Research ArticleDynamic Response of Composite Steel Lining Structure underBlast Loading

Desen Kong 12 Yu Xu1 and Cheng Song3

1School of Civil Engineering and Architecture Shandong University of Science and Technology Qingdao 266590 China2Shandong Key Laboratory of Civil Engineering Disaster Prevention and Mitigation Qingdao 266590 China3No 4 Engineering Company Ltd of China Communications Construction First Harbor Engineering Company LtdTianjin 300000 China

Correspondence should be addressed to Desen Kong skd992012sdusteducn

Received 21 November 2019 Revised 17 March 2020 Accepted 25 May 2020 Published 30 June 2020

Academic Editor Athanasios Chasalevris

Copyright copy 2020 Desen Kong et al (is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

According to the advantages of high tensile resistance and high shear strength of composite steel plate a new antiexplosionprotection method of composite steel plate lining structure is put forward (e numerical model of explosion impact of subwaytunnel with composite steel plate lining structure was established by dynamic analysis software(e transient dynamic response oflining structure with the composite steel plate was simulated when explosion occurred (e research results show that theinfluence of explosive quantity on each point of composite steel plate lining structure is different and the change of accelerationnear the centre of the detonation source is generally greater than the multiple of the increase of explosive quantity (e increase ofvelocity and displacement is basically consistent with the quantity of explosive(e influence of axial stress on the lining structureis the least and the influence of the lining structure is greater in the y-direction than in the x-direction (e research results canprovide the plan and basis for the emergency response of the subway tunnel

1 Introduction

With the acceleration of the modernization process theconstruction of subway is not only the best solution to thetraffic jam problem but also the catalyst to promote themodernization process As an effective tool to solve theinconvenience of citizens subway tunnels sometimes be-come places where terrorists carry out terrorist bombings Inorder to protect the safety of real citizens and reduce the lossof public property subway tunnel structures should havesufficient antiexplosion capability (erefore it is of greattheoretical value to study the role of composite steel plates insubway tunnel protection [1ndash3]

In the field of subway tunnel protection scholars athome and abroad have carried out a large number of ex-periments and numerical simulation studies Liu et al [4]used LS-DYNA software to carry out explosion numericalsimulation on equivalent explosive amounts of 10 kg 20 kgand 30 kg TNT and obtained the results that the structure

cannot be damaged at 10 kg the structure can be damaged at20 kg and the structure can be completely damaged at 30 kgZyskowski et al [5] studied the dynamic response of theinternal explosion load of the structure by using a reducedscale model for internal explosion simulation and a nu-merical simulation method Yan and Cao [6 7] obtained thepressure variation curves when the explosion occurred in thetunnel structure by constructing different structural modelsof underground tunnels and tunnels and conducting anumerical simulation of explosion and experimental re-search in different proportions However there are still a lotof gaps in the research on the protection of compositematerials in subway tunnels especially its protectioncharacteristics and dynamic response analysis which stillneed to be vigorously studied

A new type of explosion-proof structure of compositesteel plate lining structure was proposed Based on theknowledge of explosion mechanics and fluid dynamics anumerical model of explosive-air-composite steel plate-

HindawiShock and VibrationVolume 2020 Article ID 2693659 12 pageshttpsdoiorg10115520202693659

lining-surrounding soil was established by dynamic analysissoftware LS-DYNA(e instantaneous dynamic response oflining structure with composite steel plate when explosionoccurs was simulated and the stress characteristics of liningstructure under different explosive equivalent are obtained

2 Establishment of Numerical Model ofComposite Steel Plate LiningProtection Structure

21 Composite Steel Plate Lining Protection Structure (etraditional composite steel plate is mostly used to preventvibration and noise According to this characteristic thecomposite steel plate is extended to the tunnel protection(e two remarkable characteristics of the composite steelplate are the difference of interface bond ratio and interfaceshear strength as well as the tensile bending hardness andother properties required by protective materials (epreparation methods of composite steel plate can be dividedinto rolling method surfacing method explosive weldingmethod and explosive welding rolling method (e rollingmethod is to seal the joint between the cladding and the baseand to weld and vacuum-roll (e manufacturing process issimple but the disadvantages are obvious (e steel platespecification is small and the quality of the interface joint ispoor (e cost of using the surfacing method to make large-area steel plate is too high (e explosive welding rollingmethod is similar to the explosive welding method How-ever the explosive welding rolling method is used in China(e composite steel plate cannot be widely used due to poorcoordination (e composite steel plate is composed of twolayers of steel plate and high-strength polyester fiber (ehigh-strength polyester fiber is between two layers of steelplate and its thickness ratio is 2 1 2 which is made by theexplosive welding method (e two basic characteristics ofcomposite steel plate interface binding rate and interfaceshear strength have reached the relevant standards (ecomposite steel plate structure is as shown in Figure 1

According to the nonlinear characteristics of shock re-flection during the propagation of explosion shock wave inexplosion activities the protection steel plate adopts themodel of ordinary steel plate and takes into account thecharacteristics of laminated composite steel plate (ematerial model of protection steel plate adopts the bilinearelastoplastic constitutive model [8] (e strain rate effect ofcomposite steel plate material is expressed by Cow-perndashSymonds model [9] and its dynamic yield strength σycan be expressed as follows

σy 1 +εD

1113874 11138751p

1113890 1113891 σ0 + βEpεeffp1113872 1113873 (1)

where σ0 is the initial yield strength ε is the strain rate Ep isthe plastic hardening modulus εeffp is equivalent plasticstrain β is the hardening parameter When the parameter is0 it means follow-up hardening occurs and when the pa-rameter is 1 it means isotropic hardening occurs D and P

are strain rate parameters

22 Establishment of Composite Steel Plate Lining ProtectionStructure Model According to the engineering backgroundof Nanjing subway tunnel the explosive-air-composite steelplate-lining-surrounding soil model is established by usingfinite element software LS-DYNA [10] Figure 2 is thestructural diagram of composite steel plate lining structuremodel In the numerical simulation it is mainly divided intofive parts explosive unit air unit composite steel plate unitlining structure unit and soil unit Each part of the unit isdivided by mapping grid with the grid side length of100mm and the grid side length of 300mm in the distance ofthe soil unit Since the whole model is an axisymmetricmodel it takes 12 of the model to save the calculation time(e whole model has 961767 elements

(e model is a cylindrical shield tunnel with a soil depthof 15m (e shield tunnel has a lining thickness of 03minner diameter of 54m outer diameter of 60m andprotective steel plate thickness of 01m (e numericalsimulation of the model can be regarded as an axisymmetricproblem so a 12 model is adopted for modeling and cal-culation and a 36times36times15 cube is taken to form a wholemodel to reduce the influence of boundary effect (eequivalent TNT algorithm is used to simulate the pointsource explosion at a distance of 11m from the bottom ofthe tunnel lining structure under the equivalent of 10 kgTNT and 30 kg TNT

23 Explosive Combustion Model and ParametersBecause of the short reaction time and the fast propagationspeed of the blast wave the time of the blast wave propa-gating to the interface between the charge and the medium isvery short which can be ignored generally so only theexternal reaction of the explosion is studied

(e equivalent TNT conversion is carried out by LS-DYNA program and the keyword ldquolowast MATndashHIGHndashEXPLOSIVEndashBURNrdquo is used to simulate the detonation ofhigh-energy explosives [11] (e relevant parameters ofexplosives are listed in Table 1

In the numerical simulation of explosion the explosionsource explosive is simulated by JWL equation of state [12]and the pressure is expressed by the function of initialvolume and relative volume

P A 1 minusω

R1V1113888 1113889e

minusR1V+ B 1 minus

ωR2V

1113888 1113889eminusR2V

+ωE0

V (2)

where P is pressure A B R1 R2 and ω are the materialfunction coefficients respectively V is the relative volumeE0 is the initial internal energy per unit volume (e stateequation uses the ldquolowastEOS-JWLrdquo keyword provided by LS-DYNA program and the parameters are listed in Table 2

Steel plate

Steel plate

High-strengthpolyester

Figure 1 Composite steel plate structure

2 Shock and Vibration

24 Model Parameters of Surrounding Soil In numericalsimulation the soil structure is chosen to be a flattenedplastic foammodel and a soil with failure characteristics thatis the MAT- SOIL-AND-FOAM model [13] (e yieldfunction f of the model adopts the following formula

f J2 minus a0 + a1p + a2p2

1113872 1113873 (3)

(e soil in the numerical simulation is set by Druck-erndashPrager yield criterion which can be obtained by the angleof internal friction φ and cohesion c of soil

α sinφ

9 + 3 sin2 φ1113969

k

3

radicc cosφ

3 + sin2 φ1113969

(4)

25 Lining Structure Model and Parameters In the nu-merical simulation the lining structure adopts the h-j-cmodel which was initially used to simulate brittle materialssuch as glass and ceramics before it was developed tosimulate concrete(emodel can be well utilized to solve theconcrete and rock simulation problems in the case of high

strain rate and large deformation complex (erefore thismodel is adopted (e h-j-c model in LS-DYNA 3D is de-fined as lowastMAT-JOHENS-HOLMUST-CONCRETE (ematerial number is 115

26 AirModel and Parameters In the numerical simulationthe material model of air is assumed to be an ideal gas andthe relationship between pressure P and energy E can beexpressed as follows

P (c minus 1)E (5)

where c is the specific heat ratio of gas which takes the valueof 14 the relative density ρ0 of air takes the value of129 lowast 10minus3 kgm3 and the initial internal energy E of unitvolume takes the value of 025MPa

3 Analysis of Numerical Calculation Results

31 Stress Changes of Explosion Shock Wave on TunnelStructure For the shock wave generated by the explosion inthe subway tunnel its propagation law is very complex [14]In order to better study this kind of complex situation LS-DTYNA dynamics software is used under the equivalent of10 kg TNT and 30 kg TNT respectively 11m from thebottom of the lining When the explosion occurs under theprotection of composite steel plate the dynamic response ofthe subway tunnel only observes the air part of the modelFor mechanical properties Figures 3 and 4 are shock-wavestress nephogram of lining structure under the action of10 kg TNT and 30 kg TNT respectively

Table 1 Parameters of explosive material

Density (gcm3) Burst velocity (mmμs) Pressure CJ Bulk modulus (Pa) Shear modulus (Pa)163 0693 027 0 0

Table 2 Parameters of JWL equation of state

A B R1 R2 ω E0 V0

374 323 times 10minus 2 415 095 03 007 times 1011 10

Lining structure

Composite steel Dynamite

Air

Soil

Figure 2 Composite steel lining structure mode

Shock and Vibration 3

Considering the short action time and high frequency ofexplosion shock it only takes a few milliseconds from thezero load to the maximum load and the stress-strain be-havior of the structure under the action of shock wave ispositively correlated with the action rate of shock wave(erefore in order to better study the destructive effect ofthe peak value of explosion load the numerical model has anexplosion time of 50ms [15]

(e explosive propagates to all sides after the ex-plosion Under the influence of no obstacles the blastwave will form a spherical wave array and propagateoutwards Because the explosion point is 11 m away fromthe bottom lining the distance is relatively short so thefirst contact with the bottom of the lining will increasethe pressure generate the reflected wave and propagateto the distance With the increase of the distance the

pressure of the blast wave will continue to decreasebecause of the superposition of the shock wave (ereflection wave at the bottom overlaps with the weakenedshock wave which makes the propagation speed fasterIn about 5 ms the shock wave propagates to the toplining and then it reflects downward and spreads to thedistance Because the reflection wave overlaps manytimes in the subway section tunnel the reflection waveexperiences many peaks in each point inside the tunneland slows down its weakening effect Because the shockwave starts to spread as a spherical wave it spreads in thelining (e shock wave at the top is composed of twoparts the wave front of the spherical wave and the re-flection wave of the lining at the top (e reflection wavewill continue to reflect downward in the process ofpropagation In this process some reflection waves will

Fringe levels1152e ndash 061037e ndash 069219e ndash 078067e ndash 076914e ndash 075762e ndash 074609e ndash 073457e ndash 072305e ndash 071152e ndash 07

ndash0000e + 00

Fringe levels1152e ndash 061037e ndash 069219e ndash 078067e ndash 076914e ndash 075762e ndash 074609e ndash 073457e ndash 072305e ndash 071152e ndash 07

ndash0000e + 00

t = 05ms t = 25ms t = 6ms

t = 145ms t = 425ms t = 475ms

Figure 3 (e process of blast wave under 10 kg TNT at different time period

Fringe levels1152e ndash 061037e ndash 069219e ndash 078067e ndash 076914e ndash 075762e ndash 074609e ndash 073457e ndash 072305e ndash 071152e ndash 07

ndash0000e + 00

Fringe levels1152e ndash 061037e ndash 069219e ndash 078067e ndash 076914e ndash 075762e ndash 074609e ndash 073457e ndash 072305e ndash 071152e ndash 07

ndash0000e + 00

t = 05ms t = 25ms t = 6ms

t = 145ms t = 425ms t = 475ms

Figure 4 (e process of blast wave under 30 kg TNT at different time period

4 Shock and Vibration

A5 A10 A15 A20

A19A14A9A4

A3 A8 A13 A18

A17A12

A6

A7A2

A1 A11 A16

Figure 5 Observation points of tunnel liner

0 001 002 003 004Time (s)

005

03

02

01

0

ndash01

ndash02

ndash04

ndash03

Disp

lace

men

t (m

)

A1A5

(a)

0 001 002 003 004Time (s)

005

02

01

0

ndash01

ndash02

ndash03

Disp

lace

men

t (m

)

A6A10

(b)

0 001 002 003 004Time (s)

005

0

02

01

ndash01

ndash02

Disp

lace

men

t (m

)

A11A15

(c)

0 001 002 003 004Time (s)

005

0

01

005

01

Disp

lace

men

t (m

)

A16A20

(d)

Figure 6 Changes of displacement in y-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

Shock and Vibration 5

propagate in the opposite direction resulting in multiplestress peaks on the explosion source section 30 kg TNTCompared with 10 kg TNT the blast energy is morepowerful and the impact range of shock wave is widerFor the explosion activities in the closed structure thepeak value of shock wave is strengthened due to themultiple reflection and superposition of blast wave eachpoint experiences multiple peaks its duration is in-creased and its shock propagation law is more complexIn the early stage of explosion activities the bottom blastwave propagation is faster and in the process of prop-agation when the upper shock wave undergoes reflectionand superposition the propagation speed will beaccelerated which also accords with the characteristicsthat the blast wave is a spherical wave [16]

32 Dynamic Response of the Lining Structure under the BlastAction When an explosion occurs in the tunnel section thedisplacement velocity and acceleration of the liningstructure under the action of the explosion are importantparameters to measure the damage degree of the structure[16] In order to study the dynamic response of the liningstructure under the action of explosives equivalent to 10 kgand 30 kg under the protection of composite steel plate 20reference points were selected where the influence of thelining structure was obvious and divided into four groups(ese four groups were arranged on sections at differentdistances from the explosion source centre numberedA1ndashA20 and were 0m 3m 6m and 9m away from theexplosion centre Figure 5 is the layout diagram of eachreference point of the lining structure [17ndash19]

0 001 002 003 004Time (s)

005

2

0

ndash2

ndash4

ndash6

ndash8

Velo

city

(ms

)

A1A5

(a)

0 001 002 003 004Time (s)

005

2

1

0

ndash1

ndash2

ndash3

Velo

city

(ms

)

A1A5

(b)

0 001 002 003 004Time (s)

005

Acce

lera

tion

(ms

2 )10

3

2

ndash2

0

ndash4

ndash10

ndash8

ndash6

ndash12

A11A15

(c)

0 001 002 003 004Time (s)

005

2

15

05

0

ndash2

ndash05

Acce

lera

tion

(ms

2 )10

3

A11A15

(d)

Figure 7 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

6 Shock and Vibration

321 Dynamic Response of Lining Structure under 10 kg TNTExplosion From the numerical simulation results it can beseen that the maximum vertical displacement points of eachsection occur at two reference points at the upper wall andthe lower wall Figure 6 is the y-direction displacementchange curve at the upper wall and the lower wall of the foursections

As can be seen from the y-direction displacement changecurve shown in Figure 6 the lining structure has a dis-placement of 04 cm at section A1 (e displacement changecurve of the section closer to the explosion source decreasesrapidly after experiencing a peak value and the change trendis stable As the distance from the centre of the explosionsource increases the y-direction displacement gradually

decreases Multiple displacement peaks appear at sectionstwo three and four since the shock wave energy decaysrapidly with the increase of distance (ere is a large dif-ference between the value and section one(e displacementof the reference point at a longer distance first appears as asmall amplitude oscillation change under the reflectionsuperposition effect of the shock wave (erefore under theexplosion of 10 kg of explosives the deformation peak valueof the lining is 04 cm and the influence on the liningstructure is within the elastic range At the beginning of theexplosion the lining structure was subjected to tensile stressand had a maximum acceleration and velocity at point A1Figure 7 is a velocity and acceleration variation curve in they-direction of sections one and three

01

0

ndash01

ndash02

ndash03

Disp

lace

men

t (m

)

0 001 002 003 004Time (s)

005

A2A3A4

(a)

0 001 002 003 004Time (s)

005

A7A8A9

01

0

ndash01

ndash02

Disp

lace

men

t (m

)(b)

0 001 002 003 004Time (s)

005

A12A13A14

006

004

002

0

ndash01

ndash008

ndash006

ndash004

ndash002

Disp

lace

men

t (m

)

(c)

0 001 002 003 004Time (s)

005

A17A18A19

004

002

0

ndash006

ndash004

ndash002

Disp

lace

men

t (m

)

(d)

Figure 8 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

Shock and Vibration 7

From the velocity and acceleration change curves shownin Figure 7 it can be seen that the displacement change of thereference point of section one rapidly decays after experi-encing a peak value while the displacement change of thereference point of other sections further away experiencesmultiple peaks showing an overall weakening trend and alonger duration (is also verifies that the velocity andacceleration are affected by overpressure and the magnitudeof the impact is positively related to the distance from theexplosive source Under the action of explosion the max-imum horizontal displacement of five reference points ineach section occurs at three points on the side wall Figure 8is the x-direction displacement change curve of four sectionsat three points

From the x-direction displacement variation curveshown in Figure 8 it can be seen that the maximum dis-placement of 024 cm occurs at the reference point at the side

wall A4 instead of the reference point at the front side wallA3 In addition the impact of explosion shock wave on thedisplacement of the lining structure side wall is generallyreflected in the second peak value and the first peak value ofdisplacement variation is caused by the vacuum zone formedby the sharp consumption of air during explosion Under thesuperposition of multiple reflections of the shock wave thedisplacement changes experienced multiple peaks andshowed a weakening trend By comparing the maximumvelocity and acceleration in the x-direction with the maxi-mum velocity and acceleration in the y-direction we can seethat there is a big gap between the two

322 Dynamic Response of Lining Structure under 30 kg TNTExplosion For the influence of explosion shock wave onlining structure under the action of higher explosive

0 001 002 003 004Time (s)

005

A1A5

1

05

0

05

ndash1

ndash15

Velo

city

(ms

)

(a)

0 001 002 003 004Time (s)

005

A1A5

06

04

02

0

ndash02

ndash04

ndash06

Velo

city

(ms

)

(b)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

04

02

0

ndash02

ndash04

(c)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

02

01

0

ndash02

ndash01

ndash03

(d)

Figure 9 Changes of displacement in y-direction in sections (a) Velocity in y direction of section one (b) velocity in y direction of sectionthree (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

8 Shock and Vibration

equivalent 30 kg TNT is selected for analysis Each referencepoint is arranged in the same way as 10 kg TNT Figure 9 isthe y-direction displacement change curve at upper andlower walls of the four sections

As can be seen from the y-direction displacementchange in Figure 9 the maximum vertical displacement ofeach section occurs in two points on the upper and lowerwalls (e maximum displacement of A1 reference point ofsection one in y-direction is more than twice as much asthat of section three under the action of 10 kg TNT (edisplacement change curve shows a weakening trend as awhole (erefore the displacement of the lining structureclose to the centre of the explosion source will increase at ahigh magnification when the amount of explosive in-creases exponentially However with the increase of dis-tance the displacement will increase at a lowmagnification

and the influence will decrease gradually (ere is anobvious plastic deformation at section one It can beknown that 30 kg TNT explosive exceeds the critical pointof the plastic zone of the lining structure protected bycomposite steel plates

According to the change curve in Figure 10 the changeof velocity and acceleration in the y-direction is affecteddifferently by the change of explosive charge (e multipleincrease of explosive charge has the greatest impact on thearea close to the explosive source With the increase ofdistance the impact gradually weakens Within the range of3m from the explosive source the velocity and accelerationwill rapidly decrease after experiencing a main peak valueand tend to be stable Beyond the range of 3m from theexplosive source the velocity and acceleration will slowlydecrease after experiencing a main peak value

20

10

0

ndash10

ndash20

ndash30

ndash400 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(a)

10

0

ndash10

ndash20

ndash30

ndash40

ndash500 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(b)

Acce

lera

tion

(ms

2 )103

4

2

0

ndash2

ndash4

ndash60 001 002 003 004 005

Time (s)

A11A15

(c)

