To limit the losses due to floods, public authorities can try to foster the adoption of private measures aimed at reducing the vulnerability of dwellings. However, the efficacy and cost-efficiency of such measures to reduce material losses are not well-known. In particular, the influence of building and flood characteristics on these variables has not been thoroughly studied. A better understanding of this topic would help identify the measures that are relevant to implement in specific contexts. To address this gap, we examined the effect of building and flood characteristics on the cost, efficacy, and cost-efficiency of three groups of measures taken for existing dwellings: one consists of elevating the dwelling, one of dry proofing it, and one of using construction materials that are resistant to water or cheap to repair or replace. We combined expert judgement and computer modelling to assess their cost, efficacy, and cost-efficiency for a wide range of flood depths and durations, building characteristics, and levels of exposure. We found that the value of the building components has a positive effect on the efficacy of dry proofing and elevating a dwelling. Both the efficacy and cost of these two groups of measures increase with the size of the dwelling. Moreover, according to our results, dry proofing and elevating a dwelling are unlikely to be cost-efficient for dwellings that are not exposed to floods with a return period lower than 100 and 30 years, respectively. Our findings also highlight that it is often less expensive to use the adapted than the original materials when rebuilding a damaged dwelling. Moreover, adapting the materials of an intact dwelling is unlikely to be cost-efficient for dwellings that are not exposed to floods with a return period lower than 20 years. Our results apply to France because the damage and the installation costs of the measures are specific to France and the geometry of the dwellings considered to perform our analyses is based on French dwellings.

A flood risk can be defined as the combination of a hazard, exposed assets and populations, and their vulnerability to the hazard (e.g.

We focused on measures aimed at reducing the vulnerability of existing dwellings to floods, which we call “precautionary measures”, and analysed their efficacy, cost, and cost-efficiency. We define the cost-efficiency of a measure as the discounted sum of the difference between its annual expected efficacy and its annual cost over its lifespan. The efficacy of a precautionary measure indicates the extent to which it reduces the level of damage to a dwelling. It depends on the flood intensity. The annual expected efficacy is thus the probability-weighted average of the values of efficacy computed for all possible flood intensities.

So far, the efficacy of precautionary measures has been examined at the household level using mainly empirical approaches and expert judgement (see

All these studies assessed the efficacy of precautionary measures for particular flood events. However, the comparison of the cost and efficacy of a measure requires estimating its annual expected efficacy.

While empirical studies analyse precautionary measures in realistic settings, the results they provide are largely context-dependent, as reported by

In brief, the existing literature focuses on assessing the efficacy or cost-efficiency of precautionary measures rather than on explaining their variability. The aim of our study was to address this gap. We combined data based on expert judgement and computer modelling to analyse three types of measures (elevation, dry proofing, and component adaptations) for a wide range of flood intensities and dwellings characteristics, including the materials used for their components. More specifically, we assessed ranges of cost and efficacy of the measures and examined the influence of building and flood characteristics on these variables. For each type of measure, we also found a range of exposure level for which it is unlikely that the measure could be cost-efficient independently of the building characteristics.

In the following section, we present the measures that we focus on. We describe the method used to assess their efficacy, cost, and cost-efficiency in Sect.

We reviewed the measures recommended to reduce the vulnerability of dwellings to floods in a joint report of the French ministries in charge of environment and housing

The measures described in these reports can be classified into three categories: some aim at avoiding damage by elevating the house, storing valuables upstairs, or elevating heating and electrical utilities, for example; some at preventing the water from entering into the dwelling; and some at limiting the costs of repair and replacement of building components.

We analysed the measure that consists of elevating the house and the measures that aim at preventing the water from entering into the dwelling or at limiting the costs of repair and replacement of the building components. We refer to the first measure as the elevation strategy, to the second group of measures as the dry-proofing strategy, and to the third group of measures as the component adaptation strategy.

To avoid damage up to a given flood depth, dwellings can sometimes be elevated. According to a report of the

It is also possible to leave the slab on the ground and to construct a new floor after lifting the house.

. In both cases, an external staircase must be built to access the dwelling and utility lines must be extended.We analysed the efficacy, cost, and cost-efficiency of elevating dwellings by 50, 100, and 250 cm. We assumed that only single-storey houses can be elevated because other types of dwellings are too large.

