WANG Tian-hao， ZHANG Zhi-jie,2,3， CHENG Hao

(1. School of Instrument and Electronics, North University of China, Taiyuan 030051， China；2. Key Laboratory of Instrumentation Science & Dynamic Measurement (North University of China),Ministry of Education, Taiyuan 030051， China；3. Automatic Test Equipment and System Engineering Research Center of Shanxi Province, Taiyuan 030051， China)

Abstract： Distributed testing system has strong applicability in the field of dynamic testing, which can centrally manage the testing equipment in different locations through the local area network, and meet the new requirements of the test. Based on the theory of seismic location, the location of underground explosion center was studied. The applicability of seismic location theory to the location of underground explosion center was verified by simulating the underground explosion with LS-DYNA simulation platform. Combined with distributed testing system theory and weighting method, the optimal distribution method of test points was summarized through data analysis.

Key words： explosion center location； LS-DYNA； distributed testing system； seismic location； weighting method

0 Introduction

Distributed testing system integrates the whole testing system in the form of the local area network. It has the characteristics of high accuracy, better universality and strong applicability in the field of dynamic testing[1].

At present, there are many studies on the location of air and underwater explosion centers at home and abroad. Because the shock wave produced by explosives after underground explosion attenuates rapidly, the testing system can not collect the signals directly, so it is difficult to determine the location of the explosion centers. It is found that during the explosion, the crust will tremble and generate seismic signals. Based on this, this paper intends to study the location of the underground explosion center by using the principle of seismic location.

Seismic wave signals generated by crustal tremor propagate through soil. Seismic waves are mainly divided into S-wave and P-wave, in which P-wave travels faster and can reach the surface first[2]. Thus P-wave signals can be collected by distributed testing system on the surface and the location of the explosion center can be determined by using the principle of seismic location[3].

1 Underground explosion location method

Traditionally, earthquakes can be divided into natural earthquakes and artificial earthquakes. The so-called artificial earthquakes refer to earthquakes caused by human activities[4]. As shown in Fig.1, by measuring the azimuth, epicentral distance and focal depth can determine the location of the explosion center[5].

Fig.1 Schematic diagram of explosion center location

Focus: The source of the earthquake. The explosion position of artificial explosion is indicated in this paper.

Epicenter: The point on the surface of the earth directly above the focus is called as epicenter.

Azimuth: The rectangular coordinate system is established with the test point as the origin. The azimuth is defined as the rotation angle of the test point along the positiveXaxis pointer to the epicenter, and the test point is on the horizontal ground with the epicenter.

Epicentral distance: Distance between test point and epicenter.

Focal depth: Vertical distance from focus to epicenter[6].

1.1 Calculation method of azimuth (θ)

Acceleration values in the three directions ofX,YandZaxes generated by the explosion are respectively collected at the test points, and then the three-dimensional covariance matrix is obtained by

(1)

The eigenvalues of the covariance matrix are calculated asλ1,λ2,λ3from large to small. The eigenvalues ofλ1,λ2,λ3correspond to eigenvectors ofu1,u2,u3, which satisfy Eq.(2).αis required to satisfy the eigenvalue normalization shown in Eq.(3). Finally, the expression of azimuth angleθis obtained by polarization analysis method, as shown in Eq.(4).

u1=[u11u12u13].

(2)

(3)

(4)

1.2 Calculation method of epicentral distance (D)

In this paper, the epicentral distance is expressed byD. The collected data are mainly the P-band of seismic waves, which can be quantitatively described by the gradual change signal model as

Sω0(t)=Btexp(-At+iω0t)u(t),

(5)

whereω0is the signal main frequency;Bis the slope factor;Ais the change factor related to the signal change, the change ofAandBwill cause the difference of P-wave morphology;u(t) is a step signal. The envelope fitting model of the P-wave waveform can be obtained by transforming Hilbert into Eq.(5) as

Se(t)=Btexp(-At)u(t).

(6)

The data of 2 s in the vertical direction of the P-wave is intercepted, then the Hilbert transform is performed on the signal of 2 s, and the absolute value is taken to obtain the envelope function of the P-wave. Next, the P-wave envelope model of Eq.(6) is used to fit the above P-wave envelope function. At this point, the value ofBcan be inversely calculated. After obtaining the value ofB, the relationship betweenBand epicenter distanceDis fitted by least square method[7]. Finally, the value of epicentral distanceDcan be deduced by calculating theBvalue of each measured data. The block diagram is shown in Fig.2.

