A simulation method of site-city interaction effects based on OpenSees

Abstract

The purpose of the present invention is to solve the problem that the existing site soil stress-strain behavior mostly adopts a viscoelastic model without considering the elastic-plastic deformation of the site. Simulation method: 1. Establish a numerical model of the site soil; 2. Add information such as the nodes of the superstructure group, the superstructure and the site soil to obtain the superstructure-site soil model; 3. Gravity load the superstructure-site soil model, and the deformation behavior of the soil material is linear elastic; 4. Keep the initial stress state of the soil unchanged, and then change the deformation behavior of the soil material to elastic-plastic to obtain the initial stress field model of the soil; 5. Apply seismic excitation to the initial stress field model of the soil, and perform seismic response analysis. The present invention can reliably restore the dynamic interaction between the site soil and the superstructure group, and takes into account the influence of the nonlinear deformation of the soil on the site seismic response and the seismic interaction between the structure group and the soil.

Description

Technical Field

[0001] The invention belongs to the field of earthquake engineering, and in particular relates to a site-city interaction effect simulation method based on OpenSees. Background Art

[0002] In the complex engineering environment of the city, the existence of large-scale engineering structures causes the seismic waves on the surface to present a complex interference pattern. The vibration of the structure will serve as a new secondary source of earthquakes, further "polluting" the distribution of ground motions on the surface, which is the so-called "Site-City Interaction (SCI)".

[0003] Existing site-city interaction models mainly simulate urban buildings by using homogeneous block models, simplifying buildings into equivalent isotropic elastic bodies to simulate soil-structure interaction. The homogeneous block model has simple parameter settings, convenient application, and relatively simple mechanical behavior. Compared with the single degree of freedom model used in early SCI effect research, it has higher accuracy and can simulate the interaction between the high-order vibration modes of the structure and the site, but it requires sufficiently fine meshing to accurately capture the high-order vibration modes of the building, and the model calculation cost is relatively high.

[0004] In addition, the stress-strain behavior of the site soil is mostly assumed to be a simple viscoelastic model, without considering the elastic-plastic deformation of the site. Under the action of an earthquake, the elastic-plastic deformation of the soil will significantly change the seismic response of the site, thereby affecting the seismic interaction between soil and structure. However, most of the current studies on site-city interaction do not consider the impact of the elastic-plastic deformation behavior of the site on the urban seismic field. Summary of the invention

[0005] The purpose of the present invention is to solve the problem that the stress-strain behavior of existing site soil mostly adopts viscoelastic model without considering the elastic-plastic deformation of the site, and in order to more accurately evaluate the impact of urban building complexes on urban seismic motion fields and study the distribution characteristics of seismic motion fields in complex urban environments, a new type of refined numerical modeling and calculation method of ground-city interaction is proposed to study the spatiotemporal distribution characteristics and evolution laws of seismic motion fields in complex urban environments.

[0006] The site-city interaction effect simulation method based on OpenSees of the present invention is implemented according to the following steps:

[0007] Step 1: In the OpenSees system (the Open System for Earthquake Engineering Simulation), define the node and unit information of the site soil model, define the site soil material parameters and model boundary conditions, and establish a site soil numerical model;

[0008] The steps for setting the site soil numerical model and boundary conditions are as follows:

[0009] a. Set a free field soil column at each free field boundary on both sides of the site soil model to simulate the free field boundary, and bind the degrees of freedom of the nodes at the same height on both sides of the soil column to ensure that the soil column can restore the free field response under the action of an earthquake;

[0010] b. The site soil model is connected to the free-field soil columns on both sides through parallel viscous dampers and springs. The vertical degree of freedom of the bottom node of the site soil model is fixed, and parallel viscous dampers and springs are set in the horizontal direction. The viscous dampers and springs are simulated by zero-length units. The damping coefficient of the viscous damper is calculated using the following formula:

[0011] c=ρV s A(1)

[0012] The spring rate is calculated using the following formula:

[0013]

[0014] Where ρ is the bedrock density, V s is the bedrock shear wave velocity, α is the artificial boundary parameter, G is the site soil shear modulus, R is the distance from the site soil model center to the artificial boundary node, and A is the control area of ​​a single node;

