Rock Failure Under Dynamic Loading Conditions
Authors: Burdine N.T. 
Published: December 2007

BURDINE, N.T., SOCONY MOBIL OIL CO., INC., DALLAS, TEX

Abstract
The present investigation is concerned with the cumulative damage to rock samples when exposed to cyclic stresses under various loading conditions. Information on the response of rocks to repetitive deformational forces is an essential prerequisite to an understanding of the fundamentals of drilling. Using a laboratory designed and constructed dynamic-stress apparatus, preliminary data were obtained on cylindrical rock samples. The experiments consist of measuring the number of cycles to failure for a given axial load ( static plus dynamic). Data were obtained for various confining and pore pressures, pore fluids (air and water), frequencies of stress application and loading procedures. The results are related to failure theories and dynamic fatigue properties of other materials.

Introduction
In most conventional and new drilling processes, repetitive forces are applied to the bottom of the borehole. Furthermore, in hard-rock drilling the number of applications of the forces to a particular section of rock may become excessively large. The present investigation is concerned with the cumulative damage to rocks when exposed to cyclic stresses under various loading conditions. It is believed that the experiments will lead to a better understanding of the mechanical response of rocks to particular deformational forces and to a more efficient drillingprocedure.Thepresent investigation is the initial part of a general study of the behavior of inelastic materials under static and dynamic conditions, including both theoretical and experimental studies.

SURVEY OF FAILURE THEORIES OF MATERIALS
Few, even phenomenological, theories on rock deformation have been established because the state of knowledge of flow, fracture and strength of rocks is largely empirical. Most of the theories that do exist were originally formulated for other materials.

HOOKE'S LAW
The state of stress in continuous media is completely determined by the stress tensor and the state of deformation by the strain tensor . In the linear theory of elasticity the generalized Hooke's law is
..........................(1)
where the coefficients are the components of the elasticity tensor. For homogeneous and isotropic conditions the number of independent coefficients reduce to two, and Eq. 1 becomes
..................(2)
in which and are Lame's constants; is the kronecker delta; and is the dilation. This simplified version of Hooke's law has been used quite extensively in geophysical research where most of the information about the mechanical properties of the earth have been obtained. However, it has only limited application in rock fatigue studies.

MATERIAL BEHAVIOR
Many solids obey Hooke's law at small stresses, but for higher stresses a hysteretic effect occurs due to temporary or permanent residual deformation of the solid (inelastic deformation). Such deviations in mechanical behavior exist in varying degrees in different classes of materials. Most elastic materials have a microscopic heterogeneity due either to random distribution of anisotropic particles, or due to some preferred particle orientation, or both. Other materials are quite grossly heterogeneous. And the method of formation, particularly in rocks, oftentimes creates residual stress concentrations which have complicated states of imperfect equilibrium. Also, the thermal effects resulting from structural behavior give rise to nonuniform temperature distributions and the degradation of mechanical energy. When such bodies are exposed to certain large loading conditions, the inelastic behavior is intensified so strongly that the deformation, normally brittle, becomes ductile.
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