# Numerical simulation of dynamic process of earthquake

Numerical simulation of dynamic process of an earthquake
Yongen Cai and Ren Wang
Geodynamic Research Center of Peking University Department of Geology, Peking University, Beijing,100871, China (e-mail: yonen@pku.edu.cn; phone: 86 10 6275 5441).

Abstract
In this investigation, we use a new numerical method LDDA ( Lagrangian Discontinuous Deformation Analysis)[1-2] to simulate a dynamic process of an earthquake occurring on strike slip fault, The method can be used to solve the dynamic problem with discontinuous deformation block system, it grows up on the base of the finite element method with domain decomposition algorithm [3-4] and DDA (Discontinuous Deformation Analysis) [5] and overcomes the weakness of the classical Lagrangian multiplier method by using domain decomposition algorithm and obviously prevails over the penalty method in the satisfaction of constrain conditions. The process of solving the problem by LDDA is as follows: 1) find total contact points (Lagrangian multiplier points) between blocks according to the contact criteria of the DDA, 2) solve the forces on the contact points between blocks by domain decomposition method. 3) calculate the displacement and stresses caused by the contact forces in term of the FEM for each block. In mechanics, the earthquake occurrence can be considered as the results when the shear stress on the fault overcomes the frictional resistance of the fault. The LDDA method will be used to simulate the dynamic process by changing the frictional state of the fault[6] in the following example. The geometry of the model used in the study is shown in Fig. 1. The fault is simulated by contact element across which the displacement is discontinuous when slip occurs. The initial stress field is induced by applying displacements on the boundaries of the model. Under the state the frictional coefficient of the middle section (thick line) is changed from 1.0 to 0.1, it starts the dynamic process of fault sliting. The computed results of the dynamic process are shown in Figs. 2 and 3. Fig. 2 shows the “Seismographs” of the x-, y- components of the displacement at “station” A, B, C and D. It shows that the “elastic rebound” is about 7cm at A at time 0.03 sec. after the start of sliding, but the residual displacement found at time 5.0 sec.(quasi-static state) is less than this magnitude. At other locations the displacements are also not recovered to their initial displacement. Fig. 3 shows the contours of the change in displacement and maximum shear stress caused by earthquake at different time.

261

0.5m

D+ ?=0.1 ?=1.0 B+ A+ ?=0.1 +C 70m 25m 700m 25m 1m

1m

700m

0.5m
Fig. 1 Model geometry and boundary conditions

We see from the results that 1) the relative displacement of the fault obtained after this simulated earthquake is less than the maximum reached at the initial moment of the dynamic process, 2) The maximum shear stress drop obtained is about 38Mpa at the fault and decreases away from the fault, 3) P and S wave can not be identified at the earthquake source region. Although the material model and geometry shapes in the examples are very simple the results still reveal some very interesting phenomena and are helpful for understanding the dynamic process of earthquake events, especially for the discontinuous deformation dynamic problems. The method will be used to simulate the dynamic process of earthquake migration in a fault network

262

( ( ( ( ( ( ( ( (    

'LVSODFHPHQW; P

1RGH \$

7LPH VHF 



( ( ( ( ( ( ( ( (    

'LVSODFHPHQW< P

1RGH \$

7LPH VHF    7LPH VHF 



'LVSODFHPHQW; P

'LVSODFHPHQW< P

( ( ( ( ( ( (   

1RGH %

( ( ( ( ( (   

1RGH %

7LPH VHF   7LPH VHF 









7 LP H V HF   VH F











'LVSODFHPHQW; P

( ( ( ( ( ( (









 1RGH &

'LVSODFHPHQW< P

1RGH &

( ( ( ( ( (

7 L PH VH F    PH VHF 

7 L P H V HF   VH F










'LVSODFHPHQW< P

'LVSODFHPHQW; P

( ( ( ( (

 ( ( ( ( ( ( (









1RGH '

1RGH '

7 L PH V HF    PH V HF 

7LPH VHF  7LPH VHF 

Fig. 2 the x-, y- components of the displacement process at A, B, C and D

263

Time = 0.01sec

Time = 0.01sec

Time = 0.04sec

Time = 0.04sec

Time = 0.06sec

Time = 0.06sec

Time = 5.00sec

Time = 5.00sec

(a)

(b)

Fig. 3 a) Contours of the change of displacement. b) Contours of the change of maximum shear stress.

Acknowledgement
The support for this study was provided by the Climp Program (95-S-05), SSTC.

264

References
[1] Hilbert, L. B., Jr., Yi, W., Cook, N.G. W., Cai, Y. and Liang, G. P. (b), A new Discontinuous finite element method for interaction of many deformable bodies in geomechanics, Pro. 8th Int. Conf. Comp. Meth. adv,Geomech., 836-931, 1994. [2] Y. Cai, G. P. Liang, G. H. Shi, N. G. W. Cook, Studing an impact problem by using LDDA, Discontinuous Deformation Analysis (DDA) and Simulations of Discon-

tinuous Media, edited by Salami and Banks, 1996, TSI.
[3] Liang Guo-ping and He Jiangheng , The non comforming domain decomposition method for elliptic problems with Lagrangian Multiplies, Chinese J. Num. Math. & Appl., 15:1,8-19, 1993. [4] Printice, J. K., and Fikani, M.M., A domain decomposition technique for computational solid dynamics, Fifth International Symposium on Domain Decomposition methods for Partial Differential Equations, SIAM, Philadelphia, 541-544, 1992. [5] Shi, Geng-hua and Goodman, R. E., Two-dimensional discontinuous deformation analysis, Int. J. Numer. Anal. Meth. Geomech., 9, 541-556, 1985. [6] Wang Ren, Sun Xunying, Cai Yongen, A mathematical simulation of earthquake sequence in north China in last 700 years,Scientia Sinica(in English),Vol.26, No.1, 32-42,1983.

