Here we present the RFM results of feature importance and SRC tests for damage sample variables (Section 4.1) and tsunami fragility curves (Section 4.2) for roads (Section 4.2.1) and utility poles (Section 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. 3a & 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. 4a & 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. 4a & 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. 4b). This indicates scour is most likely to cause road damage in response to flow velocity and hydrodynamic force increasing with flow depth.
Flow velocity is the simulated hydrodynamic HIM of highest importance for utility pole damage (Fig. 4d). 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. 4d 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. 4c & 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. 3a & 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. 4) 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 <5m) network component attributes. This highlights the need to consider such attributes in the development of object-specific tsunami fragility curves for roads and utility poles.
4.2 Fragility curves
Tsunami fragility curves are presented here for roads (Section 4.2.1) and utility poles (Section 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) and hydrodynamic force (kN/m), (2) mixed attributes (damage level only), (3) construction material, and (4) capacity (roads).
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 damage level 3 in particular (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. 5a), for interpolated flow depth, and 0.2, 0.11 and 0.08, respectively (Fig. 5a), 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. 5a). Arbitrary values of 5 m/s and 10 kN/m are used as reference points to compare network component vulnerability across the flow velocity and hydrodynamic force (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. 6a). 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. 6a). For hydrodynamic force, a probability of mixed attribute roads reaching or exceeding DL1, DL2 and DL3 at 10 kN/m hydrodynamic force is 0.48, 0.32 and 0.25 respectively (Fig. 6b). 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. 6b).
There is some difference in DL1 and DL2 exceedance probability for asphalt and concrete road construction materials as tsunami flow increases (Fig. 5b & c, 6c-f), 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 and 0.01 at 10 kN/m hydrodynamic force), when compared to asphalt roads (e.g. 0.09, 0.1, 0.55 and 0.35 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, b). In Coquimbo, tsunami fragility curves representing DL1 and DL2 (Fig. 5d & e, 6g-j) are mostly lower for both collector and local roads (considerably so with flow velocity and hydrodynamic force 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 and 0.07 at 10 kN/m hydrodynamic force), when compared to local roads (e.g. 0.14, 0.16, 0.84 and 0.54 respectively).
Table 4 Summary of tsunami fragility curve parameters for roads. Pseudo r2 is calculated using the McFadden method (McFadden, 1974)
Fragility curve
|
µ
|
σ
|
r2
|
Mixed roads DMAX
|
DL1
|
1.69
|
1.20
|
0.05
|
|
DL2
|
2.14
|
1.20
|
|
|
DL3
|
2.36
|
1.20
|
|
Concrete roads DMAX
|
DL1
|
1.38
|
0.60
|
0.12
|
|
DL2
|
1.81
|
0.60
|
|
|
DL3
|
2.71
|
0.60
|
|
Asphalt roads DMAX
|
DL1
|
1.28
|
0.86
|
0.001
|
|
DL2
|
1.50
|
0.86
|
|
|
DL3
|
1.60
|
0.86
|
|
Local roads DMAX
|
DL1
|
1.19
|
0.90
|
0.08
|
|
DL2
|
1.57
|
0.90
|
|
|
DL3
|
1.59
|
0.90
|
|
Collector roads DMAX
|
DL1
|
1.66
|
0.89
|
0.08
|
|
DL2
|
1.98
|
0.89
|
|
|
DL3
|
2.41
|
0.89
|
|
Mixed roads VMAX
|
DL1
|
1.43
|
0.56
|
0.13
|
|
DL2
|
1.67
|
0.56
|
|
|
DL3
|
1.78
|
0.56
|
|
Concrete roads VMAX
|
DL1
|
1.58
|
0.59
|
0.14
|
|
DL2
|
2.01
|
0.59
|
|
|
DL3
|
2.90
|
0.59
|
|
Asphalt roads VMAX
|
DL1
|
1.35
|
0.47
|
0.12
|
|
DL2
|
1.49
|
0.47
|
|
|
DL3
|
1.55
|
0.47
|
|
Local roads VMAX
|
DL1
|
1.07
|
0.31
|
0.34
|
|
DL2
|
1.28
|
0.31
|
|
|
DL3
|
1.30
|
0.31
|
|
Collector roads VMAX
|
DL1
|
2.30
|
1.21
|
0.03
|
|
DL2
|
2.71
|
1.21
|
|
|
DL3
|
3.24
|
1.21
|
|
Mixed roads FMAX
|
DL1
|
2.37
|
1.38
|
0.13
|
|
DL2
|
2.94
|
1.38
|
|
|
DL3
|
3.22
|
1.38
|
|
Concrete roads FMAX
|
DL1
|
2.60
|
1.31
|
0.14
|
|
DL2
|
3.56
|
1.31
|
|
|
DL3
|
5.52
|
1.31
|
|
Asphalt roads FMAX
|
DL1
|
2.27
|
1.34
|
0.02
|
|
DL2
|
2.65
|
1.34
|
|
|
DL3
|
2.81
|
1.34
|
|
Local roads FMAX
|
DL1
|
1.61
|
0.97
|
0.25
|
|
DL2
|
2.16
|
0.97
|
|
|
DL3
|
2.20
|
0.97
|
|
Collector roads FMAX
|
DL1
|
3.99
|
2.51
|
0.05
|
|
DL2
|
4.85
|
2.51
|
|
|
DL3
|
5.99
|
2.51
|
|
Mixed roads IDMAX
|
DL1
|
1.91
|
1.22
|
0.09
|
|
DL2
|
2.33
|
1.22
|
|
|
DL3
|
2.53
|
1.22
|
|
Concrete roads IDMAX
|
DL1
|
2.12
|
1.34
|
0.12
|
|
DL2
|
3.04
|
1.34
|
|
|
DL3
|
4.98
|
1.34
|
|
Asphalt roads IDMAX
|
DL1
|
1.72
|
0.97
|
0.05
|
|
DL2
|
1.92
|
0.97
|
|
|
DL3
|
2.01
|
0.97
|
|
Local roads IDMAX
|
DL1
|
1.44
|
1.15
|
0.12
|
|
DL2
|
1.89
|
1.15
|
|
|
DL3
|
1.92
|
1.15
|
|
Collector roads IDMAX
|
DL1
|
1.77
|
0.81
|
0.10
|
|
DL2
|
2.03
|
0.81
|
|
|
DL3
|
2.34
|
0.81
|
|
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. 7a) for interpolated depth and 0.27, 0.20 and 0.19 respectively for simulated depth (Fig. 7a). 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. 7a) and at 4.1 m 5.3 m and 5.6 m flow depth (simulated), respectively (Fig. 7a). 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. 8a). 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. 8a). For flow hydrodynamic force 10 kN/m is used to compare component vulnerability. The probability of mixed attribute utility poles reaching or exceeding DL1, DL2 and DL3 at 10 kN/m hydrodynamic force is 0.49, 0.40 and 0.38 respectively (Fig. 8b). 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. 8b).
