Mo P 14 Resistivity Modeling of Sinkholes Effects Caused by Karst and Suffosion

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1 Mo P 14 Resistivity Modeling of Sinkholes Effects Caused by Karst and Suffosion P. Cuevas Castellanos (Universidad Autónoma de Nuevo León Facultad de Cie), V.A. Shevnin* (Moscow State University), K.V. Krivosheya (Universidad Autónoma de Nuevo León), A.M. Pavlova (Moscow state university), A.A. Ryjov (VSEGINGEO) & A.A. Bobachev (Moscow state university) SUMMARY Sinkholes caused by two different processes of karst and suffosion have some similarity and both create damages in cities, settlements and single houses in rural areas. Not once the problem was set to give forecast of sinkholes before their output on the earth surface. The authors with the help of mathematical modeling of anomalous effect above vertical cylinder and similar models tried to estimate possibilities of resistivity methods for forecast of dangerous underground sinkholes before their collapse.

Introduction Sinkholes caused by two different processes of karst and suffosion have some similarity and both create damages in cities, settlements and single houses in rural areas.

The authors with mathematical resistivity modeling tried estimating possibilities of resistivity method in forecast of sinkholes before appearance openings on the earth surface using vertical

$; б) rocks permeability arising mainly from tectonic fracturing; в) active movement of groundwater, dissolving rocks and transporting products of dissolution.$

2 Introduction Sinkholes caused by two different processes of karst and suffosion have some similarity and both create damages in cities, settlements and single houses in rural areas. Forecast of sinkholes until now is not successful. The authors with mathematical resistivity modeling tried estimating possibilities of resistivity method in forecast of sinkholes before appearance openings on the earth surface using vertical cylinder with high resistivity and similar models. More than 1/3 part of the earth surface is covered by rocks subjected to karst phenomena. For karst origin three conditions are necessary: а) soluble rocks, like gypsum, anhydrite, limestone, rock-salt, etc.; б) rocks permeability arising mainly from tectonic fracturing; в) active movement of groundwater, dissolving rocks and transporting products of dissolution. Suffosion (from Latin term suffosio) - means removal of small mineral particles by water in the filtration process. Suffosion is mainly physical process, while karst is chemical process of dissolution [Ogilvi, 1990]. In carbonate and gypsum sandy-clayish rock karst and suffosion can appear simultaneously and is called clayey karst or clayey pseudo-karst. For creation underground cavities sinkholes three conditions are necessary: 1. Rocks subjected to destruction (chemically or physically). 2. Groundwater movement. 3. Evacuation of destruction products. Figure 1 Two sinkholes in Guatemala-city have the depth 0 m. Distance between them is about 1. km. Karst and suffosion sinkholes are found in many regions on the Earth. Such sinkholes are known in Moscow, in Perm region in Russia, in Mexico and Mexico-city, in Guatemala-city (these events were incentive of this work). Investigations in Guatemala-city were performed by UNAM (Mexico) under leadership of Gerardo Cifuentes Nava (UNAM, Mexico) [Zúñiga-Lara et al., 2011] with participation of the UANL student P. Cuevas Castellanos. Authors do not know cases of successful forecast of sinkholes with geophysics before their collapse. Simplified static model of buried sinkhole Simplified mechanical model of cavity can be presented as vertical cylinder (cavity) with cupola. Cavity can grow below cupola upward (Figure 2) until the moment of collapse. Figure 2 Model of cavity begins from small volume below and grows sideways and upward. Figure 3 Growing sinkhole and channel, taking out distraction products.

Calculations can be performed in such a way. Volume of cupola (Fig.) is: Weight of cupola is. Side surface of cupola is equal Shear effort on the side surface is equal.

Maximal effort σ max, which support cupola above cavity before collapse depends on weight of cupola P and area of side contact S, which depends first of all on radius R.

3 Calculations can be performed in such a way. Volume of cupola (Fig.) is: Weight of cupola is. Side surface of cupola is equal Shear effort on the side surface is equal. In the simplest case of flat cupola above cylinder cavity we can write (Fig. 6). Maximal effort σ max, which support cupola above cavity before collapse depends on weight of cupola P and area of side contact S, which depends first of all on radius R. Vertical thickness of cupola L goes away from formula and only radius R remains. More sophisticated formulas were published in paper [Kalinin, 2006] Figure 4 Model to obtain formula of cupola stability. Figure Growing cavity and its cupola. Sinkhole resistivity modeling and results analysis Information about sinkholes in Guatemala city was an incentive to begin resistivity modeling above vertical cylinder of high resistivity. There are 2D, 2.D and 3D models used in resistivity modeling [Electrical sounding..., 1988]. 2D model means 2D object in the field of linear current electrodes. Such electrodes are not practical, but rather convenient for theoretical calculations (Figure 6). In 1960 such model was popular for analog modeling with electro-conducting paper. 2.D model means 2D object in the field of point current electrodes. In our case we used array oriented in perpendicular direction to the 2D object. 3D model means 3D object (vertical cylinder) in the field of point current electrodes. Profile in our case crosses object in its center. Why we used 2D and 2.D models when the main object is 3D? Because there is similarity and differences between these models that help understand better resistivity method's possibilities. We used vertical cylinder with squared instead of circular section due to programs possibilities. We used model of dike with width 40 m and vertical cylinder with diameter 40 m (Fig.6), like in case of sinkholes in Guatemala city (Fig.1). Lower surface is at the depth 100 m. Upper surface is at the depth from 6 to 60 m. Halfspace resistivity is equal 0 Ohm.m, and dike or cylinder resistivity Ohm.m.

