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1D and 3D resistivity inversions for geotechnical investigation

1D and 3D resistivity inversions for geotechnical investigation The resistivity method is frequently used in the investigation of the shallow parts of the earth. Interpretation of such data is usually done assuming a layered earth. However, a more complete imaging can be obtained if 3D models are used. Thirty-five vertical electrical soundings (VES) were carried out in a regular mesh at the northwestern part of Greater Cairo in order to characterize different geological units and to study their quality for building foundations. Models obtained from 1D inversion of each VES, together with borehole information, were used for construction of eight geoelectrical sections which exhibit the main geoelectrical characteristics of the geological units present in the area. The 3D inversion of the data indicated a complex subsurface electrical resistivity distribution conditioned by lithology, water content and tectonic structures. The results indicate that the subsurface consists of different geologic units such as gravel and sand, sand, clay and limestone. The main results are related to the characterization of the clay formations in the north of the survey area, which is revealed by low-resistivity values (<100  m) and sand layers associated with high-resistivity values (>600  m) depicted in the central part of the study zone. Keywords: geotechnical engineering, resistivity survey, 3D inversion (Some figures in this article are in colour only in the electronic version) 1. Introduction Resistivity data are usually interpreted assuming one- dimensional (1D) or two-dimensional (2D) models (Koefoed 1960,Loke 1997). The use of three-dimensional (3D) The construction of any structure in civil engineering demands modelling and inversion of resistivity data has increased in the knowledge of soil engineering properties obtained by the past few years taking advantage of the great development geotechnical tests. However, the number of test sites is limited, on the automatic data acquisition systems and faster computers demanding extrapolation/interpolation of the results over a and mathematical algorithms. Several algorithms have been larger area. The use of geophysical methods in civil and developed to perform 3D resistivity modelling and inversion. environmental engineering has increased in the past few years 3D forward algorithms based on the finite-difference, finite- helping to produce accurate extrapolation/interpolation of soil element and integral methods have been presented by several geotechnical properties (Ward 1990, Dannoski and Yaramanci authors (Spitzer 1998, Zhang et al 1995, Zhao and Yedlin 1999, Cosenza et al 2006,Giao et al 2003, Sultan et al 1996, Loke and Barker 1996, Tsourlos and Ogilvy 1999,Yi 2004, Soupios et al 2007). Resistivity methods are widely et al 2001, Pidlisecky et al 2007, which are just some of the used in ground investigation for building foundation analyses, papers published in the last 10 years). inspection and monitoring of dams and dikes (Karastathis et al 2002,Abu-Zeid 1994) and detection of potentially dangerous Several authors have published examples of the structures in the subsurface (Debeglia and Dupont 2002). application of 3D modelling and inversion of resistivity data. 1742-2132/08/010001+11$30.00 © 2008 Nanjing Institute of Geophysical Prospecting Printed in the UK 1 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 S Awad Sultan and F A Monteiro Santos Figure 1. Location and geological map of the study area (modified after the internal report of the Geological Survey of Egypt). Monteiro Santos et al (1997) used a 3D approach in modelling et al (2000) reported the 3D modelling of double-dipole resistivity rectangle and dipole–dipole data. Park (1998) data. Represas et al (2005) used 3D inversion of resistivity applied the method to monitor the movement of a fresh water data for geological and mining investigation. El-Quady plume through a vadose zone. Ogilvy et al (1999) applied the et al (2005) and Sultan et al (2006) applied 3D inversion 3D inversion to investigate industrial waste deposits. Weller of resistivity data investigating archaeological sites in Egypt. et al (2000) applied 3D inversion in order to better characterize Recently, Soupios et al (2007) have used 2D and 3D the induced polarization data of a simulated waste site. Stoll inversion of dipole–dipole data in combination with geological 2 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 Figure 2. Wells geological logs. 1: Gravel and sand, 2: sandstone, 3: coarse and fine sand, 4: coarse sand, 5: silty sand and 6: fine and medium sand. and geotechnical data to investigate a vacant building eastern and southeastern parts of the study area and also cover site. the wadies that cross the studied area. The Quaternary deposits In this study, the authors used 1D and 3D interpretation are composed of sand dunes, sand sheet and alluvium deposits. of resistivity data (Schlumberger soundings) to characterize The Middle Miocene deposits occur in the northern part of the different geological units that represent the stratigraphic the area and are represented by Hommath formation, which section of the study area and to study their quality for building consists of sandy limestone, clay and calcareous sandstone. foundations. Oligocene deposits represented by Gabal Ahamar formation The study area stands at the northwestern part of Greater composed of sandstone, loose sand and gravel cover the central Cairo, northward of the Cairo–Suez road, and is located part of the study area. Three boreholes, drilled in the study ◦   ◦ between latitudes of 30 06 30 and 30 08 30 E and area by the geological survey of Egypt (EGSMA 1996), with ◦   ◦ longitudes of 31 39 00 and 31 41 30 N (figure 1). The depths of 50 m indicate that the shallow part of the subsurface study area represents a flat area between El Shourk and Bdr section consists of different varieties of sand, sandstone, clay cities and was intended to be prepared for different types of and limestone (figure 2). constructions. 