1 Introduction: scope and objectives

Areas in which karst rocks are covered with different types of detrital deposits (soil, alluvial, glacial…) frequently develop alluvial dolines that constitute major hazardous zones because of the intrinsic instability of the sedimentary cover. Mantled karst development involves a complex ensemble of processes, and is controlled by numerous factors. In addition to rock dissolution, processes such as suffosion, plastic flow, brittle fracturing and collapse of the cover, among others, should also be considered (Williams 2003; Waltham et al. 2005; Ford and Williams 2007). Considering the relative influence of such processes, genetic classifications of dolines have been proposed (e.g., Gutiérrez et al. 2014; Parise 2022). Understanding their mechanisms and evolutionary patterns, in order to know the origin and behaviour of alluvial dolines and to assess their hazard, requires interdisciplinary approaches for which multiple map**, exploring and data analysis methods should be adopted (e.g., Margiotta et al. 2012; Zumpano et al. 2019; Jia et al. 2021).

A high increase in risk occurs in regions where karst interferes with anthropic activities (Brinkmann et al. 2008; Kuniansky et al. 2015; Fischer et al. 2018). Northeastern Spain (Fig. 1a) is one of such regions, owing to abundance of dolines (sinkholes) developed on Quaternary sediments overlying Neogene evaporites. In particular, urban zones at the central Ebro basin (Soriano 1992; Soriano and Simón, 1995) and the Calatayud basin (Gutiérrez and Cooper 2002) have historically suffered from their effects.

Fig. 1
figure 1

a Location of the study area (red polygon) within the Ebro Basin, Spain. 1: Paleozoic; 2: Mesozoic; 3: Paleogene; 4: Neogene; 5: Quaternary. Inset: Location within the Iberian Peninsula. b Geomorphological map of the area west of Zaragoza city, with location of the surveyed area. T1 to T4: fluvial terraces; P3 and P4: pediments correlative of T3 and T4, respectively (after Soriano 1990)

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In the surroundings of the Zaragoza city (see location in Fig. 1a, b), former agricultural areas were transformed into residential and industrial areas after filling karst depressions. No special constructive measures were taken for buildings and infrastructures at that moment, and damage on them initiated a few years later: fractures in walls, floors and ceilings of buildings (causing in some cases their almost complete destruction), subsidence or collapse in roads, breaking of water supply systems, etc. (e.g., Soriano and Simón, 1995, 2002; Guerrero et al. 2004; Galve et al. 2009; Gutiérrez et al. 2009; Pueyo-Anchuela et al. 2010b; Soriano et al. 2012).

The recurrent cases of breakage of a water supply pipeline to the Casetas district and the industrial areas west of Zaragoza city prompted the City Council to build an alternative pipe. A study of karst subsidence hazard of the new route was commissioned to our research group, for both overall hazard assessing and identifying the most dangerous segments in order to adopt special construction techniques. A detailed survey was carried out in 1991 (Gracia et al. 1991), in which both natural dolines and damages in the affected industrial district were mapped, and a spatial hazard map was elaborated on the basis of the observed active depressions and the spatial distribution of their controlling factors.

With some variations, that spatial hazard model was later applied to other studies in new areas of urban expansion in Zaragoza city, and its hazard zoning criteria were adopted by the City Council for urban planning in such areas (Simón et al. 1998). The resulting general maps have also served, for more than two decades, as a guide for detailed geotechnical studies carried out by private consultants for the construction of buildings and infrastructures. There is a generally positive perception of the reliability and usefulness of these maps among municipal technicians, private consultants and construction companies. By that time, the authors were optimistic on the possibility of spatial prediction of karst subsidence on the basis of their work (Soriano and Simón, 1995). Since then, however, no objective statistical assessment had been carried out in this respect, and therefore the factual predictive ability of the spatial hazard model have not really been tested.

The 30 years that have passed since the elaboration and the first spatial hazard map offer an excellent time perspective for advancing in two complementary lines: (i) to evaluate the predictive ability of that model, and (ii) to calculate the probabilities of temporal occurrence of karst subsidence in the different zones or categories of the map, and therefore translate this originally susceptibility map into a hazard s.s. map.

