1 Introduction

Physical infrastructure networks (e.g. transportation and energy) are crucial to the everyday functioning of society, but are at risk of damage and disruption when exposed to tsunamis. A number of contemporary observations have been made to this effect, most notably over the past two decades (Ballantyne, 2006; Edwards, 2006; Evans & McGhie, 2011; Fritz et al., 2011; Goff et al., 2006; Maruyama & Itagaki, 2017; Palliyaguru & Amaratunga, 2008; Paulik et al., 2021; Scawthorn et al., 2006; Tang et al., 2006). To effectively manage the risk from tsunamis requires risk assessment (UNISDR, 2015), including context appropriate (i.e. for local asset and hazard standards) vulnerability models.

Tsunami vulnerability models define the relationship between asset damage level and hazard intensity (e.g. tsunami flow depth; Koshimura et al., 2009). These include vulnerability and fragility curves. Vulnerability curves derive a continuous loss index or ratio as intensity increases for the given hazard intensity measure (HIM), whereas fragility curves provide the probability of exceeding different limit states (e.g. physical damage) for the given HIM (Koshimura et al., 2009). Tsunami fragility curves are typically developed from empirical asset attribute and impact data, and empirical or numerical hazard data for a specific event. The vulnerability data are, therefore, representative of the events’ hazard characteristics and local asset or component construction standards. A priority for the tsunami risk discipline is to undertake post-event hazard and impact surveys. These surveys contribute to progressively more comprehensive global datasets and inform increasingly effective disaster risk assessment. Tsunami vulnerability assessment has largely focused on building damage to date (Tarbotton et al., 2015), and there is now a need to focus on other elements of the built environment including physical infrastructure networks.

Tsunami fragility curves commonly rely on relatively large samples of empirical or modelled impact data, yet such data for physical infrastructure network components are rare and have only recently been a focus of post-event impact assessment (MLIT, 2012; Paulik et al., 2019, 2021) and physical modelling studies (Chen & Melville, 2015; Chen et al., 2017, 2018; Rossetto et al., 2014). For physical infrastructure networks, transportation and energy sector components (namely roads, bridges, port structures and utility poles), have been previously analysed for fragility curve development from empirical field surveys and physical modelling (Chua et al., 2020; Eguchi et al., 2013; Kawashima & Buckle, 2013; Koks et al., 2019; Maruyama & Itagaki, 2017; Shoji & Moriyama, 2007; Williams, et al., 2020a, 2020b). However, the relative importance of network component attribute characteristics influencing tsunami damage is understudied. These previous fragility studies typically apply tsunami flow depth as the HIM, as it has a strong correlation with impact and can be measured post-event. Empirical tsunami flow depth data can be used for interpolated hazard models (e.g. Williams, et al., 2020a, 2020b) and/or to refine and validate numerical hazard models (e.g. Aránguiz et al., 2018; Heidarzadeh et al., 2015; Jamelot et al., 2019). However tsunami hazard and impact studies are almost unanimous in that no single HIM can fully encapsulate the characteristics of tsunami impacts (Bojorquez et al., 2012; Gehl & D’Ayala, 2015; Macabuag et al., 2016a, 2016b). Furthermore, a number of studies recommend the development of tsunami fragility curves for infrastructure network components that consider tsunami flow velocity (m/s), hydrodynamic force (kN/m) and momentum flux (m3/s2) (e.g. Williams, et al., 2020a, 2020b) among other HIMs.

The present study has two objectives: (1) Analyse and discuss the factors causing damage to roads and utility poles, using empirical data collected from Coquimbo (Chile) after the 2015 Illapel tsunami; and (2) develop fragility curves on the conditional probability of physical damage levels for these network components in response to interpolated and simulated tsunami flow depth, flow velocity, hydrodynamic force and momentum flux. The data used to develop fragility curves in the present study represent network component attributes and damage levels (Paulik et al., 2021), interpolated tsunami flow depths (Williams et al., 2020a) and numerical hydrodynamic tsunami models (Aránguiz et al., 2018). To that affect, this paper provides an overview of the case-study event (Sect. 2), methodology (Sect. 3), including the empirical damage dataset (Sect. 3.1), tsunami hazard data (Sect. 3.2), variable testing for feature importance and correlation (Sect. 3.3) and fragility curve development (Sect. 3.4) using a cumulative link model method. The results of the variable importance and correlation tests are presented (Sect. 4.1), followed by the tsunami fragility curves (Sect. 4.2) for roads (Sect. 4.2.1) and utility poles (Sect. 4.2.2). A discussion of the results (Sect. 5), including their potential limitations, are then followed by conclusions of the study (Sect. 6).

2 Case Study Event

The 16 September 2015 Illapel tsunami followed a large earthquake off the central Chilean coast (Fig. 1a). The event motivated several post-event field surveys, with teams measuring and recording tsunami hazard characteristics and damage along a 700 km stretch of coastline from Chañaral to Concón (Aránguiz et al., 2016; Tomita et al., 2016). Tsunami flow depth and run-up measurements were mostly taken between La Serena and Los Vilos (Aránguiz et al., 2016) with building, physical infrastructure and environmental damage observed in Coquimbo and Los Vilos (Aránguiz et al., 2016; Contreras-López et al., 2016; Paulik et al., 2021). In Coquimbo (pop. 209,684), the maximum recorded tsunami amplitude was 4.75 m at the Port tide gauge, causing a maximum run-up height of 6.4 m (Aránguiz et al., 2016; Contreras-López et al., 2016). Physical infrastructure network damage and disruption were cited in immediate tsunami damage reports (ONEMI, 2015), however, network component damage investigations were not a primary focus of national-led post-event surveys.

