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Yujiang Li, Lianwang Chen, Yuanzhong Lu (2012). Numerical simulation on the influences of Wenchuan earthquake on the surrounding faults. Earthq Sci 25(2): 143-150. DOI: 10.1007/s11589-012-0841-7
Citation: Yujiang Li, Lianwang Chen, Yuanzhong Lu (2012). Numerical simulation on the influences of Wenchuan earthquake on the surrounding faults. Earthq Sci 25(2): 143-150. DOI: 10.1007/s11589-012-0841-7

Numerical simulation on the influences of Wenchuan earthquake on the surrounding faults

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  • Corresponding author:

    Yujiang Li, e-mail: toleeyj@126.com

  • Received Date: 05 Jan 2012
  • Accepted Date: 19 Mar 2012
  • Available Online: 30 May 2022
  • Published Date: 09 Apr 2012
  • On 12 May 2008, the devastating Wenchuan earthquake struck the Longmenshan fault zone, which comprised the eastern margin of the Tibetan Plateau, and this fault zone was predominantly a convergent boundary with a right-lateral strike-slip component. After such a large-magnitude earthquake, it was crucial to analyze the influences of the earthquake on the surrounding faults and the potential seismic activity. In this paper, a complex viscoelastic model of western Sichuan and eastern Tibet regions was constructed including the topography. Based on the findings of co-seismic static slip distribution, we calculated the stress change caused by the Wenchuan earthquake with the post-seismic relaxation into consideration. Our preliminary results indicated that: (1) The tectonic stressing rate was relatively high in Kunlun mountain pass-Jiangcuo, Ganzi-Yushu, Xianshuihe and Zemuhe faults; while in the east Kunlun and Longriba was medium; also the value was less in the Minjiang, Longmenshan, Anninghe and Huya faults. As to the Longmenshan fault, the value was 0.28×10-3 MPa/a to 0.35×10-3 MPa/a, which is coincident with the previous long recurrence interval of Wenchuan earthquake; (2) The Wenchuan earthquake not only caused the Coulomb stress decrease in the source region, but also the stress increase in the two terminals, especially the northeastern segment, which is comparatively consistent with the aftershock distribution. Meanwhile, the high concentration areas of the static slip distribution were corresponding to the Coulomb stress reductions; (3) The Coulomb stress change caused by Wenchuan earthquake showed significant increase on five major faults, which were northwestern segment of Xianshuihe fault, eastern Kunlun fault, Longriba fault, Minjiang fault and Huya fault respectively; also the Coulomb stress on the fault plane of the Yushu earthquake was faintly increased; (4) We defined the recurrence interval as the time needed to accumulate the magnitude of the stress drop, and the recurrence interval of Wenchuan earthquake was estimated about 1 714 a to 2 143 a correspondingly.

  • On 12 May 2008, the devastating Wenchuan earthquake struck the Longmenshan fault zone about 300 km (; ), which comprised the eastern margin of the Tibetan Plateau, collapsing buildings and killing thousands in major cities of Sichuan province, China. Preliminary teleseismic waveform analysis suggested that the earthquake was composed of two sub-events of 6-9 m slip on an about 33° dipping fault, the epicentral sub-event underwent oblique right-lateral thrust slip, while the northeast subevent slipped largely right-laterally (; ). After such an earthquake, it was crucial to analyze the stress transfer in the crust. Then, we employed the finite element model to study the stress change caused by Wenchuan earthquake with the post-seismic relaxation into consideration.

    In the history records, there were many earthquakes in the Longmenshan adjacent area, such as the Diexi M7.3 in 1933 (), the SongpanPingwu M7.2 double shocks in 1966 (), which were about one hundred kilometers to this fault. However, in the last three hundred years, there was no MS>6.0 earthquake in the Longmenshan fault system. Unexpectedly, the Wenchuan earthquake occurred on this fault which was seemingly inactive from the GPS observation before.

