مدل ساختاری برای بتن محصور شده با فیبرهای پلیمری تقویت شده (FRP) در نرم افزار OpenSees

ABSTRACT A modified constitutive model for FRP confined concrete in circular sections and its implementation with OpenSees programming

Lateral confinement of concrete enhances its strength and ductility significantly. By utilizing steel or fiber reinforced polymer (FRP) as confinement material, confined concrete has a higher strength and deformation capacity compared with unconfined concrete due to the tri-axial compressive status with respect to lateral confining. As a result, confined concrete has been increasingly applied in civil engineering, especially in seismic design (Park et al., 1982; Mander et al., 1988a; Shams and Saadeghvaziri, 1997). As a promising option for engineering applications, FRP have been widely introduced into the application of confined concrete, and its confinement can greatly enhance the compressive strength and ultimate strain of concrete at the same time (Samaan et al., 1998; Toutanji, 1999).

In early studies of confined concrete, the uniaxial constitutive models for steel confined concrete and FRP confined concrete were the same. However, a number of research groups showed that significant differences exist between FRP confined and steel confined concrete and that its direct use is inappropriate. This is because in most steel confined concrete models (Mander et al., 1988b), a constant confining pressure is assumed, which is the case of steel confined concrete when the steel is in plastic flow, but not the case for FRP confined concrete. As FRP composites tend to remain linearly elastic until final rupture, the lateral confining pressure in FRP confined concrete increases continuously with the increasingly hoop enlarging.

Considerable progress has been achieved in developing a constitutive model for describing FRP confined concrete over the last three decades. All these stress strain models can be classified into two categories: (a) design-oriented models, and (b) analysis-oriented models. Even though the analysis oriented models have advantages in describing detailed mechanical behavior with the inevitable complexity of the incremental process, the design oriented models can be much more effectively and practically used in engineering design. According to a comprehensive review and assessment of the FRP confined concrete constitutive models including design-oriented and analysis-oriented ones (Ozbakkaloglu et al., 2013), the design-oriented models generally performed better in predicting the ultimate strength and strain enhancement ratios. Among several typical design-oriented constitutive models listed in Table 1, the one proposed by Lam and Teng (2003) is simple and accurate in depicting the strength and ductility of FRP confined concrete members, and therefore playing an important role in their structural analysis and design). In consistence with the assessment result calibrated by 730 FRP confined concrete cylinders test database, Lam and Teng (2003)’s model is one of the top performing models (Ozbakkaloglu et al., 2013). He et al. (2013) modified Lam and Teng (2003)’s model slightly for analyzing FRP piers or columns. In this paper, the modified constitutive model, in which the ambiguity on selecting parameters empirically has been reduced, is more comprehensive and much better results are expected.

The fiber element method, which makes the structural modeling process more concise and efficient than the traditional finite element method, can be regarded as a distributed beam-system finite element method, i.e., the fiber element model is set up on the basis of a beam-system structural mechanics and uniaxial constitutive model of materials. In the fiber section, the assumptions that each fiber possesses its unique uniaxial constitutive material property, and no relative slippage exists between different fibers have been straightforwardly carried out. Spacone et al. (1996) and Monti and Spacone (2000) demonstrated the utility of the fiber element method in dealing with structural nonlinear analysis, and showed that the efficiency raised by the decrease of computational degree of freedom (DOF) and the accuracy of analysis can be successfully achieved at the same time. The schematic depiction of the fiber section of FRP confined concrete is shown in Fig. 1.

OpenSees is an open framework with high compatibility and extendibility originally developed at University of California, Berkeley and currently supported by the American Pacific Earthquake Engineering Research Center (PEER) and an ever growing community. It has been utilized by the PEER based on object oriented C++ language source code since 1997. The OpenSees platform has embedded a fiber element method into its framework since it was first launched. Therefore, the nonlinear structural analysis based on the fiber element method can be completely conducted in OpenSees software mainly through a nonlinear beam column model and plastic hinge model. Since its utility and accuracy have been well verified, widespread acceptance and broad application of OpenSees have been achieved in the earthquake engineering research field.

The characteristics of the fiber element method are consistent with the idea of the design-oriented constitutive model; however, there is still no FRP confined concrete constitutive model embedded in the OpenSees platform up to now. For this reason, a modified constitutive model for FRP confined concrete based on Lam and Teng (2003)’s model is proposed in this paper and seamlessly embedded into OpenSees through UserMat secondary development to further broaden its application in structural analysis in combination with the efficient fiber element method.