### Abstract

Two polynomial constitutive equations of nonlinear stress-strain relationship were used to construct two nonlinear 1-D wave equations with external pressure (source term) applied. Nonlinear model 1 was a concave downward curve, and nonlinear model 2 was a concave upward curve. The time-dependent stress and strain of a 300-m length were calculated. The computation for nonlinear model 1 terminated at time t = 5. 0 s. The evaluated stress versus position at different times was mainly at position x = 0 m. The stress versus position had a concave point at position x = 0. 3 m. Between x = 0 m and x = 0. 3 m, the graph of stress versus position showed a small convex upward curve. Moreover, at the two sides of x = 0. 3 m, the strain position had distinctively different slopes. The distinctive difference in the slope of strain at position x = 0. 3 m can therefore be used to estimate the rupture position of a rock. The terminal evaluation time for nonlinear model 2 was at t = 1. 55 s. The stress versus position and the strain versus position to time change were within the 0-3 m interval from the pressure end. Time increase produced the phenomenon of stress and strain solitons. These stress and strain solitons moved forward and increased in peak value with time. During the compression process, the stress and strain soliton resulted in instability which rendered the rock situation more easily broken. The position of the rock rupture might have occurred away from the pressure side.

Original language | English |
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Pages (from-to) | 1613-1620 |

Number of pages | 8 |

Journal | Arabian Journal of Geosciences |

Volume | 6 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2013 May 1 |

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### All Science Journal Classification (ASJC) codes

- Environmental Science(all)
- Earth and Planetary Sciences(all)

### Cite this

*Arabian Journal of Geosciences*,

*6*(5), 1613-1620. https://doi.org/10.1007/s12517-011-0466-5