CN115482891A - Construction method of recycled concrete mesoscopic random aggregate model based on convex polygon - Google Patents
Construction method of recycled concrete mesoscopic random aggregate model based on convex polygon Download PDFInfo
- Publication number
- CN115482891A CN115482891A CN202211174401.XA CN202211174401A CN115482891A CN 115482891 A CN115482891 A CN 115482891A CN 202211174401 A CN202211174401 A CN 202211174401A CN 115482891 A CN115482891 A CN 115482891A
- Authority
- CN
- China
- Prior art keywords
- aggregate
- model
- convex polygon
- convex
- recycled
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000010276 construction Methods 0.000 title claims abstract description 9
- 239000004570 mortar (masonry) Substances 0.000 claims abstract description 38
- 239000002245 particle Substances 0.000 claims abstract description 36
- 238000012360 testing method Methods 0.000 claims abstract description 20
- 238000004364 calculation method Methods 0.000 claims abstract description 6
- 238000000034 method Methods 0.000 claims description 24
- 239000011159 matrix material Substances 0.000 claims description 19
- 238000006467 substitution reaction Methods 0.000 claims description 14
- 230000001186 cumulative effect Effects 0.000 claims description 8
- 230000001174 ascending effect Effects 0.000 claims description 4
- 238000000342 Monte Carlo simulation Methods 0.000 claims description 3
- 238000012163 sequencing technique Methods 0.000 claims description 3
- 238000004088 simulation Methods 0.000 abstract description 4
- 238000010586 diagram Methods 0.000 description 6
- 239000000463 material Substances 0.000 description 6
- 238000002474 experimental method Methods 0.000 description 4
- 238000011160 research Methods 0.000 description 4
- 239000013598 vector Substances 0.000 description 3
- 239000002699 waste material Substances 0.000 description 3
- VEXZGXHMUGYJMC-UHFFFAOYSA-N Hydrochloric acid Chemical compound Cl VEXZGXHMUGYJMC-UHFFFAOYSA-N 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 239000011148 porous material Substances 0.000 description 2
- VEXZGXHMUGYJMC-UHFFFAOYSA-M Chloride anion Chemical compound [Cl-] VEXZGXHMUGYJMC-UHFFFAOYSA-M 0.000 description 1
- 239000000853 adhesive Substances 0.000 description 1
- 230000001070 adhesive effect Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 239000004568 cement Substances 0.000 description 1
- 239000003086 colorant Substances 0.000 description 1
- 230000006835 compression Effects 0.000 description 1
- 238000007906 compression Methods 0.000 description 1
- 238000005094 computer simulation Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000009792 diffusion process Methods 0.000 description 1
- 238000001035 drying Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000007717 exclusion Effects 0.000 description 1
- 238000010438 heat treatment Methods 0.000 description 1
- 239000000203 mixture Substances 0.000 description 1
- 238000002360 preparation method Methods 0.000 description 1
- 238000004064 recycling Methods 0.000 description 1
- 239000004576 sand Substances 0.000 description 1
- 238000004448 titration Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
- G16C60/00—Computational materials science, i.e. ICT specially adapted for investigating the physical or chemical properties of materials or phenomena associated with their design, synthesis, processing, characterisation or utilisation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/25—Design optimisation, verification or simulation using particle-based methods
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02W—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO WASTEWATER TREATMENT OR WASTE MANAGEMENT
- Y02W30/00—Technologies for solid waste management
- Y02W30/50—Reuse, recycling or recovery technologies
- Y02W30/91—Use of waste materials as fillers for mortars or concrete
Landscapes
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Computing Systems (AREA)
- General Engineering & Computer Science (AREA)
- Evolutionary Computation (AREA)
- Computer Hardware Design (AREA)
- Bioinformatics & Cheminformatics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Computational Mathematics (AREA)
- Bioinformatics & Computational Biology (AREA)
- Life Sciences & Earth Sciences (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a construction method of a mesoscopic random aggregate model of recycled concrete based on a convex polygon, which comprises the following steps: 1, determining basic parameters; 2, calculating the theoretical calculation throwing area of the aggregate of each particle size section; 3 randomly generating different ellipses; 4, randomly generating N convex polygons on the ellipse, and sequentially connecting the vertexes of the convex polygons to generate a common aggregate convex polygon model; 5 randomly generating mortar to form a recycled aggregate convex polygonal model; and 6, randomly putting the common aggregate and the recycled aggregate. The mesoscopic model obtained by the invention is closer to the mesoscopic structure of the actual recycled concrete section, so that the simulation of the random aggregate model of the convex polygonal recycled concrete can be realized, and the requirements of the actual simulation test model can be better met.
Description
Technical Field
The invention belongs to the technical field of material simulation, and particularly relates to a two-dimensional five-phase mesoscopic modeling method for recycled concrete based on a convex polygonal random aggregate model.
Background
With the rapid development of economic construction in China, the consumption of concrete materials for basic construction in China is huge, and natural resources such as gravels and the like are consumed. Meanwhile, waste concrete generated by demolishing old buildings is increasing day by day, and currently, modes mainly adopted such as landfill have great influence on the environment. The waste concrete can be prepared into recycled coarse aggregate after treatment, can be used for replacing natural aggregate to prepare recycled concrete, not only solves the problem of lack of natural aggregate resources, but also realizes recycling of the waste concrete.
In recent years, many researchers have conducted extensive studies on various properties of recycled concrete, for example, by changing the preparation method of recycled concrete, etc., the influence of factors such as the substitution rate of recycled aggregate, the adhesion rate of mortar, etc., on the mechanical properties and durability of recycled concrete is studied. The influence of the mortar aggregate on the basic mechanical property of the recycled concrete is researched by changing the strength of the mortar aggregate. Chen Long researches on preparing recycled coarse aggregates with different mortar adhesion rates in a laboratory by taking a sand rate as a variable show that the larger the adhesion rate of the recycled coarse aggregate mortar is, the larger the drying shrinkage of recycled concrete is, and the lower the compressive strength of the recycled concrete is. The lunar study found that the lower the strength of the adhering aggregate, the lower the compressive strength of the recycled concrete, and the greater the dry shrinkage. However, most of these studies are based on macroscopic experiments, and the differences of the elastic modulus and strength properties of the components of each phase are ignored.
