Modelling liquefaction-induced building damage in earthquake loss estimation

Soil Dynamics and Earthquake Engineering 26 (2006) 15–30 www.elsevier.com/locate/soildyn

Modelling liquefaction-induced building damage in earthquake loss estimation Juliet F. Bird a,*, Julian J. Bommer b, Helen Crowley c, Rui Pinho c a

Arup Geotechnics, The Arup Campus, Blythe Gate, Blythe Valley Park, Solihull, West Midlands, B90 8AE, UK b Department of Civil and Environmental Engineering, Imperial College London, SW7 2AZ, UK c European School of Advanced Studies in Reduction of Seismic Risk, c/o EUCENTRE, Via Ferrata 1, 27100 Pavia, Italy Accepted 4 October 2005

Abstract The assessment of building damage caused by liquefaction-induced ground deformations requires the definition of building capacity and vulnerability as a function of the demand, as well as damage scales to describe the state of the damaged building. This paper presents a framework for resolving these issues within the context of earthquake loss estimations, where large variations in building stock and ground conditions must be considered. The principal modes of building response to both uniform and differential ground movements are discussed and the uncertainties in their evaluation are highlighted. A unified damage scale is proposed for use in both reconnaissance and assessment of all modes of building damage, including ‘rigid body’ response of structures on stiff foundations to uniform or differential ground movements. The interaction of ground shaking and liquefaction in the context of induced structural damage is also briefly considered. The paper raises important aspects of earthquake loss estimations in regions of liquefaction potential, which remain relatively poorly defined at present. q 2005 Elsevier Ltd. All rights reserved. Keywords: Liquefaction; Ground deformation; Building damage; Earthquake loss estimations

1. Introduction The potential for earthquake-induced liquefaction to cause significant damage to buildings in earthquakes is well known. Destructive earthquakes in Kobe in 1995 and in Taiwan and Turkey in 1999 are prime examples of this, with numerous reports of buildings settling, tilting, sliding, or otherwise suffering due to the failure of the underlying soils. The impact of liquefaction has been greatest on lifelines such as roads, mainly due to the failure of bridges, and buried pipelines, as well as to port structures, the clearest case in point for the latter being the damage caused by the Kobe earthquake. Although there are cases where spectacular damage to buildings has been caused by liquefaction, such as in Adapazari due to the 1999 Kocaeli earthquake in Turkey, liquefaction-induced damage to buildings in major earthquakes typically contributes to earthquake losses only over relatively small areas [1]. Earthquake loss estimation is a technique used to quantify potential losses in a given region or to a particular portfolio of * Corresponding author. Tel.: C44-121-213-3000. E-mail address: [email protected] (J.F. Bird).

0267-7261/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2005.10.002

buildings and facilities, due to future earthquakes. The main components of an earthquake loss model are shown in Fig. 1. The scale of an earthquake loss estimation may range from an entire country to cities or even districts within cities. The larger the study area, the more likely it is that ground shaking-induced damage to buildings will dominate the overall losses, and that any secondary hazards affecting a particular zone will be of less significance. For example, in the 1999 Kocaeli earthquake in Turkey, damaging hazards included surface fault rupture, coastal subsidence, slope failures and liquefaction, but the dominant cause of damage over the entire region was undoubtedly ground shaking [1]. An estimation of building damage for the entire Kocaeli region could, therefore, reasonably concentrate on ground-shaking, but for more detailed studies within the region there is an increased likelihood that local features such as liquefiable soils will influence the results, as was seen in the city of Adapazari. The framework for estimating liquefaction damage presented in this paper is primarily intended to be applied on a local scale. Comprehensive earthquake loss estimations require interaction between Earth scientists, engineers, public and private owners of facilities, lifeline operators, planners and financiers and as such are truly multi-disciplinary. Two significant features from an engineering perspective are the regional

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HAZARDS Ground shaking Ground Failure Fault Rupture INVENTORY Buildings and Lifelines DIRECT PHYSICAL DAMAGE

INDUCED PHYSICAL DAMAGE Fire following earthquake Release of hazardous materials Flood following earthquake Debris

LOSS Social losses – casualties and shelter Direct economic impact Indirect economic impact

Fig. 1. Components of an earthquake loss estimation (after FEMA [2]).

nature of loss estimations and the fact that the models deal with existing buildings and infrastructure, about which very little may be known. Both these features present a considerable contrast to site-specific design or even site-specific assessment. Techniques used for site-specific design cannot be employed in this context, because the demands of time and data acquisition would be excessive. The objective of this paper is to obtain an assessment of the distribution amongst damage levels for a particular building stock as a consequence of an earthquake-induced liquefaction. These results can be simply translated into a direct economic loss once the total financial value of the building stock is known. However, as discussed in detail in Section 3.2, the definition of damage necessarily differs from that traditionally used in loss estimation models since a building can be rendered uninhabitable by the effects of liquefaction without suffering any structural damage to the load-bearing system. 2. Estimating liquefaction demand Methodologies for the assessment of liquefaction potential and the resulting ground deformation have been the focus of research for many years. Despite this, when it comes to determining the impact these deformations will have on existing structures, the published literature is generally inadequate [3]. There are many reasons for this, not least that the preferred design approach is to mitigate the liquefaction potential by ground improvement or site re-location. Generally, a structural engineer will determine the deformation tolerances for a structure, and the geotechnical engineer will ensure through design that these criteria are satisfied. Similarly, in the estimation of expected ground deformations, most soil mechanics theory is orientated towards the avoidance of large-scale deformations associated with ground failure, rather

