Using Least Squares Support Vector Machine to Predict the Maximum Ground Surface Settlement Caused by Shield Tunneling

Xingchun Li1,3, Xinggao Li2,* , Dajun Yuan2, Yuhai Guo4 1 School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China 2 School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China 3 School of Information Engineering, Wuyi University, Jiangmen 529020, China 4 Fourth engineering department of Beijing Municipal Construction Co., Ltd Beijing 100089, China *Corresponding author: e-mail: [email protected]

ABSTRACT Ground surface settlement caused by large diameter (>10m) shield tunneling has attracted increased concern in recent years. This settlement prediction remains a challenging and demanding task due to many influencing factors involved. The least squares support vector machine for function estimation, which is based on the theory of statistical learning, is capable of predicting the shield tunneling induced settlement. The capability is investigated with the data available from a large diameter shield tunneling project in Beijing. Eight factors included in the least squares support vector machine models, are the tunnel depth, measured N-values of the soils on tunnel roof, earth chamber pressure, shield advance rate, total thrust, cutter head torque, rotation of cutter head and injection volume per segmental ring. Observations by comparing the model predictions with the measured data reveal the models with radial basis function kernels obtain the best generalization performance according to the calculated errors. The least squares support vector machine models with radial basis function kernels are robust tools for surface settlement prediction. Moreover, with findings of the models, the explicit formula of the settlement caused by large diameter shield tunneling can be expressed in terms of the considered factors. The settlement can be easily estimated with the formula, as is of vital importance for rapid shield tunnel construction. KEYWORDS: Least squares support vector machine; ground surface settlement prediction; large diameter shield tunneling; RBF kernel

INTRODUCTION Rapid population growth in the largest cities all over the world has resulted in growing demand for mass transit systems in recent years. Shield tunnels are an indispensable component of the transportation systems because of the widespread use of the close face shield machines to construct tunnels. Particularly, the double-track tunnels with more than 10 m diameter, such as the tunnel on the Metro Line 9 in Barcelona (1), the tunnel on Beijing subway Line 14 (2), and the railway tunnel linking Beijing Railway Station and Beijing West Railway Station (3), were constructed due to the

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Vol. 22 [2017], Bund. 02 614 limited underground space. This large diameter shield tunneling is likely to cause settlement of the ground surface, which if not controlled might significantly affect nearby buildings, structures and pipelines. The magnitude of the ground surface settlement depends on a number of factors, such as depth and diameter of the tunnel, soil conditions and necessarily the shield operational parameters. How to predict the large diameter shield tunneling induced ground surface settlement remains an urgent and challenging task. Shield tunneling induced ground surface movement is a critical issue in tunnel construction and has attracted growing attention. Methods for the settlement prediction can be divided into three types: empirical, numerical and experimental. Peck (4) established the most utilized empirical method of estimating the tunneling induced surface settlements at varying distance from the centerline of the tunnel, approximating the settlements by a Gaussian function and expressing the equation for the maximum settlement, smax, in two variables: the ground volume loss and the settlement trough width coefficient. Peck's finding focused on settlements due to tunneling with traditional shields, such as an open shield. Many measured results show the settlement trough above tunnels constructed with modern earth pressure balance (EPB) and slurry shields can also be represented by the Gaussian function. The maximum settlement is one of the two key parameters of the Gaussian function, which varies with different shield tunneling methods. Based on 94 cases in Japan, Fujita (5) summarized the maximum settlements caused by tunnel construction using different types of shield machines driven through different soils, with or without additional measures (such as grouting). Based on the findings of Peck and Fujita, Fang et al. (6) proposed an empirical method to estimate the magnitude and extent of surface settlement associated with shield tunneling. Rowe and Lo (7) described a technique suitable for the numerical analysis of lined tunnels constructed in soft soil, and performed a parametric study to identify potentially significant factors affecting the settlement prediction using the authors’ plane strain elasto-plastic finite element program. Kasper and Meschke (8) presented a three- dimensional finite element simulation model for shield-driven tunnel excavation, taking into account all relevant components of the construction process including the soil, the ground water, the tunnel boring machine with frictional contact to the soil, the hydraulic jacks, the tunnel lining and the tail void grouting. Mollon et al. (9) performed the three-dimensional numerical simulations using the commercial code FLAC3D to investigate surface movements due to the applied face pressure, the overcutting, the shield conicity, the annular void behind the shield, and the tail void grout injection during a typical slurry shield tunnel excavation. Nomoto et al. (10) did a large number of centrifuge model tests for simulating the shield construction process in dry sand, and an experimental formula for estimating the surface settlement was deduced by a function of tail void thickness and cover-to- diameter ratio. Fang et al. (11) carried out indoor shield driving tests to verify the reasonableness and accuracy of the deduced equations by Nomoto et al. in 1999 for settlement prediction. Although the empirical, numerical, and experimental methods have several advantages in addressing the issue of surface settlement prediction, there are major constraints in application. The use of a Gaussian distribution allows for easy calculations of the maximum surface settlement, but has the disadvantages of oversimplification such as horizontal strata and overdependence on the accumulated experiences on ground volume loss. The numerical method seems to be a powerful tool for surface settlement estimation, but its application in engineering practice is extremely limited mainly due to the applicability of idealized analyses to real conditions. This situation arises, in part, from the difficulty in representing soil behaviors in modeling. It is clear that in-door tests can be employed to implore limited interaction features and sometimes are not realistic because of the ignorance of some basic factors. Moreover, the above-mentioned methods can’t fully and directly take into consideration the effects of the shield operational parameters such as the earth chamber pressure and shield advance rate, as not in favor of the immediate control over surface settlement during tunnel construction. Vol. 22 [2017], Bund. 02 615