Measures can be taken to prevent the water from entering into a dwelling if the flood depth stays below 1 m and the flood lasts less than 48 h. For higher flood depths or longer flood durations, the pressure on the vertical elements of the building structure can cause severe damage.

For a dwelling without a basement, the following measures must be taken together and dimensioned consistently to prevent the water from entering up to a chosen threshold: installing flood barriers, repairing faulty seals in the external walls, waterproofing the external walls, treating cracks in the external walls, installing removable covers on small openings that are below the chosen threshold, installing anti-backflow valves, ensuring that the electrical cable sleeves are watertight, and buying a pumping device

For dwellings with a basement, additional measures must be taken. We only analysed the measures which aim to prevent the water from entering into a dwelling without a basement.

. FollowingWe define “component adaptation” as a measure which consists of using building materials that are resistant to water or cheap to repair or replace. We studied component adaptations which pertain to the ceilings, the walls, the floors, and the openings. We detail in Table

Materials that limit the costs of repair or replacement after a flood.

We used a computer tool called

The efficacy and the cost of the strategies were assessed for several numerical models of dwellings. The cost of each strategy depends on the geometry of the dwellings and, in some cases, on whether the strategy is taken for an intact or damaged building and for the building materials. The efficacy is assessed by comparing the damage functions of the dwellings obtained with and without a strategy. It depends on the flood depth and duration, on the geometry of the dwellings, and on the building materials.

In this section, we describe the numerical models used as inputs, we provide an overview of how

The numerical model of a dwelling is made up of an XML file and a CSV file. The former indicates the ground floor height above ground level, the layout and size of the rooms, and the construction materials used for the building. Figure

Top view of the single-storey house. The external walls are in black, the internal walls in grey, the doors in brown, and the windows in blue.

Pieces of furniture contained in Bedroom 1 of the single-storey house (see Fig.

Originally, we had three numerical models which represent real dwellings: we visited an apartment to establish its plan and make an inventory of its furniture, the European Center for Flood Risk Prevention did the same with a single-storey house

In order to be able to generalise our results, we developed several versions of these three numerical models of dwellings by modifying the combination of the building components listed in Table

Components of the building used to develop the versions of the numerical models of dwellings.

We define the damage suffered by a good as the expected cost of the actions that must be performed after a flood in order to bring it back to its pre-flood state. Using this definition,

Some floods can last more than 144 h. The experts interviewed did not provide data regarding the vulnerability of the elementary components to such floods. Thus, we did not study the efficacy of precautionary measures for floods longer than 144 h.

in 12 h increments.For a given numerical model,

A more detailed description of

Numerous empirical and synthetic flood loss models exist.

Some empirical flood damage models include precautionary measures as explanatory variables (see for example

The damage mechanisms are more explicit in synthetic models (see for example

To our knowledge,

Modelling the elevation of a dwelling consists of choosing a threshold of flood depth below which damage should be avoided. The cost and efficacy of the strategy are deduced from this threshold.

To model the dry proofing of a dwelling, a threshold below which the water should be prevented from entering must first be chosen. The number of openings that are below the threshold is the number of flood barriers that must be installed. Then, the perimeter of the dwelling, from which the quantity of removable covers that must be installed is deduced, is computed. The perimeter is multiplied by the threshold to obtain the area on which faulty seals and cracks in the external walls must be repaired and on which the external walls must be waterproofed.

Adapting a given component of the numerical model of a dwelling boils down to replacing its original variant by the recommended one (see Table

Costs of elevating a masonry dwelling as reported by

The costs per square foot are in USD 2009.

To assess the cost of elevating a dwelling, we relied on the estimates provided by the

Costs of elevating a masonry dwelling used in our study.

The costs per square metre are in EUR 2017.

Once the costs were in euros per square foot, we converted them into euros per square metre by dividing them by 0.3048

The cost of each measure that must be implemented to dry proof a dwelling was assessed by a construction expert for the single-storey house. Knowing the characteristics of this dwelling, we estimated the cost of each measure by measurement unit. For each numerical model of a dwelling, they were multiplied by the quantities on which the measures must be applied. Table

Costs of the dry-proofing measures.

