Estimating maximum surface settlement due to EPBM

Transportation Geotechnics 18 (2019) 92–102

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Transportation Geotechnics journal homepage: www.elsevier.com/locate/trgeo

Estimating maximum surface settlement due to EPBM tunneling by Numerical-Intelligent approach – A case study: Tehran subway line 7 Sayed Rahim Moeinossadat, Kaveh Ahangari

T

⁎

Department of Mining Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

A R T I C LE I N FO

A B S T R A C T

Keywords: Subway tunnel Surface settlement FDM GEP VB

Ground settlement due to excavation of shallow tunnels is a common phenomenon. To control the settlement, one should be able to predict it, and based on it he may consider required preventions and protections. There are different methods for predicting settlement, each having some strengths and weaknesses. The main weakness of these methods is that they do not consider enough effective parameters on the settlement. The numerical methods, contrary to the empirical and analytical methods, take into account the effects of a larger number of parameters. However, ideal selection of many parameters is associated with ambiguity and difficulty and is timeconsuming. To overcome these issues, the intelligent methods are incorporated which are appropriate tools. The aim of this paper is to present a numerical-intelligent model for prediction of maximum surface settlement (Smax). At first, a section of Tehran subway line 7 was modeled using the finite difference method (FDM). Then a dataset including 100 Smax values were prepared for creating the intelligent model. Among the intelligent methods, the gene expression programming (GEP) method was selected to represent the mathematical equation and the built numerical-intelligent model explained a proper performance. The determination coefficient, R2, for both the training and testing phases was 0.976 and 0.931, respectively. At the end, the derived mathematical equation from the GEP model was prepared using the visual basic (VB) in the form of predictor software. According to accuracy of the prediction results, the presented equation and software are reliable and suitable as an alternative for the numerical modelling.

Introduction Most urban tunnels are excavated in shallow depths and soft ground; hence occurrence of deformation (especially the settlement) due to this process is relatively a common phenomenon. Precise estimation of the settlement has an important role in the safety, design and tunnel construction. By estimating this parameter, where there is possibility of occurring any damage, the above mentioned issues could be prevented or possibly some measures could be adopted to control them. Therefore, knowledge on the amount of maximum surface settlement and comparison with the allowable settlement is of great importance. There are different methods for prediction of surface settlement and among them one could refer to the empirical, analytical, numerical and recently intelligent methods. Each of these methods may have some strength and could help in solving the problem but on the other hand, it may have some weaknesses. The empirical methods are based on the experimental formulations in the past and mostly are limited to the measurements in a specific field, therefore may yield inappropriate

predictions for other areas [28,38,41,5,4,36,27,20,44,3,19,26]. Analytical methods are mostly useful for predicting the short-term maximum surface settlement. Many studies have been performed in this respect [24,46,25,12,6,13,37]. The most important weakness of the empirical and analytical methods is that they do not consider enough effective parameters on the settlement. Today use of the earth pressure balance machine (EPBM) in construction of urban tunnels is widespread. In this method of tunneling, many factors such as the tunnel geometry, ground conditions and shield operation factors influence the surface settlement. Therefore, it is hard to calculate the surface settlement just by application of the traditional methods. Numerical methods contrary to the empirical and analytical ones look into the effects of a greater number of parameters on the settlement. In the last three decades, these methods (especially FEM and FDM) have been extensively utilized in analysis of the surface settlement due to tunnel excavation, and the results show appropriate performance of these methods [39,23,1,45,29,30,34,15,9,10,11]. Nevertheless, these methods also have some constraints. Determination of

⁎ Corresponding author at: Department of Mining Engineering, Science and Research Branch, Islamic Azad University, End of North Sattari Highway, University Square, Tehran, Iran. E-mail address: [email protected] (K. Ahangari).

https://doi.org/10.1016/j.trgeo.2018.11.009 Received 9 July 2018; Received in revised form 25 November 2018; Accepted 26 November 2018 Available online 27 November 2018 2214-3912/ © 2018 Elsevier Ltd. All rights reserved.


