Prediction of TBM jamming risk in squeezing grounds using Bayesian and artificial neural networks

Rohola Hasanpour, Jamal Rostami, Jürgn Shmitt, Yilmaz Ozlik, Baak Sohraian

a Institute for Tunneling and Construction Management, Ruhr-University Bochum, Bochum, Germany

b Department of Mining Engineering, Colorado School of Mines, Golden, USA

c Department of Civil Engineering, Darmstadt University of Applied Science, Darmstadt, Germany

d Department of Mining Engineering, Hacettepe University, Ankara, Turkey

e Faculty of Mining and Metallurgical Engineering, Urmia University of Technology, Urmia, Iran

Keywords:Bayesian network (BN)Artificial neural network (ANN)Shielded tunnel boring machine (TBM)Jamming risk Numerical simulation Squeezing ground

A B S T R A C T This study presents an application of artificial neural network (ANN) and Bayesian network (BN) for evaluation of jamming risk of the shielded tunnel boring machines(TBMs)in adverse ground conditions such as squeezing grounds. The analysis is based on database of tunneling cases by numerical modeling to evaluate the ground convergence and possibility of machine entrapment. The results of initial numerical analysis were verified in comparison with some case studies. A dataset was established by performing additional numerical modeling of various scenarios based on variation of the most critical parameters affecting shield jamming. This includes compressive strength and deformation modulus of rock mass, tunnel radius, shield length, shield thickness, in situ stresses, depth of over-excavation, and skin friction between shield and rock. Using the dataset, an ANN was trained to predict the contact pressures from a series of ground properties and machine parameters.Furthermore,the continuous and discretized BNs were used to analyze the risk of shield jamming. The results of these two different BN methods are compared to the field observations and summarized in this paper. The developed risk models can estimate the required thrust force in both cases.The BN models can also be used in the cases with incomplete geological and geomechanical properties.

1. Introduction

The use of shielded tunnel boring machines (TBMs) allows machine to pass through weak grounds and adverse geological conditions. However, there is an intrinsic risk associated with tunnel construction by using these types of machines because of limited access to the excavated walls for observation of ground conditions.This is even more challenging when the machine passes through rock mass with squeezing behavior. Obviously, machines cannot address all the ground related risks and may incur delays for various reasons while coping with the field conditions.Meanwhile,if these risks are known beforehand,there might be some measures to allow better handling of the situation and to prevent major loss of ground, machine jamming or entrapment, ground support issues, and problems with groundwater, or safety concerns.

The best known and somewhat quantifiable risk in shielded tunneling through weak and squeezing grounds is the risk of shield jamming due to high in situ stresses. Shield jamming is a very serious problem and releasing a jammed shield requires manual excavation and other risky,costly,and difficult measures.To assess this risk beforehand,an estimation of the required thrust force for propelling the machine based on known ground conditions and machine thrust system at design stage prior to tunnel construction is essential.If the required thrust force was high,the shield would be susceptible to entrapment or seizure in weak rocks especially under high overburden where the ground loading on the shield and the related frictional forces exceed machine thrust capacity.

Application and evaluation of tunnel construction risks have been studied in recent years by researchers and practitioners in different projects and project settings.Some of the most important issues on this topic have been discussed in Eskesen et al.(2004)and Reilly (2005), who proved that it is essential to analyze the uncertainties for identifying and managing the risks in tunneling and underground projects. The influences of the surrounding ground strengths and buried depths on the deformation and failure mechanism of the tunnels are investigated using the transparent soil model test technique and PFC3D numerical simulation under different testing conditions by Xiang et al.(2018).Studies regarding application of Bayesian network(BN)and artificial neural network(ANN) for evaluation of risks in underground structures can be divided into several categories such as the estimation of wall deflection in deep excavations (Chua and Goh, 2005), risk assessment of road tunnels (Schubert et al., 2012), risk analysis during construction of Porto Metro tunnel (Sousa and Einstein, 2012),assessment of tunnel construction performance based on field data and using BN (Spackova, 2012) , risk assessment of tunnelinginduced damage to existing surface properties (Wang et al.,2014), developing an estimation model for evaluating groutability for improving ground in tunneling projects through sandy silt soil(Cheng and Hoang,2014),predicting tunnel squeezing levels(Feng and Jimenez,2015),safety decision support in tunnel construction(Wu et al., 2015), safety risk assessment for metro construction projects (Wang and Chen, 2017), and predicting rockburst hazards(Li et al., 2017). A study concerning examining of TBM jamming using probabilistic methods has been also reported by Mahdevari et al. (2012), in which artificial intelligence (AI) algorithms are used for predicting tunnel convergence and TBM jamming.

