effect of the soil type on the dynamic response

ISSN 0010-5082, Combustion, Explosion, and Shock Waves, 2016, Vol. 52, No. 3, pp. 363–370. c© Pleiades Publishing, Ltd., 2016.

Original Russian Text c© B. Mobaraki, M. Vaghefi.

Effect of the Soil Type on the Dynamic Response

of a Tunnel under Surface Detonation

UDC 622.235.5B. Mobarakia and M. Vaghefib

Published in Fizika Goreniya i Vzryva, Vol. 52, No. 3, pp. 119–127, May–June, 2016.Original article submitted December 10, 2014; revision submitted July 21, 2015.

Abstract: The analysis of the dynamic response of a circular tunnel in three types of soil atdifferent depths under surface detonation of a 250-kg TNT charge reveals that the tunnel peakparticle velocity and the failure zone length are sensitive to the soil type and material properties.The buried tunnel in silty clay sand has the least damage; the length of the failure zone is 5 m inthe longitudinal direction and 0 to 60◦ at the top arch.

Keywords: soil type, dynamic response, numerical simulation, underground structure, surfacedetonation, peak particle velocity.

DOI: 10.1134/S0010508216030175

INTRODUCTION

Studying the dynamic response of soil under blastloading is very important to engineers in military con-struction, pipeline construction, mining, and tunneling.Due to a very intricate structure of soil, it is very cru-cial to describe its constitutive relation when it is underblast loading.

In order to analyze and design underground struc-tures that may be subjected to blast loads, the behaviorof the whole system including the soil type, the shockwave propagation through the soil, and the structureand properties of the TNT charge, need to be simu-lated. A quick release of energy from surface detona-tion causes a rapid rise of pressure through the soil.In other words, while the detonation-induced pressurepropagates across the soil surrounding the examinedstructures, reflected waves are produced when the in-cident wave strikes the structures. These two types ofwaves produce vibrations, stresses, and strains, whichdamage the structures. Studies of the dynamic behaviorof buried structures and the blast response of soil wereconducted by many scholars. Hendron [1] summarizedthe large explosion tests carried out by the US Army

aCivil Engineering Department, Eastern MediterraneanUniversity, Famagusta, Turkey;[email protected].

bCivil Engineering Department, Persian Gulf University,75169-13817 Bushehr, Iran; [email protected].

Corps of Engineers during the years 1948 to 1952 nearunlined tunnels in sandstone. The experiment provedthat, on the average, no rock fall occurred in tunnelsuntil the peak particle velocity (PPV) umax exceeded0.9 m/s. Tunstall [2] proposed the PPV criterion to beumax = 17.5 cm/s for the rock mass rating (RMR) of 85.Fourie and Green [3] found that no cracks are formedat umax < 11 cm/s. Singh [4] confirmed that severedamage at RMR > 60 is expected to occur at umax =12–23 cm/s. Wei et al [5] investigated the damage of arock mass under blast loading through numerical sim-ulations and indicated that the RMR, loading density,and charge weight affect the damage depth. Lu et al[6] indicated that the characteristic of blasting is influ-enced by rock properties and geological structures if theelastic vibration zone approaches the charge. Jiang andZhou [7] evaluated the response of a horseshoe-shapedtunnel affected by surface detonation. They found outthat failure occurs at umax > 11 cm/s. Safaei et al.[8] estimated the half-space free-field peak stresses andPPVs for three ground media of hard rock, stiff soil, andsoft soil with two ground damping ratios and two ex-plosive charges. They concluded that the estimated re-sponse varies with respect to the ground hardness. Xiaet al. [9] studied the effects of tunnel blast excavation onthe surrounding rock mass and the lining system nextto existing tunnels for the Damaoshan highway tunnelproject. They found that no failure occurred in the lin-ing at umax < 30 cm/s.

0010-5082/16/5203-0363 c© 2016 by Pleiades Publishing, Ltd. 363

364 Mobaraki and Vaghefi

Fig. 1. Schematic diagram of the project (R is the tunnel burial depth).

