ANN Model for Prediction of Rockfill Dam Slope Stability

: Dam safety and potential failure is one of the issues with the highest risk in water resources management. The dam slope stability is adversely influenced by the natural seepage process in the dam. Thus, monitoring of the pore and total pressures in the dam core is essential in the seepage process analysis. It is possible during the dam operation period to have one or more cells malfunctioning, after years of operation. Sometimes it is technically not possible to replace the cell or the costs of the replacement are too high and not economically justified. At the Pridvorica Dam, several instruments - cells for pore and total pressure monitoring malfunctioned. The objective of this study is to develop a neural network model for the prediction of the pore and total pressure on the malfunctioning cells and to demonstrate its quick and effective practical application for identifying complex non-linear relationship between the input and output variables. The proposed approach can be a very helpful tool for modeling of the stochastic behavior of the dam in order to give adequate warning of soil pressures to prevent failures.


INTRODUCTION
Dam safety and potential failure is one of the issues with a highest risk in water resources management and it is a permanent occupation of engineers and scientists 23, 29.
Slope stability of the dam is a key factor in dam safety. The dam slope stability is adversely influenced by the natural seepage process in the dam 4, 7, 10, 12, 22, 28. The main indicator of the slope stability is the pore pressure at the slip circle of the dam 24.
Total pressure that acts at the saturated soil of the clay core of the dam is transmitted by the mineral soil skeleton and the pore water. The mineral soil skeleton carries the effective pressure p ef and the pore water carries the pore pressure p w .
The total pressure can be calculated as: Slope safety of dam is monitored by the instruments installed in the dam (pore and total pressure measurement cells). Progressively with the dam construction the instruments and devices required for dam monitoring are installed. Directly after installation, the measurement cell zero-reading is made. Zero-reading is crucial for measurement data evaluation and instrument inspection 1. The dam is equipped with instruments -pressure cells that are located in the center of the core as well as close to the filter, at the outer part of the core, to provide the monitoring of all potential slip surfaces.
During the period of the construction of the dam, the total pressure at the monitoring cell depends on the magnitude of the external pressure at the overlying compacted layer and the weight of the layer above the cell.
When pressed, the layer above the cell settles 2, 17. After the dam construction, the pressure on the cell depends on piezometric head of the filtrated water through the dam, the pressure of the material above the phreatic line and the pressure in the saturated material under the phreatic line 27.
The pore pressures at the dam are affected by the piezometric head in the reservoir and piezometric head in the river banks 5, 9. The magnitude of the registered pore pressure in the installed cell is affected by the position of the cell in the dam relative to the phreatic line in the dam.
When the registered pore pressure is greater than piezometric head defined by reservoir water level and the phreatic line, it is an indicator that the dam slope stability factor decreases. Pore pressure increasing results in decreasing of cohesion and internal friction coefficient.
Artificial neural network is a very powerful tool for solving complex data set issues 15.
It is possible during the dam operation period to have one or more cells malfunctioning, after years of operation. Sometimes it is technically not possible to replace the cell or the costs of the replacement are too high and not economically justified.
At the Pridvorica Dam, several instruments -cells for pore and total pressure monitoring malfunctioned. The problem of obtaining newly data increases. Solution of cells replacing, implying dam clay core destruction, can significantly jeopardize dam stability. Thus theoretical approaches have been considered as alternative.
There are a lot of numerical methods for dams stability analysis 814 and a lot of newly developed predictive models both statistical and deterministic in terms of displacement, leakage, peak load and piezometric head, shown as very useful tool for estimation of the slope safety.
In problems of the stochastic processes, artificial neural networks (ANN) have been found efficient and have been used successfully in water resources management for many engineering problems.
ANN application is very often in operation of the existing reservoirs 18, 19, 48 where determination of the relationship between reservoir parameters is the one of the most pressing difficulties due to possible effects to the operation of dams 13, 16, 21.
The risk function particularly occurs from reservoir release decisions.
Nevertheless the most challenging issue is forecasting the safety and stability of the dams 25.
The objective of this study is to develop a neural network model for the prediction of the pore and total pressure in the malfunctioning cell and to demonstrate its application to identifying complex non-linear relationship between the input variables and output variables.
The proposed approach can be a very helpful tool for modelling of the stochastic behavior of the dam and that could give adequate warning of soil pressures to prevent failures.

