CN115859704A - Engineering algorithm for continuous collapse damage range of reinforced concrete frame structure based on multiple regression - Google Patents
Engineering algorithm for continuous collapse damage range of reinforced concrete frame structure based on multiple regression Download PDFInfo
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Abstract
The invention relates to a multiple regression-based engineering algorithm for a continuous collapse damage range of a reinforced concrete frame structure. The method realizes the establishment of a reinforced concrete frame model and the simulation of the failure and the fracture of the member in the continuous collapse of the frame by a fiber beam model and a member failure criterion developed by MSC. Based on a collapse discrimination criterion and a multiple linear regression method, an engineering algorithm of a continuous collapse damage range of the reinforced concrete frame structure is constructed, wherein input variables of the engineering algorithm are structure parameters and initial damage parameters, and the total structural collapse damage area is used as a unique output parameter. The problems are solved: 1) The evaluation efficiency is low, and the timeliness of the result is difficult to ensure; 2) The nonlinear behavior of continuous collapse large deformation is difficult to simulate; 3) The problem that the non-professional person is difficult to operate by hands. The algorithm ensures the simplicity, applicability and reliability of rapid evaluation of the continuous collapse damage range of the frame structure, and is of great importance to the evaluation of the rationality of the structural damage.
Description
Technical Field
The invention belongs to the field of building structure disaster prevention and reduction, and relates to an engineering algorithm for a reinforced concrete frame structure continuous collapse damage range based on multiple regression.
Background
The continuous collapse refers to the large-scale damage and even collapse of the whole structure caused by the local damage and chain reaction of the engineering structure caused by unexpected events (such as fire, gas explosion, terrorist attack, vehicle impact, human design and construction errors, environmental corrosion and the like). Just as Reinforced Concrete (RC) structures may collapse locally after a failure of a partial structural failure, such a local collapse failure may propagate in different directions of the structural system, causing a chain reaction, ultimately leading to a greater range of structural collapse failures within the structural system. Because most of the existing evaluation methods related to the structure continuous collapse are numerical simulation or test methods, the evaluation efficiency is low, and the timeliness of the result is difficult to ensure; the continuous collapse damage of the large deformation of the frame has strong nonlinear characteristics, and the stress behavior of the member entering the extreme deformation is difficult to simulate; the existing method has the problems of numerous required parameters, complex calculation process and difficult realization of non-professionals. In many emergency scenes such as military affairs and rescue after disasters, the calculation speed is often required to be high, and how to establish an engineering algorithm model which is simple, convenient, easy to operate and easy to master and is used for the continuous collapse and damage range of the reinforced concrete frame structure is a problem to be solved urgently at present.
Disclosure of Invention
Based on the problems, a typical reinforced concrete frame structure and frame shear structure model library is established, the typical frame structure under various working conditions is subjected to collapse simulation by adopting a numerical simulation method, and a structural continuous collapse damage range engineering algorithm model is established by adopting a multiple linear regression method, so that a structural damage effect evaluation method is simplified, the calculation accuracy is ensured, and the calculation efficiency is greatly improved.
The purpose of the invention is realized by the following technical scheme: an engineering algorithm for a continuous collapse and damage range of a reinforced concrete frame structure comprises the following steps of:
(1) Designing and modeling a typical frame structure;
(2) Determining a frame structure continuous collapse damage mechanism and an analysis method;
(3) Carrying out typical frame structure collapse damage calculation simulation;
(4) Analyzing the collapse damage propagation area of the frame to obtain collapse judgment criteria and propagation rules;
(5) And constructing an engineering algorithm of the continuous collapse damage range of the reinforced concrete frame structure by adopting a multiple regression method based on the continuous collapse damage data and the propagation rule obtained by simulation.
Drawings
FIG. 1 is a model T section fiber;
FIG. 2 is an exemplary initial failure position of the frame structure;
FIG. 3 is a schematic diagram of an algorithmic model;
fig. 4 shows a flowchart of a collapse area evaluation algorithm.
