koneshwaran, sivalingam, thambiratnam, david p., & gallage ... · the 14th international...

13
This may be the author’s version of a work that was submitted/accepted for publication in the following source: Koneshwaran, Sivalingam, Thambiratnam, David,& Gallage, Chaminda (2013) Response of a buried tunnel to surface blast using different numerical tech- niques. In Ivanyi, P & Topping, B (Eds.) Proceedings of the Fourteenth Inter- national Conference on Civil, Structural and Environmental Engineering Computing. Civil-Comp Press, United Kingdom, pp. 1-12. This file was downloaded from: https://eprints.qut.edu.au/66699/ c Consult author(s) regarding copyright matters This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the docu- ment is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recog- nise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to [email protected] Notice: Please note that this document may not be the Version of Record (i.e. published version) of the work. Author manuscript versions (as Sub- mitted for peer review or as Accepted for publication after peer review) can be identified by an absence of publisher branding and/or typeset appear- ance. If there is any doubt, please refer to the published source. https://doi.org/10.4203/ccp.102.142

Upload: others

Post on 13-Aug-2020

3 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

This may be the author’s version of a work that was submitted/acceptedfor publication in the following source:

Koneshwaran, Sivalingam, Thambiratnam, David, & Gallage, Chaminda(2013)Response of a buried tunnel to surface blast using different numerical tech-niques.In Ivanyi, P & Topping, B (Eds.) Proceedings of the Fourteenth Inter-national Conference on Civil, Structural and Environmental EngineeringComputing.Civil-Comp Press, United Kingdom, pp. 1-12.

This file was downloaded from: https://eprints.qut.edu.au/66699/

c© Consult author(s) regarding copyright matters

This work is covered by copyright. Unless the document is being made available under aCreative Commons Licence, you must assume that re-use is limited to personal use andthat permission from the copyright owner must be obtained for all other uses. If the docu-ment is available under a Creative Commons License (or other specified license) then referto the Licence for details of permitted re-use. It is a condition of access that users recog-nise and abide by the legal requirements associated with these rights. If you believe thatthis work infringes copyright please provide details by email to [email protected]

Notice: Please note that this document may not be the Version of Record(i.e. published version) of the work. Author manuscript versions (as Sub-mitted for peer review or as Accepted for publication after peer review) canbe identified by an absence of publisher branding and/or typeset appear-ance. If there is any doubt, please refer to the published source.

https://doi.org/10.4203/ccp.102.142

Page 2: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

Response of Buried Tunnel to SurfaceBlast using Different Numerical

Techniques

Abstract

This paper presents a comparative study on the response of a buried tunnel to sur-face blast using the Arbitrary Lagrangian-Eulerian (ALE) and Smooth Particle Hy-drodynamics (SPH) techniques. Since explosive tests with real physical models areextremely risky and expensive, the results of a centrifuge test were used to validate thenumerical techniques. Numerical study shows that the ALE predictions were fasterand closer to the experimental results than those from the SPH simulations whichover predicted the strains. The findings of this research demonstrate the superiority ofthe ALE modelling techniques for the present study. They also provide a comprehen-sive understanding of the preferred ALE modelling techniques which can be used toinvestigate the surface blast response of underground tunnels.

Keywords: Explosion, tunnel, dry soil, centrifuge test, numerical modelling, strain

1 Introduction

Underground transit tunnels play an important role in addressing transportation needsin many cities, making it crucial to consider effective mitigation strategies to protectthese underground facilities against potential terrorist attacks. Therefore, the transittunnels must be designed to withstand a ground shock transmitted from a credibleexplosion. Explosive tests with real physical models are extremely risky and expensiveto investigate the tunnel response and hence the possible alternative is to use numericalmodelling techniques. These techniques have the capability to simulate the sequencesof phases, such as explosion, crater formation, ground shock, and tunnel response.The simulations also provide valuable data in a timely and cost effective manner toenable the development of design tools as well as retrofit measures, if necessary.

There are many Finite Element Methods (FEMs) available in computer hydro-codes, but selection of the appropriate numerical technique is dependent on the typeof problem and its computational cost. Deformation problems are best solved withan advanced general-purpose multi-physics simulation software LS-DYNA [1] whichoffers different numerical techniques such as Lagrangian, Eulerian, ArbitraryLagrang

1

Page 3: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

ian-Eulerian (ALE) and Smooth Particle Hydrodynamics (SPH). This paper uses ALEand SPH numerical techniques to investigate the large deformation due to an explo-sion on the ground surface and the subsequence tunnel response, and compare themodelling aspects and computational efficiencies of the two techniques.

