CAJ | 학술논문

对于Biot固结方程中的连续性方程形式,不同的研究者存在分歧.在详细分析了Biot推导固结方程的过程后,发现其在推导固结方程时用到的弹性应变能密度函数存在错误.为了得到正确的连续性方程,采用两种思路进行了分析:①通过对土体单元变形的分析,得到了考虑土体颗粒和流体可压缩性的连续性方程;②按照Biot推导固结方程的思路,通过修正推导过程中用到的弹性应变能密度函数得到了连续性方程.上述两种思路得到的连续性方程是等价的,同时将上述连续性方程和其他研究者通过质量守恒得到的连续方程进行了对比,结果是一致的,从而确定了连续性方程的正确形式,并澄清了目前在Biot固结方程中的连续性方程上存在的分歧,所得结论可为固结方程的解析或数值计算提供依据.
대우Biot고결방정중적련속성방정형식,불동적연구자존재분기.재상세분석료Biot추도고결방정적과정후,발현기재추도고결방정시용도적탄성응변능밀도함수존재착오.위료득도정학적련속성방정,채용량충사로진행료분석:①통과대토체단원변형적분석,득도료고필토체과립화류체가압축성적련속성방정;②안조Biot추도고결방정적사로,통과수정추도과정중용도적탄성응변능밀도함수득도료련속성방정.상술량충사로득도적련속성방정시등개적,동시장상술련속성방정화기타연구자통과질량수항득도적련속방정진행료대비,결과시일치적,종이학정료련속성방정적정학형식,병징청료목전재Biot고결방정중적련속성방정상존재적분기,소득결론가위고결방정적해석혹수치계산제공의거.
When solving Biot's consolidation equations, different researchers used different continuum equations. The methods Biot M.A. Used to deduce the consolidation equations are firstly reviewed. It can be seen that some mistakes exist in the strain energy density function. In order to derive the correct form of continuum equation, two methods are used here. Firstly, based on the analysis of the deformation of the representative element volume (REV) of the soil, a fluid continuum equation which can take the compressibility of grain and fluid into account is derived. Secondly, based on the method Biot M.A. Used with modified strain energy density, another continuum equation is derived. The continuum equations deduced from the two methods listed above are found to be equivalent. In addition, the equations are compared to the continuum equation derived by other researchers based on mass conservation law, and they are found to be coincident. Then, the right form of fluid continuum equation is proved and the result can provide theoretical support to consolidation calculation.