Parameterization construction method of recycled concrete two-dimensional mesoscopic numerical model

Abstract

The invention provides a parameterization construction method of a two-dimensional mesoscopic numerical model of recycled concrete. The parameterization construction method comprises the following steps: 1) calculating the particle number and the particle size of recycled concrete aggregate and the thickness of an old mortar layer; 2) constructing a geometric model of the recycled concrete two-dimensional random circular aggregate test piece; 3) constructing a geometric model of the recycled concrete two-dimensional random convex polygon aggregate test piece; (4) carrying out unstructured grid division; and 5) constructing a projection grid model of the recycled concrete. According to the method, the problem that the geometric space structure of the recycled concrete is complex can be effectively solved, the established geometric model can truly reflect the actual grading, content and shape of the aggregate in the recycled concrete, the problem that grid division is difficult can be effectively solved, and the established grid model has extremely high unit quality.

Description

Technical Field

[0001] The invention relates to the technical field of building materials, and in particular to a parameterized construction method of a two-dimensional mesoscopic numerical model of recycled concrete. Background Art

[0002] With the rapid development of the global economy, the construction industry has experienced significant growth worldwide, and the demand for construction materials has continued to increase, especially in countries such as China, India, and Brazil. However, this growth is accompanied by a large amount of resource consumption and environmental problems, such as the increase in construction waste and the intensification of carbon dioxide emissions. Therefore, studying how to better utilize construction waste has become an important topic in the current construction industry.

[0003] As a sustainable building material, recycled concrete has great application potential. The basic principle of recycled concrete is to clean, crush and grade the aggregates in the waste concrete, and then add them into a new cement matrix in a certain proportion to partially or completely replace the natural aggregates to prepare new concrete. Although recycled concrete helps to save natural resources and reduce environmental pollution, due to the complexity of its internal structure, the mechanical properties of recycled concrete at the macro and micro levels show great differences. Its performance is affected by the replacement rate of recycled aggregates, the presence of old mortar, and the characteristics of the interface transition zone. Therefore, a deep understanding of the mesostructural characteristics of recycled concrete is crucial to optimizing its macroscopic mechanical properties.

[0004] At present, some studies have used numerical simulation methods to analyze the mechanical behavior of recycled concrete. Mesoscopic mechanical models provide an effective means to understand the damage evolution inside recycled concrete. These models usually regard recycled concrete as a five-phase composite material consisting of natural aggregate, old cement mortar, new cement mortar, old interface transition zone between natural aggregate and old cement mortar, and new interface transition zone between old cement mortar and new cement mortar. Traditional mesoscopic models mostly use the shape of circular simplified aggregates and adopt a uniform structured grid division method. They do not consider the interface transition zone or simplify the interface transition zone, which is difficult to meet the requirements for model accuracy in engineering practice. Summary of the invention

[0005] In order to solve the problems of complex geometric space structure, difficult meshing and thin interface transition zone that are difficult to simulate in the mesoscopic modeling of recycled concrete, the present invention proposes a parameterized construction method for a two-dimensional mesoscopic numerical model of recycled concrete in response to the technical problems existing in the above-mentioned background technology.

[0006] In order to solve the above technical problems, the present invention provides a parameterized construction method of a two-dimensional mesoscopic numerical model of recycled concrete, which comprises the following steps:

[0007] 1) Calculate the number of particles, particle size and thickness of the old mortar layer of recycled concrete aggregate;

[0008] 2) Construction of geometric model of two-dimensional random circular aggregate specimens of recycled concrete

[0009] After the aggregate particles were generated, the geometric model of the two-dimensional random circular aggregate specimen of recycled concrete was established by the “pick-and-place method”;

[0010] 3) Construction of geometric model of two-dimensional random convex polygonal aggregate specimens of recycled concrete

[0011] First, the inscribed polygon of each outer circle of the recycled concrete circular aggregate is extended outward, and then the inscribed polygon of each inner circle of the recycled concrete circular aggregate is extended outward, until the areas of the outer circle and the inner circle are reached respectively, thus generating a geometric model of a recycled concrete two-dimensional random convex polygon aggregate specimen with the same area as the circular aggregate;

[0012] 4) Unstructured grid division

[0013] Considering the boundary of the interface transition zone between aggregate and matrix in recycled concrete and the mesh refinement of the interface transition zone, a high-quality recycled concrete mesh model is obtained by using the mesh generation algorithm of the geometric shape specified by the implicit function.

[0014] 5) Construction of recycled concrete projection grid model.

[0015] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein the step 1) specifically comprises the following steps:

[0016] 1.1) Calculate the particle number and gradation of recycled concrete aggregate

[0017] The Walraven formula is used to calculate the number of aggregate particles with different particle sizes in the two-dimensional cross section. The cumulative distribution probability of aggregate with particle size D<D0 is as follows:

[0018]

[0019] Where P k is the percentage of aggregate volume to total concrete volume; P c is the cumulative distribution probability of aggregate with particle size less than D0;

[0020] The formula for calculating the number of aggregate particles n with a particle size of D1<D<D2 in a recycled aggregate concrete specimen with a cross-sectional area of ​​A is as follows:

[0021] n=[P c (D<D2)-P c (D<D1)]×A / A i ;

[0022] In the formula, A i is the area of ​​recycled aggregate with diameter D;

[0023] 1.2) Calculate the thickness of the old mortar layer of recycled aggregate

[0024] On the premise that the volume percentage of aggregate in concrete is equal to the area percentage of aggregate at a certain section, calculate the area ratio of old mortar and natural aggregate in the recycled aggregate at a certain section, and then find the thickness of the old mortar layer in the recycled aggregate:

[0025]

[0026] Where V s ,V g Respectively represent the area occupied by old mortar and aggregate in the recycled aggregate; ρ s ,ρ g Represent the density of old mortar and aggregate respectively; m s ,m 总 Respectively represent the mass of old mortar and recycled aggregate; ω represents the mass content of old mortar; It represents the ratio of the old mortar area to the aggregate area;

[0027] The mortar layer thickness h is obtained from the ratio of the old mortar area to the aggregate area:

[0028]

[0029] Where a represents the aggregate particle size.

