等效介质理论中裂缝密度的适用性研究

为了比较裂缝等效介质理论的预测精度，本文利用物理模拟的方法制作了一组9个裂隙密度模型，其中裂隙密度从0增大到12%，裂隙厚度和直径保持不变，分别为0.12 mm和3 mm.使用0.5 MHz的纵横波换能器，采用脉冲透射法得到纵横波的速度和各向异性.然后，将基质的模量、裂缝填充物模量和裂缝参数代入等效介质理论中，计算出纵横波速度和各向异性随着裂隙密度的变化情况.通过纵横波速度的实测值与等效介质理论的定量对比，发现当裂隙密度小于12%时，Hudson理论和线性滑动理论对纵波速度的预测与实测值非常吻合.当裂隙密度小于8%时，Hudson理论和线性滑动理论对快横波速度的预测与实测值非常吻合.当裂隙密度小于9%时，各向异性自洽理论和NIA（非相互作用近似）理论对慢横波速度的预测与实测值非常吻合.通过纵横波速度各向异性实测值与理论计算值定量对比，发现当裂隙密度小于12%时，Hudson理论和线性滑动理论对纵波速度各向异性的预测与实测值更吻合；当裂隙密度小于6%时，各向异性自洽理论和NIA理论对横波速度各向异性的预测与实测值更吻合.

Physical modeling of the influence of crack density on the accuracy of effective medium theory

In order to investigate the prediction accuracy of the effective medium theory, we construct a series of crack density models, in which crack density ranges from 0 to 12%, crack aperture and diameter fix at 0.12 mm and 3 mm, respectively. We use the 0.5 MHz transducers to measure the elastic velocity and anisotropy of these crack models, then compare the measurement results with those from the effective medium theory. Comparison suggests that when the crack density is less than 12%, the Hudson theory and the Linear Slip theory's predictions about the P-wave velocity fit with experimental results very well. When the crack density is less than 8%, the Hudson theory and the Linear Slip theory's predictions about the fast S-wave velocity fit with experimental results very well. And when the crack density is less than 9%, the anisotropic SCA and the NIA's predictions about the slow S-wave velocity match with experimental results very well. In addition, when the crack density is less than 12%, the Hudson theory and the Linear Slip theory's prediction about ε fit good with experimental results. When the crack density is less than 6%, the anisotropic SCA and the NIA's prediction about γ are more consistent with real measurements.