CN114758094A - Method for efficiently constructing three-dimensional random aggregate concrete mesoscopic model - Google Patents
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Abstract
The invention provides a method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model, which comprises the following steps of: setting parameters such as concrete size, aggregate volume fraction, aggregate particle size interval, interface transition zone thickness and the like; determining aggregate gradation by adopting a fullerene gradation formula; randomly determining the average grain diameter and the number of vertexes of an aggregate by adopting an aggregate random generation function; randomly determining the vertex coordinates of each aggregate within a predetermined range of the average particle size of the aggregates; calculating the total volume of the currently generated aggregate, and constructing the irregular polyhedral aggregate by adopting a Delaunay triangulation method and a graph envelope method when the total volume of the currently generated aggregate meets the aggregate volume fraction; constructing an interface transition region by adopting a Delaunay triangulation method and a graph envelope method; and sequencing the aggregates according to the volume and randomly putting the aggregates into a concrete area. The construction method is simple and efficient, the model feeding efficiency is high, the space randomness of the aggregate is high, the universality is strong, and the method can be suitable for various working conditions in the aspect of concrete durability.
Description
Technical Field
The invention relates to the technical field of concrete mesoscopic model construction, in particular to a method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model.
Background
The experimental study of some concrete often cannot analyze and study the structural components of the microscopic level due to the limitation of factors such as fields, equipment and environment, so that the numerical study of the microscopic model becomes a powerful research means. The construction of the concrete mesoscopic model is the basis for numerical research on concrete. On the microscopic scale, concrete can be regarded as a three-phase composite material consisting of coarse aggregate, mortar and an Interface Transition Zone (ITZ) of mortar-aggregate, and the characteristics of mechanical property, durability and the like of the concrete are related to the microscopic scale characteristics of aggregate form, aggregate gradation, aggregate volume fraction, ITZ thickness and the like. The establishment of concrete mesoscopic models which are closer to the real aggregate form of concrete and meet the aggregate grading requirements of experimental research is an important hot topic nowadays.
At present, the construction methods of concrete mesoscopic models mainly comprise two types:
1) and identifying and processing the image by a scanning imaging method, distinguishing the cement matrix from the aggregate, and establishing a model. For example, chinese patent application No. 201810833630.5 discloses a mesoscopic structure reconstruction method based on the pixel characteristics of a concrete CT image, which includes automatically identifying and extracting the CT image of concrete, determining the coordinate data of a spatial object by judging the gray values of each component, and matching the unit nodes and the set of the spatial object based on the INP file data of ABAQUS to reconstruct a concrete mesoscopic model. However, the patent has the following problems: the method has low modeling efficiency and is limited by experimental equipment, and for some equipment with low resolution, the components cannot be well separated. For another example, chinese patent application No. 202110242982.5 discloses a method for generating and delivering a concrete three-dimensional aggregate with high efficiency, namely a three-dimensional residual space method, which reconstructs a three-dimensional aggregate by scanning a real concrete slice, separates and fits the aggregate into an ideal shape, extracts parameters thereof, and establishes a three-dimensional concrete mesoscopic model with different sizes and different substitution rates based on the extracted three-dimensional parameters. However, the patent has the following problems: although the efficiency of the method is improved in algorithm, real concrete is still needed, the overall efficiency is low, and in addition, the constructed model is only suitable for concrete of a specific experiment and has no universality.
2) And putting and constructing each component by a computer modeling method. For example, chinese patent application No. 202111136735.3 discloses a three-dimensional mesoscopic model modeling method for full-graded concrete containing random defects, which generates a random aggregate model with four-graded distribution by performing a random shrinkage process in accordance with aggregate grading requirements on each convex polyhedral cell element in a three-dimensional Voronoi graph with a corresponding nucleation point as a center; and the random sphere air hole defect with the required volume content is quickly introduced outside the aggregate distribution area, and finally, a full-graded concrete mesoscopic model containing the random defect is established. However, the patent has the following problems: the algorithm is high in complexity, and after the aggregate polyhedrons are divided, the shrinkage proportion is the same, so that the spatial randomness of the distribution of the aggregates is reduced. For another example, the chinese patent with application number 202011230867.8 discloses a method for constructing a concrete model with a multi-level high volume fraction, which constructs a concrete model with a multi-level high volume fraction by the processes of randomly shaking uniformly distributed seed lattices, rearranging repulsive force, dividing by weighted Voronoi, and reconstructing particles. However, the patent only establishes a two-dimensional concrete mesoscopic model, and does not construct a three-dimensional concrete mesoscopic model.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model.
