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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (6) : 1289-1300     https://doi.org/10.1007/s11709-019-0548-0
RESEARCH ARTICLE
Global sensitivity analysis of certain and uncertain factors for a circular tunnel under seismic action
Nazim Abdul NARIMAN1(), Raja Rizwan HUSSAIN2, Ilham Ibrahim MOHAMMAD1, Peyman KARAMPOUR3
1. Department of Civil Engineering, Tishk International University Sulaimani, Sulaimaniya 46001, Iraq
2. Civil Engineering Department, College of Engineering, King Saud University, Riyadh 11421, Saudi Arabia
3. Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak 38156-875, Iran
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Abstract

There are many certain and uncertain design factors which have unrevealed rational effects on the generation of tensile damage and the stability of the circular tunnels during seismic actions. In this research paper, we have dedicated three certain and four uncertain design factors to quantify their rational effects using numerical simulations and the Sobol’s sensitivity indices. Main effects and interaction effects between the design factors have been determined supporting on variance-based global sensitivity analysis. The results detected that the concrete modulus of elasticity for the tunnel lining has the greatest effect on the tensile damage generation in the tunnel lining during the seismic action. In the other direction, the interactions between the concrete density and both of concrete modulus of elasticity and tunnel diameter have appreciable effects on the tensile damage. Furthermore, the tunnel diameter has the deciding effect on the stability of the tunnel structure. While the interaction between the tunnel diameter and concrete density has appreciable effect on the stability process. It is worthy to mention that Sobol’s sensitivity indices manifested strong efficiency in detecting the roles of each design factor in cooperation with the numerical simulations explaining the responses of the circular tunnel during seismic actions.

Keywords shear waves      Sobol’s sensitivity indices      maximum principal stress      maximum overall displacement      tensile damage     
Corresponding Authors: Nazim Abdul NARIMAN   
Just Accepted Date: 28 May 2019   Online First Date: 08 July 2019    Issue Date: 21 November 2019
 Cite this article:   
Nazim Abdul NARIMAN,Raja Rizwan HUSSAIN,Ilham Ibrahim MOHAMMAD, et al. Global sensitivity analysis of certain and uncertain factors for a circular tunnel under seismic action[J]. Front. Struct. Civ. Eng., 2019, 13(6): 1289-1300.
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http://journal.hep.com.cn/fsce/EN/10.1007/s11709-019-0548-0
http://journal.hep.com.cn/fsce/EN/Y2019/V13/I6/1289
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Nazim Abdul NARIMAN
Raja Rizwan HUSSAIN
Ilham Ibrahim MOHAMMAD
Peyman KARAMPOUR
Fig.1  Finite element model of the circular tunnel
item friction angle dilation angle cohesion yield stress (Pa) absolute plastic strain
soil plasticity 35°
soil cohesion 200000 0
Tab.1  Soil Mohr Coulomb plasticity data
Fig.2  Mesh convergence analysis
certain factor symbol minimum
value
maximum
value
tunnel lining thickness (m) X1 0.3 0.5
tunnel diameter (m) X2 8 10
tunnel lining (concrete)
modulus of elasticity (GPa)
X3
17
31
tunnel lining concrete density (kg/m3) X4 2300 2500
Tab.2  Ranges of certain factors
uncertain factors symbol minimum value maximum value
peak ground acceleration (m/s2) X5 0.981 4.905
soil density (kg/m3) X6 1800 2200
soil modulus of elasticity (GPa) X7 0.2 0.25
Tab.3  Ranges of uncertain factors
sensitivity indices maximum principal stress maximum overall displacement
first effect X1 3.37 0.41
first effect X2 2.94 88.71?
first effect X3 83.76? 0.68
first effect X4 0.92 7.81
sum of first effects 90.99? 97.61?
interaction between X1 and X2 0.12 0.01
interaction between X1 and X3 0.40 0.00
interaction between X1 and X4 0.54 0.00
interaction between X2 and X3 0.68 0.00
interaction between X2 and X4 1.15 1.26
interaction between X3 and X4 2.05 0.00
total effect of X1 4.43 0.42
total effect of X2 4.89 89.98?
total effect of X3 86.89? 0.68
total effect of X4 4.66 9.07
sum of total effects 100.87?? 100.15??
Tab.4  Sensitivity indices — certain factors
Fig.3  Main effects of certain factors-maximum principal stress
Fig.4  Main effects of certain factors-maximum overall displacement
sensitivity indices maximum principal stress maximum overall displacement
first effect X5 40.81? 99.81?
first effect X6 30.3 0.07
first effect X7 26.62? 0.09
sum of first effects 97.73? 99.97?
interaction between X5 and X6 0.89 0.01
interaction between X5 and X7 0.55 0.01
interaction between X6 and X7 0.56 0.00
total effect of X5 42.25? 99.83?
total effect of X6 31.75? 0.09
total effect of X7 27.73? 0.10
sum of total effects 101.73?? 100.02??
Tab.5  Sensitivity indices — uncertain factors
Fig.5  Main effects of uncertain factors-maximum principal stress
Fig.6  Main effects of uncertain factors-maximum overall displacement
Fig.7  Variation of concrete modulus of elasticity-tensile damage. (a) Minimum value at time= 3.8 s; (b) minimum value at time= 4.1 s; (c) medium value at time= 3.8 s; (d) medium value at time= 4.1 s; (e) maximum value at time= 3.8 s; (f) maximum value at time= 4.1 s
Fig.8  Variation of tunnel diameter-stability
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