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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 83
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 130

Application of the Circumferential Notch Method to Fibre Reinforced Concrete

P.P. Procházka and A.E. Yiakoumi

Department of Structural Mechanics, Faculty of Civil Engineering, Czech Technical University Prague, Czech Republic

Full Bibliographic Reference for this paper
P.P. Procházka, A.E. Yiakoumi, "Application of the Circumferential Notch Method to Fibre Reinforced Concrete", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 130, 2006. doi:10.4203/ccp.83.130
Keywords: fibre reinforced concrete, tunnel linings, eigenparameters, Fourier series, extreme one-sided moistening, arch problem, circumferential notch method.

In this paper the problem of a fibre reinforced concrete (FRC) arch (simulating part of a tunnel lining) in difficult conditions is solved. Extremely at one-side moistened and at the other side dried, the structure is studied. Experiments with straight laminated beams are fully exploited for the creation of the arch model, which involves eigenparameters simulating the state of wetting. A Fourier series method is applied in the numerical analysis for solving the arch problem. It enables us to reduce the dimension by one for the simply supported arch. As certain experiments have been conducted with dry concrete, the comparative study is also prepared for this case but with clamped ends. In order to obtain the solution of a fixed arch, Lekhnitski's technique [2], is used.

A procedure for calculating a segment of the one-sided moistened tunnel lining constrcuted from FRC is suggested. Plastic behaviour is described by the circumferential (hoop) notch method. Here this method is completed by applying adjustable uniformly distributed eigenstrain or eigenstress fields in laminas, in which the arch is divided.

The eigenparameters can simulate many of the mechanical, swelling, wettening, and thermal properties. In our case two types of eigenstrains are employed: first, the influence of the non uniform distribution of water inside the body under consideration is simulated; the second is a simulation of plastic behaviour. In both cases, a laminate structure is created with laminate-wise uniformly distributed moisture.

In the application of shotcrete to underground structures, especially in the construction of the primary lining of tunnels, the basic research is not developed enough. This is why a particular case of arch structures simulating part of the tunnel lining is studied in this paper. It is worth noting that the application of the FRC cannot substitute in full the extent of the rebar reinforcement in the classical concrete. In order to use the FRC appropriately it is necessary to select zones, in which the positive properties come across (durability, partially increased the tensile strength, and the material modules, waterproof, etc.). Application of the FRC acts very favourably over where the bearing elements are loaded in three dimensions and where a difficult structural reinforcement complicates the engineering. For this reason the use of FRC in primary and secondary linings of tunnels is very advantageous.

Since some structures, such as tunnels, are drilled into stressed rock, the initial stress or eigenstress act out a very important role in the computation. It may simulate the previous stages of loading, and may substitute the plastic strain (eigenstrain). The last quantity can be employed in the physically nonlinear computation (e.g. plasticity, creep) by means of a kind of inverse analysis (using transformation field analysis (TFA) [4]); the development of additional eigen-stresses and consequently the behaviour of the rock can be esteemed from this measurement.

An attempt to solve the problem envisaged is given in reference [1], were explicit solution was presented under simplified conditions. Also Lekhnitski [2] published interesting solution for the axisymmetric problem. We utilize his publication for turning a simply supported arch into a clamped one. The eigenparameters have been used in many publications and have different meanings, but always they are very important and give successful results. We mention here publication [3], where the optimization using the classical variational formulation for layered structures is presented. It was proved that they are a powerful tool [4]. The Fourier series method was used in [5], where a simplified solution with one sine wave was applied.

I.S. Sokolnikoff, "Mathematical theory of elasticity", 2nd edition, McGraw-Hill, New York, 1996.
S.G. Lekhnitski, "Anisotropic plates", Gordon and Breach Sci. Publ. NYC - London - Paris, 1968.
P. Procházka, "Optimal eigenstress fields in layered structures", Journal of Computational and Applied Mathematics, 63(1-3), 475-480, 1995. doi:10.1016/0377-0427(95)00093-3
G.J. Dvorak, P. Procházka, "Thick-walled composite cylinders with optimal fiber prestress", Composites Part B: Engineering Volume 27(6), 643-649, 1996. doi:10.1016/S1359-8368(96)00001-7
T. Chen, G.J. Dvorak, Y. Benveniste, "Stress fields in composites reinforced by coated cylindrically orthotropic fibers", Mechanics of Materials 9, 17-32, 1990. doi:10.1016/0167-6636(90)90027-D

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