Experiment Study and Interpretation on Relation between Modulus of Rock and Strain Amplitude

INTRODUCTIONThe modulus of rock is one of the basic elastic parameters of the earth’s medium. Under theassumption of linear elastic theory and Poisson medium,other parameters can be calculated fromit .But the real earth mediumis nonlinear elastic and has not a simple linear relationship between stressand strain.This causes relatively big differences betweenthe dynamic andthe static modulus of rock.In nonlinear elastic theory,the Young’s modulusEis replaced bythe nonlinear elastic modul…

Experiment Study and Interpretation on Relation between Modulus of Rock and Strain Amplitude

Nonlinear elasticity of the earth medium produces a numerical difference between the dynamic and the static modulus of rock. The dynamic modulus is calculated with the ultrasonic velocity measurement, the small-cycle modulus is calculated with small cycles in the load-unload experiment,the static modulus is calculated from the slope of the stress-strain curve in the large cycle, the Young's modulus is obtained from the ratio of stress to strain in the measured point. The relationship between the modulus and the strain amplitudes is studied by changing the strain amplitude in the small cycles. The moduli obtained from different measuring methods are thus compared. The result shows that the dynamic modulus is the largest, the small-cycle modulus takes the second place, the static modulus of bigger-cycle is the third, and finally the Young's modulus is the smallest. Nonlinear modulus of rock is a function of the strain level and strain amplitude. The modulus decreases exponentially with the ascending of the strain amplitude, while increases with the ascending of the strain level. Finally, the basic concept of the P-M model is briefly introduced and the relationship between the modulus and strain amplitude is explained by the rock having different distribution densities and the different open-and-close stresses of the micro-cracks.