scale should be linearly related to the excitation amplitude; (4) The selected parameters should have clear physical meanings and be easy to estimate.

3. According to claim 1, a dimensional analysis method for earthquake response of adjacent building collision system, It is characterized in that In step (2), The matrix equation (5) consists of equations corresponding to two buildings; the first group contains n+2 coupled equations, n is the number of floors of the building on the left, and 2 is the two degrees of freedom of the foundation soil layer; similarly, the second group contains m+2 coupled equations, m is the number of floors of the building on the right; here, n≥m is assumed; Further expand formula (5) The matrices and vectors corresponding to the building structure on the left are expanded as follows (the matrices and vectors corresponding to the building on the right are similar to the left, just replace l and n with r and m respectively): in lb T ={in l1 in l2 …in ln } (12) v lb T ＝{1 …1} (13) Among them, m li , k li are the floor mass and lateral bending stiffness of the i-th floor of the left building respectively; c in formula (6) lb is the Rayleigh damping matrix of the left structure, which can be obtained from the mass matrix and stiffness matrix; The matrices and vectors corresponding to the left foundation are as follows: in ls T ={in lφ in lf } (18) in ls T ={0 m lf } (19) Among them, H i is the height of the i-th floor from the ground; the subscripts φ and f correspond to the sway deformation and horizontal deformation of the foundation, respectively; k lφ ,c lφ are the spring and damping parameters corresponding to the foundation rocking motion, k lf ,c lf are the spring and damping parameters corresponding to the horizontal motion of the foundation, and their values ​​are determined by the material and geometric characteristics of the foundation; For adjacent buildings, most scholars only consider the interaction between the building and its underlying foundation when studying the interaction between soil and structure. However, under the action of an earthquake, since the foundations of adjacent buildings are close to each other, the movement and deformation of one side will inevitably be transmitted to the other side through the intermediate soil layer, thereby affecting the seismic response of the buildings above each other. In this chapter, it is considered that the shear force and bending moment can be transmitted between the foundations, that is, the intermediate soil layer has swaying motion and horizontal motion, and the corresponding coupling term in the dynamic equation is Among them, k bsbφ ,c bsbφ are the spring and damping parameters corresponding to the swaying motion of the middle soil layer, k bsbf ,c bsbf are the spring and damping parameters corresponding to the horizontal movement of the middle soil layer; The dynamic characteristics of the circular rigid foundation on the homogeneous soil half space are simulated by using a discrete element model. The model is based on the idealization of the homogeneous soil under the foundation by a semi-infinite truncated cone. The motion of the foundation is simulated by a swing and sway model, and its parameter values ​​are given by the empirical formula: Among them, m f ,c f ,k f and m φ ,c φ ,k φ are the mass, damping and stiffness corresponding to the horizontal motion and the rocking motion in the discrete model, respectively; For the coupling effect between foundations, we have The MP pulse model fully describes the pulse characteristics of near-fault ground motion from both qualitative and quantitative aspects, and has only one mathematical expression, and the input parameters also have clear physical meanings; the MP pulse mathematical expression is as follows: Among them, γ and are the velocity pulse vibration characteristic parameter and the phase angle of the amplitude modulation simple harmonic function, both are dimensionless constants, v 0 Control pulse velocity amplitude, T p is the dominant period of earthquake motion; by adjusting γ and Different types of MP pulses are available: γ = 1.01 and Corresponding to the sliding pulse, the acceleration pulse amplitude is approximately equal to 0.879ω p v 0 ; γ = 1.01 and Corresponding to the forward directional pulse, the acceleration pulse amplitude is approximately equal to ω p v 0 ; Note that γ and are dimensionless constants, so they can be used in dimensional analysis. to represent the near-fault MP pulse.

4. The dimensional analysis method for seismic response of adjacent building collision system according to claim 1, It is characterized in that In step (3), Based on the intrinsic length scale, the adjacent building collision system considering SSSI is analyzed dimensionally, and the pulse excitation acceleration amplitude a is selected. p 、The natural angular frequency of the right structure ω R and the mass of the right structural floor m R As the basic quantity, the variables in formula (24) are dimensionless, and we get The above dimensionless parameters are substituted into the dynamic equation, the input variables are controlled, and the time-history responses of adjacent building floors under different frequency ratios are calculated based on the Newmark method, thereby obtaining the parameter influence law of the collision response.

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