A given component can be destroyed or intact when the adaptation takes place. At the level of a dwelling, we consider two situations: either all the components are destroyed or they are all intact when the adaptation takes place. In the first case, which we call the repair context, the adaptation cost is the difference between the costs of installing the recommended and the original variants of the components. In the second case, which we call the prevention context, the adaptation cost is the sum of the costs of installing the recommended variant of the components (if they are different from the original ones) and of reinstalling the original coatings (of the walls, floors, and ceilings).

We define the efficacy of a strategy for a given numerical model of a dwelling as the difference between the damage functions computed without and with the strategy.

When a dwelling is elevated by

Efficacy of the elevation, dry proofing, and component adaptation strategies implemented on the original version of the single-storey house. The two top panels show damage in euros, while the lower panel shows avoided damage in euros.

The damage function of the numerical model of a dwelling where the dry-proofing strategy is installed is equal to zero for combinations of immersion depths below or equal to the threshold and immersion durations below or equal to 48 h. For all other combinations of immersion depth and duration, dry proofing has no effect on the damage function. For example, Fig.

The efficacy of a component adaptation to reduce the vulnerability of a dwelling is the difference between the damage functions computed with the original and recommended variants of the component. Hence, the efficacy depends on the immersion depth and duration. For instance, Fig.

The maximum cost-efficiency of a strategy for a given type of dwelling (single-storey house, double-storey house, or apartment) is defined as a supremum of the cost-efficiency computed for the version for which the strategy is the most cost-efficient. It is thus a supremum of the cost-efficiency for the type of dwelling considered. In other words, for a given strategy and a given type of dwelling, the cost-efficiency of the strategy is always lower than the maximum cost-efficiency regardless of the building materials or the relationship between the flood intensity and frequency.

In this section, we mathematically define the cost-efficiency and maximum cost-efficiency of a strategy.

The cost-efficiency (CE) of a strategy is defined for a contextualised dwelling, which is a dwelling that has a given location and thus a given exposure to floods depending on their frequency. The cost-efficiency is the discounted sum of the difference between the annual expected efficacy (AEE) and the cost of the strategy over a defined time horizon (

Moreover, the annual expected efficiency of a strategy for a given dwelling is equal to

What we call maximum cost-efficiency is in fact an upper boundary of the cost-efficiency. We first computed it for each version of a given type of dwelling.

To compute the maximum cost-efficiency of a strategy

Thus, we define the maximum cost-efficiency of

We used a discount rate of 2.5 %, which is the value recommended to assess public investments in France

For each type of dwelling, we computed the maximum cost-efficiency for values of

For each strategy and type of dwelling, we searched for the combinations of the time horizon and return period for which the maximum cost-efficiency is negative. In these contexts, our results suggest that the strategy is unlikely to be cost-efficient. Indeed, unlike the cost-efficiency, the maximum cost-efficiency for a given type of dwelling does not depend on the building materials and on the relationship between the flood intensity (immersion depth and duration) and frequency. It only depends on the time horizon and return period. Thus, for the combinations of the time horizon and return period associated with a negative maximum cost-efficiency, the strategy is always cost-inefficient regardless of the building materials and of the relationship between the flood intensity and frequency.

We present the ranges of cost and efficacy and the maximum cost-efficiency of the elevation, dry proofing, and component adaptation strategies.

As shown in Table

Distribution of the cost in thousands of euros across all numerical models of dwellings.

The cost of elevating a single-storey house lies between EUR 66 000 and EUR 109 000. Thus, it is always higher that the highest value of efficacy for this strategy. It increases with the elevation and is always the highest for dwellings that have slab-on-grade foundations.

The cost of dry proofing a dwelling ranges from EUR 6000 to EUR 10 000. For a given threshold, the cost of dry proofing is always maximum for the single-storey house and minimum for the double-storey house. This is due to the fact that the single-storey house has the greatest perimeter (54 m) and the double-storey house the smallest (40 m). The area on which some measures must be applied increases with the threshold. Thus, the cost of dry proofing is greater when the threshold is 100 cm than when it is 50 cm.