Acce

lera

tion

(ms

2 )103

2

1

0

ndash1

ndash20 001 002 003 004 005

Time (s)

A11A15

(d)

Figure 10 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

Shock and Vibration 9

Under the action of 30 kg TNTexplosion the maximumhorizontal displacement of five reference points in eachsection occurs at three points on the side wall Figure 11 isthe x-direction displacement change curve of four sections atthree points By comparing the data of Figures 8 and 11 itcan be concluded that the maximum displacement at foursections in the x-direction under the action of 30 kg TNT isabout twice as large as that under the action of 10 kg TNTslightly smaller than the maximum displacement increase inthe y-direction at the same distance At the same time it canalso be obtained through the displacement change curve ofsection one and the damage effect of 30 kg TNT equivalenthas exceeded the critical point making the lining structureproduce a plastic zone

323 Variation Curve of Axial Overpressure underExplosion For the variation of overpressure effect of ex-plosion shock wave along the axial direction of liningstructure the 20 reference points A1ndashA20 are divided intofive straight lines L1 L2 L3 L4and L5 along the axialdirection the L1 straight line includes A1 A15 A11 andA16 L2 straight line includes A2 A7 A12 and A17 L3straight line includes A3 A8 A13 and A18 L4 straight lineincludes A4 A9 A14 and A19 L5 straight line includes A5A10 A15 and A20 Figures 12 and 13 are curves of axialoverpressure change under explosion of 10 kg TNT and30 kg TNT

According to the attenuation law of overpressure oneach straight line in Figure 12 the overpressure at the close

0 001 002 003 004 005Time (s)

A2A3A4

02

01

0

ndash01

ndash02

ndash03

ndash04

ndash05

Disp

lace

men

t (m

)

(a)

0 001 002 003 004 005Time (s)

A7A8A9

0

02

01

ndash01

ndash02

ndash03

ndash04

Disp

lace

men

t (m

)

(b)

0 001 002 003 004 005Time (s)

A12A13A14

Disp

lace

men

t (m

)

01

005

0

ndash005

ndash01

ndash015

ndash02

(c)

0 001 002 003 004 005Time (s)

A18A17A19

Disp

lace

men

t (m

)01

005

0

ndash005

ndash01

(d)

Figure 11 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

10 Shock and Vibration

distance from the lining structure is the strongest (eoverpressure will decrease sharply in the range of 3m andthe overpressure will decrease slowly in the range of3msim9m as a whole (is is due to the rapid compression ofair near the explosive at the initial stage of the explosionreaction concentration of energy and overpressure phe-nomenon With the increase of distance the energy willgradually diffuse [20](e axial overpressure of the referencepoint within 6m away from the centre of the explosionsource will also increase slightly which is due to the energyreceived by individual reference points increasing after theexplosion shock wave is reflected and superimposed formany times

By comparing the overpressure changes in Figures 12and 13 it can be seen that at the beginning of the explosionthe overpressure peak value of 30 kg TNT increased by aboutsix times compared with 10 kg TNT at the same referencepoint which is much larger than the increase of explosivemass Similar to the variation curve of overpressure of 10 kgTNT the overpressure is strongest at the close distance fromthe centre of the explosion source (e overpressure has

obvious attenuation at 3m from the centre of the explosionsource and the overpressure keeps a slow attenuation trendin the range of 3msim9m (e overpressure of the referencepoint in the same straight line beyond 6m will also bestrengthened which is also due to the superposition ofmultiple reflections of the explosion shock wave

4 Conclusions

(e instantaneous dynamic response of the lining structureinstalled with composite steel plate when explosion occurs issimulated by establishing a composite steel plate liningstructure model Different influencing factors are deter-mined and parameterized analysis is carried out by using themethod of comparison of different explosive equivalentexplosion effects (e following conclusions are obtained

(1) (e change of velocity acceleration and displace-ment of each reference point at the lining structure isrelated to the action of overpressure and distance Amain peak value will be formed within 3m from theexplosion source and the peak value is obviouslyhigher than other peaks With the propagation ofexplosion shock wave the function of lining struc-ture will gradually decrease

(2) (e effect of multiple increase of explosive quantityon each point of lining structure is not the same (eacceleration near the distance is generally far greaterthan the multiple increase of explosive quantitywhile the increase of velocity and displacement isbasically the same as the explosive quantity (eeffect of multiple increase of explosive quantity onacceleration velocity and displacement is reducedand the change is relatively stable at a distance (3maway from the explosive source)

(3) By comparing the data changes of acceleration velocityand displacement in each direction of the same refer-ence point it can be seen that under the action ofexplosion when the distance is relatively close theinfluence is greater the axial stress has the least influenceon the lining structure and the influence of y-directionof the lining section on the lining structure is greaterthan the other two directions

Data Availability

(e rawprocessed data used to support the findings of thisstudy have not been made available because they form partof the ongoing research

Conflicts of Interest

(e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof China (41372288) and Shandong Natural ScienceFoundation (ZR2019MEE027)

2 8 1040 6Displacement (m)

0

02

04

06

08

1

12

14Pr

essu

re (M

Pa)

L1L2L3

L4L5

Figure 12 Overpressure attenuation laws in lines of 10 kg TNT

L1L2L3

L4L5

2 8 1040 6Displacement (m)

0

1

2

3

4

5

6

7

8

Pres

sure

(MPa

)

Figure 13 Overpressure attenuation laws in lines of 30 kg TNT

Shock and Vibration 11

References

[1] Q H Meng Dynamic Response and Explosion-Resist-Ant-protection of Subway Tunnel under Terroristbom-Bing loadShandong University of Science and Technology QingdaoChina 2010

[2] D S Kong M Y Deng and Y Z Li ldquoExperimental study onmechanical deformation characteristics of inclined andstraight alternating pile groupsrdquo Advances in Civil Engi-neering vol 2020 Article ID 8394182 11 pages 2020

[3] D-S Kong Q-H Meng W-W Zhang and Q-H ZhangldquoShock responses of a metro tunnel subjected to explosiveloadsrdquo Journal of Vibration and Shock vol 31 no 12pp 69ndash72 2012

[4] J B Liu andQ S H Ni ldquoStudy on explosion protectionin ironunderground structurerdquo Journal of Vibration and Shockvol 27 no 8 pp 16ndash19 2008

[5] A Zyskowski I Sochet G Mavrot P Bailly and J RenardldquoStudy of the explosion process in a small scale experiment-structural loadingrdquo Journal of Loss Prevention in the ProcessIndustries vol 17 no 4 pp 291ndash299 2004

[6] C L Yan andD J Ma ldquoHigh resolution numerical simulationof strong explosive waves in a vesselrdquo Journal of ChinaUniversity of Science and Technology vol 25 no 1 pp 10ndash161998

[7] Y Z Cao Z S Lu and H A Guan ldquoNumerical simulation ofexplosion flow field in anti-explosion vesselrdquo Journal of ChinaUniversity of Science and Technology Chinese Journal of HighPressure Physics vol 15 no 2 pp 127ndash133 2001

[8] Y Cui Dynamic Response and Damage Assessment of DuplexHollow CFST Column Subjected to Blast Loading ChanganUniversity Xirsquoan China 2013

[9] D S Kong M X Deng and Z M Zhao ldquoSeismic interactioncharacteristics of an inclined straight alternating pile group-soil in liquefied groundrdquo Advances in Civil Engineeringvol 2019 Article ID 3758286 12 pages 2019

[10] K Z Yang and X M Yang ldquo(e propagation law of theimpulse shock wave in the tunnelrdquo Explosion and ShockWaves vol 23 no 1 pp 37ndash40 2003

[11] A L Kuhl and H Reichenbach ldquoCombustion effects inconfined explosionsrdquo Proceedings of the Combustion Institutevol 32 no 2 pp 2291ndash2298 2009

[12] D Kong M Deng Y Liu and X Tan ldquoStudy of the force anddeformation characteristics of subsea mudmat-pile hybridfoundationsrdquo Polish Maritime Research vol 25 no s3pp 43ndash53 2019

[13] S H Qu Structural Response and Damage and Ground Vi-bration of Subway Station under Internal Explosion TianjinUniversity Tianjin China 2008

[14] X L Du W Z H Liao M Z H Tian et al ldquoNumericalsimulation of flow around blast waverdquo Journal of BeijingUniversity of Technology vol 34 no 3 pp 277ndash287 2008

[15] D S Kong M X Deng and Y Xu ldquoStudy on calculation ofpile sliding interval of large-diameter steel pipe piles onoffshore platformsrdquo Mathematical Problems in Engineeringvol 2019 Article ID 3549296 8 pages 2019

[16] Y F Liu R H Liu S Q Shi et al ldquoNumerical stimulation onanalysis of reducing blast by using foam aluminumrdquo ChineseJournal of Underground Space and Engineering vol 27 no 8pp 16ndash19 2008

[17] D S Kong Y F Bai Y P Chen andM X Deng ldquoA study onthe seismic response characteristics of an oblique pile group-soil-structure with different pile capsrdquo Shock and Vibrationvol 2019 Article ID 8141045 12 pages 2019

[18] D S Kong M X Deng and Y Z Li ldquoNumerical simulation ofseismic soil-pile interaction in liquefying groundrdquo IEEEAccess vol 8 no 1 pp 195ndash204 2020

[19] D S Kong Y Liu M X Deng and X Y Zhao ldquoAnalysis ofinfluencing factors of lateral soil resistance distributioncharacteristics around monopole foundation for offshorewind powerrdquo Applied Ocean Research vol 97 Article ID102106 2020

[20] W W Zhang Study of Impulse Response and Shield Tech-nology of Subway Station under Terrorist Explosion loadShandong University of Science and Technology QingdaoChina 2010

12 Shock and Vibration

24 Model Parameters of Surrounding Soil In numericalsimulation the soil structure is chosen to be a flattenedplastic foammodel and a soil with failure characteristics thatis the MAT- SOIL-AND-FOAM model [13] (e yieldfunction f of the model adopts the following formula

f J2 minus a0 + a1p + a2p2

1113872 1113873 (3)

(e soil in the numerical simulation is set by Druck-erndashPrager yield criterion which can be obtained by the angleof internal friction φ and cohesion c of soil

α sinφ

9 + 3 sin2 φ1113969

k

3

radicc cosφ

3 + sin2 φ1113969

(4)

25 Lining Structure Model and Parameters In the nu-merical simulation the lining structure adopts the h-j-cmodel which was initially used to simulate brittle materialssuch as glass and ceramics before it was developed tosimulate concrete(emodel can be well utilized to solve theconcrete and rock simulation problems in the case of high

strain rate and large deformation complex (erefore thismodel is adopted (e h-j-c model in LS-DYNA 3D is de-fined as lowastMAT-JOHENS-HOLMUST-CONCRETE (ematerial number is 115

26 AirModel and Parameters In the numerical simulationthe material model of air is assumed to be an ideal gas andthe relationship between pressure P and energy E can beexpressed as follows

P (c minus 1)E (5)

where c is the specific heat ratio of gas which takes the valueof 14 the relative density ρ0 of air takes the value of129 lowast 10minus3 kgm3 and the initial internal energy E of unitvolume takes the value of 025MPa

3 Analysis of Numerical Calculation Results

31 Stress Changes of Explosion Shock Wave on TunnelStructure For the shock wave generated by the explosion inthe subway tunnel its propagation law is very complex [14]In order to better study this kind of complex situation LS-DTYNA dynamics software is used under the equivalent of10 kg TNT and 30 kg TNT respectively 11m from thebottom of the lining When the explosion occurs under theprotection of composite steel plate the dynamic response ofthe subway tunnel only observes the air part of the modelFor mechanical properties Figures 3 and 4 are shock-wavestress nephogram of lining structure under the action of10 kg TNT and 30 kg TNT respectively

Table 1 Parameters of explosive material

Density (gcm3) Burst velocity (mmμs) Pressure CJ Bulk modulus (Pa) Shear modulus (Pa)163 0693 027 0 0

Table 2 Parameters of JWL equation of state

A B R1 R2 ω E0 V0

374 323 times 10minus 2 415 095 03 007 times 1011 10

Lining structure

Composite steel Dynamite

Air

Soil

Figure 2 Composite steel lining structure mode

Shock and Vibration 3

Considering the short action time and high frequency ofexplosion shock it only takes a few milliseconds from thezero load to the maximum load and the stress-strain be-havior of the structure under the action of shock wave ispositively correlated with the action rate of shock wave(erefore in order to better study the destructive effect ofthe peak value of explosion load the numerical model has anexplosion time of 50ms [15]

(e explosive propagates to all sides after the ex-plosion Under the influence of no obstacles the blastwave will form a spherical wave array and propagateoutwards Because the explosion point is 11 m away fromthe bottom lining the distance is relatively short so thefirst contact with the bottom of the lining will increasethe pressure generate the reflected wave and propagateto the distance With the increase of the distance the

pressure of the blast wave will continue to decreasebecause of the superposition of the shock wave (ereflection wave at the bottom overlaps with the weakenedshock wave which makes the propagation speed fasterIn about 5 ms the shock wave propagates to the toplining and then it reflects downward and spreads to thedistance Because the reflection wave overlaps manytimes in the subway section tunnel the reflection waveexperiences many peaks in each point inside the tunneland slows down its weakening effect Because the shockwave starts to spread as a spherical wave it spreads in thelining (e shock wave at the top is composed of twoparts the wave front of the spherical wave and the re-flection wave of the lining at the top (e reflection wavewill continue to reflect downward in the process ofpropagation In this process some reflection waves will

Fringe levels1152e ndash 061037e ndash 069219e ndash 078067e ndash 076914e ndash 075762e ndash 074609e ndash 073457e ndash 072305e ndash 071152e ndash 07

ndash0000e + 00

Fringe levels1152e ndash 061037e ndash 069219e ndash 078067e ndash 076914e ndash 075762e ndash 074609e ndash 073457e ndash 072305e ndash 071152e ndash 07

ndash0000e + 00

t = 05ms t = 25ms t = 6ms

t = 145ms t = 425ms t = 475ms

Figure 3 (e process of blast wave under 10 kg TNT at different time period

Fringe levels1152e ndash 061037e ndash 069219e ndash 078067e ndash 076914e ndash 075762e ndash 074609e ndash 073457e ndash 072305e ndash 071152e ndash 07

ndash0000e + 00

Fringe levels1152e ndash 061037e ndash 069219e ndash 078067e ndash 076914e ndash 075762e ndash 074609e ndash 073457e ndash 072305e ndash 071152e ndash 07

ndash0000e + 00

t = 05ms t = 25ms t = 6ms

t = 145ms t = 425ms t = 475ms

Figure 4 (e process of blast wave under 30 kg TNT at different time period

4 Shock and Vibration

A5 A10 A15 A20

A19A14A9A4

A3 A8 A13 A18

A17A12

A6

A7A2

A1 A11 A16

Figure 5 Observation points of tunnel liner

0 001 002 003 004Time (s)

005

03

02

01

0

ndash01

ndash02

ndash04

ndash03

Disp

lace

men

t (m

)

A1A5

(a)

0 001 002 003 004Time (s)

005

02

01

0

ndash01

ndash02

ndash03

Disp

lace

men

t (m

)

A6A10

(b)

0 001 002 003 004Time (s)

005

0

02

01

ndash01

ndash02

Disp

lace

men

t (m

)

A11A15

(c)

0 001 002 003 004Time (s)

005

0

01

005

01

Disp

lace

men

t (m

)

A16A20

(d)

Figure 6 Changes of displacement in y-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

Shock and Vibration 5

propagate in the opposite direction resulting in multiplestress peaks on the explosion source section 30 kg TNTCompared with 10 kg TNT the blast energy is morepowerful and the impact range of shock wave is widerFor the explosion activities in the closed structure thepeak value of shock wave is strengthened due to themultiple reflection and superposition of blast wave eachpoint experiences multiple peaks its duration is in-creased and its shock propagation law is more complexIn the early stage of explosion activities the bottom blastwave propagation is faster and in the process of prop-agation when the upper shock wave undergoes reflectionand superposition the propagation speed will beaccelerated which also accords with the characteristicsthat the blast wave is a spherical wave [16]

32 Dynamic Response of the Lining Structure under the BlastAction When an explosion occurs in the tunnel section thedisplacement velocity and acceleration of the liningstructure under the action of the explosion are importantparameters to measure the damage degree of the structure[16] In order to study the dynamic response of the liningstructure under the action of explosives equivalent to 10 kgand 30 kg under the protection of composite steel plate 20reference points were selected where the influence of thelining structure was obvious and divided into four groups(ese four groups were arranged on sections at differentdistances from the explosion source centre numberedA1ndashA20 and were 0m 3m 6m and 9m away from theexplosion centre Figure 5 is the layout diagram of eachreference point of the lining structure [17ndash19]

0 001 002 003 004Time (s)

005

2

0

ndash2

ndash4

ndash6

ndash8

Velo

city

(ms

)

A1A5

(a)

0 001 002 003 004Time (s)

005

2

1

0

ndash1

ndash2

ndash3

Velo

city

(ms

)

A1A5

(b)

0 001 002 003 004Time (s)

005

Acce

lera

tion

(ms

2 )10

3

2

ndash2

0

ndash4

ndash10

ndash8

ndash6

ndash12

A11A15

(c)

0 001 002 003 004Time (s)

005

2

15

05

0

ndash2

ndash05

Acce

lera

tion

(ms

2 )10

3

A11A15

(d)

Figure 7 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

6 Shock and Vibration

321 Dynamic Response of Lining Structure under 10 kg TNTExplosion From the numerical simulation results it can beseen that the maximum vertical displacement points of eachsection occur at two reference points at the upper wall andthe lower wall Figure 6 is the y-direction displacementchange curve at the upper wall and the lower wall of the foursections

As can be seen from the y-direction displacement changecurve shown in Figure 6 the lining structure has a dis-placement of 04 cm at section A1 (e displacement changecurve of the section closer to the explosion source decreasesrapidly after experiencing a peak value and the change trendis stable As the distance from the centre of the explosionsource increases the y-direction displacement gradually

decreases Multiple displacement peaks appear at sectionstwo three and four since the shock wave energy decaysrapidly with the increase of distance (ere is a large dif-ference between the value and section one(e displacementof the reference point at a longer distance first appears as asmall amplitude oscillation change under the reflectionsuperposition effect of the shock wave (erefore under theexplosion of 10 kg of explosives the deformation peak valueof the lining is 04 cm and the influence on the liningstructure is within the elastic range At the beginning of theexplosion the lining structure was subjected to tensile stressand had a maximum acceleration and velocity at point A1Figure 7 is a velocity and acceleration variation curve in they-direction of sections one and three

01

0

ndash01

ndash02

ndash03

Disp

lace

men

t (m

)

0 001 002 003 004Time (s)

005

A2A3A4

(a)

0 001 002 003 004Time (s)

005

A7A8A9

01

0

ndash01

ndash02

Disp

lace

men

t (m

)(b)

0 001 002 003 004Time (s)

005

A12A13A14

006

004

002

0

ndash01

ndash008

ndash006

ndash004

ndash002

Disp

lace

men

t (m

)

(c)

0 001 002 003 004Time (s)

005

A17A18A19

004

002

0

ndash006

ndash004

ndash002

Disp

lace

men

t (m

)

(d)

Figure 8 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

Shock and Vibration 7

From the velocity and acceleration change curves shownin Figure 7 it can be seen that the displacement change of thereference point of section one rapidly decays after experi-encing a peak value while the displacement change of thereference point of other sections further away experiencesmultiple peaks showing an overall weakening trend and alonger duration (is also verifies that the velocity andacceleration are affected by overpressure and the magnitudeof the impact is positively related to the distance from theexplosive source Under the action of explosion the max-imum horizontal displacement of five reference points ineach section occurs at three points on the side wall Figure 8is the x-direction displacement change curve of four sectionsat three points

From the x-direction displacement variation curveshown in Figure 8 it can be seen that the maximum dis-placement of 024 cm occurs at the reference point at the side

wall A4 instead of the reference point at the front side wallA3 In addition the impact of explosion shock wave on thedisplacement of the lining structure side wall is generallyreflected in the second peak value and the first peak value ofdisplacement variation is caused by the vacuum zone formedby the sharp consumption of air during explosion Under thesuperposition of multiple reflections of the shock wave thedisplacement changes experienced multiple peaks andshowed a weakening trend By comparing the maximumvelocity and acceleration in the x-direction with the maxi-mum velocity and acceleration in the y-direction we can seethat there is a big gap between the two

322 Dynamic Response of Lining Structure under 30 kg TNTExplosion For the influence of explosion shock wave onlining structure under the action of higher explosive

0 001 002 003 004Time (s)

005

A1A5

1

05

0

05

ndash1

ndash15

Velo

city

(ms

)

(a)

0 001 002 003 004Time (s)

005

A1A5

06

04

02

0

ndash02

ndash04

ndash06

Velo

city

(ms

)

(b)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

04

02

0

ndash02

ndash04

(c)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

02

01

0

ndash02

ndash01

ndash03

(d)

Figure 9 Changes of displacement in y-direction in sections (a) Velocity in y direction of section one (b) velocity in y direction of sectionthree (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

8 Shock and Vibration

equivalent 30 kg TNT is selected for analysis Each referencepoint is arranged in the same way as 10 kg TNT Figure 9 isthe y-direction displacement change curve at upper andlower walls of the four sections

