An IBE simulation method for seismic response of long-span steel structures considering soil-structure interaction

Abstract

The present invention discloses an IBE simulation method for the seismic response of a large-span steel structure taking into account soil-structure interaction, and relates to the technical field of building structure seismic response simulation. The method comprises: establishing a large-span steel structure seismic response calculation model taking into account soil-structure interaction; solving the free-field response of the soil layer based on the direct stiffness method; solving the foundation stiffness matrix based on the uniformly distributed line load Green's function and boundary continuity conditions; solving the foundation free-field response based on the soil free-field response and the foundation stiffness matrix; solving the foundation scattered-field response based on 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 derive the foundation response under earthquake action; solving the column top response of the large-span steel structure based on the relationship between the large-span steel structure response and the foundation response; and solving the mid-span response of the large-span steel structure based on the motion equation of the large-span steel structure. The present invention can improve the accuracy of structural seismic response analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of building structure seismic response simulation, and more particularly to an IBE (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 impacts. They have caused serious casualties and economic losses worldwide. Ensuring the seismic safety of building structures is a key issue in structural design. In addition, multiple earthquake damage observations have shown that soil-structure interaction can aggravate the damage to building structures under earthquakes. In the 1985 7.8 magnitude earthquake in Mexico, approximately 35% of the buildings in Mexico City, more than 400 kilometers from the epicenter, were damaged due to the soft soil site, and more than 300 buildings completely collapsed. Related studies have shown that the changes in the natural frequency of the structure after considering soil-structure interaction, the mutual influence of scattered waves between foundations, and the displacement differences between supports will cause significant changes in the seismic response of the structure. The impact of soil-structure interaction on the seismic response of the structure cannot be ignored.

[0003] Existing structural seismic response analyses often consider the influence of local site conditions based on empirical formulas and simplify the consideration of traveling earthquake waves based on changes in amplitude and phase. Numerical models for structural seismic response analysis often only include the structural portion, or use springs and dampers to simplify the effects of the soil. Although some methods use the finite element method to establish an integrated soil-foundation-structure model, most of these models treat the soil as a homogeneous medium and truncate a limited range of soil to simulate a semi-infinite space region. This requires the introduction of artificial boundaries at the cutoffs of the soil model to eliminate errors caused by seismic wave reflections at the boundaries. These issues make it difficult to fully consider the effects of soil-structure interaction in existing structural seismic response analysis methods, resulting in significant uncertainty in the results.

[0004] The indirect boundary element (IBE) method is a commonly used analytical approach for solving soil-structure interaction problems. It offers advantages such as strict compliance with semi-infinite space radiation conditions, high solution accuracy, and low problem dimensionality. Therefore, it is necessary to propose an IBE simulation method for the seismic response of large-span steel structures that considers soil-structure interaction. This method fully accounts for the influence of soil-structure interaction on the seismic response of the structure and derives a calculation formula for the seismic response of a foundation-long-span steel structure model in a horizontally layered field, providing 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 existing technology. Summary of the Invention

[0006] In view of this, the present invention provides an IBE simulation method for the 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 includes 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 long-span steel structure;

[0014] The foundation free field response and the 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 can be optionally used to establish 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, with an angle of θ to the x-axis, and 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 mass per unit length M0, and the replaced soil with mass per unit length 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] Alternatively, the above method considers the large-span steel structure seismic response calculation model of soil-structure interaction, in which the soil and foundation, as well as the foundation and the base of the large-span steel structure column are rigidly connected, and no relative displacement occurs.

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

[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 sub-layer 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 sub-layer 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 * superscripts are complex material constants after considering 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 obtained.

[0029] The above method is optional. The specific content of solving the foundation stiffness matrix based on the uniformly distributed line load Green's function and boundary continuity conditions is as follows:

[0030] Under the excitation of SH wave, the foundation only produces out-of-plane displacement Δ={Δ Γ1 ,Δ Γ2} T , the foundation boundaries Γ1 and Γ2 are discretized into 2N units according to the site stratification. 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] Apply a column dummy load q to each element of the foundation 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 P = [Λ]Δ, [Λ] represents the virtual load vector applied on the boundary when the foundation produces 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 net 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 be used to solve the free-field response of the foundation without considering the foundation and the long-span steel structure based on the free-field response of the soil layer and the foundation stiffness matrix. The specific content is:

[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, g t,j (x,z) is the stress Green's function, K is the basic stiffness matrix, is the out-of-plane displacement matrix of the foundation without considering the foundation and the long-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 can optionally be used to solve the foundation scattered field response based on the motion equations 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 of the beam end is the same as the displacement of 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, which 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] The above method optionally adds the foundation free-field response and the foundation scattered-field response to obtain the specific content of the foundation response under earthquake action:

[0069] The foundation response Δ is divided into two parts: one is the foundation free field response Δ1 without considering the foundation and the long-span steel structure; the other 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 long-span steel structure based on the relationship between the long-span steel structure response and the foundation response. The specific content of solving the mid-span response of the long-span steel structure based on the motion equation of the long-span steel structure is as follows:

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

[0080]

[0081] Mid-span displacement response of long-span steel structures 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 large-span steel structures taking into account soil-structure interaction, which has the following beneficial effects:

[0084] Compared with existing structural seismic response analysis methods, the seismic response IBE simulation method proposed in this invention takes into account factors such as the change in structural natural frequency caused by soil-structure dynamic interaction and the mutual influence of scattered waves between foundations; no artificial boundaries are required during the solution, and the semi-infinite space radiation conditions are strictly met; the calculation units are only divided 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 following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any 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 the IBE simulation method for seismic response of large-span steel structures considering soil-structure interaction provided by the present invention;

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

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

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

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

[0092] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts 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 long-span steel structure;

[0099] The foundation free field response and the 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 from 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 Figure 2, the establishment of a large-span steel structure seismic response calculation model considering soil-structure interaction includes:

[0103] Incident SH wave: incident from the interface between bedrock and soil layer, with an angle of θ to the x-axis, and 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 mass per unit length M0, and the replaced soil with mass per unit length 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 calculation model of seismic response of large-span steel structures considering soil-structure interaction, the soil and foundation, as well as the foundation and the bottom of the large-span steel structure columns are rigidly connected, and no relative displacement occurs.

[0108] Furthermore, the specific content of solving the free-field response of the soil layer based on the direct stiffness method is 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 sub-layer 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 sub-layer 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 * superscripts are complex material constants after considering 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 obtained.

[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 as follows:

[0116] Under the excitation of SH wave, the foundation only produces out-of-plane displacement Δ={Δ Γ1 ,Δ Γ2} T , the foundation boundaries Γ1 and Γ2 are discretized into 2N units according to the site stratification. 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] Apply a column dummy load q to each element at the foundation 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 P = [Λ]Δ, [Λ] represents the virtual load vector applied on the boundary when the foundation produces 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 net 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, based on 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 long-span steel structure is as follows:

[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, g t,j (x,z) is the stress Green's function, K is the basic stiffness matrix, is the out-of-plane displacement matrix of the foundation without considering the foundation and the long-span steel structure. is the virtual load vector on the boundary when the foundation produces unit displacement.

[0136] Further,

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

[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 of the beam end is the same as the displacement of 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, which 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:

[0155] The foundation response Δ is divided into two parts: one is the foundation free field response Δ1 without considering the foundation and the long-span steel structure; the other 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, based on the relationship between the response of the long-span steel structure and the foundation response, the column top response of the long-span steel structure is solved. Based on the motion equation of the long-span steel structure, the specific content of the mid-span response of the long-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 structures 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 long-span steel structure to the foundation radius a is 5, 10, 20, and 40 respectively; the mass M of the long-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 large-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 is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily 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 is not limited to the embodiments shown herein but is intended to conform 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 by: 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 long-span steel structure; The foundation free field response and the foundation scattered field response are added to obtain the foundation response under earthquake action; Based on the relationship between the response of the long-span steel structure and the foundation response, the column top response of the long-span steel structure is solved. Based on the motion equation of the long-span steel structure, the mid-span response of the long-span steel structure is solved. 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, with an angle of θ to the x-axis, and 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 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 mass per unit length M0, and the replaced soil with mass per unit length 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 ; The specific content of solving the foundation scattered field response according to the motion equation of the foundation and the long-span steel structure is: 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 of the beam end is the same as the displacement of 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, which 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: Where [K] is the basic stiffness matrix; 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: The foundation response Δ is divided into two parts: one is the foundation free field response Δ1 without considering the foundation and the long-span steel structure; the other 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:

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

3. The IBE simulation method for seismic response of large-span steel structures considering soil-structure interaction according to claim 1 is characterized in that: The specific content of solving the free field response of soil layer based on direct stiffness method is 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 sub-layer 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 sub-layer 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 * superscripts are complex material constants after considering 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 obtained.

4. The IBE simulation method for seismic response of large-span steel structures considering soil-structure interaction according to claim 3 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 excitation of SH wave, the foundation only produces out-of-plane displacement Δ={Δ Γ1 ,Δ Γ2 } T , the foundation boundaries Γ1 and Γ2 are discretized into 2N units according to the site stratification. 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); Apply a column dummy load q to each element of the foundation 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 P = [Λ]Δ, [Λ] represents the virtual load vector applied on the boundary when the foundation produces 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 net 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)。 5. The IBE simulation method for seismic response of large-span steel structures 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 long-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, g t,j (x,z) is the stress Green's function, K is the basic stiffness matrix, is the out-of-plane displacement matrix of the foundation without considering the foundation and the long-span steel structure. is the virtual load vector on the boundary when the foundation produces unit displacement.

6. The IBE simulation method for seismic response of large-span steel structures considering soil-structure interaction according to claim 5 is characterized in that:

7. The IBE simulation method for seismic response of large-span steel structures considering soil-structure interaction according to claim 1 is characterized in that: 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 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 structures Δ m for:

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