CN116167129A - Method for calculating sidewall spacing in fiber reinforced concrete - Google Patents

Method for calculating sidewall spacing in fiber reinforced concrete Download PDF

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CN116167129A
CN116167129A CN202310040318.1A CN202310040318A CN116167129A CN 116167129 A CN116167129 A CN 116167129A CN 202310040318 A CN202310040318 A CN 202310040318A CN 116167129 A CN116167129 A CN 116167129A
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fiber
side wall
fibers
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黄斌
龚明子
黄伟
潘阿馨
苏艺凡
王涛
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Cccc Green Construction Xiamen Technology Co ltd
CCCC First Highway Xiamen Engineering Co Ltd
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Abstract

The invention discloses a method for calculating the distance between side walls in fiber reinforced concrete, which comprises the following steps: s1, generating a three-dimensional steel fiber space distribution model; considering the FRC matrix as an ideal state, wherein the material properties of the FRC matrix are uniformly distributed and have no influence of particle bubbles; setting a boundary of a simulated concrete matrix, randomly generating fibers by using a Monte Carlo method, randomly putting the fibers into a cube boundary space, wherein N put fibers are all positioned in the cube boundary and are mutually disjoint; s2, building a side wall effect model; inserting a plane parallel to the single side face of the cube into the model based on the fiber space distribution model established in the step S1 to serve as a sampling face; step S3, drawing P s (x) -x relationship; s4, analyzing the influence distance of the side wall effect; dividing different influencing distances, with calculation stepsThe method has the advantages of simplicity, rapidness, remarkable improvement of efficiency of calculating the influence area of the side wall effect, higher accuracy, reality fitting and the like.

Description

Method for calculating sidewall spacing in fiber reinforced concrete
Technical Field
The invention belongs to the technical field of fiber reinforced concrete, and particularly relates to a method for calculating a boundary wall distance in fiber reinforced concrete.
Background
Fiber reinforced concrete (Fiber Reinforced Concrete, FRC for short) is a generic term for a novel cement-based composite material composed of cement paste, mortar or concrete as a base material, and discontinuous short fibers or continuous long fibers as a reinforcing material, which are uniformly blended in concrete. Compared with common concrete, FRC is doped with fiber in a concrete matrix, and the bridging effect of the fiber compensates the inherent defects of the common concrete: low tensile strength, poor toughness, etc. With excellent physical and mechanical properties, FRC has been successfully applied to numerous practical projects such as bridge deck pavement, pier reinforcement, curtain wall, etc.
In recent years, as FRC is applied more widely, a large number of scholars pay more attention to research on the influence of FRC on its performance. However, conventional mechanical tests have the disadvantages of high cost, long cycle time and narrow applicability. For rapidly and accurately analyzing the mechanical properties of the composite material, the micro-mechanical analysis of the composite material based on numerical simulation is an important direction for carrying out efficient analysis and structural design on the mechanical properties of FRC.
In finite element modeling, the more the number of models and the closer to the actual structure, the more accurate the analysis result. In actual pouring, steel fibers are randomly distributed in the FRC matrix, the number is huge and the steel fibers are mutually disjoint, and the distribution of the steel fibers in the matrix is more in the middle and less in the two ends due to the influence of the template. In order to be able to truly simulate the influence of the side wall effect in the FRC, a finite element model more conforming to reality is built, and therefore the side wall effect model in the FRC needs to be studied.
The defects of the existing main research on the concrete side wall effect are as follows: 1) Cutting test analysis: cutting the test piece at different positions according to the literature 'study on mechanical properties of flow-induced fiber orientation UHPC', wherein the fiber orientation is not limited by the side wall of a die when the test piece is cut from the inside of a matrix; cutting from the test piece and the mold sidewall area, the orientation of which is limited by the mold sidewall; the research on the side wall effect of the steel fiber is mainly limited to the traditional cutting test, and the side wall effect of the steel fiber is known according to the image analysis technology after cutting. Because the cutting test is a breakage test, the consumable cost is high, the required time is long, and the method is only suitable for individual tests and cannot obtain a wide conclusion.