Fig.2 Flow chart for solving epicentral distance

1.3 Calculation method of focal depth (H)

As seen from Fig.1, in the right triangle composed of the detonation center, epicenter and test point, the epicenter distance has been calculated. Therefore, after further calculating the distance between the detonation center and the test point, the value of the focal depth can be obtained according to Pythagorean theorem as

(7)

wheret1indicates the time when the P-wave generated by the explosion arrives at the test point;t0indicates the time when the explosion occurs; andVrepresents the average velocity of the P-wave propagating underground. Because of the attenuation of seismic wave propagation and the infeasibility of underground velocity measurement, velocityVis difficult to obtain. In view of this problem, a distributed testing system is proposed[8].

Fig.3 Test layout diagram

As shown in Fig.3, the six test points are distributed on a circle with the same radius on the ground. The explosion center is located at the origin, each test point is an independent testing system. Because the test points are explosions with the same depth, the depths of all systems are theoretically the same. Choose any three testing systems as a set of Eqs.(8)-(10), whereD1,D2,D3are the epicentral distance of test points of 1, 2 and 3;t1,t2,t3are the time when seismic waves reach test points of 1, 2 and 3;t0is the initiation time; andHis the explosion depth.

(8)

(9)

(10)

The measurement data of the test point 1 in Fig.3 is obtained according to Eqs.(8)-(10), as shown in Eq.(11). It can be seen that there is only one unknownHin the formula, so this method can be used to calculate the focal depth.

(11)

Up to now, the three parameters for determining the location of the explosion center have been determined. In theory, the location of the explosion center can be determined.

2 LS-DYNA simulation

LS-DYNA finite element simulation has a good fit in the study of underground explosion. In this paper, Hyperworks is used to divide the finite element mesh, ANSYS is used to calculate K file, LS-prepost is used for post-processing analysis[9]. The simulation results are shown in Fig.4, and the left figure is the result of meshing, which defines three materials as air, soil and explosive, respectively. The attributes of materials are shown in Tables.1-3. Simulate the explosion environment of 1 m3, in which the top is air, and the explosive is located in the soil from the surface depth of 0.4 m. The right figure shows a moment intercepted during the explosion.

Fig.4 Simulation model and result

Table 2 Parameters of explosives and JWL equation

Table 3 Soil physical parameters

Distributed testing system can centralize the management of testing equipment in different locations through local area network, which meets the new testing requirements under the new situation, and the measurement accuracy is higher than that of single testing system[10].

As shown in Fig.5, eight test points are distributed on a circle with the same radius, and the distance from the test point to the epicenter is 10, 20 and 30 cm, respectively, with a cobweb distribution. After getting the data of each group, we need to analyze the whole data according to certain evaluation criteria and integrate the best results.

Fig.6 is the simulated acceleration values ofX,YandZaxes at the intercepted test point 7. The unit of abscissa is s and the unit of ordinate is g.

3 Optimal distribution of testing system

According to the calculation method of epicenter distance and azimuth angle, 24 test point data in Fig.5 are calculated as shown in Table 4.

The distance between the test point and the detonation center and the way around the explosion center will affect the experimental data.

In the actual test experiment, there may be deviation between the device layout center and the actual explosion center, resulting in that only part of the data collected by the distributed testing system is effective. In order to make the measurement results more accurate and get a more accurate way to arrange points, the 24 testing systems are divided into 6 groups: the first group (1-8), the second group (9-17), the third group (18-24), the fourth group (1-3), the fifth group (13-15) and the sixth group (19-21). The statistical results are obtained in Table 5.

Table 5 Coordinates for each group

Analysis of the 1-3 groups of data shows that the closer the test points are to the epicenter, the closer the calculated results are to the actual results. The comparison analysis between the first group and the fourth group, between the second group and the fifth group, between the third group and the sixth group show that when the distance between the testing system and the epicenter is the same, the error of the surrounding shape distribution is smaller than that of the same quadrant distribution. Due to the same distance measurement has certain limitations, it is proposed to integrate and analyze the data by using the weighted method, that is to say, the closer the test points to the epicenter, the greater their proportion, as shown in Eqs.(12)-(14).

(12)

(13)

(14)

whereHis the focal depth;XandYare the transverse and vertical coordinates of the epicenter (after azimuth and epicenter distance are determined);Hi,Xi,Yiare the parameters obtained by a single testing system. Using the above weighted formula, the epicenter coordinates are calculated as (0.52, 0.47) and the focal depth is 0.43 m. Therefore, the final location of underground explosion is (0.52, 0.47, 0.43), compared with the actual location of (0.5,0.5,0.4), the error is about 5%, which is within the normal error range. Therefore, it can be judged that the principle of seismic location is applicable to the determination of underground explosion center location.

4 Conclusion

In view of the vacancies in the research on the location of underground explosion center at home and abroad, the location of underground explosion center is analyzed by using the principle of seismic location. LS-DYNA finite element simulation platform was used to simulate the explosive explosion in the ground, and the location method was validated by analyzing the data. In addition, the distributed testing system combined with the weighting method was used to give the optimal layout.