Determination of geological strength index of jointed rock mass based on image processing
Generally, knowledge on the mechanical properties of rock mass is a prerequisite for the numerical simulation and the design of the underground structure, opening-up of mineral deposits and mining processes.
Since the early 1990s, many scholars (e.g. Hoek and Brown, 1997; Hoek et al., 2005, 2008, 2013; Hoek and Marinos, 2007) have proposed a variety of methods to determine the strength and deformation parameters of rock mass using geological strength index (GSI). The standard GSI chart considers qualitatively the surface condition and blockiness of a rock mass, and is used to estimate a value between 0 and 100 representing the overall geotechnical quality of the rock mass (Fig. 1). The GSI approach has been modified over the years and applied to characterizing the mechanical properties of rock mass by many authors (e.g. Sonmez and Ulusay, 1999; Cai et al., 2004, 2007; Sonmez et al., 2004; Bridean, 2005; Marinos et al., 2006).
The best outcomes can be achieved only by collaboration between experienced engineering geologists and geotechnical engineers. Quantifying estimates of GSI may provide a means of reducing inadvertent errors and inconsistencies by inexperienced practitioners in classifying a rock mass. Bieniawski (1989) and Hoek and Brown (1997) suggested that GSI can be related to the modified rock mass quality index Q and rock mass rating (RMR), respectively. A recent paper by Hoek et al. (2013) proposed a method for quantifying GSI using the rock quality designation (RQD), the joint condition rating of the RMR system, and the joint condition factor (JCond89) by Bieniawski (1989). Russo (2009) suggested a new approach for quantitative assessment of the GSI (Hoek et al.,1995) by means of the basic input parameters for the determination of the rock mass index (RMI), such as the elementary block volume and the joint conditions.
A recent paper by Bertuzzi et al. (2016) provided data from four different rock masses to extend the case history proposed by Hoek et al. (2013). The correlation between the GSI qualitatively assessed from the standard GSI chart and the quantified GSI was found to be fair for the datasets from the four rock masses.
Akin (2013) estimated the GSI value using the back analysis method with shear strength parameters of a failure surface in heavily jointed rock masses on a slope. The shear strength parameters of a failure surface under a specific normal stress can be determined using the material constants of the Hoek-Brown failure criterion (mb and s) as a function of the GSI value. Also, Tajdus (2010) proposed a back analysis method of the surface subsidence, which is based on the uniaxial compressive strength Rc of rock samples, as well as mining and geological conditions, to determine the GSI values of a rock mass disturbed by underground exploitation.
In recent years, several authors such as Han et al. (2014), Poulsen et al. (2015) and Wang et al. (2015a) have also suggested many methods to determine the strength and deformation parameters of rock mass using GSI. All of the above-mentioned papers focused on quantifying the GSI chart to facilitate use of the system especially by inexperienced practitioners.
Many researchers (e.g. Crosta, 1997; Castleman, 2002; Hadjigeorgiou et al., 2003; Lemy and Hadjigeorgiou, 2003; Lato et al., 2009) have investigated digital face mapping as a practical tool to characterize rock masses, which can significantly reduce the time required in the field and avoid exposure to potentially unsafe conditions.
The digital rock mass rating (DRMR) developed by Monte (2004) uses basic image processing procedures and calculations to estimate a classification rating from digital images of rock masses. The rating system incorporates fracture information collected from a discontinuity trace map (e.g. length, spacing, large-scale, roughness, rock bridge percentage, and block volume).
In this paper, we propose a method to quantitatively determine the GSI by first detecting the joints in two-dimensional (2D) photographs of a rock mass surface using the image processing technology, then determining the fractal dimension, and finally predicting the GSI using artificial neural network (ANN). The applicability of the method proposed is verified through stability analysis of the working in a coal mine.
Joint detection on the rock mass surface using image processing
Fig. 2 shows the schematic flowchart for detecting joints on the rock mass surface via image processing. The detailed steps for joint detection on the rock mass surface are described as follows.
