Abstract
Since 1989 Loma Prieta earthquake and 1994 Northridge earthquake,performance-based earthquake engineering(PBEE)has been widely recognized in both engineering practice and academic research of seismic analysis of above ground structures[1].Ground motion intensity measure(IM)is a key link between the seismic hazard analysis and structural seismic response analysis,which plays an important role in the PBEE framework.Therefore,how to define a reasonable ground motion IM which can represent earthquake intensity and reduce the dispersion of structure response has become a critical topic in the field of earthquake engineering.
In order to find suitable IMs for seismic response analysis of mountain tunnels,a two dimensional finite element model is established in this paper to simulate the nonlinear dynamic interaction between mountain tunnel and surrounding rock.The general-purposed finite element code ABAQUS is employed in this study for the nonlinear dynamic time-history analyses of mountain tunnel subjected to earthquake excitation and the numerical model is depicted in Figure 1.The model is 160 m wide and 100 m deep.The modelled tunnel has a circular cross section of radius r=5 m and its center is located 50 m below the ground surface.The lining inner radius is 4.5 m and the wall thickness is 0.5 m.The concrete lining of tunnel is simulated by the concrete damaged plasticity constitutive model and the surrounding rock is simulated by the Mohr-Coulomb constitutive model.The boundary conditions of the model are as follows:the boundary at the top of the numerical model is free and the boundary at the model bottom is artificial viscousspring boundary[2].Tied degrees of freedom boundary(TDOF)which imposes horizontal kinematic constraints to the nodes with the same burial depth at the two lateral boundaries of model are applied at the lateral boundaries of the model[3].The whole analysis process is divided into two steps to produce a more realistic simulation of seismic responses of tunnel structures.The first step is to establish geostatic stress equilibrium.Then,ground motion is applied to the bottom boundary to perform dynamic analyses.The near field ground motion without velocity pulse and far field ground motion recommended by FEMA-P695 are used as the input ground motions for the numerical study[4].Comparison of capability of the commonly used twenty IMs including the efficiency,practicality and sufficiency in assessing the engineering demand of tun_nel structures are presented in this paper[5-7].
Figure 1 Finite element model
Besides,the overall lining damage indices in compression(OLDC)and in tension(OLDT)are used as the engineering damage measures(DMs)to estimate the lining damage state.
where
is the dissipated energy of the i th element;
and 
are the damage index of the i th element in compression and tension,respectively.OLDC and OLDT reflect the cross-sectional lining damage of the mountain tunnels in single values,which can be easily correlated to scalar seismic IM.
Previous researchers found that DM-IM relationships follow a standard power law as shown in Eq.(3)[8].
which can be transformed into
This transformation allows the constants ln(a)and b to be estimated by simple linear regression of ln(DM)and ln(IM).The efficiency is characterized in terms of the dispersion of the residuals of linear regression results.The dispersion is quantified by the standard deviation of the logarithm of the residuals,denoted as σherein and can be calculated by
The numerical results of efficiency of the selected IM s are shown in Figure 2.
Figure 2 Regression analysis results for the efficiency of all IM s
Practicality refers to whether or not there is any direct correlation between an IM and the DM.If a ground motion IM is not practical,there is little or no dependence of the level of structural demand upon the level of the IM.Practicality is measured by the regression parameter b in Eq.(4).Larger b value indicates that the IM is more practical.The results of practicality of the selected IM s are shown in Figure 3.
Figure 3 Practicality comparison of candidate IM s
In addition to the discussion of efficiency and practicality of IM s,the sufficiency of IM s is also considered in this study.Sufficiency is determined by the statistical significance of the trend of the residuals from the regression between the DM and magnitude(M)or distance(R).The results of sufficiency are shown in Figure 4 and Figure 5.
Figure 4 P-values of IM s-OLDC regressions
Figure 5 P-values of IM s-OLDT regressions
Based on the criteria of efficiency,practicality and sufficiency,Arias intensity measure is the optimal IM for the seismic performance assessment of mountain tunnels.