A Study on the Crack Propagation Process in Concrete Structures Using Energy Method-Reference-Cited by-同舟云学术

A Study on the Crack Propagation Process in Concrete Structures Using Energy Method

Published:2012-10 Issue: Volume:204-208 Page:3151-3155
ISSN:1662-7482
Container-title:Applied Mechanics and Materials
language:
Short-container-title:AMM

Author:

Hu Shao Wei¹,Mi Zheng Xiang¹,Lu Jun¹

Affiliation:

1. Nanjing Hydraulic Research Institute

Abstract

The mechanical performance of concrete structures closely relates to the propagation of cracks. Depth studying energy dissipation of concrete in fracture process zone not only contributes to comprehensive understanding fracture failure mechanism of concrete, but also has significant in detecting and forecasting the cracks in actual structure. In view of this, a general equation for calculating at any time’s mean energy dissipation per unit length was given. After that, we further simplified and deduced the general equation and got a simple, practical and high accuracy numerical solution, with which Gauss integration method was used. At last, the specific steps of calculating mean energy dissipation were given by taking 10 three-point bending beams of different crack-depth ratios for an example. Compared with test dates, we found that calculated results are in good agreement with the test dates. According to results, influence of crack-depth ratio on the fracture energy was also discussed.

Publisher

Trans Tech Publications, Ltd.

Link

https://www.scientific.net/AMM.204-208.3151.pdf

Reference100 articles.

1. According to the definition of fracture energy, assumed that in any x position, we defined the energy which is used to overcome the constraints of the aggregate force in the process of the crack from 0 to ωx as the local fracture energy, and record it as, then: (7) When we got the local fracture energy of concrete in fracture process zone at any position according to the Eq. 7, energy dissipation can be got by integrating from a0 to a. (8) If the crack propagation length along the thickness is the same and material characteristics are alike, and then the fracture energy is expressed Eq. 9: (9) Now discuss how to solve the above definite integration: 1) When a0≤a≤as: if the crack is in this area, the distribution of cohesion was shown in Fig. 1, and fracture energy is: (10) Where:, . 2) When a0≤as≤a≤awo: if the crack is in this area, the distribution of cohesion was shown in Fig. 2, and fracture energy is: (11) Where: , , ,,,. Fig. 1 CTOD≤ωs Fig. 2 ωs≤CTOD≤ω0 Fig. 3 ω0≤CTOD 3) When aw0≤a: if the crack is in this area, and then ω0≤CTOD, there will be the crack of no cohesion and the macro-crack starts to propagate. In the case, the distribution of cohesion was shown in Fig. 3, and fracture energy is: (12) Where: , , ,,, Experimental verification The introduction of experiments. In this paper, four groups concrete specimens with different crack-height ratios were tested, whose sizes were 1000mm×200mm×120mm. However we only got 10 ideal test datas because some were damaged in the process of dismantling template and transporting. The mixture ratio of concrete was cementing material: sand: stone: water =1: 2. 42: 3. 21: 0. 54. Cement used P42. 5 ordinary Portland cement; sand used natural sand and the stone's diameter was 8mm-31. 5mm. Cube compressive strength of concrete was 29. 7MPa. All the beams were tested by the pressure testing machine of 5000kN. The CMOD was measured by Clip-on extensometer produced by Epsilon Company, with measurement accuracy 0. 2μm. Parameters F, CMOD and ε were collected by dynamic strain testing system and the acquisition frequency was 20Hz. Each specimen's Pmax, E, CMODc, CTODc and a were shown in the table 1. Table 1 Three-point bending beam specimen mechanical properties and dimensions Specimen NO. a0/h Fmax[kN] CMODc[μm] CTODc[μm] a[mm] Gf [N/m] Gf×[N/m] TPB25-02-01.

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