2) Aggregate side wall effect simulation: in the literature 'computer simulation of two-dimensional aggregate distribution boundary effect', aggregates are generated by a random number generation method and distributed on a rectangular concrete section, and the influence of the boundary wall effect on the equal volume aggregate grading and the Fuller aggregate grading is studied; the research on the concrete side wall effect mainly focuses on the side wall effect after the aggregate is randomly put in, but in the stereoscopic vision, the aggregate and the steel fiber show larger differences in appearance shape and mechanical property, and the algorithm is limited to two dimensions, so that the analysis error of the side wall effect exists.
Disclosure of Invention
The invention aims to provide a method for calculating the sidewall spacing in fiber reinforced concrete, which has simple and convenient formula calculation and reduces a large number of function simulation processes, and solves the problems that the conventional cutting test is a damage test, the individual test is limited and has no universality, and the aggregate and the steel fiber show larger differences in appearance shape and mechanical property, so that the sidewall effect analysis error exists.
Therefore, the technical scheme adopted by the invention is that the method for calculating the sidewall spacing in the fiber reinforced concrete comprises the following steps:
s1, generating a three-dimensional steel fiber space distribution model; considering the FRC matrix as an ideal state, wherein the material properties of the FRC matrix are uniformly distributed and have no influence of particle bubbles; setting the cubic boundary of the simulated concrete matrix, randomly generating fibers by using a Monte Carlo method, and randomly generating the fibersPutting into the boundary space of the cube, putting N fibers which are all positioned in the boundary of the cube and are not intersected with each other,
Figure BDA0004050616170000031
wherein: l (L) f 、d f 、V f V represents the length of the fiber, the diameter of the fiber, the volume doping amount of the fiber and the volume of the set cube respectively;
s2, building a side wall effect model; inserting a plane parallel to the single side face of the cube into the model based on the fiber space distribution model established in the step S1 to serve as a sampling face;
step S3, drawing P s (x) -x relationship; calculating the sum of all the cross-sectional areas of the fibers intersecting the sampling surface in the model, wherein the fiber volume fraction at a point in three-dimensional space can be represented by the area fraction of the surface intersecting the fibers on the sampling surface,
Figure BDA0004050616170000032
wherein: x is the distance between the sampling surface and the side surface of the cube; s is S f (x) The sum of the intercepted areas of all the fibers intersected with the sampling surface; s (x) is the area of the sampling surface; p (P) s (x) The area fraction of the steel fiber on the sampling surface; drawing P by taking the distance x between the sampling surface and the side edge as an abscissa and the area fraction of the steel fiber on the sampling surface as an ordinate s (x) -x, obtaining a change rule of the fiber volume fraction along with the position in the model;
s4, analyzing the influence distance of the side wall effect; the different influencing distances are divided, and the steel fibers are divided into a central area which is not influenced by the side wall effect, a surface area which is influenced by the side wall effect at one place, edge areas which are influenced by the side wall effect at two places and corner areas which are influenced by the side wall effect at three places, so that the influence degree of the side wall effect on the steel fibers in each area is analyzed.
As a priority of the above scheme, in the step S1, MATLAB is adopted to generate random numbers uniformly distributed in the interval by using the function rand, so that the requirement of random sampling can be satisfied, and the operation is simple.
Further preferably, in the step S1, the single fiber is generated by randomly generating the spatial coordinates P of one of the endpoints 1 (x 1 ，y 1 ，z 1 ) Then randomly generating included angles alpha, beta and gamma representing the X-axis, the Y-axis and the Z-axis of the fiber and three Cartesian coordinates, and taking the value range of [0,2 pi ]]The position value of the single fiber in the space is obtained, the operation is reasonable and simple, the distribution of the fiber in the space is controlled by six degrees of freedom, and therefore six values are required to be automatically generated.
