# Working State of ECC Link Slabs Used in Continuous Bridge Decks
## 5 Characterization of the ECC Link Slabs' Working State  
### The GSED-Based Investigation into the Working States of ECC Link Slabs  
The stress data of each mesh node are calculated via the constitutive relations of different materials as shown in Figure 7.  
The constitutive relations in uniaxial tension and compression prior to ultimate failure can be described by bilinear curves [42]. The constitutive relation in uniaxial tension is fitted with the tensile stress-strain curve of ECC as shown in Figure 7a [26]. The constitutive relation in compression is established by connecting those specific points as shown in Figure 7b. The unilinear stress-strain relationships of the CFT grid (elastic modulus \(E_{CFT}\) =130.2 GPa) and CFRP bar (elastic modulus \(E_{CFRP}\) =133.7 GPa) are exhibited in Figure 7c,d, respectively [43; 44]. According to these constitutive relations, the stress values are calculated. Thus, the GESD and the \(E_{j,\text{norm}}\) are obtained by Equation (1) and Equation (2), respectively. The \(E_{j,\text{norm}}\)-\(L_{j}\) curve, \(U\!F_{k}\)-\(L_{j}\) curve and \(U\!B_{k}\)-\(L_{j}\) curve for Type I ECC link slab are plotted in Figure 8, which embodies the evolving structural performance of ECC link slab from the perspective of energy. By distinguishing the intersections of \(U\!F_{k}\) and \(U\!B_{k}\) curves, the M-K criterion reveals two working state leaps in the \(E_{j,\text{norm}}\)-\(L_{j}\) curve. These two mutation points indicate the structural performance transitions of ECC link slab under loads. The first mutation point (M1: Step 9, 9 kN) is identified by investigating the whole \(E_{j,\text{norm}}\)-\(L_{j}\) curve. Then, the following mutation point (M2: Step 14, 14 kN) is identified from the \(E_{j,\text{norm}}\)-\(L_{j}\) curve segment (from M1 on). Similarly, the working state leaps of the other two link slabs are revealed from their \(E_{j,\text{norm}}\)-\(L_{j}\) curves, which are shown in Figure 9 together with the curve of Type I ECC link slab for comparison. The two mutation points (M1 and M2) can divide the working state of ECC link slab into different stages:  
Figure 5: Mesh generation. Figure 6: Contour map of shape function \(N_{1}\). Figure 7: Constitutive relations of different materials: (**a**) ECC materials in uniaxial tension; (**b**) ECC materials in compression; (**c**) CFT grid; and (**d**) CFRP bar. 1. The elastic stage. As shown in Figure 9, the \(E_{j,\text{norm}}\) grows quite slowly and the developing trend is steady before M1, representing a stable stage of ECC link slabs under the simulated traffic loading. Actually, the working behavior within this stage is mostly the elastic response of ECC material properties and cracking was not observed during this period [26]. When the magnitude of load is relatively small, the structural load-bearing capacity is mainly offered by the ECC. The effect of FRP composites is not obvious as the GSED sum of the three ECC link slabs are almost identical in the early phase. The experimental structures are of adequate stiffness and stability within this stage. 2. The elastic-plastic stage. The \(E_{j,\text{norm}}\) after M1 is relatively greater than that in the elastic stage as shown in Figure 9, speculating on the formation of micro-cracks and crack propagation afterwards. The \(E_{j,\text{norm}}\)-\(L_{j}\) curve in this stage is not that smooth due to the multiple cracking behavior of ECC materials [26]. The whole structure has transited into the elastic-plastic stage with local plastic development. It could be comprehended that the critical point M1 between elastic stage and elastic-plastic stage is the yielding point of each ECC link slab, where the working state changes from elasticity to elastoplasticity. The plastic behavior occurs at the 9 th loading step for Type I and II ECC link slabs, and the 24 th step for Type III ECC link slab. Accordingly, the yielding loads of the three types of ECC link slabs are 9 kN, 9 kN, and 24 kN, respectively.