Fragility Functions of Highway and Railway Infrastructure

Abstract

The experience of past earthquakes has revealed that highway and railway elements are quite vulnerable to earthquake shaking and induced phenomena such as soil liquefaction or landslide; damages to these elements can seriously affect the transportation of products and people in both short-term (emergency actions) and long-term period. The objective of this chapter is to propose appropriate fragility functions for roadway and railway components other than bridges that are presented separately in Chap. 9. To this end, the main typological features are summarized and a short review of earthquake damages together with damage states definitions are provided for these elements. Fragility curves from literature are collected and reviewed. In some cases these functions are modified and adapted, while in other cases new fragility curves are developed. A general procedure for the derivation of analytical fragility curves that was followed in SYNER-G is described. This approach takes into account the effect of structure geometry, ground motion characteristics, soil conditions and associated uncertainties. New fragility curves are presented for tunnels in soil, embankments, cuttings and bridge abutments based on numerical analyses due to ground shaking. Finally, the proposed fragility functions are summarized and a general scheme to identify the functionality of roadway and railway elements due to different damage levels is outlined.

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10.1 Introduction

Roadway and railway systems are complex networks of various components like bridges, roads, tunnels, embankments, retaining walls, slopes, tracks and building facilities. Past earthquakes indicate that some of these elements are quite vulnerable, and in addition, involve lengthy repair time or rerouting difficulties. For example, the disruption to the road network can strongly affect the emergency efforts immediately after the earthquake and the rebuilding and other business activities in the following period. Typical paradigms of damage to highway and railway structures can be found in recent earthquakes such as the 2011 Christchurch, New Zealand; 2010 Chile; 2009 L’Aquila, Italy; 2007 Niigata-Chuetsu Oki and 2004 Niigata-ken Chuetsu, Japan and others. In these events the damages due to geotechnical hazards were particularly important.

The complexity of elements at risk, their construction variability, and until recently, the lack of well-documented damage and loss data from strong earthquakes have made the vulnerability assessment of each component or the network as a whole, quite a complicated problem. Consideration of the spatial extension of roadway/railway networks, the interactions with other systems and the inherent uncertainties in seismic hazard and vulnerability estimates, have made the risk assessment of transportation networks a complex and challenging issue.

In the following sections, the main typological features, damage classification and definitions are given for the roadway and railway elements that considered in the SYNER-G taxonomy. A brief review of available fragility curves and their evaluation methods are presented. The existing fragility curves are limited and generally inadequate, especially for the case of induced deformations by liquefaction, lateral spreading, landslide and fault rupture. The derivation of new analytical fragility curves due to seismic shaking is described for specific components and the parameters of the proposed fragility functions are presented. In case of ground failure, preliminary fragility curves are proposed based on expert judgment, while further research is needed on this topic.

10.2 Identification of Main Typologies

Most of the roadway and railway elements are categorized as earth structures; therefore, a main typological feature is the ground type, which characterizes either a construction or its foundation and surrounding material. Different soil classification systems are available based on various soil properties. A widely used scheme is the one provided by Eurocode 8 (2004), which is based on the soil’s average shear wave velocity on the top 30 m, V_s30.

In case of roadways, the main element is the road itself, which is passing over bridges, embankments or through tunnels and other civil works. Therefore, the hierarchy of roads according to their functions and capacities is an important parameter for the description of the typologies of the roadway elements. Different classification schemes exist based on speed limits, number of lanes and other criteria.

In case of railway infrastructure, the key part is the track, which consists of elements such as rails, sleepers and ballast that transfer the static and dynamic loads to the foundation soil. Different classification schemes exist which are based on speed limits, construction materials, usage of track and other parameters.

In addition to the above main attributes, other important typological features are given in the following for each element. It is noted that bridges are presented separately in Chap. 9.

