Application of Soft Computing Techniques for Prediction of Slope Failure

Department of Mining Engineering

National Institute of Technology, Rourkela

MN591: Research Project I (Summer)

Submitted By:

Abhijeet Dutta

711MN1172

Guided By:

Prof. N. Prakash

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Table of Contents

Introduction ..................................................................................................................... 2

Literature Review ............................................................................................................ 3

Artificial Neural Network .................................................................................................. 5

Introduction .................................................................................................................. 5

Back-Propagation Algorithm: ....................................................................................... 7

Variable selection ......................................................................................................... 8

Formation of training, testing and validation sets ......................................................... 9

Neural network architecture ......................................................................................... 9

Evaluation criteria ........................................................................................................ 9

Neural network training ................................................................................................ 9

Fuzzy Inference System ................................................................................................ 11

Conclusion .................................................................................................................... 13

References .................................................................................................................... 14

Table of Figures

Figure 1: Three layer neural network ..................................................................................................... 5

Figure 2: Graphical presentation of neuron in ANN .............................................................................. 6

Figure 3: A multi-layer feedforward network .......................................................................................... 7

Figure 4: A recurrent neural network ....................................................................................................... 7

Figure 5: Input, sum-operator and bias working together for producing the output node. ............ 10

Figure 6: Flow Chart to determine the properties and analysis the Slope stability by ANN ......... 11

Figure 7: (a) Crisp Set (b) Fuzzy Set ................................................................................................... 12

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Introduction Mining is one of the earliest primary industries of human civilization. It is considered a key industry

for many countries, and it has huge ripping effects on other industries. In comparison to past

centuries, the efficiency of modern mining has been dramatically improved through the

development of associated technologies. Many innovative mining methods and theories have

been developed by a multitude of scholars and engineers. Advanced high-tech computing

technologies with improved machineries have significantly contributed to the development of the

mining industry. In fact, modern mining is an advanced amalgamation of all the fundamental

sciences. In the case of actual mining activities, the mining manager frequently encounters many

complex decision-making problems without sufficient data or precise information available to over-

come them. An inappropriate decision could endanger peoples lives and cause irreversible

damage to the mining economy, considering the huge size of the capital of mining. The main

causes of difficulties in the decision-making processes in mining can be categorized.

The determination of the non-linear behaviour of multivariate dynamic systems often presents a

challenging and demanding problem. Slope stability estimation is an engineering problem that

involves several parameters. The impact of these parameters on the stability of slopes is

investigated through the use of computational tools called neural networks. A number of networks

of threshold logic unit were tested, with adjustable weights. The computational method for the

training process was a back-propagation learning algorithm. In this paper, the input data for slope

stability estimation consist of values of geotechnical and geometrical input parameters. As an

output, the network estimates the factor of safety (FS) that can be modelled as a function

approximation problem, or the stability status (S) that can be modelled either as a function

approximation problem or as a classification model. The performance of the network is measured

and the results are compared to those obtained by means of standard analytical methods.

Since their introduction, research into the area of artificial neural networks and their applications

continue to captivate scientists and engineers from a variety of disciplines. This growing interest

among researchers is stemming from the fact that these learning machines have an excellent

performance in the issues of pattern recognition and the modelling of non-linear relationships of

multivariate dynamic systems. This paper investigates the validity of utilizing artificial neural

networks in the physical problem of slope stability prediction.

The behaviour of complex engineering mechanisms is determined by a series of interactive

parameters with interrelations not yet entirely understood.

According to Jing and Hudson (2002), Jing (2003) all numerical modelling methods (analytical

methods, basic numerical methods, Finite Element Method, Boundary Element Method, Distinct

Element Method, hybrid methods, extended numerical methods and fully coupled models) attempt

to achieve one-to-one mechanism mapping in the model. In other words, a one-to-one mechanism

occurring in reality is modelled directly such as a clear stressstrain relationship.

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Literature Review Since their introduction, research into the area of artificial neural networks and their applications

continue to captivate scientists and engineers from a variety of disciplines. This growing interest

among researchers is stemming from the fact that these learning machines have an excellent

performance in the issues of pattern recognition and the modelling of non-linear relationships of

multivariate dynamic systems. This paper investigates the validity of utilizing artificial neural

networks in the physical problem of slope stability prediction.

The term one-to-one mapping refers to the direct modelling of geometry and physical

mechanisms, either specifically or through equivalent properties. The neural network approach is

a non one-to-one mapping method. In such a model, mechanism mapping is not totally direct.

This model provides predicting capabilities; this is why it has been used for rock and soils

parameter identification and prediction.