3. Geoelectrical data and interpretation 2. Geology of the study area Thirty-five vertical electrical soundings (VES) were carried The geology of the area was studied by the geological survey out in the area under investigation (figure 3) in a regular grid of Egypt (EGSMA 1996). The surface geology consists of with spacing between soundings of approximately 500 m. The different units with ages of Quaternary, Middle Miocene and VES were executed using a Russian electronic compensator, Oligocene (figure 1). The Quaternary deposits occur in the type AE-72. The maximum current electrode spacing (AB) 3 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 S Awad Sultan and F A Monteiro Santos The IPI2WIN program deals with VES curves in the man– computer interactive regime and draws theoretical and field curves on a display screen together with the Rho(z) model curve. Three boreholes drilled in the area, where three VES were measured, were used for the correlation and calibration between the interpreted electrical data and the real geologic information. Figure 5 shows a comparison between the resistivity models and the geological logs. VES 13 and borehole D5 are located in the Gabal Ahamar formation dominated by fine and medium sand. The variation on the resistivity values is conditioned by the presence of the groundwater in the medium grain size material (corresponding to the 100  m layer at depths between 8 and 20 m). At depths between 20 and 80 m, the high-resistivity value (2000  m) is probably justified by the presence of fine sand, which is less porous and dry. The new decrease in resistivity detected at 80 m depth cannot be correlated with any borehole information, but it is probably due to the presence of sandstone. Sounding VES 31 and borehole F1 were performed in Quaternary sedimentary formations. A quite good correlation between resistivity and geological layers can be noted in the upper part of well F1 and VES 31. The relative low-resistivity layer (90  m) starting at a depth of approximately 32 m, where the sandstone layer starts, might represent the aquifer. The results of 1D inversions were combined with the geological information from boreholes in the construction of Figure 3. Location map for vertical electrical soundings (VES) and eight interpreted cross-sections: seven of them are in the W–E boreholes. direction and the eighth is in the S–N direction (figures 6 and 7). Geoelectrical cross-sections along profiles A-A and was chosen to be 500 m, aiming to obtain information about the B-B cross the northern part of the survey area represented by thicknesses and resistivities of the shallow subsurface section. wadi deposits of Quaternary age and by the Middle Miocene The VES field apparent resistivity curves are shown in figure 4. deposits (Hommath formation composed of sand and gravel, Three/four-layer models can in general explain the main clay and calcareous sandstone). The clay layer of Middle features of the curves. There are curves of the types H, A and Miocene exhibits low-resistivity values ranging from 2 to Q. The H-type curves, revealing a second conductive layer, 10  m. The models suggested the presence of this clay are dominant in the northwestern and southeastern parts of the layer in the whole north part of the survey area. This layer survey. The A- and Q-type curves are mostly represented in acts as the north limit of the aquifer. a SW–NE region that crosses the central part of the survey The geoelectrical cross-section along profile C-C area. The pattern of the curves changes slowly between represents formations of three ages: Quaternary (wadi sites. Exceptions are, however, observed in the vicinity of deposits), Middle Miocene (calcareous sandstone) and the lithological changes which are, in general, associated with Oligocene deposits (sand and sandstone). This last layer of tectonic structures like faults. Example of variations greater sand contains the groundwater aquifer and exhibits resistivity than one decade are observed between VES 11 and 6 in the ranging from 72 to 152  m but the dry sand reveals northwestern part and between VES 31 and 32 in south of very high-resistivity values ranging from 297 to 1810  m. the area, both associated with probable faults crossing the There are variations in the thicknesses of the different types area. of sand according to grain size. These variations are a consequence of the deposition cycles. The central part of the 3.1. 1D resistivity interpretation study area includes the geoelectric cross-section along profiles D-D ,E-E and F-F that exhibit the wadi deposits overlaying VES apparent resistivity data were inverted assuming layered- the Oligocene sand. The geoelectric cross-section along earth models to determine the thicknesses and true resistivities profile G-G crosses the southern part of the area, where of the successive strata below each VES site. There are the western part is represented by Oligocene deposits and several interpretation methods; some of them are graphical the eastern part is represented by wadi deposits of Quaternary (manual) and others are numerical methods. The authors age with the thickness of about 40 m overlaying the Oligocene used manual interpretation based on two-layer standard curve deposits. A normal fault (F1) dissecting the surface and Cagniard graphs (Koefoed 1960) to estimate initial models subsurface stratigraphic units intercepts the profile between for the inversion process using the IPI2WIN 2000 software. VES 31 and 32 with the downthrown towards VES 32. The 4 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 Figure 4. VES data (symbols) and model responses (lines) of the 3D model shown in figure 8, for selected sites. smoothness-constrained least-squares algorithm for inversion geoelectric cross-section H-H (figure 7) crosses the area in the N–S direction including VES 31, 26, 16, 11, 6 and (Monteiro Santos et al 1997, Represas et al 2005). The 1. This section crosses the Quaternary, Middle Miocene program uses an irregular mesh constructed for each VES and Oligocene deposits. A probable normal fault is located site, taking into account sounding parameters (AB/2 spacing between VES 6 and 11 where the contact between Middle and spatial orientation). With the meshes adopted in this work Miocene and Oligocene deposits is mapped. a numerical error lower than 3% is expected in the apparent The 1D geoelectrical cross-sections suggest that the resistivity calculations. subsurface structure is more complex than initially suspected. The 35 VES, corresponding to 490 data measurement Therefore, a 3D model is more adequate for its points, were inverted considering the subsurface domain interpretation. divided into 1920 hexahedral elements of unknown resistivity. Horizontally, the finite-element mesh was defined for each 3.2. 3D resistivity interpretation sounding, in general, with 91 × 96 nodes. In the The 3D inversion code used in this work was developed using downward direction the mesh spacing increases according the finite-element approach for forward calculations and a to the exponential law z = z exp(0.2 nz), where z m m 5 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 S Awad Sultan and F A Monteiro Santos Figure 5. Comparison between 1D models obtained from inversion of VES 31 and 13 with geological logs from wells F1 and D5, respectively. represents the thickness of the uppermost hexahedral element characterized by high-resistivity values (>500  m) alternated (0.5 m in this case) and nz is the vertical level of the element. with low-resistivity values. This discontinuous pattern can Twenty-eight nodes were used in the vertical direction. A be an artefact originated by the large spacing between VES 230  m (corresponding to the average apparent resistivity sites. The high-resistivity values become more continuous and data) uniform medium was considered for an initial model. dominant with increasing depth. These high-resistivity values The regularization