NUMERICAL SIMULATION OF RESONANT COLUMN EXPERIMENTS FOR JOINTED
ROCKS AND ITS APPLICATION IN ROCK MECHANICS
T G SITHARAM and Resmi Sebastian
ABSTRACT
Wave propagation studies across jointed rocks have significance in the fields of rock mechanics and
geophysics. The passage of a seismic wave induces strains in rocks and often, these strains are of low
magnitudes except at the vicinity of source. These low magnitude strains are generally in the elastic range
and hence elastic constants necessary for the design and analysis of strength of rock mass, can be derived
from wave velocities. Measurement of travel time velocities and measurement of resonance frequencies
are the two methods usually adopted for obtaining wave propagation velocities.
Resonant column apparatus measures wave velocities from the resonant frequencies obtained during
testing. Depending on the type vibration applied, torsional or flexural, shear and compression wave
velocities are secured. By varying the amplitude of vibrations applied, various strain levels can be
introduced and corresponding resonant frequencies and wave velocities can be calculated. The resonant
column experiments were performed on a model material, hardened Plaster of Paris (POP) samples, in
laboratory. The paper explains the preparation of samples and the working mechanism of resonant column
apparatus along with the estimation of wave velocity from resonant frequency. The numerical simulation
of resonant column apparatus using distinct element method and its validation with the experimental results
are presented in the paper.
A distinct element code is usually used to simulate the movement of materials with intersecting
discontinuities. Finite rotations and displacements of individual blocks representing the material are
permitted and new contacts between the blocks are identified as the calculation progresses. Three
dimensional Distinct Element Code (3DEC), the software intended for the numerical simulation of rock
engineering projects, can well simulate the behavior of jointed rocks under static and dynamic loading
conditions. The numerical simulation of resonant column apparatus has been performed with 3DEC
considering its efficiency in modeling jointed rocks.
The numerical modeling of the resonant column apparatus with application of torsional and flexural
vibrations to the sample is elaborated in the paper. The response of samples to a range of frequencies is
obtained and the frequency that induces maximum displacement in the sample is measured as the resonant
frequency, for any particular strain level. The displacements measured at various points of the sample
during application of vibrations are compared and presented. The numerical modeling of resonant column
apparatus with an intact sample (without joint) and a sample with a joint incorporated are explained at a
particular strain level. The resonant frequencies obtained from laboratory experiments and numerical
simulations are compared and illustrated. The resonant frequency curves obtained for a sample with joint
under torsional and flexural vibrations are shown in Figs. 1 and 2. It has been found that resonant
frequencies obtained using numerical and laboratory experiments are in good comparison and can be
extended for various strain levels and sample conditions.
1.3E-07
Displacements (m)
1.2E-07
1.1E-07
1.0E-07
Resonant frequency
curve
9.0E-08
8.0E-08
180
190
200
210
220
230
240
Resonant frequency (Hz)
Fig. 1 Resonant frequency curve obtained from numerical simulation in torsional vibration.
9.90E-07
Displacements (m)
9.85E-07
9.80E-07
9.75E-07
9.70E-07
Resonant frequency curve
9.65E-07
9.60E-07
110
120
130
140
150
160
170
Frequency (Hz)
Fig. 2 Resonant frequency curve obtained from numerical simulation in flexural vibration.
KEYWORDS
Wave velocities, Resonant frequency, Resonant Column Apparatus, Distinct Element Method, Numerical
simulation