1 Introduction

Over the last decades, the African continent has experienced fundamental changes in socioeconomic and demographic conditions. According to the United Nations (UN) Department of Economic and Social Affairs Population Division (2019), the substantial increase in the population occurring since the 1950s is expected to continue in the following decades, with an annual population growth rate of 2.5%. In 2020, the continent’s population was 1,341 million, and it is predicted to reach 2,489 million by 2050. In addition to this exponential growth, an unprecedented phenomenon of urbanisation and relocation from rural areas to cities is occurring, especially in Sub-Saharan Africa. Consequently, urban centres could triple their population by 2050 (United Nations Department of Economic and Social Affairs Population Division 2019).

Among the African nations, Malawi has one of the highest rates of population and urbanisation growth. The UN estimates the annual population increase at 2.7% (United Nations Department of Economic and Social Affairs Population Division 2019), while according to World Bank data, the last recorded annual urban population growth (for the year 2019) was 4.03% (World Bank 2019). In contrast with the majority of African countries, Malawi is characterised by a moderate earthquake hazard (Hodge et al. 2015; Goda et al. 2016) and high seismic vulnerability of the building stock (Kloukinas et al. 2020; Novelli et al. 2021; Giordano et al. 2021a). A rapid increase in population results in a higher demand for affordable housing. How this demand will be met will dramatically impact the resilience of urban centres against future natural disasters, including earthquakes.

Despite the increasing interest of international development agencies and governments in assessing the future risks of urban centres (Galasso et al. 2021), there is still a lack of extensive quantitative studies in this field. In addition, most of the studies in the literature are focused on the combined effect of climate risk and urban expansion (Muis et al. 2015; Daksiya et al. 2021), while less attention is devoted to seismic risk. Starting from recent hazard and vulnerability research for Malawi (Hodge et al. 2015; Giordano et al. 2021a; Goda et al. 2022), this paper investigates the implications of urban expansion and code enforcement on future earthquake loss for the case study of the city of Blantyre, Malawi. Blantyre is the oldest urban centre in Malawi. It represents the national hub for financial, commercial, and industrial activities and has an estimated population of more than 800,000 inhabitants (Mawenda et al. 2020). It is surrounded by several potential earthquake faults, which results in moderate seismicity (Hodge et al. 2015; Goda et al. 2016).

The analysis is carried out within a catastrophe risk modelling framework that probabilistically combines exposure, hazard, and vulnerability. Three urban expansion scenarios are investigated by assessing the Net Present Value (NPV) of the 30-year aggregated future earthquake monetary loss. For each scenario, the effect of code compliance on future constructions is considered through different sets of seismic vulnerability curves, where the uncertainty around the mean curve is propagated throughout the analysis. A summary of the paper structure is as follows:

  • Sect. 2 summarises the current seismic code previsions in Malawi and describes how these indications are incorporated in the loss analysis to reflect the presence/absence of code enforcement.

  • Sect. 3 describes the building stock exposure in Malawi and in Blantyre (number of buildings, construction typologies, building value/replacement cost) and discusses the main differences between national and city inventory.

  • Sect. 4 presents the assessment methodology adopted to quantify the earthquake-induced Expected Annual Loss Ratio (EALR = expected annual monetary loss/replacement cost) of a single building located in Blantyre. A set of EALRs, specific to each building typology within the portfolio, is subsequently used as data input for the city-scale NPV loss estimate.

  • Sect. 5 presents and discusses the results of the NPV loss assessment approach and the investigated scenarios.

2 Seismic code provisions in Malawi

Despite its location in the Eastern African Rift, risk awareness of the potential effects of seismic events is relatively low in Malawi (Goda et al. 2016, 2022). Consequently, earthquake-specific building provisions are not fully developed, as well as new seismic protection techniques (Tsiavos et al. 2021b). Currently, there are five main documents with information on seismic safe construction practices in Malawi:

  • Code of Practice for Design Loadings for Buildings, Malawi Standard MS 820:2010 (Malawi Bureau of Standards 2010);

  • Guidelines for Safer House Construction, Technical Manual (Malawi Government 2010a) and Supplementary Handbook to ‘Guidelines for Safer House Construction’ (Malawi Government 2010b).

