Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown Foundations

Xuan Guo, Zhaohua Dai and ZhiQiang Chen

## Abstract

This chapter proposes a probabilistic framework for assessing seismic and scour effects on existing river-crossing bridge structures. The emphasis is on bridge structures in rural areas, for which it has been recognized that a large number of rural bridges have unknown foundation types and further are subject to both flooding-induced scour and seismic damage. With a review of the US-based rural bridges, this chapter presents a probabilistic framework for bridge performance assessment. Using a representative rural bridge model, the fragility results for the bridge reveal that scour tends to be beneficial in reducing structural damage at slight to moderate seismic intensities and to be detrimental in increasing collapse potential at high-level intensities. The demand hazard curves further quantify probabilistically the occurrence of local damage and global collapse, and systematically reveal the complex effects of scour as a hydraulic hazard on bridge structures.

Keywords: bridge, unknown foundation, flood-induced scour, multi-hazard, resilience

## 1. Introduction

There are over 484,500 highway bridges built over river channels in the U.S., among which over 20,904 are regarded scour-critical [1]. A distinct feature of flood-induced scour is that once it starts forming around a foundation, it may accumulate or vary over the bridge's service life. Hence it is intuitive that a potentially more severe risk is that scour is combined with other extreme hazards, such as earthquakes, which may threaten bridges serving in both earthquake and flooding active regions, such as Alaska, Oregon, and California in the U.S. On the other hand, it is recognized that a large number of bridges that are in service for tens of years have unknown foundation, in the meantime, been suffering from flooding induced scour.

In a recent National Cooperative Highway Research Program (NCHRP) report published in 2006 [2], it was identified that a very large proportion of the bridges built in 1950 and 1980 had unknown foundations, although it was surprising that even 69 bridges built during 2000–2005 were concluded with the label of bridges

with unknown foundation types. Based on this report, we further extract the proportion of bridge structures with unknown foundations in different function categories under two primary groups: rural and urban. Two characteristics are observed (Figure 1). First, the bridges with unknown foundations in rural areas outnumber significantly those in urban areas (50,743 vs. 8151). Second of all, among the bridges of different functions, the local bridges are the majority with unknown foundations. Particularly, in rural areas in the US, 34,478 bridges (out of 50,743 or about 68%) have unknown foundations; whereas in the urban areas, this number is 3948 (out of 8151 or about 48%). One significant feature of these local bridges is that they are usually structurally simple, short-span with one or two bents. When seismically active regions are concerned, in the aforementioned states of Oregon and California, 801 and 993 local rural bridges with unknown foundations are identified, respectively. Two arguments are raised herein. First, the seismic performance of these simple bridges imposes a great challenge to the stakeholders when duly considering the fact that these bridges have unknown foundation type, and in the meantime, they are subject to flooding induced scour. Second, a rapid and quantitative multi-hazard assessment methodology is demanded.

To evaluate the risk and to provide decision-making for managing these bridges, a methodological and practical procedure has been proposed in [2]; and Figure 2 recreates part of the workflow. In this workflow, empirical methods are proposed to infer the foundation types and basic geometric parameters. If the foundation types can be determined, then a standard failure analysis is followed. Two additional steps are proposed if the foundation types are not inferable. If the bridge is of high priority, then field reconnaissance is needed to determine the foundation type and configuration. If not, simple risk calculation procedures are used to evaluate if the bridge's minimum performance levels are met (in terms of the annual probability of failure) are proposed. If further not, again the field reconnaissance is recommended to carry out followed by a rigorous and quantitative performance assessment procedure. With this state-of-the-practice methodological framework, however, two limitations are recognized. First, no quantitative procedure that considers the source of uncertainties (e.g., materials or scour) is found, which in nature demands a probabilistic procedure. Second, in light of the bridges that serve in seismically active areas, a multi-hazard approach is further necessary. These limitations imply the necessity of developing a quantitative and multi-hazard assessment procedure.

rural and remote areas. This is a resourcefulness measure to increase the resilience of a bridge system [3, 4], and bridges are critical links with interdependence with other infrastructure systems. Indirectly, if a decision is made regarding that the scour countermeasure be added, this would build the structural redundancy to the bridge system hence reducing the possible bridge loss, increasing the robustness property of the bridge resilience against both the potential flooding, scour, and seismic hazards. Last and above all, rural areas lack technology resources when compared with urban areas; at least due to the geospatial remoteness, any technical measure when being deployed would take a longer time. Therefore, a rapid and

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown…

With this motivation, this book chapter is organized as follows. First, Section presents systematically the proposed methodology framework for multi-hazard seismic and scour assessment. Second, a numerical experiment is proposed with a known shallow foundation type. Last, this chapter concludes with a number of

Towards a multi-hazard approach to assessing the conjunct effects of earthquakes and flooding-induced scour on the vulnerability of bridges, a probabilistic approach to bridge scour analysis is required due to its inherent uncertainties in the first place. In two recent papers, a general approach to probabilistic scour hazard modeling was reported, which starts with the deterministic scour estimation equation then incorporates model bias and random errors [5]. Furthermore, Briaud et al. [6] concluded that for shallow foundations supporting bridge structures, the design scour depth needs to be 2.0–2.5 times of the HEC-18 estimates to ensure that the

quantitative assessment procedure is essentially necessary.

remarks for practical application and future research work.

2. Probabilistic methodology

Risk management workflow (part) proposed in [2].

DOI: http://dx.doi.org/10.5772/intechopen.85158

2.1 Related work

187

Figure 2.

Besides the need for a quantitative multi-hazard framework, we further state that a rapid approach is favorable for the bridges with unknown foundations in

Figure 1. Bridges with unknown foundations in the US: (a) rural areas and (b) urban areas.

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown… DOI: http://dx.doi.org/10.5772/intechopen.85158

Figure 2. Risk management workflow (part) proposed in [2].

rural and remote areas. This is a resourcefulness measure to increase the resilience of a bridge system [3, 4], and bridges are critical links with interdependence with other infrastructure systems. Indirectly, if a decision is made regarding that the scour countermeasure be added, this would build the structural redundancy to the bridge system hence reducing the possible bridge loss, increasing the robustness property of the bridge resilience against both the potential flooding, scour, and seismic hazards. Last and above all, rural areas lack technology resources when compared with urban areas; at least due to the geospatial remoteness, any technical measure when being deployed would take a longer time. Therefore, a rapid and quantitative assessment procedure is essentially necessary.

With this motivation, this book chapter is organized as follows. First, Section presents systematically the proposed methodology framework for multi-hazard seismic and scour assessment. Second, a numerical experiment is proposed with a known shallow foundation type. Last, this chapter concludes with a number of remarks for practical application and future research work.

## 2. Probabilistic methodology

#### 2.1 Related work

Towards a multi-hazard approach to assessing the conjunct effects of earthquakes and flooding-induced scour on the vulnerability of bridges, a probabilistic approach to bridge scour analysis is required due to its inherent uncertainties in the first place. In two recent papers, a general approach to probabilistic scour hazard modeling was reported, which starts with the deterministic scour estimation equation then incorporates model bias and random errors [5]. Furthermore, Briaud et al. [6] concluded that for shallow foundations supporting bridge structures, the design scour depth needs to be 2.0–2.5 times of the HEC-18 estimates to ensure that the

with unknown foundation types. Based on this report, we further extract the proportion of bridge structures with unknown foundations in different function categories under two primary groups: rural and urban. Two characteristics are observed (Figure 1). First, the bridges with unknown foundations in rural areas outnumber significantly those in urban areas (50,743 vs. 8151). Second of all, among the bridges of different functions, the local bridges are the majority with unknown foundations. Particularly, in rural areas in the US, 34,478 bridges (out of 50,743 or about 68%) have unknown foundations; whereas in the urban areas, this number is 3948 (out of 8151 or about 48%). One significant feature of these local bridges is that they are usually structurally simple, short-span with one or two bents. When seismically active regions are concerned, in the aforementioned states of Oregon and California, 801 and 993 local rural bridges with unknown foundations are identified, respectively. Two arguments are raised herein. First, the seis-

Earthquakes - Impact, Community Vulnerability and Resilience

mic performance of these simple bridges imposes a great challenge to the stakeholders when duly considering the fact that these bridges have unknown foundation type, and in the meantime, they are subject to flooding induced scour.

Second, a rapid and quantitative multi-hazard assessment methodology is

Bridges with unknown foundations in the US: (a) rural areas and (b) urban areas.

To evaluate the risk and to provide decision-making for managing these bridges, a methodological and practical procedure has been proposed in [2]; and Figure 2 recreates part of the workflow. In this workflow, empirical methods are proposed to infer the foundation types and basic geometric parameters. If the foundation types can be determined, then a standard failure analysis is followed. Two additional steps are proposed if the foundation types are not inferable. If the bridge is of high priority, then field reconnaissance is needed to determine the foundation type and configuration. If not, simple risk calculation procedures are used to evaluate if the bridge's minimum performance levels are met (in terms of the annual probability of failure) are proposed. If further not, again the field reconnaissance is recommended to carry out followed by a rigorous and quantitative performance assessment procedure. With this state-of-the-practice methodological framework, however, two limitations are recognized. First, no quantitative procedure that considers the source of uncertainties (e.g., materials or scour) is found, which in nature demands a probabilistic procedure. Second, in light of the bridges that serve in seismically active areas, a multi-hazard approach is further necessary. These limitations imply the necessity of developing a quantitative and multi-hazard assessment procedure. Besides the need for a quantitative multi-hazard framework, we further state that a rapid approach is favorable for the bridges with unknown foundations in

demanded.

Figure 1.

186

probability of exceeding the estimated scour depth be less than 0.001, even that both HEC-18 (Sand and Clay) methods are considerably conservative compared with measured bridge scour data. Besides probabilistic scour assessment for bridge foundations, however, these two efforts did not address the multi-hazard effects on a bridge as a system if earthquakes are involved.

2.2 Mean-scour seismic fragility modeling

DOI: http://dx.doi.org/10.5772/intechopen.85158

Ψ(x) [15], to fit the data set of {(Z > z

possibly from structural materials.

