IRJET- Rock Slope Assessment using Artificial Neural Networks

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Rock Slope Assessment using Artificial Neural Networks Prashant K. Nayak1, S. Srinivas2, N. Rakesh2, G. Sanjeev Kumar2, B. Mahesh Babu2 1 Assistant

Professor, Dept. of Mining Engineering, Godavari Institute of Engineering & Technology (Autonomous), Rajahmundry, Andhra Pradesh, India.

2B. Tech Final Year Student, Dept. of Mining Engineering, Godavari Institute of Engineering & Technology (Autonomous), Rajahmundry, Andhra Pradesh, India.

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Abstract – In the risk analysis of slope stability, it is utmost necessary for a mining engineer to provide a reasonable factor of safety, which gives not only the reliability but also the economic conditions. The stability of slopes in open pit mines is of great concern because of the significant detrimental consequence’s instabilities can have. To ensure the safe and continuous economic operation of the open pit mines, it is utmost necessary to systematically assess and manage slope stability risk. For this purpose, the slope face of a study area is discretized into cells having homogenous aspect, slope angle, rock properties and joint set orientations.

In this paper, an ANN based model is developed by which the objective function i.e. Probability of failure is assessed by the combination of discontinuity parameters and slope geometry which defines the instability in rock slopes.

Key Words: Rock Slope Instability; Artificial Neural Networks; MATLAB.

1. INTRODUCTION Reliable slopes are essential to the design of an open pit mine, at all scales and at every level of project development. The slope design process, including how to gather reliable data, how to formulate the design, how to implement the design, how to assess the reliability of the outcome, and how to manage risk. If slope instabilities do develop, they must be manageable at all pit scales, from the individual benches to the overall slopes. When managing the failures, it is essential that a degree of stability is ensured to minimize risk (Read & Stacey, 2017).

Slope instability can be caused by failure occurring through weak intact rock or along pre-existing discontinuities in hard rock.

The type of rock discontinuities and its characteristics helps to determine their effect on rock mass properties. In rock mass, joints are a source of weakness and can be the source of instability. The important joint characteristics are spacing, persistence, joint roughness, aperture, and joint orientation (Gratchev, 2019).

To conduct stability analyses and develop optimum slope angles for input into pit design process, the proposed pit must be divided into design sectors that are sections of the pit with similar geological and operational characteristics. This selection is based on several criteria: the structural domain, the wall orientation, and operational considerations. Since a pit geometry is required to define, design sectors, slope design are iterative with mine planning (Fleurisson & Cojean, 2014).

To ensure the safe and economic operation of these mines, it is necessary to systematically access and manage slope stability risk. The methodology and factors that impact on rock mass slope stability risks are data collection, processing, reliability, and the partitioning of data into domains. If all geotechnical inputs and factors impacting failure modes had been considered by appropriate statistical methods, and consensus exists on the minimum volume of dislodged debris that constitutes a ‘true’ slope failure, then the statistical distribution of computing Factors of Safety (FS) could be a measure of stability risks. FoS is defined as the resisting shear strength divided by the activating force (Baczynski, 2016).

The risk is estimated as the product of probability of the potentially damaging event and its consequences. The specific failure risk may be expressed as follows: R = H × E × (V × C); where H = Probability of a potentially damaging event of a given magnitude; E = Set of elements at risk to the hazardous event; V = Vulnerability of the exposed element (s); and C = Cost. H and V variables are (+) the numbers for measuring the probability aspect of the hazard and vulnerability (Wolf, et. al, 2018). In slope design, the risks (R) associated with slope failure are defined and quantified as: R = PoF X Consequences of failure (Read & Stacey, 2017). In this paper, ANN model is developed to assess the probability of failure by assessment of slope risk by the combination of discontinuity parameters and slope geometry which defines the instability of the rock mass.

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Table - 1: Controllable factors influencing the Stability of Rock Slopes Parameter Slope Orientation Slope Angle Berms Mechanical Excavation Bulk Density Controlled Blasting Vegetation Proximal Engineering

Excavation Geometry Excavation Method Environment

Effect Appropriate orientation w.r.t. the geology reduces instability.

The lower slope angle may increase stability.

Wide berms limit the size of potential failures and retain failed material.