Figure 1
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a Location of Coquimbo region in South America. b Coquimbo city. (Basemap source ESRI contributors, 2020)

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Post-tsunami surveys prior to this event have mainly focused on systematic building damage assessments opposed to component damage sustained by transport, energy, water and telecommunications networks. Empirical information on tsunami hazard intensity, physical infrastructure component attributes and damage level are critical for analysing the fragility of individual network components. Physical infrastructure network component fragility curves can support investigations of potential service disruption to single or multiple networks affected by tsunamis. Previous studies on this event have focused on surveying the hazard to determine tsunami source characteristics (Aránguiz et al., 2016), damage observations (Aránguiz et al., 2016; Contreras-López et al., 2016; Paulik et al., 2021), interpolated and simulated hazard models (Aránguiz et al., 2018; Klapp et al., 2020) and vulnerability models for buildings (Aránguiz et al., 2018) and road network components (Williams et al., 2020a).

3 Methodology

3.1 Empirical Damage Data

Paulik et al. (2021) recorded tsunami flow depths and classified building, road and utility pole (among others) attribute damage in Coquimbo following the 2015 Illapel tsunami. Damage level (DL) classifications for roads and utility poles were categorised using a four-state ordinal scale (Fig. 2, Tables 1, 2) ranging from DL0 (No damage) to DL3 (Complete damage). Roads and utility pole attribute information, as applied in the present study, are presented in Table 3, along with the tsunami hazard characteristics. Road observation points were converted into linear road features by Williams et al. (2020a) to represent attribute and damage levels for road network components exposed to tsunami hazards. In total 24 km of roads (split into 50 m sections) and 897 utility poles were recorded in the study area (Table 2).

Figure 2
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Surveyed infrastructure network component data [modified from Paulik et al. (2021)]

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Table 1 Damage level descriptions for network components in Coquimbo survey area [modified from Paulik et al. (2021)]
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Table 2 Summary of field data collected for tsunami hazard and damage level for road and utility poles located in the study area [modified from Paulik et al. (2021)]
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Table 3 Tsunami hazard and network component characteristics
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3.2 Tsunami Hazard Data

Hydrodynamic tsunami hazard characteristics (Table 3) are estimated at road and utility pole locations using interpolated (Williams et al., 2020a; "IDmax") and simulated (Aránguiz et al., 2018; "Dmax") representations of the 2015 Illapel tsunami hazard. Both hazard models have been applied in the development of fragility curves for buildings (Aránguiz et al., 2018) and infrastructure (Williams et al., 2020a). The single hazard intensity metric (HIM), an assumed maximum tsunami flow depth, is represented by the interpolated (spline method) water surface (IDmax; m), from flow depth measurements made by Paulik et al. (2021) and interpolated by Williams et al. (2020a). Aránguiz et al. (2018) developed hydrodynamic tsunami models for the study area by means of numerical simulation, which have been validated against tsunami height measurements, from the same study, by using the root mean square (Aida, 1978). Aránguiz et al. (2018) applied the Non-hydrostatic Evolution of Ocean WAVEs (NEOWAVE) model. NEOWAVE has been previously tested with velocity measurements at Hawaii during the 2011 Tohoku tsunami (Cheung et al., 2013). Five nested grids were applied at a maximum grid resolution of 10 m, and the Li et al. (2016) earthquake source model, to quantify maximum flow depth (Dmax; m), flow velocity (Vmax; m/s), hydrodynamic force (Fmax; kN/m) and momentum flux (Mmax; m3/s2) for the main urban centre of tsunami exposed Coquimbo (Aránguiz et al. (2018); Fig. 3). The four tsunami HIMs represented by these datasets were spatially sampled, in the present study, at road and utility pole asset locations for vulnerability analysis and fragility curve development.

Figure 3
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Tsunami interpolation and numerical hazard simulations for a interpolated flow depth (wetland and beach masked; Williams et al., 2020a) b simulated flow depth (wetland and beach masked; Aránguiz et al., 2018), c interpolated flow depth (wetland and beach un-masked; Williams et al., 2020a), d simulated flow depth (wetland and beach unmasked; Aránguiz et al., 2018), e simulated flow velocity (Aránguiz et al., 2018), f simulated hydrodynamic force (Aránguiz et al., 2018) and g simulated momentum flux (Aránguiz et al., 2018) hazard intensity measures