than calculating their magnitude. Even in the field of performance-based seismic design, there is little guidance on what are acceptable damage levels due to foundation movements. The prediction of liquefaction demand comprises three stages. The first is to determine whether the soils are susceptible to liquefaction using mainly qualitative criteria such as those presented by Youd and Perkins [4]. Given a positive response to this, the likelihood of liquefaction being triggered by the scenario earthquake is required (Section 2.1). Finally, the demand, in terms of the expected ground deformations, must be defined (Section 2.2). A preference has been noted in previous papers [5,6] for the use of scenario based loss estimations over those based upon a probabilistic seismic hazard assessment (PSHA). This preference, despite the additional computational expense it entails, is reiterated herein, since to estimate both the liquefaction potential and the resulting ground deformations, the earthquake magnitude, its duration, and the source-to-site distance are fundamentally important variables, and therefore, a scenariobased approach, which explicitly defines the magnitude and distances, is essential. 2.1. Triggering of liquefaction Current standard practice for the assessment of liquefaction potential is essentially deterministic, using one of a number of published relationships between the in situ density of the soil and the cyclic shear stress induced by ground shaking (e.g. [7]). Application of deterministic methodologies goes no further than ascertaining that the factor of safety (FS) against liquefaction is greater than or less than unity. For risk assessments, the probability associated with the result FS!1 is also needed. Even where there is an apparently significant safety margin in the calculation, there may still be an associated, albeit low, probability of failure, which comes from three principal areas of uncertainty: the ground motion level, the empirical procedures used to evaluate liquefaction resistance, and the natural variability and heterogeneity of the soil properties and stratigraphy. Probabilistic approaches towards liquefaction assessment have been developed by, amongst others, Cetin et al. [8] and Rodrigue´z-Marek et al. [9], although these are not so widely used as the deterministic methods. 2.2. Quantification of permanent ground deformations The evaluation of liquefaction-induced displacements beneath a building is far from straightforward. A number of methodologies are available, all of which use different approaches and uncertain variables; none of these methods have overwhelming support in their favour compared to the others. There are multiple complex mechanisms which can cause damaging ground deformations. Table 1 summarises available methodologies for the assessment of expected liquefaction-induced ground deformations.

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Table 1 Selected methodologies for determining liquefaction-induced permanent ground deformations Reference

Description

I. Lateral ground deformation Zhang and Zhou Empirical prediction of liquefaction-induced lateral [10] spread Youd et al. [11] Equations obtained through multi-linear regression of empirical data Bardet et al. [12] Multi-linear regression of empirical data

Youd and Perkins [13] Rauch and Martin [14]

II. Settlement Tokimatsu and Seed [15]

Equations for Liquefaction Severity Index (LSI), defined as maximum lateral deformation in inches, with 0! LSI!100 Empirical prediction of liquefaction lateral spread

Charts relating in situ density measurements to earthquake induced shear strain. Laboratory and empirical data Charts relating FL to in situ density and volumetric strain

Ishihara and Yoshimine [16] III. Combined lateral and vertical movement Shamoto et al. [17] Charts for volumetric and shear strains

Variable input parametersa

Comments

M, R, T15, (N1)60, FC, D50, M, R, T15, slope (S) and free face ratio (W) M, R

Shown to be accurate within a factor of 2 Same dataset as Youd et al. [11] but in a probabilistic framework Maximum value. Single topographic/geologic environment only

(i). M, R, PGA, duration (ii). M, R, PGA, duration, Lslide, Stop, Hface (if free face present) (iii). M, R, PGA, duration, Lslide, Stop, Hface, ZFSmin, Zliq

Average displacements 3 equations, for different levels of input data; site, regional and geotechnical

(N1)60, CSR, FC

Shown to yield correct results within a factor of 2-3 [18]

FL, N1, FC

T/s 0 , Na, FC

Uses soil mechanics theory as well as empirical data.

a

T15, thickness of layer with (N1)60!15; D50, median particle size diameter; CSR, cyclic shear stress ratio; Hface, Height of free face; FC, fines content; FL, factor of safety against liquefaction; Lslide, maximum horizontal length of lateral spread; M, earthquake magnitude; N1, SPT N value corrected for overburden; Na, adjusted SPT N value (Shamoto et al., 1998); (N1)60, SPT N value adjusted for energy and overburden; PGA, peak ground acceleration; R, source-to-site distance; Stop, average slope across the surface of the lateral spread; T15, thickness of soil with SPT N!15; Vs, shear wave velocity of soil; ZFSmin, depth to minimum factor of safety against liquefaction; Zliq, depth to top of liquefied layer

Most commonly used assessment methods rely heavily on empirical data. One reason for this is the difficulty in obtaining measured in situ soil properties for input to soil mechanics theory, and the variability associated with such properties [18]. Another reason is that geotechnical analysis techniques do not generally allow for large strain deformations of soils [19]. Even where full constitutive soil models in a finite element framework are used, many of these cannot go beyond the initiation of liquefaction, at which point the procedure will typically break down and fail to converge (e.g. [20]). Furthermore, numerical models have been found to be particularly sensitive to small variations in input parameters [21], an undesirable feature in such an uncertain field as loss estimation. Youd et al. [11] state that ‘no physical theory’ exists to confirm their empirically-based relationships. For the purpose of loss estimations, empirical processes, based upon easily obtainable parameters, or at least parameters that can be estimated using a reasonable level of judgement, are preferable to complex numerical approaches [3]. The uncertainty associated with either approach should always be considered. The empirical methods shown in Table 1 are

generally accepted to be accurate only to within a factor of 2 or 3 [18,11] and their predictive capacity tends to be worst for small-to-moderate (0.3–0.75 m) deformations [21]. Selection of the calculation methodology is best made on a case-by-case basis; with categorical recommendations there is a danger that regional features, which may affect their validity in some way, are overlooked. For example, in the HAZUS methodology [22], the simplified approach for estimating lateral spread combines the Liquefaction Severity Index (LSI) relationships derived by Youd and Perkins [13] with the attenuation relationships of Sadigh et al. [23] to derive a relationship for LSI in terms of peak ground acceleration (PGA) only. Notwithstanding the simplifications involved, or the fact that significant scatter in both empirical relationships is ignored, neither of these relationships are applicable outside of the western USA, and the former is only valid for the specific environment of ‘wide active flood plains or other areas of gently-sloping late Holocene fluvial deposits’. For the prediction of lateral movements, the EPOLLS (Empirical Prediction of Liquefaction Lateral Spreading) methodology [14], has some advantageous features, in that it

