A methodology for three dimensional modeling of subsurface geologic structure in mantled karst area

Abstract

Geological defects near or beneath built-up area may lead to sudden collapse of ground surface, and cause fatal accidents with losses in human life and property. To understand the features of underground stratum structure and anomalies in mantled karst area, a three dimensional modeling methodology is developed in this paper. Firstly, Timely data is obtained through surface geology investigation and borehole data. Subsequently, Ground Penetrating Radar (GPR) survey is conducted along the survey lines, which has a mixed orthogonal distribution, and a series of two dimensional GPR profiles are obtained. Concurrently, the detailed information of underground stratum structure and anomalies is resolved by the apexes of diffraction hyperbolas and lateral changes in the reflection pattern, including size, geometry and the location. Finally, based on the integrated analysis of slices being parallel or perpendicular to survey lines, a spatial database relative to the geological map is positioned, and the three dimensional model of geological structure is reconstructed. To verify the validity of the method, an application is performed in Nan’an district in Chongqing city. The results indicate the method can provide a simple and relatively effective way for understanding the subsurface geologic condition in practice.

Keywords

Three dimensional modeling ground penetrating radar survey GPR profiles interpretation borehole surveying surface geology investigation

1. Introduction

The shape of the surface of the earth is the result of a wide set of physical and chemical processes that have acted over thousands or millions of years. The karst landscape takes its name from a region comprised between NE Italy and Slovenia dominated by outcrops of carbonate rocks [1]. In China, karst landscape distributes widely, and carbonate rocks occupy an area of approximately 3.25 million km ${}^{2}$ . Of the total area, exposed rock accounts for some 1.25 million km ${}^{2}$ , and the remaining is covered [2]. In most cases, carbonate rocks are dissolved by slightly acidic waters, which display the distinctive landforms such as karren, caves and underground drainage [3, 4, 5]. With the development of economic and urbanization, the demand for primary resources increase, including land ,water, food, building materials and electricity [5], and the dimensions of engineering construction and speed have accelerated. Owing to the effects of natural erosion and the human activities, shallow defects regularly occur. The frequently hidden character of the defects may lead to fatal accidents with losses in human life and property. As a result, indentifying the underground geological structure accurately is beneficial for avoiding geological hazards and taking effective preventive measures.

GPR (ground penetrating radar) is a kind of non-destructive geophysical detection technique. On account of high resolution, GPR has been applied extensively in many fields. Underground archeological surveying [6, 7, 8] is a typical representative. For hydraulic projects, erosion of clay core for dams [9], structural anomalies of the dam [10, 11, 12], underwater hydraulic structures [13] and the detection of multiple hidden defects [14] were conducted. Reliable data can be obtained for reasonable renovation and safety management of the projects. In geological prospecting, assess structural condition and also to locate buried objects [15, 16], investigation of near-surface fault properties [17, 18], karstic cavities and sinkholes characterization [19, 20, 21, 22, 23, 24, 25, 26, 27]. Lithology and moisture content changes [28, 29] were carried out, which would be significant for controlling the occurrence of risks. In civil engineering, detecting and mapping cracks in rock slopes [30], building stability [31], road evaluation [32], successful applications in investigation of scour pits around underwater bridge piers [33] were included.

Significant achievements have been made according to the available literature. However, the study on the boundary and geometry dimension of anomalous area is relatively small. In this paper, a three dimensional modeling methodology is developed, and the method combines geological survey with GPR survey. Geological survey is used to obtain timely data, and the detailed information of overlying units and karst cavities could be resolved by a series of two dimensional GPR profiles interpretation. Based on a spatial database relative to the geological map, the three dimensional underground geological structure could be restructured. Finally, an application is performed in Nan’an district in Chongqing city is used to verify the validity of the proposed method.

2. Methodology

The proposed method mainly includes three parts (Fig. 1).

The geological survey records are sources of geological information. Timely data is collected from geological mapping or other field works, inluding borehole, elevation and outcrop descriptions with lithological information.

Figure 1.