S.R. Moeinossadat, K. Ahangari

some of these essential parameters for the modelling is difficult and utilizing inaccurate values could result into unreal design and predictions [8]. In addition, most numerical methods are highly sensitive to the model's geometric components like model dimensions, mesh shapes and its configuration etc. Considering these issues, it becomes clear that numerical modelling is time consuming and needs experience and skillfulness. To overcome the mentioned limitations, the intelligent methods have been utilized as they are not limited by the number of input parameters, and are not time consuming and costly also they have high estimation capability. Many studies have been performed in this respect [42,22,43,32,7,14,35,2] and the results have indicated proper performance of these methods. The main defect of the previous investigations is that these intelligent models were specific to their developers and there is not an equation or specific tool to be used by other researchers in this field. This problem is eliminated in the GEP method and it has acquired capability of a general application by presenting the mathematical equations. Ahangari et al. [2] using GEP, presented the first intelligent equation for predicting the surface settlement due to excavation of tunnels by NATM. In this research, it is attempted to present a combined numericalintelligent model for predicting the settlement of Tehran subway line 7. This model would have the advantages of both methods, besides the numerical method knowledge; its intelligent part increases the ability and speed of prediction. Therefore, in case of precise predicted results it could be proposed as a suitable alternative for the numerical method or at least as a tool for preliminary estimation of the surface settlement.

Table 1 Technical features of the EPBM Tehran subway line 7 [40]. EPBM Parameters

Amount

Excavation diameter (m) External diameter (m) Internal diameter (m) Annular gap (mm) Minimum curve radius (m) Curve length Shield outside diameter Shield length (m) Type of segment Configuration of segment Segment length (m) Segment thickness (cm) Type of grout Grout Volume per ring (m3) Face pressure (kPa)

9.200 8.850 8.150 175 300 250 9.164 9.0 Universal ring 6 + 1 Key + 1 Invert 1.5 35 Two component 6.7 55

line includes a total number of 25 stations, which connect eastern Tehran to the north western part (Fig. 1). This tunneling project is divided in to two sections of north-west and east-west at the intersection of Ghazvin Street and Navab Highway, where it is being executed using two EPBMs [40]. In this investigation, the surface settlement of the beginning of south-north section located at the chainage of 12 + 600 to 12 + 710 m (between stations N7 and O7), has been modeled. The main characteristics of the tunneling machine in this section are given in Table 1.

Case study: Tehran subway line 7 Site geology Site location Fig. 2 shows the geology section of the investigated area in the chainage of 12 + 600 and 12 + 710 m between stations N7 and O7. The geotechnical model of this project was prepared using the geotechnical test results and soil classification, and based on them the soil layers in this area are categorized in four major groups. In Table 2, the

Tehran subway line 7 with a length of 27 km begins from Takhti Sport Complex, located at eastern Tehran, and after traveling about 12 km in the east-west direction, by reaching Navab Safavi Highway changes its direction and continues in the south-north direction. This

Fig. 1. Route plan of Tehran subway line 7 [10]. 93



Fig. 2. Geological section of Tehran subway line 7 in the chainage of 12 + 600 and 12 + 710 m [48].

dimensions are as follows: the transverse section dimension of the model (along the positive direction of X-axis) is 50 m (at least 5 times greater than the tunnel diameter (D)), the distance of the tunnel axis to the bottom of the model (along Z-axis) is 30 m (about 3D) and the longitudinal section dimension (along Y-axis) is 75 m (about 6 times the tunnel diameter from the excavated space to the back of the tunnel front, assuming 60 m advancement). To apply the boundary conditions, the surrounding nodes of the model along the horizontal directions (X and Y) were fixed on the X-Z and Y-Z planes, whereas the bottom model nodes at the vertical direction (Z) were fixed on the X-Z and Y-Z planes. With respect to the model dimensions the coordinates of the fixed points are X = 0 and X = 50, Y = 0 and Y = 75 and finally Z = −30, respectively. Therefore, at the model boundaries there is no horizontal displacement in the X-Z and Y-Z planes and no vertical displacement in the X-Y plane. It should be mentioned that in the modelling process, the model dimensions, size of the meshes, excavation length and similar parameters are calibrated by trial and error method. For better simulating the tunnel which is constructed by EPBM, the tunneling process was executed as being real and as sequential including the tunnel excavation, applying the support pressure to the tunnel front, installation of segment and filling the tail void behind it. The mentioned sequences were designed with more details according to Fig. 5 and were applied by the fish codes. The technical properties and features of EPB, which are implemented for modelling, are given in Table 3. The other important parameter is the face support pressure and is assumed as 50 kPa. The important point here is the live burdens at the ground surface, which is divided into two portions in this investigation: The traffic burden effect being equal to 20 kN/m2 and the burden due to buildings around the avenue being equal to 30 kN/m2. The built model with the corresponding support elements is shown in Fig. 6.