The specific objectives of the present work are:

  1. (1)

    Identifying, inventorying and map** karst subsidence damages that were visible in 2021 in the industrial district west of Zaragoza where the first study was carried out, and comparing them with those inventoried in 1991.

  2. (2)

    Comparing the damage occurred during the 1991–2021 period with the previously proposed susceptibility zonation according to an objective protocol.

  3. (3)

    Assessing the predictive ability of the 1991 spatial hazard model with a decades-long perspective.

  4. (4)

    Associating values of temporal probability to the hazard zones.

2 Geological setting

The Ebro basin (Fig. 1a) had an endorheic regime from the Late Eocene to the Late Miocene (Muñoz et al. 2002; García-Castellanos et al. 2003; Arche et al. 2010). The distribution of alluvial fans and freshwater or saline lakes conditioned the sedimentation of clastic, evaporite and carbonate materials (Muñoz et al. 2002; Pardo et al. 2004). The Neogene rocks usually show nearly horizontal bedding, although deformation structures, mostly extensional in origin, are locally present: gentle bending folds, normal faults, and systematic joint sets (Simón, 1989; Simón et al. 1999; Arlegui and Simón, 2001; Arlegui and Soriano 2003).

The Ebro River is the main drainage in the zone. During the Quaternary, a number of terrace and pediment levels have been developed associated to its progressive incision (Soriano 1990; Esnaola and Leyva 1995; Gil Marín et al. 1998; Marqués et al. 1998; Guerrero et al. 2013; Gil 2017). In the central basin, up to ten terrace levels have been identified, with relative height of 220 m to 3 m above the Ebro river (Gil 2017). Their deposits are mainly constituted by fluvial gravels that correspond to braided channels. However, aeolian sands, loess and lacustrine mudstones also exist, indicating a more complex sedimentary setting (Luzón et al. 2008, 2012; Gil et al. 2013; Gil 2017). Carbonate crusts are frequent at the top of most terraces.

Mantled karst has been active since Early Pleistocene time where such Quaternary deposits overlie evaporites, especially at the depocentre of the Neogene basin. In the Zaragoza area, dolines mainly develop on the lowest terrace levels (T1, T2 and T3; Fig. 1b). Curiously, ancient dolines helped to preserve Pleistocene sand dunes and lacustrine muds that otherwise would probably have been dismantled by subsequent floods (Luzón et al. 2008, 2012; Gil et al. 2013; Simón et al. 2014; Soriano et al. 2012, 2019). Alluvial doline development is controlled by: (1) rate of mobilisation of material by groundwater, which may occur by either dissolution of the soluble substratum or suffosion of unconsolidated materials; (2) subsidence mechanisms of the alluvial cover, either slow in the case of unconsolidated materials or sudden collapse in the case of consolidated ones (Beck 1986; Waltham 2005; Williams 2003; Gutiérrez et al. 2014).

3 Previous subsidence hazard studies in the Zaragoza area: overall view

At present, karst subsidence is an active process in the area that causes significant damage and economic losses. Numerous studies carried out in the last decades have attempted to address this problem, using different approaches: doline map**, subsidence monitoring, subsoil exploration by means of geophysical techniques, hazard assessment, etc. (Soriano and Simón, 1995; 2002; Guerrero et al. 2004; Gutiérrez et al. 2005, 2008; Lamelas et al. 2008; Galve et al. 2009; Pueyo-Anchuela et al. 2010a,b, 2015a; Soriano et al. 2012; Sevil et al. 2021).

The above-mentioned recurrent breakage of a water supply pipeline west of Zaragoza (see Sect. 1) was probably the first damage case that prompted the authorities (namely, the City Council) to promote a specific study of karst subsidence susceptibility (Gracia et al. 1991). The proposed susceptibility model, based on both observation of active dolines and spatial analysis of controlling factors, was then refined and formally published by Soriano and Simón (1995). The latter emphasized the role of an empirical algorithm that compiled geological and hydrogeological variables and allowed elaborating susceptibility maps of karst subsidence. The refined model was applied to new districts, and has served for overall urban planning and as a guide for detailed geotechnical studies in housing construction and civil engineering (Simón et al. 1998).