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provides three different levels of empirical relationship, depending on the amount of data available. An additional advantage is that the formulae estimate the average rather than the maximum displacement, which is more appropriate to the requirements of a loss estimation study. The authors also present a study of the statistical variation of horizontal movements within a lateral spread [24]. For estimation of vertical movements, both the methods of Tokimatsu and Seed [15] and Ishihara and Yoshimine [16] have been found to be accurate to within a factor of 2 or 3. Both methodologies deal with settlements caused by the change in volumetric strain as pore water pressures dissipate after liquefaction has taken place. This is only one potential cause of vertical foundation movements, others include loss of ground due to sand boiling, the vertical component of lateral deformation of a volume of soil, or ‘punching’ failure of foundations due to reduced bearing capacity [21]. All of these hazards are potentially damaging to foundations; unfortunately there are no reliable procedures for their estimation, which is currently a major shortcoming in this field. 2.3. Uncertainties associated with liquefaction demand The uncertainty associated with estimating the expected permanent ground deformation arises from the following areas: † The level of earthquake hazard in terms of the uncertainty associated with the ground-motion estimation. † The likelihood of liquefaction triggering, based upon empirical data with associated scatter (e.g. Youd et al. [7]). † The choice of appropriate methodologies and input parameters for the evaluation of liquefaction probability, liquefaction-induced permanent ground deformation, and building response. As well as the epistemic uncertainty in selecting a methodology, there will be uncertainties due to scatter, and, due to the limitations of the selected approach. † The difficulty in accurately defining the thickness and extent of different stratigraphic layers, due to natural heterogeneity of soils (e.g. Power et al. [25]) and insufficiency of available geotechnical data. † Measurement or equipment biases of in situ data. Standard penetration test (SPT) measurements have been cited as having coefficients of variation from 25 to 50% [20,26]. † The necessary simplification of soil properties and stratigraphy, since even in the unlikely event that comprehensive geotechnical data were available, it would not be feasible on a large scale to incorporate this without some approximation. Ground conditions and building types that are expected to respond in an approximately similar manner to liquefaction must be grouped into a manageable number of classifications. In reality each soil profile and building will respond differently, and understanding and thereby quantifying the effects of this grouping is one of the most significant requirements of regional damage estimations.

Furthermore, it should be noted that these uncertainties are over and above the significant epistemic uncertainties associated with the primary part of a loss estimation; building damage due to ground shaking, all of which have been shown to have a significant impact upon the estimated distributions of damage [e.g. 27,28]. 2.4. Differential movements Of particular concern in terms of assessing building damage are the expected differential settlements or differential lateral movements. Ishihara and Yoshimine [16] state that ‘because of nonhomogeneous conditions in the soil deposits, the settlements seldom occur uniformly even in small localised areas and differential settlements become the major cause of the damage to lifelines or other facilities’. An example of large differential settlements is those that occur beneath buildings located on the boundary between liquefied and non-liquefied soils. Bardet and Kapuskar [29] observed that the worst damage in the Marina district after the 1989 Loma Prieta earthquake was on such a boundary. Differential ground settlements will occur due to heterogeneity in soil stiffness and stratigraphy both laterally and with depth. Estimating differential ground movements on a regional scale has an even greater uncertainty than the estimation of uniform or average movements. This is principally because of the lack of sufficient geotechnical data; a borehole at each corner of a building would allow a reasonable estimation of the variability in the settlements, even though retaining the other uncertainties listed in the previous sub-section. In the absence of this degree of detailed geotechnical data, for convenience, the variability may be modelled as random (i.e. aleatory), assuming a statistical distribution such as normal or lognormal, with a mean and variance. Thus the distribution of differential settlements over the footprint of a building, in terms of a percentage of the absolute settlements, can be obtained. Differential lateral movements will also be caused by the variability of in situ ground conditions, but these will also have a less random component related to geometric variability in terms of increasing distance from a free face or from the toe of a slope. Rauch and Martin [24] found the variability of lateral displacements across a slope to be reasonably represented by a gamma distribution. The flow chart in Fig. 2 illustrates the input data and decisions required to identify modes of liquefaction-induced ground deformation beneath buildings in the context of a loss estimation. The relative likelihood of each mode must be evaluated and the associated magnitude of ground deformation quantified. The complexities and uncertainties in this process are significant, and Fig. 2 summarises these without dictating the choice of methodology and the level of input data, which must be decided on an individual basis. 3. Building response to liquefaction Structural damage to buildings during ground shaking is mainly due to inter-storey drift, caused by inertial forces

J.F. Bird et al. / Soil Dynamics and Earthquake Engineering 26 (2006) 15–30

Historical and geological data

Is soil susceptible to liquefaction?

Level ground?

Stop

Yes

Earthquake characteristics and geotechnical data Choice of calculation methodology

No

Regional probability of liquefaction

P(L) < X *

Stop

>X* P(L) –

Geotechnical and topographical data

Sloping face or free face?

Yes Mean and variance of expected settlement (regional)

19

Yes

Choice of calculation methodology

Mean and variance of expected lateral spreading (regional)

Flexible foundations only P(uniform settlement)

Mean and variance of expected differential settlement (local)

Mean and variance of expected differential lateral movement (local)

Fig. 2. Information required for a complete assessment of building vulnerability to liquefaction-induced ground deformations. *X is a predefined value below which the probability of liquefaction is considered negligible.

induced by the excitation of the base and by the passage of waves ascending the building. The inter-storey drift induces distress in the structural elements, leading to loss of functionality and then to load bearing capacity. Structural response to vibratory motion lends itself to analytical modelling of the elastic and inelastic deformations, permitting the development of mechanically-based methods for evaluating building vulnerability to strong ground-motion. One example of this is the capacity spectrum method embodied in the HAZUS methodology [22,30]. An alternative approach has been developed by Crowley et al. [31]. The evaluation of building vulnerability to liquefaction-induced ground deformations is less straightforward, because of the variety of ways in which buildings can respond, which creates the need to use more than one approach. The different modes of response of buildings to ground failure also creates the need for broader definitions of damage, since these cannot be based only on deformations in structural members. The first step in developing any method for evaluating building vulnerability is a classification system for buildings, based on the concept of buildings in any category having essentially the same mode of response and failure, and comparable levels of susceptibility to the earthquake hazard under consideration. Crowley et al. [31], in common with most loss estimation methodologies, define building vulnerability in terms of the structural system and the member properties (dimensions and deformation characteristics). For assessing

building response to earthquake-induced ground failure, the foundation system will also be of importance. For a portfolio of buildings, knowledge of the foundations will be more uncertain than that of the structural system, which in itself requires some significant assumptions, short of carrying out a building-bybuilding survey. Even from visual surveys, foundation types cannot be easily ascertained, and a greater depth of investigation is required. There are, however, some assumptions that can reasonably be made: for example that poorly designed buildings are likely to have poorly designed foundations, and well-designed modern buildings are more likely to have considered liquefaction susceptibility in the foundation design and to have stiff or deep foundations, or some form of ground improvement. Such assumptions necessarily add an additional level of uncertainty to an inventory, which must be considered when interpreting the results. Given that this methodology is likely to be applicable to relatively small study areas, where it is known that there is a prevalence of liquefiable soils, it is a reasonable premise that enough information on the local building stock will be available to make appropriate judgments regarding the distribution of foundation types. For example, in Adapazari, investigations after 1999 revealed that a very high percentage of the beskat1 buildings were founded on reinforced concrete 1 Literally ‘five-storied’, but used to describe 4–6 storey, reinforced concrete frame apartment blocks.

