CN112949071B - Method for calculating I-type stress intensity factor of rock-concrete interface crack under action of continuous load - Google Patents

Method for calculating I-type stress intensity factor of rock-concrete interface crack under action of continuous load Download PDF

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CN112949071B
CN112949071B CN202110249488.1A CN202110249488A CN112949071B CN 112949071 B CN112949071 B CN 112949071B CN 202110249488 A CN202110249488 A CN 202110249488A CN 112949071 B CN112949071 B CN 112949071B
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董伟
袁文岩
赵晓瑜
姚洁香
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Dalian University of Technology
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Abstract

The invention belongs to the field of safety evaluation of concrete gravity dams, and provides a method for calculating an I-type stress intensity factor of a rock-concrete interface crack under the action of continuous load.

Description

Method for calculating I-type stress intensity factor of rock-concrete interface crack under action of continuous load
Technical Field
The invention belongs to the field of safety evaluation of concrete gravity dams, and relates to a method for calculating an I-type stress intensity factor of a rock-concrete interface crack under the action of continuous load.
Background
For a concrete gravity dam located on a rock foundation, the interface of the rock foundation and a concrete dam body is a weak link. Initial defects are easily generated in an interface area due to improper pouring and maintenance during construction and load and environment effects during service, and further the safe operation of the concrete gravity dam is threatened. Numerous scholars have developed the exploration of interfacial fracture mechanism under quasi-static conditions, wherein the fracture criterion using stress intensity factor as criterion is extensively studied and widely applied. The stress intensity factor is a physical quantity reflecting the strength of a stress field of a fracture tip and is the most important evaluation index in fracture mechanics. Under quasi-static conditions, the calculation method of the stress intensity factor of the interface crack is mature, such as a displacement extrapolation method based on crack surface displacement; stress extrapolation based on stress at the leading edge of the crack tip; and (4) an interaction integration method based on the energy of the crack tip region.
It is particularly noted that concrete gravity dams typically operate under continuous water pressure. Under the action of continuous load, the materials on two sides of the interface crack generate viscoelastic deformation. Due to the high stress of the interface crack tip and the large deformation caused thereby, a stress redistribution phenomenon occurs within the structure and a stress relaxation phenomenon occurs at the interface crack tip. At this time, the interface stress intensity factor calculation method established based on the quasi-static fracture analysis is no longer applicable. According to the investigation of the inventor, the research on the fracture mechanism of the rock-concrete interface under the action of continuous load is not found at present, and a calculation method of the stress intensity factor of the interface crack considering the action of the continuous load is not provided. Based on the above, the subject group of the inventor carries out related research, and proposes and verifies a method for calculating the I-type stress intensity factor of the rock-concrete interface crack under the action of continuous load.
Disclosure of Invention
Based on the defects of the current research, the invention provides a method for calculating the I-type stress intensity factor of the rock-concrete interface crack under the action of continuous load, which can provide reference for the safety evaluation of the dam heel interface area during the service period of the concrete gravity dam.
The technical scheme of the invention is as follows:
a method for calculating I-type stress intensity factors of rock-concrete interface cracks under the action of continuous load comprises the following steps:
(1) Simulating the viscoelastic response of a rock-concrete interface according to the viscoelastic parameters of materials (rock and concrete) on two sides of the interface; extracting elastic strain energy densities of different nodes of front edge of interface crack tip from numerical simulation results
Figure BDA0002965397570000021
Further calculating the I-type stress intensity factor at the node based on the strain energy density factor theory
Figure BDA0002965397570000022
The calculation formula is shown as formula (1):
Figure BDA0002965397570000023
Figure BDA0002965397570000024
Figure BDA0002965397570000025
in the formula, E eff Is the equivalent elastic modulus of a rock-concrete interface, and the expression formula is shown in formula (2), wherein E 1 、E 2 Elastic molds for rock and concrete respectively; v is ave Is the average Poisson's ratio of rock-concrete interface, as shown in formula (3), wherein v 1 、ν 2 Poisson's ratio for rock and concrete, respectively; r is the distance from the calculation node to the crack tip point;
(2) I-type stress intensity factors of different nodes of front edge of tip of interface crack under continuous load action
Figure BDA0002965397570000026
Without distance independence, the method uses the core distance r of the front edge of the crack tip c The average value of the stress intensity factors of the internal nodes represents the stress intensity factor K of the interface crack under the action of continuous load 1 ，K 1 The calculation formula is shown in formula (4):
Figure BDA0002965397570000027
Figure BDA0002965397570000031
wherein m is the core distance r of the front edge of the crack tip c The number of the internal nodes is not less than 10; r is a radical of hydrogen c Calculated by formula (5); wherein
Figure BDA0002965397570000032
The fracture initiation toughness of the interface under quasi-static conditions is determined by a conventional fracture test; f. of t The tensile strength of the interface under quasi-static conditions was determined by conventional czochralski testing.
The invention has the beneficial effects that: according to the mechanical response of the core area of the front edge of the tip of the interface crack, the I-type stress intensity factor of the interface crack under the action of continuous load can be simply and conveniently calculated, so that the quantitative description of the stress field of the tip of the interface crack under the action of continuous load is realized, and a reference is provided for the safety evaluation of the concrete gravity dam during service.
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FIG. 1 (a) is a rock-concrete composite beam three-point bending test piece (P is an external load, S is a test piece span, and L is a test piece length), and FIG. 1 (B) is a mid-span section view of the test piece (B and D are a test piece length, a and a respectively 0 Interface initiation fracture length).
FIG. 2 shows a local area (r) of the crack tip at the interface c Core distance of the leading edge of the interfacial fracture tip).
FIG. 3 is a graph of stress intensity factor of a node within distance of the core from the leading edge of the interfacial fracture tip
Figure BDA0002965397570000033
FIG. 4 is an interfacial crack stress intensity factor K 1 Curve with time on load.
Detailed Description
In order to make the purpose, technical scheme and beneficial effects of the invention clearer, the following takes a rock-concrete composite beam three-point bending load-bearing test piece as an example, and the invention is clearly described with reference to 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 obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The three-point bending test piece of the rock-concrete composite beam described in the embodiment is shown in fig. 1, and the geometrical parameters of the test piece are as follows: l =500mm, B = D =100mm, S =400mm, a 0 =30mm. Modulus of elasticity E of rock and concrete 1 、E 2 Poisson ratio v 1 、ν 2 And the interface equivalent elastic modulus E calculated by the formulas (2) and (3) eff Average Poisson's ratio v ave Are all known; fracture toughness of interface under quasi-static loading condition
Figure BDA0002965397570000041
Tensile strength f t And r calculated from the formula (5) c Are all known; in addition, the present embodiment employs a Bailey-Norton based creep equation
Figure BDA0002965397570000042
The viscoelastic model simulates the viscoelastic response of the rock and concrete materials, so as to obtain the viscoelastic response of the rock-concrete interface, and the parameters of the viscoelastic model of the rock and concrete materials are known. The above material parameters are listed in table 1.
TABLE 1 materials parameters of rock, concrete, rock-concrete interface
Figure BDA0002965397570000043
A schematic diagram of the local area of the interface crack tip is shown in FIG. 2. Core distance r of the leading edge of the crack tip in this embodiment c There are 12 nodes inside. Under the action of continuous load P =2.27kN, the I-type stress intensity factors of different nodes in different holding time within the distance r from the front edge of the tip of the interface crack
Figure BDA0002965397570000044
As shown in fig. 3. The invention leads the core distance r of the front edge of the crack tip c I-type stress intensity factor of inner 12 nodes
Figure BDA0002965397570000051
The average value of the values is taken as the stress intensity factor K of the interface crack under the action of continuous load 1 . From this, a time-dependent change curve of the interfacial crack stress intensity factor in the present embodiment can be obtained, as shown in fig. 4.