• Tunnels: the basic parameters for the description of the typology are the construction method (bored or mined, cut-and-cover, immersed), the shape (circular, rectangular, horseshoe, etc.), the depth (surface, shallow, deep), the geological conditions (rock, alluvial), and supporting system (concrete, masonry, steel, etc.).

• Embankments, cuts and slopes: the main typological features are the geometrical parameters of the construction (i.e. slope angle, height).

• Road pavements: the basic parameter is the number of traffic lanes which is based on the functional hierarchy of the network.

• Bridge abutments: their typology is related to the structural type of bridge (e.g. stub, partial or full depth, integral abutment); other main typological features are the depth and the soil conditions of foundation and fill material behind the abutment. The depth is dependent on the surrounding topography and abutment geometry, while the backfill material behaviour depends on its compaction level.

The typological features and classification considered in SYNER-G are summarized in Table 10.1.

Table 10.1 SYNER-G taxonomy for roadway and railway network

10.3 Damage Description

Earthquake effects on roadway and railway elements can be grouped into two categories, (1) ground shaking (expressed often in terms of peak ground acceleration, PGA); and (2) ground failure such as liquefaction, fault displacement, and slope instability (expressed in terms of permanent ground deformation, PGD). A brief summary is given below for each element:

• Tunnels: Three types of deformations express the response of underground structures to seismic motions, (1) axial compression and extension, (2) longitudinal bending, and (3) ovaling/racking. Typical damages include (Owen and Scholl 1981; ALA 2001; Corigliano 2007): slope instability leading to tunnel collapse, portal failure, roof or wall collapse, invert uplift spalling, cracking or crushing of the concrete lining, slabbing or spalling of the rock around the opening, bending and buckling of reinforcing bars, pavement cracks, wall deformation, local opening of joints and obstruction of the opening.

• Embankments: When the foundation bearing capacity is lost due to static and dynamic loading, for example due to soil liquefaction, the embankment may spread laterally and settle at the same time. This could lead to lateral movement of embankment (from a few centimetres to several meters) resulting in opening of cracks in the road pavement or displacement of the railway tracks.

• Cuts and slopes: Earthquake induced landslides and rock falls can cause partial or complete blockage of the road/track as well as the structural damage to the road pavement or railway track. In addition, roads/tracks constructed in cuts and on slopes are subjected to failure or large movements of the slopes on the sides of the road/track.

• Bridge abutments/retaining walls: Approach backfills behind bridge abutments/retaining walls are vulnerable to earthquake-induced differential settlement. Approach-fill settlement has been the most commonly occurring type of highway system damage during recent earthquakes. In addition, pounding of the deck to the abutment can seriously affect the overall response of the bridge (Argyroudis et al. 2013a). This type of damage does not often result in extensive repair costs; however, it may have a serious impact on the functionality of the road network during the emergency period. In case of railway network, where the tolerance to ground deformation is lower, the impairment of functionality is more significant.

• Road pavement: Damage to road pavement can be direct (e.g. fault ruptures, settlement, lateral spreading), indirect (e.g. collapsed buildings, landslide debris, damage to underlying pipelines) or induced (e.g. restoration works).

• Railway track damage in past earthquakes have included displaced ballast, broken ties, pulled apart joints, broken rails, buckled rail, large lateral displacements and loss of vertical support for track over large distances. Signal systems have suffered limited damages in relatively low magnitude earthquakes due to broken batteries, overturned electrical relays and wrapped wires in pole lines. Such damage are often highly disruptive but can be quickly repaired. Moreover, losses might occur in larger earthquakes in terms of more extensive damage such as broken signal masts (Byers 2004).

Different damage criteria have been proposed for the fragility analysis of roadway and railway elements. The number of damage states is variable and is related with the functionality, traffic state, and/or the repair duration. In empirical and expert judgment methods, the extent of damage is described qualitatively (e.g. extent of cracks or settlements). In analytical methods the damage levels are defined based on the range of a specific damage index such as permanent ground deformation, capacity and factor of safety, which is also related to the serviceability level of the network.