As can be seen from the y-direction displacementchange in Figure 9 the maximum vertical displacement ofeach section occurs in two points on the upper and lowerwalls (e maximum displacement of A1 reference point ofsection one in y-direction is more than twice as much asthat of section three under the action of 10 kg TNT (edisplacement change curve shows a weakening trend as awhole (erefore the displacement of the lining structureclose to the centre of the explosion source will increase at ahigh magnification when the amount of explosive in-creases exponentially However with the increase of dis-tance the displacement will increase at a lowmagnification

and the influence will decrease gradually (ere is anobvious plastic deformation at section one It can beknown that 30 kg TNT explosive exceeds the critical pointof the plastic zone of the lining structure protected bycomposite steel plates

According to the change curve in Figure 10 the changeof velocity and acceleration in the y-direction is affecteddifferently by the change of explosive charge (e multipleincrease of explosive charge has the greatest impact on thearea close to the explosive source With the increase ofdistance the impact gradually weakens Within the range of3m from the explosive source the velocity and accelerationwill rapidly decrease after experiencing a main peak valueand tend to be stable Beyond the range of 3m from theexplosive source the velocity and acceleration will slowlydecrease after experiencing a main peak value

20

10

0

ndash10

ndash20

ndash30

ndash400 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(a)

10

0

ndash10

ndash20

ndash30

ndash40

ndash500 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(b)

Acce

lera

tion

(ms

2 )103

4

2

0

ndash2

ndash4

ndash60 001 002 003 004 005

Time (s)

A11A15

(c)

Acce

lera

tion

(ms

2 )103

2

1

0

ndash1

ndash20 001 002 003 004 005

Time (s)

A11A15

(d)

Figure 10 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

Shock and Vibration 9

Under the action of 30 kg TNTexplosion the maximumhorizontal displacement of five reference points in eachsection occurs at three points on the side wall Figure 11 isthe x-direction displacement change curve of four sections atthree points By comparing the data of Figures 8 and 11 itcan be concluded that the maximum displacement at foursections in the x-direction under the action of 30 kg TNT isabout twice as large as that under the action of 10 kg TNTslightly smaller than the maximum displacement increase inthe y-direction at the same distance At the same time it canalso be obtained through the displacement change curve ofsection one and the damage effect of 30 kg TNT equivalenthas exceeded the critical point making the lining structureproduce a plastic zone

323 Variation Curve of Axial Overpressure underExplosion For the variation of overpressure effect of ex-plosion shock wave along the axial direction of liningstructure the 20 reference points A1ndashA20 are divided intofive straight lines L1 L2 L3 L4and L5 along the axialdirection the L1 straight line includes A1 A15 A11 andA16 L2 straight line includes A2 A7 A12 and A17 L3straight line includes A3 A8 A13 and A18 L4 straight lineincludes A4 A9 A14 and A19 L5 straight line includes A5A10 A15 and A20 Figures 12 and 13 are curves of axialoverpressure change under explosion of 10 kg TNT and30 kg TNT

According to the attenuation law of overpressure oneach straight line in Figure 12 the overpressure at the close

0 001 002 003 004 005Time (s)

A2A3A4

02

01

0

ndash01

ndash02

ndash03

ndash04

ndash05

Disp

lace

men

t (m

)

(a)

0 001 002 003 004 005Time (s)

A7A8A9

0

02

01

ndash01

ndash02

ndash03

ndash04

Disp

lace

men

t (m

)

(b)

0 001 002 003 004 005Time (s)

A12A13A14

Disp

lace

men

t (m

)

01

005

0

ndash005

ndash01

ndash015

ndash02

(c)

0 001 002 003 004 005Time (s)

A18A17A19

Disp

lace

men

t (m

)01

005

0

ndash005

ndash01

(d)

Figure 11 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

10 Shock and Vibration

distance from the lining structure is the strongest (eoverpressure will decrease sharply in the range of 3m andthe overpressure will decrease slowly in the range of3msim9m as a whole (is is due to the rapid compression ofair near the explosive at the initial stage of the explosionreaction concentration of energy and overpressure phe-nomenon With the increase of distance the energy willgradually diffuse [20](e axial overpressure of the referencepoint within 6m away from the centre of the explosionsource will also increase slightly which is due to the energyreceived by individual reference points increasing after theexplosion shock wave is reflected and superimposed formany times

By comparing the overpressure changes in Figures 12and 13 it can be seen that at the beginning of the explosionthe overpressure peak value of 30 kg TNT increased by aboutsix times compared with 10 kg TNT at the same referencepoint which is much larger than the increase of explosivemass Similar to the variation curve of overpressure of 10 kgTNT the overpressure is strongest at the close distance fromthe centre of the explosion source (e overpressure has

obvious attenuation at 3m from the centre of the explosionsource and the overpressure keeps a slow attenuation trendin the range of 3msim9m (e overpressure of the referencepoint in the same straight line beyond 6m will also bestrengthened which is also due to the superposition ofmultiple reflections of the explosion shock wave

4 Conclusions

(e instantaneous dynamic response of the lining structureinstalled with composite steel plate when explosion occurs issimulated by establishing a composite steel plate liningstructure model Different influencing factors are deter-mined and parameterized analysis is carried out by using themethod of comparison of different explosive equivalentexplosion effects (e following conclusions are obtained

(1) (e change of velocity acceleration and displace-ment of each reference point at the lining structure isrelated to the action of overpressure and distance Amain peak value will be formed within 3m from theexplosion source and the peak value is obviouslyhigher than other peaks With the propagation ofexplosion shock wave the function of lining struc-ture will gradually decrease

(2) (e effect of multiple increase of explosive quantityon each point of lining structure is not the same (eacceleration near the distance is generally far greaterthan the multiple increase of explosive quantitywhile the increase of velocity and displacement isbasically the same as the explosive quantity (eeffect of multiple increase of explosive quantity onacceleration velocity and displacement is reducedand the change is relatively stable at a distance (3maway from the explosive source)

(3) By comparing the data changes of acceleration velocityand displacement in each direction of the same refer-ence point it can be seen that under the action ofexplosion when the distance is relatively close theinfluence is greater the axial stress has the least influenceon the lining structure and the influence of y-directionof the lining section on the lining structure is greaterthan the other two directions

Data Availability

(e rawprocessed data used to support the findings of thisstudy have not been made available because they form partof the ongoing research

Conflicts of Interest

(e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof China (41372288) and Shandong Natural ScienceFoundation (ZR2019MEE027)

2 8 1040 6Displacement (m)

0

02

04

06

08

1

12

14Pr

essu

re (M

Pa)

L1L2L3

L4L5

Figure 12 Overpressure attenuation laws in lines of 10 kg TNT

L1L2L3

L4L5

2 8 1040 6Displacement (m)

0

1

2

3

4

5

6

7

8

Pres

sure

(MPa

)

Figure 13 Overpressure attenuation laws in lines of 30 kg TNT

Shock and Vibration 11

References

[1] Q H Meng Dynamic Response and Explosion-Resist-Ant-protection of Subway Tunnel under Terroristbom-Bing loadShandong University of Science and Technology QingdaoChina 2010

[2] D S Kong M Y Deng and Y Z Li ldquoExperimental study onmechanical deformation characteristics of inclined andstraight alternating pile groupsrdquo Advances in Civil Engi-neering vol 2020 Article ID 8394182 11 pages 2020

[3] D-S Kong Q-H Meng W-W Zhang and Q-H ZhangldquoShock responses of a metro tunnel subjected to explosiveloadsrdquo Journal of Vibration and Shock vol 31 no 12pp 69ndash72 2012

[4] J B Liu andQ S H Ni ldquoStudy on explosion protectionin ironunderground structurerdquo Journal of Vibration and Shockvol 27 no 8 pp 16ndash19 2008

[5] A Zyskowski I Sochet G Mavrot P Bailly and J RenardldquoStudy of the explosion process in a small scale experiment-structural loadingrdquo Journal of Loss Prevention in the ProcessIndustries vol 17 no 4 pp 291ndash299 2004

[6] C L Yan andD J Ma ldquoHigh resolution numerical simulationof strong explosive waves in a vesselrdquo Journal of ChinaUniversity of Science and Technology vol 25 no 1 pp 10ndash161998

[7] Y Z Cao Z S Lu and H A Guan ldquoNumerical simulation ofexplosion flow field in anti-explosion vesselrdquo Journal of ChinaUniversity of Science and Technology Chinese Journal of HighPressure Physics vol 15 no 2 pp 127ndash133 2001

[8] Y Cui Dynamic Response and Damage Assessment of DuplexHollow CFST Column Subjected to Blast Loading ChanganUniversity Xirsquoan China 2013

[9] D S Kong M X Deng and Z M Zhao ldquoSeismic interactioncharacteristics of an inclined straight alternating pile group-soil in liquefied groundrdquo Advances in Civil Engineeringvol 2019 Article ID 3758286 12 pages 2019

[10] K Z Yang and X M Yang ldquo(e propagation law of theimpulse shock wave in the tunnelrdquo Explosion and ShockWaves vol 23 no 1 pp 37ndash40 2003

[11] A L Kuhl and H Reichenbach ldquoCombustion effects inconfined explosionsrdquo Proceedings of the Combustion Institutevol 32 no 2 pp 2291ndash2298 2009

[12] D Kong M Deng Y Liu and X Tan ldquoStudy of the force anddeformation characteristics of subsea mudmat-pile hybridfoundationsrdquo Polish Maritime Research vol 25 no s3pp 43ndash53 2019

[13] S H Qu Structural Response and Damage and Ground Vi-bration of Subway Station under Internal Explosion TianjinUniversity Tianjin China 2008

[14] X L Du W Z H Liao M Z H Tian et al ldquoNumericalsimulation of flow around blast waverdquo Journal of BeijingUniversity of Technology vol 34 no 3 pp 277ndash287 2008

[15] D S Kong M X Deng and Y Xu ldquoStudy on calculation ofpile sliding interval of large-diameter steel pipe piles onoffshore platformsrdquo Mathematical Problems in Engineeringvol 2019 Article ID 3549296 8 pages 2019

[16] Y F Liu R H Liu S Q Shi et al ldquoNumerical stimulation onanalysis of reducing blast by using foam aluminumrdquo ChineseJournal of Underground Space and Engineering vol 27 no 8pp 16ndash19 2008

[17] D S Kong Y F Bai Y P Chen andM X Deng ldquoA study onthe seismic response characteristics of an oblique pile group-soil-structure with different pile capsrdquo Shock and Vibrationvol 2019 Article ID 8141045 12 pages 2019

[18] D S Kong M X Deng and Y Z Li ldquoNumerical simulation ofseismic soil-pile interaction in liquefying groundrdquo IEEEAccess vol 8 no 1 pp 195ndash204 2020

[19] D S Kong Y Liu M X Deng and X Y Zhao ldquoAnalysis ofinfluencing factors of lateral soil resistance distributioncharacteristics around monopole foundation for offshorewind powerrdquo Applied Ocean Research vol 97 Article ID102106 2020

[20] W W Zhang Study of Impulse Response and Shield Tech-nology of Subway Station under Terrorist Explosion loadShandong University of Science and Technology QingdaoChina 2010

12 Shock and Vibration

Considering the short action time and high frequency ofexplosion shock it only takes a few milliseconds from thezero load to the maximum load and the stress-strain be-havior of the structure under the action of shock wave ispositively correlated with the action rate of shock wave(erefore in order to better study the destructive effect ofthe peak value of explosion load the numerical model has anexplosion time of 50ms [15]

(e explosive propagates to all sides after the ex-plosion Under the influence of no obstacles the blastwave will form a spherical wave array and propagateoutwards Because the explosion point is 11 m away fromthe bottom lining the distance is relatively short so thefirst contact with the bottom of the lining will increasethe pressure generate the reflected wave and propagateto the distance With the increase of the distance the

pressure of the blast wave will continue to decreasebecause of the superposition of the shock wave (ereflection wave at the bottom overlaps with the weakenedshock wave which makes the propagation speed fasterIn about 5 ms the shock wave propagates to the toplining and then it reflects downward and spreads to thedistance Because the reflection wave overlaps manytimes in the subway section tunnel the reflection waveexperiences many peaks in each point inside the tunneland slows down its weakening effect Because the shockwave starts to spread as a spherical wave it spreads in thelining (e shock wave at the top is composed of twoparts the wave front of the spherical wave and the re-flection wave of the lining at the top (e reflection wavewill continue to reflect downward in the process ofpropagation In this process some reflection waves will

Fringe levels1152e ndash 061037e ndash 069219e ndash 078067e ndash 076914e ndash 075762e ndash 074609e ndash 073457e ndash 072305e ndash 071152e ndash 07

ndash0000e + 00

Fringe levels1152e ndash 061037e ndash 069219e ndash 078067e ndash 076914e ndash 075762e ndash 074609e ndash 073457e ndash 072305e ndash 071152e ndash 07

ndash0000e + 00

t = 05ms t = 25ms t = 6ms

t = 145ms t = 425ms t = 475ms

Figure 3 (e process of blast wave under 10 kg TNT at different time period

Fringe levels1152e ndash 061037e ndash 069219e ndash 078067e ndash 076914e ndash 075762e ndash 074609e ndash 073457e ndash 072305e ndash 071152e ndash 07

ndash0000e + 00

Fringe levels1152e ndash 061037e ndash 069219e ndash 078067e ndash 076914e ndash 075762e ndash 074609e ndash 073457e ndash 072305e ndash 071152e ndash 07

ndash0000e + 00

t = 05ms t = 25ms t = 6ms

t = 145ms t = 425ms t = 475ms

Figure 4 (e process of blast wave under 30 kg TNT at different time period

4 Shock and Vibration

A5 A10 A15 A20

A19A14A9A4

A3 A8 A13 A18

A17A12

A6

A7A2

A1 A11 A16

Figure 5 Observation points of tunnel liner

0 001 002 003 004Time (s)

005

03

02

01

0

ndash01

ndash02

ndash04

ndash03

Disp

lace

men

t (m

)

A1A5

(a)

0 001 002 003 004Time (s)

005

02

01

0

ndash01

ndash02

ndash03

Disp

lace

men

t (m

)

A6A10

(b)

0 001 002 003 004Time (s)

005

0

02

01

ndash01

ndash02

Disp

lace

men

t (m

)

A11A15

(c)

0 001 002 003 004Time (s)

005

0

01

005

01

Disp

lace

men

t (m

)

A16A20

(d)

Figure 6 Changes of displacement in y-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

Shock and Vibration 5

propagate in the opposite direction resulting in multiplestress peaks on the explosion source section 30 kg TNTCompared with 10 kg TNT the blast energy is morepowerful and the impact range of shock wave is widerFor the explosion activities in the closed structure thepeak value of shock wave is strengthened due to themultiple reflection and superposition of blast wave eachpoint experiences multiple peaks its duration is in-creased and its shock propagation law is more complexIn the early stage of explosion activities the bottom blastwave propagation is faster and in the process of prop-agation when the upper shock wave undergoes reflectionand superposition the propagation speed will beaccelerated which also accords with the characteristicsthat the blast wave is a spherical wave [16]

32 Dynamic Response of the Lining Structure under the BlastAction When an explosion occurs in the tunnel section thedisplacement velocity and acceleration of the liningstructure under the action of the explosion are importantparameters to measure the damage degree of the structure[16] In order to study the dynamic response of the liningstructure under the action of explosives equivalent to 10 kgand 30 kg under the protection of composite steel plate 20reference points were selected where the influence of thelining structure was obvious and divided into four groups(ese four groups were arranged on sections at differentdistances from the explosion source centre numberedA1ndashA20 and were 0m 3m 6m and 9m away from theexplosion centre Figure 5 is the layout diagram of eachreference point of the lining structure [17ndash19]

0 001 002 003 004Time (s)

005

2

0

ndash2

ndash4

ndash6

ndash8

Velo

city

(ms

)

A1A5

(a)

0 001 002 003 004Time (s)

005

2

1

0

ndash1

ndash2

ndash3

Velo

city

(ms

)

A1A5

(b)

0 001 002 003 004Time (s)

005

Acce

lera

tion

(ms

2 )10

3

2

ndash2

0

ndash4

ndash10

ndash8

ndash6

ndash12

A11A15

(c)

0 001 002 003 004Time (s)

005

2

15

05

0

ndash2

ndash05

Acce

lera

tion

(ms

2 )10

3

A11A15

(d)

Figure 7 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

6 Shock and Vibration

321 Dynamic Response of Lining Structure under 10 kg TNTExplosion From the numerical simulation results it can beseen that the maximum vertical displacement points of eachsection occur at two reference points at the upper wall andthe lower wall Figure 6 is the y-direction displacementchange curve at the upper wall and the lower wall of the foursections

As can be seen from the y-direction displacement changecurve shown in Figure 6 the lining structure has a dis-placement of 04 cm at section A1 (e displacement changecurve of the section closer to the explosion source decreasesrapidly after experiencing a peak value and the change trendis stable As the distance from the centre of the explosionsource increases the y-direction displacement gradually

decreases Multiple displacement peaks appear at sectionstwo three and four since the shock wave energy decaysrapidly with the increase of distance (ere is a large dif-ference between the value and section one(e displacementof the reference point at a longer distance first appears as asmall amplitude oscillation change under the reflectionsuperposition effect of the shock wave (erefore under theexplosion of 10 kg of explosives the deformation peak valueof the lining is 04 cm and the influence on the liningstructure is within the elastic range At the beginning of theexplosion the lining structure was subjected to tensile stressand had a maximum acceleration and velocity at point A1Figure 7 is a velocity and acceleration variation curve in they-direction of sections one and three

01

0

ndash01

ndash02

ndash03

Disp

lace

men

t (m

)

0 001 002 003 004Time (s)

005

A2A3A4

(a)

0 001 002 003 004Time (s)

005

A7A8A9

01

0

ndash01

ndash02

Disp

lace

men

t (m

)(b)

0 001 002 003 004Time (s)

005

A12A13A14

006

004

002

0

ndash01

ndash008

ndash006

ndash004

ndash002

Disp

lace

men

t (m

)

(c)

0 001 002 003 004Time (s)

005

A17A18A19

004

002

0

ndash006

ndash004

ndash002

Disp

lace

men

t (m

)

(d)

Figure 8 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

Shock and Vibration 7

From the velocity and acceleration change curves shownin Figure 7 it can be seen that the displacement change of thereference point of section one rapidly decays after experi-encing a peak value while the displacement change of thereference point of other sections further away experiencesmultiple peaks showing an overall weakening trend and alonger duration (is also verifies that the velocity andacceleration are affected by overpressure and the magnitudeof the impact is positively related to the distance from theexplosive source Under the action of explosion the max-imum horizontal displacement of five reference points ineach section occurs at three points on the side wall Figure 8is the x-direction displacement change curve of four sectionsat three points

From the x-direction displacement variation curveshown in Figure 8 it can be seen that the maximum dis-placement of 024 cm occurs at the reference point at the side

wall A4 instead of the reference point at the front side wallA3 In addition the impact of explosion shock wave on thedisplacement of the lining structure side wall is generallyreflected in the second peak value and the first peak value ofdisplacement variation is caused by the vacuum zone formedby the sharp consumption of air during explosion Under thesuperposition of multiple reflections of the shock wave thedisplacement changes experienced multiple peaks andshowed a weakening trend By comparing the maximumvelocity and acceleration in the x-direction with the maxi-mum velocity and acceleration in the y-direction we can seethat there is a big gap between the two

322 Dynamic Response of Lining Structure under 30 kg TNTExplosion For the influence of explosion shock wave onlining structure under the action of higher explosive

0 001 002 003 004Time (s)

005

A1A5

1

05

0

05

ndash1

ndash15

Velo

city

(ms

)

(a)

0 001 002 003 004Time (s)

005

A1A5

06

04

02

0

ndash02

ndash04

ndash06

Velo

city

(ms

)

(b)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

04

02

0

ndash02

ndash04

(c)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

02

01

0

ndash02

ndash01

ndash03

(d)

Figure 9 Changes of displacement in y-direction in sections (a) Velocity in y direction of section one (b) velocity in y direction of sectionthree (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

8 Shock and Vibration

equivalent 30 kg TNT is selected for analysis Each referencepoint is arranged in the same way as 10 kg TNT Figure 9 isthe y-direction displacement change curve at upper andlower walls of the four sections

As can be seen from the y-direction displacementchange in Figure 9 the maximum vertical displacement ofeach section occurs in two points on the upper and lowerwalls (e maximum displacement of A1 reference point ofsection one in y-direction is more than twice as much asthat of section three under the action of 10 kg TNT (edisplacement change curve shows a weakening trend as awhole (erefore the displacement of the lining structureclose to the centre of the explosion source will increase at ahigh magnification when the amount of explosive in-creases exponentially However with the increase of dis-tance the displacement will increase at a lowmagnification

and the influence will decrease gradually (ere is anobvious plastic deformation at section one It can beknown that 30 kg TNT explosive exceeds the critical pointof the plastic zone of the lining structure protected bycomposite steel plates