Detailed Description
The invention is described in further detail below with reference to the following figures and examples:
1. a typical frame structure is designed. And analyzing the layout of the frame structure and the scheme of the structural system by combining common building structure examples such as typical multi/high-rise office buildings, broadcast communication buildings and the like. According to the actual engineering design principle and experience, a representative frame structure model is designed and built according to the national design standard of concrete structure design and the building earthquake-resistant design standard. The plane layout is designed as follows: 1) The corresponding spans of the transverse direction (x direction) and the longitudinal direction (y direction) are respectively 8 spans and 4 spans;
2) The height of the bottom layer is 4.5m, and the heights of other layers are 3.6m; 3) The earthquake fortification category is class B buildings; 4) The building site category is II, and a first group is designed and grouped; 5) The basic wind pressure is 0.45kN/m 2 The ground roughness is C type; 6) The constant load (including the self-weight of the floor) on the floor is the concrete volume weight (25 kN/m 3 ) X floor thickness + additional load (1.25 kN/m) 2 ) The live load is 2kN/m 2 . The key design parameters are: 1) The seismic fortification intensity is 6 degrees and 8 degrees, and the corresponding basic seismic acceleration values are 0.05g and 0.20g respectively; 2) The number of floors is 2, 4 and 6; 3) The single span spans 6m, 9m and 12m. A total of 18 typical frame structures are designed.
A typical framework structure is modeled. And establishing an integral structure model by adopting a fiber beam model based on MSC. A Legeron-Paultre model is selected according to the constraint effect of compressed concrete, the hysteretic behavior under cyclic reciprocating load and the 'tension rigidization effect' of the tensioned concrete. In order to consider the fracture surface effect brought by simulating the concrete fracture closure, a linear fracture closure function is adopted to simulate the rigidity recovery process of the concrete from the fracture to the compression in a tension and compression transition zone of the concrete. In the tension area, a Jiangtian whale model is adopted to simulate the tension cracking and softening behaviors of concrete so as to consider the tension rigidization effect. The skeleton line loading should reflect the constraint effect and softening behavior, using the following model:
wherein, sigma and epsilon are respectively the compressive stress and the compressive strain of the compressed concrete; sigma c0 、ε c0 Respectively the peak stress and the peak strain of the compressed concrete; s, s 1 、s 2 Is a control parameter of a stress-strain curve.
The steel bar constitutive model considers the Bauschinger effect based on the Leegeron model and reflects the phenomena of yielding, hardening and softening of the steel bar during monotonous loading, a steel bar monotonous loading curve is composed of a double-straight-line segment and a parabolic segment, and the tensioned segment is taken as an example:
wherein, sigma and epsilon are respectively stress and strain of the steel bar; e s Is the modulus of elasticity of the steel bar; f. of y 、ε y ＝f y /E s Respectively the yield strength and yield strain of the steel bar; parameter k 1 The ratio of the strain at the hardening starting point of the reinforcing steel bar to the yield strain; parameter k 2 The ratio of the peak strain to the yield strain of the steel bar; parameter k 3 The ratio of the ultimate strain to the yield strain of the steel bar; parameter k 4 Is the ratio of the peak stress to the yield strength of the steel bar. A fiber model with a T-shaped section (attached figure 1) is developed to simulate the stress of the floor slab within an effective width range; the connection of the beam, the column and the wall is considered according to the fixed constraint boundary condition; in order to coordinate the connection between different members and reduce the degree of freedom in the unit dispersion, the beams, columns and walls are divided by adopting consistent units.
2. And determining the continuous collapse damage mechanism of the frame structure. The collapse damage of the reinforced concrete frame structure is usually caused by partial component failure, however, the initial damage positions are different, and the collapse areas of the structure have larger difference. In consideration of the symmetry of the structural arrangement, typical initial failure positions are set in 5 kinds of conditions of the corner post, the penultimate post, the short-side center post, the long-side center post, and the inner center post (fig. 2).