Some recent publications on various geotechnical engineering topics are given below:

Performance monitoring of rock masses for mining geomechanics (Millar and Hudson, 1994).

Liquefaction assessment (Goh, 1995b).

Rock mass classification (Sklavounos and Sakellariou, 1995).

Estimation of load capacity of driven piles (Goh, 1995a).

Estimation of permeability of compacted clay layers (Najjar and Basheer, 1996).

Subsurface characterization (Gangopadhyay et al., 1999).

Different types of displacements of rock slopes (Deng and Lee, 2001).

Lithofacies identification (Chang et al., 2002).

Assessment of geotechnical properties (Yang and Rosenbaum, 2001).

As evidenced by the list of references above, the neural networks modelling approach has already

been applied to a variety of subjects in rock and soil mechanics. It is also evident that the method

has significant potential on account of its non 1:1 mapping and because of the fact that it may

be possible in the future for such networks to include creative ability, perception and judgement.

However, the method has not yet proved an adequate alternative to conventional modelling (Jing

and Hudson, 2002; Jing, 2003). The approach to the problem of slope stability estimation from

the perspective of artificial neural networks is not an easy task and requires sophisticated

modelling techniques, experience, deep knowledge of engineering and a vast amount of

experimental data.

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The accurate estimation of the stability of a rock or soil slope is a difficult problem mainly because

of the complexity of the physical system itself and the difficulty involved in determining the

necessary input data associated with geotechnical parameters. We are faced with a non-linear

dynamical system which is likewise spatially distributed including a further problem due to the fact

that only a rough overall (macroscopic) description of the physical and geometric characteristics

of the slope can usually be given. For the above reasons, it is difficult to determine the values of

essential input data. Neural networks provide descriptive and predictive capabilities and, for this

reason, have been applied through the range of rock and soil parameter identification and

engineering activities (Jing and Hudson, 2002; Jing, 2003). This paper is a continuation of the

research conducted by our research group (Sakellariou and Ilias, 1997; Roussos, 2000).

The following approaches will be taken for the rest of my project work:

Application of the neural network method in the field of slope stability, and investigation of the

performance and convergence of artificial neural networks.

Investigation of the accuracy and flexibility of the method when applied to specific real-world

data sets, with reference to circular failure mechanism, plane failure mechanism and wedge

failure mechanism, in soil or highly fractured rock and rock slopes. Additionally, exploration of the

data set and testing the quality of the data.

Validation of the method by comparing its results to those obtained by standard engineering

techniques and simple empirical equations.

Examination of the relative importance of the input parameters.

Estimation of the stability and the factor of safety from the perspective of a dynamic system in

which one can implement descriptive data, as the status of stability.

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Artificial Neural Network Introduction An artificial neural network (ANN), usually called neural network (NN), is a mathematical model

or computational model that is inspired by the structure and/or functional aspects of biological

neural networks. A neural network consists of an interconnected group of artificial neurons, and

it processes information using a connectionist approach to computation. They are powerful tools

for modelling, especially when the underlying data relationship is unknown. ANNs can identify

and learn correlated patterns between input data sets and corresponding target values. After

training, ANNs can be used to predict the outcome of new independent input data.

ANNs have been applied to many geotechnical engineering problems such as in pile capacity

prediction, modelling soil behaviour, site characterisation, earth retaining structures,

settlement of structures, slope stability, design of tunnels and underground openings,

liquefaction, soil permeability and hydraulic conductivity, soil compaction, soil swelling and

classification of soils.

Figure 1: Three layer neural network

Figure1 show three layer neural network consist first layer has input neurons, second layer

of hidden neurons, third layer of output neurons. Supervised neural networks are trained in

order to produce desired outputs in response to training set of inputs. It is trained by

providing it with input and matching output patterns.

It used in the modelling and controlling of dynamic systems, classifying noisy data, and

predicting future events. Unsupervised neural networks, on the other hand, are trained by letting

the network continually adjusting itself to new input. It is or Self-organisation in which an (output)

unit is trained to respond to clusters of pattern within the inputs. Reinforcement Learning is be

considered as an intermediate form of the above two types of learning. Here the learning

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machine does some action on the environment and gets a feedback response from the

environment.

For an artificial neuron, the weight is a number, and represents the synapse. A negative weight

reflects an inhibitory connection, while positive values designate excitatory connections. All

inputs are summed altogether and modified by the weights and refers as a linear combination.

Finally, an activation function controls the amplitude of the output. For example, an acceptable

range of output is usually between 0 and 1, or it could be -1 and 1.