More recent works have further explored the assessment of karst subsidence susceptibility and hazard from other viewpoints. Lamelas et al. (2008) elaborated a probability map using logistic regression, which relate predictor variables to the presence or absence of dolines. Such approach allows increasing the possibility of analysing qualitative and quantitative factors that influence karst and subsidence processes. Galve et al. (2009) elaborated susceptibility maps mostly based on two criteria: (a) proximity to known dolines, assuming the nearest neighbour distance; (b) doline density (% area occupied by dolines), adopting the highest nearest neighbour distance as the radius of a circle centred at each pixel for which the area occupied by dolines is computed.

In addition, monitoring of selected dolines has been carried out by using different techniques. Soriano and Simón (2002) calculated subsidence rates using two data sources: (i) dates of construction and repairing of buildings and pavements, and (ii) monitoring of three dolines during four years by means of high-precision levelling. Correlation between both data types is good, with the resulting subsidence rates ranging from 12 to 110 mm/year. Galve et al. (2015) used Differential Interferometric Synthetic Aperture Radar (DInSAR) techniques as a tool to locate unstable areas, especially in urbanized sectors. Sevil et al. (2021) measured ground deformation, at a doline partially inaccessible, using Terrestrial Laser Scanner (TLS). Although the results are not so good as those obtained with high-precision levelling, this technique could be the most satisfactory in absence of ground control points.

4 Methods

4.1 Conceptual bases and procedures for the 1991 spatial hazard model and hazard map

Since our purpose is comparing damage occurred during the 1991–2021 period with the spatial hazard map proposed in 1991, we should first refer to the methodology used for elaborating that map. This involves sequential acquisition and processing of spatial information, which is illustrated for a small selected area in the maps of Fig. 2 (see also Online Resources 1 and 2 for full view). Exhaustive compilation of documental and field information was carried out, including: (1) technical reports, subsoil data from mechanical drilling, geoelectrical profiles, groundwater wells at a total of 580 points or small sections distributed over an area of 124 km2; (2) four sets of aerial photographs covering the period from 1947 to 1986, which allowed identifying contours of dolines and their variations through time (Fig. 2a, b); (3) geological and geomorphological maps; (4) numerous interviews to people living or working in the area, which allowed checking the presence of dolines and knowing the date and exact location of subsidence or collapse events (especially where the latter were not clearly identified in aerial photographs, owing to small size or anthropic modifications); (5) detailed field survey including observation and map** of both natural dolines and damage in urban and industrial areas (Fig. 2c); (6) laboratory analogue modelling of karst subsidence under different physical conditions; (7) analysis of sections of relict collapses in Pleistocene fluvial terraces (Gracia et al. 1991; Soriano and Simón, 1995).

Fig. 2
figure 2figure 2

Methodological process illustrated by thematic maps of a selected portion of the study area (Polígono Europa). a Aerial photograph taken in 1957. b Doline map elaborated from successive series of aerial photographs (1946, 1957, 1970 and 1986; available from CNIG, Centro Nacional de Información Geográfica, Gobierno de España). c Damages surveyed in 1991, mapped on a 2015 orthoimage (CNIG, PNOA). d Potential susceptibility map elaborated in 1991, based on the spatial hazard index Ht that combines five variables controlling doline occurrence. e Susceptibility map of karst subsidence elaborated in 1991, by synthesizing maps b, c and d. f Damage map elaborated in 2021. Methodological process illustrated by thematic maps of a selected portion of the study area (Polígono Europa). g Damage map 1991 with 5 m buffers around damage sites, and location of survey transects. h Idem for the 2021 damage map. i Idem for the 1991–2021 residual damage map. j Segments of surveyed transects affected by damage in 2021. k Segments of surveyed transects going through 1991–2021 residual damage areas