A numerical method is used in the present studyto evaluate the dynamic response of a buried circularshape tunnel at the depths of 3.5, 7, 10.5, and 14 m,induced by surface detonation of a 250-kg TNT charge.Eventually, the effects of three different types of soil onthe blast response of the buried tunnel are considered.The numerical results are validated by using the em-pirical formulas of the US Army Corps of EngineeringManual TM5-855-1 [10].

FINITE ELEMENT MODELING

In the present paper, the detonation is modeled byusing the finite element software LS-DYNA-971. Finiteelement models are used for considering a concrete tun-nel (with a strength class of C50) with a length of 50 m,inner radius r = 3.93 m, wall thickness δ = 0.85 m,and the same area as the Kobe box shape subway tun-nel [11]. The finite element model consists of 154581elements, with 126017 elements to model the soil, 25500elements to model the air, 3060 elements to model thetunnel, and 4 elements to model the TNT charge. TheTNT charge is placed above the soil at the center of thefinite element model (Fig. 1). The dimensions of themodel are 50 ×50×30 m; however, due to the symmetryof the model, only a quarter of the project is modelled tosave the analysis time [12]. Moreover, the transitionaldisplacements of the nodes normal to the Y X and Y Zplanes are constrained, the non-reflecting boundary isutilized for two lateral surfaces and the bottom surface,and the free boundary condition is used for the upperXZ plane [13]. A combined Lagrangian-Eulerian ap-proach [14] is utilized for the tunnel, air, TNT, andsoil. The ∗CONSTRAINED LAGRANGE IN SOLID

command [15] is applied to provide the coupling mech-anism for modelling soil–tunnel interaction.

The TNT charge is modelled by the material type 8of LS-DYNA (∗MAT HIGH EXPLOSIVE BURN) [16]and the Jones–Wilkens–Lee (JWL) equation of state,which defines the pressure as a function of the relativevolume [17–19]. The standard parameters of TNT areobtained from the AUTODYN material library [15].

The air is modelled by the material type 9 of LS-DYNA (∗MAT NULL) [20] with a linear polynomialequation of state. The standard parameters of air areobtained from AUTODYN material library [15].

The material type 3 of LS-DYNA(∗MAT PLASTIC KINEMATIC) [21] is used tomodel the tunnel. An equivalent stiffness is consideredfor both concrete and steel bars.

Three types of soil used in this research aremodelled by the material type 5 of LS-DYNA(∗MAT SOIL AND FOAM) [22], which was put for-ward by Krieg [23]. These three soil types are sandyloam [24], soil medium [25], and silty clay sand [26].

BLAST WAVE PROPAGATION IN THE SOIL

Through changing the main parameters such as soiltype (sandy loam, soil medium, and silty clay sand) andthe depths of tunnel burial, the following calculationcases are obtained:

for case 1, R = 3.5 m,for case 2, R = 7 m,for case 3, R = 10.5 m,for case 4, R = 14 m.In all cases, the TNT charge mass was identical:

W = 250 kg.

Effect of the Soil Type on the Dynamic Response of a Tunnel under Surface Detonation 365

Table 1. Parameters of the free field peak pressure formula [29]

Soil type f n ρc, 106 Pa·s/mSandy loam 0.4 2.75 4.972

Soil medium 0.4 2.5 9.944

Silty clay sand 0.4 2.5 9.944

Table 2. Properties of soil

Soil type Density, kg/m3 Shear modulus, MPa Bulk compression modulus, MPa

Sandy loam 1255 1.724 5.516

Soil medium 1762 24 142

Silty clay sand 2350 34.474 15.024

Fig. 2. Pressures at target points A–D for sandy loam under detonation of a 250-kg TNT charge.