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Although both flow depth models from Aránguiz et al. (2018) and Williams et al. (2020a) use widely accepted and validated methods, there are key differences in the resulting hazard models (Figs. 3, 4). These differences are relevant to understanding the implications on the simulated hazard models (Aránguiz et al., 2018), and subsequently the fragility curves presented in Sect. 4.2 (see discussion in Sect. 5). As evident from Williams et al. (2020a), the interpolated flow depth model does not contain survey data from the wetland and Playa Changa (beach; Fig. 1), due to an inherent absence of vertical features (e.g. structures) for tsunami traces (i.e. watermarks) to be recorded against. Although this could be seen as a major limitation for fragility curve development, in this instance there were no physical infrastructure network components in these areas. For this reason, and to better compare the interpolated and simulated data, Fig. 1a, b are presented with the wetland and beach (i.e. areas with no bearing on fragility curve development for this case study) masked. Another key difference between these hazard models is the Puerto de Coquimbo (port) area (Fig. 1, Fig. 3a, b). The interpolated model (Fig. 3a) indicates relatively higher flow depths here compared to the simulated model (Fig. 3b). Conversely, the coastal esplanade (Avenida Costanera; Fig. 1) has relatively higher flow depths for the simulated model (Fig. 3b) compared to relatively lower interpolated flow depths (Fig. 3a). The simulated hazard model is generally over-estimating depth at < 2.5 m and under-estimating depth at > 2.5 m, relative to the interpolated hazard model.

Figure 4
figure 4

Flow depth for simulated (Aránguiz et al., 2018) and interpolated (Williams et al., 2020a) hazard models at each road centroid (i.e. the centre point along a linear feature) (a) and utility pole (b) location (Paulik et al., 2021)

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Non-hydrodynamic hazard data (Table 3) for scour (i.e. an undermined surface or exposed foundation below pre-event surface level) and debris strike (i.e. damage from direct debris impact force) were recorded for each network component during the field survey presented in Paulik et al. (2021). These observations were recorded for roads (scour) and utility poles (scour and debris strike).

3.3 Variable Testing for Feature Importance and Correlation

Determining the importance and relationships between variables leading to tsunami damage is critical for understanding the dependencies and uncertainties of tsunami vulnerability models. The damage sample was analysed using a random forest model (RFM) to identify non-linear and non-monotonic variable dependence and Spearman’s rank-order correlation tests (SRC) to detect monotonic relationships. Tsunami hazard (hydrodynamic and non-hydrodynamic) and network component attribute predictor variables (from Table 3) were applied in each model. Road and utility pole damage levels were the dependant variables in RFM to identify feature importance for damage.

The damage data sample was processed for RFM and SRC tests using the scikit-learn 0.24.2 package for Python. Nineteen tsunami hazard and network component attribute predictor variables (i.e. 5 hydrodynamic, 2 non-hydrodynamic, 7 road and 6 utility pole variables; Table 3) were selected and binary-coded if required prior to processing. The RFM applied 1000 trees with 4 random variables per split for both road and utility pole components, based on the square root of the predictor variable count. The number of trees represents the default setting of the algorithm. Variable feature importance is derived from RFM by mean decrease Gini, with loss in model performance when permuting the feature values indicating importance (Breiman, 2001). Here, the higher mean decrease Gini is an indicator of higher predictor variable importance for damage. The SRC test was then applied to analyse their feature importance with predictor variables applied in the RFM. The correlation test determines the strength and direction (i.e. positive or negative) of monotonic relationships between two predictor variables. The correlation significance (p value) for variable combinations was reported to indicate the relative significance of predictor variable relationships.

3.4 Fragility Curve Development

Fragility curves provide a probabilistic relationship between tsunami HIMs, and infrastructure component damage. In this study, synthesised tsunami HIM and network component attribute information are applied in cumulative link models (CLM) to construct fragility curves (Lallemant et al., 2015; Macabuag et al., 2016a, 2016b). Previous empirical fragility curves for Coquimbo roads (Williams et al., 2020a) applied ordinary least square regression methods (OLS). However, this method can result in overlapping fragility curves that are not representative of network component damage characteristics (Williams et al., 2020b). CLMs are an extension of general link models (GLMs), which use the ordinality of damage levels, where increasing damage levels correspond to increasing damage severity (Charvet et al., 2014). Damage level ordering allows cumulative probabilities to be calculated for each damage level simultaneously. Given these factors, the present study uses the CLM method for fitting fragility curves as follows:

$$P\left(DL\ge dl|HIM\right)= \Phi \left( {\widehat{\beta }}_{j}+{\widehat{\beta }}_{2 }1n\left(HIM\right)\right)$$
(1)

where Φ is the standard cumulative normal distribution function, and the probability (P) to equal or exceed a given damage state is expressed in terms of the hazard intensity metric (HIM). Fragility curves representing damage levels may converge but will not cross. This is because each cumulative probability has its own intercept \({(\widehat{\beta }}_{j})\) but shares a common slope coefficient (\({\widehat{\beta }}_{2 })\) satisfying an assumption that higher hazard intensities are required for a higher damage level (Lallemant et al., 2015; Macabuag et al., 2016a, 2016b). When data are treated as nominal rather than ordinal, as is the case for GLMs and OLS data binning, fragility curves are able to cross each other. This can occur when few damage level samples are represented in an empirical dataset. In cases where few observations represent the highest damage level, CLMs will utilise observations for the second highest damage level to fit a representative fragility curve (Lallemant et al., 2015; Williams et al., 2019). Fragility curves fitted by CLMs inherently represent the uncertainty associated with tsunami damage for a given hazard intensity, as the cumulative probability of being in any damage level (DL0 – 3) is always equal to 1, and the individual probability of falling into a given damage level is the range between each DL threshold rather than a discrete value. Fragility curve estimates of nominal-scaled and ordinal variables were evaluated with classification performance metrics. Here, the ‘accuracy’ metric evaluates correctly predicted attributes as a percentage (Baldi et al., 2000).