According to the change curve in Figure 10 the changeof velocity and acceleration in the y-direction is affecteddifferently by the change of explosive charge (e multipleincrease of explosive charge has the greatest impact on thearea close to the explosive source With the increase ofdistance the impact gradually weakens Within the range of3m from the explosive source the velocity and accelerationwill rapidly decrease after experiencing a main peak valueand tend to be stable Beyond the range of 3m from theexplosive source the velocity and acceleration will slowlydecrease after experiencing a main peak value

20

10

0

ndash10

ndash20

ndash30

ndash400 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(a)

10

0

ndash10

ndash20

ndash30

ndash40

ndash500 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(b)

Acce

lera

tion

(ms

2 )103

4

2

0

ndash2

ndash4

ndash60 001 002 003 004 005

Time (s)

A11A15

(c)

Acce

lera

tion

(ms

2 )103

2

1

0

ndash1

ndash20 001 002 003 004 005

Time (s)

A11A15

(d)

Figure 10 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

Shock and Vibration 9

Under the action of 30 kg TNTexplosion the maximumhorizontal displacement of five reference points in eachsection occurs at three points on the side wall Figure 11 isthe x-direction displacement change curve of four sections atthree points By comparing the data of Figures 8 and 11 itcan be concluded that the maximum displacement at foursections in the x-direction under the action of 30 kg TNT isabout twice as large as that under the action of 10 kg TNTslightly smaller than the maximum displacement increase inthe y-direction at the same distance At the same time it canalso be obtained through the displacement change curve ofsection one and the damage effect of 30 kg TNT equivalenthas exceeded the critical point making the lining structureproduce a plastic zone

323 Variation Curve of Axial Overpressure underExplosion For the variation of overpressure effect of ex-plosion shock wave along the axial direction of liningstructure the 20 reference points A1ndashA20 are divided intofive straight lines L1 L2 L3 L4and L5 along the axialdirection the L1 straight line includes A1 A15 A11 andA16 L2 straight line includes A2 A7 A12 and A17 L3straight line includes A3 A8 A13 and A18 L4 straight lineincludes A4 A9 A14 and A19 L5 straight line includes A5A10 A15 and A20 Figures 12 and 13 are curves of axialoverpressure change under explosion of 10 kg TNT and30 kg TNT

According to the attenuation law of overpressure oneach straight line in Figure 12 the overpressure at the close

0 001 002 003 004 005Time (s)

A2A3A4

02

01

0

ndash01

ndash02

ndash03

ndash04

ndash05

Disp

lace

men

t (m

)

(a)

0 001 002 003 004 005Time (s)

A7A8A9

0

02

01

ndash01

ndash02

ndash03

ndash04

Disp

lace

men

t (m

)

(b)

0 001 002 003 004 005Time (s)

A12A13A14

Disp

lace

men

t (m

)

01

005

0

ndash005

ndash01

ndash015

ndash02

(c)

0 001 002 003 004 005Time (s)

A18A17A19

Disp

lace

men

t (m

)01

005

0

ndash005

ndash01

(d)

Figure 11 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

10 Shock and Vibration

distance from the lining structure is the strongest (eoverpressure will decrease sharply in the range of 3m andthe overpressure will decrease slowly in the range of3msim9m as a whole (is is due to the rapid compression ofair near the explosive at the initial stage of the explosionreaction concentration of energy and overpressure phe-nomenon With the increase of distance the energy willgradually diffuse [20](e axial overpressure of the referencepoint within 6m away from the centre of the explosionsource will also increase slightly which is due to the energyreceived by individual reference points increasing after theexplosion shock wave is reflected and superimposed formany times

By comparing the overpressure changes in Figures 12and 13 it can be seen that at the beginning of the explosionthe overpressure peak value of 30 kg TNT increased by aboutsix times compared with 10 kg TNT at the same referencepoint which is much larger than the increase of explosivemass Similar to the variation curve of overpressure of 10 kgTNT the overpressure is strongest at the close distance fromthe centre of the explosion source (e overpressure has

obvious attenuation at 3m from the centre of the explosionsource and the overpressure keeps a slow attenuation trendin the range of 3msim9m (e overpressure of the referencepoint in the same straight line beyond 6m will also bestrengthened which is also due to the superposition ofmultiple reflections of the explosion shock wave

4 Conclusions

(e instantaneous dynamic response of the lining structureinstalled with composite steel plate when explosion occurs issimulated by establishing a composite steel plate liningstructure model Different influencing factors are deter-mined and parameterized analysis is carried out by using themethod of comparison of different explosive equivalentexplosion effects (e following conclusions are obtained

(1) (e change of velocity acceleration and displace-ment of each reference point at the lining structure isrelated to the action of overpressure and distance Amain peak value will be formed within 3m from theexplosion source and the peak value is obviouslyhigher than other peaks With the propagation ofexplosion shock wave the function of lining struc-ture will gradually decrease

(2) (e effect of multiple increase of explosive quantityon each point of lining structure is not the same (eacceleration near the distance is generally far greaterthan the multiple increase of explosive quantitywhile the increase of velocity and displacement isbasically the same as the explosive quantity (eeffect of multiple increase of explosive quantity onacceleration velocity and displacement is reducedand the change is relatively stable at a distance (3maway from the explosive source)

(3) By comparing the data changes of acceleration velocityand displacement in each direction of the same refer-ence point it can be seen that under the action ofexplosion when the distance is relatively close theinfluence is greater the axial stress has the least influenceon the lining structure and the influence of y-directionof the lining section on the lining structure is greaterthan the other two directions

Data Availability

(e rawprocessed data used to support the findings of thisstudy have not been made available because they form partof the ongoing research

Conflicts of Interest

(e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof China (41372288) and Shandong Natural ScienceFoundation (ZR2019MEE027)

2 8 1040 6Displacement (m)

0

02

04

06

08

1

12

14Pr

essu

re (M

Pa)

L1L2L3

L4L5

Figure 12 Overpressure attenuation laws in lines of 10 kg TNT

L1L2L3

L4L5

2 8 1040 6Displacement (m)

0

1

2

3

4

5

6

7

8

Pres

sure

(MPa

)

Figure 13 Overpressure attenuation laws in lines of 30 kg TNT

Shock and Vibration 11

References

[1] Q H Meng Dynamic Response and Explosion-Resist-Ant-protection of Subway Tunnel under Terroristbom-Bing loadShandong University of Science and Technology QingdaoChina 2010

[2] D S Kong M Y Deng and Y Z Li ldquoExperimental study onmechanical deformation characteristics of inclined andstraight alternating pile groupsrdquo Advances in Civil Engi-neering vol 2020 Article ID 8394182 11 pages 2020

[3] D-S Kong Q-H Meng W-W Zhang and Q-H ZhangldquoShock responses of a metro tunnel subjected to explosiveloadsrdquo Journal of Vibration and Shock vol 31 no 12pp 69ndash72 2012

[4] J B Liu andQ S H Ni ldquoStudy on explosion protectionin ironunderground structurerdquo Journal of Vibration and Shockvol 27 no 8 pp 16ndash19 2008

[5] A Zyskowski I Sochet G Mavrot P Bailly and J RenardldquoStudy of the explosion process in a small scale experiment-structural loadingrdquo Journal of Loss Prevention in the ProcessIndustries vol 17 no 4 pp 291ndash299 2004

[6] C L Yan andD J Ma ldquoHigh resolution numerical simulationof strong explosive waves in a vesselrdquo Journal of ChinaUniversity of Science and Technology vol 25 no 1 pp 10ndash161998

[7] Y Z Cao Z S Lu and H A Guan ldquoNumerical simulation ofexplosion flow field in anti-explosion vesselrdquo Journal of ChinaUniversity of Science and Technology Chinese Journal of HighPressure Physics vol 15 no 2 pp 127ndash133 2001

[8] Y Cui Dynamic Response and Damage Assessment of DuplexHollow CFST Column Subjected to Blast Loading ChanganUniversity Xirsquoan China 2013

[9] D S Kong M X Deng and Z M Zhao ldquoSeismic interactioncharacteristics of an inclined straight alternating pile group-soil in liquefied groundrdquo Advances in Civil Engineeringvol 2019 Article ID 3758286 12 pages 2019

[10] K Z Yang and X M Yang ldquo(e propagation law of theimpulse shock wave in the tunnelrdquo Explosion and ShockWaves vol 23 no 1 pp 37ndash40 2003

[11] A L Kuhl and H Reichenbach ldquoCombustion effects inconfined explosionsrdquo Proceedings of the Combustion Institutevol 32 no 2 pp 2291ndash2298 2009

[12] D Kong M Deng Y Liu and X Tan ldquoStudy of the force anddeformation characteristics of subsea mudmat-pile hybridfoundationsrdquo Polish Maritime Research vol 25 no s3pp 43ndash53 2019

[13] S H Qu Structural Response and Damage and Ground Vi-bration of Subway Station under Internal Explosion TianjinUniversity Tianjin China 2008

[14] X L Du W Z H Liao M Z H Tian et al ldquoNumericalsimulation of flow around blast waverdquo Journal of BeijingUniversity of Technology vol 34 no 3 pp 277ndash287 2008

[15] D S Kong M X Deng and Y Xu ldquoStudy on calculation ofpile sliding interval of large-diameter steel pipe piles onoffshore platformsrdquo Mathematical Problems in Engineeringvol 2019 Article ID 3549296 8 pages 2019

[16] Y F Liu R H Liu S Q Shi et al ldquoNumerical stimulation onanalysis of reducing blast by using foam aluminumrdquo ChineseJournal of Underground Space and Engineering vol 27 no 8pp 16ndash19 2008

[17] D S Kong Y F Bai Y P Chen andM X Deng ldquoA study onthe seismic response characteristics of an oblique pile group-soil-structure with different pile capsrdquo Shock and Vibrationvol 2019 Article ID 8141045 12 pages 2019

[18] D S Kong M X Deng and Y Z Li ldquoNumerical simulation ofseismic soil-pile interaction in liquefying groundrdquo IEEEAccess vol 8 no 1 pp 195ndash204 2020

[19] D S Kong Y Liu M X Deng and X Y Zhao ldquoAnalysis ofinfluencing factors of lateral soil resistance distributioncharacteristics around monopole foundation for offshorewind powerrdquo Applied Ocean Research vol 97 Article ID102106 2020

[20] W W Zhang Study of Impulse Response and Shield Tech-nology of Subway Station under Terrorist Explosion loadShandong University of Science and Technology QingdaoChina 2010

12 Shock and Vibration

A5 A10 A15 A20

A19A14A9A4

A3 A8 A13 A18

A17A12

A6

A7A2

A1 A11 A16

Figure 5 Observation points of tunnel liner

0 001 002 003 004Time (s)

005

03

02

01

0

ndash01

ndash02

ndash04

ndash03

Disp

lace

men

t (m

)

A1A5

(a)

0 001 002 003 004Time (s)

005

02

01

0

ndash01

ndash02

ndash03

Disp

lace

men

t (m

)

A6A10

(b)

0 001 002 003 004Time (s)

005

0

02

01

ndash01

ndash02

Disp

lace

men

t (m

)

A11A15

(c)

0 001 002 003 004Time (s)

005

0

01

005

01

Disp

lace

men

t (m

)

A16A20

(d)

Figure 6 Changes of displacement in y-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

Shock and Vibration 5

propagate in the opposite direction resulting in multiplestress peaks on the explosion source section 30 kg TNTCompared with 10 kg TNT the blast energy is morepowerful and the impact range of shock wave is widerFor the explosion activities in the closed structure thepeak value of shock wave is strengthened due to themultiple reflection and superposition of blast wave eachpoint experiences multiple peaks its duration is in-creased and its shock propagation law is more complexIn the early stage of explosion activities the bottom blastwave propagation is faster and in the process of prop-agation when the upper shock wave undergoes reflectionand superposition the propagation speed will beaccelerated which also accords with the characteristicsthat the blast wave is a spherical wave [16]

32 Dynamic Response of the Lining Structure under the BlastAction When an explosion occurs in the tunnel section thedisplacement velocity and acceleration of the liningstructure under the action of the explosion are importantparameters to measure the damage degree of the structure[16] In order to study the dynamic response of the liningstructure under the action of explosives equivalent to 10 kgand 30 kg under the protection of composite steel plate 20reference points were selected where the influence of thelining structure was obvious and divided into four groups(ese four groups were arranged on sections at differentdistances from the explosion source centre numberedA1ndashA20 and were 0m 3m 6m and 9m away from theexplosion centre Figure 5 is the layout diagram of eachreference point of the lining structure [17ndash19]

0 001 002 003 004Time (s)

005

2

0

ndash2

ndash4

ndash6

ndash8

Velo

city

(ms

)

A1A5

(a)

0 001 002 003 004Time (s)

005

2

1

0

ndash1

ndash2

ndash3

Velo

city

(ms

)

A1A5

(b)

0 001 002 003 004Time (s)

005

Acce

lera

tion

(ms

2 )10

3

2

ndash2

0

ndash4

ndash10

ndash8

ndash6

ndash12

A11A15

(c)

0 001 002 003 004Time (s)

005

2

15

05

0

ndash2

ndash05

Acce

lera

tion

(ms

2 )10

3

A11A15

(d)

Figure 7 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

6 Shock and Vibration

321 Dynamic Response of Lining Structure under 10 kg TNTExplosion From the numerical simulation results it can beseen that the maximum vertical displacement points of eachsection occur at two reference points at the upper wall andthe lower wall Figure 6 is the y-direction displacementchange curve at the upper wall and the lower wall of the foursections

As can be seen from the y-direction displacement changecurve shown in Figure 6 the lining structure has a dis-placement of 04 cm at section A1 (e displacement changecurve of the section closer to the explosion source decreasesrapidly after experiencing a peak value and the change trendis stable As the distance from the centre of the explosionsource increases the y-direction displacement gradually

decreases Multiple displacement peaks appear at sectionstwo three and four since the shock wave energy decaysrapidly with the increase of distance (ere is a large dif-ference between the value and section one(e displacementof the reference point at a longer distance first appears as asmall amplitude oscillation change under the reflectionsuperposition effect of the shock wave (erefore under theexplosion of 10 kg of explosives the deformation peak valueof the lining is 04 cm and the influence on the liningstructure is within the elastic range At the beginning of theexplosion the lining structure was subjected to tensile stressand had a maximum acceleration and velocity at point A1Figure 7 is a velocity and acceleration variation curve in they-direction of sections one and three

01

0

ndash01

ndash02

ndash03

Disp

lace

men

t (m

)

0 001 002 003 004Time (s)

005

A2A3A4

(a)

0 001 002 003 004Time (s)

005

A7A8A9

01

0

ndash01

ndash02

Disp

lace

men

t (m

)(b)

0 001 002 003 004Time (s)

005

A12A13A14

006

004

002

0

ndash01

ndash008

ndash006

ndash004

ndash002

Disp

lace

men

t (m

)

(c)

0 001 002 003 004Time (s)

005

A17A18A19

004

002

0

ndash006

ndash004

ndash002

Disp

lace

men

t (m

)

(d)

Figure 8 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

Shock and Vibration 7

From the velocity and acceleration change curves shownin Figure 7 it can be seen that the displacement change of thereference point of section one rapidly decays after experi-encing a peak value while the displacement change of thereference point of other sections further away experiencesmultiple peaks showing an overall weakening trend and alonger duration (is also verifies that the velocity andacceleration are affected by overpressure and the magnitudeof the impact is positively related to the distance from theexplosive source Under the action of explosion the max-imum horizontal displacement of five reference points ineach section occurs at three points on the side wall Figure 8is the x-direction displacement change curve of four sectionsat three points

From the x-direction displacement variation curveshown in Figure 8 it can be seen that the maximum dis-placement of 024 cm occurs at the reference point at the side

wall A4 instead of the reference point at the front side wallA3 In addition the impact of explosion shock wave on thedisplacement of the lining structure side wall is generallyreflected in the second peak value and the first peak value ofdisplacement variation is caused by the vacuum zone formedby the sharp consumption of air during explosion Under thesuperposition of multiple reflections of the shock wave thedisplacement changes experienced multiple peaks andshowed a weakening trend By comparing the maximumvelocity and acceleration in the x-direction with the maxi-mum velocity and acceleration in the y-direction we can seethat there is a big gap between the two

322 Dynamic Response of Lining Structure under 30 kg TNTExplosion For the influence of explosion shock wave onlining structure under the action of higher explosive

0 001 002 003 004Time (s)

005

A1A5

1

05

0

05

ndash1

ndash15

Velo

city

(ms

)

(a)

0 001 002 003 004Time (s)

005

A1A5

06

04

02

0

ndash02

ndash04

ndash06

Velo

city

(ms

)

(b)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

04

02

0

ndash02

ndash04

(c)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

02

01

0

ndash02

ndash01

ndash03

(d)

Figure 9 Changes of displacement in y-direction in sections (a) Velocity in y direction of section one (b) velocity in y direction of sectionthree (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

8 Shock and Vibration

equivalent 30 kg TNT is selected for analysis Each referencepoint is arranged in the same way as 10 kg TNT Figure 9 isthe y-direction displacement change curve at upper andlower walls of the four sections

As can be seen from the y-direction displacementchange in Figure 9 the maximum vertical displacement ofeach section occurs in two points on the upper and lowerwalls (e maximum displacement of A1 reference point ofsection one in y-direction is more than twice as much asthat of section three under the action of 10 kg TNT (edisplacement change curve shows a weakening trend as awhole (erefore the displacement of the lining structureclose to the centre of the explosion source will increase at ahigh magnification when the amount of explosive in-creases exponentially However with the increase of dis-tance the displacement will increase at a lowmagnification

and the influence will decrease gradually (ere is anobvious plastic deformation at section one It can beknown that 30 kg TNT explosive exceeds the critical pointof the plastic zone of the lining structure protected bycomposite steel plates

According to the change curve in Figure 10 the changeof velocity and acceleration in the y-direction is affecteddifferently by the change of explosive charge (e multipleincrease of explosive charge has the greatest impact on thearea close to the explosive source With the increase ofdistance the impact gradually weakens Within the range of3m from the explosive source the velocity and accelerationwill rapidly decrease after experiencing a main peak valueand tend to be stable Beyond the range of 3m from theexplosive source the velocity and acceleration will slowlydecrease after experiencing a main peak value

20

10

0

ndash10

ndash20

ndash30

ndash400 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(a)

10

0

ndash10

ndash20

ndash30

ndash40

ndash500 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(b)

Acce

lera

tion

(ms

2 )103

4

2

0

ndash2

ndash4

ndash60 001 002 003 004 005

Time (s)

A11A15

(c)

Acce

lera

tion

(ms

2 )103

2

1

0

ndash1

ndash20 001 002 003 004 005

Time (s)

A11A15

(d)

Figure 10 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

Shock and Vibration 9

Under the action of 30 kg TNTexplosion the maximumhorizontal displacement of five reference points in eachsection occurs at three points on the side wall Figure 11 isthe x-direction displacement change curve of four sections atthree points By comparing the data of Figures 8 and 11 itcan be concluded that the maximum displacement at foursections in the x-direction under the action of 30 kg TNT isabout twice as large as that under the action of 10 kg TNTslightly smaller than the maximum displacement increase inthe y-direction at the same distance At the same time it canalso be obtained through the displacement change curve ofsection one and the damage effect of 30 kg TNT equivalenthas exceeded the critical point making the lining structureproduce a plastic zone

323 Variation Curve of Axial Overpressure underExplosion For the variation of overpressure effect of ex-plosion shock wave along the axial direction of liningstructure the 20 reference points A1ndashA20 are divided intofive straight lines L1 L2 L3 L4and L5 along the axialdirection the L1 straight line includes A1 A15 A11 andA16 L2 straight line includes A2 A7 A12 and A17 L3straight line includes A3 A8 A13 and A18 L4 straight lineincludes A4 A9 A14 and A19 L5 straight line includes A5A10 A15 and A20 Figures 12 and 13 are curves of axialoverpressure change under explosion of 10 kg TNT and30 kg TNT

According to the attenuation law of overpressure oneach straight line in Figure 12 the overpressure at the close

0 001 002 003 004 005Time (s)

A2A3A4

02

01

0

ndash01

ndash02

ndash03

ndash04

ndash05

Disp

lace

men

t (m

)

(a)

0 001 002 003 004 005Time (s)

A7A8A9

0

02

01

ndash01

ndash02

ndash03

ndash04

Disp

lace

men

t (m

)

(b)

0 001 002 003 004 005Time (s)

A12A13A14

Disp

lace

men

t (m

)

01

005

0

ndash005

ndash01

ndash015

ndash02

(c)

0 001 002 003 004 005Time (s)

A18A17A19

Disp

lace

men

t (m

)01

005

0

ndash005

ndash01

(d)

Figure 11 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

10 Shock and Vibration

distance from the lining structure is the strongest (eoverpressure will decrease sharply in the range of 3m andthe overpressure will decrease slowly in the range of3msim9m as a whole (is is due to the rapid compression ofair near the explosive at the initial stage of the explosionreaction concentration of energy and overpressure phe-nomenon With the increase of distance the energy willgradually diffuse [20](e axial overpressure of the referencepoint within 6m away from the centre of the explosionsource will also increase slightly which is due to the energyreceived by individual reference points increasing after theexplosion shock wave is reflected and superimposed formany times