According to one aspect of the invention, a method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model is provided, which comprises the following steps:
setting concrete areas with preset length, width and height, wherein the maximum particle size of concrete aggregate is Dmax, the minimum particle size of concrete aggregate is Dmin, the volume fraction of the aggregate is Va, and the thickness of an interface transition area is t; determining aggregate gradation by adopting a fullerene gradation formula according to the set aggregate particle size range;
according to the fullerene gradation curve and the volume fraction of the aggregate, randomly determining the average particle size and the number of vertexes of the aggregate by adopting an aggregate random generation function;
randomly determining the vertex coordinates of each aggregate within a predetermined range of the average particle size of the aggregates;
calculating the total volume of the currently generated aggregate according to the vertex coordinates of the aggregate, and constructing the irregular polyhedral aggregate by adopting a Delaunay triangulation method and a graph envelope method when the total volume of the currently generated aggregate meets the volume fraction of the aggregate;
constructing a layer of interface transition region around the aggregate by adopting a Delaunay triangulation method and a graph envelope method according to the thickness of the interface transition region;
and sequencing the aggregates with the interface transition area according to the volume size, and randomly putting the aggregates into the concrete area to obtain the three-dimensional random aggregate concrete mesoscopic model.
Further, the aggregate gradation is determined by adopting a fullerene gradation formula, wherein the fullerene gradation formula is as follows:
wherein P is an aggregate volume accumulation distribution function, Di is the current aggregate average particle size, D is the aggregate average particle size, and Va is the aggregate volume fraction; n is a coefficient of 0.3 to 0.5.
Further, the average particle size and the number of vertexes of an aggregate are randomly determined by adopting an aggregate random generation function, wherein the aggregate random generation function is as follows:
wherein,
alpha is a random number of 0 to 1.
Further, the randomly determining the vertex coordinates of each aggregate within a predetermined range of the average particle size of the aggregate includes:
determining the number b of the top points of each aggregate according to the average particle size of each aggregate;
randomly selecting a point in the aggregate range as a central point of the aggregate, and recording the point as a point O;
at [0.45Di，0.55Di]Randomly determining the distance r between each vertex of the aggregate and the central point within the rangeiComprises the following steps:
ri＝0.5D0+0.05D0(2 alpha-1), wherein alpha is a random number of 0-1;
and (3) in each vertex, recording the current vertex as A and the next vertex as B, and determining the horizontal component and the vertical component of the AOB included angle in the range of [0, 2 pi/B ]:
θ'i＝2π(1+(2α-1)*β/b，
wherein, theta'i、
Is an intermediate variable, θiIs the horizontal component of the included angle of the AOB,
the included angle alpha, beta, gamma and eta are random numbers of 0-1 respectively;
converting the spherical coordinates of the top points of the aggregates into rectangular coordinates, and transforming the coordinates into:
the coordinates (xi, yi, zi) of the aggregate vertex relative to the aggregate center are obtained.
Further, the step of determining the number b of the top points of each aggregate according to the average particle size of each aggregate comprises the following steps:
when the average particle size of the aggregate is less than 5mm, the number of aggregate vertexes is 18-23;
when the average particle size of the aggregate is larger than 5mm and smaller than 9.5mm, the number of aggregate vertexes is 20-26;
when the average particle size of the aggregate is larger than 9.5mm and smaller than 18mm, the number of the aggregate vertexes is 21-28;
when the average particle size of the aggregate is larger than 18mm, the number of the aggregate vertexes is 24-32.
