1 Introduction

The catastrophic collapse of residual soil covers overlaying solution cavities in karstic limestone areas constitutes a serious geological hazard around the world (Beck and Sinclair 1986, Waltham 1989, Waltham et al. 2005). It is a well known phenomenon related to the occurrence of underground solution cavities in limestone, dolomite and gypsum terrains (Klimchouk (2000)). It is a challenge for land use planners and engineers as it affects seriously the foundations stability and performance. In urban areas, generally the sudden collapse causes damages to properties, infrastructures, and even lives. This research work deals with the problem of karst sinkhole collapse occurring in the last few years in Cheria area in NE Algeria. The first event resulted in a crater of more than 50 m, in diameter; it occurs in a non populated locality called Douamis. This first event has caused no damage to properties or human lives and so did not receive any attention from the local authorities. Recently on the 29th February 2009 at 03 a.m. a spectacular sinkhole collapsed with an elongated form of about 10–15 m large and more than a 100 m long, occurs in the center of the town of Cheria. This later event has caused severe damage to several houses, roads, water main supply, and sewages. It has caused a widespread panic among the population mainly those living too close to the crater. This time, as the phenomenon starts to affect the security and the economy of the population, the local authorities have become very aware about the danger threatening several tens of thousands of peoples. The collapse is due to a sudden rupture of the roof of a large underground karst cavity. Karst cavities are in fact widespread in the Eocene limestone forming the upper formation under the Quaternary cover in the Cheria syncline.

The problem of sinkhole collapse has been approached from several points of view. To name few, Waltham and Swift (2004) studied the stability of underground cavities under imposed loading. Modeling of collapse conditions of cavities has been carried out by Goodings and Abdulla (2002), Kaufmann and Quinif (2002) mapped the occurrence of karst cavities as a natural hazard and Yang and Drumm (2002) have studied the karst cavities as a hydrogeological hazard. In this study, it is mainly dealt with the problem of underground exploration for cavities and their stability. Site investigation procedure has been carried out using different techniques such as on site geological survey, mechanical drilling, and resistivity survey. Ground penetrating radar (GPR) has not been used as it does not give reliable results in clayey covered terrain (Mio-Plio-Quaternary filling deposit covering Eocene limestone contains clay layers) (Roth et al. 2002).

Local authorities and residents are aware about the fact that every structure in the area could well be build totally or partially on a potentially collapsible void. The extension plans of the area could no more be established without a thorough knowledge of the underground conditions including the occurrence, depth, geometry and dimensions of the karst cavities.

2 General Setting

Cheria basin which takes the name of the village located in its center is located to a 50 km to the SW of Tebessa city. It is a wide plateau of a triangular shape with an area of around 800 km2. The altitudes vary from 1,050 to 1,500 m (Fig. 1).

Fig. 1
figure 1

Location of the study area

Full size image

From a geological point of view, the studied area is a syncline structure oriented 30° to the North. It has been studied by several authors among the first stand (Durozoy et Lamber 1947). Cheria syncline consists of a stratigraphic succession of more than 1,000 m thick. Triassic, Cretaceous and Eocene constitute the main formations. The later occupy more than 80 %, the resting 20 % are composed of the Mio-Plio and Quaternary filling deposits (Chaffai et al. 1986). In its central part, Eocene limestone is intensively fractured and karstified and covered by a mantle of varying thickness constituted of a mixture of gravel sand, clays and limestone crusts. Eocene limestone outcrop in the centre of the basin and form small troughs on either side. These latter are covered by the aforementioned recent detrital materials.

The basin is dissected by two major sets of fractures trending NE–SW and NW–SE cut by a sub-orthogonal third set of N–S direction. The drainage pattern in the basin is highly controlled by these sets of fractures. It appears from a first glance at the air photographs that the distribution of karst.

From a hydrogeological point of view, Eocene limestone formation constitutes the most extensive aquifer in Cheria basin. The perennial water availability in the study area is related to the great potential of Eocene limestone aquifer. The marly-limestone bedrock (Maestrichtian) forms the lower boundary of the groundwater reservoir (Fig. 2). The thickness of the Eocene limestone aquifer increases towards the central part of the basin (Chaffai et al. 1986). The alluvial aquifer is not appreciably used for drinking water, as it used to be, because of its relatively poor quality acquired recently by agriculture, domestic and industrial pollutants. Compared to the Eocene aquifer, this later remains of limited extent and thus limited reserves. The general flow direction for both Eocene and Quaternary aquifers is from the north to the south guided most of the time by the fractures and the morphology (Fig. 3).