groups and the corresponding geotechnical tests results are presented. In this table, γ is unit weight, C is cohesion, Ø is angle of internal friction, E is Modulus of Elasticity, υ is Poisson’s ratio and K is coefficient of earth pressure. As there was no groundwater in this area the effect of pore water pressure is neglected in the calculations. Instrumentation and monitoring surface settlement With respect to the importance of Dena Building (Fig. 3a), being located above this underground structure, different tools and devices are incorporated for monitoring including the metal meter, optical points and benchmarks. To measure the building deformation, the metal meters and optical points are installed at its different parts. Furthermore, to monitor the ground surface settlement, seven benchmarks at each cross section and with a distance of 10 m are specified on the layout map as shown in Fig. 3b. The measured maximum ground surface settlement at sections A-A and B-B is reported equal to 7.1 and 6.9 mm, respectively (Fig. 3c). Numerical modelling Three-dimensional modelling of tunnel For 3D modelling of this tunnel, FLAC3D Ver. 5.0 software is utilized which is based on FDM. The soil environment is assumed as homogeneous, isotropic with elastic-perfectly plastic behavior and MohrCoulomb criterion. The segment rings and the shield were modeled with elastic behavior. Due to the axial symmetry of the structure. Which is circular, and for reducing the number of computations and increasing the modelling speed just half of the structure was modeled. The used units were; for the length (m), density (kg/m3), force (N), stress (Pa) and gravity (m/sec2). According to Fig. 4 the model Table 2 Soil grouping and geotechnical design data in the project area [48]. Layers

Engineering classification symbols (BSCS)*

Thickness (m)

γ (kg/m3)

C (kPa)

Ø (°)

E (MPa)

υ

K

Layer Layer Layer Layer

Filling ML, CL GML, GCL GWM, GML

1.2 8.0 11.6 Base

1900 1900 1900 1900

29 40 30 20

35 27 35 38

15 30 80 100

0.30 0.35 0.27 0.27

0.42 0.55 0.43 0.38

1 2 3 4

* ML: Silt, CL: Clay, GML: Silt with gravel, GCL: Clay with gravel, GWM: Well graded silty gravel. 94



(a)

(b)

(c)

Fig. 3. (a) Dena building; (b) Benchmarks layout (c) Main monitoring sections [10].

Validating the numerical model Fig. 7 shows the vertical displacement contours due to modelling of the surface settlement. To ensure maximized surface settlement and access to the final settlement trough, the modelling process was continued up to 40 steps so the tunnel advancement equals 60 m (about 6D). Then, using history of the predefined points, the surface settlement over the centerline of the driven axis of the tunnel is derived and its value is determined. The maximum surface settlement values obtained for sections A-A and B-B are 7.48 and 6.21 mm, respectively. With respect to the measured settlement values (7.1 and 6.9 mm for sections AA and B-B) it is clear that the settlement values calculated by FLAC3D have good compatibility with the measured values and shows its proper performance. According to Fig. 7, at the initial excavation step, a heave is observed behind the shield which has been referred to in the reports by different persons. According to Namazi et al. [31] and Franzius et al. [18] this heave is related to the model dimensions. These researchers believe that with increase in the model dimensions, the heave is reduced. Ng and Lee [33] relate this heave to the high lateral earth pressure or changes in the effective stress. The authors agree with both theories. To investigate this issue the modelling process is repeated with enlargement of the model dimensions at the Y-axis direction (from 75 to 90 m) and in a way that the whole tunnel structure is modeled. Although the calculation time was highly increased but the rate of heave

Fig. 4. Three-dimensional views of the created FLAC3D model for simulating surface settlement.

