In the past few decades, as a new tool for analysis of the tough geotechnical problems, artificial neural networks (ANNs) have been successfully applied to address a number of engineering problems, including deformation due to tunnelling in various types of rock mass. Unlike the classical regression methods in which a certain form for the approximation function must be presumed, ANNs do not require the complex constitutive models. Additionally, it is traced that the ANN prediction system is one of the most effective ways to predict the rock mass deformation. Furthermore, it could be envisaged that ANNs would be more feasible for the dynamic prediction of displacements in tunnelling in the future, especially if ANN models are combined with other research methods. In this paper, we summarized the stateoftheart and future research challenges of ANNs on the tunnel deformation prediction. And the application cases as well as the improvement of ANN models were also presented. The presented ANN models can serve as a benchmark for effective prediction of the tunnel deformation with characters of nonlinearity, high parallelism, fault tolerance, learning, and generalization capability.
Deformation prediction of the rock masses is one of the major subjects in determining the stability of the underground excavation projects. Recently, the tunnel construction is experiencing a very rapid growth in the complex geological formations and especially in urban areas where the low construction depth and the external loading from the buildings increase risk conditions [
Underground works system frame.
Artificial neural networks (ANNs) commence as a new tool for analysis of the fuzzy geotechnical problems. The attractiveness of ANNs comes from the information processing characteristics of the system, such as nonlinearity, high parallelism, fault tolerance, learning, and generalization capability [
ANNs are complex mathematical models inspired from biological neurons and are in fact the emulation of biological neural networks which are widely used in modelling of nonlinear systems and system identification, as shown in Figure
Biological neural networks.
Traced back to 1943, the biological neurons had been actually lively presented by psychologist McCulloch [
Artificial neuron architecture.
The artificial neuron presented in Figure
In recent years, the number of ANN models proposed is far more than 60, which encompass BP, RBF, SVM, Hopfield, SOM, and so on. Apparently, these models have different characteristics and application areas [
Application of ANN models.
Attribute  Neural network  

BP  RB  SVM  Hopfield  SOM  
MATLAB function  Newff  New, Newrbe  Svmpredict  Newp  Newc 
Application area  Approximation Prediction classification  Approximation prediction  Prediction classification  Classification  Classification 
Currently, among various ANN models, radial basis function (RBF) model and backpropagation (BP) networks have gained wide application in tunnel deformation prediction.
RBF method, as an interpolation technique in higher space dimensions, is a highefficiency feedforward neural network, which has many advantages such as strong approximation property, better global optimization performance, simple structure, and fast training speed in comparison with other feedforward networks. Meanwhile, the RBF neural network has also been widely applied in the fields of pattern recognition and nonlinear function approximation.
Typically, among the much different prediction models, BP neural network is the most popular used as a prediction method in tunnel projects for its nonlinear mapping approach capability, robustness, and easy realization, which has been used to correct the connection weights of network layers from the posterior layer to the anterior layer utilizing the difference between real output and desired output. BP network is a typical multilayer network [
Typical structure of a BP network.
BP network was firstly proposed by Werbos [
Designing a BP network architecture includes determining the number of input and output variables (i.e., neurons in input and output layers) and selecting the number of hidden layers and neurons in each hidden layer, as shown in Figure
BP network design frame.
The input data need to be normalized before the training of samples, and then the data are reflected to initial ranges after the training of samples. Based on the
Procedure of the design of BP neural network.
Currently, the underground engineering problems based on ANNs are mainly classified as two types: one is the nonlinear relationship of parameters, which is established by the given data; the other is the prediction system for the latter period based on the experience gained and the in situ test data gathered from past projects.
For the prediction system, the geotechnical engineering is certainly a complex giant system, as shown in Figure
Geotechnical engineering system [
Generally, excessive deformations in tunnels are induced by the rock mass disturbance. For mountain tunnels, loess tunnels, or urbanroad shield tunnels, the ground surface settlement and the deformation induced by tunnelling are mainly composed of three factors, as shown in Figure
Interaction of deformation factors.
Considering the different geological conditions, scale of projects, and construction approaches in the research of practical problems, we usually regard the specific and dominant influencing factors as input variables in BP networks. Meanwhile, the deformation to be predicted is taken as the target variable. In order to select the effective input variables, we should follow the two basic principles:
For the given time series
In order to predict the rock mass deformation in tunnelling, a multipleinput singleoutput BP network model is established, as shown in Figure
Sample construction of BP network.
Sample  Input layer vector  Output layer vector 