[0030] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein: the step 1) is to regard the recycled concrete as a five-phase composite material consisting of natural aggregate, old cement mortar, new cement mortar, old interface transition zone between natural aggregate and old cement mortar, and new interface transition zone between old cement mortar and new cement mortar at the mesoscopic level.

[0031] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein the process of establishing the two-dimensional recycled aggregate random distribution geometric model by the "pick and place method" in step 2) is: using the coordinates generated by the random number generator to place the aggregate particles, and checking whether the placed particles meet the requirements, the aggregates are placed in a certain space in the order from the largest particle to the smallest particle until the specified volume fraction is reached; and each aggregate randomly selects a position in a certain space for placement, and a particle of an aggregate is placed at this position. If this position overlaps with the particles of the existing aggregate, the position is reselected until a suitable non-overlapping space is found; the aggregate placement process is described by the following mathematical model:

[0032] P new =(xnew ,y new );

[0033] Where, P new is the new particle position, x new ,y new are the coordinates of the new position and should satisfy:

[0034] ‖P new -P i ‖>r i +r new ;

[0035] Where P i is the position of the existing particle, r i and r new are the radii of the existing particles and the new particles respectively.

[0036] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein the specific process of step 3) is as follows:

[0037] 3.1) Randomly generate several points on the circumference of each circular aggregate as the polygonal aggregate base frame; note that the number of base points of the large aggregate is greater than that of the small aggregate, and control the distance between the base points of the large aggregate and the small aggregate so that the centers of the large aggregate and the small aggregate are inside the generated polygonal aggregate base frame;

[0038] 3.2) The polygonal aggregate framework generated on the circumference of each circular aggregate is extended outwards in sequence until the area of ​​the circular aggregate in the inner cross section of the two-dimensional random circular aggregate specimen of recycled concrete is reached; the polygonal aggregate framework with a much smaller area than the corresponding circular aggregate is preferably selected, and the longer side is selected to extend outwards; for each vertex A1, A2, ..., A i , A i+1 , …, A n ; Polygonal aggregate base frame vertex A i The coordinates of (x i ,y i ), A i+1 The coordinates of (x i+1 ,y i+1 );

[0039] The coordinates of the new insertion point that is convex to the outward extension are:

[0040]

[0041] In the formula, R1, R2 are random numbers in the interval (0,1);

[0042] When the area of ​​the convex polygonal aggregate after extension is greater than or equal to the area of ​​the corresponding circular aggregate, the extension ends.

[0043] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete comprises: compiling automatic generation software of a convex polygonal aggregate geometric model through the steps (1) to (3), using the automatic generation software to transform the two-dimensional random circular aggregate geometric model of recycled concrete into a two-dimensional random convex polygonal aggregate geometric model of recycled concrete, wherein the two-dimensional random circular aggregate geometric model of recycled concrete and the two-dimensional random convex polygonal aggregate geometric model of recycled concrete have the same aggregate gradation, corresponding aggregate content and old mortar content, but different aggregate shapes;

[0044] The main program flow of converting the two-dimensional random circular aggregate geometric model of recycled concrete into the two-dimensional random convex polygonal aggregate geometric model of recycled concrete by using the automatic generation software of the convex polygonal aggregate geometric model is as follows:

[0045] (1) Input round aggregate information

[0046] Input information about recycled concrete circular aggregates. This information includes physical parameters such as location, gradation, and old mortar content of circular aggregates;

[0047] (2) Generate a polygonal base frame on the old mortar boundary

[0048] According to the recycled concrete circular aggregate information, a polygonal old mortar base frame is created on the old mortar boundary;

[0049] (3) Extended convex polygonal old mortar base frame;

[0050] (4) Generate a polygonal natural aggregate base frame on the natural aggregate boundary

[0051] (5) Extended polygonal natural aggregate base frame;

[0052] (6) Output convex polygon aggregate information

[0053] After completing the generation and extension of all frames, the final convex polygon aggregate information is output.

[0054] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein the newly inserted point must meet the following requirements: ① the newly inserted point cannot exceed the specimen size range; ② the newly formed side length must be greater than the set minimum value; ③ the convex condition is satisfied; ④ for the extension and convexity of the old mortar boundary, it is necessary to ensure that there is no cross-overlap between the aggregates, and the extension and convexity of the natural aggregate boundary must ensure that the extension and convexity point is within the corresponding old mortar boundary.

[0055] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein the specific process of step 4) is as follows:

[0056] 4.1) Meshing of 2D microscopic model of recycled concrete

[0057] Based on the physical analogy between the edge of the triangular element and the truss structure, the linear force-displacement relationship is used to solve the equilibrium problem in the truss structure to improve the initial mesh. The specific solution process is:

[0058] The difference between the ideal length and the current length of each edge of the triangular element is set as the spring force. The mesh is adjusted by updating the node position and recalculating the Delaunay triangulation until the node system reaches a balanced state. The node update formula is:

[0059]

[0060] In the above formula, k is the coefficient of simulating the linear spring rod, which can be set to 1. When F>0, the mesh boundary is stretched. For all internal nodes, there is a balance: For most rods, the force is repulsive, i.e., F>0, to help the nodes spread out within the entire geometric boundary;

[0061] The ideal length l0 of the side of a triangular element is described by the mesh size function h(x,y), which does not have to be equal to the actual size. The mesh size function h(x,y) gives the relative distribution over the domain;

[0062]

[0063] h(x i ,y i )=min(min(a+b*{|d(x i ,y i )|}),c);

[0064] In the above formula, d(x i ,y i ) is the distance function, {|d(x i ,y i )|} is the point (x i ,y i ) is the set of absolute values ​​of the distances from the interface to each aggregate; a, b, c are the relative size parameters of the mesh at the interface;

[0065] 4.2) Formation of boundary layer inside the mesh in the interface transition zone