As an essential part of the technology industry, artificial intelligence provides the heavy lifting for many of the most challenging problems in practical engineering. Some artificial intelligence methods were used to correlate surface settlements with key shield operational parameters, such as the artificial neural network (ANN) method by Suwansawat and Einstein (12) and Qiao et al. (13), the wavelet network method by Pourtaghi and Lotfollahi-Yaghin (14), the methods of support vector machine (SVM) and Gaussian processes by Ocak and Seker (15), the partial least squares (PLS) regression method by Bouayad et al. (16), and the decision tree classification method by Dindarloo and Siami-Irdemoosa (17). These methods can give good estimation for surface settlement if the most effective parameters are considered and a decent number of quality data are available. The least squares support vector machine (LSSVM) is a reformulation of the SVM first invented by Vapnik & Lerner in 1963 and Vapnik & Chervonenkis in 1964 (18). Adopting a least squares linear system as a loss function, LSSVM is closely related to regularization networks. Besides keeping advantages of the SVM, the LSSVM has nice properties in that its solution can be found by solving a set of linear equations making the algorithm amenable for adaptive on-line application (19). This merit of the high computational efficiency is helpful to make rapid response to large settlements in rapid shield tunnel construction. It is necessary to examine feasibility of the LSSVM to predict the large diameter shield tunneling induced surface settlement. This study employs LSSVM for surface settlement prediction, which is modeled as a function estimation problem. The efficacy of the LSSVM in function learning and estimation is demonstrated by measurements recorded in a 10.22-m diameter EPB shield-tunneling project in Beijing. The data available from the project are utilized to train and test the LSSVM models to enable the settlement prediction with inputting variables having direct physical significance.

THE 10.22 M DIAMETER EPB SHIELD TUNNELLING PROJECT

Project overview The subway system in Beijing has been increased dramatically in the last decade due to the large population and limited surface spaces. Now, Beijing is still extending its subway network while the underground space of the city is becoming more and more a scarce resource, especially at the shallow depth. For example, a double-track tunnel was arranged between Dongfengbeiqiao station and Jingshunlu station of Beijing subway Line 14. Beijing Subway Line 14 includes 4 stations and about 2.8 km of tunnels between Dongfengbeiqiao station and Jingshunlu station, as shown in Fig.1. A 10.22 m diameter EPB shield machine was chosen, after overall considerations, to excavate the tunnel. It was the first time that a so large diameter EPB shield machine was adopted in Beijing subway tunnel construction. To improve working efficiency of the 10.22 m diameter shield, the innovative construction plan was employed of first completing the continued 3.2 km long shield driving and then forming the two middle stations by enlarging the finished shield tunnel. Mastering the large diameter shield tunneling induced ground surface settlement is of great importance. The soils at the construction site can be divided into three types: backfill, clayey and sandy soils, as given in Figs.2-4. There are four types of aquifers involved: (1) perched aquifer, (2) unconfined aquifer, (3) confined aquifer I and (4) confined aquifer II, with water table of 2.98-6.79m, 5.98- 9.25m, 11.70-18.40m and 21.00-27.65m underneath the ground surface, respectively. The depth of the tunnel overburden ranges from 11.3m to 21.2m. Two elements concerning the tunnel alignment are the minimum curve radius of 350m and the maximum slope of 27‰. The water-bearing sandy soil, the shallow overburden together with the small curve radius will contribute to the large ground Vol. 22 [2017], Bund. 02 616 surface settlements if not properly dealt with. For more detailed information, refer to Guo (2013) (20).