A neuron is a real function of the input vector (x0, x2, xk). The out put is obtained as f(yj)

Where, f is a function, typically the sigmoid (logistic or tangent hyperbolic) function. A

graphical presentation of neuron is given in figure 2. Mathematically a Multi-Layer Perceptron

network is a function consisting of compositions of weighted sums of the functions

corresponding to the neurons.

Figure 2: Graphical presentation of neuron in ANN

There are several types of architecture of NNs. However, the two most widely used NNs

Feed forward networks and Recurrent networks. In a feed forward network,

information flows in one direction along connecting pathways, from the input layer via the

hidden layers to the final output layer. There is no feedback (loops) i.e., the output of any

layer does not affect that same or preceding layer. Feed-forward neural networks,

where the data O(w) from input to output units is strictly feedforward. The data processing

can extend over multiple (layers of) units, but no feedback connections are present.

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Figure 3: A multi-layer feedforward network

These networks differ from feed forward network architectures in the sense that there is at least one feedback loop. Thus, in these networks, for example, there could exist one layer with feedback connections as shown in figure below. There could also be neurons with self feed back links, i.e. the output of a neuron is fed back into itself as input.

Recurrent neural networks that do contain feedback connections. In some cases, the

activation values of the units undergo a relaxation process such that the neural network will

evolve to a stable state in which these activations do not change anymore. In other

applications, the change of the activation values of the output neurons are significant, such

that the dynamical behaviour constitutes the output of the neural network (Pearlmutter,

1990).

Figure 4: A recurrent neural network

Back-Propagation Algorithm:

The back-propagation algorithm is a non-linear extension of the least mean squares (LMS)

algorithm for multi-layer perceptrons. It is the most widely used of the neural network

paradigms and has been successfully applied in many fields of model-free function

estimation. The back propagation network (BPN) is expensive computationally, especially

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during the training process. Properly trained BPN tends to produce reasonable results when

presented with new data set inputs.

A BPN is usually layered, with each layer fully interconnected to the layers below and above

it. The first layer is the input layer, the only layer in the network that can receive external input.

The second layer is the hidden layer, in which the processing units are interconnected to the

layers below and above it. The third layer is the output layer. Each unit of the hidden layer is

interconnected with the units of the output layer. Units are not interconnected to other units

within the same layer. Each interconnection is assigned an associative connection strength,

expressed as weight (Figure 1). Weights are adjusted during the training of the network. In

BPN, the training is supervised, in which case the network is presented with target values for

each input pattern. The input space of the network is considered to be linearly separable. The

back-propagation algorithm is a non-linear extension of the least mean squares (LMS)

algorithm for multi-layer perceptrons. It is the most widely used of the neural network

paradigms and has been successfully applied in many fields of model-free function

estimation. The back propagation network (BPN) is expensive computationally, especially

during the training process. Properly trained BPN tends to produce reasonable results when

presented with new data set inputs.

A BPN is usually layered, with each layer fully interconnected to the layers below and above

it. The first layer is the input layer, the only layer in the network that can receive external input.

The second layer is the hidden layer, in which the processing units are interconnected to the

layers below and above it. The third layer is the output layer. Each unit of the hidden layer is

interconnected with the units of the output layer. Units are not interconnected to other units

within the same layer. Each interconnection is assigned an associative connection strength,

expressed as weight (Figure 1). Weights are adjusted during the training of the network. In

BPN, the training is supervised, in which case the network is presented with target values for

each input pattern. The input space of the network is considered to be linearly separable.

A BPN is usually layered, with each layer fully interconnected to the layers below and above it.

The first layer is the input layer, the only layer in the network that can receive external input. The

second layer is the hidden layer, in which the processing units are interconnected to the layers

below and above it. The third layer is the output layer. Each unit of the hidden layer is

interconnected with the units of the output layer. Units are not interconnected to other units within

the same layer. Each interconnection is assigned an associative connection strength, expressed

as weight (Figure 1). Weights are adjusted during the training of the network. In BPN, the training

is supervised, in which case the network is presented with target values for each input pattern.

The input space of the network is considered to be linearly separable.

The various steps in developing a neural network model are: summarized below & the example

is shown by metlab software.

Variable selection The input variables important for modeling variable(s) under study are selected by suitable

variable selection procedures.

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Formation of training, testing and validation sets The data set is divided into three distinct sets called training, testing and validation sets. The

training set is the largest set and is used by neural network to learn patterns present in the data.

The testing set is used to evaluate the generalization ability of a supposedly trained network. A

final check on the performance of the trained network is made using validation set.

Neural network architecture Neural network architecture defines its structure including number of hidden layers, number of

hidden nodes and number of output nodes etc. Number of hidden layers: The hidden layer(s)

provide the network with its ability to generalize. In theory, a neural network with one hidden layer

with a sufficient number of hidden neurons is capable of approximating any continuous function.

