Two and Three-Dimonsional ERT Modelling for a Buried Tunnnel

Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 7(3): 118-127 Scholarlink Research Institute Journals, 2016 (ISSN: 2141-7016) jeteas.scholarlinkresearch.com Journal of Emerging Trends Engineering and Applied Sciences (JETEAS) 7(3):118-127 (ISSN: 2141-7016) Two and Three-Dimonsional ERT Modelling for a Buried Tunnnel 1* Mostafa Ebrahimi, 2 Abed Asadi Taleshi, 3 Alireza Arab-Amiri, 4 Masoud Abbasinia 1, 2, 4 Institute of Geophysics, University of Tehran,Tehran, Iran. 3 School of Mining, Petroluem and Geophysics Engineering, Shahrood University of Technology, Shahrood, Iran. Corresponding Author: Mostafa Ebrahimi Abstract Nowadays, finding either natural or man-made hollows in the subsurface is a challenge for civil engineers. Thanks to advancements in science, geophysical methods can handle this problem. Two and three-dimensional distribution of subsurface electrical resistivity are known as electrical resistivity tomography. Nowadays, geoelectrical tomography is an inseparable part of engineering, exploration and the environmental studies. A growing number of electrical arrays have several advantages and disadvantages. Choosing appropriate array and considering the relation between array parameters and geometry of exploration target are the necessities of geophysical studies. Regarding the heterogeneous nature of the earth, it is clear that 2-D studies have obviously higher accuracy and reliability compared with 1-D. likewise, 3-D studies are more accurate and reliable compared with 2-D ones. The purpose of this study is to investigate geoelectrical response of tunnel space and its geometrical relationship with the data-acquisition parameters so as to boost the efficiency of electrical resistivity method in similar studies. For this purpose, the geological circumstances of the tunnel were twodimensionally modeled with finite difference method, assuming 3% noise, for Wenner-Alpha, Wenner- Schlumberger and Dipole-Dipole arrays. Thus, resistivity of tunnel and surrounding medium are 100 and 10 ohm-meter, respectively. Then the values of resistivity were inverted and obtained norm L1 method. For all arrays, number of electrodes and electrode spacing were considered 36 and 1 meter, respectively. Data point density, sensitivity, horizontal and vertical resolution of arrays helped to select appropriate array and find the relation between the array s geometry and geometry of tunnel. It is found that Dipole-Dipole array has higher data coverage and sensitivity compared to Wenner-Alpha and Schlumberger. The vertical distance of data points is a function of the dipole length. Meanwhile, the horizontal distance between two adjacent data points depends on the array midpoint movement. In order to detect the tunnel, the horizontal length of tunnel must be at least twice as much as horizontal distance of two adjacent data points. What is more, vertical length should be at least twice the vertical distance of two adjacent data points. Therefore, the electrode spacing must be less and equal to half of horizontal length of tunnel and dipole length should be less and equal to 1.78 times of vertical length of tunnel. 3-D forward and inverse modelling were implemented. The results of 3-D inversion of 2-D data indicate reasonable ability of this method. Expanding horizontal resolution relations among profiles leads to obtaining a clear image of anomalies which in turn results in the distances among parallel profiles should be less or equal to half of the width of anomaly along the perpendicular to profiles. In spite of efficiency of this method for mapping tunnel space, the contrast between tunnel space and surrounding medium, earth heterogeneity, high level of noise in depth and dip of tunnel are some limitations which have adverse effects on results. Keywords: apparent resistivity, tomography, theory, numerical study, modelling INTRODUCTION Existing either natural or manmade empty space is a hazard for construction. Finding these hollows and their dimensions is a challenge that should be solved. Fortunately, geophysical methods during last decades has been able to found several ways to handle this problem. The physical changes of earth features can be measured in one, two, or three dimensions depending on both aim and scale of geophysical studies. Geological terms, in geophysical exploration, the environmental and engineering studies are often accompanied by heterogeneous which means that there are physical changes of the earth in vertical and/or horizontal directions. Vertical electrical sounding is not proper to image such complex geology conditions (Aizebeokhai et al. 2011). If the assumption of depth changes of resistivity can be valid, this method is so efficient and can widely be used by geophysicists (Omosuyi et al. 2008; Raimi et al. 2011). Electrical resistivity tomography (ERT) is one of the most prevalent geophysical methods to investigate 2- D or 3-D distribution of the earth s apparent electrical resistivity which has significantly been considered, especially in environmental areas, exploration and engineering studies by researchers in recent years. (Al-Fares 2014; Dostal et al. 2014; Badmus et al. 2012). 118