Results from both numerical simulations are compared with the experimental re-sults reported by Anirban De [2, 3] to validate these modelling techniques.

2 Problem description

In geotechnical investigation, centrifuge testing uses small-scale physical model tosimulate the physical behaviour of large-scale prototype model under different load-ing conditions. Anirban De [2, 3] conducted a centrifuge testing to investigate theperformance of a buried copper tunnel subjected to surface explosion. He used a 70 gcentrifuge testing machine, where g is the gravitational acceleration. A scaled-downmodel was prepared by burying a copper tunnel in dry Nevada sand (a relative density(Dr) =60%) to simulate a depth of 3.6 m in the prototype scale. A spherical shapeexplosive was symmetrically placed above the mid-span, directly over the centerlineof the copper tunnel, such that the ground surface was tangent to the spherical surfaceof the explosive.

Centrifuge scaling laws [4] explain how a physical model and its dynamic eventsare correlated in the centrifuge test, in which the scaled-down model is sufficientlyraised to N times the gravitational acceleration. The centrifuge scaling laws allowto convert the scaled model dimension to the prototype model dimension as shownin Table 1. This paper uses the problem and experimental results to validate bothnumerical techniques.

Parameter Scaled model dimension Prototype model dimensionin a centrifuge test for numerical simulation

Copper tunnel diameter 76 mm 5.32 mCopper tunnel thickness 2.5 mm 175 mmExplosive weigh of TNT 2.6 g 892 kg

Table 1: Conversion to prototype model

3 Material constitutive models

This simulation includes the following material models in LS-DYNA for modellingair, explosive, soil and tunnel (copper);

2

Page 4: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

3.1 Air

The air is modelled as an ideal gas [1] using ’*MAT NULL’ material model with thelinear polynomial Equation of State (EOS). The pressure is expressed by;

P = C0 + C1µ+ C2µ2 + C3µ

3 +(C4 + C5µ+ C6µ

2)E0 (1)

where E0 is the initial internal energy per initial volume, C0, C1, C2, C3, C4, C5, andC6 are constant, and µ = ρ

ρ0− 1. where ρ

ρ0is the ratio of current density to initial

density.The linear polynomial equation represents an ideal gas with the gamma law EOS,

in which C0 = C1 = C2 = C3 = C6 = 0 and C4 = C5 = γ − 1.where γ is the ratio of specific heat at constant pressure per specified heat at con-

stant volume. The pressure is then denoted by;

P =(γ − 1

) ρρ0E0 (2)

where γ is an adiabatic constant for air behaving as an ideal gas (estimated value forγ = 1.4), ρ=1.29kg/m3 is the density and the initial internal energy per unit volume,E0, is estimated as 0.25MPa [5].

3.2 Explosive

The Jone-Wilkin-Lee’s EOS is used to describe the explosive as it is the most popularand easiest to calibrate. The Jone-Wilkin-Lee’s EOS defines pressure as;

P = A

(1− ω

R1V

)e−R1V +B

(1− ω

R2V

)e−R2V +

ωE

V(3)

where V is the relative volume or the expansion of explosive, E is the initial energyper volume, othersA,B,R1,R2, ω are empirically derived constants for the explosive.Table 2 shows the material parameters used for TNT (Trinitrotoluene) explosive.

ρ vD PCJ A B R1 R2 ω V E0

(g/cm3) (ms−1) (GPa) (GPa) (GPa) (kJ/m3)

1.63 6930 21 373.77 3.747 4.15 0.90 0.35 1 6.0E+006

Table 2: Material parameters for TNT explosive [6]

3

Page 5: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

3.3 Soil

This research investigates an appropriate soil model that incorporates the various soilcompositions, in particular, moisture content. By evaluating several material modelsin LS-DYNA, *MAT FHWA SOIL model was identified as a suitable soil model thatincludes strain softening, kinematic hardening, strain rate effects, element deletion,excess pore water effects and stability with no soil confinement [7, 8]. This materialmodel requires the main parameters of mass density, specific gravity, bulk modulus,shear modulus and moisture content. These soil parameters are generally determinedthrough laboratory tests. Parameters required for defining strain softening, kinematichardening, strain rate effects and pore water effects can be evaluated through labora-tory tests and/or equations in the material manual [7].