Fig. 2
figure 2

Geological cross section of the studied region

Full size image
Fig. 3
figure 3

Boundary condition map for the study area

Full size image

Karst processes are one of the most important post sedimentary factors that contribute to landscape evolution in the studied area. Unfortunately most of the Eocene limestone of Cheria area is covered by Quaternary deposits, which do not allow karst features (sinkholes, pineacles, cavities etc.) to be apparent. Nevertheless, at Youkous valley, which is not far from the study site and located at the northern periphery of the basin, karst features such as shafts, pinnacles and cavities are well exposed.

The karst underground cavities are generated by the dissolution of carbonates by the action of water and CO2. The flow of water with dissolved CO2 through preexistent fissures and cracks dissolve limestone and widens discontinuities with time. Stringfield and Rapp (1976), Ford and Williams (1989), Klimchouk (2000) have shown that over a period of 100,000 years small cracks could be widen to several meters across. The created voids evolve later by upward migration and acquire a round or dome like shape.

The stability of the resulting voids depends primarily on the cohesive or non-cohesive behavior of the roof materials. The collapse or dragging down of the overlying Quaternary cover happens when the capping material loses its integrity either by a flexural failure of just by the upward migration of the roof (Fig. 4).

Fig. 4
figure 4

Photography’s of collapses in Cheria basin

Full size image

Seasonal oscillations of the water table are also an important factor in the processes of Karstic cavity formation and growth (Hall and Metcalfe 1984; Roje-Bonacci 1997; Tharp 1999). Because of this dissolution and collapse, outcrops of palaeocollapse features that vary in size and morphology appear dispersed in the basin (Baali 2007). The recognized karst processes are both syn-sedimentary and post-sedimentary with the Quaternary deposits.

3 Characteristics of the Cheria Sinkholes

Sinkhole collapse is a well-known phenomenon in Cheria area, NE Algeria (Fig. 1). It has been reported that during the last century small diameter sinkholes appear from time to time in Cheria area without making any harm to people or infrastructures. They were not considered as a challenge to security or safety and so they were not of some concern to population or of local authorities.

The water level was then close to the surface, mainly in the southern part of the basin. The wells drilled for underground water extraction show that voids were encountered at a depth between 1 and 50 m. The voids vary in height, between 1 m to several meters throughout the area. In recent years, two large events of cover collapse sinkholes were recorded. The first event resulted in a crater of more than 50 m, in diameter, occurs in a non-populated locality called Douamis (Fig. 4). This first event has caused no damage and did not receive any attention from the local authorities. Recently on 29 February 2009 at 03 a.m., a spectacular sinkhole collapsed with a diameter of more than a hundred meters in the center of the town of Cheria, Harkat Bouziane Avenue (Fig. 4). This later event has caused severe damage to several houses, roads, water main supply and sewages. It has caused a widespread panic among the population mainly those living too close to the crater. This time, as the phenomenon starts to affect the security and the economy of the population, the local authorities have become aware about the danger threatening several 10,000 of peoples. The collapse is due to a sudden rupture of the roof of a large underground karst cavity.

4 Site Investigation

Site investigation is carried out by several techniques, geological map, aerial photos, field survey; geophysical techniques etc. Aerial photographs did not show any hint that lead to cavity detection. In our opinion, aerial photographs are not very helpful because of the cyclic use of the land; every time the land is worked, traces of small subsidence is erased so they cannot be seen on photographs (Kaufmann and Quinif 2002). The consultation of the ANRH (Agence Nationale des Ressources Hydrauliques) archive show that on all wells dug in the area, for water extraction, voids were encountered at depths varying between 1 and 50 m. Falls of drilling tools and total loss of the mud during the drilling process were reported by the drillers. The falls, which corresponds, to the height of the caverns varies from less than a meter to few meters (Table 1). The drilling logs show that cavities and fractures occur at the same horizon. Fractures are more frequent and occur above and below the cavities. Eocene limestones are affected by fractures and cavities in more than one level as shown on logs. On the other hand, pictures obtained by a down the hole camera (Fig. 5) has shown that the limestone is highly karstified up to a depth of 50 meters. The size of the voids decreases in size as we go deeper. Dissolution features such as voids and cavernous looking rocks occurs frequently on preexisting fissures. Small blocks and stones with a chalky appearance could also be seen. Further down, the volume of the voids decreases and become more related to the layers boundary. Dissolution features are of few centimeters wide stretched horizontally between layers.

