Large-span steel structure earthquake response IBE simulation method considering soil-structure interaction

Abstract

The invention discloses a large-span steel structure earthquake response IBE simulation method considering soil-structure interaction, and relates to the technical field of building structure earthquake response simulation. Comprising the following steps: establishing a large-span steel structure earthquake response calculation model considering soil-structure interaction; solving a soil layer free field response based on a direct stiffness method; solving a basic stiffness matrix based on a uniform wiring load Green function and a boundary continuity condition; solving a basic free field response according to the soil layer free field response and the basic stiffness matrix; solving a basic scattered field response according to the motion equations of the foundation and the large-span steel structure; adding the foundation free field response and the foundation scattered field response to obtain a foundation response under the earthquake action; according to the relation between the large-span steel structure response and the foundation response, the large-span steel structure column top response is solved, and according to the motion equation of the large-span steel structure, the large-span steel structure mid-span response is solved. The accuracy of structural earthquake response analysis can be improved.

Description

Technical Field

[0001] The invention relates to the technical field of building structure seismic response simulation, and more particularly to an IBE simulation method for seismic response of a large-span steel structure taking soil-structure interaction into consideration. Background Art

[0002] Earthquakes are highly destructive, difficult to predict, and have a wide range of impact. They have caused serious casualties and economic losses worldwide. How to ensure the earthquake safety of building structures is a key issue in structural design. In addition, multiple earthquake damage observations have shown that soil-structure interaction will aggravate the degree of damage to building structures under earthquakes. In the 1985 Mexico 7.8 earthquake, due to the influence of soft soil sites, about 35% of the buildings in Mexico City, more than 400 kilometers away from the epicenter, were damaged and more than 300 buildings collapsed completely. Related studies have shown that the change in the natural frequency of the structure after considering the soil-structure interaction, the mutual influence of scattered waves between foundations, and the displacement difference between supports will cause significant changes in the seismic response of the structure. The influence of soil-structure interaction on the seismic response of the structure cannot be ignored.

[0003] In the existing structural seismic response analysis, the influence of local site conditions is often considered based on empirical formulas, and the earthquake wave effect is simplified based on the changes in amplitude and phase; the numerical model of structural seismic response analysis often only includes the structural part, or uses springs and damping to simplify the soil effect. Although some methods have established a soil-foundation-structure overall model based on the finite element method, most of these models regard the soil as a homogeneous medium and intercept a limited range of soil to simulate a semi-infinite space area. It is necessary to introduce artificial boundaries at the cutoff of the soil model to eliminate the errors caused by the reflection of seismic waves on the boundaries. The above problems make it difficult to fully consider the influence of soil-structure interaction in the existing structural seismic response analysis methods, and the results are subject to great uncertainty.

[0004] The indirect boundary element (IBE) method is a commonly used analysis method for solving soil-structure interaction problems. It has the advantages of strictly satisfying the semi-infinite space radiation conditions, high solution accuracy, and low problem dimension. Therefore, it is necessary to propose an IBE simulation method for the seismic response of large-span steel structures considering soil-structure interaction, fully consider the influence of soil-structure interaction on the seismic response of the structure, derive the seismic response calculation formula of the horizontal layered field underground foundation-large-span steel structure model, and provide theoretical support for the seismic design of the structure.

[0005] Therefore, it is an urgent problem for those skilled in the art to propose an IBE simulation method for the seismic response of large-span steel structures that takes into account soil-structure interaction to solve the difficulties existing in the prior art. Summary of the invention

[0006] In view of this, the present invention provides an IBE simulation method for seismic response of large-span steel structures taking into account soil-structure interaction, which effectively improves the accuracy of structural seismic response analysis.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] An IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction comprises the following steps:

[0009] Establish a calculation model for the seismic response of large-span steel structures considering soil-structure interaction;

[0010] Solve the free field response of soil layer based on direct stiffness method;

[0011] Solve the foundation stiffness matrix based on the uniformly distributed line load Green's function and boundary continuity conditions;

[0012] According to the free-field response of the soil layer and the foundation stiffness matrix, the free-field response of the foundation without considering the foundation and the long-span steel structure is solved;

[0013] Solve the foundation scattered field response based on the motion equations of the foundation and the long-span steel structure;

[0014] The foundation free field response and foundation scattered field response are added to obtain the foundation response under earthquake action;

[0015] According to the relationship between the response of the large-span steel structure and the foundation response, the column top response of the large-span steel structure is solved. According to the motion equation of the large-span steel structure, the mid-span response of the large-span steel structure is solved.