(1) Converting the color image of rock mass to black and white one
To detect the joints on the image of jointed rock mass, the contrast of the image should be analyzed. We convert the natural color image to black and white one using the gray level conversion function as follows (Castleman, 2002):
Smoothing and sharpening
To emphasize the joints, the image needs to be smoothed and sharpened using the corresponding masks. Smoothing and sharpening can be performed by image enhancement technique using following equation (William, 2007):
An image may be influenced by noise and interference from several sources, including electrical sensor noise, photographic grain noise and especially blast-induced cracks. Therefore, corrosion and swelling operations in automatic and manual procedures must be performed for the binary images in order to remove unnecessary noise which may cause errors in joint detection. Particularly, the manual procedure removes the blast-induced cracks on the joint trace maps, while comparing the results of automatic detection with those of in situ survey.
Detection of the joints
After removing the unnecessary noise, we detect the joints remained on the binary image.
Generally, edge and line locations on the binary track map can be easily found from the distribution of white pixels under black background. For implementation, we use two major classes of specific edge and line detection: first- and second-order derivatives.
The details are explained in William (2007). Here, we automatically collect properties of the joint set, such as trace length, joint intensity, joint spacing and roughness, from the discontinuity trace maps for 4 sides (left and right walls, face and roof) in underground mine working. However, in the middle section of the existing operation working, which has already been driven, we collect the properties for only three sides (left and right walls, and roof).
Fractal property of joints on rock mass surface
In recent years, many researchers including Jiang et al. (2006) and Alameda-Hernandez et al. (2014) investigated the methods for determining joint roughness coefficient (JRC) on the rock mass surface using the following parameters derived from digitized profiles: fractal dimension (D), first-derivative root-mean-square (Z2), and roughness profile index or profile sinuosity (RP).
Odling (1994), Fardin et al. (2004), Nazarov and Nazarova (2008), Wnuk and Yavari (2008), and Wang et al. (2015b) proposed the correlations between the fractal dimension and joint properties on the rock mass surface, such as JRC and roughness exponent of fracture surfaces. On the basis of above researches, joints in rock masses may be treated in some cases as statistically self-similar (fractal property), and therefore can be characterized using their fractal dimension.
The fractal dimension of a 2D rock mass surface can be calculated with the following equation (Kulatilake et al., 1997):
where ri is the length of section, and N(ri) is the number of joints in lattice network with length of section ri.
Since joints of rock mass surface generally lie on a 2D plane, it is natural to consider the problem using 2D model of fractal dimension, rather than three-dimensional (3D) model. When determining the fractal dimension for joint on rock mass surface, the study area is subsequently subdivided by mesh, the size of which is chosen between 1/64 and 1/2 along the column and row.
We first divide the image into 2n (n ¼ 0e6) for detecting joints of standard surfaces according to the rock mass classification given by Hoek and Brown (1997), then count the number of joints by size of lattice network, and finally calculate the fractal dimension of 6 types of standard surfaces for rock masses. The fractal dimensions are listed in Table 1.
As shown in Table 1, we can find that the 2nd to 6th types of standard surfaces of rock masses have clearly 2D fractal dimensions.
The first type of standard surface, however, has fractal dimension of approximately 0.99, which does not belong to 2D surface. This is due to that the first type of standard surface possesses 1e2 groups of joint sets. This may be a very important issue. Hence Table 1 can be used as an alternative tool that enables to quantify standard rock masses in GSI chart given by Hoek and Brown (1997).
Prediction of the GSI by ANN
The development of ANN started as an attempt to understand the operation of the human brain and mimic its assessment capabilities, in other words, to be able to decide and act under uncertainty or even deal with situations having limited previous experience. ANNs are mathematic models consisting of interconnected processing nodes (neurons) under a pre specified topology (layers).