algorithm proposed by Sasaki (1989)was might correspond predominantly to gravel and loose sand. adopted in this work. The results presented in this section The low-resistivity values might be due to the groundwater have been obtained using a regularization parameter of 0.3, presence. The transition between high- and low-resistivity which corresponds to the better fitting between data and model zones in the southern and eastern parts of the survey area responses. This result was obtained after several inversion runs correlates very well with the transition from Gabal Ahmar and with different parameters. An initial homogeneous medium Quaternary formations mainly represented by alluvium, sand of 230  m was used. This value corresponds to the average dune and sand sheet. The presence of groundwater might of the measured apparent resistivity values. be responsible for the low resistivity of these formations. In The results are presented in figure 8 as horizontal slices the south the transition between Gabal Ahmar and Quaternary of the resistivity model. This model was obtained after 16 formations is represented by a normal fault. To the east the 3D iterations. The comparison between measured and calculated resistivity model suggests that the Gabal Ahmar formation apparent resistivity curves is shown in figure 4.The misfit is deeper and covered by Quaternary sediments. The 3D between data and model responses varies between soundings: model agrees, in general, with the 1D ones. The main a huge misfit is observed at site 33 (VES 33). A high misfit difference is verified in the northern part of the survey area for is observed at shortest AB/2 spacing for VES 11, 12, 17, 25 deep structures. This difference will be analysed in the next and 28. For the majority of the soundings the fit is quite good, section. with rms error lower than 12%. The Hommath formation (sandy limestone, clay) at the 4. Sensitivity tests northern part of the area is revealed as a low-resistivity zone (resistivity < 100  m). The high content in clay might be The sensitivity of the data to some features in the 3D model the reason for the low-resistivity values. This agrees with was studied considering two models derived from the final the results obtained from 1D inversion for the intermediate inversion model shown in figure 8. In the first model (A) the layers. The main differences between 1D and 3D models in resistivity of all the elements between 300 and 700  mwas this part of the survey area are noted in the deep structures changed to 300  m. This change mainly affects the structures that were revealed to be more conductive in the 3D model— resistivity values lesser than 100  m are noted in the 3D in the central part of the survey area. For the soundings located model in contrast to the 1D results, where values ranging from to the north and south of the survey, the changes on apparent 150 to 200  m are observed. The central part of the survey resistivity curves correspond to changes on lateral structures. area, which corresponds to the Gabal Ahmar formation, is In the second model (B) the resistivity of all the elements at 6 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 (A)(E ) (B) (F ) (C ) (G) (D) Figure 6. W–E geoelectrical cross-section with results of boreholes, resistivity values in  m. a depth greater than 100 m was changed to 700  m. This in VES 3). In contrast to the 3D model, the 1D models change corresponds to an increase in the resistivity of deep obtained from VES located in the northern part of the survey northern and southern structures. This also corresponds to a area suggest resistive deep bedrock (probably made up of slight decrease of the deep structures in the central part of the limestone). survey area. The model responses at nine selected sites are shown in Model A allows us to study the importance of the high figure 9. In this figure the responses obtained with models resistivity (mainly associated with the Oligocene formations A and B are compared with experimental data and with the in the centre of the survey area) in the model responses. responses of the best-inverted model shown in figure 8. Model B was motivated by the discrepancy observed in deep The decrease in the resistivity (model A) does not structures in 1D and 3D models and the misfit between data affect soundings located to the north and south out of and the 3D model response for largest AB/2 spacing at the survey area (VES 3, 8 and 33), showing that high some soundings located in the north part of the area (e.g. apparent resistivity measured for large AB/2 spacing is not 7 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 S Awad Sultan and F A Monteiro Santos Figure 7. Geoelectric cross-section along profile H-H , resistivity values in  m. depth: 0 to 4 m depth: 4 to 8 m depth: 8 to 12 m 825500 825500 825500 Tm 825000 825000 825000 824500 824500 824500 824000 Q 824000 824000 To 823500 823500 823500 823000 823000 823000 F1 822500 822500 822500 679500 680500 681500 679500 680500 681500 679500 680500 681500 W <--- Distance in m ---> E depth: 12 to 16 m depth: 16 to 25 m depth: 25 to 40 m 825500 825500 825500 825000 825000 825000 824500 824500 824500 824000 824000 824000 823500 823500 823500 823000 823000 823000 822500 822500 822500 679500 680500 681500 679500 680500 681500 679500 680500 681500 depth: 40 to 60 m depth: 60 to 100 m depth > 100 m 825500 825500 825500 825000 825000 825000 824500 824500 824500 824000 824000 824000 823500 823500 823500 823000 823000 823000 822500 822500 822500 679500 680500 681500 679500 680500 681500 679500 680500 681500 ohm-m Figure 8. Horizontal slices from the 3D resistivity model. Dashed lines in the first slice represent the contours of the main geological units. VES location is represented by crosses. Tm: Miocene deposits, Q: Quaternary deposits and To: Oligocene deposits. S <--- Distance in m ---> N Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 Figure 9. Results of the sensitivity tests at some chosen sites. Dots are the observed data, best 3D resistivity model responses are represented by a continuous black line (1), responses for the model where resistivities in the range 300–700  m are changed to 300  mare represented by a dashed-dot line (2). The short-dashed line represents the responses of a model with structures deeper than 100 m changed to 700  m(3). originated by lateral effects caused by the high-resistivity 5. Discussion central structures. Soundings carried out in the Oligocene formations (VES 13, 18, 23 and 28) have great sensitivity Attempts to relate geotechnical properties (such as unit weight, to this decrease in resistivity suggesting that high-resistivity water content, liquid limit, plastic limit, liquidity index, Oligocene formations are thick. undrained shear strength, compression ratio, effective stress, grain size dimension, cone resistance, among several others) Soundings located in the northern part of the area, such to geoelectrical results are not so frequent. The relatively few as VES 3, show a better fit (mainly for large AB/2 