Applicability of Neural Network in Rock Classification of Mountain Tunnel
2019 Volume 60 Issue 5 Pages 758-764
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2019 Volume 60 Issue 5 Pages 758-764
In construction projects of mountain tunnels, with a purpose of improving accuracies of rock classifications in preliminary survey, we have studied applicability of Artificial Neural Network (ANN). One characteristics of ANN is that it does not require defining clear formula correlating data input and output, by using its learning function. Leveraging the characteristics, accuracy of rock classification improved by using geophysical datasets (seismic velocity and resistivity) at a tunnel face and surrounding. Also, ANN has a problem of reduced applicability caused by over learning to training data. It is possible to avoid the over learning problem by increasing training dataset, but it is not easy to accumulate complete dataset of geophysical properties and actual rock classification obtained in construction stage. We found that it is important to collect various tunnel data without much deviation, for accumulating training datasets effectively in the future.
This Paper was Originally Published in Japanese in Journal of the Society of Materials Science, Japan 67 (2018) 354–359. In order to more precisely explain, we add vertical axis label as Estimated rock mass class and horizontal axis label as Actual rock mass class in Fig. 3 and Fig. 4.
In construction projects of mountain tunnels, a problem that often occurs is the disparity between rock mass conditions expected during survey and design, and the actual conditions found during the construction phase, resulting in significant increase in construction costs. Owing to the strong need to reduce construction costs in recent years, a significant increase in construction cost during the construction phase is often not acceptable. One of the reasons for such disparity is that mountain tunnels are linear structures that involve a large overburden that prevents obtaining in advance a thorough understanding of ground conditions through a preliminary geological survey. This is owing to budget and time restrictions or technical limitations. However, it is necessary to improve the accuracy in assessing rock mass conditions during survey and design.
In Japan, preliminary surveys of mountain tunnels consist in general of surface geological surveys, seismic prospection, and a boring survey. Then, rock mass classification is carried out according to a rock mass classification table.1) In the classification according to the rock mass classification table, rock mass classes are defined according to such information as rock type, seismic velocity, boring core, and overburden. In general, standard shoring is applied according to the classification. In recent times, it was often the case that the use of explosives was restricted, and electrical resistivity prospecting was carried out instead of seismic exploration. However, the results were mostly used as a supplementary reference for the geological interpretation of the rock mass.
On the other hand, rock mass classification based on the tunnel face evaluation score is becoming increasingly common.2,3) The tunnel face evaluation score is based on scores assigned to such criteria as the compression strength of bedrock at the tunnel face, weathering pattern, fissure interval, fissure conditions, groundwater conditions, and conditions of rock deterioration by water. Judgments regarding rock mass classification are based on the scores. When information regarding tunnel face evaluation scores is not obtained, a problem that arises is how to estimate rock mass conditions at the tunnel face during the preliminary survey.
Regarding the preliminary survey, geophysical prospecting is the only method that permits obtaining physical properties along the tunnel route. For this reason, in order to improve the accuracy of rock mass classification, it is important to make effective use of the physical properties obtained in geophysical prospecting (seismic velocity and resistivity). However, owing to the complex relations between these physical properties and such criteria as the compression strength of the bedrock, weathering pattern, fissure conditions, and groundwater conditions, it is difficult to formulate a simple correlation between geophysical quantities and rock mass conditions at the tunnel face. On the other hand, the authors attempt to conduct the classification using a neural network (ANN: artificial neural network) owing to its ability to associate input and output data through a learning function without requiring a clear formulation between them.4)
Regarding the use of an ANN for rock classification in mountain tunnels, there is ongoing research on rock mass ratings (RMRs), which are a kind of bedrock classification.5) The target of that research is to use ANNs for automatic RMR rating, which has been proposed in the form of a complex table. However, no comparison was carried out between the obtained RMR and actual rock mass conditions at the tunnel face. By contrast, in the present research, we use ANNs to perform rock mass classification at the tunnel face based on information obtained through preliminary surveys.
In prior research carried out by the authors, a simple ANN containing one input layer, one hidden layer, and one output layer was used.4) In recent years, it has become possible to build more complex ANN structures. Thus, in order to achieve higher accuracy in rock mass classification, in the present research, we build ANN structures containing more hidden layers and investigate their properties (e.g., in terms of adaptability to non-trained data). Here, since the objective is to improve the accuracy of the classification in the preliminary survey, tunnel face prediction in surveys carried out during the construction work is excluded from our target scope.
