**3. Input variables**

The geometry, material, level of natural ground line, soil type, seismic event, and upper level of bedrock constitute the required input for each embankment and are addressed in the following sub-sections.

*Geometry:* The ideal case for obtaining the geometry of a given embankment is to carry out an on-site inspection. Should there be difficulties encountered in gathering such on-site information, however, the embankment geometry may be taken from the bridge plans. It is assumed that utilizing data from a finalized set of bridge plans will not affect the accuracy of the final seismic ranking and priority list for a given embankment case. Embankment slopes are assumed to be free of any evidence of impending failure, swampy conditions, or other terrain conditions that might be relevant to their stability. For a typically irregular slope, an idealization of the slope has to be performed in such a way that results in the lowest seismic slope stability *C/D* ratio. It is assumed that the material that might have been used for erosion protection of the slope will not greatly influence the resulting seismic slope stability, and therefore is not considered as an input parameter. The embankment slope geometry is identified by its height (*H*) and the idealized inclination (*b*) (Figure 1). The water table is assumed to be located below the embankment base in order to obtain the most critical seismic stability conditions. Analysis shall be carried out on both ends of each bridge and the most critical embankment slope at either end, which results in the lower seismic slope stability *C/D* ratio*,* shall be considered in the ranking analysis and priority list.

204 Earthquake Engineering

This Chapter addresses the technical component of embankment prioritization and is well-

In order to achieve the objective of this study, a flowchart is generated to assess the seismic vulnerability of multiple bridge embankments simultaneously. The embankment geometry, material, type of underlying soil, elevation of natural ground line, upper level of bedrock, and expected seismic event in accordance with associated seismic zone maps constitute the variables for each embankment. This methodology results in calculating the seismic slope stability capacity/demand (*C/D*) ratio, estimated displacement, and liquefaction potential of each bridge embankment for the respective expected seismic event. Seismic vulnerability ranking and prioritization of embankments are conducted by using the "Kentucky Embankment Stability Rating" (*KESR*) model. Three categories are identified in the KESR model to represent the failure risk of the embankments. A priority list of the embankments

In general, data regarding soil types and depth of bedrock are not available for many existing bridge embankments to allow for detailed seismic analysis and risk assessment. This Chapter provides a methodology that enables identifying the embankments that are susceptible to failure during a seismic event. Having categorized the embankments in a designated region according to the respective failure risk, a priority list that includes the most critical bridge embankments can then be highlighted. When site-specific data for a bridge embankment is available, it can be used to obtain the list of seismically deficient embankments. When site-specific data for a bridge embankment is not available, the proposed methodology outlines an approach to estimate the information that is required to obtain the priority list. It is understood that the resulting seismic risk of a specific embankment may not be very accurate due to limited available data or lack thereof. However, the estimated data and strength parameters that are available for utilization shall be assessed by a qualified geo-technical engineer in order to ensure valid results. In order to facilitate the application of the proposed ranking methodology, assumptions, calculations, and required checks are presented along with the parameters of each embankment. The parameters of each embankment include the respective geometry, material, seismic event, upper level of bedrock, level of natural ground line, soil type, and anticipated failure types. The following sections: input variables, embankment vulnerability analysis, ranking parameters, category identification, and ranking and prioritization are provided to outline

The geometry, material, level of natural ground line, soil type, seismic event, and upper level of bedrock constitute the required input for each embankment and are addressed in

suited to a reliability-based model for seismic risk assessment.

with the highest seismic risk can be generated for any set of embankments.

all of the necessary steps to achieve the study objective.

**3. Input variables** 

the following sub-sections.

**2. Seismic vulnerability and ranking of bridge embankments** 

*Materials, Natural Ground Line and Soil Properties:* The soil profile at a bridge site is often composed of naturally deposited soils rather than controlled fill. The profile usually consists of multiple layers of different soils and the contact between softer foundations and stiffer bedrock soils is typically irregular. Defining the soil conditions at a site requires detailed site-specific sub-surface exploration that is not available at the majority of existing bridge embankment sites. Therefore, another approach is employed herein to specify the soil types and properties of applicable sites. It is assumed that any soil outside the embankment zone at a bridge site has uniform un-drained shear strength. The soil is considered to be in continuous contact with the bedrock layer, where the bedrock acts as a layer possessing high strength at some depth below the embankment.

Soil data is dependent on the level of the Natural Ground Line (*NGL*), shown in Figure 1. Both the "*Geologic Quadrant Maps of the United States"* that are provided in "*United States Geologic Survey* (*USGS*)" maps [2] and the "*Soil Conservation Service, Soil Survey"* maps that are reported by "*United States Department of Agriculture* (*USDA*)" [3] are used to identify the soil type underneath an embankment. The way by which either map is chosen is based on the level of the *NGL* as compared to the embankment base. Whenever the level of the *NGL* is above the level of the embankment base by more than 1.5 m. (5 ft), the analysis is solely based on the soil data obtained from the "*Geologic Quadrangle Maps of the United States",*  provided by *USGS* [2]. Otherwise, the soil data is derived from the "*Soil Conservation Service, Soil Survey",* provided by *USDA* [3].