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(a)

(b)

∆v

∆v

Fig. 3. Schematic illustration of frame buildings with stiff shallow foundations subjected to liquefaction-induced ground deformations: (a) Uniform vertical settlements, and (b) differential vertical settlements leading to rigid-body rotation of structure and foundation.

mat foundations of 1–1.5 m thickness [32]. For a study area the size of Adapazari it is feasible to gather such information through dialogue with local engineers and builders, whereas for a larger region, such as the model compiled for the whole of Turkey [5], such depth of investigation is clearly unrealistic. 3.1. Rigid-body and differential movements There are a number of deformation modes that buildings may experience when subject to liquefaction-induced ground deformations [33]. These modes can be divided into two broad categories: rigid-body movements, whereby the structure moves without significant internal deformation, and differential movements. The type of response will depend primarily on the foundation type: for shallow foundations, the distinction will be whether these are rigid (Fig. 3) or flexible (Fig. 4). A review of field reports from recent earthquakes [1] revealed a much larger number of occurrences of rigid body damage rather than structural damage to buildings on flexible (i.e. unrestrained) foundations. Hundreds of buildings were reported to have settled or tilted in the earthquakes in Turkey and Taiwan in 1999 and the Philippines in 1990, amongst many others. A notable example of structural damage, caused by differential foundation movement, is the failure of the low-rise wooden structures of the Marine Laboratory at Moss Landing following the Loma Prieta earthquake in 1989 [34]. Other cases have been reported in the 1999 Kocaeli and Chi–Chi earthquakes (e.g. Fig. 5) but overall there are relatively few such reports. Notwithstanding the scarcity of case histories, this failure mode clearly represents a genuine hazard to buildings. Marino [35] notes that the most common earthquake-induced foundation damage is separation of foundation elements, resulting from the irregularity of foundation settlement due to lateral spreading, inducing tension, bending or tilting in shallow foundations. The smaller number of reports of structural damage due to differential foundation movements may be because in many cases even fairly flexible foundations have sufficient relative stiffness, compared to soft underlying soils, to cause structures to behave as rigid bodies. Alternatively, it is possible that,

because the damage more closely resembles damage caused by ground shaking, comprising cracking and yielding of structural members, it is not always immediately identified as being due to ground failure. However, this explanation seems improbable considering the building shown in Fig. 5 for example, where the ground deformation is obvious. Fig. 6 summarises the modes of response to ground deformations for any given structural and foundation classification. Where ground deformation causes ‘rigid body’ building response, the important consideration for determining the damage state is the acceptability of the system performance. The damage state cannot be easily classified in terms of the deformations of structural members, therefore there is no apparent analytical solution in this case, and an empirical solution is required. Where there is sufficient flexibility in the foundations for the walls or columns to move independently and thus differentially (as depicted in Fig. 4), the response is referred to as ‘structural damage’, because the damage occurs in the structural elements and is related to the deformation induced in them. Analytical solutions are possible in this case; a procedure for estimating expected damage levels in the framework of an earthquake loss estimation is presented by Bird et al. [33]. These solutions are compatible with the displacement-based earthquake loss assessment methodology presented by Crowley et al. [31]. 3.2. Building damage states and losses Where building response to ground failure comprises structural damage, as described above, damage states can be classified using the same schemes used for structural damage caused by ground shaking, e.g. Table 2. Such schemes are an important component of loss estimations, in allowing analysis and presentation of results, comparison with field observations, and providing users with an understanding of the physical condition of different classes of buildings, and consequences in terms of repair and occupancy. The absence of rigid body rotation failures related to ground deformations, such as tilting, settlement or sliding, from most existing damage scales has been discussed previously [e.g. 1,

J.F. Bird et al. / Soil Dynamics and Earthquake Engineering 26 (2006) 15–30

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(a)

Rotational failure of columns

∆v (b)

Hinges form in beams

∆v Fig. 4. Schematic illustration of frame buildings with flexible shallow foundations to liquefaction-induced ground deformations: (a) Differential vertical settlements due to soil variability, and (b) differential settlement at the centre of a multi-bay frame.

36]. Even where there is no, or minor, damage to the structural elements of such buildings, they must be considered to be damaged, where damage may be defined as ‘a change in the condition of the structure that adversely affects its future structural performance’ [37]. In extreme cases, such as the buildings shown in Fig. 7, the damage state is complete, since the buildings are only suitable for demolition. In this context, damage can only be defined in terms of the consequences for the building use and the safety of the contents and inhabitants. However, the actual cost of the kind of failure illustrated in Fig. 7 could potentially be even higher than that due to complete structural collapse, since in addition to the replacement cost of the building there will be the costs associated with the demolition of the tilted or settled building, and excavation of the existing foundations. Figure 8 illustrates another possible failure whereby settlement causes damage to the floor slab; this may not be damage to the main load-carrying system, but it will represent a weakening of the structure due to loss of diaphragm action. At the same time, the disruption to the function of the building could be very severe. As mentioned previously, there is no analytical approach for the estimation of damage levels of buildings that have rotated as a rigid-body, since there is no structural demand (apart from possible PKD effects at larger rotations). Therefore the

damage state of a rotated or settled building is best described using empirical solutions, classifying the damage level in terms of the functionality and reparability of the building. Damage can be considered according to three criteria: aesthetic, where the movements are perceptible to the owners or inhabitants but do not impact the functionality; serviceability, or in the worst case, stability. Damage to a building that has settled uniformly may include: damage to the ground floor slab (Fig. 8), sand ejecta filling the ground floor, disruption to services, damage due to dragging down of adjacent attached buildings and serviceability issues related to change of levels of doors and entrances. Additionally there may be aesthetic issues due to level differences between a settled building and neighbouring buildings, or sidewalks. The damage state will be related to the extent of settlement and ease of repair. Unacceptable settlement or tilt may require structural remedial works in the form of jacking-up and underpinning, or by grout injection. In the worst cases, repair costs may be excessive and the buildings will be demolished. For consistency with the structural damage levels described in Table 2, both rotational and settlement limits must also be related to the repair cost ratio, although determining the cost of foundation repairs is significantly more complex than structural repairs. Issues that complicate the estimation of likely repair

