An engineering algorithm for damage extent of reinforced concrete frame structures based on multiple regression

Abstract

The present application relates to a kind of engineering algorithm of reinforced concrete frame structure continuous collapse damage range based on multiple regression.The present application realizes the establishment of reinforced concrete frame model and the simulation of component failure and fracture in frame continuous collapse by the fiber beam model and component failure criterion developed by MSC.Marc and the introduction of life and death unit algorithm.Based on collapse criterion and multiple linear regression method, the input variable is structural parameter and initial damage parameter, and the engineering algorithm of reinforced concrete frame structure continuous collapse damage range is constructed, with the total area of structure collapse damage as the only output parameter.1) The efficiency of evaluation is low, and it is difficult to ensure the timeliness of the results;2) It is difficult to simulate the large deformation nonlinear behavior of continuous collapse;3) Non-professionals are difficult to operate.The algorithm ensures the simplicity, applicability and reliability of the rapid evaluation of the damage range of frame structure continuous collapse, which is crucial for the rationality evaluation of structural damage.

Description

Technical Field

[0001] This invention belongs to the field of disaster prevention and mitigation in building structures and involves an engineering algorithm based on multiple regression to determine the damage range of continuous collapse of reinforced concrete frame structures. Background Technology

[0002] Progressive collapse refers to the large-scale damage or even collapse of an engineering structure caused by localized damage resulting from unexpected events (such as fires, gas explosions, vehicle collisions, human design and construction errors, environmental corrosion, etc.). Just as reinforced concrete (RC) structures may experience localized collapse after the failure of some components, this localized collapse failure can propagate along different directions within the structural system, causing a chain reaction and ultimately leading to a larger-scale structural collapse. Current methods for assessing progressive collapse are mostly numerical simulations or experimental methods, which suffer from low assessment efficiency and difficulty in ensuring the timeliness of results. Progressive collapse failure of frames with large deformations exhibits strong nonlinear characteristics, making it difficult to simulate the stress behavior of components under ultimate deformation. Existing methods require numerous parameters and involve complex calculations, making them difficult for non-professionals to implement. However, in many emergency scenarios such as military operations and disaster relief, there is often a high demand for computational speed. Therefore, establishing a simple, easy-to-use, and easily masterable engineering algorithm model for assessing the damage range of progressive collapse in reinforced concrete frame structures is a pressing problem that needs to be solved. Summary of the Invention

[0003] Based on the above problems, this study established a model library of typical reinforced concrete frame structures and frame-shear wall structures. Numerical simulation methods were used to simulate the collapse of typical frame structures under various working conditions. An engineering algorithm model for the range of continuous collapse damage was established through multiple linear regression, which simplified the method for assessing structural damage effects and greatly improved computational efficiency while ensuring computational accuracy.

[0004] The objective of this invention is achieved through the following technical solution: an engineering algorithm for determining the damage range of a progressively collapsing reinforced concrete frame structure, comprising the following steps:

[0005] (1) Design and model typical framework structures;

[0006] (2) Determine the damage mechanism and analysis method of progressive collapse of frame structures;

[0007] (3) Perform collapse and damage calculation simulations of typical frame structures;

[0008] (4) Analyze the area of ​​damage spread from the collapsed frame to obtain the collapse judgment criteria and propagation law;

[0009] (5) Based on the continuous collapse damage data and propagation law obtained from the simulation, an engineering algorithm for the continuous collapse damage range of reinforced concrete frame structures is constructed using the multiple regression method. Attached Figure Description

[0010] Figure 1 T-section fiber model;

[0011] Figure 2 Typical initial failure locations of frame structures;

[0012] Figure 3 Algorithm model diagram;

[0013] Figure 4 Flowchart of the collapse area assessment algorithm. Detailed Implementation

[0014] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments:

