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Dieterich, Eugen

doi:10.1007/978-3-642-99540-8_8

Cited by 13 publications

(20 citation statements)

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“…This unification utilized a characteristic slip distance (which is a property of the slip surface). The resulting friction laws may be said to be of a rate and state dependent type ; they can manifest behavior which, depending on the modeled friction experiment, appears as any of the simpler types of friction mentioned earlier (DIETERICH, 1978(DIETERICH, , 1979aRUINA, 1980RUINA, , 1983. Recent experiments of RUINA (1980), TEUFEL (1981), JOHNSON (1981) and HIGGS (1981) lend support for these rate and state dependent friction laws.…”

Section: Intr~d~jction Stick-slip Motions Are the Results Of Interactionmentioning

confidence: 91%

“…In yet another simple friction law, the friction stress decreases with slip displacement, in a 'slip-weakening' sense, after slip begins following stationary contact (RABINOWICZ, 1958(RABINOWICZ, , 1959BYERLEE, 1970). Over the years attempts have been made to associate these two kinds of friction laws (JENKIN and EWING, 1877 ;RABINOWICZ, 1958RABINOWICZ, , 1959DIETERICH, 1978DIETERICH, , 1979a and to include combinations of them in stability analysis of frictional sliding. A more comprehensive friction law has been proposed by DIETERICH (1978DIETERICH ( , 1979a) based on his experiments with rocks and is similar to a proposal of RABINOWICZ (1958) based on experiments with metals (SAMPSON et al, 1943).…”

Section: Intr~d~jction Stick-slip Motions Are the Results Of Interactionmentioning

confidence: 99%

“…Over the years attempts have been made to associate these two kinds of friction laws (JENKIN and EWING, 1877 ;RABINOWICZ, 1958RABINOWICZ, , 1959DIETERICH, 1978DIETERICH, , 1979a and to include combinations of them in stability analysis of frictional sliding. A more comprehensive friction law has been proposed by DIETERICH (1978DIETERICH ( , 1979a) based on his experiments with rocks and is similar to a proposal of RABINOWICZ (1958) based on experiments with metals (SAMPSON et al, 1943). The original motivation of DIETERICI~ (1978, 1979a) and RABINOWICZ (1958) in proposing these laws was to unite the observed dependence of 'static' friction stress on time of nominally (see RUINA, 1983) stationary contact with the inverse dependence of steady sliding friction stress on slip rate.…”

Section: Intr~d~jction Stick-slip Motions Are the Results Of Interactionmentioning

confidence: 99%

“…The simple one state variable constitutive law proposed by RUINA (1980RUINA ( , 1983 as representative of experiments on slip at constant normal stress 0 over a range of positive x and motivated as an approximation to a more complex law by DIETERICH (1979aDIETERICH ( , 1980DIETERICH ( , 1981, is…”

Section: Constitutive Relation With One State Variablementioning

confidence: 99%

“…We note as a curiosity that when il = e -1, the apparent asymptote and numerically found solid line coincide. DIETERICH (1978), in arguing for the importance of spring stiffness in stick-slip, has presented a qualitative analysis applicable to the case just studied. His reasoning, applied to the friction law considered here, is as follows.…”

Section: Perturbations Of a Steadily Sliding System One State Variabmentioning

confidence: 99%

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Slip motion and stability of a single degree of freedom elastic system with rate and state dependent friction