Regarding the adaptation of all building components, if it takes place on a damaged building (repair context), it is often less expensive to adapt the dwelling than to install the original variants of the components again. More precisely, it is the case for 91 % of the 5184 numerical models of dwellings. On the contrary, if the dwelling is intact when the adaptation takes place (prevention context), the mean cost of adapting all components is approximately 4 times higher than the cost of dry proofing. In the prevention context, the minimum costs relate to versions of the dwellings for which the original variants of the components are highly similar to the recommended ones. Note that we did not compute numerical models of dwellings that were made up of all the recommended variants of the components. The cost and efficacy of adapting all building components of such dwellings would be null. The highest adaptation costs relate to versions of the dwellings for which almost all components must be adapted.

Figure

Efficacy of the three strategies for a duration of immersion of 24 or 72 h.

More specifically, the efficacy of elevating a dwelling increases with the value of elevation and with the value of the components of the dwelling. For this strategy, the highest efficacy is obtained for numerical models of dwellings which contain a lot of wooden components (joist boards, parquet, and opening frames and shutters in wood). The highest efficacy is observed for an immersion depth equal to the elevation value.

As for dry proofing, its efficacy increases with the threshold, the value of the components of the dwelling, and the floor area. The highest maximum efficacies relate to the single-storey house and the lowest to the double-storey house because the former has the largest floor area (133.5 m

Adapting all components can sometimes generate the same or a higher level of damage than keeping all the original components. This is the case for the 576 versions of each type of dwelling, which originally have masonry internal walls and tiles or textiles as coatings of floors. There is indeed a probability greater than zero that the adapted walls in plaster must be replaced for immersion depths greater than or equal to 30 cm, no matter the immersion duration. On the contrary, the probability that masonry walls must be replaced for immersion durations lower than 72 h is equal to zero. This type of wall needs only to be repaired in such cases. As a consequence, for some immersion depths, the elementary damage function of an internal wall in plaster is above the one of a masonry internal wall for immersion durations lower than 72 h. Negative levels of efficacy are observed only for dwellings which originally have tiles or textile as coatings of floors because the high efficacy of replacing parquet floors by sealed tiling floors compensates the negative efficacy of replacing masonry walls by walls in plaster. The efficacy of adapting all components is always positive for immersion durations higher than or equal to 72 h. The variance in the efficacy increases with the quantity of building components to adapt.

Table

Distribution of efficacy in thousands of euros across all numerical models of dwellings and all combinations of immersion depth and duration.

Figure

Sign of the maximum cost-efficiency of each strategy.

For the analysed values of the time horizon, it is never cost-efficient to elevate a single-storey house which is only exposed to floods with a return period higher than 30 years. If the dwelling has slab-on-grade foundations, the minimum return period for which it could be cost-efficient to elevate a dwelling is 20 years approximately.

Similarly, according to our results, adapting all building components is never cost-efficient for intact dwellings that are not exposed to floods that have a return period of less than 20 years. However, when component adaptations take place on a damaged dwelling, our results do not indicate ranges of the time horizon and return period for which this strategy is never cost-efficient.

Regarding dry proofing, the results are similar for the three types of dwellings and are not affected by the threshold. They suggest that dry proofing is never cost-efficient for dwellings that are not exposed to floods with a return period of 100 years or less.

Except in the case of adapting all the building components of a damaged building, we observe that the maximum return period for which a strategy is cost-efficient increases with the time horizon. For instance, for a dwelling that must be entirely dry proofed again after 20 years and that is not exposed to floods with a return period of less than 60 years, this strategy will never be cost-efficient.

We assessed the cost and efficacy of some precautionary measures by taking into account some characteristics of the dwellings (their building components and size), parameters of the measures, grouped in strategies (their dimension or implementation context), and flood characteristics (immersion depth and duration). Then, we computed the maximum cost-efficiency of each strategy for several combinations of the time horizon and return period. We could thus identify exposure levels for which it is unlikely that the strategies could be cost-efficient.