By comparing the overpressure changes in Figures 12and 13 it can be seen that at the beginning of the explosionthe overpressure peak value of 30 kg TNT increased by aboutsix times compared with 10 kg TNT at the same referencepoint which is much larger than the increase of explosivemass Similar to the variation curve of overpressure of 10 kgTNT the overpressure is strongest at the close distance fromthe centre of the explosion source (e overpressure has

obvious attenuation at 3m from the centre of the explosionsource and the overpressure keeps a slow attenuation trendin the range of 3msim9m (e overpressure of the referencepoint in the same straight line beyond 6m will also bestrengthened which is also due to the superposition ofmultiple reflections of the explosion shock wave

4 Conclusions

(e instantaneous dynamic response of the lining structureinstalled with composite steel plate when explosion occurs issimulated by establishing a composite steel plate liningstructure model Different influencing factors are deter-mined and parameterized analysis is carried out by using themethod of comparison of different explosive equivalentexplosion effects (e following conclusions are obtained

(1) (e change of velocity acceleration and displace-ment of each reference point at the lining structure isrelated to the action of overpressure and distance Amain peak value will be formed within 3m from theexplosion source and the peak value is obviouslyhigher than other peaks With the propagation ofexplosion shock wave the function of lining struc-ture will gradually decrease

(2) (e effect of multiple increase of explosive quantityon each point of lining structure is not the same (eacceleration near the distance is generally far greaterthan the multiple increase of explosive quantitywhile the increase of velocity and displacement isbasically the same as the explosive quantity (eeffect of multiple increase of explosive quantity onacceleration velocity and displacement is reducedand the change is relatively stable at a distance (3maway from the explosive source)

(3) By comparing the data changes of acceleration velocityand displacement in each direction of the same refer-ence point it can be seen that under the action ofexplosion when the distance is relatively close theinfluence is greater the axial stress has the least influenceon the lining structure and the influence of y-directionof the lining section on the lining structure is greaterthan the other two directions

Data Availability

(e rawprocessed data used to support the findings of thisstudy have not been made available because they form partof the ongoing research

Conflicts of Interest

(e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof China (41372288) and Shandong Natural ScienceFoundation (ZR2019MEE027)

2 8 1040 6Displacement (m)

0

02

04

06

08

1

12

14Pr

essu

re (M

Pa)

L1L2L3

L4L5

Figure 12 Overpressure attenuation laws in lines of 10 kg TNT

L1L2L3

L4L5

2 8 1040 6Displacement (m)

0

1

2

3

4

5

6

7

8

Pres

sure

(MPa

)

Figure 13 Overpressure attenuation laws in lines of 30 kg TNT

Shock and Vibration 11

References

[1] Q H Meng Dynamic Response and Explosion-Resist-Ant-protection of Subway Tunnel under Terroristbom-Bing loadShandong University of Science and Technology QingdaoChina 2010

[2] D S Kong M Y Deng and Y Z Li ldquoExperimental study onmechanical deformation characteristics of inclined andstraight alternating pile groupsrdquo Advances in Civil Engi-neering vol 2020 Article ID 8394182 11 pages 2020

[3] D-S Kong Q-H Meng W-W Zhang and Q-H ZhangldquoShock responses of a metro tunnel subjected to explosiveloadsrdquo Journal of Vibration and Shock vol 31 no 12pp 69ndash72 2012

[4] J B Liu andQ S H Ni ldquoStudy on explosion protectionin ironunderground structurerdquo Journal of Vibration and Shockvol 27 no 8 pp 16ndash19 2008

[5] A Zyskowski I Sochet G Mavrot P Bailly and J RenardldquoStudy of the explosion process in a small scale experiment-structural loadingrdquo Journal of Loss Prevention in the ProcessIndustries vol 17 no 4 pp 291ndash299 2004

[6] C L Yan andD J Ma ldquoHigh resolution numerical simulationof strong explosive waves in a vesselrdquo Journal of ChinaUniversity of Science and Technology vol 25 no 1 pp 10ndash161998

[7] Y Z Cao Z S Lu and H A Guan ldquoNumerical simulation ofexplosion flow field in anti-explosion vesselrdquo Journal of ChinaUniversity of Science and Technology Chinese Journal of HighPressure Physics vol 15 no 2 pp 127ndash133 2001

[8] Y Cui Dynamic Response and Damage Assessment of DuplexHollow CFST Column Subjected to Blast Loading ChanganUniversity Xirsquoan China 2013

[9] D S Kong M X Deng and Z M Zhao ldquoSeismic interactioncharacteristics of an inclined straight alternating pile group-soil in liquefied groundrdquo Advances in Civil Engineeringvol 2019 Article ID 3758286 12 pages 2019

[10] K Z Yang and X M Yang ldquo(e propagation law of theimpulse shock wave in the tunnelrdquo Explosion and ShockWaves vol 23 no 1 pp 37ndash40 2003

[11] A L Kuhl and H Reichenbach ldquoCombustion effects inconfined explosionsrdquo Proceedings of the Combustion Institutevol 32 no 2 pp 2291ndash2298 2009

[12] D Kong M Deng Y Liu and X Tan ldquoStudy of the force anddeformation characteristics of subsea mudmat-pile hybridfoundationsrdquo Polish Maritime Research vol 25 no s3pp 43ndash53 2019

[13] S H Qu Structural Response and Damage and Ground Vi-bration of Subway Station under Internal Explosion TianjinUniversity Tianjin China 2008

[14] X L Du W Z H Liao M Z H Tian et al ldquoNumericalsimulation of flow around blast waverdquo Journal of BeijingUniversity of Technology vol 34 no 3 pp 277ndash287 2008

[15] D S Kong M X Deng and Y Xu ldquoStudy on calculation ofpile sliding interval of large-diameter steel pipe piles onoffshore platformsrdquo Mathematical Problems in Engineeringvol 2019 Article ID 3549296 8 pages 2019

[16] Y F Liu R H Liu S Q Shi et al ldquoNumerical stimulation onanalysis of reducing blast by using foam aluminumrdquo ChineseJournal of Underground Space and Engineering vol 27 no 8pp 16ndash19 2008

[17] D S Kong Y F Bai Y P Chen andM X Deng ldquoA study onthe seismic response characteristics of an oblique pile group-soil-structure with different pile capsrdquo Shock and Vibrationvol 2019 Article ID 8141045 12 pages 2019

[18] D S Kong M X Deng and Y Z Li ldquoNumerical simulation ofseismic soil-pile interaction in liquefying groundrdquo IEEEAccess vol 8 no 1 pp 195ndash204 2020

[19] D S Kong Y Liu M X Deng and X Y Zhao ldquoAnalysis ofinfluencing factors of lateral soil resistance distributioncharacteristics around monopole foundation for offshorewind powerrdquo Applied Ocean Research vol 97 Article ID102106 2020

[20] W W Zhang Study of Impulse Response and Shield Tech-nology of Subway Station under Terrorist Explosion loadShandong University of Science and Technology QingdaoChina 2010

12 Shock and Vibration

propagate in the opposite direction resulting in multiplestress peaks on the explosion source section 30 kg TNTCompared with 10 kg TNT the blast energy is morepowerful and the impact range of shock wave is widerFor the explosion activities in the closed structure thepeak value of shock wave is strengthened due to themultiple reflection and superposition of blast wave eachpoint experiences multiple peaks its duration is in-creased and its shock propagation law is more complexIn the early stage of explosion activities the bottom blastwave propagation is faster and in the process of prop-agation when the upper shock wave undergoes reflectionand superposition the propagation speed will beaccelerated which also accords with the characteristicsthat the blast wave is a spherical wave [16]

32 Dynamic Response of the Lining Structure under the BlastAction When an explosion occurs in the tunnel section thedisplacement velocity and acceleration of the liningstructure under the action of the explosion are importantparameters to measure the damage degree of the structure[16] In order to study the dynamic response of the liningstructure under the action of explosives equivalent to 10 kgand 30 kg under the protection of composite steel plate 20reference points were selected where the influence of thelining structure was obvious and divided into four groups(ese four groups were arranged on sections at differentdistances from the explosion source centre numberedA1ndashA20 and were 0m 3m 6m and 9m away from theexplosion centre Figure 5 is the layout diagram of eachreference point of the lining structure [17ndash19]

0 001 002 003 004Time (s)

005

2

0

ndash2

ndash4

ndash6

ndash8

Velo

city

(ms

)

A1A5

(a)

0 001 002 003 004Time (s)

005

2

1

0

ndash1

ndash2

ndash3

Velo

city

(ms

)

A1A5

(b)

0 001 002 003 004Time (s)

005

Acce

lera

tion

(ms

2 )10

3

2

ndash2

0

ndash4

ndash10

ndash8

ndash6

ndash12

A11A15

(c)

0 001 002 003 004Time (s)

005

2

15

05

0

ndash2

ndash05

Acce

lera

tion

(ms

2 )10

3

A11A15

(d)

Figure 7 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

6 Shock and Vibration

321 Dynamic Response of Lining Structure under 10 kg TNTExplosion From the numerical simulation results it can beseen that the maximum vertical displacement points of eachsection occur at two reference points at the upper wall andthe lower wall Figure 6 is the y-direction displacementchange curve at the upper wall and the lower wall of the foursections

As can be seen from the y-direction displacement changecurve shown in Figure 6 the lining structure has a dis-placement of 04 cm at section A1 (e displacement changecurve of the section closer to the explosion source decreasesrapidly after experiencing a peak value and the change trendis stable As the distance from the centre of the explosionsource increases the y-direction displacement gradually

decreases Multiple displacement peaks appear at sectionstwo three and four since the shock wave energy decaysrapidly with the increase of distance (ere is a large dif-ference between the value and section one(e displacementof the reference point at a longer distance first appears as asmall amplitude oscillation change under the reflectionsuperposition effect of the shock wave (erefore under theexplosion of 10 kg of explosives the deformation peak valueof the lining is 04 cm and the influence on the liningstructure is within the elastic range At the beginning of theexplosion the lining structure was subjected to tensile stressand had a maximum acceleration and velocity at point A1Figure 7 is a velocity and acceleration variation curve in they-direction of sections one and three

01

0

ndash01

ndash02

ndash03

Disp

lace

men

t (m

)

0 001 002 003 004Time (s)

005

A2A3A4

(a)

0 001 002 003 004Time (s)

005

A7A8A9

01

0

ndash01

ndash02

Disp

lace

men

t (m

)(b)

0 001 002 003 004Time (s)

005

A12A13A14

006

004

002

0

ndash01

ndash008

ndash006

ndash004

ndash002

Disp

lace

men

t (m

)

(c)

0 001 002 003 004Time (s)

005

A17A18A19

004

002

0

ndash006

ndash004

ndash002

Disp

lace

men

t (m

)

(d)

Figure 8 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

Shock and Vibration 7

From the velocity and acceleration change curves shownin Figure 7 it can be seen that the displacement change of thereference point of section one rapidly decays after experi-encing a peak value while the displacement change of thereference point of other sections further away experiencesmultiple peaks showing an overall weakening trend and alonger duration (is also verifies that the velocity andacceleration are affected by overpressure and the magnitudeof the impact is positively related to the distance from theexplosive source Under the action of explosion the max-imum horizontal displacement of five reference points ineach section occurs at three points on the side wall Figure 8is the x-direction displacement change curve of four sectionsat three points

From the x-direction displacement variation curveshown in Figure 8 it can be seen that the maximum dis-placement of 024 cm occurs at the reference point at the side

wall A4 instead of the reference point at the front side wallA3 In addition the impact of explosion shock wave on thedisplacement of the lining structure side wall is generallyreflected in the second peak value and the first peak value ofdisplacement variation is caused by the vacuum zone formedby the sharp consumption of air during explosion Under thesuperposition of multiple reflections of the shock wave thedisplacement changes experienced multiple peaks andshowed a weakening trend By comparing the maximumvelocity and acceleration in the x-direction with the maxi-mum velocity and acceleration in the y-direction we can seethat there is a big gap between the two

322 Dynamic Response of Lining Structure under 30 kg TNTExplosion For the influence of explosion shock wave onlining structure under the action of higher explosive

0 001 002 003 004Time (s)

005

A1A5

1

05

0

05

ndash1

ndash15

Velo

city

(ms

)

(a)

0 001 002 003 004Time (s)

005

A1A5

06

04

02

0

ndash02

ndash04

ndash06

Velo

city

(ms

)

(b)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

04

02

0

ndash02

ndash04

(c)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

02

01

0

ndash02

ndash01

ndash03

(d)

Figure 9 Changes of displacement in y-direction in sections (a) Velocity in y direction of section one (b) velocity in y direction of sectionthree (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

8 Shock and Vibration

equivalent 30 kg TNT is selected for analysis Each referencepoint is arranged in the same way as 10 kg TNT Figure 9 isthe y-direction displacement change curve at upper andlower walls of the four sections

As can be seen from the y-direction displacementchange in Figure 9 the maximum vertical displacement ofeach section occurs in two points on the upper and lowerwalls (e maximum displacement of A1 reference point ofsection one in y-direction is more than twice as much asthat of section three under the action of 10 kg TNT (edisplacement change curve shows a weakening trend as awhole (erefore the displacement of the lining structureclose to the centre of the explosion source will increase at ahigh magnification when the amount of explosive in-creases exponentially However with the increase of dis-tance the displacement will increase at a lowmagnification

and the influence will decrease gradually (ere is anobvious plastic deformation at section one It can beknown that 30 kg TNT explosive exceeds the critical pointof the plastic zone of the lining structure protected bycomposite steel plates

According to the change curve in Figure 10 the changeof velocity and acceleration in the y-direction is affecteddifferently by the change of explosive charge (e multipleincrease of explosive charge has the greatest impact on thearea close to the explosive source With the increase ofdistance the impact gradually weakens Within the range of3m from the explosive source the velocity and accelerationwill rapidly decrease after experiencing a main peak valueand tend to be stable Beyond the range of 3m from theexplosive source the velocity and acceleration will slowlydecrease after experiencing a main peak value

20

10

0

ndash10

ndash20

ndash30

ndash400 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(a)

10

0

ndash10

ndash20

ndash30

ndash40

ndash500 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(b)

Acce

lera

tion

(ms

2 )103

4

2

0

ndash2

ndash4

ndash60 001 002 003 004 005

Time (s)

A11A15

(c)

Acce

lera

tion

(ms

2 )103

2

1

0

ndash1

ndash20 001 002 003 004 005

Time (s)

A11A15

(d)

Figure 10 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

Shock and Vibration 9

Under the action of 30 kg TNTexplosion the maximumhorizontal displacement of five reference points in eachsection occurs at three points on the side wall Figure 11 isthe x-direction displacement change curve of four sections atthree points By comparing the data of Figures 8 and 11 itcan be concluded that the maximum displacement at foursections in the x-direction under the action of 30 kg TNT isabout twice as large as that under the action of 10 kg TNTslightly smaller than the maximum displacement increase inthe y-direction at the same distance At the same time it canalso be obtained through the displacement change curve ofsection one and the damage effect of 30 kg TNT equivalenthas exceeded the critical point making the lining structureproduce a plastic zone

323 Variation Curve of Axial Overpressure underExplosion For the variation of overpressure effect of ex-plosion shock wave along the axial direction of liningstructure the 20 reference points A1ndashA20 are divided intofive straight lines L1 L2 L3 L4and L5 along the axialdirection the L1 straight line includes A1 A15 A11 andA16 L2 straight line includes A2 A7 A12 and A17 L3straight line includes A3 A8 A13 and A18 L4 straight lineincludes A4 A9 A14 and A19 L5 straight line includes A5A10 A15 and A20 Figures 12 and 13 are curves of axialoverpressure change under explosion of 10 kg TNT and30 kg TNT

According to the attenuation law of overpressure oneach straight line in Figure 12 the overpressure at the close

0 001 002 003 004 005Time (s)

A2A3A4

02

01

0

ndash01

ndash02

ndash03

ndash04

ndash05

Disp

lace

men

t (m

)

(a)

0 001 002 003 004 005Time (s)

A7A8A9

0

02

01

ndash01

ndash02

ndash03

ndash04

Disp

lace

men

t (m

)

(b)

0 001 002 003 004 005Time (s)

A12A13A14

Disp

lace

men

t (m

)

01

005

0

ndash005

ndash01

ndash015

ndash02

(c)

0 001 002 003 004 005Time (s)

A18A17A19

Disp

lace

men

t (m

)01

005

0

ndash005

ndash01

(d)

Figure 11 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

10 Shock and Vibration

distance from the lining structure is the strongest (eoverpressure will decrease sharply in the range of 3m andthe overpressure will decrease slowly in the range of3msim9m as a whole (is is due to the rapid compression ofair near the explosive at the initial stage of the explosionreaction concentration of energy and overpressure phe-nomenon With the increase of distance the energy willgradually diffuse [20](e axial overpressure of the referencepoint within 6m away from the centre of the explosionsource will also increase slightly which is due to the energyreceived by individual reference points increasing after theexplosion shock wave is reflected and superimposed formany times

By comparing the overpressure changes in Figures 12and 13 it can be seen that at the beginning of the explosionthe overpressure peak value of 30 kg TNT increased by aboutsix times compared with 10 kg TNT at the same referencepoint which is much larger than the increase of explosivemass Similar to the variation curve of overpressure of 10 kgTNT the overpressure is strongest at the close distance fromthe centre of the explosion source (e overpressure has

obvious attenuation at 3m from the centre of the explosionsource and the overpressure keeps a slow attenuation trendin the range of 3msim9m (e overpressure of the referencepoint in the same straight line beyond 6m will also bestrengthened which is also due to the superposition ofmultiple reflections of the explosion shock wave

4 Conclusions

(e instantaneous dynamic response of the lining structureinstalled with composite steel plate when explosion occurs issimulated by establishing a composite steel plate liningstructure model Different influencing factors are deter-mined and parameterized analysis is carried out by using themethod of comparison of different explosive equivalentexplosion effects (e following conclusions are obtained

(1) (e change of velocity acceleration and displace-ment of each reference point at the lining structure isrelated to the action of overpressure and distance Amain peak value will be formed within 3m from theexplosion source and the peak value is obviouslyhigher than other peaks With the propagation ofexplosion shock wave the function of lining struc-ture will gradually decrease

(2) (e effect of multiple increase of explosive quantityon each point of lining structure is not the same (eacceleration near the distance is generally far greaterthan the multiple increase of explosive quantitywhile the increase of velocity and displacement isbasically the same as the explosive quantity (eeffect of multiple increase of explosive quantity onacceleration velocity and displacement is reducedand the change is relatively stable at a distance (3maway from the explosive source)

(3) By comparing the data changes of acceleration velocityand displacement in each direction of the same refer-ence point it can be seen that under the action ofexplosion when the distance is relatively close theinfluence is greater the axial stress has the least influenceon the lining structure and the influence of y-directionof the lining section on the lining structure is greaterthan the other two directions

Data Availability

(e rawprocessed data used to support the findings of thisstudy have not been made available because they form partof the ongoing research

Conflicts of Interest

(e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof China (41372288) and Shandong Natural ScienceFoundation (ZR2019MEE027)

2 8 1040 6Displacement (m)

0

02

04

06

08

1

12

14Pr

essu

re (M

Pa)

L1L2L3

L4L5

Figure 12 Overpressure attenuation laws in lines of 10 kg TNT

L1L2L3

L4L5

2 8 1040 6Displacement (m)

0

1

2

3

4

5

6

7

8

Pres

sure

(MPa

)

Figure 13 Overpressure attenuation laws in lines of 30 kg TNT

Shock and Vibration 11

References

[1] Q H Meng Dynamic Response and Explosion-Resist-Ant-protection of Subway Tunnel under Terroristbom-Bing loadShandong University of Science and Technology QingdaoChina 2010

[2] D S Kong M Y Deng and Y Z Li ldquoExperimental study onmechanical deformation characteristics of inclined andstraight alternating pile groupsrdquo Advances in Civil Engi-neering vol 2020 Article ID 8394182 11 pages 2020

[3] D-S Kong Q-H Meng W-W Zhang and Q-H ZhangldquoShock responses of a metro tunnel subjected to explosiveloadsrdquo Journal of Vibration and Shock vol 31 no 12pp 69ndash72 2012

[4] J B Liu andQ S H Ni ldquoStudy on explosion protectionin ironunderground structurerdquo Journal of Vibration and Shockvol 27 no 8 pp 16ndash19 2008

[5] A Zyskowski I Sochet G Mavrot P Bailly and J RenardldquoStudy of the explosion process in a small scale experiment-structural loadingrdquo Journal of Loss Prevention in the ProcessIndustries vol 17 no 4 pp 291ndash299 2004

[6] C L Yan andD J Ma ldquoHigh resolution numerical simulationof strong explosive waves in a vesselrdquo Journal of ChinaUniversity of Science and Technology vol 25 no 1 pp 10ndash161998

[7] Y Z Cao Z S Lu and H A Guan ldquoNumerical simulation ofexplosion flow field in anti-explosion vesselrdquo Journal of ChinaUniversity of Science and Technology Chinese Journal of HighPressure Physics vol 15 no 2 pp 127ndash133 2001

[8] Y Cui Dynamic Response and Damage Assessment of DuplexHollow CFST Column Subjected to Blast Loading ChanganUniversity Xirsquoan China 2013