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Fig. 5. Liquefaction induced damage of a technical school building after the 1999 Chi–Chi earthquake. (Courtesy: Marshall Lew, Los Angeles Tall Buildings Structural Design Council).

costs of buildings that have undergone rigid body deformation include the strength of the foundations to survive the planned remedial action, which may not be easily determined, and regional variabilities in construction practices and tolerance to

BUILDING CLASSIFICATION

FOUNDATION CLASSIFICATION

damage. The apartment building shown in Fig. 7(b) tilted by approximately 5 degrees and was subsequently demolished, whereas Hwang et al. [38] report buildings that tilted by up to 9 degrees in the Chi-Chi earthquake and were repaired using oil jacks to re-level them. Proposed limits for grouping the rigid body response of buildings to ground failure into similar ranges that coincide with structural damage definitions are presented in Table 3. This scale enables comparison of damage in different regions and different earthquakes as well as providing improved descriptors of predicted damage distributions. Sources of information for determining acceptable levels include reports from past earthquakes, technical papers related to earthquake damage levels, and published tolerances for non-earthquake related foundation deformations [39]. These limits have a high associated uncertainty due to the lack of available data regarding repair methods and costs for settled and rotated buildings. There are clearly many factors influencing rigid body damage levels that are both difficult to define and to quantify. Therefore the body of field data needs to be significantly expanded, and supplemented with local knowledge and judgement; without this it is not possible to quantify the uncertainties associated with these limits. The limits presented in Table 3 for stiff foundations subjected to ground deformations are compared in Fig. 9 with vulnerability curves derived for reinforced concrete frame buildings on flexible foundations [33]. The former are deterministic, in that they ignore the variability in building dimensions associated with the grouping of many buildings into a single classification. The latter include variability in the geometric and material properties, but not in the demand. An

MODE OF GROUND DEFORMATION

SOLUTION FOR DAMAGE ESTIMATION

Uniform vertical Differential vertical Flexible foundations

Differential lateral

‘Structural damage’. Analytical solutions possible

Combined lateral and vertical Uniform vertical

RC Frame Buildings

Stiff shallow foundations OR floating piles

Differential vertical Differential lateral

‘Rigid body’ response. Empirical solutions required.

Combined lateral and vertical Uniform vertical Differential vertical Piles to firm stratum

Differential lateral Combined lateral and vertical

Fig. 6. Modes of liquefaction-induced damage within one building classification.

Significant damage is unlikely and can be ignored on a regional scale Outside the scope of this paper

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Table 2 Structural damage state descriptions for RC frame buildings (after Crowley et al. [31]) Structural damage band

Description

None to slight

Linear elastic response, flexural or shear type hairline cracks (!1.0 mm) in some members, no yielding in any critical section Member flexural strengths achieved, limited ductility developed, crack widths reach 1.0 mm, initiation of concrete spalling Significant repair required to building, wide flexural or shear cracks, buckling of longitudinal reinforcement may occur Repair of building not feasible either physically or economically, demolition after earthquake required, could be due to shear failure of vertical elements or excessive displacement

Moderate Extensive Complete

intersection of the vertical line with vulnerability curve for that limit state at a probability of failure, Pf, of 0.5 would suggest nominal agreement between the two. For rigid body rotations there is a slightly lower tolerance to small movements, being controlled by aesthetic issues rather than the qualitative parameter of yield stress, but higher tolerances to larger movements, being less sensitive to increasing movements than in the case of structural deformations. 4. Liquefaction in earthquake loss estimation models The subject of this paper must be put into context by reiterating that for buildings the liquefaction component of a loss estimation model is, in the majority of cases, less significant to the final results than the ground shaking component (e.g. [1]). Nonetheless, the fact that liquefaction is a secondary hazard in the context of earthquake-induced losses by no means diminishes its importance. There is a need for comprehensive methodologies capable of estimating damage caused by all expected hazards to all elements of a region’s infrastructure. Any methodology to be added into a loss estimation should provide a pragmatic solution to the issues of spatial uncertainty and variability in ground conditions and exposed building stock, while still producing a realistic and meaningful estimation of the expected damage distribution as a result of earthquake hazards. The particular requirements of a framework for incorporating liquefaction into a loss model are: 1. Consistency with other components of the model, in terms of complexity, accuracy and treatment of uncertainties. 2. Appropriate input data, commensurate with available resources for a regional study, where detailed in situ measurements are unlikely to be feasible in terms of cost or time. 3. Compatibility of results with the estimation of damage caused by ground shaking, i.e. using consistent damage definitions as described in the previous section. In terms of accuracy, the optimum approach would be to predict the probability of liquefaction, the expected ground deformation and the resulting damage to buildings using in situ geotechnical data and detailed building inventory data including foundation type. This would require specialist input, and above all, analysis to determine the building response, and is therefore likely to be prohibitive. The

pragmatic solution therefore seeks to deal with all the uncertainties, rather than eliminate (or ignore) them. 4.1. HAZUS In terms of recognising the need to have a ‘ground-failure component’ and including all of the necessary steps to analyse damage due to ground failure, the HAZUS [22] loss-estimation methodology has made a significant contribution to the field. In particular, the HAZUS methodology is advantageous to loss modellers in being comprehensive, openly available, and fully documented. Recognising the low level of geotechnical and building inventory data that most loss estimations have to use, HAZUS presents a simplified approach that seeks to resolve the contradictory demands of minimising the amount of additional data required and producing realistic estimates of the resulting damage. It is the only published method for evaluating building damage due to ground failure that does so in a detailed manner, taking account of the expected mode of failure and foundation type. Previous methodologies such as ATC-13 [40] simply applied a factor to the calculated ground shaking-induced damage to estimate the additional damage due to ground failure. Nonetheless, there are many additional uncertainties generated through the simplifying assumptions made in HAZUS, and these are poorly constrained and considered. Bird et al. [36] showed that despite the use of published references and logical analysis to determine the expected ground deformations, the procedure is based in a large part on subjective judgement, and therefore has no particular advantage over other empirically-based procedures. The principal shortcomings of the HAZUS ground-failure component relate not to the assumptions and over-simplifications made in the treatment of ground failure, discussed by Bird et al. [36], but rather to what it fails to do, namely: † It does not distinguish between different shallow foundation systems, i.e. flexible or stiff, which will respond very differently to ground failure † The thickness of the liquefied layer is not evaluated; clearly this will influence the extent of the damage. Without in situ data, to do so is almost impossible, which highlights the difficulty in attempting to incorporate liquefaction without such data. † It does not consider different building responses to uniform or differential foundation deformations, and how these will