95



Fig. 5. Designed excavation sequences for simulating EPBM process in numerical modelling.

decreased somehow according to the Namazi et al. [31] and Franzius et al. [18] opinions. Nevertheless, this heave still was present which could be related to the high lateral earth pressure or change in the effective stress (The Ng and Lee [33] opinion). It should be mentioned that the corresponding surface settlement of the new model was somehow less than that of the original model, hence the results of the original model are acceptable and fulfill the problem’s requirements. Another point that should be referred to is the occurred pre-settlements at the tunnel face and before reaching the excavation machine. In other words, in the first initial steps of excavation, there is no pre-settlement ahead of the tunnel face (due to the excavation operation in the previous stages) and as settlement at the point is equal to sum of the settlements occurred in the previous stages and after excavation, it is expected that the final settlement in the initial parts of tunnel is less than those in other parts. An obvious example of the discussed issue is depicted in the corresponding figure, in which the maximum surface settlement is seen at a distance from the start of the model.

Fig. 6. Views of tunnel vertical section and related structural support elements.

numerical model has the potential of creating a new databank which is possible through changing the effective parameters on the settlement and repeating the modelling. Implementation of this approach, while helps achieving the above mentioned goals makes it possible to look into the impact of effective parameters on the surface settlement.

Artificial modelling and dataset making The results obtained from predicting the maximum surface settlement in the numerical model were close to the measured values and this proved validity of the built model. Therefore the corresponding Table 3 Properties of support elements used in modelling. Parameters

Element type

Constitutive model type

Internal diameter (m)

External diameter (m)

Thickness (cm)

E (GPa)

υ

γ (kg/m3)

Shield Segment Grout

Shell Shell Zone

Elastic Elastic Mohr–Coulomb

9.0 8.2 8.9

9.2 8.9 9.2

10.0 35.0 15.0

200 27 1

0.25 0.20 0.25

7840 2400 1200

96



Fig. 7. Contour of Z-Displacement (Vertical displacement) for section A-A.

subway line 7, the different parameters values that were used in the numerical model, are explained below:

First, it is essential to select the properties of the base model, then while assuming other parameters as constant, each dependent parameter is changed and modelling is performed. The base model properties are selected based on the mean geotechnical parameters values of the studied section. This was done using Eq. (1).

XAve =

• Values of C are considered with intervals equal to 3 kPa as 10, 13, 16, …, 37 and 40 kPa • Values of Ø are considered as 15.0, 17.5, 20.0, …, 37.5 and 40° • Values of E are considered as 30, 37, 44, …, 93 and 100 MPa • Values of γ are considered as 1700, 1735, 1770, …, 2015 and 2050 kg/m • Values of Z are considered as 10, 13, 16, …, 37 and 40 m • Values of υ are considered as 0.200, 0.215, 0.230, …, 0.335 and 0.350 • Values of K are considered as 0.35, 0.39, 0.43, …, 0.71 and 0.75 • Values of σ are considered as 0,10, 20, …, 90 and 100 kPa • Values of σ are considered as 0.0, 7.5, 15.0, …, 67.5 and 75.0 kPa

(XLayer1 ∗ TLayer1 + ·····+XLayern ∗ TLayern ) TLayer1 + ·····+TLayern

(1)

3

In this equation XAve is the mean value of the parameter, XLayer1 is the parameter value of the first layer, TLayer1 is thickness of the first layer and it is repeated for other layers. For example to measure the mean value of cohesion the corresponding equation was utilized and its value in the base model was assumed to be equal to 34 kPa. These computations were performed for all the parameters and on this basis the angle of internal friction was found to be equal to 32°, modulus of elasticity 57 MPa, Poisson’s ratio 0.30 and the coefficient of earth pressure 0.48. The corresponding values of other parameters including the properties of structural elements and other properties are assumed similar to the initial modelling.

t

s

As is seen, 11 values are considered for each dependent parameter, and the number of the parameters is nine; therefore, there is a total number of 99 new models and considering the original model (base model), 100 numerical models were built. After building the models, the values of 11 variables of each parameter were drawn against its corresponding surface settlement in a diagram and the results are given in Fig. 8. Considering Fig. 8 the main derived results are as follows:

Effective parameters and their renege As stated before, the main issue concerning the empirical equations is that they do not consider all the effective parameters on the settlement phenomenon. To solve this problem and provide a more precise tool for predicting the settlement, first the effective parameters on the settlement should be identified and then the amount of these effects should be investigated. With respect to the previous investigations and the needed parameters for FDM modelling, in this section all the nine parameters including cohesion (C), angle of internal friction (Ø), Modulus of Elasticity (E), unit weight (γ), depth (Z), Poisson’s ratio (υ), coefficient of earth pressure (K), face support pressure (σt) and Surface surcharge (σs) are investigated. The other parameters such as the tunnel diameter and support elements including the thickness and width of segment, strength of the grout etc. are significant but as these parameters were kept constant during the project, they were ignored as input parameters in the numerical-intelligent model. According to Table 2, representing the project properties of Tehran

• The C, Ø, E were inversely proportional to the S • • • • 97

max. However, decrease in the amount of Smax due to the Ø is of greater importance with respect to other two parameters. Contrary to the three previous parameters, the Z, γ and σs parameters values are directly proportional to that of Smax. It is known that tunnel construction at enough higher depths, roof falls resulted effects will be petered out before reaching the ground surface [47]. Therefore, it is expected that there is an inverse relationship between the Z and the Smax values However it was not due to taking the other parameters (especially the σt) as constant. Increase in the value of such parameters as υ, K and σt results in



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Fig. 8. Effect of various parameters on maximum surface settlement.

•

γ had the minimum effect, respectively. Introduction of the parameter K as the most effective dependent parameter is with hesitation as it is expected that the roles of geometric and strength parameters are more important. The main reason for reaching this conclusion is the selected range for changes in the parameters. For more explanation, in case that the difference between the maximum and minimum values of K is less than the assumed value (0.40), the results may vary. However, as stated before, the selected the range for variation in the parameters values is based on Tehran subway line 7 characteristics.

reduction of Smax value. Among them, the coefficient of earth pressure has a relatively greater importance and possesses a somehow complicated relation. The components of ground volume loss (VL) during EPB tunneling process include, volume loss at the tunnel face (Vf), volume loss around shield (Vs) and volume loss in tail void (Vt). With increase in the face support pressure, Vf decreases toward zero at the tunnel front and this causes reduced surface settlement. However, this reduction continues up to the base surface settlement and from that time on, remains constant because Vs and Vt also are not continued for a long time.

Intelligent modelling

Table 4 demonstrates the effect (in percentage) of each parameter on reducing the maximum surface settlement value and the relative effect of each of them is calculated. Based on the obtained results, K and

Gene expression programming (GEP) Ferreira [16] proposed a new algorithm based on the genetic algorithm (GA) and genetic programming (GP) called GEP. The new evolutionary algorithm was created to overcome many GA and GP limitations [21]. Fig. 9 shows GEP algorithm in which selection starts with five elements. This method consists of two main sections called chromosomes and expression tree (ET). This algorithm generates some compound preliminary genes made of some chromosomes randomly; each gene indicates a mathematical function. Then each gene is converted into an ET. In other words, a fixed-length string character is used in this method for presenting each solution. It has a tree-like structure and the ETs can be written as mathematical equations [21]. Each ET is made of two parts called function set and terminal set (Fig. 10). In the next stage, the real and the predicted values are compared. If the obtained results correspond to the stopping criteria determined at the beginning, GEP process will be stopped. In case the stopping criteria are satisfied, some chromosomes will be selected and mutated by roulette wheel sampling method for finding new chromosomes. The operation

Table 4 Percentage of effective parameters for reducing maximum surface settlement. Effective parameters

Range Minimum

K Z Ø E σs σt C υ γ

0.35 10.0 15.0 30.0 0.0 0.0 10.0 0.20 1700.0

Relevant Smax

Affect amount

Maximum 0.75 40.0 40.0 100.0 100.0 75.0 40.0 0.35 2050.0

11.63 0.57 26.03 10.67 5.03 8.27 7.57 6.95 5.72

−7.63 9.94 5.66 3.95 10.24 5.75 5.96 5.82 6.56

*

Absolute

Relative

165.6 94.3 78.3 63.0 50.9 30.5 21.3 16.3 12.8

31.1 17.7 14.7 11.8 9.5 5.7 4.0 3.1 2.4

* Amount of Smax less than zero is dedicated surface heave. 98



Table 5 Parameters settings of the GEP algorithm for creating intelligent model. Parameters General

