CN113325164B - Method for analyzing three-dimensional expansion process of concrete I-shaped crack - Google Patents
Method for analyzing three-dimensional expansion process of concrete I-shaped crack Download PDFInfo
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Abstract
The invention belongs to the technical field of concrete fracture analysis, and provides a method for analyzing a three-dimensional expansion process of a concrete I-shaped crack. According to the method, the three-line distribution model of the fracture toughness and the three-line distribution model of the fracture energy can be obtained by considering the thickness boundary effect according to the fracture toughness and the fracture energy of the concrete measured under the static condition. And (3) introducing a virtual crack model and a crack propagation criterion considering the thickness effect, namely simulating the three-dimensional propagation process of the concrete I-shaped crack to obtain a crack propagation track at any time along the thickness direction.
Description
Technical Field
The invention belongs to the technical field of concrete fracture analysis, and relates to a method for analyzing a three-dimensional expansion process of a concrete I-shaped crack.
Background
The propagation of cracks in concrete is a potential threat to the safety and stability of the structure. Researchers at home and abroad develop the research on concrete fracture mechanics and provide a plurality of famous concrete fracture models, such as a virtual fracture model, a fracture zone model, an equivalent elastic fracture model, a two-parameter model, a double-K model and the like. The double-K fracture model proposed by scholars in China divides the fracture propagation process into three stages of fracture initiation, fracture stable propagation and fracture instability propagation, and proposes the concept of concrete fracture initiation toughness for the first time. The fracture toughness is a parameter for representing the fracture resistance of the material, and is a fracture tip stress intensity factor of the structure under the fracture load and the initial fracture length. On the basis, Wuzhimin and Dongwei propose a fracture propagation criterion taking fracture toughness as a criterion, consider the fracture propagation as one new fracture, and further analyze the fracture propagation process in the test piece in the loading process. It should be noted that the current research is based on two-dimensional plane assumption, and the three-dimensional constant-section structure is simplified into the problem of plane stress or plane strain with thickness. In fact, due to the side wall effect, the poisson effect under the load action and the boundary effect of the material performance in the pouring process of the test piece, the stress state and the material performance of the test piece with the equal section are different along the thickness direction of the test piece. At this time, fracture analysis based on the two-dimensional plane hypothesis cannot accurately analyze the real fracture performance of the structure, and even more, cannot accurately simulate the real expansion process of the fracture. Therefore, it is necessary to provide a method for analyzing the three-dimensional propagation process of concrete cracks.
In the existing research, a student considers the boundary effect of the concrete fracture energy along the ligament direction and the boundary effect in the thickness direction, proposes a boundary effect model of the fracture energy, and applies the model to fracture analysis of concrete. The fracture initiation toughness characterizes the crack resistance of the material, and controls key parameters of fracture initiation and propagation. However, a distribution model considering the fracture toughness along the thickness boundary is not proposed at present, and a concrete three-dimensional crack propagation analysis method taking the fracture toughness as a criterion is not proposed.
Disclosure of Invention
Based on the defects of the current research, the applicant performs a great amount of thickness-variable concrete fracture tests, provides a concrete fracture toughness distribution model considering the thickness boundary effect by combining with numerical simulation, analyzes the three-dimensional expansion process of the concrete I-shaped crack by introducing a virtual crack model considering the cohesive action of a fracture process area in the crack expansion process, and provides reference for the stability analysis of the engineering solid structure crack.
A method for analyzing a three-dimensional expansion process of a concrete I-shaped crack comprises the following steps:
(1) and (3) providing a three-line distribution model of the concrete fracture toughness considering the thickness boundary effect. For a test piece with any thickness, according to the fracture toughness calculated under the two-dimensional assumption condition, the distribution rule of the fracture toughness along the thickness direction can be obtained, the expression along the thickness is shown as formula (1), and the distribution diagram is shown as figure 1.
Wherein b is a position in the thickness direction of the specimen,
for fracture toughness at different positions b in the thickness direction, K ini The thickness is the calculated fracture toughness of the test piece under the two-dimensional assumption, d max The maximum aggregate particle size of the concrete, and B the thickness of the test piece.
(2) Introducing a virtual crack model, and representing the cohesive action of a concrete fracture process area by applying cohesive force, so as to soften the relation between the virtual crack opening and the cohesive stress described by the constitutive model. In the three-dimensional crack analysis process of concrete, the thickness boundary effect of the fracture energy is considered, the three-line type distribution model of the concrete fracture initiation toughness is provided by considering the thickness boundary effect, the distribution rule of the fracture energy along the thickness direction can be obtained according to the fracture energy calculated under the two-dimensional assumption condition, the expression of the distribution along the thickness is shown in the formula (2), and the distribution diagram is shown in the figure 2.