4 Results

Here we present the RFM results of feature importance and SRC tests for damage sample variables (Sect. 4.1) and tsunami fragility curves (Sect. 4.2) for roads (Sect. 4.2.1) and utility poles (Sect. 4.2.2).

4.1 Feature Importance and Correlation Tests for Damage Sample Variables

Road and utility pole damage sample variables were applied in RFM and SRC. The RFM identifies the relative importance of tsunami hazard and network component attribute variables in determining physical damage, then SRC confirms importance with correlation of the monotonic relationship. Here, we focus on reporting the importance and relationships of tsunami hazards (hydrodynamic and non-hydrodynamic) and network component attributes for road and utility pole damage.

The RFM indicates scour is of high importance for roads and utility pole damage, as is debris strike for utility pole damage (Fig. 5a, c). The SRC tests confirm importance, demonstrating significant positive correlations between damage and scour (0.67–0.68, p value < 0.01) for roads, and debris impact (0.76, p value < 0.01) for utility poles (Fig. 6a, c). Scour also demonstrates a moderate positive relationship with both interpolated (0.29, p value < 0.01) and simulated (0.38, p value < 0.01) flow depth (Fig. 6a, b). Simulated flow depth shows a moderate to significant positive relationship with flow velocity and hydrodynamic force, coinciding with a positive monotonic relationship with scour (Fig. 6b). This indicates scour is most likely to cause road damage in response to flow velocity and hydrodynamic force increasing with flow depth.

Figure 5
figure 5

Random Forest model feature importance for DRb variables. a Roads interpolated dataset b roads simulated dataset, c utility poles interpolated dataset and d utility poles simulated dataset

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Figure 6
figure 6

Spearman’s rank correlation matrix presenting the rho and significance (p) (below rho) values of tsunami hazard and component attribute variable correlation with DL. a Roads interpolated dataset, b roads simulated dataset, c utility poles interpolated dataset and d utility poles simulated dataset

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Flow velocity is the simulated hydrodynamic HIM of highest importance for utility pole damage (Fig. 6d). A positive monotonic relationship is observed with debris impact, which demonstrates a high importance for causing utility pole damage. Incidence of debris impact for utility poles in built-up areas will be relatively higher when debris entrained in tsunami flows increase in response to increasing flow velocity and hydrodynamic force. Here, Fig. 6d demonstrates a positive relationship with all interpolated and simulated hydrodynamic HIMs, indicating debris impact and utility pole damage is more likely as hazard intensity increases. Similarly, scour is a variable of relatively higher importance for utility pole damage (Fig. 6c, d) and demonstrates a positive relationship with hydrodynamic HIMs. These observations highlight non-hydrodynamic hazards in response to hydrodynamic HIMs have a key influence on utility pole damage.

Overall, the RFM shows road and utility pole network component attributes have lower importance for physical damage compared to hydrodynamic and non-hydrodynamic hazards. Gini coefficients of < 0.05 are observed for most attributes. The exception is for road network components, where distance from coastline and number of lanes exceeded 0.1 relative to the interpolated and simulation hydrodynamic HIMs respectively (Fig. 5a, b). Despite a low Gini coefficient, distance from coastline also shows relatively higher importance for utility pole damage. This is expected as the negative monotonic relationships observed between distance from coastline and hydrodynamic HIMs indicates hazard intensities decrease with distance inland. Lower hazard intensities further reduce the potential for road and utility pole damage from scour or debris impact. While not clearly demonstrated by the RFM, SRC tests (Fig. 6) demonstrate positive monotonic relationships between damage levels and road (e.g. surface: asphalt and unsealed, capacity: local, culvert) and utility pole (i.e. steel, height < 5 m) network component attributes. This highlights the need to consider such attributes in the development of object-specific roads and utility poles tsunami fragility curves.

4.2 Fragility Curves

Tsunami fragility curves are presented here for roads (Sect. 4.2.1) and utility poles (Sect. 4.2.2). Fragility curve parameters are reported in Tables 4 & 5. The tsunami fragility curves each reflect a variation in damage probability due to (1) HIM (interpolated depth (m), simulated flow depth (m), flow velocity (m/s), hydrodynamic force (kN/m), and momentum flux (m3/s2), (2) mixed attributes (damage level only), (3) construction material, and (4) capacity (roads).