Fig 1: Route between Dongfengbeiqiao and Jingshunzhan station on Beijing subway Line 14.

Fig 2: Longitudinal section between Dongfengbeiqiao station and Jiangtai Station.

Fig 3: Longitudinal section between Jiangtai station and Gaojiayuan Station.

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Fig 4: Longitudinal section between Gaojiayuan station and Jingshunlu Station.

Type selection and special design of the used shield machine Three types of factors influence the selection between EPB and slurry shields: economic, technical and geological, and a thorough and detailed discussion is often needed. However, the use of a 10.22 m diameter EPB shield in this project can be justified by two reasons: (1) the accumulated experiences and skills with the wide use of the 6.15 m diameter EPB shields in Beijing area, and (2) no enough ground surface space for a sophisticated separation plant for the slurry shield. The used machine is presented in Fig.5 and the spoke-type cutter head with the opening ratio of 65% adopted mainly based on experiences of using machines in Beijing subway construction.

Fig: the used 10.22 m diameter EPB shield. The EPB shield uses the excavated material (muck) by the cutting wheel as the support medium to maintain the stability of the cutting face, and the supporting pressure is heavily dependent on the plastic flow of the muck in earth chamber. Particularly, that ensure high plastic flow of the muck matters when operating the 10.22 m diameter EPB shield, because the excavated volume per meter by the 10.22 m diameter shield is nearly 2.8 times greater than the ever-used 6.15 m diameter shield. Necessary components are considered for the 10.22 m diameter shield to achieve plastic flow of the muck in the chamber. Twelve additive injection ports (six for foam and six for slurry) are provided at the cutting wheel, bulkhead and crew conveyor of the machine. Besides the fixed blades attached to the cutting wheel and bulkhead, the motor driven mixing device is provided, as presented in Fig. 6. The provided device can actively and efficiently mix the excavated soil with the injected additives, thus ensuring plastic flow of the muck. Other important technical features of the shield are summarized in Table 1. Vol. 22 [2017], Bund. 02 618

Fig 6: the provided motor driven mixing device behind cutting wheel.

Table 1: Important technical parameters of the shield. Items Parameters Excavation diameter (mm) 10220 External diameter (mm) 10000 Internal diameter (mm) 9000 Segment thickness (mm) 500 Segment ring width (mm) 1800 Configuration of segments 9 (8+1 keystone) Machine length (mm) 11550 Cutterhead rotational speed (r/min) 0-0.68 Advance rate (mm/min) 0-85 Total thrust (kN) 108000 Maximum torque coefficient α=32.2 Working torque (kN·m) 22896-34344

Monitoring ground surface settlement and data available for building the LSSVM models

Table 2: Data available for building the LSSVM model. TD ECP SAR TT CHT RCH IVPR s No. MCSs NSTR max Notes (m) (kPa) (mm/min) (kN) (kN·m) (r/min) (m3) (mm) 1 DB-01 11.4 15 159 48 30437 7555.68 0.64 12.2 -24.0 2 DB-02 11.4 15 157 51 31382 8586.00 0.62 14.1 -18.3

3 DB-03 11.4 15 163 50 32731 7899.12 0.63 15.2 -16.4 4 DB-04 11.4 15 161 51 31627 8242.56 0.64 16.6 -15.3 et 5 DB-07 15.0 15 169 55 33261 7212.24 0.61 13.8 -18.1 6 DB-08 16.5 15 172 59 35124 8929.44 0.63 12.7 -17.3 Training s 7 DB-09 17.9 16 176 64 35628 9616.32 0.66 13.0 -16.2 8 DB-11 18.2 16 189 69 37613 12020.4 0.56 11.9 -15.6 9 DB-12 18.5 16 186 70 37569 10303.2 0.55 14.2 -17.1 Vol. 22 [2017], Bund. 02 619