Minimize disturbance of rock mass reduces instability.

Can produce induced instability.

Use to minimize induced stability.

Roots dilate discontinuities, increases stress and weathering.

Position of other structures can influence stability.

Table - 2: Uncontrollable factors influencing the Stability of Rock Slopes Parameter Meteorology

Geology & Geotechnics

Topography

Rainfall Temperature Freeze/Thaw Intact Rock Properties Discontinuity Properties In-situ Stress Earthquakes Pre-existing Slides Pre-existing Relief

Effect Water pressures drive instability. Water increases weathering.

Temperature affects weathering.

Ice wedging acts as driving force on failure masses.

Determines excavation method and can induced instability due to excavation method.

Shear strength, orientation, frequency, aperture, roughness, and infill influence the scale and the likelihood of instabilities.

Increase in stress deceases overall stability.

Increases the destabilizing forces on the slope.

Can be reactivated due to excavate and may have post-peak shear strength.

Determines the geometry of the design.

Table - 3: FoS and PoF acceptance criteria values (Read & Stacey, 2009).

Slope scale

Consequence of failure

Bench

Low-high Low Medium High Low Medium High

Inter-ramp

Overall

FoS (Min) (Static) 1.1 1.15-1.2 1.2 1.2-1.3 1.2-1.3 1.3 1.3-1.5

Acceptance criteria FoS (Min) (Dynamic) NA 1.0 1.0 1.1 1.0 1.05 1.1

PoF (Max) P [FoS ≤ 1] 25-50% 25% 20% 10% 15-20% 5-10% ≤5%

Fig - 1 - Correlation between velocity of slope movement and movement classification and sensitivity to environmental factors (Vaziri, et. al, 2010).

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Fig - 2 - Risk Acceptability Criteria (Steffen et al., 2006).

2. Rock Slope Assessment - Case Study 2.1 Project Background The SRP OC - II Expansion Project is proposed to operate in the Srirampur Area where one opencast mine is already in operation under the name of SRP OC - II Project. The proposed project is expansion of SRP OC - II Project. SRP OC - II Expansion Project is proposed with method of mining/technology (i.e. Opencast with Shovel Dumper combination technology), the Hazards were identified based on the previous experience of the SRP OC - II Project with the following criteria. The following are the possible hazards identified for the proposed project basing on the Tasks/Activities/Workplaces involved: For Pit Slope Stability - The ultimate working depth of the proposed quarry is between 120 m to 350 m. There may be chances of slope failure, where the depth is more.

Identified Hazards

Slope Stability

Mechanism

Control The overall pit slope varies from 400 to Failure of Pit Slope when 420. This has been done to ensure safe pit the depth is more and slope for the prevalent strata conditions. intercepted by a number For Slope stability, care is taken while of faults. forming the batter on the east side of the quarry fault zone by pre-split blasting.

Action The movement of the slope shall be observed by installing subsidence movement pillars.

The surveyor should ensure frequently.

The derived values are likely to be valid for the entire quarry. The slope stability analysis was done based on the data of rock mass discontinuity parameters and geometric parameters. It may however be prudent, from time to time, to re-examine the local changes in the different geotechnical parameters.

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3. METHODOLOGY 3.1 Derivation of Factor of Safety (FoS) Index The FoS Parameter is derived from a standard set of calculations which use the parameter values as input. The logic of the derivation of the FoS Parameter is that Primary parameter values are derived related to the potential for each type of failure on a slope. Each type of failure is assumed to act independently, and they therefore follow separate calculation paths. Calculation of the FoS Index involves multiplying the Primary parameters by successive Secondary parameters and adding other relevant Primary parameters.

3.2 Input Parameters and Data Collection Input Parameters for calculation of FoS Index are failure specific and a complete set of parameters are required for each potential failure observed on the rock slope and the remaining parameters are slope angle, slope height, and ground water level.

The relevant parameters are as follows: 1.

Potential failure plane discontinuities: Dip and azimuth, Join Spacing, Trace Length, Aperture, Block Sizes, Weathering adjacent to potential failure, Rock Strength and Ground water Conditions.

Potential failure dimension: Height, Width, and Depth (Depth for Toppling only; can be calculated for Plane and Wedge).

2.