Further, the method for constructing the irregular polyhedral aggregate by adopting the Delaunay triangulation method and the graph envelope method comprises the following steps:
and constructing a triangular cone mesh by traversing each vertex of the aggregate by adopting a Delaunay triangulation method, only reserving the surface on the outermost side of the graph by adopting a graph enveloping method, and deleting the rest triangular cones to obtain the irregular polyhedral aggregate.
Further, after calculating the total volume of the currently generated aggregate according to the vertex coordinates of the aggregate, the method further comprises the following steps:
judging whether the total volume of the currently generated aggregate meets the requirement of the aggregate volume fraction; and if the total volume of the currently generated aggregate does not meet the requirement of the aggregate volume fraction, returning to the step of randomly determining the average particle size and the number of the top points of the aggregate by adopting an aggregate random generation function according to the fullerene grading curve and the aggregate volume fraction.
Further, the method for constructing a layer of interface transition region around the aggregate by adopting a Delaunay triangulation method and a graphical envelope method comprises the following steps:
and (3) expanding the vertex coordinates of the aggregate outwards:
and after the vertex coordinates of the interface transition area are obtained, constructing a triangular cone grid by traversing each vertex of the interface transition area through a Delaunay triangulation method, only reserving the surface on the outermost side of the graph by adopting a graph enveloping method, and deleting the rest triangular cones to obtain the irregular polyhedral aggregate.
Further, the aggregate with the interface transition region is sorted according to the volume size and randomly thrown into the concrete region, and the method comprises the following steps:
traversing all the aggregates, and sequencing the aggregates from large to small according to the volume;
the aggregates are put in sequence from large to small according to the volume, and the coordinates of the center point of the aggregates are as follows:
wherein r ismaxThe maximum distance between the top point and the center of the aggregate; e is the minimum spacing between aggregates; alpha, beta and gamma are random numbers of 0-1 respectively;
and (4) calculating the distance between the aggregate centers, and finishing the aggregate feeding when the distance between the aggregate centers is larger than the sum of the external spherical radii of the two aggregates.
Further, after the calculating the distance between the aggregate centers, the method further comprises: and judging whether the aggregates are overlapped or not according to the distance between the aggregate centers, if the distance between the aggregate centers is smaller than the sum of the external sphere radii of the two aggregates, judging that the aggregates are overlapped, and adding the aggregates again until the aggregate is added.
Compared with the prior art, the invention has the following beneficial effects:
1. the method for efficiently constructing the three-dimensional random aggregate concrete mesoscopic model has the advantages that the method is simple and efficient in process, and the generated concrete model is high in aggregate space randomness and closer to the form and distribution of real concrete aggregates; moreover, the model adopts adjustable fullerene gradation, and can meet the requirements of various gradations and the volume fraction of the aggregate.
2. According to the method for efficiently constructing the three-dimensional random aggregate concrete mesoscopic model, the Delaunay triangulation and graphic envelope method is adopted, and the generated polyhedral aggregate does not need to be judged for the concavity and convexity, so that the model construction process is simpler and more efficient.
3. The method for efficiently constructing the three-dimensional random aggregate concrete mesoscopic model can generate concrete models with different shapes and types of aggregates by changing initial parameters (such as the maximum aggregate particle size, the minimum aggregate particle size, the number of aggregate vertexes and the like), and the model comprises a mortar-aggregate interface transition area, so that the method has strong universality and wide application range, can meet the requirements of most experiments and numerical value researches, and can be suitable for various working conditions in the aspect of concrete durability.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a schematic flow chart of a method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model according to an embodiment of the invention;
FIG. 2 is a graph of an aggregate particle size density distribution function and a resulting aggregate particle size density distribution used in an example of the present invention;
FIG. 3 is a schematic diagram of a Delaunay triangulation method employed in embodiments of the present invention;
FIG. 4 is a schematic diagram of aggregate construction by a graphical envelope method according to an embodiment of the present invention;
FIG. 5 is a schematic illustration of an Interfacial Transition Zone (ITZ) constructed in accordance with an embodiment of the present invention;
FIG. 6 is a schematic diagram of the embodiment of the invention after the aggregate is put;
FIG. 7 is a schematic diagram of a final three-dimensional random aggregate concrete mesoscopic model in an embodiment of the invention.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will aid those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any manner. It should be noted that variations and modifications can be made by persons skilled in the art without departing from the spirit of the invention. All falling within the scope of the present invention.