189

The seismic fragility or the probability of structural damage given a seismic IM

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown…

defined value of the demand variable. The expression Z > z\* defines a limit state that indicates occurrence of a certain level of damage or even collapse. For measuring the seismic intensity, a sufficient IM should be chosen. Peak ground acceleration (PGA) is often used as an objective scalar measure of seismic intensity. When a structure is considered, the spectral displacement (Sd) and spectral acceleration (Sa) defined at the structure's modal period (Tn) are two commonly used measures. In this chapter, Sa is adopted; particularly, Sa measured at the fixed-base first-mode period of the bridge model is usedWhen the sample values ofIM and Z are available, a fitting function in terms of IM = x is usually used to fit the conditional probability P(Z > z\* | IM), denoted by Ψ(x). The most popular approach is to enforce a monotonically increasing function bounded by [0, 1], such as the Lognormal cumulative distribution function

\* is a specifically

can be modeled as a conditional probability, P(Z > z\* | IM), where z

\*

<sup>Ψ</sup>ð Þ¼ <sup>x</sup> P Z . <sup>z</sup> <sup>∗</sup> ð Þ <sup>j</sup>IM <sup>¼</sup> <sup>x</sup> <sup>≈</sup> <sup>Φ</sup>

rates a designated scour condition in terms of a deterministic SD value, y

<sup>Ψ</sup>ð Þ¼ <sup>x</sup> P Z . <sup>z</sup> <sup>∗</sup> <sup>j</sup>IM <sup>¼</sup> <sup>x</sup>; SD <sup>¼</sup> <sup>y</sup> <sup>∗</sup> ð Þ<sup>≈</sup> <sup>Φ</sup><sup>y</sup> <sup>∗</sup>

random variable, a bivariate fragility model becomes of interest:

)i, IMi | i = 1 …N}:

where μ and β are the mean and standard deviation parameters of the Lognormal cumulative function, respectively. Based on the sample data, a general approach to parameter estimation is the maximum likelihood estimation (MLE) method [25]. This method is adopted in this chapter and formulation details are found in [25]. When scour depth (SD) is considered in seismic fragility analysis, an easy treatment is to compute seismic demands using the SFS bridge model that incorpo-

The expression in Eq. 2 represents the seismic fragility considering a deterministic scour depth, wherein the uncertainties come from external seismic inputs and

<sup>Ψ</sup>ð Þ¼ <sup>x</sup>; <sup>y</sup> P Z . <sup>z</sup> <sup>∗</sup> ð Þ <sup>j</sup>IM <sup>¼</sup> <sup>x</sup>; SD <sup>¼</sup> <sup>y</sup> (3)

If one considers scour as a type of hazard and then treats scour depth as a

If the conditional probability model in Eq. 3 is fitted by a bivariate Lognormal function, a fragility surface model is achieved. A fragility surface model has its merit in expressing the true fragility of a structure when multiple hazards are affecting the structure [26] or multiple parameters are used to describe one hazardous effect [27]. As implied in Eq. 6, one may consider fitting the conditional probability by a bivariate function in terms of both seismic intensity and scour depth as independent variables and then study the resulting seismic-scour fragility surface. However, a significant difference of scour effects from seismic effects as illustrated previously is that scour may cause beneficial effects (i.e., reduction of force demands). This implies that the fragility when partially conditional on scour may decrease as the scour depth increases. With the fragility partially depending on seismic measure IM (which often designates a monotonic increasing relation), the resulting fragility surface from Eq. 3 may be nonmonotonic, which causes difficulty

ln x � μ β

(1)

ln x � μ β

\* :

(2)

For a system-level multi-hazard assessment of seismic and scour effects (termed seismic-scour effects hereafter), a number of efforts are found. Wang et al. investigate the vulnerability of scoured pile-foundation supported bridges through probabilistic fragility surface analysis [7]. However, in their work, scour was treated deterministically. Dong et al. proposed a multi-hazard assessment approach to studying bridge performance considering time-variant structural deterioration; however, scour uncertainty was not considered either [8]. Prasad and Banerjee investigated the seismic risk of four example bridges considering scour variations [9, 10]. While studying the characteristics of seismic fragility curves, however, only system-level displacement-based demands (i.e., drift demands at the deck level) were used, which led to the conclusion that scour always increases seismic fragility. Several recent efforts are found on probabilistic calibration of load-resistance factors that are used to combine scour condition with seismic and other design forces [11–13]. No quantitative and probabilistic framework is found to date that is able to comprehensively assess the conjunct seismic-scour effects on river-crossing bridge's vulnerability. In the following, a probabilistic framework is proposed that aims to output seismic-scour integrated fragility and probabilistic demand hazard. The focus is then on the experimental results and observations based on a simple shallow-foundation supported bridge model, followed by the conclusions in the last section.

For assessing performance and vulnerability of structures considering seismic hazards, two probabilistic analysis tools are usually employed, which are probabilistic seismic fragility analysis (PSFA) and probabilistic seismic demand analysis (PSDA). PSFA can be applied to identify the probability of a defined limit-state (e.g., structural damage or collapse) conditional on one or multiple measures of seismic intensity [14–17]. PSDA is used to assess structural vulnerability by estimating the annual probability of a structural demand exceeding a varying demand parameter without conditioning on the input hazard [18, 19]. The output of the PSDA model is a demand hazard curve that is analogous to a seismic hazard curve (from probabilistic seismic hazard analysis, PSHA). Since the demand hazard curve is an essential component of the probabilistic performance-based seismic design framework [20], PSDA has been frequently used for assessing building structures [21, 22] and bridge structures [23, 24].

Different from general multi-hazard analysis wherein two or more hazards appear as a joint occurrence of two independent events that may be generalized as external forces applied to structures (but independent to structures), earthquake and scour should be treated distinctly. Different from loading-based hazards, scour primarily leads to modification of the geometric boundary condition of the soilfoundation-structure (SFS) bridge system. This boundary modification further results in reduction in foundation stiffness, and nonlinear foundation bearing and lateral capacities as demonstrated previously. To account for such changes, a system-level modeling approach needs to be adopted considering SFSI subjected to dynamic loadings (e.g., earthquakes). This in turn leads to an unfavorable situation, wherein the SFS bridge system is not invariant; rather, it is subject to significant modification in terms of foundation impedance and nonlinear capacities due to the varying scour (treated as a hazard).

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown… DOI: http://dx.doi.org/10.5772/intechopen.85158

### 2.2 Mean-scour seismic fragility modeling

probability of exceeding the estimated scour depth be less than 0.001, even that both HEC-18 (Sand and Clay) methods are considerably conservative compared with measured bridge scour data. Besides probabilistic scour assessment for bridge foundations, however, these two efforts did not address the multi-hazard effects on

For a system-level multi-hazard assessment of seismic and scour effects (termed seismic-scour effects hereafter), a number of efforts are found. Wang et al. investigate the vulnerability of scoured pile-foundation supported bridges through probabilistic fragility surface analysis [7]. However, in their work, scour was treated deterministically. Dong et al. proposed a multi-hazard assessment approach to studying bridge performance considering time-variant structural deterioration; however, scour uncertainty was not considered either [8]. Prasad and Banerjee investigated the seismic risk of four example bridges considering scour variations [9, 10]. While studying the characteristics of seismic fragility curves, however, only system-level displacement-based demands (i.e., drift demands at the deck level) were used, which led to the conclusion that scour always increases seismic fragility. Several recent efforts are found on probabilistic calibration of load-resistance factors that are used to combine scour condition with seismic and other design forces [11–13]. No quantitative and probabilistic framework is found to date that is able to comprehensively assess the conjunct seismic-scour effects on river-crossing bridge's vulnerability. In the following, a probabilistic framework is proposed that aims to output seismic-scour integrated fragility and probabilistic demand hazard. The focus is then on the experimental results and observations based on a simple shallow-foundation supported bridge model, followed by the conclusions in the

For assessing performance and vulnerability of structures considering seismic hazards, two probabilistic analysis tools are usually employed, which are probabilistic seismic fragility analysis (PSFA) and probabilistic seismic demand analysis (PSDA). PSFA can be applied to identify the probability of a defined limit-state (e.g., structural damage or collapse) conditional on one or multiple measures of seismic intensity [14–17]. PSDA is used to assess structural vulnerability by estimating the annual probability of a structural demand exceeding a varying demand parameter without conditioning on the input hazard [18, 19]. The output of the PSDA model is a demand hazard curve that is analogous to a seismic hazard curve (from probabilistic seismic hazard analysis, PSHA). Since the demand hazard curve is an essential component of the probabilistic performance-based seismic design framework [20], PSDA has been frequently used for assessing building structures

Different from general multi-hazard analysis wherein two or more hazards appear as a joint occurrence of two independent events that may be generalized as external forces applied to structures (but independent to structures), earthquake and scour should be treated distinctly. Different from loading-based hazards, scour primarily leads to modification of the geometric boundary condition of the soilfoundation-structure (SFS) bridge system. This boundary modification further results in reduction in foundation stiffness, and nonlinear foundation bearing and lateral capacities as demonstrated previously. To account for such changes, a system-level modeling approach needs to be adopted considering SFSI subjected to dynamic loadings (e.g., earthquakes). This in turn leads to an unfavorable situation, wherein the SFS bridge system is not invariant; rather, it is subject to significant modification in terms of foundation impedance and nonlinear capacities due to the

a bridge as a system if earthquakes are involved.

Earthquakes - Impact, Community Vulnerability and Resilience

last section.

[21, 22] and bridge structures [23, 24].

varying scour (treated as a hazard).

188

The seismic fragility or the probability of structural damage given a seismic IM can be modeled as a conditional probability, P(Z > z\* | IM), where z \* is a specifically defined value of the demand variable. The expression Z > z\* defines a limit state that indicates occurrence of a certain level of damage or even collapse. For measuring the seismic intensity, a sufficient IM should be chosen. Peak ground acceleration (PGA) is often used as an objective scalar measure of seismic intensity. When a structure is considered, the spectral displacement (Sd) and spectral acceleration (Sa) defined at the structure's modal period (Tn) are two commonly used measures. In this chapter, Sa is adopted; particularly, Sa measured at the fixed-base first-mode period of the bridge model is usedWhen the sample values ofIM and Z are available, a fitting function in terms of IM = x is usually used to fit the conditional probability P(Z > z\* | IM), denoted by Ψ(x). The most popular approach is to enforce a monotonically increasing function bounded by [0, 1], such as the Lognormal cumulative distribution function Ψ(x) [15], to fit the data set of {(Z > z \* )i, IMi | i = 1 …N}:

$$\Psi(\mathbf{x}) = P(Z > z^\* \, | \, \mathrm{IM} = \mathbf{x}) \approx \Phi\left(\frac{\ln \pi - \mu}{\beta}\right) \tag{1}$$

where μ and β are the mean and standard deviation parameters of the Lognormal cumulative function, respectively. Based on the sample data, a general approach to parameter estimation is the maximum likelihood estimation (MLE) method [25]. This method is adopted in this chapter and formulation details are found in [25].