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All this information was processed for defining spatial distribution of both the dolines and the physical parameters that determine karst susceptibility, according to conceptual and experimental knowledge on genetic mechanisms and evolutionary patterns. On these bases, elaboration of the spatial hazard model by Gracia et al. (1991) followed four steps:

  1. (1)

    Defining spatial distribution of dolines, approached by map** natural karst depressions on four sets of aerial photographs (years 1946, 1957, 1970 and 1986) at scales from 1:18,000 to 1:43,000. As an example, Fig. 2a shows the 1957 aerial photograph, in which anthropic activities had not masked too much the natural landforms. Since the occurrence of visible dolines vary through time, such diachronic analysis is necessary, as recurrently recognized in many studies (e.g., Soriano and Simón, 1995, 2002; Festa et al. 2012; Pueyo-Anchuela et al. 2015b, 2017). In our case, a composite of the four maps (1946, 1957, 1970 and 1986; Fig. 2b) was used for computing the density of dolines, expressed as the number of unit dolines per km2. A unit doline was defined as that with a diameter ranging from 10 to 100 m, which is a realistic standard size in the region.

  2. (2)

    Analysing regional variation of quantitative and qualitative variables (geologic, hydrologic and anthropic) that control doline development (Palmquist 1979; Beck 1986; Lamoreaux and Newton 1986; White et al. 1986; Upchurch and Littlefield 1988; Soriano 1992; Soriano et al. 1994). Maps of the following variables were elaborated from drilling data, geoelectrical profiles, groundwater wells, and geological information: (1) thickness of Quaternary deposits; (2) height of the Neogene-Quaternary boundary; (3) grain size of alluvial cover; (4) lithology and solubility of the Neogene; (5) fracture patterns; (6) geotechnical parameters of the alluvial cover; (7) groundwater-table contours and inferred groundwater flow paths; (8) depth of the water table below the topographic surface; (9) thickness of saturated alluvial cover; (10) maximum annual variation of the water table; (11) sulphate content in groundwater; (12) total solid residuum in groundwater; (13) electrical conductivity.

  3. (3)

    Systematic comparison between digitized versions of maps derived form steps 1 and 2, by using the application Cartographie for Macintosh, a software that at that time could be considered as a simple and innovative "proto-GIS". The optimum combination able to reasonably explain the doline distribution involved variables 1, 2, 3, 10 and 11. Briefly, the data suggest that dolines mostly develop in areas with: (i) low sulphate content in groundwater; (ii) coarse grain size of the alluvial cover; (iii) ‘paleogullies’ able to concentrate groundwater flow at the Neogene-Quaternary boundary; (iv) high annual variation of the water table, and (v) small thickness of the alluvial cover. These five variables were submitted to multivariate analysis in order to weight them adequately and therefore obtain the algorithm that provided the best regression with doline density. A so defined spatial hazard index Ht combining these five variables gives an estimate of the potential (“theoretical”) spatial probability of doline occurrence:

    $$H_{t} \, = \,{85}0 \, / \, (0.{5}S\, + \,{7}0I_{b} \, + \,{5}L\, + \,{2}0T_{Q} {-}{125}V_{w} )$$

where S = sulphate content in groundwater (in ppm), Ib = semiquantitative height index of the Neogene-Quaternary boundary (value ranging from 1 to 5 according to the relative position with respect to ‘paleogully’ topography), L = % of lutite in the alluvial cover, TQ = thickness of the alluvial cover (in m), and Vw = maximum annual height variation of the water table (in m) (Gracia et al. 1991; Simón et al. 1991; Soriano et al. 1994; Soriano and Simón, 1995).

  1. (4)

    Elaboration of susceptibility maps. Spatial distribution of the spatial hazard index Ht results in a potential spatial hazard map (Fig. 2d). The underlying notion of this map is that where the most relevant controlling factors occur, dissolution and dragging of alluvial materials are very likely active in the subsoil. Although their effects on the topographic surface may not yet be apparent, it is probable that in the more or less near future subsidence will occur.