spacing) published results relating mechanical properties to electrical when the resistivity of deep structures increases (model B). properties seem to be contradictory (Cosenza et al 2006, This shows that deep structures in that part of the 3D model Endres and Clement 1998, Braga et al 1999, Giao et al are not well resolved. Soundings carried out in the centre of 2003). The only correlation that seems to be well understood the survey area (VES 18, 23) are not affected by resistivity and well established is the interdependence between electrical changes originating from model B. Soundings located in the resistivity and water content. Quaternary formations (VES 16, 28 and 33) have strong A relatively good correlation between the 1D and 3D sensitivity to deep resistivity, showing that deep structures resistivity models and the geology can be noted for the upper in the southern part have resistivity significantly lesser than layers. The relatively high resistivity (160  m) at depths 700  m. 9 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 S Awad Sultan and F A Monteiro Santos between 18 and 40 m represents the combined response of electrical data: a case study at Garchy in France J. Appl. Geophys. 60 165–78 the gravel and of the coarse and fine sand formations. In the Dannoski G and Yaramanci U 1999 Estimation of water content and north part of the survey area the models show a decrease in porosity using combined radar and geoelectrical measurements the resistivity (to 2–5  m in 1D models) approximately at Eur. J. Env. Eng. Geophys. 4 71–85 10–20 m depth. This change in the resistivity correlates quite Debeglia N and Dupont F 2002 Some critical factors for engineering well with the beginning of a clay layer. and environmental microgravity investigations J. Appl. Geophys. 50 435–54 Clay layers are important in civil engineering. For El-Quady G, Monteiro Santos F A, Hassaneen A Gh and Trindade L example, clay minerals have a great affinity for water. Some 2005 3-D inversion of VES data from Saqqara archaeological clay minerals swell easily and may double in thickness when area Egypt Near Surf. Geophys. 227–33 wet. The process by which some clay minerals swell when Endres A L and Clement W P 1998 Relating cone penetrometer test they take up water is reversible. Swelling clay expands or information to geophysical data: a case study Symp. Application of Geophysics to Engineering and Environmental contracts in response to changes in environmental factors (wet Problems (SAGEEP98) (Chicago, USA) and dry conditions, temperature). According to Velde (1995), Geological Survey of Egypt (EGSMA) 1996 Geological and hydration and dehydration can vary the thickness of a single geophysical studies on new Hilioplis City, Geol. Surv. of clay particle by almost 100%. Therefore, any construction Egypt, Internal report (12/1996) built on soil containing swelling clays may be subject to Giao P H, Chung S G, Kim DY and Tanaka H 2003 Electrical structural damage caused by seasonal swelling of the clay imaging and laboratory resistivity testing for geotechnical investigation of Pusan clay deposits J. Appl. Geophys. portion of the soil. 52 157–75 IPI2Win-1D Program 2000 Programs set for 1-D VES data 6. Conclusions interpretation, Dept. of Geophysics, Geological Faculty, Moscow University, Russia Geophysical surveys can contribute to identify subsurface Karastathis V K, Karmis P N, Drakatos G and Stavrakakis G 2002 zones which are inappropriate for the construction of building Geophysical methods contributing to the testing of concrete dams. Application at the Marathon Dam J. Appl. Geophys. foundations. Electric imaging produced from resistivity data 50 247–60 proved to be a useful tool in clay layer detection. Koefoed O 1960 A generalized Cagniard graph for interpretation of The results presented here show that the survey area geoelectric sounding data Geophys. Prospect. 8 459–69 has a complex subsurface electrical resistivity distribution, Loke M H and Barker R D 1996 Practical techniques for 3D conditioned by lithology, water content and tectonic structures. resistivity surveys and data inversion Geophys. Prospect. From a civil engineering point of view the main results are 44 499–523 Loke M H 1997 Rapid 2D resistivity inversion using the related to the characterization of the clay and sand (Oligocene least-squares method RES2DINV Program Manual (Penang, age) layers. Clay soils are more susceptible to subsidence Malaysia) being also strongly affected by environmental conditions Monteiro Santos F A, Andrade Afonso A R and Mendes-Victor L A (Soupios et al 2007). Therefore, special care is recommended 1997 Study of the Chaves geothermal field using 3D resistivity if foundation footings are to be constructed in the northern part modeling J. Appl. Geophys. 37 85–102 of the survey area. Ogilvy R, Meldrum P and Chambers J 1999 Imaging of industrial waste deposits and buried quarry geometry by 3-D resistivity tomography Eur. J. Env. Eng. Geophys. 3 103–13 Acknowledgments Park S 1998 Fluid migration in the vadose zone from 3-D inversion of resistivity monitoring data Geophysics 63 41–51 The first author (Sultan Awad Sultan) is indebted to the Pidlisecky A, Haber E and Knight R 2007 RESINVM3D: a 3D ˜ ˆ Fundac ¸ao para a Ciencia e Tecnologia (Portugal) for his resistivity inversion package Geophysics 72 H1-H10 support through the post-doctor fellowship of reference Represas P, Monteiro Santos F A, Mateus A, Figueiras J, (SFRH\BPD\22116\2005). This work was partly developed Barroso M, Martins R, Oliveira V, Nolasco da Silva M and Matos J X 2005 A case study of two and three-dimensional in the scope of the scientific cooperation agreement between inversion of dipole–dipole data: the Enfermarias Zn–Pb Centro de Geofisica da Universidade de Lisboa, Portugal (Ag,Sb,Au) prospect (Moura, Portugal) Near Surf. Geophys. (CGUL) and the National Research Institute for Astronomy 3 21–31 and Geophysics, Egypt (NRIAG). Robertson P K and Campanella R G 1983 Interpretation of cone penetrometer test: Part I. Sand Can. Geotech. J. 20 References 718–33 Sasaki Y 1989 Two-dimensional joint inversion of magnetotelluric and dipole–dipole resistivity data Geophysics 54 254–62 Abu-Zeid N 1994 Investigation of channel seepage areas at the Song Y, Cho S-J, Chung SH and Suh J H 2001 Three-dimensional existing Kaffrein Dam Site (Jordan) using electrical resistivity measurements J. Appl. Geophys. 32 163–75 imaging of subsurface structures using resistivity data Andrews R J, Barker R and Heng L M 1995 The application of Geophys. Prospect. 49 483–97 electrical tomography in the study of the unsaturated zone in Soupios P M, Georgakopoulos P, Papadopoulos N, Saltas V, chalk at three sites in Cambridgeshire, United Kingdom Andeadakis A, Vallianatos F, Sarris A and Makris J P 2007 Hydrogeol. J. 3 17–31 Use of engineering geophysics to investigate a site for a Braga A, Malagutti W, Dourado J and Change H 1999 Correlation building foundation J. Geophys. Eng. 4 94–103 of electrical resistivity and induced polarization data with Spitzer K 1998 The three-dimensional DC sensitivity for surface geotechnical survey standard peretration test measurements J. and subsurface sources Geophys. J. Int. 134 736–46 Environ. Eng. Geophys. 