**5. FE Evaluation process – System behavior analysis**

The previous section indicates that the goals of the vulnerability evaluation influences the selection of FE modeling options including software (structural or general purpose), level of analysis (2D or 3D), element selection (structural or continuum), connectivity (rigid connec‐ tions or flexible bearings), boundary conditions (fixed, flexible, or absorbing). These choices not only influence the behavior and response details that may be estimated and Visualized, they also determine what output measures are available for estimating physical damage, performance characteristics, and vulnerability.

In the MEMA UM campus study [17], a basic analysis approach was established that was followed throughout all the studies. Before proceeding to the complex nonlinear dynamic time history analysis, linear static and eigenvalue preliminary analyses were first performed. The **10** 1 study of a

**12** Figure 10

**12** 6 stiffness mass

be made partially transparent)

(piles and springs not visible below water free surface; water and soil layers need to

linear static gravity load analysis requires processing of all parameters and procedures involved in estimating the stiffness properties of the system. It is relatively fast computation‐ ally and enables visual and quantitative confirmation of element connectivity and effect of support fixity (fixed base models), support flexibility (soil springs), or absorbing boundary conditions (SSI models). The eigenvalue analysis requires processing of all parameters and procedures involved in estimating the mass properties of the system. The analysis is also relatively fast computationally and yields mode shapes and frequencies. These modal properties provide insight into the expected dynamic response characteristics under earth‐ quake loading. **11** 4 supported support **11** 7 only primarily **11** 16 engineering engineering ones **11** 28 -system - System **11** 33-34 visualized. They Visualized, they **12** 2 rapid relatively fast computationally

Pier 1

ground motion applied to footing springs

deck and intermediate bents.

events.

Pier 2

Pier 3 

FE Based Vulnerability Assessment of Highway Bridges Exposed to Moderate Seismic Hazard

6-DOF Concrete Piled Footing Springs (Typ.)

**Figure 11.** Model [16] of typical 3-span continuous concrete box girder bent for Coldwater River bridge carrying two lanes of interstate highway traffic; concrete pier columns and footing piles modeled with frame elements; box girder flanges and webs and footing pile cap modeled with shell elements; footings modeled with equivalent 6-DOF springs;

Figure 12 illustrates some of the benefits of performing the preliminary analyses before proceeding to the nonlinear time history response analysis. The issues of stiffness and mass distribution become evident from the plotting and animation of the mode shapes associated with global movements of the system. These shapes may be broadly categorized as ones that involve significant net movement of the center of mass of the system and those that do not (sometimes called breathing modes). In the case of the campus bridge shown, it is seen that the mode involving transverse movement of the mass center becomes coupled with a rotational movement because of the skew of the deck necessitated by the angle between the centerlines of the street carried and the one crossed. Also visualized in the case shown in Figure 12 is the effect of the SSI, in this case the embankments and abutments interacting with the main span

Behavior similar to that observed for the MEMA UM campus study bridge is found in the case of the MDOT study bridge. Figure 13 shows the transverse mode shape for the fixed base model. The bridge proportions (both deck length to width and deck span to column height ratios) and skew angle are different in the two cases. The translational and rotational coupling

The eigenvalue analyses not only provide insight regarding the expected deformation patterns, they also provide the frequencies associated with these characteristic modes. These frequencies provide quantitative information which provide insight into the expected influence of the SSI effects as well as the dominance of deformation modes associated with specific earthquake

The influence of SSI was examined in detail in the MDOT study which included ambient vibration measurements using a portable array of accelerometers [11, 14]. Simultaneous readings were taken at each bent location under excitation of the bridge by truck traffic. Using

is less pronounced, and the transverse column bending is more pronounced.

Pier 4 

http://dx.doi.org/10.5772/55334

197

3-DOF Bearing Link Element (Typ.)

**12** 10 model Model **13** 2 model Model **Figure 10.** Model of typical intermediate bent for Coldwater River bridge [16] carrying two lanes of interstate high‐ way traffic; concrete piles and cap modeled as frame elements (section behavior modeled with axial-bending interac‐ tion using fiber model); ground motion applied to soil springs

linear static gravity load analysis requires processing of all parameters and procedures involved in estimating the stiffness properties of the system. It is relatively fast computation‐ ally and enables visual and quantitative confirmation of element connectivity and effect of support fixity (fixed base models), support flexibility (soil springs), or absorbing boundary conditions (SSI models). The eigenvalue analysis requires processing of all parameters and procedures involved in estimating the mass properties of the system. The analysis is also relatively fast computationally and yields mode shapes and frequencies. These modal properties provide insight into the expected dynamic response characteristics under earth‐

3

quake loading.