[0016] The above method optionally establishes a large-span steel structure seismic response calculation model considering soil-structure interaction, including:

[0017] Incident SH wave: incident from the interface between bedrock and soil layer, incident at an angle θ to the x-axis, with a circular frequency of ω;

[0018] Soil model: The horizontally layered half-space soil model includes bedrock and overlying soil layers, and the bedrock shear wave velocity is β R , mass density is ρ R , the damping ratio is ξ R , the soil layer thickness is D, the shear wave velocity is β L , mass density is ρ L , the damping ratio is ξ L ;

[0019] Foundation model: two identical semicircular rigid foundations with radius a and unit length mass M0, and the replaced soil unit length mass M S ;

[0020] Large-span steel structure model: including beams and columns, the natural frequency of the steel structure is ω b , the damping ratio is ξ b , the shear wave velocity is β b ; The beam is simplified to an Euler-Bernoulli beam with a span of L and a mass per unit length of M b ; The column height is H, and the stiffness of a single column is K b .

[0021] In the above method, optionally, the soil and foundation, as well as the foundation and the bottom of the column of the large-span steel structure in the large-span steel structure seismic response calculation model considering soil-structure interaction are rigidly connected, and no relative displacement occurs.

[0022] The above method is optional. The specific content of solving the free field response of soil layer based on direct stiffness method is:

[0023] The soil layer is divided into N sub-layers according to the natural stratification of the soil layer and the calculation accuracy requirements, and the free field overall stiffness matrix [S] is integrated;

[0024] Calculate the load matrix of each sublayer interface when SH wave is incident [Q] = {0,0,…,0,Q R} T , Q R =[S R ]v SH ;

[0025] According to the direct stiffness method [Q] = [S] [V], the displacement at the interface of each sublayer is obtained [V] = {v1,v 2, …,v N ,v N+1} T , then the out-of-plane displacement and stress of any point (x, z) in the lth layer of the soil are:

[0026] v(x,z)=[A SH exp(ikt L z)+B SH exp(-ikt L z)]exp(-ikx)exp(iωt) (1)

[0027] τ yz (x,z)=-ikt L G L *[A SH exp(ikt L z)-B SH exp(-ikt L z)]exp(-ikx)exp(iωt) (2)

[0028] Among them, v SH is the displacement amplitude of the bedrock surface when the SH wave is incident from the bedrock; the corresponding symbols with * in the superscript are the complex material constants after considering the material damping; z∈(0,d l ), d l is the thickness of the lth sublayer; A SH and B SH By v l , z = 0 and v l+1 , z = d l Two displacement values ​​are found.

[0029] The above method optionally solves the foundation stiffness matrix based on the uniformly distributed line load Green's function and boundary continuity conditions as follows:

[0030] Under the SH wave excitation, the foundation only produces an out-of-plane displacement Δ={Δ Γ1 ,Δ Γ2} T , according to the site stratification, the basic boundaries Γ1 and Γ2 are discretized into 2N units respectively. When the rotation angle is very small, the displacement U(x,z) on the boundaries Γ1 and Γ2 are respectively:

[0031] U(x,z)=

[10] {Δ Γ1 ,Δ Γ2} T =[Ω(x,z)]Δ…(x,z)∈Γ1 (3)

[0032] U(x,z)=

[01] {Δ Γ1 ,Δ Γ2} T =[Ω(x,z)]Δ…(x,z)∈Γ2 (4)

[0033] A column dummy load q is applied to each element at the base boundary Γ j (j=1,2,…,4N), let the virtual load vector P={q1,q2,…,q 4N} T , then the displacement and stress at any point on the boundary are:

[0034] U(x,z)=[g u (x,z)]P…(x,z)∈Γ (5)

[0035] T(x,z)=[g t (x,z)]P…(x,z)∈Γ (6)

[0036] According to the displacement continuity condition, the displacement of any point (x, z) on the foundation boundary satisfies:

[0037] [g u(x,z)]P=[Ω(x,z)]Δ…(x,z)∈Γ (7)

[0038] For a linear system, assuming that P = [Λ]Δ, [Λ] represents the virtual load vector applied to the boundary when the foundation produces a unit displacement, then equation (7) is:

[0039] [g u (x,z)][Λ]=[Ω(x,z)]…(x,z)∈Γ (8)

[0040] The matrix [Λ] is obtained from this, and the matrix [Λ] is substituted into formula (6) to obtain:

[0041] T(x,z)=[g t (x,z)][Λ]Δ…(x,z)∈Γ (9)

[0042] According to the relationship between force and stress, the total external force acting on the foundation is:

[0043] F = ∫ Γ [Ω(x,z)] T T(x,z)dS(10)

[0044] Substituting equation (9) into equation (10) yields the foundation stiffness matrix [K]:

[0045] F = ∫ Γ [Ω(x,z)] T [g t (x,z)][Λ]ΔdS=[K]Δ(11)

[0046] [K] = ∫ Γ [Ω(x,z)] T [g t (x,z)][Λ]dS(12)

[0047] The above method can optionally solve the free field response of the foundation without considering the foundation and the long-span steel structure according to the free field response of the soil layer and the foundation stiffness matrix as follows:

[0048]

[0049] Among them, U f (x,z) is the free field displacement on the boundaries Γ1 and Γ2 when the SH wave is incident, T f (x,z) is the traction force on the boundaries Γ1 and Γ2 when the SH wave is incident, Ω1 and Ω2 are the basic shape functions, and g t,j (x,z) is the stress Green's function, K is the basic stiffness matrix, is the displacement matrix of the foundation plane without considering the foundation and the large-span steel structure. is the virtual load vector on the boundary when the foundation produces unit displacement.

[0050] The above method is optional.

[0051] The above method optionally solves the foundation scattered field response according to the motion equation of the foundation and the long-span steel structure as follows:

[0052] The basic inertia force is:

[0053]

[0054] Since most of the mass of the steel structure is concentrated in the beam, the out-of-plane motion is manifested as the horizontal displacement of the beam. According to the equilibrium equation of the single-particle system under earthquake action:

[0055]

[0056] Then the displacement of the top of the steel structure column relative to the foundation is:

[0057]

[0058] Simplifying the steel structure beam into an Euler-Bernoulli beam, the out-of-plane displacement of any point on the beam satisfies:

[0059]

[0060] Among them, k b is the shear wave number of the beam, k b =ω / β b Since the displacement at the beam end is the same as the displacement at the column top, equation (18) has two special solutions at the beam ends x = 0 and x = L:

[0061] u b (0) = Δ b Γ1 +Δ Γ1 =κΔ Γ1 ,u b (L) = Δ b Γ2 +Δ Γ2 =κΔ Γ2 (19)

[0062] in, The displacement of any point on the beam is:

[0063]

[0064] The reaction force generated at both ends of the beam is calculated, that is, the inertia force of the long-span steel structure:

[0065]

[0066] Basic mass inertia force F 01 and F 02 And the mass inertia force F of the large-span steel structure b1 and F b2 The resulting scattered field response Δ2 is:

[0067]

[0068] In the above method, optionally, the foundation free field response and the foundation scattered field response are added to obtain the specific content of the foundation response under earthquake action:

[0069] The foundation response Δ is divided into two parts: one part is the foundation free field response Δ1 without considering the foundation and the long-span steel structure; the other part is the scattered field response Δ2 generated by the foundation inertia force and the long-span steel structure inertia force:

[0070]

[0071] Substitute equation (23) into equation (22), and let

[0072] Then we have:

[0073]

[0074] That is:

[0075]

[0076] In summary, the basic response Δ is:

[0077]

[0078] The above method can optionally solve the column top response of the large-span steel structure according to the relationship between the response of the large-span steel structure and the foundation response. The specific content of solving the mid-span response of the large-span steel structure according to the motion equation of the large-span steel structure is:

[0079] Displacement response of column top of long-span steel structure Δ b for:

[0080]

[0081] Mid-span displacement response of long-span steel structure Δ m for:

[0082]