At the outset of the Civil and Mechanical Systems Program of the National Sci-ence Foundation (NSF), Nevada sand (a relative density (Dr) of 60%) was used forcentrifuge tests by Anirban De [2]. In 1992, Arulmoli et al. [9] conducted an exten-sive laboratory test for the Nevada sand with different Dr values including: 40% and60% in the VELACS (Verification of Liquefaction Analyses by Centrifuge Studies)Program.

The Cyclic Triaxial Test data for dry Nevada sand at Dr =60% [9] reported themain soil parameters such as mass density and specific gravity as 1.6g/cm3 and 2.67respectively. Based on the initial void ratio, porosity of the sand was derived as 0.4.Anriban De [2] presented data for density (ρ) versus sound speed (c) and this was usedfor back-calculation of shear modulus (G) as 56.0 MPa. The Bulk modules (K) wasderived as 146.0 MPa from Poisson’s ratio of the Nevada sand (υ) = 0.33 [2].

3.4 Copper (tunnel material)

The copper tunnel is modelled using *MAT PLASTICIY KINEMATIC material modelwhich incorporates both non-linear material behaviour and high strain rate effects dueto the ground shock. Material parameters for copper [10, 11] are described in Table 3.The main parameters include mass density (ρ), Young’s modules (E), Poisson’s ratio(υ), yield stress (σy), tangent modules (Etan), hardening parameter (β) and strain rateparameters (C) & (P ) for Cowper Symonds strain rate model.

ρ E υ σy Etan β C P(g/cm3) (GPa) (MPa) (MPa) (s−1)

8.93 117 0.35 400 100 1.0 1.346e+6 5.286

Table 3: Material parameters for copper

4

Page 6: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

4 Numerical models

4.1 ALE simulation

Symmetric modelling capabilities are important to reduce computation costs by con-sidering a quarter symmetry-geometrical numerical model. The Anirban De [2, 3]test was first simulated with ALE capabilities in LS-DYNA. A numerical model forthe simulation is shown in Fig 1(a) and model was used to represent the Lagrangianstructure composed of two major parts of the copper tunnel and soil.

16.00 m20.00 m

15.0

0 m

3.60

m

R=2.66 m

X

Z

Y

SOILSOIL

TUNNEL (Copper)

(a) A quarter symmetrical model (Lagrangianstructure)

SOILSOIL

ALE (Background mesh)

TUNNEL (Copper)

EXPLOSIVE (ALE)

(b) Coupling with ALE background mesh

Figure 1: ALE simulation

The eight-node solid elements are used with different spatial discretisation solvers.Lagrangian meshes model the soil and copper tunnel while ALE meshes (backgroundmesh) are used separately to model the surrounding air and explosive. A mesh consis-tency condition is achieved through a series of cases with different meshes to capturethe analytical solution in the limit of a mesh refinement process. The Lagrangianstructure uses smaller elements in the region adjacent to the explosive as well as forthe structure, while larger size elements are used for the far field region.

The spherical shape explosive is defined into the background mesh using *INITIALVOLUME FRACTION GEOMETRY, by specifying its radius and detonation point.

The contact interface between the soil and copper tunnel is defined using *CON-TACT AUTOMATIC SURFACE TO SURFACE. The translational displacements ofsymmetry boundariesXZ and Y Z plans are constrained in the normal direction whilethe non-reflecting boundary condition is applied to the other two lateral planes and thebase is fixed in all directions to represent the bed rock.

Minimising the computational cost is essential in the numerical modelling tech-

5

Page 7: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

nique which relates to a time-ordered sequence of interrelated phases describing theentire simulation. As such, LS-DYNA’s restart feature enables breaking the entire sim-ulation into three stages such as stress initialisation, ALE/Lagrangian coupling, anddeletion of ALE background mesh. The stress initialisation phase sees the simula-tion using a time-dependent mass damping option *DAMPING GLOBAL to imposenear-critical damping until the preload is established in the model, as illustrated in Fig1(a).

