**10. Embankment properties**

218 Earthquake Engineering

the next 50 years exceeds 80%.

**9. Bridges in the commonwealth of Kentucky** 

bridge embankments on or over I-24 in western Kentucky.

generated for the 127 bridges on or over I-24 in western Kentucky.

evaluation studies as well as post-earthquake inspection.

Bridges in the western region of the Commonwealth of Kentucky are located near the New Madrid seismic zone, which is potentially one of the most destructive fault zones in the United States. It extends through the Mississippi River Valley and encompasses 26 counties in western Kentucky in the area of its strongest influence. Studies have shown that the probability of an earthquake with a 6.3 magnitude on the Richter scale to hit this area within

Passing through seven counties in western Kentucky, I-24 is considered a vital transportation link for the commonwealth of Kentucky. I-24 passes through McCracken, Livingston, Marshall, Lyon, Trigg, Caldwell, and Christian counties in western Kentucky (Figure 4). The objective of this part of the Chapter is to investigate the seismic risk of all

In order to achieve the study objective, a means of accessing which embankments qualify as "most critical" is required. The methodology presented earlier in this Chapter is applied to assess the seismic vulnerability of I-24 bridge embankments. The embankment geometry, materials, type and properties of underlying soil, elevation of the natural ground line, and upper level of bedrock are estimated for each embankment. The minimum seismic slope stability capacity/demand, (*C/D)min* ratio, embankment displacement, and liquefaction potential of each bridge embankment are calculated. Bridge embankments along I-24 in western Kentucky are assigned one of three possible categories to represent their seismic failure risk. A final priority list of the embankments with the highest seismic risk is

**On-Site Inspection of I-24 Bridges in Western Kentucky:** On-site inspection of the bridges, including photographing different structural components of each bridge, was carried out. The on-site inspection records form an invaluable source that assists in pre-earthquake

**I-24 Bridge Inventory in Western Kentucky:** One objective of the on-site inspection is to have an informative source of accurate and updated bridge records, which are required for most assessment studies including the current study of seismic ranking and prioritization of I-24 bridge embankments in western Kentucky. Another objective of the on-site inspection is to provide engineers and transportation officials with information delineating the current bridges' conditions in order to facilitate future comparisons with post-earthquake conditions immediately after future earthquakes. Through these comparisons, significant changes can be reported and further studies can be carried out. All the bridges and embankments along I-24 in western Kentucky were visually inspected, photographed and the records were stored in a database. The on-site inspection represents a significant supplement to the "asbuilt" bridge plans. A comprehensive inventory of the bridges was compiled by review of the "as-built" bridge plans, construction and maintenance records, and on-site inspection forms. The inventory provides an essential data record, which is utilized for risk assessment of I-24 bridges and embankments in western Kentucky. A one-page sample of the I-24

The geometry of each bridge embankment on or over I-24 in western Kentucky is taken from the bridge plans. The geometry of the 127 studied embankments is classified into five types (Figure 5*a*-5*e*). An embankment has either a single slope or double slopes separated by a perm. The inventory of I-24 bridge embankments in western Kentucky shows that a given slope has one of three possible inclinations (1:1, 2:1, or 3:1), where the first number of the ratio represents the horizontal unit and the second number represents the vertical unit. The drawings shown in Figure 5*a*-5*d* are for cases where the feature crossed by the bridge is either a highway or a railway. The drawing shown in Figure 5*e* is found when the bridge crosses a waterway. The embankment slope geometry is identified by its height (*H*) and the idealized inclination (*b*) (Figure 6). The analysis is carried out on both ends of each bridge and the most critical embankment slope at either end; whichever analysis results in a lower seismic slope stability *C/D* ratio is considered in the seismic vulnerability ranking.