4 123–30 Stoll J B, Haak V and Spitzer K 2000 Electrical double-dipole Cosenza P, Marmet E, Rejiba F, Cui Y J, Tabbagh A and experiment in the German Continental Deep Drilling Program Charley Y 2006 Correlation between geotechnical and (KTB) J. Geophys. Res. 105 21319–31 10 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 Sultan S A et al 2004 Geoelectrical application for solving Ward S H 1990 Resistivity and induced polarization methods geotechnical problems at two localities in greater Cairo, Egypt Geotechnical and Environmental Geophysics ed S Ward NRIAG J. Geophys. 3 51–64 (Tulsa: Society of Exploration Geophysicists) pp 147–89 Sultan S A, Monteiro Santos F A and Helal A 2006 A study of the Weller A, Frangos W and Seichter M 2000 Three-dimensional groundwater seepage at Hibis Temple using geoelectrical data, inversion of induced polarization data from simulated waste Kharga Oasis, Egypt Near Surf. Geophys. 347–54 J. Appl. Geophys. 44 67–83 Zhang J, Mackie R L and Madden T R 1995 3-D resistivity forward Tsourlos P I and Ogilvy R D 1999 An algorithm for the 3-D inversion of tomographic resistivity and induced polarisation modelling and inversion using conjugate gradients Geophysics data: preliminary results J. Balkan Geophys. Soc. 2 30–45 60 1313–25 Velde B 1995 Composition and mineralogy of clay minerals Origin Zhao S K and Yedlin M J 1996 Some refinements on the and Mineralogy of Clays ed B Velde (New York: Springer) finite-difference method for 3-D dc resistivity modeling pp 8–42 Geophysics 61 1301–7 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Geophysics and Engineering Oxford University Press

1D and 3D resistivity inversions for geotechnical investigation

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Oxford University Press
Copyright
© 2008 Nanjing Institute of Geophysical Prospecting
ISSN
1742-2132
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1742-2140
DOI
10.1088/1742-2132/5/1/001
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Abstract

The resistivity method is frequently used in the investigation of the shallow parts of the earth. Interpretation of such data is usually done assuming a layered earth. However, a more complete imaging can be obtained if 3D models are used. Thirty-five vertical electrical soundings (VES) were carried out in a regular mesh at the northwestern part of Greater Cairo in order to characterize different geological units and to study their quality for building foundations. Models obtained from 1D inversion of each VES, together with borehole information, were used for construction of eight geoelectrical sections which exhibit the main geoelectrical characteristics of the geological units present in the area. The 3D inversion of the data indicated a complex subsurface electrical resistivity distribution conditioned by lithology, water content and tectonic structures. The results indicate that the subsurface consists of different geologic units such as gravel and sand, sand, clay and limestone. The main results are related to the characterization of the clay formations in the north of the survey area, which is revealed by low-resistivity values (<100  m) and sand layers associated with high-resistivity values (>600  m) depicted in the central part of the study zone. Keywords: geotechnical engineering, resistivity survey, 3D inversion (Some figures in this article are in colour only in the electronic version) 1. Introduction Resistivity data are usually interpreted assuming one- dimensional (1D) or two-dimensional (2D) models (Koefoed 1960,Loke 1997). The use of three-dimensional (3D) The construction of any structure in civil engineering demands modelling and inversion of resistivity data has increased in the knowledge of soil engineering properties obtained by the past few years taking advantage of the great development geotechnical tests. However, the number of test sites is limited, on the automatic data acquisition systems and faster computers demanding extrapolation/interpolation of the results over a and mathematical algorithms. Several algorithms have been larger area. The use of geophysical methods in civil and developed to perform 3D resistivity modelling and inversion. environmental engineering has increased in the past few years 3D forward algorithms based on the finite-difference, finite- helping to produce accurate extrapolation/interpolation of soil element and integral methods have been presented by several geotechnical properties (Ward 1990, Dannoski and Yaramanci authors (Spitzer 1998, Zhang et al 1995, Zhao and Yedlin 1999, Cosenza et al 2006,Giao et al 2003, Sultan et al 1996, Loke and Barker 1996, Tsourlos and Ogilvy 1999,Yi 2004, Soupios et al 2007). Resistivity methods are widely et al 2001, Pidlisecky et al 2007, which are just some of the used in ground investigation for building foundation analyses, papers published in the last 10 years). inspection and monitoring of dams and dikes (Karastathis et al 2002,Abu-Zeid 1994) and detection of potentially dangerous Several authors have published examples of the structures in the subsurface (Debeglia and Dupont 2002). application of 3D modelling and inversion of resistivity data. 1742-2132/08/010001+11$30.00 © 2008 Nanjing Institute of Geophysical Prospecting Printed in the UK 1 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 S Awad Sultan and F A Monteiro Santos Figure 1. Location and geological map of the study area (modified after the internal report of the Geological Survey of Egypt). Monteiro Santos et al (1997) used a 3D approach in modelling et al (2000) reported the 3D modelling of double-dipole resistivity rectangle and dipole–dipole data. Park (1998) data. Represas et al (2005) used 3D inversion of resistivity applied the method to monitor the movement of a fresh water data for geological and mining investigation. El-Quady plume through a vadose zone. Ogilvy et al (1999) applied the et al (2005) and Sultan et al (2006) applied 3D inversion 3D inversion to investigate industrial waste deposits. Weller of resistivity data investigating archaeological sites in Egypt. et al (2000) applied 3D inversion in order to better characterize Recently, Soupios et al (2007) have used 2D and 3D the induced polarization data of a simulated waste site. Stoll inversion of dipole–dipole data in combination with geological 2 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 Figure 2. Wells geological logs. 1: Gravel and sand, 2: sandstone, 3: coarse and fine sand, 4: coarse sand, 5: silty sand and 6: fine and medium sand. and geotechnical data to investigate a vacant building eastern and southeastern parts of the study area and also cover site. the wadies that cross the studied area. The Quaternary deposits In this study, the authors used 1D and 3D interpretation are composed of sand dunes, sand sheet and alluvium deposits. of resistivity data (Schlumberger