# Blast Damage Assessment of Symmetrical Box-Shaped Underground Tunnel According to Peak Particle Velocity (PPV) and Single Degree of Freedom (SDOF) Criteria

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Blast Damage Assessment Methods of a Box-Shaped Tunnel

_{c}). Thus, various damage levels were suggested corresponding to the value of y

_{c}, which is set to be the mid-height lateral displacement of the structural member to reduce uncertainties in predicting the critical deflections, as shown in Table 2. This damage criterion was used by Mussa et al. [26] in order to assess the damage level of a box-shaped tunnel.

## 2. Numerical Modelling

#### 2.1. Geometry Details and Meshing

#### 2.2. Material Model

#### 2.2.1. Air

_{0}, C

_{1}, C

_{2}, C

_{3}, C

_{4}, C

_{5}, and C

_{6}are constants, and E

_{0}is represented the initial internal energy per unit volume. The adopted EOS symbolizes an ideal gas that was dominated by a gamma law, whereas the constants (C

_{0}, C

_{1}, C

_{2}, C

_{3}, and C

_{6}) are equal to 0 and (C

_{4}, and C

_{5}) are equal to γ − 1. Accordingly, the equation of pressure can be rewritten, as follows:

#### 2.2.2. Tunnel

_{r}). The maximum principal stress for failure (SIGF) [24] is assumed to be the f

_{c}and is equal to 61.18 MPa. A smeared modelling option available in Material 16 was used to simulate the rebar due to a large number of model elements, as well as its ability to deliver reasonable results within lower cost and time than that needed by discrete models [36]. Strain rate sensitivity was defined for the concrete and rebar by using dynamic increase factor (DIF) curves, as shown in Figure 2. The DIF curve was obtained during a laboratory test conducted in UKM University on concrete with a compressive strength of 61.18 MPa via the split Hopkinson pressure bar (SHPB) impact test within a strain rate range of up to 103.87 s

^{–1}[37]

_{.}For steel, the DIF of grade 60 rebar was determined by using Malvar‘s equation [38]. Table 4 shows the tunnel parameters, where SIGF is the unconfined concrete compressive strength (f

_{c}), P

_{r}is the Poisson ratio of concrete, E

_{r}is the elastic modulus of steel, PE

_{r}is the reinforcement percentage, PR

_{r}is the Poisson ratio of steel, and SIGY is the steel yield stress (${\mathrm{f}}_{\mathrm{y}}$).

#### 2.2.3. Soil

_{u}is the bulk modulus at the unloading path, a

_{0}, a

_{1}, and a

_{2}are the constants of the yield function, and P

_{cut}is the pressure cut-off of the tensile fracture [24,44].

#### 2.2.4. TNT

_{1}, R

_{2}, ω are constants, and V is indicated to the relative volume of the explosive material [24]. Table 7 shows the adopted parameters of the TNT charge [33].

#### 2.3. Boundary Condition

#### 2.4. Arbitrary Lagrangian Eulerian (ALE) Solver

## 3. Results and Discussions

#### 3.1. Validation of Numerical Models

#### 3.1.1. Peak Pressure of Blast Waves into the Soil

_{p}is the peak pressure of blast wave into the soil (MPa); f is the coupling factor, which equals to 0.14 for the surface blast in air; n and $\mathsf{\rho}\mathrm{c}$ are the attenuation and acoustic impedance coefficients of the sandy loam soil, which are equal 2.75 and 4.972, respectively, as described in TM5-855-1 [50]; R is the distance to the explosion centre in m; and, W is the weight of the explosive charge in kg. A similar approach was used by several scholars to validate the propagation of explosion waves into the soil [3,23,25,26,51].

#### 3.1.2. Validation of Tunnel Dynamic Response

#### 3.2. Propagation of Blast Wave

#### 3.2.1. Soil

#### 3.2.2. Tunnel

#### 3.3. Damage Assessment Results

#### 3.3.1. PPV Method

#### 3.3.2. SDOF Method

_{c}) of the mid-height structural member, as shown in Table 2 above. Accordingly, y

_{c}was set to be the maximum numerical displacement of the tunnel, which occurred at the roof centre. The results revealed that the tunnel roof centre with 250 mm lining thickness collapsed at burial depths of 4 and 6 m. On the other hand, the lining thickness of 500 mm showed a considerable decrease in the lateral displacement. Nevertheless, the roof centre has recorded a high damage level at the burial depth of 4 m due to the high intensity of blast waves.