Accurate identification of the soil characteristics requires detailed site-specific subsurface exploration. This approach is expensive, and such data is not available for the majority of the bridge embankments along I-24 in western Kentucky. Pflazer [14] reported on the use of existing geo-technical data to supplement site investigations. Another approach to specify the soil type and its properties is to use existing geological and agricultural maps. The source of soil data is dependent on the *NGL* (Figure 5*f*-5*g*). The *USGS* and the *USDA*  are used to identify the soil type underneath an embankment. The way by which either

Bridge Embankments – Seismic Risk Assessment and Ranking 221

**Figure 6.** Example of bridge embankment geometry and materials

estimated from the *USGS maps.* 

map is chosen for a given bridge site is based on the level of the "*Natural Ground Line*" (*NGL*) as compared to the respective embankment base (Figures 2*f*, 2*g,* and 3). Whenever the level of the *NGL* is above the level of the embankment base by more than 1.50 m (5 ft), the soil type is solely identified in accordance with the *USGS* maps. Whenever the level of the *NGL* is either above the level of the embankment base by less than 1.50 m (5 ft) or below the level of the embankment base, the soil type is based on both the *USGS* maps, and the *USDA* maps. After specifying the soil type, conservative soil characteristics including shear strength and mass density are estimated. The upper and lower soil layers' types (Figure 5) for embankments in McCracken County are provided in Table 6. Shear strength and mass density for bridge embankments are derived following the guidelines presented earlier. Data regarding the level below which a hard stratum (stiff bedrock layer) exists is not available for the majority of bridge embankment sites along I-24 in western Kentucky. The upper level of the stiff bedrock layer, which falls within the range from the embankment base down to the upper level of the hard stratum, is initially

**Figure 5.** Embankments along I-24 in western Kentucky: geometry classification (Figs. a, b, c, d, e), level of "Natural Ground Line" (NGL) and source of the soil data (Figs. f, g)

**Figure 6.** Example of bridge embankment geometry and materials

**Figure 5.** Embankments along I-24 in western Kentucky: geometry classification (Figs. a, b, c, d, e), level

of "Natural Ground Line" (NGL) and source of the soil data (Figs. f, g)

map is chosen for a given bridge site is based on the level of the "*Natural Ground Line*" (*NGL*) as compared to the respective embankment base (Figures 2*f*, 2*g,* and 3). Whenever the level of the *NGL* is above the level of the embankment base by more than 1.50 m (5 ft), the soil type is solely identified in accordance with the *USGS* maps. Whenever the level of the *NGL* is either above the level of the embankment base by less than 1.50 m (5 ft) or below the level of the embankment base, the soil type is based on both the *USGS* maps, and the *USDA* maps. After specifying the soil type, conservative soil characteristics including shear strength and mass density are estimated. The upper and lower soil layers' types (Figure 5) for embankments in McCracken County are provided in Table 6. Shear strength and mass density for bridge embankments are derived following the guidelines presented earlier. Data regarding the level below which a hard stratum (stiff bedrock layer) exists is not available for the majority of bridge embankment sites along I-24 in western Kentucky. The upper level of the stiff bedrock layer, which falls within the range from the embankment base down to the upper level of the hard stratum, is initially estimated from the *USGS maps.* 