soundings) to characterize The Middle Miocene deposits occur in the northern part of the different geological units that represent the stratigraphic the area and are represented by Hommath formation, which section of the study area and to study their quality for building consists of sandy limestone, clay and calcareous sandstone. foundations. Oligocene deposits represented by Gabal Ahamar formation The study area stands at the northwestern part of Greater composed of sandstone, loose sand and gravel cover the central Cairo, northward of the Cairo–Suez road, and is located part of the study area. Three boreholes, drilled in the study ◦   ◦ between latitudes of 30 06 30 and 30 08 30 E and area by the geological survey of Egypt (EGSMA 1996), with ◦   ◦ longitudes of 31 39 00 and 31 41 30 N (figure 1). The depths of 50 m indicate that the shallow part of the subsurface study area represents a flat area between El Shourk and Bdr section consists of different varieties of sand, sandstone, clay cities and was intended to be prepared for different types of and limestone (figure 2). constructions. 3. Geoelectrical data and interpretation 2. Geology of the study area Thirty-five vertical electrical soundings (VES) were carried The geology of the area was studied by the geological survey out in the area under investigation (figure 3) in a regular grid of Egypt (EGSMA 1996). The surface geology consists of with spacing between soundings of approximately 500 m. The different units with ages of Quaternary, Middle Miocene and VES were executed using a Russian electronic compensator, Oligocene (figure 1). The Quaternary deposits occur in the type AE-72. The maximum current electrode spacing (AB) 3 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 S Awad Sultan and F A Monteiro Santos The IPI2WIN program deals with VES curves in the man– computer interactive regime and draws theoretical and field curves on a display screen together with the Rho(z) model curve. Three boreholes drilled in the area, where three VES were measured, were used for the correlation and calibration between the interpreted electrical data and the real geologic information. Figure 5 shows a comparison between the resistivity models and the geological logs. VES 13 and borehole D5 are located in the Gabal Ahamar formation dominated by fine and medium sand. The variation on the resistivity values is conditioned by the presence of the groundwater in the medium grain size material (corresponding to the 100  m layer at depths between 8 and 20 m). At depths between 20 and 80 m, the high-resistivity value (2000  m) is probably justified by the presence of fine sand, which is less porous and dry. The new decrease in resistivity detected at 80 m depth cannot be correlated with any borehole information, but it is probably due to the presence of sandstone. Sounding VES 31 and borehole F1 were performed in Quaternary sedimentary formations. A quite good correlation between resistivity and geological layers can be noted in the upper part of well F1 and VES 31. The relative low-resistivity layer (90  m) starting at a depth of approximately 32 m, where the sandstone layer starts, might represent the aquifer. The results of 1D inversions were combined with the geological information from boreholes in the construction of Figure 3. Location map for vertical electrical soundings (VES) and eight interpreted cross-sections: seven of them are in the W–E boreholes. direction and the eighth is in the S–N direction (figures 6 and 7). Geoelectrical cross-sections along profiles A-A and was chosen to be 500 m, aiming to obtain information about the B-B cross the northern part of the survey area represented by thicknesses and resistivities of the shallow subsurface section. wadi deposits of Quaternary age and by the Middle Miocene The VES field apparent resistivity curves are shown in figure 4. deposits (Hommath formation composed of sand and gravel, Three/four-layer models can in general explain the main clay and calcareous sandstone). The clay layer of Middle features of the curves. There are curves of the types H, A and Miocene exhibits low-resistivity values ranging from 2 to Q. The H-type curves, revealing a second conductive layer, 10  m. The models suggested the presence of this clay are dominant in the northwestern and southeastern parts of the layer in the whole north part of the survey area. This layer survey. The A- and Q-type curves are mostly represented in acts as the north limit of the aquifer. a SW–NE region that crosses the central part of the survey The geoelectrical cross-section along profile C-C area. The pattern of the curves changes slowly between represents formations of three ages: Quaternary (wadi sites. Exceptions are, however, observed in the vicinity of deposits), Middle Miocene (calcareous sandstone) and the lithological changes which are, in general, associated with Oligocene deposits (sand and sandstone). This last layer of tectonic structures like faults. Example of variations greater sand contains the groundwater aquifer and exhibits resistivity than one decade are observed between VES 11 and 6 in the ranging from 72 to 152  m but the dry sand reveals northwestern part and between VES 31 and 32 in south of very high-resistivity values ranging from 297 to 1810  m. the area, both associated with probable faults crossing the There are variations in the thicknesses of the different types area. of sand according to grain size. These variations are a consequence of the deposition cycles. The central part of the 3.1. 1D resistivity interpretation study area includes the geoelectric cross-section along profiles D-D ,E-E and F-F that exhibit the wadi deposits overlaying VES apparent resistivity data were inverted assuming layered- the Oligocene sand. The geoelectric cross-section along earth models to determine the thicknesses and true resistivities profile G-G crosses the southern part of the area, where of the successive strata below each VES site. There are the western part is represented by Oligocene deposits and several interpretation methods; some of them are graphical the eastern part is represented by wadi deposits of Quaternary (manual) and others are numerical methods. The authors age with the thickness of about 40 m overlaying the Oligocene used manual interpretation based on two-layer standard curve deposits. A normal fault (F1) dissecting the surface and Cagniard graphs (Koefoed 1960) to estimate initial models subsurface stratigraphic units intercepts the profile between for the inversion process using the IPI2WIN 2000 software. VES 31 and 32 with the downthrown towards VES 32. The 4 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 Figure 4. VES data (symbols) and model responses (lines) of the 3D model shown in figure 8, for selected sites. smoothness-constrained least-squares algorithm for inversion geoelectric cross-section H-H (figure 7) crosses the area in the N–S direction including VES 31, 26, 16, 11, 6 and (Monteiro Santos et al 1997, Represas et al 2005). The 1. This section crosses the Quaternary, Middle Miocene program uses an irregular mesh constructed for each VES and Oligocene deposits. A probable normal fault is located site, taking into account sounding parameters (AB/2 spacing between VES 6 and 11 where the contact between Middle and spatial orientation). With the meshes adopted in this work Miocene and Oligocene deposits is mapped. a numerical error lower than 3% is expected in the apparent The 1D geoelectrical cross-sections suggest that the resistivity calculations. subsurface structure is more complex than initially suspected. The 35 VES, corresponding to 490 data measurement Therefore, a 3D model is more adequate for its points, were inverted considering the subsurface domain interpretation. divided into 1920 hexahedral elements of unknown resistivity. Horizontally, the finite-element mesh was defined for each 3.2. 