## 4. Comparison between Damage Assessment Methods

#### Proposed Damage Criteria and Equation of the PVV Method

^{–6}× T × W + 0.019156 D

^{2}− 6.48000 × 10

^{−7}× T

^{2}+ 1.00580 × 10

^{−7}× W

^{2}

^{2}), which is recommended to be close to 1, with a minimum value of 0.8 [55,56]. Furthermore, the variances between the Predicted and Adjusted (R

^{2}) have to be less than 0.2 and the adequate precision (AP) greater than 4 to achieve a clear signal of the model [57].

## 5. Conclusions

- The numerical validation results revealed a good consistency with technical manual (TM5-855-1) at depths between 1 and 7 m within differences ranging from 1.01–18.70%. However, the results diverged at large depths of more than 8 m with differences ranging between 40.48 and 60%.
- The pressure contours proved that the blast waves travelled inside the soil in a hemispherical shape before and after inserting the tunnel structure, which considerably reduced the values of incident pressure by obstructing the propagation of blast waves to large depths.
- The pressure contours of the tunnel revealed that the peak reflected pressure that occurred immediately before the incident pressure reached its highest value, which means that the total energy of the blast waves transferred from the soil to the tunnel lining.
- Using of SDOF method to assess the damage levels of a box-shaped tunnel was more reliable and harmonic with the tunnel failure modes as compared with the PPV method at the studied cases of lining thickness, burial depth, and explosive charge weight.
- The assessment of tunnel damage based on the proposed damage criteria and the equation of the PVV method matched considerably with the results of the SDOF method. Hence, these criteria might be broadly adopted by engineers to ensure an accurate design of underground box-shaped tunnel structures exposed to massive surface explosions.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