Fig - 3a - Discontinuity Dip, Azimuth & Trace Length.

Fig - 3b - Resolution of the fracture frequency for one set.

Geotechnical Parameters - Initial Parameter Indices from Discontinuity - Slope Geometry Relationships Plane Orientation Dip azm 30-45 +/- 20 30-45 +/- 20 30-45 +/- 20 30-45 +/- 20 45-70 +/- 20 45-70 +/- 20 45-70 +/- 20 45-70 +/- 20 70-90 +/- 20 70-90 +/- 20 70-90 +/- 20 70-90 +/- 20

The plane must dip >300 at an azimuth of slope of a slope azm +/- 200 & plane dip < slope dip.

Plane failure

Criteria

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Slope Orientation <45 45-60 60-70 70-90 <45 45-60 60-70 70-90 <45 45-60 60-70 70-90

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Initial Parameter 0.5 1.0 1.0 1.0 0 0.3 0.8 1.0 0 0 0 0.5

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FoS Parameter Stable Stable Stable Stable Stable Stable Stable Stable Stable Stable Stable Stable

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Set 1 Dip 30-45 30-45 30-45 30-45 30-45 30-45 30-45 30-45 30-45 30-45 30-45 45-70 45-70 45-70 45-70 45-70 45-70 45-70 70-90 70-90 70-90

Intersection must dip >600 toward (slope azm + 180) +/- 20 & plane must dip <300 toward slope azm +/- 20.

Toppling Plane

Criteria

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Wedge Plane Orientation Set 1 Set 2 azm Dip azm +20-90 30-45 -20-90 +20-90 30-45 -20-90 +20-90 30-45 -20-90 +20-90 30-45 -20-90 +20-90 45-70 -20-90 +20-90 45-70 -20-90 +20-90 45-70 -20-90 +20-90 45-70 -20-90 +20-90 70-90 -20-90 +20-90 70-90 -20-90 +20-90 70-90 -20-90 +20-90 70-90 -20-90 +20-90 45-70 -20-90 +20-90 45-70 -20-90 +20-90 45-70 -20-90 +20-90 45-70 -20-90 +20-90 70-90 -20-90 +20-90 70-90 -20-90 +20-90 70-90 -20-90 +20-90 70-90 -20-90 +20-90 70-90 -20-90 +20-90 70-90 -20-90 +20-90 70-90 -20-90 +20-90 70-90 -20-90

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azm +20-90 +20-90 >90 +20-90 +20-90 >90 >90 +20-90 +20-90 >90 >90 +20-90 +20-90 >90 +20-90 +20-90 >90 >90 +20-90 >90 >90

Toppling Plane Orientation Set 2 Dip azm Dip 30-45 -20-90 <30 30-45 >90 <30 30-45 >90 <30 45-70 -20-90 <30 45-70 >90 <30 45-70 -20-90 <30 45-70 >90 <30 70-90 -20-90 <30 70-90 >90 <30 70-90 -20-90 <30 70-90 >90 <30 45-70 -20-90 <30 45-70 >90 <30 45-70 >90 <30 70-90 -20-90 <30 70-90 >90 <30 70-90 -20-90 <30 70-90 >90 <30 70-90 -20-90 <30 70-90 -20-90 <30 70-90 >90 <30

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Slope Orientation Dip <45 45-60 60-70 70-90 <45 45-60 60-70 70-90 <45 45-60 60-70 70-90 <45 45-60 60-70 70-90 <45 45-60 60-70 70-90 <45 45-60 60-70 70-90

Set 3 azm +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20 +/- 20

Initial Parameter

FoS Parameter

0.09 0.16 0.16 0.16 0.18 0.37 0.37 0.37 0.25 0.5 0.5 0.5 0.15 0.45 0.67 0.77 0.16 0.49 0.70 0.87 0.12 0.30 0.57 0.86

Fail Fail Fail Fail Fail Fail Fail Fail Fail Fail Fail Fail Stable Stable Stable Stable Stable Stable Stable Stable Stable Stable Stable Stable

Initial Parameter 0 0 0 0 0 0 0 0 0 0 0 0 0 0.06 0 0 0.12 0.24 0.04 0.27 0.27

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Mode

ψp < Фp – Stable X / Y < tan ψp – Topple

Dip 30-45 30-45 30-45 30-45 30-45 30-45 30-45 30-45 30-45 30-45 30-45 30-45 45-70 45-70 45-70 45-70 45-70 45-70 45-70 45-70 70-90 70-90 70-90 70-90

Intersection must be formed from planes from separate sets.