3D resistivity interpretation sounding, in general, with 91 × 96 nodes. In the The 3D inversion code used in this work was developed using downward direction the mesh spacing increases according the finite-element approach for forward calculations and a to the exponential law z = z exp(0.2 nz), where z m m 5 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 S Awad Sultan and F A Monteiro Santos Figure 5. Comparison between 1D models obtained from inversion of VES 31 and 13 with geological logs from wells F1 and D5, respectively. represents the thickness of the uppermost hexahedral element characterized by high-resistivity values (>500  m) alternated (0.5 m in this case) and nz is the vertical level of the element. with low-resistivity values. This discontinuous pattern can Twenty-eight nodes were used in the vertical direction. A be an artefact originated by the large spacing between VES 230  m (corresponding to the average apparent resistivity sites. The high-resistivity values become more continuous and data) uniform medium was considered for an initial model. dominant with increasing depth. These high-resistivity values The regularization algorithm proposed by Sasaki (1989)was might correspond predominantly to gravel and loose sand. adopted in this work. The results presented in this section The low-resistivity values might be due to the groundwater have been obtained using a regularization parameter of 0.3, presence. The transition between high- and low-resistivity which corresponds to the better fitting between data and model zones in the southern and eastern parts of the survey area responses. This result was obtained after several inversion runs correlates very well with the transition from Gabal Ahmar and with different parameters. An initial homogeneous medium Quaternary formations mainly represented by alluvium, sand of 230  m was used. This value corresponds to the average dune and sand sheet. The presence of groundwater might of the measured apparent resistivity values. be responsible for the low resistivity of these formations. In The results are presented in figure 8 as horizontal slices the south the transition between Gabal Ahmar and Quaternary of the resistivity model. This model was obtained after 16 formations is represented by a normal fault. To the east the 3D iterations. The comparison between measured and calculated resistivity model suggests that the Gabal Ahmar formation apparent resistivity curves is shown in figure 4.The misfit is deeper and covered by Quaternary sediments. The 3D between data and model responses varies between soundings: model agrees, in general, with the 1D ones. The main a huge misfit is observed at site 33 (VES 33). A high misfit difference is verified in the northern part of the survey area for is observed at shortest AB/2 spacing for VES 11, 12, 17, 25 deep structures. This difference will be analysed in the next and 28. For the majority of the soundings the fit is quite good, section. with rms error lower than 12%. The Hommath formation (sandy limestone, clay) at the 4. Sensitivity tests northern part of the area is revealed as a low-resistivity zone (resistivity < 100  m). The high content in clay might be The sensitivity of the data to some features in the 3D model the reason for the low-resistivity values. This agrees with was studied considering two models derived from the final the results obtained from 1D inversion for the intermediate inversion model shown in figure 8. In the first model (A) the layers. The main differences between 1D and 3D models in resistivity of all the elements between 300 and 700  mwas this part of the survey area are noted in the deep structures changed to 300  m. This change mainly affects the structures that were revealed to be more conductive in the 3D model— resistivity values lesser than 100  m are noted in the 3D in the central part of the survey area. For the soundings located model in contrast to the 1D results, where values ranging from to the north and south of the survey, the changes on apparent 150 to 200  m are observed. The central part of the survey resistivity curves correspond to changes on lateral structures. area, which corresponds to the Gabal Ahmar formation, is In the second model (B) the resistivity of all the elements at 6 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 (A)(E ) (B) (F ) (C ) (G) (D) Figure 6. W–E geoelectrical cross-section with results of boreholes, resistivity values in  m. a depth greater than 100 m was changed to 700  m. This in VES 3). In contrast to the 3D model, the 1D models change corresponds to an increase in the resistivity of deep obtained from VES located in the northern part of the survey northern and southern structures. This also corresponds to a area suggest resistive deep bedrock (probably made up of slight decrease of the deep structures in the central part of the limestone). survey area. The model responses at nine selected sites are shown in Model A allows us to study the importance of the high figure 9. In this figure the responses obtained with models resistivity (mainly associated with the Oligocene formations A and B are compared with experimental data and with the in the centre of the survey area) in the model responses. responses of the best-inverted model shown in figure 8. Model B was motivated by the discrepancy observed in deep The decrease in the resistivity (model A) does not structures in 1D and 3D models and the misfit between data affect soundings located to the north and south out of and the 3D model response for largest AB/2 spacing at the survey area (VES 3, 8 and 33), showing that high some soundings located in the north part of the area (e.g. apparent resistivity measured for large AB/2 spacing is not 7 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 S Awad Sultan and F A Monteiro Santos Figure 7. Geoelectric cross-section along profile H-H , resistivity values in  m. depth: 0 to 4 m depth: 4 to 8 m depth: 8 to 12 m 825500 825500 825500 Tm 825000 825000 825000 824500 824500 824500 824000 Q 824000 824000 To 823500 823500 823500 823000 823000 823000 F1 822500 822500 822500 679500 680500 681500 679500 680500 681500 679500 680500 681500 W <--- Distance in m ---> E