3. And determining a frame structure continuous collapse damage analysis method. And (3) simulating local component failure by adopting instant dismantling of the vertical component. The process is as follows: 1) Calculating a static equilibrium state of the whole structure under the action of vertical gravity load by adopting a static analysis algorithm; 2) Instantly removing a target component by adopting a living and dead unit technology to simulate the initial local structural damage and trigger the power collapse of the whole structure; 3) Non-linear kinetic analysis was performed and subsequent component failure and breakage were allowed until the structure reached failure or a new steady state was reached. For the condition that a single vertical component is damaged, respectively carrying out finite element numerical simulation analysis on five different working conditions according to the difference of the initial damaged component load bearing area and the constraint level of the peripheral structure; for the condition that a plurality of vertical components are damaged, the damage effect is usually that the peripheral vertical components are damaged by taking a room as a unit, an initial collapse damage position is determined by a method of a single vertical component, then the vertical component adjacent to the column is added as an initial damage component by taking the room where the column is located as the center, and then collapse damage simulation is carried out.
4. And analyzing the frame collapse damage propagation area to obtain a collapse judgment criterion. The judgment criterion refers to American DOD standard and Chinese building structure collapse resistance design standard and simulation verification: the 2 nd criterion is that if the structural collapse damage is caused by dismantling a certain layer of vertical bearing force member, the continuous collapse damage is also considered to occur to the floors below the collapse damage position under the stacking effect of the upper structure.
5. And analyzing the damage propagation area caused by frame collapse to obtain a propagation rule. When the structure collapses continuously, the upper floor slab area directly supported by the initial destruction column collapses firstly, namely, the vertical collapse destruction occurs, meanwhile, the floor load of the area is transmitted to the peripheral columns through the lintel to cause the overloading of the columns, if the subsequent failure occurs to the columns, the collapse can be transmitted to the upper floor slab area along the horizontal direction, namely, the horizontal collapse destruction occurs, and further vertical propagation of the collapse is caused, and through the summary analysis of the law of the collapse embodiment, the collapse is always transmitted to the direction with less peripheral vertical components by taking the initial destruction component as the center (the horizontal constraint rigidity and the bearing capacity are low). The propagation law is therefore: if all rooms in the initial collapse damage area are not collapsed, giving priority to the propagation sequence of the area damaged by the vertical members; the collapse directions are divided into a main collapse direction and a secondary collapse direction. And (3) the main collapse damage is preferentially propagated along the direction with the minimum column and wall number in the x-axis direction and the y-axis direction, and if the minimum direction area is collapsed, the propagation direction represented by the value with the second lowest value is taken, and the propagation directions are analogized in turn. If there is an equality, propagation is preferentially carried out in the short side direction of the structure. And if the initial damage region completely collapses, considering horizontal collapse propagation, and assuming that the collapse transmission condition of the next region is calculated only after the area of the previous region completely collapses during the collapse propagation, wherein the collapse region takes a room directly connected with the initial damage member as a core and sequentially diffuses in four directions.
