Constitutive Parameter Adjustment for Mechanized Tunneling with Reference to Sub-system Effects Chenyang Zhao1(B) , Arash Alimardani Lavasan1 , Thomas Barciaga1 , Raoul H¨ olter1 , Maria Datcheva2 , and Tom Schanz1 1
Chair of Foundation Engineering, Soil and Rock Mechanics, Ruhr-Universit¨ at Bochum, Geb¨ aude IC 5/115, Universit¨ atsstr¨ ae 150, 44801 Bochum, Germany
[email protected] 2 Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., bl. 4, 1113 Sofia, Bulgaria
Abstract. In this research, the effect of sub-system on model response for mechanized tunneling process has been taken into consideration. The main aim of this study is to modify the constitutive parameters in a way that the best agreement between numerical results and measurements is obtained. The sub-system includes supporting pressure at the face of the TBM, contraction along the TBM-shield and grouting pressure in the annular gap. The commercially available finite element code, PLAXIS is adopted to simulate the construction process. The soil behavior during the excavation is numerically reproduced by utilizing Hardening Soil model with small strain stiffness (HSsmall). The constitutive parameters are obtained via sensitivity and back analyses while they have been calibrated based on the real measurement of Western Scheldt tunnel in the Netherlands. Both local and global sensitivity analyses are used to distinguish which parameters are most influencing the soil deformation. Thereafter, the model validation is accomplished by applying different scenarios for face pressure distributions with respect to the slope of the tunnel. In addition, the effect of contraction factor is modified individually or coupled with the variation of grouting pressure. Evaluating the influence of the sub-system is conducted to assess its effects on the model responses and to seek the possibility to decrease the disagreement between the calculated displacement and real measured data. Keywords: Mechanized tunneling · Numerical simulation analysis · Meta-modeling · Back analysis · Sub-system
1
· Sensitivity
Introduction
In order to overcome the plight that limited space can be used for public transportation in urban area, shield supported tunneling has been widely applied. c Springer International Publishing Switzerland 2015 I. Dimov et al. (Eds.): NMA 2014, LNCS 8962, pp. 217–225, 2015. DOI: 10.1007/978-3-319-15585-2 24
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Numerical simulation as an efficient and useful tool can be conducted to predict the soil deformation before and during the tunnel construction. This paper mainly focuses on the effects of sub-system on numerical model response. The sub-system includes the face pressure in front of Tunnel Boring Machine (TBM), contraction along the TBM-shield and grouting pressure at the tail of TBM [1]. To avoid the collapse of soil at the excavation face of TBM, face pressure is applied to maintain the balance against with the earth pressure. Conicity shape of TBM means the cross sectional area at the tail is smaller than the front of TBM. It makes the excavation process efficient. Contraction factor is applied to simulate the volume loss due to overcut zone, it increases from the front towards the tail of TBM and keeps constant along the lining segments. Grouting pressure is injected at the tail of TBM to fill the gap between the lining segments and surrounding soils, which aims to decrease the surface settlement. The Western Scheldt tunnel is located under the Scheldt river in the Netherlands and it is constructed by slurry shield TBM. The tunnel has a length of 6.6 Km and the diameter is 11.33 m. The thickness of each lining segment is 0.45 m and its length is 2.00 m. The total length of TBM is 10.95 m and there is some additional length for the cutting head. The excavation domain consists of several clay and sand layers. The mechanical properties of soil layers are summarized in [2]. Water level is about 1.5 m below the ground surface during tunnel construction.
2 2.1
Methodology Numerical Simulation of Mechanized Tunneling
Mechanized excavation of Western Scheldt tunnel is simulated via commercially available finite element code P LAXIS. To reproduce the soil behavior during tunnel excavation, Hardening soil model with small strain stiffness (HSsmall) is implemented [3,4]. The initial soil constitutive parameters are given in Table 1. Due to the absence of in situ investigation, some parameters are assumed by authors according to the type of soil and other existing parameters. A total length of 88 m tunnel excavation is simulated in this paper, and the tunnel has an inclination of 4.3 %. The TBM-shield and the lining segments are modeled as circular plate elements with linear elastic model. Young’s modulus of lining segment and TBM-shield is 22 MPa and 210 MPa, respectively. Poisson ratio of lining segment and TBM-shield is 0.1 and 0.3, respectively. Based on some trial analyses, the final mesh discretization and boundary condition are selected in a way that the model response is independent to them. The 3D FE-model has dimensions of 150 m long in X-axis direction, 100 m wide in Y-axis direction and 71 m deep in Z-axis direction (See Fig. 1). These dimensions only represent half of the model due to the symmetry condition. Furthermore, a discretized mesh with a total number of 26,538 10-node tetrahedral elements is adopted.