[0015] Step 2: Add the superstructure group nodes and the material information of the superstructure, set the contact surface between the superstructure and the site soil, and obtain the superstructure-site soil model;

[0016] The simulation method of the superstructure is as follows:

[0017] The superstructure is simulated by a bending-shear coupling multi-degree-of-freedom system. The superstructure is connected to the site soil through equivalent degrees of freedom to ensure that the site soil and the superstructure move together. The superstructure is composed of rigidly connected bending beams and shear beams. The bending beams and shear beams are connected through equivalent degrees of freedom. The bending beam stiffness EI0 and the shear beam stiffness GA0 are calculated by the following formula:

[0018]

[0019]

[0020] Where ω1 is the first-order vibration mode natural circular frequency of the superstructure, ρ b is the structural mass per unit height, H is the structural height, α0 is the bending-shear stiffness ratio of the structure, and γ is the eigenvalue parameter;

[0021] Step 3: Gravity analysis of the site-urban building complex interaction model:

[0022] Gravity loading is performed on the superstructure-site soil model to obtain the initial stress field distribution of the soil. During the gravity loading stage, the deformation behavior of the soil material is linear elastic. At the same time, the displacement of the boundary nodes at both ends of the site soil model is fixed, and the boundary node reaction force is recorded;

[0023] Step 4: Change the deformation behavior of soil material from linear elastic to elastoplastic:

[0024] After the gravity analysis is completed, the initial stress state of the soil is kept unchanged, the displacement information of the soil is cleared, the displacement constraints of the boundary nodes at both ends of the site soil model are released, and the boundary node reaction force recorded in step 3 is applied to the boundary nodes. The deformation behavior of the soil material is changed to elastic-plastic through material update processing, and the model of the initial stress field of the soil is obtained;

[0025] Step 5: Apply seismic excitation to the model of the soil initial stress field and conduct seismic response analysis to complete the simulation of the site-city interaction effect.

[0026] Compared with the prior art, the site-city interaction effect simulation method based on OpenSees in the present invention includes the following

[0027] Beneficial effects:

[0028] 1. The present invention adopts the time-domain finite element method, which can reliably restore the dynamic interaction between the site soil and the upper structure group under complex terrain conditions and stratum conditions, and adopts an absorptive boundary to reduce the influence of the reflection of the scattered waves generated by the upper structure group at the model boundary on the simulation results;

[0029] 2. The present invention uses elastic-plastic materials to simulate the stress-strain behavior of soil, taking into account the influence of nonlinear deformation of soil on site seismic response and structural group-soil seismic interaction;

[0030] 3. The present invention adopts a simplified bending-shear coupling model to simulate the superstructure, which can reliably restore the dynamic response of the structure under seismic dynamics, and the number of grids required is far less than that of the traditional homogeneous block model, which can greatly reduce the calculation cost of the numerical model. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 This is a flow chart of a method for simulating site-city interaction effects based on OpenSees;

[0032] Figure 2 It is a simplified model schematic diagram of the bending-shear multi-degree-of-freedom system of the upper structure in the embodiment;

[0033] Figure 3This is a schematic diagram of the distribution of the upper structure group in the embodiment;

[0034] Figure 4 It is a structural schematic diagram of the numerical model of the site soil in the embodiment;

[0035] Figure 5 It is a comparison diagram of the linear model and the nonlinear model in the embodiment. DETAILED DESCRIPTION

[0036] Specific implementation method 1: This implementation method is based on the OpenSees site-city interaction effect simulation method according to the following steps:

[0037] Step 1: In the OpenSees system (the Open System for Earthquake Engineering Simulation), define the node and unit information of the site soil model, define the site soil material parameters and model boundary conditions, and establish a site soil numerical model;

[0038] The steps for setting the site soil numerical model and boundary conditions are as follows:

[0039] a. Set a free field soil column at each free field boundary on both sides of the site soil model to simulate the free field boundary, and bind the degrees of freedom of the nodes at the same height on both sides of the soil column to ensure that the soil column can restore the free field response under the action of an earthquake;