Claims (1)

1. A method for calculating I-type stress intensity factors of rock-concrete interface cracks under the action of continuous load is characterized by comprising the following steps:
(1) Simulating the viscoelasticity response of the rock-concrete interface according to the viscoelasticity parameters of the rock and concrete materials on the two sides of the interfaceThe preparation method comprises the following steps of; extracting elastic strain energy densities of different nodes of front edge of interface crack tip from numerical simulation results
Figure FDA0002965397560000011
Further calculating the I-type stress intensity factor at the node based on the theory of strain energy density factor
Figure FDA0002965397560000012
Figure FDA0002965397560000013
The calculation formula is shown as formula (1):
Figure FDA0002965397560000014
Figure FDA0002965397560000015
Figure FDA0002965397560000016
in the formula, E eff Is the equivalent elastic modulus of a rock-concrete interface, and the expression formula is shown in formula (2), wherein E 1 、E 2 Elastic dies of rock and concrete respectively; v is ave Is the average Poisson's ratio of rock-concrete interface, as shown in formula (3), wherein v 1 、ν 2 Poisson's ratio for rock and concrete, respectively; r is the distance from the calculation node to the crack tip point;
(2) I-type stress intensity factors of different nodes of front edge of tip of interface crack under continuous load action
Figure FDA0002965397560000017
Without distance independence, the method uses the core distance r of the front edge of the crack tip c Of stress intensity factors of internal nodesThe average value represents the stress intensity factor K of the interface crack under the action of continuous load 1 ，K 1 The calculation formula is shown in formula (4):
Figure FDA0002965397560000018
Figure FDA0002965397560000019
wherein m is the core distance r of the front edge of the crack tip c The number of the internal nodes is not less than 10; r is c Calculated by formula (5); wherein
Figure FDA00029653975600000110
The fracture toughness of the interface under the quasi-static condition is determined by a conventional fracture test; f. of t The tensile strength of the interface under quasi-static conditions was determined by the Czochralski test.
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Citations (2)

* Cited by examiner, † Cited by third party
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
CN112067460A (en) * 2020-05-25 2020-12-11 长江大学 Method for testing stress intensity factor in fracture process of layered rock interface

Patent Citations (2)

* Cited by examiner, † Cited by third party
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
CN112067460A (en) * 2020-05-25 2020-12-11 长江大学 Method for testing stress intensity factor in fracture process of layered rock interface

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
四点剪切条件下岩石-混凝土界面裂缝扩展过程研究;陆超等;《水利与建筑工程学报》;20151015(第05期);全文 *

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