In 2-D imaging of resistivity, it is assumed that the subsurface medium changes vertically and laterally along a profile. A vast number of studies have been done based on this assumption and in such relatively complex geological conditions (Amidu & Olayinka 2006; Ayolabi et al. 2013). Subsurface terrains have inherently three-dimensional features. Consequently, two-dimensional assumption is rejected which in turn results in creating anomalies out of plane in the resistivity models and it leads to wrong interpretation (Bently & Gharibi 2004). As a result, threedimensional work can boost the efficiency of resistivity measurement and generate a threedimensional interpretation model. In recent years, data-acquisition facilities and processing software make progress which is followed by more accurate and faster results. Three-dimensional studies of resistivity are carried out in two ways: 1. Using parallel profiles data which can produce three-dimensional models (Leucci et al. 2007; Aizebeokhai et al. 2013(. 2. Three-dimensional data which can produce threedimensional models. (Badmus et al. 2011; Negri et al. 2008). In the second method, electrodes are usually placed in a square or rectangular grid with constant electrode spacing arranged on both x and y directions (Figure 2).The most common arrays in three-dimensional surveys are the pole-pole, pole-dipole and dipoledipole. Other arrays due to poor data coverage in the margin of electrodes are not much effective Measurement of electrical resistivity is done by different electrode arrays (Figure 1).Wenner (Alpha- Beta-Gamma), Wenner- Schlumberger, dipole-dipole, pole-dipole and pole- pole are the most commonlyused arrays. Figure 1. As is shown, geoelectrical arrays, in which P 1 and P 2 are potential electrodes, C 1 and C 2, are current electrodes, respectively. K is geometric factor Each geoelectrical array has some advantages and disadvantages.some factors, in particular sensitivity to background noise, signal to noise ratio, anomaly effect, maximum of interpretable depth and the resolution of final geoelectrical models, play a vital role in difference of these arrays with each other (Aber & Meshin Chi Asl 2010). For instance, Schlumberger array has a good vertical resolution. Thus, it is the most appropriate array for electrical sounding. Wenner-alpha and dipole-dipole arrays are the most commonly-used arrays in two-dimensional tomography. Dipole-dipole and Wenner arrays have the maximum penetration depth and signal to noise ratio (Rey et al. 2013). However, the Wenner array is more sensitive to vertical changes compared to Dipole-dipole and schlumberger arrays. Dipole-dipole array is sensitive to lateral changes of resistivity. Figure 2. Electrode arrays which were used for a 5 6 grid in resistivity data acquisition (Aizebeokhai 2010). In the resistivity method, we have two types of forward and inverse modeling like other geophysical methods. The measured values in the field operations are called apparent resistivity. Interpolating these parameters leads to production of resistivity pseudo section which is a perspective of subsurface distribution of apparent resistivity. Producing a reliable model of apparent resistivity distribution is possible in the inversion method of apparent values. Calculating response of synthetic models is the main aim of forward modeling. The methods which used to solve forward modeling problems are including: 1. Integral equation method of Hohmann (1975) 2. Network method of Pelton et al. (1978) 3. Finite Element Method of Silvester & Ferrari (1990) 4. Finite difference, Mufti (1976). 119