CASE STUDY
This study focuses on the Pridvorica Dam as a case study. This dam is located in the South West of Serbia.
The Pridvorica Dam was built in the year 1983 and the main purpose of this reservoir was solving the water supply problem of the town Blace.
Concerning the technical data one can say that Pridvorica is a rockfill dam, 44.5 m high and with central vertical clay core -sealing element.
The upstream face slope is 1:2, 1:2.5 and downstream face slope is 1:1.9, 1:2. The volume of the construction fill material is 120 000 m 3 and the reservoir capacity is 832 000 m 3 .
In the frame of technical observation of this dam, slope stability is being appraised measuring of pore and total pressures in the clay core.

Figure 1 Arrangement of instruments in the dam
After the dam construction, the initial filling of the reservoir was conducted.
The control over the first filling evidenced the seepage on the downstream slope and flanks of the dam that indicated the failure in the grout curtain. Hence, the remedial grouting, through the constructed embankment dam was performed in year 1986 to control this seepage.
After the remedial grouting through the dam, the other problem occurred, namely at the cross section 5 ( Fig. 1), cells P 2 and T 2 , located at the contact of the dam with the fundament (505.00 masl) and the cell T 5 (516.00 masl) malfunctioned.
The cells T 1 and P 1 (505.00 masl) located at the cross section 5 as well, are still in operation.
Pressures measured data-set date, from the installation moment in 1980, up-to-date.
This study aims to investigate the possibility of predicting the data on malfunctioned cells using the existing measurement data.

PREDICTION MODEL
Before proceeding to the description of the solutions to the above problems we will describe the basics of feed-forward neural networks used as the core approximant throughout our work.
An example of a feed-forward neural network 11 is given in Fig. 2.

Figure 2 Feed-forward ANN
It is a fully connected network with one hidden layer. n, n 0 and n' are the number of neurons in the input, hidden, and output layer, respectively. θ ji is the threshold of the i-th neuron in the j-th layer, while w(p, i)(q, j) is the weight of the connection between the j-th neuron in the p-th layer and the i-th neuron in the q-th layer.
The neurons belonging to the hidden layer are activated by the following function: For the neurons in the output layer we use: where: -λ 1 and λ 2 are constants, while -z i and y i are the responses of the neurons in the hidden and the output layer, respectively (25).
where: -x j are the input signals of the corresponding neurons. Arrows in the Fig. 2 mark the signal transfer between neurons. Indices: i, h, and o, in this figure, stand for input, hidden, and output, respectively.
The value associated with an arrow expresses the fact that the output signal of the neuron from the previous layer is multiplied by a constant, here referred to as the weight, w(i, j), before it excites a neuron in the next layer. The network is fully connected, i.e. all w(i, j) are nonzero.
For the set of weights connecting the input and the hidden layer we have: i = 1, 2, ..., n i , j = 1,2, ..., n h , while for the set connecting the hidden and output layer we have: In this paper we will use artificial neural networks (ANNs) for predicting the data on malfunctioned cells installed in the body of the dam, as described earlier in the paper.