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Table 1. Soil constitutive parameters for HSsmall model Parameter Soil layers Dike K1
Z1
BK1
BK2
GZ2
K2
Unit
ϕ
20
22
34
28
28
34
40
[◦ ]
ψ
0
0
4
0
0
4
0
[◦ ]
c
5
5
6.4
20
20
11.4
40
[kN/m2 ]
ref E50 ref Eoed ref Eur Gref 0
11 000 24 000
35 000
25 000 30 000
30 000
50 000
[kN/m2 ]
11 000 24 000
35 000
25 000 30 000
30 000
50 000
[kN/m2 ]
30 000 60 000
80 000
60 000 100 000 90 000
γ0.7
0.0002 0.0002
0.0002
0.0002 0.0002
0.0002
0.00015 [-]
m
0.7
0.7
0.5
0.7
0.7
0.5
0.7
[-]
γunsat
19
18
18
18
17
17
17
[kN/m3 ]
γsat
20
20
19
21
19.3
20.2
20
[kN/m3 ]
180 000 [kN/m2 ]
40 000 150 000 140 000 65 000 100 000 110 000 150 000 [kN/m2 ]
K0nc
0.66
0.63
0.44
0.53
0.53
0.40
0.36
[-]
OCR
1.0
1.0
1.0
2.7
2.8
2.5
3.0
[-]
Fig. 1. 3D model geometry
According to the construction reality, the face pressure increases with the advancement of the TBM due to changing the embedment depth. In initial prediction, the face pressure distribution keeps constant for all the excavation stages and the value linearly increases from 137 kN/m2 at tunnel’s crown to 250 kN/m2 at tunnel’s bottom. To simulate the volume loss caused by overcut and conicity of TBM, contraction factor is applied to the plate elements which represent the TBM and lining segments. It increases linearly from 1.4 % at the front of TBM towards 3.8 % at the tail of TBM. Since in reality, the measured surface settlement is quite large and the value of applied grouting pressure is uncertain, the grouting pressure is not considered in the initial prediction.
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The consequential excavation process is modeled by staged calculation. The TBM is simulated as 12 m long plate elements. In each excavation, the TBM advances 2.0 m which is the length of one lining segment. The soil elements in front of TBM is deactivated and the face pressure is activated. Additionally, the contraction factor is activated when TBM-shield material is assigned to the plate elements. The installation of lining segments are modeled by assigning lining segment material to the plate elements at the tail of TBM. 2.2
Sensitivity and Back Analyses
Sensitivity analysis is an important and efficient tool to estimate the key parameters for geotechnical applications. There are two main groups of sensitivity analyses, Local Sensitivity Analysis (LSA) and Global Sensitivity Analysis (GSA). For LSA, the model response with respect to the input parameters is evaluated at a given local point and based on the calculation of derivatives. Therefore, the information provided by LSA highly depends on the given local point and the step size used in approximation of derivatives. The result may be not reliable for non-linear models. While GSA explores the whole space of input parameters which makes the result independent of the model nature. In this paper, Variance-Based (VB) method of GSA is applied to evaluate the uncertainty of input parameters. Composite scaled sensitivity index CSSj and total effect sensitivity index ST i are defined as [5,9]: CSSj =
yi (xj + Δxj ) − yi (xj ) Δyi 1 m (SSi,j )2 , SSi,j = xj = xj (1) i=1 m Δxj Δxj Si =
yA )2 yA T yCi − n (¯ (yB − yCi )T (yB − yCi ) , ST i = 2 yA T yA − n (¯ yA ) 2yB T yB − 2n (¯ yB )2
(2)
Equation (1) indicates the sensitivity information provided by i-th observation points for the estimation of j-th parameter. In this research, Δxj = 0.1xj . yi (xj ) is scalar of model response for i-th observation point calculated with corresponding input scalar of j-th parameter xj . m = 8 is the number of observation points. In Eq. (2), A and B are two independent (n, k) matrices and Ci, whose columns are copied from matrix B except the i-th column copied from its corresponding column in A. yA , yB , and yCi are vectors of model responses calculated with corresponding input vector of matrices A, B, and Ci, respec¯B are the mean value of model response calculated with all the tively. y ¯A and y input vectors of yA and yB . Back analysis has been widely used in engineering problems [6,7]. It is employed to identify the unknown parameters with field measurements. In this paper, Partial Swarm Optimization (PSO) algorithm [8] is implemented in back analysis to find the best optimized values of selected parameters.