[0015] 1. Design a typical frame structure. Analyze the layout and structural system scheme of the frame structure, using typical multi-story / high-rise office buildings and broadcasting / communication buildings as examples of common building structures. Based on practical engineering design principles and experience, and in accordance with the national design codes "Code for Design of Concrete Structures" and "Code for Seismic Design of Buildings," design and construct a representative frame structure model. Its plan layout is as follows: 1) The spans in the transverse (x-direction) and longitudinal (y-direction) directions are 8 spans and 4 spans respectively; 2) The ground floor height is 4.5 m, and the heights of other floors are 3.6 m; 3) The seismic fortification category is Class B; 4) The building site category is Class II, and the design group is Group 1; 5) The basic wind pressure is 0.45 kN / m³. 2 The surface roughness is Class C; 6) The dead load on the floor (roof) (including the self-weight of the floor slab) is the unit weight of concrete (taken as 25kN / m³). 3 × floor slab thickness + additional load (taken as 1.25 kN / m) 2 The live load is 2 kN / m. 2 The key design parameters are: 1) seismic fortification intensity of 6 degrees and 8 degrees, corresponding to basic seismic acceleration values ​​of 0.05 g and 0.20 g, respectively; 2) number of floors of 2, 4 and 6; 3) single span of 6 m, 9 m and 12 m. A total of 18 typical frame structures were designed.

[0016] A typical frame structure is modeled. A fiber beam model based on MSC.Marc is used to establish the overall structural model. Considering the constraint effect of compressed concrete, the hysteretic behavior under cyclic loading, and the "tensile stiffening effect" of tensile concrete, the Légeron-Paultre model is selected for the monotonic loading envelope of the concrete constitutive model under compression in this patent. To simulate the crack surface effect caused by concrete crack closure, a linear crack closure function is used in the transition zone between tension and compression to simulate the stiffness recovery process of concrete from cracking to compression. In the tension zone, the Jiang Jianjing model is used to simulate the tensile cracking and softening behavior of concrete to consider the "tensile stiffening effect." The skeleton line loading should reflect the constraint effect and softening behavior; the following model is used:

[0017]

[0018] In the formula, These represent the compressive stress and compressive strain of the compressed concrete, respectively. , , represent the peak stress and peak strain of the compressed concrete, respectively; s, s1, and s2 are the control parameters of the stress-strain curve.

[0019] The steel reinforcement constitutive model, based on the Légeron model, considers the Bauschinger effect and reflects the yielding, hardening, and softening phenomena of steel reinforcement under monotonic loading. The monotonic loading curve of the steel reinforcement consists of three parts: a double straight line segment and a parabolic segment. Taking the tension segment as an example:

[0020]

[0021] In the formula, These represent the stress and strain of the reinforcing steel, respectively. This refers to the elastic modulus of the reinforcing steel. These are the yield strength and yield strain of the reinforcing steel, respectively; parameters This represents the ratio of the initial hardening strain to the yield strain of the steel reinforcement; parameters. This is the ratio of peak strain to yield strain of the reinforcing steel; parameter. This represents the ratio of the ultimate strain to the yield strain of the reinforcing steel; parameters. This represents the ratio of peak stress to yield strength in steel reinforcement. A T-section fiber model was also developed (see attached). Figure 1 The simulation assumes the stress on the floor slab within the effective width range; the connections of beams, columns and walls are considered according to fixed constraint boundary conditions; in order to facilitate the coordination of connections between different components and reduce the degrees of freedom, the beams, columns and walls are divided into consistent elements for element discretization.

[0022] 2. Determine the damage mechanism of progressive collapse in frame structures. The collapse of reinforced concrete frame structures is usually caused by the failure of local components; however, the collapse area varies significantly depending on the initial failure location. Considering the symmetry of the structural layout, typical initial failure locations are set at five scenarios: corner columns, the second-to-last column, the short-side middle column, the long-side middle column, and the internal middle column (see appendix). Figure 2 ).