The dependency on the *USDA* maps in this case can be attributed to the fact that the top 1.5 m. (5 ft) soil can be accurately obtained from these maps. Shear strengths are assigned as done so by [4] for non-cohesive soil materials, which were derived from analysis of standard penetration tests (Table 1). When a range of values is given for the shear strength of a given soil, the lowest value is assigned to accommodate for the anticipated liquefaction potential at many bridge sites [5]. The shear strength assigned for cohesive soils in Table 1 is chosen after examining commensurately accurate un-confined compression data. Shear strengths assigned to the embankment fill are adjusted to reflect the cyclic loading effects between undrained failure for both cohesive and saturated cohesion-less soils, in addition to the intermediate behavior between drained and un-drained for dry and partially saturated soils. The density and shear strength of the embankment soils are conservatively estimated by assuming that marginal compaction may have occurred during construction. Should there be more accurate soil properties, they may replace those provided in Table 1.

Bridge Embankments – Seismic Risk Assessment and Ranking 207

**Table 1.** Density and strength of soils and embankments

required to resist the 500-year seismic event.

**4. Embankment vulnerability analysis** 

rather than providing only the required derivations and equations.

*Seismic Event:* The input Peak Ground Acceleration (*PGA*), which is the maximum bedrock acceleration at a designated embankment site, is obtained from seismic maps that are generated for specific seismic events. The choice of the seismic event is based on the importance and anticipated performance of the bridge as well as its geographic location on the seismic maps. The seismic maps to define the acceleration coefficient based on a uniform risk method of seismic hazard can be used. The probability that the acceleration coefficient will not be exceeded for a 50-year event is estimated to be 90%, with an expected return period is of 475 years [6]. Alternatively, seismic maps that may have been generated by State Departments of Transportation can be used. For the Commonwealth of Kentucky 50-year, 250-year, and 500-year seismic events were developed [7]. These events have a 90% probability of not being exceeded in 50 years, 250 years, and 500 years, respectively. All but four of the bridges and their embankments on priority routes in western Kentucky are required to withstand the 50-year and 250-year seismic events. The four other bridges are

The potential for slope displacement to occur during an earthquake is assessed using a twodimensional limit equilibrium stability analysis. Sutterer et al. [8] summarized the stability analysis using numerical formulation of both critical circular and wedge–shaped failures (Figure 2). Sutterer et al. [4] reported that pseudo-static analysis of homogeneous slopes showed that seismically loaded embankments with uniform foundation soils, and slope inclinations flatter than 1 horizontal to 1 vertical and steeper than 4 horizontal to 1 vertical, most probably fail in a base failure mode. Steeper slopes may be subjected to a toe circle failure type in the embankment alone (Figure 2). Regardless, most highway bridge embankments fall within the range dominated by base failures. In assessing the seismic vulnerability of each embankment, both failure types are considered in the proposed methodology, and the one that results in a lower *C/D* ratio is considered. This Chapter defines a process to assign the seismic risk, rank and priority of a set of bridge embankments

**Figure 1.** Bridge embankment representation for seismic ranking

*Upper Level of Bedrock Layer:* Data regarding the level under which a hard stratum, stiff bedrock layer, exists is not available for the majority of existing embankment sites; especially for small bridges. An initial assumption of the upper level of this hard stratum is estimated from the "*Geologic Quadrant Maps of the United States"* [2]. The actual upper level of the stiff bedrock layer specifically falls within the range from the level of the embankment base down to the top level of the hard stratum. For the sake of seismic risk assessment of a bridge embankment, few upper levels of the bedrock layer within that range are considered. Wherever the upper level of the bedrock layer is not known at a bridge site, the following three assumptions of this level are made, and the most critical case is considered in the ranking analysis: (1) at the same level of the embankment base; (2) at the bottom level of the lower soil layer, which is also the upper level of the hard stratum; and (3) at mid-height of the lower soil layer. Other assumptions of the top level of the bedrock layer may be considered if those assumptions yield a lower seismic slope stability *C/D* ratio. The top level of the bedrock layer, adopted in the ranking analysis, is the assumed elevation that results in the lowest seismic slope stability *C/D* ratio.


**Table 1.** Density and strength of soils and embankments

206 Earthquake Engineering

at many bridge sites [5]. The shear strength assigned for cohesive soils in Table 1 is chosen after examining commensurately accurate un-confined compression data. Shear strengths assigned to the embankment fill are adjusted to reflect the cyclic loading effects between undrained failure for both cohesive and saturated cohesion-less soils, in addition to the intermediate behavior between drained and un-drained for dry and partially saturated soils. The density and shear strength of the embankment soils are conservatively estimated by assuming that marginal compaction may have occurred during construction. Should there