6. And constructing an engineering algorithm of the continuous collapse damage range of the reinforced concrete frame structure by adopting a multiple regression method based on the continuous collapse damage data and the propagation rule obtained by simulation. The work studied included:
1) Carrying out model research on the collapse damage engineering algorithm by combining theoretical analysis and simulation experiment results, constructing a functional relation among damaged parts, structural characteristic parameters (span, floor number and seismic fortification intensity) and collapse damage areas of a typical building with a frame structure, and determining a basic model frame of the collapse damage effect engineering algorithm;
2) Calibrating parameters of the algorithm model according to the statistical analysis result of the progressive collapse area of a large number of early typical structure examples;
3) And analyzing the change rule of the calculation result of the algorithm model when various structural parameters and design indexes change, comparing and analyzing the change rule with the calculation simulation result of the continuous collapse of the early-stage integral structure, and determining that the model meets the requirement of objective rules. The algorithm establishment process is shown in the attached 3
Under the condition that the plane position and the damage quantity of the initial damage component are kept the same, the influence of the change of the design parameters on the structural collapse damage area is considered respectively. And (2) establishing a functional relation between the collapse failure area of a single floor and the seismic fortification intensity, the floor number, the single span and the number of the layers of the initial failure member by adopting a multivariate linear regression method while keeping the structure type and the plane arrangement position of the initial failure member to be the same, wherein beta is a parameter:
y＝β 0 +β 1 x 1 +β 2 x 2 +β 3 x 3 +β 4 x 4 +β 5 x 1 x 2 +β 6 x 1 x 3 +β 7 x 1 x 4 +β 8 x 2 x 3 +β 9 x 2 x 4 +β 10 x 3 x 4 +β 11 x 1 x 2 x 3 +β 12 x 1 x 2 x 4 +β 13 x 1 x 3 x 4 +β 14 x 2 x 3 x 4 +β 15 x 1 x 2 x 3 x 4
wherein x is 1 Representing seismic fortification intensity;
x 2 the number of the representative floors;
x 3 represents a single span;
x 4 representing the number of layers in which the initial failure member is located.
7. The parameters in the multiple linear regression method are calibrated in the following way: each example corresponds to a collapse damage area statistical result, so that an n-dimensional vector is used for storing and counting the obtained collapse damage area, wherein n represents the number of examples corresponding to the plane position of the initial damage, the number of examples corresponding to the frame structure at a single initial damage position, and m represents the number of considered independent variables to form an n multiplied by m matrix to solve the value of the parameter.
In the algorithm, the value of n in the corner column or the corner wall is 1, the value of the penultimate column or the inner wall is 2, the value of the center pillar or the inner column is 3, the value of the center pillar in the long side is 4, and the value of the center pillar in the short side is 5,m, which represent the seismic fortification intensity, the floor number, the single span and the floor number where the initial destruction component is located (for example, x is 11 The corresponding seismic fortification intensity when initial damage occurs at the 1 position):
8. and (4) constructing an engineering algorithm of the continuous collapse and damage range of the reinforced concrete frame structure by adopting a multiple regression method (shown in the attached figure 4). The earthquake fortification intensity, the floor number, the single span, the number of the initial damage members and the plane position of the initial damage column are used as input parameters, the total structural collapse damage area is used as an output parameter, and the corresponding relation between the input parameters and the output parameters is respectively established as a structural collapse damage area evaluation theoretical model. And substituting the positions of different initial collapse damage planes into corresponding functional relational expressions according to a hierarchy system to obtain a predicted value of the structural collapse damage area, and comparing the predicted value with an actual value obtained through statistics. And confirming the model meeting the precision requirement, and reselecting a more proper mathematical expression and parameter fitting algorithm for the model not meeting the statistical rule and the precision requirement until the precision meets the requirement.
Claims (9)
1. A engineering algorithm for a progressive collapse damage range of a reinforced concrete frame structure based on multiple regression is characterized by comprising the following steps of:
(1) Designing and establishing a typical frame structure model database;
(2) Determining a frame structure continuous collapse damage mechanism and an analysis method;
(3) Carrying out typical frame structure collapse damage calculation simulation;
(4) Analyzing the collapse damage propagation area of the frame to obtain collapse judgment criteria and propagation rules;
(5) And constructing an engineering algorithm of the continuous collapse damage range of the reinforced concrete frame structure by adopting a multiple regression method based on the continuous collapse damage data and the propagation rule obtained by simulation.
2. The engineering algorithm for the progressive collapse and damage range of the reinforced concrete frame structure as claimed in claim 1, wherein the step (1) of designing and establishing the typical frame structure model database is based on a fiber beam model to establish an overall structure model database, and the overall structure model database covers frame structure models under a plurality of different design parameters.
3. The engineering algorithm for the progressive collapse damage range of the reinforced concrete frame structure as claimed in claim 1, wherein typical initial damage positions in the determination of the progressive collapse damage mechanism of the frame structure in the step (2) are corner posts, penultimate posts, short side center posts, long side center posts and inner center posts of the frame structure.