In practice, neural network with one and occasionally two hidden layers are widely used and have

to perform very well.

Number of hidden nodes: There is no magic formula for selecting the optimum number of hidden

neurons. However, some thumb rules are available for calculating number of hidden neurons. A

rough approximation can be obtained by the geometric pyramid rule proposed by Masters (1993).

For a three layer network with n input and m output neurons, the hidden layer would have

sqrt(n*m) neurons.

Activation function: Activation functions are mathematical formula that determine the output of a

processing node. Each unit takes its net input and applies an activation function to it. Non linear

functions have been used as activation functions such as logistic, tanh etc. Transfer functions

such as sigmoid are commonly used because they are nonlinear and continuously differentiable

which are desirable for network learning.

Evaluation criteria

The most common error function minimized in neural networks is the sum of squared errors. ther error functions offered by different software include least absolute deviations, least fourth powers, asymmetric least squares and percentage differences.

Neural network training

Training a neural network to learn patterns in the data involves iteratively presenting it with

examples of the correct known answers. The objective of training is to find the set of weights

between the neurons that determine the global minimum of error function. This involves

decision regarding the number of iteration i.e., when to stop training a neural network and the

selection of learning rate.

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Figure 5: Input, sum-operator and bias working together for producing the output node.

Various researchers have used ANN to predict to the slope stability or slope failure or factor of

safety. The Back propagation neural network is used to calculate the factor of safety. Nine input

parameters and one output parameter are used in the analysis. The output parameter is the factor

of the safety of the slopes, the input parameters are the height of slope, the inclination of slope,

the height of water level, the depth of firm base, the cohesion of soil, the friction angle of soil, the

unit weight of soil, but the important input parameters are horizontal and vertical seismic

coefficients.

Slope failures are complex natural phenomena that constitute a serious natural hazard in many

countries. To prevent or mitigate the landslide damage, slope-stability analyses and stabilization

require an understanding and evaluation of the processes that govern the behavior of the slopes.

The factor of safety based on an appropriate geotechnical model as an index of stability, is

required in order to evaluate slope stability. Many variables are involved in slope stability

evaluation and the calculation of the factor of safety requires geometrical data, physical data on

the geologic materials and their shear-strength parameters (cohesion and angle of internal

friction), information on pore-water pressures, etc.

The determination of the non-linear behaviour of multivariate dynamic systems often presents a

challenging and demanding problem. The impact of these parameters on the stability of slopes is

investigates through the use of computational tools called neural networks. The input data for

slope stability estimation consist of values of geotechnical and geometrical input parameters. The

network estimates the factor of safety (FS) that can be modelled as a function approximation

problem, or the stability status (S) that can be modelled either as a function approximation

problem or as a classification model. The performance of the network is measured and the results

are compared to those obtained by means of standard analytical methods.

A series of ANNs were created in order to predict the safety factor and estimate stability against

the circular failure mechanism and the wedge failure mechanism.

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Ann and fuzzy set could primarily be used in two ways in slope stability. One is prediction of

various strength and physic-mechanical properties by previously used properties.

Other is direct prediction of factor of safety or stability based on simulation of huge data set or

incorporating the case studies.

The rock slopes have important role for the design and excavation in various open pit mine and

also civil engineering projects all around the world. Initial the condition and friction angle can be

trained by neural network. Input parameter of compressive strength and later on cohesion and

friction angle were calculated by compressive strength and these properties were used as input

for finite difference code to analyzing slope stability and determine the factor of safety.

Figure 6: Flow Chart to determine the properties and analysis the Slope stability by ANN

Fuzzy Inference System Fuzzy logic is a form of many-valued logic and it deals with reasoning that is approximate rather

than fixed and exact. The nature of uncertainty in a slope design is a very important that should

considered. Fuzzy set theory was developed specially to deal with uncertainties that are

nonrandom in nature.

The fuzzy set was first introduced in 1965 by Lofti Zadeh as a mathematical way to represent

linguistic vagueness . It can be considered as a generalization of classical set theory. In a classical

set, an element belongs to or does not belong to a set. That is, the membership of an element is

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crisp (0, 1), and an A crisp set of real objects are described by a unique membership function

such as XA in fig.7(a).

Figure 7: (a) Crisp Set (b) Fuzzy Set

Contrary, a fuzzy set is a generalization of an ordinary set which assign the degree of membership

for each element to range over the unit interval between 0 and 1 as shown in fig. 7(b). In addition,

fuzzy set theory can be used for developing rule-based models which combine physical insights,

expert knowledge and numerical data in a transparent way that closely resembles the real world.