(piles and springs not visible below water free surface; water and soil layers need to

**12** 6 stiffness mass

be made partially transparent)

**12** 10 model Model **13** 2 model Model

**11** 28 -system - System

**11** 4 supported support **11** 7 only primarily

**11** 16 engineering engineering ones

**11** 33-34 visualized. They Visualized, they

**12** 2 rapid relatively fast computationally

/

Bearing Load (Typ.)

196 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

Soil spring (Typ.)

Soil spring

tion using fiber model); ground motion applied to soil springs

(Typ.) Soil

**Figure 10.** Model of typical intermediate bent for Coldwater River bridge [16] carrying two lanes of interstate high‐ way traffic; concrete piles and cap modeled as frame elements (section behavior modeled with axial-bending interac‐

Soil Layer 1

> Soil Layer 2

> > Layer 3

Water

**10** 1 study of a

**12** Figure 10

**Figure 11.** Model [16] of typical 3-span continuous concrete box girder bent for Coldwater River bridge carrying two lanes of interstate highway traffic; concrete pier columns and footing piles modeled with frame elements; box girder flanges and webs and footing pile cap modeled with shell elements; footings modeled with equivalent 6-DOF springs; ground motion applied to footing springs

Figure 12 illustrates some of the benefits of performing the preliminary analyses before proceeding to the nonlinear time history response analysis. The issues of stiffness and mass distribution become evident from the plotting and animation of the mode shapes associated with global movements of the system. These shapes may be broadly categorized as ones that involve significant net movement of the center of mass of the system and those that do not (sometimes called breathing modes). In the case of the campus bridge shown, it is seen that the mode involving transverse movement of the mass center becomes coupled with a rotational movement because of the skew of the deck necessitated by the angle between the centerlines of the street carried and the one crossed. Also visualized in the case shown in Figure 12 is the effect of the SSI, in this case the embankments and abutments interacting with the main span deck and intermediate bents.

Behavior similar to that observed for the MEMA UM campus study bridge is found in the case of the MDOT study bridge. Figure 13 shows the transverse mode shape for the fixed base model. The bridge proportions (both deck length to width and deck span to column height ratios) and skew angle are different in the two cases. The translational and rotational coupling is less pronounced, and the transverse column bending is more pronounced.

The eigenvalue analyses not only provide insight regarding the expected deformation patterns, they also provide the frequencies associated with these characteristic modes. These frequencies provide quantitative information which provide insight into the expected influence of the SSI effects as well as the dominance of deformation modes associated with specific earthquake events.

The influence of SSI was examined in detail in the MDOT study which included ambient vibration measurements using a portable array of accelerometers [11, 14]. Simultaneous readings were taken at each bent location under excitation of the bridge by truck traffic. Using

**Figure 12.** Eigenvalue analysis results for the MEMA UM campus study bridge models [17]; top figures show plan and isometric views of fixed based model transverse mode causing bent and abutment column deformation; bottom fig‐ ures show comparable modes for SSI model; skew of roadway alignment introduces coupling of translation and rota‐ tion of the deck mass as well as bending and torsion of the deck; the resistance provided by the embankment is apparent from the contact developed during rotation

a point on the bridge deck as a reference point, frequency response functions were derived that eliminated the influence of the excitation, and system response frequencies were extracted corresponding with excellent correlation to the 3D model SSI case without any model param‐ eter modification. Accelerometers were then moved to the abutments and frequency extraction performed [11] revealing evidence of the participation of the abutments in the transverse mode shape comparable to the one in Figure 13.

In the MEMA bridge study, the preliminary analyses were again performed prior to time history analysis. Figure 14 shows that the fundamental mode of vibration for a typical intermediate bent in the interstate highway river crossing is one involving net translation of the deck and corresponding bending of the piles which were designed as axially loaded members. Consideration of the eccentricity of the deck mass with respect to the center of resistance of the soil-pile system provides for expectation of an overturning moment. Such a moment would generate an increase of axial force in one of the batter piles which would combine with the bending action.
