According to the generalized Hooke Law, the
elastic strain energy released from the unit rock mass under the triaxial compression test is (Xie et al., 2011):
The
elastic strain energy of the ith beam element is:
According to energy theory, the rock dynamic elastic modulus is the embodiment of dynamic elastic parameters under dynamic load, and its value reflects the quality of rock's elastic bearing performance; the rock damping ratio represents the ratio of the total energy consumed by the rock to its
elastic strain energy during the single loading period.
For each specimen, three major factors [3], including energy dissipation ([E.sub.h]),
elastic strain energy ([E.sub.e]), and equivalent viscous damping ratio ([[xi].sub.eq]), were calculated for each hysteric loop with MATLAB.
where U is the total energy stored in the infinite plate, [U.sub.t] represents the initial total
elastic strain energy, [U.sub.c] is the total
elastic strain energy released by the crack on the upper and lower surfaces of the crack length of 2a, W is the work performed by the external force, and [U.sub.s] is the free surface energy.
Remembering now that the stress can also be thought of as an energy density, we can ask, What is the contribution of the singular stress field near the crack to the total
elastic strain energy in the solid?
As the high
elastic strain energy accumulated in the rock masses is greater than the energy consumed by rock failure, imbalance of the rock mass structure occurs and the excess energy causes the rock to explode and emitted rock debris", he explained.
In the relation above value of [E.sub.D] is absorbed energy inside full loop which corresponds complete level of a cycle ([A.sub.loop]) and [E.sub.S0] is
elastic strain energy corresponds force maximum ([F.sub.max]) and displacement ([D.sub.max])obtained in a cycle of cyclic graph which have been shown on the following force-displacement figure (figure
With the advance of mining extraction,
elastic strain energy gradually accumulates in front coal body of mining face.