Table 1 Eocene limestone logs description according to Gaud. DHW-Tébessa 1978
Full size table
Fig. 5
figure 5

Photography’s of cavities obtained by a down the hole camera at varying depths (46.6 and 55 m) in Cheria basin

Full size image

Multielectrode resistivity testing was also conducted using a dipole–dipole electrode array. The concepts of electrical imaging are well described in the geophysical literature (LaBrecque et al. 1996). Resistivity measurements are made for a large number of sets of four electrodes. Given these measurements, it is possible to solve numerically for a resistivity distribution that results in a set of calculated resistivity measurements that best fits with the measured response.

The array is widely used in resistivity and induced-polarization surveys, because of the low electromagnetic coupling between the current and potential circuits. Furthermore, this array is very sensitive to horizontal changes in resistivity. Hence it is good at mapping vertical structures such as dikes and cavities.

Two electric parallel profiles of 60 m long each and 10 m apart were carried out. The electrode spacing for these lines was 4 m. The length of the scan line was chosen on the basis of the space available in the town and the supposed dimension of the cavities. Resistivity profiles were created through an inversion process and were used for characterization of the subsurface. The inversion process is discussed in de Groot-Hedlin and Constable (1990) and Loke and Barker (1996). The resulting profiles illustrate trends in resistivity that may be interpreted to represent subsurface features of interest. Abrupt changes in resistivity are smoothed during the inversion process. Resistivity profiles obtained at the site typically showed an irregular surface at the contrast between low- and high-resistivity materials. Subsurface anomalies of high and low resistivity were also observed. The results obtained were compared to the log supplied by the LTPE (Laboratoire de Travaux Publique Est) as part of the site investigation procedure. The electric tomography cross sections show a good fit with the boring logs. High resistivity regions coincide well with voids (Fig. 6). Whereas, low resistivity zones which show, in 2D, a sub circular like shape correspond to paleocollapse features (Lamont-Black et al. 2002) They are mainly formed by fine unconsolidated moist filling materials. Fehdi et al. (2011) using the same technique have shown, at Douamis locality, that borings and 2D resistivity tomography were in a good agreement, they both show that underground void occurs at 2–6 m underground.

Fig. 6
figure 6

The result of 2D inversion of dipole–dipole electrode array data from the study area

Full size image

5 Stability Analysis of Karst Cavities

Several authors have studied the condition of stability of underground cavities in natural and man made cavities. Abdullah and Goodings (1996, 2002) have used geotechnical centrifuge to replicate full-scale sinkhole development over underground cavities in weakly cemented sandstone. He showed that when the ratio of roof thickness (T) to cavity width (W) is less than 0.25, failure occurs. While When T/W was greater than or equal to 0.31 a stable arch is formed and the roof is stable. Waltham and Swift (2004) used plaster scale models and Finite Element models (FEM), in order to simulate failure mechanisms and ultimate failure loads. Insitu testing was carried out using full-scale test, where a cavity roof in Triassic sandstone was loaded to failure in Nottingham (Waltham and Swift 2004). This experiment was then used to validate the numerical results obtained considering material of the same properties as Nottingham sandstone using Flac 2D (L. Zhengxin). Several other authors such as Davis et al. (1980), Tharp (1999) and have used with success the limit analysis technique to study the stability of underground openings in an undrained state.

The effect of underground water fluctuation is also of a paramount importance. Sowers (1975) described the occurrence of two large sinkholes after 3 days of pumping. In Florida, Benson and La Fountain (1984), Currin and Barfus (1989) reported that sinkhole frequency increases during spring dry season. The reason is more probably the lowering of the water table. It is in part due to the loss of the buoyant support as a result of water table lowering. They also occur as a result of rainfalls that come after prolonged period of draught. The reason this time is the downward, force induced by the percolating water. Passage of heavy vehicle, explosives from neighboring quarries and imposed loading on the roof cavity are also a common cause of sinkhole collapse Gertje and Jeriminas (1989); usually the collapse occurs days or weeks later.

In this study, the stability assessment is carried out using Falc 2D software and considering karst cavities with varying dimensions. The reason is that in Cheria area, underground cavities exist in varying dimensions, from one meter to more than 50 m across. They also occur at a depth of less than a meter to several tens of meters with varying rock mass properties. Hence, cavity width and roof thickness are varied in order to model all the possible scenarios. For rock properties, Young Modulus (E), Poisson Ratio (μ), Uniaxial Compressive Strength (UCS), Uniaxial Tensile Strength (UTS), Rock Density, and Shear Strength, expressed as Cohesion (c) and Friction Angle (ϕ) were determined. The Rock Mass Rating (RMR) (Bieniawski 1973) was also determined as we are dealing with rock mass. The RMR is used to account for rock mass properties rather than intact rock properties. The available data were based upon laboratory and full-scale tests. Table 2 shows the initial mechanical properties assumed for modeling.