Bridge Embankments – Seismic Risk Assessment and Ranking 223

**Table 6.** Types of upper and lower soil layers for embankment sites in McCracken County, western

Kentucky

**Table 5.** Inventory of I-24 bridges in McCracken County, western Kentucky


**Table 5.** Inventory of I-24 bridges in McCracken County, western Kentucky

**Table 6.** Types of upper and lower soil layers for embankment sites in McCracken County, western Kentucky

Other upper levels of the bedrock layer within that range are also considered, and the controlling case is the one that results in the lowest seismic slope stability *C/D* ratio. The input *PGA* at a designated embankment site is obtained from seismic maps generated by [7] for 50-year, 250-year, and 500-year events. The 50-year, 250-year, and 500-year events are seismic events with a 90% probability of not being exceeded in 50 years, 250 years, and 500 years, respectively. Figure 4 illustrates an example of the anticipated *PGA* of all counties in the Commonwealth of Kentucky during the 250-year seismic event. The peak ground acceleration for McCracken County during the 250-year event is 0.19 *g,* where *g* is the gravitational acceleration. Other anticipated *PGAs* of all counties in the Commonwealth of Kentucky during the 50-year and 500-year seismic events can be found in the Kentucky Transportation Center report [11]. With the exception of the parallel bridges at the Cumberland River crossing, and at the Tennessee River crossing, each bridge and their embankments along I-24 in western Kentucky is evaluated for the 50-year and 250 year seismic events, for which valuable input data is taken from a study conducted by Street et al. [7]. During the 50-year seismic event, the bridges are expected to behave elastically without any disruption to traffic. During the 250-year seismic event, partial damage to the bridges is permitted, and the bridges are expected to remain accessible to emergency traffic. I-24 parallel bridges at the Cumberland River and at Tennessee River crossings are evaluated for the 250-year seismic event and the maximum credible 500-year seismic event. Detailed evaluation of these bridges and their embankments are presented elsewhere [11].

Bridge Embankments – Seismic Risk Assessment and Ranking 225

ratio of *Ay*/*Amax*, where *Ay* is the acceleration causing yielding in the embankment slope and *Amax.* is equal to the *PGA*. The displacement of the slope with a specified *PGA* exceeding the *Ay* is estimated. At intervals for which the *PGA* exceeds *Ay* (*Y* is less than 1.0), the occurrence of slope displacement is expected. Decreasing *Ay* results in increasing the magnitude of the embankment displacement, correspondingly. As the seismic slope stability of an embankment decreases, a larger displacement is expected, providing a stronger indication of an at-risk embankment than that obtained from the (*C/D)min.* ratio analysis. One advantage of this methodology is that the analysis eliminates the misleading condition of how to assess an embankment that has (*C/D)min.* ratio1.0, and instead forces a consideration of the possible embankment displacement. The vulnerability rating for a designated soil is based on quantitative assessment of liquefaction susceptibility and the anticipated magnitude of the acceleration coefficient [1]. Bridges subjected to low liquefaction potential shall be

It is stipulated that it is not necessary to calculate liquefaction potential for the bridge sites, which are required to resist a seismic acceleration of less than 0.09 *g* [1]. The majority of the area surrounding the fault in the New Madrid Seismic Zone lies on fluvial and alluvial deposits and sandy soils. Defining the liquefaction potential is a matter of considerable concern during the seismic assessment of bridges and their embankments in this region. Western Kentucky encompasses several major bodies of water, including the Ohio River, Mississippi River, Barkley Lake, and Kentucky Lake. These bodies of water cause the saturated soils within the area to be highly susceptible to liquefaction potential. The proximity to these four bodies of water necessitates particular concern when examining the liquefaction potential for bridge sites along I-24 in western

The method to calculate the liquefaction potential is dependent on the availability of the soil boring logs. Whenever the boring logs of an embankment site along I-24 in western Kentucky are not available, the susceptibility of an embankment soil to liquefaction is classified in one of three ways. High susceptibility is associated with saturated loose sands, saturated silty sands, or non-plastic sands. A bridge that crosses a waterway is often constructed on loose saturated cohesionless deposits that are most susceptible to liquefaction. Moderate susceptibility is associated with medium dense soils, such as

Whenever the boring logs of an embankment site along I-24 in western Kentucky are available, the liquefaction potential of the bridge site is accurately determined by the method developed by Seed et al. [9, 10] and reported earlier in this Chapter. This method includes the following four steps: (1) determination of time history of shear stresses induced by the earthquake ground motion; (2) converting the time history to an equivalent number of stress cycles; (3) calculation of the cyclic shear stresses required to cause liquefaction in the same number of stress cycles; and (4) judging the liquefaction potential by comparing the shear stress induced during the earthquake with that required

compacted sand soils. Low susceptibility is associated with dense soils.

assigned a low vulnerability rating.

Kentucky.

to cause liquefaction.