Table 4 Summary of tsunami fragility curve parameters for roads. Pseudo r2 is calculated using the McFadden method (McFadden, 1974)
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Table 5 Summary of tsunami fragility curve parameters for utility poles. Pseudo r2 is calculated using the McFadden method (McFadden, 1974)
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4.2.1 Roads

A flow depth of 2 m is used here to consistently compare network component vulnerability across curves since this depth has been previously defined as a critical threshold for reaching DL3 (Williams, et al., 2019). The probability of mixed attribute roads (i.e. all construction material and capacity types) reaching or exceeding DL1, DL2 and DL3 at 2 m flow depth is 0.16, 0.09 and 0.07, respectively (Fig. 7a), for interpolated flow depth, and 0.2, 0.11 and 0.08, respectively (Fig. 7a), for simulated flow depth. The results indicate there is a 0.5 probability of reaching or exceeding DL1, DL2 and DL3 at 6.8 m, 10.2 m and 12.4 m flow depth (interpolated) respectively and 5.4 m, 8.4 m, and 10.6 m respectively for flow depth (simulated) for mixed attribute roads (Fig. 7a). Arbitrary values of 5 m/s, 10 kN/m and 10 m3/s2 are used as reference points to compare network component vulnerability across the flow velocity, hydrodynamic force and momentum flux (respectively) fragility curves. The probability of mixed attribute roads reaching or exceeding DL1, DL2 and DL3 at 5 m/s flow velocity is 0.63, 0.46 and 0.38 respectively (Fig. 8a). There is a 0.5 probability of reaching or exceeding DL1, DL2 and DL3 at 4.2 m/s, 5.3 m/s and 5.9 m/s velocity respectively for mixed attribute roads (Fig. 8a). For hydrodynamic force, a probability of mixed attribute roads reaching or exceeding DL1, DL2 and DL3 at 10 kN/m is 0.48, 0.32 and 0.25 respectively (Fig. 8b). There is a 0.5 probability of reaching or exceeding DL1, DL2 and DL3 at 10.6 kN/m, 18.6 kN/m and 25 kN/m hydrodynamic force respectively for mixed attribute roads (Fig. 8b). For momentum flux, a probability of mixed attribute roads reaching or exceeding DL1, DL2 and DL3 at 10 m3/s2 is 0.82, 0.7 and 0.62 respectively (Fig. 8b). There is a 0.5 probability of reaching or exceeding DL1, DL2 and DL3 at 2.4 m3/s2, 4.5 m3/s2 and 6.2 m3/s2 respectively for mixed attribute roads (Fig. 8c).

Figure 7
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Tsunami fragility curves using IDmax and Dmax for mixed road attributes (a), concrete (b) and asphalt (c) construction roads, and local (d) and collector (e) capacity roads

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Figure 8
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Tsunami fragility curves using Vmax, Fmax and Mmax (left to right) for mixed road attributes (a–c), concrete (d–f) and asphalt (g–i) construction roads, and local (j–l) and collector (m–o) capacity roads

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There is some difference in DL1 and DL2 exceedance probability for asphalt and concrete road construction materials as tsunami flow increases (Fig. 7b, c, 8d-i), with higher probabilities indicated for concrete construction over asphalt construction. However, there are considerably lower probabilities of DL3 exceedance for concrete construction (e.g. 0.04 at 2 m interpolated flow depth, 0.0 at 2 m simulated flow depth, 0.01 at 5 m/s flow velocity, 0.01 at 10 kN/m hydrodynamic force and 0.11 at 10 m3/s2 momentum flux), when compared to asphalt roads (e.g. 0.09, 0.1, 0.55, 0.35 and 0.79 respectively).

Road capacity, in this study, is used as a proxy for construction standards where field data is absent. Higher capacity ‘collector’ roads are often built to a higher standard than lower capacity ‘local’ roads and are potentially more resistant to tsunami forces (Williams et al., 2020a, 2020b). In Coquimbo, tsunami fragility curves representing DL1 and DL2 (Fig. 7d, e, 6j-o) are mostly lower for both collector and local roads (considerably so with flow velocity, hydrodynamic force and momentum flux as HIMs). However, collector roads have far lower probability of reaching or exceeding DL3 (e.g. 0.02 at 2 m interpolated flow depth, 0.03 at 2 m simulated flow depth, 0.09 at 5 m/s flow velocity, 0.07 at 10 kN/m hydrodynamic force and 0.2 m3/s2 momentum flux), when compared to local roads (e.g. 0.14, 0.16, 0.84, 0.54 and 0.96 respectively).

4.2.2 Utility Poles

The probability of mixed attribute utility poles (i.e. all construction materials and pole heights) reaching or exceeding DL1, DL2 and DL3 at 2 m flow depth is 0.28, 0.17 and 0.13 respectively (Fig. 9a) for interpolated depth and 0.27, 0.20 and 0.19 respectively for simulated depth (Fig. 9a). There is a 0.5 probability of reaching or exceeding DL1, DL2 and DL3 at 3.1 m, 3.9 m and 4.5 m flow depth (interpolated), respectively, (Fig. 9a) and at 4.1 m 5.3 m and 5.6 m flow depth (simulated), respectively (Fig. 9a). The probability of mixed attribute utility poles reaching or exceeding DL1, DL2 and DL3 at 5 m/s flow velocity is 0.52, 0.43 and 0.41, respectively (Fig. 10a). There is a 0.5 probability of reaching or exceeding DL1, DL2 and DL3 at 4.8 m/s, 6.1 m/s and 6.4 m/s flow velocity, respectively, for mixed attribute utility poles (Fig. 10a). For hydrodynamic force the probability of mixed attribute utility poles reaching or exceeding DL1, DL2 and DL3 at 10 kN/m is 0.49, 0.40 and 0.38 respectively (Fig. 10b). There is a 0.5 probability of reaching or exceeding DL1, DL2 and DL3 at 10.2 kN/m, 16.2 kN/m and 18 kN/m hydrodynamic force respectively for mixed attribute roads (Fig. 10b). For momentum flux the probability of mixed attribute utility poles reaching or exceeding DL1, DL2 and DL3 at 10 m3/s2 is 0.77, 0.7 and 0.66 respectively (Fig. 10c). There is a 0.5 probability of reaching or exceeding DL1, DL2 and DL3 at 2 kN/m, 3.2 kN/m and 4 kN/m hydrodynamic force respectively for mixed attribute roads (Fig. 10c).