Flow of the proposed method. (a) Geological survey records (b) GPR survey (c) Geological structure reconstruction.

To understand the features of stratum structure and karst cave, a RIS-K2 instrument by the IDS company (Italy) was used in the study, using 80 MHz shielded antenna. The GPR instrument is equipped with data acquisition software (K2FastWave software) and data processing software (GresWin 2). The survey parameters were set to record one scanning datum for every 2.5 cm at a speed of approximately 1 m/s. Each scan curve was composed of 512 individual data points. GPR survey is employed along survey lines. To obtain high-quality information data, the instrument was deployed close to the ground surface along the survey lines. Owing the different attribute of media it penetrates, part of the signals emitted will be reflected at the interface between various materials. The reflected signals can be received, magnified and digitized by the receiver, and then sent to the mainframe for storage. The signal of GPR profiles are enhanced through data processing and the more accurate and better visual geophysical signatures are represented, the general operation sequence of data processing is (1) vertical bandpass filter, (2) move start time, (3) background removal, (4) linear gain, and (5) smoothed gain. Finally, based on the principle of the GPR signal behavior, a time to depth conversion was performed, using Eq. (1).

$\displaystyle h=vt/2$ (1)

Where $t$ is two-way reflection time and $v$ (110 m/mms) is the propagation velocity in the media.

Detailed information is shown through images interpretation, including the embedded depth, the boundary of karst caves and the thickness of soil and interlayer, a spatial coordinate system relative to the geological map could be easily positioned.

Finally, Based the spatial database integrated analysis of slices being parallel or perpendicular to survey lines, the three dimensional model of underground geological structure is reconstructed.

3. Analysis of GPR response signatures

To characterize the GPR response signatures on geometric effect and geophysical property change, GPR profile analysis of three culverts in Chongqing were performed.

Figure 2.

Culvert 1: (a) picture of culvert 1 in the field (A present vegetation is extremely developed at a localized area, B and C are the defects in structure); (b) diagram of culvert 1’s dimension.

Figure 2a shows a section of culvert 1 in the field, and the stratum structure could be delineated through exposed region. There is a river below the culvert, and vegetation is extremely developed at a localized area. Refer to field measurements, the thickness of overlying concrete pavement is 0.2 m, sandstone is the bed rock. The apex of culvert is 1.24 m from ground surface, and the span reaches 3.23 m (Fig. 2b).

Figure 3.

Labeled GPR profile of culvert 1 after processing. ( $L_{1}$ is the interface of different medias; B and C present the change of image in lateral direction; red quasi-hyperbolic curve is the reflection from the top of culvert 1, and green quasi-hyperbolic curve is the inter-formational multiples appear, which is contribute to the filled material; A and D are signal weaken zone.

Labeled GPR profile of culvert 1 is presented in Fig. 3, which was acquired parallel to the road cut. Electromagnetic wave is sensitive to different electric parameters [33]. The continuity of profile was disrupted by lithology change at 0.2 m depth, interface $L_{1}$ was determined (Fig. 3). The reflection characteristic was consistent with the space position between pavement and bedrock (Fig. 2b). Comparing the images of area B and area C in Fig. 2a with those in Fig. 3 respectively, lateral changes in signals indicate the difference in bedrock structure. The hyperbola (labeled by red curve in Fig. 3) was caused by the diffraction on the top boundary of the culvert, the buried depth of culvert was 1.24 m inferred from the coordinate of apex in depth. The space between culvert and the river was filled with air, hyperbola (labeled by green curve in Fig. 3) generates from multiple interferential reflections. Owing to the high relative permittivity of fresh water, reflection from the base of the culvert was absent on the profile (area D in Fig. 3). The effects of vegetation lifting the antenna from the rock surface and of overhanging regions could not be avoided, and the weakening zone appears (area A in Fig. 3).

Figure 4.

Culvert 2: (a) picture of culvert 2 in the field and (b) diagram of culvert 2’s dimension.

Figure 5.