#### **11. Vulnerability analysis of I-24 bridge embankment in Kentucky**

For a bridge on or over I-24 in western Kentucky, the potential of an embankment slope to displace during a designated earthquake event is assessed using the two-dimensional limit equilibrium stability analysis. During the seismic vulnerability evaluation of each embankment, the possibility of occurrence of either circular or wedge–shaped slope failure [11] is investigated and the one that results in the lesser *C/D* ratio is considered in the ranking process. *Kh* equals to 2/3 of the *PGA*. The ranking and prioritization procedure of the embankments is based on three main parameters: (1) seismic slope stability (*C/D)min.* ratio, (2) embankment displacement, and (3) liquefaction potential at the embankment site. For embankments with (*C/D)min.* ratio against sliding1.0, estimation of how far the embankment actually displaces during the ground excitation is necessary. Hence, the displacement of the embankment is calculated. The maximum acceleration (*Amax.*) for a specified seismic event is identified for a designated embankment. For slope displacement to occur, the maximum acceleration must exceed the acceleration causing yielding in the embankment slope (*Ay*). The (*C/D)min.* ratio is calculated for each embankment, and is used to assign a rank for each embankment relative to the other embankments along I-24 in western Kentucky.

Assuming that the yield displacement is equal to *Khf*, which corresponds to the (*C/D)min.* ratios for all the possible failure cases, the resulting 'Yield Factor' (*Y*) is estimated as the ratio of *Ay*/*Amax*, where *Ay* is the acceleration causing yielding in the embankment slope and *Amax.* is equal to the *PGA*. The displacement of the slope with a specified *PGA* exceeding the *Ay* is estimated. At intervals for which the *PGA* exceeds *Ay* (*Y* is less than 1.0), the occurrence of slope displacement is expected. Decreasing *Ay* results in increasing the magnitude of the embankment displacement, correspondingly. As the seismic slope stability of an embankment decreases, a larger displacement is expected, providing a stronger indication of an at-risk embankment than that obtained from the (*C/D)min.* ratio analysis. One advantage of this methodology is that the analysis eliminates the misleading condition of how to assess an embankment that has (*C/D)min.* ratio1.0, and instead forces a consideration of the possible embankment displacement. The vulnerability rating for a designated soil is based on quantitative assessment of liquefaction susceptibility and the anticipated magnitude of the acceleration coefficient [1]. Bridges subjected to low liquefaction potential shall be assigned a low vulnerability rating.

224 Earthquake Engineering

embankments are presented elsewhere [11].

western Kentucky.

Other upper levels of the bedrock layer within that range are also considered, and the controlling case is the one that results in the lowest seismic slope stability *C/D* ratio. The input *PGA* at a designated embankment site is obtained from seismic maps generated by [7] for 50-year, 250-year, and 500-year events. The 50-year, 250-year, and 500-year events are seismic events with a 90% probability of not being exceeded in 50 years, 250 years, and 500 years, respectively. Figure 4 illustrates an example of the anticipated *PGA* of all counties in the Commonwealth of Kentucky during the 250-year seismic event. The peak ground acceleration for McCracken County during the 250-year event is 0.19 *g,* where *g* is the gravitational acceleration. Other anticipated *PGAs* of all counties in the Commonwealth of Kentucky during the 50-year and 500-year seismic events can be found in the Kentucky Transportation Center report [11]. With the exception of the parallel bridges at the Cumberland River crossing, and at the Tennessee River crossing, each bridge and their embankments along I-24 in western Kentucky is evaluated for the 50-year and 250 year seismic events, for which valuable input data is taken from a study conducted by Street et al. [7]. During the 50-year seismic event, the bridges are expected to behave elastically without any disruption to traffic. During the 250-year seismic event, partial damage to the bridges is permitted, and the bridges are expected to remain accessible to emergency traffic. I-24 parallel bridges at the Cumberland River and at Tennessee River crossings are evaluated for the 250-year seismic event and the maximum credible 500-year seismic event. Detailed evaluation of these bridges and their