The embodiment of the invention provides a method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model, and with reference to fig. 1, the method comprises the following steps:
s1, setting a concrete area with the length of L, the width of W and the height of H according to specific experimental requirements, wherein the maximum particle size of concrete aggregate is Dmax, the minimum particle size is Dmin, Va is the volume fraction of the aggregate, and the thickness of an interface transition area is t; determining aggregate gradation by adopting a fullerene gradation formula according to the set aggregate particle size range;
s2, randomly determining the average particle size and the number of vertexes of an aggregate by adopting an aggregate random generation function according to the fullerene grading curve and the aggregate volume fraction Va set in the S1;
s3, randomly determining the vertex coordinates of each aggregate in the preset range of the average particle size of the aggregates generated in S2;
s4, calculating the total volume of the currently generated aggregate according to the vertex coordinates of the aggregate determined in S3, and when the total volume of the currently generated aggregate meets the aggregate volume fraction Va set in S1, constructing an irregular polyhedral aggregate by adopting a Delaunay triangulation method and a graph envelope method, otherwise, repeating the steps S2-S4;
s5, constructing a layer of interface transition area around the aggregate by adopting a Delaunay triangulation method and a graph envelope method according to the thickness t of the interface transition area set in the S1;
and S6, sorting the aggregates constructed by the S4 with the interface transition area generated by the S5 according to the volume size, and randomly putting the aggregates into the concrete area set in the S1 to obtain the three-dimensional random aggregate concrete mesoscopic model.
The method for constructing the three-dimensional random aggregate concrete mesoscopic model in the embodiment of the invention has the advantages that the process is simple and efficient, the space randomness of the generated concrete model aggregates is high, and the shape and distribution of the generated concrete model aggregates are closer to those of real concrete aggregates; moreover, the model adopts adjustable fullerene gradation, and can meet the requirements of various gradations and the volume fraction of the aggregate.
In some preferred embodiments, in step S1, the determining aggregate grading using a fullerene grading formula includes: the formula of the fullerene grading is as follows:
wherein P is an aggregate volume accumulation distribution function, Di is the current aggregate average particle size, D is the aggregate average particle size, and Va is the aggregate volume fraction; n is a coefficient of 0.3-0.5, and can be adjusted according to specific experimental requirements.
In some preferred embodiments, in step S2, randomly determining an average particle diameter and a vertex number of the aggregate by using an aggregate random generation function, includes: the aggregate random generation function is:
wherein,
alpha is a random number of 0 to 1.
In some preferred embodiments, in step S3, randomly determining the vertex coordinates of each aggregate within a predetermined range of the average particle size of the aggregates generated in S2 includes:
s31, determining the number b of the vertex points according to the average particle size of each aggregate;
s32, randomly selecting a point in the aggregate range as a central point of the aggregate, and recording the point as a point O;
s33, in order to avoid aggregate from generating sharp corners which affect the mechanical property, the angle is set to be 0.45Di，0.55Di]Randomly determining the distance r between each vertex of the aggregate and the central point within the rangeiComprises the following steps:
ri＝0.5D0+0.05D0(2 α -1); wherein alpha is a random number of 0-1;
it should be noted that the aggregate range can be adjusted according to experimental requirements, and the aggregate shape tends to be regular as the interval is larger and the probability of sharp corners of the aggregate is larger.
S34, traversing each vertex, recording the current vertex as A, recording the next vertex as B, and determining the horizontal component and the vertical component of the AOB included angle in the range of [0, 2 pi/B ]:
θ'i＝2π(1+(2α-1)*β/b，
wherein, theta'i、
Is an intermediate variable, θiIs the horizontal component of the included angle of the AOB,
the included angle alpha, beta, gamma and eta are random numbers of 0-1 respectively;
s35, converting the spherical coordinates of the top point of the aggregate into rectangular coordinates, and converting the coordinates into:
the coordinates (xi, yi, zi) of the aggregate vertex relative to the aggregate center are obtained.