Domestic scholars take the water-cement ratio, the replacement rate of recycled aggregates and the like as influencing factors, and make a great deal of research on the mechanical properties of recycled concrete, such as compression resistance, tensile resistance and the like. Feng Shuai and the like control the mortar coverage area of recycled aggregate by a microwave heating method, and study the influence of the mortar coverage area on the durability and mechanical properties of recycled concrete. Hu Xin, cui Zhenglong, etc. the effect of the adhesion rate of mortar on the performance of recycled concrete was investigated by testing the adhesion rate of mortar to different recycled aggregates by hydrochloric acid titration. These studies are mostly based on macroscopic experiments, in which the differences in the elastic modulus and strength properties of the materials of the phases are neglected.
Since the recycled concrete has more remarkable unevenness and complicated internal structure than the general concrete. From the perspective of the complicated structure inside the recycled concrete material, it is necessary to study the influence of each phase composition on the performance of the recycled concrete material, and the method can provide a basis for further improving the performance of the recycled concrete material.
With the development of computer information technology, building a computer model of a recycled concrete mesostructure is an important research hotspot. As the random aggregate model can more accurately reflect the failure mechanism of concrete, the establishment of the random aggregate model of recycled concrete arouses the interest of more and more scholars. Jiang Baoku and the like establish a circular-based recycled concrete random aggregate model, study the tensile mechanical property of the recycled concrete, and simulate the two-dimensional diffusion process of chloride ions in the recycled concrete; xu Mengchan establishes an elliptical two-dimensional recycled concrete mesoscopic structure, and researches the influence of mesoscopic component interface thickness on the mechanical property of recycled concrete; CN114239345A establishes a recycled concrete mesoscopic model based on the recycled aggregate of concentric circles; CN112464523A constructs a recycled concrete mesoscopic model based on oval recycled aggregate. However, these models are too idealized regardless of whether they are oval or round, and are greatly different from the actual aggregate shape. CN113591195A constructs a microscopic model of recycled concrete with a concentric convex polygon, but the method simply treats the attached mortar as wrapping the outer ring of the convex polygon by one layer, which is different from the actual recycled concrete.
Until now, there has been no method for constructing a more realistic mesoscopic random aggregate model of recycled concrete.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a construction method of a mesoscopic random aggregate model of recycled concrete based on a convex polygon, so that a more real recycled concrete model can be constructed, and the popularization and the efficient application of the recycled concrete are facilitated.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a construction method of a mesoscopic random aggregate model of recycled concrete based on a convex polygon, which is characterized by comprising the following steps of:
step 1: acquiring basic parameters, including: rectangular section size of recycled concrete test piece, namely width W of test piece section, height H of test piece section and aggregate volume ratio P k Size of sieve with holes [ D ] min ,D 2 …D i-1 ,D i ,D i+1 …D max ]The recycled aggregate substitution rate R and the mortar adhesion content level; wherein D is min Denotes the minimum particle diameter of the aggregate, D max Represents the maximum particle size of the aggregate; d i Indicates the size of the ith screen;
step 2: according to an aggregate grade curve Walraven formula of a Fuller grade curve under a two-dimensional plane, calculating the theoretical calculation throwing area { S ] of the aggregates in each grade range i I =2,3, …, max }, where S i Indicates that the particle size range is (D) i-1 ,D i ) The feeding area is calculated theoretically for the aggregate;
and step 3: establishing a plane rectangular coordinate system by taking a left lower corner point of a rectangular section of the test piece as a coordinate origin, the transverse direction of the rectangular section as an x axis and the longitudinal direction of the rectangular section as a y axis, and generating a plane rectangular domain with the width of W and the height of H;
and 4, step 4: initializing i = max;
and 5: randomly generating a number R epsilon (0,1) based on a Monte Carlo method, and if R is less than or equal to R, generating a grain size range (D) i-1 ,D i ) The normal aggregate convex polygon model of (1), if r>R, the generation size range is (D) i-1 ,D i ) The recycled aggregate convex polygonal model; wherein R represents the substitution rate of recycled aggregate;
and 6: the particle size range is judged to be (D) i-1 ,D i ) Whether the generated aggregate convex polygon model simultaneously meets the boundary condition and the aggregate interference condition or not, and if so, the size fraction range is within (D) i-1 ,D i ) The convex polygon model of the aggregate is put into the plane rectangular domain, and the size fraction range is calculated to be (D) i-1 ,D i ) The area a of the s-th charged aggregate is S =1,2, …, L; otherwise, returning to the step 5; until a particle size range (D) is obtained i-1 ,D i ) L cumulative charging area for charging aggregate
Until formula (1) is satisfied;
A i ∈((1-σ)S i ,(1+σ)S i ) (1)
in formula (1), σ represents a parameter between (0,1);
and 7: assigning i-1 to i, returning to step 4 to execute in sequence until i<2 so as to obtain the cumulative charging area { A of the aggregates in each size fraction range i |i＝2,3,…,max}；
And 8: calculating the aggregate total input area ratio S A And the area ratio S of the attached old mortar M The method is used for constructing a mesoscopic random aggregate model of the recycled concrete.
The construction method of the recycled concrete mesoscopic random aggregate model based on the convex polygon is also characterized in that a boundary function of a planar rectangular domain in the step 3 is obtained by using a formula (2):
in the formula (2), x 1 、x 2 、y 1 、y 2 Are the arguments of the four boundary line equations.
The step of generating the common aggregate convex polygon model in the step 5 comprises the following steps:
step 5.1a: randomly generating an ellipse E, and making the longer half shaft a of the ellipse E belong to 0.5 (D) i-1 ,D i+1 )；
Step 5.2a: randomly generating N angles
Taking the center of the ellipse E as a starting point, generating N rays according to N angles, and respectively intersecting the N rays with the ellipse E to obtain N points; wherein,
representing the included angle between the jth ray and the positive direction of the x axis of the plane rectangular coordinate system;
step 5.3a: sequencing the N angles in an ascending order, sequentially calculating the difference value between two adjacent angles, and if any difference value is smaller than the set angle delta, returning to the step 5.2a for sequential execution; otherwise, executing step 5.4a;
step 5.4a: and calculating to obtain the coordinates of N points on the ellipse E according to the N angles and the general parameter equation of the ellipse, and connecting all the vertexes in sequence to obtain the common aggregate convex polygon model.