Number of Chromosomes Head size Number of Genes Linking function Function set

30 10 6 Addition (+) +, −, ×, ÷, √, 3√, ^2, ^3, arctan, tanh, exp, ln. RMSE

Fitness function error type Genetic operators

Numerical constants

Mutation rate IS Transposition rate RIS Transposition rate Inversion rate One-point recombination rate Two-point recombination rate Gene recombination rate Gene transposition

0.05 0.10 0.10 0.10 0.30

Constants per gene Data type Lower bound Upper bound

2 Floating- Point −10 +10

0.30 0.10 0.10

the same time with the highest compatibility (Table 5). Fig. 11 illustrates the determination coefficient for predictions made by the numerical-intelligent model for two phases of training and testing, which shows its high precision. To derive the mathematical equation of the model, the rule of converting ETs to equations is incorporated and Eq. (2) was obtained [17]. The predicted results by the numerical-intelligent model for the two training and testing phases, based on different assessment criteria, are given in Table 6. As is seen, the corresponding model in both the training and testing phases had a very precise performance.

Fig. 9. GEP algorithm [21].

⎧ 21 7 ⎪ −4.081 2 ⎞ + ⎛ (K / υ ) ⎞ Smax = − ⎛ ⎨ ⎝ σs − 4.081 ⎠ ⎝ 7.495 ⎠ ⎪ ⎩ ⎜

⎟

⎜

⎟

3

Z + 6.521 ⎞ ⎞ + (ln(tanhυ)) ⎟⎞ + ⎜⎛ ⎛1 − ⎛ ⎝ Ø − 4.081 ⎠ ⎠ ⎝⎝ ⎠ 6 K ⎞ + ln ⎛ 3 ⎝ (υ ∗ tanh(ln(Z − 5.274))) ⎠ ⎜

⎟

⎜

⎟

(((tanh2 σs )((tanhC ) σt )) + E ) ⎞ +⎛ Z ⎝ ⎠ ⎜

⎟

( (

⎛ ln +⎜ ⎜ ⎝ Fig. 10. An example of the tree obtained in the GEP and its relevant mathematical equation.

(E − 8.502) (γ / Z )

) ) − (tanh(Z /−8.502)) K

2

⎞⎫ ⎪ ⎟ ⎟⎬ ⎪ ⎠⎭

(2)

where Smax is maximum surface settlement (mm), C is cohesion (kPa), Ø is angle of internal friction (◦), E is Modulus of Elasticity (MPa), γ is unit weight (kg/m3), Z is depth (m), υ is Poisson’s ratio, K is coefficient of earth pressure, σt is face support pressure (kPa) and σs is surface surcharge (kPa). The built numerical-intelligent model was finally converted to a mathematical equation to be more applicable. However, it is a relatively complex and long equation and may yield undesired results due to the computational errors. Hence, to overcome this problem and for increasing the prediction speed, use was made of visual basic (VB) to promote its application. Fig. 12 shows a figure of the software page. This figure shows an example of the software application for prediction of the maximum surface settlement at section A-A. The input parameters at this section are calculated based on Eq. (1) and were input to the software and finally a value equal to 8.33 mm was estimated for

iterates until satisfying stopping criteria [16,21].

Prediction of Smax by GEP In this section, the data bank obtained from the artificial numerical modelling is implemented for the intelligent modelling. For building the GEP model, use has been made of GeneXproTools (Ver. 5). 100 datasets were divided randomly in to two groups of training and testing. For this purpose, 70 datasets (70%) were considered for creating the model and 30 datasets (30%) were considered for its evaluation. Using the trial and error method some configurations are applied in this software to select a model with minimum error and at 99



(a)

(b)

Fig. 11. Coefficient of determination (R2) between calculated and predicted values of maximum surface settlement (a) Training phase (b) Testing phase.

have good extrapolation capabilities.

