CAJ | 학술논문

针对圆形隧道的弹塑性解析中许多能更好地反映岩石特性的本构模型由于数学求解的困难而得不到广泛应用的问题，进行新的尝试。首先，基于单一曲线和体积不可压缩假设，总结完善一种更为简便的解析方法。其次，运用该解析方法，针对6种不同的本构模型，计算围岩的弹性区和塑性区应力、塑性区半径、围岩平衡方程、围岩自承地应力上下限等，得到精确或近似的解析表达式。针对线性软化本构模型，引入Lambert函数给出塑性区半径R的解析表达式，论证围岩平衡曲线中R的取值范围。针对Nelder非线性软化本构模型，引入幂函数给出拐点横坐标以及拐点处降模量的近似计算式。当峰后为Weibull非线性软化本构模型时，由于whittaker函数无法求反函数和极限，故而提出以Gauss公式拟合整条围岩平衡曲线，再以Gauss反函数的求解得到塑性区半径的新思路。最后，对比分析6种本构模型的解析结果之间的差异后得出，非线弹性情况下得到的围岩自承地应力上限比线弹性情况下高，而应力集中系数低，应力集中位置偏离弹塑区边界位于弹性区内，切向应力再分布曲线上不会出现尖角，这些都与实际更为相符。因此，不论是软岩或是硬岩，使用连续而光滑的本构模型进行弹塑性分析可以得到更为符合实际的结果。
침대원형수도적탄소성해석중허다능경호지반영암석특성적본구모형유우수학구해적곤난이득불도엄범응용적문제，진행신적상시。수선，기우단일곡선화체적불가압축가설，총결완선일충경위간편적해석방법。기차，운용해해석방법，침대6충불동적본구모형，계산위암적탄성구화소성구응력、소성구반경、위암평형방정、위암자승지응력상하한등，득도정학혹근사적해석표체식。침대선성연화본구모형，인입Lambert함수급출소성구반경R적해석표체식，론증위암평형곡선중R적취치범위。침대Nelder비선성연화본구모형，인입멱함수급출괴점횡좌표이급괴점처강모량적근사계산식。당봉후위Weibull비선성연화본구모형시，유우whittaker함수무법구반함수화겁한，고이제출이Gauss공식의합정조위암평형곡선，재이Gauss반함수적구해득도소성구반경적신사로。최후，대비분석6충본구모형적해석결과지간적차이후득출，비선탄성정황하득도적위암자승지응력상한비선탄성정황하고，이응력집중계수저，응력집중위치편리탄소구변계위우탄성구내，절향응력재분포곡선상불회출현첨각，저사도여실제경위상부。인차，불론시연암혹시경암，사용련속이광활적본구모형진행탄소성분석가이득도경위부합실제적결과。
A lot of constitutive models,representing the properties of rock well,have not been utilized widely because of the difficulty in elastoplastic solution. So,based on the single curve and constant volume hypothesis, an analytical method that can be used more conveniently was summed up and modified firstly. Using this method, the stress of elastic and plastic zones,radius of plastic zone,equilibrium equation and superior and inferior limits of self-support geostress of surrounding rock after excavation were calculated accurately or approximately. In view of linear softening constitutive model,Lambert function was introduced to calculate the radius of plastic zone R and its range in equilibrium curve of surrounding rock proved. For the Nelder nonlinear softening model, an exponential function was used to describe approximately the abscissa of inflection point and softening modulus. When the Weibull model was taken to represent the post-peak mechanical behaviour,since it is difficult to get the inverse function and limit of Whittaker function,a new idea,fitting the whole equilibrium curve with Gauss function and computing the radius of plastic zone by solving the inverse function of Gauss,was proposed. Then, comparison was taken between these results derived from six constitutive models and it is found that the superior limit of self-support geostress of surrounding rock was higher,the stress concentration factor was lower,the position that stress concentrates was in elastic zone,deviating from the interface between elastic and plastic zones,and the wedge angle in the tangential stress redistribution curve disappeared under nonlinear elastic condition,which is consistent with the practice. Therefore,for either soft or hard rock,a more perfect result from elastoplastic solution can be obtained by taking a smooth and continuous constitutive model.