Recently, a multivariate adaptive regression splines (MARS)approach has been developed by Goh et al. (2018) that allows to map all influencing parameters to surface settlements for an earth pressure balance (EPM) TBM tunneling. Regarding the extensive plane-strain finite element analyses of braced diaphragm walls,the MARS method has been also used for inverse parameter identification of the soil relative stiffness ratio as well as inverse parameter estimation of the wall system stiffness to determine the appropriate wall size during preliminary design phase (Zhang et al.,2017). Zhang et al. (2019) also employed the MARS approach for determining horizontal wall deflection envelope for braced excavations in clays based on a series of three-dimensional (3D) finite element analyses using the hardening soil (HS) model.

A practical approach has been proposed by Lü et al. (2017a) for the reliability assessment of rock tunnel excavations using the moving least squares method (MLSM). Considering the groundsupport interaction and the parametric uncertainties, Lü et al.(2017b) employed a reliability-based design optimization (RBDO)method in a rock tunnel support system to study the design variables of the minimum shotcrete thickness and the optimal installation position for the rock tunnel case. Furthermore, the probability of slope system failure with surrogate models based on the least-squares support vector machine(LS-SVM)regression was investigated by Ji et al.(2017),proving that the LS-SVM model can reasonably capture the global characteristics of complex slopes only when all the relevant soil layers are treated probabilistically.

Most of the existing risk analysis systems deal only with the effects of random geological and construction uncertainties on the time and cost of construction. Sources of risk related to machine and performance scenarios of the shielded TBM tunneling that can impact the tunneling process have not been considered in most of risk analysis systems. Furthermore, entering all main TBM, tunnel and performance parameters in statistical calculations and systematic risk analysis of tunneling by shielded TBMs, based on 3D numerical simulation and measured data, and studies about a certain risk such as shield jamming are not commonly found in the literature.

Various parameters such as rock mass properties,TBM features,tunnel geometry, and performance data are required for assessing the risk of shield jamming (Hasanpour et al., 2017). Taking these parameters into account, this study aims at developing new risk models based on BN and ANN by using the results of a fully 3D numerical simulation of tunneling with a single shielded TBM.

The risk of shield jamming by calculation of the required thrust force is aimed to be evaluated numerically for different combinations of rock mass and TBM parameters. To perform the BN and ANN analyses, a dataset of shield jamming events based on the numerical results was prepared and analyzed as a subset for learning the ANN algorithm and with the aid of the augmented naive Bayes(ANB)that predicts the probabilities of shield jamming.Then, the predictions of the proposed Bayesian structure were validated using 10-fold cross-validation.

The developed risk models of this study enable understanding of the way and the extent that the involved parameters affect the shield jamming. The results show that the proposed model is a suitable tool for prediction of the contact loads on the shield in unexcavated zones of the tunnel as well as in new tunnels to be excavated in a similar geological environment.

2. Effective parameters on shield jamming

For developing a risk model for shield jamming, a risk registry should be established.For this purpose,the effective parameters on shield jamming were identified and used in the numerical analyses and the corresponding results were used for establishing the required database. The most significant controlling parameters for ground convergence are the uniaxial compressive strength of intact rock (UCS), the geological strength index (GSI), Hoek-Brown material constant(mi),elastic modulus of intact rock(Ei),in situ stress(P0), excavation/tunnel radius (R), overboring or overcut (ΔR),shield length (L), and the skin friction coefficient between shield and rock (μ).