To show the compressive wave propagation in thesoil (free field), a number of target points are chosen;they are situated within the range of 2–10 m from theTNT charge [27]. As in our recent paper [28], the finiteelement results of the three types of soil are validated byusing the free field pressures obtained from the empiricalformula recommended by the TM5-855-1 manual

pmax = 0.407fρc(R/W 1/3)−n, (1)

where pmax is the peak pressure, f is the coupling fac-tor for the explosion, which is dependent on the scaleddepth of the explosion as f = d/W 1/3, d is the depthof the centroid of the explosive charge, W is the chargeweight, ρc is the acoustic impedance, R is the distancefrom the source, and n is the attenuation coefficient.

In the TM5-855-1 manual, which includes a totalof five types of soil, sandy loam is described as type

4, while soil medium and silty clay sand are describedas type 3. Table 1 shows the parameters that are ob-tained from the TM5-855-1 manual for sandy loam, soilmedium, and silty clay sand [29]. The detonation wavethat travels in the soil can be describes as travellingthrough three phases that consist of soil particles, air,and water. Dry soil consists of soil particles and air,whereas fully saturated soil consists of soil particles andwater. Eventually, the whole process of propagationand attenuation of compressive waves through the threetypes of dry soil is presented.

Figure 2 illustrates numerical compressive waves atdifferent depths. For comparison, Fig. 3 shows the nu-merical and empirical values of the peak pressures atdepths of 2 to 10 m. The results of the finite elementanalysis agree fairly well with the empirical predictions.


Fig. 3. Peak pressure attenuation versus the scaleddistance for sandy loam (a), soil medium (b), andsilty clay sand (c) under detonation of a 250-kg TNTcharge: (1) numerical results; (2) TM 5-855-1 re-sults; (3) best fit of numerical results.

Table 3. Effective peak stress of all tunnel cases

under detonation of a 250-kg TNT charge

Soil type Casenumber

σeff , MPa

1 25.7

Sandy loam2 7.34

3 1.87

4 0.697

1 26.5

Soil medium2 8.86

3 2.26

4 0.708

1 33.1

Silty clay sand2 9.72

3 2.78

4 1.15

The peak pressure decreases with an increase in the dis-tance from the blast, due to damping of compressivewaves in the soil [30]. For sandy loam, the peak pres-sures decrease by 46, 76, and 92% at depths of 5, 6,and 7 m, respectively, in comparison with the depth of4 m (Fig. 3a). The corresponding reduction of the peakpressures for soil medium and silty clay sand under thesame conditions is 54, 69, and 86% (Fig. 3b) and 47,77, and 90% (Fig. 3c).

COMPARISONS OF THE DYNAMICRESPONSE OF THE TUNNELIN THREE TYPES OF SOIL

The blast analysis creates several time history re-sponses, such as pressure, stress, strain, vibration, andvelocity, in all directions for all nodes and elements [31].In order to study the effect of the soil type on the blastresponse of the tunnel and also the variation of the tun-nel PPV in different soils, a target element is selected torecord its dynamic response history [32]. This elementis on the top of the tunnel (Fig. 4a). As this elementsuffers intensive vibration, it is one of the most criticalpoints of the tunnel. Figure 4b shows the PPV versusthe scaled distance R/W 1/3 (R = 3.5, 7, 10.5, and 14 m)of the selected element for all calculation cases. The re-sults indicate that the PPV depends on the soil type.The blast shock distribution in soil is a complex eventdepending on the charge geometry, loading density, andsoil dynamic constitutive properties.


Fig. 4. Vertical peak velocity at the target point (a) versus the scaled distance (b) under detonation of a250-kg TNT charge: (1) sandy loam; (2) soil medium; (3) silty clay sand.

Fig. 5. Damage zone for the tunnel situated in sandy loam under detonation of a 250-kg TNT charge.

For cohesive soils, the volume of the air-filled voidsis the key factor for the wave reduction rate, whereas therelative density is the main factor that affects the ratesof wave reduction in non-cohesive soils. As the relativedensity is not always accessible, the dry unit weight maybe used. Soils with low relative densities (high volumeof air voids) reduce the blast shock faster than soilswith high relative densities (low volume of air voids).With an increase in the scaled distance, the PPV is

seen to decrease. Moreover, the PPV attenuation ratesare almost identical for the tunnels situated in sandyloam and soil medium. The tunnel situated in sandyloam has the least PPV due to its poor constructionand the lowest relative density among the three typesof soil. As was mentioned in [33], the relative density isthe main parameter for the dynamic behavior in non-cohesive soils.