The process of generating the recycled aggregate convex polygon model in the step 5 comprises the following steps:
on the basis of generating the common aggregate convex polygon model, randomly selecting N from N vertexes of the common aggregate convex polygon model according to level 1 2 continuous vertexes are randomly selected in the inner part of the common aggregate convex polygon model, so that N is obtained 1 +2 points are connected in sequence to obtain an adhesion mortar polygonal model, and the adhesion mortar polygonal model and the residual N-N points are connected 1 Polygonal part formed by connecting vertexesThe recycled aggregate convex polygonal model is formed by the components together.
The judging mode of whether the convex polygon model in the step 6 meets the boundary condition is as follows:
if the general circumscribed ellipse parameter equation of the convex polygon aggregate model and the four boundary linear equations in the formula (2) are not solved, the convex polygon aggregate model satisfies the boundary condition of the throwing area, otherwise, the convex polygon aggregate model does not satisfy the boundary condition.
The particle size range in the step 6 is (D) i-1 ,D i ) The judging mode of whether the aggregate convex polygon model meets the aggregate interference condition is as follows:
step 6.1: the size fraction is judged to be in the range of (D) i-1 ,D i ) Whether the center of the external ellipse of the convex polygonal aggregate model is in the interior of any one of the thrown convex polygonal aggregate model or not is judged, if yes, the condition of aggregate interference is not met, and if not, the step 6.2 is executed;
step 6.2: the calculated size fraction is in (D) i-1 ,D i ) The quadratic matrix A of the external ellipse of the convex polygonal model of the aggregate is calculated, and the generalized characteristic polynomial of the quadratic matrix A and the quadratic matrix B of the external ellipse of any one thrown convex polygonal model of the aggregate is calculated; judging whether the generalized characteristic polynomial has two different positive roots or not, if so, indicating that the circumscribed ellipses corresponding to the quadratic matrix A, B are separated, and executing the step 6.3; otherwise, executing step 6.4;
step 6.3: continuously judging whether the quadric form matrix A is separated from the circumscribed ellipses of other thrown aggregate convex polygon models or not, and indicating that the particle size range is (D) when the quadric form matrix A is separated from the circumscribed ellipses of other thrown aggregate convex polygon models only i-1 ,D i ) The convex polygon model of the aggregate meets the aggregate interference condition, and the judging process is exited;
step 6.4: sequentially judging the size fraction range to be (D) i-1 ,D i ) Whether all the vertexes of the convex-polygonal model of the aggregate are in the interior of all the thrown convex-polygonal models of the aggregate, if so, the size range is shown to be (D) i-1 ,D i ) The convex polygon model of the aggregate does not meet the aggregate interference condition, otherwise, the step 6.5 is executed;
step 6.5: the size fraction is judged to be in the range of (D) i-1 ,D i ) Whether any line segment between all vertexes of the aggregate convex polygon model has an intersection relation with any line segment between vertexes of all thrown aggregate convex polygon models exists, if yes, the aggregate interference condition is not met, and if not, the aggregate interference condition is met.
Compared with the prior art, the invention has the beneficial effects that:
1. compared with the existing recycled concrete model, the method has the advantages that the old mortar attaching model is randomly generated on the periphery of the common aggregate model, so that the adopted recycled concrete model based on the convex polygon is more consistent with the recycled concrete microscopic structure under the real condition, the shape and the position of the attached mortar are more real, and the simulation result is more accurate.
2. Compared with the existing recycled concrete mesoscopic model, the method can control the replacement rate of the recycled aggregate and the adhesion content of the old mortar by changing the input parameters, and can be used for simulating and researching the influence of the adhesion amount, the replacement rate and the like of the mortar of the recycled aggregate on various properties of the recycled concrete.
3. Compared with the existing recycled concrete mesoscopic model, the boundary condition judgment and the aggregate interference judgment in the invention are stricter and more accurate, and the filling rate of the aggregate is improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic view of a recycled aggregate model according to the present invention;
FIG. 3 is a boundary condition decision diagram of the present invention;
FIG. 4 is a diagram of the intersection of a convex polygon according to the present invention;
FIG. 5a is a diagram illustrating a line segment intersection method according to the present invention;
FIG. 5b is a schematic view of the present invention showing the intersection of line segments;
FIG. 6a is a schematic diagram of a model of a recycled concrete mesoscopic random aggregate with a substitution rate of 30% according to the present invention;
FIG. 6b is a schematic diagram of a model of a recycled concrete mesoscopic random aggregate with a 50% substitution rate according to the present invention;
FIG. 6c is a schematic diagram of a model of the recycled concrete mesoscopic random aggregate with a substitution rate of 100% according to the present invention.
Detailed Description
In this embodiment, as shown in fig. 1, a method for constructing a mesoscopic random aggregate model of recycled concrete based on a convex polygon is to generate a polygonal old mortar model based on the convex polygon random aggregate, so that the old mortar model is randomly attached, and the effect of controlling the content of the old mortar can be achieved by controlling the number of vertexes of the polygon, so as to better conform to the mesoscopic structure of the recycled concrete under real conditions. Specifically, the method comprises the following steps:
step 1: acquiring basic parameters, including: rectangular section size of recycled concrete test piece, namely width W of test piece section, height H of test piece section and aggregate volume ratio P k (aggregate volume in percent of total volume of recycled concrete), size of mesh [ D min ,D 2 …D i-1 ,D i ,D i+1 …D max ]The recycled aggregate substitution rate R is an element (0,1) and the mortar adhesion content level; wherein D is min Denotes the minimum particle diameter of the aggregate, D max Represents the maximum particle diameter of the aggregate; d i Indicates the size of the ith screen;
and 2, step: determining the area proportion of aggregate of each grade according to an aggregate grade curve of a Fuller grade curve under a two-dimensional plane, namely a Walraven formula shown in a formula (1), and calculating the theoretical calculated throwing area { S } of the aggregate in each grade range according to a formula (2) i I =2,3, …, max }, where S i Indicates that the particle size range is (D) i-1 ,D i ) The feeding area is calculated theoretically for the aggregate;
S i ＝[P i (D＜D i )-P i-1 (D＜D i-1 )]×W×H (2)
in the formulae (1) and (2), P (D)<D 0 ) The particle diameter D of aggregate in the section is smaller than the sieve pore D 0 General summary of the scopeRate, P k The volume of the aggregate accounts for the total volume of the recycled concrete, D max Is the maximum particle diameter of the aggregate, S i Indicates that the particle diameter is in the range of (D) i-1 ,D i ) The aggregate charging area, P, is calculated according to the theory i (D<D i ) The particle diameter D of aggregate in the section is smaller than the sieve pore D i The probability in the range, W, is the section width of the test piece, and H is the section height of the test piece.