GPR profile of culvert 2: (a) radargram after processing (E is the anomalous region) and (b) labeled image after processing (F, G, H and I are the apexes of diffraction hyperbolas).

Culvert 2 underlies the thick compacted sandstone (Fig. 4a). After field investigation, the section is irregular quadrilateral, and the actual dimension is shown in Fig. 4b. Anomaly E was confirmed through processed imagines (Fig. 5a). Hyperbolas appear at the turning points, the records indicate coordinates as follows: F (1.8 m, 1.04 m), G (2.15 m, 1.04 m), H (1.75 m, 1.6 m), I (2.23 m, 1.6 m). Linking the four points together, the boundary of anomaly can be determined (Fig. 5b). As shown by the results of validation, the error is 0.02 m in depth and horizontal direction.

Figure 6.

Culvert 3: (a) picture in the field and (b) diagram of actual dimension.

Figure 7.

GPR profile of culvert 3: (a) radargram after processing (G and K are the anomalous regions) and (b) labeled image after processing (L, M, N and Q are the apexes of diffraction hyperbolas).

The third sample is subsurface concrete pipe, which is surrounded by vegetation (Fig. 6a). The concrete pipe situates below 0.5 m thick soil, and the diameter of it is 0.35 m (Fig. 6b). A pair of hyperbolas in area G characterizes circle section signatures (Fig. 7a). Meanwhile, there is the black-white-black alteration in the image, because the permittivity of air is lower than concrete. Under the assumption of homogeneous soil and rock (neglecting medium depolarization and dispersion effects), the distance of apexes in depth represent the diameter. According to coordinates L (1.2, 0.5), M (1.2, 0.85), the buried depth of the pipe is 0.5 m and the diameter is 0.35 m (Fig. 7b). The coordinate of L in x direction is 1.2 m, which is corresponding to the actual location (Fig. 6b). In addition, anomaly K appears on the profile, which indicates there may be another buried pipe at the depth of 0.95 m.

4. Three dimensional modeling

On the basis of profile analysis above, the GPR response signatures on geometric effect and geophysical property change were concluded. The accuracy of dimension and boundary determined by the apexes of diffraction hyperbolas and lateral changes in the reflection pattern has been also demonstrated. Next, these conclusions will be used to generate 3D modeling in practice.

4.1 Site description

A planning area is situated on the Nan’an district in Chongqing, and study area is located in the south of the region (Fig. 8).

Figure 8.

Location of study area.

Figure 9.

Images of study site. (a) Layout of survey. All the intersections numbered from 1 to 15 are regarded as the control stations, which get ready for the subsequent study. (b) Image of site.

The study area is an eroded hilly landform. The topographic dip direction is 21 ${}^{\circ}$ , and the slope angle varies between 15 ${}^{\circ}$ to 36 ${}^{\circ}$ . In the meanwhile, the weather is subtropical climate type, and the annual average temperature varies from 16.5 ${{}^{\circ}}$ to 18.5 ${{}^{\circ}}$ . Thin soil covers the entire field, and thick limestone is the main component of the bedrock in the subsurface. In addition, the preliminary geological survey indicates the presence of an adverse geological phenomenon. In particular, various natural karst caves appear in the partial region.

Considering local environment and satisfactory data, the layout of this survey lines had a mixed orthogonal distribution, with an interval of 1 m. A number of strings were used as guideline for each profile to ensure the straightness and parallelism (Fig. 9a and b).

4.2 Integrated data acquisition

4.2.1 Geological survey records

1. Surface geology investigation

According to the geological map, the coordinates of control stations from 1 to 15 are shows in Table 1.

Table 1
Spatial coordinates of control stations

NumberCoordinate	$x$	$y$	$z$
1	0	0	438.4
2	1	0	438.2
3	2	0	438.1
4	3	0	438
5	4	0	437.9
6	0	1	437.9
7	1	1	437.8
8	2	1	437.7
9	3	1	437.6
10	4	1	437.5
11	0	2	437.5
12	1	2	437.4
13	2	2	437.3
14	3	2	437.2
15	4	2	437.1

Figure 10.