In some preferred embodiments, in step S31, determining the number of vertexes b according to the average particle diameter of each aggregate includes:
when the average particle size of the aggregate is less than 5mm, the number of aggregate vertexes is 18-23;
when the average particle size of the aggregate is larger than 5mm and smaller than 9.5mm, the number of aggregate vertexes is 20-26;
when the average particle size of the aggregate is larger than 9.5mm and smaller than 18mm, the number of the aggregate vertexes is 21-28;
when the average particle size of the aggregate is larger than 18mm, the number of the aggregate vertexes is 24-32.
In some preferred embodiments, in step S4, the Delaunay triangulation method and the graph envelope method are used to construct irregular polyhedral aggregates, including: and constructing a triangular cone mesh by traversing each vertex of the aggregate by adopting a Delaunay triangulation method, only reserving the surface on the outermost side of the graph by adopting a graph enveloping method, and deleting the rest triangular cones to obtain the irregular polyhedral aggregate. By adopting the Delaunay triangulation and the graph enveloping method, the generated polyhedral aggregate does not need to judge the concavity and convexity, so that the model building process is simpler and more efficient.
In some preferred embodiments, in step S4, after calculating the total volume of the currently generated aggregates according to the aggregate vertex coordinates determined in S3, the method further comprises:
judging whether the total volume of the currently generated aggregate meets the requirement of the aggregate volume fraction; and if the total volume of the currently generated aggregate does not meet the requirement of the aggregate volume fraction, returning to the step S2.
In some preferred embodiments, in step S5, a Delaunay triangulation method and a graphical envelope method are used to construct a layer of interface transition region around the aggregate, including:
expanding the coordinates of the vertex of the aggregate outwards:
after vertex coordinates of the interface transition area are obtained, a Delaunay triangulation method is adopted, a triangular cone mesh is constructed at every four vertexes of the interface transition area, only the surface of the outermost side of the graph is reserved by adopting a graph enveloping method, and the rest triangular cones are deleted to obtain the irregular polyhedral aggregate. By adopting the Delaunay triangulation and the graphical envelope method, the generated interface transition area has the same thickness, namely the interface transition area is equal to the distance between the aggregates everywhere, and the algorithm is simple and efficient.
In some preferred embodiments, in step S6, the aggregates of the S4 construction with the S5 generated interface transition region are sorted by volume size and randomly placed into the concrete region set in S1, including:
s61, traversing all the aggregates, and sorting the aggregates from large to small according to the volume;
s62, sequentially adding aggregates according to the volume from large to small, wherein the coordinates of the center point of the aggregates are as follows:
wherein r ismaxThe maximum distance between the top point and the center of the aggregate; e is the minimum spacing between aggregates; alpha, beta and gamma are random numbers of 0-1 respectively;
and S63, calculating the distance between the aggregate centers, and finishing the aggregate feeding when the distance between the aggregate centers is larger than the sum of the external sphere radii of the two aggregates.
In some preferred embodiments, after calculating the distance between the aggregate centers, further comprising: and judging whether the aggregates are overlapped or not according to the distance between the aggregate centers, if the distance between the aggregate centers is smaller than the sum of the external sphere radii of the two aggregates, judging that the aggregates are overlapped, and adding the aggregates again until the aggregate is added.
According to the invention, a Delaunay triangulation method and a graph enveloping method are adopted, the aggregate library is established firstly, and then the aggregates are put in, so that the space randomness of the aggregates is high, the shape and distribution of the aggregates are close to those of real concrete aggregates, and the construction process is simple and efficient. The method for efficiently constructing the three-dimensional random aggregate concrete mesoscopic model in the embodiment of the invention is explained in more detail by a specific embodiment.
Setting a cube concrete with the length of 50mm, the width of 50mm and the height of 50mm, setting the particle size range of aggregate to be 2.5 mm-10 mm, setting the volume fraction of the aggregate to be 50%, and setting the thickness of an interface transition region to be 60 mu m.
