Trans. Tianjin Univ. 2008, 14:563-568 DOI 10.1007/s12209-008-0097-4 © Tianjin University and Springer-Verlag 2008
Numerical Simulation of Dynamic Response of an Existing Subway Station Subjected to Internal Blast Loading HU Qiuyun(胡秋韵), YU Haitao(禹海涛), YUAN Yong(袁
勇)
(Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China)
Abstract：In order to design and retrofit a subway station to resist an internal blast, the distribution of blast loading and its effects on structures should be investigated firstly. In this paper, the behavior of a typical subway station subjected to different internal blast loadings was analyzed. It briefly introduced the geometric characteristics and material constitutive model of an existing two-layer and three-span frame subway station. Then three cases of different explosive charges were considered to analyze the dynamic responses of the structure. Finally, the maximum principal stress, displacement and velocity of the columns in the three cases were obtained and discussed. It concluded that the responses of the columns are sensitive to the charge of explosive and the distance from the detonation. It’s also found that the stairs between the two layers have significant effects on the distribution of the maximum principal stress of the columns in the upper layer. The explicit dynamic nonlinear finite element software——ANSYS/LS-DYNA was used in this study. Keywords ：internal blast loading；subway station；numerical analysis；dynamic response
Subway stations are important joints for underground traffic. They usually locate in downtown district with large population. Once an internal explosion happens in a subway station, it might result in deaths or injures to people, collapse or damage to subway station, and adverse vibration to surrounding buildings nearby. The harmful effects are no less than those of an upground blast. That is just the reason why a subway station becomes one of the targets for terrorists. The blast events in subway stations, such as, in Paris (1995), in Moscow (2004), and in London (2005) have caused to hundreds of deaths and injuries, considerable damages of subway structures, and interruption of traffic system. With the rapid development of underground construction and the potential threaten of terrorism, engineers and researchers have made extensive efforts on the research of underground structures to resist blast loadings. Since it’s hard to conduct a full scale in-site experiment, numerical techniques are usually applied to simulating blast events. A number of researches have done plenty of work to analyze the wave propagation [1,2] and dynamic responses of underground structures[3,4] subjected to blast loading. However, there is few work focusing on complex underground structures such as
Accepted date: 2008-07-15. HU Qiuyun, female, born in 1983, doctorate student. Correspondence to HU Qiuyun, E-mail:
[email protected].
subway stations, and the structures subjected to internal blast. In this paper, with the available commercial software ANSYS/LS-DYNA, the numerical model of a typical two-layer and three-span frame subway station is established. The TNT charges of 5 kg, 10 kg and 40 kg are considered to analyze the dynamic responses of the structure under different explosion loadings. The dynamic responses (including the maximum principal stress, displacement and velocity) of the columns are presented and discussed.
1
Computational method
The ANSYS/LS-DYNA software used in this study combines the LS-DYNA explicit finite element program with the ANSYS program. The explicit method used by LS-DYNA provides fast solutions for short-time, large deformation dynamics, quasi-static problems with large deformations, multiple non-linearity, and complex contact/impact problems. In this study, the general simulation is carried out by using the arbitrary LagrangianEulerian (ALE) method, which involves modeling the explosive and air with the ALE multi-material mesh,
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and modeling reinforced concrete structures and surrounding soil with the Lagrangian mesh.
2
Numerical model
2.1
Typical subway station The subway station in this study is a typical twolayer station of 21.2 m in width (X-axis), 12.02 m in height (Y-axis) and about 200 m in length (Z-axis). The depth of soil above the top surface of the station is 3.5 m. The thickness of the roof plate, side walls, bottom plate, middle plate and platform is 0.8 m, 0.8 m, 0.9 m, 0.4 m and 0.2 m respectively. The cross section of columns is 0.6 m×0.9 m, and space distance between them is 5.7 m in X-axis and 8.5m in Z-axis. The explosive is assumed to be situated in the middle of the cross section and at 1.2 m height above the platform. The geometric layout of the subway station and the explosive point are shown in Fig.1. The numerical model of the subway station is shown in Fig.2.
plate, beams, columns and platform), surrounding soil, TNT and air as shown in Fig.3. The element of SOLID164 defined by eight nodes is adopted for the 3D model. The bound of soil is assumed as 6 m below the bottom plate and 6 m beyond the side walls. The whole domain is assumed to be axial symmetric, so 1/4 of the model is established in this study. The calculated length of the station is 28 m away from the explosive point, because it was found that the further increase in the length of the structure has insignificant effects on the wave propagation, and the blast wave has negligible influence on the further structure. The opening in middle plate represents the hatch for stairs between the two layers (shown in Fig.2). The nodes transitional displacement normal to the symmetry planes (XY and YZ planes) is constrained, which forms the symmetry boundary condition. Nonreflected boundary condition was considered in all the other boundaries except the ground surface, which adopts free boundary condition.