When scour depth (SD) is considered in seismic fragility analysis, an easy treatment is to compute seismic demands using the SFS bridge model that incorporates a designated scour condition in terms of a deterministic SD value, y \* :

$$\Psi(\mathbf{x}) = P(Z \ge \mathbf{z}^\* | IM = \mathbf{x}, \mathbf{SD} = \mathbf{y}^\*) \approx \Phi\_{\mathbf{y}^\*} \left( \frac{\ln \mathbf{x} - \mu}{\beta} \right) \tag{2}$$

The expression in Eq. 2 represents the seismic fragility considering a deterministic scour depth, wherein the uncertainties come from external seismic inputs and possibly from structural materials.

If one considers scour as a type of hazard and then treats scour depth as a random variable, a bivariate fragility model becomes of interest:

$$\Psi(\mathbf{x}, \mathbf{y}) = \mathbf{P}(Z \succeq \mathbf{z}^\* \, | \, \text{IM} = \mathbf{x}, \mathbf{SD} = \mathbf{y}) \tag{3}$$

If the conditional probability model in Eq. 3 is fitted by a bivariate Lognormal function, a fragility surface model is achieved. A fragility surface model has its merit in expressing the true fragility of a structure when multiple hazards are affecting the structure [26] or multiple parameters are used to describe one hazardous effect [27]. As implied in Eq. 6, one may consider fitting the conditional probability by a bivariate function in terms of both seismic intensity and scour depth as independent variables and then study the resulting seismic-scour fragility surface. However, a significant difference of scour effects from seismic effects as illustrated previously is that scour may cause beneficial effects (i.e., reduction of force demands). This implies that the fragility when partially conditional on scour may decrease as the scour depth increases. With the fragility partially depending on seismic measure IM (which often designates a monotonic increasing relation), the resulting fragility surface from Eq. 3 may be nonmonotonic, which causes difficulty ¼ ESD½ � Ψð Þ x; y

in interpreting such a surface. To retain the traditional simplicity in a fragility curve, it is more straightforward to marginalize out the scour depth as a random variable. Based on the law of total probability, one has

$$\begin{aligned} \mathbf{P}(\mathbf{Z} \rhd \mathbf{z}^\* | \mathbf{IM} = \mathbf{x}) &= \\ \mathbf{I} = \int \mathbf{P}(\mathbf{Z} \rhd \mathbf{z}^\* | \mathbf{IM} = \mathbf{x}, \mathbf{SD} = \mathbf{y}) f\_{\mathbf{SD}}(\mathbf{y}) d\mathbf{y} \end{aligned} \tag{4}$$

In addition, seismic hazard models can be obtained from the web portal of the United States Geological Survey (USGS) for a given site in the United States [29]. One key step in PSHA is to select an appropriate seismic IM type. Traditionally, peak ground acceleration (PGA) and spectral acceleration (Sa) at a certain natural period (Tn) are commonly used [30]. In this chapter, the USGS'seismic hazard

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown…

For local bridge scour (scour around bridge foundation), two primary estimation methods exist as described in Hydraulic Engineering Circular No. 18 [31], which is termed the HEC-18 Sand and HEC-18 Clay. The HEC-18 Clay method was developed at the Texas A&M University, which was designed to predict scour depths in cohesive fine-grained soils (e.g., clay) and was once termed the SRICOS-EFA method [32]. Using the HEC-18 Clay method, the scour depth is the function of time over the period of the hydrograph. First, this method predicts the maximum

where R is Reynolds number equal to νDp/υ, v is the upstream velocity, Dp is the diameter of the pier, and υ is the water viscosity (10�<sup>6</sup> s/m2 at 20°C). The time-

depth in Eq. 1, the time at which a given velocity is applied, and the initial rate of

^yt <sup>¼</sup> <sup>t</sup> 1 y\_ i <sup>þ</sup> <sup>t</sup> y^max

where t with a unit of year is the time over which a given velocity is applied and

Based on the deterministic estimation described in Eqs. 8 and 9, multiplicative correction factors are considered to account for the bias and random errors inherent in the deterministic models, which leads to the probabilistic scour modeling [5] and is termed probabilistic scour hazard analysis in this chapter (PScHA to be different

In Bolduc et al. [5], by adopting a Lognormal distribution for scour depth, the

� � <sup>þ</sup> Log ^yt

time-dependent scour estimation from Eq. 9; N(0;1) represents a Normal random variable with zero mean and unit variance; σ<sup>y</sup> is therefore the standard deviation of the Lognormal variable yt. This implies that when these deterministic parameters, θy, ^yt and σ<sup>y</sup> are available, a probability density function for the distribution of the scour depth can be defined using a Lognormal distribution, denoted by fSD(yt) in this chapter. Given fSD(y), the scour hazard can be analytically expressed as

depicted as a curve quantifies the probability of exceeding a scour-depth value at a bridge site; the only distinction is that different from the annual POEs as used in a seismic hazard model, a scour hazard model defined above is calculated at a certain

<sup>0</sup> f SDð Þy dy. Similar to the seismic hazard curve, this model when

probabilistic scour depth is formulated in a Logarithm expression:

� � <sup>¼</sup> Log <sup>θ</sup><sup>y</sup>

where θ<sup>y</sup> is a parameter accounting for the model bias; ^yt

Log yt

^ymax <sup>¼</sup> <sup>0</sup>:18R<sup>0</sup>:<sup>635</sup> (8)

, is defined by linking the maximum scour

� � <sup>þ</sup> <sup>σ</sup>yNð Þ <sup>0</sup>; <sup>1</sup> (10)

is the deterministic and

(9)

model in terms of SAs is adopted.

scour ^ymax as:

scour:

from PSHA).

HSD yt

191

� � <sup>¼</sup> <sup>1</sup> � <sup>Ð</sup> yt

year of service.

2.5 Probabilistic scour hazard analysis

DOI: http://dx.doi.org/10.5772/intechopen.85158

dependent scour depth, denoted by ^yt

y\_<sup>i</sup> denotes the initial rate of scour.

$$P(Z \ge z^\* \, | IM = \infty) \approx \Phi\_{MS} \left(\frac{\ln \varkappa - \mu}{\beta}\right) \tag{5}$$

where fSD(y) is the probability density function for the scour depth as a random variable and E[] defines the mathematical expectation operator. In Eq. 4, the seismic fragility is defined by integrating out scour depth as a random variable, which is equivalent to the mathematical mean of the bivariate fragility upon the scour depth distribution. Due to this analytical meaning, a notion of mean-scour (MS) fragility is proposed in this chapter. In the meantime, the analytical expression of the meanscour fragility P Z . <sup>z</sup> <sup>∗</sup> ð Þ <sup>j</sup>IM <sup>¼</sup> <sup>x</sup> means that the fragility model can be directly estimated by fitting the simulated data set using the Lognormal model in Eq. 5.

#### 2.3 Seismic-scour integrated demand modeling

Traditional PSDA assesses the performance of a structure by probabilistically predicting the seismic response in terms of the probability of exceedance for a limit state defined by Z > z, where z is a varying demand value. The resulting function, Hz(z) = P(Z > z), is termed probabilistic demand hazard model. In the original efforts [e.g., [18]], a probabilistic demand hazard model (or strictly speaking the mean annual frequency of the exceedance event for a response demand) is evaluated based on the summation over seismic sources described by magnitudes and site distance. In more recent literature, a probabilistic demand hazard model for evaluating the seismic performance of a structure has been defined in a continuous form [19]:

$$H\_Z(\mathbf{z}) = \int P(Z \ge \mathbf{z} | IM = \mathbf{x}) | \mathbf{d}H\_{IM}(\mathbf{x}) | \tag{6}$$

where P Zð Þ . zjIM ¼ x defines the likelihood that the structural demand Z exceeds a post-elastic demand value z, and dHIM(x) defines the derivative of the seismic hazard model (the absolute sign is necessary since the derivative is negative).

It is noted that Eq. 6 considers one (seismic) hazard. If flooding-induced scour as a hazardous condition is considered, the integrated seismic-scour demand hazard, denoted by HSS(z), is proposed, which is based on a simple extension of Eq. 6:

$$H\_{\rm SS}(\mathbf{z}) = \int \left[ P(Z \ge \mathbf{z} | \mathbf{IM} = \mathbf{x}, \mathbf{SD} = \mathbf{y}) \mathbf{d} H\_{\rmIM}(\mathbf{x}) \mathbf{d} H\_{\rm SD}(\mathbf{y}) \right] \tag{7}$$

where HIM(x) and HSD(y) are the probabilistic seismic hazard and scour hazard models, respectively. The demand hazard model in Eq. 7 involves probabilistic models of seismic and scour hazards. The two hazard models are introduced below.

#### 2.4 Probabilistic seismic hazard analysis

The probabilistic seismic hazard analysis (PSHA) attempts to define the probability of exceedance (POE) for an IM variable x that is exceeded annually, denoted by HIM(x). In practice, PSHA can be analytically conducted for a given site [28].

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown… DOI: http://dx.doi.org/10.5772/intechopen.85158

In addition, seismic hazard models can be obtained from the web portal of the United States Geological Survey (USGS) for a given site in the United States [29]. One key step in PSHA is to select an appropriate seismic IM type. Traditionally, peak ground acceleration (PGA) and spectral acceleration (Sa) at a certain natural period (Tn) are commonly used [30]. In this chapter, the USGS'seismic hazard model in terms of SAs is adopted.