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Fig. 2. Numerical prediction of (a) transverse surface settlement (b) longitudinal surface settlement
3
Results
Figure 2 shows the surface settlements when the initially guessed parameters are assigned. It can be found that the affected zone calculated by FE-model is wider than the real measured data in both transverse and longitudinal directions. For improvement, both local and global sensitivity analyses are applied to estimate the key parameters and reduce the degrees of system freedom. Results of LSA and GSA are given in Fig. 3. It is obvious that parameters of sand layer (Z1) play the most important role in soil deformation due to the fact that tunnel is excavated in Z1 layer. According to the result of GSA, sensitivity of parameter changes with the variation of observation points. Displacements of points above the tunnel are most sensitivity to the friction angle, this is because of the dominating plastic ref and deformation. While for observation points far away from the tunnel, Eur ref G0 generate increasing importance, which is due to the gradually increasing elastic deformation. Since ground settlements at observation points 1–3 are most ref ref and Eur of Z1 and K1 layers, they are selected as the key sensitive to ϕ, Eoed parameters which need to be modified by back analysis. Surface settlements calculated with modified soil parameters are showed in Fig. 2. In order to further improve the results, effects of sub-systems on model response are studied. Different scenarios are described in Table 2. Figure 4 describes the influence of face pressure. Scenario 1 uses the same pressure distribution described in former simulation. Considering the slope of tunnel, depth dependent face pressure is applied in scenario 2 to study the effect of varying face pressure on model response. Since in reality, face pressure keeps at a low level in the first several excavations before increasing to a high level, scenario 3 is applied to simulate the reality. The result shows high face pressure decreases the surface settlement in longitudinal direction. It means depth dependent face pressure increases the face stability when the earth pressure and water pressure
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Fig. 3. Results of (a) LSA (b) GSA
increase with the advancement of TBM. Overall, depth dependent face pressure provides surface settlement profiles which match the real measurement better. Table 2. Different scenarios to study the sub-system effects No. of scenario Description of sub-system Face pressure Contraction factor Grouting pressure 1
Constant
1.4 % to 3.8 %
Not applied
2
Depth dependent 1.4 % to 3.8 %
Not applied
3
Depth dependent 1.4 % to 3.8 %
Not applied
4
Constant
1.26 % to 3.42 %
Not applied
5
Constant
1.54 % to 4.18 %
Not applied
6
Constant
1.54 % to 4.18 %
75 kPa (constant)
7
Constant
1.54 % to 4.18 %
150 kPa (constant)
Figure 5 shows the effects of contraction factor on model response. The value of contraction factor is decreased and increased 10 % respectively in Scenario 4 and Scenario 5. It is obvious that contraction factor has important effect on surface settlements in both transverse and longitudinal directions. This is due to the fact that surface settlement is mainly caused by the volume loss of soil during mechanized excavation. In the above simulations, only face pressure and contraction factor are applied to the numerical model. Based on Scenario 5, grouting pressure is applied together with the increased contraction factor to seek possibility to decrease the disagreement between the numerical result and real measurements. The results are given in Fig. 6. It is clear that surface settlement profiles are highly affected by the grouting
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Fig. 4. Effect of face pressure on (a) transverse surface settlement (b) longitudinal surface settlement
Fig. 5. Effect of contraction factor on (a) transverse surface settlement (b) longitudinal surface settlement
Fig. 6. Effect of grouting pressure on (a) transverse surface settlement (b) longitudinal surface settlement
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pressure. In transverse direction, new prediction well matches measured data for small deformation area. While for large deformation area, there is significant disagreement between the calculated and measured data. The possible reason is that soil constitutive parameters are optimized in the model where grouting pressure is not applied. The result would be improved by modifying the soil parameters via back analysis.
4
Conclusions
Both local and global sensitivity analyses are applied to distinguish the key parameter which governs the model response. It is found that surface settlement above the tunnel is most sensitive to the friction angle and stiffness of soil. Depth dependent face pressure performs better in predicting the soil deformation when tunnel has an inclination. Surface settlement mainly comes from the volume loss of tunnel excavation, contraction factor influences both transverse and longitudinal ground displacement, especially for the observation points above the tunnel. Grouting pressure can be applied to decrease the large surface settlement caused by volume loss during excavation. Modified input parameters of sub-system decrease the disagreement between calculated result and real measured data. Acknowledgments. This research has been supported by the German Research Foundation (DFG) through the Collaborative Research Center (SFB 837). The first author is sponsored through a scholarship by China Scholarships Council (CSC). These supports are gratefully acknowledged.
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