The damage states in Table 10.2, in terms of permanent ground deformation (PGD), have been proposed in SYNER-G and have been used for roadway and railway components. In particular, a mean value of PGD was estimated for minor, moderate, and extensive/complete damage based on a range of values (min, max) from a review of the literature. In Table 10.3 the damage states for each component are defined and also correlated to the serviceability of the network (Table 10.4).

Table 10.2 Definition of damage states for roadway and railway elements (embankments, cuts, abutments, slopes, tracks) in SYNER-G

Table 10.3 Description of damage states for roadway/railway components in SYNER-G

Table 10.4 Description of damage states for roadway/railway components in SYNER-G (cont.)

10.4 Review of Existing Fragility Functions

The existing fragility functions are based on empirical, analytical or expert judgment methods. Most of the available fragility curves follow a lognormal cumulative distribution. The number of damage states and the type of intensity measure vary depending on the method and the element at risk. Most common intensity measure types (IMTs) are peak ground acceleration (PGA) when ground shaking is the cause of damage or permanent ground deformation (PGD) in case of ground failure. A brief review of existing fragility functions for roadway and railway elements is given in the following. The corresponding review of methods and IMTs for bridges is provided in Chap. 9.

10.4.1 Tunnels

Until recently, the vulnerability assessment of tunnels has mainly been based on expert judgment (ATC13 1985; NIBS 2004) or empirical fragility curves (ALA 2001; Corigliano 2007) derived from actual damage in past earthquakes. In the study by Corigliano (2007) all deep tunnels are classified in one category and the proposed fragility curves are given as functions of peak ground velocity (PGV) for none/slight and moderate damage. The HAZUS approach (NIBS 2004) is based on judgment and limited empirical data set by Dowding and Rozen (1978) and Owen and Scholl (1981), providing fragility curves both for ground shaking (PGA) and ground failure (PGD). In ALA approach tunnels are distinguished based on geology conditions and quality of construction. Fragility curves are given as functions of PGA for three damage states. The parameters of the lognormal distribution in terms of medians (μ) and standard deviations (β) are given in Table 10.5. The fragility curves are illustrated in Figs. 10.1 and 10.2.

Table 10.5 Fragility function parameters for tunnels (ALA 2001)

Fig. 10.1

Fragility curves for tunnels in rock

Fig. 10.2

Fragility curves for tunnels in alluvial and cut and cover (ALA 2001)

A limited number of numerical approaches for the fragility analysis of tunnels are available. Salmon et al. (2003) presented analytical fragility curves for bored and cut and cover tunnels of the BART project as a function of PGA (ground shaking) and PGD (fault offset). These curves are site specific and their use is limited to the BART project. In the framework of LessLoss (2007) project, Argyroudis and Pitilakis (2007) proposed a preliminary set of analytical fragility curves for circular (bored) tunnels due to permanent ground deformation (PGD).

In the SYNER-G project new analytical fragility curves were proposed for shallow/metro tunnels in alluvial soil for different conditions (circular/bored and rectangular/cut and cover) due to ground shaking (see 10.5.2). In case of permanent ground deformations the generic fragility curves by HAZUS methodology can be applied as a first approximation, however further research is needed on this topic.

10.4.2 Embankments, Cuts and Slopes

Maruyama et al. (2010) proposed empirical curves for expressway embankments based on damage datasets from recent earthquakes in Japan. The fragility functions relate the number of damage incidents per km of expressway to PGV. Lagaros et al. (2009) proposed analytical fragility curves for embankments based on pseudostatic slope stability analyses, through Monte Carlo simulation method and neural network metamodels. The damage states are defined based on factor of safety, while the main purpose of the study is to highlight the computational effort of different approaches. The ATC-13 (1985) approach provided fragility curves for six slope classes, which are defined by the critical acceleration based on expert opinion as a function of earthquake intensity MMI. Finally, an expert judgment approach to determining the physical vulnerability of roads for a given debris flow volume is proposed by Winter et al. (2013). Damage probabilities were assessed based on a detailed questionnaire to experts.