[0083] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses an IBE simulation method for seismic response of a large-span steel structure taking into account soil-structure interaction, and its beneficial effects are:

[0084] Compared with the existing structural seismic response analysis methods, the seismic response IBE simulation method proposed in the present invention takes into account factors such as the change in the structural natural frequency caused by the soil-structure dynamic interaction and the mutual influence of scattered waves between foundations; no artificial boundary is required during the solution and the semi-infinite space radiation conditions are strictly met; the calculation units are divided only at the boundaries, the problem dimension is reduced by one dimension compared with other methods, and the calculation efficiency is high, which can effectively improve the accuracy and speed of structural seismic response analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0086] Figure 1 A flowchart of an IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction provided by the present invention;

[0087] Figure 2 The overall flow chart of an IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction provided by the present invention;

[0088] Figure 3 A diagram of a large-span steel structure seismic response calculation model considering soil-structure interaction provided by the present invention;

[0089] Figure 4 Basic response diagrams under different structural spans provided by the embodiments of the present invention; wherein 4a is a basic response diagram of L / a=5, 4b is a basic response diagram of L / a=10, 4c is a basic response diagram of L / a=20, and 4d is a basic response diagram of L / a=40;

[0090] Figure 5 The top response diagrams of the large-span steel structure columns under different structural spans provided by the embodiment of the present invention; wherein 5a is the top response diagram of the large-span steel structure column with L / a=5, 5b is the top response diagram of the large-span steel structure column with L / a=10, 5c is the top response diagram of the large-span steel structure column with L / a=20, and 5d is the top response diagram of the large-span steel structure column with L / a=40;

[0091] Figure 6The mid-span response diagrams of large-span steel structures under different structural spans provided in the embodiments of the present invention; among them, 6a is the mid-span response diagram of the large-span steel structure with L / a=5, 6b is the mid-span response diagram of the large-span steel structure with L / a=10, 6c is the mid-span response diagram of the large-span steel structure with L / a=20, and 6d is the mid-span response diagram of the large-span steel structure with L / a=40. DETAILED DESCRIPTION

[0092] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0093] See also Figure 1 and Figure 2 As shown, the present invention discloses an IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction, comprising the following steps:

[0094] Establish a calculation model for the seismic response of large-span steel structures considering soil-structure interaction;

[0095] Solve the free field response of soil layer based on direct stiffness method;

[0096] Solve the foundation stiffness matrix based on the uniformly distributed line load Green's function and boundary continuity conditions;

[0097] According to the free-field response of the soil layer and the foundation stiffness matrix, the free-field response of the foundation without considering the foundation and the long-span steel structure is solved;

[0098] Solve the foundation scattered field response based on the motion equations of the foundation and the long-span steel structure;

[0099] The foundation free field response and foundation scattered field response are added to obtain the foundation response under earthquake action;

[0100] According to the relationship between the response of the large-span steel structure and the foundation response, the column top response of the large-span steel structure is solved. According to the motion equation of the large-span steel structure, the mid-span response of the large-span steel structure is solved.

[0101] Specifically, the response of the long-span steel structure is calculated by the foundation response, which is the sum of the free field response without considering the foundation and the long-span steel structure and the scattered field response generated by the inertial force of the foundation and the long-span steel structure.

[0102] For further information, see Figure 3 As shown in the figure, the calculation model of seismic response of large-span steel structure considering soil-structure interaction includes:

[0103] Incident SH wave: incident from the interface between bedrock and soil layer, incident at an angle θ to the x-axis, with a circular frequency of ω;

[0104] Soil model: The horizontally layered half-space soil model includes bedrock and overlying soil layers, and the bedrock shear wave velocity is β R , mass density is ρ R , the damping ratio is ξ R , the soil layer thickness is D, the shear wave velocity is β L , mass density is ρ L , the damping ratio is ξ L ;

[0105] Foundation model: two identical semicircular rigid foundations with radius a and unit length mass M0, and the replaced soil unit length mass M S ;

[0106] Large-span steel structure model: including beams and columns, the natural frequency of the steel structure is ω b , the damping ratio is ξ b , the shear wave velocity is β b ; The beam is simplified to an Euler-Bernoulli beam with a span of L and a mass per unit length of M b ; The column height is H, and the stiffness of a single column is K b .

[0107] Furthermore, in the seismic response calculation model of the large-span steel structure considering soil-structure interaction, the soil and foundation, and the foundation and the bottom of the large-span steel structure column are all rigidly connected, and no relative displacement occurs.

[0108] Furthermore, the specific contents of solving the free field response of soil layer based on direct stiffness method are as follows:

[0109] The soil layer is divided into N sub-layers according to the natural stratification of the soil layer and the calculation accuracy requirements, and the free field overall stiffness matrix [S] is integrated;

[0110] Calculate the load matrix of each sublayer interface when SH wave is incident [Q] = {0,0,…,0,Q R} T , Q R =[S R ]v SH ;

[0111] According to the direct stiffness method [Q] = [S] [V], the displacement at the interface of each sublayer is obtained [V] = {v1,v 2, …,v N ,v N+1} T , then the out-of-plane displacement and stress of any point (x, z) in the lth layer of the soil are:

[0112] v(x,z)=[A SH exp(ikt L z)+B SH exp(-ikt L z)]exp(-ikx)exp(iωt) (1)

[0113] τ yz (x,z)=-ikt L G L *[A SH exp(ikt L z)-B SH exp(-ikt L z)]exp(-ikx)exp(iωt) (2)

[0114] Among them, v SH is the displacement amplitude of the bedrock surface when the SH wave is incident from the bedrock; the corresponding symbols with * in the superscript are the complex material constants after considering the material damping; z∈(0,d l ), d l is the thickness of the lth sublayer; A SH and B SH By v l , z = 0 and v l+1 , z = d l Two displacement values ​​are found.

[0115] Furthermore, the specific content of solving the foundation stiffness matrix based on the uniformly distributed line load Green's function and boundary continuity conditions is:

[0116] Under the SH wave excitation, the foundation only produces an out-of-plane displacement Δ={Δ Γ1 ,Δ Γ2} T , according to the site stratification, the basic boundaries Γ1 and Γ2 are discretized into 2N units respectively. When the rotation angle is very small, the displacement U(x,z) on the boundaries Γ1 and Γ2 are respectively:

[0117] U(x,z)=

[10] {Δ Γ1 ,Δ Γ2} T =[Ω(x,z)]Δ…(x,z)∈Γ1 (3)

[0118] U(x,z)=

[01] {Δ Γ1 ,Δ Γ2} T =[Ω(x,z)]Δ…(x,z)∈Γ2 (4)

[0119] A column dummy load q is applied to each element at the base boundary Γ j(j=1,2,…,4N), let the virtual load vector P={q1,q2,…,q 4N} T , then the displacement and stress at any point on the boundary are:

[0120] U(x,z)=[g u (x,z)]P…(x,z)∈Γ (5)

[0121] T(x,z)=[g t (x,z)]P…(x,z)∈Γ (6)

[0122] According to the displacement continuity condition, the displacement of any point (x, z) on the foundation boundary satisfies:

[0123] [g u (x,z)]P=[Ω(x,z)]Δ…(x,z)∈Γ (7)

[0124] For a linear system, assuming that P = [Λ]Δ, [Λ] represents the virtual load vector applied to the boundary when the foundation produces a unit displacement, then equation (7) is:

[0125] [g u (x,z)][Λ]=[Ω(x,z)]…(x,z)∈Γ (8)

[0126] The matrix [Λ] is obtained from this, and the matrix [Λ] is substituted into formula (6) to obtain:

[0127] T(x,z)=[g t (x,z)][Λ]Δ…(x,z)∈Γ (9)

[0128] According to the relationship between force and stress, the total external force acting on the foundation is:

[0129] F = ∫ Γ [Ω(x,z)] T T(x,z)dS(10)

[0130] Substituting equation (9) into equation (10) yields the foundation stiffness matrix [K]:

[0131] F = ∫ Γ [Ω(x,z)] T [g t (x,z)][Λ]ΔdS=[K]Δ(11)

[0132] [K] = ∫ Γ [Ω(x,z)] T [g t (x,z)][Λ]dS(12)

[0133] Furthermore, according to the free-field response of the soil layer and the foundation stiffness matrix, the specific content of solving the free-field response of the foundation without considering the foundation and the large-span steel structure is:

[0134]

[0135] Among them, U f (x,z) is the free field displacement on the boundaries Γ1 and Γ2 when the SH wave is incident, T f (x,z) is the traction force on the boundaries Γ1 and Γ2 when the SH wave is incident, Ω1 and Ω2 are the basic shape functions, and g t,j (x,z) is the stress Green's function, K is the basic stiffness matrix, is the displacement matrix of the foundation plane without considering the foundation and the large-span steel structure. is the virtual load vector on the boundary when the foundation produces unit displacement.

[0136] Furthermore,

[0137] Furthermore, the specific contents of solving the foundation scattered field response according to the motion equations of the foundation and the long-span steel structure are as follows:

[0138] The basic inertia force is:

[0139]

[0140] Since most of the mass of the steel structure is concentrated in the beam, the out-of-plane motion is manifested as the horizontal displacement of the beam. According to the equilibrium equation of the single-particle system under earthquake action:

[0141]

[0142] Then the displacement of the top of the steel structure column relative to the foundation is:

[0143]

[0144] Simplifying the steel structure beam into an Euler-Bernoulli beam, the out-of-plane displacement of any point on the beam satisfies:

[0145]

[0146] Among them, k b is the shear wave number of the beam, k b =ω / β b Since the displacement at the beam end is the same as the displacement at the column top, equation (18) has two special solutions at the beam ends x = 0 and x = L:

[0147] u b (0) = Δ b Γ1 +Δ Γ1=κΔ Γ1 ,u b (L) = Δ b Γ2 +Δ Γ2 =κΔ Γ2 (19)

[0148] in, The displacement of any point on the beam is:

[0149]

[0150] The reaction force generated at both ends of the beam is calculated, that is, the inertia force of the long-span steel structure:

[0151]

[0152] Basic mass inertia force F 01 and F 02 And the mass inertia force F of the large-span steel structure b1 and F b2 The resulting scattered field response Δ2 is:

[0153]

[0154] Furthermore, by adding the foundation free field response and the foundation scattered field response, the specific content of the foundation response under earthquake action is obtained as follows:

[0155] The foundation response Δ is divided into two parts: one part is the foundation free field response Δ1 without considering the foundation and the long-span steel structure; the other part is the scattered field response Δ2 generated by the foundation inertia force and the long-span steel structure inertia force:

[0156]

[0157] Substitute equation (23) into equation (22), and let

[0158] Then we have:

[0159]

[0160] That is:

[0161]

[0162] In summary, the basic response Δ is:

[0163]

[0164] Furthermore, according to the relationship between the response of the large-span steel structure and the foundation response, the top response of the large-span steel structure column is solved. According to the motion equation of the large-span steel structure, the specific content of the mid-span response of the large-span steel structure is solved as follows:

[0165] Displacement response of column top of long-span steel structure Δ b for:

[0166]

[0167] Mid-span displacement response of long-span steel structure Δ m for:

[0168]

[0169] In a specific embodiment, the SH wave incident angle θ = 90°; the stiffness ratio of the soil to the long-span steel structure ε = β L L / (β b a) is 2; the ratio of soil thickness D to foundation radius a is 2; the bedrock shear wave velocity β R and soil shear wave velocity β L The ratio is 2, and the rigid foundation condition takes β R =β L =7200m / s; bedrock density ρ R and soil density ρ L The ratio of the span L of the large-span steel structure to the foundation radius a is 5, 10, 20, and 40 respectively; the mass M of the large-span steel structure is 0.05. b and the mass of excavated soil M S The ratio of foundation mass M0 to excavated soil mass M S The ratio is 1.

[0170] Figure 4 4a-4d in the figure are the foundation response curves under different structural spans. Figure 5 5a-5d in the figure are the response curves of the top of the long-span steel structure column. Figure 6 6a-6d in the figure are mid-span response curves of large-span steel structures. Figure 4-Figure 6 The displacement of the medium rigid foundation condition is represented by the dotted line, and the x-coordinate is the dimensionless frequency η=ωa / β L .

[0171] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0172] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An IBE simulation method for seismic response of large-span steel structures considering soil-structure interaction, characterized in that: The following steps are involved: Establish a calculation model for the seismic response of large-span steel structures considering soil-structure interaction; Solve the free field response of soil layer based on direct stiffness method; Solve the foundation stiffness matrix based on the uniformly distributed line load Green's function and boundary continuity conditions; According to the free-field response of the soil layer and the foundation stiffness matrix, the free-field response of the foundation without considering the foundation and the long-span steel structure is solved; Solve the foundation scattered field response based on the motion equations of the foundation and the long-span steel structure; The foundation free field response and foundation scattered field response are added to obtain the foundation response under earthquake action; According to the relationship between the response of the large-span steel structure and the foundation response, the column top response of the large-span steel structure is solved. According to the motion equation of the large-span steel structure, the mid-span response of the large-span steel structure is solved.

2. The IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction according to claim 1 is characterized in that: The establishment of a large-span steel structure seismic response calculation model considering soil-structure interaction includes: Incident SH wave: incident from the interface between bedrock and soil layer, incident at an angle θ to the x-axis, with a circular frequency of ω; Soil model: The horizontally layered half-space soil model includes bedrock and overlying soil layers, and the bedrock shear wave velocity is β R , mass density is ρ R , the damping ratio is ξ R , the soil layer thickness is D, the shear wave velocity is β L , mass density is ρ L , the damping ratio is ξ L ; Foundation model: two identical semicircular rigid foundations with radius a and unit length mass M0, and the replaced soil unit length mass M S ; Large-span steel structure model: including beams and columns, the natural frequency of the steel structure is ω b , the damping ratio is ξ b , the shear wave velocity is β b ; The beam is simplified to an Euler-Bernoulli beam with a span of L and a mass per unit length of M b ; The column height is H, and the stiffness of a single column is K b .

3. The IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction according to claim 1 is characterized in that: In the calculation model of seismic response of large-span steel structure considering soil-structure interaction, the soil and foundation, as well as the foundation and the bottom of the column of large-span steel structure are rigidly connected, and no relative displacement occurs.

4. The IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction according to claim 1 is characterized in that: The specific contents of solving the free field response of soil layer based on direct stiffness method are as follows: The soil layer is divided into N sub-layers according to the natural stratification of the soil layer and the calculation accuracy requirements, and the free field overall stiffness matrix [S] is integrated; Calculate the load matrix of each sublayer interface when SH wave is incident [Q] = {0,0,…,0,Q R } T , Q R =[S R ]v SH ; According to the direct stiffness method [Q] = [S] [V], the displacement at the interface of each sublayer is obtained [V] = {v1,v 2, …,v N ,v N+1 } T , then the out-of-plane displacement and stress of any point (x, z) in the lth layer of the soil are: v(x,z)=[A SH exp(ikt L z)+B SH exp(-ikt L z)]exp(-ikx)exp(iωt) (1) τ yz (x,z)=-ikt L G L *[A SH exp(ikt L z)-B SH exp(-ikt L z)]exp(-ikx)exp(iωt) (2) Among them, v SH is the displacement amplitude of the bedrock surface when the SH wave is incident from the bedrock; the corresponding symbols with * in the superscript are the complex material constants after considering the material damping; z∈(0,d l ), d l is the thickness of the lth sublayer; A SH and B SH By v l , z = 0 and v l+1 , z = d l Two displacement values ​​are found.

5. The IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction according to claim 1 is characterized in that: The specific content of solving the foundation stiffness matrix based on the uniformly distributed line load Green's function and boundary continuity conditions is: Under the SH wave excitation, the foundation only produces an out-of-plane displacement Δ={Δ Γ1 ,Δ Γ2 } T , according to the site stratification, the basic boundaries Γ1 and Γ2 are discretized into 2N units respectively. When the rotation angle is very small, the displacement U(x,z) on the boundaries Γ1 and Γ2 are respectively: U(x,z)=[10]{Δ Γ1 ,Δ Γ2 } T =[Ω(x,z)]Δ…(x,z)∈Γ1 (3) U(x,z)=[01]{Δ Γ1 ,Δ Γ2 } T =[Ω(x,z)]Δ…(x,z)∈Γ2 (4) A column dummy load q is applied to each element at the base boundary Γ j (j=1,2,…,4N), let the virtual load vector P={q1,q2,…,q 4N } T , then the displacement and stress at any point on the boundary are: U(x,z)=[g u (x,z)]P…(x,z)∈Γ (5) T(x,z)=[g t (x,z)]P…(x,z)∈Γ (6) According to the displacement continuity condition, the displacement of any point (x, z) on the foundation boundary satisfies: [g u (x,z)]P=[Ω(x,z)]Δ…(x,z)∈Γ (7) For a linear system, assuming that P = [Λ]Δ, [Λ] represents the virtual load vector applied to the boundary when the foundation produces a unit displacement, then equation (7) is: [g u (x,z)][Λ]=[Ω(x,z)]…(x,z)∈Γ (8) The matrix [Λ] is obtained from this, and the matrix [Λ] is substituted into formula (6) to obtain: T(x,z)=[g t (x,z)][Λ]Δ…(x,z)∈Γ (9) According to the relationship between force and stress, the total external force acting on the foundation is: F=∫ Γ [Ω(x,z)] T T(x,z)dS (10) Substituting equation (9) into equation (10) yields the foundation stiffness matrix [K]: F=∫ Γ [Ω(x,z)] T [g t (x,z)][Λ]ΔdS=[K]Δ (11) [K]=∫ Γ [Ω(x,z)] T [g t (x,z)][Λ]dS (12)。 6. The IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction according to claim 1 is characterized in that: According to the free-field response of the soil layer and the foundation stiffness matrix, the specific content of solving the free-field response of the foundation without considering the foundation and the large-span steel structure is: Among them, U f (x,z) is the free field displacement on the boundaries Γ1 and Γ2 when the SH wave is incident, T f (x,z) is the traction force on the boundaries Γ1 and Γ2 when the SH wave is incident, Ω1 and Ω2 are the basic shape functions, and g t,j (x,z) is the stress Green's function, K is the basic stiffness matrix, is the displacement matrix of the foundation plane without considering the foundation and the large-span steel structure. is the virtual load vector on the boundary when the foundation produces unit displacement.

7. The IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction according to claim 6 is characterized in that:

8. The IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction according to claim 1 is characterized in that: The specific contents of solving the foundation scattered field response according to the motion equations of the foundation and the long-span steel structure are as follows: The basic inertia force is: Since most of the mass of the steel structure is concentrated in the beam, the out-of-plane motion is manifested as the horizontal displacement of the beam. According to the equilibrium equation of the single-particle system under earthquake action: Then the displacement of the top of the steel structure column relative to the foundation is: Simplifying the steel structure beam into an Euler-Bernoulli beam, the out-of-plane displacement of any point on the beam satisfies: Among them, k b is the shear wave number of the beam, k b =ω / β b Since the displacement at the beam end is the same as the displacement at the column top, equation (18) has two special solutions at the beam ends x = 0 and x = L: you b (0)=D b Γ1 +D Γ1 =kD Γ1 , u b (L)=Δ b Γ2 +D Γ2 =kD Γ2 (19) in, The displacement of any point on the beam is: The reaction force generated at both ends of the beam is calculated, that is, the inertia force of the long-span steel structure: Basic mass inertia force F 01 and F 02 And the mass inertia force F of the large-span steel structure b1 and F b2 The resulting scattered field response Δ2 is:

9. The IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction according to claim 1, characterized in that: By adding the foundation free field response and the foundation scattered field response, the specific content of the foundation response under earthquake action is obtained as follows: The foundation response Δ is divided into two parts: one part is the foundation free field response Δ1 without considering the foundation and the long-span steel structure; the other part is the scattered field response Δ2 generated by the foundation inertia force and the long-span steel structure inertia force: Substitute equation (23) into equation (22), and let Then we have: That is: In summary, the basic response Δ is:

10. The IBE simulation method for seismic response of a large-span steel structure considering soil-structure interaction according to claim 1, characterized in that: According to the relationship between the response of the large-span steel structure and the foundation response, the top response of the large-span steel structure column is solved. According to the motion equation of the large-span steel structure, the specific content of solving the mid-span response of the large-span steel structure is as follows: Displacement response of column top of long-span steel structure Δ b for: Mid-span displacement response of long-span steel structure Δ m for:

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