[0023] 3. Determine the method for progressive collapse damage analysis of frame structures. The method involves simulating local component failure by instantaneously removing vertical components. The process is as follows: 1) Calculate the static equilibrium state of the overall structure under vertical gravity load using a static analysis algorithm; 2) Use the birth and death element technique to instantaneously remove the target component to simulate initial local structural failure, triggering dynamic collapse of the overall structure; 3) Conduct nonlinear dynamic analysis, allowing subsequent component failure and fracture, until the structure reaches failure or a new stable state. For the failure of a single vertical component, finite element numerical simulation analysis is performed for five different working conditions based on the load-bearing area of ​​the initially failing component and the constraint level of the surrounding structure. For the failure of multiple vertical components, the damage effect is usually caused by damage to surrounding vertical components at the room level. First, determine the initial collapse failure location using the method for a single vertical component. Then, with the room containing the column as the center, add adjacent vertical components as initial failure components, and then simulate the collapse failure.

[0024] 4. Analyze the area of ​​damage propagation from frame collapse to obtain collapse criteria. The criteria are based on the US DOD standard and the Chinese "Standard for Design of Building Structures Against Collapse" and simulation verification: Criterion 1 is that when the vertical displacement of the structure exceeds 1 / 5 of the span or the horizontal displacement exceeds 1 / 20 of the story height, the area directly connected to the above-mentioned components can be identified as the area where collapse failure occurs. Criterion 2 is that if the removal of a vertical bearing member of a certain floor causes structural collapse failure, then the floors below the location of the collapse failure are considered to have also experienced progressive collapse failure under the load of the superstructure.

[0025] 5. Analyze the propagation area of ​​frame collapse damage to obtain the propagation law. When a structure experiences progressive collapse, the upper floor slab area directly supported by the initially failed column will collapse first, i.e., vertical collapse failure. Simultaneously, the floor load in this area propagates to the surrounding columns through the lintels, causing these columns to be overloaded. If these columns subsequently fail, the collapse will propagate horizontally to this area, i.e., horizontal collapse failure, and cause further vertical propagation of collapse. Through summarizing and analyzing the laws of collapse examples, it was found that the collapse always propagates from the initially failed member as the center to the direction with fewer surrounding vertical members (where the horizontal constraint stiffness and bearing capacity are low). Therefore, the propagation law is as follows: if the rooms in the initially collapsed area have not all collapsed, the propagation order of the areas with vertical member failure is prioritized; the collapse direction is divided into the primary collapse direction and the secondary collapse direction. The primary collapse failure preferentially propagates along the direction with the fewest columns and walls in both the x-axis and y-axis directions. If the area in the smallest direction has already collapsed, the direction represented by the second smallest value is taken for propagation, and so on. If equal values ​​exist, propagation is prioritized along the shorter side of the structure. If the entire initial failure area collapses, horizontal collapse propagation is considered, and it is assumed that the collapse propagation of the next area only begins after the entire area of ​​the previous area has collapsed. The collapse area is centered on the room directly connected to the initially failed component and spreads sequentially in four directions.

[0026] 6. Based on the progressive collapse damage data and propagation patterns obtained from simulations, an engineering algorithm for determining the damage range of progressive collapse in reinforced concrete frame structures is constructed using multiple regression. The research includes:

[0027] 1) Combine theoretical analysis and simulation results to conduct research on collapse failure engineering algorithm models, construct the functional relationship between the damage location, structural characteristic parameters (span, number of floors, seismic fortification intensity) and the collapse failure area of ​​typical frame structure buildings, and determine the basic model framework of collapse failure effect engineering algorithm;

[0028] 2) Based on the statistical analysis results of the continuous collapse area of ​​a large number of typical structural examples in the early stage, the parameters of the algorithm model are calibrated;

[0029] 3) Analyze the changing patterns of the algorithm model's calculation results when various structural parameters and design indicators change, and compare them with the previous simulation results of the overall structural progressive collapse to confirm that the model conforms to objective laws. The algorithm establishment process is shown in Appendix 3.