#### 2.5 Probabilistic scour hazard analysis

in interpreting such a surface. To retain the traditional simplicity in a fragility curve, it is more straightforward to marginalize out the scour depth as a random

P Z . <sup>z</sup> <sup>∗</sup> ð Þ <sup>j</sup>IM <sup>¼</sup> x, SD <sup>¼</sup> <sup>y</sup> <sup>f</sup> SDð Þ<sup>y</sup> <sup>d</sup><sup>y</sup>

where fSD(y) is the probability density function for the scour depth as a random variable and E[] defines the mathematical expectation operator. In Eq. 4, the seismic fragility is defined by integrating out scour depth as a random variable, which is equivalent to the mathematical mean of the bivariate fragility upon the scour depth distribution. Due to this analytical meaning, a notion of mean-scour (MS) fragility is proposed in this chapter. In the meantime, the analytical expression of the meanscour fragility P Z . <sup>z</sup> <sup>∗</sup> ð Þ <sup>j</sup>IM <sup>¼</sup> <sup>x</sup> means that the fragility model can be directly estimated by fitting the simulated data set using the Lognormal model in Eq. 5.

Traditional PSDA assesses the performance of a structure by probabilistically predicting the seismic response in terms of the probability of exceedance for a limit state defined by Z > z, where z is a varying demand value. The resulting function, Hz(z) = P(Z > z), is termed probabilistic demand hazard model. In the original efforts [e.g., [18]], a probabilistic demand hazard model (or strictly speaking the mean annual frequency of the exceedance event for a response demand) is evaluated based on the summation over seismic sources described by magnitudes and site distance. In more recent literature, a probabilistic demand hazard model for evaluating the seis-

mic performance of a structure has been defined in a continuous form [19]:

where P Zð Þ . zjIM ¼ x defines the likelihood that the structural demand Z exceeds a post-elastic demand value z, and dHIM(x) defines the derivative of the seismic hazard model (the absolute sign is necessary since the derivative is negative). It is noted that Eq. 6 considers one (seismic) hazard. If flooding-induced scour as a hazardous condition is considered, the integrated seismic-scour demand hazard, denoted by HSS(z), is proposed, which is based on a simple extension of Eq. 6:

where HIM(x) and HSD(y) are the probabilistic seismic hazard and scour hazard

The probabilistic seismic hazard analysis (PSHA) attempts to define the probability of exceedance (POE) for an IM variable x that is exceeded annually, denoted by HIM(x). In practice, PSHA can be analytically conducted for a given site [28].

models, respectively. The demand hazard model in Eq. 7 involves probabilistic models of seismic and scour hazards. The two hazard models are introduced below.

ð

ln x � μ β � �

P Zð Þ . zjIM ¼ x ∣dHIMð Þ x ∣ (6)

P Zð Þ . zjIM ¼ x; SD ¼ y dHIMð Þ x dHSDð Þy (7)

(4)

(5)

variable. Based on the law of total probability, one has

Earthquakes - Impact, Community Vulnerability and Resilience

¼ Ð

2.3 Seismic-scour integrated demand modeling

HZð Þ¼ z

HSSð Þ¼ z

2.4 Probabilistic seismic hazard analysis

190

ð ð

P Z . <sup>z</sup> <sup>∗</sup> <sup>ð</sup> <sup>j</sup>IM <sup>¼</sup> <sup>x</sup>Þ ¼

P Z . <sup>z</sup> <sup>∗</sup> ð Þ <sup>j</sup>IM <sup>¼</sup> <sup>x</sup> <sup>≈</sup> <sup>Φ</sup>MS

¼ ESD½ � Ψð Þ x; y

For local bridge scour (scour around bridge foundation), two primary estimation methods exist as described in Hydraulic Engineering Circular No. 18 [31], which is termed the HEC-18 Sand and HEC-18 Clay. The HEC-18 Clay method was developed at the Texas A&M University, which was designed to predict scour depths in cohesive fine-grained soils (e.g., clay) and was once termed the SRICOS-EFA method [32]. Using the HEC-18 Clay method, the scour depth is the function of time over the period of the hydrograph. First, this method predicts the maximum scour ^ymax as:

$$
\hat{y}\_{\text{max}} = \mathbf{0}.\mathbf{18}R^{0.635} \tag{8}
$$

where R is Reynolds number equal to νDp/υ, v is the upstream velocity, Dp is the diameter of the pier, and υ is the water viscosity (10�<sup>6</sup> s/m2 at 20°C). The timedependent scour depth, denoted by ^yt , is defined by linking the maximum scour depth in Eq. 1, the time at which a given velocity is applied, and the initial rate of scour:

$$
\hat{\mathcal{Y}}\_t = \frac{t}{\frac{1}{\hat{\mathcal{Y}}\_i} + \frac{t}{\hat{\mathcal{Y}}\_{\text{max}}}} \tag{9}
$$

where t with a unit of year is the time over which a given velocity is applied and y\_<sup>i</sup> denotes the initial rate of scour.

Based on the deterministic estimation described in Eqs. 8 and 9, multiplicative correction factors are considered to account for the bias and random errors inherent in the deterministic models, which leads to the probabilistic scour modeling [5] and is termed probabilistic scour hazard analysis in this chapter (PScHA to be different from PSHA).

In Bolduc et al. [5], by adopting a Lognormal distribution for scour depth, the probabilistic scour depth is formulated in a Logarithm expression:

$$\log\left[\boldsymbol{y}\_{t}\right] = \text{Log}\left[\boldsymbol{\theta}\_{\text{y}}\right] + \text{Log}\left[\boldsymbol{\hat{y}}\_{t}\right] + \sigma\_{\text{y}}\mathbf{N}(\mathbf{0};\mathbf{1})\tag{10}$$

where θ<sup>y</sup> is a parameter accounting for the model bias; ^yt is the deterministic and time-dependent scour estimation from Eq. 9; N(0;1) represents a Normal random variable with zero mean and unit variance; σ<sup>y</sup> is therefore the standard deviation of the Lognormal variable yt. This implies that when these deterministic parameters, θy, ^yt and σ<sup>y</sup> are available, a probability density function for the distribution of the scour depth can be defined using a Lognormal distribution, denoted by fSD(yt) in this chapter. Given fSD(y), the scour hazard can be analytically expressed as HSD yt � � <sup>¼</sup> <sup>1</sup> � <sup>Ð</sup> yt <sup>0</sup> f SDð Þy dy. Similar to the seismic hazard curve, this model when depicted as a curve quantifies the probability of exceeding a scour-depth value at a bridge site; the only distinction is that different from the annual POEs as used in a seismic hazard model, a scour hazard model defined above is calculated at a certain year of service.

## 3. Experimental results

#### 3.1 Simple bridge model

The bridge chosen in this chapter has a shallow foundation system with a full embedment depth that is constructed in a hard-soil (e.g., cohesive clay) river bed. The bridge has three spans of concrete decks supported by two concrete columns. Such a bridge is commonly used in practice for short-span river passing when the foundation soil is relatively hard (e.g., clay) [33]. In addition, by analyzing a shallow foundation-supported bridge model, the probabilistic assessment can be readily conducted. It is noted, nevertheless, the framework developed and demonstrated in this chapter can be easily adapted for assessing existing bridges with deep foundation systems (e.g., piles) in soft-soil river bed provided a finite-element (FE) based SFS model is provided. Figure 3 illustrates a simple bridge model, which is considered as a representative rural local river-crossing bridge. The bridge is a three-span (27 m + 36 m + 27 m) continuous structure supported by two piers on two separate shallow foundations. This bridge model was used in the author's previous work [34]. 1. Local strain ductility: defined as the ratio of the strain demand (|ϵmax|) at the base of the concrete pier to the compressive yielding strain (ϵy) of the concrete,

μ<sup>s</sup> = |ϵmax|/ϵy. Since the local strain at the surface is proportional to the curvature, ϵ = ρ r, where r is the diameter of the circular column, one can define an equivalent local curvature ductility demand. Hereinafter, local strain

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown…

2. System drift ductility: defined as the ratio of the transverse system drift demand at the mid-span of the bridge deck (|umax|) to the bridge's yielding drift (uy) at the fixed-end boundary condition, μ<sup>d</sup> = |umax|/uy. For the bridge

The local strain ductility demand μ<sup>s</sup> reflects the degree of local inelasticity occurred to the bridge's concrete piers. For bridge structures, the ranges for using local strain ductility demand to characterize different damage levels are well defined (e.g., [36]). In general, when given a limit state of μ<sup>s</sup> > 1, it implies the onset of local damage or indication of slight damage. A larger threshold may be used to define higher-level structural damage, such as 2 < μ<sup>s</sup> < 4 for moderate damage or μ<sup>s</sup> > 4 for extensive damage. Fragility models resulting from these higher-level damage limit-states are not reported in this chapter. The system drift ductility demand indicates the degree of global displacement, which in general consists of structural deformation and foundation-induced rigid-body motion (e.g., sliding and rocking) as a SFS system. In this chapter, if μ<sup>d</sup> is larger than seven (μ<sup>d</sup> > 7), the onset of system collapse limit-state is defined (usually a drift ductility of 5–10 is used to define bridge collapse in the literature; herein a median value of 7 is used) [37, 38]. We particularly note that for a scoured SFS bridge, it may be biased to define a limit-state using the system-level ductility demand to indicate structural damage in local members. Especially when considering an extreme scour, a limit-state in the range of 2 < μ<sup>d</sup> < 3 may be dominated by the rigid-body displacement from the substructure with linear-elastic or insignificant inelastic structural deformation; in this case, structural damage may not reach to the expected level (e.g., μ<sup>s</sup> < 1).