Geomechanical and geometrical properties of a single shielded TBM and mechanical properties of the machine considered in the numerical studies are given in Tables 1 and 2, respectively. The shield thickness was assumed to be 3 cm. Considering these parameters in the numerical analyses, a parametric study for determining the required thrust force for each combination of rock mass and the TBM properties was conducted for more than 400 models and they are used as outputs in BN and ANN.

3. Numerical modeling

For calculation of the required thrust force, it is essential to evaluate the complex interaction between rock mass,machine and its main components within tunneling through squeezingconditions. For this purpose, FLAC3D was used to investigate the stress-deformation relationship of the rock mass in an excavated tunnel with a single shielded TBM. A typical 3D block model and discretization of the model of a single shielded TBM are shown in Fig.1.

Table 1 Geomechanical and geometrical dimensions used in numerical investigations(Hasanpour et al., 2018).

Table 2 Mechanical features of the machine (Hasanpour et al., 2018).

Fig.1. Screenshots of (a) the block model of the ground and (b) discretization of the 3D model.

The developed 3D model allows for realistic evaluation of ground loading on the shields and calculation of the required thrust force. It is considered that the in situ stress varies linearly with depth H,i.e.P0=γH,where γ is the unit weight of the rock,and the ratio between the horizontal and vertical stress components(σh/σv)in the rock mass is equal to 1,or K0=1,for long and deep tunneling.The rock mass was assumed to follow a linearly elastic-perfectly plastic behavior according to the Hoek-Brown failure criterion.Contact between the cutterhead and the rock mass,as well as that between the shield and rock mass,has been modeled by using the interface elements on both tunnel and shield boundaries, in consideration of the gap between them according to non-uniform overcut around the shielded TBM. For numerical modeling of a single shielded TBM, a number of drilling stages and their design are chosen to represent true configuration of the cutterhead and the shield specifications.A full description of the excavation stages,modeling procedure and validation of the numerical results with field data in selected tunneling projects can be found in Hasanpour(2014) and Hasanpour et al. (2014).

4. Establishing dataset based on numerical results

4.1. Parameters used for ground description

Given the uniaxial compressive strength (UCS) of intact rock,Hoek-Brown material constant(mi),geological strength index(GSI)and elastic modulus (Ei) of intact rock, one can calculate the compressive strength and deformation modulus of rock mass as follows (Hoek and Brown,1997; Hoek and Diederichs, 2006):

where mbis a reduced value of the material constant mi;s and a are the constants for the rock mass; D is the disturbance factor and it was assumed as zero for excavation by a TBM;and σcmand Ermare respectively the compressive strength and the deformation modulus of rock mass, which are used for presenting the geomechanical characteristic of the rock mass.

4.2. TBM and tunnel parameters

Plotting the required thrust force, Fr, versus the product of the shield radius,length,and in situ stress,RLP0,in the database shows a good correlation between RLP0and the required thrust force(see Fig.2).This observation proves that these three parameters are the most significant parameters that affect the shield jamming. By increasing R,L and P0,it is necessary to provide more thrust force to overcome frictional forces between the shield and the rock mass.Due to high impact of the RLP0on the shield jamming,one may use“thrust index” to normalize the required thrust force. While it accounts for the geometry of the TBM and magnitude of in situ stresses, it allows for better distinction of impacts of other geological parameters (Hasanpour et al., 2018). This index can be defined as follows:

Fig.2. Diagram of the required thrust force vs.thrust index(Hasanpour et al.,2018).R2 represents the coefficient of determination.

Fig. 3. Distributions of five geological and geometrical parameters considered in prediction of the risk of shield jamming.ΔR and μ represent the overcut and friction coefficient,respectively; and SD represents the standard deviation.

JTBM= RLP0(6)

Thrust index (JTBM) is considered here for representing the in situ stress and the TBM geometrical parameters.It should be noted that the distribution around the straight line (i.e. the deviations from the linearity) shown in Fig. 2 is due to variation of the other parameters, such as the geological properties of rock mass, which are used as input into the model.