Intersection must dip >300 and daylight on the slope.

Wedge failure

Criteria

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Factors for Observed Failure Condition Multiplicative Parameters Parameter Plane Failure Observed Wedge Failure Observed Toppling Observed Failure Additive Parameters Parameter Plane Failure Wedge Failure Toppling Failure

Parameter Value 1 1 2

Not Observed Not Observed Not Observed

Parameter Value 0.5 0.5 0.5

Parameter Value 1 1 2

Multiplicative Multiplicative Multiplicative

Type Initial Initial Initial

Discontinuity Size and Spacing Factors

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Spacing Factor Persistence Factor Aperture Factor Block sizes Factor

Indices of each type of failure are multiplied by the principle spacing factors and persistence factors for each relevant joint set.

Criteria

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Description Extremely close spacing Very close spacing Close spacing Moderate spacing Wide spacing Very wide spacing Extremely wide spacing Description Very low persistence Low persistence Medium persistence High persistence Very high persistence Description Very tight Tight Partly open Open Moderately wide Wide Very wide Extremely wide Cavernous Description Very large blocks Large blocks Medium-sized blocks Small blocks Very small blocks Crushed rock

Joint spacing (m) <0.02 0.02–0.06 0.06–0.2 0.2–0.6 0.6–2 2–6 >6 Trace length (m) <1 1–3 3–10 10–20 > 20 Aperture (mm) < 0.1 0.1–0.25 0.25–0.5 0.5–2.5 2.5–10 > 10 10–100 100–1000 > 1000 Jv (joints/m3) <1 1–3 3–10 10–30 30–60 > 60

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Parameter Value 9 6.5 2.25 1 0.35 0.11 0 Parameter Value 0.25 1 4 16 56 Parameter Value 0 0.11 0.35 1 1.2 1.3 >1.4 >1.4 >1.4 Parameter Value 0 0.25 1 4 16 56

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Type Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative Type Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative Type Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative Type Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative

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GW Factor

Strength Factor

Weathering Factor

Weathering Strength and Water Factors Option Fresh Slight Moderate Highly Complete Residual Parameter Weak Moderate strong Strong Very strong Parameter None Minor Moderate Extreme

Parameter Value 1 1 1.2 1.5 2 2.5 Parameter Value 2 1.5 1 1 Parameter Value 1 1.1 1.2 1.3

Type Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative Multiplicative Type Multiplicative Multiplicative Multiplicative Type Multiplicative Multiplicative Multiplicative Multiplicative

Geometric Parameters Factor Slope Angle

Slope Height

Range 30-450 45-600 60-700 70-900 3-6m 6-12m 12-20m >20m

Parameter Value 0 0.5 1 1.5 0 0.5 1 1.5

Type Additive Additive Additive Additive Additive Additive Additive Additive

4. BUILDING NEURAL NETWORK MODEL The neural network design process has 7 steps: (1) Collect data; (2) Create the network; (3) Configure the network; (4) Initialize the weights and biases; (5) Train the network; (6) Validate the network (post-training analysis); and (7) Use the network. An ANN is a group of interconnected artificial neurons, interacting with one another in a concerted manner. Feed forward networks have one-way connections, from the input to the output layer. Here, the neurons are arranged in the form of layers. Neurons in one layer get inputs from the previous layer and feed their outputs to the next layer. The last layer is called the output layer. Layers between the input and output layers are called hidden layers and are termed multi-layered networks.

The number of hidden layers and neurons in the hidden layer is usually defied by trial and error method. ANN studyâ&#x20AC;&#x2122;s input, output relationships by suitably adjusting the synaptic weights in a process known as training.

In supervised learning, target values or desired responses are known and are given to ANN during training so that ANN can adjust its weights to try to match its output to the target values. Before the learning algorithms are applied to update the weights, all the weights are initialized randomly (Haykin, 1999). The network using this set of inputs produces its own outputs.