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J.F. Bird et al. / Soil Dynamics and Earthquake Engineering 26 (2006) 15–30

Ruptured ground floor slab

∆v

∆v

Fig. 8. Potential building response due to uniform vertical settlements in level, homogeneous ground.

relationships between uncertain input and predicted results, are all ignored. To estimate building damage due to a geotechnical phenomenon, as HAZUS attempts to do, with the only input data being a susceptibility rating between none and very high, according to the ratings presented by Youd and Perkins [4], is intuitively flawed. Expected earthquake losses due to liquefaction cannot be estimated in the absence of any geotechnical information, at least not in a quantitative manner, and not from the limited information currently available in this field. The authors believe that to do so represents an unrealistic simplification, because of the complex and unquantified uncertainties associated with the subsequent results. 4.2. An improved framework for ground-failure induced losses

Fig. 7. Buildings damaged beyond repair due to rigid body rotation caused by foundation failure in the city of Adapazari, Turkey, after the 1999 Kocaeli earthquake: (a) rotation only, (b) combined settlement and rotation. Photos courtesy of the Earthquake Engineering Field Investigation Team (EEFIT).

vary with superstructure and foundation type is not considered. † Natural variability of soil properties, epistemic uncertainties related to the choice of calculation methodology, and

Relative to the uncertainties associated with the groundshaking demand and building response, those associated with the occurrence and consequences of liquefaction are, if not larger, certainly more complex, and a number of additional variables, with large associated uncertainties, are necessary to define them. Analytical solutions have been developed for building vulnerability to ground deformations, for buildings on flexible footings, presented by Bird et al. [33]. These have the advantage of being based upon straightforward structural mechanics rather than empirical data, and are fully compatible with the estimation of ground shaking-induced structural damage presented by Crowley et al. [31], thus satisfying the three requirements listed at the beginning of Section 4. Furthermore, the probabilistic framework allows rigorous treatment of the associated uncertainties. Fig. 10 illustrates the principal stages in the evaluation of building damage in a region with liquefaction potential. Complete definition of each stage in Fig. 10 becomes complex. The illustration shown in the figure uses the analytical procedures presented by Bird et al. [33]. The uncertainties within this procedure are described in Section 2.3.

J.F. Bird et al. / Soil Dynamics and Earthquake Engineering 26 (2006) 15–30

25

Table 3 Suggested limit states for rigid body settlement and rotation due to earthquake-induced ground deformations beneath RC frame buildings [39] Damage state

Structural damage (see Table 2 for full description)

Additional description (rigid body deformation)

Settlement (D) only

Rotation (q) only

Slight Moderate

Hairline cracks only Some cracks in load-bearing elements

Extensive

Wide cracks and buckling of longitudinal reinforcement Repair not feasible, shear failures or excessive displacement

Repairs may be necessary for aesthetic reasons Repairable damage, serviceability and/or functionality affected Uninhabitable, but repairable

D%0.1 m 0.1 m!D%0. 3m 0.3 m!D%1. 0m R1.0 m

q%0.68 1/100 0.68!q%2.38 1/ 100–1/25 2.38!q%4.68 1/ 25–1/12.5 qR4.68R1/12.5

Demolition cheaper than repair. Structural integrity affected, possible instability

4.3. Combining liquefaction and ground-shaking hazards The complex issue of combined ground shaking and liquefaction has been touched upon in many previous publications. Post-earthquake field reports of tilted or settled buildings that do not exhibit any signs of structural damage or distress due to ground shaking, are common, suggesting a ‘base isolation’ effect, whereby the softening of the ground due to liquefaction significantly increases the period of the ground shaking, such that for most typical structural periods the spectral accelerations are very low. Despite the theoretical and observational support to this hypothesis, it has been clearly demonstrated (e.g. [1,41]) that some strong shaking will occur before the pore water pressures have built up sufficiently for liquefaction to initiate. A number of case histories of reports of buildings damaged by both shaking and liquefaction are presented by Bird and Bommer [1]. Furthermore, as Bray and Stewart [42] reasonably observe, where a building has collapsed, which many would if subjected to strong ground shaking followed by liquefaction, it is impossible to determine the extent of liquefaction-induced deformations. This remains a complex and somewhat controversial issue. Presently, it can be concluded that the ‘base-isolation’ effect of liquefaction cannot be reliably predicted and cannot therefore be guaranteed, either for design or assessment. Two potential scenarios are described below: 1. The two hazards do not interact, therefore, any group of buildings has a probability P(X) of being affected by liquefaction, and a probability of 1KP(X) of being damaged by ground shaking. The final damage distribution can therefore be estimated as follows:

2. The two hazards do interact, i.e. the final damage state of any building is a function of both the initial damage caused by ground shaking and any subsequent damage caused by liquefaction. In this case the final damage distribution is calculated as follows: PðDSÞ Z PðLÞPðDSjShaking plus LiquefactionÞ C ð1KPðLÞÞPðDSjShaking onlyÞ

(2)

In this scenario, the strong ground shaking, even though shorter than the full duration, is of sufficient amplitude and duration to cause some initial damage to the building. When the building is still in some damage state less than collapse, the subsequent deformation imposed on it due to liquefaction causes further damage, either by increasing the deformation of the columns (Fig. 4) or by causing the damaged building to settle and rotate (Fig. 3). The final damage state is thus a function of the damage 1 0.9 0.8 0.7 0.6 vertical lines show suggested rigid body limits for a 4m wide building rotating due to differential settlement beneath its base

0.5 0.4 0.3

PðDSÞ Z PðLÞPðDSjLiquefactionÞ C ð1KPðLÞÞPðDSjShakingÞ

If the probability of liquefaction is negligible, then damage will be due to ground shaking only, and if the occurrence of liquefaction is certain (i.e. P(L)Z1) then damage will be due to liquefaction only.