[0066] During the mesh generation process, when the nodes are within a certain range hp from the geometric boundary of the aggregate, these nodes will be "pulled back" to the nearest position on the boundary of the interface transition zone; the thickness of the interface transition zone is h, and it is assumed that the distance from the aggregate to the geometric boundary of the aggregate is ±h / 2 as the interface transition zone, and the points within the range hp from the boundary of the interface transition zone need to be moved and corrected to the nearest point on its boundary; the node correction distance hp can be taken as 20% to 50% of the thickness of the interface transition zone h, that is, hp = 0.2h to 0.5h, to ensure that the correction range is reasonable;

[0067] The first-order Taylor approximation is used to calculate the node correction distance vector to form the internal boundary layer; the correction distance refers to the correction amount of the node from the current position to the nearest interface transition zone boundary; assuming a node P and interface function F(P) are given, the corrected node position P′ can be obtained by the formula:

[0068] P' = P + ΔP;

[0069] And the node correction distance vector ΔP is approximately calculated by the first-order Taylor expansion:

[0070]

[0071] 4.3) Meshing of 2D microscopic model of recycled concrete

[0072] 4.3.1) Create uniformly distributed nodes within the geometric boundary, corresponding to equilateral triangle elements;

[0073] 4.3.2) Calculate the size function h(x,y) of each node and use the rejection sampling method with 1 / h(x i ,y i ) 2 The probability of selecting nodes is 1 / 2; the mesh refinement gradient inside and outside the natural aggregate is set respectively, and the maximum mesh size is specified;

[0074] 4.3.3) Enter the main loop of mesh optimization, and continuously iterate and optimize the node positions until a certain convergence standard is met

[0075] 4.3.4) Terminate the loop. The termination condition is determined by the maximum motion displacement of the node in the current iteration. The maximum motion displacement of the node is obtained by the following formula:

[0076]

[0077] Where ΔP max is the maximum motion displacement of all nodes in the current iteration; Δx i and Δy i are the displacements of the ith node in the x and y directions, respectively.

[0078] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein the specific steps of step 4.3.3) entering the main loop of grid optimization are as follows:

[0079] 4.3.3.1) Remove triangular meshes whose centroids are outside the geometric boundary;

[0080] 4.3.3.2) Calculate the ideal triangle side length through the mesh size function h(x,y), adjust the side length and move nodes based on the difference with the actual side length;

[0081] 4.3.3.3) If a node moves outside the geometric boundary of the two-dimensional random circular aggregate specimen geometric model of recycled concrete and the two-dimensional random convex polygonal aggregate specimen geometric model of recycled concrete after updating, move it back to the nearest point on its boundary to avoid node loss;

[0082] 4.3.3.4) Set the node correction distance hp, and pull the points within the interface transition zone hp back to the boundary of the interface transition zone to form an internal boundary layer.

[0083] The parameterized construction method of the two-dimensional microscopic numerical model of recycled concrete, wherein: the specific process of the step (5) is: firstly establish a geometric model of the recycled concrete specimen and mesh it, then project the recycled concrete aggregate to the grid unit area; determine its unit type by judging the relative position of each grid unit node; finally, assign material parameters to the generated units.

[0084] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein the process of determining its unit type is: when all nodes of the unit fall in the natural aggregate area, this unit will be defined as a natural aggregate unit; when all nodes fall in the old mortar area, this unit is defined as an old mortar unit; when all nodes fall in the new mortar area, this unit is defined as a new mortar unit; and when some nodes are in the natural aggregate area and some fall in the old mortar area, they will be defined as old interface transition zone units; when some nodes are in the old mortar area and some fall in the new mortar area, this unit is a new interface transition zone unit.

[0085] By adopting the above technical solution, the present invention has the following beneficial effects:

[0086] The parametric construction method of the two-dimensional mesoscopic numerical model of recycled concrete of the present invention is reasonably conceived and can effectively solve the problem of complex geometric space structure of recycled concrete; through parametric construction, the geometric model of recycled concrete can truly reflect the actual gradation, content and shape of aggregate, ensuring the authenticity and accuracy of the model, and providing a reliable basis for mechanical analysis at the mesoscopic level.

[0087] The present invention proposes a new method for optimizing unstructured meshes with interface alignment, which successfully solves the problem of difficult traditional mesh division. The present invention refines the mesh of the interface transition zone while considering the interface transition zone between aggregate and matrix in recycled concrete, and generates a mesh model with extremely high unit quality by using a mesh generation algorithm of geometric shapes specified by implicit functions. The established mesh model not only improves the accuracy of finite element analysis, but also effectively reduces the amount of calculation and improves the calculation efficiency.

[0088] The present invention has significant advantages in the parametric construction and high-quality meshing of the mesoscopic numerical model of recycled concrete, solves the key problems in the prior art, is suitable for recycled concrete specimen models of different shapes and sizes, and provides strong technical support for the numerical simulation and engineering application of recycled concrete. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0090] Figure 1 Construct a flow chart for a two-dimensional mesoscopic numerical model of recycled concrete;

[0091] Figure 2 This is a schematic diagram of the mesostructure of recycled concrete;

[0092] Figure 3 This is a schematic diagram of the mesostructure of recycled convex aggregate concrete;

[0093] Figure 4 Generate schematic diagrams for new vertices;

[0094] Figure 5 Generate process diagrams for polygonal aggregates;

[0095] Figure 6 The main program flow chart for establishing polygonal aggregate model;

[0096] Figure 7 Schematic diagram of the process of generating the geometric model of random convex polygon aggregate of recycled concrete ( Figure 6 Middle: (a) Random circular aggregate model of recycled concrete, (b) Generate an inscribed polygon on the outer circle (blue line) and extend it outward as the outer boundary of the convex recycled aggregate (black line), (c) Generate an inscribed polygon on the inner circle (blue line) and extend it outward as the outer boundary of the convex natural aggregate (black line), (d) Random convex polygonal aggregate model of recycled concrete);

[0097] Figure 8 This is a diagram of the interface layer formation process;

[0098] Fig. 9 This is a diagram of the mesh generation process;

[0099] Fig.10 Schematic diagram of mesh quality;

[0100] Fig.11 It is a schematic diagram of the projection grid model;

[0101] Fig.12 It is the projection grid model and unit mass diagram of the circular aggregate recycled concrete square slab;

[0102] Fig.13 This is the projection grid model and unit mass diagram of the convex aggregate recycled concrete square slab. DETAILED DESCRIPTION

[0103] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0104] The present invention is further explained below in conjunction with specific implementation modes.