(a) Local enlarged
(b) Finite element mesh
Fig.3 Finite element mesh and local enlarged Fig.1
Layout of the subway station and the explosive point
Fig.2 Numerical model of the subway station (1/4 symmetrical model)
2.2
FEM model The FEM model consists of reinforced concrete structure (side walls, roof plate, bottom plate, middle
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2.3
Material constitutive models The response of concrete under shock loading is a complex nonlinear and rate-dependent process. A number of dynamic constitutive models for concrete have been proposed in the past [5]. In this study, the interaction of steel bars and concrete is not considered. According to the principle of equivalent stiffness EI, the stiffness of steel bars are converted and added to the stiffness of concrete. Plastic Kinematic Model [6] is adopted to simulate the behavior of reinforced concrete under blast loading. This model is suitable to describe isotropic and kinematic hardening plasticity with rate effects. The main parameters of this model are listed in Tab.1. The dynamic behavior of surrounding soil is described by Soil_and_Foam Model [6]. The main parameters of this model are listed in Tab.2.
HU Qiuyun et al: Numerical Simulation of Dynamic Response of an Existing Subway Station Subjected to Internal Blast Loading Tab.1 Mass density/ (kg·m−3) 2. 5×103
Main parameters of reinforced concrete model (*Mat_Plastic_Kinematic)
Young’s modulus/Pa 5×1010
Poisson’s ratio
Yielding stress/Pa
0.18
3.5×107
Tab.2 Mass density/(kg·m−3) 1.88×103
Hardening parameter 1
Failure strain for eroding elements 0.01
Main parameters of soil model (*Mat_Soil_and_Foam) Shear modulus/Pa 5.14×107
The high explosive burn and the Jones-Wilkins-Lee (JWL) equation of state (EOS) [6] are used to model the detonation of the TNT explosive. The JWL equation of state defines the pressure as ω ⎞ − R1V ω ⎞ − R2V ω E0 ⎛ ⎛ p = A ⎜1 − e + B ⎜1 − + ⎟ ⎟e V ⎝ R1V ⎠ ⎝ R2V ⎠ (1) where the parameters are assumed as A =3.74×1011 Pa, 9 B =3.23×10 Pa, R =4.15, R =0.95, ω =0.38 and 9 3 E =7×10 J/m . The mass density of TNT ρ =1 630 3 kg/m , detonation velocity vD =6 930 m/s and ChapmanJouget pressure pCJ =2.1×1010 Pa. Air is modeled by Null material model and the LINEAR_POLYNOMIA equation of state. The JWL 1
Tangent modulus/Pa 1×109
Bulk modulus/Pa 2.4×1010
A0 6.2×108
A1 1.67×104
A2 0.112 6
equation of state defines the pressure as p = C0 + C1μ + C2 μ 2 + C3 μ 3 + ( C4 + C5 μ + C6 μ 2 )
(2) where the parameters are assumed as C0 =−1×10 ， C1 =0 ， C2 =0 ， C3 =0 ， C4 =0.4 ， C5 =0.4 and C6 =0. The mass density of air ρ =1.292 9 kg/m3 and the initial internal energy per unit reference specific volume E0 = 2.5×105 J/m3. 5
2
0
3
Numerical results and discussions
Fig.4—Fig.6 show the dynamic responses of the columns.