Figure 9
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Tsunami fragility curves using IDmax and Dmax for mixed utility pole material (a) and concrete (b), steel (c), and timber (d) construction

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Figure 10
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Tsunami fragility curves using Vmax, Fmax and Mmax (left to right) for mixed utility pole material (a–c) and concrete (d–f), steel (g–i), and timber (j–l) construction

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Utility pole construction material appears to influence fragility (Figs. 9b-d, 10d-l). At 2 m flow depth, there is a probability of reaching or exceeding DL1, DL2 and DL3 of 0.08, 0.05 and 0.03 (interpolated) and 0.06, 0.03 and 0.03 (simulated) for concrete poles, 0.40, 0.23 and 0.19 (interpolated) and 0.44, 0.34 and 0.32 (simulated) for steel poles, and 0.36, 0.20 and 0.16 (interpolated) and 0.40, 0.23 and 0.19 (simulated) for timber poles (Fig. 9b-h). The probability of utility poles reaching or exceeding DL3 at 5 m/s flow velocity is 0.21, 0.48 and 0.46 for concrete, steel and timber construction respectively (Fig. 10d, g & j). The probability of utility poles reaching or exceeding DL3 at 10 kN/m hydrodynamic force is 0.07, 0.59 and 0.31, for concrete, steel and timber construction respectively (Fig. 10e, h & k). The probability of utility poles reaching or exceeding DL3 at 10 m3/s2 momentum flux is 0.13, 0.88 and 0.26, for concrete, steel and timber construction respectively (Fig. 10f, i & l).

5 Discussion

Flow depth is the adopted HIM for many tsunami fragility curves (Sect. 1; e.g. Koshimura et al., 2009; Suppasri et al., 2013). However, other hydrodynamic HIMs are often cited as being more important (De Risi et al., 2017; Macabuag et al., 2016a, 2016b; Song et al., 2017). Here we analysed the relative importance of flow depth (interpolated and simulated), flow velocity and hydrodynamic force (Sect. 4.1). Flow depth showed high importance for physical damage to roads and utility poles (Sect. 4.1). This is not to say that hydrodynamic features of tsunamis are un-important, with respect to direct damage, and it is likely these factors contribute to damage through other actions. Non-hydrodynamic hazards, such as scour and debris strike, showed high importance for physical damage and likely exacerbate damage.

Previous studies have investigated debris potential for tsunami impact assessment of buildings (Macabuag et al., 2016a, 2016b; Naito et al., 2014; Shafiei et al., 2016). However, examples of tsunami debris-based fragility assessment of physical infrastructure are scarce [e.g. Kameshwar et al. (2021) and Williams et al. (2020a)]. Scour, being the strongest variable in RFM and SRC testing (Fig. 5 & Fig. 6) for roads (and second highest for utility poles), and debris strike the strongest for utility poles. This indicates a direction for further investigating the non-hydrodynamic impacts from tsunamis. Next steps would be to determine when and where scour and debris strike are most important, with further investigation into the relationships between hydrodynamic force, soil conditions (scour) and land-use to improve scour and debris strike potential estimations. This work, for scour and debris impact, could be undertaken with existing tsunami impact datasets (e.g. Tohoku 2011, Illapel 2015, and Sulawesi 2018) and progressed further by future field observations. Ultimately this could progress the tsunami hazard field, beyond the use of traditional hazard maps for impact assessment, by enhancing these with non-hazard parameters (debris potential, land-use, ground conditions etc.). The importance of scour for component damage presented in this study supports previous studies (Chen et al., 2013; Yeh et al., 2013) that have observed considerable scour-based damage for roads. The distribution of scour observed in the Illapel event is consistent with observations made following the 2018 Sulawesi tsunami (Paulik et al., 2019; Williams et al., 2020b), in that high concentrations were observed along a coastal esplanade (i.e. along Avenida Costanera) and low concentrations observed > 50 m from the shoreline. This may indicate a relative importance of the scour-causing conditions (e.g. ground conditions and land-use) for relatively small tsunami events (e.g. 2015 Illapel and 2018 Sulawesi tsunamis) in contrast to larger subduction zone events (e.g. 2004 Indian Ocean and 2011 Tohoku tsunamis) where scour is still observed at high concentrations further inland (i.e. > 50 m).