The first sample 


⋮ 


The ( 





The ( 


Multipleinput singleoutput BP network model.
Afterwards, samples learning and training based on BP network are conducted. The stable network structure, connection weights, and neuron thresholds can be obtained after learning and training. Then the tunnel deformation prediction model based on BP network can be established. When the variables of samples to be predicted are input to the BP network, the output variables of samples can be obtained correspondingly.
Because of the complex relationships among these factors which have influences on the soil deformation, it is very important to select the influence factors when the model is established. In the prediction model, the output variables are the solutions to be desired; meanwhile, the input variables are the influence factors of the output variables. The number of neurons in the input layer should be designed according to the requirements of the output layer. The size and range of the original space are determined by the input layer of the network, and the number of neurons in the input layer should be matched with the field monitoring data. The successful application of the networks depends on the full knowledge of problems to be solved. Therefore, what the problem to be solved by using the neural network must be clear first; then, based on the field monitoring data, several issues need to be addressed: input variables which determine the problem, output variables which are the solutions to the problem, value range of variables, and corresponding results. After the problem is determined, the number of neurons in the input layer and output layer is determined accordingly.
With regard to the number of neurons in the hidden layer of BP network, it is important to note that the number is obtained mainly through the accumulated experience and the in situ test data gathered from past projects without an exact analytical expression. And the determination of the number of neurons should be in conformity with two basic principles of less iterated number and strong fault tolerance. Additionally, for the general BP network, the number of neurons in the hidden layer can be obtained as follows [
Since the first shield tunnel was completed in London 170 years ago, shield tunnelling is greatly popular with its flexibility, costeffectiveness, and little impact on ground traffic and surface structures [
Ground settlements in different construction stages [
Typically, for the aforementioned problems, Qu [
The training samples selected are given in Table
Training samples for ground settlement prediction [
Test number 












1  11.8  15.2  5.91  9.78  6.34  0.35  1.7  14  20  47.3  4.77 
2  28.1  32.8  5.42  13.3  6.40  0.25  1.5  31.65  40  9.6  9.71 
3  32.4  10.7  11.17  14.5  6.40  0.25  1.7  31.65  60  22.0  5.37 
4  31.1  44.1  40.75  20  6.25  0.30  1.3  33  30  4.3  9.77 
5  11.9  13.8  5.22  11.9  6.34  0.40  2.0  14  20  21.2  7.25 
6  12.1  13.7  5.21  12  6.34  0.35  1.7  14  30  55.3  7.46 
Prediction model of shield tunnel ground deformation.
Then, the samples learning and training are conducted using neural network toolbox in MATLAB, which can be used to establish the nonlinear relations between inputs and output parameters. And the prediction results, as shown in Figure
Prediction results of training samples.
From the prediction results, as shown in Table
Comparison between prediction results and in situ test data [
Test number 




Prediction data  Test data  Absolute error  Relative error  Prediction data  Test data  Absolute error  Relative error  
1  42.3  47.3  −5  −0.11  4.19  4.77  −0.58  −0.12 
2  11.9  9.6  2.3  0.24  10.05  9.71  0.34  0.04 
3  25.3  22  3.3  0.15  6.47  5.37  1.1  0.2 
4  4.9  4.3  0.6  0.14  11.59  9.77  1.82  0.19 
5  20.7  21.2  −0.5  −0.02  6.34  7.25  −0.91  −0.13 
6  48.6  55.3  −6.7  −0.12  6.21  7.46  −1.25  −0.17 
Additionally, Sun and Yuan [
Simulative results of training samples.
Simulative results of test samples.
Moreover, concerning the shield tunnelling construction and measurement development in time sequence, Wang et al. [
The maximal ground upheaval and settlement change in the targeted area with tunnelling of 10 m.
From the previous section, it can be seen that the prediction of ground surface settlement due to shield tunnelling using the ANN models is effective concerning the combined influence of factors, for example, geological environment, physical parameters of TBM, and construction craft.
According to NATM, the monitoring and measurement are crucial for safety evaluation in NATM tunnelling. Typically, the tunnel deformation monitoring during excavation is relatively an important item, especially tunnelling in harsh geological areas.
Recent years have seen an increased interest in the prediction of tunnel performance, notably the rock mass deformation. For the prediction of rock masses deformation in front of the working face according to the given geological and construction conditions, a substantial research effort has been undertaken. Based on results of FEM simulation, Chang et al. [
Procedure of the design of combination prediction model [
On the basis of predecessors’ research results on the tunnel deformation, Jian [
Key points for displacement field of underground tunnels [
The neural network for double faults model, which had the highest prediction accuracy, was selected after 64 neural networks for
Test number  Point 11  Point 14  Point 15  