    Based on the latest achievements about active tectonics, velocity structure in western Sichuan and eastern Tibet regions, a finite element model is constructed to simulate the stress change following the Wenchuan earthquake. The model incorporates five key features: (1) The boundary is determined as follows: 26°N-37°N in latitude and 90°E-108°E in longitude, also the depth reaches 100 km; (2) The model includes five layers with the topography into consideration, and all these faults in the model are simulated by the frictional contact, that is to say, contact elements have zero thickness; (3) The faults in the model are discontinuities and have deformable contact elements on their surface that obey the Coulomb failure criterion; (4) The Longmenshan fault zone has a high dipping angle near surface and low-angle at depth, and this kind of listric shape favors significant strain to form great earthquakes; (5) The crustal velocity structure and density are known in advance (; ; ), and the elastic parameters can be inferred (Table 1), the viscosity follows the previous results (; ).

    Table  1.  Material properties of the crust and upper mantle
     | Show Table
    DownLoad: CSV

    The finite element model is composed entirely of eight-node viscoelastic elements (Figure 1). It consists of 135 547 elements with 141 527 active nodes. The surface elevation is mainly based on the SRTM (Shuttle Radar Topography Mission) elevation data (http://srtm.csi.cgiar.org/). Since the Longmenshan fault zone has a high dipping angle near surface and low-angle at depth, we use the listric shape to simulate the fracture surface morphology, and this kind of shape favors significant strain or energy accumulation to form great earthquakes (). As the earthquake preparation process generally takes several hundred to several thousand years and even longer, to a certain extent, the rock stress-strain accumulation presents the rheological properties. Therefore, it is necessary to consider the rheological properties of the medium.

    Figure 1. Three dimensional discretization model. F1 to F10 represent the Kunlun mountain pass-Jiangcuo, eastern Kunlun, Longriba, Minjiang, Huya, Longmenshan, Ganzi-Yushu, Xianshuihe, Anninghe and Zemuhe faults, respectively, and the geometric parameters are in details in Table 2 according to the recent findings (Xu et al., 2008), while the right is the digital elevation increased by five times around the Sichuan basin, and the elevation difference was obvious
    Figure  1.  Three dimensional discretization model. F1 to F10 represent the Kunlun mountain pass-Jiangcuo, eastern Kunlun, Longriba, Minjiang, Huya, Longmenshan, Ganzi-Yushu, Xianshuihe, Anninghe and Zemuhe faults, respectively, and the geometric parameters are in details in Table 2 according to the recent findings (), while the right is the digital elevation increased by five times around the Sichuan basin, and the elevation difference was obvious
    Table  2.  Geometric parameters of the major active faults
     | Show Table
    DownLoad: CSV

    Among the previous researches, the Maxwell body or the power-law fluid was widely used in the earthquake-related fields (; ), the relaxation and creep characteristics of the Maxwell body have shown a similar fluid nature property, in which the stress reduces to zero, or the strain increases infinitely with time, and this may not match the crustal rheological characteristics. As a nonlinear constitutive relation, the power-law fluid needs the higher convergence value. In the end, we choose the standard linear solid constitutive in this paper. And the creep and relaxation equations of this constitutive relation are

    (1)

    and

    (2)

    where p1=η/(E1+E2), q0=E1·E2/(E1+E2), q1=E1·η/ (E1+E2), τ=q1/q0=η/E2, E1, E2 represent the Young's modulus and η the viscosity.

    As we all know, the Maxwell body shows a similar fluid properties, and as a solid medium with the rheological properties, the standard linear solid is more realistic than the Maxwell or Kelvin body, and the creep and relaxation characteristics are shown in Figure 2. For the creep equation, the strain increases to a constant with the invariable stress, not the infinite; while for the relaxation equation, the stress reduces to a constant with the invariable strain, not zero.

    Figure 2. Creep (a) and relaxation (b) curves of the standard linear solid body where E0 and E∞ represent the Young's modulus in the initial and the infinite time, while ε0 and ε∞ represent the strain in the same condition, σ0 represents the initial stress
    Figure  2.  Creep (a) and relaxation (b) curves of the standard linear solid body where E0 and E represent the Young's modulus in the initial and the infinite time, while ε0 and ε represent the strain in the same condition, σ0 represents the initial stress

    GPS velocity observations are interpolated and extrapolated across the model and boundary condition areas, and the model is loaded according to a thousand year displacements, then the tectonic stressing rate is evaluated. Meanwhile, the model base is freely slipping laterally but cannot move vertically, and the model free surface is fully deformable. All constraints are imposed on the model as described above; before any constrain is introduced, the model is subjected to gravity for a ten thousand years period required to fully compress under its own weight.