10 DB-13 17.1 16 173 60 35143 8242.56 0.61 12.8 -18.0 11 DB-14 16.4 34 176 65 36721 8242.56 0.66 14.2 -22.9 12 DB-15 16.0 34 169 62 35627 7899.12 0.65 15.1 -22.6 13 DB-16 16.0 17 184 68 37797 6868.80 0.68 14.6 -15.4 14 DB-17 16.1 34 126 54 33354 5495.04 0.70 12.4 -33.8 15 DB-19 16.1 34 182 65 32658 6181.92 0.68 12.9 -26.9

16 DB-20 16.1 34 179 68 33452 7899.12 0.66 13.5 -24.5 17 DB-21 16.1 34 185 62 34123 6868.80 0.63 14.1 -23.3 Test s et 18 DB-22 16.1 33 183 64 35746 6525.36 0.71 16.2 -20.4 To aid the information-orientated construction, ground surface settlement monitoring was carried out over the whole period of shield tunneling, if ground surface permitted. As shown in Figs.2-4, thirty-six monitoring cross sections (MCSs) in all were arranged on ground surface along the tunnel route, which are denoted as “DB-i (i=1,2,3,……,36)”. It is necessary to point out that the monitored settlements for some cross sections are not complete due to various reasons, and not given herein. The surface settlement is decided by both geological conditions and shield operational parameters. For the former, the tunnel depth (TD) and measured N-values of the soil on tunnel roof (NSTR) are considered in the LSSVM models; for the latter, key operational parameters included are the earth chamber pressure (ECP), shield advance rate (SAR), total thrust (TT), cutter head torque (CHT), rotation of cutter head (RCH) and the injection volume per ring (IVPR). The data available for building the LSSVM model for surface settlement prediction are list in Table 2.

LSSVM MODEL FOR PREDICTING MAXIMUM SURFACE SETTLEMENT

LSSVM for function estimation The LSSVMs are based on the theory of statistical learning, using techniques of classification and function estimation. The issue of the surface settlement prediction belongs to the latter. Consider a given training set of N data points, N , with input data x∈Rn and output y∈R, where Rn and R {xyii, }i=1 are the n-dimensional and one-dimensional vector space, respectively. The input variables employed are the tunnel depth, N-value of the soil on tunnel roof, earth chamber pressure, shield advance rate, total thrust, cutter head torque, rotation of cutter head and the injection volume per ring, which are denoted as x1, x2, x3, x4, x5, x6, x7 and x8, respectively. The output, y, represents the maximum surface settlement. So, in this study x = [ x1, x2, x3, x4, x5, x6, x7, x8] and y = [smax]. In feature space, LSSVM models adopt the form:

yx( ) = wTϕ ( x) + b (1)

where the feature map φ(·) maps the input data into a higher dimensional feature space; w is an adjustable weight vector; and b is the scalar threshold. In LSSVM for function estimation, the following optimization problem is formulated. Vol. 22 [2017], Bund. 02 620

N 11T 2 minJ( we , ) = ww + γ ei (2) we, ∑ 22i=1

subject to the equality constrains:

yx( ) = wTϕ ( x) + b + e, i = 1, ⋅⋅⋅ , N ii (3)

where γ is the regularization constant; ei is the error variable; N is the number of data. This is a form of ridge regression, and can be solved by constructing the following Lagrangian function (18).

N T L( wbe,,;α) = J( we ,) −∑ αϕi{ w( x i) ++ b e ii − y} (4) i=1

where αi is the Lagrange multiplier. With Equation (4) and using conditions for optimality and Mercer's condition, the resulting LSSVM model for surface settlement prediction can be written as

N

yx( ) = ∑αii Kxx( , ) + b (5) i=1

where K(·) is the kernel function. Mathematically equivalent to regularization networks and Gaussian processes (usually without bias term), this solution, which can be expressed analytically in terms of the input parameters and can sample first and second order statistics, is easy to analyze.