These are compared with the target outputs and the difference between them, called the error, is used for modifying the weights. The architecture of MLP is a multi-layered feed-forward neural network, in which nonlinear elements (neurons) are arranged in successive layers and the information flows unidirectionally, that is from the input layer to the output layer through hidden layers. MLP is trained by using supervised algorithms known as the back-propagation algorithm.

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The backpropagation (BP) algorithm allows experimental acquisition of input/output mapping knowledge within multilayer networks. There are basically two passes through the different layers of the network: a feed-forward pass and a backward pass.

In the forward pass, an input pattern is submitted and propagated through the network, layer by layer. A set of outputs is produced as the actual response of the network. During the forward pass, the synaptic weights are all fixed, and in the backward pass, the synaptic weights are all adjusted, depending on the error between the actual output and the target output.

The process is continued until all the input patterns from the training set are learned with an acceptable overall error. The error is cumulative and computed over the entire training set. This computation is called the training epoch. During the testing phase, the trained network it operates in a feed-forward manner (Haykin 1999).

The performance of the back-propagation algorithm depends on following: 1.

2.

3.

4.

5.

Initial weights - The network weights are initialized to small random values. The initialization strongly affects the final solution.

The transfer function of the Nodes - For calculating the value of δ in the backward pass, the requirement is that the activation function should be differentiable.

Learning rate - The effectiveness and convergence of back propagation algorithm depend significantly on the value of the learning rate η. By trial and error, the value of the learning rate provides an optimum solution. The value is lesser than 1.

Momentum coefficient - The momentum term is generally used to accelerate the convergence of the error BP algorithm.

This involves the use of momentum coefficient α. This is a simple method of increasing the rate of learning and yet avoids the danger of instability. The value chosen is generally lesser than 1.

Number of hidden neurons - The optimal number of hidden nodes in any network for solving any given problem is determined by trial and error. Hidden units play a critical role in the operation of multilayer perceptron with BP algorithm learning as they act as feature detectors.

5. Supervised Learning - Using Neural Network Fitting Tools In this work, the ANN model was developed by using MATLAB R2016b software for windows. Data for functional fitting problems are set up in a neural network by organizing the data into two matrices, the input matrix X and the target matrix T. Input ‘data’ is a 350 x 7 matrix, representing static data of 350 samples of 7 elements. Target ‘data’ is a 350 x 1 matrix, representing static data of 350 samples of 1elements. Then divides input vectors and target vectors into three sets as follows: (a) 60% is used for training; (b) 20% are used to validate that the network is generalizing and to stop training over fitting, and (c) 20% are used as a completely independent test of network generalization.

a

b

Fig - 4 - Three independent data sets for (a) Independent and (b) Split Sample testing (Priddy & Keller, 2005).

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a

b

Fig - 5 - Block diagram: (a) Training Stage and (b) Operation stage (Priddy and Keller, 2005).

For training the ANN, Scaled Conjugate Gradient (trainscg) is recommended as it uses gradient calculations which are more memory efficient than the Jacobian calculations i.e. Two algorithms Levenberg-Marquardt and Bayesian Regularization. The training continued until the validation error failed to decrease for six iterations (validation stop). From a given random initialization of the network, every 'run' produces distinct results. We get distinct results from those depicted here, but if the modelling process goes well, we should expect results of the same quality. If we click Performance in the training window; a plot of the training errors; validation errors; and test errors appeared. The only sign of the derivative is used to determine the direction of the weight updates.

6. RESULTS AND DISCUSSIONS The model is validated by comparing the results with the remaining 140 rock slope cases and found that the predicted results are having a very close relationship with the actual results. The value of correlation coefficient, R is found to be 0.99 and having a very low RMSE value of 0.05. The Simulink model for ANN is shown in Fig 7. Hence, it is concluded that ANN can be used as a good prediction tool for slope stability risk analysis. The Error Histogram of the network is shown above, the blue bars represent the training data, the green bars represent the validation data, and the red bars represent testing data. The histogram gives the indication of outliners, which are data points where the fit is significantly worse than most data. In this case, most errors fall between -25.03 and 25.7. These outliners give the idea to determine if the data is bad, or if those data points are different than the rest of the data set. The magnitude of the derivative has no effect on the weight update. The update value for each weight and bias is increased by a predefined value whenever derivative of the performance function w.r.t. that weight has the same sign for the two successive iterations. The update value is decreased by that value whenever the derivative w.r.t. that weight changes signs from the previous iteration.

