## 1 Introduction  
Near-field ground motions (NF) differ from ordinary (far-field) ground motions. The proximity to the fault renders the effect of the global displacements and the mutual displacements of the opposite sides of the fault very evident in the records: (i) the vertical motion component maximum values often exceeds the horizontal component [1]; long period velocity pulses can be generated by (ii) earthquake directivity and (iii) fling-step [2], (iv) differential input displacements at the base of the piers [3]. For (i), in structures prone to axial force variation, the combined effect of horizontal and vertical motions can bring to severe structural demand [4]. Case (ii) happens due to the focusing of wave energy along the fault in the direction of rupture, when this latter propagates towards the site (forward directivity) and when the velocity of propagation is slightly slower than the shear wave velocity, causing the seismic energy to arrive in a large pulse of motion [5]. In this case, the pulses in the velocity time series are generally double-sided, and they are stronger in the component of motion normal to the fault strike. Case (iii) (fling-step) occurs when the earthquake causes major surface rupture. In this case, there is a slow increase of stresses in the earth crust over long periods of time. Then, the stresses are abruptly released causing a permanent offset in the displacement time series [6]. Fling-step effects produce single-sided pulses. For dip-slip faults, also these effects are observed in the component of motion normal to the fault strike. Case (iv), differential displacements, will not be treated here even though the authors discussed possible input generations and relative effects in various publications [7; 8]. Near-fault effects on bridges are usually investigated by means of Nonlinear Response History Analyses (NRHA) [9; 10; 11; 12]. Consequently, a method frequently used to assess the response of structures to NF is Incremental Dynamic Analysis (IDA) [13], which requires the execution of several NRHA using a set of ground motion records. NRHA allows for the proper estimation of the seismic demand and capacity of structures in the time domain considering the horizontal and vertical components of the seismic action (the vertical one is relevant for NF events). Due to the significant amount of time required for analysis and complexity required to perform several NRHAs and to the specific complexity of the dynamic method, it is useful to investigate alternative static methods that can provide results with lower computational effort. For these reasons, some authors proposed the use of pushover analyses to investigate the response of bridge structures under near-fault seismic input [14; 15]. In [16; 17; 18], the authors of the paper at hand proposed an incremental (in terms of seismic intensity) pushover-based procedure (specifically developed for bridges) named IMPA\(\beta\), and discussed the validity in case of far-field records (FF). The procedure employs the envelope of a single-run conventional uniform pushover analysis (UPA) and of a modal pushover analysis (MPA), to determine the seismic demands for each intensity level considered. In the case of NF ground motions, the vertical action becomes relevant; therefore, its consideration or neglect thereof should be discussed. In this work, this issue has been considered and the necessity of performing vertical and horizontal pushover has been evaluated by testing the IMPA\(\beta\) procedure substituting MPA with the Extended Modal Pushover Analysis (EMPA) [19], which considers all the components of the records. Nonetheless, as discussed in SS2, EMPA results were coincident with MPA. Scope of the work presented is therefore the evaluation of this innovative procedure proposed for bridges to be proposed also in case of near-fault events. This activity was performed testing a review of the IMPA\(\beta\) in order to obtain a procedure more suitable for near-fault events.