The value of the building components by square metre has a positive effect on the efficacy of dry proofing and elevating a dwelling, while it does not affect the cost of these strategies. Hence, the more expensive the components of a dwelling, the more relevant it can be to elevate or dry proof it. By contrast, both the efficacy and the cost of dry proofing and elevation increase with the flood depth below which damage must be avoided and with the size of the dwelling. Consequently, these parameters do not affect the maximum cost-efficiency of dry proofing and elevation. According to our results, these strategies are unlikely to be cost-efficient for dwellings only exposed to floods with a return period higher than 100 and 30 years, respectively.

The efficacy of adapting the building components strongly depends on their original materials. It can even be negative for floods that last less than 72 h if the internal walls are originally in masonry. The cost of adapting the building components is influenced by the adaptation context and by the original materials. If the adaptation takes place on an already-damaged building, it is most of the time less expensive to adapt it than to reinstall the original variants of the components. However, it costs approximately EUR 40 000 on average to adapt an intact building. Since the cost and efficacy both increase with the quantity of components to adapt, the maximum cost-efficiency does not depend on the size of the dwelling. Adapting an intact dwelling that is not exposed to floods with a return period lower than 20 years is unlikely to be cost-efficient. In a repair context, we could not identify exposure levels for which it is never cost-efficient to adapt all building components.

Note that the cost-efficiency of all strategies increases with their lifespan and with the level of exposure in terms of frequency of floods.

According to

Similarly to our results, those of

We did not find studies which analyse specifically the efficacy, cost, or cost-efficiency of adapting all the building components. However,

According to

Our results seem reliable, since they are mostly in line with previous studies. They suggest that elevating or adapting the building components of intact dwellings that are not exposed to frequent floods (i.e. with a return period lower than 30 years) should not be fostered by policymakers who wish to limit material damage due to floods. However, after a flood, it could be efficient to take advantage of the reconstruction phase to adapt the building components, since it is often less expensive to install the recommended components than to rebuild dwellings as they were before the event. Given that the post-disaster recovery often occurs in a climate of urgency, it could be useful to design in advance policy tools to help people adapt their dwelling during this phase.

Moreover, policymakers should not promote the installation of dry-proofing measures in dwellings that are not exposed to floods with a return period lower than 100 years.

Besides the level of exposure, the building components should be taken into account to assess the vulnerability of the dwellings and thus the relevance of implementing precautionary measures that sometimes generate higher costs than benefits.

Decisions regarding the allocation of public funds to communicate about the strategies considered here or to subsidise their installation cannot be based solely on the present study because of several limits relating either to its perimeter or to the method on which it relies. Several limits due to the method are linked to the assumptions and data used in

We only took into account the damage in terms of monetary losses and did not consider the impact of the strategies on the damage related to human health. While the latter is unlikely to be influenced by component adaptations, it could be reduced by dry proofing and even more by elevating the dwelling.

Moreover, our results cannot be used to identify a range of exposures for which it is likely that the studied precautionary measures would efficiently reduce monetary losses. Contextualised studies are required to finely relate the efficiency of precautionary measures to the characteristics of a dwelling and its level of exposure to floods.

Our results are mainly relevant for relatively slow riverine floods. Indeed,

Moreover, our results apply to France because we used French data to estimate the costs of the measures, the database of elementary damage functions of

We only studied the efficacy and cost-efficiency of the strategies for dwellings that are exposed to floods that do not last more than 144 h because the experts interviewed to develop the elementary damage functions of

Our results also depend on the geometry of the dwellings used to develop the numerical models. For instance, dry proofing was only analysed for dwellings that do not contain a basement.

We analysed three types of precautionary measures in a non-contextualised setting. This novel approach enabled us to explore the influence of several building and flood characteristics on the cost and efficacy of the precautionary measures and to find ranges of exposure for which they are unlikely to be cost-efficient. In particular, we found that adapting all the building components or elevating an existing dwelling is unlikely to be cost-efficient if the probability of occurrence of floods is lower than

CR modelled the elevation strategy, analysed the data, and wrote the article. HB modelled the other strategies. FG developed

The authors declare that they have no conflict of interest.

This research has been supported by the Ministère de la Transition écologique et Solidaire (grant no. 2102049246).

This paper was edited by Kai Schröter and reviewed by two anonymous referees.