In the framework of SYNER-G, new analytical fragility curves have been developed as functions of PGA, for embankments and cuts of different heights and soil conditions (see Sect. 10.5.4). In case of roads and tracks on slopes new fragility curves were proposed following the approach adopted by Pitilakis et al. (2010). In particular, the threshold PGD values of Table 10.2 were used for the estimation of the corresponding PGA medians based on the model by Bray and Travasarou (2007). The slopes were classified through the yield acceleration coefficient k_y (Table 10.6, Figs. 10.3 and 10.4).

Table 10.6 Fragility function parameters for roads and tracks on slopes

Fig. 10.3

Fragility curves at various damage states and different yield coefficients (k_y) for roads on slope (Kaynia 2013)

Fig. 10.4

Fragility curves at various damage states and different yield coefficients (k_y) for tracks on slope (Kaynia 2013)

10.4.3 Retaining Walls and Approach Fills

The ATC-13 (1985) approach provided damage probability matrices for retaining walls for different levels of MMI based on expert opinion. Salmon et al. (2003) reported analytical fragility curves for retaining walls of the BART project as functions of PGA. However, the typological characteristics of the walls are not given; therefore, the fragility functions are considered as project specific. REDARS methodology (Werner et al. 2006) provides threshold values of PGD for different damage levels, related to the repair cost, duration and traffic states of bridge approach fills and road pavements for California highways. They are based on expert judgment and are not given in the form of fragility functions.

In the framework of SYNER-G, new analytical curves for bridge abutments on shallow foundations are proposed as functions of PGA for different soil conditions and abutment heights (see Sect. 10.5.3).

10.4.4 Road Pavements and Railway Tracks

HAZUS methodology (NIBS 2004) includes fragility curves for major and urban roads as functions of PGD (fault offset, liquefaction, landslide) (Table 10.7, Fig. 10.5). These curves have been validated in SYNER-G using observed damage in road pavements during past earthquakes in Greece. The results indicated a good agreement between the estimated and observed damages (Kaynia et al. 2011). The aforementioned functions, which are based on expert judgment, are also suggested for railway tracks in HAZUS methodology. However, the tolerance of railways to damage is lower and therefore these functions are generally considered unsatisfactory. In SYNER-G, new PGD thresholds to different damage states have been proposed for railway tracks. These values are applied for the derivation of fragility functions for railway tracks subjected to ground failure (Table 10.8 and Fig. 10.6). As a first approximation, these fragility curves can be applied for road pavements and railway tracks subjected to permanent ground deformations (e.g. by liquefaction, fault crossing, and landslide) independently of their location on embankment, cut, slope or flat ground. However, further investigation is needed on this subject to study the effects of soil and topography conditions as well as the peculiarities of each component.

Table 10.7 Fragility function parameters for road pavements

Fig. 10.5

Fragility curves for road pavements subjected to ground failure (NIBS 2004)

Table 10.8 Fragility function parameters for railway tracks

Fig. 10.6

Fragility curves for railway tracks subjected to ground failure (Kaynia 2013)

10.5 New Analytical Fragility Curves for Ground Shaking

The existing fragility curves for roadway and railway components are mainly based on empirical or expert judgment approaches both for ground shaking and ground failure. In many cases they do not cover adequately the typologies, soil conditions and ground motion characteristics. In the framework of SYNER-G, new analytical fragility curves were developed for tunnels in alluvial soil and roadway/railway bridge abutments, embankments and cuts subjected to ground shaking. In the following, a brief description of the general procedure for the derivation of the analytical fragility curves is given. Next, the main modeling issues are described, and finally, the parameters of the new fragility curves are summarized for each component. The response of roadway and railway infrastructures due to earthquake-induced geohazards such as landslides and ground failure needs further research in order to develop adequate fragility curves for all elements.

