CN113722960A - Three-dimensional numerical simulation method for humidity migration and drying shrinkage cracking - Google Patents

Three-dimensional numerical simulation method for humidity migration and drying shrinkage cracking Download PDF

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CN113722960A
CN113722960A CN202111016001.1A CN202111016001A CN113722960A CN 113722960 A CN113722960 A CN 113722960A CN 202111016001 A CN202111016001 A CN 202111016001A CN 113722960 A CN113722960 A CN 113722960A
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严成增
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Abstract

The invention provides a three-dimensional numerical simulation method for humidity migration and shrinkage cracking, which comprises the steps of dividing a solution domain into a plurality of polyhedral entity units, selectively arranging public units between adjacent polyhedral entity units, calculating the moisture mass flow of each node in each entity unit according to the humidity transfer between the nodes in the entity units, and obtaining the total moisture mass flow of each node; updating the humidity of each node according to a finite difference integral strategy, expressing the humidity distribution of the entity units by using the humidity of each node in each entity unit, calculating the shrinkage stress, and applying the shrinkage stress on the entity units as a body load to calculate a stress field; and deleting the broken public units, and separating the entity units on two sides of the public surface to be separated until the humidity transfer and drying shrinkage cracking simulation is completed. The technical scheme provided by the invention has the beneficial effects that: the three-dimensional numerical simulation method can be used for carrying out three-dimensional numerical simulation on humidity migration and shrinkage cracking in soil or other materials.

Description

Three-dimensional numerical simulation method for humidity migration and drying shrinkage cracking
Technical Field
The invention relates to the technical field of civil engineering, geotechnical engineering and geological engineering, in particular to a three-dimensional numerical simulation method for humidity migration and shrinkage cracking.
Background
The problems of humidity migration and shrinkage cracking in soil bodies or other materials relate to engineering application problems of civil engineering, geotechnical engineering, geological engineering and the like. With the development of computer hardware and the development of computational simulation technology, the numerical simulation method gradually becomes a powerful tool for analyzing and calculating humidity migration and shrinkage cracking. At present, the main calculation methods for solving the problems of humidity migration and shrinkage cracking are finite element and discrete element methods. The finite element method can well simulate the humidity migration, but the crack initiation, expansion, intersection and the like of the crack are difficult to process. The discrete element method is further divided into bulk discrete elements and particle discrete elements. The discrete elements of the block require complete cutting of the whole solution domain, and although various non-continuous problems can be solved, the initiation, expansion and intersection of cracks in the block are difficult to process; the discrete elements of the particles require complicated calibration of the input parameters because the microscopic input parameters cannot be directly corresponding to the measured material parameters. Thus, these methods still have many problems in simulating moisture migration and drying cracking problems in soil or other materials.
Disclosure of Invention
In view of the above, embodiments of the present invention provide a three-dimensional numerical simulation method for humidity migration and drying shrinkage cracking.
The embodiment of the invention provides a three-dimensional numerical simulation method for humidity migration and drying shrinkage cracking, which comprises the following steps:
s1, dividing the solving domain into a plurality of polyhedral entity units through grid division;
s2 optionally setting a common unit between adjacent said entity units;
s3 calculating the moisture mass flow of each node in each entity unit according to the humidity transfer among the nodes in the entity unit;
s4 regards the common cell set at step S2 as not present, and then performs the humidity migration calculation; obtaining the total moisture mass flow of each node according to the moisture mass flow of each node in the entity unit; according to a finite difference integral strategy, updating the humidity of each node by using the total moisture mass flow of each node, and expressing the humidity distribution of each entity unit by using the humidity of each node in each entity unit to complete the three-dimensional numerical simulation of the humidity migration of the whole solution domain;
s5, calculating shrinkage stress according to the humidity distribution of the solid units;
s6, applying the shrinkage stress on the solid unit as a body load to calculate a stress field;
s7, judging whether the common unit is broken or not according to the stress field for the entity unit provided with the common unit; for the entity units without the common units, calculating the tensile stress and the shear stress of the common plane of the entity units according to the stress field, and determining whether the entity units on the two sides of the common plane are separated;
s8, the broken common units are deleted, the entity units on two sides of the common surface to be separated are separated, and the steps S1-S8 are repeated in a circulating mode until the humidity migration and drying shrinkage cracking simulation is completed.