  • Safer House Construction Guidelines (Bureau TNM 2016);

  • Safer Schools Construction Guidelines (World Bank and Malawi Government 2019);

  • Malawi Building Regulations (MBR) 2019 (Malawi Government 2019) incorporates and summarises most of the information reported in the previous documents.

According to MBR-2019 (Malawi Government 2019), “Malawi is zoned as an earthquake-prone area. Because of its narrow banana shape, all areas shall be taken as equally vulnerable to earthquakes. All buildings shall be designed for horizontal ground accelerations of 10% probability of exceedance in 50 years (0.24 g). Buildings with post-disaster function shall be designed for accelerations of 10% probability of exceedance in 100 years (0.3 g). Seismic structural provisions shall be in accordance with the Code of Practice for Design Loadings for Buildings, Malawi Standard MS 820”. These levels of ground shaking are particularly critical for non-engineered, Unreinforced Fired Brick masonry buildings (UFB) (Novelli et al. 2021; Giordano et al. 2021a). Therefore, the technical indications reported by the Malawian guidelines mainly refer to masonry. In addition, UFBs represent a large proportion of the current building stock and, as observed on-site, the primary construction type for new settlements (Kloukinas et al. 2020; Novelli et al. 2021). The main indications provided by MBR-19 on UFBs can be summarised as follows:

  1. (i)

    Foundations. Buildings should be realised on plinths in fired bricks/field stones and cement mortar masonry or concrete. The minimum foundation depth should be 700 mm for gravel/sandy soil and 1000 mm for clay. If additional resources are available, a 75–100 mm thick Reinforced Concrete (RC) foundation slab should be realised.

  2. (ii)

    Walls. The height of walls should be less than 12 times their thickness (t); therefore, for a typical height of 2.5 m, t should be at least 230 mm. The maximum unsupported length (i.e., the distance between two consecutive cross-walls) should be less than 18 × t; therefore, for t = 230 mm, the limit is 4.0 m. The connection between adjacent walls must be ensured through effective brick layouts, avoiding vertical alignment of head joints. To avoid Out-Of-Plane (OOP) failure, buttresses should be realised if the length of unrestrained walls exceeds the maximum limit. A regular masonry bond should be adopted (e.g., English bond). Horizontal and vertical mortar joints should be properly filled with 10 mm thick cement mortar. The verticality of walls should be ensured. In addition, heavy masonry gables should be avoided when acting as unrestrained cantilevers.

  3. (iii)

    Horizontal/vertical reinforcement of walls. Metal wires should be placed every four courses of bricks. One steel bar (D16 mm) should be positioned at any intersection between walls.

  4. (iv)

    Reinforced concrete ring beam at roof/lintel level. The recommended dimension for the lintel ring beam is 150 mm × t, with four D12 mm longitudinal bars and D6 mm stirrups at 150 mm spacing. The indicated dimension for the roof level ring beam is 75–100 mm × t. The reinforcement of the beam comprises two D12 mm longitudinal bars and D6 stirrups at 150 mm spacing.

The last two provisions (iii and iv) correspond to a consistent improvement of seismic capacity (e.g. Dauda et al. 2021). However, due to cost implications, the use of steel reinforcement in Malawian constructions is very limited (Malawi Government 2010a) and, therefore, not considered in this study. As discussed previously (Giordano et al. 2021a), the key aspect of the seismic vulnerability of UFBs lies in the wall construction quality (point ii). Non-code-conforming Malawian buildings are highly vulnerable to OOP damage, characterised by a lack of wall-to-wall/wall-to-roof connections. On the contrary, if OOP action is controlled through appropriate construction detailing (point ii), masonry walls are more likely to sustain In-Plane (IP) damage, avoiding premature damage at lower ground shaking intensities (Silva et al. 2022, Sharma et al. 2021).