Rice

Ruina

et al. 1984

Journal of the Mechanics and Physics of Solids

515

450

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WE CONSIDER quasistatic motion and stability of a single degree of freedom elastic system undergoing frictional slip. The system is represented by a block (slider) slipping at speed V and connected by a spring of stillness k to a point at which motion is enforced at speed V,. We adopt rate and state dependent frictional constitutive relations for the slider which describe approximately experimental results of Dieterich and Ruina over a range of slip speeds % In the simplest relation the friction stress depends additively on a term A In V and a state variable 0; the state variable B evolves, with a characteristic slip distance, to the value -B In K where the constants A, Bare assumed to satisfy B > A > 0. Limited results are presented based on a similar friction Iaw using two state variables.Linearized stability analysis predicts constant slip rate motjon at V0 to change from stable to unstable with a decrease in the spring stiffness k below a critical value k,,. At neutral stability oscillations in slip rate are predicted. A nonhnear analysis of shp motions given here uses the Hopf bifurcation technique, direct determination of phase plane trajectories, Liapunov methods and numerical integration of the equations of motion. Small but finite amplitude limit cycles exist for one value of k, if one state variable is used. With two state variables oscillations exist for a small range of k which undergo period doubling and then lead to apparently chaotic motions as k is decreased.Perturbations from steady sliding are imposed by step changes in the imposed load point motion. Three cases are considered : (1) the load point speed V0 is suddenly increased; (2) the load point is stopped for some time and then moved again at a constant rate; and (3) the load point displacement suddenly jumps and then stops. In all cases, for all values of k, sufficiently large perturbations lead to instability. Primary conclusions are: (I) "stick-slip" instability is possible in systems for which steady sliding is stable, and (2) physical manifestation of quasistatic oscillations is sensitive to material properties, stiffness, and the nature and magnitude of toad perturbations.t Visiting, Division of Applied Sciences, Harvard University, 1981-3. 167

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Section: Intr~d~jction Stick-slip Motions Are the Results Of Interactionmentioning

confidence: 91%

Section: Intr~d~jction Stick-slip Motions Are the Results Of Interactionmentioning

confidence: 99%

Section: Intr~d~jction Stick-slip Motions Are the Results Of Interactionmentioning

confidence: 99%

Section: Constitutive Relation With One State Variablementioning

confidence: 99%

Section: Perturbations Of a Steadily Sliding System One State Variabmentioning

confidence: 99%

See 3 more Smart Citations

Slip motion and stability of a single degree of freedom elastic system with rate and state dependent friction

Rice

Ruina

et al. 1984

Journal of the Mechanics and Physics of Solids

515

450

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Temporal earthquake forecasting

Ong¹,

Nielsen

Giani

et al. 2022

Preprint

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Convolutional Neural Networks (CNNs) can detect patterns that are otherwise difficult to identify and have been shown to excel in predicting fault characteristics in laboratory shear experiments and slow slip \emph{in situ}. Here we show that during the precursory phase of some natural earthquakes, a subtle change in the seismic background signal occurs that can be identified by a suitably designed CNN, and used as a probabilistic forecasting tool. We use 31 earthquakes of $\textrm{M} \textrm{w}\geq 6$ in Japan and vicinity, between March 2012 and February 2020, all recorded by station IU MAJO (Japan main island) except one recorded by station IU MA2 (Kamtchatka). The CNN is trained on 24 events, where a 16 mn time window preceding each earthquake is labelled as precursory (presumably containing a strong precursory signal), and another 16 mn time window far from the time of earthquake occurrence is labelled as noise (presumably containing weak or no precursory signal). The 7 remaining events were used for testing. The CNN achieves 98\% training accuracy and a 96\% testing accuracy in discriminating noise and precursor windows.

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Detection of earthquake precursors using neural networks

Ong¹,

Nielsen

Giani

et al. 2022

Preprint

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Convolutional Neural Networks (CNNs) can detect patterns that are otherwise difficult to identify and have been shown to excel in predicting fault characteristics in laboratory shear experiments and slow slip \emph{in situ}. Here we show that a suitably designed CNN can be trained to identify some precursory change in the seismic signal preceding some large natural earthquakes by up to a few hours, with a variable success rate. We use 65 $\textrm{M} w\geq 6$ events in the NE pacific in and around Japan from 2012 to 2022. By repeating the training/testing cycle with variable random initial weights, we obtained up to 98\% in training accuracy and 96\% in testing accuracy in discriminating noise and precursor windows. In the $\sim 3$ hours preceding the earthquakes, the network identifies precursors progressively more frequently as earthquake time approaches. A final subset of more recent seismic events was used for a further verification, with mixed results. While the network appears to differentiate noise and precursor with a statistically positive incidence, the results are highly variable depending on the events that are analysed, with poor potential for generalisation.

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Cited by 13 publications

References 0 publications

Slip motion and stability of a single degree of freedom elastic system with rate and state dependent friction

Slip motion and stability of a single degree of freedom elastic system with rate and state dependent friction

Temporal earthquake forecasting

Detection of earthquake precursors using neural networks

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