The ANN is an information processing method created with the purpose of letting a computer imitate the mechanism of the human brain.6,7) The advantage of an ANN is its nonlinear processing capability. Thanks to its learning function, there is no need to formulate the relation between explanatory variables and the target variable.
The structure of the ANN used in the present research is shown in Fig. 1. An ANN consists of an input layer, hidden layers, and an output layer. The number of neurons in the input layer corresponds to the number of input data of the ANN, and the number of neurons in the output layer corresponds to the number of output data of the ANN. In the example of Fig. 1, the number of input and output data are 3 and 2, respectively. There are no restrictions regarding the number of hidden layers and the number of neurons in each hidden layer. The user can define them arbitrarily. In general, the ability to perform more complex tasks is enhanced by increasing the number of layers and neurons.
Structure of ANN.
The output from a neuron corresponds to the input to a neuron located in the next layer. Here, a weight is applied to the value output by a neuron before being input into the next neuron. For instance, in the example of Fig. 1, the output signal from the first neuron of the input layer is multiplied by weight W111 before being input into the first neuron of the hidden layer. Each neuron has a bias value that is added to the sum of the input signals, resulting in the internal voltage. The output value is defined based on the internal voltage. In most cases, the internal voltage is converted to the output value using a sigmoid function. In order to find values of weights and biases for the neurons, a method called back-propagation is used. In this method (learning method), weights and biases are adjusted based on previously known data sets that are used as training data. References on this method can be found in the existing literature.4,6,7)
The two following issues are expected concerning the application of ANNs to rock mass classification for mountain tunnels. First, the relations between physical values obtained through physical surveys (seismic velocity and resistivity) and the classification at the tunnel face are not clear, and therefore there is no guarantee that an accurate estimation of the classification is possible. Another issue is the possibility that an unexpected (improper) output may result when the input is not in the training data (in other words, it becomes impossible to solve problems different from the training data). This problem is called overlearning. Overlearning tends to occur when the number of parameters (number of weights and biases in the neurons) is large with respect to the amount of training data. For this reason, a complex ANN may result in a narrow range of applicability. Overlearning can be controlled by increasing the amount of training data. However, complete data related to mountain tunnels, comprising the seismic velocity, resistivity, and the classification at the tunnel face are extremely scarce. Thus, in the present research, we study the effect of overlearning on the accuracy of the classification using an ANN with a small amount of training data and complex ANN structures.
In the present research, we use data from two tunnels (referred to as tunnel R and tunnel B) consisting of crystalline rock mass. For each tunnel, Fig. 2 shows the seismic velocity, resistivity, and rock mass classification at the tunnel face upon the execution of the construction. As shown in the figure, no clear correlation can be observed between the seismic velocity and rock mass classification, or between the resistivity and rock mass classification. As seismic velocity and resistivity decrease, the occurrence of poor rock mass tends to simply follow the sequence B, CI, CII, D, in increasing order of poor rock mass. The seismic velocity is distributed in a range between 3 to 4 km/s and around 5 km/s for tunnel R. On the other hand, tunnel B contains speeds of 4 km/s and above, with a distribution slightly different from that of tunnel R. The same happens with the resistivity: tunnel B tends to show a lower resistivity than tunnel R, with a slightly different distribution.
Relationship with seismic velocity, resistivity and rock classification.
The input data for the ANN in the present research consist of the seismic velocity, resistivity, and overburden. In general, seismic velocity is related to bedrock hardness. However, it increases with overburden owing to the influence of overburden pressure. For this reason, in order to assess bedrock hardness at the tunnel excavation position, it is desirable that the seismic velocity considers the effect of overburden. Moreover, in terms of resistivity, if we consider that gaps become smaller owing to overburden pressure, it is necessary to consider overburden in the same way as seismic velocity. Therefore, information regarding overburden was also included as an input to the ANN.
Considering the accuracy of geophysical prospecting, the result does not necessarily correspond to the geophysical properties at the tunnel face. The position may suffer a horizontal or vertical bias. For this reason, the accuracy of rock mass classification is expected to improve if data corresponding to an area close to the tunnel face are input. Thus, in the present research, we consider two cases concerning the input of data at the tunnel face position, and one case concerning the input of data around the tunnel face. Table 1 lists the ANN attributes for each case. In Case 1, the seismic velocity (Vp), resistivity (ρ), and overburden (D) at the tunnel face are used as inputs. The input data are taken in 10 m intervals at the tunnel excavation positions. Moreover, in order to normalize the order of the seismic velocity, resistivity, and overburden, we consider common logarithms for resistivity and overburden. For the ANN, we consider three hidden layers, each one containing 10 neurons. In Case 2, we also consider seismic velocity, resistivity, and overburden at the tunnel face, similar to Case 1. As a structure more complex than that of Case 1, we consider three hidden layers, each containing 33 neurons. In Case 2, we study the effect of making the ANN model more complex. In Case 3, seismic velocities at the tunnel face and in locations 50 m back and forth with respect to the tunnel face at the excavation position are used as inputs in addition to the resistivity and overburden. The ANN model also contains three hidden layers as in Case 2, each containing 33 neurons.