Based on the limit states defined previously, Figure 4(a) shows the probability of local damage defined by μ<sup>s</sup> > 1 considering four designated scour-depth values (No scour; Scour S1 with z = 2.8 m; S2 with z = 4.0 m; S3 with z = 4.2 m). In addition, the mean-scour (MS) fragility curve according to Eq. 5 is shown as well. Figure 4(b) uses the same configuration for plotting the fragility curves in terms of the defined collapse limit-state (μ<sup>d</sup> > 7). It is noted that material uncertainties are

Figure 4(a) indicates that the probability of damage is insignificant (less than

, which is the Expected Earthquake design level). In addition, at the NS

10%) if Sa (T1) < 0.33 g (equivalently corresponding to an annual POE of

(i.e., z = 0 m) and the S1 level of scour depth (i.e., z = 2.8 m), the probability of damage quickly approaches to a high probability (>50%) when the spectral acceleration becomes larger than 0.5 g (or an equivalent 0.38% annual POE). The general trend is that if the scour depth increases when the IM is greater than 0.33 g, the probability of damage decreases significantly. Especially, when the scour reaches the full-depth of the foundation (S2), the probability of damage dramatically reduces; for example, at Sa (T1) = 1.19 g (about 4.1 <sup>10</sup><sup>4</sup> annual POE or subject to the MCE-level earthquake), the probability of damage is around 5%, whereas it is 95% compared with the N1 case (z = 2.8 m). This observation is consistent with the

not considered in the two fragility illustrations in Figure 4.

model considered herein, the yielding drift is about 6.1 cm.

ductility demand (μs) is used.

DOI: http://dx.doi.org/10.5772/intechopen.85158

3.3 Fragility analysis results

9.2 <sup>10</sup><sup>3</sup>

193

The height of the circular piers is 9.0 m with a diameter of 1.4 m. The steel ratio of the column is about 1.3%. The foundation is constructed on hard clay with a density of 1700 kg/m<sup>3</sup> and with a small-strain shear wave velocity of 260 m/s. The thickness of the foundation is 2.4 m, with the transverse width being 2.8 m and the longitudinal length being 3.3 m, respectively. In this experiment, the embedment depth of foundations is 4.0 m. For bridges with unknown foundation, such full embedment depth can be determined through field inspection methods (for example, for shallow foundations, one can use a drilling device to drill through the footing to determine the elevation of the footing bottom). The simplified configuration of the bridge is shown in Figure 3. A three-dimensional finite-element (FE) model for the bridge is developed to simulate the bridge using the OpenSees framework [35]. The FE modeling and the details about beam-column elements, footing elements, material uncertainties, sampling scheme, and the nonlinear time-history analysis details are found in this work as well. Particularly, we consider a target service period of 50 years among its 75-year design life. The purpose is to mimic the situation of an existing bridge that is subject to progressive scour after 50 years of service.

#### 3.2 Demand variables

A variety of response demand parameters can be extracted. In this chapter two demand variables are considered in the following fragility and demand modeling.

Figure 3. Bridge configuration (unit: m).

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown… DOI: http://dx.doi.org/10.5772/intechopen.85158


The local strain ductility demand μ<sup>s</sup> reflects the degree of local inelasticity occurred to the bridge's concrete piers. For bridge structures, the ranges for using local strain ductility demand to characterize different damage levels are well defined (e.g., [36]). In general, when given a limit state of μ<sup>s</sup> > 1, it implies the onset of local damage or indication of slight damage. A larger threshold may be used to define higher-level structural damage, such as 2 < μ<sup>s</sup> < 4 for moderate damage or μ<sup>s</sup> > 4 for extensive damage. Fragility models resulting from these higher-level damage limit-states are not reported in this chapter. The system drift ductility demand indicates the degree of global displacement, which in general consists of structural deformation and foundation-induced rigid-body motion (e.g., sliding and rocking) as a SFS system. In this chapter, if μ<sup>d</sup> is larger than seven (μ<sup>d</sup> > 7), the onset of system collapse limit-state is defined (usually a drift ductility of 5–10 is used to define bridge collapse in the literature; herein a median value of 7 is used) [37, 38]. We particularly note that for a scoured SFS bridge, it may be biased to define a limit-state using the system-level ductility demand to indicate structural damage in local members. Especially when considering an extreme scour, a limit-state in the range of 2 < μ<sup>d</sup> < 3 may be dominated by the rigid-body displacement from the substructure with linear-elastic or insignificant inelastic structural deformation; in this case, structural damage may not reach to the expected level (e.g., μ<sup>s</sup> < 1).

#### 3.3 Fragility analysis results

Based on the limit states defined previously, Figure 4(a) shows the probability of local damage defined by μ<sup>s</sup> > 1 considering four designated scour-depth values (No scour; Scour S1 with z = 2.8 m; S2 with z = 4.0 m; S3 with z = 4.2 m). In addition, the mean-scour (MS) fragility curve according to Eq. 5 is shown as well. Figure 4(b) uses the same configuration for plotting the fragility curves in terms of the defined collapse limit-state (μ<sup>d</sup> > 7). It is noted that material uncertainties are not considered in the two fragility illustrations in Figure 4.

Figure 4(a) indicates that the probability of damage is insignificant (less than 10%) if Sa (T1) < 0.33 g (equivalently corresponding to an annual POE of 9.2 <sup>10</sup><sup>3</sup> , which is the Expected Earthquake design level). In addition, at the NS (i.e., z = 0 m) and the S1 level of scour depth (i.e., z = 2.8 m), the probability of damage quickly approaches to a high probability (>50%) when the spectral acceleration becomes larger than 0.5 g (or an equivalent 0.38% annual POE). The general trend is that if the scour depth increases when the IM is greater than 0.33 g, the probability of damage decreases significantly. Especially, when the scour reaches the full-depth of the foundation (S2), the probability of damage dramatically reduces; for example, at Sa (T1) = 1.19 g (about 4.1 <sup>10</sup><sup>4</sup> annual POE or subject to the MCE-level earthquake), the probability of damage is around 5%, whereas it is 95% compared with the N1 case (z = 2.8 m). This observation is consistent with the

3. Experimental results

Earthquakes - Impact, Community Vulnerability and Resilience

3.1 Simple bridge model

50 years of service.

Figure 3.

192

Bridge configuration (unit: m).

3.2 Demand variables

The bridge chosen in this chapter has a shallow foundation system with a full embedment depth that is constructed in a hard-soil (e.g., cohesive clay) river bed. The bridge has three spans of concrete decks supported by two concrete columns. Such a bridge is commonly used in practice for short-span river passing when the foundation soil is relatively hard (e.g., clay) [33]. In addition, by analyzing a shallow foundation-supported bridge model, the probabilistic assessment can be readily conducted. It is noted, nevertheless, the framework developed and demonstrated in this chapter can be easily adapted for assessing existing bridges with deep foundation systems (e.g., piles) in soft-soil river bed provided a finite-element (FE) based SFS model is provided. Figure 3 illustrates a simple bridge model, which is considered as a representative rural local river-crossing bridge. The bridge is a three-span (27 m + 36 m + 27 m) continuous structure supported by two piers on two separate shallow foundations. This bridge model was used in the author's previous work [34]. The height of the circular piers is 9.0 m with a diameter of 1.4 m. The steel ratio

of the column is about 1.3%. The foundation is constructed on hard clay with a density of 1700 kg/m<sup>3</sup> and with a small-strain shear wave velocity of 260 m/s. The thickness of the foundation is 2.4 m, with the transverse width being 2.8 m and the longitudinal length being 3.3 m, respectively. In this experiment, the embedment depth of foundations is 4.0 m. For bridges with unknown foundation, such full embedment depth can be determined through field inspection methods (for example, for shallow foundations, one can use a drilling device to drill through the footing to determine the elevation of the footing bottom). The simplified configuration of the bridge is shown in Figure 3. A three-dimensional finite-element (FE) model for the bridge is developed to simulate the bridge using the OpenSees framework [35]. The FE modeling and the details about beam-column elements, footing elements, material uncertainties, sampling scheme, and the nonlinear time-history analysis details are found in this work as well. Particularly, we consider a target service period of 50 years among its 75-year design life. The purpose is to mimic the situation of an existing bridge that is subject to progressive scour after

A variety of response demand parameters can be extracted. In this chapter two demand variables are considered in the following fragility and demand modeling.

subjected to high-intensity earthquakes and greater scout depths, the potential threat is system collapse. Therefore, it is rational to state that increasing scour depth is only beneficial when subjected to weak to moderate-intensity earthquakes (e.g.,

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown…

theless, the probability of collapse rises for each scour condition when Sa

Figure 4(b) shows the probability of collapse defined based on the drift ductility demand at the bridge deck. This figure indicates that the probability of collapse increases as the scour depth and the seismic intensity levels increase. Specifically, the conditional probability of collapse is close to zero when Sa (T1) < 0.7 g. None-

(T1) > 0.7 g. For a NS system, the probability of collapse is 4% if Sa (T1) = 1.19 g or considering a MCE level earthquake. By contrast, the corresponding probability for a scour system with the scour depth of 4.2 m is about 9%, which is about 2.25 times of that for the NS system. Accordingly, scour is detrimental by increasing the probability of collapse at all levels of ground motions, but much significantly when

The above fragility curves are constructed at designated scour conditions (NS, S1, S2, and S3). However, for an in-service bridge, its scour depth may be completely unknown; therefore, one may not be able to designate a scour depth. Based on Eq. 5, Figure 4(a) and (b) also report the resulting MS fragility curves. First, one can observe that the MS fragility curve at either of the limit states lies between the fragility curve at the S1 condition (z = 2.8 m) and the one at the NS condition (no scour or z = 0 m), although it is worthy to mention that this observa-

tion depends on the probabilistic scour hazard modeling at a specific site.

Second, similar observations in the trend of the MS curves as IM increases are still seen compared with the curves at the designated scour depths. Considering the smaller difference of the MS fragility curves from the curves at the S1 condition yet significant difference from the curves at the S2 and S3 conditions, one may assert that scour survey is critical in terms of the potential high risk resulting from a possibly greater scour depth. Nonetheless, if an accurate scour depth is not available, the proposed probabilistic MS fragility modeling becomes instrumental to

The seismic-scour integrated demand hazard curves can be approximated as expressed in Eq. 7. With the two ductility demand measures, Figure 5 reports the demand hazard curves, wherein the vertical axis indicates the probability of exceeding a demand variable that is marked in the horizontal axis (which is either μ<sup>s</sup> or μd). The two illustrations in Figure 5 provide a comparison between the cases of considering scour vs. not considering scour (in both cases, material uncertainties, denoted by "mu," are considered). Among them, Figure 5(a) illustrates the demand hazard curves in terms of the local strain ductility variable; whereas

First of all, the demand hazard curves in Figure 5 reveal the effects of scour as a source of hazard on the bridge structure. In terms of the local strain ductility μ<sup>s</sup> in Figure 5(a), the POEs in the range of μ<sup>s</sup> < 2.1 indicates that scour lowers the probability of structural damage in bridge piers, which is consistent with the previous fragility study. However, in the range of 2.1 < μ<sup>s</sup> < 4.1, scour increases the probability of damage, which is not revealed in the fragility study since such limitstate of 2 < μ<sup>s</sup> < 4 is not defined. It is noted that in both ranges, scour effect is insignificant due to the fact that scour-depth (SD) as a random variable has been integrated out numerically; therefore, it should be roughly regarded as a "mean"

in the case of the bridge model herein, Sa(T1) < 0.8 g).