3 Blantyre’s building stock exposure

In data-scarce regions, exposure information can be inaccurate and is generally characterised by low granularity. For instance, a recent scenario-based earthquake risk assessment study for Malawi by Goda et al. (2022) has shown that different exposure databases lead to a 30% variation of the regional seismic risk for rural areas of the central-southern part of the country. In this work, the exposure model of Blantyre is extracted from the Modelling Exposure Through Earth Observation Routines (METEOR) database (Ghosh et al. 2018), (https://meteor-project.org/data/) which includes Level 1 (global-quality) exposure data for about fifty low-to-middle income counties. This database was also considered in the scenario-based analysis developed by Goda et al. (2022). METEOR data does not contain extensive country-specific information but has the advantage of being structured for catastrophe modelling applications. The geospatial resolution of the data is 15-arcsecond (approximately 500 m at the equator). Each cell of the database grid contains estimates of the number of buildings, the total building floor area, the construction typologies, and the Total Building Value (TBV) within the cell. The TBV is the current estimate of the reconstruction cost of all the buildings within the cell (i.e. replacement cost, not including the land cost). This last quantity is one of the most uncertain pieces of information in the database, as the literature lacks official data on construction costs in Malawi. One of the few sources of construction cost data for Malawi was provided by UN-HABITAT (2010) in relation to reconstruction projects after the 2009 Karonga earthquake sequence (Chapola and Gondwe 2016). It indicates that 45 m2 “houses constructed using locally made burnt brick, mud and cement mortar, timber for the roof structure and joinery, and iron sheeting for roofs” cost approximately USD 2400, including labour. Although this value is similar to the one provided by METEOR for the corresponding building class (USD 2986), comparing a 2010 cost with a 2018 estimate is challenging, given the complex and untracked evolution of develo** economies like Malawi’s. For the scope of this work, and in the absence of more accurate exposure information, the METEOR TBV data are considered acceptable. In the following subsections, a brief overview of the METEOR exposure data is reported to highlight the general characteristics of the building inventory and the main differences between the national exposure and Blantyre’s exposure.

3.1 National building exposure

The Malawi METEOR exposure model includes around 344,000 data entities whose aggregated results are reported in Fig. 1. The construction taxonomy adopted in METEOR, and retrieved in this study, is reported in Table 1.

Fig. 1
figure 1

Exposure data of the Malawian building stock. Pie charts generated by processing and aggregating data from METEOR (https://meteor-project.org/data/): a Number of Buildings (NoB) of each construction type Total NoB = 3.396 M; b Total Building Value (TBV) for each construction type—Total TBV = USD 21.665 billion; c NoB per IBV level and estimated floor area

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Table 1 Construction typology taxonomy adopted in this study and corresponding vulnerability models
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Figure 1a reports the breakdown of the total number of buildings (3.396 M) by construction typology. At the national level, a large predominance of unreinforced structures is observed. The most common typologies are adobe structures (A), mud walls structures (M), and unreinforced brick masonry structures (UFB), each accounting for about 30% of the total. The same breakdown, expressed in TBV, is reported in Fig. 1b. In this case, it is observed that ~ 40% of the national exposure TBV (USD 21.665 billion total) is represented by UFB constructions, while the contributions of A and M buildings are 20% and 23.5%, respectively. The difference between building count distribution and TBV distribution is justified by the lower economic value of A and M buildings with respect to UFBs. Figure 1c shows the proportion of buildings with the four Individual Building Value (IBV) levels considered in the database: USD 2986, USD 8467, USD 22,097, and USD 32,325. These IBV levels correspond to different estimated floor areas (Fig. 1d): 46 m2, 65 m2, 85 m2 and 140 m2. From Fig. 1c, it is observed that ~ 60% of the buildings have IBV = USD 2986 and a floor area of 46 m2. About 34% of the inventory is constituted by buildings with IBV of USD 8467 and a floor area of 65 m2. Only a limited proportion of the total (~ 8%) is characterised by higher IBV (> USD 20 k).

3.2 Blantyre building exposure

Analogous data analysis has been carried out for Blantyre by selecting and processing the grid cells data within the administrative area (240 km2, population density of about 3334 people/km2), which is shown in Fig. 2. Figure 2a reports the geospatial distribution of the NoB, while Fig. 2b reports the distribution of TBV. The total NoB for the considered area is 217,000, while the total TBV is USD 3.263 billion. This corresponds to 6.39% of the total national NoB and 15% of the national TBV. Therefore, from a building stock TBV perspective, Blantyre is a potential hotspot of risk accumulation. Within Blantyre, there is a good spatial correlation between NoB and TBV, i.e. densely urbanised areas define the zones of high TBV.