4.3. Performance factors

Overboring around shield (overcut) and friction coefficient between shield and ground(μ)are considered as performance factors that can considerably affect the shield jamming.Increasing overcut reduces the loads on the shield and leads to lower frictional forces against the machine. However, it allows larger deformations around the tunnel that creates massive plastic zones of overstressed ground. The impact of non-uniform overcut as a most effective performance factor on the shield jamming was considered in the parametric studies and risk analysis.A more comprehensive discussion of the impact of overcut on the shield jamming can be found in Hasanpour et al. (2018).

The other important factor that should be considered in assessing the risk of shield jamming is the skin friction coefficient,or friction between ground and shield skin. The magnitude of friction coefficient between shield and ground, which is direct result of the friction coefficient,influences the amount of frictional forces formed around the shield due to ground loading. The effect of lubrication on mitigating jamming risk, which has been considered by reducing the value of friction coefficient,is also used for developing the risk models.For this purpose,the required thrust force was calculated for various ranges of friction coefficients.

4.4. Distribution of the input parameters

Fig.3 illustrates the histogram of the five geological parameters selected for this parametric study, with normal curve overly, to predict the risk of shield jamming.These parameters were used for subsequent analysis using BNs.These histograms show the range of values used in the simulation,for which predictions could be valid.It is suggested that the predictions and analysis of the shield jamming risk for future cases should be confined to these ranges. By gathering new data from upcoming tunneling projects and verification of the numerical models, this range can be extended for applicability of the methodology.

5. Discretization of the parameters

For discretization of the variables,it is essential to determine the appropriate interval steps for each set of variables.In this study,the interval steps of each variable were selected based on their impacts on the required thrust force calculated.Table 3 shows the intervals considered for the input parameters of the developed BN with their minimum and maximum values. In addition to the five variables used for estimating the required thrust force, the difference between the installed and the operational thrust forces (available thrust force,Fd)is used in the BN analysis for predicting the risk of shield jamming.

The jamming risk,JR,is defined as the ratio of the required thrust force estimated by the model to the operational thrust force, and can be calculated as follows:

where Frand Fdare the estimated required thrust and the maximum operational thrust, respectively. If the required thrust force is higher than the operational thrust force or JR＞1,the shield jamming is anticipated.It should be noted that the employed rock mass and the TBM parameters are generally selected to evaluate jamming events. However, the developed BN can be applied to cases with variables slightly outside of the selected ranges.

6. Artificial neural network (ANN)

A set of computer algorithms is utilized in ANNs using the input data to estimate the objective parameter while minimizing the errors,which are the differential values between the predicted and real outputs. The back-propagation neural network (BPN) is the most frequently used algorithm that is applied for training neural networks as it is capable of acting like a functional estimator between input and output data. BPN refers to as the fact that any mistake made by the network during the training procedure gets sent backward,in an attempt to correct the predicted output and to teach the network what is right and wrong. The BPN, as shown in Fig.4,is composed of an input layer,one or more hidden layers and an output layer.

Several ANN models were examined for establishing a relationship between the objective or dependent variable of the required thrust force and the independent variables including tunnel geometry, the main component of the TBM, and the rock mass properties. Three principal steps consist of defining the network architecture, and training and testing the network were involved into the model.The datasets corresponding to the results from 400 numerical analyses on various properties of the rock mass and the shielded TBM were prepared and used for modeling and assessing the prediction performance of the models.Each dataset is composed of eight input parameters given in Fig. 4. The target parameter is the calculated values for the required thrust force,Fsh.The inputs in the network were used for training of the ANN algorithm adopting three different algorithms including the Levenberg-Marquardt back-propagation algorithm, Bayesian regularization algorithm and scaled conjugate gradient,and the results were compared to each other.

Number of neurons included in the hidden layer can be determined through trial and error. This was done by respectively choosing 70%,15%and 15%of the datasets as the network training,the validation and the network testing sets. Several experiments with different network architectures were tested to identify appropriate combinations. Some selected results using trial-anderror experimentation are listed in Table 4. According to Table 4,the optimum configuration of the model is obtained by applying the Bayesian regularization algorithm with 8,10 and 1 topologies(8-10-1) as the input, neurons, and output layers, respectively. It should be noted that the mean squared error (MSE) is commonly used in ANN model for evaluating the model performance.