Log of borehole CK8: R ${}_{1}$ (the mixture of bondless rock blocks and granular soils), R ${}_{2}$ (Gray middling weathering limestone), R ${}_{3}$ (clay).

2. Boreholes and sampling

According to information gathered from a log of borehole CK8 drilled 20.8 m, the area is underlain by the following stratigraphic units from top to base (Fig.9):

(1)

Unit R ${}_{1}$ is a mixture of bondless rock blocks and granular soils, the thickness of it is 0.4 m. In addition, unit R ${}_{1}$ composed of intense weathered limestone with clayey soil. In the meanwhile, rock block accounts for 50% to 60% of the total amount, the size of it rock blocks generally ranges from 50 mm to 400 mm, and the maximum value may reach 400 mm.

(2)

Gray middling weathering limestone is the major constituent of unit R ${}_{2}$ . R ${}_{2}$ has a thickness from 0.4 m to 2 m and from 7.8 m to 20.8 m respectively. The thick layered structure and cryptocrystalline result in good strength and integrity.

(3)

Corresponding to unit R ${}_{3}$ , the karstic residue between 2.0 m and 7.8 m depth consists of clay, which is yellow and in plastic state.

Table 2

Depth of interfaces (m)

	1	2	3	4	5
Point
Interface 1	0.4	0.65	0.55	0.65	0.55
Interface 2	2.25	1.74	1.9	2.15	1.69
Point	6	7	8	9	10
Interface 1	0.42	0.3	0.35	0.42	0.24
Interface 2	2.06	2.02	2.01	1.97	2.11
Point	11	12	13	14	15
Interface 1	0.22	0.15	0.18	0.16	0.11
Interface 2	2.01	1.6	1.75	1.65	2.01

Figure 11.

GPR profile of geological cross-section along L ${}_{1}$ .

Figure 12.

Oscillogram after proper operation.

Figure 13.

GPR profiles of geological cross sections along L ${}_{1}$ : (a) GPR profile of geological cross sections along L ${}_{1}$ after processing. (b) Labeled GPR profile of geological cross sections along L ${}_{1}$ after processing. B and D are the reflections from the top of the karst cavities. C and E represent reflections from the top of the karst cavities.

4.2.2 GPR profiles interpretation

Figure 11 is the GPR profile of geological cross section along L ${}_{1}$ . x axis is the distance along the survey line, and the vertical axis represents location in depth direction. On the whole, the black-white-black alteration exists above the depth of about 2 meters, and there are irregular reflections in the rest part. Firstly, the top region was selected to be analyzed. The continuity is disrupted at about 0.6 m, which represents the existence of interface. Moreover, the width of amplitude changed, which also indicates different feature of the substance. Clicking the determined point (Fig.12a), locating on the vertical line which go through control station numbered from 1 to 15 (Fig.10a), then the accurate location can be read (Fig.12b). Repeating the operation to other cross sections, the embedded depths of interfaces can be obtained (Table 2).

Figure 14.

GPR profiles of the geological cross -sections along L ${}_{2}$ : (a) GPR profile of geological cross sections along L ${}_{2}$ after processing. (b) Labeled GPR profile of geological cross sections along L ${}_{2}$ after processing. B and D are the reflections from the top of the karst cavities. (B ${}_{1}$ , C ${}_{1}$ ; B ${}_{2}$ , C ${}_{2})$ are reflections from the top of the karst cavities, and (D ${}_{1}$ , E ${}_{1}$ ; D ${}_{2}$ , E ${}_{2})$ represent reflections from the bottom of the karst cavities.

Figure 15.

GPR profiles of the geological cross -sections along L ${}_{3}$ : (a) GPR profile of geological cross sections along L ${}_{3}$ after processing. (b) Labeled GPR profile of geological cross sections along L ${}_{3}$ after processing. B and D are the reflections from the top of the karst cavities. (B ${}_{21}$ , C ${}_{21}$ ; B ${}_{3}$ , C ${}_{3})$ are reflections from the top of the karst cavities, and (D ${}_{2}$ , E ${}_{2}$ ; D ${}_{3}$ , E ${}_{3})$ represent reflections from the bottom of the karst cavities.