Further preferably, in the step S1, the length l of the fiber is based on f Diameter d f And alpha, beta and gamma, and the other end point P of the fiber is obtained 2 Space coordinates (x) 2 ，y 2 ，z 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Judging whether the position value of the single fiber in the space is within a set cube boundary, and if the position value exceeds the boundary, regenerating the fiber to avoid the interference of the fiber positioned outside the cube boundary with the analysis result of the side wall effect.
Further preferably, in the step S1, it is sequentially determined whether the newly generated single fiber located in the boundary of the set cube intersects with other existing fibers, whether the minimum distance between the two line segments is larger than the diameter of the fiber is determined, if so, the fiber needs to be regenerated, so as to avoid the area fraction of the steel fiber on the intersecting sampling surface of the fiber and interfere with the analysis result of the side wall effect.
Further preferably, in the steps S1 to S3, when analyzing the sidewall effect, the average result of 1000 three-dimensional steel fiber space distribution models generated by each parameter is researched, so that the change rule of the fiber volume fraction is ensured to be a smooth curve, and the accuracy of the fiber volume fraction can be ensured.
The invention has the beneficial effects that:
(1) The Monte Carlo method is used for randomly generating fibers, the fibers are randomly thrown into a cube boundary space, N thrown fibers are all located in the cube boundary and are mutually disjoint, a real FRC matrix is fully simulated, the method is suitable for simulating the influence of a side wall effect on steel fibers in the FRC matrix, a plane parallel to a single side face of the cube is inserted to serve as a sampling face, the fiber area fraction is obtained by the ratio of the cross-sectional area of the steel fibers on the sampling face to the area of the sampling face, then a relation curve of the fiber area fraction and the distance edge length is drawn, the influence of the side wall effect on the steel fibers on the sampling face is obtained, the calculation steps are simple and quick, and the efficiency of calculating the influence area of the side wall effect can be remarkably improved.
(2) Compared with the computer simulation limited by two-dimensional aggregate distribution boundary effect, the method has the advantages that the universality is low, the established three-dimensional fiber space distribution cube model is wide in application range, different types of fiber reinforced concrete matrixes can be simulated according to reality, the universality is strong, the influence of the side wall effect of steel fibers in the three-dimensional space is more in line with the structural design of actual engineering, the simulation experiment accuracy of the side wall effect is higher, and the reality is attached.
(3) Drawing P by taking the distance x between the sampling surface and the side edge as an abscissa and the area fraction of the steel fiber on the sampling surface as an ordinate s (x) And (3) obtaining a relation curve of x, namely obtaining a change rule of the fiber volume fraction in the model along with the position, fully knowing the internal condition of the fiber reinforced concrete matrix, dividing different influence intervals into the influence of no side wall, one side wall effect, two side wall effects and three side wall effects, indicating the influence degree of the side wall effect on different areas of the fiber reinforced concrete matrix, and accurately knowing the influence of the side wall effect on the fiber reinforced concrete matrix from multiple directions and multiple angles, wherein the division is reasonable.
In conclusion, the method has the advantages of simple and rapid calculation steps, remarkably improved efficiency of calculating the influence area of the side wall effect, higher accuracy, reality fitting and the like.
Drawings
FIG. 1 is a flow chart of the steps of the present invention.
Fig. 2 is a flow chart of fiber random generation.
Fig. 3 is a schematic representation of the fiber structure produced in an ideal FRC matrix.
Fig. 4 is a schematic diagram of a sample plane intercepting fiber process.
Fig. 5 is a schematic cross-sectional view of a sampling plane intersecting a fiber.
FIG. 6 is P s (x) -x.
Fig. 7 is a schematic view of the surface area of a fiber reinforced concrete matrix affected by one side wall effect, the edge area affected by two side wall effects, and the corner area affected by three side wall effects.