265

Numerical simulation of dynamic process of earthquake.pdf
Numerical simulation of dynamic process of earthquake_电力/水利_工程科技_专业资料。Numerical simulation of dynamic process of an earthquake Yongen Cai and Ren...
Numerical Simulation of Failure Process of Concrete....pdf
Numerical Simulation of Failure Process of Concrete Under Compression Based on...Numerical simulation of fracture process of concrete under dynamic impact. ...
Numerical simulation of dynamic process of an earthquake.unkown
Abstract In this investigation, we use a new numerical method LDDA ( ...[1-2] to simulate a dynamic process of an earthquake occurring on strike...
The numerical simulation study of the dynamic evolutionary ....unkown
The numerical simulation study of the dynamic evolutionary processes in an ...earthquake recurrence process and the dynamic evolutionary processes in an ...
Numerical simulation of dynamic thermal process during double....pdf
Numerical simulation of dynamic thermal process during doublesided asymmetrical TIG backing weld_专业资料。CNAWEDI 12 . rh2 HI LNGVo.0No1Mac 01 1 Numeia...
Numerical Simulation of Dynamic Response of Supple Nets_论文_....pdf
Numerical Simulation of Dynamic Response of Supple Nets_水产渔业_农林牧渔_专业资料。维普资讯 http://www.cqvip.com CiaOca n/erg,Vo.0,N3P4346hn enE...
Dynamic experiment and numerical simulation of solute ....pdf
Dynamic experiment and numerical simulation of solute transmission in heap leaching processing_化学_自然科学_专业资料。维普资讯 http://www.cqvip.com JCn.ot ...
Numerical Simulation of Seismic Ground Motion Isolation Using....pdf
Numerical Simulation of Seismic Ground Motion ...Earthquake Engineering and Soil Dynamics IV GSP ...process of prediction of mechanical behavior in ...
Numerical simulation of cutting process of the slice ....pdf
Numerical simulation of cutting process of the slice components cutting machine_机械/仪表_工程科技_专业资料。JunlfHriIsttoenly(eee)o.7N.,00oraoab ntuefT...
Numerical simulation of dynamic process for liquid film ....pdf
Numerical simulation of dynamic process for liquid film spreading by lattice Boltzmann met_林学_农林牧渔_专业资料。J.Cent.South Univ.(2014)21:32473253...
NUMERICAL SIMULATION OF PROPAGATION AND BREAKING PROCESSES OF....pdf
NUMERICAL SIMULATION OF PROPAGATION AND BREAKING PROCESSES OF A FOCUSED WAVES GROUP_物理_自然科学_专业资料。399 Avlbeoieatail nl anwww.cecdic.osinertm eo...
Numerical Simulation of Chemical Engineering Processes.pdf
Numerical Simulation of Chemical Engineering Processes...One key issue to run e ciently this process ... in Parallel Computational Fluid Dynamics: ...
NUMERICAL SIMULATION OF FRICTION STIR WELDING PROCESS.pdf
NUMERICAL SIMULATION OF FRICTION STIR WELDING PROCESS_英语学习_外语学习_教育... processes were performed utilizing Eulerian Computational Fluid Dynamics codes,...
Numerical Simulation on Failure Process in Brittle and ....pdf
Numerical Simulation on Failure Process in Brittle and Heterogeneous Matrix Filled with Randoml_专业资料。维普资讯 http://www.cqvip.com JunlfWua iesyo e...
Numerical Simulation of Dynamic Response of A Net Cage for ....pdf
Numerical Simulation of Dynamic Response of A Net Cage for Flatfish in Waves_建筑/土木_工程科技_专业资料。ChinaOceanE” Vol 28 No 1 PP 43 56 @2014 ...
Pseudo-dynamic test and numerical simulation of high-strength....pdf
Pseudo-dynamic test and numerical simulation of high-strength concrete frame structure reinforc_专业资料。Vl.0No-01.21 EARTHQUAKE ENGIERIAND NGIEENG BRATON...
Numerical Simulation on Coseismic Effect of the November 14, ....pdf
Numerical Simulation on Coseismic Effect of the November 14, 2001 Great Kunlun Earthquake, North_专业资料。维普资讯 http://www.cqvip.com EatqaeReerhi iar...
Numerical simulation of standing waves for ultrasonic ....pdf
Numerical simulation of standing waves for ultrasonic purification of magnesium alloy melt_机械/仪表_工程科技_专业资料。舞 TasNofru tScCia021)32s8 rn.neos...
Numerical Simulation of Dynamic Response of an Existing ....pdf
Numerical Simulation of Dynamic Response of an Existing Subway Station Subiected to Internal Bl_专业资料。Trn.iniUnv20. :66 sTaj i.0815358an4DOI 0...
Numerical Simulation on Dynamic Bending Strength of Three-....pdf
Numerical Simulation on Dynamic Bending Strength of Three-Graded Concrete Beam Based on Meso-Mec_专业资料。维普资讯 http://www.cqvip.com TasTaj i.0813135...