- Kong, L.; Jin, F.; Jiang, M. Analysis of the way and scale of terroristic raid. Blasting
**2007**, 24, 29–88. [Google Scholar] - Verma, H.K.; Samadhiya, N.K.; Singh, M.; Goel, R.K.; Singh, P.K. Blast induced rock mass damage around tunnels. Tunn. Underg. Space Technol.
**2018**, 71, 149–158. [Google Scholar] [CrossRef] - Koneshwaran, S. Blast Response and Sensitivity Analysis of Segmental Tunnel; Queensland University of Technology: Brisbane, Australia, 2014. [Google Scholar]
- Koneshwaran, S.; Thambiratnam, D.P.; Gallage, C. Blast Response of Segmented Bored Tunnel Using Coupled SPH–FE Method in Structures; Elsevier: Amsterdam, The Netherlands, 2015. [Google Scholar]
- Buonsanti, M.; Leonardi, G. 3-D simulation of tunnel structures under blast loading. Arch. Civ. Mech. Eng.
**2013**, 13, 128–134. [Google Scholar] [CrossRef] - Koneshwaran, S.; Thambiratnam, D.P.; Gallage, C. Response of segmented bored transit tunnels to surface blast. Adv. Eng. Softw.
**2015**, 89, 77–89. [Google Scholar] [CrossRef] - Davies, M. Dynamic soil structure interaction resulting from blast loading. Centrifuge
**1994**, 94, 319–324. [Google Scholar] - Davies, M.; Williams, A. Centrifuge modelling the protection of buried structures subjected to blast loading. In Structures under Shock and Impact II, Proceedings of the Second International Conference, Portsmouth, UK, 16–18 June 1992; Thomas Telford Publishing: London, UK, 1992. [Google Scholar]
- De, A. Numerical simulation of surface explosions over dry, cohesionless soil. Comput. Geotech.
**2012**, 43, 72–79. [Google Scholar] [CrossRef] - De, A.; Morgante, A.N.; Zimmie, T.F. Mitigation of blast effects on underground structure using compressible porous foam barriers. In Poromechanics V, Proceedings of the Fifth Biot Conference on Poromechanics, Vienna, Austria, 10–12 July 2013; American Society of Civil Engineers: Reston, VA, USA, 2013. [Google Scholar]
- Kutter, B.L.; O’Leary, L.M.; Thompson, P.Y.; Lather, R. Gravity-scaled tests on blast-induced soil-structure interaction. J. Geotech. Eng.
**1988**, 114, 431–447. [Google Scholar] [CrossRef] - Whittaker, J. Centrifugal and Numerical Modeling of Buried Structures. A Centrifuge Study of the Behavior of Buried Conduits under Airblast Loads; Department of Civil Environmental and Architectural Engineering, University of Colorado Boulder: Boulder, CO, USA, 1987; Volume 3. [Google Scholar]
- Liu, H. Damage of cast-iron subway tunnels under internal explosions. In Geo-Frontiers 2011: Advances in Geotechnical Engineering; American Society of Civil Engineers: Reston, VA, USA, 2011; pp. 1524–1533. [Google Scholar]
- Liu, H. Soil-structure interaction and failure of cast-iron subway tunnels subjected to medium internal blast loading. J. Perform. Constr. Facil.
**2011**, 26, 691–701. [Google Scholar] [CrossRef] - Choi, S.; Wang, J.; Munfakh, G.; Dwyre, E. 3D nonlinear blast model analysis for underground structures. In GeoCongress 2006: Geotechnical Engineering in the Information Technology Age; American Society of Civil Engineers: Reston, VA, USA, 2006; pp. 1–6. [Google Scholar]
- Hu, Q.; Yuan, Y. Numerical Simulation of Internal Blast Effects on a Subway Station, in Computational Structural Engineering; Springer: Berlin/Heidelberg, Germany, 2009; pp. 699–706. [Google Scholar]
- Yu, H.; Wang, Z.; Yuan, Y.; Li, W. Numerical analysis of internal blast effects on underground tunnel in soils. Struct. Infrastruct. Eng.