Kernels considered The LSSVM capabilities are controlled by the choice of the kernel functions. This allows the user to solve complex regression problems by choosing appropriate kernels. The study aims at investigating the capability of a LSSVM model to predict shield tunneling induced ground surface settlement. So three widely used and simple kernels are used: the linear, polynomial and radial basis function (RBF). The kernels are listed below:

T Kxx( ,ii ) = x x (6)

Td2 Kxx( ,ii ) =+≥ ( xx t ) , t 0 (7)

2 −−xx Kxx( , ) = exp(i ) (8) i σ 2

where d, t and σ are constants of the kernels. The program LS-SVMlab1.8 under the GNU General Public License, constructed using MATLAB by De Brabanter et al. (21), is employed to build the models for surface settlement prediction. In the program, there are three optimization algorithms: simplex method for all kernels, grid search method only for 2-dimensional tuning parameter optimization, and line search method used with the linear kernel. The regularization and kernel parameters are determined in two steps. First, for every kernel, the Coupled Simulated Annealing (CSA) determines suitable starting points for every method. The CSA uses the acceptance temperature to control the variance of the acceptance probabilities with a control scheme, thus resulting in an improved optimization efficiency. The search limits of the CSA method are set to Vol. 22 [2017], Bund. 02 621

[exp(−10), exp(10)]. Second, these starting points are then given to one of the three optimization routines above to find the optimal parameters through the cross-validation method according to the cost estimation. Four cross-validation methods are provided in the program: leave-one-out, L-fold, robust L-fold and generalized cross-validation. The simplex method and the leave-one-out cross- validation are selected in the study.

RESULTS AND DISCUSSIONS Performances of the LSSVM models for surface settlement prediction are evaluated based on the error indices of the absolute error (AE), relative error (RE), Root Mean Square Error (RMSE) and the mean absolute percentage error (MAPE). The former two indices are used to assess the prediction precision of one single sample, while the latter two are fit for error evaluation of the sample set. They are given as follows:

AE = yip, − y i (9)

RE=( yip, − y i) y i (10)

m 1 2 RMSE = ∑( yip, − y i) (11) m i=1

m 1 yyip, − i MAPE = ∑ (12) myi=1 i

where yi and yi,p are the field measured and the predicted surface settlement, respectively, and m is the number of the prediction points. Using the program LS-SVMlab1.8 under the GNU General Public License (21), the calculation steps for the LSSVM models are as follows: (1) Dividing the available samples into the training set and the test set; (2) Determing values of the parameter the models with different kernels by the program LS- SVMlab1.8; (3) With the Equations 9-12, calculating the error indices.

Table 3: Errors of training set when determining regularization and kernel parameter using linear kernel. Measured Predicted AE RMSE No. MCSs RE MAPE data (mm) results (mm) (mm) (mm) 1 DB-01 -24.0 -21.9 2.1 8.6% 2 DB-02 -18.3 -19.3 1.0 5.2% 3 DB-03 -16.4 -16.9 0.5 2.9% 0.97 2.69% 4 DB-04 -15.3 -15.3 0.0 0.3% 5 DB-07 -18.1 -18.9 0.8 4.5% Vol. 22 [2017], Bund. 02 622

6 DB-08 -17.3 -18.0 0.7 4.0% 7 DB-09 -16.2 -16.6 0.4 2.4% 8 DB-11 -15.6 -16.1 0.5 3.1% 9 DB-12 -17.1 -15.1 2.0 11.9% 10 DB-13 -18 -19.1 1.1 5.8% 11 DB-14 -22.9 -22.6 0.3 1.3% 12 DB-15 -22.6 -22.9 0.3 1.1% 13 DB-16 -15.4 -15.5 0.1 0.4% 14 DB-17 -33.8 -33.1 0.7 2.2% The data presented in Table 2 are used to build the LSSVM models. The former fourteen samples are treated as the training set, and the latter four samples as the test set. In the case of the linear kernel, the initial value of γ is 1.6 determined by the CSA, and its optimal 1.5 attained by the simplex method. The computation results of the model are listed in Tables 3 and 4. For the training set, RMSE = 0.97 mm and MAPE = 3.84%; for the test set, RMSE = 0.73 mm, MAPE =2.69%. The findings of α and b are given below.

