# Working State of ECC Link Slabs Used in Continuous Bridge Decks
## 5 Characterization of the ECC Link Slabs' Working State
### Working State Modes Based on Strains and Displacements  
The structural responses at representative locations should exhibit some features relevant to the working state of the whole structure. The working state modes are defined as the dependences of strains/displacements measured in the experiment on both the locations of measuring points and the loading steps, which are formulated as follows,  
\[\left\{\mathbf{S}\right\}=\left\{ \begin{array}{ccccc}s_{11}&\dots&s_{1j}& \dots&s_{1n}\\ \vdots&\ddots&&\\ s_{i1}&&s_{ij}&&\vdots\\ \vdots&&&\ddots&\\ s_{m1}&&\dots&&s_{mn}\end{array} \right\}, \tag{14}\]  
Figure 10: Structural toughness indices of Type I and Type II ECC link slabs. \[\{\mathbf{D}\}=\left\{ \begin{array}{cccccc}d_{11}&\ldots&d_{1j}&\ldots&d_{1n}\\ \vdots&\ddots&&\\ d_{i1}&&d_{ij}&&\vdots\\ \vdots&&&\ddots&\\ d_{m1}&&\ldots&&d_{mn}\end{array} \right\}, \tag{15}\]  
where \(s_{ij}\) and \(d_{ij}\) refer to the strains and displacements of the \(i\)th measuring point at the \(j\)th loading step, respectively; \(m\) is the number of measuring points and \(n\) is the number of loading steps. The Type II ECC link slab is exampled to demonstrate the working state modes since it contains all series of strain measuring points as well as the two critical points through the whole working state. The working state mode of Type II ECC link slab can be divided into five groups, including the strains measured along the top midline (S\({}_{\text{top}}\)), the strains measured along the side midline (S\({}_{\text{side}}\)), the strains of the CFT grids (S\({}_{\text{grid}}\)), the strains of the reinforcing steels embedded in the link slab (S\({}_{\text{steel}}\)), and the displacement at the mid location of the link slab (D\({}_{\text{m}}\)). The strain-based working state modes are plotted in Figure 11, where the local working behavior characteristics can be perceived in terms of \"shape\" and \"incremental amplitude\". The displacement-based working state mode is represented by the relationship between D\({}_{\text{m}}\) and loading steps, as shown in Figure 12.  
Figure 11: Strain-based working state modes for various groups: (**a**) S\({}_{\text{top}}\)-based working state mode; (**b**) S\({}_{\text{side}}\)-based working state mode; (**c**) S\({}_{\text{grid}}\)-based working state mode; and (**d**) S\({}_{\text{steel}}\)-based working state mode. Figure 11 vividly exhibits the development of working state modes where the red dash lines correspond to the critical loading steps of yielding/initial failure for Type II ECC link slab. It can be seen from Figure 11a that S\({}_{\text{top}}\) grows at quite a slow pace before M1 and then a sudden change in the incremental amplitude of S\({}_{\text{top}}\) is observed around M1. Thereafter, another mutation of S\({}_{\text{top}}\) happens in the wake of M2. The developing rate of the S\({}_{\text{top}}\) at T1 and T3 is faster than the others, indicating that these zones are the weak parts of Type II ECC link slab. The strains along the side grow obviously faster than those along the top, as shown in Figure 11b. Before M1, the strain values at the five points are basically in a straight line (approximately at the same level), due to the flat state within this zone. After M1, the strains near the top surface develop much faster than those interior ones, indicating that the flat state begins to feature the nonlinearity to some extent. This could be attributed to the formation of micro-cracks around M1. The development of strains is accelerated with the crack propagation after M1. Moreover, all the measuring points along the side have transited into the tension state after M2 and the subsequent plastic deformation is considerable. It is illustrated in Figure 11b that the qualitative transformation from the sectional flat state to the non-flat state occurs when the load reaches the critical point M1 and this irreversible change becomes more remarkable after M2.