**2016**, 12, 1090–1105. [Google Scholar] [CrossRef] - Tiwari, R.; Chakraborty, T.; Matsagar, V. Dynamic analysis of a twin tunnel in soil subjected to internal blast loading. Indian Geotech. J.
**2016**, 46, 369–380. [Google Scholar] [CrossRef] - Tiwari, R.; Chakraborty, T.; Matsagar, V. Dynamic analysis of underground tunnels subjected to internal blast loading. In Proceedings of the World Congress of Computational Mechanics (WCCM XI), Barcelona, Spain, 20–25 July 2014. [Google Scholar]
- Tiwari, R.; Chakraborty, T.; Matsagar, V. Dynamic Analysis of Tunnel in Soil Subjected to Internal Blast Loading. Geotech. Geol. Eng.
**2017**, 35, 1491–1512. [Google Scholar] [CrossRef] - Hibbitt, Karlsson, and Sorensen. ABAQUS/Explicit: User’s Manual; Hibbitt, Karlsson and Sorenson Incorporated: Rhode Island, NY, USA, 2001; Volume 1. [Google Scholar]
- Luo, K.-S.; Wang, Y.; Zhao, Y.-T.; Hunag, L.-K. Numerical simulation of section subway tunnel under surface explosion. J. PLA Univ. Sci. Technol.
**2007**, 6, 022. [Google Scholar] - Yang, Y.; Xie, X.; Wang, R. Numerical simulation of dynamic response of operating metro tunnel induced by ground explosion. J. Rock Mech. Geotech. Eng.
**2010**, 2, 373–384. [Google Scholar] - Ls-Dyna, L. Keyword User’s Manual; Livermore Software Technology Corporation: Livermore, CA, USA, 2007. [Google Scholar]
- Mobaraki, B.; Vaghefi, M. Numerical study of the depth and cross-sectional shape of tunnel under surface explosion. Tunn. Undergr. Space Technol.
**2015**, 47, 114–122. [Google Scholar] [CrossRef] - Mussa, M.H.; Mutalib, A.A.; Hamid, R.; Naidu, S.R.; Radzi, N.A.M.; Abedini, M. Assessment of damage to an underground box tunnel by a surface explosion. Tunn. Undergr. Space Technol.
**2017**, 66, 64–76. [Google Scholar] [CrossRef] - Fallah, A.S.; Louca, L. Pressure–impulse diagrams for elastic-plastic-hardening and softening single-degree-of-freedom models subjected to blast loading. Int. J. Impact Eng.
**2007**, 34, 823–842. [Google Scholar] [CrossRef] - Hendron, A. Engineering of Rock Blasting on Civil Projects; Hall, W.J., Ed.; Structural and Geotechnical Mechanics, a Volume Honoring NM Newmark; Prentice-Hall: Englewood Cliffs, NJ, USA, 1977; pp. 242–277. [Google Scholar]
- Kendorski, F.; Jude, C.; Duncan, W. Effect of blasting on shotcrete drift linings. Min. Eng.
**1973**, 25, 38–41. [Google Scholar] - Nakano, K.-I.; Okada, S.; Furukawa, K.; Nakagawa, K. Vibration and cracking of tunnel lining due to adjacent blasting. Doboku Gakkai Ronbunshu
**1993**, 462, 53–62. [Google Scholar] [CrossRef] - Perea, C.; Alcala, J.; Yepes, V.; Gonzalez-Vidosa, F.; Hospitaler, A. Design of reinforced concrete bridge frames by heuristic optimization. Adv. Eng. Softw.
**2008**, 39, 676–688. [Google Scholar] [CrossRef] - Henrych, J.; Major, R. The Dynamics of Explosion and Its Use; Elsevier: Amsterdam, The Netherlands, 1979. [Google Scholar]
- Autodyn, A. Interactive Non-Linear Dynamic Analysis Software, Version 12, User’s Manual; SAS IP Inc.: Cary, NC, USA, 2009. [Google Scholar]
- Wang, Y.; Lee, S. Experimental study of water tank under impulsive loading. Arch. Civ. Mech. Eng.
**2015**, 15, 986–996. [Google Scholar] [CrossRef] - Jiang, N.; Zhou, C. Blasting vibration safety criterion for a tunnel liner structure. Tunn. Undergr. Space Technol.
**2012**, 32, 52–57. [Google Scholar] [CrossRef] - Jendele, L.; Cervenka, J.; Saouma, V.; Pukl, R. On the choice between discrete or smeared approach in practical structural FE analyses of concrete structures. In Proceedings of the Fourth International Conference on Analysis of Discontinuous Deformation Glasgow, Scotland, UK, 6–8 June 2001. [Google Scholar]
- Mohamed, H.; Mussa, A.A.M. Roszilah Hamid, and Sudharshan N. Raman, Dynamic Properties of High Volume Fly Ash Nanosilica (HVFANS) Concrete Subjected to Combined Effect of High Strain Rate and Temperature. Latin Am. J. Solids Struct.