α = [-0.6451 0.2984 0.1499 -0.0135 0.2554 0.2188 0.1231 0.1517 - (13) 0.6387 0.3295 -0.0934 0.0800 0.0183 -0.2343]T

b = 8.5149e-016 (14)

Table 4: Errors of test set when determining regularization and kernel parameter using linear kernel. Measured Predicted AE RMSE No. MCSs RE MAPE data (mm) results (mm) (mm) (mm) 15 DB-19 -26.9 -26.0 0.9 3.4% 16 DB-20 -24.5 -24.6 0.1 0.6% 0.73 2.69% 17 DB-21 -23.3 -23.6 0.3 1.5% 18 DB-22 -20.4 -19.3 1.1 5.3% In the case of the RBF kernel, the initial values of γ and σ are 1365.7 and 57.1, respectively, and their optimal values are 1206.7 and 58.8, respectively. The computation results of the model are listed in Tables 5 and 6. For the training set, RMSE = 0.12 mm and MAPE = 0.57%; for the test set, RMSE = 0.47 mm, MAPE = 2.06%. The findings of α and b are listed below.

α = [-42.9553 40.0339 15.9245 -18.7611 18.9842 -33.2414 18.3398 (15) 30.3491 -43.3623 16.2261 -35.1803 23.4436 17.3153 -7.1161] T

b = -2.1468 (16)

Table 5: Errors of training set when determining regularization and kernel parameters using RBF kernel. Measured Predicted RMSE No. MCSs AE (mm) RE MAPE data (mm) results (mm) (mm) 1 DB-01 -24.0 -23.8 0.2 0.7% 0.12 0.57% 2 DB-02 -18.3 -18.5 0.2 0.9% Vol. 22 [2017], Bund. 02 623

3 DB-03 -16.4 -16.5 0.1 0.4% 4 DB-04 -15.3 -15.2 0.1 0.5% 5 DB-07 -18.1 -18.2 0.1 0.4% 6 DB-08 -17.3 -17.2 0.1 0.8% 7 DB-09 -16.2 -16.3 0.1 0.5% 8 DB-11 -15.6 -15.7 0.1 0.8% 9 DB-12 -17.1 -16.9 0.2 1.0% 10 DB-13 -18.0 -18.1 0.1 0.4% 11 DB-14 -22.9 -22.8 0.1 0.6% 12 DB-15 -22.6 -22.7 0. 0.4% 13 DB-16 -15.4 -15.5 0.1 0.5% 14 DB-17 -33.8 -33.8 0.0 0.1%

Table 6: Errors of test set when determining regularization and kernel parameters using RBF kernel. Measured Predicted RMSE No. MCSs AE (mm) RE MAPE data (mm) results (mm) (mm) 15 DB-19 -26.9 -26.6 0.3 1.3% 16 DB-20 -24.5 -24.2 0.3 1.2% 0.47 2.06% 17 DB-21 -23.3 -23.9 0.6 2.6% 18 DB-22 -20.4 -21.0 0.6 3.2% In the case of the polynomial kernel, the initial values of γ, t, and d are 4827.3, 19.7 and 3.0, respectively, and their optimal values are 9660.5, 40.1 and 3.0, respectively. The computation results of the model are listed in Tables 7 and 8. For the training set, RMSE = 0.0 mm and MAPE = 0.00%; for the test set, RMSE = 0.63 mm, MAPE = 2.51%. The findings of α and b are given below.

α = 1.0e-004*[-0.7628 0.6746 0.8016 -0.6256 0.1423 -0.5492 0.6092 (17) 0.2292 -0.3976 0.1189 -0.8073 0.4041 0.2865 -0.1240] T

b = 0.2121 (18)

Table 7: Errors of training set when determining regularization and kernel parameters using polynomial kernel. Measured Predicted AE RMSE No. MCSs RE MAPE data (mm) results (mm) (mm) (mm) 1 DB-01 -24.0 -24.0 0.0 0.0 2 DB-02 -18.3 -18.3 0.0 0.0 3 DB-03 -16.4 -16.4 0.0 0.0 4 DB-04 -15.3 -15.3 0.0 0.0 0.00 0.00% 5 DB-07 -18.1 -18.1 0.0 0.0 6 DB-08 -17.3 -17.3 0.0 0.0 7 DB-09 -16.2 -16.2 0.0 0.0 8 DB-11 -15.6 -15.6 0.0 0.0 Vol. 22 [2017], Bund. 02 624