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In this case, the result is reasonable because of the following: (1) The final mean-square error is small; (b) The test set error, and the validation set error has similar characteristics (green & red lines in the plot); and (c) No significance over fitting has occurred by iteration 6 (where the best validation performance occurs). The coefficient of correlation is used to determine the relative correlation and the goodness of fit between the predicted and observed data. A suggested guide for values of |R| between 0.0 and 1.0: (1) |R| > 0.8 => Strong correlation exists between two sets of variables; (2) 0.2 < |R| < 0.8 => Correlation exists between the two sets of variables: and (3) |R| < 0.2 => Weak correlation exists between the two sets of variables. The regression plot gives the value of R for training, testing, and validation in Fig 6. From the regression plot, it was found that the value of R equals to 0.99 which is very close to unity. Hence, it can be stated that the prediction results bear a close relationship between the input variables.

Fig - 6 - Regression Plot showing the value of R for training, testing, and validation.

Fig - 7 - Simulink Model for ANN.

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Fig - 8 - Performance Plot for Predicted ANN Model.

Fig - 9 - Training State Plot for showing Gradient and Validation check with epoch.

Fig -10 - Error Histogram Plot of Predicted ANN Model.

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7. CONCLUSIONS     

Risk-based design provides enough quantitative information to: (a) Define acceptable risks in terms of safety and economics; and (b) Assess relative risks for different slope configurations.

The results of the analytical analyses form the basis for more vigorous numerical analysis which serves to verify and validate the recommended discontinuity sets, slope angles and the open pit geometry.

Before the slope designs are accepted, they must be aligned with the slope failure criteria that require the walls of the pit to be stable for the required life of the pit, which may extend into closure.

Discontinuity data recording should be simultaneously carried out with quarrying operations. It will provide a guideline for carrying out excavations in other parts of the deposit.

Finally, implement the steps as recommended in the DGMS Circular No.2, 2010 to control slope failures.

REFERENCES 1.

2.

Abramson, L. W. (1996), Slope Stability and Stabilisation Methods. Wiley, New York.

Xia-Ting Feng (2017), Rock Mechanics and Engineering, Vol. 3: Analysis, Modeling & Design, Ch.-25, Open pit slope design, Read & Stacey, pp 785-818.

3. Kyle Rollins, Dimitrios Zekkos, Geotechnical Engineering State of the Art and Practice (2012), Ch - 6, Assessment of Slope Stability, American Society of Civil Engineers.

4. Chowdhury, R. N., Geotechnical slope analysis, Performance indicators and basic probability concepts, (2010), Ch-3, pp 111 - 126, Taylor & Francis Group.

5. Vaziri A., Moore L., Hosam Ali H., Monitoring systems for warning impending failures in slopes and open pit mines, Nat Hazards (2010) 55:501–512.

6. Haykin, S. (1999). Neural Networks—A Comprehensive Foundation. Prentice Hall, Upper Saddle River, New Jersey.

7. Smith, J., Machine Learning with Neural Networks using MATLAB, (2017), Create Space Independent Publishing Platform.

8. Priddy K. L., and Keller P.E. (2005). ‘Artificial Neural Networks - An Introduction’, SPIE - The International Society for Optical Engineering, Bellingham, Washington.

9. Chaturvedi, D. K., Modeling and Simulation of Systems using MATLAB and Simulink, (2010), Ch-10, pp 503 - 511, Taylor & Francis Group.

10. Demuth H. and Beale M. (2010), Neural Network Toolbox for Use with MATLAB. The Math Works Inc., Natick, Mass.

11. Fleurisson, A., and Cojean, R., Error Reduction in Slope Stability Assessment. Bhattacharya, Lieberwirth and Klein; Surface Mining Methods, Technology and Systems. Vol. 1, Wide, 41p, 2014.

AUTHOR Mr. Prashant K. Nayak, Assistant Professor, Department of Mining Engineering, Godavari Institute of Engineering & Technology (Autonomous), Rajahmundry, Andhra Pradesh, India.

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