depth: 12 to 16 m depth: 16 to 25 m depth: 25 to 40 m 825500 825500 825500 825000 825000 825000 824500 824500 824500 824000 824000 824000 823500 823500 823500 823000 823000 823000 822500 822500 822500 679500 680500 681500 679500 680500 681500 679500 680500 681500 depth: 40 to 60 m depth: 60 to 100 m depth > 100 m 825500 825500 825500 825000 825000 825000 824500 824500 824500 824000 824000 824000 823500 823500 823500 823000 823000 823000 822500 822500 822500 679500 680500 681500 679500 680500 681500 679500 680500 681500 ohm-m Figure 8. Horizontal slices from the 3D resistivity model. Dashed lines in the first slice represent the contours of the main geological units. VES location is represented by crosses. Tm: Miocene deposits, Q: Quaternary deposits and To: Oligocene deposits. S <--- Distance in m ---> N Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 Figure 9. Results of the sensitivity tests at some chosen sites. Dots are the observed data, best 3D resistivity model responses are represented by a continuous black line (1), responses for the model where resistivities in the range 300–700  m are changed to 300  mare represented by a dashed-dot line (2). The short-dashed line represents the responses of a model with structures deeper than 100 m changed to 700  m(3). originated by lateral effects caused by the high-resistivity 5. Discussion central structures. Soundings carried out in the Oligocene formations (VES 13, 18, 23 and 28) have great sensitivity Attempts to relate geotechnical properties (such as unit weight, to this decrease in resistivity suggesting that high-resistivity water content, liquid limit, plastic limit, liquidity index, Oligocene formations are thick. undrained shear strength, compression ratio, effective stress, grain size dimension, cone resistance, among several others) Soundings located in the northern part of the area, such to geoelectrical results are not so frequent. The relatively few as VES 3, show a better fit (mainly for large AB/2 spacing) published results relating mechanical properties to electrical when the resistivity of deep structures increases (model B). properties seem to be contradictory (Cosenza et al 2006, This shows that deep structures in that part of the 3D model Endres and Clement 1998, Braga et al 1999, Giao et al are not well resolved. Soundings carried out in the centre of 2003). The only correlation that seems to be well understood the survey area (VES 18, 23) are not affected by resistivity and well established is the interdependence between electrical changes originating from model B. Soundings located in the resistivity and water content. Quaternary formations (VES 16, 28 and 33) have strong A relatively good correlation between the 1D and 3D sensitivity to deep resistivity, showing that deep structures resistivity models and the geology can be noted for the upper in the southern part have resistivity significantly lesser than layers. The relatively high resistivity (160  m) at depths 700  m. 9 Downloaded from https://academic.oup.com/jge/article-abstract/5/1/1/5127447 by DeepDyve user on 21 May 2020 S Awad Sultan and F A Monteiro Santos between 18 and 40 m represents the combined response of electrical data: a case study at Garchy in France J. Appl. Geophys. 60 165–78 the gravel and of the coarse and fine sand formations. In the Dannoski G and Yaramanci U 1999 Estimation of water content and north part of the survey area the models show a decrease in porosity using combined radar and geoelectrical measurements the resistivity (to 2–5  m in 1D models) approximately at Eur. J. Env. Eng. Geophys. 4 71–85 10–20 m depth. This change in the resistivity correlates quite Debeglia N and Dupont F 2002 Some critical factors for engineering well with the beginning of a clay layer. and environmental microgravity investigations J. Appl. Geophys. 50 435–54 Clay layers are important in civil engineering. For El-Quady G, Monteiro Santos F A, Hassaneen A Gh and Trindade L example, clay minerals have a great affinity for water. Some 2005 3-D inversion of VES data from Saqqara archaeological clay minerals swell easily and may double in thickness when area Egypt Near Surf. Geophys. 227–33 wet. The process by which some clay minerals swell when Endres A L and Clement W P 1998 Relating cone penetrometer test they take up water is reversible. Swelling clay expands or information to geophysical data: a case study Symp. Application of Geophysics to Engineering and Environmental contracts in response to changes in environmental factors (wet Problems (SAGEEP98) (Chicago, USA) and dry conditions, temperature). According to Velde (1995), Geological Survey of Egypt (EGSMA) 1996 Geological and hydration and dehydration can vary the thickness of a single geophysical studies on new Hilioplis City, Geol. Surv. of clay particle by almost 100%. Therefore, any construction Egypt, Internal report (12/1996) built on soil containing swelling clays may be subject to Giao P H, Chung S G, Kim DY and Tanaka H 2003 Electrical structural damage caused by seasonal swelling of the clay imaging and laboratory resistivity testing for geotechnical investigation of Pusan clay deposits J. Appl. Geophys. portion of the soil. 52 157–75 IPI2Win-1D Program 2000 Programs set for 1-D VES data 6. Conclusions interpretation, Dept. of Geophysics, Geological Faculty, Moscow University, Russia Geophysical surveys can contribute to identify subsurface Karastathis V K, Karmis P N, Drakatos G and Stavrakakis G 2002 zones which are inappropriate for the construction of building Geophysical methods contributing to the testing of concrete dams. Application at the Marathon Dam J. Appl. Geophys. foundations. Electric imaging produced from resistivity data 50 247–60 proved to be a useful tool in clay layer detection. Koefoed O 1960 A generalized Cagniard graph for interpretation of The results presented here show that the survey area geoelectric sounding data Geophys. Prospect. 8 459–69 has a complex subsurface electrical resistivity distribution, Loke M H and Barker R D 1996 Practical techniques for 3D conditioned by lithology, water content and tectonic structures. resistivity surveys and data inversion Geophys. Prospect. From a civil engineering point of view the main results are 44 499–523 Loke M H 1997 Rapid 2D resistivity inversion using the related to the characterization of the clay and sand (Oligocene least-squares method RES2DINV Program Manual (Penang, age) layers. Clay soils are more susceptible to subsidence Malaysia) being also strongly affected by environmental conditions Monteiro Santos F A, Andrade Afonso A R and Mendes-Victor L A (Soupios et al 2007). Therefore, special care is recommended 1997 Study of the Chaves geothermal field using 3D resistivity if foundation footings are to be constructed in the northern part modeling J. Appl. Geophys. 37 85–102 of the survey area. 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Journal of Geophysics and Engineering – Oxford University Press

Published: Mar 6, 2008

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