Fig. 6. Damage zone for the tunnel situated in the soil medium under detonation of a 250-kg TNT charge.

Fig. 7. Damage zone for the tunnel situated in silty clay sand under detonation of a 250-kg TNT charge.

FAILURE MODE ANALYSISOF THE TUNNEL

The uniaxial compression strength of the C50 con-crete σmax = 23.1 MPa is used to model all tun-nel cases. The tunnel fracture is simulated by using∗MAT ADD EROSION for the above-mentioned maxi-mum principal stress at failure [21, 34]. In other words,when the principal stress of the tunnel reaches the fail-ure stress, the material is removed from consideration.The failure of the tunnels situated in sandy loam, soil

medium, and silty clay sand in case 1 are schematicallydepicted in Figs. 5–7, respectively. Figures 5a, 6a, and7a show the stress distributions just before failure. Fig-ures 5c, 6c, and 7c represent the fringe levels and stressdistributions at the end of failure. According to the vonMises failure criterion, the roof of the tunnel covered bysandy loam is collapsed. The length of the failure zoneis 6 m in the longitudinal direction of the tunnel (Z)and 0–60◦ at the top arch. Almost all upper elementsof the roof of the tunnel situated in the soil mediumare destroyed, and the length of the failure zone is the


same as that of the buried tunnel in sandy loam. It canbe seen that the same destruction occurs for the tun-nel situated in silty clay sand (0–60◦ at the top arch),but the length of the damage zone is smaller (5 m inthe Z direction). By comparing the main parameters ofthree types of soil (Table 2), it is obvious that silty claysand is firmer than the two others because of its highshear strength and relative density. Therefore, due toits firm construction and solidity, silty clay sand can bethe best support for the tunnel among the soil typesmentioned. It can be concluded that the soil propertiesshould be carefully considered in order to estimate theeffect of the blast load on buried structures. However,it has been verified that the model used and the type ofsoil chosen in LS-DYNA have no effect on the diameterof the crater created by underground detonations [35].

Table 3 presents the effective peak stresses σeff (ac-cording to the von Mises criterion) for all tunnel cases,which indicate how the tunnel depth affects its safetyagainst blast loads. The effective peak stress reduc-tion trends are different for different types of soil. Forexample, for the buried tunnel in sandy loam, the ef-fective peak stresses in cases 2, 3, and 4 are smaller by71.4, 92.7, and 97.3% than that in case 1, respectively,which is close to the values for the tunnel covered bysoil medium: 66.6, 91.5, and 97.3%, but differs fromthat for the buried tunnel situated in silty clay sand,where the effective peak stresses in cases 2, 3, and 4 aresmaller by 70.6, 91.6, and 96.5% as compared to case 1,respectively.

CONCLUSIONS

The scale reduction of the peak pressures at differ-ent depths in sandy loam, soil medium, and silty claysand has been computed by the finite element method.In sandy loam, the peak pressures decrease by 46, 76,and 92% at depths of 5, 6, and 7 m as compared to thatof 4 m, respectively. In the soil medium, the peak pres-sures decrease by 54, 69, and 86%, respectively. Thecorresponding values of the peak pressure reduction insilty clay sand are 47, 77, and 90%.

For cohesive soils, the volume of the air-filled voidsis the key factor for the wave reduction rate, whereasthe relative density is the main factor that affects therates of wave reduction in non-cohesive soils.

The computations of the vertical peak velocities ofthe target element for all the tunnel cases show that theleast value of this parameter is reached for the tunnelsituated in sandy loam due to its lowest relative densityamong the three types of soil considered in the presentstudy.

According to the von Mises failure criterion, thedamage zones have been computed for the buried tunnelin all soils. The tunnel situated in silty clay sand hasthe least damage because of its high shear strength andfirm construction.

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effect of the soil type on the dynamic response

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