10.5.1 Key Modeling Issues and Treatment of Uncertainties

The general procedure followed in SYNER-G for the derivation of analytical fragility curves for roadway and railway elements is described by Argyroudis et al. (2013b). The effects of soil conditions and ground motion characteristics on the element’s response are taken into account by using different typical soil profiles and seismic input motions. The response of the free field soil profiles is calculated through 1D numerical analysis with increasing ground motion amplitude at the seismic basement (V_s > 800 m/s). 2D dynamic or quasi-static analysis is used for the non-linear seismic response of the soil-structure. This approach allows the evaluation of fragility curves considering the distinctive features of the element geometries, the input motion characteristics and the soil properties.

The level of damage is described by a damage index expressing the exceedance of certain limit states (Table 10.2), and the fragility curves are estimated based on the evolution of damage index with increasing earthquake acceleration, considering the associated uncertainties. An example is given in Fig. 10.7 where the different points indicate the results of the analyses in terms of damage index for different levels of earthquake shaking. The solid line is produced based on a regression analysis in which the median threshold value of the intensity measure to cause the i_th damage state is estimated based on the definition of damage index (mean values in Table 10.2). The fragility curve is described by a lognormal distribution function which is defined by two parameters, the median threshold value of the earthquake intensity measure type IMT (e.g. PGA) required to cause the i _th damage state and β _tot is the total standard deviation which describes the total variability associated with each fragility curve. Three primary sources of uncertainty are usually considered (NIBS 2004), namely the definition of damage states, β_DS, the response and resistance (capacity) of the element, β_C, and the earthquake input motion (demand), β_D. The total uncertainty is estimated as the root of the sum of the squares of the component dispersions assuming that they are stochastically independent lognormal-distributed random variables.

Fig. 10.7

Example of evolution of damage with earthquake intensity measure and definition of threshold median value for the damage state i, and definition of standard deviation (β_D) due to input motion (demand)

In the absence of a more rigorous estimation, the uncertainty parameters can be obtained from the literature (e.g. NIBS 2004). However, the uncertainty associated with seismic demand (β_D), is described by the variability in response due to the variability of ground motion in numerical simulations.

10.5.2 Shallow Tunnels

Numerical fragility curves for shallow metro (urban) tunnels in alluvial deposits were developed by considering structural parameters, local soil conditions and – input ground motion characteristics. In particular, the transverse seismic response of the tunnel due to upward travelling shear waves was evaluated under quasi-static conditions by applying on the tunnel cross-section and the surrounding soil the free field seismic ground deformations, which were calculated independently though 1D equivalent linear analysis. Different tunnel cross-sections, input motions and soil profiles were employed. By defining the damage levels according to the exceedance of strength capacity of the most critical sections of the tunnel, the fragility curves were constructed as functions of the level and the type of seismic excitation. The comparison between the new fragility curves and the existing empirical ones has highlighted the important role of the local soil conditions (Argyroudis and Pitilakis 2012).

10.5.2.1 Damage States

The damage states of existing empirical fragility curves are based on a qualitative damage description from past earthquakes. In particular the damage index (DI) is defined as the ratio between the bending moment demand, M, and the capacity bending moment of the tunnel cross-section, M_Rd. This definition is compatible with the use of displacements, according to the equal displacement approximation. Based on previous experience of damages in shallow tunnels and applying engineering judgment, four damage states were considered due to ground shaking. They refer to minor, moderate, extensive and complete damage of the tunnel lining as described in Table 10.9.