[0040] b. The site soil model is connected to the free-field soil columns on both sides through parallel viscous dampers and springs. The vertical degree of freedom of the bottom node of the site soil model is fixed, and parallel viscous dampers and springs are set in the horizontal direction. The viscous dampers and springs are simulated by zero-length units. The damping coefficient of the viscous damper is calculated using the following formula:

[0041] c=ρV s A(1)

[0042] The spring rate is calculated using the following formula:

[0043]

[0044] Where ρ is the bedrock density, V s is the bedrock shear wave velocity, α is the artificial boundary parameter, G is the site soil shear modulus, R is the distance from the site soil model center to the artificial boundary node, and A is the control area of ​​a single node;

[0045] Step 2: Add the superstructure group nodes and the material information of the superstructure, set the contact surface between the superstructure and the site soil, and obtain the superstructure-site soil model;

[0046] The simulation method of the superstructure is as follows:

[0047] The superstructure is simulated by a bending-shear coupling multi-degree-of-freedom system. The superstructure is connected to the site soil through equivalent degrees of freedom to ensure that the site soil and the superstructure move together. The superstructure is composed of rigidly connected bending beams and shear beams. The bending beams and shear beams are connected through equivalent degrees of freedom. The bending beam stiffness EI0 and the shear beam stiffness GA0 are calculated by the following formula:

[0048]

[0049]

[0050] Where ω1 is the first-order vibration mode natural circular frequency of the superstructure, ρ b is the structural mass per unit height, H is the structural height, α0 is the bending-shear stiffness ratio of the structure, and γ is the eigenvalue parameter;

[0051] Step 3: Gravity analysis of the site-urban building complex interaction model:

[0052] Gravity loading is performed on the superstructure-site soil model to obtain the initial stress field distribution of the soil. During the gravity loading stage, the deformation behavior of the soil material is linear elastic. At the same time, the displacement of the boundary nodes at both ends of the site soil model is fixed, and the boundary node reaction force is recorded;

[0053] Step 4: Change the deformation behavior of soil material from linear elastic to elastoplastic:

[0054] After the gravity analysis is completed, the initial stress state of the soil is kept unchanged, the displacement information of the soil is cleared, the displacement constraints of the boundary nodes at both ends of the site soil model are released, and the boundary node reaction force recorded in step 3 is applied to the boundary nodes. The deformation behavior of the soil material is changed to elastic-plastic through material update processing, and the model of the initial stress field of the soil is obtained;

[0055] Step 5: Apply seismic excitation to the model of the soil initial stress field and conduct seismic response analysis to complete the simulation of the site-city interaction effect.

[0056] In the site-city interaction effect simulation method based on OpenSees, the present implementation method first defines the node and unit information of the site soil model, defines the site soil material parameters and model boundary conditions, and establishes a two-dimensional site soil numerical model. The model is distributed along the thickness direction (z direction) and width direction (x direction) of the site soil. Then, the nodes, units and material information of the upper structure group are added, and the contact surface between the structure and the site soil is set. The gravity analysis of the site-city building complex interaction model is performed, and then the deformation behavior of the soil material is transformed from linear elasticity to elastoplasticity. The model is subjected to seismic response analysis. The initial state of the model adopts the initial stress field of the soil calculated by the above method, and the seismic excitation is applied to the bottom of the model in the form of force.

[0057] Specific implementation method 2: The difference between this implementation method and specific implementation method 1 is that the maximum height of the grid size of the site soil model in step 1 is determined by the following formula:

[0058]

[0059] Where V s represents the shear wave velocity of the softest soil layer, f max Indicates the maximum frequency of the input ground motion.

[0060] Specific implementation method three: The difference between this implementation method and specific implementation methods one or two is that in step one, the site soil is simulated using the two-dimensional FourNodeQuad unit in OpenSees, the unit thickness is set to 1m, and the constitutive relationship adopts a multi-yield surface elastic-plastic constitutive model, that is, the PressureIndependMultiYield material in OpenSees.

[0061] Specific implementation method 4: The difference between this implementation method and any one of specific implementation methods 1 to 3 is that the artificial boundary parameter α in formula (2) in step 1 is set to 0.5.