*Upper Level of Bedrock Layer:* Data regarding the level under which a hard stratum, stiff bedrock layer, exists is not available for the majority of existing embankment sites; especially for small bridges. An initial assumption of the upper level of this hard stratum is estimated from the "*Geologic Quadrant Maps of the United States"* [2]. The actual upper level of the stiff bedrock layer specifically falls within the range from the level of the embankment base down to the top level of the hard stratum. For the sake of seismic risk assessment of a bridge embankment, few upper levels of the bedrock layer within that range are considered. Wherever the upper level of the bedrock layer is not known at a bridge site, the following three assumptions of this level are made, and the most critical case is considered in the ranking analysis: (1) at the same level of the embankment base; (2) at the bottom level of the lower soil layer, which is also the upper level of the hard stratum; and (3) at mid-height of the lower soil layer. Other assumptions of the top level of the bedrock layer may be considered if those assumptions yield a lower seismic slope stability *C/D* ratio. The top level of the bedrock layer, adopted in the ranking analysis, is the assumed elevation that results in

be more accurate soil properties, they may replace those provided in Table 1.

**Figure 1.** Bridge embankment representation for seismic ranking

the lowest seismic slope stability *C/D* ratio.

*Seismic Event:* The input Peak Ground Acceleration (*PGA*), which is the maximum bedrock acceleration at a designated embankment site, is obtained from seismic maps that are generated for specific seismic events. The choice of the seismic event is based on the importance and anticipated performance of the bridge as well as its geographic location on the seismic maps. The seismic maps to define the acceleration coefficient based on a uniform risk method of seismic hazard can be used. The probability that the acceleration coefficient will not be exceeded for a 50-year event is estimated to be 90%, with an expected return period is of 475 years [6]. Alternatively, seismic maps that may have been generated by State Departments of Transportation can be used. For the Commonwealth of Kentucky 50-year, 250-year, and 500-year seismic events were developed [7]. These events have a 90% probability of not being exceeded in 50 years, 250 years, and 500 years, respectively. All but four of the bridges and their embankments on priority routes in western Kentucky are required to withstand the 50-year and 250-year seismic events. The four other bridges are required to resist the 500-year seismic event.

#### **4. Embankment vulnerability analysis**

The potential for slope displacement to occur during an earthquake is assessed using a twodimensional limit equilibrium stability analysis. Sutterer et al. [8] summarized the stability analysis using numerical formulation of both critical circular and wedge–shaped failures (Figure 2). Sutterer et al. [4] reported that pseudo-static analysis of homogeneous slopes showed that seismically loaded embankments with uniform foundation soils, and slope inclinations flatter than 1 horizontal to 1 vertical and steeper than 4 horizontal to 1 vertical, most probably fail in a base failure mode. Steeper slopes may be subjected to a toe circle failure type in the embankment alone (Figure 2). Regardless, most highway bridge embankments fall within the range dominated by base failures. In assessing the seismic vulnerability of each embankment, both failure types are considered in the proposed methodology, and the one that results in a lower *C/D* ratio is considered. This Chapter defines a process to assign the seismic risk, rank and priority of a set of bridge embankments rather than providing only the required derivations and equations.

The horizontal earthquake acceleration in the seismic slope stability analysis often ranges from 50% to 100% of the *PGA* assigned for the embankment site. The *PGA* is often a single spike of motion of a very brief duration and causes little if any significant displacement. A horizontal earthquake acceleration (*Kh*) equals to two-thirds of the *PGA* is selected in the proposed methodology. This assumption accounts for those embankments in which the seismic acceleration either never exceeds the yield acceleration or very briefly exceeds the yield acceleration, and results in little or no displacement.

Bridge Embankments – Seismic Risk Assessment and Ranking 209

(1)

(2)

**Table 2.** Categories of bridge embankment behavior during a seismic event

*cb*

1 21

*D KD H*

<sup>1</sup> *D b d d r dr bx x* 40 2 1 3 3 3 6 3 3 (4)

(3)

2 2

2 2 <sup>2</sup>

3 2 3 2

<sup>2</sup> *D* 40 2 ( 3 2 ( ( 2 )) 2 (( 1 ) (1 2 )) 3 3 6 6 ) *b bd d d r d d r br x dx rx* (5)

where *λ* is the ratio of *S2/S1*, *S2* is the embankment soil un-drained shear strength and *γ2* is the embankment soil density (Table 1). For the values of *x* and *r* that result in the lowest factor of safety, designated *xc* and *rc*, the term in brackets of Eq. 1 has to be calculated and is called the stability number for the designated slope. The use of Eq. 1 in a spreadsheet with an optimization function provides reliable estimates of these parameters over the designated

*h RR S FS*

where *cb FS* is the factor of safety against circular base failure, *S1* is the un-drained shear strength of the soil beneath the embankment, *H* is the embankment height (Figure 1), and *γ<sup>1</sup>* is the density of the soil layer (Table 1). The parameters *R1*, *R2*, *D1*, and *D2* are obtained from

*<sup>r</sup>*

<sup>1</sup> (9 (1 ) 40 (1 ) 480 ) *<sup>d</sup> <sup>R</sup> d dr r*

12 1

1 40 ( 12 ) ( 2) *<sup>d</sup> R rd r*

*r*

Equations (2), (3), (4), and (5), respectively.

2