3-D modelling can be similarly done by finite element and finite difference methods. Inverse modelling finds a model with the most similar responses to the field data. We are in search of model in which estimates physical properties as an ideal mathematical representation of earth. Least square method (Inman 1975) is one of proposed methods to solve inverse problem (Treitel & Lines 2001). The main purpose of paper is investigating 3-D and 2-D geoelectrical response of an empty subsurface space (tunnel) which is followed by finding the best relation between parameters of data acquisition and tunnel s geometry. Figure 2 is a synthetic model of tunnel. In this model, apparent resistivity of tunnel and surrounding are 100 and 10 ohm-meter, respectively. This modelling was implemented by RES2DMOD software and finite difference method with assuming 3% noise. The number of electrodes and electrode spacing were considered 36 and 1 meter, respectively. Figure 3 depicts the synthetic model of tunnel and its physical properties. In order to choose appropriate array for detecting tunnel, the geoelectrical response of three arrays including dipole-dipole, Wenner-alpha and Wenner-Schlumberger were calculated. 2-D forward and inverse modelling were implemented by RES2DMOD and RES2DINV software. 3-D modelling was done by RES3DINV and RES3DINV for forward modeling and inverse modeling, respectively. In the subsequent stage, we explain forward and inverse modeling by use of these programs in more details. METHOD In forward modeling, values of apparent resistivity are calculated based on physical characteristics of model. Nowadays, the finite element and finite difference methods are widely used to solve electrical potential equation. These methods consider the subsurface environment as a series of blocks and calculate potential values at intersection of blocks and then calculate the apparent resistivity values for each block (Loke 2002). To begin with, tunnel structure was designed as a two-dimensional model and tunnel structure is assumed as an empty space. Therefore, apparent resistivity value is considered much more than surroundings. Figure 3. Synthetic model of the tunnel Inversion was done by RES2DINV software and norm L1 method. As matter of fact, application of this method is mainly attributed to the tunnel s sharp boundary with the surroundings. The purpose of this method is optimizing fitting error (Loke et al. 2003). During inversion process, initial parameters of model change to minimize the errors of the field apparent resistivity values and calculated resistivity. These changes will continue until reaching the desired level of error. Figure 4 shows inversion sections of these three arrays 120

Figure 4. Inversion sections of calculated apparent resistivity of synthetic model using dipole-dipole (up), Wenner- schlumberger (middle) and Wenner- alpha (down) arrays (dashed square shows tunnel location). Figure 5. Sensitivity sections of dipole-dipole (up), Wenner- Schlumberger (middle) and Wenner-alpha (down) arrays. Horizontal resolution means lateral distance between As is seen, the dipole-dipole model has higher two measure points, with the same depth which has vertical and lateral resolution as well as in this array; equal electrode spacing. Vertical resolution is the apparent resistivity anomaly is highly matched to location of tunnel. Because this array benefit from high quality of dense measure points and sensitivity vertical length between two points with the same offset. This can be different, for various types of arrays. section Fig.5. 121

Table 1 illustrates the relation between modeling depth and data acquisition parameters for three types of arrays (Hamidou-Tamssur 2013; Ebrahimi & Abbasinia 2015). In this table, L, n, a and Z e are the array length, leap number, potential electrode spacing and modelling depth, respectively. According to this table, dipole-dipole array benefit from a better vertical resolution and is more appropriate to detect the tunnel. Data density, sensitivity, horizontal and vertical resolution of dipole-dipole array has relation with operation parameters. According to Table 1, the vertical distance of points is a function of the dipole length. Table 1. Relation between modeling depth, survey parameters and vertical resolution Array Wenner Alpha W-SCH n=1 n=2 n=3 Dipole-Dipole n=1 n=2 n=3 Z e/a 0.52 0.52 0.93 1.32 0.42 0.7 0.96 Z e/l 0.17 0.17 0.19 0.19 0.14 0.17 0.19 Vertical resolution 0.52a 0.39a 0.26a Meanwhile, the horizontal length depends on the array midpoint movement. By the way, the number of leaps between the dipoles controls penetration depth. Totally, the volume of measurement points can be controlled by changing these three parameters, which have direct relation with the quality section. Figure 6 is a hypothetical case of data density around the tunnel space. In order for three-dimensional modeling of tunnel condition, a grid was designed with 33 10 nodes (electrodes) and one meter electrode spacing. Figure 6. The position of hypothetical data points related to tunnel geometry Figure 7. Horizontal sections of three- dimensional model of tunnel 122