[0030] While maintaining the same initial failure location and number of damaged components, the impact of changes in design parameters on the collapse damage area of ​​the structure is considered. Keeping the structural type and initial failure component location the same, a multiple linear regression method is used to establish a functional relationship between the collapse damage area of ​​a single floor and the seismic fortification intensity, number of floors, single span, and the number of floors containing the initial failure component, where β is a parameter.

[0031]

[0032] Where x1 represents the seismic fortification intensity;

[0033] x2 represents the floor number;

[0034] x3 represents the single span;

[0035] x4 represents the layer number where the initial damaged component was located.

[0036] 7. The parameters in the multiple linear regression method are calibrated as follows: each case corresponds to a statistical result of the collapse damage area. Therefore, the statistically obtained collapse damage area is stored in an n-dimensional vector, where n represents the number of cases corresponding to the plane position of the initial failure, the number of cases corresponding to the frame structure under a single initial failure position, and m represents the number of independent variables considered. The n×m matrix is ​​used to solve for the parameter values. After obtaining the functional relationship of the single-story collapse area, it is only necessary to multiply it by the number of floors of the structure to obtain the collapse damage area of ​​the frame structure under different conditions.

[0037] In this algorithm, n is 1 for corner pillars or corner walls, 2 for the second-to-last pillar or internal wall, 3 for middle pillars or internal pillars, 4 for middle pillars on longer sides, and 5 for middle pillars on shorter sides (e.g., x). 11 (Refers to the seismic fortification intensity corresponding to the initial failure at location 1).

[0038]

[0039] 8. An engineering algorithm for constructing the damage range of progressive collapse of reinforced concrete frame structures using multiple regression (see appendix). Figure 4Using seismic fortification intensity, number of stories, single span, number of stories where the initial failure member is located, and the planar location of the initial failure column as input parameters, and the total collapse damage area of ​​the structure as the output parameter, a correspondence between the input and output parameters is established as a theoretical model for assessing the structural collapse damage area. For different initial collapse damage planar locations, the corresponding functional relationships are substituted according to a hierarchical system to obtain the predicted value of the structural collapse damage area, which is then compared with the statistically obtained actual value. Models that meet the accuracy requirements are validated; for models that do not meet the statistical regularity and accuracy requirements, more suitable mathematical expressions and parameter fitting algorithms are selected until the accuracy requirements are met.