There is a positive monotonic relationship between flow depth and flow velocity, hydrodynamic force and momentum flux in the SRC tests (Fig. 5b, d). This indicates flow depth could be a fair proxy for indicative flow velocity, hydrodynamic force and momentum flux, and vice versa, in the application of fragility curves for roads and utility poles. This is consistent with previous studies (Maruyama & Itagaki, 2017; Williams, et al., 2020a, 2020b) that propose, but do not test, this relationship. However, this is inconsistent with a number of studies (Song et al., 2017; Wang et al., 2020) that claim flow depth is not a reliable metric for assessing tsunami hazard and damage relationships. One implication of this finding is that while velocity, hydrodynamic force and momentum flux are important HIMs, flow depth is of the greatest importance, and could therefore be used as a reliable proxy for tsunami exposure, impact and risk assessment of transport and electric infrastructure networks. Velocity, hydrodynamic force and momentum flux are used in the present study as data were readily available (Aránguiz et al., 2018) and is used in other fragility studies (Klapp et al., 2020; Park et al., 2017; Qu et al., 2019; Turner, 2015). However, since these metrics did not show considerable importance (Fig. 5) suggests that their derived fragility curves could be considered less reliable than those derived from inundation depth in this study. Hydrodynamic force has an almost complete correlation with momentum flux (99–100%; Fig. 6b, d), and is certainly because the hazard model uses a fixed drag coefficient and density (Aránguiz et al., 2018), meaning the expression of hazard is essentially the momentum flux scaled by a constant. Because of this, and despite some quantified importance of hydrodynamic force presented Fig. 5b & d, it is the least reliable HIM for application of the synthesised fragility curves in the present study. More work should also be done in the future to correlate these relationships between network components and HIMs. Because interpolated flow depth is the most commonly used HIM for tsunami fragility assessment (e.g. Koshimura et al., 2009; Maruyama & Itagaki, 2017; Mas et al., 2020) this, and future, suites of empirical and numerical tsunami fragility curves could be applied to refine tsunami impact and risk assessment. Applying weightings to multiple HIM-specific fragility curves, supported by variable correlation testing (i.e. from this study and future studies), is one potential method to enhance tsunami risk assessment for physical infrastructure network components. Future studies could consider a reasonable range of uncertainty of the hazard data and assess how that propagates to fragility curves.

Roads in Coquimbo performed poorly when compared with the 2011 Tohoku event and performed considerably well when compared with the 2018 Sulawesi event (Fig. 11). In the 2011 Tohoku tsunami, the probability of complete damage (i.e. DL3) at 5 m flow depth was 0.10 (Williams et al., 2020a), compared to 0.23 (interpolated depth) and 0.27 (simulated depth) reported in the present study (Fig. 11a). It should be noted that these use a GLM method, with manual data binning, as do the Illapel fragility curves from the same study. Using the same dataset, but different fragility curve development methods (Sect. 3.4), Coquimbo roads are shown to perform worse in the present study [e.g. 0.53 probability of exceeding/reaching DL3 at 5 m (interpolated depth) and 0.27 (simulated depth)] than indicated by Williams et al. (2020a), (e.g. 0.12 probability of reaching or exceeding DL3 at 5 m). The CLM method, used in the present study, is considered to be appropriate for fitting curves to datasets of this nature (Lallemant et al., 2015; Williams et al., 2019, 2020b), implying that this study has refined the event fragility curves in a way that would have higher levels of damage modelled for subsequent impact and risk assessments. This study, therefore, represents an improvement to the field, and a case could be made to similarly improve the comparable road component fragility curves for the 2011 Tohoku tsunami event (Graf et al., 2014; Williams et al., 2020a). The most directly comparable previous study for road fragility curves are from the 2018 Sulawesi tsunami (also CLM method), which has a 0.57 probability of reaching or exceeding DL3 at 5 m flow depth (Williams et al., 2020b). With respect to utility poles, the low threshold for pole damage (e.g. 0.56 of reaching or exceeding DL3 at 5 m (interpolated depth) and 0.46 (simulated depth) is lower in the present study, compared to pole fragility analysed for the 2018 Sulawesi tsunami (e.g. 0.86 of reaching or exceeding DL3 at 5 m).

Figure 11
figure 11

Comparison with previous studies using flow depth as a HIM, for mixed construction a roads and b utility poles

Full size image

In the present study, the estimated accuracy for all mixed construction fragility curves is > 70% (generally accepted threshold for “good” accuracy), with the lowest bound at 51% (Steel poles, Dmax) and up to 95% (Concrete poles; Tables 4 & 5). However, these values are representative of the dominant damage level at a given HIM (i.e. the damage level with the highest probability). To better quantify uncertainty, future studies should look to comparing the accuracy of fragility curves derived at one geographical setting (e.g. Coquimbo) for estimating empirical damage at other geographical settings (e.g. 2011 Tohoku or 2018 Sulawesi tsunami damage datasets). While it is typical to compare fragility curves with previous relative studies (e.g. Fig. 11; Aránguiz et al., 2018; De Risi et al., 2017; Mas et al., 2020; Williams et al., 2020b), future studies could look to better quantify uncertainty by further testing. The growing catalogue of post-event empirical damage, hazard, and fragility datasets, provides wider scope for increasingly sophisticated and credible tsunami impact assessment in the future. A variation on 4-teir (DL0 – 3) infrastructure damage levels could also improve the synthesised fragility curves presented in this study. Many have very limited ranges between DL2 & 3 thresholds, due to a low amount of DL2 data available, and may lend themselves to a 3-teir damage level model with DL2 representing unrepairable to complete damage. This would remove the indicative uncertainty with low DL2 datasets presented in this study but would provide less risk outputs. Inversely, curves with small ranges between DL2 & 3 thresholds may simply represent a minimal amount of increased hazard intensity required to exceed DL3 once in DL2.