And step 3: establishing a plane rectangular coordinate system by taking a left lower corner point of a rectangular section of the test piece as a coordinate origin, the transverse direction of the rectangular section as an x axis and the longitudinal direction of the rectangular section as a y axis, and generating a plane rectangular domain with the width of W and the height of H, wherein a boundary function of the rectangle is a formula (3);
in the formula (3), x 1 、x 2 、y 1 、y 2 Are the arguments of the four boundary line equations.
And 4, step 4: initializing i = max, and sequentially adding aggregates according to the order of size fractions from large to small;
and 5: randomly generating a number R epsilon (0,1) based on a Monte Carlo method, and if R is less than or equal to the substitution rate R of the recycled aggregate, generating the particle size range of (D) i-1 ,D i ) The common aggregate convex polygon model comprises the following steps:
step 5.1a: randomly generating an ellipse E, and making the longer half shaft a of the ellipse E belong to 0.5 (D) i-1 ,D i+1 ) Randomly generating a minor axis b and a major axis a (a)>b) Calculating the value of the minor semi-axis b as mua, randomly generating an ellipse central coordinate (m, n) satisfying the formula (4), randomly generating an included angle alpha between the major axis direction of the ellipse and the positive direction of the x axis of the plane rectangular coordinate system in (0, pi), and generating an ellipse with random position and any inclination angle based on a general parameter equation of the ellipse of the formula (5);
in the formula (4), b is a minor semi-axis of the ellipse E, W is the width of the cross section of the test piece, H is the height of the cross section of the test piece, and m and n are respectively the horizontal and vertical coordinates of the center of the ellipse E.
Only one case where the ellipse E generated according to the above equation intersects the boundary is shown in fig. 3.
In the formula (5), x and y are respectively the horizontal and vertical coordinates of any point on the ellipse E, a and b are respectively the semi-major axis and semi-minor axis of the ellipse E, alpha is the included angle between the major axis of the ellipse E and the positive direction of x, and m and n are respectively the horizontal and vertical coordinates of the center of the ellipse E.
Step 5.2a: randomly generating N angles
N e (7,11); taking the center of the ellipse E as a starting point, generating N rays according to N angles, and respectively intersecting the N rays with the ellipse E to obtain N points; wherein,
representing the included angle between the jth ray and the positive direction of the x axis of the plane rectangular coordinate system;
step 5.3a: the N angles are sorted in an ascending order, the difference values between two adjacent angles are calculated in sequence, if any difference value is smaller than the set angle delta, the step 5.2a is returned to be executed in sequence, the N angles are generated again randomly, and long and thin deformed aggregates with large side length difference are avoided; otherwise, executing step 5.4a;
step 5.4a: and calculating to obtain the coordinates of N points on the ellipse E according to the general parameter equation (5) of the N angles and the ellipse, and connecting each vertex in sequence to obtain the common aggregate convex polygon model.
If r>The replacement ratio R of recycled aggregate is such that the produced particle size is within the range of (D) i-1 ,D i ) The recycled aggregate convex polygon model comprises the following specific steps: on the basis of generating a common aggregate convex polygon model, according to the level, forming a common aggregate convex polygon modelRandomly selecting N from N vertexes of model 1 And the continuous vertexes are used as partial vertexes of the old mortar polygonal model. As shown in FIG. 2, when the level is 'small', N 1 When 3 is taken, the grade is 'mean', N 1 When 4 is taken, the grade is 'big', N 1 And 5, taking. With N 1 The mortar adhesion content increases. And randomly selecting 2 points in the interior of the common aggregate convex polygonal model so as to obtain N 1 +2 points are connected in sequence to obtain an adhering mortar polygonal model, and the adhering mortar polygonal model and the rest N-N 1 And polygonal parts formed by connecting the vertexes jointly form the recycled aggregate convex polygonal model.
And 6: the particle size range is judged to be (D) i-1 ,D i ) Whether the generated aggregate convex polygon model simultaneously meets the boundary condition and the aggregate interference condition or not, and if so, the size fraction range is within (D) i-1 ,D i ) The convex polygon model of the aggregate is put into a plane rectangular domain, and the size fraction range is calculated to be (D) i-1 ,D i ) The area a of the s-th charged aggregate is S =1,2, …, L (when the aggregate model is a recycled aggregate convex polygon model, the area F of the adhesive mortar polygon model in the kth recycled aggregate convex polygon model is calculated k ，k＝1,2,…,L 1 . ) (ii) a Otherwise, returning to the step 5; when the fraction (D) i-1 ,D i ) Cumulative aggregate charging area A i Theoretical calculated area S less than this size fraction i Returning to the step 5 to continue throwing the aggregate in the size fraction section; a. The i Greater than S i When the aggregate is not put into the container, the last aggregate is abandoned, and the smaller aggregate is generated in the size fraction section again to continue to be put into the container until the obtained size fraction range is (D) i-1 ,D i ) L cumulative charging area for charging aggregate
Until formula (6) is satisfied;
A i ∈((1-σ)S i ,(1+σ)S i ) (6)
in the formula (6), σ represents a parameter between (0,1); in order to make the cumulative feeding area of each grain fractionA i As close as possible to the theoretical calculated area S of the fraction i And σ may take 0.2.