Table 3 The intervals employed for input parameters of the BN.

Table 4 Specification of the studied ANN models.

Fig. 5. (a) Performance error plot of the optimum MLP for model No. 8, and (b) Normal distribution of the errors.

Fig. 6. Regression plots corresponding to the optimum MLP for model No. 8. Output refers to contact pressures obtained from numerical studies, and target is the amount of required thrust force calculated by ANN.

Fig. 7. ANN architecture used for prediction of the required thrust force.

Fig. 5a shows performance error plot of the optimum MLP(multi-layer perceptron) for model No. 8, with best training performance. Normal distribution of errors produced in order to calibrate the process is also depicted in Fig. 5b, representing a highly satisfied normal distribution of errors (targets-outputs) around zero.

The best validation performance with the lowest MSE value is shown in Fig. 6. The best results are for the cases that the tansigmoid and the linear transfer functions are respectively used as the neurons of the hidden and the output layers by applying the Bayesian regularization, as illustrated in Fig. 7.

7. Bayesian network (BN)

7.1. BN structure

The BNs have advantage over the other approaches because they can be implemented in case of limited input information and incomplete data(Uusitalo,2007)and also,can offer acceptable predictions of outputs based on limited datasets(Kontkanen et al.,1997;Feng and Jimenez,2015).The first step in the BN modeling is defining the structure of the network.The defined structure should accurately account for the conditional independency and dependency relationships between the associated discretized inputs variables (Li et al.,2017).Eight parameters,as shown in Table 3,are selected for defining the dataset in the BN modeling. Among these parameters,the tunnel radius(R),the shield length(L)and the initial stress(P0)are classified into a unique category called thrust index(JTBM).Hence,the five input parameters including Erm,σrm,μ,DR and JTBMare used for describing the attribute vectors for the required thrust force in the BN modeling. These vectors can be given as X1= (σrm, Erm, ΔR, μ,JTBM). For developing the aimed BN model for assessment of the required thrust force,the conditional probability,P(Fr|X1),should be determined.Furthermore,to assess the risk of TBM entrapment,the required thrust force (Fr) and the available thrust force (Fd) are selected as the attribute vectors for jamming risk(JR),which is stated as X2=(Fr,Fd).To estimate the risk of shield jamming,the multiple conditional probability of P(JR|X2)should be determined.

Fig. 8. BN organizational structure used in this study.

In this study, 400 available datasets resulting from numerical analysis were replicated to about 3600 datasets by using different values for skin friction coefficient(μ)and the available thrust force(Fd).The dataset was trained by the ANB algorithm according to the BN structure, as shown in Fig. 8. Using regression analysis, it was proven that there is a weak correlation between the input parameters for all datasets. Controlling correlation coefficients is due to the fact that the presence of conditional dependence between parameters can affect the results of risk analysis considerably.

To define a BN model,the discretized data should be analyzed by an appropriate learning algorithm.In this study,the ANB structure learning algorithm was used for data analysis. We used the ANB algorithm due to its simplicity in comparison with the other algorithms. Furthermore, by employing the ANB, an acyclic directed graph with the class variable can be provided and used as the parent of all the other variables.It is also capable of structuring and adding further connections between the feature variables to calculate the possible dependence among them and conditional probabilities on the class variable (Bayesfusion, 2016). Fig. 9 illustrates the structure of an ANB classifier developed here for estimating the risk of shield jamming.The amounts of the conditional probabilities of the analyzed database using the ANB algorithm are also given in this figure.

7.2. Belief updating

A belief updating can be implemented to examine the posterior probability distribution for a set of given evidences in risk analysis(Korb and Nicholson,2010).This process can be applied when there are an incomplete set of observations. The aim here is to compute the posterior probability of jamming risk with given data. The calculations can be performed using various algorithms based on stochastic sampling approaches such as the probabilistic logic sampling, the likelihood sampling, the backward sampling, the adaptive importance sampling (AIS), and the evidence prepropagation importance sampling (EPIS). In this study, the most commonly used approach, i.e. the probabilistic logic sampling algorithm(Li et al.,2017),was used for updating of the beliefs and the results are illustrated in Fig.10.