[0062] Specific implementation mode 5: This implementation mode is different from specific implementation modes 1 to 4 in that the thickness of the free-field soil column unit in step a is set to 1000 times the thickness of the site soil model unit.

[0063] Specific implementation method 6: The difference between this implementation method and any one of specific implementation methods 1 to 5 is that the value of α0 in formula (3) of step 2 ranges from 0 to 20.

[0064] Specific implementation method seven: The difference between this implementation method and specific implementation method six is ​​that for frame shear wall and frame core tube structure, the α0 value range is 0 to 1.5; for frame structure with lateral force resisting components, the α0 value range is 1.5 to 6; for pure frame structure, the α0 value range is 6 to 20.

[0065] Specific implementation eight: This implementation differs from specific implementations one to seven in that the calculation formula of the characteristic value parameter γ in formula (3) of step two is:

[0066]

[0067] Specific implementation method 9: The difference between this implementation method and specific implementation methods 1 to 8 is that in step 2, the curved beam in the upper structure is simulated by the elasticBeamColumn unit in OpenSees, and the shear beam is simulated by the twoNodeLink unit in OpenSees.

[0068] Specific implementation method ten: This implementation method is different from any one of specific implementation methods one to nine in that in step five, the seismic excitation is applied from the bottom in the form of force.

[0069] Embodiment: This example is based on the OpenSees site-city interaction effect simulation method and is implemented according to the following steps:

[0070] Step 1: In the OpenSees system (open system for earthquake engineering simulation), define the site soil model nodes and (grid) unit information (including node number and coordinates, unit number, node number contained in the unit, unit thickness, etc.), define the site soil material parameters and model boundary conditions, and establish a two-dimensional site soil numerical model. The two-dimensional site soil numerical model is distributed along the site soil thickness direction (z direction) and width direction (x direction);

[0071] Select the soil section to be studied, establish the site-city interaction model, and divide the numerical model grid; in this example, the width of the site soil numerical model is 2500m, the soil layer thickness is 40m, the soil layer shear wave velocity is 100m / s, and the maximum height of the numerical model grid size is determined by the following formula:

[0072]

[0073] Among them, V s represents the shear wave velocity of the softest soil layer, f max Indicates the maximum frequency of the input ground motion. In this example, the numerical model, the maximum frequency of the input ground motion is 5Hz, so the numerical model grid size height is set to 2m, and the grid horizontal width is 5m;

[0074] In this example, the site soil is simulated using a two-dimensional FourNodeQuad unit with the unit thickness set to 1m. Its constitutive relationship uses a multi-yield surface elastoplastic constitutive model, namely the PressureIndependMultiYield material in OpenSees.

[0075] The steps to set boundary conditions are as follows:

[0076] a. Set a thicker free-field soil column at the free-field boundary on both sides of the model to simulate the free-field boundary, and bind the node degrees of freedom at the same height on both sides of the soil column to ensure that the soil column can restore the free-field response under earthquake action. In this example, the thickness of the free-field soil column unit is set to 1000 times the thickness of the site soil model unit, and the width of the soil column is set to 600m;

[0077] b. The vertical degrees of freedom of the bottom nodes of the fixed site soil model are set at each node in the horizontal direction and between the free field soil column and the viscous damper and spring are connected in parallel. The viscous damper and spring are simulated by zero-length units. The damping coefficient of the viscous damper is calculated by the following formula:

[0078] c=ρV s A

[0079] The spring rate is calculated using the following formula:

[0080]

[0081] Where ρ is the bedrock density, V s is the bedrock shear wave velocity, α is the artificial boundary parameter, in this embodiment, the value of α is 0.5, G is the site soil shear modulus, R is the distance from the center of the site soil model to the artificial boundary node, and A is the control area of ​​a single node;

[0082] c. Connect the site soil model with the free-field soil columns on both sides through parallel viscous dampers and spring units. The damping coefficient of the damper and the spring stiffness coefficient are calculated in the same way as above.