[9] D S Kong M X Deng and Z M Zhao ldquoSeismic interactioncharacteristics of an inclined straight alternating pile group-soil in liquefied groundrdquo Advances in Civil Engineeringvol 2019 Article ID 3758286 12 pages 2019

[10] K Z Yang and X M Yang ldquo(e propagation law of theimpulse shock wave in the tunnelrdquo Explosion and ShockWaves vol 23 no 1 pp 37ndash40 2003

[11] A L Kuhl and H Reichenbach ldquoCombustion effects inconfined explosionsrdquo Proceedings of the Combustion Institutevol 32 no 2 pp 2291ndash2298 2009

[12] D Kong M Deng Y Liu and X Tan ldquoStudy of the force anddeformation characteristics of subsea mudmat-pile hybridfoundationsrdquo Polish Maritime Research vol 25 no s3pp 43ndash53 2019

[13] S H Qu Structural Response and Damage and Ground Vi-bration of Subway Station under Internal Explosion TianjinUniversity Tianjin China 2008

[14] X L Du W Z H Liao M Z H Tian et al ldquoNumericalsimulation of flow around blast waverdquo Journal of BeijingUniversity of Technology vol 34 no 3 pp 277ndash287 2008

[15] D S Kong M X Deng and Y Xu ldquoStudy on calculation ofpile sliding interval of large-diameter steel pipe piles onoffshore platformsrdquo Mathematical Problems in Engineeringvol 2019 Article ID 3549296 8 pages 2019

[16] Y F Liu R H Liu S Q Shi et al ldquoNumerical stimulation onanalysis of reducing blast by using foam aluminumrdquo ChineseJournal of Underground Space and Engineering vol 27 no 8pp 16ndash19 2008

[17] D S Kong Y F Bai Y P Chen andM X Deng ldquoA study onthe seismic response characteristics of an oblique pile group-soil-structure with different pile capsrdquo Shock and Vibrationvol 2019 Article ID 8141045 12 pages 2019

[18] D S Kong M X Deng and Y Z Li ldquoNumerical simulation ofseismic soil-pile interaction in liquefying groundrdquo IEEEAccess vol 8 no 1 pp 195ndash204 2020

[19] D S Kong Y Liu M X Deng and X Y Zhao ldquoAnalysis ofinfluencing factors of lateral soil resistance distributioncharacteristics around monopole foundation for offshorewind powerrdquo Applied Ocean Research vol 97 Article ID102106 2020

[20] W W Zhang Study of Impulse Response and Shield Tech-nology of Subway Station under Terrorist Explosion loadShandong University of Science and Technology QingdaoChina 2010

12 Shock and Vibration

321 Dynamic Response of Lining Structure under 10 kg TNTExplosion From the numerical simulation results it can beseen that the maximum vertical displacement points of eachsection occur at two reference points at the upper wall andthe lower wall Figure 6 is the y-direction displacementchange curve at the upper wall and the lower wall of the foursections

As can be seen from the y-direction displacement changecurve shown in Figure 6 the lining structure has a dis-placement of 04 cm at section A1 (e displacement changecurve of the section closer to the explosion source decreasesrapidly after experiencing a peak value and the change trendis stable As the distance from the centre of the explosionsource increases the y-direction displacement gradually

decreases Multiple displacement peaks appear at sectionstwo three and four since the shock wave energy decaysrapidly with the increase of distance (ere is a large dif-ference between the value and section one(e displacementof the reference point at a longer distance first appears as asmall amplitude oscillation change under the reflectionsuperposition effect of the shock wave (erefore under theexplosion of 10 kg of explosives the deformation peak valueof the lining is 04 cm and the influence on the liningstructure is within the elastic range At the beginning of theexplosion the lining structure was subjected to tensile stressand had a maximum acceleration and velocity at point A1Figure 7 is a velocity and acceleration variation curve in they-direction of sections one and three

01

0

ndash01

ndash02

ndash03

Disp

lace

men

t (m

)

0 001 002 003 004Time (s)

005

A2A3A4

(a)

0 001 002 003 004Time (s)

005

A7A8A9

01

0

ndash01

ndash02

Disp

lace

men

t (m

)(b)

0 001 002 003 004Time (s)

005

A12A13A14

006

004

002

0

ndash01

ndash008

ndash006

ndash004

ndash002

Disp

lace

men

t (m

)

(c)

0 001 002 003 004Time (s)

005

A17A18A19

004

002

0

ndash006

ndash004

ndash002

Disp

lace

men

t (m

)

(d)

Figure 8 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

Shock and Vibration 7

From the velocity and acceleration change curves shownin Figure 7 it can be seen that the displacement change of thereference point of section one rapidly decays after experi-encing a peak value while the displacement change of thereference point of other sections further away experiencesmultiple peaks showing an overall weakening trend and alonger duration (is also verifies that the velocity andacceleration are affected by overpressure and the magnitudeof the impact is positively related to the distance from theexplosive source Under the action of explosion the max-imum horizontal displacement of five reference points ineach section occurs at three points on the side wall Figure 8is the x-direction displacement change curve of four sectionsat three points

From the x-direction displacement variation curveshown in Figure 8 it can be seen that the maximum dis-placement of 024 cm occurs at the reference point at the side

wall A4 instead of the reference point at the front side wallA3 In addition the impact of explosion shock wave on thedisplacement of the lining structure side wall is generallyreflected in the second peak value and the first peak value ofdisplacement variation is caused by the vacuum zone formedby the sharp consumption of air during explosion Under thesuperposition of multiple reflections of the shock wave thedisplacement changes experienced multiple peaks andshowed a weakening trend By comparing the maximumvelocity and acceleration in the x-direction with the maxi-mum velocity and acceleration in the y-direction we can seethat there is a big gap between the two

322 Dynamic Response of Lining Structure under 30 kg TNTExplosion For the influence of explosion shock wave onlining structure under the action of higher explosive

0 001 002 003 004Time (s)

005

A1A5

1

05

0

05

ndash1

ndash15

Velo

city

(ms

)

(a)

0 001 002 003 004Time (s)

005

A1A5

06

04

02

0

ndash02

ndash04

ndash06

Velo

city

(ms

)

(b)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

04

02

0

ndash02

ndash04

(c)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

02

01

0

ndash02

ndash01

ndash03

(d)

Figure 9 Changes of displacement in y-direction in sections (a) Velocity in y direction of section one (b) velocity in y direction of sectionthree (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

8 Shock and Vibration

equivalent 30 kg TNT is selected for analysis Each referencepoint is arranged in the same way as 10 kg TNT Figure 9 isthe y-direction displacement change curve at upper andlower walls of the four sections

As can be seen from the y-direction displacementchange in Figure 9 the maximum vertical displacement ofeach section occurs in two points on the upper and lowerwalls (e maximum displacement of A1 reference point ofsection one in y-direction is more than twice as much asthat of section three under the action of 10 kg TNT (edisplacement change curve shows a weakening trend as awhole (erefore the displacement of the lining structureclose to the centre of the explosion source will increase at ahigh magnification when the amount of explosive in-creases exponentially However with the increase of dis-tance the displacement will increase at a lowmagnification

and the influence will decrease gradually (ere is anobvious plastic deformation at section one It can beknown that 30 kg TNT explosive exceeds the critical pointof the plastic zone of the lining structure protected bycomposite steel plates

According to the change curve in Figure 10 the changeof velocity and acceleration in the y-direction is affecteddifferently by the change of explosive charge (e multipleincrease of explosive charge has the greatest impact on thearea close to the explosive source With the increase ofdistance the impact gradually weakens Within the range of3m from the explosive source the velocity and accelerationwill rapidly decrease after experiencing a main peak valueand tend to be stable Beyond the range of 3m from theexplosive source the velocity and acceleration will slowlydecrease after experiencing a main peak value

20

10

0

ndash10

ndash20

ndash30

ndash400 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(a)

10

0

ndash10

ndash20

ndash30

ndash40

ndash500 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(b)

Acce

lera

tion

(ms

2 )103

4

2

0

ndash2

ndash4

ndash60 001 002 003 004 005

Time (s)

A11A15

(c)

Acce

lera

tion

(ms

2 )103

2

1

0

ndash1

ndash20 001 002 003 004 005

Time (s)

A11A15

(d)

Figure 10 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

Shock and Vibration 9

Under the action of 30 kg TNTexplosion the maximumhorizontal displacement of five reference points in eachsection occurs at three points on the side wall Figure 11 isthe x-direction displacement change curve of four sections atthree points By comparing the data of Figures 8 and 11 itcan be concluded that the maximum displacement at foursections in the x-direction under the action of 30 kg TNT isabout twice as large as that under the action of 10 kg TNTslightly smaller than the maximum displacement increase inthe y-direction at the same distance At the same time it canalso be obtained through the displacement change curve ofsection one and the damage effect of 30 kg TNT equivalenthas exceeded the critical point making the lining structureproduce a plastic zone

323 Variation Curve of Axial Overpressure underExplosion For the variation of overpressure effect of ex-plosion shock wave along the axial direction of liningstructure the 20 reference points A1ndashA20 are divided intofive straight lines L1 L2 L3 L4and L5 along the axialdirection the L1 straight line includes A1 A15 A11 andA16 L2 straight line includes A2 A7 A12 and A17 L3straight line includes A3 A8 A13 and A18 L4 straight lineincludes A4 A9 A14 and A19 L5 straight line includes A5A10 A15 and A20 Figures 12 and 13 are curves of axialoverpressure change under explosion of 10 kg TNT and30 kg TNT

According to the attenuation law of overpressure oneach straight line in Figure 12 the overpressure at the close

0 001 002 003 004 005Time (s)

A2A3A4

02

01

0

ndash01

ndash02

ndash03

ndash04

ndash05

Disp

lace

men

t (m

)

(a)

0 001 002 003 004 005Time (s)

A7A8A9

0

02

01

ndash01

ndash02

ndash03

ndash04

Disp

lace

men

t (m

)

(b)

0 001 002 003 004 005Time (s)

A12A13A14

Disp

lace

men

t (m

)

01

005

0

ndash005

ndash01

ndash015

ndash02

(c)

0 001 002 003 004 005Time (s)

A18A17A19

Disp

lace

men

t (m

)01

005

0

ndash005

ndash01

(d)

Figure 11 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

10 Shock and Vibration

distance from the lining structure is the strongest (eoverpressure will decrease sharply in the range of 3m andthe overpressure will decrease slowly in the range of3msim9m as a whole (is is due to the rapid compression ofair near the explosive at the initial stage of the explosionreaction concentration of energy and overpressure phe-nomenon With the increase of distance the energy willgradually diffuse [20](e axial overpressure of the referencepoint within 6m away from the centre of the explosionsource will also increase slightly which is due to the energyreceived by individual reference points increasing after theexplosion shock wave is reflected and superimposed formany times

By comparing the overpressure changes in Figures 12and 13 it can be seen that at the beginning of the explosionthe overpressure peak value of 30 kg TNT increased by aboutsix times compared with 10 kg TNT at the same referencepoint which is much larger than the increase of explosivemass Similar to the variation curve of overpressure of 10 kgTNT the overpressure is strongest at the close distance fromthe centre of the explosion source (e overpressure has

obvious attenuation at 3m from the centre of the explosionsource and the overpressure keeps a slow attenuation trendin the range of 3msim9m (e overpressure of the referencepoint in the same straight line beyond 6m will also bestrengthened which is also due to the superposition ofmultiple reflections of the explosion shock wave

4 Conclusions

(e instantaneous dynamic response of the lining structureinstalled with composite steel plate when explosion occurs issimulated by establishing a composite steel plate liningstructure model Different influencing factors are deter-mined and parameterized analysis is carried out by using themethod of comparison of different explosive equivalentexplosion effects (e following conclusions are obtained

(1) (e change of velocity acceleration and displace-ment of each reference point at the lining structure isrelated to the action of overpressure and distance Amain peak value will be formed within 3m from theexplosion source and the peak value is obviouslyhigher than other peaks With the propagation ofexplosion shock wave the function of lining struc-ture will gradually decrease

(2) (e effect of multiple increase of explosive quantityon each point of lining structure is not the same (eacceleration near the distance is generally far greaterthan the multiple increase of explosive quantitywhile the increase of velocity and displacement isbasically the same as the explosive quantity (eeffect of multiple increase of explosive quantity onacceleration velocity and displacement is reducedand the change is relatively stable at a distance (3maway from the explosive source)

(3) By comparing the data changes of acceleration velocityand displacement in each direction of the same refer-ence point it can be seen that under the action ofexplosion when the distance is relatively close theinfluence is greater the axial stress has the least influenceon the lining structure and the influence of y-directionof the lining section on the lining structure is greaterthan the other two directions

Data Availability

(e rawprocessed data used to support the findings of thisstudy have not been made available because they form partof the ongoing research

Conflicts of Interest

(e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof China (41372288) and Shandong Natural ScienceFoundation (ZR2019MEE027)

2 8 1040 6Displacement (m)

0

02

04

06

08

1

12

14Pr

essu

re (M

Pa)

L1L2L3

L4L5

Figure 12 Overpressure attenuation laws in lines of 10 kg TNT

L1L2L3

L4L5

2 8 1040 6Displacement (m)

0

1

2

3

4

5

6

7

8

Pres

sure

(MPa

)

Figure 13 Overpressure attenuation laws in lines of 30 kg TNT

Shock and Vibration 11

References

[1] Q H Meng Dynamic Response and Explosion-Resist-Ant-protection of Subway Tunnel under Terroristbom-Bing loadShandong University of Science and Technology QingdaoChina 2010

[2] D S Kong M Y Deng and Y Z Li ldquoExperimental study onmechanical deformation characteristics of inclined andstraight alternating pile groupsrdquo Advances in Civil Engi-neering vol 2020 Article ID 8394182 11 pages 2020

[3] D-S Kong Q-H Meng W-W Zhang and Q-H ZhangldquoShock responses of a metro tunnel subjected to explosiveloadsrdquo Journal of Vibration and Shock vol 31 no 12pp 69ndash72 2012

[4] J B Liu andQ S H Ni ldquoStudy on explosion protectionin ironunderground structurerdquo Journal of Vibration and Shockvol 27 no 8 pp 16ndash19 2008

[5] A Zyskowski I Sochet G Mavrot P Bailly and J RenardldquoStudy of the explosion process in a small scale experiment-structural loadingrdquo Journal of Loss Prevention in the ProcessIndustries vol 17 no 4 pp 291ndash299 2004

[6] C L Yan andD J Ma ldquoHigh resolution numerical simulationof strong explosive waves in a vesselrdquo Journal of ChinaUniversity of Science and Technology vol 25 no 1 pp 10ndash161998

[7] Y Z Cao Z S Lu and H A Guan ldquoNumerical simulation ofexplosion flow field in anti-explosion vesselrdquo Journal of ChinaUniversity of Science and Technology Chinese Journal of HighPressure Physics vol 15 no 2 pp 127ndash133 2001

[8] Y Cui Dynamic Response and Damage Assessment of DuplexHollow CFST Column Subjected to Blast Loading ChanganUniversity Xirsquoan China 2013

[9] D S Kong M X Deng and Z M Zhao ldquoSeismic interactioncharacteristics of an inclined straight alternating pile group-soil in liquefied groundrdquo Advances in Civil Engineeringvol 2019 Article ID 3758286 12 pages 2019

[10] K Z Yang and X M Yang ldquo(e propagation law of theimpulse shock wave in the tunnelrdquo Explosion and ShockWaves vol 23 no 1 pp 37ndash40 2003

[11] A L Kuhl and H Reichenbach ldquoCombustion effects inconfined explosionsrdquo Proceedings of the Combustion Institutevol 32 no 2 pp 2291ndash2298 2009

[12] D Kong M Deng Y Liu and X Tan ldquoStudy of the force anddeformation characteristics of subsea mudmat-pile hybridfoundationsrdquo Polish Maritime Research vol 25 no s3pp 43ndash53 2019

[13] S H Qu Structural Response and Damage and Ground Vi-bration of Subway Station under Internal Explosion TianjinUniversity Tianjin China 2008

[14] X L Du W Z H Liao M Z H Tian et al ldquoNumericalsimulation of flow around blast waverdquo Journal of BeijingUniversity of Technology vol 34 no 3 pp 277ndash287 2008

[15] D S Kong M X Deng and Y Xu ldquoStudy on calculation ofpile sliding interval of large-diameter steel pipe piles onoffshore platformsrdquo Mathematical Problems in Engineeringvol 2019 Article ID 3549296 8 pages 2019

[16] Y F Liu R H Liu S Q Shi et al ldquoNumerical stimulation onanalysis of reducing blast by using foam aluminumrdquo ChineseJournal of Underground Space and Engineering vol 27 no 8pp 16ndash19 2008

[17] D S Kong Y F Bai Y P Chen andM X Deng ldquoA study onthe seismic response characteristics of an oblique pile group-soil-structure with different pile capsrdquo Shock and Vibrationvol 2019 Article ID 8141045 12 pages 2019

[18] D S Kong M X Deng and Y Z Li ldquoNumerical simulation ofseismic soil-pile interaction in liquefying groundrdquo IEEEAccess vol 8 no 1 pp 195ndash204 2020

[19] D S Kong Y Liu M X Deng and X Y Zhao ldquoAnalysis ofinfluencing factors of lateral soil resistance distributioncharacteristics around monopole foundation for offshorewind powerrdquo Applied Ocean Research vol 97 Article ID102106 2020

[20] W W Zhang Study of Impulse Response and Shield Tech-nology of Subway Station under Terrorist Explosion loadShandong University of Science and Technology QingdaoChina 2010

12 Shock and Vibration

From the velocity and acceleration change curves shownin Figure 7 it can be seen that the displacement change of thereference point of section one rapidly decays after experi-encing a peak value while the displacement change of thereference point of other sections further away experiencesmultiple peaks showing an overall weakening trend and alonger duration (is also verifies that the velocity andacceleration are affected by overpressure and the magnitudeof the impact is positively related to the distance from theexplosive source Under the action of explosion the max-imum horizontal displacement of five reference points ineach section occurs at three points on the side wall Figure 8is the x-direction displacement change curve of four sectionsat three points

From the x-direction displacement variation curveshown in Figure 8 it can be seen that the maximum dis-placement of 024 cm occurs at the reference point at the side

wall A4 instead of the reference point at the front side wallA3 In addition the impact of explosion shock wave on thedisplacement of the lining structure side wall is generallyreflected in the second peak value and the first peak value ofdisplacement variation is caused by the vacuum zone formedby the sharp consumption of air during explosion Under thesuperposition of multiple reflections of the shock wave thedisplacement changes experienced multiple peaks andshowed a weakening trend By comparing the maximumvelocity and acceleration in the x-direction with the maxi-mum velocity and acceleration in the y-direction we can seethat there is a big gap between the two

322 Dynamic Response of Lining Structure under 30 kg TNTExplosion For the influence of explosion shock wave onlining structure under the action of higher explosive

0 001 002 003 004Time (s)

005

A1A5

1

05

0

05

ndash1

ndash15

Velo

city

(ms

)

(a)

0 001 002 003 004Time (s)

005

A1A5

06

04

02

0

ndash02

ndash04

ndash06

Velo

city

(ms

)

(b)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

04

02

0

ndash02

ndash04

(c)

0 001 002 003 004Time (s)

005

A11A15

Acce

lera

tion

(ms

2 )10

3

02

01

0

ndash02

ndash01

ndash03

(d)

Figure 9 Changes of displacement in y-direction in sections (a) Velocity in y direction of section one (b) velocity in y direction of sectionthree (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

8 Shock and Vibration

equivalent 30 kg TNT is selected for analysis Each referencepoint is arranged in the same way as 10 kg TNT Figure 9 isthe y-direction displacement change curve at upper andlower walls of the four sections

As can be seen from the y-direction displacementchange in Figure 9 the maximum vertical displacement ofeach section occurs in two points on the upper and lowerwalls (e maximum displacement of A1 reference point ofsection one in y-direction is more than twice as much asthat of section three under the action of 10 kg TNT (edisplacement change curve shows a weakening trend as awhole (erefore the displacement of the lining structureclose to the centre of the explosion source will increase at ahigh magnification when the amount of explosive in-creases exponentially However with the increase of dis-tance the displacement will increase at a lowmagnification

and the influence will decrease gradually (ere is anobvious plastic deformation at section one It can beknown that 30 kg TNT explosive exceeds the critical pointof the plastic zone of the lining structure protected bycomposite steel plates

According to the change curve in Figure 10 the changeof velocity and acceleration in the y-direction is affecteddifferently by the change of explosive charge (e multipleincrease of explosive charge has the greatest impact on thearea close to the explosive source With the increase ofdistance the impact gradually weakens Within the range of3m from the explosive source the velocity and accelerationwill rapidly decrease after experiencing a main peak valueand tend to be stable Beyond the range of 3m from theexplosive source the velocity and acceleration will slowlydecrease after experiencing a main peak value

20

10

0

ndash10

ndash20

ndash30

ndash400 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(a)

10

0

ndash10

ndash20

ndash30

ndash40

ndash500 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(b)

Acce

lera

tion

(ms

2 )103

4

2

0

ndash2

ndash4

ndash60 001 002 003 004 005

Time (s)