Next, detailed analysis was carried out in the rest zone. To get a better result, the profile was labeled (Fig. 13). It can be found that there are a number of irregular reflection waves in the depth of 1.5 m–10 m. Under further analysis, two pairs of hyperbolas were marked with the red curve, which were caused by diffraction on the top and bottom of circular sections of karst caves (Fig. 13b). Coordinates of apexes of the hyperbolic reflection can be read from image, they are B (1, 1.5), C (1, 2.5), D (1, 5) and E (1, 6.5). So the diameters are 1 m and 1.5 m respectively.

The radergram of geological cross sections along L ${}_{2}$ and L ${}_{3}$ (Figs 14 and 15) were similar to Fig. 5. From radiolocation theory, it is known [35, 36] that in order for a strong coherent reflection to be obtained, the first Fresnel zone at the centre frequency of the antenna should be at least the same size as the target. For L ${}_{2}$ it can be inferred that the karst caves boundary ranging from 2.8 m to 3.5 m and from 5.0 m to 7.0 m in depth, and ranging from 1 m to 2 m in x axis direction (Fig. 14). In the same way, the lengths of rectangular are 0.7 m, 1 m, 1.8 m and 2 m respectively for L ${}_{3}$ (Fig. 15). Comparing the GPR profile interpretation of geological cross section along L ${}_{2}$ with boring log in the same position, it suggests that the regions may be affected by karst process are at the depth of 2–7.9 m and 2–7.8 m respectively. The results are in agreement with each other.

Figure 16.

The GPR profiles of the geological cross-sections along T ${}_{1}$ : (a) GPR profile of geological cross sections along T ${}_{1}$ after processing. (b) Labeled GPR profile of geological cross sections along T ${}_{1}$ after processing. B ${}_{4}$ and C ${}_{4}$ are reflections from the top and the bottom of the karst cavities, and (D ${}_{4}$ , E ${}_{4}$ ; D ${}_{5}$ , E ${}_{5}$ ) are reflections from the top and the bottom of the interlayer.

Figure 17.

The GPR profiles of the geological cross-sections along T ${}_{2}$ : (a) GPR profile of geological cross sections along T ${}_{2}$ after processing. (b) Labeled GPR profile of geological cross sections along T ${}_{2}$ after processing. B ${}_{5}$ and C ${}_{5}$ are reflections from the top and the bottom of the karst cavities, and (D ${}_{6}$ , E ${}_{6}$ ; D ${}_{7}$ , E ${}_{7}$ ) are reflections from the top and the bottom of the interlayer.

Figures 16–20 show the GPR profiles along the rest five survey lines (T ${}_{1}$ , T ${}_{2}$ , T ${}_{3}$ , T ${}_{4}$ , T ${}_{5}$ ). The diameters of circular sections are 0.5 m, 0.5 m, 0.5 m, 1.5 m and 0.7 m from T ${}_{1}$ to T ${}_{5}$ respectively. Information gathered from the log of borehole CK8, indicates there may be soft interlayer. All the profiles include acclivitous interlayer between two straight lines, which go through the whole section. According to the profiles of T ${}_{1}$ and T ${}_{2}$ , there are also declivitous interlayers in the two cross sections, and especially intersections exist among interlayer in different direction (Figs 16 and 17). Beside the location can be read from the profiles.

Figure 18.

The GPR profiles of the geological cross-sections along T ${}_{3}$ : (a) GPR profile of geological cross sections along T ${}_{3}$ after processing. (b) Labeled GPR profile of geological cross sections along T ${}_{2}$ after processing. B ${}_{6}$ and C ${}_{6}$ are reflections from the top and the bottom of the karst cavities, and (D ${}_{8}$ , E ${}_{8}$ ) are reflections from the top and the bottom of the interlayer.

Figure 19.