Fig 1(b) describes the background mesh insertion into the preloaded Lagrangianmodel with ALE/Lagrangian coupling using *CONSTRAINED LAGRANGE IN SOLID. ALE/Lagrangian coupling phase is more expensive than the other two phases asit deals with Fluid Structure Interaction (FSI) which is complex to solve analytically.However, the duration for the blast load transfer from ALE domain to Lagrangianparts is considerably small, as is evident from Fig 2. It can be observed from the KEvs. time plot that the KE of ALE background mesh is sufficiently reduced to zero inabout 180 ms.

020406080

100120140160180200

1000 1050 1100 1150 1200

KE

(MJ)

Time (ms)

KE of ALE baground mesh

Figure 2: KE vs. Time plot of ALE baground mesh

The restart features of *DELETE PART and *DELETE FSI allow the removalof the redundant ALE background mesh and ALE/Lagrangian coupling respectively.Deletion of these redundant elements significantly reduces the computational time.The simulation continues with the remaining lagrangian structure until the coppertunnel response comes to rest.

4.2 SPH simulation

The Anirban De [2, 3] test was further simulated using SPH simulations. The part ofthe soil experiencing large deformations and the explosive were modelled with SPHparticles while the rest of the model was based on the Lagrange FEM elements. Thenear field soil domain dimension was effectively evaluated as a ”3.50m x 3.50m x2.76m” box filled with SPH particles, as shown in Fig 3(a). The SPH particles were10mm in diameter for both the soil and explosive. The surrounding outside space ofthe explosive is assumed to be a vacuum which ignores the later interaction process

6

Page 8: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

between the explosion-produced gas and surrounding air. The coupling interactionbetween the SPH and Lagrange FEM is formed by the penalty based contact *CONTACT AUTOMATIC SURFACE TO SURFACE. Though the boundary conditionswere identical to the ALE model, a special symmetry boundary *BOUNDARY SPHSYMMETRY PLANE was applied to those SPH particles.

The same dimensions and material parameters as those used in ALE simulation areused in this simulation, as shown in Fig 3(a).

SOILSOIL

TUNNEL (Copper)

SOILSOIL (SPH)

3.50 m 3.50 m

2.76

m

(a) A quarter symmetrical model (with Soil(SPH))

SOILSOIL

TUNNEL (Copper)

SOILSOIL (SPH) SOILEXPLOSIVE (SPH)

(b) Insertion of explosive (SPH)

Figure 3: SPH simulation

The simulation considers the two stages of initialisation and blast analysis. A modelas shown in Fig 3(a) is used for stress initialisation with a time-dependent mass damp-ing. After initialisation, Fig 3(b) illustrates the insertion of explosive SPH particlesinto the preloaded model.

5 Results and discussion

This section compares the numerical results with a known experiment, as illustratedin Section 2. Before performing the transient (blast) analysis, the stress initialisationphase brought both numerical models to a steady-state preload in 1000 ms. The blastload was applied to both models by detonating the explosive at 1000 ms.

5.1 Shock wave propagation

Blast-induced ground shock from the surface explosion travels in the soil in the formof hemispherical waves as shown in Fig 4. Both simulations show that the area ofwave front expands with the wave propagation which reached the tunnel surface after7 ms of explosion.

7

Page 9: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

(a) Shockwave propagation in ALE simulation (b) Shockwave propagation in SPH simulation

Figure 4: Shockwave propagation through soil

5.2 Tunnel response

The stabilised tunnel started to respond dynamically when the shock wave reached thetunnel upper surface. Fig 5 illustrates the shock wave propagation sequence throughthe tunnel during the ALE simulation. Fig 5(a) demonstrates that the tunnel responsecommenced at t = 1007 ms and that the shock wave propagation in the longitudinaldirection is faster than the circumferential direction while positive and negative phasesof stress contours change with time.

(a) t =1007ms (b) t =1009ms (c) t =1014ms

(d) t =1019ms (e) t =1024ms (f) t =1029ms

Figure 5: Pressure contours on the tunnel (ALE simulation)

Fig 6(a) illustrates the four measuring points in a half-symmetrical prototype modelabout the mid-span [3] which validate the tunnel response. In the centrifuge test,measuring points AS1 and AS2 were introduced along the surface of tunnel crownto record the axial strains while measuring points CS1 and CS2 on either side of thespringline at mid-span recorded the circumferential strains. Three gauge points wereonly considered in the numerical model by considering the symmetry, as shown inFig 6(b). The circumferential strain at Gauge 3 simulated the experimental results atcorresponding points CS1 and CS2.

