Study of Earthquake Triggering in a Heterogeneous Crust Using a New Finite Element Model

Hu, Changjin; Zhou, Yijie; Cai, Yongen; Wang, Chi‐Yuen

doi:10.1785/gssrl.80.5.799

Cited by 7 publications

(18 citation statements)

References 52 publications

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“…Herein we refer to an earthquake fault as a zone with finite thickness [ Evans , 1990; Caine et al , 1996; Schulz and Evans , 2000; Li et al , 2002; Gudmundsson , 2004]. Thus in a mechanical model, the occurrence of an earthquake may be considered as material softening/weakening or damage in the fault zone, which may be simulated by reducing the shear modulus of the material in the fault zone [ Hu et al , 2009a, 2009b]. …”

Section: Quasi‐static Model Of a Fault Earthquakementioning

confidence: 99%

“…Two basic equations can be obtained on basis of the principle of virtual work. One equation solves for preseismic displacement u t or strain ε t [ Hu et al , 2009b]:

\int_{V} {\overset{ε}{true}}^{T} D {bold-italicε}^{t} d V = \int_{V} {\tilde{boldu}}^{T} f^{t} d V + \int_{S_{2}} {\overset{u}{true}}^{T} {boldq}^{t} d S - \int_{V} {\tilde{bold-italicε}}^{T} σ^{0} d V

where

{\tilde{boldu}}^{T}

and

{\tilde{bold-italicε}}^{T}

are the virtual displacement and virtual strain, respectively,

{bold-italicσ}^{t} = {[σ_{italicxx} σ_{italicyy} σ_{italiczz} τ_{italicyz} τ_{italicxz} τ_{italicxy}]}^{T}

and

{bold-italicε}^{t} = {[ε_{italicxx} ε_{italicyy} ε_{italiczz} γ_{italicyz} γ_{italicxz} γ_{italicxy}]}^{T}

are the stress and strain at time t , respectively,

f^{t}

and

q^{t}

are body force and traction force, respectively, and

boldD

and

σ_{}^{0}

are the material matrix and initial or previous stresses, respectively.…”

Section: Quasi‐static Model Of a Fault Earthquakementioning

confidence: 99%

“…The second equation solves the co‐ and postseismic displacement,

Δ u

and strain

Δ ε

, caused by an earthquake [ Hu et al , 2009b]:

\int_{V} {\tilde{bold-italicε}}^{T} true(boldD - normalΔ boldD true) normalΔ bold-italicε d V = \int_{V} {\tilde{bold-italicε}}^{T} normalΔ D {bold-italicε}^{t} d V - \int_{V} {\tilde{bold-italicε}}^{T} normalΔ {bold-italicσ}^{0} d V + \int_{V} {\tilde{boldu}}^{T} true(normalΔ boldf true) d V + \int_{S_{2}} {\tilde{boldu}}^{T} true(normalΔ boldq true) d S_{2}

where

Δ bold-italicε = boldL Δ boldu

is the co‐ or postseismic strain field in the domain V , and

Δ boldD

Δ σ^{0}

Δ boldf

, and

Δ boldq

are the changes in the material matrix, stress matrix, body force, and traction force, respectively.…”

Section: Quasi‐static Model Of a Fault Earthquakementioning

confidence: 99%

“…If fault healing is considered in the postseismic process, the

Δ boldD

is a function of time. If

Δ boldf

and

Δ boldq

are much smaller than the contribution of the first term of the right side of equation (2) during an earthquake sequence or a quasi‐earthquake cycle, equation (2) can be reduced to

\int_{V} {\tilde{bold-italicε}}^{T} true(boldD - normalΔ boldD true) normalΔ bold-italicε d V = \int_{V} {\tilde{bold-italicε}}^{T} normalΔ D {bold-italicε}^{t} d V - \int_{V} {\tilde{bold-italicε}}^{T} normalΔ {bold-italicσ}^{0} d V .

Compared with the previous equations [ Hu et al , 2009b], the initial stress field

{bold-italicσ}_{}^{0}

and its change

Δ σ^{0}

are involved in equations (1)–(3). The material in the lower crust and upper mantle is viscoelastic according to the Maxwell model, which is different from the elastic material in previous work [ Hu et al , 2009b].…”

Section: Quasi‐static Model Of a Fault Earthquakementioning

confidence: 99%

“…On the basis of Coulomb failure criterion neglecting rock cohesion, which is much less than the shear stress in depth, a dimensionless earthquake triggering factor, C = | τ n |/( μσ n ), and its change, Δ C = C a − C b , are defined [ Hu et al , 2009b], where τ n and σ n are the shear and normal stresses on the fault, respectively, μ is the internal frictional coefficient, or effective frictional coefficient, and C a and C b are the post‐ and preseismic C values. C ≥ 1 implies that the Mohr's circle touches or crosses the Coulomb failure envelope and earthquakes may be triggered, and C < 1 implies that the circle is below the envelope, and no earthquakes are expected.…”

Section: Quasi‐static Model Of a Fault Earthquakementioning

confidence: 99%

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Effects of large historical earthquakes, viscous relaxation, and tectonic loading on the 2008 Wenchuan earthquake

Cai

Wang

2012

J. Geophys. Res.

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The 2008 Wenchuan earthquake (M7.9) occurred on the Longmenshan Fault in Sichuan, China. Both the seismicity and slip rate of the fault are lower than those of other faults in the region. By incorporating large earthquakes in the region during the past 222 years into our investigation, the effects of historical earthquakes, viscous relaxation, and tectonic loading on the Wenchuan earthquake were studied, using a quasi‐static, finite element model. In this model, we first simulated an initial stress field constrained by fault slip rates obtained by GPS and geologic observations in the region. We then simulated earthquakes by fault softening. The results show that tectonic loading has the most significant effect on the Longmenshan Fault, whereas viscous relaxation of the lower crust and upper mantle has the least effect. The effects of the historical earthquakes are variable; some promote the earthquake potential and others retard the earthquake potential.

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Section: Quasi‐static Model Of a Fault Earthquakementioning

confidence: 99%

“…Two basic equations can be obtained on basis of the principle of virtual work. One equation solves for preseismic displacement u t or strain ε t [ Hu et al , 2009b]:

\int_{V} {\overset{ε}{true}}^{T} D {bold-italicε}^{t} d V = \int_{V} {\tilde{boldu}}^{T} f^{t} d V + \int_{S_{2}} {\overset{u}{true}}^{T} {boldq}^{t} d S - \int_{V} {\tilde{bold-italicε}}^{T} σ^{0} d V

where

{\tilde{boldu}}^{T}

and

{\tilde{bold-italicε}}^{T}

are the virtual displacement and virtual strain, respectively,

{bold-italicσ}^{t} = {[σ_{italicxx} σ_{italicyy} σ_{italiczz} τ_{italicyz} τ_{italicxz} τ_{italicxy}]}^{T}

and

{bold-italicε}^{t} = {[ε_{italicxx} ε_{italicyy} ε_{italiczz} γ_{italicyz} γ_{italicxz} γ_{italicxy}]}^{T}

are the stress and strain at time t , respectively,

f^{t}

and

q^{t}

are body force and traction force, respectively, and

boldD

and

σ_{}^{0}

are the material matrix and initial or previous stresses, respectively.…”

Section: Quasi‐static Model Of a Fault Earthquakementioning

confidence: 99%

“…The second equation solves the co‐ and postseismic displacement,

Δ u

and strain

Δ ε

, caused by an earthquake [ Hu et al , 2009b]:

\int_{V} {\tilde{bold-italicε}}^{T} true(boldD - normalΔ boldD true) normalΔ bold-italicε d V = \int_{V} {\tilde{bold-italicε}}^{T} normalΔ D {bold-italicε}^{t} d V - \int_{V} {\tilde{bold-italicε}}^{T} normalΔ {bold-italicσ}^{0} d V + \int_{V} {\tilde{boldu}}^{T} true(normalΔ boldf true) d V + \int_{S_{2}} {\tilde{boldu}}^{T} true(normalΔ boldq true) d S_{2}

where

Δ bold-italicε = boldL Δ boldu

is the co‐ or postseismic strain field in the domain V , and

Δ boldD

Δ σ^{0}

Δ boldf

, and

Δ boldq

are the changes in the material matrix, stress matrix, body force, and traction force, respectively.…”

Section: Quasi‐static Model Of a Fault Earthquakementioning

confidence: 99%

“…If fault healing is considered in the postseismic process, the

Δ boldD

is a function of time. If

Δ boldf

and

Δ boldq

are much smaller than the contribution of the first term of the right side of equation (2) during an earthquake sequence or a quasi‐earthquake cycle, equation (2) can be reduced to