In the formula, G t G is the fracture energy calculated for the test piece under the two-dimensional assumption condition for the thickness as the fracture energy at different positions b in the thickness direction.
(3) And (5) providing a concrete three-dimensional crack propagation criterion. In the three-dimensional expansion analysis of the concrete I-shaped crack, a test piece is divided into a plurality of parts along the thickness direction, each part of the thickness is not more than the maximum aggregate grain diameter of the test piece, cohesive stress calculated by the fracture energy and the material tensile strength of the position is applied to different thickness parts, and a stress intensity factor caused by external load is used
Stress intensity factor caused by cohesion at the position
Is greater than the fracture initiation toughness at the location
When this position is extended. The criterion can be expressed as equations (3), (4), (5).
The invention has the beneficial effects that: according to the concrete fracture toughness and the fracture energy measured under the static condition, a fracture toughness three-line distribution model and a fracture energy three-line distribution model considering the thickness boundary effect can be obtained. And (3) introducing a virtual crack model and a crack propagation criterion considering the thickness effect, namely simulating the three-dimensional propagation process of the concrete I-shaped crack to obtain a crack propagation track at any time along the thickness direction.
Drawings
FIG. 1 is a three-line model of the fracture toughness distribution of concrete taking into account thickness boundary effects.
Fig. 2 is a concrete fracture energy triplet distribution model considering thickness boundary effect.
FIG. 3 is a diagram illustrating the construction of a semi-structural finite element model in numerical simulation.
Fig. 4 is a comparison of crack propagation trajectories at different times obtained by numerical simulation with test results. Wherein (a) is the peak load P max The crack surface profile is obtained by a time dyeing method test; (b) is peak load P max A test and numerical comparison graph of the crack propagation track at the moment; (c) is 75% P after peak max The crack surface profile is obtained by a time dyeing method test; (d) is 75% P after peak max Time crack extension railTest and value comparison graphs of traces; (e) is 50% P after the peak max The crack surface profile is obtained by a time dyeing method test; (f) is 50% P after the peak max A test and numerical comparison graph of the crack propagation track at the moment; (g) is 25% P after peak max The crack surface profile is obtained by a time dyeing method test; (h) is 25% P after peak max A test and numerical comparison graph of the crack propagation track at the moment; (i) is 5% P after the peak max The crack surface profile is obtained by a time dyeing method test; (j) is 5% P after the peak max And (3) comparing the test and the value of the crack propagation track at the moment.
Detailed Description
In order to make the purpose, technical scheme and beneficial effects of the invention clearer, the following specifically describes the concrete I-type three-dimensional crack propagation process by taking a rock-concrete three-point bending test piece as an example and combining the accompanying drawings. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
(1) Three-point concrete bending beam test
The size of a concrete three-point bending beam test piece is 500mm multiplied by 100mm, the initial crack is positioned in the center of the bottom of the test piece, the length of the crack is 30mm, and the span of the support is 400 mm. The concrete material has the following basic mechanical properties: the compressive strength is 37.6MPa, the tensile strength is 3.2MPa, the elastic modulus is 31.6GPa, and the Poisson ratio is 0.2. The three-point bending beam test adopts a displacement loading mode, and the loading rate is 0.05 mm/min. The test shows that the concrete has the crack initiation load of 3207N, the fracture energy of 117.08N/m and the crack initiation toughness of 1.39 MPa.m 1/2 。
(2) Three-linear distribution model for concrete fracture toughness and fracture energy
According to the concrete fracture toughness and the fracture energy measured by the test, a fracture toughness and fracture energy trilinear distribution model of the concrete considering the thickness boundary effect can be obtained by the formulas (1) and (2).
(3) Numerical simulation of crack propagation process in three-point bending test
And simulating the three-dimensional crack propagation process of the concrete tested by the three-point bending beam by using ANSYS finite element software. Due to the symmetry in the thickness direction, a half-structure finite element model is established in the numerical simulation, and is divided into every 2mm in the thickness direction, and a model diagram is shown in fig. 3. Since the fracture energy and the fracture initiation toughness are different at different positions in the thickness direction, the cohesive constitutive relation and the fracture propagation criterion of each part are considered separately in the numerical simulation. When the comprehensive stress intensity factor at a certain position along the thickness direction reaches the cracking toughness at the position, the crack at the position is cracked. And modeling again after the crack is initiated, and repeating the analysis until the crack is expanded to penetrate through the whole interface. The crack propagation trajectory at different times obtained by numerical simulation is compared with the test result, for example, as shown in fig. 4, in which the blue line is the numerical simulation result and the orange line is the test result.