Firstly, distinguishing boundary conditions of the aggregate convex polygon model: if the general circumscribed ellipse parameter equation (5) of the convex polygon aggregate model and the four boundary linear equations in the equation (3) are not solved, the convex polygon model satisfies the boundary condition of the throwing area, otherwise, the convex polygon model does not satisfy the boundary condition. The convex polygon model of the aggregate meeting the boundary condition further judges the interference condition of the aggregate, and judges that the size fraction range is in (D) according to the following steps i-1 ,D i ) Whether the aggregate convex polygon model meets the aggregate interference condition is as follows:
step 6.1: judging the size range to be (D) i-1 ,D i ) Whether the center of the external ellipse of the convex polygonal aggregate model is in the interior of any one of the thrown convex polygonal aggregate model or not is judged, if yes, the condition of aggregate interference is not met, and if not, the step 6.2 is executed;
step 6.2: in order to improve the efficiency of aggregate interference judgment, whether the convex polygon inside the convex polygon is interfered is judged by utilizing interference judgment between the ellipses, if the circumscribed ellipse of the convex polygon is not interfered with the thrown convex polygon, the convex polygon is not interfered with other convex polygons necessarily, and is thrown into the plane rectangular domain generated in the step 3 directly, otherwise, strict interference judgment of the convex polygon is required. The interference discrimination between ellipses is based on algebraic condition decision: if the generalized eigenvalues of the quadratic matrices of the two ellipses a and B (the roots of the generalized eigenequation f (λ) = 0) have two distinct positive real roots, the ellipses are separated, otherwise they are not separated. The particle size range is calculated by the formula (7) as (D) i-1 ,D i ) A quadratic matrix A of the external ellipse of the convex polygonal aggregate model is calculated, and a generalized characteristic polynomial of the quadratic matrix A and a quadratic matrix B of the external ellipse of any one thrown convex polygonal aggregate model is calculated; judging whether two different orthomorphic roots exist in the generalized characteristic polynomial (formula (8)), if so, indicating that the circumscribed ellipses corresponding to the quadratic matrix A, B are separated, and executing the step 6.3; otherwise, it can judgeInterrupting the external ellipse of the aggregate convex polygonal model and the external ellipse of the thrown aggregate convex polygonal model to generate interference, further performing interference judgment on the convex polygon, and executing the step 6.4;
in the formula (8), A represents a quadratic matrix of an external ellipse, m and n are horizontal and vertical coordinates of the center of the ellipse, a and b are respectively a long semi-axis and a short semi-axis of the ellipse, and alpha is an included angle between the long axis of the ellipse and the positive direction of x.
f(λ)＝det(λA+B)＝0 (8)
In the formula (3), A and B are quadric form matrixes of any two circumscribed ellipses, and f (lambda) is a generalized characteristic polynomial of the ellipses A and B.
Step 6.3: continuously judging whether the quadric form matrix A is separated from the external ellipses of other thrown aggregate convex polygon models or not, and indicating that the size range is (D) when the quadric form matrix A is separated from the external ellipses of other thrown aggregate convex polygon models only i-1 ,D i ) The aggregate convex polygon model meets the aggregate interference condition, and the judging process is quitted;
step 6.4: the intersection of the convex polygons includes three cases as shown in FIG. 4, and the size fraction range is sequentially judged to be (D) i-1 ,D i ) Whether all the vertexes of the convex-polygonal model of the aggregate are in the interior of all the thrown convex-polygonal models of the aggregate, if so, the size range is shown to be (D) i-1 ,D i ) If not, judging that the aggregate convex polygon model does not have the interference types shown in the cases 1 and 2, further judging whether the situation 3 points do not contain intersection, and executing the step 6.5;
step 6.5: judging the size range to be (D) i-1 ,D i ) Whether any line segment between all vertexes of the aggregate convex polygon model is intersected with any line segment between the vertexes of all the thrown aggregate convex polygon models or not is judged, if yes, the aggregate interference condition is not met, and if not, the aggregate interference condition is met. Further judging whether two line segments intersect (see fig. 5 a)Shown), a "rapid exclusion experiment" was first performed: judging whether rectangles taking the two line segments as diagonals are intersected or not according to coordinates of end points of the two line segments, if not, obviously not intersecting the two line segments, and if so, carrying out a next step of 'straddle experiment': if the two line segments AB, CD intersect, two conditions must be satisfied:
(1) The two points C and D are respectively arranged on two sides of the line segment AB;
(2) The two points A and B are respectively arranged on two sides of the line segment CD;
as shown in fig. 5b, based on the knowledge of the vector cross product and the vector product, if c <0 in equation (9), C, D two points are on both sides of the line segment AB, and if f <0 is calculated by equation (10), A, B two points are on both sides of the line segment CD. The CD intersects when c <0 and f <0 line segment AB, otherwise does not intersect.
And 7: assigning i-1 to i, returning to the step 4 for sequential execution, and sequentially putting the aggregate models of all the particle sizes according to the sequence of big first and small second until i<2 until now, the cumulative aggregate charging area { A) in each size range is calculated i |i＝2,3,…,max}；
And step 8: the aggregate total charging area ratio S is calculated according to the formula (11) A And the area ratio S of the attached old mortar M The method is used for constructing a mesoscopic random aggregate model of the recycled concrete.
S in formula (11) A And S M Respectively the aggregate total throwing area ratio and the attached old mortar area ratio, A i Is (D) i-1 ,D i ) The actual area of aggregate feeding in the size fraction, max is the number of the hole sieves, and W and H are respectively the testWidth and height of cross-section of the member, L 1 Number of particles to feed recycled aggregate, F k The area of the adhering mortar polygonal model in the kth recycled aggregate convex polygonal model.