Further, step S3 includes the steps of:
s3.1, according to the Gaussian divergence theorem, solving the humidity gradient in the polyhedral entity unit and the humidity gradient
Figure BDA0003239893960000021
Comprises the following steps:
Figure BDA0003239893960000022
wherein w is humidity, V is the area of the polyhedral solid unit,
Figure BDA0003239893960000023
is the unit external normal vector, w, of the face opposite to the node l in the polyhedral solid elementlIs the temperature, S, of node l in the solid element of the polyhedron(l)Is the area of the face opposite to the node l in the polyhedral solid unit;
s3.2 setting the humidity migration in the polyhedral entity unit to be in direct proportion to the humidity gradient, and passing the humidity gradient
Figure BDA0003239893960000031
Obtaining the mass flow rate m of water along the i direction unit cross section area in unit timeiComprises the following steps:
Figure BDA0003239893960000032
in the formula, kijIs the humidity conductivity tensor, w is the humidity;
s3.3 according to step S3.1 and step S3.2, the mass flow of water flowing into the node l of the polyhedral solid unit is as follows:
Figure BDA0003239893960000033
further, step S4 includes the steps of:
s4.1, the total water mass flow of the polyhedron solid unit inflow node l is as follows:
Figure BDA0003239893960000034
in the formula, TiA polyhedral solid element representing a common node l;
s4.2 in the next time step Δ t, the humidity of node l can be updated according to the following formula:
Figure BDA0003239893960000035
in the formula, MsIs the dry mass of the entire material.
Further, in step S5, the calculation formula of the shrinkage stress is:
Δσij＝-δij3KαΔw；
in the formula: delta sigmaijFor the shrinkage stress, i is 1,2,3, j is 1,2,3, K is the bulk modulus, α is the shrinkage coefficient, Δ w is the change in humidity, δijIs the permutated tensor.
Further, in step S6, the stress field may be calculated by using any one of Finite Element (FEM), mixed finite-discrete element (FDEM), Discrete Element (DEM), Discontinuous Deformation Analysis (DDA), and numerical prevalence (NMM).
Further, in step S1, the polyhedral solid cell may be gridded for one or more of an N-face body (N is a natural number and is greater than or equal to 4) and a three-dimensional voronoi.
Further, in step S2, the common unit between adjacent polyhedral solid units is one of a joint unit, an interface unit, and a coherence unit.
The technical scheme provided by the embodiment of the invention has the following beneficial effects: the three-dimensional numerical simulation method for humidity migration and shrinkage cracking can simulate the humidity migration in soil or other materials very conveniently, and meanwhile, because the crack propagation is along the boundary of the solid unit, when the crack initiation, the crack propagation and the grid division are simulated, the crack initiation, the crack propagation and the grid division do not need to be tracked, and the crack initiation, the crack propagation and the crack intersection of any complex crack can be simulated very conveniently.
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FIG. 1 is a humidity migration calculation model in a three-dimensional numerical simulation method of humidity migration and drying shrinkage cracking provided by the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be further described with reference to the accompanying drawings.
The embodiment of the invention provides a three-dimensional numerical simulation method for humidity migration and drying shrinkage cracking, which comprises the following steps:
s1, dividing the solution domain into a plurality of polyhedral solid units through grid division, wherein the polyhedral solid units can be subjected to grid division for one or more of N-face body (N is a natural number and is more than or equal to 4) and three-dimensional voronoi.
S2 optionally arranging a common unit between adjacent solid units (with or without a common unit between adjacent polyhedral solid units), wherein the common unit is one of a joint unit, an interface unit and a coherence unit.
S3 calculating a moisture mass flow rate for each node within each of the physical units based on the moisture transfer between the nodes within the physical unit.
Specifically, step S3 includes the steps of:
s3.1, according to the Gaussian divergence theorem, solving the humidity gradient in the polyhedral entity unit and the humidity gradient
Figure BDA0003239893960000051
Comprises the following steps:
Figure BDA0003239893960000052
wherein w is humidity, V is the area of the polyhedral solid unit,
Figure BDA0003239893960000053
is the unit external normal vector, w, of the face opposite to the node l in the polyhedral solid elementlIs the temperature, S, of node l in the solid element of the polyhedron(l)Is the area of the face opposite to the node l in the polyhedral solid unit;
s3.2 setting the humidity migration in the polyhedral entity unit to be in direct proportion to the humidity gradient, and passing the humidity gradient
Figure BDA0003239893960000054
Obtaining the mass flow rate m of water along the i direction unit cross section area in unit timeiComprises the following steps:
Figure BDA0003239893960000055
in the formula, kijAnd is the humidity conductivity tensor, w is the humidity, also known as the water content, defined as the mass of water in the material divided by the dry mass of the entire material.