[0105] like Figure 1 As shown, this embodiment provides a parameterized construction method of a two-dimensional mesoscopic numerical model of recycled concrete, which includes the following steps:

[0106] S100, calculate the particle number and particle size of recycled concrete aggregate and the thickness of the old mortar layer;

[0107] At the microscopic level, recycled aggregate concrete is considered as a five-phase composite material consisting of natural aggregate, old cement mortar, new cement mortar, old interface transition zone between natural aggregate and old cement mortar, and new interface transition zone between old cement mortar and new cement mortar. Figure 2 shown.

[0108] S101. Calculate the particle number and gradation of recycled concrete aggregate

[0109] The Walraven formula is used to calculate the number of aggregate particles with different particle sizes in the two-dimensional cross section. The cumulative distribution probability of aggregate with particle size D<D0 is as follows:

[0110]

[0111] Where P kIt is the percentage of aggregate volume to total concrete volume, generally 0.75; P c is the cumulative distribution probability of aggregate with particle size less than D0.

[0112] The formula for calculating the number of aggregate particles n with a particle size of D1<D<D2 in a recycled aggregate concrete specimen with a cross-sectional area of ​​A is as follows:

[0113] n=[P c (D<D2)-P c (D<D1)]×A / A i ;

[0114] In the formula, A i is the area of ​​recycled aggregate with diameter D.

[0115] S102, thickness of recycled aggregate old mortar layer

[0116] The volume percentage of aggregate in concrete is basically equal to the area percentage of aggregate at a certain section. From this, the area ratio of old mortar and natural aggregate in the recycled aggregate at a certain section can be calculated, and then the thickness of the old mortar layer in the recycled aggregate can be calculated.

[0117]

[0118] Where V s ,V g Respectively represent the area occupied by old mortar and aggregate in recycled aggregate, ρ s ,ρ g Represent the density of old mortar and aggregate, m s ,m 总 Respectively represent the mass of old mortar and recycled aggregate, ω represents the mass content of old mortar, It represents the ratio of old mortar area to aggregate area.

[0119] The mortar layer thickness h is obtained from the area ratio.

[0120]

[0121] In the formula, a represents the aggregate particle size.

[0122] S200, Construction of geometric model of two-dimensional random circular aggregate specimens of recycled concrete

[0123] After the aggregate particles are generated, the aggregate needs to be placed in a certain space. The present invention adopts the "pick-and-place method" to establish a two-dimensional recycled aggregate random distribution geometric model; specifically: the "pick-and-place method" is used to place the aggregates in a certain space in the order from the largest particle to the smallest particle until the specified volume fraction is reached; starting from the largest particle instead of the smallest particle, the aggregate is placed in the specified space, which can greatly improve the efficiency of the aggregate placement algorithm; the coordinates generated by the random number generator are used to place the aggregate particles, and it is checked whether the placed particles meet the requirements; and each aggregate randomly selects a position in a certain space for placement, and a particle of an aggregate is placed at this position; if this position overlaps with the particles of the existing aggregate, the position is reselected until a suitable non-overlapping space is found; the aggregate placement process is described by the following mathematical model:

[0124] P new =(x new ,y new );

[0125] Where, P new is the new particle position, x new ,y new are the coordinates of the new position and should satisfy:

[0126] ‖P new -P i ‖>r i +r new ;

[0127] Where P i is the position of the existing particle, r i and r new are the radii of the existing particles and the new particles respectively.

[0128] S300, Geometric model of two-dimensional random convex polygonal aggregate specimens of recycled concrete

[0129] Based on the geometric model of the two-dimensional random circular aggregate specimen of recycled concrete, a random polygonal aggregate specimen model is generated. Specifically, the inscribed polygon of each outer circle of the recycled concrete circular aggregate is extended outward, and then the inscribed polygon of each inner circle of the recycled concrete circular aggregate is extended outward until the area of ​​the outer circle and the inner circle are reached respectively, so that the geometric model of the two-dimensional random convex polygonal aggregate specimen of recycled concrete with the same area as the circular aggregate is generated, as shown in FIG. Figure 3 shown.

[0130] S301, randomly generate several points on the circumference of each circular aggregate as a polygonal aggregate base frame. Note that the number of base points of the large aggregate is greater than the number of base points of the small aggregate, and control the distance between the base points of the large aggregate and the small aggregate so that the centers of the large aggregate and the small aggregate are inside the generated polygonal aggregate base frame.

[0131] S302, sequentially extending the polygonal aggregate base frame generated on the circumference of each circular aggregate outward until the area of ​​the inner cross section of the two-dimensional random circular aggregate specimen of recycled concrete occupied by the circular aggregate is reached; preferentially selecting a polygonal aggregate base frame that is much smaller than the area of ​​the corresponding circular aggregate, and selecting a longer side to extend outward;

[0132] like Figure 4 As shown, for each vertex A1, A2, ..., A of any polygonal aggregate base frame i , A i+1 , …, A n ; Polygonal aggregate base frame vertex A i The coordinates of (x i ,y i ), A i+1 The coordinates of (x i+1 ,y i+1 );

[0133] The coordinates of the new insertion point that is convex to the outward extension are:

[0134]

[0135] Where R1 and R2 are random numbers in the interval (0,1).

[0136] At the same time, the newly inserted points must meet the following requirements: ① The newly inserted points cannot exceed the specimen size range; ② The newly formed side length must be greater than the set minimum value; ③ The convex condition must be met; ④ For the extension and convexity of the old mortar boundary, it is necessary to ensure that there is no cross-overlap between the aggregates, and the extension and convexity of the natural aggregate boundary must ensure that the extension and convexity points are within the corresponding old mortar boundary.

