CAJ | 학술논문

基于非饱和多孔介质动力方程，研究了充满2种流体的非饱和多孔介质动力响应问题，并分别给出了2种边界条件作用下非饱和半无限多孔介质一维瞬态响应积分形式解。首先，运用正弦与余弦变换法将偏微分方程组变换为常微分方程组。然后，运用状态空间法求解此常微分方程组，得到变换域内解析解。最后，通过正弦与余弦反变换，给出非饱和半无限多孔介质一维瞬态响应积分形式解。该方法的优点是积分解中被积函数为实函数，给数值计算带来极大的方便。通过算例分析，验证了本文结果的正确性，证实了非饱和多孔介质内存在3种类型压缩波，分析了3类压缩波作用下多孔介质内固体和2种流体间的相位关系。
기우비포화다공개질동력방정，연구료충만2충류체적비포화다공개질동력향응문제，병분별급출료2충변계조건작용하비포화반무한다공개질일유순태향응적분형식해。수선，운용정현여여현변환법장편미분방정조변환위상미분방정조。연후，운용상태공간법구해차상미분방정조，득도변환역내해석해。최후，통과정현여여현반변환，급출비포화반무한다공개질일유순태향응적분형식해。해방법적우점시적분해중피적함수위실함수，급수치계산대래겁대적방편。통과산례분석，험증료본문결과적정학성，증실료비포화다공개질내존재3충류형압축파，분석료3류압축파작용하다공개질내고체화2충류체간적상위관계。
Based on the basic equations for unsaturated porous media,the transient response of an unsaturated semi-infinite porous medium saturated with water and oil was studied. The integral solutions for the one-dimensional transient response of an unsaturated semi-infinite porous medium with two types of nonhomogeneous boundary conditions were developed. Using the sine and cosine transforms,the basic equations were first transformed into a set of ordinary differential equations. Then,the state-space method was employed to solve these equations and the analytical solution in the transform domain was obtained. Finally,the integral solutions were obtained by using the inverse sine and cosine transforms. The integrands of the integral solutions were real functions,which had great advantages on the numerical calculations. Numerical examples were provided to verify the validity of the proposed solutions and investigated the dynamic behavior of unsaturated porous media,and it was verified that three types of compressional waves exists in unsaturated porous media that contained two immiscible fluids.