A composite of such potential or “theoretical” spatial hazard map (Fig. 2d) and the evidenced or actual doline map (Fig. 2b, c) gave rise to the final karst subsidence spatial hazard map (Fig. 2e; Gracia et al. 1991). Seven categories were defined for it (their original nomenclature is kept):

Category 1 Very high actual hazard. Urban areas where active, present-day subsidence were evidenced by damage in buildings and pavements. Agricultural areas where active sinkholes were observed in at least two among the four series of aerial photographs.

Category 2 High actual hazard. Areas located either (i) on dolines observed in at least one aerial photograph set, with a 10 to 15-m-wide “safety belt” around them, or (ii) within a 15–30-m-wide belt around zones of Category 1 (current subsidence frequently occurs in the form of small collapses located at the edges of ancient, expanding dolines).

Category 3 High theoretical hazard (Ht > 1.5).

Category 4 Medium theoretical hazard (1.5 ≥ Ht > 1.3).

Category 5a Medium–Low theoretical hazard (1.3 ≥ Ht > 1.15).

Category 5b Low theoretical hazard (1.15 ≥ Ht > 1.0).

Category 6 Very low theoretical hazard (Ht ≤ 1.0).

4.2 The 2021 survey and data processing

The new survey achieved in January 2021 has mainly consisted, as that in 1991, in detailed observation and map** of damage in buildings and pavements of the industrial district west of Zaragoza. A systematic survey was made along 101 transects with a total length of 28,566 m (see example in Fig. 2g,h,i; complete transects in Fig. 3), in which cracks and shear bands in building walls, floors and ceilings, as well as subsidence signs in pavements, were carefully and exhaustively inventoried (Fig. 2f). The whole information was georeferenced and processed using a Geographic Information System managed in QGis software, in which previous maps generated during the 1991 research (those depicted in Fig. 2) were also incorporated.

Fig. 3
figure 3

Detailed damage map of the entire study area from the 2021 survey (with 5 m buffers)

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Maps of damage reported in 1991 and 2021 for the selected example area are shown in Fig. 2c, f, respectively. Such dual spatial information gives rise to a “residual map” of new damage occurred between 1991 and 2021. For integrating them, both maps should adopt a standardized format able to be submitted to an objective, quantified comparison procedure. The standardization adopted is based on applying a buffer with a 5 m radius around each damage sign (Fig. 2g, h), such buffer working as a “pixel” or minimum damage unit for data processing. Such assumption is realistic seeing at the actual size of surficial karst effects and the response of buildings: (i) the standard diameter of new visible dolines in urbanized areas is usually in the range of 5–10 m; (ii) the minimum horizontal portion of a wall or pavement affected at each single damage site also approaches such length. Both Fig. 2g, h depict the trace of transects surveyed in 2021, which in the case of the 1991 represent “virtual transects” that allow comparison of both data layers.

The 1991–2021 residual damage map has been automatically obtained in QGis by addition of damage buffer maps of 1991 and 2021, then subtraction of that of 1991 (Fig. 2i). Intersection of the selected transects with damage buffers in the 2021 damage map (thick segments in Fig. 2j) provides the fraction of each transect affected by karst subsidence at present. Intersection with damage buffers in the residual map (thick segments in Fig. 2k) provides the fraction affected by new karst subsidence propagating during the period 1991–2021. From both spatial damage scenarios, the total accumulated percentage within each zone of the 1991 susceptibility map (category areas in Fig. 2e) will approach the predictive capability of the model: our hypothesis is that such percentages will be systematically and significantly greater for zones with a high-level subsidence susceptibility.