S3.3 according to step S3.1 and step S3.2, the mass flow of water flowing into the node l of the polyhedral solid unit is as follows:
Figure BDA0003239893960000056
s4, regarding the public unit set in the step S2 as nonexistent, if not set, no processing is needed, and then the humidity migration calculation is carried out; obtaining the total moisture mass flow of each node according to the moisture mass flow of each node in the entity unit; and according to a finite difference integration strategy, updating the humidity of each node by using the total moisture mass flow of each node, and expressing the humidity distribution of each entity unit by using the humidity of each node in each entity unit to complete the three-dimensional numerical simulation of the humidity migration of the whole solution domain.
Specifically, step S4 includes the steps of:
s4.1, the total water mass flow of the polyhedron solid unit inflow node l is as follows:
Figure BDA0003239893960000061
in the formula, TiA polyhedral solid element representing a common node l;
s4.2 in the next time step Δ t, the humidity of node l can be updated according to the following formula:
Figure BDA0003239893960000062
in the formula, MsIs the dry mass of the entire material.
S5, calculating the shrinkage stress according to the humidity distribution of the solid unit, wherein the calculation formula of the shrinkage stress is as follows:
Δσij＝-δij3KαΔw；
in the formula: delta sigmaijFor the shrinkage stress, i is 1,2,3, j is 1,2,3, K is the bulk modulus, α is the shrinkage coefficient, Δ w is the change in humidity, δijIs the permutated tensor.
S6 applies the shrinkage stress as a body load to the solid element to calculate a stress field, where the stress field may be calculated by using any one of Finite Element (FEM), mixed finite-discrete element (FDEM), Discrete Element (DEM), Discontinuous Deformation Analysis (DDA), and numerical prevalence (NMM).
S7, judging whether the common unit is broken or not according to the stress field for the entity unit provided with the common unit; for the entity units without the common units, calculating the tensile stress and the shear stress of the common plane of the entity units according to the stress field, and determining whether the entity units on the two sides of the common plane are separated;
s8, the broken common units are deleted, the entity units on two sides of the common surface to be separated are separated, and the steps S1-S8 are repeated in a circulating mode until the humidity migration and drying shrinkage cracking simulation is completed.
The following describes the three-dimensional numerical simulation method of moisture migration and shrinkage cracking according to the present invention by way of a specific example.
In this embodiment, a solution domain is subjected to mesh division by taking a polyhedral entity unit as a tetrahedral unit as an example.
Constructing the 3D humidity diffusion model shown in FIG. 1, equating 1/4 mass of all tetrahedral units connected with a node to the node, and representing the humidity distribution of the whole area by using the humidity of the node, wherein the humidity at any point in the tetrahedral units can be obtained by linear interpolation of the humidity of four nodes of the tetrahedron. In FIG. 1, the junction nodes of the nodal units are the common nodes of the tetrahedron and the nodal units, such as nodes 1-7 in FIG. 1, and the humidity of these discrete nodes is used to characterize the humidity field throughout the continuum. The following describes how the humidity field of the entire continuum is calculated based on the topological connections shown in fig. 1.
Taking node 1 in fig. 1 as an example, there are 8 tetrahedral units connected to node 1, where Δ 1236, Δ 1346, Δ 1456, Δ 1526, Δ 1237, Δ 1347, Δ 1457, and Δ 1527 are all tetrahedral units, and 8 in fig. 1 is a common unit disposed between adjacent polyhedral solid units. Since the humidity of the nodes 2,3, 4, 5, 6, 7 directly connected to the node 1 may be different from that of the node 1, humidity diffusion may occur in these areas. Take one of the tetrahedral units Δ 1236 connected to node 1 as an example. Assuming that the humidity field distribution within a tetrahedral cell follows a linear distribution, the humidity gradient at any point within the same tetrahedral cell is a constant and can be expressed as:
Figure BDA0003239893960000071
by the gaussian divergence theorem, formula (1) can be written as:
Figure BDA0003239893960000072
wherein V is the area of the tetrahedral unit,
Figure BDA0003239893960000073
is the unit normal vector, w, of the plane subtended by the nodes, l, of the tetrahedronlIs the temperature, S, of node l in the tetrahedral unit(l)Is the area of the face subtended by node l in the tetrahedral cell.