DOI: http://dx.doi.org/10.5772/intechopen.85158

the seismic intensity approaches to the MCE level.

quantitatively assess the seismic-scour effects.

Figure 5(b) presents the system drift-ductility hazard curves.

3.4 Demand analysis results

195

#### Figure 4.

Fragility model at different scour depths without considering material uncertainties: (a) probability of structural damage at the column base and (b) probability of system collapse.

aforementioned literature that softened foundations in the context of seismic soilstructure interaction tend to lead to less structural damage or smaller base-shear force demands [11]. However, it should be pointed out that when the bridge is

#### Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown… DOI: http://dx.doi.org/10.5772/intechopen.85158

subjected to high-intensity earthquakes and greater scout depths, the potential threat is system collapse. Therefore, it is rational to state that increasing scour depth is only beneficial when subjected to weak to moderate-intensity earthquakes (e.g., in the case of the bridge model herein, Sa(T1) < 0.8 g).

Figure 4(b) shows the probability of collapse defined based on the drift ductility demand at the bridge deck. This figure indicates that the probability of collapse increases as the scour depth and the seismic intensity levels increase. Specifically, the conditional probability of collapse is close to zero when Sa (T1) < 0.7 g. Nonetheless, the probability of collapse rises for each scour condition when Sa (T1) > 0.7 g. For a NS system, the probability of collapse is 4% if Sa (T1) = 1.19 g or considering a MCE level earthquake. By contrast, the corresponding probability for a scour system with the scour depth of 4.2 m is about 9%, which is about 2.25 times of that for the NS system. Accordingly, scour is detrimental by increasing the probability of collapse at all levels of ground motions, but much significantly when the seismic intensity approaches to the MCE level.

The above fragility curves are constructed at designated scour conditions (NS, S1, S2, and S3). However, for an in-service bridge, its scour depth may be completely unknown; therefore, one may not be able to designate a scour depth. Based on Eq. 5, Figure 4(a) and (b) also report the resulting MS fragility curves. First, one can observe that the MS fragility curve at either of the limit states lies between the fragility curve at the S1 condition (z = 2.8 m) and the one at the NS condition (no scour or z = 0 m), although it is worthy to mention that this observation depends on the probabilistic scour hazard modeling at a specific site.

Second, similar observations in the trend of the MS curves as IM increases are still seen compared with the curves at the designated scour depths. Considering the smaller difference of the MS fragility curves from the curves at the S1 condition yet significant difference from the curves at the S2 and S3 conditions, one may assert that scour survey is critical in terms of the potential high risk resulting from a possibly greater scour depth. Nonetheless, if an accurate scour depth is not available, the proposed probabilistic MS fragility modeling becomes instrumental to quantitatively assess the seismic-scour effects.

#### 3.4 Demand analysis results

The seismic-scour integrated demand hazard curves can be approximated as expressed in Eq. 7. With the two ductility demand measures, Figure 5 reports the demand hazard curves, wherein the vertical axis indicates the probability of exceeding a demand variable that is marked in the horizontal axis (which is either μ<sup>s</sup> or μd). The two illustrations in Figure 5 provide a comparison between the cases of considering scour vs. not considering scour (in both cases, material uncertainties, denoted by "mu," are considered). Among them, Figure 5(a) illustrates the demand hazard curves in terms of the local strain ductility variable; whereas Figure 5(b) presents the system drift-ductility hazard curves.

First of all, the demand hazard curves in Figure 5 reveal the effects of scour as a source of hazard on the bridge structure. In terms of the local strain ductility μ<sup>s</sup> in Figure 5(a), the POEs in the range of μ<sup>s</sup> < 2.1 indicates that scour lowers the probability of structural damage in bridge piers, which is consistent with the previous fragility study. However, in the range of 2.1 < μ<sup>s</sup> < 4.1, scour increases the probability of damage, which is not revealed in the fragility study since such limitstate of 2 < μ<sup>s</sup> < 4 is not defined. It is noted that in both ranges, scour effect is insignificant due to the fact that scour-depth (SD) as a random variable has been integrated out numerically; therefore, it should be roughly regarded as a "mean"

aforementioned literature that softened foundations in the context of seismic soilstructure interaction tend to lead to less structural damage or smaller base-shear force demands [11]. However, it should be pointed out that when the bridge is

Fragility model at different scour depths without considering material uncertainties: (a) probability of

structural damage at the column base and (b) probability of system collapse.

Earthquakes - Impact, Community Vulnerability and Resilience

Figure 4.

194

4. Conclusions

DOI: http://dx.doi.org/10.5772/intechopen.85158

increased due to scour.

is available.

197

This chapter begins with a review of studying bridges with unknown foundations, which can be impacted by both flooding induced scour and earthquakes. Using the data from the United States (US), it is recognized that a large number of bridges have foundation types not identified in the database; in the meantime, many of these bridges serve in rural areas. With this fact, this chapter states that is essential to develop a probabilistic and multi-hazard framework to assess these bridges, although they are often simple in configuration. Such methodological framework can be treated as a resourcefulness measure to improve the resilience of rural bridges, hence local civil infrastructure systems in general (as bridges are interconnected with the functions of other infrastructure systems), and communities. With this motivation, this chapter presents a comprehensive probabilistic framework for assessing the effects of scour on the seismic response of existing bridge structures. Through a case-based assessment using a representative bridge model, several important observations are quantitatively revealed. These include:

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown…

• The fragility curves at designated scour depths or the proposed mean-scour seismic fragility curves indicate that scour tends to be beneficial in reducing structural damage at slight to moderate seismic intensities. However, the concern should be raised at strong seismic intensities, wherein even with a lowered probability of structural damage, the collapse potential is significantly

• The demand hazard curves systematically reveal the complex effects of seismic attacks and scour conditions on exceeding any local structural deformation or

meantime, scour systematically increases the probability of exceedance at any system drift ductility level, and more significantly at a larger demand level; or equivalently, scour in general increases the likelihood of system collapse when

• Material uncertainties can be ignored if solely for evaluating the effects of scour. If ignored, the proposed framework provides a computationally efficient approach to performing an integrated seismic-scour assessment for bridge structures. However, if material uncertainties considered, the computational cost is much increased since more parametric finiteelement models are included, which results in excessive nonlinear static pushover analysis in the framework. To mitigate this, one may choose a small and unique set of ground motions (e.g., only one motion is used in

system drift demands. These effects include that scour can lower the probability of exceeding a local strain ductility demand at small values compared to the case where scour is not considered; nonetheless, scour can increase the probability of exceedance at larger demand values. In the

compared with the case of no consideration of bridge scour.

this chapter) at different seismic intensity levels.

To this end, we envision that the proposed probabilistic framework and the associated numerical implementation in this chapter may provide a rapid means for assessing the conjunct seismic and scour effects on existing river-crossing bridges, particularly the simple bridges in the rural areas. We further note that the proposed probabilistic framework can be adapted when it is used to assess the effects of flood-induced scour on other bridge types (e.g., deep-foundation supported bridges in soft soils), provided that a finite-element based nonlinear model for the bridge

Figure 5.

Probabilistic demand hazard curves considering scour and material uncertainties (denoted by "mu") vs. considering "mu" only: (a) strain ductility demand hazard curves and (b) drift ductility demand hazard curves.

effect of the scour. In terms of the system drift ductility μ<sup>d</sup> in Figure 4(b), the overall trend is that the probability of exceeding any specified μ<sup>d</sup> increases due to the consideration of scour. This is especially evident when μ<sup>d</sup> is greater than 5. This implies that at larger drift ductility levels, wherein the likelihood of system collapse is defined, scour tends to increase the probability of system collapse. Due to these observations, we state that the probabilistic demand hazard modeling provides a more comprehensive approach to evaluating the effects of scour on the seismic response and the vulnerability of bridge structures.

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown… DOI: http://dx.doi.org/10.5772/intechopen.85158

## 4. Conclusions

This chapter begins with a review of studying bridges with unknown foundations, which can be impacted by both flooding induced scour and earthquakes. Using the data from the United States (US), it is recognized that a large number of bridges have foundation types not identified in the database; in the meantime, many of these bridges serve in rural areas. With this fact, this chapter states that is essential to develop a probabilistic and multi-hazard framework to assess these bridges, although they are often simple in configuration. Such methodological framework can be treated as a resourcefulness measure to improve the resilience of rural bridges, hence local civil infrastructure systems in general (as bridges are interconnected with the functions of other infrastructure systems), and communities. With this motivation, this chapter presents a comprehensive probabilistic framework for assessing the effects of scour on the seismic response of existing bridge structures. Through a case-based assessment using a representative bridge model, several important observations are quantitatively revealed. These include:

	- Material uncertainties can be ignored if solely for evaluating the effects of scour. If ignored, the proposed framework provides a computationally efficient approach to performing an integrated seismic-scour assessment for bridge structures. However, if material uncertainties considered, the computational cost is much increased since more parametric finiteelement models are included, which results in excessive nonlinear static pushover analysis in the framework. To mitigate this, one may choose a small and unique set of ground motions (e.g., only one motion is used in this chapter) at different seismic intensity levels.