5 Results

5.1 Results of the 2021 survey

The complete results of the field survey carried out in January 2021 are depicted in the map of Fig. 3 (see also Online Resource 3 for full view). As made for the survey carried out in 1991, the following individual damage signs observed in buildings and pavements are represented: (i) tilting of buildings; (ii) cracks in pavements and walls with indication of sinking direction; (iii) visible subsidence in pavements and natural soils, with schematic contours of sinking zones and directions of maximum slope; (iv) vertical and horizontal cracks in walls; (v) subsidence centres, either observed or inferred. Buffers with radius = 5 m around each damage sign, as well as traces of the surveyed transects are also depicted. Several examples of such deformation types in the surveyed industrial area are shown in Fig. 4. Distribution of damage in 2021 does not significantly differ from that in 1991 (see Online Resource 1, map 1.4, and Online Resource 3, map 3.2, for overall comparison), although its density has increased in many zones. Intersection of the surveyed transects with 2021 damage areas in the buffer map of Fig. 3 indicates that 20,1% of the total surveyed length is affected (5,747 m of 28,563 m; see Table 1). This percentage is about twice that obtained for the 1991 damage map (10.2%, 2,903 m of 28,563 m). Higher damage degrees are mainly reported in the central sector of the study area (Fig. 3; Online Resource 3, map 3.2). Only two sectors, La Torre Outlet and Polígono Portazgo, show a lower degree of damage than that observed in 1991. Nevertheless, it should be taken into account that a great part of those areas have been remodelled during the last decade (including demolition of an old factory, re-urbanization, and building of the new commercial centre La Torre Outlet), so that any vestige of previous damage has been obliterated.

Fig. 4
figure 4

Examples of deformation types inventoried in the study area. a Visible subsidence centre in pavement with concentric cracks. b Tilted building. c Oblique cracks in a wall, indicating a subsidence centre to the right. d Open expansion joint. e Tilted pavement and wall. f Cracks in a road

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Table 1 Overall computation of damage share among zones of the 1991 susceptibility map: percentages of transects intersecting damage areas in 1991, 2021, and residual damage 1991–2021
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5.2 Residual map of damage occurred between 1991 and 2021

After adding the damage buffer maps of 1991 and 2021, and then subtracting that of 1991), the residual damage map 1991–2021 has been obtained (see example for the selected zone in Fig. 2i; full map in Online Resource 3, 3.3). It shows how new damage zones developed between 1991 and 2021 are mainly clustered in the central sector (Polígono Europa) and, to a lesser extent, in the NW and SE sectors (Polígono Ruiseñores-El Olivar and Portazgo, respectively). Such areas highly coincide with those damaged before 1991. Intersection of the surveyed transects with damage areas in this residual map indicates that a 14,5% of the total surveyed length has undergone new karst subsidence during the 1991–2021 period (Table 2).

Table 2 Comparison, within each susceptibility zone, between the accumulated length of damage buffers and the total length of the surveyed transects
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5.3 Comparison of the 2021 damage map with the 1991 susceptibility map

Comparison of the damage map elaborated from the 2021 survey with the 1991 susceptibility map allows assessing the overall predictive capability of the latter. Table 1 provides a first approach. It shows the absolute length of transects affected by (i) damage in 1991, (ii) damage in 2021, and (iii) residual damage 1991–2021, and how they are shared among the distinct zones of the 1991 susceptibility map. The same information is graphically depicted in Fig. 5. Nevertheless, such share itself is not significant on its own, since the surfaces occupied by the susceptibility zones are not uniform in size.

Fig. 5
figure 5

Percentages of transects going through damaged areas, shared among zones of the 1991 susceptibility map. Damaged areas observed in 1991 and 2021, and newly damaged areas (inferred from residual damage map 1991–2021) are distinguished

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The key task is computing, within each zone, the accumulated length of damage buffers and comparing it with the total length of the surveyed transects. The results are synthesized in Fig. 6 and Table 2. It can be seen how such percentage systematically increases from Category 5b (low potential or “theoretical” hazard; 7.7% of transect length affected by karst subsidence damage) to Category 1 (very high evidenced hazard; 38.0% affected).