Step two, according to the set aggregate particle size range, determining the optimal aggregate gradation by adopting a fullerene gradation formula, wherein an aggregate gradation curve is shown as a curve in fig. 2, and the adopted fullerene gradation formula is as follows:
wherein P is aggregate volume accumulation distribution function, DiIs the current average particle size of the aggregate, D is a particle size smaller than the current particle size of the aggregate, VaTaking 50 percent of aggregate volume fraction and DmaxThe maximum particle size of the aggregate is 10mm, and n is 0.5.
Step three, randomly determining the average particle diameter D of each aggregate according to the fullerene grading curve and the volume fraction of the aggregatesiThe particle size density of the produced aggregate is shown in fig. 2, and the random generation function of the aggregate is as follows:
wherein,
alpha is a random number of 0 to 1.
Step four, randomly determining the vertex coordinates of the aggregates in the range of 0.45-0.55 times of the average particle size of each aggregate, wherein the specific operation steps are as follows:
4.1) determining the number of vertexes b according to the average particle diameter of each aggregate:
when the average particle size of the aggregate is less than 5mm, the number of aggregate vertexes is 18-23;
when the average particle size of the aggregate is larger than 5mm and smaller than 9.5mm, the number of aggregate vertexes is 20-26;
when the average particle size of the aggregate is larger than 9.5mm and smaller than 18mm, the number of the aggregate vertexes is 21-28;
when the average particle size of the aggregate is larger than 18mm, the number of the aggregate vertexes is 24-32.
It should be noted that the number of vertices b can be arbitrarily adjusted by those skilled in the art according to the specific experimental requirements.
4.2) randomly selecting one point in the aggregate range as the center point of the aggregate, and recording the point as a point O.
4.3) at [0.45Di，0.55Di]Randomly determining the distance r between each vertex and the center of the aggregate within the rangeiComprises the following steps:
ri＝0.5D0+0.05D0(2α-1)，
wherein alpha is a random number of 0-1.
4.4) traversing each vertex, recording the current vertex as A and the next vertex as B, and determining the horizontal component and the vertical component of the AOB included angle in the range of [0, 2 pi/B ]:
θ'i＝2π(1+(2α-1)*β/b，
wherein, theta'i、
Is an intermediate variable, θiIs the horizontal component of the included angle of the AOB,
the included angle alpha, beta, gamma and eta are random numbers of 0-1 respectively.
4.5) converting the spherical coordinates of the top points of the aggregates into rectangular coordinates, and transforming the coordinates into:
obtaining the coordinates (x) of the top point of the aggregate relative to the center of the aggregatei，yi，zi)。
Step five, calculating the total volume of the currently generated aggregate, and if the requirement of the number of the aggregates is not met, repeating the step three and the step four; and if the requirement of the volume fraction of the aggregate is met, the next step is carried out. When the volume fraction requirement of 50% is reached, 957 aggregates are formed.
And step six, constructing a triangular pyramid grid by adopting a Delaunay triangulation method and traversing each vertex of the aggregate, wherein every four vertices are constructed as shown in figure 3. And (3) adopting a pattern enveloping method, reserving the outermost surface, and removing the rest triangular cones to obtain the irregular polyhedral aggregate, as shown in figure 4.
Step seven, expanding the coordinates of the top point of the aggregate outwards according to the thickness of the interface transition area:
after the vertex coordinates of the interface transition region are obtained, the interface transition region is generated by using a Delaunay triangulation method, as shown in fig. 5.
Step eight, randomly putting the aggregate into a concrete area, and specifically comprising the following steps:
8.1) traversing all the aggregates, and sorting the aggregates from large to small according to the volume.
8.2) the aggregates are put in sequence from large to small according to the volume, and the coordinates of the center point of the aggregates are as follows:
wherein r ismaxThe maximum distance between the top point and the center of the aggregate; e is the minimum spacing between the aggregates, and is taken to be 0.5 mm; alpha, beta and gamma are random numbers of 0-1 respectively.
8.3) judging whether the aggregates are overlapped: calculating the distance between the aggregate centers, and finishing the aggregate feeding when the distance between the aggregate centers is larger than the sum of the external spherical radii of the two aggregates; and when the distance between the centers of the aggregates is smaller than the sum of the external spherical radii of the two aggregates, putting the aggregates again until the aggregate is put, wherein the putting is completed as shown in fig. 6.