[0137] When the area of ​​the polygon after convexification is greater than or equal to the corresponding circle area, the convexification ends. Figure 5 shown.

[0138] The method of the above steps S100-S300 is used to compile automatic generation software for the convex polygonal aggregate geometric model, and the automatic generation software is used to transform the two-dimensional random circular aggregate geometric model of recycled concrete into a two-dimensional random convex polygonal aggregate geometric model of recycled concrete. The aggregate grading, corresponding aggregate content and old mortar content of the two-dimensional random circular aggregate geometric model of recycled concrete and the two-dimensional random convex polygonal aggregate geometric model of recycled concrete are the same, but the aggregate shape is different.

[0139] The main program flow of using this automatic generation software to transform the two-dimensional random circular aggregate geometric model of recycled concrete into the two-dimensional random convex polygonal aggregate geometric model of recycled concrete is as follows (e.g. Figure 6 ):

[0140] (1) Input round aggregate information

[0141] Input information about recycled concrete circular aggregates. This information includes physical parameters such as location, gradation, and old mortar content of circular aggregates;

[0142] (2) Generate a polygonal base frame on the old mortar boundary

[0143] According to the recycled concrete circular aggregate information, a polygonal old mortar base frame is created on the old mortar boundary;

[0144] (3) Extended convex polygonal old mortar base frame;

[0145] (4) Generate a polygonal natural aggregate base frame on the natural aggregate boundary

[0146] (5) Extended polygonal natural aggregate base frame;

[0147] (6) Output convex polygon aggregate information

[0148] After completing the generation and extension of all frames, the final convex polygon aggregate information is output.

[0149] like Figure 7 The figure shows the generation process of the two-dimensional random convex polygonal aggregate geometric model of recycled concrete: (a) Two-dimensional random circular aggregate model of recycled concrete; (b) Generate an inscribed polygon on the outer circle (blue line); and extend it outward as the outer boundary of the convex recycled aggregate (black line); (c) Generate an inscribed polygon on the inner circle (blue line), and extend it outward as the outer boundary of the convex natural aggregate (black line); (d) Two-dimensional random convex polygonal aggregate geometric model of recycled concrete.

[0150] S400, unstructured meshing

[0151] After generating the geometric model of the two-dimensional random circular aggregate specimen of recycled concrete and the geometric model of the two-dimensional random convex polygonal aggregate specimen of recycled concrete, it is necessary to mesh them. In order to generate high-quality meshes, the mesh generation algorithm of the geometric shape specified by the implicit function is used, the boundary of the interface transition zone and the mesh refinement are considered, and the optimization and application are applied to the recycled concrete model to obtain a high-quality recycled concrete mesh model.

[0152] S401. Meshing of 2D microscopic model of recycled concrete

[0153] Based on the physical analogy between the edges of triangular elements and truss structures, the linear force-displacement relationship is used to solve the equilibrium problem in the truss structure to improve the initial mesh; the specific solution process is:

[0154] The difference between the ideal length and the current length of each edge of the triangular element is set as the spring force, and the mesh is adjusted by updating the node position and recalculating the Delaunay triangulation (any set of points can be triangulated by the Delaunay algorithm, that is, generating triangular elements that meet the Delaunay conditions and ensuring that no point is located within the circumscribed circle of any triangle) until the node system reaches a state of equilibrium; when the node moves, the mesh is optimized by recalculating the Delaunay triangulation or by local updating to improve the unit quality; in the equilibrium state, the unit tends to have a high quality, and this method can be extended to higher dimensions.

[0155] The force F on each edge of a triangle element depends on the difference between its current length l and its ideal length l0:

[0156]

[0157] Where k is the coefficient for simulating a linear spring bar and can be set to 1. When F>0, the mesh boundary is stretched. For all internal nodes, there is a balance: For most rods, the force is repulsive (F>0) to help the node expand within the entire geometric boundary. This means that when the current length is near the ideal length, F should be greater than zero. This can be achieved by appropriately scaling the desired ideal length, usually 20% (Fscale=1.2).

[0158] The ideal length l0 of the side of the triangular element is described by the mesh size function h(x,y). Note that h(x,y) does not have to be equal to the actual size. The mesh size function gives the relative distribution over the domain. To avoid large changes in the element size, this is achieved by limiting the gradient in h(x,y).

[0159]

[0160] h(x i ,y i )=min(min(a+b*{|d(x i ,y i )|}),c);

[0161] Among them, d(x i ,y i ) is the distance function, {|d(x i ,y i )|} is the point (x i ,y i ) is the set of absolute values ​​of the distances to each aggregate interface; a, b, c are the relative size parameters of the mesh at the interface.

[0162] S402, formation of boundary layer inside the grid in the interface transition zone

[0163] During the mesh generation process, when nodes are within a certain range hp from the aggregate geometric boundary (the "certain range" here means that the distance between the node and the aggregate geometric boundary is less than a certain threshold. The nodes within this range will be corrected to the position closest to the interface transition zone boundary, usually this threshold is several millimeters), these nodes will be "pulled back" to the position closest to the interface transition zone boundary. Figure 8 , the thickness of the interface transition zone is h, and the node correction distance is hp. Then we can simply assume that the distance from the aggregate to the geometric boundary ±h / 2 is the interface transition zone, and the points within the range of hp from the boundary of the interface transition zone need to be moved and corrected to the nearest point on its boundary; the node correction distance hp can be taken as 20% to 50% of the thickness of the interface transition zone h, that is, hp = 0.2h to 0.5h, to ensure that the correction range is reasonable;

[0164] The first-order Taylor approximation is used to calculate the node correction distance vector to form the internal boundary layer; the correction distance refers to the correction amount of the node from the current position to the nearest interface transition zone boundary; assuming a point P and an interface function F(P) are given, the corrected node position P′ can be obtained by the following formula:

[0165] P' = P + ΔP;

[0166] And the node correction distance vector ΔP is approximately calculated by the first-order Taylor expansion:

[0167]