The physical conditions of the tunnel were designed in a way that the apparent resistivity of tunnel was 10 times more than surroundings. Figure 7 shows the tunnel model as horizontal sections. As is shown, the tunnel has lateral expansion in two directions. The tunnel space begins from the depth of 0.35m and ends at depth of 5.8 m. The thickness of each section is 0.35 m. In terms of previous section; the best array to measure apparent resistivity in complex structure is dipole-dipole array. Assuming the measurement in x direction, the values of apparent resistivity for eleven profiles with one-meter distance were obtained. Figure 8 illustrates pseudo-sections of model as horizontal sections. As a result of greater distance of measure points in Figure 8 the resolution of deeper sections is less than shallow sections Figure 8. Apparent resistivity pseudo-sections calculated in x direction Figure 9. Horizontal slices of inversion results 123

Figure 10. Vertical sections of inversion results along x axis Figure 11. Sensitivity sections of three- dimensional inversion Inversion of three-dimensional data was implemented by RES3DINV software. Figure 9 and 10 show results of inversion as horizontal slices and vertical sections. 124 Figure 11 shows the horizontal slices of inversion sensitivity. In order to have a better representation of tunnel geometry, inversion outputs were imported to VOXLER software. This software can display data in three-dimensional form.

Figure 12. Geophysical model of tunnel space CONCLUSION Sensitivity and two-dimensional inversion sections represent high capability of dipole-dipole array to detect the tunnel space. As to Figure 6, to detect the tunnel, we need at least two horizontal and vertical points in apparent resistivity sections. The horizontal length of tunnel must be at least twice as much as horizontal length of measurement points; also its vertical length should be at least twice as much as vertical length of both measurement points. As the following relations (equations1-6), for horizontal and vertical resolution of dipole-dipole array, the vertical length of the tunnel should be more and equal to twice of 0.26 dipole length and its horizontal length must be more and equal to twice of the electrode spacing. (Ebrahimi & Abbasinia 2015). H ES (1) R V 0.26 D R (2) L And H L(T) 2 H R (3) V L(T) 2 V R (4) Thus: ES H L(T) / 2 (5) D L 1.78 V L(T) (6) In relation 1, it has assumed that horizontal resolution is equal to electrode spacing in data acquisition. Moreover, In relation 2, since geophysical survey is done with Dipole-Dipole method and according to table 1, vertical resolution with the same offset is equal to 0.26 Dipole length. Ebrahimi & Abbasinia (2015) proved equations 3-6. Where, HR and VR are horizontal and vertical resolutions, HL(T) and VL(T) are horizontal and vertical length of tunnel, ES and DL are electrode spacing and dipole length, respectively. As mentioned above, a wide range of Dipole-Dipole capacities have been proved. In order to detect tunnel, these relations suggest that the smaller values of electrode spacing and dipole length are more accurate. It should be noted that the smaller dipole length limits the exploration depth. Thus, there is an uncertainty. In terms of this uncertainty, data acquisition would be considered by these parameters. The results of threedimensional inversion of two-dimensional data indicate reasonable ability of this method at threedimensional imaging of subsurface targets. Thus, there is a good correlation between the outputs and Figure 9 and 10. Using the inversion algorithm of the norm L1 highly helps to detect the location of tunnel boundaries. Since there is a decrease of dipole-dipole sensitivity array with increase of depth, accuracy and reliability of inversion results decrease as the increase of depth. Expanding horizontal resolution relations between the profiles can lead to gaining a clear image of anomalies. Distance between parallel profiles should be less or equal to half of the width of anomaly along the perpendicular to profiles. Results show that three-dimensional imaging of a tunnel with electrical resistivity tomography method is possible, but there are some limitations which have several effects on efficiency, including the contrast between tunnel space and surrounding medium, earth heterogeneity, high noise level, depth and dip of tunnel. REFERENCES Aber, H. & MeshinChi Asl, M.S. 2010. Present a proper pattern for choose best electrode array based on geological structure investigating in geoelectrical tomography in order to get the highest resolution image of the surface, the 1th international applied geological congress, Islamic Azad University, April 26-28. Aizebeokhai, A.P., 2010. Acquisition geometry and inversion of 3D geoelectrical resistivity imaging data for environmental and engineering investigation, PhD thesis in applied geophysics, Covenant University, Ota, Ogun state, Nigeria. 125

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