**11. Vulnerability analysis of I-24 bridge embankment in Kentucky** 

For a bridge on or over I-24 in western Kentucky, the potential of an embankment slope to displace during a designated earthquake event is assessed using the two-dimensional limit equilibrium stability analysis. During the seismic vulnerability evaluation of each embankment, the possibility of occurrence of either circular or wedge–shaped slope failure [11] is investigated and the one that results in the lesser *C/D* ratio is considered in the ranking process. *Kh* equals to 2/3 of the *PGA*. The ranking and prioritization procedure of the embankments is based on three main parameters: (1) seismic slope stability (*C/D)min.* ratio, (2) embankment displacement, and (3) liquefaction potential at the embankment site. For embankments with (*C/D)min.* ratio against sliding1.0, estimation of how far the embankment actually displaces during the ground excitation is necessary. Hence, the displacement of the embankment is calculated. The maximum acceleration (*Amax.*) for a specified seismic event is identified for a designated embankment. For slope displacement to occur, the maximum acceleration must exceed the acceleration causing yielding in the embankment slope (*Ay*). The (*C/D)min.* ratio is calculated for each embankment, and is used to assign a rank for each embankment relative to the other embankments along I-24 in

Assuming that the yield displacement is equal to *Khf*, which corresponds to the (*C/D)min.* ratios for all the possible failure cases, the resulting 'Yield Factor' (*Y*) is estimated as the It is stipulated that it is not necessary to calculate liquefaction potential for the bridge sites, which are required to resist a seismic acceleration of less than 0.09 *g* [1]. The majority of the area surrounding the fault in the New Madrid Seismic Zone lies on fluvial and alluvial deposits and sandy soils. Defining the liquefaction potential is a matter of considerable concern during the seismic assessment of bridges and their embankments in this region. Western Kentucky encompasses several major bodies of water, including the Ohio River, Mississippi River, Barkley Lake, and Kentucky Lake. These bodies of water cause the saturated soils within the area to be highly susceptible to liquefaction potential. The proximity to these four bodies of water necessitates particular concern when examining the liquefaction potential for bridge sites along I-24 in western Kentucky.

The method to calculate the liquefaction potential is dependent on the availability of the soil boring logs. Whenever the boring logs of an embankment site along I-24 in western Kentucky are not available, the susceptibility of an embankment soil to liquefaction is classified in one of three ways. High susceptibility is associated with saturated loose sands, saturated silty sands, or non-plastic sands. A bridge that crosses a waterway is often constructed on loose saturated cohesionless deposits that are most susceptible to liquefaction. Moderate susceptibility is associated with medium dense soils, such as compacted sand soils. Low susceptibility is associated with dense soils.

Whenever the boring logs of an embankment site along I-24 in western Kentucky are available, the liquefaction potential of the bridge site is accurately determined by the method developed by Seed et al. [9, 10] and reported earlier in this Chapter. This method includes the following four steps: (1) determination of time history of shear stresses induced by the earthquake ground motion; (2) converting the time history to an equivalent number of stress cycles; (3) calculation of the cyclic shear stresses required to cause liquefaction in the same number of stress cycles; and (4) judging the liquefaction potential by comparing the shear stress induced during the earthquake with that required to cause liquefaction.

Liquefaction potential of few embankment sites along I-24 in western Kentucky is estimated using standard penetration tests (*SPT*) provided by the 'Kentucky Transportation Cabinet, Department of Materials and Geotechnical Testing.' For the rest of the bridge embankments along I-24 in western Kentucky, any judgment of the liquefaction potential is solely based on the surrounding soil type. The soil type is obtained from the *USGS* and *USDA* maps. A detailed method to predict the liquefaction potential is shown in Zatar et al. [12, 13].

Bridge Embankments – Seismic Risk Assessment and Ranking 227

**Table 7.** Seismic ranking for I-24 bridge embankments in McCracken County for a 250-year event

County, western Kentucky