FIG. 8 is a schematic illustration of a central region of a fiber reinforced concrete matrix unaffected by a sidewall.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
referring to fig. 1 to 8, a method for calculating the distance between the side walls in the fiber reinforced concrete comprises the following specific implementation steps:
s1, generating a three-dimensional steel fiber space distribution model; the fiber reinforced concrete matrix is regarded as ideal, and the material properties are uniformly distributed and have no influence of particle bubbles.
Setting a cube boundary of a fiber reinforced concrete matrix, randomly generating fibers by using a Monte Carlo method, and randomly throwing the fibers into a cube boundary space, wherein N thrown fibers are all positioned in the cube boundary and are mutually disjoint.
Figure BDA0004050616170000061
/>
Wherein: l (L) f 、d f 、V f V represents the length of the fiber, the diameter of the fiber, the volume of the fiber, and the volume of the set cube, respectively.
For example, when the test piece is a cube of 50X 50mm in size, the length l of the steel fiber f =13 mm, diameter d f =0.2 mm, steel fiber volume incorporation was 2%.
The number N of the fibers is as follows:
Figure BDA0004050616170000062
in step S1, MATLAB is adopted to generate random numbers uniformly distributed in the interval by using a function rand, so that the requirement of random sampling can be met.
In step S1, the single fiber is generated by randomly generating the spatial coordinates P of one of the endpoints 1 (x 1 ，y 1 ，z 1 ) Then randomly generating included angles alpha, beta and gamma representing the X-axis, the Y-axis and the Z-axis of the fiber and three Cartesian coordinates, and taking the value range of [0,2 pi ]]Thereby obtaining the position value of the single fiber in the space.
In step S1, based on the length l of the fiber f Diameter d f And alpha, beta and gamma, and the other end point P of the fiber is obtained 2 Space coordinates (x) 2 ，y 2 ，z 2 ) The method comprises the steps of carrying out a first treatment on the surface of the And judging whether the position value of the single fiber in the space is within the set cubic boundary, and if the position value exceeds the boundary, regenerating the fiber.
In step S1, it is sequentially determined whether the newly generated single fiber located in the boundary of the set cube intersects with other existing fibers, whether the minimum distance between the two line segments is larger than the diameter of the fiber is determined, and if so, the fiber needs to be regenerated.
Judging whether the second fiber input later is intersected with the first fiber before, and judging whether the minimum distance between the two line segments is larger than the diameter of the fiber or not. The method for calculating the minimum distance between the two line segments is as follows:
1) Line segment l which will represent two fibres in space 1 、l 2 Record l 1 Is P at two ends 1 、P 2 ；l 2 Is Q of 1 、Q 2 The method comprises the steps of carrying out a first treatment on the surface of the L is then 1 、l 2 Available vector
Figure BDA0004050616170000071
The expression is shown in the following formula.
Figure BDA0004050616170000072
Figure BDA0004050616170000073
2) Any point on the straight line where the two line segments lie is shown as follows.
Figure BDA0004050616170000074
Figure BDA0004050616170000075
Wherein lambda is 1 、λ 2 Then each represents an arbitrary point on the line. The problem of solving the shortest distance between two straight lines can be equivalent to an optimization problem under boundary conditions, as shown in the following equation.
Figure BDA0004050616170000081
3) Solving equation 5, the minimum condition can be seen:
Figure BDA0004050616170000082
the expansion of the equation simplifies the system of equations that can be obtained, as shown in the following equation.
Figure BDA0004050616170000083
/>
Figure BDA0004050616170000084
4) Solving the equation set to obtain lambda 1 、λ 2 In the case of a value of λ 1 、λ 2 Is l 1 、l 2 Analyzing whether the drop foot is positioned on the line segment l 1 、l 2 Further, the calculation of the minimum distance is classified into 3 cases according to the above:
case a: when lambda is 1 ∈[0,1]And lambda is 2 ∈[0,1]It is indicated that both feet are located above the respective line segment, and that the minimum distance between the two straight lines is equal to the length of the common vertical line.