Fig. 6
figure 6

Histograms computing, within each susceptibility zone, the accumulated length of damage buffers and its percentage with respect to the total length of the surveyed transects. a Transects going through 1991 damaged areas. b Idem 2021. c Idem for the newly damaged areas (residual 2021–1991 map). The curve shows how the percentage of damage systematically increases from zones of Category 5b (low potential hazard) up to zones of Category 1 (very high evidenced hazard)

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5.4 Comparison of the residual 1991–2021 damage map with the 1991 susceptibility map

Comparison of the residual 1991–2021 damage map with the 1991 susceptibility map, in the same way as in Sect. 5.3, allows assessing the predictive ability of the model specifically for the zones not damaged prior to 1991. The results are synthesized in the same Fig. 6 and Table 2. It can be seen how such percentage also increases systematically between Category 5b (low potential hazard; 7.7% of transect length affected by karst subsidence damage) up to zones of Category 1 (very high evidenced hazard; 19.4% affected).

6 Interpretation and discussion

The results obtained are clear in quantitative terms, but require critical discussion in order to assess their significance. The percentages of transects affected by damage within the different hazard zones can be considered as a suitable approach to the probability of occurrence of new damage. The 1991 hazard model is obviously not deterministic: the maximum hazard zones cannot be expected to have a 100% probability of being damaged within a certain time period (determinable or not); neither can the minimum hazard zones be completely safe from damage.

If we focus on areas that had no deformation before 1991 (residual 1991–2021 damage map), our results indicate that very high hazard areas would have around 20% of probability of damage in a 30-years period, while low hazard areas only have 7%. The difference may not seem too conspicuous, but it is quite significant for optimizing any urban planning that aims to rigorously assess the economic costs that damage due to karst subsidence could cause.

This estimate represents only a minimum for the hypothetical occurrence of deformation. It should be assumed that, between 1991 and 2021, considerable damage would have occurred as a continuation of that already existing in 1991. With the methodology used, it has not been possible to quantitatively evaluate this damage or to differentiate it from the pre-1991 deformation, since our maps of spatial distribution only take into account the occurrence of damage, but not its intensity. For computing the latter, we should have measured, during both the 1991 and the 2021 campaigns, e.g., the width of fissures or the dip of tilted pavements. By carrying out the subtraction (damage recorded in 2021) –(damage recorded in 1991) in GIS, we implicitly assume that the damage currently observed at a given point where damage was reported in 1991 already existed entirely in that year. Therefore, they are not computed as damage for the 1991–2021 period, even though they may have actually continued to progress after 1991. If it would be effectively computed within the 1991–2021 period, the adjustment and significance of the results would probably be much better.

Since our field observations do not allow discriminating, within the areas already damaged in 1991, those that have continued to be damaged after that year, we can adopt another extreme scenario for probability estimation: in all these damaged areas, we can suppose that karstic subsidence and deformation have persisted after 1991. Within this scenario, the 2021 damage map would provide an approximation to the maximum probability of damage occurrence in a 30-year period: 38% for areas of Category 1, while only 7.7% for areas of Category 5b.

Accepting that both options represent extreme scenarios, the most realistic probability is represented by the range between them: it can be estimated that the very high hazard areas in our 1991 hazard map (Category 1) have an approximate probability between 19 and 38% of suffering damage from karst subsidence within a 30-year period, and that the probability systematically decreases as the hazard level decreases, until reaching about 8% for the low hazard areas (Category 5b).

On the other hand, the results allow approaching a comparison between the probability of damage up to 1991 (about 20 years since the development of the industrial district) and the new damage recorded between 1991 and 2021 (30 years). Although the incremental deformation of that recorded in 1991 is not computed, our results indicate that, in that first period, deformation affected ca.10% of the land urbanized in the early 1970s (10.2% of the total length of the surveyed transects), while in the following 30 years it spread to another ca.15% (computed in 14.6% of the surveyed transects) and continued in an undetermined portion of the area already affected. Seeing at the duration of both periods (~ 20 and 30 years, respectively), we can therefore infer that the rate of occurrence of new damage has remained quite uniform: ~ 0.51 and 0.48% of new damaged areas per year, respectively.

Such virtual persistence of the deformation rate allows translating our numerical results (i.e., percentages of damage occurrence during the 30-year period) into approximate annual probability of damage for each hazard one: from 0.6–1.3% for Category 1, to 0.3% for Category 5b (Table 3).