Example (b): the method comprises the following steps of constructing a random microscopic model of the recycled concrete based on the convex polygon:
step 1: determining basic parameters:
the section width W =100mm and the height H =100mm of the recycled concrete test piece, and the aggregate volume accounts for the total volume percentage P of the recycled concrete k =0.75, minimum aggregate particle size D min =4.75mm, maximum aggregate particle diameter D max =25mm, the screen mesh size is 4.75mm,9.5mm,16mm,19mm,25mm, the substitution rate of the recycled aggregate is respectively 30%,50%,100%, namely R =0.3,0.5,1;
step 2: calculating the area ratio of the aggregates of each size fraction in the aggregate feeding area:
according to the Walraven formula, calculating to obtain the aggregate with the particle size of 19-25 mm and the input area of 674mm 2 The aggregate with the grain size of 16-19 mm is put in the area of 494mm 2 The aggregate feeding area with the grain size of 9.5-16 mm is 1401mm 2 The aggregate feeding area with the grain size of 4.75-9.5 mm is 1434mm 2 The total charging area of the aggregate accounts for 40 percent.
And step 3: establishing a plane rectangular coordinate system by taking a left lower corner point of a rectangular section of the test piece as a coordinate origin, the transverse direction of the rectangular section as an x axis and the longitudinal direction of the rectangular section as a y axis, and generating a plane rectangular domain with the width of W and the height of H;
and 4, step 4: initializing i =5;
and 5: randomly generating a number R = rand (1) in the range of (0,1), and when R ≦ R, generating a size fraction in the range of (D) 4 ,D 5 ) The common aggregate convex polygon model: randomly generating the number of vertexes N =6+ randi (3,1) of the common aggregate convex polygonal model, and randomly generating N angles
Utilizing Matlab to embed function sort function pair
Performing ascending sequencing, sequentially calculating the difference value between two adjacent angles, and if the difference value is less than the set angle delta = pi/6, randomly generating N angles again
Calculating N vertex coordinates according to an ellipse parameter equation, sequentially connecting the N vertices by using a Matlab built-in function fill, and filling colors to obtain a common aggregate convex polygon model; if r>R, the generation size range is (D) i-1 ,D i ) The recycled aggregate convex polygon model: determining the number N of vertexes of the old mortar polygon on the basis of generating a convex polygon model of the common aggregate 1 : when level ='s', N 1 =3; when level ='m', N 1 =4; when level = 'b', N 1 =5; and randomly taking 2 points in the convex polygon and connecting the points in sequence by using fill function (N) 1 + 2) carrying out point and color filling to obtain a regenerated aggregate random polygon model attached with old mortar;
and 6: firstly, the particle size range is judged to be (D) i-1 ,D i ) Whether the generated aggregate convex polygon model meets boundary conditions and aggregate interference conditions is judged: and (3) judging whether the parameter equation (4) of any position of the ellipse and the four boundary straight line equations (5) respectively have solutions by using a Matlab built-in function solution, if not, indicating that the convex polygon model meets the boundary condition of the throwing area, and carrying out next aggregate interference judgment, otherwise, returning to the step 5. And further judging the aggregate interference condition by the aggregate convex polygon model meeting the boundary condition: and (3) judging whether the center of the external ellipse of the newly generated convex polygonal aggregate is inside any one of the placed aggregate convex polygonal models or not by using a Matlab built-in function inpogon, if so, indicating that the aggregate interference condition is not met, returning to the step 5 to regenerate the aggregate convex polygonal model, otherwise, performing interference judgment between next ellipses, and sequentially judging the position relationship between the newly generated convex polygonal aggregate external ellipse and all generated ellipses. Solving two of any two ellipses by utilizing Matlab built-in function eig (A, B)If there are two different negative roots, the generalized eigenvalues of the minor forms a and B can be determined that the ellipses a and B are separated from each other (when the generalized eigenvalue is found by the Matlab built-in function eig (a, B), f (λ) = det (λ a-B) is defined as a generalized eigenpolynomial). If the newly generated convex polygon circumscribed ellipse is separated from the generated convex polygon circumscribed ellipse, directly throwing the convex polygon circumscribed ellipse; otherwise, carrying out the next judgment; sequentially judging whether all vertexes of the newly generated convex polygon are outside all the thrown aggregate convex polygon models or not by utilizing a Matlab built-in function inpegg, if not, returning to the step 5, and if not, performing next judgment; and respectively calculating cross products and dot product operations between vectors by using cross functions and dot functions in Matlab, sequentially judging whether all edges, namely line segments, of the newly generated convex polygon are intersected with all edges of the generated convex polygon, and if all line segments are not intersected, smoothly putting in the convex polygon. Otherwise, the step 5 is returned. And (4) recording the area of the aggregate of the successfully-thrown aggregate convex polygon model, and if the aggregate model is a regenerated aggregate model, recording the area of the mortar-attached polygon.
And 7: assigning i-1 to i, and then returning to the step 4 to execute the sequence until i is less than 2, thereby obtaining the accumulated throwing area of each size range; when the accumulated feeding area of the aggregate of a certain size fraction is smaller than the theoretical calculation area of the size fraction, continuously feeding the aggregate of the size fraction; when the accumulated throwing area is larger than the theoretical calculation area, giving up the throwing of the last aggregate, generating a smaller aggregate again in the particle size section, continuing to throw the aggregate until the accumulated throwing area of the current particle size aggregate reaches 0.98-1.02 times of the theoretical calculation area of the particle size aggregate, and throwing the aggregate of the next particle size until all the particle size sections are thrown;
and step 8: calculating the aggregate total throwing area ratio S A And the area ratio S of the attached old mortar M 。
FIG. 6a is a schematic representation of a microscopically random aggregate model of recycled concrete with a substitution rate of 30% and levels of ' S ','m ' and ' b ', calculated to obtain S when the level is ' S A 41.25% of S M Is 2.54%; when the level is' m A 42.39%, S M Is 8.29 percent; when level is 'b' S A 41.85%, S M The content was 12.65%. FIG. 6b is a schematic representation of a mesoscopic random aggregate of recycled concrete with a substitution rate of 50% and levels of "S", "m" and "b", calculated to give S when the level is "S A 40.98%, S M 4.20 percent; s when level is' m A 41.33% of S M 9.99 percent; when level is 'b' S A 41.76% of S M The content was 32.78%. FIG. 6c is a schematic representation of a mesoscopic random aggregate of recycled concrete with a substitution rate of 100% and levels of "S", "m" and "b", calculated to give S when the level is "S A 41.69% of S M 9.32%; when the level is' m A 41.45%, S M 25.02%; when level is 'b' S A 42.01%, S M Is 55.04%.