Table 10.9 Definition of damage states for tunnel lining

10.5.2.2 Model Parameters

Two typical tunnel sections were considered, a circular (bored) tunnel with a 10 m diameter and a rectangular (cut and cover) one-barrel frame with dimensions 16 × 10 m. The lining of the circular tunnel is composed of 0.50 m thick precast concrete segments, while the rectangular tunnel has 0.9 m thick concrete walls, 1.2 m thick roof slab and 1.4 m thick base slab. The circular and rectangular tunnel was placed at 10 m and 3.5 m depths, respectively. Fourteen ideal soil deposits were considered corresponding to ground types B, C and D of Eurocode 8 (2004), ranged according to the shear wave velocity, V _s30, values. Three different soil thicknesses equal to 30, 60 and 120 m were assumed, and typical values of the different soil parameters were selected for each soil layer.

Records on rock sites from different earthquakes were selected such that their average response spectrum matched fairly well the response spectrum of Eurocode 8. These earthquake records were used as input motion in 1D ground response analyses. The records were scaled from 0.1 to 0.7 g and applied at the base of the soil model in order to calculate the induced stresses in the tunnel as a function of PGA and finally to estimate the fragilty curves (Argyroudis and Pitilakis 2012).

10.5.2.3 1D and 2D Numerical Analyses

The imposed quasi-static seismic ground displacements were computed using 1D equivalent linear approach with the code EERA (Bardet et al. 2000). The variations of shear modulus G/G_o (where G_o is the initial shear modulus) and damping ratio with the shear strain level γ were defined according to the available data in the literature as a function of plasticity index and effective stress. The PGA value computed on the surface of each soil profile was selected as the representative IMT in the fragility curves.

A plane strain ground model with the tunnel cross-section was analysed using the finite element code PLAXIS 2D (Plaxis 1998). Prior to the application of the imposed displacement, a set of initial static analyses was performed to properly model the initial static conditions, the excavation of the tunnel and the construction of the lining. The behaviour of the tunnel lining is assumed to be linear elastic, while the soil was characterized by a Mohr-Coulomb yield criterion in all the stages of the analysis. Figure 10.8 shows a representative example of the tunnel response after imposing the shear ground displacements.

Fig. 10.8

Example of 2D analysis of tunnel: deformed mesh (a), total moment and axial forces of the circular (b) and rectangular (c) tunnel lining (soil profile: type B, depth: 60 m; input motion: Kypseli, 0.3 g)

10.5.2.4 Derivation of Fragility Curves

For the derivation of fragility curves the general procedure described in Sect. 10.5.1 is followed. In particular, the median PGA value for each damage state is based on the relationship between the computed damage indices versus PGA on the free field and the definitions of damage states given in Table 10.9. A value equal to 0.4 was assigned for the uncertainty associated with the definition of damage states, β_DS, following the approach of HAZUS (NIBS 2004) for buildings; the uncertainty due to the capacity, β_C, is assigned equal to 0.3 according to analyses for bored tunnels of BART system (Salmon et al. 2003). The last source of uncertainty, associated with seismic demand, is described by the standard deviation of the damage indices that have been calculated for the different input motions at each level of PGA. The parameters of the lognormal distribution in terms of medians and standard deviations are given in Table 10.10 and the corresponding fragility curves are shown in Figs. 10.9 and 10.10.

Table 10.10 Parameters of numerical fragility curves for urban tunnels in different ground types

Fig. 10.9

Fragility curves for circular (bored) metro/urban tunnel section

Fig. 10.10

Fragility curves for rectangular (cut and cover) metro/urban tunnel section

10.5.3 Bridge Abutments

New analytical fragility curves for bridge abutment-approach fill system were developed in SYNER-G (Argyroudis et al. 2013b). The response of the abutment was evaluated from dynamic analyses with an increasing level of seismic shaking following the general procedure briefly described in Sect. 10.5.1. In particular, the soil behaviour was simulated through a 2D fully coupled FE model using an elasto-plastic criterion. A calibration procedure was followed in order to account for the dependency of both stiffness and damping on the ground strain level. The effect of soil conditions and ground motion characteristics in the global soil and structure response was taken into account by considering different typical soil profiles and seismic input motions. The performance of the wall, and thus the level of damage, was described by the settlement observed on the backfill.