Case b: when lambda is 1 ∈[0,1]And is also provided with
Figure BDA0004050616170000085
Or->
Figure BDA0004050616170000086
And lambda is 2 ∈[0,1]It is illustrated that only one drop foot is located on the line segment and the other drop foot is located on the extension of the line segment. Let the drop foot lie on the line segment be l 1 The line segment of the drop foot on the extension line is l 2 At this time the minimum distance is equal to l 2 Upper end point closer to the foot drop to l 1 Distance of foot drop.
Case c: when (when)
Figure BDA0004050616170000087
And->
Figure BDA0004050616170000088
It is stated that both the drop feet are located on the extension line of the line segment, and the minimum distance is equal to the distance between the endpoints of the two line segments near the drop feet.
After the minimum distance between the fibers is found, the distance is compared with the fiber diameter, and if the distance is smaller than the fiber diameter, the intersection between the fibers is indicated, and the fibers need to be discarded, otherwise, the two fibers are indicated not to be intersected.
S2, building a side wall effect model; based on the fiber space distribution model established in the step S1, a plane parallel to the single side face of the cube is inserted into the model as a sampling surface.
Step S3, drawing P s (x) -x relationship; the sum of all fiber cross-sectional areas intersecting the sampling plane in the model is calculated, and the fiber volume fraction at a point in three-dimensional space can be represented by the area fraction of the intersecting plane with the fibers on the sampling plane.
Figure BDA0004050616170000091
Wherein: x is the distance between the sampling surface and the side surface of the cube; s is S f (x) The sum of the intercepted areas of all the fibers intersected with the sampling surface; s (x) is the area of the sampling surface; p (P) s (x) Is the area fraction of steel fibers on the sampling surface.
Drawing P by taking the distance x between the sampling surface and the side edge as an abscissa and the area fraction of the steel fiber on the sampling surface as an ordinate s (x) -x, obtaining a change rule of the fiber volume fraction along with the position in the model;
in the step S1-S3, when the side wall effect is analyzed, 1000 three-dimensional steel fiber space distribution models are generated for each parameter, and the average result is researched, so that the change rule of the fiber volume fraction is ensured to be a smooth curve.
As the number of models increases, the fiber volume fraction exhibits a certain law of variation. When the number of the models is equal to 1000, the change rule of the volume fraction presents a smooth curve, so that 1000 model averaging results are generated for each parameter in the analysis of the side wall effect for research.
S4, analyzing the influence distance of the side wall effect; the different influencing distances are divided, and the steel fibers are divided into a central area which is not influenced by the side wall effect, a surface area which is influenced by the side wall effect at one place, edge areas which are influenced by the side wall effect at two places and corner areas which are influenced by the side wall effect at three places, so that the influence degree of the side wall effect on the steel fibers in each area is analyzed.
As shown in fig. 7 and 8, the numbers on the cuboid indicate the extent of the influence of the side wall effect on the area, such as the cube with the number 3 at the corner, and indicate that the side wall effect with three-sided boundaries affects the fiber distribution in the area, and fig. 7 shows a schematic diagram of the surface area affected by one side wall effect, the edge area affected by two side wall effects, and the corner area affected by three side wall effects.
Fig. 8 shows a schematic view of a central area unaffected by the side wall, numbered 0 at the core, where the steel fibers are not affected by the side wall effect, and are approximately evenly distributed.