The three-dimensional irregular aggregate concrete mesoscopic model obtained finally is shown in fig. 7. The model has high space randomness of the aggregate, and is closer to the form and distribution of real concrete aggregate; the model comprises a mortar-aggregate interface transition area, has strong universality and wide application range, can meet the requirements of most experiments and numerical value researches, and is suitable for various working conditions in the aspect of concrete durability.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes and modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The above-described preferred features may be used in any combination without conflict with each other.
Claims (10)
1. A method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model is characterized by comprising the following steps:
setting concrete areas with preset length, width and height, wherein the maximum particle size of concrete aggregate is Dmax, the minimum particle size of concrete aggregate is Dmin, the volume fraction of the aggregate is Va, and the thickness of an interface transition area is t; determining aggregate gradation by adopting a fullerene gradation formula according to a set aggregate particle size range;
according to the fullerene grading curve and the volume fraction of the aggregate, randomly determining the average particle size and the number of vertexes of the aggregate by adopting an aggregate random generation function;
randomly determining the vertex coordinates of each aggregate within a predetermined range of the average particle size of the aggregates;
calculating the total volume of the currently generated aggregate according to the vertex coordinates of the aggregate, and constructing the irregular polyhedral aggregate by adopting a Delaunay triangulation method and a graph envelope method when the total volume of the currently generated aggregate meets the volume fraction of the aggregate;
constructing a layer of interface transition area around the aggregate by adopting a Delaunay triangulation method and a graph envelope method according to the thickness of the interface transition area;
and sequencing the aggregates with the interface transition area according to the volume size, and randomly putting the aggregates into the concrete area to obtain the three-dimensional random aggregate concrete mesoscopic model.
2. The method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model according to claim 1, wherein the aggregate grading is determined by using a fullerene grading formula, wherein the fullerene grading formula is as follows:
wherein P is an aggregate volume accumulation distribution function, Di is the current aggregate average particle size, D is the aggregate average particle size, and Va is the aggregate volume fraction; n is a coefficient of 0.3 to 0.5.
3. The method for efficiently constructing the three-dimensional random aggregate concrete mesoscopic model according to claim 1, wherein the average particle size and the number of vertexes of an aggregate are randomly determined by adopting an aggregate random generation function, wherein the aggregate random generation function is as follows:
wherein,
alpha is a random number of 0 to 1.
4. The method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model according to claim 1, wherein the randomly determining the vertex coordinates of each aggregate within a predetermined range of the average particle size of the aggregate comprises:
determining the number b of the top points of each aggregate according to the average particle size of each aggregate;
randomly selecting a point in the aggregate range as a central point of the aggregate, and recording the point as a point O;
at [0.45Di，0.55Di]Randomly determining the distance r between each vertex of the aggregate and the central point within the rangeiComprises the following steps:
ri＝0.5D0+0.05D0(2 alpha-1), wherein alpha is a random number of 0-1;
and (3) in each vertex, recording the current vertex as A and the next vertex as B, and determining the horizontal component and the vertical component of the AOB included angle in the range of [0, 2 pi/B ]:
θi'＝2π(1+(2α-1)*β/b，
wherein, theta'i、
Is an intermediate variable, θiIs the horizontal component of the included angle of the AOB,
the included angle alpha, beta, gamma and eta are random numbers of 0-1 respectively;
converting the spherical coordinates of the top points of the aggregates into rectangular coordinates, and transforming the coordinates into:
coordinates (xi, yi, zi) of the aggregate vertex relative to the aggregate center are obtained.
5. The method for efficiently constructing the three-dimensional random aggregate concrete mesoscopic model according to claim 4, wherein the step of determining the number b of the vertexes of each aggregate according to the average particle size of each aggregate comprises the following steps:
when the average particle size of the aggregate is less than 5mm, the number of aggregate vertexes is 18-23;
when the average particle size of the aggregate is larger than 5mm and smaller than 9.5mm, the number of aggregate vertexes is 20-26;
when the average particle size of the aggregate is larger than 9.5mm and smaller than 18mm, the number of the aggregate vertexes is 21-28;
when the average particle size of the aggregate is larger than 18mm, the number of the aggregate vertexes is 24-32.
