Biot 理论与修正的 Biot 理论比较及讨论

摘要

对Biot理论和修正的Biot理论中的波动方程进行了详细推导，注明了每个参数的量纲和准确含义，并基于修正的 Biot 理论导出了三种不同形式的波动方程；对两种理论进行比较，得到了 Biot 弹性系数表达式，并分析了两者的应力及其对应关系；最后，着重对易被混淆的孔隙流体压力符号的正方向和含义，以及基本方程中部分参数的定义式进行了讨论，有助于更好地理解、应用 Biot 理论和修正的 Biot 理论。%The wave equations of Biot theory and modified Biot one were derived,and the dimension and correct definition of each parameter in the equations were clearly indicated.Based on the modified Biot theory,three different forms of wave equations were derived as well.Then,by comparing those two theories,the expressions of Biot elastic coefficients were obtained,and the stresses of the two theories and their correspondences were analyzed.Finally, particularly,the positive direction and meaning of pore-fluid pressure sign and the definitions of part parameters in the fundamental equations were discussed to be helpful for understanding and using the two theories.