To this end, we envision that the proposed probabilistic framework and the associated numerical implementation in this chapter may provide a rapid means for assessing the conjunct seismic and scour effects on existing river-crossing bridges, particularly the simple bridges in the rural areas. We further note that the proposed probabilistic framework can be adapted when it is used to assess the effects of flood-induced scour on other bridge types (e.g., deep-foundation supported bridges in soft soils), provided that a finite-element based nonlinear model for the bridge is available.

effect of the scour. In terms of the system drift ductility μ<sup>d</sup> in Figure 4(b), the overall trend is that the probability of exceeding any specified μ<sup>d</sup> increases due to the consideration of scour. This is especially evident when μ<sup>d</sup> is greater than 5. This implies that at larger drift ductility levels, wherein the likelihood of system collapse is defined, scour tends to increase the probability of system collapse. Due to these observations, we state that the probabilistic demand hazard modeling provides a more comprehensive approach to evaluating the effects of scour on the seismic

Probabilistic demand hazard curves considering scour and material uncertainties (denoted by "mu") vs. considering "mu" only: (a) strain ductility demand hazard curves and (b) drift ductility demand hazard

response and the vulnerability of bridge structures.

Earthquakes - Impact, Community Vulnerability and Resilience

Figure 5.

curves.

196

## Acknowledgements

The first author gratefully acknowledges the support from the grants from National Natural Science Foundation of China (Grant Number 51708484). Both authors appreciate the funding from a project supported by the University of Missouri Research Board titled "Design-oriented Scoured Foundation Modeling for Bridge Performance Analysis." The second author's rural resilience research is partially supported by the National Science Foundation (NSF) of the USA under the Award Number IIA-1355406.

References

0309098343

NCHRP Project 24-25

2003;19(4):733-752

3639-3649

[1] Hunt BE. Monitoring Scour Critical Bridges: A Synthesis of Highway Practice (NCHRP Synthesis 396). Washington, D.C.: Transportation Research Board; 2009 Report No.:

DOI: http://dx.doi.org/10.5772/intechopen.85158

Earthquake Engineering & Structural Dynamics. 2013;42(10):1451-1467

[9] Prasad GG, Banerjee S. The Impact of

[10] Banerjee S, Prasad GG. Analysis of

[11] Ghosn M, Moses F, Wang J. NCHRP Report 489: Design of Highway Bridges for Extreme Events. Washington, DC: Transportation Research Board; 2004

[12] Alipour A, Shafei B, Shinozuka M. Reliability-based calibration of load and resistance factors for design of RC bridges under multiple extreme events: Scour and earthquake. Journal of Bridge

[13] Wang Z, Padgett JE, Dueñas-Osorio L. Risk-consistent calibration of load factors for the design of reinforced concrete bridges under the combined effects of earthquake and scour hazards. Engineering Structures. 2014;79:86-95

[14] Karim KR, Yamazaki F. A simplified method of constructing fragility curves for highway bridges. Earthquake Engineering & Structural Dynamics.

[15] Shinozuka M, Feng MQ, Lee J, Naganuma T. Statistical analysis of fragility curves. Journal of Engineering Mechanics. 2000;126(12):1224-1231

[16] Nielson BG, DesRoches R. Seismic fragility methodology for highway

2003;32(10):1603-1626

Engineering. 2012;18(5):362-371

Flood-induced Scour on Seismic Fragility Characteristics of Bridges. Journal of Earthquake Engineering.

Bridge Performance under the Combined Effect of Earthquake and Flood-Induced Scour. In: Bilal MA, editor. Vulnerability, Uncertainty, and

Risk: Analysis, Modeling, and Management. Hyattsville, Maryland:

ASCE; 2011. pp. 889-896

2013;17(6):803-828

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown…

[2] Stein S, Sedmera K. Risk-Based Managment Guidelines for Scour at Bridges National Cooperative Highway. Research Program; 2006. Contract No.:

[3] Bruneau M, Chang SE, Eguchi RT, Lee GC, O'Rourke TD, Reinhorn AM, et al. A framework to quantitatively assess and enhance the seismic resilience of communities. Earthquake spectra.

[4] Cimellaro GP, Reinhorn AM, Bruneau M. Framework for analytical quantification of disaster resilience. Engineering Structures. 2010;32(11):

[5] Bolduc LC, Gardoni P, Briaud J-L. Probability of exceedance estimates for scour depth around bridge piers. Journal of Geotechnical and Geoenvironmental Engineering. 2008;134(2):175-184

[6] Briaud J-L, Gardoni P, Yao C. Statistical, risk, and reliability analyses of bridge scour. Journal of Geotechnical and Geoenvironmental Engineering.

[7] Wang Z, Song W, Li T, editors. Combined fragility surface analysis of earthquake and scour hazards for bridge. In: Proceedings of 15th World Conference on Earthquake Engineering.

[8] Dong Y, Frangopol DM, Saydam D. Time-variant sustainability assessment of seismically vulnerable bridges subjected to multiple hazards.

2013;140(2):04013011

Lisbon, Portugal. 2012

199

## Author details

Xuan Guo<sup>1</sup> , Zhaohua Dai<sup>2</sup> and ZhiQiang Chen<sup>3</sup> \*

1 College of Civil Science and Engineering, Yangzhou University, Yangzhou, Jiangsu, China

2 School of Civil Engineering, Nanjing Forestry University, Nanjing, China

3 School of Computing and Engineering, University of Missouri, Kansas City, USA

\*Address all correspondence to: chenzhiq@umkc.edu

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown… DOI: http://dx.doi.org/10.5772/intechopen.85158

## References

Acknowledgements

Award Number IIA-1355406.

Author details

, Zhaohua Dai<sup>2</sup> and ZhiQiang Chen<sup>3</sup>

\*Address all correspondence to: chenzhiq@umkc.edu

provided the original work is properly cited.

\*

1 College of Civil Science and Engineering, Yangzhou University, Yangzhou,

2 School of Civil Engineering, Nanjing Forestry University, Nanjing, China

3 School of Computing and Engineering, University of Missouri, Kansas City, USA

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

Xuan Guo<sup>1</sup>

198

Jiangsu, China

The first author gratefully acknowledges the support from the grants from National Natural Science Foundation of China (Grant Number 51708484). Both authors appreciate the funding from a project supported by the University of Missouri Research Board titled "Design-oriented Scoured Foundation Modeling for Bridge Performance Analysis." The second author's rural resilience research is partially supported by the National Science Foundation (NSF) of the USA under the

Earthquakes - Impact, Community Vulnerability and Resilience

[1] Hunt BE. Monitoring Scour Critical Bridges: A Synthesis of Highway Practice (NCHRP Synthesis 396). Washington, D.C.: Transportation Research Board; 2009 Report No.: 0309098343

[2] Stein S, Sedmera K. Risk-Based Managment Guidelines for Scour at Bridges National Cooperative Highway. Research Program; 2006. Contract No.: NCHRP Project 24-25

[3] Bruneau M, Chang SE, Eguchi RT, Lee GC, O'Rourke TD, Reinhorn AM, et al. A framework to quantitatively assess and enhance the seismic resilience of communities. Earthquake spectra. 2003;19(4):733-752

[4] Cimellaro GP, Reinhorn AM, Bruneau M. Framework for analytical quantification of disaster resilience. Engineering Structures. 2010;32(11): 3639-3649

[5] Bolduc LC, Gardoni P, Briaud J-L. Probability of exceedance estimates for scour depth around bridge piers. Journal of Geotechnical and Geoenvironmental Engineering. 2008;134(2):175-184

[6] Briaud J-L, Gardoni P, Yao C. Statistical, risk, and reliability analyses of bridge scour. Journal of Geotechnical and Geoenvironmental Engineering. 2013;140(2):04013011

[7] Wang Z, Song W, Li T, editors. Combined fragility surface analysis of earthquake and scour hazards for bridge. In: Proceedings of 15th World Conference on Earthquake Engineering. Lisbon, Portugal. 2012

[8] Dong Y, Frangopol DM, Saydam D. Time-variant sustainability assessment of seismically vulnerable bridges subjected to multiple hazards.

Earthquake Engineering & Structural Dynamics. 2013;42(10):1451-1467

[9] Prasad GG, Banerjee S. The Impact of Flood-induced Scour on Seismic Fragility Characteristics of Bridges. Journal of Earthquake Engineering. 2013;17(6):803-828

[10] Banerjee S, Prasad GG. Analysis of Bridge Performance under the Combined Effect of Earthquake and Flood-Induced Scour. In: Bilal MA, editor. Vulnerability, Uncertainty, and Risk: Analysis, Modeling, and Management. Hyattsville, Maryland: ASCE; 2011. pp. 889-896

[11] Ghosn M, Moses F, Wang J. NCHRP Report 489: Design of Highway Bridges for Extreme Events. Washington, DC: Transportation Research Board; 2004

[12] Alipour A, Shafei B, Shinozuka M. Reliability-based calibration of load and resistance factors for design of RC bridges under multiple extreme events: Scour and earthquake. Journal of Bridge Engineering. 2012;18(5):362-371

[13] Wang Z, Padgett JE, Dueñas-Osorio L. Risk-consistent calibration of load factors for the design of reinforced concrete bridges under the combined effects of earthquake and scour hazards. Engineering Structures. 2014;79:86-95

[14] Karim KR, Yamazaki F. A simplified method of constructing fragility curves for highway bridges. Earthquake Engineering & Structural Dynamics. 2003;32(10):1603-1626

[15] Shinozuka M, Feng MQ, Lee J, Naganuma T. Statistical analysis of fragility curves. Journal of Engineering Mechanics. 2000;126(12):1224-1231

[16] Nielson BG, DesRoches R. Seismic fragility methodology for highway

bridges using a component level approach. Earthquake Engineering & Structural Dynamics. 2007;36(6): 823-839

[17] Hwang H, Liu JB, Chiu Y-H. Seismic Fragility Analysis of Highway Bridges. Urbana, IL: Mid-America Earthquake Center; 2001

[18] Bazzurro P, Cornell CA. Seismic hazard analysis of nonlinear structures. I: Methodology. Journal of Structural Engineering. 1994;120(11):3320-3344

[19] Cornell CA, Jalayer F, Hamburger RO, Foutch DA. Probabilistic basis for 2000 SAC federal emergency management agency steel moment frame guidelines. Journal of Structural Engineering. 2002;128(4):526-533

[20] Cornell CA, Krawinkler H. Progress and challenges in seismic performance assessment. PEER Center News. 2000; 3(2):1-3

[21] Luco N. Probabilistic Seismic Demand Analysis, SMRF Connection Fractures, and Near-Source Effects. Stanford, California: Stanford University; 2002

[22] Tothong P, Luco N. Probabilistic seismic demand analysis using advanced ground motion intensity measures. Earthquake Engineering & Structural Dynamics. 2007;36(13):1837-1860

[23] Tondini N, Stojadinovic B. Probabilistic seismic demand model for curved reinforced concrete bridges. Bulletin of Earthquake Engineering. 2012;10(5):1455-1479

[24] Mackie K, Stojadinovic B. Probabilistic seismic demand model for California highway bridges. Journal of Bridge Engineering. 2001;6(6):468-481

[25] Baker JW. Efficient analytical fragility function fitting using dynamic structural analysis. Earthquake Spectra. 2015;31(1):579-599

Washington, DC: Federal Highway

DOI: http://dx.doi.org/10.5772/intechopen.85158

Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown…

multihazard framework for assessing flood scour and earthquake effects on bridge failure. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering.