The data sets used in the study are 229 for tunnel R and 109 for tunnel B, and 338 in total. Regarding rock mass classification, which corresponds to the output, we assign 1 to rock mass D, 2 to rock mass CII, 3 to rock mass CI, and 4 to rock mass B. Rock mass classes and quantized data (1 to 4 as indicated above) of actual tunnel faces are given as training data. The number of iterations for the back-propagation method is set to 1000. For the calculations, the neural network module PyBrain 0.3 for the Python language is used. Table 1 also shows the error during training (sum of squared residuals normalized by the number of data). The training error is approximately equivalent for Case 1 and Case 2; Case 3 shows a smaller error than Case 1 and Case 2, with better matching to the training data.
(1) Results of rock mass classification for Case 1 and Case 2
We performed rock mass classification using seismic velocity, resistivity, and overburden at the tunnel face position as input data. Using an ANN, the rock mass is classified according to the output: D for an output smaller than 1.5, CII for an output smaller than 2.5, CI for an output smaller than 3.5, and B for an output of 3.5 or above.
The matching rate and difference rate of the output estimated by the ANN (hereinafter referred to as the estimated rock mass class) and the actual rock class (hereinafter referred to as the actual rock class) are shown in Table 2. The matching rate is about 60% for both Case 1 and Case 2. In both cases, differences between the estimated and actual rock mass classes relate mostly to poor rock mass classification. No significant difference was found between Case 1 and Case 2 in terms of matching and difference rates.
Figure 3 shows a histogram of the actual rock mass classes for each rock mass class. The distribution found in the histogram is about the same for Case 1 and Case 2. No data was found where the estimated rock mass class was B. In rock masses where the estimated classification was CI, the predominant rock mass class found in the actual data was CI, with a larger number of good (rock mass class B) than poor (rock mass class CII) classifications. In rock masses where the estimated classification was CII, the predominant rock mass class found in the actual data was CII, with an approximately equal number of poor (rock mass class D) and good (rock mass class CI) classifications. In rock masses where the estimated classification was D, even though they corresponded to the actual rock mass class in most cases, a few data with rock mass classification good (rock mass class CII) were found. Considering the frequent occurrence of incorrect classification as poor in rock masses classified as CI, as shown in Table 2, we consider that as a whole, the results tend to lead to a poor rock mass classification. Comparing the results of Case 1 and Case 2, we conclude that the accuracy of rock mass classification does not improve by constructing more complex ANN structures.
Histograms of real rock class for each predicted rock class by ANN.
(2) Rock mass classification result for Case 3
We performed rock mass classification with respect to a tunnel perforation position 50 m before and after the tunnel face using seismic velocity, resistivity, and overburden as input data. However, we excluded from the classification scope those segments where no data were available 50 m before and after the tunnel face, for instance, in areas near the tunnel portal.
The matching rate and difference rate between the rock mass classification estimated by the ANN and the actual rock mass classification are listed in Table 2. The matching rate between the predicted rock mass classification and the actual rock mass classification is higher than in Case 1 and Case 2. However, the difference rate relative to the poor rock mass class, which increased compared to Case 1 and Case 2, whereas the difference rate relative to the good rock mass class decreased. As shown in Fig. 3, in Case 3, a few examples of class B were found among the estimated rock mass classes. Regarding rock mass classes estimated as CI, the difference rate relative to a good rock mass (B rock mass class) was practically none, whereas the difference rate relative to a poor rock mass (CII rock mass class) was larger than in Case 1 and Case 2. Considering that the amount of data estimated as pertaining to the CI rock mass class is large, it is possible that this may be the reason for the larger difference rate relative to the bad rock mass class in Case 3 compared to Case 1 and Case 2. For rock mass classes estimated as CII, the amount of mismatching data was smaller than in Case 1 and Case 2. For rock mass classes estimated as D, no mismatching data were found.
From the above, we conclude that on the whole, the accuracy of rock mass classification improved in Case 3 compared to Case 1 and Case 2. In this way, we confirmed the effectiveness of introducing data related to the tunnel face in the input.
