Vertical Acceleration Analytical Approaches

The analytical model was developed in particular to investigate the moment and shear demands in integral bridge girder-to-cap connections under various earthquake load scenarios. Since the influence of vertical ground motion is a particular area of concern for such connections, special attention was given to appropriate methods for incorporating vertical acceleration effects into this analysis. Three approaches for modeling vertical ground motion were considered: (1) modeling the vertical acceleration as constant pseudostatic upward or downward force along the bridge superstructure, (2) using a time- history analysis incorporating horizontal ground motion data from actual earthquake events and modeling the vertical acceleration as two-thirds the magnitude of the horizontal acceleration, and (3) using time-history ground motion data for both horizontal and vertical acceleration as recorded in actual earthquake events. All three of these approaches have been used in similar analytical efforts and are discussed in the following sections.

6.3.1.Constant Vertical Acceleration

From a modeling standpoint, a simple way to incorporate vertical acceleration effects is to use a static force based on the structure’s mass and the expected vertical acceleration. With this method the definition of the load is straightforward, the analysis tends to be stable, and the results are easily interpretable. The challenge with this method is using a meaningful vertical acceleration and associated constant force. Studies continue to investigate likely magnitudes of vertical acceleration during earthquake events, but regional effects like topography, soil type, and proximity to fault make such predictions very difficult.

6.3.2.Vertical Acceleration as a Function of Horizontal Acceleration

Much of the recent research effort related to vertical acceleration has focused on comparing magnitudes of peak ground acceleration (PGA) in the horizontal and vertical directions. A common practice is to use 2/3 as the ratio of peak vertical to peak horizontal acceleration (V/H), but it is currently recognized that this practice is not always conservative. Because of the complexity of the relationship, many of the current efforts related to modeling vertical acceleration utilize numerical parametric approaches to develop V/H estimates. These algorithms are developed to learn the nonlinear relationships between predictive variables and the V/H ratio directly from the ground motion data, such as the study by Tezcan and Cheng (2012). Many other studies in the past couple of decades have proposed similar models using site and ground motion parameters, such as Gulerce and Ambrahamson (2011), Kalkan and Bulkan (2004), and Ambraseys and Simpson (1996).

These and similar studies have shown that the V/H ratio is typically less than or equal to 2/3. A study by Yang and Lee (2007) investigated the vertical and horizontal ground motion characteristics during the earthquake in Niigata-ken Chuetsu, Japan, in 2004. This study showed that V/H was typically less than or equal to 2/3 for this data set, but for a few sites the ratio was as high as 1. The study concluded that the V/H ratio was strongly dependent on spectra frequency, site-to-source distance, and site condition. It showed that the V/H ratio could be significantly higher than 2/3 at short periods, in near-field regions, and at extremely long periods.

6.3.3.Horizontal and Vertical Ground Motion

The studies mentioned above focus on the V/H ratio, taking V as the magnitude of the vertical PGA and H as the magnitude of the horizontal PGA. The limitation of this method is that it utilizes the peak values from both the vertical and horizontal directions, but these peak values rarely occur at the same time. Thus, using the V/H ratio to predict vertical ground motion based on horizontal ground motion is likely to be overly conservative. One of the only studies that considered simultaneous vertical and horizontal accelerations was conducted by Ambraseys and Douglas (2000), along with a follow-up study in 2003. These studies mentioned the limitation of omitting consideration of simultaneous behavior: “A major draw-back of the acceleration ratio…for practical purposes is that in an earthquake the maximum ground or response accelerations in the vertical and horizontal direction occur at different times.”

However, in a couple significant earthquake events the peaks have been verified to occur at almost the same time, especially for near-fault rock sites. Figure 6.1a shows the ground motion for two such sites, the Pacoima Dam during the 1994 Northridge event and Eureka Canyon Road during the 1989 Loma Prieta Event. The peak vertical motion (middle line on both records) occurs at almost exactly the same time as the peaks in the two horizontal directions (top and bottom lines on both records). Interestingly, the near-fault non-rock sites do not show similar behavior, as indicated by the records in Figure 6.1b that are also from the Northridge event. Comparing these records shows the difficulty of developing a one-size-fits-all approach to predicting vertical acceleration based on horizontal ground motion.

a. Rock sites from the 1994 Northridge event (top) and the 1989 Loma Prieta event (bottom)

b. Close soil sites from the 1994 Northridge event

Figure 6.1. Horizontal and vertical component acceleration time histories from the 1994 Northridge and 1989 Loma Prieta events (Silva, 1997)