A11A15

(c)

Acce

lera

tion

(ms

2 )103

2

1

0

ndash1

ndash20 001 002 003 004 005

Time (s)

A11A15

(d)

Figure 10 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

Shock and Vibration 9

Under the action of 30 kg TNTexplosion the maximumhorizontal displacement of five reference points in eachsection occurs at three points on the side wall Figure 11 isthe x-direction displacement change curve of four sections atthree points By comparing the data of Figures 8 and 11 itcan be concluded that the maximum displacement at foursections in the x-direction under the action of 30 kg TNT isabout twice as large as that under the action of 10 kg TNTslightly smaller than the maximum displacement increase inthe y-direction at the same distance At the same time it canalso be obtained through the displacement change curve ofsection one and the damage effect of 30 kg TNT equivalenthas exceeded the critical point making the lining structureproduce a plastic zone

323 Variation Curve of Axial Overpressure underExplosion For the variation of overpressure effect of ex-plosion shock wave along the axial direction of liningstructure the 20 reference points A1ndashA20 are divided intofive straight lines L1 L2 L3 L4and L5 along the axialdirection the L1 straight line includes A1 A15 A11 andA16 L2 straight line includes A2 A7 A12 and A17 L3straight line includes A3 A8 A13 and A18 L4 straight lineincludes A4 A9 A14 and A19 L5 straight line includes A5A10 A15 and A20 Figures 12 and 13 are curves of axialoverpressure change under explosion of 10 kg TNT and30 kg TNT

According to the attenuation law of overpressure oneach straight line in Figure 12 the overpressure at the close

0 001 002 003 004 005Time (s)

A2A3A4

02

01

0

ndash01

ndash02

ndash03

ndash04

ndash05

Disp

lace

men

t (m

)

(a)

0 001 002 003 004 005Time (s)

A7A8A9

0

02

01

ndash01

ndash02

ndash03

ndash04

Disp

lace

men

t (m

)

(b)

0 001 002 003 004 005Time (s)

A12A13A14

Disp

lace

men

t (m

)

01

005

0

ndash005

ndash01

ndash015

ndash02

(c)

0 001 002 003 004 005Time (s)

A18A17A19

Disp

lace

men

t (m

)01

005

0

ndash005

ndash01

(d)

Figure 11 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

10 Shock and Vibration

distance from the lining structure is the strongest (eoverpressure will decrease sharply in the range of 3m andthe overpressure will decrease slowly in the range of3msim9m as a whole (is is due to the rapid compression ofair near the explosive at the initial stage of the explosionreaction concentration of energy and overpressure phe-nomenon With the increase of distance the energy willgradually diffuse [20](e axial overpressure of the referencepoint within 6m away from the centre of the explosionsource will also increase slightly which is due to the energyreceived by individual reference points increasing after theexplosion shock wave is reflected and superimposed formany times

By comparing the overpressure changes in Figures 12and 13 it can be seen that at the beginning of the explosionthe overpressure peak value of 30 kg TNT increased by aboutsix times compared with 10 kg TNT at the same referencepoint which is much larger than the increase of explosivemass Similar to the variation curve of overpressure of 10 kgTNT the overpressure is strongest at the close distance fromthe centre of the explosion source (e overpressure has

obvious attenuation at 3m from the centre of the explosionsource and the overpressure keeps a slow attenuation trendin the range of 3msim9m (e overpressure of the referencepoint in the same straight line beyond 6m will also bestrengthened which is also due to the superposition ofmultiple reflections of the explosion shock wave

4 Conclusions

(e instantaneous dynamic response of the lining structureinstalled with composite steel plate when explosion occurs issimulated by establishing a composite steel plate liningstructure model Different influencing factors are deter-mined and parameterized analysis is carried out by using themethod of comparison of different explosive equivalentexplosion effects (e following conclusions are obtained

(1) (e change of velocity acceleration and displace-ment of each reference point at the lining structure isrelated to the action of overpressure and distance Amain peak value will be formed within 3m from theexplosion source and the peak value is obviouslyhigher than other peaks With the propagation ofexplosion shock wave the function of lining struc-ture will gradually decrease

(2) (e effect of multiple increase of explosive quantityon each point of lining structure is not the same (eacceleration near the distance is generally far greaterthan the multiple increase of explosive quantitywhile the increase of velocity and displacement isbasically the same as the explosive quantity (eeffect of multiple increase of explosive quantity onacceleration velocity and displacement is reducedand the change is relatively stable at a distance (3maway from the explosive source)

(3) By comparing the data changes of acceleration velocityand displacement in each direction of the same refer-ence point it can be seen that under the action ofexplosion when the distance is relatively close theinfluence is greater the axial stress has the least influenceon the lining structure and the influence of y-directionof the lining section on the lining structure is greaterthan the other two directions

Data Availability

(e rawprocessed data used to support the findings of thisstudy have not been made available because they form partof the ongoing research

Conflicts of Interest

(e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof China (41372288) and Shandong Natural ScienceFoundation (ZR2019MEE027)

2 8 1040 6Displacement (m)

0

02

04

06

08

1

12

14Pr

essu

re (M

Pa)

L1L2L3

L4L5

Figure 12 Overpressure attenuation laws in lines of 10 kg TNT

L1L2L3

L4L5

2 8 1040 6Displacement (m)

0

1

2

3

4

5

6

7

8

Pres

sure

(MPa

)

Figure 13 Overpressure attenuation laws in lines of 30 kg TNT

Shock and Vibration 11

References

[1] Q H Meng Dynamic Response and Explosion-Resist-Ant-protection of Subway Tunnel under Terroristbom-Bing loadShandong University of Science and Technology QingdaoChina 2010

[2] D S Kong M Y Deng and Y Z Li ldquoExperimental study onmechanical deformation characteristics of inclined andstraight alternating pile groupsrdquo Advances in Civil Engi-neering vol 2020 Article ID 8394182 11 pages 2020

[3] D-S Kong Q-H Meng W-W Zhang and Q-H ZhangldquoShock responses of a metro tunnel subjected to explosiveloadsrdquo Journal of Vibration and Shock vol 31 no 12pp 69ndash72 2012

[4] J B Liu andQ S H Ni ldquoStudy on explosion protectionin ironunderground structurerdquo Journal of Vibration and Shockvol 27 no 8 pp 16ndash19 2008

[5] A Zyskowski I Sochet G Mavrot P Bailly and J RenardldquoStudy of the explosion process in a small scale experiment-structural loadingrdquo Journal of Loss Prevention in the ProcessIndustries vol 17 no 4 pp 291ndash299 2004

[6] C L Yan andD J Ma ldquoHigh resolution numerical simulationof strong explosive waves in a vesselrdquo Journal of ChinaUniversity of Science and Technology vol 25 no 1 pp 10ndash161998

[7] Y Z Cao Z S Lu and H A Guan ldquoNumerical simulation ofexplosion flow field in anti-explosion vesselrdquo Journal of ChinaUniversity of Science and Technology Chinese Journal of HighPressure Physics vol 15 no 2 pp 127ndash133 2001

[8] Y Cui Dynamic Response and Damage Assessment of DuplexHollow CFST Column Subjected to Blast Loading ChanganUniversity Xirsquoan China 2013

[9] D S Kong M X Deng and Z M Zhao ldquoSeismic interactioncharacteristics of an inclined straight alternating pile group-soil in liquefied groundrdquo Advances in Civil Engineeringvol 2019 Article ID 3758286 12 pages 2019

[10] K Z Yang and X M Yang ldquo(e propagation law of theimpulse shock wave in the tunnelrdquo Explosion and ShockWaves vol 23 no 1 pp 37ndash40 2003

[11] A L Kuhl and H Reichenbach ldquoCombustion effects inconfined explosionsrdquo Proceedings of the Combustion Institutevol 32 no 2 pp 2291ndash2298 2009

[12] D Kong M Deng Y Liu and X Tan ldquoStudy of the force anddeformation characteristics of subsea mudmat-pile hybridfoundationsrdquo Polish Maritime Research vol 25 no s3pp 43ndash53 2019

[13] S H Qu Structural Response and Damage and Ground Vi-bration of Subway Station under Internal Explosion TianjinUniversity Tianjin China 2008

[14] X L Du W Z H Liao M Z H Tian et al ldquoNumericalsimulation of flow around blast waverdquo Journal of BeijingUniversity of Technology vol 34 no 3 pp 277ndash287 2008

[15] D S Kong M X Deng and Y Xu ldquoStudy on calculation ofpile sliding interval of large-diameter steel pipe piles onoffshore platformsrdquo Mathematical Problems in Engineeringvol 2019 Article ID 3549296 8 pages 2019

[16] Y F Liu R H Liu S Q Shi et al ldquoNumerical stimulation onanalysis of reducing blast by using foam aluminumrdquo ChineseJournal of Underground Space and Engineering vol 27 no 8pp 16ndash19 2008

[17] D S Kong Y F Bai Y P Chen andM X Deng ldquoA study onthe seismic response characteristics of an oblique pile group-soil-structure with different pile capsrdquo Shock and Vibrationvol 2019 Article ID 8141045 12 pages 2019

[18] D S Kong M X Deng and Y Z Li ldquoNumerical simulation ofseismic soil-pile interaction in liquefying groundrdquo IEEEAccess vol 8 no 1 pp 195ndash204 2020

[19] D S Kong Y Liu M X Deng and X Y Zhao ldquoAnalysis ofinfluencing factors of lateral soil resistance distributioncharacteristics around monopole foundation for offshorewind powerrdquo Applied Ocean Research vol 97 Article ID102106 2020

[20] W W Zhang Study of Impulse Response and Shield Tech-nology of Subway Station under Terrorist Explosion loadShandong University of Science and Technology QingdaoChina 2010

12 Shock and Vibration

equivalent 30 kg TNT is selected for analysis Each referencepoint is arranged in the same way as 10 kg TNT Figure 9 isthe y-direction displacement change curve at upper andlower walls of the four sections

As can be seen from the y-direction displacementchange in Figure 9 the maximum vertical displacement ofeach section occurs in two points on the upper and lowerwalls (e maximum displacement of A1 reference point ofsection one in y-direction is more than twice as much asthat of section three under the action of 10 kg TNT (edisplacement change curve shows a weakening trend as awhole (erefore the displacement of the lining structureclose to the centre of the explosion source will increase at ahigh magnification when the amount of explosive in-creases exponentially However with the increase of dis-tance the displacement will increase at a lowmagnification

and the influence will decrease gradually (ere is anobvious plastic deformation at section one It can beknown that 30 kg TNT explosive exceeds the critical pointof the plastic zone of the lining structure protected bycomposite steel plates

According to the change curve in Figure 10 the changeof velocity and acceleration in the y-direction is affecteddifferently by the change of explosive charge (e multipleincrease of explosive charge has the greatest impact on thearea close to the explosive source With the increase ofdistance the impact gradually weakens Within the range of3m from the explosive source the velocity and accelerationwill rapidly decrease after experiencing a main peak valueand tend to be stable Beyond the range of 3m from theexplosive source the velocity and acceleration will slowlydecrease after experiencing a main peak value

20

10

0

ndash10

ndash20

ndash30

ndash400 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(a)

10

0

ndash10

ndash20

ndash30

ndash40

ndash500 001 002 003 004 005

Time (s)

Velo

city

(ms

)

A1A5

(b)

Acce

lera

tion

(ms

2 )103

4

2

0

ndash2

ndash4

ndash60 001 002 003 004 005

Time (s)

A11A15

(c)

Acce

lera

tion

(ms

2 )103

2

1

0

ndash1

ndash20 001 002 003 004 005

Time (s)

A11A15

(d)

Figure 10 Velocity and acceleration curves in y-direction on each section (a) Velocity in y-direction of section one (b) velocity in y-direction of section three (c) acceleration of section one in y-direction and (d) acceleration of section three in y-direction

Shock and Vibration 9

Under the action of 30 kg TNTexplosion the maximumhorizontal displacement of five reference points in eachsection occurs at three points on the side wall Figure 11 isthe x-direction displacement change curve of four sections atthree points By comparing the data of Figures 8 and 11 itcan be concluded that the maximum displacement at foursections in the x-direction under the action of 30 kg TNT isabout twice as large as that under the action of 10 kg TNTslightly smaller than the maximum displacement increase inthe y-direction at the same distance At the same time it canalso be obtained through the displacement change curve ofsection one and the damage effect of 30 kg TNT equivalenthas exceeded the critical point making the lining structureproduce a plastic zone

323 Variation Curve of Axial Overpressure underExplosion For the variation of overpressure effect of ex-plosion shock wave along the axial direction of liningstructure the 20 reference points A1ndashA20 are divided intofive straight lines L1 L2 L3 L4and L5 along the axialdirection the L1 straight line includes A1 A15 A11 andA16 L2 straight line includes A2 A7 A12 and A17 L3straight line includes A3 A8 A13 and A18 L4 straight lineincludes A4 A9 A14 and A19 L5 straight line includes A5A10 A15 and A20 Figures 12 and 13 are curves of axialoverpressure change under explosion of 10 kg TNT and30 kg TNT

According to the attenuation law of overpressure oneach straight line in Figure 12 the overpressure at the close

0 001 002 003 004 005Time (s)

A2A3A4

02

01

0

ndash01

ndash02

ndash03

ndash04

ndash05

Disp

lace

men

t (m

)

(a)

0 001 002 003 004 005Time (s)

A7A8A9

0

02

01

ndash01

ndash02

ndash03

ndash04

Disp

lace

men

t (m

)

(b)

0 001 002 003 004 005Time (s)

A12A13A14

Disp

lace

men

t (m

)

01

005

0

ndash005

ndash01

ndash015

ndash02

(c)

0 001 002 003 004 005Time (s)

A18A17A19

Disp

lace

men

t (m

)01

005

0

ndash005

ndash01

(d)

Figure 11 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

10 Shock and Vibration

distance from the lining structure is the strongest (eoverpressure will decrease sharply in the range of 3m andthe overpressure will decrease slowly in the range of3msim9m as a whole (is is due to the rapid compression ofair near the explosive at the initial stage of the explosionreaction concentration of energy and overpressure phe-nomenon With the increase of distance the energy willgradually diffuse [20](e axial overpressure of the referencepoint within 6m away from the centre of the explosionsource will also increase slightly which is due to the energyreceived by individual reference points increasing after theexplosion shock wave is reflected and superimposed formany times

By comparing the overpressure changes in Figures 12and 13 it can be seen that at the beginning of the explosionthe overpressure peak value of 30 kg TNT increased by aboutsix times compared with 10 kg TNT at the same referencepoint which is much larger than the increase of explosivemass Similar to the variation curve of overpressure of 10 kgTNT the overpressure is strongest at the close distance fromthe centre of the explosion source (e overpressure has

obvious attenuation at 3m from the centre of the explosionsource and the overpressure keeps a slow attenuation trendin the range of 3msim9m (e overpressure of the referencepoint in the same straight line beyond 6m will also bestrengthened which is also due to the superposition ofmultiple reflections of the explosion shock wave

4 Conclusions

(e instantaneous dynamic response of the lining structureinstalled with composite steel plate when explosion occurs issimulated by establishing a composite steel plate liningstructure model Different influencing factors are deter-mined and parameterized analysis is carried out by using themethod of comparison of different explosive equivalentexplosion effects (e following conclusions are obtained

(1) (e change of velocity acceleration and displace-ment of each reference point at the lining structure isrelated to the action of overpressure and distance Amain peak value will be formed within 3m from theexplosion source and the peak value is obviouslyhigher than other peaks With the propagation ofexplosion shock wave the function of lining struc-ture will gradually decrease

(2) (e effect of multiple increase of explosive quantityon each point of lining structure is not the same (eacceleration near the distance is generally far greaterthan the multiple increase of explosive quantitywhile the increase of velocity and displacement isbasically the same as the explosive quantity (eeffect of multiple increase of explosive quantity onacceleration velocity and displacement is reducedand the change is relatively stable at a distance (3maway from the explosive source)

(3) By comparing the data changes of acceleration velocityand displacement in each direction of the same refer-ence point it can be seen that under the action ofexplosion when the distance is relatively close theinfluence is greater the axial stress has the least influenceon the lining structure and the influence of y-directionof the lining section on the lining structure is greaterthan the other two directions

Data Availability

(e rawprocessed data used to support the findings of thisstudy have not been made available because they form partof the ongoing research

Conflicts of Interest

(e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof China (41372288) and Shandong Natural ScienceFoundation (ZR2019MEE027)

2 8 1040 6Displacement (m)

0

02

04

06

08

1

12

14Pr

essu

re (M

Pa)

L1L2L3

L4L5

Figure 12 Overpressure attenuation laws in lines of 10 kg TNT

L1L2L3

L4L5

2 8 1040 6Displacement (m)

0

1

2

3

4

5

6

7

8

Pres

sure

(MPa

)

Figure 13 Overpressure attenuation laws in lines of 30 kg TNT

Shock and Vibration 11

References

[1] Q H Meng Dynamic Response and Explosion-Resist-Ant-protection of Subway Tunnel under Terroristbom-Bing loadShandong University of Science and Technology QingdaoChina 2010

[2] D S Kong M Y Deng and Y Z Li ldquoExperimental study onmechanical deformation characteristics of inclined andstraight alternating pile groupsrdquo Advances in Civil Engi-neering vol 2020 Article ID 8394182 11 pages 2020

[3] D-S Kong Q-H Meng W-W Zhang and Q-H ZhangldquoShock responses of a metro tunnel subjected to explosiveloadsrdquo Journal of Vibration and Shock vol 31 no 12pp 69ndash72 2012

[4] J B Liu andQ S H Ni ldquoStudy on explosion protectionin ironunderground structurerdquo Journal of Vibration and Shockvol 27 no 8 pp 16ndash19 2008

[5] A Zyskowski I Sochet G Mavrot P Bailly and J RenardldquoStudy of the explosion process in a small scale experiment-structural loadingrdquo Journal of Loss Prevention in the ProcessIndustries vol 17 no 4 pp 291ndash299 2004

[6] C L Yan andD J Ma ldquoHigh resolution numerical simulationof strong explosive waves in a vesselrdquo Journal of ChinaUniversity of Science and Technology vol 25 no 1 pp 10ndash161998

[7] Y Z Cao Z S Lu and H A Guan ldquoNumerical simulation ofexplosion flow field in anti-explosion vesselrdquo Journal of ChinaUniversity of Science and Technology Chinese Journal of HighPressure Physics vol 15 no 2 pp 127ndash133 2001

[8] Y Cui Dynamic Response and Damage Assessment of DuplexHollow CFST Column Subjected to Blast Loading ChanganUniversity Xirsquoan China 2013

[9] D S Kong M X Deng and Z M Zhao ldquoSeismic interactioncharacteristics of an inclined straight alternating pile group-soil in liquefied groundrdquo Advances in Civil Engineeringvol 2019 Article ID 3758286 12 pages 2019

[10] K Z Yang and X M Yang ldquo(e propagation law of theimpulse shock wave in the tunnelrdquo Explosion and ShockWaves vol 23 no 1 pp 37ndash40 2003

[11] A L Kuhl and H Reichenbach ldquoCombustion effects inconfined explosionsrdquo Proceedings of the Combustion Institutevol 32 no 2 pp 2291ndash2298 2009

[12] D Kong M Deng Y Liu and X Tan ldquoStudy of the force anddeformation characteristics of subsea mudmat-pile hybridfoundationsrdquo Polish Maritime Research vol 25 no s3pp 43ndash53 2019

[13] S H Qu Structural Response and Damage and Ground Vi-bration of Subway Station under Internal Explosion TianjinUniversity Tianjin China 2008

[14] X L Du W Z H Liao M Z H Tian et al ldquoNumericalsimulation of flow around blast waverdquo Journal of BeijingUniversity of Technology vol 34 no 3 pp 277ndash287 2008

[15] D S Kong M X Deng and Y Xu ldquoStudy on calculation ofpile sliding interval of large-diameter steel pipe piles onoffshore platformsrdquo Mathematical Problems in Engineeringvol 2019 Article ID 3549296 8 pages 2019

[16] Y F Liu R H Liu S Q Shi et al ldquoNumerical stimulation onanalysis of reducing blast by using foam aluminumrdquo ChineseJournal of Underground Space and Engineering vol 27 no 8pp 16ndash19 2008

[17] D S Kong Y F Bai Y P Chen andM X Deng ldquoA study onthe seismic response characteristics of an oblique pile group-soil-structure with different pile capsrdquo Shock and Vibrationvol 2019 Article ID 8141045 12 pages 2019

[18] D S Kong M X Deng and Y Z Li ldquoNumerical simulation ofseismic soil-pile interaction in liquefying groundrdquo IEEEAccess vol 8 no 1 pp 195ndash204 2020

[19] D S Kong Y Liu M X Deng and X Y Zhao ldquoAnalysis ofinfluencing factors of lateral soil resistance distributioncharacteristics around monopole foundation for offshorewind powerrdquo Applied Ocean Research vol 97 Article ID102106 2020

[20] W W Zhang Study of Impulse Response and Shield Tech-nology of Subway Station under Terrorist Explosion loadShandong University of Science and Technology QingdaoChina 2010