Table 3 Interpretative, approximate temporal probability of damage due to karst subsidence within each hazard zone (30-year and annual probability)
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A factor that has probably contributed to the fit between the predictions of our 1991 spatial hazard model and the distribution of new damaged areas is the safety belt that was defined around each historic doline. Such belts, regardless of whether or not they showed damage to the walls and pavements of the industrial area in 1991, were included in the category of high actual hazard zones (Category 2). The evolutionary tendency of alluvial sinkholes to enlarge through the appearance of small coalescent collapses on their periphery (Soriano and Simón, 1995; Simón et al. 2008; Galve et al. 2015; Pueyo-Anchuela et al. 2013, 2017) results in a particular concentration of new damage close to the doline edges. Good examples are located in the Polígono Europa and the former Polígono Pikolín (present-day La Torre Outlet) (Fig. 7). Other examples are provided by recent cases of buildings that have been seriously damaged precisely within those safety belts (Gutiérrez et al. 2009; Pueyo- Anchuela et al. 2012; Sevil et al. 2020). The tendency to widen the limits of the subsidence areas has also been recognized in Pleistocene dolines (Soriano et al. 2019).

Fig. 7
figure 7

Detailed maps showing clustering of recent and present-day damage at the edges of historical dolines. a Polígono Europa. b Former Polígono Pikolín, present-day La Torre Outlet (modified from Simón et al. 2008)

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The relevance of having defined these safety belts, and their successful predictive ability, is supported by statistics. In 1991, such Category 2 areas showed damage in only 3.6% of transects. This result is logical considering that they were adjacent to areas that did suffer massive damage, but showed little damage themselves (otherwise they would have been included in Category 1). In the 2021 survey, this percentage has increased up to 15.5%, becoming of the same order as in Category 1 areas (20.4%).

7 Conclusions

About 10% of the industrial area west of Zaragoza city, urbanized in the early 1970s, had been affected in 1991 by damage derived from karst subsidence. In the following 30 years, damage spread to another ~ 15% of that area, and continued in an undetermined portion already affected. The rate of occurrence of new damage has remained quite uniform around 0.5% in area per year.

Comparing the present-day (year 2021) map of zones damaged by karstic processes with the susceptibility map elaborated in 1991, we can conclude that the predictive ability of the latter is good in general. The total percentage of area currently damaged within each hazard category systematically increases from zones of Category 5 (very low hazard level; 7.4%) up to those of Category 1 (very high hazard level; 39.5%). A similar pattern is found for the residual damage map (damaged areas in 2021 minus damaged areas in 1991): 7.4% for Category 5 increasing up to 20.4% for Category 1. Therefore, the model shows the same predictive ability specifically for the zones not damaged prior to 1991.

Both comparative exercises imply end-member scenarios for damage computation: (i) that based on the present-day map would involve the assumption that the entire damage mapped in 2021 has been in progress between 1991 and 2021 (i.e. every deformation observed in 1991 has continued to be active in the following years); (ii) computation based on the residual map assumes that damage currently observed in walls or pavements already deformed in 1991 existed entirely in that year (i.e. tilting or cracks have not progressed in the following 30 years). Both scenarios represent hypotheses of maximum and minimum damage occurrence, respectively, for the 1991–2021 period. The actual occurrence should be within the range defined by both end-members; we therefore infer that the areas of highest subsidence hazard in our 1991 hazard map (Category 1) have an approximate probability between 19 and 38% of suffering damage over a 30-year period (annual probability ~ 0.6–1.3%), and that the former systematically decreases as the hazard level decreases, until reaching about 8% for the lowest hazard areas (Category 5; annual probability ~ 0.3%),). The difference is quite significant, and it should be seriously considered for optimizing urban or industrial planning in the Zaragoza area, and hence minimizing the economic costs derived from karst subsidence.

Safety belts that were defined around the historic dolines and classified as high actual hazard zones (Category 2) in our 1991 hazard map have contributed to the predictive ability of the latter. They represent a useful tool for assessing the probability of future ground subsidence, as demonstrated by recent cases of buildings that have been damaged within those belts indeed.