岩石模量与应变振幅关系的实验研究及理论解释

地球介质的非线性弹性造成了岩石动态和静态弹性模量在数值上的差异。本文用超声波速度测量得到岩石的动模量，用含有小循环的加卸载实验得到小循环模量，用大循环的应力、应变曲线斜率得到静模量，用测点的应力、应变之比得到杨氏模量。通过改变小循环的应变振幅来研究模量与应变振幅的关系，进而比较用不同测量方法得到的模量值的差异。结果表明，动模量值最大，小循环模量值次之，大循环静模量值再次之，而杨氏模量最小。岩石非线性模量既是所受应变水平的函数，也是应变振幅的函数，模量随应变振幅的增加以指数形式下降，随应变水平增加以指数形式上升。最后简要介绍了P-M模型的基本概念，用岩石中微裂缝具有不同的分布密度，不同的打开和关闭压力来解释模量与应变振幅的关系。

Experiment Study and Interpretation on Relation between Modulus of Rocks and Strain Amplitudes

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