    All modeling presented here is conducted using the ANSYS finite element program. ANSYS employs the Newton-Raphson approach to solve nonlinear problems. In this method a load is subdivided into a series of increments applied over several steps. Before each solution this method evaluates the out-of-balance load vector. If the convergence criteria are not satisfied, the load vector is reevaluated, the stiffness matrix is updated, and a new solution is obtained until the problem converges.

    An earthquake can be modeled as an elastic dislocation solutions in an elastic half-space (Okada, 1992), which makes the estimation of stress transfer and prediction of the aftershock distribution available immediately after an earthquake, and it is widely used nowadays (; ; ). When the Wenchuan earthquake occurred, numerous Coulomb failure stress studies have been carried out. calculated the stress change in the vicinity of the Longmenshan fault zone and estimated the earthquake probability. did a similar analysis to forecast the seismic rate and distribution of damaging shocks using the calculated stress changes and the observed background seismicity. used an updated earthquake source model and the fault geometry as well as kinematic parameters to attempt a better assessment of the earthquake potentials in the region, also to evaluate the Coulomb failure stress assuming different effective friction coefficients; the results are in general agreements with previous studies. used the PSGRN/PSCMP software and the Crust 2.0 model to study the stress change caused by Wenchuan earthquake, and also the uncertainty deduced from the effective friction coefficient. Unfortunately, the shortcomings such as the coupled viscoelastic relaxation effect and inhomogeneous medium treatment were obvious (), the initial stress was also not included. However, the initial stress not only made the fault plane stress state more complex, but also affected the distribution of Coulomb stress (), while the finite element method was relatively flexible.

    Calculated changes in stress tensor components are resolved on the interest planes, and changes in failure stress are related to triggering or inhibition of future earthquakes (). Usually, the Coulomb stress change is used to explain patterns of seismicity (; ). The Coulomb failure criterion is defined as

    (3)

    where Δτ is the shear stress acting on the receiver fault (positive in the fault slip direction), μ is the friction coefficient, Δσn is the change in normal stress acting on the receiver fault (positive for unclamping), Δp is the pore pressure change. The effect of friction reduction due to pore pressure can be represented by an equivalent friction coefficient μ'=μ(1−B), in which B is the Skempton coefficient in the range of 0-1 (), then Δσfτ+μσn, also in our calculation, we are assuming the equivalent friction coefficient value of μ'=0.4.

    Tectonic stressing rate is simulated on the finite element model with the GPS constraints, and this period lasts one thousand years. After one thousand years the Wenchuan earthquake is simulated by displacing the Longmenshan fault with the slip distribution of . From Figure 3 we can conclude that the stressing rate is relatively high in Kunlun mountain pass-Jiangcuo, Ganzi-Yushu, Xianshuihe and Zemuhe faults; while the east Kunlun and Longriba is medium; also the value is less in the Minjiang, Longmenshan, Anninghe and Huya faults. As to the Longmenshan fault, the value is 0.28×10−3 MPa/a to 0.35×10−3 MPa/a, which is coincident with the previous long recurrence interval of Wenchuan earthquake (; ; ; ).

    Figure 3. Tectonic stressing rate on the mainly active faults in the upper crust. F1 to F10 represent the Kunlun mountain pass–Jiangcuo, eastern Kunlun, Longriba, Minjiang, Huya, Longmenshan, Ganzi-Yushu, Xianshuihe, Anninghe and Zemuhe faults, respectively
    Figure  3.  Tectonic stressing rate on the mainly active faults in the upper crust. F1 to F10 represent the Kunlun mountain pass–Jiangcuo, eastern Kunlun, Longriba, Minjiang, Huya, Longmenshan, Ganzi-Yushu, Xianshuihe, Anninghe and Zemuhe faults, respectively

    The Coulomb failure stress change on a receiver fault not only depends on the fault geometry (strike, dip and rake) and friction coefficient, but also the geometry of the source fault, as well as the coseismic slip of the source earthquake (). Before the findings of co-seismic static slip distribution was introduced (Figure 4), the model was subjected to gravity for a ten-thousand-year period required to fully compress under its own weight, then with the post-seismic relaxation into consideration, the Coulomb failure stress change caused by the Wenchuan earthquake was examined in detail, as shown in Figure 5.

    Figure 4. Distribution of the coseismic displacement in the seismogenic fault (After Ji and Hayes, 2008)
    Figure  4.  Distribution of the coseismic displacement in the seismogenic fault (After )
    Figure 5. Coulomb stress change on major faults caused by the Wenchuan earthquake. The fault names are the same as those in Figure 3
    Figure  5.  Coulomb stress change on major faults caused by the Wenchuan earthquake. The fault names are the same as those in Figure 3

    The Wenchuan earthquake not only caused the Coulomb failure stress decrease in the source region, but also the stress increase in the two terminals, especially the northeastern segment, which is comparatively consistent with the aftershock distribution. Meanwhile, the high concentration area of the static slip distribution was corresponding to the stress reduction; the Coulomb failure stress change caused by Wenchuan earthquake was significantly increased on five major fault segments, which were northwestern segment of Xianshuihe fault, eastern Kunlun fault, Longriba fault, Minjiang fault and Huya fault respectively, also the Coulomb failure stress on the fault plane of the Yushu earthquake was faintly increased. The earthquake also decreased the Coulomb failure stress on the southeastern segment of Xianshuihe fault, Anninghe fault, especially on the southeastern segment of Xianshuihe fault with the stress reduction of 0.3 MPa, respectively. The Coulomb failure stress change on the fault plane of Zemuhe was nearly zero, indicating no significant influence of the Wenchuan earthquake on the fault. In short, the Coulomb stress change was mainly increasing in the area north of the Longmenshan fault zone while the south was different degrees of reduction.

    From the point of the excavation trenches after the earthquake, both the central and frontier-range faults of the Longmenshan had shown at least two seismic events with the size of the Wenchuan earthquake, and the preliminary results were of characteristic earthquake type (; ). We defined the recurrence interval as the time needed to accumulate the magnitude of the stress drop. In line with our result of the tectonic stressing rate in Figure 3, the recurrence interval of Wenchuan earthquake in the Longmenshan fault was estimated about 1 714 a to 2 143 a correspondingly, which was comparatively consistent with the other methods, such as the paleoseismic evidence, fault slip rate, earthquake moment rate and GPS observation data (; ; ; ; ).

    The 12 May 2008 Wenchuan earthquake caused grievous losses, yet its legacy included possible large shocks in the near future around the Sichuan basin. In view of this point, GPS-derived displacement was used to distort a finite element model of western Sichuan and eastern Tibet, and the tectonic stressing rate was given. Based on the findings of co-seismic static slip distribution deduced from the teleseismic waveform analysis, the Coulomb failure stress change caused by the Wenchuan earthquake was introduced with the post-seismic relaxation into consideration, then the preliminary results showed that the effect was changed in partition in the area north of the Longmenshan fault; the effect was mainly loaded while in the south uploaded. That is to say, if such an earthquake in the future is observed on the stressed parts of the Xianshuihe, east Kunlun, Longriba, Minjiang and Huya faults, it would provide support for hypothesis that large shocks are now also more likely to happen where the static stress imparted by the mainshock has risen. Finally, the recurrence interval of the Longmenshan fault was estimated about 1 714 a to 2 143 a correspondingly. Furthermore, the postseismic effect such as the afterslip was ignored in this paper, which will be done later.

    Thanks are given to Professor Yongge Wan and the three anonymous reviewers for their helpful suggestions, also to Yanxing Li and Chen Ji for providing the data. This work was financially supported by Basic Science and Research from the Institute of Crustal Dynamics, China Earthquake Administration (ZDJ2012-09, ZDJ2010-12), and the National Key Technology Research and Development Program (2008BAC38B04).

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