Modeling of the nonlinear resonant response in sedimentary rocks

Conference · Fri Apr 03 04:00:00 EDT 2009

OSTI ID:988312

Ten Cate, James A ^[1]; Shankland, Thomas J ^[1]; Vakhnenko, Vyacheslav O ^[2]; Vakhnenko, Oleksiy ^[2]

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1. Los Alamos National Laboratory
2. NON LANL

We suggest a model for describing a wide class of nonlinear and hysteretic effects in sedimentary rocks at longitudinal bar resonance. In particular, we explain: hysteretic behaviour of a resonance curve on both its upward and downward slopes; linear softening of resonant frequency with increase of driving level; gradual (almost logarithmic) recovery of resonant frequency after large dynamical strains; and temporal relaxation of response amplitude at fixed frequency. Starting with a suggested model, we predict the dynamical realization of end-point memory in resonating bar experiments with a cyclic frequency protocol. These theoretical findings were confirmed experimentally at Los Alamos National Laboratory. Sedimentary rocks, particularly sandstones, are distinguished by their grain structure in which each grain is much harder than the intergrain cementation material. The peculiarities of grain and pore structures give rise to a variety of remarkable nonlinear mechanical properties demonstrated by rocks, both at quasistatic and alternating dynamic loading. Thus, the hysteresis earlier established for the stress-strain relation in samples subjected to quasistatic loading-unloading cycles has also been discovered for the relation between acceleration amplitude and driving frequency in bar-shaped samples subjected to an alternating external drive that is frequency-swept through resonance. At strong drive levels there is an unusual, almost linear decrease of resonant frequency with strain amplitude, and there are long-term relaxation phenomena such as nearly logarithmic recovery (increase) of resonant frequency after the large conditioning drive has been removed. In this report we present a short sketch of a model for explaining numerous experimental observations seen in forced longitudinal oscillations of sandstone bars. According to our theory a broad set of experimental data can be understood as various aspects of the same internally consistent pattern. Furthermore, the suggested theory will be shown to predict the dynamical realization of hysteresis with end-point memory, figuratively resenlbling its well-known quasistatic prototype.

• Research Organization: Los Alamos National Laboratory (LANL)
• Sponsoring Organization: DOE
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 988312
• Report Number(s): LA-UR-09-02145; LA-UR-09-2145
• Country of Publication: United States
• Language: English

Related Subjects

58 GEOSCIENCES
ACCELERATION
AMPLITUDES
HYSTERESIS
LANL
MECHANICAL PROPERTIES
MESONS
OSCILLATIONS
PORE STRUCTURE
RELAXATION
RESONANCE
SANDSTONES
SEDIMENTARY ROCKS
SIMULATION
STRAINS