**2018**, 15. [Google Scholar] [CrossRef] - Malvar, L.J.; Crawford, J.E. Dynamic increase factors for steel reinforcing bar. In Proceedings of the 28th DDESB Seminar, Orlando, FL, USA, August 1998. [Google Scholar]
- Krieg, R.D. A Simple Constitutive Description for Cellular Concrete; Sandia National Laboratories: Albuquerque, NM, USA, 1972. [Google Scholar]
- Foster, W.A., Jr.; Johnson, C.E.; Chiroux, R.C.; Way, T.R. Finite element simulation of cone penetration. Appl. Math. Comput.
**2005**, 162, 735–749. [Google Scholar] [CrossRef] - Yu, H.; Yuan, Y.; Yu, G.; Liu, X. Evaluation of influence of vibrations generated by blasting construction on an existing tunnel in soft soils. Tunn. Undergr. Space Technol.
**2014**, 43, 59–66. [Google Scholar] [CrossRef] - Bailey, A.C.; Johnson, C.E. A soil compaction model for cylindrical stress states. Trans. ASAE
**1989**, 32, 822–825. [Google Scholar] [CrossRef] - Kulak, R.F.; Bojanowski, C. Modeling of cone penetration test using SPH and MM-ALE approaches. In Proceedings of the 8th European LS-DYNA Users Conference, Strasbourg, France, 23–24 May 2011. [Google Scholar]
- Shin, J.-H.; Moon, H.-G.; Chae, S.-E. Effect of blast-induced vibration on existing tunnels in soft rocks. Tunn. Undergr. Space Technol.
**2011**, 26, 51–61. [Google Scholar] [CrossRef] - Cheng, D.; Hung, C.; Pi, S. Numerical simulation of near-field explosion. J. Appl. Sci. Eng.
**2013**, 16, 61–67. [Google Scholar] - Xie, L.; Lu, W.B.; Zhang, Q.B.; Jiang, Q.H.; Wang, G.H.; Zhao, J. Damage evolution mechanisms of rock in deep tunnels induced by cut blasting. Tunn. Undergr. Space Technol.
**2016**, 58, 257–270. [Google Scholar] [CrossRef] - Li, D.; Zheng, Z.L.; Liu, C.Y.; Zhang, G.-X.; Lian, Y.; Tian, Y.; Xiao, Y.; Xie, X. Dynamic response of rectangular prestressed membrane subjected to uniform impact load. Arch. Civ. Mech. Eng.
**2017**, 17, 586–598. [Google Scholar] [CrossRef] - Hallquist, J.O. LS-DYNA theory manual. Livermore Softw. Technol. Corp.
**2006**, 3, 25–31. [Google Scholar] - Alia, A.; Souli, M. High explosive simulation using multi-material formulations. Appl. Ther. Eng.
**2006**, 26, 1032–1042. [Google Scholar] [CrossRef] - US Army Engineers Waterways Experimental Station. Fundamentals of Protective Design for Conventional Weapons; TM5-855-1; US Army Engineers Waterways Experimental Station: Vicksburg, MS, USA, 1986. [Google Scholar]
- Mussa, M.H.; Mutalib, A.A. Numerical analysis of underground tunnels induced by ground truck explosion. In Proceedings of the CAASR International Conference on Innovative Engineering and Technologies & Advanced Theoretical Computer Applications, Bangkok, Thailand, 27–28 November 2015. [Google Scholar]
- Tabatabaei, Z.S.; Volz, J.S. A comparison between three different blast methods in LS-DYNA: LBE, MM-ALE, Coupling of LBE and MM-ALE. In Proceedings of the 12th International LS-DYNA Users Conference, Dearborn, MI, USA, 5–7 June 2012. [Google Scholar]
- Mutalib, A.A.; Bakhary, N. Empirical Formulae to Predict Pressure and Impulsive Asymptotes for P–I Diagrams of RC Columns Strengthened with FRP. J. Teknol.
**2011**, 55, 27–38. [Google Scholar] [CrossRef] - Vaughn, N.; Polnaszek, C. Design-Expert
^{®}Software; Stat-Ease, Inc.: Minneapolis, MN, USA, 2007. [Google Scholar] - Joglekar, A.; May, A. Product excellence through design of experiments. Cereal Foods World
**1987**, 32, 857–868. [Google Scholar] - Noordin, M.Y.; Venkatesh, V.C.; Sharif, S.; Elting, S.; Abdullah, A. Application of response surface methodology in describing the performance of coated carbide tools when turning AISI 1045 steel. J. Mater. Process. Technol.
**2004**, 145, 46–58. [Google Scholar] [CrossRef] [Green Version] - Montgomery, D.C. Design and Analysis of Experiments 6th Edition with Design Expert Software; John Wiley & Sons: New York, NY, USA, 2004. [Google Scholar]