Fig. 2
figure 2

Geospatial representation of Blantyre’s administrative area exposure. Maps generated by processing and aggregating data from METEOR (https://meteor-project.org/data/): a NoB distribution; b TBV distribution. Note: uncoloured cells have no building exposure according to METEOR

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In terms of construction typologies, the exposure in Blantyre differs considerably from the one at the national level. Figure 3a shows that UFBs represent 48.33% of the total number of buildings, while the proportions of A and M constructions are lower, at 11.62% and 19.67%, respectively. A similar trend is observed in Fig. 3b, where 49.56% of the TBV is represented by UFBs, while A and M account for 10.25% and 18.99%, respectively. In this regard, it is noted that the actual number of UFB constructions reached 80% of the total, as emerged from local building survey data (Kloukinas et al. 2020). In Fig. 3c-d, the exposure distribution by TBV-floor area bands is reported. Approximately half of the building stock is constituted by buildings of TBV = USD 8,467 and a floor area of 65 m2, while the other half is by buildings of TBV = USD 22,097 and a floor area of 85 m2. This last statistic explains why Blantyre represents, from a TBV perspective, an important proportion of the national building stock. Table 3 of the Appendix reports the full breakdown of the exposure data by typology, TBV, and floor area.

Fig. 3
figure 3

Exposure data of Blantyre’s building stock. Pie charts generated by processing and aggregating data from METEOR (https://meteor-project.org/data/): a Number of Buildings (NoB) of each construction type—Total NoB = 217 103; b TBV for each construction type—Total TBV = USD 3,263 billion; c NoB per IBV level and estimated floor area

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4 Expected Annual Loss Ratio (EALR) at asset scale

The EALR is a key parameter in catastrophe risk assessment (e.g. De Risi et al. 2018; Giordano et al. 2020c, 2021b) and insurance applications (e.g. Sly and Ma 2013). It incorporates in a single number the earthquake vulnerability characteristics of the considered asset and the seismic hazard probability at the asset’s location. The EALR is calculated by solving the following integral (e.g. Porter 2018):

$${\text{EALR}} = \mathop \int \limits_{0}^{\infty } y\left( s \right)\left( {\frac{{ - {\text{d}}G\left( s \right)}}{{{\text{d}}s}}} \right){\text{d}}s$$
(1)

where G(s) represents the hazard at the given location, i.e., the relationship between an earthquake Intensity Measure (IM), such as the Peak Ground Acceleration (PGA) and its Mean Annual Frequency of Exceedance (MAF); y(s) is the building vulnerability curve, which describes the relationship between an IM and the Damage Ratio (DR, i.e., damage repair cost/IBV). The integral in Eq. (1) is executed overall levels of shaking, s. The following subsections present the hazard and vulnerability information utilised to estimate the EALR for the construction typologies present in Blantyre.

4.1 Seismic hazard in Blantyre

Blantyre covers an area of more than 200 square kilometres. Consequently, different locations within Blantyre are characterised by different hazard intensity levels, given the different seismic source distances and different geological/geotechnical conditions across the city. To capture this spatial variability of the hazard, a specific microzonation study (e.g. Ansal et al. 2010; De Risi et al. 2019) would be required. However, this level of detail is unachievable given the lack of ground data available in Malawi and is out of the scope of this work. In this analysis, the seismic hazard is assumed constant within Blantyre’s city limit and is represented by a single probabilistic hazard curve G(s). The curve (Fig. 4) has been calculated by adopting the hazard data of the Africa Hazard Model developed by the Global Earthquake Model (GEM) Foundation (Poggi et al. 2017). It is important to note that the current GEM model does not incorporate recent findings on active fault traces and seismogenic sources in Malawi, which might result in a significant increase in the earthquake hazard throughout the country (Williams et al. 2021).