Prediction data (mm)  Test data (mm)  Error (%)  Prediction data (mm)  Test data (mm)  Error (%)  Prediction data (mm)  Test data (mm)  Error (%)  
1  −5.12  −4.46  14.8  −1.33  −1.76  24.43  −1.12  −0.78  43.59 
2  −16.21  −11.71  38.43  −4.25  −5.43  21.73  −3.45  −3.23  6.81 
3  1.93  2.22  13.06  −0.78  −0.60  30.00  −22.56  −27.23  17.15 
4  63.38  59.16  7.13  −82.24  −90.55  9.18  −45.68  −40.88  11.74 
5  0.75  0.57  31.58  −0.52  −0.23  126.09  −1.21  −1.16  4.31 
6  −5.28  −5.77  8.49  −11.37  −9.38  21.22  −1.16  −1.06  9.43 
7  −7.01  −6.79  3.24  −3.26  −2.14  52.34  −2.15  −1.79  20.11 
8  −113.42  −107.30  5.70  −23.29  −26.49  12.08  −21.64  −26.50  18.34 
9  −72.22  −64.17  12.54  −13.04  −13.20  1.21  −14.06  −13.17  6.76 
10  −0.94  −0.67  40.30  −1.61  −1.75  8.00  −0.44  −0.25  76.00 
The normal analysis (prediction of the deformation induced by the tunnelling through the given mechanics parameters of rock masses) and the back analysis (prediction of the mechanics parameters of rock masses through the given deformation) are closely interrelated and inseparable from each other, especially when the mechanics parameters of rock masses are difficult to be obtained and the number of that is limited in the practical projects. Thus, the prediction of the mechanics parameters of rock masses through the in situ test data is of great significance [
Typically, in order to address the problems of the model complex and slow speed in problem solving for all conventional displacement back analyses, Yun et al. [
Training error curve in MATLAB.
From Table
Comparison between monitoring data and training results [
Sample  Monitoring data  Training results  