**Figure 2.**Full range of dynamic increase factor (DIF) at different strain rates for (

**a**) concrete, and (

**b**) steel.

**Figure 6.**Convergence study of tunnel response with a lining thickness of 250 mm by using mesh sizes of (

**a**) 125 mm, and (

**b**) 250 mm.

**Figure 8.**Propagation and pressure contours of blast waves inside the soil: (

**a**) before tunnel insertion; (

**b**) after tunnel insertion; and, (

**c**) the formation of a crater.

**Figure 10.**Time histories of vertical velocity and reflected pressure for the tunnel roof centre at a burial depth of (

**a**) 4 m, and (

**b**) 6 m.

**Figure 11.**Time history of lateral displacement for tunnel roof centre at burial depth of (

**a**) 4 m, and (

**b**) 6 m.

**Figure 12.**Failure modes of the tunnel roof centre at a depth of 6 m during a container explosion with lining thickness of (

**a**) 250 mm, (

**b**) 500 mm.

Damage Level | Peak Particle Velocity (m/s) |
---|---|

Safe | 0–0.9 |

Intermittent failure (IF) | 0.9–1.8 |

Local failure (LF) | 4 |

General failure (GF) | 12 |

Tight Closure (TC) | NA |

Damage Level | Lateral Displacement (mm) |
---|---|

Safe | y_{c} < 20 |

Medium damage (MD) | 20 < y_{c} < 40 |

High damage (HD) | 40 < y_{c} < 80 |

Collapse (C) | y_{c} > 80 |

C_{0} | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | $\mathsf{\rho}$ (kg/m^{3}) | ${\mathbf{E}}_{0}$ (MPa) | ${\mathbf{V}}_{0}$ |
---|---|---|---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 0.4 | 0.4 | 0 | 1.29 | 0.25 | 1 |

$\mathsf{\rho}$ (kg/m^{3}) | ${\mathbf{f}}_{\mathbf{c}}$ (MPa) | P_{r} | E_{r} (MPa) | PE_{r} (%) | PR_{r} | ${\mathbf{f}}_{\mathbf{y}}$ (MPa) |
---|---|---|---|---|---|---|

2430 | 61.18 | 0.19 | 200,000 | 0.45 | 0.3 | 500 |

$\mathsf{\rho}$ (kg/m^{3}) | G (MPa) | K_{u} (MPa) | a_{0} | a_{1} | a_{2} | P_{cut} (MPa) |
---|---|---|---|---|---|---|

1255 | 1.7240 | 5.5160 | 0 | 0 | 0.8702 | 0 |

True Volumetric Strain | 0.05 | 0.1 | 0.15 | 0.2 | 0.25 | 0.3 | 0.33 |

Pressure (MPa) | 0.02 | 0.05 | 0.07 | 0.12 | 0.2 | 0.34 | 0.5 |

$\mathsf{\rho}$ (kg/m^{3}) | υ_{D} (m/s) | P_{cut} (MPa) | A (MPa) | B (MPa) | R_{1} | R_{2} | ω | ${\mathbf{V}}_{0}$ | ${\mathbf{E}}_{0}$ (MPa) |
---|---|---|---|---|---|---|---|---|---|

1630 | 6930 | 2.1 × 10^{4} | 3.738 × 10^{5} | 3.747 × 10^{3} | 4.15 | 0.9 | 0.35 | 1 | 6000 |

**Table 8.**Comparison of TM5 and numerical peak pressures at different depths into soil during a container truck explosion.

Depth (m) | Peak Pressure (MPa) | Differences (%) | |
---|---|---|---|

TM5 | Numerical Results | ||

1 | 178.78 | 183.6 | 2.70 |

2 | 26.58 | 31.55 | 18.70 |

3 | 8.71 | 7.78 | 11.95 |

4 | 3.95 | 3.99 | 1.01 |

5 | 2.14 | 2.52 | 17.76 |

6 | 1.30 | 1.52 | 16.92 |

7 | 0.85 | 0.93 | 9.41 |

8 | 0.59 | 0.42 | 40.48 |

9 | 0.42 | 0.27 | 55.55 |

10 | 0.32 | 0.20 | 60 |

**Table 10.**Velocity and displacement values of a tunnel roof centre at different explosive charge weights, lining thicknesses, and burial depths.

Depth (m) | Thickness (mm) | Velocity (mm/ms) | Displacement (mm) | ||||||
---|---|---|---|---|---|---|---|---|---|