As shown in Fig. 1 and Table 1, GSI and the fractal dimension are represented using different values according to joint properties on rock mass surface, respectively. Therefore, GSI is closely related with the fractal dimension, as mentioned in the literature (Fardin et al., 2004; Jiang et al., 2006; Alameda-Hernandez et al., 2014). Recently, ANN is widely used in engineering practice. For example, back-propagation (BP) ANN is used to predict deformation modulus and GSI of jointed rock mass (Lemy and Hadjigeorgiou, 2003; Sonmez et al., 2006). The BP networks consist of an input layer, one or more hidden layers and an output layer. Each layer is composed of different processing units (also called neurons), connected to the units of the next layer. A transfer function processes input data that reach the corresponding neuron. To differentiate between different processing units, values called biases are introduced in the transfer functions.
These biases are referred to as the temperature of a neuron. During training of the network, data are processed through the network, until they reach the output layer (forward pass). In this layer, the output is compared to the GSI value (the “true” output) obtained from Fig. 1. The difference or error between both is processed back through the network (backward pass) by updating the individualweights of the connections and the biases of the individual neurons. The input and output data aremostly represented as vectors called training pairs. The process asmentioned above is repeated for all the training pairs in the dataset, until the network error converges to a minimum threshold defined by a corresponding cost function.
We have used 3-layer BP ANN for predicting the GSI of the surface of jointed rock mass. In 3-layer BP network, output signal yk is expressed as
index is changed from zero (very good, i.e. very rough and fresh unweathered surface) to 100 (very poor, i.e. slickenside and highly weathered surface).
Here, the number of neurons of hidden layer is first set to three and it is finally determined via learning procedure to establish the most effective ANN structure. As a result of learning with one by one increasing the neurons number of hidden layer, the learning error is minimized at 13 neurons, when the highest accuracy of ANN learning is reached. The transfer function between input layer and hidden one is tansigmoid and that between hidden layer and output one is purelin.
In general, the output vector, containing all yk of the neurons of the output layer, is not the same as the true output vector y* k (i.e. the GSI value obtained from Fig.1). The mean square error (Ek) between these vectors is made during processing the inputeoutput vector pair and can be calculated as follows:
Fig. 4 shows a change of the squared sum of learning errors according to the learning iteration.
As a result, we set up the mean square error as 103 and the maximum learning number as 1500 times. After training 1028 times, the mean square error of the ANN is reached to threshold error, and the relative error between the GSI value predicted by
ANN and the GSI value given in the GSI chart is below 3.6% (Table 2). Fig. 5 shows the interface, coded by using built-in tools of MATLAB 7.0, such as image processing, fractal analysis and ANN, based on the proposed method.
We present an example for determining the GSI value of rock mass around the working at Kangdong Coal Mine Complex in Korean Peninsula. The Coal Mine Complex is exploiting anthracite seam, formed during the Permian period, upper Paleozoic era.
The considered working, as main haulage drift, is driven into relatively stable rock mass, which mainly consists of sandstone as a footwall of the target coal seam. The rock mass is slightly weathered with one or two groups of joint sets, and the uniaxial compressive strength of rock samples is approximately 88 MPa, which corresponds to the class I rock according to rock mass classification determined from total ratings (Bieniawski, 1978).
Images of rock mass in a working of about 800 m long are taken every 10 m spacing. In total, we have taken 240 images on rock mass for left and right walls, and roof side. Fig. 6 shows an example for some sections. Results of determining the GSI value for every section are listed in Table 3. As shown in Table 3, GSI values vary between 88 and 93 in the considered sections.
In this study, we propose a method to quantitatively determine the GSI using images of in situ jointed rock mass. An application example is given to verify the applicability of the method. Conclusions are drawn as follows:
(1) The GSI chart of jointed rock mass given by Hoek and Brown (1997) can be quantified by combining image processing, fractal theory and ANN. Especially, the fractal dimension in Table 1 can be used as an alternative tool to quantify standard rock masses in GSI chart.
(2) The proposed method is comparably objective and does not need rich experience.
(3) This method must be further improved, so that it can be applied to loose and soft rock mass.
Kunui Hong a,*, Eunchol Han b, Kwangsong Kang a
a Faculty of Mining Engineering, Kim Chaek University of Technology, Pyongyang, Democratic People’s Republic of Korea
b School of Engineering and Science, Kim Chaek University of Technology, Pyongyang, Democratic People’s Republic of Korea