4 h1 A M N B A Profile Linear current electrode B Linear current electrode Earth surface h1 Vertical cylinder Vertical dike h2 Figure 6 Models 2D, 2.D and 3D for resistivity modeling. We used programs developed for resistivity modeling in Moscow state university at the end of 80-th on the base on integral equation method: IE2DL, IE2DP1 and IE3D1 [Electrical sounding..., 1988]. The program IE2DL is similar to analog modeling on electro-conducting paper or 2D modeling of the field of linear current electrodes. The program IE2DP1 is for 2D modeling of the field of point current electrodes when array orientation is perpendicular to 2D body. The program IE3D1 calculates the field of point current electrodes near 3D object. These three programs can calculate ERT profiles. Three other programs were developed by A.A.Ryjov: the first "3DMod" is similar to IE3D1, the second "Cylinder" calculates influence of horizontal cylinder in the field of point current electrodes, the third "Sphere" calculates influence of sphere in the field of point current electrodes. These programs calculate only results of resistivity profiling with unmovable current electrodes. Though model of sinkhole has the best approximation as vertical cylinder that can be calculated in the programs IE3D1 and 3DMod, other programs, as our experience shows, can help in study of effects of local inhomogeneities. The program IE2DL allows fast and simple model creation and fast calculation. That is why first calculations were performed with IE2DL. In this case we used model of rectangular vertical dike with low boundary at 100 m depth and top boundary at 6, 13, 37 and 60 m. Anomaly value we calculated dividing ρ a value in epicenter of anomaly on ρ 1 =0 Ohm.m (resistivity of surrounding medium). For each of six programs we obtained dependences of anomaly from the depth of top boundary (fig.7) Figure 7 a Anomaly value versus depth of top boundary for six programs: 1 - IE2DL; 2 - IE2DP1; 3 - Cylinder; 4-3DMod; - IE3D1; 6 - Sphere Figure 7 b Anomaly value versus depth of top boundary for the programs IE3D1 () and 3DMod (4). 4

The most high anomalies in fig.7,a are obtained for IE2DL program, after that for vertical dike and point current electrodes, low anomaly for vertical cylinder.

5 The most high anomalies in fig.7,a are obtained for IE2DL program, after that for vertical dike and point current electrodes, low anomaly for vertical cylinder. Anomaly depends on current density near the object: dike for linear current electrodes, dike for point current electrodes, vertical cylinder and sphere, this situation is clear. Figure 7, b shows that two similar programs 3DMod and IE3D1 give similar results. Vertical cylinder with 40 m diameter can be found when the depth of its top surface is no more than 0 m. Calculations in ERT regime (IE2DL, IE2DP1, IE3D1) were inverted with the program Res2DInv (Geotomo Software). Top boundary was at 6, 13, 37 and 60 m, low boundary at 100 m. We used AMN+MNB array with spacings AO between 7. and 122. m, step between electrodes - m. Figure 8 gives clear presentation of a problem found. When low boundary is at 100 m in inversion result its position seems to be at 20 m. For 3D object (vertical cylinder) current density and sensitivity to object diminishes rapidly with depth and influence of the cylinder on ERT field disappeares. We calculated also several models for different positions of low boundary. Variation of low boundary Figure 8 2D inversion. Vertical cylinder. Top Figure 9 2D inversion. Vertical cylinder. Top boundary is at 6 m, low boundary at 100 m. boundary is at 6 m, low boundary at 13 m. In figure 9 there is model with top boundary at 6 and low boundary at 13 m. Visually low boundary seems a bit deeper (at 1 m). In figure 10 there is model with top boundary at 6 and low boundary at 37 m. Visually low boundary seems to be at 20 m. In figure 11 there is model with top boundary at 6 and low boundary at 60 m. Visually low boundary seems to be at 20 m. We think that we found principal restriction of ERT in estimating low boundary of vertical cylinder. When top boundary is at 6 m, low boundary can be found at depth until 20 m. Deeper situated low boundary can not be found. The cylinder diameter is 40 m. Figure 10 2D inversion. Vertical cylinder. Figure 11 2D inversion. Vertical cylinder. Top Top boundary is at 6 m, low boundary at 37 m. boundary is at 6 m, low boundary at 60 m. Conclusions Modeling shown that vertical cylinder of high resistivity and diameter 40 m can be found by ERT when its upper edge is at the depth until 0 m.

6 Lower edge is more difficult element of vertical cylinder and its depth can be estimated with great errors. ERT is more oriented on finding horizontal boundaries and local bodies, but not vertical ones. References Kalinin, E.V. [2006] Engineering-geological calculations and modeling. Moscow, MSU edition, 2006, 248. (In Russian). Ogilvi, A.A. [1990] Fundamentals of engineering geophysics. Moscow., Nedra, 01. (In Russian). Electrical sounding of geological medium. Moscow university edition, part 1, 1988, 170 pp., part 2, 1992, 200 pp. ISBN Zúñiga, L.R., Chavez, R., Cifuentes, G., Hernandez, E., Tejero, A. and Monzon, A. [2001] Determination of High Risk Zones in Urban Areas. Near Surface Geophysics, EAGE conference, 2011, Leicester, United Kingdom. P31.

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