摘要
为深入研究某围岩气体渗流解析计算方法在数学上的严谨性和物理上的合理性,进而验证其在工程应用上的可行性,针对内含空腔围岩中气体渗流动力学问题,利用达西定律和合理的数学假设,严格推导了围岩内裂隙区和孔隙区中气体最远到达位置关于渗透率之间的比例关系。根据基本的物理认识和工程施工安全预估需求,通过严密地数学推导,证明了"爆室空腔与围岩间不存在热传递"和"对于进入围岩裂隙或孔隙的气体取围岩裂隙或孔隙的压力与体积作为该部分气体的压力与体积"这两个重要前提假设的合理性。最后,给出了气体在围岩中到达某位置所用时间的解析计算公式的详细推导过程,并利用实验数据证明了该公式应用于工程实践的可行性。
The purpose of this paper is to further study the rigorousness in mathematics and rationality in physics of some analytical calculation method for the gas seepage problem of surrounding rock,and thereby validate the feasibility of the method in engineering application.By focusing on the gas seepage dynamic problem of surrounding rock with an internal cavity,on the basis of the Dacy’s law and some reasonable mathematical hypothesises,the proportion relationship of the maximum gas leakage distances in the crack region and the pore region,as a function of the permeabilities of the crack region and the pore region,has been derived strictly.According to some basic physics and the requirements in the engineering construction safety estimations,by ultilizing some strict mathematical derivations,the rationality of the following two assumptions has been proved.The first assumption is that there is no heat transfer between the explosion cavity and the surrounding rock.The other assumption is that the volume and the pressure of the gas leaking into the surrounding rock equal to the volume and the pressure of the corresponding crack region or the pore region in the surrounding rock respectively.Finally,the derivation process of the analytic formula for the arrival time of the gas arriving at some specified location in the surrounding rock is proposed in detail.Moreover,the results of the analytic formula agree very well with the experimental data,which has verified the feasibility of the analytic formula applying to engineering practice.
作者
钟巍
田宙
王铁良
Zhong Wei;Tian Zhou;Wang Tieliang(Northwest Institute of Nuclear Technology,Xi’an 710024,P.R.China;School of Mathematical Sciences,Peking University,Beijing 100871,P.R.China)
出处
《地下空间与工程学报》
CSCD
北大核心
2020年第1期35-42,共8页
Chinese Journal of Underground Space and Engineering
基金
国家自然科学基金(91330205).
关键词
内含空腔围岩
气体渗流
达西定律
解析公式
裂隙区
孔隙区
渗流时间
surrounding rock with an internal cavity
gas seepage
Darcy’s law
analytical formula
crack region
pore region
arrival time of the gas seepage