Pf | ∆ FV

Complete

0.2

(1)

LS1

0.1

LS2

LS3

0 0

where DS damage state (e.g. slight, moderate, extensive or complete) P(L) Probability of liquefaction. This should be most onerous combination of TL (thickness of liquefied layer) and P(L) with respect to the damage distribution, therefore, a number of scenarios may need to be considered.

0.2

0.4

0.6

Differential Settlement of Foundations, ∆

0.8 FV

(m)

Fig. 9. Comparison of rigid body rotational limits with vulnerability curves for differential settlements by Bird et al. [33]; curves are derived for poor quality RC frame buildings, with 4 m beam length, with flexible foundations. Vertical lines are for 4 m wide buildings with stiff foundations. LS1, boundary between slight and moderate damage; LS2, boundary between moderate and extensive damage; LS3, boundary between extensive and complete damage.

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J.F. Bird et al. / Soil Dynamics and Earthquake Engineering 26 (2006) 15–30

Fig. 10. A framework for estimating damage in a zone of liquefaction susceptibility. The principal components are in the column on the left-hand side of the figure, and a simplified illustration is shown on the right. This example considers P(L)Z0.5, differential vertical movements only and RC frame buildings with flexible foundations. S, slight; M, moderate; E, extensive; C, complete damage (see Table 2). F(PGDjUV) signifies the CDF of PGD given that the ground deformation is uniform vertical etc.

state reached at the onset of liquefaction, and hence, how much capacity remains to resist the liquefaction demand. One suggested approach for including combined damage would be to calibrate building vulnerabilities to liquefaction

with field observations such that the complexities of the hazard interaction are implicitly included. A more rigorous approach for determining the overall damage for the second scenario above (i.e. interaction), when there is sufficient data to do so, is

J.F. Bird et al. / Soil Dynamics and Earthquake Engineering 26 (2006) 15–30

briefly considered. However, it is recognised that there remain difficulties in determining when this will occur as opposed to the first scenario (i.e. no interaction), and that such assessments may in many cases be beyond the scope of a loss estimation model. Nonetheless, the procedure described below is a useful illustration of the potential influence of liquefaction following ground shaking. A simplified behaviour model to determine the displacement capacity at the end of ground shaking is illustrated in Fig. 11. If the structure has not exceeded its yield capacity, i.e. it has remained elastic, then the full displacement capacity is available to resist liquefaction. If, however, either the yield capacity or the second limit state, which defines the boundary between moderate and extensive damage, has been exceeded, then it is nominally assumed that such buildings are, on average, half way between the two limits, and the remaining capacity is calculated accordingly. The capacity is calculated making the simplifying assumption that the unloading path has the same gradient as the initial loading path. If the structure has suffered complete damage due to ground shaking (i.e. it has failed the third limit state), then it cannot be further damaged by the occurrence of ground failure. A further simplifying assumption has been made that all damage due to ground shaking occurs in the first part of the earthquake and the liquefaction-induced ground deformation will occur towards the end of, or subsequent to the earthquake. This ignores the potential for low-frequency ground shaking or low-frequency ground oscillations after the onset of liquefaction. A further assumption is made in Fig. 11 that the same structural element is loaded by both ground-shaking and ground deformation. This is likely to be the case for buildings exhibiting column sway (soft-storey) behaviour under ground shaking, followed by deformation beneath flexible foundations as shown in Fig. 4(a). Based upon this model of ‘residual’ capacity at the end of cyclic loading due to ground shaking, the schematic diagram shown in Fig. 12 can be followed to obtain the final damage state. Building Classification

27

(a)

LS1

F slight

LS2 moderate

∆y

∆’ LS2

LS3 extensive

∆ LS2

complete

∆ LS3

Average available displacement capacity of structure exceeding LS1 at end of ground shaking

Displacement Capacity

(b)

LS1

F

slight

LS2 moderate

∆y

∆’ LS2

LS3 extensive

∆ LS2

complete

∆ LS3

Average available displacement capacity of structure exceeding LS1 at end of ground shaking

Displacement Capacity

Fig. 11. Schematic illustration of force–displacement paths for a structural element exceeding each limit state.: (a) to the end of the strong ground shaking cycle (b) from the onset of liquefaction, showing the average available capacity the element will have left to resist liquefaction-induced deformations.

Damage state at end of strong shaking

Potential damage states after liquefaction

Slight Moderate Slight

Extensive Complete Moderate

Moderate RC Frame Buildings. Pad footings

Extensive Complete

Extensive

Extensive Complete

Complete

Complete

Fig. 12. Cumulative structural damage due to ground shaking followed by liquefaction.

J.F. Bird et al. / Soil Dynamics and Earthquake Engineering 26 (2006) 15–30

In order to implement the procedure shown in Fig. 12, an important variable is the degree to which the occurrence of liquefaction will modify the demand compared to the case where no liquefaction occurs. It is hypothesised that in this case the peak acceleration will still occur, but the number of cycles of strong motion would be reduced. 4.4. Application of the new framework A demonstration of the approach described in the preceding sections and summarised in Fig. 10 is briefly presented using measurements and observations from central Adapazari in the 1999 Kocaeli earthquake. The data from Adapazari allow an estimation of both the strength of ground shaking and the magnitude of the liquefaction-induced permanent ground deformation. This means that some of the uncertainty associated with the estimation of the demand is reduced. The remaining uncertainty relates to the spatial variability across the study region, and the natural heterogeneity of the ground conditions. The example presented considers the semihypothetical case of reinforced-concrete frame buildings on flexible foundations subjected to the same level demand as the buildings in central Adapazari, which were in reality mainly on stiff raft foundations. The ground shaking demand in downtown Adapazari must be estimated using attenuation relationships, since there were no strong-motion instruments in the immediate area. However there were sufficient strong-motion records from the near-fault region to guide the selection of an appropriate attenuation relationship and hence a degree of reliability in the calculated response spectra, as described by Bird et al. [36]. Thus the variability of demand is modelled by allowing a range of site classifications from D to E, and a range of source-site distances of 6–8 km. Almost no lateral spreading was observed in Adapazari, therefore only settlement-induced damage is considered. The ground deformation demand has been estimated from the range of settlements reported for individual buildings by Yoshida et al. [43], assuming that these are directly analogous to the differential settlements in the ground beneath the buildings. The median and standard deviation of the differential settlements have been calculated from the data, where the median differential settlement was 8 cm, with a lognormal standard deviation of 0.6 (i.e. the data required at Step 4 in Fig. 10). These values are significantly lower that the maximum settlements reported in Adapazari, which exceeded 1.0 m in areas, because they are differential values across the footprint of a single building. For a 4 m wide building on rigid foundations, 8 cm corresponds to a rotation of 1/50 or approximately 18 which appears a reasonable estimate of the median value based upon the observations of Bray and Stewart [42]. Additional information required to enable an estimation of liquefaction-induced damage includes: † The proportion of buildings not affected by liquefaction. In central Adapazari, at least 60% of the buildings surveyed by