9 DB-12 -17.1 -17.1 0.0 0.0 10 DB-13 -18.0 -18.0 0.0 0.0 11 DB-14 -22.9 -22.9 0.0 0.0 12 DB-15 -22.6 -22.6 0.0 0.0 13 DB-16 -15.4 -15.4 0.0 0.0 14 DB-17 -33.8 -33.8 0.0 0.0 It is observed from Tables 3-8 that the predicted results vary with different kernels and the RBF and the polynomial kernel perform more favorably than the linear kernel. Large errors occur when the models with linear kernels. When the polynomial kernel is used, the errors are minor on account of the self-adaptive adjustment of d. When adopting RBF kernels, the errors of the training set are greater than those of the polynomial kernels, while the errors of the test set are the less. The RBF kernel has the good generalization performance for the issue of the maximum surface settlement prediction, and is easy to use for the RBF kernel has less hyper-parameters than the polynomial kernel. Table 8: Errors of test set when determining regularization and kernel parameters using polynomial kernel. Measured Predicted AE RMSE No. MCSs RE MAPE data (mm) results (mm) (mm) (mm) 15 DB-19 -26.9 -26.3 0.6 2.3% 16 DB-20 -24.5 -24.1 0.4 1.7% 0.63 2.51% 17 DB-21 -23.3 -23.6 0.3 1.3% 18 DB-22 -20.4 -21.4 1.0 4.7%

Analytical expressions for the maximum surface settlements in terms of the influencing factors discussed above can be gotten by substituting Equations 13-18 of the calculated results of α and b into Equation (5). Using these expressions, the maximum surface settlement can be easily and rapidly predicted, as provides more time to take precautions against the possible worst-case scenarios and is particularly important to rapid shield tunnel construction.

DISCUSSION AND CONCLUSION Using the program LS-SVMlab1.8 under the GNU General Public License (21) and the data from the 10.22 m diameter shield tunneling project in Beijing, the capability is examined of the LSSVM model to predict shield tunneling induced ground surface settlement. Computation results show the LSSVM is a robust tool and can take into consideration effects of the shield operational parameters and soil conditions on surface settlement. The parameters considered in the LSSVM models are not limited those included in this study, and more parameters can be added if necessary. (1) With suitable kernels such as the RBF and polynomial kernels, the LSSVM models give very good approximations of the surface settlements. Meanwhile, The RBF kernel attains the best generalization performance for the issue of the maximum surface settlement prediction according to the calculated RMSE and MAPE, and is easy to use in the engineering practice for the RBF kernel has less hyper- parameters than the polynomial kernel. (2) From the LSSVM model, the explicit formula of the maximum surface settlement, expressed in terms of all the considered factors, can be obtained. With the formula, the maximum surface settlement can be rapidly predicted. Measures and countermeasures can be adopted in time according to the predicted results during rapid shield tunnel construction. Vol. 22 [2017], Bund. 02 625

(3) The data for building the LSSVM models are from the already finished 10.22 m diameter shield tunnel construction and only a certain number of samples available. With intentionally collected more representative samples, it is expected the LSSVM models with RBF kernels achieve better performances. CONFLICT OF INTEREST The authors confirm that this article content has no conflict of interest.

ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support by the National Basic Research Program of China under Grant 2015CB057800.

