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J. R. Rice, “A Path Independent Integral and Approximate Analysis of Strain Concentration by Notches and Cracks,” Journal Applied Mechanics, Vol. 35, 1968, pp. 379-386.

has been cited by the following article:

  • TITLE: Strengthening of Sewerage Systems with Composites Plates: Numerical Optimization

    AUTHORS: Stephan Kesteloot, Chafika Djelal, Idriss Benslimane, Saïd Baraka

    KEYWORDS: Sewerage Systems, Carbon Plates, Concrete, Repair, Reinforcement, Finites Elements

    JOURNAL NAME: Materials Sciences and Applications, Vol.2 No.3, March 7, 2011

    ABSTRACT: Sewerage systems are subject to many types of degradation. In France, an estimated 10% of the total systems length requires work due to structural degradation. At present, there is no method to localised rehabilitation of man-entry sewers. Laboratory tests have validated localised methods that involve bonding composite plates to the sewer. Those tests were performed on pre-damaged (multi-cracked) ovoid test pieces. The degradation observed was a longitudinal crack opened at the crown. The tests were performed under vertical loading. Our Study concerns the application of partial lining of sewer with composites plates. The composite strengtheners used were 1.2 mm thick pultruded carbon plates. A series of experiments were carried out on reinforced-concrete ovoids (T180) strengthened and unstrengthened by carbon plates in the keystone. After this test, a vertically-loaded ovoid was subjected to three-dimensional modelling in order to determinate its structural behavior and collapse mechanism. Knowledge of the latter make it possible to limit the areas in need of strengthening. An ovoid strengthened by composite plates adhered to the damaged areas was also modelled. Using real case data, modelling was carried out using a finite-element computational software program. This program allows cracking to be monitored until the structure collapses. Many conventional approaches using intensity factors k and contour integrals J have already been reported in the literature. We used methods for restituting energy G. Because nonlinear elasticity was being calculated, the constitutive laws of the various materials had to be taken into account. These constitutive laws describe the evolution of the materials. Moreover, those laws are subject to deformation limits. The simulated models were homogeneously meshed with physically nonlinear, triangular elements. The test results were then compared to those of the digital models. Partial lining of a sewer with composite plates, compared to a traditional reinforced-concrete lining, achieves a cost reduction of about 55%.