Fig. 4
figure 4

Representative hazard curve for Blantyre calculated with the GEM Africa Hazard Model (Poggi et al. 2017). Interested readers could consult the GEM OpenQuake Hazard Map Viewer where the full country hazard is reported (https://maps.openquake.org/map/global-seismic-hazard-map/#3/32.00/-2.00)

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4.2 Vulnerability models

Several models exist in the literature about building stock vulnerability models (e.g. Kappos et al. 2006). According to the exposure data reported in Fig. 3, there are nine construction typologies in Blantyre. Ideally, for each of these typologies, two vulnerability models would be considered to represent code-conforming (-C) buildings and informal (-I) (i.e., non-code-conforming) buildings. However, as discussed in Sect. 2, code-conforming vulnerability curves are utilised for UFB buildings only, as UFBs constitute most of Blantyre’s building stock (Fig. 3) and are widely used for new settlements in Malawi (Kloukinas et al. 2020). Sections 4.2.1 and 4.2.2 present the vulnerability models for UFBs, while Sect. 4.2.3 briefly reports the vulnerability curves used for the remaining construction classes. The main difference between UFB-I and UFB-C is that the most critical collapse mechanisms (e.g. overturning) are prevented in favour of stable mechanisms (e.g. in-plane failure).

4.2.1 Informal UFB buildings

Non-code-conforming UFB (UFB-I) vulnerability models are derived from a set of country-specific damage fragility curves by Giordano et al. (2021a). The methodology adopted to derive fragility curves consists of three steps (Giordano et al. 2021a):

  • Stochastic generation of typological buildings. Generation of a representative ensemble of UFB Malawian buildings by using 327 construction geometries collected on site (Novelli et al. 2021). For each geometry, the mechanical properties of masonry are defined probabilistically by considering a database of experimental tests of local masonry (Kloukinas et al. 2019).

  • IP and OOP capacity assessment. The damage assessment of each masonry building is assessed with IP/OOP nonlinear static (pushover) analyses. The IP capacity is estimated with detailed macro-modelling finite element analyses (Pelà et al. 2013; McKenna 2016; Petracca et al. 2017), while the OOP capacity is quantified with an analytical mechanics-based closed-form procedure (Giordano et al. 2020a, b).

  • Fragility curve derivation. For each pushover analysis, a set of damage state fragilities is generated by adopting two methodologies: Static PushOver to Incremental Dynamic Analysis SPO2IDA (Vamvatsikos and Cornell 2006) and the Capacity Spectrum Method (Freeman 1978; Lagomarsino 2015; Giordano et al. 2020b), where damage states are defined in terms of displacement thresholds on the pushover curve. The exceedance probability of generic damage is subsequently defined as a function of PGA.

Figure 5 displays the fragility curves for UFB-I buildings for different Damage States (DS). The solid-grey lines represent the fragility curves of the individual buildings of the stochastic portfolio. The solid red line represents the mean fragility curve (m) of the building class for the given DS, while the orange and green lines define the confidence intervals around the mean (m ± σ, i.e. standard deviation). The building class vulnerability curve is subsequently calculated by convoluting the DS fragility curves through the Consequence Functions (CF) (e.g. Giordano et al. 2021b). Specifically, the CF defines the relationship between earthquake damage and corresponding mean damage repair cost. CF is expressed as a percentage of the IBV of the considered building type. By adopting the recommendations provided by Martins and Silva (2020), the CF for slight, moderate, extensive, and near-collapse damage are taken as 5%, 20%, 60%, and 100% of IBV, respectively. According to the same reference, to account for the uncertainties around these values, a normal distribution with Coefficient of Variation (CoV) of 0.3, 0.2, 0.1 and 0.0 is accounted for slight, moderate, extensive and near collapse damage, respectively (Martins and Silva 2020).

Fig. 5
figure 5

Fragility curves for UFB-I buildings in Malawi: a DS1, slight damage, b DS2, moderate damage, c DS3, extensive damage, d DS4, near collapse

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Figure 7a reports the average vulnerability curve for UFB-I buildings (solid grey line) together with three pairs of confidence intervals. The first pair of intervals (CF—triangle markers) considers the variability (± σ) of the CF values. The second pair of intervals (Fr—dashed and dashed-dotted grey lines) considers the variability around the mean DS fragility curves (displayed in Fig. 5). Lastly, the third pair of intervals (Fr + CF—cross markers) allows for the combination of the two sources of uncertainty described above. It is observed that the Fr variability gives a large dispersion around the mean curve, while the uncertainties of the CF values have a limited impact on the vulnerability results.