Claims (6)

1. The method for calculating the sidewall spacing in the fiber reinforced concrete is characterized by comprising the following steps of:
s1, generating a three-dimensional steel fiber space distribution model; the fiber reinforced concrete matrix is regarded as an ideal state, and the material properties of the fiber reinforced concrete matrix are uniformly distributed and have no influence of particle bubbles; setting a cube boundary of a fiber reinforced concrete matrix, randomly generating coordinates of fibers by using a Monte Carlo method, randomly throwing the coordinates into a cube boundary space, wherein N thrown fibers are all positioned in the cube boundary and are mutually disjoint,
Figure FDA0004050616160000011
wherein: l (L) f 、d f 、V f V represents the length of the fiber, the diameter of the fiber, the volume doping amount of the fiber and the volume of the set cube respectively;
s2, building a side wall effect model; inserting a plane parallel to the single side face of the cube into the model based on the fiber space distribution model established in the step S1 to serve as a sampling face;
step S3, drawing P s (x) -x relationship; calculating the sum of all the cross-sectional areas of the fibers intersecting the sampling surface in the model, wherein the fiber volume fraction at a point in three-dimensional space can be represented by the area fraction of the surface intersecting the fibers on the sampling surface,
Figure FDA0004050616160000012
wherein: x is the distance between the sampling surface and the side surface of the cube; s is S f (x) The sum of the intercepted areas of all the fibers intersected with the sampling surface; s (x) is the area of the sampling surface; p (P) s (x) The area fraction of the steel fiber on the sampling surface; drawing P by taking the distance x between the sampling surface and the side edge as an abscissa and the area fraction of the steel fiber on the sampling surface as an ordinate s (x) -x, obtaining a change rule of the fiber volume fraction along with the position in the model;
s4, analyzing the influence distance of the side wall effect; the different influencing distances are divided, and the steel fibers are divided into a central area which is not influenced by the side wall effect, a surface area which is influenced by the side wall effect at one place, edge areas which are influenced by the side wall effect at two places and corner areas which are influenced by the side wall effect at three places, so that the influence degree of the side wall effect on the steel fibers in each area is analyzed.
2. The method for calculating the sidewall spacing in the fiber reinforced concrete according to claim 1, wherein: in the step S1, MATLAB is adopted to generate random numbers uniformly distributed in the interval by using a function rand, so that the requirement of random sampling can be met.
3. The method for calculating the sidewall spacing in the fiber reinforced concrete according to claim 1, wherein: in the step S1, the single fiber is generated by randomly generating the spatial coordinates P of one endpoint 1 (x 1 ，y 1 ，z 1 ) Then randomly generating included angles alpha, beta and gamma of the fiber and the X axis, the Y axis and the Z axis of the Cartesian coordinate, and taking the value range of [0,2 pi ]]Since α, β, γ are generated by random numbers, their cosine values are also random. Thus, it is possible to directly produce [ -1,1]Is a random number cosα, cosβ, cosγ. Based on the length l of the fiber f Diameter d f With cos alpha, cos beta, cos gamma, the spatial coordinates of the other end point P2 of the fiber are obtained (x 2 ，y 2 ，z 2 ) Thereby obtaining the position value of the single fiber in the space.
4. A method for calculating the sidewall spacing in fiber reinforced concrete according to claim 3, wherein: in the step S1, the length l of the fiber is based f Diameter d f And alpha, beta and gamma, and the other end point P of the fiber is obtained 2 Space coordinates (x) 2 ，y 2 ，z 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Judging whether the position value of single fiber in space is in the boundary of set cube or not, if it is out of boundary, regenerating said fiber。
5. The method for calculating the sidewall spacing in the fiber reinforced concrete according to claim 4, wherein: in the step S1, it is sequentially determined whether the newly generated single fiber located in the boundary of the set cube intersects with other existing fibers, whether the minimum distance between the two line segments is larger than the diameter of the fiber is determined, and if so, the fiber needs to be regenerated.
6. The method for calculating the sidewall spacing in the fiber reinforced concrete according to claim 1, wherein: in the steps S1-S3, when the side wall effect is analyzed, 1000 three-dimensional steel fiber space distribution models are generated for each parameter, and the average result is researched, so that the change rule of the fiber volume fraction is ensured to be a smooth curve.
CN202310040318.1A 2023-01-13 2023-01-13 Method for calculating sidewall spacing in fiber reinforced concrete Pending CN116167129A (en)

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