The GPR profiles of the geological cross-sections along T ${}_{4}$ : (a) GPR profile of geological cross sections along T ${}_{4}$ after processing. (b) Labeled GPR profile of geological cross sections along T ${}_{4}$ after processing. B ${}_{7}$ and C ${}_{7}$ are reflections from the top and the bottom of the karst cavities, and (D ${}_{9}$ , E ${}_{9}$ ) are reflections from the top and the bottom of the interlayer.

4.2.3 Geological structure reconstruction

In summary, eight geological cross sections in two different directions were built up, combining the detailed information of GPR profiles interpretation and elevation value of 15 control points. The tridimensional internal structure can be generated through the integrated analysis of 2D GPR profiles (Fig. 21).

Figure 20.

The GPR profiles of the geological cross-sections along T ${}_{5}$ : (a) GPR profile of geological cross sections along T ${}_{5}$ after processing. (b) Labeled GPR profile of geological cross sections along T ${}_{4}$ after processing. B ${}_{8}$ and C ${}_{8}$ are reflections from the top and the bottom of the karst avities, and (D ${}_{10}$ , E ${}_{10}$ ) are reflections from the top and the bottom of the interlayer.

Figure 21.

The 3D model of study site: (a) is the tridimensional external structure and (b) is the tridimensional internal structure.

5. Discussion

Geological mapping is always regarded as a reliable method, the detailed information like the thick of the stratum, the elevation of the bottom and so on could be obtained. However, the high cost and randomness of it limit the objective reflection to underground karst landform in a large-scale range. The application of GPR profiling methods allows spatially dense over large area to be conducted within a limited period of time. On the contrary, the results obtained through the interpretation of GPR profiles are also influenced by natural and artificial factors. Combining GPR with borehole surveying can make full use of the advantages of the two methods, the effective explanation of underground geological condition may be figured out.

Timely data is collected during geological mapping .GPR is an effective method for reconnaissance survey, and the interpretation of 2D profiles is precise. With a mixed orthogonal distribution of dense survey lines, sufficient real data could be collected. Therefore, it’s reasonable to generate three-dimensional model through the integrated analysis of slices, which may provide reference for understanding geological condition in practice.

6. Conclusion

With the transmission of electromagnetic wave in the underground, reflection would form on the boundary of the objects. The response characteristics of GPR profiles caused by the change of geometry and filler were summarized. When the section is circular, hyperbolas in pair appear because of the diffraction on the boundary of the section. The reflection pattern of rectangular section is approximate to circular section. However, the flat curve existed in the front of the image is the main difference. Additionally, the GPR profile of triangular section displays an intersection of two straight lines. Various kinds of infill materials will also make the profiles show slightly different. In the case of water, metal, wet clay or sludge, negative reflection forms in the front of profile. When the space is full of air, positive reflection appears in the same position.

Timely data is collected during geological mapping or other field works, consisting of borehole, elevation and outcrop descriptions with lithological information. The distribution of overlying units and characteristics of cavities is resolved by the apexes of diffraction hyperbolas and lateral changes in the reflection pattern of 2D GPR profiles, including size, geometry and location within the soluble rock. With a mixed orthogonal distribution of dense survey lines, sufficient real data could be collected. It is reasonable to built the tridimensional internal structure through the integrated analysis of vertical as well as horizontal slices characteristics. An application in an area in Chongqing province vertified that the methodology could provide a simple and effective way for understanding the subsurface geologic condition in practice.

Footnotes

Acknowledgments

This work was supported from the Fundamental Research Funds for the Natural Science Fund of China [grant number 51478065]; the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry; the National Twelfth Five Year Plan of Science and Technology Support Project [grant number 2012BAJ22B06].

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A methodology for three dimensional modeling of subsurface geologic structure in mantled karst area

Abstract

Keywords

1. Introduction

2. Methodology

4.1 Site description

4.2.1 Geological survey records

Table 1 Spatial coordinates of control stations

6. Conclusion

Footnotes

Acknowledgments

References

Table 1
Spatial coordinates of control stations