[35] Mazzoni S, McKenna F, Scott MH, Fenves GL. OpenSees command language manual. Berkley, CA: Pacific Earthquake Engineering Research

[36] Choi E, DesRoches R, Nielson B. Seismic fragility of typical bridges in moderate seismic zones. Engineering Structures. 2004;26(2):187-199

[37] Dutta A, Mander J, editors. Seismic fragility analysis of highway bridges. In: Proceedings of the INCEDE-MCEER Center-to-Center Project Workshop on Earthquake Engineering Frontiers in Transportation Systems. 1998

[38] Kim S-H, Feng MQ. Fragility analysis of bridges under ground motion with spatial variation. International Journal of Non-Linear Mechanics. 2003;

38(5):705-721

201

[34] Guo X, Chen Z. Lifecycle

Administration; 2002

2015;2(2):C4015004

(PEER) Center; 2006;264

[26] Lee KH, Rosowsky DV. Fragility analysis of woodframe buildings considering combined snow and earthquake loading. Structural Safety. 2006;28(3):289-303

[27] Seyedi D, Gehl P, Douglas J, Davenne L, Mezher N, Ghavamian S. Development of seismic fragility surfaces for reinforced concrete buildings by means of nonlinear timehistory analysis. Earthquake Engineering & Structural Dynamics. 2010;39(1):91-108

[28] Baker JW. An introduction to probabilistic seismic hazard analysis. 2013. Online report: https://web. stanford.edu/~bakerjw/Publications/ Baker\_(2008)\_Intro\_to\_PSHA\_v1\_3.pdf (last access time: March 4, 2019)

[29] USGS. Seismic Design Maps & Tools; 2015. Available from: http://earth quake.usgs.gov/hazards/designmaps/

[30] Kafali C, Grigoriu M. Seismic fragility analysis: Application to simple linear and nonlinear systems. Earthquake Engineering & Structural Dynamics. 2007;36(13):1885-1900

[31] Arneson LA, Zevenbergen LW, Lagasse PF, Clopper PE. Evaluating Scour at Bridges (HEC-18). Washington, D.C.: U.S. Department of Transportation, Federal Highway Administration; 2012

[32] Briaud J-L, Ting FC, Chen H, Gudavalli R, Perugu S, Wei G. SRICOS: Prediction of scour rate in cohesive soils at bridge piers. Journal of Geotechnical and Geoenvironmental Engineering. 1999;125(4):237-246

[33] Kimmerling RE, Bachus RC, Mayne PW, Scheider JA, Zettler TE. Geotechnical Engineering Circular No. 6, Shallow Foundations (FHWA-IF-02-054). Multi-Hazard Assessment of Seismic and Scour Effects on Rural Bridges with Unknown… DOI: http://dx.doi.org/10.5772/intechopen.85158

Washington, DC: Federal Highway Administration; 2002

bridges using a component level approach. Earthquake Engineering & Structural Dynamics. 2007;36(6):

[17] Hwang H, Liu JB, Chiu Y-H. Seismic Fragility Analysis of Highway Bridges. Urbana, IL: Mid-America Earthquake

Earthquakes - Impact, Community Vulnerability and Resilience

structural analysis. Earthquake Spectra.

[26] Lee KH, Rosowsky DV. Fragility analysis of woodframe buildings considering combined snow and earthquake loading. Structural Safety.

[27] Seyedi D, Gehl P, Douglas J, Davenne L, Mezher N, Ghavamian S. Development of seismic fragility surfaces for reinforced concrete buildings by means of nonlinear time-

history analysis. Earthquake

Engineering & Structural Dynamics.

[28] Baker JW. An introduction to probabilistic seismic hazard analysis. 2013. Online report: https://web. stanford.edu/~bakerjw/Publications/ Baker\_(2008)\_Intro\_to\_PSHA\_v1\_3.pdf (last access time: March 4, 2019)

[29] USGS. Seismic Design Maps & Tools; 2015. Available from: http://earth quake.usgs.gov/hazards/designmaps/

[30] Kafali C, Grigoriu M. Seismic fragility analysis: Application to simple

Earthquake Engineering & Structural Dynamics. 2007;36(13):1885-1900

[31] Arneson LA, Zevenbergen LW, Lagasse PF, Clopper PE. Evaluating Scour at Bridges (HEC-18). Washington, D.C.: U.S. Department of Transportation, Federal Highway Administration; 2012

[32] Briaud J-L, Ting FC, Chen H, Gudavalli R, Perugu S, Wei G. SRICOS: Prediction of scour rate in cohesive soils at bridge piers. Journal of Geotechnical and Geoenvironmental Engineering.

[33] Kimmerling RE, Bachus RC, Mayne PW, Scheider JA, Zettler TE. Geotechnical Engineering Circular No. 6, Shallow Foundations (FHWA-IF-02-054).

1999;125(4):237-246

linear and nonlinear systems.

2015;31(1):579-599

2006;28(3):289-303

2010;39(1):91-108

[18] Bazzurro P, Cornell CA. Seismic hazard analysis of nonlinear structures. I: Methodology. Journal of Structural Engineering. 1994;120(11):3320-3344

[19] Cornell CA, Jalayer F, Hamburger RO, Foutch DA. Probabilistic basis for

[20] Cornell CA, Krawinkler H. Progress and challenges in seismic performance assessment. PEER Center News. 2000;

[21] Luco N. Probabilistic Seismic Demand Analysis, SMRF Connection Fractures, and Near-Source Effects. Stanford, California: Stanford

[22] Tothong P, Luco N. Probabilistic seismic demand analysis using advanced ground motion intensity measures. Earthquake Engineering & Structural Dynamics. 2007;36(13):1837-1860

[23] Tondini N, Stojadinovic B.

[24] Mackie K, Stojadinovic B.

[25] Baker JW. Efficient analytical fragility function fitting using dynamic

2012;10(5):1455-1479

200

Probabilistic seismic demand model for curved reinforced concrete bridges. Bulletin of Earthquake Engineering.

Probabilistic seismic demand model for California highway bridges. Journal of Bridge Engineering. 2001;6(6):468-481

2000 SAC federal emergency management agency steel moment frame guidelines. Journal of Structural Engineering. 2002;128(4):526-533

823-839

Center; 2001

3(2):1-3

University; 2002

[34] Guo X, Chen Z. Lifecycle multihazard framework for assessing flood scour and earthquake effects on bridge failure. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering. 2015;2(2):C4015004

[35] Mazzoni S, McKenna F, Scott MH, Fenves GL. OpenSees command language manual. Berkley, CA: Pacific Earthquake Engineering Research (PEER) Center; 2006;264

[36] Choi E, DesRoches R, Nielson B. Seismic fragility of typical bridges in moderate seismic zones. Engineering Structures. 2004;26(2):187-199

[37] Dutta A, Mander J, editors. Seismic fragility analysis of highway bridges. In: Proceedings of the INCEDE-MCEER Center-to-Center Project Workshop on Earthquake Engineering Frontiers in Transportation Systems. 1998

[38] Kim S-H, Feng MQ. Fragility analysis of bridges under ground motion with spatial variation. International Journal of Non-Linear Mechanics. 2003; 38(5):705-721

Chapter 12

Jonas Eliasson

1. Introduction

numerically stable domain.

203

Abstract

and Tsunamis

Earthquake-Generated Landslides

Large earthquakes generate tsunamis, but when it also triggers a landslide, the tsunami may become enormous. Slide scars on the continental shelf of the North Atlantic Ocean show this. For estimating the tsunami, a translatory wave theory has been suggested. Slide data are used to estimate the amplitude of the displacement wave. The amplitudes are used to obtain wave heights at a reference point outside the breaker zone. Energy transmission formulas are used to find the wave height transfer coefficients from the source area to a reference point. Tsunami risk from several sources at a reference point is quantified using stochastic processes, and estimations of a hazard curve for the probability of landslide occurrence are carried out. The sensitivity of the hazard curve to uncertainties in determining the wave height from the individual sources turns can be evaluated. In two case studies, the Tohoku tsunami and earthquake in 2011 in Japan is found to be caused by a coseismic slip and a landslide in combination, and a hazard curve for a reference

point south of Iceland is found for tsunamis in the North Atlantic Ocean.

The main difficulty in tsunami hazard assessment is to estimate the generation of wave energy at the source. In many cases, this is simply solved by running a CFD model and estimating the ocean surface amplitude at the source [1] from it. This estimate of the amplitudes involves many problems and can be very uncertain, when the measured amplitudes are small, but a better method is still to be found. Sometimes it is better to estimate the initial wave itself, and when that is done, the energy transmission from the source to the point of impact can be quite accurately modeled in CFD models [2–4], if the shallow water wave equations are in the

Strong earthquakes cause large deformations of the surface of the earth, so tsunamis are more often than not strengthened by landslides triggered by the earthquake. Often the triggering earthquake does not contribute any significant amount of energy to the tsunami wave, and this seems to be the general case in the

There have also been speculations in the scientific community about the danger

of tsunamis in the North Atlantic from gigantic glacial flood waves of volcanic origin, (jökulhlaups), emerging on the south coast of Iceland. In this case, there is a well-defined probability of occurrence [5] and clear geological evidence of the

North Atlantic, where few dangerous tsunamis are reported.

Keywords: earthquake, tsunami, landslide, hazard

## Chapter 12