In the ANN, the results may not be as expected when data other than the training data are used as the input, owing to overlearning. Thus, we investigated the matching and difference rates when a model is trained using data from tunnel R or B, and data from the other tunnel are used as input.
Table 3 lists the respective matching and difference rates when data from tunnel R are used for training the ANN, and data from tunnels R and B are used as input data. The matching rate when data from tunnel R are used to train the ANN, and data from tunnel R are also used as the input, is 79.4%. When data from tunnel B are used to train the ANN and data from tunnel B are also used as the input, the matching rate is 95.5%, which is considerably high. On the other hand, when data from tunnel R are used to train the ANN and data from tunnel B are used as the input, the matching rate is 57.4%. When data from tunnel B are used to train the ANN and data from tunnel R are used as the input, the matching rate is 39.3%, i.e., the matching rate is low. In other words, the adaptability of the ANN to non-trained data is low. In terms of the difference rate, if data from tunnel R are used to train the ANN and data from tunnel B are used as input, the difference rate relative to the poor rock mass is high. By contrast, when data from tunnel B are used to train the ANN and data from tunnel R are used as input, the difference rate relative to a good rock mass is high. Thus, we can see that the characteristics of the ANN are largely influenced by the characteristics of the training data.
Two methods can be considered in order to reduce overlearning: reducing the number of hidden layers and the number of neurons in each layer (reducing the number of unknown parameters), and increasing the training data. Reducing the number of hidden layers and the number of neurons in each layer involves the issue of how to determine the optimal number of hidden layers and neurons in each layer. Moreover, in order to achieve better performance using a smaller number of hidden layers and neurons, it is also necessary to consider ANN construction methods that do not rely on back-propagation. Here, we do not consider methods that reduce the number of hidden layers and neurons in each layer. Instead, we consider ways to increase the amount of training data.
(1) Preparing training data by introducing variations
Geophysical data obtained by geophysical surveys are subject to uncertainty. This uncertainty is supposed to grow with the size of the overburden. On the other hand, the uncertainty involved in rock mass classification at the tunnel face during the execution phase of the construction work is considered to be small. (Strictly speaking, there is some uncertainty in the rock mass classification at the tunnel face conducted by engineers, but that is neglected here.) As a way to consider the uncertainty embedded in the geophysical survey data used as input, we prepare multiple training data containing variations, which are introduced using random numbers. This is done in order to increase the training data in a virtual manner. It is expected that by increasing the degree of uncertainty and the number of random numbers introduced, it will be possible to reduce the effect of overlearning.
The following is a method to create training data containing variations. Since there is no established method to quantitatively evaluate the uncertainty of multiple phenomena, we assume here that there is a ±20% uncertainty in the geophysical survey data. For each item of geophysical data input into the ANN, 100 uniform random samples are generated in a range from 0.8 to 1.2. The geophysical survey data are multiplied by these random numbers to generate training data containing variations. Here, the number of random samples of 100 was selected based on restrictions related to computation time.
Concretely speaking, seismic velocity data taken approximately 50 m before and beyond the tunnel face, and resistivity data, are multiplied by the random numbers above to generate training data. The overburden does not contain any uncertainty because it can be determined from the tunnel excavation depth and earth altitude. Therefore, it is not multiplied by a random number. Thanks to the processing above, the apparent amount of training data becomes 100 times larger. Regarding the rock mass class, uncertainty is not considered because it corresponds to the actual rock mass class at the tunnel face.
There are cases where the output, which corresponds to the rock mass class, may assume a different value even though the same value is input into the ANN. In order to allow this situation, the number of neurons in the output layer is set to 4. Each neuron outputs the probability of resulting in a rock mass class of B, CI, CII, or D. For this reason, the value of each neuron in the output layer of the training data is (1,0,0,0) for rock mass class B, (0,1,0,0) for rock mass class CI, (0,0,1,0) for rock mass class CII, and (0,0,0,1) for rock mass class D. Depending on the input data, the output from the ANN may be smaller than 0 or greater than 1. In that case, if the output is smaller than 0, it is corrected to 0, and if the output is greater than 1, it is corrected to 1. Moreover, the outputs from all neurons in the output layer are normalized so that they sum up to 1. By doing so, the outputs from the ANN can be viewed as the probability of belonging to each rock mass class.
Regarding hidden layers, a total number of three hidden layers containing 33 neurons each are set, as was done previously.