[0168] S403. Meshing of 2D microscopic model of recycled concrete

[0169] Taking a 100×100mm two-dimensional specimen as an example, a recycled round aggregate with a radius of 25mm is placed in the center of the specimen, where the thickness of the old mortar is 5mm and the interface transition zone is 1mm; the process of meshing the specimen is as follows:

[0170] S4031. Create uniformly distributed nodes within the geometric boundary, corresponding to equilateral triangle units, such as Fig. 9 (a) shows an equilateral triangle grid with a side length of 1 mm;

[0171] S4032, calculate the size function h(x,y) of each node, and use the rejection sampling method to calculate the size function h(x,y) of each node. i ,y i ) 2The probability of selecting nodes is 1 / 2 (in order to adjust the mesh size more accurately, it is necessary to select nodes through rejection sampling, which is a way of selecting nodes with a specific probability in the model area); set the mesh refinement gradient inside and outside the natural aggregate separately, and specify the maximum mesh size; such as Fig. 9 As shown in (b), inside the natural aggregate, the mesh refinement gradient is 1, outside the natural aggregate, the mesh refinement gradient is 0.2, and the maximum mesh size is specified to be 3 mm.

[0172] S4033, enter the main loop, the node position is continuously iteratively optimized until a certain convergence standard is met; and the main loop steps are as follows:

[0173] ① Remove the triangular mesh whose centroid is outside the geometric boundary;

[0174] ② Calculate the ideal triangle side length through the grid size function h(x,y), adjust the side length and move the nodes based on the difference with the actual side length; Fig. 9 (c) shows the Delaunay triangulation diagram after the first node movement;

[0175] ③ If a node moves outside the geometric boundaries of the two-dimensional random circular aggregate specimen geometric model of recycled concrete and the two-dimensional random convex polygonal aggregate specimen geometric model of recycled concrete after updating, it will be moved back to the nearest point on its boundary to avoid node loss;

[0176] ④ Set the node correction distance hp, pull the points at a certain distance from the interface transition zone hp back to the boundary of the interface transition zone to form an internal boundary layer.

[0177] S4034, terminate the loop. The termination condition is determined by the maximum motion displacement of the node in the current iteration. The maximum motion displacement of the node is obtained by the following formula:

[0178]

[0179] In the formula, ΔP max is the maximum motion displacement of all nodes in the current iteration; Δx i and Δy i are the displacements of the ith node in the x and y directions, respectively.

[0180] like Fig. 9 (d) Fig. 9 (e) and Fig. 9As shown in (f), assuming that the interface transition zone is 1mm, these are the Delaunay mesh diagrams after the 1st, 5th and 100th iterations. It can be seen from the figure that as the iteration proceeds, the mesh quality becomes higher and higher, and the final triangular elements are almost equilateral. A commonly used mesh quality evaluation index is the ratio of the radius of the largest inscribed circle (multiplied by 2) to the radius of the smallest circumscribed circle:

[0181]

[0182] Where a, b, c are the side lengths. As a rule of thumb, if q>0.5 for all triangles, the result is good.

[0183] Fig.10 Respectively Fig. 9 (d) Fig. 9 (e) and Fig. 9 (f) Histogram after calculating the grid quality, given by Fig.10 It can be seen that with the iteration to optimize the mesh quality, the quality and uniformity of the mesh units generated by the algorithm are getting better and better. At the 100th iteration, q>0.6 for all units, and the average quality is 0.9359, that is, the generated mesh quality is extremely high.

[0184] It should be noted that since the natural aggregate unit strength is often high, it rarely suffers damage under load. At the same time, in order to reduce the calculation scale, different mesh refinement parameters are adopted inside and outside the natural aggregate to reduce the overall degrees of freedom of the specimen.

[0185] S500, Recycled Concrete Projection Grid Model

[0186] First, the overall model of the recycled concrete specimen is established and meshed. Then, the recycled concrete aggregate (including circular aggregate and convex polygonal aggregate) is projected to the grid unit area. The unit type is determined by judging the relative position of the unit nodes, and the material parameters of the generated units are assigned. When all the nodes of the unit fall in the natural aggregate area, this unit will be defined as a natural aggregate unit; when all the nodes fall in the old mortar area, this unit is defined as an old mortar unit; when all the nodes fall in the new mortar area, this unit is defined as a new mortar unit; and when some nodes are in the natural aggregate area and some fall in the old mortar area, they will be defined as old interface transition zone units; when some nodes are in the old mortar area and some fall in the new mortar area, this unit is a new interface transition zone unit. Finally, the material parameters of the generated units are assigned. Fig.11(a), the light blue area represents the new mortar matrix, the blue area represents the old mortar matrix, the red area is the natural aggregate, and the white thin layer area around the recycled aggregate particles is the interface transition zone. In addition, using the same method, a high-quality projection mesh model can also be generated for the convex aggregate concrete model, such as Fig.11 (b) as shown.

[0187] Example Application

[0188] In the following example, a 100mm×100mm square specimen is used as a representative. It is assumed that the aggregate consists of three types of particle sizes: coarse aggregate, medium aggregate and fine aggregate, with diameters of 17.5, 12.5 and 7.5mm respectively, the aggregate content is 40%, the content of old mortar attached to the aggregate is 42%, the thickness of the interface transition zone is 0.25mm, and the number of particles of each size of aggregate is calculated using the Walraven formula. In the meshing, it is assumed that the initial mesh size is 0.25mm and the node correction range of the interface transition zone is 0.2mm. The random circular aggregate and convex polygonal aggregate specimen models of concrete and recycled concrete are established respectively, as shown in Figure 1. Figure 12-13 As shown in the figure, it can be seen that the average unit quality of each model is above 0.94, indicating that the units in each model are almost equilateral, and the model has a higher mesh quality. In addition, compared with the traditional mesh division, the mesh division method in the patent method can generate a background mesh model with adjustable thickness in the interface transition zone. In addition, by controlling the mesh encryption gradient, the number of degrees of freedom can be significantly reduced, and the mesh quality and uniformity are better.

[0189] (a) 100mm×100mm round aggregate recycled concrete square slab

[0190] Number of nodes: 50923; number of elements: 101285; average element quality: 0.9440.