It is crucial that the differences in the synthesised fragility curves (Sect. 4.2) be considered and acknowledged in any subsequent application (i.e. risk assessment). In the case of this study, particular attention must be given to the implications of the two differing, but widely accepted, methods of tsunami hazard assessment used in the respective studies (Sect. 3.2; Aránguiz et al., 2018; Williams et al., 2020a). These differences have led to the variation seen in the synthesised fragility curves, which are compared in Sect. 4.2. Some key differences in flow depth distribution are in the wetland, Playa Changa (beach) and Puerto de Coquimbo (port) area, as described in Sect. 3.2 (Figs. 1 & 3). Subsequently, these key differences could have implications on the accuracy of the flow velocity hydrodynamic force and momentum flux models (Fig. 3e–g) underlaid by the Aránguiz et al. (2018) simulated flow depth model. In this context, a suggested approach to the application of these synthesised fragility curves is to consider which are the most appropriate (i.e. during the impact assessment stage of a risk assessment framework), or consider the application of both sets of fragility curves (if appropriate) with a resulting range of damage values (and, potentially, subsequent disruption and/or loss). The tsunami hazard models (Sect. 3.2) are also limited in their lack of consideration for topography (in areas with low-density empirical data), macroroughness (buildings), flow direction and flow duration.

It is also crucial that the local hazard and network component conditions are considered when applying tsunami fragility curves. The 2015 Illapel tsunami was a relatively small event by historical standards. It was also documented as producing relatively long wave-lengths given its regional subduction zone earthquake origins – meaning a slow deterioration of wave energy inland (Heidarzadeh et al., 2015). Comparably (with the only other available suite of CLM tsunami fragility curves for physical infrastructure network components for an event of this magnitude), the 2018 Sulawesi tsunami was documented as a notably short wave-length (traveling ~ 0.3 km inland), given it was a local-source event (Aránguiz et al., 2020). Conversely, the 2011 Tohoku tsunami, which has available GLM fragility curves for physical infrastructure network components (Williams et al., 2020a), was documented as having considerably long wave-lengths (traveling ~ 11 km inland). In this context, the fragility curves developed in the present study would not be as appropriate to apply to events of higher or smaller wavelengths as much as the other events’ (Sulawesi and Tohoku) fragility curves would not necessarily be appropriate for an event comparable to the 2015 Illapel tsunami. The levels of shaking experienced in each respective case-study, and therefore it’s bearing on interpolated component damage levels, varies considerably (11.5–21.5 g in Miyagi and Iwate Prefectures (Tohoku) and 11.5–40.1 g in Palu (Sulawesi) compared with 0.20–0.29 g in Coquimbo (Illapel)) and should be considered in any application of fragility curves for impact and risk assessment (USGS, 2015).

6 Conclusions

This study analysed tsunami vulnerability of infrastructure network components exposed during the 2015 Illapel tsunami in Coquimbo, Chile. Hydrodynamic HIMs from interpolated and simulated tsunami hazard models for the event were used to develop fragility curves for roads and utility poles. A four-tier classification of structural damage was used, from ‘No damage’ through to ‘Complete damage’. The methodology applied in this paper overcomes the limitations of in-field tsunami hazard surveys by incorporating simulated hydrodynamic models, the HIMs of which were not possible to capture from field surveys alone.

A Random Forest Model and Spearman’s Rank correlation test were applied to analyse variable importance and monotonic relationships between tsunami hazards and physical infrastructure network component damage levels (DL). These models and tests revealed scour for roads, and debris impact and scour for utility poles, were highly important and strongly correlated with DLs. Of the hazard specific variables flow depth was the strongest and had the highest correlation with DLs, while flow velocity and hydrodynamic force were also important but considerably second and third to depth. The SRC tests also demonstrated that flow depth was strongly correlated with flow velocity and hydrodynamic force, indicating it could be a fair proxy for velocity and force, and vice versa.

This hybrid hazard methodology provides higher-resolution fragility analysis than with previous studies. The cumulative link model methodology, used to fit fragility curves, represents an improvement to the previously developed general link model fragility curves for the same road damage dataset. Roads demonstrated both higher and lower vulnerability compared to those analysed in previous events, with 0.23 probability of reaching or exceeding DL3 at 5 m flow depth, compared with 0.1 and 0.57 for the 2011 Tohoku tsunami and 2018 Sulawesi tsunami, respectively. Utility poles demonstrated lower vulnerability than those exposed in the 2018 Sulawesi tsunami, with a 0.56 and 0.86 probability of reaching or exceeding DL3 respectively. These curves can be applied to future tsunami impact and risk assessments. Application of the synthesised fragility curves in other geospatial areas should be carefully evaluated, considering the uncertainties of local hazard and network component characteristics.