Table 4 lists the matching and difference rates between rock mass classes estimated by the ANN and those actually observed. The expected value is calculated by rounding the obtained output probabilities multiplied by the values of the rock mass class (1 to 4) assigned as follows: 1 for rock mass D, 2 for rock mass CII, 3 for rock mass CI, and 4 for rock mass B. As shown in the shaded part of the table, the matching rate when data from tunnel R are used to train the ANN and data from tunnel B are used as the input is 34.8%, which is lower than the result shown in Table 3. On the other hand, the matching rate when data from tunnel B are used to train the ANN and data from tunnel R are used as the input is 44.3%, which is slightly higher than the result shown in Table 3. However, there is no evident improvement as a whole. These results are obtained when an uncertainty of 20% is attributed to the geophysical data. This results in a range from 2.4 to 3.6 km/s for a seismic velocity of 3 km/s, or from 4.0 to 6.0 km/s for a seismic velocity of 5.0 km/s. As can be seen in Fig. 2, the obtained ranges cover approximately the data of tunnels R and T, and therefore the assumed uncertainty does not seem to be too small. There is also a possibility that the results may change if the amount of random numbers is increased even more (e.g. 1,000 or 10,000 times rather than 100), but in that case, more consideration is needed in terms of computation time.
(2) Preparing training data by extracting data at random from tunnels R and B
It was not possible to reduce the effect of overlearning by virtually increasing the amount of training data through the introduction of uncertainty to the geophysical survey data used as the input. Therefore, in essence, it is desirable to accumulate a large amount of tunnel data and use them for training. However, in practice, it is difficult to accumulate a large amount of data containing seismic velocity, resistivity, and rock mass classification at the tunnel face during the construction phase. Moreover, it is probably difficult to reduce the effect of overlearning by accumulating a large amount of similar data.
As shown in Fig. 2, the distributions of seismic velocity, resistivity, and rock mass class differ for tunnels R and B. In other words, population distributions differ for tunnels R and B. Thus, we consider borrowing part of the data for training the ANN of tunnels R and B. Thus, even if the number of data is small, we can use data whose population contains a lot of variety for training. Concretely speaking, half the data from tunnels R and B are extracted at random and used as training data for the ANN.
Table 5 lists the matching and difference rates between rock mass classes estimated by the ANN trained above, where data from tunnels R and B are used as inputs, and actual rock mass classes. The matching rate for tunnels R and B is approximately 70%. Figure 4 shows a histogram of the estimated and actual rock mass classes. In the case of tunnel R, even though the estimated rock mass classes contain a relatively large number of samples of rock mass class CII for those estimated to be of class CI, the estimated rock mass classes in general match the actual classes relatively well. However, in the case of tunnel B, for a large number of data, the estimated rock mass class is CI, while the actual class is CII. Moreover, compared to tunnel R, the matching rate between the estimated and actual rock mass classes is lower. A possible cause is the influence of the number of training data extracted from R, which corresponds to approximately twice the number of data extracted from B. Even so, compared to an ANN where only data from tunnel R or B are used, the matching rate between the estimated and actual rock mass classes is higher. Therefore, it is effective to use tunnel data with a distribution that differs from that of the population for the purpose of training an ANN.
Comparison with predicted and real rock classification.
In the present research, we investigated the applicability of an ANN to rock mass classification of mountain tunnels. The insights obtained through our research are as follows:
Thanks to the learning capability of the ANN, there is no need to formulate the relations between explanatory variables and the target value, and complex models can be easily constructed. On the other hand, overlearning constitutes an important problem. A general approach to decrease overlearning is to reduce the number of parameters of the model (number of hidden layers and neurons in each layer) as much as possible. Methodologies for selecting an optimal model were not discussed in the present research and remain an issue to be addressed in the future. Another approach to reducing the influence of overlearning is increasing the amount of training data. However, it is not straightforward to accumulate a large amount of tunnel data containing seismic velocity, resistivity, and rock mass classification at the tunnel face during the construction phase. For this reason, in order to build an ANN in an effective manner with few training data, it is important to accumulate tunnel data containing a large variety of population distributions. We propose to accumulate not only data containing differences in types of rock such as crystalline or sedimentary rocks, but also data exhibiting different distributions based on the understanding of distributions of geophysical properties according to rock mass classification for different tunnels. Moreover, the content of the training data is important. In the present research, we built an ANN where the training data used were extracted at random, half from tunnel R and half from tunnel B, but the amount of training data extracted from tunnel R was about twice that extracted from tunnel B. The results of rock mass classification using the ANN constructed as above exhibited higher accuracy when data from tunnel R were used as the input than when data from tunnel B were used. This suggests that consideration is needed in the choice of data to be used for training.