REFERENCES 1. C. Deulofeu, H. Schwarz, U. Maidl and M. Comulada, “Data management for highly mechanized shield tunnelling in the construction of the Line 9 Metro Barcelona”, in World Tunnel Congress 2007 and 33rd ITA/AITES Annual General Assembly, 2007, pp. 1521-1526. 2. J. Liu, F. Wang, S. He, E. Wang and H. Zhou, “Enlarging a large-diameter shield tunnel using the Pile-Beam-Arch method to create a metro station”, Tunn. Undergr. Sp. Tech., vol. 49, no. 6, pp. 130-143, 2015. 3. F. He, “Analysis on Adaptability of Slurry Shield Cutterhead and Cutters in Beijing Railway Underground Connecting Line Project”, Tunnel Construction, vol. 31, no. 4, pp. 416-425, 2011. 4. R.B. Peck, “Deep excavations and tunnelling in soft ground”, in Proceedings of the 7th international Conference on Soil Mechanics and Foundation Engineering, State-of-the- Art volume, 1969, pp. 225-290. 5. K. Fujita, “Prediction of surface settlements caused by shield tunneling”, in Proceedings of the International Conference on Soil Mechanics, Vol. 1, 1982, pp. 239-246. 6. Y.S. Fang, J.S. Lin and C.S. Su, “An estimation of ground settlement due to shield tunnelling by the Peck-Fujita method”, Can. Geotech. J., vol. 31, no. 3, pp. 431-443, 1994. 7. R.K. Rowe and K.Y. Lo, “A method of estimating surface settlement above tunnels constructed in soft ground”, Can. Geotech. J., vol. 20, no. 1, pp. 11-22, 1983. 8. T. Kasper and G. Meschke, “A 3D finite element simulation model for TBM tunnelling in soft ground”, Int. J. Numer. Anal. Meth. Geomech., vol. 28, no. 14, pp. 1441-1460, 2004. 9. G. Mollon, D. Dias and A. Soubra, “Probabilistic analyses of tunneling-induced ground movements”, Acta Geotech., vol. 8, no. 2, pp. 181-199, 2013. 10. T. Nomoto, S. Imamura, T. Hagiwara, O. Kusakabe and N. Fujii, “Shield tunnel construction in centrifuge”, J. Geotech. Geoenviron. Eng., vol. 125, no. 4, pp. 289-300, 1999. 11. Y. Fang, Z. Yang, G. Cui and C. He, “Prediction of surface settlement process based on model shield tunnel driving test”, Arab J. Geosci., vol. 8. no. 10, pp. 7787-7796, 2015. Vol. 22 [2017], Bund. 02 626

12. S. Suwansawat and H. H. Einstein, “Artificial neural networks for predicting the maximum surface settlement caused by EPB shield tunneling”, Tunn. Undergr. Sp. Tech., vol. 21, no. 2, pp. 133-150, 2006. 13. J. Qiao, J. Liu, W. Guo and Y Zhang, “Artificial neural network to predict the surface maximum settlement by shield tunneling”, Intelligent Robotics and Applications, Lecture Notes in Computer Science, Vol. 6424, 2010, pp. 257-265. 14. A. Pourtaghi and M. A. Lotfollahi-Yaghin, “Wavenet ability assessment in comparison to ANN for predicting the maximum surface settlement caused by tunneling”, Tunn. Undergr. Sp. Tech., vol. 28, no. 3, pp. 257-271, 2012. 15. I. Ocak and S. E. Seker, “Calculation of surface settlements caused by EPBM tunneling using artificial neural network, SVM, and Gaussian processes”, Environ. Earth Sci., vol. 70, no. 3, pp. 1263-1276, 2013. 16. D. Bouayad, F. Emeriault and M. Maza, “Assessment of ground surface displacements induced by an earth pressure balance shield tunneling using partial least squares regression”, Environ. Earth Sci., vol. 73, no. 11, pp. 7603-7616, 2015. 17. S. R. Dindarloo and E. Siami-Irdemoosa, “Maximum surface settlement based classification of shallow tunnels in soft ground”, Tunn. Undergr. Sp. Tech., vol. 49, no. 6, pp. 320-327, 2015. 18. J. A. K. Suykens, T. V. Gestel, J. D. Brabanter, B. D. Moor and J. Vandewalle, Least squares support vector machines. Singapore: World Scientific Publishing Company, 2002. 19. A. Kuh, “Least squares kernel methods and applications”, Soft Computing in Communications, Part 4, Studies in Fuzziness and Soft Computing, Vol. 136, Springer Berlin Heidelberg, 2004, pp. 365-387. 20. Y. Guo, “Study on ground surface movement induced by large-diameter earth pressure balance shield tunneling”, China Civil Engineering Journal, vol. 46, no. 11, pp. 128-137, 2013. (in Chinese). 21. K. De Brabanter, P. Karsmakers, F. Ojeda, C. Alzate, J. De Brabanter, K. Pelckmans, B. De Moor, J. Vandewalle and J. A. K. Suykens, LS-SVMlab toolbox user's guide version 1.8, Internal Report 10-146, ESAT-SISTA, K. U. Leuven (Leuven, Belgium), 2010.

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Editor’s note. This paper may be referred to, in other articles, as: Xingchun Li, Xinggao Li, Dajun Yuan, Yuhai Guo: “Using Least Squares Support Vector Machine to Predict the Maximum Ground Surface Settlement Caused by Shield Tunneling” Electronic Journal of Geotechnical Engineering, 2017 (22.02), pp 613-626. Available at ejge.com.