[0191] (b) 100mm×100mm convex aggregate recycled concrete square slab

[0192] Number of nodes: 52066; number of elements: 103563; average element quality: 0.9429.

[0193] The present invention can effectively solve the problem of complex geometric space structure of recycled concrete. The established geometric model can truly reflect the actual gradation, content and shape of aggregate in recycled concrete. It can also effectively solve the problem of difficult grid division. The established grid model has extremely high unit quality.

[0194] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A parameterized construction method for a two-dimensional mesoscopic numerical model of recycled concrete, characterized in that: The following steps are involved: 1) Calculate the number of particles, particle size and thickness of the old mortar layer of recycled concrete aggregate; 2) Construction of geometric model of two-dimensional random circular aggregate specimens of recycled concrete After the aggregate particles are generated, the geometric model of the two-dimensional random circular aggregate specimen of recycled concrete is established by the "pick-and-place method"; 3) Construction of geometric model of two-dimensional random convex polygonal aggregate specimens of recycled concrete First, the inscribed polygon of each outer circle of the recycled concrete circular aggregate is extended outward, and then the inscribed polygon of each inner circle of the recycled concrete circular aggregate is extended outward, until the areas of the outer circle and the inner circle are reached respectively, thus generating a geometric model of a recycled concrete two-dimensional random convex polygon aggregate specimen with the same area as the circular aggregate; 4) Unstructured grid division Considering the boundary of the interface transition zone between aggregate and matrix in recycled concrete and the mesh refinement of the interface transition zone, a high-quality recycled concrete mesh model is obtained by using the mesh generation algorithm of the geometric shape specified by the implicit function. 5) Construction of recycled concrete projection grid model.

2. The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: The step 1) specifically comprises the following steps: 1.1) Calculate the particle number and gradation of recycled concrete aggregate The Walraven formula is used to calculate the number of aggregate particles with different particle sizes in the two-dimensional cross section. The cumulative distribution probability of aggregate with particle size D<D0 is as follows: Where P k is the percentage of aggregate volume to total concrete volume; P c is the cumulative distribution probability of aggregate with particle size less than D0; The formula for calculating the number of aggregate particles n with a particle size of D1<D<D2 in a recycled aggregate concrete specimen with a cross-sectional area of ​​A is as follows: n=[P c (D<D2)-P c (D<D1)]×A / A i ; In the formula, A i is the area of ​​recycled aggregate with diameter D; 1.2) Calculate the thickness of the old mortar layer of recycled aggregate On the premise that the volume percentage of aggregate in concrete is equal to the area percentage of aggregate at a certain section, calculate the area ratio of old mortar and natural aggregate in the recycled aggregate at a certain section, and then find the thickness of the old mortar layer in the recycled aggregate: Where V s ,V g Respectively represent the area occupied by old mortar and aggregate in the recycled aggregate; ρ s ,ρ g Represent the density of old mortar and aggregate respectively; m s ,m 总 Respectively represent the mass of old mortar and recycled aggregate; ω represents the mass content of old mortar; It represents the ratio of the old mortar area to the aggregate area; The mortar layer thickness h is obtained from the ratio of the old mortar area to the aggregate area: In the formula, a represents the aggregate particle size.

3. The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: The step 1) is to regard the recycled concrete as a five-phase composite material consisting of natural aggregate, old cement mortar, new cement mortar, old interface transition zone between natural aggregate and old cement mortar, and new interface transition zone between old cement mortar and new cement mortar at a microscopic level.

4. The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that The process of establishing a two-dimensional recycled aggregate random distribution geometric model by the "pick-and-place method" in step 2) is as follows: using the coordinates generated by the random number generator to place aggregate particles, and checking whether the placed particles meet the requirements, placing the aggregates in a certain space in the order from the largest particle to the smallest particle until the specified volume fraction is reached; and each aggregate randomly selects a position in a certain space for placement, and places an aggregate particle at this position. If this position overlaps with the existing aggregate particles, the position is reselected until a suitable non-overlapping space is found; the aggregate placement process is described by the following mathematical model: P new =(x new ,y new ); Where, P new is the new particle position, x new ,y new are the coordinates of the new position and should satisfy: ||P new -P i ||>r i +r new ; Where P i is the position of the existing particle, r i and r new are the radii of the existing particles and the new particles respectively.

5. The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: The specific process of step 3) is as follows: 3.1) Randomly generate several points on the circumference of each circular aggregate as the polygonal aggregate base frame; note that the number of base points of the large aggregate is greater than that of the small aggregate, and control the distance between the base points of the large aggregate and the small aggregate so that the centers of the large aggregate and the small aggregate are inside the generated polygonal aggregate base frame; 3.2) The polygonal aggregate framework generated on the circumference of each circular aggregate is extended outwards in sequence until the area of ​​the circular aggregate in the inner cross section of the two-dimensional random circular aggregate specimen of recycled concrete is reached; the polygonal aggregate framework with a much smaller area than the corresponding circular aggregate is preferably selected, and the longer side is selected to extend outwards; for each vertex A1, A2, ..., A i , A i+1 , …, A n ; Polygonal aggregate base frame vertex A i The coordinates of (x i ,y i ), A i+1 The coordinates of (x i+1 ,y i+1 ); The coordinates of the new insertion point that is convex to the outward extension are: In the formula, R1, R2 are random numbers in the interval (0,1); When the area of ​​the convex polygonal aggregate after extension is greater than or equal to the area of ​​the corresponding circular aggregate, the extension ends.