4.2.2 Code-conforming UFB buildings

In the same way, as for the UFB-I typology, code-conforming UFB (UFB-C) vulnerability curves are derived from damage fragilities developed by Giordano et al. (2021a). Figure 6 shows the original fragility curves, from slight damage to near collapse, with the corresponding confidence intervals. It is worth noting that the variability of the bundle of fragility curves is quite large. Therefore, the two confidence intervals m ± σ have been cut off at zero (lower limit) and one (upper limit). Most of these building fragilities are characterised by a bimodal feature, which is a consequence of the multi-facade fragility analysis method adopted by Giordano et al. (2021a). By adopting the same approach described in Sect. 4.2.1, the average vulnerability curve and the confidence intervals for different sources of variability have been calculated (Fig. 7b). As observed in the UFB-I model, the Fr uncertainty around the mean vulnerability is much larger than the CF contribution. Figure 7 allows a direct comparison of the vulnerability curves for the two building typologies. The capacity at 50% damage ratio shifts from 0.15 g to 0.55 g moving from informal to code-compliant construcitons. In addition, the range of variability around the UFB-C curve appears larger than the corresponding value for UFB-I. This is a consequence of the different damage patterns experienced by UFB-I and UFB-C buildings. Lacking wall-to-wall and wall-to-floor connections, UFB-Is are mainly affected by one-way OOP damage. Many research studies have shown that one-way OOP seismic capacity is mainly determined by wall height and thickness and only secondarily by the mechanical characteristics of masonry (Doherty et al. 2002; Lagomarsino 2015; Giordano et al. 2020a). The wall thickness and height of Malawi buildings are relatively constant (most of the buildings are one brick thick and one story in elevation); therefore, the dispersion of OOP fragility curves is moderately low. On the contrary, UFB-C fragilities are mainly determined by the variable in-plane geometry and by the uncertain nonlinear mechanical properties of masonry, which result in a larger dispersion of the results (Giordano et al. 2021a).

Fig. 6
figure 6

Fragility curves for UFB-C buildings in Malawi: a DS1, slight damage, b DS2, moderate damage, c DS3, extensive damage, d DS4, near collapse

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Fig. 7
figure 7

a Mean vulnerability curve for Malawian UFB-I buildings and corresponding confidence intervals. b Mean vulnerability curve for Malawian UFB-C buildings and corresponding confidence intervals

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4.2.3 Other construction typologies

As described in Sect. 3.2, together with UFB buildings, according to (Ghosh et al. 2018), there are eight additional construction typologies in Blantyre. The vulnerability curves of these building types have been retrieved from the GEM vulnerability database (Martins and Silva 2020), in line with the GEM Africa Risk Model. Figure 8 shows the complete set of vulnerability curves adopted in this study, while Table 1 reports the corresponding GEM taxonomy codification. It is observed that UFB-C vulnerability models are reasonably well aligned with unreinforced typologies from GEM, which were calculated without accounting for OOP damage potential.

Fig. 8
figure 8

Mean vulnerability curves for Blantyre: UFB mean curves developed in this study and GEM vulnerability curves for other construction typologies

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4.3 Expected annual loss ratio (EALR) of individual assets

Once hazard and vulnerability are defined, the EALR can be quantified by solving the integral of Eq. (1). Figure 9 reports the results for the full set of construction typologies. As expected, UFB-I buildings are characterised by the largest EALR (0.25%), while the remaining typologies have EALR < 0.03%. As observed from the vulnerability plots, UFB-C displays a larger dispersion around the mean with respect to UFB-I.

Fig. 9
figure 9

EALR for different construction typologies in Blantyre. Error bars in UFB-I and UFB-C indicate the EALR values for m ± σ (Fr + CF) vulnerability curves

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5 Aggregated future loss at the city scale