Claims (1)
1. A method for analyzing a three-dimensional expansion process of a concrete I-shaped crack is characterized by comprising the following steps:
(1) providing a three-line distribution model of concrete fracture toughness considering thickness boundary effect
For a test piece with any thickness, according to the fracture toughness calculated under the two-dimensional assumption condition, the distribution rule of the fracture toughness along the thickness direction is obtained, and the expression along the thickness distribution is shown as formula (1):
wherein b is a position in the thickness direction of the specimen,
for fracture toughness at different positions b in the thickness direction, K ini Calculated fracture toughness, d, for the test piece under two-dimensional assumptions max The maximum aggregate particle size of the concrete, and B the thickness of the test piece;
(2) introducing a virtual crack model, representing the cohesive action of a concrete fracture process area by applying cohesive force, and softening a constitutive model to describe the relation between the opening of a virtual crack and the cohesive stress; in the concrete three-dimensional crack analysis process, the thickness boundary effect of the fracture energy is considered, a concrete fracture initiation toughness three-line distribution model considering the thickness boundary effect is provided, the distribution rule of the fracture energy in the thickness direction is obtained according to the fracture energy calculated under the two-dimensional assumption condition, and the expression of the distribution along the thickness is shown as a formula (2):
in the formula, G t The fracture energy at different positions b along the thickness direction is shown, and G is the fracture energy calculated by the test piece under the two-dimensional assumed condition;
(3) put forward the three-dimensional crack propagation criterion of concrete
In the three-dimensional expansion analysis of the concrete I-shaped crack, a test piece is divided into a plurality of parts along the thickness direction, each part of the thickness is not more than the maximum aggregate grain diameter of the test piece, cohesive stress calculated by the fracture energy and the tensile strength of the material at the position is applied to the positions with different thicknesses, and a stress intensity factor caused by external load is used
Stress intensity factor caused by cohesion at the position
Is greater than the fracture initiation toughness at the location
When, the position expands;
this criterion can be expressed as the formulae (3), (4), (5):
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Citations (4)
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|---|---|---|---|---|
| CN103760036A (en) * | 2014-01-08 | 2014-04-30 | 黄河水利委员会黄河水利科学研究院 | Testing method of steel fiber reinforced concrete fracture test crack initiation load |
| CN105004611A (en) * | 2015-05-06 | 2015-10-28 | 河海大学 | Method for studying material mechanics behaviors of concrete crack process zone |
| CN109507041A (en) * | 2018-10-18 | 2019-03-22 | 上海宝冶集团南京建筑有限公司 | A kind of I-II mixed mode fracture property test method of concrete |
| CN109668782A (en) * | 2018-12-04 | 2019-04-23 | 大连理工大学 | A method of measurement concrete initial fracture toughness |
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103760036A (en) * | 2014-01-08 | 2014-04-30 | 黄河水利委员会黄河水利科学研究院 | Testing method of steel fiber reinforced concrete fracture test crack initiation load |
| CN105004611A (en) * | 2015-05-06 | 2015-10-28 | 河海大学 | Method for studying material mechanics behaviors of concrete crack process zone |
| CN109507041A (en) * | 2018-10-18 | 2019-03-22 | 上海宝冶集团南京建筑有限公司 | A kind of I-II mixed mode fracture property test method of concrete |
| CN109668782A (en) * | 2018-12-04 | 2019-04-23 | 大连理工大学 | A method of measurement concrete initial fracture toughness |
Non-Patent Citations (4)
| Title |
|---|
| Rock-Concrete Interfacial Crack Propagation under Mixed Mode I-II Fracture;Dong, W et al.;《JOURNAL OF ENGINEERING MECHANICS》;20180630;第144卷(第6期);第1-13页 * |
| 混凝土I型裂缝扩展准则比较研究;王璀瑾 等;《工程力学》;20160531;第33卷(第5期);第89-96、105页 * |
| 混凝土断裂参数厚度尺寸效应的定量表征与机理分析;徐世烺 等;《土木工程学报》;20170531;第50卷(第5期);第57-71页 * |
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