(a) Charge of TNT: 5 kg
(b) Charge of TNT: 10 kg
(c) Charge of TNT: 40 kg
Fig.4
The maximum principal stress time-histories of columns in three cases
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Considering the quantity of explosive which a terrorist could take with won’t be too much, three cases of TNT charge are assumed: 5 kg (case 1), 10 kg (case 2) and 40 kg (case 3). Because columns are the important and vulnerable members of the subway station under an internal explosion, the analysis of dynamic response focuses on the columns in this paper. The columns are divided into two sets, as shown in Fig.2. One contains columns in the lower layer where the explosion happens, i.e. columns A1, A2, A3 and A4. The other contains columns in the upper layer, i.e. columns B1, B2, B3 and B4. It is found from the contours that the maximum value of the maximum principal stress of columns occurs at the foot of columns, and the maximum values of Xdisplacement and X-velocity take place in the middle of the columns. The time history of the maximum principal stress of each column is obtained from the element in bottom corner of each column, and the time histories
of X-displacement and X-velocity are obtained from the elements in the middle of the columns. 3.1 The maximum principal stress The plus value of the maximum principal stress is tensile stress, while the negative value is compressive stress. As shown in Fig.4, the time-depend trends of the maximum principal stress in the same column in different cases are almost the same, but the peak values are totally different from each other. Every column experiences several peak values of the maximum principal stress because of the complex incidence and reflection of the blast wave in the subway station. Column A1 is the nearest one away from the detonation, so its peak value of the maximum principal stress is much higher than that of others. It suffers the maximum principal stress of 10.21 MPa (at about 6.5 ms), 17.44 MPa (at about 6 ms) and 43.18 MPa (at about 5 ms) when the charge is 5 kg, 10 kg and 40 kg respectively. For column A2, A3 and A4,
(a) Charge of TNT: 5 kg
(b) Charge of TNT: 10 kg
(c) Charge of TNT: 40 kg
Fig.5 X-displacement time-histories of columns in three cases
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HU Qiuyun et al: Numerical Simulation of Dynamic Response of an Existing Subway Station Subjected to Internal Blast Loading
with the increase of distance away from the detonation, the peak value of the maximum principal stress declines from 3.78 MPa to 1.87 MPa in case 1, from 6.92 MPa to 2.47 MPa in case 2 and from 17.36 MPa to 3.73 MPa incase 3. For columns in the upper layer, the peak value of the maximum principal stress of column B2 is larger than that of column B1, because column B2 is close to the stairs (the hatch in the middle plate) from which the blast wave propagated to the upper layer. 3.2 Time-history responses of displacement It is obviously in Fig.5 that the maximum Xdisplacement for all the three cases occurs at column A1 in lower layer, and at column B1 in upper layer. With the condition of the charge is 5 kg, the X-displacement values of all the columns are lower than 0.4 mm except that column A1 is 0.73 mm. With the increase of the TNT charge, the maximum X-displacement at column A1 in-
creases from 1.5 mm in case 2 to 3.5 mm in case 3. In general, the X-displacement of columns increases with the adding of the charge of TNT, and declines with the growing of distance away from the detonation. 3.3 Time-history responses of velocity Fig.6 shows the time histories of X-velocity at the middle of the columns in three cases. Similarly to the displacement, the X-velocity of columns increases with the adding of the charge of TNT, and attenuates with the growing of distance away from the detonation. The allowable criteria of velocity for transportation tunnels given in the Safety Regulations for Blasting Practices[7] is 10 cm/s. According to this value, columns A1 and B1 in case 1, columns A1, A2 and B1 in case 2 and columns A1, A2, A3, B1 and B2 in case 3 are threatened by the explosion.
(a) Charge of TNT: 5 kg
(b) Charge of TNT: 10 kg
(c) Charge of TNT: 40 kg
Fig.6 X-velocity time--histories of columns in three cases
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Conclusions
Numerical simulation was conducted to investigate the response of columns in a typical two-layer and threespan frame subway station subjected to three cases of internal blast loadings. The results showed that the response of columns is mainly dependent on the charge of explosives and the distance away from the detonation. The hatch in the middle plate plays an important role to the distribution of the maximum principal stress of the columns in the upper layer. There were 6 columns in case 1, 10 columns in case 2 and 18 columns in case 3 whose X-velocity is more than the allowable value given in the Safety Regulations for Blasting Practices.
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References ［1］ Rigas F, Sklavounos S. Experimentally validated 3-D simulation of shock waves generated by dense explosives in confined complex geometries ［J］． Journal of Hazardous Materials, 2005,121(1/2/3):23-30. ［2］ Zhou Xiaoqing, Hao Hong, Li Zhongxian. Numerical simulation of an underground structure under a hypo-
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