To assess the effect of urban expansion and code-enforcement at city scale, the 30-year NPV of aggregated seismic loss is considered a representative parameter for comparison. The general formulation for estimating the aggregated NPV for a single building is

$${\text{NPV}}_{{{\text{building}}}} = \mathop \sum \limits_{n = 1}^{{T_{p} }} \frac{{{\text{EALR}} \times {\text{IBV}}}}{{\left( {1 + \rho } \right)^{n} }}$$
(2)

where \(T_{p}\) is the considered time frame (in this case, 30 years), EALR is the expected annual loss ratio of the building’s construction typology, IBV is the individual replacement cost of the considered building, and \(\rho\) is the real discount rate, assumed as 5% as suggested by a recent World Bank study (Ramirez Cortes and Mayrhofer 2019). The city-level version of Eq. (2), which accounts for urban expansion, is

$${\text{NPV}}_{{{\text{city}}}} = \mathop \sum \limits_{{{\text{BT}} = 1}}^{{\# {\text{BT}}}} \mathop \sum \limits_{{{\text{FA}} = 1}}^{{\# {\text{FA}}}} \left[ {{\text{EALR}}_{{{\text{BT}}}} \cdot {\text{IBV}}_{{{\text{BT}},{\text{FA}}}} \cdot \mathop \sum \limits_{n = 1}^{{T_{p} }} \frac{1}{{\left( {1 + \rho } \right)^{n} }} \cdot N_{{{\text{BT}},{\text{FA}}}} \cdot \left( {1 + r_{{{\text{ue}},{\text{BT}},{\text{FA}}}} } \right)^{n} } \right]$$
(3)

where BT is a given building typology (list in Fig. 9), #BT is the total number of building typologies; FA is the floor area band (Fig. 3c), #FA is the total number of floor area bands, \(N_{{{\text{BT}},{\text{FA}}}}\) is the total number of buildings having typology BT and floor area band FA, \(r_{{{\text{ue}},{\text{BT}},{\text{FA}}}}\) is the urban expansion rate of the class of buildings having building typology BT and floor area band FA.

5.1 Effect of building code enforcement

Code compliance has been demonstrated as a critical factor for seismic risk (Tsiavos et al. 2021a). Two scenarios are considered to assess the effect of building code enforcement:

  • In Scenario 1—no code enforcement. All existing and future buildings are assumed to be informal UFBs (UFB-I).

  • In Scenario 2—code enforcement. All existing UFB buildings are assumed to be informal (UFB-I model). All future buildings, due to urban expansion, are assumed to be code-conforming UFBs (UFB-C model).

5.2 Effect of urban expansion

For the urban expansion effect, four scenarios are considered (rue is the average city-level expansion rate):

  • Scenario A (baseline): rue = 0%. No urban growth.

  • Scenario B: rue = 2.3%. The urban growth in Blantyre is assumed to be proportional to the expected population growth in Malawi, as reported in the UN prospects (United Nations Department of Economic and Social Affairs Population Division 2019).

  • Scenario C: rue = 4.0%. The urban growth in Blantyre is assumed to be proportional to the World Bank’s estimate of urban population growth in Malawi (World Bank 2019).

  • Scenario D: rue = 5.3%. The building stock expansion is assumed to be proportional to the expected land use/land cover changes in Blantyre, as analysed by Mawenda et al. (2020).

5.3 Discussion of the results

Figures. 10,11, 12, 13, 14, 15 and 16 report the combined scenarios for code-enforcement and urban expansion effects. In detail:

  • Scenario 1/2-A is reported in Fig. 10. Figure 10a shows the evolution of the building stock in Blantyre over the next 30 years. Given that rue = 0%, this scenario assumes no modifications in the number of buildings and results in no difference between Scenario 1-A and Scenario 2-A. The year-by-year NPV aggregated earthquake loss is reported in Fig. 10b. It is observed that UFB-I buildings, which represent a large proportion of the building stock (more than 100 k assets), are the main drivers of the loss. The mean NPV aggregated loss over a 30-year period is equal to 69.0 M$, while the m ± σ uncertainty interval is 48.1 M$ to 91.7 M$.

  • Scenario 1-B is reported in Fig. 11. Figure 11a shows that 2.3% urban expansion means a two-fold increase in the total number of buildings in the 30-year period (from 237 to 444 k buildings). As assumed by the model, the increase is exclusively driven by UFBs as they represent the most adopted construction type for new settlements in Malawi (Kloukinas et al. 2020). In this scenario, UFB-I constructions are considered. The total 30-year NPV aggregated loss estimate is 110.6 M$, which is about 60% higher than Scenario 1/2-A.

