Prediction of Load Capacity Variation in FRP Bonded Concrete Specimens Using Brownian Motion

Tayyebeh Mohammadi,Chao Zhu,Baolin Wan,Jian-Guo Dai

doi:10.1155/2015/632912

Abstract

In wet lay-up process, dry fiber sheets are saturated with a polymer and applied to the concrete surface by hand. This causes relatively large variation in properties of the cured FRP composite material. It is hard to know the exact mechanical properties of the FRP constructed by wet lay-up process. In addition, the stiffness of FRP changes during debonding process due to different amount of concrete attached to the debonded FRP at different locations. It is also inevitable to have considerable variations in the strength of concrete. Therefore, the behaviour of FRP bonded concrete members varies among specimens even when the same materials are used. The variation of localized FRP stiffness and concrete strength can be combined in a single parameter as variation of the localized interfacial fracture energy. In an effort to effectively model the effects of the variation of interfacial fracture energy on the load versus deflection responses of FRP bonded concrete specimens subjected to Mode I and Mode II loading, a random white noise using a one-dimensional standard Brownian motion is added to the governing equations, yielding stochastic differential equations. By solving these stochastic equations, the bounds of load carrying capacity variation with 95% probability are found for different experimental tests.

Highlights

Extensive research has clearly shown that externally bonded fiber reinforced polymer (FRP) composites have good potential for use in strengthening of concrete members [1,2,3]
There are some variations in FRP stiffness and concrete strength, the localized strength
The manufacturers provide the properties of the fiber sheets, such as Young’s modulus and design sheet thickness, based on the tests in laboratories. When it is used in field, the properties of the FRP are affected by the curing process and defects such as gouges or deep scratches which may occur through the instalment of FRP [7, 8]

Summary

Introduction

Extensive research has clearly shown that externally bonded fiber reinforced polymer (FRP) composites have good potential for use in strengthening of concrete members [1,2,3]. The concepts of Brownian motion and white noise from probability theory are used to find the fracture energy range instead of variations of the FRP stiffness and concrete strength separately. A random white noise is added to the fracture energy parameter in the governing equations to model fluctuating differences between actual and theoretical values of FRP stiffness and concrete strength. The governing equations for FRP debonding from concrete subjected to Mode I (normal stress perpendicular to the interface) and Mode II (in-plane shear stress parallel to the interface) loadings become stochastic differential equations, where the driven noise is a one-dimensional standard Brownian motion By solving these equations and comparing the results with the experimental data, the ranges of load carrying capacity with 95% probability are found for different experimental tests

Background on Brownian Motion

FRP-to-Concrete Interface under Mode II Loading Condition

FRP-to-Concrete Interface under Mode I Loading Condition

Findings

Conclusion