Modelling Behaviour of One Cell
First, we will present results considering only one cell, P 2 . Since this pressure measurement cell malfunctioned, there exist measurement data only from the period when this cell was working properly, which is a short time period.
The first idea was to use data measured on T 1 cell since these two cells are on the same position in the dam, so there is a presumption that there is some relation among parameters measured on these cells. We thus hope that this correlation could help us in reproducing activity of P 2 cell. Measured data are given in the Tab. 1 (values are scalar and for results interpretation calibration factors are used) and refer to the period when P 2 and T 1 were correct, i.e. before P 2 malfunctioned. Based on these data, a neural network was supposed to be trained, so it can model dependency between P 2 and T 1 . The obtained model should give predictive values of P 2 for input values of T 1 , because we have got measured values of T 1 for a very long time period, for about twenty years.
The structure of this network is of crucial importance. Namely, the values of P 2 are very close, in the small range of values. In some cases, even, we have the same output values (P 2 ) for different input values (T 1 ) -for example, 8866 is output for 7239, 7182, 7193 and 7190.
This implies that we should have more information on the network input that should better determine the output. We propose here a solution which includes one more ANN input.
This additional input is previous value of P 2 (value from the previous measurement), because we estimated that this previous value is of great importance, since the change in the pressure is relative to the previous value, as well as it depends on the current value of T 2 . This situation requires modified ANN structure, i.e. a recurrent artificial neural network. In the Fig. 3 we presented generalized schematic of a recurrent ANN, where both time-delayed inputs and outputs exist. For our problem, we need only time-delayed output, i.e. output from the previous time instance (previous measurement), so our ANN should have two inputs and one output.
Inputs are: current value of T 1 and previous value of P 2 , and output is current value of P 2 . A steepest-descent based training algorithm was implemented for ANN training 30. The number of hidden neurons, n, was found by trial and error after several iterations starting with an estimation based on that in 3. The goal was to find the optimum n that leads to a satisfactory classification.
Using too many neurons would increase the training time, but using too few would starve the network of the resources needed to solve the problem. Also, an excessive number of hidden neurons may cause the over-fitting problem that was avoided by implementation of a concept described in 20, 26. In fact, after the choice of its first value as an initial guess, according to Masters 20, it was raised until acceptable approximation was obtained. The value of the obtained error was 4.74  10 −5 . In that way the simplest (optimal) ANN was created avoiding, at the same time, the over-fitting problem.
Artificial neural network was trained using data given in the Tab. 1. It is a recurrent neural network with one hidden layer. The number of hidden layers was restricted to one. After training was completed, the number of hidden neurons in the resulting ANN was ten. This number of hidden neurons may look too high, but this is necessary since input data are similar, so greater number of neurons is needed in order to distinguish the data. In order to predict behaviour of P 2 , we needed to use more measured samples of T 1 as an excitation.
These data refer to a period when P 2 malfunctioned, and only T 1 worked properly. Since ANN captured dependency between P 2 and T 1 , we expect that when having information about T 1 behaviour, ANN can predict behaviour of P 2 . Obtained data are given in Tab. 2 and these are predicted values of P 2 .
Measured values of T 1 for a certain period of time are presented in Fig. 4. Note that 29 samples are given, 19 from the first table (used for ANN training), and 10 from the second (used for prediction).
The results are given in Fig. 5, measured and predicted data for P 2 . Notice that first 19 values are measured, and next ten values are predicted, so we obtained dependency of P 2 over a longer period of time. We can notice from the figures that P 2 tracks T 1 , so we obtained good results, since these cells are placed on the same point, and they should have similar change over time. The second idea for predicting P 2 is to use measured values of all pore cells. The presumption is that all these values are dependent on one another, so we will try to capture this dependency using an ANN. In order to obtain it, we trained an ANN that has 15 inputs (pore pressures from P 1 to P 16 , except P 2 ), and the output of the ANN is pore pressure P 2 .
The positions of these cells are given in Fig. 1.
The obtained ANN is excited by the data given in Tab. 4, so we got predicted values of P 2 , given in the last column of Tab. 4.
These predicted values refer to a time period when P 2 malfunctioned, but other cells still worked correctly, so we have measured values on all the cells except P 2 . These data are represented in Fig. 6, along with the measured data.
It must be emphasized that we predicted 10 values, but we can predict as many values as it is needed using the same methodology, i.e. as many measured values from 15 cells we have.

Modelling the Behaviour of Two Cells
Data used for the ANN training are given in Tab. 5.
We used the same methodology in order to determine values of the total pressures that should have been measured by T 2 and T 5 , since these cells also malfunctioned. Another ANN was trained, having 8 inputs (total pressure T 1 , T 3 , T 4 , T 6 , T 7 , T 8 , T 9 , T 10 ), and two outputs (T 2 , T 5 ). The number of hidden neurons was 15. The obtained ANN is excited by the data given in Tab. 6, so we got predicted values of T 2 and T 5 , given in the last two columns of Tab. 6. Dependencies of T 2 and T 5 are given in Figs. 7 and 8.

CONCLUSION AND RECOMMENDATIONS
Most of the world's existing dams have been built after the Second World War, which increases the interest in the dam health monitoring.
Dam behavior is difficult to predict with high accuracy.
The dam safety assessment is a very complex issue due to the uniqueness of each of dam structure and site, and specific interaction between dam and foundations. Environmental impact and forces are strongly involved in the dam behavior.
In this paper prediction ANN model was applied in order to obtain accurate prediction of pore and total pressure data at any instrument in the dam where the measuring cells malfunctioned.
We found that the prediction of the pore pressures at the malfunctioned cell is possible using the values at the nearby total pressure measurement cell. Further, the prediction of the values at the malfunctioned total pressure cell is possible using the values of all pore pressure cells in the dam body. In addition we achieved the prediction of the values at the two total pressure measurement cells using the measurement of all total pressure cells in the dam body. The obtained results indicate a high degree of correlation between the input and output data, thus the application of this method is justified and possible.
Once developed, the neural network model can be used as a predictive management tool for further monitoring activities.
Application of ANN offers a significant potential in the technical supervision of dams when the problem with malfunctioning cell occurs. This approach is theoretically and economically justified, without quite complicated and expensive replacing the cells, providing an insight in the overall stability of the dam.
Structural safety is high priority problem in engineering and thus the theoretical models should be highly tested 6.