  • Scenario 2-B is reported in Fig. 12. The overall increase in the number of buildings remains the same as in Scenario 1-B, but new constructions are code-conforming rather than informal (UFB-C, growing from 0 to 200 k buildings in 30 years). The total NPV aggregated loss equals 72.05 M$, approximately equal to the corresponding value for Scenario 1/2-A. Therefore, for an expansion rate of 2.3%, the benefit of code-enforcement would reflect in ~ 40 M$ loss reduction.

  • Scenario 1-C is reported in Fig. 13. Figure 13a shows that a 4% urban growth results in a three-fold increase in the number of buildings in the 30-year period. The corresponding 30-year NPV aggregated loss (Fig. 13b), which is driven by the UFB-I contribution, is equal to 154.1 M$.

  • Scenario 2-C is reported in Fig. 14. Figure 14b shows the total aggregated NPV loss where the 30-year value is 75.21 M$. This estimate is approximately half of the corresponding no-code enforcement scenario (1-C) (~ 80 M$ loss reduction).

  • Scenario 1-D is reported in Fig. 15. Figure 15a shows that a 5.3% urban growth results in a five-fold increase of Blantyre’s building stock in the 30-year period. The corresponding NPV aggregated loss (Fig. 15b) stands at 197.6 M$.

  • Lastly, Scenario 2-D is reported in Fig. 16. As for the previous scenarios, the code enforcement results in a considerable reduction of the NPV aggregated loss. Figure 16b shows a 30-year loss of 78.38 M$, which is less than half of the corresponding value for Scenario 1-D.

Fig. 10
figure 10

Scenario 1/2-A: a number of buildings versus time, b NPV aggregated loss versus time

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Fig. 11
figure 11

Scenario 1-B: a number of buildings versus time, b NPV aggregated loss versus time

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Fig. 12
figure 12

Scenario 2-B: a number of buildings versus time, b NPV aggregated loss versus time

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Fig. 13
figure 13

Scenario 1-C: a number of buildings versus time, b NPV aggregated loss versus time

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Fig. 14
figure 14

Scenario 2-C: a number of buildings versus time, b NPV aggregated loss versus time

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Fig. 15
figure 15

Scenario 1-D: a number of buildings versus time, b NPV aggregated loss versus time

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Fig. 16
figure 16

Scenario 2-D: a number of buildings versus time, b NPV aggregated loss versus time

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A summary of the 30-year NPV aggregated loss data is displayed in Fig. 17, and the mean values are presented in Table 2. The red-solid line, which collects the no-code enforcement mean results (1-A, 1-B, 1-C, 1-D), displays a nonlinear positive trend for increasing values of rue. The dispersion around the mean value, which propagates from the uncertainties around the vulnerability curves, results in a CoV of about 25%. The black-solid line collects the loss results for the code enforcement scenarios (2-A, 2-B, 2-C, 2-D). In this case, the increase of rue has a negligible effect on the 30-year NPV aggregated loss. This is a direct consequence of the consistently lower EALR of UFB-C with respect to UFB-I. Therefore, in no-code enforcement scenarios, the monetary loss is driven by the existing UFB-I buildings. The confidence interval around the mean curve, represented by the black dotted lines, corresponds to CoV ≈ 45%.

Fig. 17
figure 17

Comparison of the investigated scenarios in terms of 30-year NPV aggregated loss

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Table 2 Comparison of the investigated scenarios
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6 Conclusions

Malawian cities are experiencing rapid urban growth, representing a critical driver of future earthquake risk. To quantitatively assess the crucial role of seismic code enforcement in growing urban centres, this study has investigated a set of potential future expansion scenarios for the city of Blantyre. By looking at the 30-years aggregated loss estimates, it appears that a lack of code enforcement can amplify the seismic loss in the order of 100 M$ (up to 152% increase). In contrast, by ensuring adequate construction detailing of unreinforced masonry buildings, which is the most common construction typology in the country, the aggregated loss would remain almost unaffected by the exposure growth. From an engineering point of view, masonry walls should adhere to building rules on (i) verticality; (ii) maximum height-to-thickness ratio; (iii) maximum unsupported length-to-thickness ratio; (iv) brick layouts; (v) presence of buttresses; (vi) wall-to-wall and wall-to-floor connections; (vii) effective mortar joints. In conclusion, these analyses suggest that investing in code enforcement should be considered a highly effective disaster risk reduction measure as it enables resilient urban development against earthquake risk.