12 Shock and Vibration

Under the action of 30 kg TNTexplosion the maximumhorizontal displacement of five reference points in eachsection occurs at three points on the side wall Figure 11 isthe x-direction displacement change curve of four sections atthree points By comparing the data of Figures 8 and 11 itcan be concluded that the maximum displacement at foursections in the x-direction under the action of 30 kg TNT isabout twice as large as that under the action of 10 kg TNTslightly smaller than the maximum displacement increase inthe y-direction at the same distance At the same time it canalso be obtained through the displacement change curve ofsection one and the damage effect of 30 kg TNT equivalenthas exceeded the critical point making the lining structureproduce a plastic zone

323 Variation Curve of Axial Overpressure underExplosion For the variation of overpressure effect of ex-plosion shock wave along the axial direction of liningstructure the 20 reference points A1ndashA20 are divided intofive straight lines L1 L2 L3 L4and L5 along the axialdirection the L1 straight line includes A1 A15 A11 andA16 L2 straight line includes A2 A7 A12 and A17 L3straight line includes A3 A8 A13 and A18 L4 straight lineincludes A4 A9 A14 and A19 L5 straight line includes A5A10 A15 and A20 Figures 12 and 13 are curves of axialoverpressure change under explosion of 10 kg TNT and30 kg TNT

According to the attenuation law of overpressure oneach straight line in Figure 12 the overpressure at the close

0 001 002 003 004 005Time (s)

A2A3A4

02

01

0

ndash01

ndash02

ndash03

ndash04

ndash05

Disp

lace

men

t (m

)

(a)

0 001 002 003 004 005Time (s)

A7A8A9

0

02

01

ndash01

ndash02

ndash03

ndash04

Disp

lace

men

t (m

)

(b)

0 001 002 003 004 005Time (s)

A12A13A14

Disp

lace

men

t (m

)

01

005

0

ndash005

ndash01

ndash015

ndash02

(c)

0 001 002 003 004 005Time (s)

A18A17A19

Disp

lace

men

t (m

)01

005

0

ndash005

ndash01

(d)

Figure 11 Changes of displacement in x-direction in sections (a) Reference point of section one (b) reference point of section two (c)reference point of section three and (d) reference point of section four

10 Shock and Vibration

distance from the lining structure is the strongest (eoverpressure will decrease sharply in the range of 3m andthe overpressure will decrease slowly in the range of3msim9m as a whole (is is due to the rapid compression ofair near the explosive at the initial stage of the explosionreaction concentration of energy and overpressure phe-nomenon With the increase of distance the energy willgradually diffuse [20](e axial overpressure of the referencepoint within 6m away from the centre of the explosionsource will also increase slightly which is due to the energyreceived by individual reference points increasing after theexplosion shock wave is reflected and superimposed formany times

By comparing the overpressure changes in Figures 12and 13 it can be seen that at the beginning of the explosionthe overpressure peak value of 30 kg TNT increased by aboutsix times compared with 10 kg TNT at the same referencepoint which is much larger than the increase of explosivemass Similar to the variation curve of overpressure of 10 kgTNT the overpressure is strongest at the close distance fromthe centre of the explosion source (e overpressure has

obvious attenuation at 3m from the centre of the explosionsource and the overpressure keeps a slow attenuation trendin the range of 3msim9m (e overpressure of the referencepoint in the same straight line beyond 6m will also bestrengthened which is also due to the superposition ofmultiple reflections of the explosion shock wave

4 Conclusions

(e instantaneous dynamic response of the lining structureinstalled with composite steel plate when explosion occurs issimulated by establishing a composite steel plate liningstructure model Different influencing factors are deter-mined and parameterized analysis is carried out by using themethod of comparison of different explosive equivalentexplosion effects (e following conclusions are obtained

(1) (e change of velocity acceleration and displace-ment of each reference point at the lining structure isrelated to the action of overpressure and distance Amain peak value will be formed within 3m from theexplosion source and the peak value is obviouslyhigher than other peaks With the propagation ofexplosion shock wave the function of lining struc-ture will gradually decrease

(2) (e effect of multiple increase of explosive quantityon each point of lining structure is not the same (eacceleration near the distance is generally far greaterthan the multiple increase of explosive quantitywhile the increase of velocity and displacement isbasically the same as the explosive quantity (eeffect of multiple increase of explosive quantity onacceleration velocity and displacement is reducedand the change is relatively stable at a distance (3maway from the explosive source)

(3) By comparing the data changes of acceleration velocityand displacement in each direction of the same refer-ence point it can be seen that under the action ofexplosion when the distance is relatively close theinfluence is greater the axial stress has the least influenceon the lining structure and the influence of y-directionof the lining section on the lining structure is greaterthan the other two directions

Data Availability

(e rawprocessed data used to support the findings of thisstudy have not been made available because they form partof the ongoing research

Conflicts of Interest

(e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof China (41372288) and Shandong Natural ScienceFoundation (ZR2019MEE027)

2 8 1040 6Displacement (m)

0

02

04

06

08

1

12

14Pr

essu

re (M

Pa)

L1L2L3

L4L5

Figure 12 Overpressure attenuation laws in lines of 10 kg TNT

L1L2L3

L4L5

2 8 1040 6Displacement (m)

0

1

2

3

4

5

6

7

8

Pres

sure

(MPa

)

Figure 13 Overpressure attenuation laws in lines of 30 kg TNT

Shock and Vibration 11

References

[1] Q H Meng Dynamic Response and Explosion-Resist-Ant-protection of Subway Tunnel under Terroristbom-Bing loadShandong University of Science and Technology QingdaoChina 2010

[2] D S Kong M Y Deng and Y Z Li ldquoExperimental study onmechanical deformation characteristics of inclined andstraight alternating pile groupsrdquo Advances in Civil Engi-neering vol 2020 Article ID 8394182 11 pages 2020

[3] D-S Kong Q-H Meng W-W Zhang and Q-H ZhangldquoShock responses of a metro tunnel subjected to explosiveloadsrdquo Journal of Vibration and Shock vol 31 no 12pp 69ndash72 2012

[4] J B Liu andQ S H Ni ldquoStudy on explosion protectionin ironunderground structurerdquo Journal of Vibration and Shockvol 27 no 8 pp 16ndash19 2008

[5] A Zyskowski I Sochet G Mavrot P Bailly and J RenardldquoStudy of the explosion process in a small scale experiment-structural loadingrdquo Journal of Loss Prevention in the ProcessIndustries vol 17 no 4 pp 291ndash299 2004

[6] C L Yan andD J Ma ldquoHigh resolution numerical simulationof strong explosive waves in a vesselrdquo Journal of ChinaUniversity of Science and Technology vol 25 no 1 pp 10ndash161998

[7] Y Z Cao Z S Lu and H A Guan ldquoNumerical simulation ofexplosion flow field in anti-explosion vesselrdquo Journal of ChinaUniversity of Science and Technology Chinese Journal of HighPressure Physics vol 15 no 2 pp 127ndash133 2001

[8] Y Cui Dynamic Response and Damage Assessment of DuplexHollow CFST Column Subjected to Blast Loading ChanganUniversity Xirsquoan China 2013

[9] D S Kong M X Deng and Z M Zhao ldquoSeismic interactioncharacteristics of an inclined straight alternating pile group-soil in liquefied groundrdquo Advances in Civil Engineeringvol 2019 Article ID 3758286 12 pages 2019

[10] K Z Yang and X M Yang ldquo(e propagation law of theimpulse shock wave in the tunnelrdquo Explosion and ShockWaves vol 23 no 1 pp 37ndash40 2003

[11] A L Kuhl and H Reichenbach ldquoCombustion effects inconfined explosionsrdquo Proceedings of the Combustion Institutevol 32 no 2 pp 2291ndash2298 2009

[12] D Kong M Deng Y Liu and X Tan ldquoStudy of the force anddeformation characteristics of subsea mudmat-pile hybridfoundationsrdquo Polish Maritime Research vol 25 no s3pp 43ndash53 2019

[13] S H Qu Structural Response and Damage and Ground Vi-bration of Subway Station under Internal Explosion TianjinUniversity Tianjin China 2008

[14] X L Du W Z H Liao M Z H Tian et al ldquoNumericalsimulation of flow around blast waverdquo Journal of BeijingUniversity of Technology vol 34 no 3 pp 277ndash287 2008

[15] D S Kong M X Deng and Y Xu ldquoStudy on calculation ofpile sliding interval of large-diameter steel pipe piles onoffshore platformsrdquo Mathematical Problems in Engineeringvol 2019 Article ID 3549296 8 pages 2019

[16] Y F Liu R H Liu S Q Shi et al ldquoNumerical stimulation onanalysis of reducing blast by using foam aluminumrdquo ChineseJournal of Underground Space and Engineering vol 27 no 8pp 16ndash19 2008

[17] D S Kong Y F Bai Y P Chen andM X Deng ldquoA study onthe seismic response characteristics of an oblique pile group-soil-structure with different pile capsrdquo Shock and Vibrationvol 2019 Article ID 8141045 12 pages 2019

[18] D S Kong M X Deng and Y Z Li ldquoNumerical simulation ofseismic soil-pile interaction in liquefying groundrdquo IEEEAccess vol 8 no 1 pp 195ndash204 2020

[19] D S Kong Y Liu M X Deng and X Y Zhao ldquoAnalysis ofinfluencing factors of lateral soil resistance distributioncharacteristics around monopole foundation for offshorewind powerrdquo Applied Ocean Research vol 97 Article ID102106 2020

[20] W W Zhang Study of Impulse Response and Shield Tech-nology of Subway Station under Terrorist Explosion loadShandong University of Science and Technology QingdaoChina 2010

12 Shock and Vibration

distance from the lining structure is the strongest (eoverpressure will decrease sharply in the range of 3m andthe overpressure will decrease slowly in the range of3msim9m as a whole (is is due to the rapid compression ofair near the explosive at the initial stage of the explosionreaction concentration of energy and overpressure phe-nomenon With the increase of distance the energy willgradually diffuse [20](e axial overpressure of the referencepoint within 6m away from the centre of the explosionsource will also increase slightly which is due to the energyreceived by individual reference points increasing after theexplosion shock wave is reflected and superimposed formany times

By comparing the overpressure changes in Figures 12and 13 it can be seen that at the beginning of the explosionthe overpressure peak value of 30 kg TNT increased by aboutsix times compared with 10 kg TNT at the same referencepoint which is much larger than the increase of explosivemass Similar to the variation curve of overpressure of 10 kgTNT the overpressure is strongest at the close distance fromthe centre of the explosion source (e overpressure has

obvious attenuation at 3m from the centre of the explosionsource and the overpressure keeps a slow attenuation trendin the range of 3msim9m (e overpressure of the referencepoint in the same straight line beyond 6m will also bestrengthened which is also due to the superposition ofmultiple reflections of the explosion shock wave

4 Conclusions

(e instantaneous dynamic response of the lining structureinstalled with composite steel plate when explosion occurs issimulated by establishing a composite steel plate liningstructure model Different influencing factors are deter-mined and parameterized analysis is carried out by using themethod of comparison of different explosive equivalentexplosion effects (e following conclusions are obtained

(1) (e change of velocity acceleration and displace-ment of each reference point at the lining structure isrelated to the action of overpressure and distance Amain peak value will be formed within 3m from theexplosion source and the peak value is obviouslyhigher than other peaks With the propagation ofexplosion shock wave the function of lining struc-ture will gradually decrease

(2) (e effect of multiple increase of explosive quantityon each point of lining structure is not the same (eacceleration near the distance is generally far greaterthan the multiple increase of explosive quantitywhile the increase of velocity and displacement isbasically the same as the explosive quantity (eeffect of multiple increase of explosive quantity onacceleration velocity and displacement is reducedand the change is relatively stable at a distance (3maway from the explosive source)

(3) By comparing the data changes of acceleration velocityand displacement in each direction of the same refer-ence point it can be seen that under the action ofexplosion when the distance is relatively close theinfluence is greater the axial stress has the least influenceon the lining structure and the influence of y-directionof the lining section on the lining structure is greaterthan the other two directions

Data Availability

(e rawprocessed data used to support the findings of thisstudy have not been made available because they form partof the ongoing research

Conflicts of Interest

(e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the Natural Science Foundationof China (41372288) and Shandong Natural ScienceFoundation (ZR2019MEE027)

2 8 1040 6Displacement (m)

0

02

04

06

08

1

12

14Pr

essu

re (M

Pa)

L1L2L3

L4L5

Figure 12 Overpressure attenuation laws in lines of 10 kg TNT

L1L2L3

L4L5

2 8 1040 6Displacement (m)

0

1

2

3

4

5

6

7

8

Pres

sure

(MPa

)

Figure 13 Overpressure attenuation laws in lines of 30 kg TNT

Shock and Vibration 11

References

[1] Q H Meng Dynamic Response and Explosion-Resist-Ant-protection of Subway Tunnel under Terroristbom-Bing loadShandong University of Science and Technology QingdaoChina 2010

[2] D S Kong M Y Deng and Y Z Li ldquoExperimental study onmechanical deformation characteristics of inclined andstraight alternating pile groupsrdquo Advances in Civil Engi-neering vol 2020 Article ID 8394182 11 pages 2020

[3] D-S Kong Q-H Meng W-W Zhang and Q-H ZhangldquoShock responses of a metro tunnel subjected to explosiveloadsrdquo Journal of Vibration and Shock vol 31 no 12pp 69ndash72 2012

[4] J B Liu andQ S H Ni ldquoStudy on explosion protectionin ironunderground structurerdquo Journal of Vibration and Shockvol 27 no 8 pp 16ndash19 2008

[5] A Zyskowski I Sochet G Mavrot P Bailly and J RenardldquoStudy of the explosion process in a small scale experiment-structural loadingrdquo Journal of Loss Prevention in the ProcessIndustries vol 17 no 4 pp 291ndash299 2004

[6] C L Yan andD J Ma ldquoHigh resolution numerical simulationof strong explosive waves in a vesselrdquo Journal of ChinaUniversity of Science and Technology vol 25 no 1 pp 10ndash161998

[7] Y Z Cao Z S Lu and H A Guan ldquoNumerical simulation ofexplosion flow field in anti-explosion vesselrdquo Journal of ChinaUniversity of Science and Technology Chinese Journal of HighPressure Physics vol 15 no 2 pp 127ndash133 2001

[8] Y Cui Dynamic Response and Damage Assessment of DuplexHollow CFST Column Subjected to Blast Loading ChanganUniversity Xirsquoan China 2013

[9] D S Kong M X Deng and Z M Zhao ldquoSeismic interactioncharacteristics of an inclined straight alternating pile group-soil in liquefied groundrdquo Advances in Civil Engineeringvol 2019 Article ID 3758286 12 pages 2019

[10] K Z Yang and X M Yang ldquo(e propagation law of theimpulse shock wave in the tunnelrdquo Explosion and ShockWaves vol 23 no 1 pp 37ndash40 2003

[11] A L Kuhl and H Reichenbach ldquoCombustion effects inconfined explosionsrdquo Proceedings of the Combustion Institutevol 32 no 2 pp 2291ndash2298 2009

[12] D Kong M Deng Y Liu and X Tan ldquoStudy of the force anddeformation characteristics of subsea mudmat-pile hybridfoundationsrdquo Polish Maritime Research vol 25 no s3pp 43ndash53 2019

[13] S H Qu Structural Response and Damage and Ground Vi-bration of Subway Station under Internal Explosion TianjinUniversity Tianjin China 2008

[14] X L Du W Z H Liao M Z H Tian et al ldquoNumericalsimulation of flow around blast waverdquo Journal of BeijingUniversity of Technology vol 34 no 3 pp 277ndash287 2008

[15] D S Kong M X Deng and Y Xu ldquoStudy on calculation ofpile sliding interval of large-diameter steel pipe piles onoffshore platformsrdquo Mathematical Problems in Engineeringvol 2019 Article ID 3549296 8 pages 2019

[16] Y F Liu R H Liu S Q Shi et al ldquoNumerical stimulation onanalysis of reducing blast by using foam aluminumrdquo ChineseJournal of Underground Space and Engineering vol 27 no 8pp 16ndash19 2008

[17] D S Kong Y F Bai Y P Chen andM X Deng ldquoA study onthe seismic response characteristics of an oblique pile group-soil-structure with different pile capsrdquo Shock and Vibrationvol 2019 Article ID 8141045 12 pages 2019

[18] D S Kong M X Deng and Y Z Li ldquoNumerical simulation ofseismic soil-pile interaction in liquefying groundrdquo IEEEAccess vol 8 no 1 pp 195ndash204 2020

[19] D S Kong Y Liu M X Deng and X Y Zhao ldquoAnalysis ofinfluencing factors of lateral soil resistance distributioncharacteristics around monopole foundation for offshorewind powerrdquo Applied Ocean Research vol 97 Article ID102106 2020

[20] W W Zhang Study of Impulse Response and Shield Tech-nology of Subway Station under Terrorist Explosion loadShandong University of Science and Technology QingdaoChina 2010

12 Shock and Vibration

References

[1] Q H Meng Dynamic Response and Explosion-Resist-Ant-protection of Subway Tunnel under Terroristbom-Bing loadShandong University of Science and Technology QingdaoChina 2010

[2] D S Kong M Y Deng and Y Z Li ldquoExperimental study onmechanical deformation characteristics of inclined andstraight alternating pile groupsrdquo Advances in Civil Engi-neering vol 2020 Article ID 8394182 11 pages 2020

[3] D-S Kong Q-H Meng W-W Zhang and Q-H ZhangldquoShock responses of a metro tunnel subjected to explosiveloadsrdquo Journal of Vibration and Shock vol 31 no 12pp 69ndash72 2012

[4] J B Liu andQ S H Ni ldquoStudy on explosion protectionin ironunderground structurerdquo Journal of Vibration and Shockvol 27 no 8 pp 16ndash19 2008

[5] A Zyskowski I Sochet G Mavrot P Bailly and J RenardldquoStudy of the explosion process in a small scale experiment-structural loadingrdquo Journal of Loss Prevention in the ProcessIndustries vol 17 no 4 pp 291ndash299 2004

[6] C L Yan andD J Ma ldquoHigh resolution numerical simulationof strong explosive waves in a vesselrdquo Journal of ChinaUniversity of Science and Technology vol 25 no 1 pp 10ndash161998

[7] Y Z Cao Z S Lu and H A Guan ldquoNumerical simulation ofexplosion flow field in anti-explosion vesselrdquo Journal of ChinaUniversity of Science and Technology Chinese Journal of HighPressure Physics vol 15 no 2 pp 127ndash133 2001

[8] Y Cui Dynamic Response and Damage Assessment of DuplexHollow CFST Column Subjected to Blast Loading ChanganUniversity Xirsquoan China 2013

[9] D S Kong M X Deng and Z M Zhao ldquoSeismic interactioncharacteristics of an inclined straight alternating pile group-soil in liquefied groundrdquo Advances in Civil Engineeringvol 2019 Article ID 3758286 12 pages 2019

[10] K Z Yang and X M Yang ldquo(e propagation law of theimpulse shock wave in the tunnelrdquo Explosion and ShockWaves vol 23 no 1 pp 37ndash40 2003

[11] A L Kuhl and H Reichenbach ldquoCombustion effects inconfined explosionsrdquo Proceedings of the Combustion Institutevol 32 no 2 pp 2291ndash2298 2009

[12] D Kong M Deng Y Liu and X Tan ldquoStudy of the force anddeformation characteristics of subsea mudmat-pile hybridfoundationsrdquo Polish Maritime Research vol 25 no s3pp 43ndash53 2019

[13] S H Qu Structural Response and Damage and Ground Vi-bration of Subway Station under Internal Explosion TianjinUniversity Tianjin China 2008

[14] X L Du W Z H Liao M Z H Tian et al ldquoNumericalsimulation of flow around blast waverdquo Journal of BeijingUniversity of Technology vol 34 no 3 pp 277ndash287 2008

[15] D S Kong M X Deng and Y Xu ldquoStudy on calculation ofpile sliding interval of large-diameter steel pipe piles onoffshore platformsrdquo Mathematical Problems in Engineeringvol 2019 Article ID 3549296 8 pages 2019

[16] Y F Liu R H Liu S Q Shi et al ldquoNumerical stimulation onanalysis of reducing blast by using foam aluminumrdquo ChineseJournal of Underground Space and Engineering vol 27 no 8pp 16ndash19 2008

[17] D S Kong Y F Bai Y P Chen andM X Deng ldquoA study onthe seismic response characteristics of an oblique pile group-soil-structure with different pile capsrdquo Shock and Vibrationvol 2019 Article ID 8141045 12 pages 2019

[18] D S Kong M X Deng and Y Z Li ldquoNumerical simulation ofseismic soil-pile interaction in liquefying groundrdquo IEEEAccess vol 8 no 1 pp 195ndash204 2020

[19] D S Kong Y Liu M X Deng and X Y Zhao ldquoAnalysis ofinfluencing factors of lateral soil resistance distributioncharacteristics around monopole foundation for offshorewind powerrdquo Applied Ocean Research vol 97 Article ID102106 2020

[20] W W Zhang Study of Impulse Response and Shield Tech-nology of Subway Station under Terrorist Explosion loadShandong University of Science and Technology QingdaoChina 2010

12 Shock and Vibration