Setting the proportional relation between the water transport and the water content gradient in the unit, combining the formula (2), and the mass flow m of the water along the i direction and the unit cross section area in the unit timei(i ═ 1,2,3) is:
Figure BDA0003239893960000074
in the formula, kijIs the tensor of the humidity conductivity coefficient, and w is the water content, which is defined as the mass of water in the soil divided by the dry mass of the soil.
Thus, the mass flow rate of water per unit time flowing from tetrahedral cell Δ 1236 into node 1 can be calculated by:
Figure BDA0003239893960000081
in the formula (I), the compound is shown in the specification,
Figure BDA0003239893960000082
the outer normal unit vector of the face subtended by node 1.
Thus, the mass flow rate M of water flowing into the node 1 in the tetrahedral unit delta 1236 can be obtainedΔ1236→1. Similar to the aboveWe can find the mass flow of water into the node 1 from other tetrahedral units directly connected to the node 1. Thus, the total mass flow of moisture per unit time into node 1 can be expressed as:
Figure BDA0003239893960000083
then, during the next time step Δ t, the humidity of node 1 may be updated according to the following equation:
Figure BDA0003239893960000084
in this way, the humidity of the node 1 at the next time step is updated, and the updating of the humidity of the remaining discrete nodes can be similarly obtained according to the method. Accordingly, the evolution of the humidity field of the whole solution domain can be obtained.
The shrinkage stress is then calculated from the humidity distribution according to the following formula:
Δσij＝-δij3KαΔw (7)
applying the shrinkage stress as a body load to the tetrahedral unit, wherein the equivalent node force caused by the shrinkage stress is as follows:
Figure BDA0003239893960000085
in the formula (I), the compound is shown in the specification,
Figure BDA0003239893960000086
is the external normal unit vector, S, of the face subtended by the node l in a tetrahedral cell(l)The area of the face of a tetrahedral cell node/pair.
Then, taking the mixed finite-discrete element method as an example, the stress field is calculated and whether the joint unit or the interface unit or the coherent unit is broken or not is judged.
And finally, according to the circulation of the steps, the calculation of humidity migration and shrinkage cracking in the soil body or other materials can be completed.
The above specific implementation is only an example of a tetrahedral unit, and the rest is one or more entity units of a pentahedron, a hexahedron, a three-dimensional voronoi unit, other arbitrary polyhedrons, and the like, and the calculation procedures are similar to the above, and are included in the protection scope of the present invention.
The features of the embodiments and embodiments described herein above may be combined with each other without conflict.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (7)

1. A three-dimensional numerical simulation method for humidity migration and shrinkage cracking is characterized by comprising the following steps:
s1, dividing the solving domain into a plurality of polyhedral entity units through grid division;
s2 optionally setting a common unit between adjacent said entity units;
s3 calculating the moisture mass flow of each node in each entity unit according to the humidity transfer among the nodes in the entity unit;
s4 regards the common cell set at step S2 as not present, and then performs the humidity migration calculation; obtaining the total moisture mass flow of each node according to the moisture mass flow of each node in the entity unit; according to a finite difference integral strategy, updating the humidity of each node by using the total moisture mass flow of each node, and expressing the humidity distribution of each entity unit by using the humidity of each node in each entity unit to complete the three-dimensional numerical simulation of the humidity migration of the whole solution domain;
s5, calculating shrinkage stress according to the humidity distribution of the solid units;
s6, applying the shrinkage stress on the solid unit as a body load to calculate a stress field;
s7, judging whether the common unit is broken or not according to the stress field for the entity unit provided with the common unit; for the entity units without the common units, calculating the tensile stress and the shear stress of the common plane of the entity units according to the stress field, and determining whether the entity units on the two sides of the common plane are separated;
s8, the broken common units are deleted, the entity units on two sides of the common surface to be separated are separated, and the steps S1-S8 are repeated in a circulating mode until the humidity migration and drying shrinkage cracking simulation is completed.