Sedan | Van | SDT | Container | Sedan | Van | SDT | Container | ||

4 | 250 | 0.050 | 0.333 | 1.522 | 5.634 | 12.788 | 29.27 | 69.928 | 352.18 |

500 | 0.068 | 0.250 | 1.105 | 3.205 | 0.513 | 1.927 | 7.867 | 56.016 | |

750 | 0.053 | 0.265 | 0.955 | 3.010 | 0.433 | 1.657 | 6.311 | 27.540 | |

6 | 250 | 0.012 | 0.046 | 0.263 | 1.688 | 6.459 | 18.124 | 32.365 | 122.290 |

500 | 0.047 | 0.208 | 0.208 | 0.931 | 0.177 | 1.674 | 1.674 | 10.320 | |

750 | 0.021 | 0.067 | 0.232 | 1.081 | 0.153 | 0.487 | 1.440 | 7.862 | |

8 | 250 | 0.003 | 0.016 | 0.058 | 0.433 | 4.222 | 10.963 | 22.154 | 58.725 |

500 | 0.035 | 0.046 | 0.083 | 0.552 | 0.092 | 0.268 | 0.713 | 3.028 | |

750 | 0.028 | 0.059 | 0.059 | 0.500 | 0.079 | 0.617 | 0.617 | 2.624 |

Depth (m) | Thickness (mm) | PPV Method | SDOF Method | ||||||
---|---|---|---|---|---|---|---|---|---|

Sedan | Van | SDT | Container | Sedan | Van | SDT | Container | ||

4 | 250 | Safe | Safe | IF | GF | Safe | MD | HD | C |

500 | Safe | Safe | IF | LF | Safe | Safe | Safe | HD | |

750 | Safe | Safe | IF | LF | Safe | Safe | Safe | MD | |

6 | 250 | Safe | Safe | Safe | IF | Safe | Safe | MD | C |

500 | Safe | Safe | Safe | IF | Safe | Safe | Safe | Safe | |

750 | Safe | Safe | Safe | IF | Safe | Safe | Safe | Safe | |

8 | 250 | Safe | Safe | Safe | Safe | Safe | Safe | MD | HD |

500 | Safe | Safe | Safe | Safe | Safe | Safe | Safe | Safe | |

750 | Safe | Safe | Safe | Safe | Safe | Safe | Safe | Safe |

Lining Thickness (mm) | Safe | Intermittent Failure (IF) | Local Failure (LF) | General Failure (GF) |
---|---|---|---|---|

250 | >0.058 | >0.433 | >1.688 | ≤1.688 |

500 | >1.105 | >3.205 | ≤3.205 | NA |

750 | >3.010 | ≤3.010 | NA | NA |

Depth (m) | Thickness (mm) | Damage Level | |||
---|---|---|---|---|---|

Sedan | Van | SDT | Container | ||

4 | 250 | Safe | IF | LF | GF |

500 | Safe | Safe | Safe | LF | |

750 | Safe | Safe | Safe | IF | |

6 | 250 | Safe | Safe | IF | GF |

500 | Safe | Safe | Safe | Safe | |

750 | Safe | Safe | Safe | Safe | |

8 | 250 | Safe | Safe | IF | LF |

500 | Safe | Safe | Safe | Safe | |

750 | Safe | Safe | Safe | Safe |

Model | R^{2} | Adjusted R^{2} | Predicted R^{2} | Adequate Precision (AP) |
---|---|---|---|---|

Quadratic | 0.8213 | 0.7595 | 0.5998 | 16.2171 |

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## Share and Cite

**MDPI and ACS Style**

Mussa, M.H.; Mutalib, A.A.; Hamid, R.; Raman, S.N.
Blast Damage Assessment of Symmetrical Box-Shaped Underground Tunnel According to Peak Particle Velocity (PPV) and Single Degree of Freedom (SDOF) Criteria. *Symmetry* **2018**, *10*, 158.
https://doi.org/10.3390/sym10050158

**AMA Style**

Mussa MH, Mutalib AA, Hamid R, Raman SN.
Blast Damage Assessment of Symmetrical Box-Shaped Underground Tunnel According to Peak Particle Velocity (PPV) and Single Degree of Freedom (SDOF) Criteria. *Symmetry*. 2018; 10(5):158.
https://doi.org/10.3390/sym10050158

**Chicago/Turabian Style**

Mussa, Mohamed H., Azrul A. Mutalib, Roszilah Hamid, and Sudharshan N. Raman.
2018. "Blast Damage Assessment of Symmetrical Box-Shaped Underground Tunnel According to Peak Particle Velocity (PPV) and Single Degree of Freedom (SDOF) Criteria" *Symmetry* 10, no. 5: 158.
https://doi.org/10.3390/sym10050158