# Stressing State Analysis of CFST Arch Supports in Deep Roadway Based on NSF Method
## 5 Stressing State Analysis of the CFST Arch Support-A  
### Gsed-Based Stressing State Mode and Characteristic Parameter  
Here, GSED values calculated by Equations (2) and (3) are chosen as the characteristic parameter to study the structural working behavior of the support-A, and in order to avoid the influence of unit and better investigate the developing tendency, the GSED values are normalized by the Equation (4). Correspondingly, the characteristic parameter \(E_{j,\mathrm{norm}}\) is plotted under load \(F_{j}\) curve to reflect the changing characteristics of structural stressing state. Then the M-K criterion are applied to the \(E_{j,\mathrm{norm}}\)-\(F_{j}\) curve, hence the three mutation points of the stressing state are detected, respectively \(Q=700\) kN (from 0 kN to ultimate load \(U\)), \(L=400\) kN (from 0 kN to \(Q\)) and \(R=800\) kN (from load \(Q\) to \(U\)), shown in Figure 6. Evidently, before load \(L\) the \(E_{j,\mathrm{norm}}\)-\(F_{j}\) curve manifests almost linear growth, signifying that the whole support-A is in quite stable elastic stressing state. Thereafter, the curve increases still slowly and steadily, but in a curvilinear shape, which could be indicated that the support generates a certain plastic deformation and enters stable elastic-plastic stressing state. When it comes to load \(Q\), the curve increases within a narrow range probably due to the further plastic development of the support, implying that the support basically goes into plastic stressing state. Then, as the load exceeds load \(R\), the curve develops sharply and rapidly, which embodies a trend completely different from the previous one. At this stage, the support enters a quite unstable stressing state until the ultimate load \(U\), reflecting the qualitative change of the support. Therefore, load \(R\) is defined as the failure load of the support, which is updated the existing failure load (ultimate load). The updated failure load is revealed according to the natural law from quantitative change to qualitative change of a system, which represents the starting point of the support's failure process. The determination of the load is not based on any assumption, which reflects inherent mutation characteristic of the structural stressing state. That is to say, the mutation load of the structural stressing state is determinate and could be taken as the reference to the determination of structural design load.  
Figure 6: \(Cont.\)  
Hence, the structural stressing state of CFST arch support-A could be divided into four stages by characteristic loads \(L\), \(Q\) and \(R\): (1) Before load \(L\), the support is in a very stable elastic stressing state and load \(L\) is defined as the demarcation point between structural elastic and elastic-plastic stressing state stages; (2) between loads \(L\) and \(Q\), the support begin to enter the nonlinear stressing state, namely elastic-plastic stressing state stage, correspondingly load \(Q\) is defined as the demarcation point between structural elastic-plastic and plastic stressing state stages; (3) from load \(Q\) to \(R\), the support is in the plastic stressing state stage, but \(E_{j,\text{norm}}\) still keeps a relative stable growth, revealing quantitative change instead of qualitative change; (4) after load \(R\), the stressing state of the support changes suddenly and qualitatively until the ultimate load \(U\) and this stage could be defined as failure stressing state.