Utility pole construction material appears to influence fragility (Fig. 7b-h). 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. 7b-h). The probability of utility poles reaching or exceeding DL1, DL2 and DL3 at 5 m/s flow velocity is 0.21, 0.48 and 0.46 for concrete, steel and timber construction respectively (Fig. 8c, e & g). The probability of utility poles reaching or exceeding DL1, DL2 and DL3 at 10 kN/m hydrodynamic force is 0.07, 0.59 and 0.31, for concrete, steel and timber construction respectively (Fig. 8d, f & h).
Table 5 Summary of tsunami fragility curve parameters for utility poles. Pseudo r2 is calculated using the McFadden method (McFadden, 1974)
Fragility curve
|
|
µ
|
σ
|
r2
|
Mixed poles DMAX
|
DL1
|
1.41
|
1.15
|
0.05
|
|
DL2
|
1.67
|
1.15
|
|
|
DL3
|
1.72
|
1.15
|
|
Concrete poles DMAX
|
DL1
|
5.50
|
3.04
|
0.02
|
|
DL2
|
6.29
|
3.04
|
|
|
DL3
|
6.47
|
3.04
|
|
Steel poles DMAX
|
DL1
|
0.79
|
0.67
|
0.08
|
|
DL2
|
0.97
|
0.67
|
|
|
DL3
|
1.01
|
0.67
|
|
Timber poles DMAX
|
DL1
|
4.32
|
13.43
|
0.00
|
|
DL2
|
11.70
|
14.98
|
|
|
DL3
|
13.61
|
15.26
|
|
Mixed poles VMAX
|
DL1
|
1.56
|
1.12
|
0.04
|
|
DL2
|
1.81
|
1.12
|
|
|
DL3
|
1.87
|
1.12
|
|
Concrete poles VMAX
|
DL1
|
1.91
|
0.66
|
0.10
|
|
DL2
|
2.10
|
0.66
|
|
|
DL3
|
2.14
|
0.66
|
|
Steel poles VMAX
|
DL1
|
1.15
|
1.87
|
0.01
|
|
DL2
|
1.62
|
1.87
|
|
|
DL3
|
1.72
|
1.87
|
|
Timber poles VMAX
|
DL1
|
1.07
|
1.03
|
0.04
|
|
DL2
|
1.59
|
1.03
|
|
|
DL3
|
1.70
|
1.03
|
|
Mixed poles FMAX
|
DL1
|
2.33
|
2.06
|
0.07
|
|
DL2
|
2.81
|
2.06
|
|
|
DL3
|
2.91
|
2.06
|
|
Concrete poles FMAX
|
DL1
|
5.30
|
2.70
|
0.06
|
|
DL2
|
6.03
|
2.70
|
|
|
DL3
|
6.19
|
2.70
|
|
Steel poles FMAX
|
DL1
|
1.31
|
1.78
|
0.06
|
|
DL2
|
1.78
|
1.78
|
|
|
DL3
|
1.88
|
1.78
|
|
Timber poles FMAX
|
DL1
|
1.86
|
4.12
|
0.02
|
|
DL2
|
3.92
|
4.12
|
|
|
DL3
|
4.39
|
4.12
|
|
Mixed poles IDMAX
|
DL1
|
1.11
|
0.73
|
0.19
|
|
DL2
|
1.40
|
0.73
|
|
|
DL3
|
1.50
|
0.73
|
|
Concrete poles IDMAX
|
DL1
|
2.43
|
1.23
|
0.13
|
|
DL2
|
2.71
|
1.23
|
|
|
DL3
|
2.99
|
1.23
|
|
Steel poles IDMAX
|
DL1
|
0.86
|
0.69
|
0.17
|
|
DL2
|
1.20
|
0.69
|
|
|
DL3
|
1.30
|
0.69
|
|
Timber poles IDMAX
|
DL1
|
1.05
|
0.98
|
0.08
|
|
DL2
|
1.53
|
0.98
|
|
|
DL3
|
1.65
|
0.98
|
|