6. The method for efficiently constructing the three-dimensional random aggregate concrete mesoscopic model according to claim 1, wherein the constructing irregular polyhedral aggregates by adopting a Delaunay triangulation method and a graphical envelope method comprises the following steps:
and constructing a triangular cone mesh by traversing each vertex of the aggregate by adopting a Delaunay triangulation method, only reserving the surface on the outermost side of the graph by adopting a graph enveloping method, and deleting the rest triangular cones to obtain the irregular polyhedral aggregate.
7. The method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model according to claim 1, further comprising, after calculating the total volume of the currently generated aggregates according to the vertex coordinates of the aggregates:
judging whether the total volume of the currently generated aggregate meets the requirement of the aggregate volume fraction; and if the total volume of the currently generated aggregate does not meet the requirement of the aggregate volume fraction, returning to the step of randomly determining the average particle size and the number of the top points of the aggregate by adopting an aggregate random generation function according to the fullerene grading curve and the aggregate volume fraction.
8. The method for efficiently constructing the three-dimensional random aggregate concrete mesoscopic model according to claim 1, wherein the step of constructing a layer of interface transition region around the aggregates by adopting a Delaunay triangulation method and a graphical envelope method comprises the following steps:
and (3) expanding the vertex coordinates of the aggregate outwards:
and after the vertex coordinates of the interface transition area are obtained, constructing a triangular cone grid by traversing each vertex of the interface transition area through a Delaunay triangulation method, only reserving the surface on the outermost side of the graph by adopting a graph enveloping method, and deleting the rest triangular cones to obtain the irregular polyhedral aggregate.
9. The method for efficiently constructing the three-dimensional random aggregate concrete mesoscopic model according to claim 1, wherein the aggregates with the interface transition region are sorted according to the volume size and are randomly thrown into the concrete region, and the method comprises the following steps:
traversing all the aggregates, and sequencing the aggregates from large to small according to the volume;
the aggregates are put in sequence from large to small according to the volume, and the coordinates of the center point of the aggregates are as follows:
wherein r ismaxThe maximum distance between the top point and the center of the aggregate; e is the minimum spacing between the aggregates; alpha, beta and gamma are random numbers of 0-1 respectively;
and (3) calculating the distance between the centers of the aggregates, and finishing the feeding of the aggregates when the distance between the centers of the aggregates is larger than the sum of the external spherical radii of the two aggregates.
10. The method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model according to claim 9, further comprising, after said calculating the distance between aggregate centers: and judging whether the aggregates are overlapped or not according to the distance between the aggregate centers, if the distance between the aggregate centers is smaller than the sum of the external sphere radii of the two aggregates, judging that the aggregates are overlapped, and adding the aggregates again until the aggregate is added.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115266717A (en) * | 2022-07-22 | 2022-11-01 | 天津大学 | Concrete segregation degree evaluation method and device |
| CN116451305A (en) * | 2023-03-10 | 2023-07-18 | 哈尔滨工业大学 | Coarse aggregate geometric modeling method based on real concrete bridge |
| CN118133493A (en) * | 2024-01-04 | 2024-06-04 | 哈尔滨工业大学 | Construction method of concrete model of three-dimensional concave-convex polyhedron random aggregate, electronic equipment and storage medium |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115266717A (en) * | 2022-07-22 | 2022-11-01 | 天津大学 | Concrete segregation degree evaluation method and device |
| CN116451305A (en) * | 2023-03-10 | 2023-07-18 | 哈尔滨工业大学 | Coarse aggregate geometric modeling method based on real concrete bridge |
| CN118133493A (en) * | 2024-01-04 | 2024-06-04 | 哈尔滨工业大学 | Construction method of concrete model of three-dimensional concave-convex polyhedron random aggregate, electronic equipment and storage medium |
| CN118133493B (en) * | 2024-01-04 | 2024-08-30 | 哈尔滨工业大学 | Construction method of concrete model of three-dimensional concave-convex polyhedron random aggregate, electronic equipment and storage medium |
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