Fig 7 shows the comparison of axial and circumferential strain history during bothALE and SPH simulations at two locations. Fig 7(a) highlights that peak axial strain in

8

Page 10: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

10.6 m

SpringlineCS2

CS1

AS1AS2

(a) A half-symmetrical prototype model

10.6 m

Springline

Gauge 1Gauge 2

Gauge 3

(b) A quater-symmetrical numerical model

Figure 6: Arrangement of measuring points

the SPH simulation is about 7 per cent more than the ALE simulation. Both readingsshows a noticeable fluctuation in strain after 1075 ms. Although the observation issimilar during the positive phase of the circumferential strain at Gauge 3, as illustratedin Fig 7(b), the peak circumferential strain at the positive phase is about 7 per cent lessthan in the ALE simulation.

-1800

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

200

1000 1050 1100 1150

Mic

rost

rain

Time (ms)

Axial strain at Gauge 1 (ALE)

Axial strain at Gauge 1 (SPH)

(a) Axial strains at Gauge 1

-1600

-1200

-800

-400

0

400

800

1200

1000 1050 1100 1150

Mir

cost

rain

Time (ms)

Circumferential strain at Gauge 3 (ALE)

Circumferential strain at Gauge 3 (SPH)

(b) Circumferential strains at Gauge 3

Figure 7: Comparison of axial and circumferential strains

Fig 8 compares the strain history of Gauge 2 with a known experimental result ofthe centrifuge test [2]. The ALE predictions are much closer than the SPH simulationwhich conservatively over predicted the strains. This could be due to the assumption inthe SPH simulation that the surrounding of the explosive SPH particles was consideredto be a vacuum. This assumption ignored the importance of SPH explosive particlesinteraction with the air. Therefore, energy imparted from the explosive into the soil inSPH simulation was significantly larger than the ALE simulation.

Fig 9 compares the magnitudes of peak axial and circumferential strains at Gauge 1and Gauge 3 respectively with respect to the equivalent scaled distance of R/W 1/3 tothe explosive. Results for these strains obtained from both ALE and SPH simulationsare compared with those from the centrifuge test [2]. In Fig 9(a), there is a discrepancyin the peak axial strain between the centrifuge test and the numerical simulations.It was also observed in the numerical simulations in [2] which could be due to anexperimental limitation, that is, the movement of the copper pipe may be influencedby its two end conditions. A real tunnel in an infinite soil medium has no movement

9

Page 11: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

-750

-500

-250

0

250

500

750

1000 1050 1100 1150M

icro

stra

in

Time elapsed (ms)

Axial strain at AS2 (Centrifuge)Axial strain at Gauge 2 (ALE)Axial strain at Gauge 2 (SPH)

Figure 8: Comparison of axial strain between numerical and centrifuge test

restrictions, but the experimental model had restrictions from all directions in the boxcontaining the soil. These constrained boundaries may have restricted the motion ofsoil structure interaction.

500

750

1000

1250

1500

1750

2000

2250

0.325 0.375 0.425 0.475 0.525 0.575 0.625

Peak

mir

cost

rain

Scaled distance (m/kg1/3)

Axial strain at AS1 (Centrifuge)Axial strain at Guage 1 (ALE)Axial strain at Guage 1 (SPH)

AS1

(a) Comparison of peak axial strains

500

750

1000

1250

1500

1750

2000

0.64 0.69 0.74 0.79 0.84 0.89 0.94 0.99 1.04 1.09 1.14

Peak

mir

cost

rain

Scaled distance (m/kg1/3)

Circumferential strain at CS1 & CS2 (Centrifuge)Circumferential strain at Gauge 3 (ALE)Circumferential strain at Gauge 3 (SPH)

CS1

CS2

(b) Comparison of peak circumferential strains

Figure 9: Comparison of peak axial and circumferential strains

The circumferential strains at Gauge 3 obtained from the numerical simulationswere compared with the experimental results, as illustrated in Fig 9(b). The compar-isons show that the numerical best-fit line is close to the experimental value at CS2,but there is some discrepancy with the value at CS1. In addition to the above men-tioned reasons of boundaries, this discrepancy may also result from the displacementof the explosive from its initial orientation during the experiment which is very diffi-cult, particularly, in the centrifuge test. Also the gauge showing the smaller readingmay not have been firmly fixed to the pipe surface, causing further discrepancy in theresults. In all cases, SPH simulation results are comparatively more than the ALE witha variation from 5 % to 7 %.