1  0.0130  0.300  0.0027  0.20  0.01255  0.3001  0.002710  0.1991 
2  0.0130  0.325  0.0033  0.45  0.01434  0.3349  0.003310  0.4246 
3  0.0130  0.350  0.0039  0.70  0.01231  0.3485  0.003919  0.7002 
4  0.0365  0.300  0.0033  0.70  0.03577  0.2945  0.003325  0.7004 
5  0.0365  0.325  0.0039  0.20  0.04477  0.3273  0.003561  0.3097 
6  0.0365  0.350  0.0027  0.45  0.03810  0.3448  0.002668  0.4696 
7  0.0600  0.300  0.0039  0.45  0.06053  0.3033  0.003864  0.4498 
8  0.0600  0.325  0.0027  0.70  0.05486  0.3296  0.003062  0.6121 
9  0.0600  0.350  0.0033  0.20  0.05526  0.3420  0.003311  0.1909 
The model established is simple which readily addresses the problem and is more likely to get accurate solutions. What is more, it can be commonly used in underground engineering for displacement back analysis. The BP algorithm is probably used to inverse the mechanical parameters of tunnel surrounding rock. The application of back analysis method is indispensable in the stability analysis of the tunnel rock masses and in informational design.
Unlike the classical calculation methods in which a certain form for the approximation function must be presumed, ANN models for tunnel rock masses present better flexibility, stronger nonlinearity, and lower values of prediction error; details are as follows:
The qualitative descriptions of rock mass properties, such as rock mass grade, weathering degree, and influence degree of geological structure, can be taken as the input variables. Moreover, there is no limitation of the number of the input variables.
Parameters processing and prediction accuracy can be modified manually and the data can be incomplete and inaccurate.
It is effective to address problems without certain solution methods.
On the subject of the deformation prediction in tunnelling projects, except for the ANN approach, extensive numerical investigations, which include finite element method, boundary element method, and semianalytical method, have been performed. Considering the large amount of calculation and the inaccuracy of modelling, however, numerical methods have many limitations and defects, especially for the deformation prediction during the real tunnel excavation. Typically, based on the experience gained from past projects, Zhou [
Although the development of BP neural networks for modelling and prediction of performance of mechanical excavators, such as TBM, and circular saw machines, has been well accepted through the scientific community, they still have some limitations including the slow rate of learning, “black box” nature, greater computational burden, proneness to overfitting, and entrapment in local minima [
In recent years, great improvements have been made in this area, and many powerful methods have been developed for the prediction of performance with high efficiency in tunnelling. For instance, Yan [
Due to the heterogeneity and nonlinearity of the rock mass, the prediction of the rock mass deformation in tunnelling is indispensable for optimization of the tunnel construction while simultaneously observing the safety requirements. For this purpose, ANN has been successfully applied in the deformation prediction and displacement back analysis, which seems to have good potential of timesaving and costeffectiveness. The present paper reviews the stateoftheart of the field of ANN technology in tunnel performance prediction. By the application case analysis and summary mentioned above, we can obtain the following conclusions and perspectives.
(1) ANNs have some extruding advantages, including selflearning ability, selforganized ability, high nonlinearity, good fault tolerance capability, and calculation inaccuracy. The application case analysis shows that the prediction of the rock mass deformation based on ANNs has a preferable applicability. In other words, the ANN prediction modelling is one of the most effective ways to predict the rock mass deformation, which is more practical for the dynamic prediction of displacements in tunnelling.
(2) Currently, the application of ANNs in the engineering field is well known to engineering sciences with the mature technology. And the neural network toolbox of the MATLAB software has been used for building the BP network code to establish the model. In this way, the relationship between the dependent variable of deformation and the independent variables of geomechanical parameters can be established. Obviously, it can be envisaged that ANNs would be more suitable for the analysis of engineering problems in the coming years, especially if ANN models are combined with other research methods.
(3) What is crucial in the BP network modelling for prediction of the rock mass deformation in tunnelling is finding the influence factors. These influence factors, as input variables, must be endowed with dynamic changes and be easy to obtain. Meanwhile, the monitoring data for network training must be sufficient, accurate, and scientific, which should be modified or rejected if necessary. The prediction ability, additionally, can be improved when the content of samples increases.
(4) Application of ANNs combined with many finite element software programs, consisting of ANSYS, ABAQUS, MIDAS/GTS, and so forth, can be readily used to pinpoint the sensitive factors which determine the deformation of rock masses in tunnelling. According to the previous finite element analysis, however, it is generally hypothesized that the rock mass is homogenous and continuous, which is quite different from actual field conditions. Therefore, the ingathering of training samples as well as precision discrimination of output variables should be considered carefully.
(5) In most cases, however, ANN prediction system has the limitation of timelag effect. Based on the experience gained and the in situ test data gathered from previous projects, we can develop the ANN prediction system for the prediction of engineering problems in the later construction stages. Finally, taking our results into consideration, we reasonably believe that the future prediction system of the rock mass deformation based on ANNs would be more realtime, dynamic, and successive, which holds great promise for the construction safety.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is partially supported by the Science and Technology Coordinating Innovative Engineering Project of Shaanxi Province (no. 2015KTZDGY010502), the Industrial Research Project of Science and Technology Department of Shaanxi Province (no. 2015GY185), and the Collaborative Innovation Project of Shaanxi Province (no. 2015XT33).