2. The three-dimensional numerical simulation method of humidity migration and shrinkage cracking according to claim 1, wherein the step S3 comprises the steps of:
s3.1, according to the Gaussian divergence theorem, solving the humidity gradient in the polyhedral entity unit and the humidity gradient
Figure FDA0003239893950000011
Comprises the following steps:
Figure FDA0003239893950000021
wherein w is humidity, V is the area of the polyhedral solid unit,
Figure FDA0003239893950000022
is the unit external normal vector, w, of the face opposite to the node l in the polyhedral solid elementlIs the temperature, S, of node l in the solid element of the polyhedron(l)Is the area of the face opposite to the node l in the polyhedral solid unit;
s3.2 setting the humidity migration in the polyhedral entity unit to be in direct proportion to the humidity gradient, and passing the humidity gradient
Figure FDA0003239893950000023
Obtaining the mass flow rate m of water along the i direction unit cross section area in unit timeiComprises the following steps:
Figure FDA0003239893950000024
in the formula, kijIs the humidity conductivity tensor, w is the humidity;
s3.3 according to step S3.1 and step S3.2, the mass flow of water flowing into the node l of the polyhedral solid unit is as follows:
Figure FDA0003239893950000025
3. the three-dimensional numerical simulation method of humidity migration and shrinkage cracking according to claim 2, wherein the step S4 comprises the steps of:
s4.1, the total water mass flow of the polyhedron solid unit inflow node l is as follows:
Figure FDA0003239893950000026
in the formula, TiA polyhedral solid element representing a common node l;
s4.2 in the next time step Δ t, the humidity of node l can be updated according to the following formula:
Figure FDA0003239893950000027
in the formula, MsIs the dry mass of the entire material.
4. The method for three-dimensional numerical simulation of humidity migration and shrinkage cracking according to claim 3, wherein in step S5, the shrinkage stress is calculated by the formula:
Δσij＝-δij3KαΔw；
in the formula: delta sigmaijFor the shrinkage stress, i is 1,2,3, j is 1,2,3, K is the bulk modulus, α is the shrinkage coefficient, Δ w is the change in humidity, δijTo replace sheetsAmount of the compound (A).
5. The method for three-dimensional numerical simulation of moisture migration and shrinkage cracking according to claim 1, wherein the stress field is calculated in step S6 by using any one of Finite Element (FEM), mixed finite-discrete element (FDEM), Discrete Element (DEM), Discontinuous Deformation Analysis (DDA), and numerical prevalence (NMM).
6. The method for three-dimensional numerical simulation of humidity migration and shrinkage cracking according to claim 1, wherein in step S1, the polyhedral solid cells are gridded for one or more of N-hedron (N is a natural number and is greater than or equal to 4) and three-dimensional voronoi.
7. The method for three-dimensional numerical simulation of moisture migration and shrinkage cracking according to claim 1, wherein in step S2, the common unit between adjacent polyhedral solid units is one of a joint unit, an interface unit and a cohesive unit.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109063257A (en) * 2018-07-02 2018-12-21 山东科技大学 A kind of coal and rock subregion water filling seepage flow-damage-stress coupling method for numerical simulation
CN109101675A (en) * 2018-06-19 2018-12-28 中国地质大学（武汉） A kind of simulation solid material thermal fracture method
US20190309604A1 (en) * 2016-08-16 2019-10-10 Halliburton Energy Services, Inc. Methods and systems of modeling fluid diversion treatment operations
CN111709161A (en) * 2020-04-27 2020-09-25 中国水利水电科学研究院 Concrete panel drying shrinkage analysis and control method

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20190309604A1 (en) * 2016-08-16 2019-10-10 Halliburton Energy Services, Inc. Methods and systems of modeling fluid diversion treatment operations
CN109101675A (en) * 2018-06-19 2018-12-28 中国地质大学（武汉） A kind of simulation solid material thermal fracture method
CN109063257A (en) * 2018-07-02 2018-12-21 山东科技大学 A kind of coal and rock subregion water filling seepage flow-damage-stress coupling method for numerical simulation
CN111709161A (en) * 2020-04-27 2020-09-25 中国水利水电科学研究院 Concrete panel drying shrinkage analysis and control method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
CHENGZENG YAN等: "A 2D FDEM-based moisture diffusion–fracture coupling model for simulating soil desiccation cracking", 《ACTA GEOTECHNICA》, vol. 16, no. 8, pages 2609 - 2628, XP037536051, DOI: 10.1007/s11440-021-01297-4 *

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