5.3 Comparison of computational efficiency

Computer simulations were conducted using ten parallel processors in two stages ofstress initialisation and blast analysis. Table 4 shows the comparison of quantity and

10

Page 12: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

computational time for those models. In the stress initialisation, the ALE simulationwas much faster than the SPH simulations as the ALE simulation dealt with onlyLagrangian elements. The CPU time required for the SPH simulation of the blastanalysis is 2.5 times more than the ALE simulation. Over all, the ALE simulation isfaster than the SPH simulation for surface explosion.

ALE simulation SPH simulationInitialisation Blast analysis Initialisation Blast analysis

No. of finite elements 135464 320936 131844 131844No. of SPH particles - - 36288 36426Duration simulation (ms) 1000 180 1000 180Timestep (µs) 1.06E+01 5.91E+00 1.06E+01 5.91E+00Total CPU time 5:26:37 55:39:52 103:06:20 140:25:01

Table 4: Comparison of computational efficiency

6 Conclusion

Two numerical modelling techniques of ALE and SPH have been presented in thispaper for simulating the buried tunnel response due to surface explosion using anadvanced general-purpose commercial software LS-DYNA. Both simulations showthat axial and circumferential deformations of the tunnel decrease with the increasein distance from the explosive. The ALE simulation was the faster and reasonablyclose to reported strain measurements from the centrifuge test, compared to the SPHsimulation which conservatively over predicted the strains. Though the SPH methodhas some favourable features, the CPU time required for the simulation and the overprediction of results, makes this approach less attractive for treating surface explosionproblems.

The ALE fluid structure interaction technique however, will not be able to handleproblems in which the explosive is buried in the soil. The SPH simulation on the otherhand, can treat problems regard less of the explosive location and orientation.

References[1] LSTC., Ls-dyna keyword user’s manual v971, livermore software

technology corporation(lstc), California, USA.[2] A. De, Numerical simulation of surface explosions over dry, cohe-

sionless soil, Computers and Geotechnics 43 (0) (2012) 72–79.[3] M. Anirban De, F. Thomas F. Zimmie, Modeling of surface blast

effects on underground structures.

11

Page 13: Koneshwaran, Sivalingam, Thambiratnam, David P., & Gallage ... · the 14th International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press

[4] Kramer, Geotechnical Earthquake Engineering, Pearson Education,1996.

[5] R. W. Yubing Yang, Xiongyao Xie, Numerical simulation of dy-namic response of operating metro tunnel induced by ground ex-plosion, Journal of Rock Mechanics and Geotechnical Engineering(2010) 373–384.

[6] Z. Wang, Y. Lu, H. Hao, K. Chong, A full coupled numerical analysisapproach for buried structures subjected to subsurface blast, Com-puters & Structures 83 (4-5) (2005) 339–356.

[7] B. A. Lewis, Manual for LS-DYNA Soil Material Model 147,Federal Highway Administration, McLEAN, VA, publication No.FHWA-HRT-095 (2004).

[8] M. Saleh, L. Edwards, Application of a soil model in the numericalanalysis of landmine interaction with protective structures., in: 26thInternational symposium on blastics MIAMI, FL, September 12-16,2011.

[9] K. Arulmoli, K. Muraleetharan, M. Hossain, Velacs verification ofliquefaction analyses by centrifuge studies laboratory testing pro-gram soil data report, Tech. rep., The Earth Technology Corp.,Project No.90-0562,Irvine, California (March 1992).

[10] D. Matuska, Hull users’ manual, Tech. rep., DTIC Document (1984).[11] M. Peroni, L. Peroni, A. Dallocchio, Thermo-mechanical model

identification of a strengthened copper with an inverse method, in:DYMAT 2009-9th International Conference on the Mechanical andPhysical Behaviour of Materials under Dynamic Loading, Vol. 2,2009, pp. 1367–1373.

12