Fig. 9. Structure of an ANB classifier employed to predict the risk of shield jamming.

7.3. K-fold cross-validation

The developed BN model is validated by means of K-fold crossvalidation method as a most prevailing cross-validation technique that allows verifying a model using the same dataset by dividing them into K parts of equal size in terms of the training and the testing subsets. The training and testing data are repeated K times in which the validation technique trains network on K-1 parts,and tests it on the last,Kth part,with a dissimilar part of the data being specified for testing(Bayesfusion, 2016).

Validation of the BN model was performed using the 10-fold cross-validation method (K = 10), not only for the estimation of the required thrust force, but also for the prediction of the risk of shield jamming. To evaluate the outcomes from cross-validation analysis, the receiver operating characteristic (ROC) curves, which are showing the quality of a model independent of the classification decision, are given for showing the state of jamming risk (see Fig.11).The quality of most states(AUC values or larger area under the curve), based on the conducted 10-fold cross-validation, is above 70%,and this proves that the BN is able to provide predictions with relatively high and acceptable accuracy.

8. Discussion

The outcomes of this study can be used in the cases with similar geological conditions and machine parameters. Nonetheless, the inherent uncertainties of the geological parameters such as variations in ground characteristics and localized stress states in the ground are not considered within evaluations of jamming risk using the proposed risk models. The risk model for such variational conditions, if determined beforehand, can be presented as a range of jamming risks.

Fig.10. The results of belief updating of a given dataset.

Fig.11. ROC curves with relevant AUC amounts for each of the states of the jamming risk.

The results of this study are based on dataset obtained from the numerical results. Although it was an attempt to develop a comprehensive 3D model so that the main affecting parameters of the ground, single shielded TBM and machine performance, were correctly simulated,the limitations of the numerical simulation for modeling the ground behavior should be added to the list of uncertainties when using the proposed model for assessment of the jamming risks.

The impact of advance rate on shield jamming has not been considered in this study. TBM advance rate is affected by many geological and geotechnical factors that can lead to standstill and stoppage of TBM for cutterhead inspections. This causes high loading on shield and consequently increases the jamming risk of the shield. Furthermore, the time-dependent characteristics such as creep and consolidation of the ground should be taken into account when assessing the jamming risk.

9. Conclusions

At the design stage of a tunneling project by shielded TBM, the practical and predictive methods such as ANN,BN,and fuzzy logic methods can be used for preliminary estimation of the TBM performance parameters,such as the required thrust force in order to avoid jamming event within boring process. This study aimed at providing a framework at the design stage of a tunnel for systematic analysis of jamming risk in the single shielded TBMs based on 3D numerical simulations.For this purpose,two risk models based on BN and ANN were developed to assess the risks of machine entrapment. The models consider the machine diameter and length, thrust, and ground properties to evaluate the risk of encountered frictional forces that could exceed machine thrust and lead to jamming in squeezing ground.The results indicate that the developed risk models can be applied for probabilistic prediction of the risk of shield jamming in tunneling through weak rocks with squeezing behavior.

The model developed for this particular task is implemented through the use of ANN method that allows identification and understanding of both the way and the extent that the involved parameters affect the shield jamming. This study also shows the importance of early identification of the jamming risk and application of early precaution methods such as implementing overcuts,lubrication,and ground improvements to avoid shield entrapment and all related risks,delays, and costs.It should be also noted that the main focus of the current study was to assess the feasibility of using BN and ANN methods for predicting JRbased on the machine and geological inputs. Ongoing studies will expand on application of AI methods to develop pertinent charts and formulae to allow for evaluation of JRbased on the same input parameters.

Declaration of Competing Interest

We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

Thanks to Alexander von Humboldt Foundation for financial support of the first author.