Bray and Stewart [42] did not suffer any ground failure. This value ignores the buildings which collapsed and therefore made it impossible to determine the occurrence of ground failure and could therefore be an over-estimate of the true value. This can be compared with a factor of 75% assumed in HAZUS to represent the area of ground that would not liquefy even given a high susceptibility to liquefaction. † The proportion of buildings affected by liquefaction where the settlements were uniform rather than differential. The presence of relatively stiff raft foundations in Adapazari would certainly have influenced this by increasing the likelihood of uniform settlements. A nominal factor of 10% has been assigned for illustrative purposes. The damage distribution has been predicted as follows: (i) Ground shaking damage to RC frame buildings, using the methodology presented by Crowley et al. [6]. (ii) Liquefaction damage to RC frame buildings with flexible foundations due to differential settlements using the analytical solutions presented by Bird et al. [33]. (iii) Combined ground-shaking and liquefaction, assuming ‘base-isolation’, i.e. the two hazards are mutually exclusive, and 60% of the buildings are damaged by ground shaking only, the other 40% by liquefaction only. (iv) Combined ground shaking and liquefaction with no ‘base-isolation’ i.e. over the 40% of the area where liquefaction occurs, buildings are damaged by ground shaking then liquefaction, as suggested in Fig. 12. Since the demand is predetermined for the sake of this illustration, it is possible to inspect the hypothetical distributions of damage due to both ground shaking and liquefaction in the same locality. Fig. 13 shows that liquefaction alone is less damaging to the RC frame buildings than ground shaking alone. Combining the two hazards in the manner suggested in Fig. 12 would increase 0.8 shaking

Percentage of affected buildings

28

differential settlement

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Slight

Moderate

Extensive

Complete

Fig. 13. Comparison of damage distributions due to ground shaking only or liquefaction-induced differential settlements only.

J.F. Bird et al. / Soil Dynamics and Earthquake Engineering 26 (2006) 15–30

0.8 shaking only

Proportion of buildings

0.7 0.6

shaking and liquefaction

0.5

shaking or liquefaction (base isolation)

0.4 0.3 0.2 0.1 0 Slight

Moderate

Extensive

Complete

Fig. 14. Comparison of the two damage scenarios described in Section 4.3 to the damage caused by ground shaking only.

the overall level of damage as shown in Fig. 14. Only damage caused by differential settlement to RC frame buildings with flexible foundations is considered in the liquefaction scenario, ignoring many of the complexities associated with different foundation types and damage mechanisms. Fig. 14 shows the importance of the debate as to whether ‘base isolation’ will occur, since, the computed damage distributions and their consequences are significantly different for the two scenarios in Section 4.3. An incorrect assumption of no interaction between the two hazards could produce unconservative results. 5. Discussion The role of engineering judgement in the estimation of liquefaction-induced damage in earthquake loss models warrants a brief discussion. There is a tendency in earthquake loss estimations to seek to standardise procedures such that they can be applied to different regions by different users in order to obtain comparable results. This feature is particularly desirable for insurance companies, and is the basis of the ground failure component of the HAZUS methodology [22], which contains many simplifications, including ‘hidden’ simplifications based upon the developers’ judgement. In the field of geotechnical engineering, the role of judgement is particularly significant, and, when extended to the field of liquefaction engineering, it is essential to deal with uncertainties ranging from the choice of the most appropriate methodology to the selection of input parameters. No framework could be developed that is universally applicable to all regions and ground conditions, thus it is imperative that decisions are made on the basis of individual studies. Probabilistic methods as presented by Crowley et al. [31] and Bird et al. [33], therefore, have a doubly important role to play, since as well as representing spatial variability they are required to describe the uncertainties related to these judgements. In the context of evaluating building damage caused by liquefaction-induced ground deformations, separate solutions are required for buildings on stiff shallow foundations, which

29

will respond as rigid bodies to deformations at foundation level, and those on flexible (i.e. unrestrained) shallow foundations, which will undergo structural deformations. As there is no obvious analytical solution to the former case, suggested limits have been proposed in Table 3, based largely upon empirical criteria. There remains an urgent need for improved field data for the calibration of such scales. There is a significant gap in current field survey data relating to postearthquake repair methods for damaged buildings. In parallel with this is a need for improved analytical solutions, such as those presented by Bird et al. [33], since even an improved empirical database will be small and sporadic in comparison to those used to evaluate other insurance premiums. For piled foundations many of the issues to consider are similar, i.e. the consequences of pile deformation on the supported building. Additional complexities must also be introduced such as the founding level of the piles compared to the thickness of the liquefied layer, and the lateral resistance capacity of the piles. Methods for the identification of liquefaction susceptibility, and the potential for the initiation of liquefaction under a given level of shaking, continue to be developed and refined, but without the capability to determine what this will mean for the affected infrastructure, the usefulness of such methods is inevitably limited. The variability and uncertainty relating to the demand remains a major issue for the evaluation of liquefaction-induced damage. Probabilistic procedures are needed for the estimation of both average and differential horizontal and vertical ground movements before a complete methodology can be developed. This has been identified as one of the present challenges of geotechnical earthquake engineering (e.g. [44,21]). This paper has shown that to incorporate liquefactioninduced damage into an earthquake loss model, following the framework shown in Fig. 10, is a complicated procedure. However, failure to consider each of these issues can produce significant errors in the resulting damage estimations. Full consideration as to the necessity of introducing liquefaction into a loss model must be made [1]. Where it is deemed an essential component of the model, then the additional data and computational requirements described in this paper should be incorporated. Acknowledgements The work of the first and third authors was respectively funded through a Marie Curie fellowship and the SAFERR Research Training Network from the European Commission. Financial assistance from the EPSRC and Arup is also gratefully acknowledged. The authors are grateful to the anonymous reviewer for constructive comments that improved the manuscript. References [1] Bird JF, Bommer JJ. Earthquake losses due to ground failure. Eng Geol 2004;75(2):147–79.

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