An element of the variable can be a member of the fuzzy set through a membership function that

can take values in the range from 0 to 1. Membership functions (MF) can either be chosen by the

user arbitrarily based on the users experience or can also be designed using machine learning

methods (e.g., artificial neural networks, genetic algorithms, etc.). There are different shapes of

membership functions; triangular, trapezoidal, piecewise-linear, Gaussian, bell shaped, etc. The

fuzzy rules provide a system for describing complex (uncertain, vague) systems by relating input

and output parameters using linguistic variables. A fuzzy ifthen rule assumes the form if x is A

then y is B, where A and B are linguistic values defined by fuzzy sets on universes of discourse

X and Y, respectively.

Fuzzy inference is the process of formulating an input fuzzy set map to an output fuzzy set using

fuzzy logic. In fact, the core section of a fuzzy system is the FIS part, which combines the facts

obtained from the fuzzification with the rule base and conducts the fuzzy reasoning process.

Generally, the basic structure of a FIS consists of three conceptual components, rule base,

database, and reasoning mechanism. A rule base contains a selection of fuzzy rules and a

database defines the membership functions used in the fuzzy rules. A reasoning mechanism

performs the fuzzy reasoning based on the rules and given facts to derive a reasonable output or

conclusion. There are several FISs that have been employed in various applications. The most

commonly used include:

Mamdani Fuzzy Model;

Takagi-Sugeno-Kang fuzzy (TSK) model;

Tsukamoto fuzzy model;

Singleton fuzzy model.

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The differences between these FISs lie in the consequents of their fuzzy rules, and thus their

aggregation and defuzzification procedures differ accordingly. Defuzzification is a process of

reducing an aggregated (or clipped) fuzzy set into a crisp number, presumably the most

representative value of that fuzzy set interval. There are two methods which are generally used

for defuzzification i.e. Centre of area (Centroid) method and Ranking index method.

The Mamdani Fuzzy model is often used in geotechnical problems because of its simplicity and

effectiveness to handle linguistic variables. Basically, rule base, database and reasoning

mechanism are three conceptual elements of a FIS. The fuzzy rules constitute the rule base and

the database determines the membership functions associated with the inputs parameters to be

used in the rule base while the reasoning mechanism provides the platform to derive an adequate

conclusion (output) by using fuzzy logic. At this stage the extraction of a crisp set from a fuzzy

set, called defuzzification is performed.

Fuzzy logic provides an inference structure that enables the human reasoning capabilities to be

applied to artificial knowledge-based systems. Fuzzy logic provides a means for converting

linguistic strategy into control actions and thus offers a high-level computation.Fuzzy logic

provides mathematical strength to the emulation of certain perceptual and linguistic attributes

associated with human cognition, whereas the science of neural networks provides a new

computing tool with learning and adaptation capabilities. The theory of fuzzy logic provides an

inference mechanism under cognitive uncertainty, computational neural networks offer exciting

advantages such as learning, adaptation, fault tolerance, parallelism, and generalization.

Neuro-fuzzy inference systems have been used in many areas in civil engineering applications.

A stability assessment model for epimetamorphic rock slopes has been developed by using

Adaptive Neuro-Fuzzy Inference System (ANFIS) for its capacity of dynamic nonlinear analyses.

the inference system is employed to predict the stability of the slope by choosing bulk density ,

the height H, the inclination , the shear strength parameters c and , of the slope as inputs, while

the stability state as output.

Conclusion In order to forecast the factor of safety (FS) or the status of stability (S) in the case of rock or soil

slopes, the factors that influence FS and S have to be determined. The output layer is composed

of a single output parameter, either the factor of safety FS, or the status of stability. Considering

the uncertain problems of stability analysis which have the characteristics of random and

fuzziness, the author uses the maximum membership degree principle to analyze and evaluate

the slope stability. Ridge distribution in effect factor of quantity and trapezium distribution in the

effect factor of ration are applied here to construct membership function. The method of two class

synthesis assessment is adopted to analyze the stability of slope. The slope stability is assessed

by each factor such as cohesion, internal angle of friction, UCS, slope angle, etc. The membership

functions and the distribution of the proportion of importance can also be applied to analyze the

stability of similar slopes. The judgment of fuzzy comprehensive evaluation as the input of neural

network by MATLAB. Then final judgment is transported out through the neural network that

possess learning ability. Since ANN models have the learning ability, therefore it is of much

practical use and it shall be used in further prediction of those slopes which are vulnerable to

natures stability disturbing properties like moisture content and other factors like cohesion, angle

of internal friction, density, etc. which are inherent properties of rocks.

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