4. The engineering algorithm for determining the progressive collapse damage range of the reinforced concrete frame structure as claimed in claim 1, wherein in the step (2), the component failure is realized by using a life-dead cell algorithm, the structural components meeting the damage criterion are deleted, and the internal force is released, so that the component failure and fracture in the progressive collapse process are accurately simulated, and the accurate simulation of the collapse damage propagation and the internal force redistribution is realized.
5. The engineering algorithm for the progressive collapse and damage range of the reinforced concrete frame structure as claimed in claim 1, wherein in the method for analyzing the progressive collapse of the frame structure in the step (2), the specific analysis flow is as follows:
1) Before the vertical component is dismantled, the static force balance state of the whole structure under the action of vertical load is calculated by adopting a static force analysis algorithm;
2) Instantly removing a target component by adopting a life-death unit technology to simulate the initial local structural damage and triggering the power collapse of the whole structure;
3) Non-linear kinetic analysis was performed until the structure reached destruction or a steady state was reached.
6. The engineering algorithm for the progressive collapse damage range of the reinforced concrete frame structure as claimed in claim 1, wherein the analysis of the frame collapse damage propagation area in the step (4) obtains the collapse criterion and the collapse criterion in the propagation law as follows:
1) During the vertical continuous collapse propagation 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 layer height, the area directly connected with the member can be judged as a collapse and damage area;
2) When the horizontal continuous collapse propagation which initially damages the peripheral structure is carried out: if the vertical bearing force members on a certain floor are dismantled to cause structural collapse damage, the floors below the position where the collapse damage occurs are considered to also have continuous collapse damage under the stacking effect of the upper structure.
7. The engineering algorithm for the continuous collapse damage range of the reinforced concrete frame structure as claimed in claim 1, wherein the analysis of the frame collapse damage propagation area in the step (4) obtains the collapse discrimination criteria and the collapse propagation rules in the propagation rules as follows:
1) If all rooms in the initially collapsed and damaged area are not collapsed, the propagation sequence of the areas with damaged vertical members is considered preferentially, and the propagation sequence is as follows: the direction with the least number of vertical components is the main collapsing direction, and the direction with the second least to last is the secondary collapsing direction;
2) If the initial damage area is totally collapsed, horizontal collapse propagation is considered, and the propagation sequence is as follows: the direction pointing from the initial failure region to the direction in which the number of vertical members is the smallest is the primary collapse direction, and the direction from the last to the next smallest is the secondary collapse direction.
8. The engineering algorithm for the continuous collapse and damage range of the reinforced concrete frame structure as claimed in claim 1, wherein in the engineering algorithm for the continuous collapse and damage range of the reinforced concrete frame structure in the step (5), each coefficient is solved by converting a linear equation set into a matrix operation form in order to calibrate undetermined coefficients in the equation set; storing the independent variable obtained by statistics by using an n multiplied by m matrix, wherein n is the number of the arithmetic examples corresponding to the plane position where the initial damage is located; m represents the number of the considered independent variables, and the coefficient vector is solved through a transposition matrix and an inverse matrix.
9. The engineering algorithm for the progressive collapse damage range of the reinforced concrete frame structure as claimed in claim 1, wherein in the engineering algorithm for the progressive collapse damage range of the reinforced concrete frame structure in the step (5), when the damaged component belongs to components at different initial damage positions, in order to effectively identify the formula to be called, a hierarchy is established for different initial damage positions of the vertical component: corner post > penultimate root post > long side center post or short side center post > interior post, where corner post priority is highest, interior post priority is lowest, and the long side center post and short side center post are unlikely to fail simultaneously.
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| CN117454698A (en) * | 2023-10-27 | 2024-01-26 | 华中科技大学 | Numerical simulation method for fiber drawing performance in concrete |
| CN117454698B (en) * | 2023-10-27 | 2024-05-07 | 华中科技大学 | Numerical simulation method for fiber drawing performance in concrete |
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