10.5.3.1 Model Parameters

Representative and simplified bridge abutment geometries with two different heights equal to 6.0 and 7.5 m were modeled as cantilever retaining wall (Fig. 10.11). The bridge deck is supported by the abutment on bearings while its total load is simulated by a vertical load equal to 200 kN.

Fig. 10.11

Properties of soil/backfill/abutment under study

Five real earthquake records were selected such that their average response spectrum matched fairly well the response spectrum of Eurocode 8 on rock. The earthquake records were from: Kocaeli 1999, Gebze; Hector Mine 1999, Hector; Parnitha 1999, Kypseli; Loma Prieta 1989, Diamond Height; Umbria Marche 1998, Gubbio-Piana. The time histories of these records were scaled from 0.1 to 0.5 g and were applied at the base of the soil model in order to calculate the response of the backfill-abutment due to an increasing level of seismic intensity.

Two ideal soil deposits of 50 m, corresponding to ground types C and D in Eurocode 8 were considered. Typical values of the soil parameters were selected for both the soil profile and the backfill. The 1D ground response analyses were performed using 1D equivalent linear approach with the code EERA (Bardet et al. 2000). A calibration procedure was followed in order to account for the dependency of both stiffness and damping on the strain level. Details for the model parameters are given in Argyroudis et al. (2013b).

The numerical simulations were performed using the finite element code PLAXIS 2D (Plaxis 2011). A close-up of the mesh employed in the study is shown in Fig. 10.12. All the analyses were carried out by performing a set of initial static stages to simulate the initial weight, the installation of the abutment and the backfill, followed by the dynamic analyses.

Fig. 10.12

Finite element mesh used in the analyses of bridge abutment

10.5.3.2 Derivation of Fragility Curves

The derivation of the fragility curves from the results of the numerical simulations was similar to that presented in Sect. 10.5.1. The threshold PGD values of Table 10.2 were used for the estimation of median PGA values for each damage state through the corresponding diagrams that describe the evolution of damage with PGA. The parameters of the fragility curves are presented in Table 10.11. The fragility curves for complete damage are derived based on extrapolation of the available computed results. Damage records from a recent earthquake in Japan were used to validate the proposed fragility curves (Argyroudis et al. 2013b) (Figs. 10.13 and 10.14).

Table 10.11 Parameters of numerical fragility curves for roadway and railway abutments in different ground types

Fig. 10.13

Fragility curves for road abutments, ground type C (left) and D (right)

Fig. 10.14

Fragility curves for railway abutments, ground type C (left) and D (right)

10.5.4 Embankments and Cuts

New analytical fragility curves for embankments and cuts were developed in SYNER-G. The response of the system was evaluated based on dynamic analyses with increasing level of seismic intensity following the procedure described in Sect. 10.5.1. Further developments for the seismic performance and fragility assessment of roadway embankments are provided in Argyroudis and Kaynia (2013).

10.5.4.1 Model Parameters

Representative geometries are considered with heights equal to 2.0 and 4.0 m for the embankment and 4.0 and 6.0 m for the cut; preliminary analyses indicated that typical engineered cuttings shallower than 4.0 m are practically not vulnerable to earthquake shaking. The top width of the embankment and the bottom width of the cut is 20 m. The same earthquake records used in the analysis of bridge abutments were applied in these analyses. The earthquake time histories were scaled from 0.1 to 0.7 g and the response of embankment/cut is calculated as a function of PGA on the ground surface.

Two ideal soil deposits of 50 m corresponding to ground types C and D with shear wave velocity (V_s30) in the range defined by Eurocode 8 were considered similar to those used in case of abutments. Typical values of soil properties are selected for the embankment. The numerical simulations are performed with the finite element code PLAXIS 2D (Plaxis 2011). A close-up of the models is shown in Fig. 10.15.