Table 2 Measured mechanical properties of the Eocene limestone
Full size table

6 Results and Discussion

In this study the above intact rock, strength parameters are kept fixe throughout the modeling procedure. The RMR is however, varied according to the local rock discontinuity conditions.

In the FLAC 2D software, the geometry model is set first with the appropriate boundary conditions. Then material properties and material model are specified. The failure criteria used is the Mohr–Coulomb fitted to the studied rock mass by way of it’s RMR to obtain a rock mass failure envelope (Bieniawski 1976).

The geometry model consists of a rectangular cavity located at a depth (D) with a roof thickness (T). The roof thickness, the cavity width, the imposed load and the RMR are varied in order to assess the influence of every parameter on the overall stability of the cavity. The modeling results show that for a given RMR and a cavity width the resistance to failure increases as the roof thickness increases (Fig. 7). When the roof thickness, the imposed load and the cavity width are kept fixe the resistance to failure increases as the RMR increases. For instance, a 6 m wide cavity with a roof thickness of 2 m, the resistance to failure increases from 4 MPa when RMR equals 20, to 10 MPa when RMR becomes 40 (Fig. 7).

Fig. 7
figure 7

Graphs showing the relationship between imposed loading and the critical roof thickness for different values of RMR

Full size image

The results also show that when the imposed load, 1 MPa, and the RMR are kept fix (Fig. 8), the relationship between cavity width and roof thickness, at failure, is of a linear form. For an RMR of 40, the ratio of roof thickness to cavity width is about 0.30. This ration is of almost 0.40 for an RMR of 30 and around 0.75 for RMR = 20 (Fig. 8). It can be easily seen that in the case of Cheria Eocene limestone where RMR is 40, an underground cavity can be considered stable if the ratio of the roof thickness to the cavity width is above 0.30 under an imposed load of 1 MPa (10 tones over an area of 1 m2).

Fig. 8
figure 8

Graphs showing the relationship between roof thickness and width of the cavity for different values of RMR

Full size image

For a cavity with a varying width and a constant RMR the roof displays more resistance to failure as it thickens. At the onset of failure (Fig. 8) shows that as the cavity width increases roof thickness also increases in a linear fashion. The same relationship remains applicable for all the assumed RMR values covered by this study. The Douamis cover collapse sinkhole with a diameter of around 50 m display visually a thickness of more than 8 m. The W/T ratio is then about 0.16. For the city center sinkhole, the W/T ration is approximately 0.2. Both of these ratios occur on the unsafe side (under the curve) of the critical line.

It has been reported that ground water fluctuation causes sinkhole to form in karst environment. The principal mechanism of water effect lies in the lake of buoyancy as water table drops. The pressure caused by moving water, towards the cavity as a result of drawdown or rainfall also contributes significantly to failure. The effect of ground water fluctuation is modeled in this study; the results show that when the piezometric head decreases rapidly from a level above the cavity roof to another below it, failure occurs (Fig. 9).

Fig. 9
figure 9

The influence of groundwater fluctuation on the stability of an underground cavity. a Cavity is dry, in this phase the vertical displacement had not approach to the boundary of failure, b cavity is submerged in this phase the vertical displacement disappeared and the stability is reinforced, c water table is under the roof of the cavity and the vertical displacement appear widely but had not approach to the boundary of failure, d cavity is emerged (water table is decreased under the cavity floor), in this phase failure occur.

Full size image

7 Conclusion

The results presented in this paper illustrate that resistivity survey is a geophysical method well suited for the detection and mapping of sinkholes in karstic areas. The dipole–dipole resistivity and the processing of the gathered data to obtain underground tomography conducted here have proved to be a powerful mapping tool for the subsurface conditions of the complex geometry of the karstic areas.

Geological study and borehole drilling were of a big support to geophysical techniques in locating underground cavities as well as in the assessment their depth, geometry, dimensions, etc.

It has been found that under an imposed loading, the stability of the karst cavities depends on the geo-mechanical parameters (RMR, GSI, and E) of the host rock as well as the depth and dimensions of the gallery. It increases with RMR, GSI, E and depth and decreases as the cavity becomes wider. The calculation results shows that a ratio (roof thickness to gallery width) of 0.2 and more indicate a stable conditions. The two collapsed sinkholes, the one at Douamis and the other at the city center have W/T ratios of 0.16 and 0.2, respectively.

The results obtained in this work constitute a road map for the identification of the underground karst cavities and the assessment of their stability. The localization of the underground cavities with the electric tomography method throughout the area and the use of the W/T stability diagrams one can locate the stable and the unstable cavities. This processes lead directly to the establishment of a sinkhole collapse hazard map. The establishment of a hazard map is not the scope of the present paper.