Claims

1. An engineering algorithm for determining the damage range of progressive collapse of reinforced concrete frame structures based on multiple regression, characterized in that, Includes the following steps: (1) Design and establish a reinforced concrete frame structure model database, establish an overall structural model based on the fiber beam model, and take the corner column, the second to last column, the short side middle column, the long side middle column and the internal middle column as typical initial failure locations; the structural model database covers frame structure models under multiple different design parameters; (2) Conduct a continuous collapse simulation for the typical initial failure location: Before removing the vertical components, use static analysis to calculate the static equilibrium state of the overall structure under vertical gravity load; use the birth and death element technology to instantly remove the target vertical components and trigger the dynamic collapse of the overall structure; carry out nonlinear dynamic analysis, and delete the subsequent structural components that reach the failure criterion and release their internal forces during the analysis until the structure reaches the failure state or a new stable state; (3) Determine the collapse damage area and count the single-layer collapse damage area based on the response of the continuous collapse simulation, wherein, 1) When the vertical continuous collapse propagates within the initial damage range: when the vertical displacement of the structure exceeds 1 / 5 of the span or the horizontal displacement exceeds 1 / 20 of the floor height, the area directly connected to the above-mentioned components can be determined as the collapse damage area; 2) When the horizontal continuous collapse propagates around the initial damage structure: if the removal of a vertical bearing component of a certain floor causes the structure to collapse, it is considered that the floors below the collapse damage location also experience continuous collapse damage under the load of the upper structure; (4) Analyze the propagation of the collapsed area to obtain the collapse propagation law, which includes the collapse propagation direction and propagation order determined according to the following rules: If the rooms in the initial collapsed area do not all collapse, the propagation order of the vertical component damage area is determined first, and the collapse direction is divided into the main collapse direction and the secondary collapse direction. The number of vertical components is counted along the x-axis and y-axis of the structural plane. The number of vertical components includes the number of column and wall vertical components. The direction with the fewest vertical components is determined as the main collapse direction, and the direction with the second fewest vertical components is determined as the secondary collapse direction; if the number of vertical components is the smallest If the area corresponding to the direction with the fewest vertical components has collapsed, then the next direction is selected in order of increasing number of vertical components for propagation, and so on. If the number of vertical components in different directions is equal, then the propagation is prioritized along the shorter side of the structure. If the entire initial damaged area has collapsed, then the horizontal collapse propagation is considered. The direction from the initial damaged area to the direction with the fewest vertical components is the primary collapse direction, and the direction to the direction with the second fewest vertical components is the secondary collapse direction. The collapse propagation of the next area is only calculated after the entire area of ​​the previous area has collapsed. The collapse spreads outward in four directions from the room directly connected to the initially damaged component as the core. (5) Based on the single-story collapse damage area statistically obtained in step (3), construct a multivariate linear regression function relationship: while keeping the structure type, the plane position of the initial damaged component and the number of the initial damaged component the same, take the single-story collapse damage area as the dependent variable and the seismic fortification intensity, the number of floors, the single span and the number of floors where the initial damaged component is located as the independent variables, and establish the functional relationship between the single-story collapse damage area and each independent variable; (6) The seismic fortification intensity, number of floors, single span, number of floors where the initial failure member is located, and plane position of the initial failure member of the reinforced concrete frame structure to be analyzed are used as input parameters, and the total collapse damage area of ​​the structure is used as output parameter. According to the functional relationship corresponding to the plane position of the initial failure member, the seismic fortification intensity, number of floors, single span, and number of floors where the initial failure member is located are substituted into the functional relationship to obtain the predicted value of the single-floor collapse damage area. The predicted value of the single-floor collapse damage area is multiplied by the number of floors of the structure to obtain the predicted value of the total collapse damage area of ​​the structure.

2. The engineering algorithm according to claim 1, characterized in that, The fiber beam model includes a T-section fiber model, used to simulate the stress on the floor slab within the effective width range; the fiber beam model considers the constraint effect of compressed concrete, the hysteretic behavior under cyclic loading, the tensile stiffening effect of tensile concrete, and the Bauschinger effect of steel reinforcement.

3. The engineering algorithm according to claim 1, characterized in that, The reinforced concrete frame structure model has a plan layout of 8 spans in the horizontal direction and 4 spans in the vertical direction, with a floor height of 4.5 m on the ground floor and 3.6 m on the other floors; the seismic fortification intensity is 6 degrees or 8 degrees, the number of floors is 2, 4 or 6, and the single span is 6 m, 9 m or 12 m.

4. The engineering algorithm according to claim 1, characterized in that, In the case of multiple vertical components failing, the initial collapse location is first determined by the method for single vertical component failure. Then, taking the room where the column is located at the initial collapse location as the center, the adjacent vertical components are added as the initial failure components, and a continuous collapse simulation is performed.

5. The engineering algorithm according to claim 1, characterized in that, When multiple vertical components that have been damaged belong to different initial damage positions, the function relationship to be substituted is determined according to the priority order of corner column, second to last column, long side middle column or short side middle column, and internal column. The internal column is the internal middle column as described in claim 1. The corner column has the highest priority and the internal column has the lowest priority. The long side middle column and the short side middle column are not damaged at the same time.

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