6. The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: The automatic generation software of the convex polygonal aggregate geometric model is compiled through the steps (1) to (3), and the two-dimensional random circular aggregate geometric model of recycled concrete is transformed into a two-dimensional random convex polygonal aggregate geometric model of recycled concrete by using the automatic generation software, wherein the two-dimensional random circular aggregate geometric model of recycled concrete and the two-dimensional random convex polygonal aggregate geometric model of recycled concrete have the same aggregate gradation, corresponding aggregate content and old mortar content, but different aggregate shapes; The main program flow of converting the two-dimensional random circular aggregate geometric model of recycled concrete into the two-dimensional random convex polygonal aggregate geometric model of recycled concrete by using the automatic generation software of the convex polygonal aggregate geometric model is as follows: (1) Input round aggregate information Input information about recycled concrete circular aggregates. This information includes physical parameters such as location, gradation, and old mortar content of circular aggregates; (2) Generate a polygonal base frame on the old mortar boundary According to the recycled concrete circular aggregate information, a polygonal old mortar base frame is created on the old mortar boundary; (3) Extended convex polygonal old mortar base frame; (4) Generate a polygonal natural aggregate base frame on the natural aggregate boundary (5) Extended polygonal natural aggregate base frame; (6) Output convex polygon aggregate information After completing the generation and extension of all frames, the final convex polygon aggregate information is output.

7. The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete according to claim 5, characterized in that: The newly inserted points must meet the following requirements: ① The newly inserted points cannot exceed the specimen size range; ② The newly formed side length must be greater than the set minimum value; ③ The convex condition must be met; ④ For the extension and convexity of the old mortar boundary, it is necessary to ensure that there is no cross-overlap between the aggregates, and the extension and convexity of the natural aggregate boundary must ensure that the extension and convexity points are within the corresponding old mortar boundary.

8. The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete according to claim 5, characterized in that: The specific process of step 4) is as follows: 4.1) Meshing of 2D microscopic model of recycled concrete Based on the physical analogy between the edge of the triangular element and the truss structure, the linear force-displacement relationship is used to solve the equilibrium problem in the truss structure to improve the initial mesh. The specific solution process is: The difference between the ideal length and the current length of each edge of the triangular element is set as the spring force. The mesh is adjusted by updating the node position and recalculating the Delaunay triangulation until the node system reaches a balanced state. The node update formula is: In the above formula, k is the coefficient of simulating the linear spring rod, which can be set to 1. When F>0, the mesh boundary is stretched. For all internal nodes, there is a balance: For most rods, the force is repulsive, i.e., F>0, to help the nodes spread out within the entire geometric boundary; The ideal length l0 of the side of a triangular element is described by the mesh size function h(x,y), which does not have to be equal to the actual size. The mesh size function h(x,y) gives the relative distribution over the domain; h(x i ,y i )=min(min(a+b*{|d(x i ,y i )}),c); In the above formula, d(x i ,y i ) is the distance function, {|d(x i ,y i )|} is the point (x i ,y i ) is the set of absolute values ​​of the distances from the interface to each aggregate; a, b, c are the relative size parameters of the mesh at the interface; 4.2) Formation of boundary layer inside the mesh in the interface transition zone During the mesh generation process, when the nodes are within a certain range hp from the geometric boundary of the aggregate, these nodes will be "pulled back" to the nearest position on the boundary of the interface transition zone; the thickness of the interface transition zone is h, and it is assumed that the distance from the aggregate to the geometric boundary of the aggregate is ±h / 2 as the interface transition zone, and the points within the range hp from the boundary of the interface transition zone need to be moved and corrected to the nearest point on its boundary; the node correction distance hp can be taken as 20% to 50% of the thickness of the interface transition zone h, that is, hp = 0.2h to 0.5h, to ensure that the correction range is reasonable; The first-order Taylor approximation is used to calculate the node correction distance vector to form the internal boundary layer; the correction distance refers to the correction amount of the node from the current position to the nearest interface transition zone boundary; assuming a node P and interface function F(P) are given, the corrected node position P′ can be obtained by the formula: P' = P + ΔP; And the node correction distance vector ΔP is approximately calculated by the first-order Taylor expansion: 4.3) Meshing of 2D microscopic model of recycled concrete 4.3.1) Create uniformly distributed nodes within the geometric boundary, corresponding to equilateral triangle elements; 4.3.2) Calculate the size function h(x,y) of each node and use the rejection sampling method with 1 / h(x i ,y i ) 2 The probability of selecting a node; Set the mesh refinement gradient inside and outside the natural aggregate separately, and specify the maximum mesh size; 4.3.3) Enter the main loop of mesh optimization, and continuously iterate and optimize the node positions until a certain convergence standard is met 4.3.4) Terminate the loop. The termination condition is determined by the maximum motion displacement of the node in the current iteration. The maximum motion displacement of the node is obtained by the following formula: Where ΔP max is the maximum motion displacement of all nodes in the current iteration; Δx i and Δy i are the displacements of the ith node in the x and y directions, respectively.

9. The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete according to claim 8, characterized in that the specific steps of entering the main loop of grid optimization in step 4.3.3) are as follows: 4.3.3.1) Remove triangular meshes whose centroids are outside the geometric boundary; 4.3.3.2) Calculate the ideal triangle side length through the mesh size function h(x,y), adjust the side length and move nodes based on the difference with the actual side length; 4.3.3.3) If a node moves outside the geometric boundary of the two-dimensional random circular aggregate specimen geometric model of recycled concrete and the two-dimensional random convex polygonal aggregate specimen geometric model of recycled concrete after updating, move it back to the nearest point on its boundary to avoid node loss; 4.3.3.4) Set the node correction distance hp, and pull the points within the interface transition zone hp back to the boundary of the interface transition zone to form an internal boundary layer.

10. The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: The specific process of step (5) is as follows: firstly, a geometric model of the recycled concrete specimen is established and meshed, and then the recycled concrete aggregate is projected into the mesh unit area; the unit type is determined by judging the relative position of each mesh unit node; and finally, the material parameters are assigned to the generated units.

11. The method for parameterizing the two-dimensional mesoscopic numerical model of recycled concrete according to claim 10, characterized in that , the process of determining its unit type is: when all the nodes of the unit fall in the natural aggregate area, this unit will be defined as a natural aggregate unit; when all the nodes fall in the old mortar area, this unit is defined as an old mortar unit; when all the nodes fall in the new mortar area, this unit is defined as a new mortar unit; and when some nodes are in the natural aggregate area and some fall in the old mortar area, they will be defined as old interface transition zone units; when some nodes are in the old mortar area and some fall in the new mortar area, this unit is a new interface transition zone unit.

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