Table 6 GEP Model results to predict maximum surface settlement. Phase

R2

RMSE

MAE

Train Test

0.976 0.931

0.582 0.494

0.397 0.346

Discussion and conclusion In this paper to present a numerical-intelligent model, Tehran subway line 7 was simulated. Using FLAC3D the two sections A-A and BB were modeled in the chainage of 12 + 600 and 12 + 710 m and then the calculated surface settlement was compared to the measured values using the monitoring tools, which proved validity of the numerical model. After ensuring the good performance of the numerical model, a total number of 100 artificial models were built to produce the new data banks. For each of the 100 models one a parameter out of the nine dependent parameters was changed. Thus sensitivity of the independent parameter Smax to each of the dependent parameters could

Smax. This value is appropriate in comparison with the measured value by monitoring (7.1 mm) and the computed value by FLAC3D (7.48 mm) and demonstrates appropriate performance of the equation and the numerical-intelligent software. As the range for the nine effective parameters in the artificial simulation, using the FLAC3D and GEP modelling is known, the software was designed in a way that it would not accept values outside of this range, as the intelligent methods do not

Fig. 12. An example of prediction Smax for Section A-A by using numerical-intelligent software. 100



References

be analyzed. The range of changes in parameters was selected in a logical way and based on the project information, and among the maximum and minimum values corresponding to each of them some uniform distances were selected to perform simulation in a better way. The new data bank after being incorporated in the intelligent model was analyzed. Sensitivity analysis of each parameter showed the parameters of coefficient of earth pressure (K) and depth (Z) had the highest impact and unit weight (γ) and Poisson’s ratio (υ) had the least impact. Caution should be exercised considering the obtained results, for example, the tunnel depth, which is introduced as the most effective dependent parameter, has a direct relationship with the Smax. Whereas, as it is expected, provided the tunnel is deep enough, roof falls resulted effects will be petered out before reaching the surface. Contradiction between this theory and the results of the numerical analysis is due to the artificial change of the depth parameter in the condition where other controlling parameters of the settlement such as the support pressure, strength of the surrounding mass etc. are taken constant. In practice with increase in depth, vertical stress (σV) is increased and consequently the present pore, cracks and joints and as a whole such indices as the porosity are decreased and this causes increase in the parameters of density, uniaxial compressive strength etc. Therefore expecting reduced settlement is rational. Also comparing the effects of the parameters, it became clear that K has the highest effect in minimizing the surface settlement, whereas it was expected that the role of geometric and strength parameters is greater. The main reason to reach this conclusion was the increased range assumed for this parameter. Therefore, it should be stated that in practice it is not possible to investigate the effect of changes in a parameter on the surface settlement while taking other parameters as constants. Even in cases where the number of collected data is high, the complexity of EPB tunneling method causes limited results for this type of sensitivity analysis. In continuation, based on the nine input parameters that all are essential for a numerical modelling and using the GEP method, a model was presented for prediction of the surface settlement. After building the GEP model and deriving the mathematical equation underlying it, the equation was converted to the numerical-intelligent predictive software using the VB programming language, which is the outcome of this article. Finally, with respect to the discussed issues in this research, the following results are obtained:

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• Due to the complexity associated with the problem of predicting • • • • •

settlement and the effect of each parameter upon other parameters, sensitivity analysis of the parameters in the case that one parameter is changed and other parameters are kept constant is impossible in practice and could only yield limited results. Increase in the value of face support pressure (σt) causes reduced volume loss at the tunnel front and consequently reduction in the surface settlement. This reduction continues up to the base surface settlement and from this point on it remains constant because the loss around the shield and within the till pores is continued. The determination coefficient of prediction in the numerical-intelligent model for the phases of training and testing were 0.976 and 0.936, respectively. Considering the precision of the results its validity is confirmed and due to the observed saving in time and cost, it could be accounted as a suitable alternative for the numerical methods. The presented software due to lack of computational errors, ease of application and its speed in estimation is preferred over the presented equation. Eventually, it should be noted the presented model and equation in this study have limitations. Some other effective parameters such as water condition, grouting pressure and filling, etc. were ignored because of lack of data. So, it could be proposed for future research in this field.

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