Claims (6)
1. A construction method of a recycled concrete mesoscopic random aggregate model based on a convex polygon is characterized by comprising the following steps:
step 1: acquiring basic parameters, including: rectangular section size of recycled concrete test piece, namely width W of test piece section, height H of test piece section and aggregate volume ratio P k Size of sieve with holes [ D ] min ,D 2 …D i-1 ,D i ,D i+1 …D max ]The recycled aggregate substitution rate R and the mortar adhesion content level; wherein D is min Denotes the minimum particle diameter of the aggregate, D max Represents the maximum particle size of the aggregate; d i Indicates the size of the ith screen;
and 2, step: according to an aggregate grade curve Walraven formula of a Fuller grade curve under a two-dimensional plane, calculating the theoretical calculation throwing area { S ] of the aggregates in each grade range i I =2,3, …, max }, where S i Indicates that the particle size range is (D) i-1 ,D i ) The feeding area is calculated theoretically for the aggregate;
and step 3: establishing a plane rectangular coordinate system by taking a left lower corner point of a rectangular section of the test piece as a coordinate origin, the transverse direction of the rectangular section as an x axis and the longitudinal direction of the rectangular section as a y axis, and generating a plane rectangular domain with the width of W and the height of H;
and 4, step 4: initializing i = max;
and 5: randomly generating a number R epsilon (0,1) based on a Monte Carlo method, and if R is less than or equal to R, generating a size fraction range (D) i-1 ,D i ) The normal aggregate convex polygon model of (1), if r>R, the generation size range is (D) i-1 ,D i ) The recycled aggregate convex polygonal model; wherein R represents the substitution rate of recycled aggregate;
step 6: the particle size range is judged to be (D) i-1 ,D i ) Whether the generated aggregate convex polygon model simultaneously meets the boundary condition and the aggregate interference condition or not, and if so, the size fraction range is within (D) i-1 ,D i ) The convex polygon model of the aggregate is put into the plane rectangular domain, and the size fraction range is calculated to be (D) i-1 ,D i ) Area a of aggregate to be charged at s-th is S =1,2, …, L; otherwise, returning to the step 5; until a particle size in the range of (D) is obtained i-1 ,D i ) L cumulative charging area for charging aggregate
Satisfying the formula (1);
A i ∈((1-σ)S i ,(1+σ)S i )(1)
in formula (1), σ represents a parameter between (0,1);
and 7: after i-1 is assigned to i, the step 4 is returned to and the sequential execution is carried out until i<2 so as to obtain the cumulative charging area { A of the aggregates in each size fraction range i |i＝2,3,…,max}；
And 8: calculating the aggregate total throwing area ratio S A And the area ratio S of the attached old mortar M The method is used for constructing a mesoscopic random aggregate model of the recycled concrete.
2. The method for constructing the convex polygon-based mesoscopic random aggregate model of recycled concrete according to claim 1, wherein the boundary function of the planar rectangular domain in step 3 is obtained by using the following formula (2):
in the formula (2), x 1 、x 2 、y 1 、y 2 Are the arguments of the four boundary line equations.
3. The method for constructing a convex polygon-based recycled concrete mesoscopic random aggregate model according to claim 1, wherein the step of generating a common aggregate convex polygon model in the step 5 comprises:
step 5.1a: randomly generating an ellipse E, and making the longer half shaft a of the ellipse E belong to 0.5 (D) i-1 ,D i+1 )；
Step 5.2a: randomly generating N angles
Taking the center of the ellipse E as a starting point, generating N rays according to N angles, and respectively intersecting the N rays with the ellipse E to obtain N points; wherein,
representing the included angle between the jth ray and the positive direction of the x axis of the plane rectangular coordinate system;
step 5.3a: sequencing the N angles in an ascending order, sequentially calculating the difference value between two adjacent angles, and if any difference value is smaller than the set angle delta, returning to the step 5.2a for sequential execution; otherwise, executing step 5.4a;
step 5.4a: and calculating to obtain the coordinates of N points on the ellipse E according to the N angles and the general parameter equation of the ellipse, and connecting each vertex in sequence to obtain the common aggregate convex polygon model.
4. The method for constructing the convex polygon-based recycled concrete mesoscopic random aggregate model according to claim 1, wherein the step 5 of generating the recycled aggregate convex polygon model comprises the following steps:
on the basis of generating the common aggregate convex polygon model, randomly selecting N from N vertexes of the common aggregate convex polygon model according to level 1 Continuous vertexes, and randomly selecting 2 points in the interior of the common aggregate convex polygon model so as to convert N into N 1 +2 points are connected in sequence to obtain an adhesion mortar polygonal model, and the adhesion mortar polygonal model and the residual N-N points are connected 1 And polygonal parts formed by connecting the vertexes jointly form a recycled aggregate convex polygonal model.
5. The method for constructing the recycled concrete mesoscopic random aggregate model based on the convex polygon as claimed in claim 2, wherein the judging manner of whether the convex polygon model meets the boundary condition in the step 6 is as follows:
if the general circumscribed ellipse parameter equation of the convex polygon aggregate model and the four boundary linear equations in the equation (2) are not solved, the convex polygon aggregate model meets the boundary condition of the throwing area, and otherwise, the convex polygon aggregate model does not meet the boundary condition.
