Experiment Study Of Third-order Elastic Constants Of Rock And The Distribution Of Acoustic Velocity Around Borehole With Stress

The development and application of acoustoelasticity theoryprovides a new way for measuring in-situ stresses. It’s a typicalacoustoelasticity problems that a small disturbance in wave field isinspired under the finite static stress on nonlinear shape variation. Thethird order elastic modulus is a very important parameter in nonlinearacoustics. The third order elastic modulu sound velocity and in-situ stressbased on the acoustoelasticity theory.So in recent years, the measurementof the third order elastic modulus for rock has been an important topicwhich has aroused the attention among the scholars to research. Inaddition, the in-situ stress will induce equivalent anisotropic medium onthe consideration of nonlinear static deformation. There will appear stressconcentration problem when the medium around borehole is subjected tostress,thus affecting the velocity distribution of around.That provides usnew information on in-situ stress. Therefore scholars have carried outmany theoretical and experimental work in recent years. Theexperimental measurements of velocity distribution under stess aroundthe borehole mainly aimed at p wave around the open hole at home andabroad. The experimental measurements of velocity distribution of shearwave under stess around casing drilling has not yet been carried out.Fromwhat has been discussed above, the main idea of the article is theexperiment study of third-order elastic constants of rock and thedistribution of acoustic velocity around borehole with stress.Firstly, the equations of stress induced anisotropy field equationswas deduced(Piola Kirchhoff equation) as well as the equivalent elastic modulus under the arbitrary triaxial stress induced. The group velocitywas deduced according to the ’Christoffel equation which was given bythe equation of motion and plane wave solution. Also,the value of phasevelocity along arbitrary direction under the three-dimensional stress wasgiven. The results show that:the medium under uniaxial stress presentsthe characteristics of the transversely isotropic.;The medium underunequal biaxial stress present the characteristics of orthogonal anisotropic;The medium under the unequal triaxial stress also presents the orthogonalanisotropy, but the presence of the third axial stress makes the azimuthanisotropy of group velocity and phase velocity weaken at the same levelof stress.Secondly, to achieve the inversion of third-order modulus of rock bythe measurement of the velocity of p wave and two shear wave thatvary with the change of the stress and propagate along the direction of therock sample thickness.The value of the third order elastic modulus frominversion is almost the same with that from experimental measurements.Lastly, stress concentrations around a laboratory borehole producemeasurable variations in acoustic velocity.Writer measure the azimuthalvelocity variations caused by borehole stress concentrations with nylonsamples.Results show that it is quite straightforward to determine thedirection of maximum uniaxial stress (perpendicular to the borehole)from azimuthal velocity variations. The azimuth of minimum velocityis the direction of maximum uniaxial stress. Then, stick on the steel pipeon the wall of the drilling hole of the samples of nylon. Writer measurethe azimuthal velocity variations caused by borehole stress concentrationsin the same way.Compared with the result of the nylon without steel pipe,the azimuth of maximum velocity has been changed,and velocityvariations caused by borehole stress concentrations is become complex.