[0083] Step 2: Add the superstructure group nodes and the material information of the superstructure (including the elastic modulus of the superstructure material, etc.), and set the contact surface between the superstructure and the site soil;

[0084] In this example, the superstructure is simulated by a bending-shear coupling multi-degree-of-freedom system, and the superstructure model consists of a rigidly connected bending beam and a shear beam. The bending beam is simulated by the elasticBeamColumn unit in OpenSees, and the shear beam is simulated by the twoNodeLink unit in OpenSees. The bending beam and the shear beam are connected by equivalent degrees of freedom to ensure that the bending beam and the shear beam move together. The superstructure and the site soil are connected by equivalent degrees of freedom to ensure that the site soil and the superstructure move together. The bending beam stiffness EI and the shear beam stiffness GA are calculated by the following formulas:

[0085]

[0086]

[0087] Among them, α0 controls the bending-shear stiffness ratio of the structure, and the eigenvalue parameter γ i It can be determined by the following formula:

[0088]

[0089] In this example, the α0 value is related to γ i They are 2.5 and 1.95 respectively.

[0090] In this example, a densely distributed group of structures is selected as the research object. Each group of buildings consists of 9 identical buildings, with a fixed distance between buildings of d = 20m, a building width of L = 30m, a building height of H = 87m, a first vibration mode natural vibration period of 1.79s, and a structural mass of m b =783×10 3 kg, the schematic diagram of building complex distribution is as follows Figure 3 shown.

[0091] Step 3: Conduct gravity analysis on the site-urban building complex interaction model;

[0092] Gravity loading is performed on the superstructure-site soil model to obtain the initial stress field distribution of the soil. During the gravity loading stage, the deformation behavior of the soil material is linear elastic. In addition, the displacement of the boundary nodes at both ends of the site soil model is fixed by the sp command in OpenSees to approximately simulate the free site conditions under static load, and the boundary node reaction force is recorded by the recorder command in OpenSees;

[0093] Step 4: Change the deformation behavior of soil material from linear elastic to elastoplastic;

[0094] After the gravity analysis is completed, the initial stress state of the soil is kept unchanged, the displacement information of the soil is cleared, and the displacement constraints of the boundary nodes at both ends of the site soil model are released through the remove sp command in OpenSees. The boundary node reaction force recorded in step 3 is applied to the boundary nodes, and the deformation behavior of the soil material is changed to elastic-plastic through material update processing to obtain the model of the initial stress field of the soil.

[0095] Step 5: Conduct seismic response analysis on the model;

[0096] The initial state of the model adopts the initial stress field of the soil calculated by the above method, and the seismic excitation is applied to the bottom of the model in the form of force.

[0097] Through the above steps, the present invention establishes a refined numerical modeling and calculation method for earthquake response of site-city dynamic interaction. The structure of the site soil numerical model is as follows: Figure 4As shown in Figure 2, the influence of the superstructure group on the site seismic response under nonlinear conditions is analyzed. The transfer function of the urban ground motion relative to the free site motion (excluding the superstructure) is defined as the ratio of the Fourier spectra of the two, as follows: Figure 5 As shown. Figure 5 It can be seen that compared with the linear elastic model, the transfer function calculated by the nonlinear model proposed in the present invention has a more complex distribution in the frequency domain, indicating that the nonlinear deformation behavior of the site soil will increase the complexity of the site-city dynamic interaction. The method proposed in the present invention can be used to evaluate the temporal and spatial distribution laws and characteristics of the seismic field in a complex urban environment under nonlinear conditions, which becomes the basis of the urban resilience assessment framework.