6. The method for constructing a mesoscopic random aggregate model of recycled concrete based on convex polygons as claimed in claim 1, wherein the particle size range in step 6 is (D) i-1 ,D i ) The judging mode of whether the aggregate convex polygon model meets the aggregate interference condition is as follows:
step 6.1: the size fraction is judged to be in the range of (D) i-1 ,D i ) Whether the center of the external ellipse of the convex polygonal aggregate model is in the interior of any one of the thrown convex polygonal aggregate model or not is judged, if yes, the condition of aggregate interference is not met, and if not, the step 6.2 is executed;
step 6.2: the calculated size fraction is in (D) i-1 ,D i ) The quadratic matrix A of the external ellipse of the convex polygonal model of the aggregate is calculated, and the generalized characteristic polynomial of the quadratic matrix A and the quadratic matrix B of the external ellipse of any one thrown convex polygonal model of the aggregate is calculated; judging whether the generalized characteristic polynomial has two different positive roots or notIf yes, the circumscribed ellipses corresponding to the quadratic matrix A, B are separated, and step 6.3 is executed; otherwise, executing step 6.4;
step 6.3: continuously judging whether the quadric form matrix A is separated from the external ellipses of other thrown aggregate convex polygon models or not, and indicating that the size range is (D) when the quadric form matrix A is separated from the external ellipses of other thrown aggregate convex polygon models only i-1 ,D i ) The aggregate convex polygon model meets the aggregate interference condition, and the judging process is quitted;
step 6.4: sequentially judging the size fraction range to be (D) i-1 ,D i ) Whether all the vertexes of the convex-polygonal model of the aggregate are in the interior of all the thrown convex-polygonal models of the aggregate, if so, the size range is shown to be (D) i-1 ,D i ) The convex polygon model of the aggregate does not meet the aggregate interference condition, otherwise, the step 6.5 is executed;
step 6.5: the size fraction is judged to be in the range of (D) i-1 ,D i ) Whether any line segment between all vertexes of the aggregate convex polygon model is intersected with any line segment between the vertexes of all the thrown aggregate convex polygon models or not is judged, if yes, the aggregate interference condition is not met, and if not, the aggregate interference condition is met.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211174401.XA CN115482891A (en) | 2022-09-26 | 2022-09-26 | Construction method of recycled concrete mesoscopic random aggregate model based on convex polygon |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211174401.XA CN115482891A (en) | 2022-09-26 | 2022-09-26 | Construction method of recycled concrete mesoscopic random aggregate model based on convex polygon |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115482891A true CN115482891A (en) | 2022-12-16 |
Family
ID=84394824
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211174401.XA Pending CN115482891A (en) | 2022-09-26 | 2022-09-26 | Construction method of recycled concrete mesoscopic random aggregate model based on convex polygon |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115482891A (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN116663378A (en) * | 2023-05-23 | 2023-08-29 | 合肥工业大学 | Grading optimization method considering morphology of reclaimed sand particles |
| CN116913432A (en) * | 2023-07-25 | 2023-10-20 | 中国人民解放军陆军工程大学 | Reconstruction method of propellant simulated filling model based on polygonal grid |
| CN117077501A (en) * | 2023-10-17 | 2023-11-17 | 中南大学 | Heterogeneous steel slag concrete permeability coefficient calculation method |
-
2022
- 2022-09-26 CN CN202211174401.XA patent/CN115482891A/en active Pending
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN116663378A (en) * | 2023-05-23 | 2023-08-29 | 合肥工业大学 | Grading optimization method considering morphology of reclaimed sand particles |
| CN116663378B (en) * | 2023-05-23 | 2024-06-04 | 合肥工业大学 | Grading optimization method considering morphology of reclaimed sand particles |
| CN116913432A (en) * | 2023-07-25 | 2023-10-20 | 中国人民解放军陆军工程大学 | Reconstruction method of propellant simulated filling model based on polygonal grid |
| CN117077501A (en) * | 2023-10-17 | 2023-11-17 | 中南大学 | Heterogeneous steel slag concrete permeability coefficient calculation method |
| CN117077501B (en) * | 2023-10-17 | 2024-01-09 | 中南大学 | Heterogeneous steel slag concrete permeability coefficient calculation method |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN115482891A (en) | Construction method of recycled concrete mesoscopic random aggregate model based on convex polygon | |
| Zhang et al. | 3D meso-scale modeling of reinforcement concrete with high volume fraction of randomly distributed aggregates | |
| CN110706352B (en) | Concrete three-phase mesoscopic model construction and internal chloride ion erosion numerical simulation method based on polygonal random aggregate | |
| Leschok et al. | 3D printing facades: Design, fabrication, and assessment methods | |
| Ma et al. | A novel numerical scheme for random parameterized convex aggregate models with a high-volume fraction of aggregates in concrete-like granular materials | |
| Wu et al. | Mesoscopic study of the mechanical properties of coral aggregate concrete under complex loads | |
| CN104899393A (en) | Modeling method of dispersed-phase reinforced composite material meso-structure | |
| Wang et al. | Strength improvement of cement emulsified asphalt mixture through aggregate gradation design | |
| Qin et al. | Numerical analysis of fracturing behavior in fully-graded concrete with oversized aggregates from mesoscopic perspective | |
| Fu et al. | Experimental and DEM investigation of axially-loaded behaviours of IWP-based structures | |
| CN113591195A (en) | Construction method of recycled concrete mesoscopic model based on random polygonal aggregate | |
| Zheng et al. | Mesoscale models and uniaxial tensile numerical simulations of concrete considering material heterogeneity and spatial correlation | |
| Yao et al. | Literature review on the discrete element method in asphalt mixtures | |
| CN115050431B (en) | Modeling analysis method for three-dimensional microstructure of cement stabilized recycled aggregate | |
| Nguyen et al. | Numerical approach to predict the flexural damage behavior of pervious concrete | |
| Jin et al. | Experimental and computational modeling of chloride transport behavior in fully recycled coarse aggregate concrete | |
| Daynes | High stiffness topology optimised lattice structures with increased toughness by porosity constraints | |
| CN117113686A (en) | Concrete aggregate two-dimensional geometric structure random generation method based on coordinate grid | |
| CN115525961B (en) | Method for analyzing binding power of heterogeneous bottom-sealing concrete and steel casing | |
| Guo et al. | A 3D FEM mesoscale numerical analysis of concrete tensile strength behaviour | |
| Zhu et al. | Buildability of complex 3D-printed concrete geometries using Peridynamics | |
| Wei et al. | Mesoscopic asphalt pavement response analysis using a random aggregate generation-based concurrent multiscale method | |
| CN115205486A (en) | Concrete three-dimensional microscopic numerical model construction method and chloride ion transmission simulation system | |
| CN114925590A (en) | Aggregate generation algorithm and construction method of reclaimed water stable aggregate discrete element numerical model | |
| Liang et al. | Rapid method for building a two-dimensional model of mixed aggregate concrete |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |