### Abstract

The fan-shaped mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface, simulating the propagation of shear ruptures in super brittle rocks, is analyzed. Such ruptures appear in the Earth's crust at seismogenic depths. They propagate due to the nucleation of oblique tensile microcracks, leading to the formation of a fan domino-structure in the rupture head. A laboratory physical model was created which demonstrates the process of fan-structure wave propagation. Equations of the dynamics of rotational motion of slabs as a mechanical system with a finite number of degrees of freedom are obtained. Based on the Merson method of solving the Cauchy problem for systems of ordinary differential equations, the computational algorithm taking into account contact interaction of slabs is developed. Within the framework of a simplified mathematical model of dynamic behavior of a fan-shaped system in the approximation of a continuous medium, the approximate estimates of the length of a fan depending on the velocity of its motion are obtained. It is shown that in the absence of friction a fan can move with any velocity that does not exceed the critical value, which depends on the size, the moment of inertia of slabs, the initial angle and the elasticity coefficient of bonds. In the presence of friction a fan stops. On the basis of discrete and continuous models, the main qualitative features of the behavior of a fan-structure moving under the action of applied tangential forces, whose values in a laboratory physical model are regulated by a change in the inclination angle of the rupture plane, are analyzed. Comparison of computations and laboratory measurements and observations shows good correspondence between the results.

Original language | English |
---|---|

Pages (from-to) | 1139-1152 |

Number of pages | 14 |

Journal | Journal of Applied Mathematics and Technical Physics |

Volume | 58 |

Issue number | 7 |

DOIs | |

Publication status | Published - Dec 2017 |

### Cite this

*Journal of Applied Mathematics and Technical Physics*,

*58*(7), 1139-1152. https://doi.org/10.1134/S0021894417070100

}

*Journal of Applied Mathematics and Technical Physics*, vol. 58, no. 7, pp. 1139-1152. https://doi.org/10.1134/S0021894417070100

**Analysis of Fan Waves in a Laboratory Model Simulating the Propagation of Shear Ruptures in Rocks.** / Tarasov, B. G.; Sadovskii, V. M.; Sadovskaya, O. V.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Analysis of Fan Waves in a Laboratory Model Simulating the Propagation of Shear Ruptures in Rocks

AU - Tarasov, B. G.

AU - Sadovskii, V. M.

AU - Sadovskaya, O. V.

PY - 2017/12

Y1 - 2017/12

N2 - The fan-shaped mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface, simulating the propagation of shear ruptures in super brittle rocks, is analyzed. Such ruptures appear in the Earth's crust at seismogenic depths. They propagate due to the nucleation of oblique tensile microcracks, leading to the formation of a fan domino-structure in the rupture head. A laboratory physical model was created which demonstrates the process of fan-structure wave propagation. Equations of the dynamics of rotational motion of slabs as a mechanical system with a finite number of degrees of freedom are obtained. Based on the Merson method of solving the Cauchy problem for systems of ordinary differential equations, the computational algorithm taking into account contact interaction of slabs is developed. Within the framework of a simplified mathematical model of dynamic behavior of a fan-shaped system in the approximation of a continuous medium, the approximate estimates of the length of a fan depending on the velocity of its motion are obtained. It is shown that in the absence of friction a fan can move with any velocity that does not exceed the critical value, which depends on the size, the moment of inertia of slabs, the initial angle and the elasticity coefficient of bonds. In the presence of friction a fan stops. On the basis of discrete and continuous models, the main qualitative features of the behavior of a fan-structure moving under the action of applied tangential forces, whose values in a laboratory physical model are regulated by a change in the inclination angle of the rupture plane, are analyzed. Comparison of computations and laboratory measurements and observations shows good correspondence between the results.

AB - The fan-shaped mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface, simulating the propagation of shear ruptures in super brittle rocks, is analyzed. Such ruptures appear in the Earth's crust at seismogenic depths. They propagate due to the nucleation of oblique tensile microcracks, leading to the formation of a fan domino-structure in the rupture head. A laboratory physical model was created which demonstrates the process of fan-structure wave propagation. Equations of the dynamics of rotational motion of slabs as a mechanical system with a finite number of degrees of freedom are obtained. Based on the Merson method of solving the Cauchy problem for systems of ordinary differential equations, the computational algorithm taking into account contact interaction of slabs is developed. Within the framework of a simplified mathematical model of dynamic behavior of a fan-shaped system in the approximation of a continuous medium, the approximate estimates of the length of a fan depending on the velocity of its motion are obtained. It is shown that in the absence of friction a fan can move with any velocity that does not exceed the critical value, which depends on the size, the moment of inertia of slabs, the initial angle and the elasticity coefficient of bonds. In the presence of friction a fan stops. On the basis of discrete and continuous models, the main qualitative features of the behavior of a fan-structure moving under the action of applied tangential forces, whose values in a laboratory physical model are regulated by a change in the inclination angle of the rupture plane, are analyzed. Comparison of computations and laboratory measurements and observations shows good correspondence between the results.

KW - fan-shaped mechanism

KW - Lagrange equations

KW - Euler equation

KW - traveling waves

KW - computational algorithm

KW - EARTHQUAKE ACTIVITY

KW - HARD ROCKS

KW - MECHANISM

KW - COMPRESSION

KW - GROWTH

U2 - 10.1134/S0021894417070100

DO - 10.1134/S0021894417070100

M3 - Article

VL - 58

SP - 1139

EP - 1152

JO - Journal of Applied Mathematics and Technical Physics

JF - Journal of Applied Mathematics and Technical Physics

SN - 0021-8944

IS - 7

ER -