Fig. 10.15

Finite element mesh used in the analyses of embankment (up) and cut (down)

10.5.4.2 Derivation of Fragility Curves

The derivation of fragility curves was based on a diagram of the computed damage indices in terms of average total permanent ground deformation, PGD, on embankment or cut surface, versus PGA on the ground surface as illustrated in Fig. 10.8. A relationship was established by linear regression analysis relating PGD to PGA on the ground surface in the free field. The median threshold value of PGA was then obtained for each damage state based on the aforementioned relationship and the definitions given in Table 10.2. The lognormal standard deviation, β_tot, which describes the total variability associated with each fragility curve, was estimated as described in Sect. 10.5.1. The estimated parameters of the fragility curves are presented in Tables 10.12 and 10.13. The derived curves are plotted in Figs. 10.16, 10.17, 10.18, and 10.19 for roadway and railway elements. For simplicity and in order to avoid intersection of the different fragility curves in case of the embankments, the plots are given for an average lognormal standard deviation equal to 0.9 for ground type C and 0.8 for ground type D.

Table 10.12 Parameters of numerical fragility curves for roadway and railway embankments in different ground types

Table 10.13 Parameters of numerical fragility curves for roadway and railway cuts in different ground types

Fig. 10.16

Fragility curves for road embankments in ground type C (left) and D (right)

Fig. 10.17

Fragility curves for railway embankments in ground type C (left) and D (right)

Fig. 10.18

Fragility curves for road cuts in ground type C (left) and D (right)

Fig. 10.19

Fragility curves for railway cuts in ground type C (left) and D (right)

10.6 Conclusions and Recommendations

A brief review of available fragility curves and their evaluation methods were presented for roadway and railway elements. The main typological features and damage states definitions were summarized. Tunnels, embankments, road pavements, slopes, cuts, railway tracks and bridge abutments are earth structures and are thus directly affected by the local soil conditions. In the framework of SYNER-G new analytical fragility curves are proposed for urban tunnels in alluvial soil, embankments and cuts, and bridge abutments for roadways and railways subjected to ground shaking. The effects of soil type and ground motion characteristics were taken into account by using typical soil profiles and seismic input motions. The response of the soil profiles was calculated through 1D equivalent linear analyses, while the non-linear response of the soil-structure system was calculated through 2D quasi-static or dynamic analyses. The available fragility curves for ground failure are limited; therefore, the case of the vulnerability of roadway and railway components due to liquefaction, landslide, rock-falls and fault rupture should further be investigated.

The proposed fragility functions for roadway and railway elements based on past and new developments presented herein are outlined in Table 10.14. Fragility functions for tunnels, embankments, cuts, slopes and bridge abutments correspond to ground shaking intensity in terms of PGA on the surface, while those for road pavements and railway tracks are referred to ground failure in terms of permanent ground displacements.

Table 10.14 Summary of proposed fragility functions for road/rail elements under ground shaking and ground failure

The performance of a roadway system, at the component level, can be described through the reduction of functional traffic lanes due to damage, which is directly connected to the reduction of speed and capacity of the system. The general scheme in Table 10.15 can be used as a basis to estimate the functionality of roadway components due to different damage levels. Three levels of functionality are described, namely, open, partially open, and closed. The partially open state is defined based on the number of lanes of the undamaged road (Table 10.16), which is based on the REDARS approach (Werner et al. 2006). It is noted that the partially open state is not applied when the roadway has a single traffic lane. A general scheme for the functionality of railway elements is given in Table 10.17 where three levels of functionality are described (fully functional, functional but with speed restrictions, not functional/closed).

Table 10.15 General proposal for functionality of roadway elements

Table 10.16 Definition of functionality of roadway elements in relation to open traffic lanes before and after the earthquake

Table 10.17 General proposal for functionality of railway elements