Claims

1. The site-city interaction effect simulation method based on OpenSees is characterized by The simulation method is implemented in the following steps: Step 1: In the OpenSees system, define the node and unit information of the site soil model, define the site soil material parameters and model boundary conditions, and establish the site soil numerical model; The steps for setting the site soil numerical model and boundary conditions are as follows: a. Set a free field soil column at each free field boundary on both sides of the site soil model to simulate the free field boundary, and bind the degrees of freedom of the nodes at the same height on both sides of the soil column to ensure that the soil column can restore the free field response under the action of an earthquake; b. The site soil model is connected to the free-field soil columns on both sides through parallel viscous dampers and springs. The vertical degree of freedom of the bottom node of the site soil model is fixed, and parallel viscous dampers and springs are set in the horizontal direction. The viscous dampers and springs are simulated by zero-length units. The damping coefficient of the viscous damper is calculated using the following formula (1): c=ρV s A(1) The spring stiffness coefficient is calculated using the following formula (2): Where ρ is the bedrock density, V s is the bedrock shear wave velocity, α is the artificial boundary parameter, G is the site soil shear modulus, R is the distance from the site soil model center to the artificial boundary node, and A is the control area of ​​a single node; Step 2: Add the superstructure group nodes and the material information of the superstructure, set the contact surface between the superstructure and the site soil, and obtain the superstructure-site soil model; The simulation method of the superstructure is as follows: The superstructure is simulated by a bending-shear coupling multi-degree-of-freedom system. The superstructure is connected to the site soil through equivalent degrees of freedom to ensure that the site soil and the superstructure move together. The superstructure is composed of rigidly connected bending beams and shear beams. The bending beams and shear beams are connected through equivalent degrees of freedom. The bending beam stiffness EI0 and the shear beam stiffness GA0 are calculated by the following formula: Where ω1 is the first-order vibration mode natural circular frequency of the superstructure, ρ b is the structural mass per unit height, H is the structural height, α0 is the bending-shear stiffness ratio of the structure, and γ is the eigenvalue parameter; Step 3: Gravity analysis of the site-urban building complex interaction model: Gravity loading is performed on the superstructure-site soil model to obtain the initial stress field distribution of the soil. During the gravity loading stage, the deformation behavior of the soil material is linear elastic. At the same time, the displacement of the boundary nodes at both ends of the site soil model is fixed, and the boundary node reaction force is recorded; Step 4: Change the deformation behavior of soil material from linear elastic to elastoplastic: After the gravity analysis is completed, the initial stress state of the soil is kept unchanged, the displacement information of the soil is cleared, the displacement constraints of the boundary nodes at both ends of the site soil model are released, and the boundary node reaction force recorded in step 3 is applied to the boundary nodes. The deformation behavior of the soil material is changed to elastic-plastic through material update processing, and the model of the initial stress field of the soil is obtained; Step 5: Apply seismic excitation to the model of the soil initial stress field and conduct seismic response analysis to complete the simulation of the site-city interaction effect.

2. The method for simulating site-city interaction effects based on OpenSees according to claim 1, characterized in that The maximum height of the mesh size of the site soil model in step 1 is determined by the following formula: Where V s represents the shear wave velocity of the softest soil layer, f max Indicates the maximum frequency of the input ground motion.

3. The method for simulating site-city interaction effects based on OpenSees according to claim 1, characterized in that In step 1, the site soil is simulated using the two-dimensional FourNodeQuad unit in OpenSees, the unit thickness is set to 1m, and the constitutive relationship adopts the multi-yield surface elastoplastic constitutive model, that is, the PressureIndependMultiYield material in OpenSees.

4. The method for simulating site-city interaction effects based on OpenSees according to claim 1, characterized in that In step 1, the artificial boundary parameter α in formula (2) is set to 0.

5.

5. The method for simulating site-city interaction effects based on OpenSees according to claim 1, characterized in that In step a, the thickness of the free-field soil column unit is set to 1000 times the thickness of the site soil model unit.

6. The method for simulating site-city interaction effects based on OpenSees according to claim 1, characterized in that The value of α0 in formula (3) of step 2 ranges from 0 to 20.

7. The method for simulating site-city interaction effects based on OpenSees according to claim 6, characterized in that For frame shear wall and frame core tube structures, the α0 value ranges from 0 to 1.5; for frame structures with lateral force resisting components, the α0 value ranges from 1.5 to 6; for pure frame structures, the α0 value ranges from 6 to 20.

8. The method for simulating site-city interaction effects based on OpenSees according to claim 1, characterized in that The calculation formula of the eigenvalue parameter γ in formula (3) of step 2 is:

9. The method for simulating site-city interaction effects based on OpenSees according to claim 1, characterized in that In step 2, the curved beams in the upper structure are simulated using the elasticBeamColumn unit in OpenSees, and the shear beams are simulated using the twoNodeLink unit in OpenSees.

10. The method for simulating site-city interaction effects based on OpenSees according to claim 1, characterized in that In step 5, the seismic excitation is applied from the bottom in the form of force.

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